Abstract group 4096.ol: $C_4^4.C_2^4$

• Label: 4096.ol
• Order: \( 2^{12} \)
• Exponent: \( 2^{3} \)
• Nilpotent: yes
• Solvable: yes
• $\card{G^{\mathrm{ab}}}$: \( 2^{9} \)
• $\card{Z(G)}$: \( 2^{7} \)
• $\card{\Aut(G)}$: \( 2^{34} \)
• $\card{\mathrm{Out}(G)}$: \( 2^{29} \)
• Perm deg.: not computed
• Trans deg.: $2048$
• Rank: $5$

Group information

Description:	$C_4^4.C_2^4$
Order:	\(4096\)\(\medspace = 2^{12} \)
Exponent:	\(8\)\(\medspace = 2^{3} \)
Automorphism group:	Group of order \(17179869184\)\(\medspace = 2^{34} \)
Composition factors:	$C_2$ x 12
Nilpotency class:	$3$
Derived length:	$2$

This group is nonabelian, a $p$-group (hence nilpotent, solvable, supersolvable, monomial, elementary, and hyperelementary), and metabelian.

Group statistics

Order	1	2	4	8
Elements	1	159	864	3072	4096
Conjugacy classes	1	47	336	640	1024
Divisions	1	47	192	160	400
Autjugacy classes	1	10	21	6	38

Dimension	1	2	4	8
Irr. complex chars.	512	384	128	0	1024
Irr. rational chars.	32	80	176	112	400

Minimal presentations

Permutation degree:	not computed
Transitive degree:	$2048$
Rank:	$5$
Inequivalent generating 5-tuples:	not computed

Minimal degrees of faithful linear representations

	Over $\mathbb{C}$	Over $\mathbb{R}$	Over $\mathbb{Q}$
Irreducible	none	not computed	none
Arbitrary	not computed	not computed	not computed

Constructions

Presentation:	${\langle a, b, c, d, e, f \mid a^{8}=b^{8}=c^{2}=d^{4}=e^{4}=f^{2}=[a,d]= \!\cdots\! \rangle}$
Matrix group:	$\left\langle \left(\begin{array}{rr} 9 & 0 \\ 0 & 1 \end{array}\right), \left(\begin{array}{rr} 1 & 8 \\ 0 & 1 \end{array}\right), \left(\begin{array}{rr} 17 & 0 \\ 0 & 1 \end{array}\right), \left(\begin{array}{rr} 7 & 12 \\ 4 & 3 \end{array}\right), \left(\begin{array}{rr} 1 & 4 \\ 0 & 1 \end{array}\right), \left(\begin{array}{rr} 9 & 0 \\ 0 & 9 \end{array}\right), \left(\begin{array}{rr} 9 & 0 \\ 2 & 3 \end{array}\right), \left(\begin{array}{rr} 1 & 16 \\ 0 & 1 \end{array}\right), \left(\begin{array}{rr} 1 & 28 \\ 20 & 21 \end{array}\right), \left(\begin{array}{rr} 17 & 0 \\ 0 & 17 \end{array}\right), \left(\begin{array}{rr} 1 & 16 \\ 16 & 17 \end{array}\right), \left(\begin{array}{rr} 1 & 24 \\ 8 & 25 \end{array}\right) \right\rangle \subseteq \GL_{2}(\Z/32\Z)$
Direct product:	$C_2$ $\, \times\, $ $(C_4^4.C_2^3)$
Semidirect product:	$(C_4^4.D_4)$ $\,\rtimes\,$ $C_2$	$(C_4^3.D_4)$ $\,\rtimes\,$ $C_8$	$(C_4^3.C_2^3)$ $\,\rtimes\,$ $D_4$	$(C_4^4.C_2^3)$ $\,\rtimes\,$ $C_2$	all 21
Trans. wreath product:	not isomorphic to a non-trivial transitive wreath product
Non-split product:	$C_4^4$ . $C_2^4$	$(C_4^4.D_4)$ . $C_2$	$(C_4^3\times C_8)$ . $D_4$ (2)	$C_4^4$ . $(C_2\times D_4)$ (2)	all 560

Elements of the group are displayed as matrices in $\GL_{2}(\Z/{32}\Z)$.

Homology

Abelianization:	$C_{2}^{3} \times C_{8}^{2} $
Schur multiplier:	$C_{2}^{9} \times C_{4} \times C_{8}$
Commutator length:	$1$

Subgroups

There are 212187 subgroups in 67115 conjugacy classes, 11867 normal (71 characteristic).

Characteristic subgroups are shown in this color. Normal (but not characteristic) subgroups are shown in this color.

Special subgroups

Center:	$Z \simeq$ $C_2^3\times C_4^2$	$G/Z \simeq$ $C_2^2\times D_4$
Commutator:	$G' \simeq$ $C_2\times C_4$	$G/G' \simeq$ $C_2^3\times C_8^2$
Frattini:	$\Phi \simeq$ $C_2\times C_4^3$	$G/\Phi \simeq$ $C_2^5$
Fitting:	$\operatorname{Fit} \simeq$ $C_4^4.C_2^4$	$G/\operatorname{Fit} \simeq$ $C_1$
Radical:	$R \simeq$ $C_4^4.C_2^4$	$G/R \simeq$ $C_1$
Socle:	$\operatorname{soc} \simeq$ $C_2^5$	$G/\operatorname{soc} \simeq$ $C_2^3:C_4^2$
2-Sylow subgroup:	$P_{ 2 } \simeq$ $C_4^4.C_2^4$

Hi

Subgroup diagram and profile

Classes of subgroups up to conjugation

No diagram available: subgroups only stored up to automorphism

Classes of subgroups up to automorphism

No diagram available

Normal subgroups

No diagram available: subgroups only stored up to automorphism

Normal subgroups up to automorphism

No diagram available

Classes of subgroups up to conjugation

Order 4096: $C_4^4.C_2^4$

Order 2048: $C_4^4.C_2^3$ x 16, $C_2\times C_4^3.C_2^4$ x 4, $C_2\times C_2^3.C_2^5.C_2^2$ x 4, $C_4^4.D_4$ x 2, $C_4^4.D_4$ x 2, $C_2\times C_4\times C_4^3.C_2^2$, $C_2\times C_4^4.C_2^2$, $C_4^4.C_2^3$

Order 1024: $C_4^3.C_2^4$ x 32, $C_2\times C_4^3.C_2^3$ x 32, $C_4^4.C_2^2$ x 32, $(C_2\times D_4).C_8^2$ x 32, $C_4^4.C_2^2$ x 20, $C_4^4.C_2^2$ x 16, $C_4\times C_4^3.C_2^2$ x 12, $C_4^2:C_8^2$ x 12, $C_2\times C_2^3.C_2^5.C_2$ x 8, $C_2\times (C_2\times C_4^3).C_2^2$ x 8, $C_4^3.C_4^2$ x 8, $C_4\times C_4^3.C_2^2$ x 4, $C_2^2\times C_4^3.C_2^2$ x 4, $C_2\times C_4\times C_2^3.C_4^2$ x 4, $C_2\times (C_2\times C_4^3).C_2^2$ x 4, $C_2\times C_2^4.C_2^4.C_2$ x 4, $C_2\times C_4^3.D_4$ x 4, $C_8\times C_2^3.C_2^4$ x 4, $C_4^3.C_4^2$ x 4, $C_2\times C_4^3\times C_8$ x 3, $C_4^4.C_4$ x 3, $C_2\times C_2^3.C_2^5.C_2$ x 2, $C_2\times C_4\times C_2^2.(C_4\times D_4)$ x 2, $C_2\times C_2^4.C_2^4.C_2$ x 2, $C_2^2\times C_4^3.C_2^2$ x 2, $C_2\times C_4^3.C_2^3$ x 2, $C_2^6.C_2^4$ x 2, $C_4^3.C_2^4$ x 2, $C_4^3.C_2^4$ x 2, $C_2\times C_4^4.C_2$

Order 512: $C_4^3.D_4$ x 128, $D_4:C_8^2$ x 128, $C_4^3.C_2^3$ x 120, $C_8\times C_2^3.C_2^3$ x 112, $C_4^3.D_4$ x 96, $C_4^3.C_2^3$ x 72, $C_4^3.C_2^3$ x 64, $C_4^3.D_4$ x 64, $C_4^2.(C_4\times D_4)$ x 64, $C_4^3.C_2^3$ x 60, $C_4^3.D_4$ x 56, $C_4^3\times C_8$ x 40, $C_4^3:C_8$ x 36, $C_2^2\times C_4^2\times C_8$ x 34, $C_4^3.D_4$ x 32, $C_4^3.D_4$ x 32, $C_4^3.D_4$ x 28, $C_4^4:C_2$ x 24, $C_4^2:C_4\times C_8$ x 24, $C_2\times C_4^2.C_4^2$ x 16, $C_4^2.C_2^5$ x 16, $C_2^3.C_8^2$ x 14, $C_4^3.C_2^3$ x 12, $C_2^5.C_4^2$ x 12, $C_2^4.C_2^5$ x 12, $C_2^5.C_4^2$ x 12, $(C_2^2\times C_4^2):C_8$ x 12, $(D_4\times C_2^3):C_8$ x 8, $C_2\times C_4^2.C_4^2$ x 8, $C_2^3.(C_8\times D_4)$ x 8, $C_4^2.C_2^5$ x 8, $C_4^3.C_2^3$ x 6, $C_2^5.C_4^2$ x 6, $C_4^3:C_2^3$ x 4, $C_4^3:C_2^3$ x 3, $C_2^4.C_2^5$ x 3, $C_2^3\times C_8^2$ x 2, $C_2^4\times C_4\times C_8$ x 2, $C_2\times C_4^4$

Order 256: $C_2\times C_4^2\times C_8$ x 560, $C_4^3.C_2^2$ x 448, $C_4^3.C_2^2$ x 320, $C_4^2.C_2^4$ x 320, $C_4^2.C_2^4$ x 296, $C_4^2.D_8$ x 256, $C_4^2.D_8$ x 256, $C_2^4.C_4^2$ x 192, $C_4^3.C_4$ x 180, $C_2^4.C_2^4$ x 168, $(C_2^2\times C_8):D_4$ x 168, $C_2^2.C_8^2$ x 144, $C_4.C_8^2$ x 144, $C_2^3\times C_4\times C_8$ x 134, $C_4^2.C_4^2$ x 128, $C_4^3:C_2^2$ x 120, $C_4^2.C_4^2$ x 120, $C_4:C_8^2$ x 112, $C_4^3:C_2^2$ x 108, $C_4^3.C_4$ x 108, $C_2^4.C_4^2$ x 96, $C_2^4.C_4^2$ x 96, $(C_2\times C_4^2):C_8$ x 84, $C_4.C_8^2$ x 64, $C_2^2.(C_8\times D_4)$ x 56, $C_4^3:C_4$ x 36, $C_2^2\times C_8^2$ x 32, $C_2^4.C_4^2$ x 30, $C_4^2.C_2^4$ x 24, $C_2^4:C_4^2$ x 18, $C_4^4$ x 16, $C_2^2\times C_4^3$ x 15, $C_2^4:C_4^2$ x 12, $C_2^4.C_2^4$ x 12, $C_4^2:C_2^4$ x 12, $C_2^5:C_8$ x 12, $C_2^3.C_2^5$ x 12, $C_2^3.C_2^5$ x 12, $C_2^5\times C_8$ x 4, $C_2^3.C_2^5$ x 3, $C_2^4\times C_4^2$ x 2, $C_4^2:C_2^4$

Order 128: $C_4^2.C_2^3$ x 1760, $C_2^2\times C_4\times C_8$ x 1624, $C_4^2\times C_8$ x 1184, $C_4^2.D_4$ x 1024, $C_4^3:C_2$ x 480, $D_4\times C_4^2$ x 448, $C_4^2:C_2^3$ x 444, $C_4^2.C_2^3$ x 444, $C_4^2.D_4$ x 416, $C_2^3.C_4^2$ x 384, $C_4^2:C_8$ x 336, $C_2\times C_4^3$ x 288, $C_2^3:C_4^2$ x 288, $C_2^3.C_2^4$ x 252, $C_4^2:C_8$ x 240, $C_2^3.C_4^2$ x 240, $C_2^4:C_8$ x 240, $C_4:C_4\times C_8$ x 224, $C_4^2.D_4$ x 192, $C_2^3.C_2^4$ x 180, $C_2.C_8^2$ x 176, $C_2^4\times C_8$ x 172, $C_4^2.D_4$ x 128, $C_2^3\times C_4^2$ x 105, $C_2^3:C_4^2$ x 96, $C_2^4.C_2^3$ x 84, $C_2\times C_8^2$ x 80, $C_2^3.C_2^4$ x 54, $C_4^2:C_2^3$ x 42, $C_2^3.C_4^2$ x 18, $C_2^5:C_4$ x 18, $C_2^4.D_4$ x 12, $C_2^5\times C_4$ x 6, $D_4\times C_2^4$ x 4

Order 64: $C_2\times C_4\times C_8$ x 4256, $C_4^2:C_2^2$ x 2640, $C_8\times D_4$ x 1664, $C_2^3\times C_8$ x 1448, $C_4^2.C_4$ x 1320, $C_2^2\times C_4^2$ x 1180, $C_2^3:C_8$ x 768, $C_4^3$ x 672, $C_2^3.C_2^3$ x 624, $C_2^2:C_4^2$ x 576, $D_4:C_8$ x 512, $C_2^4:C_4$ x 360, $C_4:C_4^2$ x 336, $C_4^2:C_2^2$ x 280, $C_2^2.C_4^2$ x 240, $C_2^4\times C_4$ x 237, $C_2^3.D_4$ x 222, $D_4\times C_2^3$ x 162, $C_2^2.C_4^2$ x 144, $C_4^2:C_4$ x 120, $C_8^2$ x 32, $C_2^6$ x 2

Order 32: $C_2\times C_4^2$ x 3216, $C_2^2\times C_8$ x 3056, $C_4\times D_4$ x 2496, $C_4\times C_8$ x 1952, $C_2^3\times C_4$ x 1830, $C_2^3:C_4$ x 1152, $C_2^2\times D_4$ x 1148, $C_2^2.D_4$ x 660, $C_4:C_8$ x 624, $C_2^2:C_8$ x 384, $C_4:D_4$ x 288, $C_2.C_4^2$ x 144, $C_2^5$ x 77

Order 16: $C_2^2\times C_4$ x 3660, $C_2\times D_4$ x 1656, $C_2\times C_8$ x 1600, $C_4^2$ x 1568, $C_2^2:C_4$ x 576, $C_2^4$ x 551, $C_4:C_4$ x 312

Order 8: $C_2\times C_4$ x 1896, $C_2^3$ x 955, $D_4$ x 400, $C_8$ x 160

Order 4: $C_2^2$ x 427, $C_4$ x 192

Order 2: $C_2$ x 47

Order 1: $C_1$

Classes of subgroups up to automorphism

Order 4096: $C_4^4.C_2^4$

Order 2048: $C_2\times C_4^3.C_2^4$, $C_4^4.C_2^3$, $C_2\times C_4\times C_4^3.C_2^2$, $C_2\times C_2^3.C_2^5.C_2^2$, $C_2\times C_4^4.C_2^2$, $C_4^4.D_4$, $C_4^4.D_4$, $C_4^4.C_2^3$

Order 1024: $C_4^4.C_2^2$ x 3, $C_2\times C_4^3\times C_8$ x 2, $C_4^4.C_2^2$ x 2, $C_4\times C_4^3.C_2^2$ x 2, $C_4^4.C_4$ x 2, $C_2\times C_4^3.D_4$ x 2, $C_4^2:C_8^2$ x 2, $C_4^3.C_4^2$ x 2, $C_4^3.C_2^4$, $C_2\times C_4^3.C_2^3$, $C_4\times C_4^3.C_2^2$, $C_2^2\times C_4^3.C_2^2$, $C_2\times C_2^3.C_2^5.C_2$, $C_2\times C_4^4.C_2$, $C_2\times C_4\times C_2^3.C_4^2$, $C_2\times C_4\times C_2^2.(C_4\times D_4)$, $C_2\times C_2^4.C_2^4.C_2$, $C_2\times (C_2\times C_4^3).C_2^2$, $C_2\times C_2^3.C_2^5.C_2$, $C_4^4.C_2^2$, $C_2^2\times C_4^3.C_2^2$, $C_2\times C_4^3.C_2^3$, $C_2\times C_2^4.C_2^4.C_2$, $C_2\times (C_2\times C_4^3).C_2^2$, $C_2^6.C_2^4$, $C_4^3.C_2^4$, $C_4^3.C_2^4$, $C_8\times C_2^3.C_2^4$, $C_4^3.C_4^2$, $(C_2\times D_4).C_8^2$

Order 512: $C_2^2\times C_4^2\times C_8$ x 12, $C_4^3.C_2^3$ x 9, $C_4^3:C_8$ x 8, $C_4^3\times C_8$ x 8, $C_4^3.C_2^3$ x 7, $C_4^4:C_2$ x 6, $C_4^3.D_4$ x 6, $C_4^3.C_2^3$ x 5, $C_4^3.D_4$ x 4, $C_2^3.C_8^2$ x 4, $C_4^3.C_2^3$ x 4, $C_4^3.C_2^3$ x 4, $C_2^4.C_2^5$ x 4, $C_8\times C_2^3.C_2^3$ x 4, $(C_2^2\times C_4^2):C_8$ x 4, $C_4^3.D_4$ x 3, $C_4^3:C_2^3$ x 2, $C_4^3:C_2^3$ x 2, $(D_4\times C_2^3):C_8$ x 2, $C_4^3.C_2^3$ x 2, $C_2\times C_4^2.C_4^2$ x 2, $C_2^5.C_4^2$ x 2, $C_2^5.C_4^2$ x 2, $C_2^4.C_2^5$ x 2, $C_4^2:C_4\times C_8$ x 2, $C_2^5.C_4^2$ x 2, $C_2^3.(C_8\times D_4)$ x 2, $C_4^3.D_4$ x 2, $C_4^3.D_4$ x 2, $C_4^2.C_2^5$ x 2, $C_2\times C_4^2.C_4^2$, $C_4^2.C_2^5$, $C_2^3\times C_8^2$, $C_2\times C_4^4$, $D_4:C_8^2$, $C_4^2.(C_4\times D_4)$, $C_4^3.D_4$, $C_4^3.D_4$, $C_2^4\times C_4\times C_8$

Order 256: $C_2\times C_4^2\times C_8$ x 49, $C_2^3\times C_4\times C_8$ x 24, $C_4^3.C_4$ x 19, $C_2^4.C_2^4$ x 15, $C_4^3:C_2^2$ x 15, $C_4^3:C_2^2$ x 12, $C_4^2.C_2^4$ x 10, $C_2^2.C_8^2$ x 8, $C_4^3:C_4$ x 8, $(C_2\times C_4^2):C_8$ x 8, $C_2^2\times C_4^3$ x 8, $C_4^3.C_4$ x 8, $C_4^3.C_2^2$ x 8, $C_2^4.C_4^2$ x 7, $C_4^4$ x 6, $(C_2^2\times C_8):D_4$ x 6, $C_2^4.C_4^2$ x 6, $C_4^2.C_4^2$ x 5, $C_2^4.C_4^2$ x 5, $C_4.C_8^2$ x 5, $C_2^4.C_2^4$ x 4, $C_4^2:C_2^4$ x 4, $C_4^2.C_2^4$ x 4, $C_2^3.C_2^5$ x 4, $C_2^3.C_2^5$ x 4, $C_2^4:C_4^2$ x 4, $C_4^2.C_2^4$ x 4, $C_2^4.C_4^2$ x 3, $C_2^2.(C_8\times D_4)$ x 3, $C_4^3.C_2^2$ x 3, $C_4:C_8^2$ x 3, $C_4^2.D_8$ x 3, $C_2^2\times C_8^2$ x 3, $C_4^2.C_4^2$ x 2, $C_2^4:C_4^2$ x 2, $C_2^5:C_8$ x 2, $C_2^3.C_2^5$ x 2, $C_2^5\times C_8$, $C_4^2:C_2^4$, $C_2^4\times C_4^2$, $C_4.C_8^2$, $C_4^2.D_8$

Order 128: $C_2^2\times C_4\times C_8$ x 100, $C_2\times C_4^3$ x 46, $C_4^2\times C_8$ x 41, $C_4^2:C_2^3$ x 30, $C_2^3\times C_4^2$ x 27, $D_4\times C_4^2$ x 21, $C_4^2.C_2^3$ x 20, $C_2^3.C_2^4$ x 20, $C_2^3:C_4^2$ x 19, $C_4^2:C_8$ x 17, $C_2^3.C_4^2$ x 14, $C_2^3.C_2^4$ x 14, $C_4^2.C_2^3$ x 13, $C_2^4\times C_8$ x 12, $C_4^3:C_2$ x 12, $C_2^4.C_2^3$ x 8, $C_2^4:C_8$ x 8, $C_2^3.C_2^4$ x 8, $C_4^2:C_8$ x 6, $C_4^2:C_2^3$ x 6, $C_4^2.D_4$ x 5, $C_2^3.C_4^2$ x 4, $C_4^2.D_4$ x 4, $C_2.C_8^2$ x 4, $C_2^4.D_4$ x 4, $C_2^5:C_4$ x 4, $C_4^2.D_4$ x 4, $C_2^3:C_4^2$ x 4, $C_4:C_4\times C_8$ x 3, $C_2^3.C_4^2$ x 3, $C_2\times C_8^2$ x 3, $D_4\times C_2^4$ x 2, $C_2^5\times C_4$ x 2, $C_4^2.D_4$

Order 64: $C_2^2\times C_4^2$ x 132, $C_2\times C_4\times C_8$ x 126, $C_4^2:C_2^2$ x 58, $C_4^3$ x 48, $C_2^3\times C_8$ x 48, $C_2^4\times C_4$ x 28, $C_4^2.C_4$ x 26, $C_2^3.D_4$ x 20, $C_4:C_4^2$ x 18, $C_2^4:C_4$ x 18, $C_2^2:C_4^2$ x 17, $D_4\times C_2^3$ x 15, $C_2^3.C_2^3$ x 10, $C_2^2.C_4^2$ x 10, $C_4^2:C_2^2$ x 9, $C_2^3:C_8$ x 8, $C_2^2.C_4^2$ x 8, $C_4^2:C_4$ x 6, $C_8\times D_4$ x 4, $D_4:C_8$, $C_2^6$, $C_8^2$

Order 32: $C_2\times C_4^2$ x 199, $C_2^3\times C_4$ x 118, $C_2^2\times C_8$ x 70, $C_4\times C_8$ x 45, $C_2^2\times D_4$ x 33, $C_2^2.D_4$ x 26, $C_4\times D_4$ x 24, $C_2^3:C_4$ x 22, $C_2^5$ x 10, $C_4:C_8$ x 8, $C_2.C_4^2$ x 6, $C_4:D_4$ x 4, $C_2^2:C_8$ x 2

Order 16: $C_2^2\times C_4$ x 188, $C_4^2$ x 80, $C_2\times C_8$ x 39, $C_2^4$ x 33, $C_2\times D_4$ x 25, $C_4:C_4$ x 8, $C_2^2:C_4$ x 6

Order 8: $C_2\times C_4$ x 117, $C_2^3$ x 48, $C_8$ x 6, $D_4$ x 5

Order 4: $C_2^2$ x 33, $C_4$ x 21

Order 2: $C_2$ x 10

Order 1: $C_1$

Normal subgroups (quotient in parentheses)

Order 4096: $C_4^4.C_2^4$ ($C_1$)

Order 2048: $C_4^4.C_2^3$ ($C_2$) x 16, $C_2\times C_4^3.C_2^4$ ($C_2$) x 4, $C_2\times C_2^3.C_2^5.C_2^2$ ($C_2$) x 4, $C_4^4.D_4$ ($C_2$) x 2, $C_4^4.D_4$ ($C_2$) x 2, $C_2\times C_4\times C_4^3.C_2^2$ ($C_2$), $C_2\times C_4^4.C_2^2$ ($C_2$), $C_4^4.C_2^3$ ($C_2$)

Order 1024: $C_4^3.C_2^4$ ($C_2^2$) x 32, $(C_2\times D_4).C_8^2$ ($C_2^2$) x 32, $C_4^4.C_2^2$ ($C_2^2$) x 16, $C_4^4.C_2^2$ ($C_4$) x 16, $C_4^4.C_2^2$ ($C_2^2$) x 16, $C_2\times C_2^3.C_2^5.C_2$ ($C_2^2$) x 8, $C_4\times C_4^3.C_2^2$ ($C_2^2$) x 8, $C_2\times (C_2\times C_4^3).C_2^2$ ($C_4$) x 8, $C_4^2:C_8^2$ ($C_2^2$) x 8, $C_4^4.C_2^2$ ($C_2^2$) x 8, $C_4^4.C_2^2$ ($C_4$) x 8, $C_4^3.C_4^2$ ($C_2^2$) x 8, $C_2^2\times C_4^3.C_2^2$ ($C_4$) x 4, $C_2\times (C_2\times C_4^3).C_2^2$ ($C_4$) x 4, $C_2\times C_2^4.C_2^4.C_2$ ($C_4$) x 4, $C_4^3.C_4^2$ ($C_2^2$) x 4, $C_2\times C_4^3\times C_8$ ($C_2^2$) x 3, $C_4^4.C_4$ ($C_2^2$) x 3, $C_2\times C_2^3.C_2^5.C_2$ ($C_2^2$) x 2, $C_2\times C_2^4.C_2^4.C_2$ ($C_4$) x 2, $C_2\times C_4^3.C_2^3$ ($C_2^2$) x 2, $C_2^6.C_2^4$ ($C_2^2$) x 2, $C_2\times C_4^3.D_4$ ($C_2^2$) x 2, $C_4^3.C_2^4$ ($C_4$) x 2, $C_2\times C_4^4.C_2$ ($C_2^2$)

Order 512: $C_4^2.(C_4\times D_4)$ ($C_2\times C_4$) x 64, $C_4^3.D_4$ ($C_8$) x 64, $C_4^3.D_4$ ($C_2^3$) x 32, $C_4^3.D_4$ ($C_2\times C_4$) x 32, $C_4^3.C_2^3$ ($C_8$) x 32, $C_8\times C_2^3.C_2^3$ ($C_2\times C_4$) x 32, $C_4^3.D_4$ ($C_2^3$) x 32, $C_4^3.D_4$ ($C_2\times C_4$) x 32, $C_4^3.D_4$ ($C_2\times C_4$) x 32, $C_4^3.C_2^3$ ($C_2^3$) x 16, $C_4^3.C_2^3$ ($D_4$) x 16, $C_2\times C_4^2.C_4^2$ ($C_2\times C_4$) x 16, $C_4^3.C_2^3$ ($C_2\times C_4$) x 16, $C_4^2.C_2^5$ ($C_2\times C_4$) x 16, $C_4^2:C_4\times C_8$ ($C_2\times C_4$) x 16, $C_2^2\times C_4^2\times C_8$ ($C_2\times C_4$) x 12, $C_4^4:C_2$ ($C_2\times C_4$) x 12, $C_4^3:C_8$ ($C_2^3$) x 12, $C_4^3:C_8$ ($C_2\times C_4$) x 12, $C_4^3\times C_8$ ($C_2^3$) x 12, $C_4^3\times C_8$ ($C_2\times C_4$) x 12, $C_4^3.C_2^3$ ($C_2^3$) x 8, $C_4^3.C_2^3$ ($C_2^3$) x 8, $C_4^3.C_2^3$ ($C_2\times C_4$) x 8, $C_2^2\times C_4^2\times C_8$ ($D_4$) x 8, $C_4^3.D_4$ ($C_2^3$) x 8, $C_4^3.D_4$ ($C_2\times C_4$) x 8, $C_4^3\times C_8$ ($D_4$) x 8, $C_4^3.D_4$ ($C_2^3$) x 8, $C_4^3.C_2^3$ ($C_2\times C_4$) x 6, $C_4^3.C_2^3$ ($C_2^3$) x 6, $C_2^2\times C_4^2\times C_8$ ($C_2^3$) x 6, $C_2^4.C_2^5$ ($C_2\times C_4$) x 6, $(C_2^2\times C_4^2):C_8$ ($C_2\times C_4$) x 6, $(D_4\times C_2^3):C_8$ ($C_2\times C_4$) x 4, $C_2\times C_4^2.C_4^2$ ($C_2\times C_4$) x 4, $C_4^4:C_2$ ($C_2^3$) x 4, $C_2^3.(C_8\times D_4)$ ($C_2\times C_4$) x 4, $C_4^2.C_2^5$ ($C_2\times C_4$) x 4, $C_4^3:C_2^3$ ($C_2\times C_4$) x 3, $C_2^4.C_2^5$ ($C_2\times C_4$) x 3, $C_4^3:C_2^3$ ($C_2^3$) x 2, $C_2\times C_4^4$ ($C_2^3$)

Order 256: $C_4^2.D_8$ ($C_2\times C_8$) x 256, $C_4^3.C_2^2$ ($C_2\times C_8$) x 128, $C_4^2.C_2^4$ ($C_2\times C_8$) x 128, $C_4^2.C_4^2$ ($C_2^2\times C_4$) x 64, $C_2\times C_4^2\times C_8$ ($C_2\times D_4$) x 64, $C_4^2.C_2^4$ ($C_2^2\times C_4$) x 64, $C_2\times C_4^2\times C_8$ ($C_2^2\times C_4$) x 60, $C_4^3:C_2^2$ ($C_2\times C_8$) x 48, $C_4^3.C_4$ ($C_2\times C_8$) x 48, $C_2\times C_4^2\times C_8$ ($C_2\times C_8$) x 48, $C_2\times C_4^2\times C_8$ ($C_2^2:C_4$) x 48, $C_4^2.C_2^4$ ($C_2\times C_8$) x 32, $(C_2^2\times C_8):D_4$ ($C_2\times C_8$) x 32, $C_4.C_8^2$ ($C_2\times D_4$) x 32, $C_2^4.C_2^4$ ($C_4^2$) x 24, $C_2^4.C_2^4$ ($C_2^2\times C_4$) x 24, $(C_2\times C_4^2):C_8$ ($C_2^2\times C_4$) x 24, $C_4^3.C_4$ ($C_2^2\times C_4$) x 24, $C_2\times C_4^2\times C_8$ ($D_4:C_2$) x 24, $C_4^2.C_2^4$ ($C_2^2\times C_4$) x 16, $C_2^3\times C_4\times C_8$ ($C_2^2:C_4$) x 16, $C_2^2.(C_8\times D_4)$ ($C_2^2\times C_4$) x 16, $(C_2^2\times C_8):D_4$ ($C_2^2\times C_4$) x 16, $C_4^2.C_4^2$ ($C_2^2\times C_4$) x 16, $C_2\times C_4^2\times C_8$ ($\OD_{16}$) x 16, $C_4^3:C_4$ ($C_4^2$) x 12, $C_4^3:C_4$ ($C_2^2\times C_4$) x 12, $C_4^2.C_2^4$ ($C_2^2\times C_4$) x 12, $C_2^3\times C_4\times C_8$ ($C_2^2\times C_4$) x 12, $C_4^3:C_2^2$ ($C_4^2$) x 12, $C_4^3:C_2^2$ ($C_2^2\times C_4$) x 12, $C_4^3:C_2^2$ ($C_2^2\times C_4$) x 12, $C_4^3.C_4$ ($C_2^4$) x 12, $C_4^3.C_4$ ($C_2^2\times C_4$) x 12, $C_2\times C_4^2\times C_8$ ($C_2^4$) x 12, $C_2^3\times C_4\times C_8$ ($C_2\times D_4$) x 8, $C_2^4.C_2^4$ ($C_4^2$) x 6, $C_4^4$ ($C_2^2\times C_4$) x 6, $C_4^2:C_2^4$ ($C_2^2\times C_4$) x 6, $C_2^3.C_2^5$ ($C_4^2$) x 6, $C_2^3.C_2^5$ ($C_2^2\times C_4$) x 6, $C_2^2\times C_4^3$ ($C_2^2\times C_4$) x 6, $C_4^4$ ($D_4:C_2$) x 4, $C_4^4$ ($C_2\times D_4$) x 4, $C_4^3:C_2^2$ ($C_2^4$) x 4, $C_2^2\times C_4^3$ ($D_4:C_2$) x 4, $C_2^2\times C_4^3$ ($C_2\times D_4$) x 4, $C_2^3.C_2^5$ ($C_4^2$) x 3, $C_4^4$ ($C_2^4$) x 2, $C_4^2:C_2^4$ ($C_4^2$), $C_2^2\times C_4^3$ ($C_2^4$)

Order 128: $C_4^2.D_4$ ($C_2^2\times C_8$) x 256, $C_4^2:C_8$ ($C_2^2\times C_8$) x 96, $C_4^2\times C_8$ ($C_2^2\times C_8$) x 96, $C_4^3:C_2$ ($C_2^2\times C_8$) x 96, $C_4^3:C_2$ ($C_4\times C_8$) x 96, $C_2^2\times C_4\times C_8$ ($C_2^3:C_4$) x 88, $C_4^2.D_4$ ($C_2^2\times C_8$) x 64, $C_4^2\times C_8$ ($C_2^2:C_8$) x 64, $C_4^2.C_2^3$ ($C_2^2\times C_8$) x 64, $C_2^2\times C_4\times C_8$ ($C_2^2:C_8$) x 64, $C_2\times C_4^3$ ($C_4\times D_4$) x 48, $C_4^2\times C_8$ ($C_4\times D_4$) x 48, $C_4^2:C_2^3$ ($C_2^2\times C_8$) x 48, $C_4^2.C_2^3$ ($C_2^2\times C_8$) x 48, $C_2^2\times C_4\times C_8$ ($\OD_{16}:C_2$) x 48, $C_2^2\times C_4\times C_8$ ($C_2^2\times C_8$) x 48, $C_2^2\times C_4\times C_8$ ($C_4\times D_4$) x 48, $C_2^3.C_2^4$ ($C_4\times C_8$) x 48, $C_4^2\times C_8$ ($C_2\times \OD_{16}$) x 32, $C_2\times C_4^3$ ($D_8:C_2$) x 24, $C_2\times C_4^3$ ($C_2^2\times C_8$) x 24, $C_4^2\times C_8$ ($D_4:C_2^2$) x 24, $C_4^2\times C_8$ ($C_2^2\times D_4$) x 24, $C_4^2:C_2^3$ ($C_4\times C_8$) x 24, $C_2^4.C_2^3$ ($C_2\times C_4^2$) x 24, $C_4^2.C_2^3$ ($C_2^3\times C_4$) x 24, $C_2^2\times C_4\times C_8$ ($C_2^3\times C_4$) x 24, $C_2^3.C_2^4$ ($C_2\times C_4^2$) x 24, $C_2^3.C_2^4$ ($C_4\times C_8$) x 24, $C_2\times C_4^3$ ($D_4:C_2^2$) x 22, $C_2\times C_4^3$ ($\OD_{16}:C_2$) x 16, $C_4^2\times C_8$ ($C_4:D_4$) x 16, $C_2^3\times C_4^2$ ($C_4\times D_4$) x 16, $C_2^2\times C_4\times C_8$ ($C_2^2\times D_4$) x 16, $C_2^2\times C_4\times C_8$ ($C_2\times \OD_{16}$) x 16, $C_2^2\times C_4\times C_8$ ($C_4:D_4$) x 16, $C_2\times C_4^3$ ($C_2^3\times C_4$) x 15, $C_2\times C_4^3$ ($C_2^2\times D_4$) x 14, $C_2\times C_4^3$ ($C_4^2:C_2$) x 12, $C_2\times C_4^3$ ($C_2^3:C_4$) x 12, $C_2\times C_4^3$ ($C_2\times C_4^2$) x 12, $C_4^2:C_2^3$ ($C_2^3\times C_4$) x 12, $C_4^2:C_2^3$ ($C_2\times C_4^2$) x 12, $C_2^3.C_2^4$ ($C_2\times C_4^2$) x 12, $C_2^3.C_2^4$ ($C_2^3\times C_4$) x 12, $C_2^3.C_2^4$ ($C_2\times C_4^2$) x 12, $C_2\times C_4^3$ ($Q_{16}:C_2$) x 8, $C_2\times C_4^3$ ($C_2\times \OD_{16}$) x 8, $C_4^2\times C_8$ ($C_4:D_4$) x 8, $C_4^2\times C_8$ ($C_4^2:C_2$) x 8, $C_2^4\times C_8$ ($C_2^3:C_4$) x 8, $C_2^2\times C_4\times C_8$ ($C_4:D_4$) x 8, $C_2^2\times C_4\times C_8$ ($C_4^2:C_2$) x 8, $C_2^4.D_4$ ($C_2\times C_4^2$) x 6, $C_4^2:C_2^3$ ($C_2\times C_4^2$) x 4, $C_2^3\times C_4^2$ ($C_4^2:C_2$) x 4, $C_2^3\times C_4^2$ ($C_2^3:C_4$) x 4, $C_2^3\times C_4^2$ ($C_2\times C_4^2$) x 4, $C_2^3\times C_4^2$ ($C_2^3\times C_4$) x 3, $D_4\times C_2^4$ ($C_2\times C_4^2$) x 2, $C_2^3\times C_4^2$ ($D_4:C_2^2$) x 2, $C_2^3\times C_4^2$ ($C_2^2\times D_4$) x 2, $C_2\times C_4^3$ ($C_2^5$)

Order 64: $C_2\times C_4\times C_8$ ($C_8\times D_4$) x 192, $C_2\times C_4\times C_8$ ($C_2^3:C_8$) x 160, $C_2^3.C_2^3$ ($C_2\times C_4\times C_8$) x 96, $C_2\times C_4\times C_8$ ($C_8:D_4$) x 64, $C_4^3$ ($C_8\times D_4$) x 64, $C_4^2:C_2^2$ ($C_8^2$) x 64, $C_2^2\times C_4^2$ ($C_8\times D_4$) x 64, $C_2^2\times C_4^2$ ($C_2^2:C_4^2$) x 56, $C_2^2\times C_4^2$ ($C_4^2:C_2^2$) x 56, $C_2\times C_4\times C_8$ ($C_2^3.C_2^3$) x 48, $C_2\times C_4\times C_8$ ($C_8.C_2^3$) x 48, $C_2\times C_4\times C_8$ ($C_2^3\times C_8$) x 48, $C_2\times C_4\times C_8$ ($C_4^2:C_2^2$) x 48, $C_4^2:C_4$ ($C_2\times C_4\times C_8$) x 48, $C_4^2:C_2^2$ ($C_2\times C_4\times C_8$) x 48, $C_4^2:C_2^2$ ($C_2\times C_4\times C_8$) x 48, $C_4^2:C_2^2$ ($C_2^3\times C_8$) x 48, $C_4^2.C_4$ ($C_2^3\times C_8$) x 48, $C_4^3$ ($D_8:C_4$) x 32, $C_4^3$ ($\SD_{16}:C_4$) x 32, $C_2^3\times C_8$ ($C_2^3:C_8$) x 32, $C_2^2\times C_4^2$ ($C_8.C_2^3$) x 32, $C_2^2\times C_4^2$ ($D_8:C_4$) x 32, $C_2^2\times C_4^2$ ($D_8:C_4$) x 32, $C_2^2\times C_4^2$ ($\SD_{16}:C_4$) x 32, $C_4^3$ ($C_2\times C_4\times C_8$) x 24, $C_4^3$ ($C_8:C_2^3$) x 24, $C_4^3$ ($C_2^3\times C_8$) x 24, $D_4\times C_2^3$ ($C_2\times C_4\times C_8$) x 24, $C_2^3.D_4$ ($C_2\times C_4\times C_8$) x 24, $C_2^2\times C_4^2$ ($C_2\times C_4\times C_8$) x 24, $C_2\times C_4\times C_8$ ($(C_2^2\times C_8):C_2$) x 16, $C_2\times C_4\times C_8$ ($C_2^2\times \OD_{16}$) x 16, $C_2\times C_4\times C_8$ ($C_2^3:D_4$) x 16, $C_4^3$ ($C_2^3.D_4$) x 16, $C_4^3$ ($C_2^3.D_4$) x 16, $C_4^3$ ($C_2^3:C_8$) x 16, $C_4^3$ ($\OD_{16}:C_4$) x 16, $C_4^3$ ($C_8.C_2^3$) x 16, $C_4^3$ ($C_4^2.C_4$) x 16, $C_2^3\times C_8$ ($(C_2^2\times C_8):C_2$) x 16, $C_2^3\times C_8$ ($C_2^3.C_2^3$) x 16, $C_2^3\times C_8$ ($C_2^4:C_4$) x 16, $C_2^2\times C_4^2$ ($C_2^3.D_4$) x 16, $C_2^2\times C_4^2$ ($C_2^3.D_4$) x 16, $C_2^2\times C_4^2$ ($C_2^3:C_8$) x 16, $C_2^2\times C_4^2$ ($\OD_{16}:C_4$) x 16, $C_2^2\times C_4^2$ ($C_4^2.C_4$) x 16, $C_2^2\times C_4^2$ ($C_4^2:C_2^2$) x 16, $C_4^3$ ($C_4^2.C_2^2$) x 12, $C_4^3$ ($C_4^2.C_2^2$) x 12, $C_4^3$ ($C_4^2:C_2^2$) x 12, $C_2^3.D_4$ ($C_2^2\times C_4^2$) x 12, $C_2^2\times C_4^2$ ($C_8:C_2^3$) x 12, $C_2^2\times C_4^2$ ($C_2^3\times C_8$) x 12, $C_2^2\times C_4^2$ ($C_4^2.C_2^2$) x 12, $C_2^2\times C_4^2$ ($C_4^2.C_2^2$) x 12, $C_2^2\times C_4^2$ ($C_4^2:C_2^2$) x 11, $C_2^2\times C_4^2$ ($C_2^4:C_4$) x 11, $C_2^2\times C_4^2$ ($C_2^2\times C_4^2$) x 11, $C_2\times C_4\times C_8$ ($C_4^2:C_2^2$) x 8, $C_2\times C_4\times C_8$ ($C_4^2:C_2^2$) x 8, $C_4^3$ ($C_4\times \OD_{16}$) x 8, $C_4^3$ ($Q_{16}:C_2^2$) x 8, $C_4^3$ ($C_2^2\times \OD_{16}$) x 8, $C_4^3$ ($C_4^2.C_2^2$) x 8, $C_2^4\times C_4$ ($C_2^2:C_4^2$) x 8, $C_2^2\times C_4^2$ ($C_4\times \OD_{16}$) x 8, $C_2^2\times C_4^2$ ($C_4^2.C_2^2$) x 8, $C_4^3$ ($D_4:C_2^3$) x 6, $C_4^3$ ($C_4^2:C_2^2$) x 4, $C_4^3$ ($C_2^3:D_4$) x 4, $D_4\times C_2^3$ ($C_2^2\times C_4^2$) x 4, $C_2^4\times C_4$ ($C_4^2:C_2^2$) x 4, $C_2^2\times C_4^2$ ($Q_{16}:C_2^2$) x 4, $C_2^2\times C_4^2$ ($C_2^2\times \OD_{16}$) x 4, $C_2^2\times C_4^2$ ($C_4^2:C_2^2$) x 4, $C_2^2\times C_4^2$ ($C_2^3:D_4$) x 4, $C_2^2\times C_4^2$ ($C_2^4\times C_4$) x 3, $C_4^3$ ($D_4\times C_2^3$) x 2, $C_4^3$ ($C_4^2:C_2^2$) x 2, $C_4^3$ ($C_4^2:C_2^2$) x 2, $C_2^2\times C_4^2$ ($D_4:C_2^3$) x 2, $C_2^2\times C_4^2$ ($D_4\times C_2^3$) x 2, $C_2^2\times C_4^2$ ($C_4^2:C_2^2$) x 2, $C_2^2\times C_4^2$ ($C_4^2:C_2^2$) x 2, $C_2^4\times C_4$ ($C_4^2:C_2^2$), $C_2^4\times C_4$ ($C_2^4:C_4$), $C_2^4\times C_4$ ($C_2^2\times C_4^2$)

Order 32: $C_2\times C_4^2$ ($D_8:C_8$) x 128, $C_2\times C_4^2$ ($\SD_{16}:C_8$) x 128, $C_2\times C_4^2$ ($C_4^2.C_2^3$) x 128, $C_4\times C_8$ ($C_4^2.C_2^3$) x 96, $C_2\times C_4^2$ ($D_4:C_4^2$) x 96, $C_2\times C_4^2$ ($C_2^3.C_4^2$) x 96, $C_2^2\times C_8$ ($C_4^2.D_4$) x 64, $C_4:D_4$ ($C_2\times C_8^2$) x 64, $C_4\times C_8$ ($C_4^2.D_4$) x 64, $C_2\times C_4^2$ ($C_4^2.D_4$) x 64, $C_2\times C_4^2$ ($C_4^2.D_4$) x 64, $C_2\times C_4^2$ ($C_4^2.D_4$) x 48, $C_2\times C_4^2$ ($C_4^2.C_2^3$) x 48, $C_2\times C_4^2$ ($C_4^2.D_4$) x 40, $C_2\times C_4^2$ ($C_4^2.D_4$) x 40, $C_2\times C_4^2$ ($C_4^2.C_2^3$) x 40, $C_2^2\times D_4$ ($C_2\times C_8^2$) x 32, $C_2^3\times C_4$ ($D_4.C_4^2$) x 32, $C_2^3\times C_4$ ($D_4:C_4^2$) x 32, $C_2^3\times C_4$ ($C_2^3.C_4^2$) x 32, $C_2^2\times C_8$ ($C_2^4:C_8$) x 32, $C_4\times C_8$ ($C_4^2.C_2^3$) x 32, $C_2\times C_4^2$ ($D_4.C_4^2$) x 32, $C_2\times C_4^2$ ($C_8\times \OD_{16}$) x 32, $C_2\times C_4^2$ ($C_4^2.C_2^3$) x 32, $C_2\times C_4^2$ ($C_4^2.C_2^3$) x 32, $C_2\times C_4^2$ ($C_2^2\times C_4\times C_8$) x 30, $C_2^2\times D_4$ ($C_2^2\times C_4\times C_8$) x 24, $C_2^2.D_4$ ($C_2^2\times C_4\times C_8$) x 24, $C_2\times C_4^2$ ($C_4^2:D_4$) x 24, $C_2^3\times C_4$ ($C_2^3:C_4^2$) x 23, $C_2\times C_4^2$ ($C_4^2.C_2^3$) x 20, $C_2\times C_4^2$ ($C_2^4.D_4$) x 20, $C_2\times C_4^2$ ($C_2^4.D_4$) x 20, $C_2\times C_4^2$ ($C_2^4:C_8$) x 20, $C_2\times C_4^2$ ($C_2^3.C_4^2$) x 20, $C_2^3\times C_4$ ($D_4.C_4^2$) x 16, $C_2^3\times C_4$ ($C_4^2.D_4$) x 16, $C_2^3\times C_4$ ($C_4^2.C_2^3$) x 16, $C_2^3\times C_4$ ($C_4^2.C_2^3$) x 16, $C_2^2\times C_8$ ($(C_2^3\times C_8):C_2$) x 16, $C_2^2\times C_8$ ($C_2^3.C_2^4$) x 16, $C_2\times C_4^2$ ($D_4.C_4^2$) x 16, $C_2\times C_4^2$ ($C_8.C_2^4$) x 16, $C_2\times C_4^2$ ($C_4^2.D_4$) x 16, $C_2\times C_4^2$ ($C_4^2.D_4$) x 16, $C_2\times C_4^2$ ($C_8^2:C_2$) x 16, $C_2\times C_4^2$ ($C_2\times C_8^2$) x 16, $C_2\times C_4^2$ ($C_4^2.C_2^3$) x 16, $C_2\times C_4^2$ ($C_4^2.C_2^3$) x 16, $C_2\times C_4^2$ ($C_4^2:C_2^3$) x 16, $C_2^3\times C_4$ ($D_4.C_4^2$) x 12, $C_2\times C_4^2$ ($\OD_{16}:D_4$) x 12, $C_2\times C_4^2$ ($D_4.C_4^2$) x 12, $C_2\times C_4^2$ ($C_4^3:C_2$) x 12, $C_2\times C_4^2$ ($C_4^3:C_2$) x 12, $C_2\times C_4^2$ ($C_4^3:C_2$) x 12, $C_2\times C_4^2$ ($D_4\times C_4^2$) x 12, $C_2\times C_4^2$ ($C_2^3.C_4^2$) x 10, $C_2^3\times C_4$ ($C_4^2.D_4$) x 8, $C_2^3\times C_4$ ($C_4^2.D_4$) x 8, $C_2^3\times C_4$ ($C_4^2.C_2^3$) x 8, $C_2^3\times C_4$ ($C_4^2.C_2^3$) x 8, $C_2^3\times C_4$ ($C_4^2:C_2^3$) x 8, $C_2^3\times C_4$ ($C_4^2:D_4$) x 8, $C_2\times C_4^2$ ($C_4^2.D_4$) x 8, $C_2\times C_4^2$ ($C_4^2.D_4$) x 8, $C_2\times C_4^2$ ($C_4^2.C_2^3$) x 8, $C_2^3\times C_4$ ($C_2^2\times C_4\times C_8$) x 6, $C_2\times C_4^2$ ($C_8:C_2^4$) x 6, $C_2\times C_4^2$ ($C_2^4\times C_8$) x 6, $C_2\times C_4^2$ ($C_4^2.C_2^3$) x 6, $C_2\times C_4^2$ ($C_4^2.C_2^3$) x 6, $C_2\times C_4^2$ ($C_4^2:C_2^3$) x 6, $C_2\times C_4^2$ ($C_2^3.C_2^4$) x 6, $C_2\times C_4^2$ ($C_2^3.C_2^4$) x 6, $C_2^3\times C_4$ ($C_4^2:C_2^3$) x 4, $C_2^3\times C_4$ ($C_4^2.C_2^3$) x 4, $C_2^3\times C_4$ ($C_4^2.C_2^3$) x 4, $C_2^3\times C_4$ ($C_2^4.D_4$) x 4, $C_2^3\times C_4$ ($C_2^4.D_4$) x 4, $C_2^3\times C_4$ ($(C_2^3\times C_8):C_2$) x 4, $C_2^3\times C_4$ ($C_2^4:C_8$) x 4, $C_2^3\times C_4$ ($C_2^3.C_4^2$) x 4, $C_2^3\times C_4$ ($C_4^3:C_2$) x 4, $C_2^3\times C_4$ ($C_4^3:C_2$) x 4, $C_2^3\times C_4$ ($C_4^3:C_2$) x 4, $C_2^3\times C_4$ ($D_4\times C_4^2$) x 4, $C_2\times C_4^2$ ($C_4^2.C_2^3$) x 4, $C_2\times C_4^2$ ($\OD_{16}:D_4$) x 4, $C_2\times C_4^2$ ($C_4^2.C_2^3$) x 4, $C_2\times C_4^2$ ($(C_2^3\times C_8):C_2$) x 4, $C_2^3\times C_4$ ($C_2^3.C_4^2$) x 2, $C_2^3\times C_4$ ($C_2^3.C_2^4$) x 2, $C_2^3\times C_4$ ($C_2^3.C_2^4$) x 2, $C_2\times C_4^2$ ($Q_{16}:C_2^3$) x 2, $C_2\times C_4^2$ ($C_2^3\times \OD_{16}$) x 2, $C_2\times C_4^2$ ($C_4^2:C_2^3$) x 2, $C_2\times C_4^2$ ($C_2^4:D_4$) x 2, $C_2^5$ ($C_2^3:C_4^2$), $C_2^3\times C_4$ ($C_4^2:C_2^3$), $C_2^3\times C_4$ ($C_2^5:C_4$), $C_2^3\times C_4$ ($C_2^3\times C_4^2$), $C_2\times C_4^2$ ($C_4^2:C_2^3$), $C_2\times C_4^2$ ($C_4^2:C_2^3$)

Order 16: $C_4^2$ ($D_4:(C_4\times C_8)$) x 128, $C_2^2\times C_4$ ($D_4:(C_4\times C_8)$) x 128, $C_4^2$ ($C_4^3.C_2^2$) x 64, $C_4^2$ ($C_4^2.C_2^4$) x 64, $C_4^2$ ($C_4^2.C_2^4$) x 64, $C_2^2\times C_4$ ($C_4^3.C_2^2$) x 64, $C_2^2\times C_4$ ($C_4^3.C_2^2$) x 64, $C_2^2\times C_4$ ($C_2\times D_4:C_4^2$) x 44, $C_2^2\times C_4$ ($C_2^4.C_4^2$) x 44, $C_2^2\times C_4$ ($C_2\times D_4.C_4^2$) x 40, $C_2\times C_8$ ($(C_2^2\times C_8):D_4$) x 32, $C_4^2$ ($C_8\times C_4:D_4$) x 32, $C_4^2$ ($C_2^2:C_8^2$) x 32, $C_4^2$ ($C_4^2.C_2^4$) x 32, $C_4^2$ ($C_4^2.C_2^4$) x 32, $C_2^2\times C_4$ ($C_8\times C_4:D_4$) x 32, $C_2^2\times C_4$ ($D_4.(C_4\times C_8)$) x 32, $C_2^2\times C_4$ ($C_2^2:C_8^2$) x 32, $C_2^2\times C_4$ ($C_4^2.C_2^4$) x 32, $C_2^2\times C_4$ ($C_4^2.C_2^4$) x 32, $C_2^2\times C_4$ ($C_4^2.C_2^4$) x 32, $C_2^2\times C_4$ ($C_4^2.C_2^4$) x 32, $C_4^2$ ($C_4^3.C_2^2$) x 24, $C_2^2\times C_4$ ($C_4^3.C_2^2$) x 24, $C_2^2\times C_4$ ($C_8^2.C_2^2$) x 24, $C_2^2\times C_4$ ($C_2^4.C_4^2$) x 22, $C_2^2\times C_4$ ($C_2\times D_4.C_4^2$) x 20, $C_4^2$ ($C_4^3.C_2^2$) x 16, $C_4^2$ ($C_4^3.C_2^2$) x 16, $C_4^2$ ($C_4^3.C_2^2$) x 16, $C_4^2$ ($C_4^3.C_2^2$) x 16, $C_4^2$ ($C_4^3.C_2^2$) x 16, $C_4^2$ ($C_8^2:C_2^2$) x 16, $C_2\times D_4$ ($C_2^2\times C_8^2$) x 16, $C_2^2\times C_4$ ($C_4^3.C_2^2$) x 16, $C_2^2\times C_4$ ($C_4^3.C_2^2$) x 16, $C_2^2\times C_4$ ($C_4^3.C_2^2$) x 16, $C_2^2\times C_4$ ($C_4^3.C_2^2$) x 16, $C_2^2\times C_4$ ($C_4^3.C_2^2$) x 16, $C_2^2\times C_4$ ($C_4^3.C_2^2$) x 16, $C_2^2\times C_4$ ($C_4^3.C_2^2$) x 16, $C_2^2\times C_4$ ($C_4^2.C_2^4$) x 16, $C_2^2\times C_4$ ($C_4^2.C_2^4$) x 16, $C_2^2\times C_4$ ($C_4^2.C_2^4$) x 16, $C_2^2\times C_4$ ($C_4^2.C_2^4$) x 16, $C_2^2\times C_4$ ($C_8^2.C_2^2$) x 16, $C_2^2\times C_4$ ($C_2^4.C_2^4$) x 14, $C_4^2$ ($C_4^2.C_2^4$) x 12, $C_4^2$ ($C_4^2.C_2^4$) x 12, $C_2^2\times C_4$ ($(C_2\times D_4).C_4^2$) x 12, $C_4^2$ ($C_4^2.C_2^4$) x 8, $C_4^2$ ($C_4^2.C_2^4$) x 8, $C_4^2$ ($C_4^3.C_2^2$) x 8, $C_4^2$ ($C_4^3.C_2^2$) x 8, $C_4^2$ ($C_4^2.(C_2\times D_4)$) x 8, $C_4^2$ ($C_4^2.(C_2\times D_4)$) x 8, $C_4^2$ ($(C_2^2\times C_8):D_4$) x 8, $C_4^2$ ($C_4^2:\OD_{16}$) x 8, $C_4^2$ ($C_8^2:C_2^2$) x 8, $C_4^2$ ($C_2^2\times C_8^2$) x 8, $C_2^4$ ($C_2\times D_4.C_4^2$) x 8, $C_2^2\times C_4$ ($C_4^2.C_2^4$) x 8, $C_2^2\times C_4$ ($C_4^2.C_2^4$) x 8, $C_2^2\times C_4$ ($C_4^3.C_2^2$) x 8, $C_2^2\times C_4$ ($C_4^3.C_2^2$) x 8, $C_2^2\times C_4$ ($C_4^3.C_2^2$) x 8, $C_2^2\times C_4$ ($C_4^2.(C_2\times D_4)$) x 8, $C_2^2\times C_4$ ($C_4^2.(C_2\times D_4)$) x 8, $C_2^2\times C_4$ ($C_4^3:C_2^2$) x 8, $C_2^2\times C_4$ ($(C_2^2\times C_8):D_4$) x 8, $C_2^2\times C_4$ ($C_4^2:\OD_{16}$) x 8, $C_2^2\times C_4$ ($C_8^2.C_2^2$) x 8, $C_2^2\times C_4$ ($C_8^2:C_2^2$) x 8, $C_2^2\times C_4$ ($C_4^2.C_2^4$) x 6, $C_2^2\times C_4$ ($C_4^2.(C_2\times D_4)$) x 6, $C_4^2$ ($C_4^2.C_2^4$) x 4, $C_4^2$ ($C_4^2.C_2^4$) x 4, $C_4^2$ ($C_4^2.C_2^4$) x 4, $C_4^2$ ($C_4^2.C_2^4$) x 4, $C_4^2$ ($(C_2\times \OD_{16}):D_4$) x 4, $C_4^2$ ($(C_2\times \OD_{16}):D_4$) x 4, $C_2^4$ ($C_2\times D_4:C_4^2$) x 4, $C_2^4$ ($C_2\times D_4.C_4^2$) x 4, $C_2^4$ ($(C_2\times D_4).C_4^2$) x 4, $C_2^4$ ($C_2^4.C_4^2$) x 4, $C_2^2\times C_4$ ($C_4^2.C_2^4$) x 4, $C_2^2\times C_4$ ($C_4^2.C_2^4$) x 4, $C_2^2\times C_4$ ($C_4^2.C_2^4$) x 4, $C_2^2\times C_4$ ($C_4^2.C_2^4$) x 4, $C_2^2\times C_4$ ($C_4^2:C_2^4$) x 4, $C_2^2\times C_4$ ($C_2^3.C_2^5$) x 4, $C_2^2\times C_4$ ($(C_2\times \OD_{16}):D_4$) x 4, $C_2^2\times C_4$ ($(C_2\times \OD_{16}):D_4$) x 4, $C_2^2\times C_4$ ($C_8^2:C_2^2$) x 4, $C_2^2\times C_4$ ($C_2^2\times C_8^2$) x 4, $C_4^2$ ($C_4^2.C_2^4$) x 3, $C_2^2\times C_4$ ($C_2^3\times C_4\times C_8$) x 3, $C_4^2$ ($C_4^2.C_2^4$) x 2, $C_4^2$ ($C_4^2.C_2^4$) x 2, $C_2^4$ ($C_2^4.C_2^4$) x 2, $C_2^4$ ($C_4^2.(C_2\times D_4)$) x 2, $C_2^4$ ($C_2^4.C_4^2$) x 2, $C_2^2\times C_4$ ($C_4^2.C_2^4$) x 2, $C_2^2\times C_4$ ($C_4^2.C_2^4$) x 2, $C_2^2\times C_4$ ($C_2^5.D_4$) x 2, $C_2^2\times C_4$ ($C_2^5.D_4$) x 2, $C_2^2\times C_4$ ($(C_2^4\times C_8):C_2$) x 2, $C_2^2\times C_4$ ($C_2^5:C_8$) x 2, $C_2^2\times C_4$ ($C_4^2.C_2^4$) x 2, $C_2^2\times C_4$ ($C_4^3:C_2^2$) x 2, $C_2^2\times C_4$ ($C_4^3:C_2^2$) x 2, $C_2^2\times C_4$ ($C_4^3:C_2^2$) x 2, $C_2^2\times C_4$ ($C_4^3:C_2^2$) x 2, $C_4^2$ ($C_4^2.C_2^4$), $C_2^4$ ($C_2^4:C_4^2$), $C_2^2\times C_4$ ($C_4^2.C_2^4$), $C_2^2\times C_4$ ($C_2^3.C_2^5$), $C_2^2\times C_4$ ($C_2^3.C_2^5$)

Order 8: $C_2\times C_4$ ($D_4:C_8^2$) x 128, $C_2\times C_4$ ($C_4^2.(C_4\times D_4)$) x 80, $C_2\times C_4$ ($C_2^2.C_4^3.C_2$) x 64, $C_2\times C_4$ ($C_4^3.D_4$) x 40, $C_2\times C_4$ ($C_4^2.C_2^4.C_2$) x 32, $C_2\times C_4$ ($C_2\times C_2^3.(C_4\times D_4)$) x 32, $C_2\times C_4$ ($C_2^2.C_4^3.C_2$) x 32, $C_2\times C_4$ ($C_4^3.C_2^3$) x 32, $C_2\times C_4$ ($C_4^3.C_2^3$) x 32, $C_2\times C_4$ ($C_8\times C_2^3.C_2^3$) x 24, $C_2\times C_4$ ($C_2^3:C_8^2$) x 20, $C_2^3$ ($C_4^2.C_2^4.C_2$) x 16, $C_2^3$ ($C_4^2.(C_4\times D_4)$) x 16, $C_2^3$ ($(C_2\times C_4^2).C_2^4$) x 16, $C_2^3$ ($C_2\times C_2^3.(C_4\times D_4)$) x 16, $C_2\times C_4$ ($C_4^2.C_2^4.C_2$) x 16, $C_2\times C_4$ ($D_4\times C_8^2$) x 16, $C_2\times C_4$ ($C_4^2.C_2^4.C_2$) x 16, $C_2\times C_4$ ($C_2\times C_4^2.C_2^3.C_2$) x 16, $C_2\times C_4$ ($(C_2\times C_4^3).C_2^2$) x 16, $C_2\times C_4$ ($(C_2\times C_4^3).C_2^2$) x 16, $C_2\times C_4$ ($(C_2\times C_4^3).C_2^2$) x 12, $C_2\times C_4$ ($C_4^3.D_4$) x 12, $C_2^3$ ($C_4^2.C_2^4.C_2$) x 8, $C_2^3$ ($C_2\times C_4^2.C_2^3.C_2$) x 8, $C_2^3$ ($(C_2\times C_4^3).C_2^2$) x 8, $C_2^3$ ($C_4^3.D_4$) x 8, $C_2^3$ ($(C_2^2\times C_8^2).C_2$) x 8, $C_2^3$ ($(C_2^3\times C_8).C_2^3$) x 8, $C_2^3$ ($C_8\times C_2^3.C_2^3$) x 8, $C_2\times C_4$ ($(C_2\times C_4^3).C_2^2$) x 8, $C_2\times C_4$ ($(C_2^2\times C_8^2).C_2$) x 8, $C_2\times C_4$ ($C_2\times (C_2^3\times C_8).C_2^2$) x 8, $C_2\times C_4$ ($C_2\times C_4^2.C_2^4$) x 8, $C_2\times C_4$ ($C_2\times C_4^2.C_2^4$) x 8, $C_2\times C_4$ ($C_4^2.C_2^5$) x 8, $C_2\times C_4$ ($C_2^2\times C_4^2.C_2^3$) x 8, $C_2\times C_4$ ($(C_2^3\times C_8).C_2^3$) x 8, $C_2\times C_4$ ($C_4^3.C_2^3$) x 6, $C_2\times C_4$ ($C_8^2.C_2^3$) x 6, $C_2^3$ ($(C_2^2\times C_8^2).C_2$) x 4, $C_2^3$ ($C_2^3:C_8^2$) x 4, $C_2^3$ ($C_2^2\times C_2^2.(C_4\times D_4)$) x 4, $C_2^3$ ($(C_2\times C_4^3).C_2^2$) x 4, $C_2^3$ ($C_2^4.C_2^4.C_2$) x 4, $C_2^3$ ($C_4^3.D_4$) x 4, $C_2\times C_4$ ($(C_2^2\times C_8^2).C_2$) x 4, $C_2\times C_4$ ($C_4^3.C_2^3$) x 4, $C_2\times C_4$ ($C_4^3.C_2^3$) x 4, $C_2\times C_4$ ($C_4^3.C_2^3$) x 4, $C_2\times C_4$ ($C_2\times C_2.C_4^3.C_2$) x 4, $C_2\times C_4$ ($C_2\times (C_4^2\times C_8).C_2$) x 4, $C_2\times C_4$ ($C_2\times C_4^3.C_2^2$) x 4, $C_2\times C_4$ ($C_2\times (C_2^2\times C_8).C_2^3$) x 4, $C_2\times C_4$ ($C_2\times C_4^2.C_2^4$) x 4, $C_2\times C_4$ ($C_2\times C_4^2.C_2^4$) x 4, $C_2\times C_4$ ($C_2^2\times C_4^2.C_2^3$) x 4, $C_2\times C_4$ ($C_2^2\times C_4^2.C_2^3$) x 4, $C_2\times C_4$ ($C_8^2.C_2^3$) x 4, $C_2\times C_4$ ($C_2^4.C_2^4.C_2$) x 4, $C_2^3$ ($C_2^2\times D_4:C_4^2$) x 2, $C_2^3$ ($C_2^2\times C_4.C_4^2.C_2$) x 2, $C_2^3$ ($C_2\times (C_2^3\times C_8).C_2^2$) x 2, $C_2^3$ ($C_2^5.C_4^2$) x 2, $C_2\times C_4$ ($C_2\times C_4^3.C_2^2$) x 2, $C_2\times C_4$ ($C_2\times C_4^3.C_2^2$) x 2, $C_2\times C_4$ ($C_2\times C_4.(C_2\times C_4):D_4$) x 2, $C_2\times C_4$ ($C_2\times (C_2\times C_4^2).C_2^3$) x 2, $C_2\times C_4$ ($C_2\times C_4.(C_2\times C_4):D_4$) x 2, $C_2\times C_4$ ($C_2\times C_4.(C_2\times C_4:D_4)$) x 2, $C_2\times C_4$ ($(D_4\times C_2^3):C_8$) x 2, $C_2\times C_4$ ($C_2\times (C_2^2\times C_8).C_2^3$) x 2, $C_2\times C_4$ ($C_8^2.C_2^3$) x 2, $C_2\times C_4$ ($C_2^2\times C_8\times \OD_{16}$) x 2, $C_2^3$ ($C_2\times C_4.(C_2\times C_4\times D_4)$), $C_2^3$ ($C_2^5.C_4^2$), $C_2^3$ ($C_2^4.C_2^5$), $C_2\times C_4$ ($C_2\times (C_2^3\times C_4).C_2^3$), $C_2\times C_4$ ($C_2\times (C_2^3\times C_4).C_2^3$), $C_2\times C_4$ ($C_2^2\times C_4^2.C_2^3$), $C_2\times C_4$ ($C_2^3\times C_8^2$)

Order 4: $C_2^2$ ($C_4^3.C_2^4$) x 48, $C_4$ ($C_2\times C_4^3.C_2^3$) x 32, $C_2^2$ ($(C_2\times C_4^3).C_2^3$) x 16, $C_2^2$ ($C_4^2.(C_8\times D_4)$) x 16, $C_2^2$ ($C_4^3.C_2^4$) x 16, $C_4$ ($C_4^2.(C_8\times D_4)$) x 16, $C_4$ ($C_2\times C_4^3.C_2^3$) x 12, $C_2^2$ ($(C_2\times C_4^3).C_2^3$) x 8, $C_2^2$ ($C_2^4.C_2^4.C_2^2$) x 8, $C_2^2$ ($(C_2\times C_4^3).C_2^3$) x 8, $C_4$ ($C_2^4.C_2^4.C_2^2$) x 8, $C_4$ ($(C_2\times C_4^3).C_2^3$) x 8, $C_4$ ($C_2\times C_4^3.C_2^3$) x 6, $C_2^2$ ($C_2\times C_4^2.C_2^4.C_2$) x 4, $C_2^2$ ($C_2\times C_4^2.C_2^4.C_2$) x 4, $C_2^2$ ($C_2\times C_2^2.C_2^5.C_2^2$) x 4, $C_2^2$ ($C_2\times C_2^2.C_2^5.C_2^2$) x 4, $C_4$ ($C_2\times C_4^3.C_2^3$) x 4, $C_4$ ($C_2\times C_4^3.C_2^3$) x 4, $C_2^2$ ($C_2\times C_2^3.C_2^4.C_2^2$) x 3, $C_2^2$ ($C_2\times C_4^2.C_2^4.C_2$) x 2, $C_2^2$ ($C_2\times C_4^2.C_2^4.C_2$) x 2, $C_2^2$ ($C_2\times (C_2^3\times C_4).C_2^4$) x 2, $C_2^2$ ($C_2\times C_4^2.C_2^4.C_2$) x 2, $C_2^2$ ($C_2\times C_2^4.C_2^4.C_2$) x 2, $C_2^2$ ($C_4^3.C_2^4$) x 2, $C_4$ ($C_2\times C_4^3.C_2^3$) x 2, $C_4$ ($C_2\times C_4^3.C_2^3$) x 2, $C_4$ ($C_4^3.C_2^4$) x 2, $C_2^2$ ($C_2\times (C_2^3\times C_4).C_2^4$), $C_2^2$ ($C_2\times (C_2^3\times C_4).C_2^4$), $C_2^2$ ($C_2\times C_2^3.C_2^4.C_2^2$), $C_2^2$ ($C_2^2\times (C_2\times C_4^2).C_2^3$)

Order 2: $C_2$ ($C_4^4.C_2^3$) x 16, $C_2$ ($C_2\times C_4^3.C_2^4$) x 6, $C_2$ ($C_2\times (C_2\times C_4^3).C_2^3$) x 2, $C_2$ ($C_2\times (C_2\times C_4^3).C_2^3$) x 2, $C_2$ ($C_4^3.C_2^5$) x 2, $C_2$ ($C_2\times (C_2\times C_4^3).C_2^3$), $C_2$ ($C_2\times (C_2\times C_4^3).C_2^3$), $C_2$ ($C_2\times C_2^4.C_2^4.C_2^2$)

Order 1: $C_1$ ($C_4^4.C_2^4$)

Normal subgroups up to automorphism (quotient in parentheses)

Order 4096: $C_4^4.C_2^4$ ($C_1$)

Order 2048: $C_2\times C_4^3.C_2^4$ ($C_2$), $C_4^4.C_2^3$ ($C_2$), $C_2\times C_4\times C_4^3.C_2^2$ ($C_2$), $C_2\times C_2^3.C_2^5.C_2^2$ ($C_2$), $C_2\times C_4^4.C_2^2$ ($C_2$), $C_4^4.D_4$ ($C_2$), $C_4^4.D_4$ ($C_2$), $C_4^4.C_2^3$ ($C_2$)

Order 1024: $C_2\times C_4^3\times C_8$ ($C_2^2$) x 2, $C_4^4.C_4$ ($C_2^2$) x 2, $C_4^3.C_4^2$ ($C_2^2$) x 2, $C_4^3.C_2^4$ ($C_2^2$), $C_2^2\times C_4^3.C_2^2$ ($C_4$), $C_2\times C_2^3.C_2^5.C_2$ ($C_2^2$), $C_4^4.C_2^2$ ($C_2^2$), $C_4^4.C_2^2$ ($C_4$), $C_2\times C_4^4.C_2$ ($C_2^2$), $C_2\times C_2^4.C_2^4.C_2$ ($C_4$), $C_2\times (C_2\times C_4^3).C_2^2$ ($C_4$), $C_2\times C_2^3.C_2^5.C_2$ ($C_2^2$), $C_4\times C_4^3.C_2^2$ ($C_2^2$), $C_4^4.C_2^2$ ($C_2^2$), $C_2\times C_4^3.C_2^3$ ($C_2^2$), $C_2\times C_2^4.C_2^4.C_2$ ($C_4$), $C_2\times (C_2\times C_4^3).C_2^2$ ($C_4$), $C_2^6.C_2^4$ ($C_2^2$), $C_2\times C_4^3.D_4$ ($C_2^2$), $C_4^2:C_8^2$ ($C_2^2$), $C_4^3.C_2^4$ ($C_4$), $C_4^4.C_2^2$ ($C_2^2$), $C_4^4.C_2^2$ ($C_4$), $C_4^3.C_4^2$ ($C_2^2$), $(C_2\times D_4).C_8^2$ ($C_2^2$)

Order 512: $C_2^2\times C_4^2\times C_8$ ($C_2\times C_4$) x 4, $C_2^2\times C_4^2\times C_8$ ($C_2^3$) x 3, $C_2^2\times C_4^2\times C_8$ ($D_4$) x 3, $C_4^3.C_2^3$ ($C_2^3$) x 2, $C_4^3:C_2^3$ ($C_2\times C_4$) x 2, $C_4^3.C_2^3$ ($C_2\times C_4$) x 2, $C_4^3.C_2^3$ ($C_2^3$) x 2, $C_4^4:C_2$ ($C_2\times C_4$) x 2, $C_2^4.C_2^5$ ($C_2\times C_4$) x 2, $C_2^4.C_2^5$ ($C_2\times C_4$) x 2, $C_4^3:C_8$ ($C_2^3$) x 2, $C_4^3:C_8$ ($C_2\times C_4$) x 2, $(C_2^2\times C_4^2):C_8$ ($C_2\times C_4$) x 2, $C_4^3\times C_8$ ($C_2^3$) x 2, $C_4^3\times C_8$ ($D_4$) x 2, $C_4^3\times C_8$ ($C_2\times C_4$) x 2, $C_4^3.C_2^3$ ($C_2^3$), $C_4^3.D_4$ ($C_2^3$), $C_4^3.D_4$ ($C_2\times C_4$), $C_4^3.C_2^3$ ($D_4$), $C_2\times C_4^2.C_4^2$ ($C_2\times C_4$), $C_4^3:C_2^3$ ($C_2^3$), $C_4^3.C_2^3$ ($C_2\times C_4$), $C_4^3.C_2^3$ ($C_8$), $(D_4\times C_2^3):C_8$ ($C_2\times C_4$), $C_4^3.C_2^3$ ($C_2^3$), $C_4^3.C_2^3$ ($C_2\times C_4$), $C_2\times C_4^2.C_4^2$ ($C_2\times C_4$), $C_4^2.C_2^5$ ($C_2\times C_4$), $C_4^4:C_2$ ($C_2^3$), $C_2\times C_4^4$ ($C_2^3$), $C_4^2:C_4\times C_8$ ($C_2\times C_4$), $C_8\times C_2^3.C_2^3$ ($C_2\times C_4$), $C_4^3.D_4$ ($C_2^3$), $C_4^3.D_4$ ($C_2\times C_4$), $C_2^3.(C_8\times D_4)$ ($C_2\times C_4$), $C_4^3.D_4$ ($C_2^3$), $C_4^2.(C_4\times D_4)$ ($C_2\times C_4$), $C_4^3.D_4$ ($C_2\times C_4$), $C_4^3.D_4$ ($C_2^3$), $C_4^3.D_4$ ($C_2\times C_4$), $C_4^3.D_4$ ($C_8$), $C_4^2.C_2^5$ ($C_2\times C_4$)

Order 256: $C_2\times C_4^2\times C_8$ ($C_2\times D_4$) x 9, $C_2\times C_4^2\times C_8$ ($C_2^2\times C_4$) x 7, $C_2^3\times C_4\times C_8$ ($C_2\times D_4$) x 5, $C_2\times C_4^2\times C_8$ ($C_2^2:C_4$) x 5, $C_2^3\times C_4\times C_8$ ($C_2^2:C_4$) x 4, $C_2^2\times C_4^3$ ($C_2^2\times C_4$) x 4, $C_2^3\times C_4\times C_8$ ($C_2^2\times C_4$) x 3, $C_2\times C_4^2\times C_8$ ($C_2^4$) x 3, $C_4^3:C_4$ ($C_4^2$) x 2, $C_4^3:C_4$ ($C_2^2\times C_4$) x 2, $C_2^4.C_2^4$ ($C_4^2$) x 2, $C_2^4.C_2^4$ ($C_2^2\times C_4$) x 2, $C_2^4.C_2^4$ ($C_4^2$) x 2, $C_4^4$ ($C_2\times D_4$) x 2, $C_4^4$ ($C_2^2\times C_4$) x 2, $C_4^2:C_2^4$ ($C_2^2\times C_4$) x 2, $C_4^2.C_2^4$ ($C_2^2\times C_4$) x 2, $(C_2\times C_4^2):C_8$ ($C_2^2\times C_4$) x 2, $C_4^3:C_2^2$ ($C_2\times C_8$) x 2, $C_4^3:C_2^2$ ($C_4^2$) x 2, $C_4^3:C_2^2$ ($C_2^2\times C_4$) x 2, $C_2^3.C_2^5$ ($C_4^2$) x 2, $C_2^3.C_2^5$ ($C_4^2$) x 2, $C_4^3:C_2^2$ ($C_2^2\times C_4$) x 2, $C_2^3.C_2^5$ ($C_2^2\times C_4$) x 2, $C_2^2\times C_4^3$ ($C_2\times D_4$) x 2, $C_4^3.C_4$ ($C_2\times C_8$) x 2, $C_4^3.C_4$ ($C_2^2\times C_4$) x 2, $C_4^3.C_4$ ($C_2^4$) x 2, $C_4^3.C_4$ ($C_2^2\times C_4$) x 2, $C_2\times C_4^2\times C_8$ ($C_2\times C_8$) x 2, $C_2\times C_4^2\times C_8$ ($D_4:C_2$) x 2, $C_4^2.C_4^2$ ($C_2^2\times C_4$), $C_4^4$ ($C_2^4$), $C_4^4$ ($D_4:C_2$), $C_4^2:C_2^4$ ($C_4^2$), $C_4^2.C_2^4$ ($C_2\times C_8$), $C_4^2.C_2^4$ ($C_2^2\times C_4$), $C_2^2.(C_8\times D_4)$ ($C_2^2\times C_4$), $C_4^3:C_2^2$ ($C_2^4$), $C_2^2\times C_4^3$ ($C_2^4$), $C_2^2\times C_4^3$ ($D_4:C_2$), $C_4^2.D_8$ ($C_2\times C_8$), $C_4^3.C_2^2$ ($C_2\times C_8$), $(C_2^2\times C_8):D_4$ ($C_2\times C_8$), $(C_2^2\times C_8):D_4$ ($C_2^2\times C_4$), $C_4^2.C_4^2$ ($C_2^2\times C_4$), $C_2\times C_4^2\times C_8$ ($\OD_{16}$), $C_4.C_8^2$ ($C_2\times D_4$), $C_4^2.C_2^4$ ($C_2\times C_8$), $C_4^2.C_2^4$ ($C_2^2\times C_4$)

Order 128: $C_2^2\times C_4\times C_8$ ($C_2^3:C_4$) x 11, $C_2\times C_4^3$ ($C_4\times D_4$) x 8, $C_2\times C_4^3$ ($C_2^3\times C_4$) x 6, $C_2\times C_4^3$ ($C_2^2\times D_4$) x 5, $C_2^2\times C_4\times C_8$ ($C_2^2\times D_4$) x 5, $C_2\times C_4^3$ ($D_4:C_2^2$) x 4, $C_2\times C_4^3$ ($C_2^3:C_4$) x 4, $C_2\times C_4^3$ ($C_2\times C_4^2$) x 4, $C_2^3\times C_4^2$ ($C_4\times D_4$) x 4, $C_2\times C_4^3$ ($C_4^2:C_2$) x 3, $C_2^4\times C_8$ ($C_2^3:C_4$) x 3, $C_2^3\times C_4^2$ ($C_2\times C_4^2$) x 3, $C_2^2\times C_4\times C_8$ ($C_2^3\times C_4$) x 3, $C_2^2\times C_4\times C_8$ ($C_2^2\times C_8$) x 3, $C_2\times C_4^3$ ($D_8:C_2$) x 2, $C_2\times C_4^3$ ($C_2^2\times C_8$) x 2, $C_4^2:C_8$ ($C_2^2\times C_8$) x 2, $C_4^2\times C_8$ ($D_4:C_2^2$) x 2, $C_4^2\times C_8$ ($C_2^2\times D_4$) x 2, $C_4^2\times C_8$ ($C_2^2\times C_8$) x 2, $C_4^2\times C_8$ ($C_4\times D_4$) x 2, $C_4^2:C_2^3$ ($C_4\times C_8$) x 2, $C_4^2:C_2^3$ ($C_2^3\times C_4$) x 2, $C_4^2:C_2^3$ ($C_2^2\times C_8$) x 2, $C_4^2:C_2^3$ ($C_2\times C_4^2$) x 2, $C_2^4.D_4$ ($C_2\times C_4^2$) x 2, $C_2^3\times C_4^2$ ($C_2^2\times D_4$) x 2, $C_2^3\times C_4^2$ ($C_2^3\times C_4$) x 2, $C_2^3\times C_4^2$ ($C_4^2:C_2$) x 2, $C_2^3\times C_4^2$ ($C_2^3:C_4$) x 2, $C_2^4.C_2^3$ ($C_2\times C_4^2$) x 2, $C_4^2.C_2^3$ ($C_2^3\times C_4$) x 2, $C_4^2.C_2^3$ ($C_2^2\times C_8$) x 2, $C_2^2\times C_4\times C_8$ ($C_2^2:C_8$) x 2, $C_2^2\times C_4\times C_8$ ($\OD_{16}:C_2$) x 2, $C_2^2\times C_4\times C_8$ ($C_2\times \OD_{16}$) x 2, $C_2^2\times C_4\times C_8$ ($C_4:D_4$) x 2, $C_2^2\times C_4\times C_8$ ($C_4^2:C_2$) x 2, $C_2^2\times C_4\times C_8$ ($C_4\times D_4$) x 2, $C_4^3:C_2$ ($C_2^2\times C_8$) x 2, $C_4^3:C_2$ ($C_4\times C_8$) x 2, $C_2^3.C_2^4$ ($C_4\times C_8$) x 2, $C_2^3.C_2^4$ ($C_2\times C_4^2$) x 2, $C_2^3.C_2^4$ ($C_4\times C_8$) x 2, $C_2^3.C_2^4$ ($C_2\times C_4^2$) x 2, $C_2^3.C_2^4$ ($C_2^3\times C_4$) x 2, $C_2^3.C_2^4$ ($C_2\times C_4^2$) x 2, $C_2\times C_4^3$ ($C_2^5$), $C_2\times C_4^3$ ($Q_{16}:C_2$), $C_2\times C_4^3$ ($\OD_{16}:C_2$), $C_2\times C_4^3$ ($C_2\times \OD_{16}$), $C_4^2.D_4$ ($C_2^2\times C_8$), $C_4^2\times C_8$ ($C_2^2:C_8$), $C_4^2\times C_8$ ($C_2\times \OD_{16}$), $C_4^2\times C_8$ ($C_4:D_4$), $C_4^2\times C_8$ ($C_4^2:C_2$), $C_4^2\times C_8$ ($C_4:D_4$), $D_4\times C_2^4$ ($C_2\times C_4^2$), $C_4^2:C_2^3$ ($C_2\times C_4^2$), $C_2^3\times C_4^2$ ($D_4:C_2^2$), $C_4^2.D_4$ ($C_2^2\times C_8$), $C_4^2.C_2^3$ ($C_2^2\times C_8$), $C_2^2\times C_4\times C_8$ ($C_4:D_4$)

Order 64: $C_2^2\times C_4^2$ ($C_4^2:C_2^2$) x 12, $C_2^2\times C_4^2$ ($C_2^2:C_4^2$) x 11, $C_2^2\times C_4^2$ ($C_2^4:C_4$) x 5, $C_2^2\times C_4^2$ ($C_2^2\times C_4^2$) x 5, $C_2\times C_4\times C_8$ ($C_2^3:C_8$) x 4, $C_2\times C_4\times C_8$ ($C_2^3.C_2^3$) x 4, $C_2^2\times C_4^2$ ($C_2\times C_4\times C_8$) x 4, $C_2^2\times C_4^2$ ($C_4^2:C_2^2$) x 4, $C_2\times C_4\times C_8$ ($C_2^3\times C_8$) x 3, $C_2^4\times C_4$ ($C_2^2:C_4^2$) x 3, $C_2^3\times C_8$ ($C_2^3:C_8$) x 3, $C_2^3\times C_8$ ($C_2^4:C_4$) x 3, $C_2^2\times C_4^2$ ($C_8.C_2^3$) x 3, $C_2\times C_4\times C_8$ ($C_8.C_2^3$) x 2, $C_2\times C_4\times C_8$ ($C_2^2\times \OD_{16}$) x 2, $C_2\times C_4\times C_8$ ($C_4^2:C_2^2$) x 2, $C_2\times C_4\times C_8$ ($C_4^2:C_2^2$) x 2, $C_2\times C_4\times C_8$ ($C_4^2:C_2^2$) x 2, $C_2\times C_4\times C_8$ ($C_8\times D_4$) x 2, $C_2^3.C_2^3$ ($C_2\times C_4\times C_8$) x 2, $C_4^2:C_4$ ($C_2\times C_4\times C_8$) x 2, $C_4^3$ ($C_2\times C_4\times C_8$) x 2, $C_4^3$ ($D_4:C_2^3$) x 2, $C_4^3$ ($C_8:C_2^3$) x 2, $C_4^3$ ($C_2^3\times C_8$) x 2, $C_4^3$ ($C_4^2.C_2^2$) x 2, $C_4^3$ ($C_4^2.C_2^2$) x 2, $C_4^3$ ($C_4^2:C_2^2$) x 2, $C_4^3$ ($C_8\times D_4$) x 2, $D_4\times C_2^3$ ($C_2\times C_4\times C_8$) x 2, $C_2^4\times C_4$ ($C_4^2:C_2^2$) x 2, $C_2^3\times C_8$ ($(C_2^2\times C_8):C_2$) x 2, $C_2^3\times C_8$ ($C_2^3.C_2^3$) x 2, $C_4^2:C_2^2$ ($C_2\times C_4\times C_8$) x 2, $C_4^2:C_2^2$ ($C_2\times C_4\times C_8$) x 2, $C_4^2:C_2^2$ ($C_2^3\times C_8$) x 2, $C_2^3.D_4$ ($C_2\times C_4\times C_8$) x 2, $C_2^3.D_4$ ($C_2^2\times C_4^2$) x 2, $C_2^2\times C_4^2$ ($C_2^3.D_4$) x 2, $C_2^2\times C_4^2$ ($C_2^3.D_4$) x 2, $C_2^2\times C_4^2$ ($\OD_{16}:C_4$) x 2, $C_2^2\times C_4^2$ ($C_4\times \OD_{16}$) x 2, $C_2^2\times C_4^2$ ($D_4\times C_2^3$) x 2, $C_2^2\times C_4^2$ ($C_2^4\times C_4$) x 2, $C_2^2\times C_4^2$ ($C_8:C_2^3$) x 2, $C_2^2\times C_4^2$ ($C_2^3\times C_8$) x 2, $C_2^2\times C_4^2$ ($C_4^2.C_2^2$) x 2, $C_2^2\times C_4^2$ ($C_4^2.C_2^2$) x 2, $C_2^2\times C_4^2$ ($D_8:C_4$) x 2, $C_2^2\times C_4^2$ ($\SD_{16}:C_4$) x 2, $C_2^2\times C_4^2$ ($C_8\times D_4$) x 2, $C_4^2.C_4$ ($C_2^3\times C_8$) x 2, $C_2\times C_4\times C_8$ ($(C_2^2\times C_8):C_2$), $C_2\times C_4\times C_8$ ($C_2^3:D_4$), $C_2\times C_4\times C_8$ ($C_8:D_4$), $C_4^3$ ($C_2^3.D_4$), $C_4^3$ ($C_2^3.D_4$), $C_4^3$ ($C_2^3:C_8$), $C_4^3$ ($\OD_{16}:C_4$), $C_4^3$ ($C_4\times \OD_{16}$), $C_4^3$ ($D_4\times C_2^3$), $C_4^3$ ($Q_{16}:C_2^2$), $C_4^3$ ($C_8.C_2^3$), $C_4^3$ ($C_2^2\times \OD_{16}$), $C_4^3$ ($C_4^2:C_2^2$), $C_4^3$ ($C_4^2.C_2^2$), $C_4^3$ ($C_4^2:C_2^2$), $C_4^3$ ($C_4^2:C_2^2$), $C_4^3$ ($C_2^3:D_4$), $C_4^3$ ($D_8:C_4$), $C_4^3$ ($\SD_{16}:C_4$), $C_4^3$ ($C_4^2.C_4$), $D_4\times C_2^3$ ($C_2^2\times C_4^2$), $C_2^4\times C_4$ ($C_4^2:C_2^2$), $C_2^4\times C_4$ ($C_2^4:C_4$), $C_2^4\times C_4$ ($C_2^2\times C_4^2$), $C_4^2:C_2^2$ ($C_8^2$), $C_2^2\times C_4^2$ ($C_2^3:C_8$), $C_2^2\times C_4^2$ ($D_4:C_2^3$), $C_2^2\times C_4^2$ ($Q_{16}:C_2^2$), $C_2^2\times C_4^2$ ($C_2^2\times \OD_{16}$), $C_2^2\times C_4^2$ ($C_4^2:C_2^2$), $C_2^2\times C_4^2$ ($C_4^2.C_2^2$), $C_2^2\times C_4^2$ ($C_4^2:C_2^2$), $C_2^2\times C_4^2$ ($C_4^2:C_2^2$), $C_2^2\times C_4^2$ ($C_2^3:D_4$), $C_2^2\times C_4^2$ ($D_8:C_4$), $C_2^2\times C_4^2$ ($C_4^2.C_4$), $C_2^2\times C_4^2$ ($C_4^2:C_2^2$)

Order 32: $C_2^3\times C_4$ ($C_2^3:C_4^2$) x 8, $C_2\times C_4^2$ ($C_4^2.C_2^3$) x 6, $C_2\times C_4^2$ ($C_2^2\times C_4\times C_8$) x 6, $C_2\times C_4^2$ ($D_4:C_4^2$) x 4, $C_2\times C_4^2$ ($C_2^3.C_4^2$) x 4, $C_2\times C_4^2$ ($C_4^2.D_4$) x 4, $C_2^3\times C_4$ ($D_4:C_4^2$) x 3, $C_2^2\times C_8$ ($C_2^4:C_8$) x 3, $C_2\times C_4^2$ ($C_8.C_2^4$) x 3, $C_2\times C_4^2$ ($C_4^2.D_4$) x 3, $C_2\times C_4^2$ ($C_4^2.D_4$) x 3, $C_2\times C_4^2$ ($C_2^4.D_4$) x 3, $C_2\times C_4^2$ ($C_2^4.D_4$) x 3, $C_2\times C_4^2$ ($C_2^3.C_4^2$) x 3, $C_2\times C_4^2$ ($C_2^3.C_4^2$) x 3, $C_2\times C_4^2$ ($C_4^3:C_2$) x 3, $C_2\times C_4^2$ ($C_4^3:C_2$) x 3, $C_2\times C_4^2$ ($C_4^2:D_4$) x 3, $C_2\times C_4^2$ ($C_2^3.C_2^4$) x 3, $C_2\times C_4^2$ ($C_2^3.C_2^4$) x 3, $C_2^2\times D_4$ ($C_2^2\times C_4\times C_8$) x 2, $C_2^3\times C_4$ ($D_4.C_4^2$) x 2, $C_2^3\times C_4$ ($D_4.C_4^2$) x 2, $C_2^3\times C_4$ ($C_2^3.C_4^2$) x 2, $C_2^3\times C_4$ ($C_4^2.D_4$) x 2, $C_2^3\times C_4$ ($C_4^2:C_2^3$) x 2, $C_2^3\times C_4$ ($C_4^2.C_2^3$) x 2, $C_2^3\times C_4$ ($D_4.C_4^2$) x 2, $C_2^3\times C_4$ ($C_2^2\times C_4\times C_8$) x 2, $C_2^2\times C_8$ ($C_4^2.D_4$) x 2, $C_2^2\times C_8$ ($(C_2^3\times C_8):C_2$) x 2, $C_2^2\times C_8$ ($C_2^3.C_2^4$) x 2, $C_4\times C_8$ ($C_4^2.C_2^3$) x 2, $C_2^2.D_4$ ($C_2^2\times C_4\times C_8$) x 2, $C_2\times C_4^2$ ($C_8:C_2^4$) x 2, $C_2\times C_4^2$ ($C_2^4\times C_8$) x 2, $C_2\times C_4^2$ ($C_4^2.C_2^3$) x 2, $C_2\times C_4^2$ ($C_4^2.C_2^3$) x 2, $C_2\times C_4^2$ ($C_4^2:C_2^3$) x 2, $C_2\times C_4^2$ ($\OD_{16}:D_4$) x 2, $C_2\times C_4^2$ ($C_4^2.C_2^3$) x 2, $C_2\times C_4^2$ ($C_4^2.C_2^3$) x 2, $C_2\times C_4^2$ ($C_4^2.C_2^3$) x 2, $C_2\times C_4^2$ ($C_2^4:C_8$) x 2, $C_2\times C_4^2$ ($D_4.C_4^2$) x 2, $C_2\times C_4^2$ ($C_4^3:C_2$) x 2, $C_2\times C_4^2$ ($D_4\times C_4^2$) x 2, $C_2^5$ ($C_2^3:C_4^2$), $C_2^2\times D_4$ ($C_2\times C_8^2$), $C_2^3\times C_4$ ($C_4^2:C_2^3$), $C_2^3\times C_4$ ($C_2^5:C_4$), $C_2^3\times C_4$ ($C_2^3\times C_4^2$), $C_2^3\times C_4$ ($C_4^2.C_2^3$), $C_2^3\times C_4$ ($C_4^2.D_4$), $C_2^3\times C_4$ ($C_4^2.D_4$), $C_2^3\times C_4$ ($C_4^2.C_2^3$), $C_2^3\times C_4$ ($C_4^2.C_2^3$), $C_2^3\times C_4$ ($C_4^2.C_2^3$), $C_2^3\times C_4$ ($C_4^2.C_2^3$), $C_2^3\times C_4$ ($C_4^2:C_2^3$), $C_2^3\times C_4$ ($C_2^4.D_4$), $C_2^3\times C_4$ ($C_2^4.D_4$), $C_2^3\times C_4$ ($(C_2^3\times C_8):C_2$), $C_2^3\times C_4$ ($C_2^4:C_8$), $C_2^3\times C_4$ ($C_2^3.C_4^2$), $C_2^3\times C_4$ ($C_2^3.C_4^2$), $C_2^3\times C_4$ ($C_4^3:C_2$), $C_2^3\times C_4$ ($C_4^3:C_2$), $C_2^3\times C_4$ ($C_4^2:D_4$), $C_2^3\times C_4$ ($C_2^3.C_2^4$), $C_2^3\times C_4$ ($C_4^3:C_2$), $C_2^3\times C_4$ ($C_2^3.C_2^4$), $C_2^3\times C_4$ ($D_4\times C_4^2$), $C_4:D_4$ ($C_2\times C_8^2$), $C_4\times C_8$ ($C_4^2.D_4$), $C_4\times C_8$ ($C_4^2.C_2^3$), $C_2\times C_4^2$ ($D_4.C_4^2$), $C_2\times C_4^2$ ($D_4.C_4^2$), $C_2\times C_4^2$ ($D_8:C_8$), $C_2\times C_4^2$ ($\SD_{16}:C_8$), $C_2\times C_4^2$ ($Q_{16}:C_2^3$), $C_2\times C_4^2$ ($C_2^3\times \OD_{16}$), $C_2\times C_4^2$ ($C_4^2:C_2^3$), $C_2\times C_4^2$ ($C_4^2.C_2^3$), $C_2\times C_4^2$ ($C_4^2:C_2^3$), $C_2\times C_4^2$ ($C_4^2:C_2^3$), $C_2\times C_4^2$ ($C_2^4:D_4$), $C_2\times C_4^2$ ($C_4^2.D_4$), $C_2\times C_4^2$ ($C_4^2.D_4$), $C_2\times C_4^2$ ($C_4^2.D_4$), $C_2\times C_4^2$ ($C_4^2.D_4$), $C_2\times C_4^2$ ($\OD_{16}:D_4$), $C_2\times C_4^2$ ($C_4^2.D_4$), $C_2\times C_4^2$ ($C_4^2.D_4$), $C_2\times C_4^2$ ($C_8^2:C_2$), $C_2\times C_4^2$ ($C_8\times \OD_{16}$), $C_2\times C_4^2$ ($C_2\times C_8^2$), $C_2\times C_4^2$ ($C_4^2.C_2^3$), $C_2\times C_4^2$ ($C_4^2.C_2^3$), $C_2\times C_4^2$ ($C_4^2.C_2^3$), $C_2\times C_4^2$ ($C_4^2.C_2^3$), $C_2\times C_4^2$ ($C_4^2.C_2^3$), $C_2\times C_4^2$ ($C_4^2.C_2^3$), $C_2\times C_4^2$ ($C_4^2:C_2^3$), $C_2\times C_4^2$ ($(C_2^3\times C_8):C_2$)

Order 16: $C_2^2\times C_4$ ($C_2^4.C_2^4$) x 5, $C_2^2\times C_4$ ($C_2\times D_4:C_4^2$) x 5, $C_2^2\times C_4$ ($C_2^4.C_4^2$) x 5, $C_2^2\times C_4$ ($C_2^4.C_4^2$) x 5, $C_2^2\times C_4$ ($C_2\times D_4.C_4^2$) x 3, $C_2^2\times C_4$ ($C_2\times D_4.C_4^2$) x 3, $C_2^2\times C_4$ ($(C_2\times D_4).C_4^2$) x 3, $C_2^2\times C_4$ ($C_4^2.(C_2\times D_4)$) x 3, $C_2\times C_8$ ($(C_2^2\times C_8):D_4$) x 2, $C_4^2$ ($C_4^2.C_2^4$) x 2, $C_4^2$ ($C_4^2.C_2^4$) x 2, $C_4^2$ ($C_4^2.C_2^4$) x 2, $C_4^2$ ($C_4^3.C_2^2$) x 2, $C_2^2\times C_4$ ($C_4^2.C_2^4$) x 2, $C_2^2\times C_4$ ($C_4^2.C_2^4$) x 2, $C_2^2\times C_4$ ($C_2^3\times C_4\times C_8$) x 2, $C_2^2\times C_4$ ($C_4^3.C_2^2$) x 2, $C_2^2\times C_4$ ($D_4:(C_4\times C_8)$) x 2, $C_2^2\times C_4$ ($C_4^3.C_2^2$) x 2, $C_2^2\times C_4$ ($C_8^2.C_2^2$) x 2, $C_4^2$ ($C_4^2.C_2^4$), $C_4^2$ ($C_4^2.C_2^4$), $C_4^2$ ($C_4^2.C_2^4$), $C_4^2$ ($C_4^2.C_2^4$), $C_4^2$ ($C_4^2.C_2^4$), $C_4^2$ ($C_4^2.C_2^4$), $C_4^2$ ($C_4^2.C_2^4$), $C_4^2$ ($C_4^2.C_2^4$), $C_4^2$ ($C_4^2.C_2^4$), $C_4^2$ ($C_4^3.C_2^2$), $C_4^2$ ($C_4^3.C_2^2$), $C_4^2$ ($C_4^3.C_2^2$), $C_4^2$ ($C_4^3.C_2^2$), $C_4^2$ ($C_4^3.C_2^2$), $C_4^2$ ($C_8\times C_4:D_4$), $C_4^2$ ($C_4^2.(C_2\times D_4)$), $C_4^2$ ($C_4^2.(C_2\times D_4)$), $C_4^2$ ($C_4^3.C_2^2$), $C_4^2$ ($(C_2\times \OD_{16}):D_4$), $C_4^2$ ($(C_2\times \OD_{16}):D_4$), $C_4^2$ ($(C_2^2\times C_8):D_4$), $C_4^2$ ($C_4^2:\OD_{16}$), $C_4^2$ ($C_4^3.C_2^2$), $C_4^2$ ($D_4:(C_4\times C_8)$), $C_4^2$ ($C_4^3.C_2^2$), $C_4^2$ ($C_2^2:C_8^2$), $C_4^2$ ($C_4^2.C_2^4$), $C_4^2$ ($C_4^2.C_2^4$), $C_4^2$ ($C_4^2.C_2^4$), $C_4^2$ ($C_4^2.C_2^4$), $C_4^2$ ($C_8^2:C_2^2$), $C_4^2$ ($C_8^2:C_2^2$), $C_4^2$ ($C_2^2\times C_8^2$), $C_2^4$ ($C_2^4.C_2^4$), $C_2^4$ ($C_2^4:C_4^2$), $C_2^4$ ($C_2\times D_4.C_4^2$), $C_2^4$ ($C_2\times D_4:C_4^2$), $C_2^4$ ($C_2\times D_4.C_4^2$), $C_2^4$ ($(C_2\times D_4).C_4^2$), $C_2^4$ ($C_2^4.C_4^2$), $C_2^4$ ($C_4^2.(C_2\times D_4)$), $C_2^4$ ($C_2^4.C_4^2$), $C_2\times D_4$ ($C_2^2\times C_8^2$), $C_2^2\times C_4$ ($C_4^2.C_2^4$), $C_2^2\times C_4$ ($C_4^2.C_2^4$), $C_2^2\times C_4$ ($C_4^2.C_2^4$), $C_2^2\times C_4$ ($C_4^2.C_2^4$), $C_2^2\times C_4$ ($C_4^2.C_2^4$), $C_2^2\times C_4$ ($C_4^2.C_2^4$), $C_2^2\times C_4$ ($C_4^2.C_2^4$), $C_2^2\times C_4$ ($C_4^2:C_2^4$), $C_2^2\times C_4$ ($C_2^5.D_4$), $C_2^2\times C_4$ ($C_2^5.D_4$), $C_2^2\times C_4$ ($(C_2^4\times C_8):C_2$), $C_2^2\times C_4$ ($C_2^5:C_8$), $C_2^2\times C_4$ ($C_4^2.C_2^4$), $C_2^2\times C_4$ ($C_4^2.C_2^4$), $C_2^2\times C_4$ ($C_4^3:C_2^2$), $C_2^2\times C_4$ ($C_4^3:C_2^2$), $C_2^2\times C_4$ ($C_2^3.C_2^5$), $C_2^2\times C_4$ ($C_2^3.C_2^5$), $C_2^2\times C_4$ ($C_4^3:C_2^2$), $C_2^2\times C_4$ ($C_2^3.C_2^5$), $C_2^2\times C_4$ ($C_4^3:C_2^2$), $C_2^2\times C_4$ ($C_4^3.C_2^2$), $C_2^2\times C_4$ ($C_4^3.C_2^2$), $C_2^2\times C_4$ ($C_4^3.C_2^2$), $C_2^2\times C_4$ ($C_4^3.C_2^2$), $C_2^2\times C_4$ ($C_4^3.C_2^2$), $C_2^2\times C_4$ ($C_4^3.C_2^2$), $C_2^2\times C_4$ ($C_4^3.C_2^2$), $C_2^2\times C_4$ ($C_8\times C_4:D_4$), $C_2^2\times C_4$ ($C_4^3.C_2^2$), $C_2^2\times C_4$ ($C_4^2.(C_2\times D_4)$), $C_2^2\times C_4$ ($C_4^2.(C_2\times D_4)$), $C_2^2\times C_4$ ($C_4^3.C_2^2$), $C_2^2\times C_4$ ($C_4^3:C_2^2$), $C_2^2\times C_4$ ($(C_2\times \OD_{16}):D_4$), $C_2^2\times C_4$ ($(C_2\times \OD_{16}):D_4$), $C_2^2\times C_4$ ($(C_2^2\times C_8):D_4$), $C_2^2\times C_4$ ($C_4^2:\OD_{16}$), $C_2^2\times C_4$ ($C_4^3.C_2^2$), $C_2^2\times C_4$ ($C_4^3.C_2^2$), $C_2^2\times C_4$ ($D_4.(C_4\times C_8)$), $C_2^2\times C_4$ ($C_2^2:C_8^2$), $C_2^2\times C_4$ ($C_4^2.C_2^4$), $C_2^2\times C_4$ ($C_4^2.C_2^4$), $C_2^2\times C_4$ ($C_4^2.C_2^4$), $C_2^2\times C_4$ ($C_4^2.C_2^4$), $C_2^2\times C_4$ ($C_4^2.C_2^4$), $C_2^2\times C_4$ ($C_4^2.C_2^4$), $C_2^2\times C_4$ ($C_4^2.C_2^4$), $C_2^2\times C_4$ ($C_4^2.C_2^4$), $C_2^2\times C_4$ ($C_8^2.C_2^2$), $C_2^2\times C_4$ ($C_8^2.C_2^2$), $C_2^2\times C_4$ ($C_8^2:C_2^2$), $C_2^2\times C_4$ ($C_8^2:C_2^2$), $C_2^2\times C_4$ ($C_2^2\times C_8^2$)

Order 8: $C_2\times C_4$ ($C_4^2.(C_4\times D_4)$) x 3, $C_2\times C_4$ ($C_4^3.D_4$) x 3, $C_2\times C_4$ ($C_8\times C_2^3.C_2^3$) x 3, $C_2\times C_4$ ($C_4^3.D_4$) x 3, $C_2\times C_4$ ($C_2^3:C_8^2$) x 2, $C_2\times C_4$ ($C_4^3.C_2^3$) x 2, $C_2\times C_4$ ($C_8^2.C_2^3$) x 2, $C_2\times C_4$ ($(C_2\times C_4^3).C_2^2$) x 2, $C_2^3$ ($C_4^2.C_2^4.C_2$), $C_2^3$ ($C_4^2.(C_4\times D_4)$), $C_2^3$ ($(C_2\times C_4^2).C_2^4$), $C_2^3$ ($C_2\times C_2^3.(C_4\times D_4)$), $C_2^3$ ($C_4^2.C_2^4.C_2$), $C_2^3$ ($C_2\times C_4^2.C_2^3.C_2$), $C_2^3$ ($(C_2\times C_4^3).C_2^2$), $C_2^3$ ($C_4^3.D_4$), $C_2^3$ ($(C_2^2\times C_8^2).C_2$), $C_2^3$ ($(C_2^2\times C_8^2).C_2$), $C_2^3$ ($C_2^3:C_8^2$), $C_2^3$ ($C_2^2\times C_2^2.(C_4\times D_4)$), $C_2^3$ ($C_2^2\times D_4:C_4^2$), $C_2^3$ ($C_2^2\times C_4.C_4^2.C_2$), $C_2^3$ ($C_2\times (C_2^3\times C_8).C_2^2$), $C_2^3$ ($C_2^5.C_4^2$), $C_2^3$ ($C_2\times C_4.(C_2\times C_4\times D_4)$), $C_2^3$ ($C_2^5.C_4^2$), $C_2^3$ ($C_2^4.C_2^5$), $C_2^3$ ($(C_2^3\times C_8).C_2^3$), $C_2^3$ ($C_8\times C_2^3.C_2^3$), $C_2^3$ ($(C_2\times C_4^3).C_2^2$), $C_2^3$ ($C_2^4.C_2^4.C_2$), $C_2^3$ ($C_4^3.D_4$), $C_2\times C_4$ ($C_4^2.C_2^4.C_2$), $C_2\times C_4$ ($C_4^2.C_2^4.C_2$), $C_2\times C_4$ ($D_4\times C_8^2$), $C_2\times C_4$ ($C_4^2.C_2^4.C_2$), $C_2\times C_4$ ($C_2\times C_2^3.(C_4\times D_4)$), $C_2\times C_4$ ($C_2\times C_4^2.C_2^3.C_2$), $C_2\times C_4$ ($(C_2\times C_4^3).C_2^2$), $C_2\times C_4$ ($(C_2^2\times C_8^2).C_2$), $C_2\times C_4$ ($(C_2^2\times C_8^2).C_2$), $C_2\times C_4$ ($C_4^3.C_2^3$), $C_2\times C_4$ ($C_2\times C_4^3.C_2^2$), $C_2\times C_4$ ($C_2\times C_4^3.C_2^2$), $C_2\times C_4$ ($C_4^3.C_2^3$), $C_2\times C_4$ ($C_4^3.C_2^3$), $C_2\times C_4$ ($C_2\times C_2.C_4^3.C_2$), $C_2\times C_4$ ($C_2\times (C_4^2\times C_8).C_2$), $C_2\times C_4$ ($C_2\times (C_2^3\times C_8).C_2^2$), $C_2\times C_4$ ($C_2\times C_4.(C_2\times C_4):D_4$), $C_2\times C_4$ ($C_2\times (C_2\times C_4^2).C_2^3$), $C_2\times C_4$ ($C_2\times C_4.(C_2\times C_4):D_4$), $C_2\times C_4$ ($C_2\times C_4^3.C_2^2$), $C_2\times C_4$ ($C_2\times C_4.(C_2\times C_4:D_4)$), $C_2\times C_4$ ($C_2\times (C_2^3\times C_4).C_2^3$), $C_2\times C_4$ ($C_2\times (C_2^3\times C_4).C_2^3$), $C_2\times C_4$ ($(D_4\times C_2^3):C_8$), $C_2\times C_4$ ($C_2\times (C_2^2\times C_8).C_2^3$), $C_2\times C_4$ ($C_2\times (C_2^2\times C_8).C_2^3$), $C_2\times C_4$ ($C_2\times C_4^2.C_2^4$), $C_2\times C_4$ ($C_2\times C_4^2.C_2^4$), $C_2\times C_4$ ($C_4^2.C_2^5$), $C_2\times C_4$ ($C_2^2\times C_4^2.C_2^3$), $C_2\times C_4$ ($C_2\times C_4^2.C_2^4$), $C_2\times C_4$ ($C_2\times C_4^2.C_2^4$), $C_2\times C_4$ ($C_2^2\times C_4^2.C_2^3$), $C_2\times C_4$ ($C_2^2\times C_4^2.C_2^3$), $C_2\times C_4$ ($C_8^2.C_2^3$), $C_2\times C_4$ ($C_8^2.C_2^3$), $C_2\times C_4$ ($C_2^2\times C_4^2.C_2^3$), $C_2\times C_4$ ($C_2^2\times C_8\times \OD_{16}$), $C_2\times C_4$ ($C_2^3\times C_8^2$), $C_2\times C_4$ ($D_4:C_8^2$), $C_2\times C_4$ ($(C_2^3\times C_8).C_2^3$), $C_2\times C_4$ ($C_2^4.C_2^4.C_2$), $C_2\times C_4$ ($C_2^2.C_4^3.C_2$), $C_2\times C_4$ ($C_4^3.C_2^3$), $C_2\times C_4$ ($C_2^2.C_4^3.C_2$), $C_2\times C_4$ ($C_4^3.C_2^3$), $C_2\times C_4$ ($(C_2\times C_4^3).C_2^2$), $C_2\times C_4$ ($(C_2\times C_4^3).C_2^2$)

Order 4: $C_2^2$ ($C_4^3.C_2^4$) x 2, $C_2^2$ ($C_2\times C_2^3.C_2^4.C_2^2$) x 2, $C_4$ ($C_2\times C_4^3.C_2^3$) x 2, $C_4$ ($C_2\times C_4^3.C_2^3$) x 2, $C_2^2$ ($C_2\times (C_2^3\times C_4).C_2^4$), $C_2^2$ ($C_2\times C_4^2.C_2^4.C_2$), $C_2^2$ ($C_2\times C_4^2.C_2^4.C_2$), $C_2^2$ ($C_2\times C_4^2.C_2^4.C_2$), $C_2^2$ ($C_2\times (C_2^3\times C_4).C_2^4$), $C_2^2$ ($C_2\times C_4^2.C_2^4.C_2$), $C_2^2$ ($(C_2\times C_4^3).C_2^3$), $C_2^2$ ($(C_2\times C_4^3).C_2^3$), $C_2^2$ ($C_2\times (C_2^3\times C_4).C_2^4$), $C_2^2$ ($C_2^4.C_2^4.C_2^2$), $C_2^2$ ($C_2\times C_2^3.C_2^4.C_2^2$), $C_2^2$ ($C_2^2\times (C_2\times C_4^2).C_2^3$), $C_2^2$ ($C_2\times C_4^2.C_2^4.C_2$), $C_2^2$ ($C_2\times C_2^2.C_2^5.C_2^2$), $C_2^2$ ($(C_2\times C_4^3).C_2^3$), $C_2^2$ ($C_2\times C_2^4.C_2^4.C_2$), $C_2^2$ ($C_2\times C_2^2.C_2^5.C_2^2$), $C_2^2$ ($C_4^2.(C_8\times D_4)$), $C_2^2$ ($C_4^3.C_2^4$), $C_2^2$ ($C_4^3.C_2^4$), $C_4$ ($C_2\times C_4^3.C_2^3$), $C_4$ ($C_2\times C_4^3.C_2^3$), $C_4$ ($C_2\times C_4^3.C_2^3$), $C_4$ ($C_2\times C_4^3.C_2^3$), $C_4$ ($C_2^4.C_2^4.C_2^2$), $C_4$ ($C_2\times C_4^3.C_2^3$), $C_4$ ($(C_2\times C_4^3).C_2^3$), $C_4$ ($C_4^2.(C_8\times D_4)$), $C_4$ ($C_4^3.C_2^4$)

Order 2: $C_2$ ($C_2\times C_4^3.C_2^4$) x 2, $C_2$ ($C_2\times (C_2\times C_4^3).C_2^3$), $C_2$ ($C_2\times (C_2\times C_4^3).C_2^3$), $C_2$ ($C_2\times (C_2\times C_4^3).C_2^3$), $C_2$ ($C_4^4.C_2^3$), $C_2$ ($C_2\times C_2^4.C_2^4.C_2^2$), $C_2$ ($C_2\times (C_2\times C_4^3).C_2^3$), $C_2$ ($C_4^3.C_2^5$)

Order 1: $C_1$ ($C_4^4.C_2^4$)

Series

Derived series

$C_4^4.C_2^4$

$\rhd$

$C_2\times C_4$

$\rhd$

$C_1$

Chief series

$C_4^4.C_2^4$

$\rhd$

$C_4^4.D_4$

$\rhd$

$C_2\times C_4^4.C_2$

$\rhd$

$C_2\times C_4^4$

$\rhd$

$C_2^2\times C_4^3$

$\rhd$

$C_2\times C_4^3$

$\rhd$

$C_2^2\times C_4^2$

$\rhd$

$C_2^3\times C_4$

$\rhd$

$C_2^2\times C_4$

$\rhd$

$C_2^3$

$\rhd$

$C_2^2$

$\rhd$

$C_2$

$\rhd$

$C_1$

Lower central series

$C_4^4.C_2^4$

$\rhd$

$C_2\times C_4$

$\rhd$

$C_2$

$\rhd$

$C_1$

Upper central series

$C_1$

$\lhd$

$C_2^3\times C_4^2$

$\lhd$

$C_2\times C_4^3\times C_8$

$\lhd$

$C_4^4.C_2^4$

Supergroups

This group is a maximal subgroup of 2 larger groups in the database.

This group is a maximal quotient of 0 larger groups in the database.

Character theory

Complex character table

The $1024 \times 1024$ character table is not available for this group.

Rational character table

See the $400 \times 400$ rational character table (warning: may be slow to load).