Abstract group 8192.sg: $(C_4^2\times C_8).C_4^3$

• Label: 8192.sg
• Order: \( 2^{13} \)
• Exponent: \( 2^{4} \)
• Nilpotent: yes
• Solvable: yes
• $\card{G^{\mathrm{ab}}}$: \( 2^{7} \)
• $\card{Z(G)}$: 32
• $\card{\Aut(G)}$: \( 2^{24} \)
• $\card{\mathrm{Out}(G)}$: \( 2^{16} \)
• Perm deg.: not computed
• Trans deg.: not computed
• Rank: $3$

Group information

Description:	$(C_4^2\times C_8).C_4^3$
Order:	\(8192\)\(\medspace = 2^{13} \)
Exponent:	\(16\)\(\medspace = 2^{4} \)
Automorphism group:	Group of order \(16777216\)\(\medspace = 2^{24} \)
Composition factors:	$C_2$ x 13
Nilpotency class:	$4$
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	16
Elements	1	31	992	2048	5120	8192
Conjugacy classes	1	19	92	272	320	704
Divisions	1	19	64	112	60	256
Autjugacy classes	1	17	68	112	32	230

Dimension	1	2	4	8	16	32
Irr. complex chars.	128	288	240	48	0	0	704
Irr. rational chars.	8	52	100	48	24	24	256

Minimal presentations

Permutation degree:	not computed
Transitive degree:	not computed
Rank:	$3$
Inequivalent generating triples:	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:	${\langle a, b, c, d, e \mid c^{8}=d^{8}=e^{4}=[a,b]=[a,d]=[d,e]=1, a^{8}= \!\cdots\! \rangle}$
Matrix group:	$\left\langle \left(\begin{array}{rr} 1 & 8 \\ 0 & 1 \end{array}\right), \left(\begin{array}{rr} 17 & 0 \\ 0 & 17 \end{array}\right), \left(\begin{array}{rr} 9 & 26 \\ 6 & 7 \end{array}\right), \left(\begin{array}{rr} 1 & 16 \\ 0 & 1 \end{array}\right), \left(\begin{array}{rr} 9 & 0 \\ 0 & 9 \end{array}\right), \left(\begin{array}{rr} 31 & 16 \\ 8 & 15 \end{array}\right), \left(\begin{array}{rr} 3 & 0 \\ 0 & 3 \end{array}\right), \left(\begin{array}{rr} 1 & 16 \\ 16 & 17 \end{array}\right), \left(\begin{array}{rr} 31 & 30 \\ 4 & 3 \end{array}\right), \left(\begin{array}{rr} 3 & 1 \\ 0 & 1 \end{array}\right), \left(\begin{array}{rr} 17 & 0 \\ 0 & 1 \end{array}\right), \left(\begin{array}{rr} 25 & 24 \\ 8 & 9 \end{array}\right), \left(\begin{array}{rr} 9 & 4 \\ 0 & 1 \end{array}\right) \right\rangle \subseteq \GL_{2}(\Z/32\Z)$
Direct product:	not computed
Semidirect product:	not computed
Trans. wreath product:	not isomorphic to a non-trivial transitive wreath product
Possibly split product:	$(C_4^2.C_4^3)$ . $Q_8$ (2)	$(C_8^2.C_4^2)$ . $Q_8$ (2)	$(C_8^2.C_4^2)$ . $Q_8$ (2)	$(C_4^3.Q_8)$ . $C_4^2$ (2)	all 1184

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

Homology

Abelianization:	$C_{4}^{2} \times C_{8} $
Schur multiplier:	$C_{2}^{5} \times C_{4}$
Commutator length:	$1$

Subgroups

There are 3086 normal subgroups (2348 characteristic).

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

Special subgroups

Center:	a subgroup isomorphic to $C_2^2\times C_8$
Commutator:	a subgroup isomorphic to $C_2\times C_4\times C_8$
Frattini:	a subgroup isomorphic to $C_2^2\times C_4\times C_8^2$
Fitting:	not computed
Radical:	not computed
Socle:	not computed
2-Sylow subgroup:	$P_{ 2 } \simeq$ $(C_4^2\times C_8).C_4^3$

Hi

Subgroup diagram and profile

Classes of subgroups up to conjugation

No diagram available: inclusions not computed

Classes of subgroups up to automorphism

No diagram available: inclusions not computed

Normal subgroups

No diagram available: inclusions not computed

Normal subgroups up to automorphism

No diagram available: inclusions not computed

Classes of subgroups up to conjugation

All subgroups of index up to 8 (order at least 1024) are shown, as well as all normal subgroups of any index.

Order 8192: $(C_4^2\times C_8).C_4^3$

Order 4096: $C_8^2.C_4^3$, $(C_4\times C_8^2).C_4^2$, $(C_4\times C_8^2).C_4^2$, $(C_4\times C_8^2).C_4^2$, $(C_4\times C_8^2).C_4^2$, $(C_4\times C_8^2).C_4^2$, $(C_4\times C_8^2).C_4^2$

Order 2048: $(C_2\times C_8^2).D_8$ x 6, $(C_4\times C_8).C_8^2$ x 6, $(C_2\times C_8^2).D_8$ x 6, $C_4^3.(C_4\times C_8)$ x 6, $(C_4\times C_8).C_4^3$ x 6, $(C_2\times C_8^2).D_8$ x 4, $(C_4\times C_8).C_4^3$ x 4, $(C_4\times C_8).C_4^3$ x 2, $C_2\times C_8^2.C_4^2$ x 2, $C_2\times C_8^2.D_8$ x 2, $C_2\times C_8^2.D_8$ x 2, $(C_2\times C_8^2).D_8$ x 2, $C_2^2\times C_8^2.D_4$ x 2, $C_2\times C_4^3.C_4^2$ x 2, $C_4^3.(C_4\times D_4)$, $C_2\times C_4^3.C_4^2$, $C_2^7.C_2^4$, $(C_4\times C_8).C_4^3$, $(C_4\times C_8).C_4^3$, $(C_4^2\times C_8).C_4^2$, $(C_4^2\times C_8).C_4^2$, $(C_4^2\times C_8).C_4^2$, $(C_4^2\times C_8).C_4^2$, $(C_2\times C_8^2).C_4^2$, $(C_2\times C_8^2).C_4^2$, $(C_2\times C_8^2).C_4^2$, $(C_4\times C_8).C_4^3$, $C_2\times C_8^2.C_4^2$, $C_2^2\times C_8^2.D_4$, $(C_2\times C_8^2).C_4^2$, $C_2\times C_8^2.C_4^2$, $C_2\times C_8^2.C_4^2$, $(C_4\times C_8).C_4^3$

Order 1024: $C_8^2.C_4^2$ x 22, $C_4^2.C_4^3$ x 18, $C_8^2.C_4^2$ x 16, $C_8^2.C_4^2$ x 16, $C_4^3.\OD_{16}$ x 15, $C_4^3.C_4^2$ x 10, $(C_4\times C_8^2):C_4$ x 10, $C_4^3.C_4:C_4$ x 8, $C_8^2.D_8$ x 8, $C_8^2.D_8$ x 8, $C_8^2.C_4^2$ x 8, $C_8^2.C_4^2$ x 8, $C_8^2.C_4^2$ x 8, $C_4^2.C_4^3$ x 8, $C_4^2.C_4^3$ x 8, $C_4^2.C_4^3$ x 6, $(C_2\times C_4^3).D_4$ x 6, $(C_2\times C_4^3).D_4$ x 6, $C_8^2.C_4^2$ x 6, $C_8^2.C_4^2$ x 6, $C_8^2.C_4^2$ x 5, $C_8^2.C_4^2$ x 4, $C_8^2.C_4^2$ x 4, $C_8^2.C_4^2$ x 4, $C_8^2.C_4^2$ x 4, $(C_2^3\times C_8).D_8$ x 4, $(C_2\times C_4^3).D_4$ x 4, $C_4^2.C_4^3$ x 4, $C_4^2.C_4^3$ x 4, $C_8^2.C_4^2$ x 4, $C_8^2.C_4^2$ x 4, $C_4^2.C_4^3$ x 3, $C_4^2.C_4^3$ x 3, $C_8^2.C_2^4$ x 3, $C_8^2.C_4^2$ x 3, $C_8^2.C_4^2$ x 3, $C_2\times C_4^2:\OD_{32}$ x 3, $C_4^3.C_4^2$ x 2, $C_4^3.C_4^2$ x 2, $C_4^2.(C_2^3\times C_8)$ x 2, $C_2^3\times C_8\times C_{16}$ x 2, $C_8^2.C_4^2$ x 2, $C_8^2.C_4^2$ x 2, $C_8^2.C_4^2$ x 2, $C_4^2.C_4^3$ x 2, $(C_2\times C_4^3).D_4$ x 2, $(C_4^2\times C_{16}):C_2^2$ x 2, $C_4^2.(C_2^3\times C_8)$ x 2, $(C_2^3\times C_8).D_8$ x 2, $C_8^2.C_2^4$ x 2, $C_8^2.C_4^2$ x 2, $C_4^2.(C_2^3\times C_8)$ x 2, $C_8^2.C_2^4$ x 2, $(C_2^2\times C_8^2):C_4$ x 2, $C_2^2\times C_8^2:C_4$ x 2, $(C_2^2\times C_8^2).C_4$ x 2, $C_8^2.C_2^4$ x 2, $(C_2^2\times C_8^2):C_4$ x 2, $C_4^2.C_4^3$ x 2, $C_4^3.C_2^4$, $C_2^2\times C_4\times C_8^2$, $(C_2\times C_4^3).D_4$, $C_8^2.C_2^4$, $C_2^2\times C_4^2:C_{16}$, $C_4^2.C_4^3$, $C_4^2.C_4^3$, $C_4^2.C_4^3$, $C_4^2.(C_2^2\times Q_{16})$, $C_2^5.(C_2\times D_8)$, $C_2^2\times C_4^2:C_{16}$, $(C_2^2\times C_4^2).D_8$, $C_4^2.(C_2^2\times D_8)$, $(C_2^2\times C_4^2).D_8$, $C_4^2.(C_2^2\times Q_{16})$, $C_4^2.(C_2^2\times D_8)$, $C_4^2.(C_2^2\times Q_{16})$, $C_4^2.(C_2^2\times C_4^2)$, $C_4^3.C_4^2$, $(C_2^2\times C_8^2).C_4$, $C_4^2.C_4^3$, $C_4^3.C_2^4$, $C_4^3.C_4^2$

Order 512: $C_2\times C_4\times C_8^2$ x 24, $C_2^2\times C_8\times C_{16}$ x 20, $C_8^2.C_8$ x 16, $C_8^2.C_8$ x 12, $(C_2\times C_8^2).C_4$ x 8, $C_4^3.C_2^3$ x 8, $(C_2\times C_4^3).C_4$ x 8, $C_8^2.C_8$ x 8, $C_4^2:\OD_{32}$ x 8, $C_4^3.D_4$ x 6, $C_2\times C_8^2.C_4$ x 4, $C_2\times C_8^2.C_4$ x 4, $(C_2\times C_8^2):C_4$ x 4, $(C_2\times C_8^2):C_4$ x 4, $(C_2\times C_8^2):C_4$ x 4, $(C_2\times C_8^2):C_4$ x 4, $C_2^3\times C_8^2$ x 4, $C_8^2.D_4$ x 4, $C_4^3.C_8$ x 4, $C_4^3.Q_8$ x 4, $(C_4^2\times C_8):C_4$ x 4, $(C_2^2\times C_8).C_4^2$ x 4, $C_2^2\times C_4^2\times C_8$ x 3, $C_4^3.C_2^3$ x 2, $C_4^3.C_2^3$ x 2, $C_4^2.C_2^5$ x 2, $C_2\times C_4^3.C_4$ x 2, $C_2^5.\OD_{16}$ x 2, $(C_4^2\times C_8):C_4$ x 2, $C_2^3.(C_4\times D_8)$ x 2, $C_8.C_4^3$ x 2, $C_4^2.(C_2^2\times D_4)$, $C_4^2.(C_2^2\times Q_8)$

Order 256: $C_2^2\times C_8^2$ x 80, $C_4\times C_8^2$ x 64, $C_2\times C_4^2\times C_8$ x 48, $C_2\times C_8\times C_{16}$ x 32, $C_4^2.C_2^4$ x 16, $C_2^3\times C_4\times C_8$ x 10, $(C_2\times C_8).C_4^2$ x 8, $C_4^2.(C_2\times D_4)$ x 8, $C_4^2:C_{16}$ x 8, $C_2\times C_8.C_4^2$ x 8, $C_8^2.C_4$ x 8, $C_8^2.C_4$ x 8, $C_8^2:C_4$ x 8, $C_8^2:C_4$ x 8, $C_4^3.C_2^2$ x 8, $C_4^3.C_2^2$ x 8, $C_4^3.C_4$ x 4, $C_4^2.\OD_{16}$ x 4, $(C_2\times C_8).C_4^2$ x 4, $C_4^2.D_8$ x 4, $C_4^2.(C_2\times Q_8)$ x 4, $C_4^2.(C_2\times Q_8)$ x 4, $C_4^2.C_2^4$ x 4, $C_4^2.C_2^4$ x 4, $C_2\times C_4^2.D_4$ x 2, $C_4^2.(C_2\times Q_8)$ x 2, $C_2^5.Q_8$ x 2, $C_2^5.D_4$ x 2, $C_2\times C_8.C_4^2$ x 2, $(C_2\times C_8):C_4^2$ x 2, $C_4^2.C_2^4$ x 2, $C_4^2.C_2^4$ x 2, $C_2^2\times C_4^3$

Order 128: $C_2\times C_8^2$ x 256, $C_2^2\times C_4\times C_8$ x 166, $C_4^2\times C_8$ x 96, $C_4^2.D_4$ x 16, $C_4^2.D_4$ x 16, $C_2\times C_4^3$ x 12, $C_4^2.D_4$ x 8, $C_2^4.Q_8$ x 8, $C_2^3.D_8$ x 8, $C_8.C_4^2$ x 8, $C_8:C_4^2$ x 8, $C_8\times C_{16}$ x 8, $C_8:\OD_{16}$ x 8, $C_8:\OD_{16}$ x 8, $C_2^4\times C_8$ x 6, $C_4^2.Q_8$ x 4, $C_4^2.Q_8$ x 4, $C_4^2.D_4$ x 4, $C_4^2.D_4$ x 4, $C_2^4.Q_8$ x 4, $C_2^4.D_4$ x 4, $C_2^3\times C_4^2$ x 3

Order 64: $C_2\times C_4\times C_8$ x 460, $C_8^2$ x 128, $C_2^3\times C_8$ x 84, $C_2^2\times C_4^2$ x 40, $C_4^3$ x 16, $C_8:C_8$ x 8, $C_8:C_8$ x 8, $C_2^3.Q_8$ x 8, $C_2^2.D_8$ x 8, $C_2^4\times C_4$ x 3

Order 32: $C_4\times C_8$ x 208, $C_2^2\times C_8$ x 184, $C_2\times C_4^2$ x 120, $C_2^3\times C_4$ x 42, $C_2^5$

Order 16: $C_2^2\times C_4$ x 100, $C_2\times C_8$ x 96, $C_4^2$ x 64, $C_2^4$ x 7

Order 8: $C_2\times C_4$ x 72, $C_2^3$ x 19, $C_8$ x 16

Order 4: $C_2^2$ x 19, $C_4$ x 16

Order 2: $C_2$ x 7

Order 1: $C_1$

Classes of subgroups up to automorphism

not computed

Normal subgroups (quotient in parentheses)

Order 8192: $(C_4^2\times C_8).C_4^3$ ($C_1$)

Order 4096: $C_8^2.C_4^3$ ($C_2$), $(C_4\times C_8^2).C_4^2$ ($C_2$), $(C_4\times C_8^2).C_4^2$ ($C_2$), $(C_4\times C_8^2).C_4^2$ ($C_2$), $(C_4\times C_8^2).C_4^2$ ($C_2$), $(C_4\times C_8^2).C_4^2$ ($C_2$), $(C_4\times C_8^2).C_4^2$ ($C_2$)

Order 2048: $(C_2\times C_8^2).D_8$ ($C_4$) x 4, $(C_2\times C_8^2).D_8$ ($C_4$) x 4, $(C_4\times C_8).C_8^2$ ($C_4$) x 4, $(C_2\times C_8^2).D_8$ ($C_4$) x 4, $C_4^3.(C_4\times C_8)$ ($C_4$) x 4, $(C_4\times C_8).C_4^3$ ($C_4$) x 4, $C_2\times C_8^2.C_4^2$ ($C_2^2$) x 2, $C_4^3.(C_4\times D_4)$ ($C_2^2$), $C_2\times C_4^3.C_4^2$ ($C_2^2$), $C_2^7.C_2^4$ ($C_2^2$), $(C_4^2\times C_8).C_4^2$ ($C_4$), $(C_4^2\times C_8).C_4^2$ ($C_4$), $(C_4^2\times C_8).C_4^2$ ($C_4$), $(C_4^2\times C_8).C_4^2$ ($C_4$), $C_2^2\times C_8^2.D_4$ ($C_2^2$), $(C_4\times C_8).C_4^3$ ($C_2^2$)

Order 1024: $C_8^2.C_4^2$ ($C_2\times C_4$) x 8, $C_4^2.C_4^3$ ($C_2\times C_4$) x 6, $C_4^3.\OD_{16}$ ($C_2\times C_4$) x 6, $C_4^3.C_4^2$ ($C_2\times C_4$) x 4, $C_4^2.C_4^3$ ($D_4$) x 4, $(C_2^3\times C_8).D_8$ ($C_8$) x 4, $(C_2\times C_4^3).D_4$ ($C_8$) x 4, $(C_2\times C_4^3).D_4$ ($C_8$) x 4, $(C_2\times C_4^3).D_4$ ($C_8$) x 4, $C_8^2.C_4^2$ ($C_2\times C_4$) x 4, $(C_4\times C_8^2):C_4$ ($C_2\times C_4$) x 4, $C_8^2.C_4^2$ ($C_2\times C_4$) x 2, $C_8^2.C_4^2$ ($Q_8$) x 2, $C_8^2.C_4^2$ ($D_4$) x 2, $C_4^2.(C_2^3\times C_8)$ ($C_2\times C_4$) x 2, $C_2^3\times C_8\times C_{16}$ ($D_4$) x 2, $C_4^2.C_4^3$ ($Q_8$) x 2, $C_8^2.C_4^2$ ($Q_8$) x 2, $C_8^2.C_4^2$ ($D_4$) x 2, $C_8^2.C_4^2$ ($D_4$) x 2, $C_8^2.C_4^2$ ($C_2\times C_4$) x 2, $(C_2^2\times C_8^2):C_4$ ($D_4$) x 2, $(C_2^2\times C_8^2).C_4$ ($D_4$) x 2, $C_2\times C_4^2:\OD_{32}$ ($D_4$) x 2, $C_4^3.C_2^4$ ($C_2\times C_4$), $C_2^2\times C_4\times C_8^2$ ($C_2^3$), $(C_2\times C_4^3).D_4$ ($C_2\times C_4$), $C_4^2.(C_2^2\times C_4^2)$ ($C_2\times C_4$), $C_4^3.C_2^4$ ($C_2\times C_4$)

Order 512: $C_2\times C_4\times C_8^2$ ($D_4:C_2$) x 10, $C_2^2\times C_8\times C_{16}$ ($C_2^2:C_4$) x 8, $C_8^2.C_8$ ($C_4:C_4$) x 8, $C_2\times C_4\times C_8^2$ ($C_2^2\times C_4$) x 6, $C_2\times C_4\times C_8^2$ ($C_2\times D_4$) x 5, $C_4^3.D_4$ ($C_2\times C_8$) x 4, $(C_2\times C_8^2).C_4$ ($\SD_{16}$) x 4, $C_2\times C_8^2.C_4$ ($C_4:C_4$) x 4, $C_2\times C_8^2.C_4$ ($C_2^2:C_4$) x 4, $(C_2\times C_8^2):C_4$ ($C_4:C_4$) x 4, $(C_2\times C_8^2):C_4$ ($C_2^2:C_4$) x 4, $C_4^3.C_2^3$ ($\OD_{16}$) x 4, $C_4^3.C_2^3$ ($C_2\times C_8$) x 4, $C_8^2.D_4$ ($C_4^2$) x 4, $(C_2\times C_4^3).C_4$ ($C_2\times C_8$) x 4, $(C_2\times C_4^3).C_4$ ($C_4^2$) x 4, $C_2^2\times C_8\times C_{16}$ ($\SD_{16}$) x 4, $C_2^2\times C_8\times C_{16}$ ($C_4:C_4$) x 4, $C_8^2.C_8$ ($C_4:C_4$) x 4, $C_8^2.C_8$ ($C_4^2$) x 4, $C_8^2.C_8$ ($C_4:C_4$) x 4, $C_8^2.C_8$ ($C_2^2:C_4$) x 4, $C_8^2.C_8$ ($C_4^2$) x 4, $C_4^2:\OD_{32}$ ($C_4:C_4$) x 4, $C_4^2:\OD_{32}$ ($C_2^2:C_4$) x 4, $C_4^3.C_8$ ($C_2^2:C_4$) x 4, $C_8^2.C_8$ ($C_2^2:C_4$) x 4, $C_8^2.C_8$ ($C_4^2$) x 4, $C_2\times C_4\times C_8^2$ ($C_2\times Q_8$) x 3, $C_2^3\times C_8^2$ ($C_2\times D_4$) x 3, $C_4^3.D_4$ ($C_4^2$) x 2, $(C_2\times C_8^2).C_4$ ($Q_{16}$) x 2, $(C_2\times C_8^2).C_4$ ($D_8$) x 2, $(C_2\times C_8^2):C_4$ ($\SD_{16}$) x 2, $(C_2\times C_8^2):C_4$ ($D_8$) x 2, $(C_2\times C_8^2):C_4$ ($Q_{16}$) x 2, $(C_2\times C_8^2):C_4$ ($\SD_{16}$) x 2, $C_4^3.C_2^3$ ($C_4^2$) x 2, $C_4^3.C_2^3$ ($C_4:C_4$) x 2, $C_4^2.C_2^5$ ($C_2^2:C_4$) x 2, $C_2\times C_4^3.C_4$ ($C_2\times C_8$) x 2, $C_2^5.\OD_{16}$ ($C_2\times C_8$) x 2, $C_2^2\times C_8\times C_{16}$ ($Q_{16}$) x 2, $C_2^2\times C_8\times C_{16}$ ($D_8$) x 2, $C_4^3.Q_8$ ($C_2\times C_8$) x 2, $C_4^3.Q_8$ ($C_4^2$) x 2, $(C_4^2\times C_8):C_4$ ($\OD_{16}$) x 2, $(C_4^2\times C_8):C_4$ ($C_2\times C_8$) x 2, $(C_2^2\times C_8).C_4^2$ ($\OD_{16}$) x 2, $(C_2^2\times C_8).C_4^2$ ($C_2\times C_8$) x 2, $(C_4^2\times C_8):C_4$ ($C_4^2$) x 2, $C_2^3.(C_4\times D_8)$ ($C_2\times C_8$) x 2, $C_8.C_4^3$ ($C_4:C_4$) x 2, $C_4^2.(C_2^2\times D_4)$ ($C_2^2:C_4$), $C_4^2.(C_2^2\times Q_8)$ ($C_2^2:C_4$), $C_2^2\times C_4^2\times C_8$ ($D_4:C_2$), $C_2^2\times C_4^2\times C_8$ ($C_2\times D_4$), $C_2^2\times C_4^2\times C_8$ ($C_2^2\times C_4$), $C_2^3\times C_8^2$ ($D_4:C_2$)

Order 256: $C_2^2\times C_8^2$ ($C_4\times D_4$) x 13, $C_4\times C_8^2$ ($C_4\times D_4$) x 12, $C_2^2\times C_8^2$ ($D_8:C_2$) x 12, $C_4\times C_8^2$ ($C_4^2:C_2$) x 10, $C_2\times C_4^2\times C_8$ ($C_4\times D_4$) x 9, $C_4\times C_8^2$ ($C_4\times Q_8$) x 8, $C_2\times C_8\times C_{16}$ ($D_4:C_4$) x 8, $C_2\times C_8\times C_{16}$ ($C_2.C_4^2$) x 8, $C_2\times C_8\times C_{16}$ ($Q_8:C_4$) x 8, $C_4^2:C_{16}$ ($C_2.C_4^2$) x 8, $C_2\times C_8.C_4^2$ ($C_4:C_8$) x 8, $C_4^3.C_2^2$ ($C_4:C_8$) x 8, $C_4^2.C_2^4$ ($C_2^2:C_8$) x 8, $C_2\times C_4^2\times C_8$ ($\OD_{16}:C_2$) x 6, $C_2^2\times C_8^2$ ($C_2\times \SD_{16}$) x 6, $C_2\times C_4^2\times C_8$ ($C_4^2:C_2$) x 5, $C_2^2\times C_8^2$ ($C_2^2:Q_8$) x 5, $C_2^2\times C_8^2$ ($C_4:D_4$) x 5, $C_4\times C_8^2$ ($C_4^2:C_2$) x 4, $C_4\times C_8^2$ ($C_4.Q_8$) x 4, $C_4\times C_8^2$ ($C_2^2.D_4$) x 4, $C_4\times C_8^2$ ($C_2^2:Q_8$) x 4, $C_4\times C_8^2$ ($C_4:D_4$) x 4, $C_4\times C_8^2$ ($C_2^2.D_4$) x 4, $C_4\times C_8^2$ ($C_2\times C_4^2$) x 4, $C_4^3.C_4$ ($C_4\times C_8$) x 4, $C_4^2.\OD_{16}$ ($C_4\times C_8$) x 4, $C_2\times C_8\times C_{16}$ ($C_8:C_4$) x 4, $C_2\times C_8\times C_{16}$ ($C_8:C_4$) x 4, $(C_2\times C_8).C_4^2$ ($C_4\times C_8$) x 4, $(C_2\times C_8).C_4^2$ ($C_8:C_4$) x 4, $(C_2\times C_8).C_4^2$ ($C_4\times C_8$) x 4, $C_4^2.D_8$ ($C_4\times C_8$) x 4, $C_4^2.(C_2\times D_4)$ ($C_4\wr C_2$) x 4, $C_8^2.C_4$ ($C_8:C_4$) x 4, $C_8^2.C_4$ ($C_8:C_4$) x 4, $C_8^2.C_4$ ($D_4:C_4$) x 4, $C_8^2.C_4$ ($Q_8:C_4$) x 4, $C_8^2:C_4$ ($C_8:C_4$) x 4, $C_8^2:C_4$ ($C_8:C_4$) x 4, $C_8^2:C_4$ ($D_4:C_4$) x 4, $C_8^2:C_4$ ($Q_8:C_4$) x 4, $C_4^3.C_2^2$ ($C_8:C_4$) x 4, $C_4^3.C_2^2$ ($C_4\times C_8$) x 4, $C_4^2.C_2^4$ ($C_4\wr C_2$) x 4, $C_4^2.C_2^4$ ($C_2.C_4^2$) x 4, $C_2^2\times C_8^2$ ($Q_{16}:C_2$) x 4, $C_2^2\times C_8^2$ ($D_8:C_2$) x 4, $C_2^2\times C_8^2$ ($C_2^2.D_4$) x 4, $C_2^2\times C_8^2$ ($C_2^3:C_4$) x 4, $C_2\times C_4^2\times C_8$ ($C_2\times \OD_{16}$) x 3, $C_2\times C_4^2\times C_8$ ($C_2^2\times C_8$) x 3, $C_2\times C_4^2\times C_8$ ($C_2^2.D_4$) x 3, $C_2\times C_4^2\times C_8$ ($C_2^2:Q_8$) x 3, $C_2\times C_4^2\times C_8$ ($C_4\times Q_8$) x 3, $C_2\times C_4^2\times C_8$ ($C_2\times C_4^2$) x 3, $C_2^2\times C_8^2$ ($C_2\times Q_{16}$) x 3, $C_2^2\times C_8^2$ ($C_2\times D_8$) x 3, $C_2^2\times C_8^2$ ($C_4^2:C_2$) x 3, $C_2^2\times C_8^2$ ($C_4^2:C_2$) x 3, $C_2^2\times C_8^2$ ($C_2^2.D_4$) x 3, $C_4\times C_8^2$ ($C_4:Q_8$) x 2, $C_4\times C_8^2$ ($C_4^2:C_2$) x 2, $C_4\times C_8^2$ ($C_2^3:C_4$) x 2, $C_2^3\times C_4\times C_8$ ($\OD_{16}:C_2$) x 2, $C_2^3\times C_4\times C_8$ ($C_4:D_4$) x 2, $C_4^2.(C_2\times D_4)$ ($D_4:C_4$) x 2, $C_4^2.(C_2\times D_4)$ ($Q_8:C_4$) x 2, $C_4^2.(C_2\times Q_8)$ ($C_4\wr C_2$) x 2, $C_4^2.(C_2\times Q_8)$ ($Q_8:C_4$) x 2, $C_4^2.(C_2\times Q_8)$ ($D_4:C_4$) x 2, $C_4^2.(C_2\times Q_8)$ ($C_4\wr C_2$) x 2, $C_2\times C_4^2.D_4$ ($C_2^2:C_8$) x 2, $C_4^2.(C_2\times Q_8)$ ($C_2^2:C_8$) x 2, $C_2^5.Q_8$ ($C_2^2:C_8$) x 2, $C_2^5.D_4$ ($C_2^2:C_8$) x 2, $C_2\times C_8.C_4^2$ ($C_2.C_4^2$) x 2, $(C_2\times C_8):C_4^2$ ($C_2.C_4^2$) x 2, $C_2\times C_4^2\times C_8$ ($C_4^2:C_2$) x 2, $C_2\times C_4^2\times C_8$ ($C_2^2.D_4$) x 2, $C_2\times C_4^2\times C_8$ ($C_2^3:C_4$) x 2, $C_4^2.C_2^4$ ($D_4:C_4$) x 2, $C_4^2.C_2^4$ ($Q_8:C_4$) x 2, $C_4^2.C_2^4$ ($C_4\wr C_2$) x 2, $C_4^2.C_2^4$ ($Q_8:C_4$) x 2, $C_4^2.C_2^4$ ($D_4:C_4$) x 2, $C_4^2.C_2^4$ ($C_4\wr C_2$) x 2, $C_2^2\times C_8^2$ ($C_4^2:C_2$) x 2, $C_2^2\times C_8^2$ ($C_2^2\wr C_2$) x 2, $C_2^3\times C_4\times C_8$ ($C_2\times \OD_{16}$), $C_2^3\times C_4\times C_8$ ($C_2^2\times C_8$), $C_2^3\times C_4\times C_8$ ($C_2^2.D_4$), $C_2^3\times C_4\times C_8$ ($C_2^2\wr C_2$), $C_2^3\times C_4\times C_8$ ($C_4\times D_4$), $C_2^3\times C_4\times C_8$ ($C_2^3:C_4$), $C_2^2\times C_4^3$ ($C_4\times D_4$), $C_2\times C_4^2\times C_8$ ($C_4.Q_8$), $C_2\times C_4^2\times C_8$ ($C_4^2:C_2$), $C_2\times C_4^2\times C_8$ ($C_4:D_4$), $C_2\times C_4^2\times C_8$ ($C_2^2\wr C_2$), $C_2^2\times C_8^2$ ($C_4:Q_8$), $C_2^2\times C_8^2$ ($C_4:D_4$), $C_2^2\times C_8^2$ ($C_4.Q_8$), $C_2^2\times C_8^2$ ($C_4\times Q_8$)

Order 128: $C_2\times C_8^2$ ($C_4\times \SD_{16}$) x 22, $C_4^2.D_4$ ($Q_8:C_8$) x 12, $C_2\times C_8^2$ ($C_4\times Q_{16}$) x 11, $C_2\times C_8^2$ ($C_4\times D_8$) x 11, $C_2^2\times C_4\times C_8$ ($C_8\times D_4$) x 11, $C_4^2\times C_8$ ($C_2^3.C_2^3$) x 10, $C_2\times C_8^2$ ($C_2^3.C_2^3$) x 10, $C_2\times C_8^2$ ($C_2^3.C_2^3$) x 10, $C_4^2\times C_8$ ($C_4:C_4^2$) x 9, $C_4^2\times C_8$ ($C_8\times D_4$) x 8, $C_8\times C_{16}$ ($C_4.C_4^2$) x 8, $C_8:\OD_{16}$ ($D_4:C_8$) x 8, $C_4^2.D_4$ ($C_2^2.C_4^2$) x 8, $C_2\times C_8^2$ ($C_2^3.D_4$) x 8, $C_2\times C_8^2$ ($C_4^2.C_2^2$) x 8, $C_2\times C_8^2$ ($C_8:D_4$) x 8, $C_2^2\times C_4\times C_8$ ($C_8:D_4$) x 8, $C_2^2\times C_4\times C_8$ ($C_4^2:C_2^2$) x 8, $C_2\times C_8^2$ ($C_4:C_4^2$) x 7, $C_2\times C_8^2$ ($C_2^2:C_4^2$) x 7, $C_2^2\times C_4\times C_8$ ($C_2^3.C_2^3$) x 7, $C_2^2\times C_4\times C_8$ ($C_8:D_4$) x 7, $C_4^2\times C_8$ ($\OD_{16}:C_4$) x 6, $C_4^2\times C_8$ ($C_2^3.C_2^3$) x 6, $C_2\times C_8^2$ ($C_2^3.C_2^3$) x 6, $C_2\times C_8^2$ ($\SD_{16}:C_4$) x 6, $C_2\times C_8^2$ ($C_2^3.D_4$) x 6, $C_2^2\times C_4\times C_8$ ($\OD_{16}:C_4$) x 6, $C_4^2\times C_8$ ($C_2^2:C_4^2$) x 5, $C_2^2\times C_4\times C_8$ ($C_2^3.D_4$) x 5, $C_2^2\times C_4\times C_8$ ($C_2^3.D_4$) x 5, $C_4^2.D_4$ ($Q_8:C_8$) x 4, $C_4^2.D_4$ ($D_4:C_8$) x 4, $C_4^2.Q_8$ ($Q_8:C_8$) x 4, $C_4^2.Q_8$ ($D_4:C_8$) x 4, $C_2^4.Q_8$ ($Q_8:C_8$) x 4, $C_2^4.Q_8$ ($D_4:C_8$) x 4, $C_2^3.D_8$ ($Q_8:C_8$) x 4, $C_2^3.D_8$ ($D_4:C_8$) x 4, $C_8.C_4^2$ ($C_4.C_4^2$) x 4, $C_8.C_4^2$ ($C_4^2:C_4$) x 4, $C_8:C_4^2$ ($C_4.C_4^2$) x 4, $C_8:C_4^2$ ($C_4^2:C_4$) x 4, $C_4^2\times C_8$ ($C_2^3.C_2^3$) x 4, $C_4^2\times C_8$ ($C_8:Q_8$) x 4, $C_4^2\times C_8$ ($C_8\times Q_8$) x 4, $C_4^2\times C_8$ ($C_8:D_4$) x 4, $C_4^2\times C_8$ ($C_8:D_4$) x 4, $C_4^2\times C_8$ ($C_4^2.C_2^2$) x 4, $C_4^2\times C_8$ ($C_4^2.C_4$) x 4, $C_4^2.D_4$ ($D_4:C_8$) x 4, $C_8:\OD_{16}$ ($Q_8:C_8$) x 4, $C_8:\OD_{16}$ ($D_4:C_8$) x 4, $C_4^2.D_4$ ($C_4.C_4^2$) x 4, $C_4^2.D_4$ ($C_4^2:C_4$) x 4, $C_4^2.D_4$ ($C_4.C_4^2$) x 4, $C_4^2.D_4$ ($C_4^2:C_4$) x 4, $C_2\times C_8^2$ ($C_2^3.D_4$) x 4, $C_2\times C_8^2$ ($C_2^2.Q_{16}$) x 4, $C_2\times C_8^2$ ($C_2^2.D_8$) x 4, $C_2\times C_8^2$ ($C_2^3.D_4$) x 4, $C_2\times C_8^2$ ($C_2^3.D_4$) x 4, $C_2\times C_8^2$ ($C_8.Q_8$) x 4, $C_2\times C_8^2$ ($C_8.D_4$) x 4, $C_2\times C_8^2$ ($C_4.Q_{16}$) x 4, $C_2\times C_8^2$ ($C_4.D_8$) x 4, $C_2\times C_8^2$ ($C_2^3.D_4$) x 4, $C_2\times C_8^2$ ($C_2^3.D_4$) x 4, $C_2\times C_8^2$ ($Q_8.Q_8$) x 4, $C_2\times C_8^2$ ($D_4.Q_8$) x 4, $C_2\times C_8^2$ ($C_2^2:Q_{16}$) x 4, $C_2\times C_8^2$ ($C_8:D_4$) x 4, $C_2\times C_8^2$ ($\OD_{16}:C_4$) x 4, $C_2^4.Q_8$ ($C_2^2.C_4^2$) x 4, $C_2^4.D_4$ ($C_2^2.C_4^2$) x 4, $C_2^2\times C_4\times C_8$ ($C_2^3.D_4$) x 4, $C_2^2\times C_4\times C_8$ ($C_2^2:C_4^2$) x 4, $C_2^2\times C_4\times C_8$ ($C_2^2:Q_{16}$) x 4, $C_2^2\times C_4\times C_8$ ($C_8:D_4$) x 4, $C_2^2\times C_4\times C_8$ ($C_8:Q_8$) x 4, $C_2^2\times C_4\times C_8$ ($C_8\times Q_8$) x 4, $C_2^2\times C_4\times C_8$ ($D_8:C_4$) x 4, $C_2^2\times C_4\times C_8$ ($D_8:C_4$) x 4, $C_2^2\times C_4\times C_8$ ($C_8:D_4$) x 4, $C_2^2\times C_4\times C_8$ ($C_4^2.C_2^2$) x 4, $C_2^2\times C_4\times C_8$ ($C_4^2.C_4$) x 4, $C_2\times C_4^3$ ($C_8:D_4$) x 3, $C_2\times C_4^3$ ($C_8\times D_4$) x 3, $C_4^2\times C_8$ ($C_2\times C_4\times C_8$) x 3, $C_2\times C_8^2$ ($C_2^3.C_2^3$) x 3, $C_2\times C_8^2$ ($C_2^3.C_2^3$) x 3, $C_2\times C_8^2$ ($C_2^3.D_4$) x 3, $C_2\times C_8^2$ ($D_8:C_4$) x 3, $C_2\times C_8^2$ ($Q_{16}:C_4$) x 3, $C_2\times C_8^2$ ($C_2^2.D_8$) x 3, $C_2\times C_8^2$ ($C_2^3.D_4$) x 3, $C_2^2\times C_4\times C_8$ ($(C_2^2\times C_8):C_2$) x 3, $C_2^2\times C_4\times C_8$ ($C_2^3:C_8$) x 3, $C_2^2\times C_4\times C_8$ ($C_2\times C_4\times C_8$) x 3, $C_2^2\times C_4\times C_8$ ($C_2^3.C_2^3$) x 3, $C_2^2\times C_4\times C_8$ ($C_2^3.C_2^3$) x 3, $C_2^2\times C_4\times C_8$ ($C_8.D_4$) x 3, $C_2\times C_4^3$ ($C_2^2:C_4^2$) x 2, $C_4^2\times C_8$ ($C_4\times \OD_{16}$) x 2, $C_4^2\times C_8$ ($C_2^3.C_2^3$) x 2, $C_4^2\times C_8$ ($C_2^3.D_4$) x 2, $C_4^2\times C_8$ ($C_2^3.D_4$) x 2, $C_4^2\times C_8$ ($C_4^2:C_4$) x 2, $C_4^2\times C_8$ ($C_4^2.C_2^2$) x 2, $C_4^2\times C_8$ ($C_4^2.C_4$) x 2, $C_2\times C_8^2$ ($C_2^3.D_4$) x 2, $C_2\times C_8^2$ ($C_4^2:C_4$) x 2, $C_2\times C_8^2$ ($C_8:Q_8$) x 2, $C_2\times C_8^2$ ($C_8:Q_8$) x 2, $C_2\times C_8^2$ ($C_8:D_4$) x 2, $C_2\times C_8^2$ ($C_2^2.Q_{16}$) x 2, $C_2\times C_8^2$ ($C_2^3.D_4$) x 2, $C_2\times C_8^2$ ($C_2^3.D_4$) x 2, $C_2\times C_8^2$ ($C_2^2.D_8$) x 2, $C_2\times C_8^2$ ($Q_8:Q_8$) x 2, $C_2\times C_8^2$ ($D_4:Q_8$) x 2, $C_2\times C_8^2$ ($Q_8:Q_8$) x 2, $C_2\times C_8^2$ ($D_4:Q_8$) x 2, $C_2\times C_8^2$ ($Q_8.D_4$) x 2, $C_2\times C_8^2$ ($D_4.D_4$) x 2, $C_2\times C_8^2$ ($D_4.D_4$) x 2, $C_2\times C_8^2$ ($D_4:D_4$) x 2, $C_2\times C_8^2$ ($C_2^3.D_4$) x 2, $C_2^2\times C_4\times C_8$ ($C_2^2.Q_{16}$) x 2, $C_2^2\times C_4\times C_8$ ($C_2^2.D_8$) x 2, $C_2^2\times C_4\times C_8$ ($C_4\times \OD_{16}$) x 2, $C_2^2\times C_4\times C_8$ ($C_2^3.C_2^3$) x 2, $C_2^2\times C_4\times C_8$ ($C_2^3.D_4$) x 2, $C_2^2\times C_4\times C_8$ ($C_8.D_4$) x 2, $C_2^2\times C_4\times C_8$ ($Q_8.D_4$) x 2, $C_2^2\times C_4\times C_8$ ($D_4.D_4$) x 2, $C_2^2\times C_4\times C_8$ ($D_4.D_4$) x 2, $C_2^2\times C_4\times C_8$ ($D_4:D_4$) x 2, $C_2^2\times C_4\times C_8$ ($\SD_{16}:C_4$) x 2, $C_2^2\times C_4\times C_8$ ($C_4\times \SD_{16}$) x 2, $C_2^2\times C_4\times C_8$ ($C_4^2.C_2^2$) x 2, $C_2^2\times C_4\times C_8$ ($C_4^2.C_4$) x 2, $C_2\times C_4^3$ ($C_2^3.C_2^3$), $C_2\times C_4^3$ ($C_2^3.C_2^3$), $C_2\times C_4^3$ ($C_2^3.D_4$), $C_2\times C_4^3$ ($C_4:C_4^2$), $C_4^2\times C_8$ ($C_4.C_4^2$), $C_4^2\times C_8$ ($C_4^2:C_4$), $C_4^2\times C_8$ ($C_4^2:C_4$), $C_4^2\times C_8$ ($C_2^3.D_4$), $C_4^2\times C_8$ ($C_2^3.D_4$), $C_4^2\times C_8$ ($C_2^2.C_4^2$), $C_4^2\times C_8$ ($C_4^3$), $C_2^4\times C_8$ ($(C_2^2\times C_8):C_2$), $C_2^4\times C_8$ ($C_2^3:C_8$), $C_2^4\times C_8$ ($C_8.D_4$), $C_2^4\times C_8$ ($C_8.D_4$), $C_2^4\times C_8$ ($C_8:D_4$), $C_2^4\times C_8$ ($C_8\times D_4$), $C_2^3\times C_4^2$ ($C_2^3.D_4$), $C_2^3\times C_4^2$ ($C_8:D_4$), $C_2^3\times C_4^2$ ($C_8\times D_4$), $C_2\times C_8^2$ ($C_4^2:C_4$), $C_2\times C_8^2$ ($C_4^2:C_4$), $C_2\times C_8^2$ ($C_2^3.D_4$), $C_2\times C_8^2$ ($C_4^2:C_4$), $C_2\times C_8^2$ ($C_2^2.C_4^2$), $C_2\times C_8^2$ ($C_4:Q_{16}$), $C_2\times C_8^2$ ($C_4:D_8$), $C_2\times C_8^2$ ($C_4:Q_{16}$), $C_2\times C_8^2$ ($C_4:\SD_{16}$), $C_2\times C_8^2$ ($Q_8:D_4$), $C_2\times C_8^2$ ($C_4:D_8$), $C_2\times C_8^2$ ($C_2^2:Q_{16}$), $C_2\times C_8^2$ ($C_2^2:\SD_{16}$), $C_2\times C_8^2$ ($Q_8:D_4$), $C_2\times C_8^2$ ($D_4:D_4$), $C_2^2\times C_4\times C_8$ ($C_4.C_4^2$), $C_2^2\times C_4\times C_8$ ($C_2^3.C_2^3$), $C_2^2\times C_4\times C_8$ ($C_2^3.D_4$), $C_2^2\times C_4\times C_8$ ($C_2^4:C_4$), $C_2^2\times C_4\times C_8$ ($C_4:C_4^2$), $C_2^2\times C_4\times C_8$ ($C_2^2.C_4^2$), $C_2^2\times C_4\times C_8$ ($C_8.D_4$), $C_2^2\times C_4\times C_8$ ($C_4:Q_{16}$), $C_2^2\times C_4\times C_8$ ($C_4:\SD_{16}$), $C_2^2\times C_4\times C_8$ ($Q_8:D_4$), $C_2^2\times C_4\times C_8$ ($C_4:D_8$), $C_2^2\times C_4\times C_8$ ($C_2^2:Q_{16}$), $C_2^2\times C_4\times C_8$ ($C_2^2:\SD_{16}$), $C_2^2\times C_4\times C_8$ ($Q_8:D_4$), $C_2^2\times C_4\times C_8$ ($D_4:D_4$), $C_2^2\times C_4\times C_8$ ($D_8:C_4$), $C_2^2\times C_4\times C_8$ ($Q_{16}:C_4$), $C_2^2\times C_4\times C_8$ ($C_4\times Q_{16}$), $C_2^2\times C_4\times C_8$ ($C_4\times D_8$)

Order 64: $C_2\times C_4\times C_8$ ($C_4^2.D_4$) x 12, $C_2\times C_4\times C_8$ ($C_4^2.D_4$) x 12, $C_2\times C_4\times C_8$ ($C_2.(C_8\times D_4)$) x 10, $C_2\times C_4\times C_8$ ($C_2.(C_8\times D_4)$) x 10, $C_2\times C_4\times C_8$ ($C_4:C_4\times C_8$) x 9, $C_2\times C_4\times C_8$ ($C_2^4.C_2^3$) x 9, $C_2\times C_4\times C_8$ ($C_4^2.D_4$) x 8, $C_2\times C_4\times C_8$ ($(C_2\times C_4).D_8$) x 8, $C_2\times C_4\times C_8$ ($C_4.(C_4\times D_4)$) x 8, $C_2\times C_4\times C_8$ ($D_4:C_4^2$) x 8, $C_8^2$ ($(C_2\times C_4).D_8$) x 8, $C_8^2$ ($C_4.(C_4\times D_4)$) x 8, $C_8:C_8$ ($C_4^2.D_4$) x 8, $C_8:C_8$ ($C_4^2.D_4$) x 8, $C_2^3.Q_8$ ($C_4^2.D_4$) x 8, $C_2^2.D_8$ ($C_4^2.D_4$) x 8, $C_2\times C_4\times C_8$ ($C_2^3.D_8$) x 6, $C_2\times C_4\times C_8$ ($C_2^3.Q_{16}$) x 6, $C_2\times C_4\times C_8$ ($Q_8:C_4^2$) x 6, $C_2\times C_4\times C_8$ ($D_4:C_4^2$) x 6, $C_2\times C_4\times C_8$ ($C_2^3.C_4^2$) x 6, $C_2\times C_4\times C_8$ ($\SD_{16}:C_8$) x 6, $C_2\times C_4\times C_8$ ($C_8\times \SD_{16}$) x 6, $C_2\times C_4\times C_8$ ($C_4^2.D_4$) x 6, $C_2\times C_4\times C_8$ ($C_4^2.D_4$) x 6, $C_2\times C_4\times C_8$ ($C_4^2.D_4$) x 6, $C_2\times C_4\times C_8$ ($C_4^2.D_4$) x 6, $C_8^2$ ($Q_8:C_4^2$) x 6, $C_8^2$ ($D_4:C_4^2$) x 6, $C_2\times C_4\times C_8$ ($C_4.(C_4\times D_4)$) x 5, $C_2\times C_4\times C_8$ ($C_2^3.C_4^2$) x 5, $C_2\times C_4\times C_8$ ($C_2^4.C_2^3$) x 5, $C_8^2$ ($C_8:C_4^2$) x 5, $C_8^2$ ($C_8:C_4^2$) x 5, $C_2\times C_4\times C_8$ ($C_4^2:Q_8$) x 4, $C_2\times C_4\times C_8$ ($(C_2\times C_4):\SD_{16}$) x 4, $C_2\times C_4\times C_8$ ($C_4^3:C_2$) x 4, $C_2\times C_4\times C_8$ ($(C_2\times C_4).D_8$) x 4, $C_2\times C_4\times C_8$ ($C_4.(C_4\times Q_8)$) x 4, $C_2\times C_4\times C_8$ ($\OD_{16}.D_4$) x 4, $C_2\times C_4\times C_8$ ($\OD_{16}.Q_8$) x 4, $C_2\times C_4\times C_8$ ($C_4^2:D_4$) x 4, $C_2\times C_4\times C_8$ ($\OD_{16}.D_4$) x 4, $C_2\times C_4\times C_8$ ($C_2^3.D_8$) x 4, $C_2\times C_4\times C_8$ ($C_2^4.D_4$) x 4, $C_2\times C_4\times C_8$ ($(C_4\times C_8):C_4$) x 4, $C_2\times C_4\times C_8$ ($C_4^2.D_4$) x 4, $C_2\times C_4\times C_8$ ($C_4^2:C_8$) x 4, $C_2\times C_4\times C_8$ ($D_4.C_4^2$) x 4, $C_2\times C_4\times C_8$ ($D_4.C_4^2$) x 4, $C_2\times C_4\times C_8$ ($C_2^4.D_4$) x 4, $C_2\times C_4\times C_8$ ($C_4^2.C_2^3$) x 4, $C_2\times C_4\times C_8$ ($D_4.\SD_{16}$) x 4, $C_2^3\times C_8$ ($C_4^2.D_4$) x 4, $C_2^3\times C_8$ ($C_4^2.D_4$) x 4, $C_8^2$ ($(C_2\times C_4):\SD_{16}$) x 4, $C_8^2$ ($(C_2\times C_4).D_8$) x 4, $C_8^2$ ($C_4.(C_4\times Q_8)$) x 4, $C_2^2\times C_4^2$ ($C_4^2:D_4$) x 4, $C_2^2\times C_4^2$ ($\OD_{16}.D_4$) x 4, $C_2\times C_4\times C_8$ ($C_4.(C_4\times D_4)$) x 3, $C_2\times C_4\times C_8$ ($C_4.(C_4\times D_4)$) x 3, $C_2\times C_4\times C_8$ ($C_4.(C_4\times D_4)$) x 3, $C_2\times C_4\times C_8$ ($C_4.(C_4\times D_4)$) x 3, $C_2\times C_4\times C_8$ ($(C_2\times C_4).D_8$) x 3, $C_2\times C_4\times C_8$ ($C_4.(C_4\times D_4)$) x 3, $C_2\times C_4\times C_8$ ($C_4.(C_4\times D_4)$) x 3, $C_2\times C_4\times C_8$ ($C_4.(C_4\times D_4)$) x 3, $C_2\times C_4\times C_8$ ($(C_2\times C_4).D_8$) x 3, $C_2\times C_4\times C_8$ ($Q_8.Q_{16}$) x 3, $C_2\times C_4\times C_8$ ($D_4.Q_{16}$) x 3, $C_2\times C_4\times C_8$ ($Q_8.D_8$) x 3, $C_2\times C_4\times C_8$ ($D_4.D_8$) x 3, $C_2\times C_4\times C_8$ ($C_8:Q_{16}$) x 3, $C_2\times C_4\times C_8$ ($C_8:\SD_{16}$) x 3, $C_2\times C_4\times C_8$ ($C_8:\SD_{16}$) x 3, $C_2\times C_4\times C_8$ ($C_8:D_8$) x 3, $C_2\times C_4\times C_8$ ($Q_8:\OD_{16}$) x 3, $C_2\times C_4\times C_8$ ($C_4^2.C_2^3$) x 3, $C_2\times C_4\times C_8$ ($D_4:\OD_{16}$) x 3, $C_2\times C_4\times C_8$ ($D_4.\OD_{16}$) x 3, $C_2\times C_4\times C_8$ ($C_8:Q_{16}$) x 3, $C_2\times C_4\times C_8$ ($C_8:\SD_{16}$) x 3, $C_2\times C_4\times C_8$ ($C_8:\SD_{16}$) x 3, $C_2\times C_4\times C_8$ ($C_8:D_8$) x 3, $C_2\times C_4\times C_8$ ($D_8:C_8$) x 3, $C_2\times C_4\times C_8$ ($Q_{16}:C_8$) x 3, $C_2\times C_4\times C_8$ ($C_8\times Q_{16}$) x 3, $C_2\times C_4\times C_8$ ($C_8\times D_8$) x 3, $C_2\times C_4\times C_8$ ($C_2^3:C_4^2$) x 3, $C_2\times C_4\times C_8$ ($C_2^4.C_2^3$) x 3, $C_2^3\times C_8$ ($C_4.(C_4\times D_4)$) x 3, $C_8^2$ ($(C_2\times C_4).Q_{16}$) x 3, $C_8^2$ ($C_4.(C_4\times Q_8)$) x 3, $C_8^2$ ($C_4.(C_4\times Q_8)$) x 3, $C_8^2$ ($(C_2\times C_4).D_8$) x 3, $C_2^2\times C_4^2$ ($C_4^2.D_4$) x 3, $C_2^2\times C_4^2$ ($C_2^3.\OD_{16}$) x 3, $C_2\times C_4\times C_8$ ($C_4^2.D_4$) x 2, $C_2\times C_4\times C_8$ ($C_4^2.D_4$) x 2, $C_2\times C_4\times C_8$ ($C_4^2.D_4$) x 2, $C_2\times C_4\times C_8$ ($C_4^2.D_4$) x 2, $C_2\times C_4\times C_8$ ($(C_2\times C_4):D_8$) x 2, $C_2\times C_4\times C_8$ ($(C_2\times C_4):Q_{16}$) x 2, $C_2\times C_4\times C_8$ ($C_4^2.D_4$) x 2, $C_2\times C_4\times C_8$ ($C_4^2.D_4$) x 2, $C_2\times C_4\times C_8$ ($C_4^2.Q_8$) x 2, $C_2\times C_4\times C_8$ ($(C_2\times C_4):\SD_{16}$) x 2, $C_2\times C_4\times C_8$ ($(C_2\times C_4):D_8$) x 2, $C_2\times C_4\times C_8$ ($(C_2\times C_4):Q_{16}$) x 2, $C_2\times C_4\times C_8$ ($(C_2\times C_4):\SD_{16}$) x 2, $C_2\times C_4\times C_8$ ($C_2^3.\OD_{16}$) x 2, $C_2\times C_4\times C_8$ ($C_2^4.D_4$) x 2, $C_2\times C_4\times C_8$ ($C_2^3.\OD_{16}$) x 2, $C_2\times C_4\times C_8$ ($C_2^4.D_4$) x 2, $C_2\times C_4\times C_8$ ($C_8:C_4^2$) x 2, $C_2\times C_4\times C_8$ ($C_8.C_4^2$) x 2, $C_2\times C_4\times C_8$ ($C_8.C_4^2$) x 2, $C_2\times C_4\times C_8$ ($Q_8:C_4^2$) x 2, $C_2\times C_4\times C_8$ ($D_4:C_4^2$) x 2, $C_2\times C_4\times C_8$ ($C_4^2.D_4$) x 2, $C_2\times C_4\times C_8$ ($C_4^2.D_4$) x 2, $C_2\times C_4\times C_8$ ($(C_4\times C_8):C_4$) x 2, $C_2\times C_4\times C_8$ ($C_4^2:C_8$) x 2, $C_2\times C_4\times C_8$ ($C_2^4.D_4$) x 2, $C_2\times C_4\times C_8$ ($C_2^3.D_8$) x 2, $C_2\times C_4\times C_8$ ($C_8.C_4^2$) x 2, $C_2\times C_4\times C_8$ ($C_4^2.C_2^3$) x 2, $C_2\times C_4\times C_8$ ($D_4.\SD_{16}$) x 2, $C_2\times C_4\times C_8$ ($C_8:Q_{16}$) x 2, $C_2\times C_4\times C_8$ ($C_8:\SD_{16}$) x 2, $C_2\times C_4\times C_8$ ($Q_8:Q_{16}$) x 2, $C_2\times C_4\times C_8$ ($D_4:Q_{16}$) x 2, $C_2\times C_4\times C_8$ ($C_2^3.C_4^2$) x 2, $C_2\times C_4\times C_8$ ($C_2.C_4^3$) x 2, $C_4^3$ ($C_2.(C_8\times D_4)$) x 2, $C_4^3$ ($C_2.(C_8\times D_4)$) x 2, $C_4^3$ ($C_2^3.\OD_{16}$) x 2, $C_4^3$ ($C_2^3.C_4^2$) x 2, $C_4^3$ ($C_2^4.C_2^3$) x 2, $C_2^3\times C_8$ ($C_4^2.D_4$) x 2, $C_2^3\times C_8$ ($C_4^2.D_4$) x 2, $C_2^3\times C_8$ ($C_2.(C_8\times D_4)$) x 2, $C_2^3\times C_8$ ($C_2.(C_8\times D_4)$) x 2, $C_2^3\times C_8$ ($C_2^3.\OD_{16}$) x 2, $C_2^3\times C_8$ ($C_2^3.\OD_{16}$) x 2, $C_2^3\times C_8$ ($C_2^3.C_4^2$) x 2, $C_2^3\times C_8$ ($C_4^2.D_4$) x 2, $C_2^3\times C_8$ ($C_4^2.D_4$) x 2, $C_2^3\times C_8$ ($C_4^2.C_2^3$) x 2, $C_2^3\times C_8$ ($D_4.\SD_{16}$) x 2, $C_2^3\times C_8$ ($\SD_{16}:C_8$) x 2, $C_2^3\times C_8$ ($C_8\times \SD_{16}$) x 2, $C_2^3\times C_8$ ($C_4^2.D_4$) x 2, $C_2^3\times C_8$ ($C_4^2.D_4$) x 2, $C_2^3\times C_8$ ($C_4^2.D_4$) x 2, $C_2^3\times C_8$ ($C_4^2.D_4$) x 2, $C_8^2$ ($C_4^2.D_4$) x 2, $C_8^2$ ($C_4^2.D_4$) x 2, $C_8^2$ ($C_4^2.D_4$) x 2, $C_8^2$ ($(C_2\times C_4):D_8$) x 2, $C_8^2$ ($(C_2\times C_4):Q_{16}$) x 2, $C_8^2$ ($C_4^2.D_4$) x 2, $C_8^2$ ($C_4^2.Q_8$) x 2, $C_8^2$ ($C_2^4.D_4$) x 2, $C_8^2$ ($C_4^2.Q_8$) x 2, $C_8^2$ ($C_4^2.Q_8$) x 2, $C_8^2$ ($C_4^2.Q_8$) x 2, $C_8^2$ ($C_2^4.D_4$) x 2, $C_8^2$ ($C_8:C_4^2$) x 2, $C_8^2$ ($Q_8:C_4^2$) x 2, $C_8^2$ ($D_4:C_4^2$) x 2, $C_8^2$ ($C_2^4.D_4$) x 2, $C_2^2\times C_4^2$ ($C_2.(C_8\times D_4)$) x 2, $C_2^2\times C_4^2$ ($C_2.(C_8\times D_4)$) x 2, $C_2^2\times C_4^2$ ($\OD_{16}.D_4$) x 2, $C_2^2\times C_4^2$ ($C_2^3.D_8$) x 2, $C_2^2\times C_4^2$ ($C_2^3.Q_{16}$) x 2, $C_2^2\times C_4^2$ ($C_2^3.\OD_{16}$) x 2, $C_2^2\times C_4^2$ ($C_2^3.C_4^2$) x 2, $C_2\times C_4\times C_8$ ($C_4^2.D_4$), $C_2\times C_4\times C_8$ ($C_4^2.D_4$), $C_2\times C_4\times C_8$ ($\OD_{16}.D_4$), $C_2\times C_4\times C_8$ ($\OD_{16}.D_4$), $C_2\times C_4\times C_8$ ($C_4^2.D_4$), $C_2\times C_4\times C_8$ ($C_4^2.D_4$), $C_2\times C_4\times C_8$ ($\OD_{16}.Q_8$), $C_2\times C_4\times C_8$ ($\OD_{16}.Q_8$), $C_2\times C_4\times C_8$ ($C_4^2.Q_8$), $C_2\times C_4\times C_8$ ($C_4^2.Q_8$), $C_2\times C_4\times C_8$ ($C_4.(C_4\times D_4)$), $C_2\times C_4\times C_8$ ($(C_2\times C_4).Q_{16}$), $C_2\times C_4\times C_8$ ($C_4.(C_4\times Q_8)$), $C_2\times C_4\times C_8$ ($C_4.(C_4\times Q_8)$), $C_2\times C_4\times C_8$ ($(C_2\times C_4).D_8$), $C_2\times C_4\times C_8$ ($\OD_{16}.D_4$), $C_2\times C_4\times C_8$ ($\OD_{16}.D_4$), $C_2\times C_4\times C_8$ ($C_2^4.D_4$), $C_2\times C_4\times C_8$ ($C_2^3.D_8$), $C_2\times C_4\times C_8$ ($C_2^4.D_4$), $C_2\times C_4\times C_8$ ($C_2^3.Q_{16}$), $C_2\times C_4\times C_8$ ($C_2^4.D_4$), $C_2\times C_4\times C_8$ ($C_2^3.D_8$), $C_2\times C_4\times C_8$ ($(C_2\times C_8).D_4$), $C_2\times C_4\times C_8$ ($(C_2\times C_8).D_4$), $C_2\times C_4\times C_8$ ($C_4^2.D_4$), $C_2\times C_4\times C_8$ ($C_4^2.D_4$), $C_2\times C_4\times C_8$ ($C_4^2.D_4$), $C_2\times C_4\times C_8$ ($C_4^2.D_4$), $C_2\times C_4\times C_8$ ($C_2^3.Q_{16}$), $C_2\times C_4\times C_8$ ($C_2^3.D_8$), $C_2\times C_4\times C_8$ ($C_8:C_4^2$), $C_2\times C_4\times C_8$ ($C_8:C_4^2$), $C_2\times C_4\times C_8$ ($C_2^3.C_4^2$), $C_2\times C_4\times C_8$ ($C_2^3.C_4^2$), $C_2\times C_4\times C_8$ ($C_2^3.C_4^2$), $C_2\times C_4\times C_8$ ($C_8:C_4^2$), $C_2\times C_4\times C_8$ ($C_4^2\times C_8$), $C_2\times C_4\times C_8$ ($C_8.Q_{16}$), $C_2\times C_4\times C_8$ ($D_4.Q_{16}$), $C_2\times C_4\times C_8$ ($Q_8:D_8$), $C_2\times C_4\times C_8$ ($C_8:D_8$), $C_4^3$ ($C_4.(C_4\times D_4)$), $C_4^3$ ($C_4:C_4\times C_8$), $C_4^3$ ($C_2^3.C_4^2$), $C_4^3$ ($C_2^3.C_4^2$), $C_4^3$ ($C_2^4.C_2^3$), $C_4^3$ ($C_2.C_4^3$), $C_2^4\times C_4$ ($\OD_{16}.D_4$), $C_2^4\times C_4$ ($C_4^2.D_4$), $C_2^4\times C_4$ ($C_2^3.\OD_{16}$), $C_2^3\times C_8$ ($\OD_{16}.D_4$), $C_2^3\times C_8$ ($\OD_{16}.D_4$), $C_2^3\times C_8$ ($\OD_{16}.Q_8$), $C_2^3\times C_8$ ($\OD_{16}.Q_8$), $C_2^3\times C_8$ ($C_4.(C_4\times D_4)$), $C_2^3\times C_8$ ($\OD_{16}.D_4$), $C_2^3\times C_8$ ($\OD_{16}.D_4$), $C_2^3\times C_8$ ($(C_2\times C_8).D_4$), $C_2^3\times C_8$ ($(C_2\times C_8).D_4$), $C_2^3\times C_8$ ($C_4.(C_4\times D_4)$), $C_2^3\times C_8$ ($C_4:C_4\times C_8$), $C_2^3\times C_8$ ($C_2^3.C_4^2$), $C_2^3\times C_8$ ($C_2^3.C_4^2$), $C_2^3\times C_8$ ($C_2^3.C_4^2$), $C_2^3\times C_8$ ($C_2^3.C_4^2$), $C_2^3\times C_8$ ($Q_8.Q_{16}$), $C_2^3\times C_8$ ($D_4.Q_{16}$), $C_2^3\times C_8$ ($Q_8.D_8$), $C_2^3\times C_8$ ($D_4.D_8$), $C_2^3\times C_8$ ($C_8.Q_{16}$), $C_2^3\times C_8$ ($D_4.Q_{16}$), $C_2^3\times C_8$ ($C_8:Q_{16}$), $C_2^3\times C_8$ ($C_8:\SD_{16}$), $C_2^3\times C_8$ ($Q_8:D_8$), $C_2^3\times C_8$ ($C_8:D_8$), $C_2^3\times C_8$ ($C_8:\SD_{16}$), $C_2^3\times C_8$ ($C_8:D_8$), $C_2^3\times C_8$ ($Q_8:\OD_{16}$), $C_2^3\times C_8$ ($C_4^2.C_2^3$), $C_2^3\times C_8$ ($D_4:\OD_{16}$), $C_2^3\times C_8$ ($D_4.\OD_{16}$), $C_2^3\times C_8$ ($C_8:Q_{16}$), $C_2^3\times C_8$ ($C_8:\SD_{16}$), $C_2^3\times C_8$ ($C_8:\SD_{16}$), $C_2^3\times C_8$ ($C_8:D_8$), $C_2^3\times C_8$ ($D_8:C_8$), $C_2^3\times C_8$ ($Q_{16}:C_8$), $C_2^3\times C_8$ ($C_8\times Q_{16}$), $C_2^3\times C_8$ ($C_8\times D_8$), $C_8^2$ ($C_4^2.D_4$), $C_8^2$ ($C_4^2.D_4$), $C_8^2$ ($C_4^2.D_4$), $C_8^2$ ($C_4^2.D_4$), $C_8^2$ ($C_4^2.Q_8$), $C_8^2$ ($C_4^2.Q_8$), $C_8^2$ ($C_4.(C_4\times D_4)$), $C_8^2$ ($C_4.(C_4\times D_4)$), $C_8^2$ ($C_4.(C_4\times D_4)$), $C_8^2$ ($(C_2\times C_4).D_8$), $C_8^2$ ($(C_2\times C_4):\SD_{16}$), $C_8^2$ ($(C_2\times C_4):D_8$), $C_8^2$ ($(C_2\times C_4):Q_{16}$), $C_8^2$ ($(C_2\times C_4):\SD_{16}$), $C_8^2$ ($C_2^4.D_4$), $C_8^2$ ($C_2^3.D_8$), $C_8^2$ ($C_2^4.D_4$), $C_8^2$ ($C_2^3.Q_{16}$), $C_8^2$ ($C_4.(C_4\times D_4)$), $C_8^2$ ($C_4.(C_4\times D_4)$), $C_8^2$ ($C_4.(C_4\times D_4)$), $C_8^2$ ($(C_2\times C_4).D_8$), $C_8^2$ ($C_2^4.D_4$), $C_8^2$ ($C_2^3.D_8$), $C_8^2$ ($C_4^2.Q_8$), $C_8^2$ ($C_4^2.Q_8$), $C_8^2$ ($C_2^3.Q_{16}$), $C_8^2$ ($C_2^3.D_8$), $C_8^2$ ($C_4^2.D_4$), $C_8^2$ ($C_4^2.D_4$), $C_8^2$ ($C_4^2.D_4$), $C_8^2$ ($C_4^2.D_4$), $C_8^2$ ($C_2^4.D_4$), $C_8^2$ ($C_2^3.D_8$), $C_2^2\times C_4^2$ ($\OD_{16}.D_4$), $C_2^2\times C_4^2$ ($(C_2\times C_4):\SD_{16}$), $C_2^2\times C_4^2$ ($(C_2\times C_4):D_8$), $C_2^2\times C_4^2$ ($(C_2\times C_4):Q_{16}$), $C_2^2\times C_4^2$ ($(C_2\times C_4):\SD_{16}$), $C_2^2\times C_4^2$ ($C_4.(C_4\times D_4)$), $C_2^2\times C_4^2$ ($C_4:C_4\times C_8$), $C_2^2\times C_4^2$ ($C_2^3.C_4^2$), $C_2^2\times C_4^2$ ($C_2^3.C_4^2$), $C_2^2\times C_4^2$ ($C_2^3:C_4^2$), $C_2^2\times C_4^2$ ($C_2^4.C_2^3$), $C_2^2\times C_4^2$ ($C_2^3.C_4^2$)

Order 32: $C_2\times C_4^2$ ($(C_4\times C_8).D_4$) x 8, $C_4\times C_8$ ($C_2^2.(C_4\times D_8)$) x 6, $C_2\times C_4^2$ ($(C_4\times C_8).D_4$) x 6, $C_2\times C_4^2$ ($(C_4\times C_8).D_4$) x 6, $C_2\times C_4^2$ ($(C_4\times C_8):D_4$) x 6, $C_2\times C_4^2$ ($C_4.(C_8\times D_4)$) x 6, $C_2^3\times C_4$ ($\OD_{16}:(C_2\times C_8)$) x 5, $C_2^3\times C_4$ ($(C_4\times C_8).D_4$) x 4, $C_2^3\times C_4$ ($\OD_{16}:(C_2\times C_8)$) x 4, $C_2^2\times C_8$ ($\OD_{32}.D_4$) x 4, $C_2^2\times C_8$ ($(C_2\times C_{16}).D_4$) x 4, $C_2^2\times C_8$ ($C_{16}.D_8$) x 4, $C_2^2\times C_8$ ($C_2^2.(C_8\times D_4)$) x 4, $C_2^2\times C_8$ ($C_4^3.C_2^2$) x 4, $C_2^2\times C_8$ ($C_4^2.D_8$) x 4, $C_2^2\times C_8$ ($C_4^3.C_2^2$) x 4, $C_2^2\times C_8$ ($(C_4\times C_8):D_4$) x 4, $C_2^2\times C_8$ ($C_4.(C_8\times D_4)$) x 4, $C_2^2\times C_8$ ($C_4^2.D_8$) x 4, $C_2^2\times C_8$ ($C_4^2.Q_{16}$) x 4, $C_2^2\times C_8$ ($C_4^2.Q_{16}$) x 4, $C_2^2\times C_8$ ($C_4^2.D_8$) x 4, $C_4\times C_8$ ($(C_2\times C_8).C_4^2$) x 4, $C_4\times C_8$ ($C_4^3.C_2^2$) x 4, $C_4\times C_8$ ($C_4^2.D_8$) x 4, $C_4\times C_8$ ($C_4^3.C_2^2$) x 4, $C_4\times C_8$ ($(C_4\times C_8):D_4$) x 4, $C_4\times C_8$ ($C_4.(C_8\times D_4)$) x 4, $C_4\times C_8$ ($C_4^2.D_8$) x 4, $C_4\times C_8$ ($C_4^2.Q_{16}$) x 4, $C_4\times C_8$ ($C_4^2.Q_{16}$) x 4, $C_4\times C_8$ ($C_4^2.D_8$) x 4, $C_2\times C_4^2$ ($C_2^2.(C_8\times D_4)$) x 4, $C_2\times C_4^2$ ($(C_4\times C_8).D_4$) x 4, $C_2\times C_4^2$ ($\OD_{16}:(C_2\times C_8)$) x 4, $C_2^2\times C_8$ ($C_4.(C_4\times Q_{16})$) x 3, $C_2^2\times C_8$ ($C_4.(C_4\times Q_{16})$) x 3, $C_2^2\times C_8$ ($C_4.(C_4\times D_8)$) x 3, $C_2^2\times C_8$ ($C_4.(C_4\times D_8)$) x 3, $C_4\times C_8$ ($C_2^2.(C_4\times Q_{16})$) x 3, $C_4\times C_8$ ($C_2^2.(C_4\times D_8)$) x 3, $C_4\times C_8$ ($(C_2\times C_8):C_4^2$) x 3, $C_4\times C_8$ ($(C_2\times C_8):C_4^2$) x 3, $C_4\times C_8$ ($C_4.C_4^3$) x 3, $C_4\times C_8$ ($C_4.(C_4\times D_8)$) x 3, $C_4\times C_8$ ($C_4.(C_4\times D_8)$) x 3, $C_4\times C_8$ ($C_4.(C_4\times Q_{16})$) x 3, $C_4\times C_8$ ($C_4.(C_4\times D_8)$) x 3, $C_2\times C_4^2$ ($C_4^2:\SD_{16}$) x 3, $C_2\times C_4^2$ ($C_4^2:D_8$) x 3, $C_2\times C_4^2$ ($C_4^2:Q_{16}$) x 3, $C_2\times C_4^2$ ($C_4^2:\SD_{16}$) x 3, $C_2\times C_4^2$ ($(C_2\times C_8):\SD_{16}$) x 3, $C_2\times C_4^2$ ($(C_2\times C_8):D_8$) x 3, $C_2\times C_4^2$ ($(C_2\times C_8):Q_{16}$) x 3, $C_2\times C_4^2$ ($(C_2\times C_8):\SD_{16}$) x 3, $C_2^3\times C_4$ ($(C_4\times C_8).D_4$) x 2, $C_2^3\times C_4$ ($(C_4\times C_8).D_4$) x 2, $C_2^3\times C_4$ ($(C_4\times C_8):D_4$) x 2, $C_2^3\times C_4$ ($C_4.(C_8\times D_4)$) x 2, $C_2^2\times C_8$ ($C_4^2.C_4^2$) x 2, $C_2^2\times C_8$ ($C_4^2.C_4^2$) x 2, $C_2^2\times C_8$ ($C_4^2.C_4^2$) x 2, $C_2^2\times C_8$ ($C_4^2.C_4^2$) x 2, $C_2^2\times C_8$ ($C_{16}.D_8$) x 2, $C_2^2\times C_8$ ($C_{16}.D_8$) x 2, $C_2^2\times C_8$ ($C_2^4.C_4^2$) x 2, $C_2^2\times C_8$ ($\OD_{16}.C_4^2$) x 2, $C_2^2\times C_8$ ($C_2^2.(C_8\times D_4)$) x 2, $C_2^2\times C_8$ ($C_2^2.(C_8\times D_4)$) x 2, $C_2^2\times C_8$ ($\OD_{16}.C_4^2$) x 2, $C_2^2\times C_8$ ($C_2^2.(C_8\times D_4)$) x 2, $C_2^2\times C_8$ ($(C_4\times C_8).D_4$) x 2, $C_2^2\times C_8$ ($C_4^2.D_8$) x 2, $C_2^2\times C_8$ ($C_4^2.Q_{16}$) x 2, $C_2^2\times C_8$ ($C_4.(C_4\times D_8)$) x 2, $C_2^2\times C_8$ ($(C_4\times C_8).Q_8$) x 2, $C_2^2\times C_8$ ($C_4.(C_8\times D_4)$) x 2, $C_2^2\times C_8$ ($C_4.(C_8\times D_4)$) x 2, $C_2^2\times C_8$ ($C_4.(C_8\times D_4)$) x 2, $C_2^2\times C_8$ ($C_2.(C_8\times D_8)$) x 2, $C_2^2\times C_8$ ($C_2.(C_8\times Q_{16})$) x 2, $C_2^2\times C_8$ ($C_4.(C_8\times Q_8)$) x 2, $C_2^2\times C_8$ ($C_4.(C_8\times Q_8)$) x 2, $C_2^2\times C_8$ ($C_2.(C_8\times D_8)$) x 2, $C_2^2\times C_8$ ($C_4.(C_8\times D_4)$) x 2, $C_2^2\times C_8$ ($C_4.(C_8\times D_4)$) x 2, $C_2^2\times C_8$ ($C_4.(C_8\times D_4)$) x 2, $C_2^2\times C_8$ ($C_2.(C_8\times D_8)$) x 2, $C_2^2\times C_8$ ($Q_8:(C_4\times C_8)$) x 2, $C_2^2\times C_8$ ($D_4:(C_4\times C_8)$) x 2, $C_2^2\times C_8$ ($C_8\times Q_8:C_4$) x 2, $C_2^2\times C_8$ ($C_8\times D_4:C_4$) x 2, $C_4\times C_8$ ($C_4^2.C_4^2$) x 2, $C_4\times C_8$ ($C_4^2.C_4^2$) x 2, $C_4\times C_8$ ($C_4^2.C_4^2$) x 2, $C_4\times C_8$ ($C_4^2.C_4^2$) x 2, $C_4\times C_8$ ($(C_2\times C_4^3):C_2$) x 2, $C_4\times C_8$ ($(C_2\times C_8).C_4^2$) x 2, $C_4\times C_8$ ($(C_2^2\times C_8).D_4$) x 2, $C_4\times C_8$ ($C_2^2.(C_4\times Q_{16})$) x 2, $C_4\times C_8$ ($C_2^2.(C_4\times D_8)$) x 2, $C_4\times C_8$ ($(C_2\times C_4^3).C_2$) x 2, $C_4\times C_8$ ($(C_2\times C_8).C_4^2$) x 2, $C_4\times C_8$ ($(C_2\times C_8).C_4^2$) x 2, $C_4\times C_8$ ($C_4^3:C_4$) x 2, $C_4\times C_8$ ($(C_2^2\times C_8).D_4$) x 2, $C_4\times C_8$ ($C_2^2.(C_4\times Q_{16})$) x 2, $C_4\times C_8$ ($C_2^2.(C_4\times D_8)$) x 2, $C_4\times C_8$ ($C_4^3:C_4$) x 2, $C_4\times C_8$ ($(C_4\times C_8).D_4$) x 2, $C_4\times C_8$ ($C_4^2.D_8$) x 2, $C_4\times C_8$ ($C_4^2.Q_{16}$) x 2, $C_4\times C_8$ ($C_4.(C_4\times D_8)$) x 2, $C_4\times C_8$ ($(C_4\times C_8).Q_8$) x 2, $C_4\times C_8$ ($C_4.(C_8\times D_4)$) x 2, $C_4\times C_8$ ($C_4.(C_8\times D_4)$) x 2, $C_4\times C_8$ ($C_4.(C_8\times D_4)$) x 2, $C_4\times C_8$ ($C_2.(C_8\times D_8)$) x 2, $C_4\times C_8$ ($C_2.(C_8\times Q_{16})$) x 2, $C_4\times C_8$ ($C_4.(C_8\times Q_8)$) x 2, $C_4\times C_8$ ($C_4.(C_8\times Q_8)$) x 2, $C_4\times C_8$ ($C_2.(C_8\times D_8)$) x 2, $C_4\times C_8$ ($C_4.(C_8\times D_4)$) x 2, $C_4\times C_8$ ($C_4.(C_8\times D_4)$) x 2, $C_4\times C_8$ ($C_4.(C_8\times D_4)$) x 2, $C_4\times C_8$ ($C_2.(C_8\times D_8)$) x 2, $C_4\times C_8$ ($Q_8:(C_4\times C_8)$) x 2, $C_4\times C_8$ ($D_4:(C_4\times C_8)$) x 2, $C_4\times C_8$ ($C_8\times Q_8:C_4$) x 2, $C_4\times C_8$ ($C_8\times D_4:C_4$) x 2, $C_2\times C_4^2$ ($(C_2\times D_4).C_4^2$) x 2, $C_2\times C_4^2$ ($(C_2\times C_4^3):C_2$) x 2, $C_2\times C_4^2$ ($(C_2\times C_8).C_4^2$) x 2, $C_2\times C_4^2$ ($C_2^2.(C_4\times D_8)$) x 2, $C_2\times C_4^2$ ($(C_2\times C_4^3).C_2$) x 2, $C_2\times C_4^2$ ($C_2^2.(C_8\times D_4)$) x 2, $C_2\times C_4^2$ ($(C_2\times D_4).C_4^2$) x 2, $C_2\times C_4^2$ ($C_2^4.D_8$) x 2, $C_2\times C_4^2$ ($C_2^5.D_4$) x 2, $C_2\times C_4^2$ ($C_4^2.(C_2\times D_4)$) x 2, $C_2\times C_4^2$ ($C_4.(C_4\times D_8)$) x 2, $C_2\times C_4^2$ ($(C_2\times C_8):Q_{16}$) x 2, $C_2\times C_4^2$ ($(C_2\times C_8):\SD_{16}$) x 2, $C_2\times C_4^2$ ($\OD_{16}:(C_2\times C_8)$) x 2, $C_2^5$ ($\OD_{16}:(C_2\times C_8)$), $C_2^3\times C_4$ ($(C_2\times D_4):C_4^2$), $C_2^3\times C_4$ ($(C_2\times D_4).C_4^2$), $C_2^3\times C_4$ ($C_2^4.C_4^2$), $C_2^3\times C_4$ ($\OD_{16}.C_4^2$), $C_2^3\times C_4$ ($\OD_{16}:C_4^2$), $C_2^3\times C_4$ ($C_2^2.(C_8\times D_4)$), $C_2^3\times C_4$ ($(C_2^2\times C_8).D_4$), $C_2^3\times C_4$ ($(C_2\times C_4^2).D_4$), $C_2^3\times C_4$ ($C_2^4.C_4^2$), $C_2^3\times C_4$ ($C_4^2:\SD_{16}$), $C_2^3\times C_4$ ($C_4^2:D_8$), $C_2^3\times C_4$ ($C_4^2:Q_{16}$), $C_2^3\times C_4$ ($C_4^2:\SD_{16}$), $C_2^3\times C_4$ ($(C_2\times C_8):\SD_{16}$), $C_2^3\times C_4$ ($(C_2\times C_8):D_8$), $C_2^3\times C_4$ ($C_4.(C_4\times Q_{16})$), $C_2^3\times C_4$ ($(C_2\times D_4).Q_{16}$), $C_2^3\times C_4$ ($(C_2\times C_8):\SD_{16}$), $C_2^3\times C_4$ ($(C_2\times C_8):D_8$), $C_2^3\times C_4$ ($(C_2\times C_8):Q_{16}$), $C_2^3\times C_4$ ($(C_2\times C_8):\SD_{16}$), $C_2^2\times C_8$ ($(C_2\times D_4).C_4^2$), $C_2^2\times C_8$ ($(C_2\times Q_8).C_4^2$), $C_2^2\times C_8$ ($(C_2\times C_8).C_4^2$), $C_2^2\times C_8$ ($(C_2\times C_8).C_4^2$), $C_2^2\times C_8$ ($C_2^2.C_4^3$), $C_2^2\times C_8$ ($C_2^2.C_4^3$), $C_2^2\times C_8$ ($C_2^2.C_4^3$), $C_2^2\times C_8$ ($C_2^2.C_4^3$), $C_2^2\times C_8$ ($C_4.(C_4\times D_8)$), $C_2^2\times C_8$ ($C_4.(C_4\times Q_{16})$), $C_2^2\times C_8$ ($C_4.(C_4\times D_8)$), $C_2^2\times C_8$ ($(C_2\times C_8).D_8$), $C_2^2\times C_8$ ($C_4.(C_4\times Q_{16})$), $C_2^2\times C_8$ ($(C_2\times C_8).Q_{16}$), $C_2^2\times C_8$ ($C_4.(C_4\times D_8)$), $C_2^2\times C_8$ ($C_4.(C_4\times D_8)$), $C_2^2\times C_8$ ($(C_4\times C_8).Q_8$), $C_2^2\times C_8$ ($(C_2\times C_8).D_8$), $C_2^2\times C_8$ ($C_4.(C_4\times D_8)$), $C_2^2\times C_8$ ($C_4.(C_4\times D_8)$), $C_2^2\times C_8$ ($C_4.(C_4\times Q_{16})$), $C_2^2\times C_8$ ($C_4.(C_4\times D_8)$), $C_2^2\times C_8$ ($(C_2\times C_8):\SD_{16}$), $C_2^2\times C_8$ ($(C_2\times C_8):D_8$), $C_2^2\times C_8$ ($C_4^2.(C_2\times D_4)$), $C_2^2\times C_8$ ($C_4.(C_4\times D_8)$), $C_2^2\times C_8$ ($(C_2\times C_8):Q_{16}$), $C_2^2\times C_8$ ($(C_2\times C_8):\SD_{16}$), $C_2^2\times C_8$ ($C_4.(C_4\times Q_{16})$), $C_2^2\times C_8$ ($(C_2\times D_4).Q_{16}$), $C_2^2\times C_8$ ($(C_8\times Q_8):C_4$), $C_2^2\times C_8$ ($(C_8\times D_4):C_4$), $C_2^2\times C_8$ ($(C_8\times Q_8):C_4$), $C_2^2\times C_8$ ($(C_8\times D_4):C_4$), $C_2^2\times C_8$ ($(C_8\times Q_8):C_4$), $C_2^2\times C_8$ ($(C_8\times D_4):C_4$), $C_2^2\times C_8$ ($(C_8\times Q_8):C_4$), $C_2^2\times C_8$ ($(C_8\times D_4):C_4$), $C_2^2\times C_8$ ($C_4.(C_4\times D_8)$), $C_2^2\times C_8$ ($(C_2\times C_8).C_4^2$), $C_2^2\times C_8$ ($(C_2\times C_8).C_4^2$), $C_2^2\times C_8$ ($(C_2\times C_8).C_4^2$), $C_2^2\times C_8$ ($C_8:(C_4\times C_8)$), $C_2^2\times C_8$ ($C_8:(C_4\times C_8)$), $C_2^2\times C_8$ ($C_8^2:C_4$), $C_2^2\times C_8$ ($C_8^2:C_4$), $C_2^2\times C_8$ ($(C_4\times C_8).D_4$), $C_2^2\times C_8$ ($(C_4\times C_8).D_4$), $C_2^2\times C_8$ ($C_4.(C_4\times Q_{16})$), $C_2^2\times C_8$ ($C_4.(C_4\times D_8)$), $C_2^2\times C_8$ ($(C_8\times Q_8):C_4$), $C_2^2\times C_8$ ($(C_8\times D_4):C_4$), $C_2^2\times C_8$ ($(C_8\times Q_8):C_4$), $C_2^2\times C_8$ ($(C_8\times D_4):C_4$), $C_4\times C_8$ ($(C_2\times Q_8):C_4^2$), $C_4\times C_8$ ($(C_2\times D_4):C_4^2$), $C_4\times C_8$ ($C_4^2.C_4^2$), $C_4\times C_8$ ($C_4^2.C_4^2$), $C_4\times C_8$ ($C_4^2.C_4^2$), $C_4\times C_8$ ($C_4^2.C_4^2$), $C_4\times C_8$ ($C_2^2.(C_4\times Q_{16})$), $C_4\times C_8$ ($C_2^2.(C_4\times D_8)$), $C_4\times C_8$ ($C_2^5.D_4$), $C_4\times C_8$ ($C_2^4.D_8$), $C_4\times C_8$ ($C_4.C_4^3$), $C_4\times C_8$ ($C_4.C_4^3$), $C_4\times C_8$ ($C_4.C_4^3$), $C_4\times C_8$ ($C_4.(C_4\times D_8)$), $C_4\times C_8$ ($C_4.(C_4\times Q_{16})$), $C_4\times C_8$ ($(C_2\times C_8).D_8$), $C_4\times C_8$ ($(C_2\times C_8).D_8$), $C_4\times C_8$ ($C_4.(C_4\times D_8)$), $C_4\times C_8$ ($(C_2\times C_8).Q_{16}$), $C_4\times C_8$ ($C_4.(C_4\times D_8)$), $C_4\times C_8$ ($C_4.(C_4\times D_8)$), $C_4\times C_8$ ($(C_4\times C_8).Q_8$), $C_4\times C_8$ ($(C_2\times C_8).D_8$), $C_4\times C_8$ ($C_4.(C_4\times Q_{16})$), $C_4\times C_8$ ($C_4.(C_4\times Q_{16})$), $C_4\times C_8$ ($C_4.(C_4\times D_8)$), $C_4\times C_8$ ($C_4.(C_4\times D_8)$), $C_4\times C_8$ ($(C_2\times C_8):\SD_{16}$), $C_4\times C_8$ ($(C_2\times C_8):D_8$), $C_4\times C_8$ ($C_4^2.(C_2\times D_4)$), $C_4\times C_8$ ($C_4.(C_4\times D_8)$), $C_4\times C_8$ ($(C_2\times C_8):Q_{16}$), $C_4\times C_8$ ($(C_2\times C_8):\SD_{16}$), $C_4\times C_8$ ($C_4.(C_4\times Q_{16})$), $C_4\times C_8$ ($(C_2\times D_4).Q_{16}$), $C_4\times C_8$ ($(C_8\times Q_8):C_4$), $C_4\times C_8$ ($(C_8\times D_4):C_4$), $C_4\times C_8$ ($(C_8\times Q_8):C_4$), $C_4\times C_8$ ($(C_8\times D_4):C_4$), $C_4\times C_8$ ($(C_8\times Q_8):C_4$), $C_4\times C_8$ ($(C_8\times D_4):C_4$), $C_4\times C_8$ ($(C_8\times Q_8):C_4$), $C_4\times C_8$ ($(C_8\times D_4):C_4$), $C_4\times C_8$ ($C_4.(C_4\times D_8)$), $C_4\times C_8$ ($(C_2\times C_8).C_4^2$), $C_4\times C_8$ ($(C_2\times C_8).C_4^2$), $C_4\times C_8$ ($(C_2\times C_8).C_4^2$), $C_4\times C_8$ ($C_8:(C_4\times C_8)$), $C_4\times C_8$ ($C_8:(C_4\times C_8)$), $C_4\times C_8$ ($C_8^2:C_4$), $C_4\times C_8$ ($C_8^2:C_4$), $C_4\times C_8$ ($(C_4\times C_8).D_4$), $C_4\times C_8$ ($(C_4\times C_8).D_4$), $C_4\times C_8$ ($C_4.(C_4\times Q_{16})$), $C_4\times C_8$ ($C_4.(C_4\times D_8)$), $C_4\times C_8$ ($(C_8\times Q_8):C_4$), $C_4\times C_8$ ($(C_8\times D_4):C_4$), $C_4\times C_8$ ($(C_8\times Q_8):C_4$), $C_4\times C_8$ ($(C_8\times D_4):C_4$), $C_2\times C_4^2$ ($C_2^2.C_4^3$), $C_2\times C_4^2$ ($(C_2\times D_4):C_4^2$), $C_2\times C_4^2$ ($(C_2\times Q_8).C_4^2$), $C_2\times C_4^2$ ($(C_2\times Q_8):C_4^2$), $C_2\times C_4^2$ ($(C_2\times D_4):C_4^2$), $C_2\times C_4^2$ ($C_2^2.(C_4\times Q_{16})$), $C_2\times C_4^2$ ($C_2^2.(C_4\times D_8)$), $C_2\times C_4^2$ ($C_2^4.C_4^2$), $C_2\times C_4^2$ ($(C_2\times C_8):C_4^2$), $C_2\times C_4^2$ ($(C_2\times C_8):C_4^2$), $C_2\times C_4^2$ ($\OD_{16}.C_4^2$), $C_2\times C_4^2$ ($\OD_{16}:C_4^2$), $C_2\times C_4^2$ ($C_2^2.(C_8\times D_4)$), $C_2\times C_4^2$ ($C_2^2.(C_4\times Q_{16})$), $C_2\times C_4^2$ ($C_2^2.(C_4\times D_8)$), $C_2\times C_4^2$ ($(C_2^2\times C_8).D_4$), $C_2\times C_4^2$ ($(C_2\times C_4^2).D_4$), $C_2\times C_4^2$ ($C_2^4.C_4^2$), $C_2\times C_4^2$ ($C_2^2.C_4^3$), $C_2\times C_4^2$ ($C_2^2.C_4^3$), $C_2\times C_4^2$ ($(C_2\times C_8):\SD_{16}$), $C_2\times C_4^2$ ($(C_2\times C_8):D_8$), $C_2\times C_4^2$ ($C_4.(C_4\times Q_{16})$), $C_2\times C_4^2$ ($(C_2\times D_4).Q_{16}$)

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

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

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

Order 2: $C_2$ ($C_8^2.(C_4\times D_8)$) x 4, $C_2$ ($(C_2^2\times C_4^2\times C_8).C_2^3$) x 2, $C_2$ ($C_4^3.(C_4\times C_4:C_4)$)

Order 1: $C_1$ ($(C_4^2\times C_8).C_4^3$)

Normal subgroups up to automorphism (quotient in parentheses)

not computed

Series

Derived series	not computed
Chief series	not computed
Lower central series	not computed
Upper central series	not computed

Supergroups

This group is a maximal subgroup of 3 larger groups in the database.

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

Character theory

Complex character table

The $704 \times 704$ character table is not available for this group.

Rational character table

See the $256 \times 256$ rational character table (warning: may be slow to load).