Abstract group 7114752.a: $C_{193}:C_{192}^2$

• Label: 7114752.a
• Order: \( 2^{12} \cdot 3^{2} \cdot 193 \)
• Exponent: \( 2^{6} \cdot 3 \cdot 193 \)
• Nilpotent: no
• Solvable: yes
• $\card{G^{\mathrm{ab}}}$: \( 2^{12} \cdot 3^{2} \)
• $\card{Z(G)}$: \( 2^{6} \cdot 3 \)
• $\card{\Aut(G)}$: \( 2^{18} \cdot 3^{2} \cdot 193 \)
• $\card{\mathrm{Out}(G)}$: \( 2^{12} \cdot 3 \)
• Perm deg.: not computed
• Trans deg.: not computed
• Rank: $2$

Group information

Description:	$C_{193}:C_{192}^2$
Order:	\(7114752\)\(\medspace = 2^{12} \cdot 3^{2} \cdot 193 \)
Exponent:	\(37056\)\(\medspace = 2^{6} \cdot 3 \cdot 193 \)
Automorphism group:	Group of order \(455344128\)\(\medspace = 2^{18} \cdot 3^{2} \cdot 193 \)
Composition factors:	$C_2$ x 12, $C_3$ x 2, $C_{193}$
Derived length:	$2$

This group is nonabelian, metacyclic (hence solvable, supersolvable, monomial, and metabelian), and an A-group.

Group statistics

Order	1	2	3	4	6	8	12	16	24	32	48	64	96	192	193	386	579	772	1158	1544	2316	3088	4632	6176	9264	12352	18528	37056
Elements	1	387	1160	1932	4248	8496	17760	35520	72576	145152	293376	586752	1179648	4730880	192	192	384	384	384	768	768	1536	1536	3072	3072	6144	6144	12288	7114752
Conjugacy classes	1	3	8	12	24	48	96	192	384	768	1536	3072	6144	24576	1	1	2	2	2	4	4	8	8	16	16	32	32	64	37056
Divisions	1	3	4	6	12	12	24	24	48	48	96	96	192	384	1	1	1	1	1	1	1	1	1	1	1	1	1	1	964

Minimal presentations

Permutation degree:	not computed
Transitive degree:	not computed
Rank:	$2$
Inequivalent generating pairs:	not computed

Minimal degrees of linear representations for this group have not been computed

Constructions

Presentation:	$\langle a, b \mid a^{192}=b^{37056}=1, b^{a}=b^{35329} \rangle$
Matrix group:	$\left\langle \left(\begin{array}{rr} 1 & 1 \\ 0 & 1 \end{array}\right), \left(\begin{array}{rr} 1 & 0 \\ 0 & 5 \end{array}\right), \left(\begin{array}{rr} 5 & 0 \\ 0 & 116 \end{array}\right) \right\rangle \subseteq \GL_{2}(\F_{193})$
Direct product:	$C_{64}$ $\, \times\, $ $C_3$ $\, \times\, $ $F_{193}$
Semidirect product:	$C_{193}$ $\,\rtimes\,$ $C_{192}^2$	$(C_{12352}:C_{64})$ $\,\rtimes\,$ $C_3^2$			more information
Trans. wreath product:	not computed
Possibly split product:	$F_{193}$ . $C_{192}$	$C_{192}$ . $F_{193}$	$D_{386}$ . $C_{96}^2$	$C_{37056}$ . $C_{192}$	all 321

Elements of the group are displayed as words in the presentation generators from the presentation above.

Homology

Abelianization:	$C_{192}^{2} \simeq C_{64}^{2} \times C_{3}^{2}$
Schur multiplier:	not computed
Commutator length:	not computed

Subgroups

There are 2216 normal subgroups (143 characteristic).

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

Special subgroups

Center:	$Z \simeq$ $C_{192}$	$G/Z \simeq$ $F_{193}$
Commutator:	$G' \simeq$ $C_{193}$	$G/G' \simeq$ $C_{192}^2$
Frattini:	$\Phi \simeq$ $C_{32}$	$G/\Phi \simeq$ $C_6\times F_{193}$
Fitting:	$\operatorname{Fit} \simeq$ $C_{37056}$	$G/\operatorname{Fit} \simeq$ $C_{192}$
Radical:	$R \simeq$ $C_{193}:C_{192}^2$	$G/R \simeq$ $C_1$
Socle:	$\operatorname{soc} \simeq$ $C_{1158}$	$G/\operatorname{soc} \simeq$ $C_{32}\times C_{192}$
2-Sylow subgroup:	$P_{ 2 } \simeq$ $C_{64}^2$
3-Sylow subgroup:	$P_{ 3 } \simeq$ $C_3^2$
193-Sylow subgroup:	$P_{ 193 } \simeq$ $C_{193}$

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 2 (order at least 3557376) are shown, as well as all normal subgroups of any index.

Order 7114752: $C_{193}:C_{192}^2$

Order 3557376: $C_{96}\times D_{193}.C_{96}$ x 2, $C_{192}\times C_{193}:C_{96}$

Order 2371584: $C_{64}\times D_{193}.C_{96}$ x 3, $C_{192}\times C_{193}:C_{64}$

Order 1778688: $C_{9264}:C_{192}$ x 4, $C_3\times C_{386}.C_2.C_8^2.C_6.C_2$, $C_{37056}.C_{48}$, $C_{18528}:C_{96}$

Order 1185792: $C_{32}\times F_{193}$ x 6, $C_{12352}:C_{96}$ x 3, $C_{18528}:C_{64}$ x 2, $C_{12352}.C_{96}$

Order 889344: $C_{24}\times F_{193}$ x 8, $C_{9264}:C_{96}$ x 2, $C_{9264}.C_{96}$ x 2, $C_{18528}.C_{48}$, $C_{37056}.C_{24}$, $C_{18528}:C_{48}$

Order 790528: $C_{12352}:C_{64}$

Order 592896: $C_{16}\times F_{193}$ x 12, $C_{3088}:C_{192}$ x 4, $C_{12352}:C_{48}$ x 3, $C_{6176}:C_{96}$ x 3, $C_{6176}.C_{96}$ x 3, $C_{18528}:C_{32}$, $C_{12352}.C_{48}$, $C_{18528}.C_{32}$

Order 444672: $C_{12}\times F_{193}$ x 16, $C_{4632}.C_{96}$ x 4, $C_{4632}:C_{96}$ x 4, $C_{9264}.C_{48}$ x 2, $C_{18528}:C_{24}$, $C_{9264}:C_{48}$, $C_{18528}.C_{24}$, $C_{37056}.C_{12}$, $C_{9264}.C_{48}$

Order 395264: $C_{6176}:C_{64}$ x 2, $C_{12352}:C_{32}$

Order 296448: $C_8\times F_{193}$ x 24, $C_{1544}:C_{192}$ x 8, $C_{3088}.C_{96}$ x 6, $C_{3088}:C_{96}$ x 6, $C_{6176}.C_{48}$ x 3, $C_{12352}:C_{24}$ x 3, $C_{6176}:C_{48}$ x 3, $C_{3088}.C_{96}$ x 2, $C_{3088}:C_{96}$ x 2, $C_{18528}.C_{16}$, $C_{18528}:C_{16}$, $C_{12352}.C_{24}$

Order 222336: $C_6\times F_{193}$ x 32, $C_{2316}:C_{96}$ x 8, $C_{2316}.C_{96}$ x 8, $C_{4632}.C_{48}$ x 4, $C_{9264}.C_{24}$ x 2, $C_{4632}.C_{48}$ x 2, $C_{4632}:C_{48}$ x 2, $C_{18528}.C_{12}$, $C_{37056}.C_6$, $C_{9264}:C_{24}$, $C_{18528}:C_{12}$, $C_{9264}.C_{24}$

Order 197632: $C_{3088}:C_{64}$ x 4, $C_{12352}:C_{16}$, $C_{6176}:C_{32}$, $C_{6176}.C_{32}$

Order 148224: $C_4\times F_{193}$ x 48, $C_{2316}:C_{64}$ x 16, $C_{1544}:C_{96}$ x 12, $C_{1544}.C_{96}$ x 12, $C_{3088}.C_{48}$ x 6, $C_{1544}.C_{96}$ x 4, $C_{1544}:C_{96}$ x 4, $C_{12352}:C_{12}$ x 3, $C_{6176}:C_{24}$ x 3, $C_{6176}.C_{24}$ x 3, $C_{3088}.C_{48}$ x 3, $C_{3088}:C_{48}$ x 3, $C_{3088}.C_{48}$ x 2, $C_{3088}:C_{48}$, $C_{3088}.C_{48}$, $C_{18528}.C_8$, $C_{18528}:C_8$, $C_{12352}.C_{12}$

Order 111168: $C_3\times F_{193}$ x 64, $C_{579}:C_{192}$ x 16, $C_{1158}:C_{96}$ x 16, $C_{579}:C_{192}$ x 8, $C_{579}:C_{192}$ x 4, $C_{2316}.C_{48}$ x 4, $C_{2316}:C_{48}$ x 4, $C_{4632}.C_{24}$ x 2, $C_{579}:C_{192}$ x 2, $C_{1158}.C_{96}$, $C_{9264}.C_{12}$, $C_{9264}:C_{12}$, $C_{4632}.C_{24}$, $C_{18528}.C_6$, $C_{4632}:C_{24}$, $C_{12352}:C_3^2$

Order 98816: $C_{1544}:C_{64}$ x 8, $C_{3088}.C_{32}$ x 2, $C_{3088}:C_{32}$ x 2, $C_{6176}:C_{16}$, $C_{6176}.C_{16}$, $C_{12352}:C_8$

Order 74112: $C_2\times F_{193}$ x 96, $C_{1158}:C_{64}$ x 32, $D_{193}:C_{192}$ x 24, $C_{772}:C_{96}$ x 24, $D_{193}:C_{192}$ x 12, $C_3\times C_{193}:(C_2\times C_{64})$ x 8, $C_{2316}:C_{32}$ x 8, $D_{193}:C_{192}$ x 6, $C_{1544}.C_{48}$ x 6, $C_{1544}:C_{48}$ x 6, $D_{193}:C_{192}$ x 4, $D_{193}:C_{192}$ x 3, $C_{12352}:C_6$ x 3, $C_{3088}:C_{24}$ x 3, $C_{3088}.C_{24}$ x 3, $C_{6176}:C_{12}$ x 3, $C_3\times C_{193}:(C_4\times C_{32})$ x 2, $C_{24}\times C_{193}:C_{16}$ x 2, $D_{193}:C_{192}$ x 2, $C_3\times C_{193}:(C_4\times C_{32})$, $C_{18528}.C_4$, $C_{12352}.C_6$, $C_{3088}:C_{24}$, $C_{18528}.C_4$

Order 55584: $C_{579}:C_{96}$ x 32, $C_{579}:C_{96}$ x 8, $C_{1158}:C_{48}$ x 8, $C_{579}:C_{96}$ x 4, $C_{2316}:C_{24}$ x 2, $C_{579}:C_{96}$ x 2, $C_{2316}.C_{24}$ x 2, $C_{24}\times C_{193}:C_{12}$, $C_{96}\times C_{193}:C_3$, $C_3\times C_{193}:C_{96}$, $C_{9264}.C_6$, $C_{4632}.C_{12}$

Order 49408: $C_{772}:C_{64}$ x 16, $C_{1544}.C_{32}$ x 4, $C_{1544}:C_{32}$ x 4, $C_{3088}.C_{16}$ x 2, $C_{3088}.C_{16}$, $C_{3088}:C_{16}$, $C_{6176}.C_8$, $C_{6176}:C_8$, $C_{12352}:C_4$

Order 37056: $F_{193}$ x 192, $C_{193}:C_{192}$ x 64, $C_{386}:C_{96}$ x 48, $C_{193}:C_{192}$ x 48, $C_{193}:C_{192}$ x 24, $C_{1158}:C_{32}$ x 16, $C_{193}:C_{192}$ x 16, $C_{193}:C_{192}$ x 12, $D_{193}:C_{96}$ x 12, $C_{772}:C_{48}$ x 12, $C_{193}:C_{192}$ x 8, $C_{772}.C_{48}$ x 6, $D_{193}:C_{96}$ x 6, $C_3\times C_{193}:C_{64}$ x 4, $C_{2316}:C_{16}$ x 4, $D_{193}:C_{96}$ x 4, $C_{193}:C_{192}$ x 3, $C_{12352}:C_3$ x 3, $C_{3088}:C_{12}$ x 3, $C_{1544}:C_{24}$ x 3, $C_{1544}.C_{24}$ x 3, $C_{6176}:C_6$ x 3, $D_{193}:C_{96}$ x 3, $C_3\times C_{193}:C_{64}$ x 2, $D_{193}:C_{96}$ x 2, $C_{24}\times C_{193}:C_8$, $C_3\times C_{193}:(C_4\times C_{16})$, $C_3\times C_{193}:(C_2\times C_{32})$, $C_{48}\times C_{193}:C_4$, $C_{96}\times D_{193}$, $C_{37056}$, $C_{193}:C_{192}$

Order 36864: $C_{192}^2$

Order 27792: $C_{579}:C_{48}$ x 16, $C_{579}:C_{48}$ x 4, $C_{1158}:C_{24}$ x 4, $C_3\times C_{193}:C_{48}$ x 2, $C_{12}\times C_{193}:C_{12}$, $C_{24}\times C_{193}:C_6$, $C_3\times C_{193}:C_{48}$, $C_{48}\times C_{193}:C_3$, $C_3\times C_{193}:(C_2\times C_{24})$

Order 24704: $C_{386}:C_{64}$ x 32, $D_{193}:C_{64}$ x 8, $C_{772}:C_{32}$ x 8, $D_{193}:C_{64}$ x 4, $C_{1544}.C_{16}$ x 2, $C_{1544}:C_{16}$ x 2, $D_{193}:C_{64}$ x 2, $C_{64}\times D_{193}$, $C_{3088}.C_8$, $C_{3088}:C_8$, $D_{193}:C_{64}$, $C_{6176}:C_4$

Order 18528: $C_{193}:C_{96}$ x 96, $C_{193}:C_{96}$ x 32, $C_{193}:C_{96}$ x 24, $C_{386}:C_{48}$ x 24, $C_{193}:C_{96}$ x 12, $C_3\times C_{193}:C_{32}$ x 8, $C_{1158}:C_{16}$ x 8, $C_{772}:C_{24}$ x 6, $C_{193}:C_{96}$ x 6, $D_{193}:C_{48}$ x 6, $C_{193}:C_{96}$ x 4, $C_{32}\times C_{193}:C_3$ x 3, $C_8\times C_{193}:C_{12}$ x 3, $C_{3088}:C_6$ x 3, $D_{193}:C_{48}$ x 3, $C_{193}:C_{96}$ x 3, $C_3\times C_{193}:(C_2\times C_{16})$ x 2, $C_{2316}:C_8$ x 2, $C_{193}:C_{96}$ x 2, $C_{1544}:C_{12}$, $C_{48}\times D_{193}$, $D_{193}:C_{48}$, $C_{18528}$, $C_{193}:C_{96}$

Order 13896: $C_{579}:C_{24}$ x 8, $C_3\times C_{193}:C_{24}$ x 2, $C_6\times C_{193}:C_{12}$ x 2, $C_{12}\times C_{193}:C_6$, $C_3\times C_{193}:C_{24}$, $C_{4632}:C_3$

Order 12352: $C_{193}:C_{64}$ x 64, $C_{386}:C_{32}$ x 16, $C_{193}:C_{64}$ x 16, $C_{193}:C_{64}$ x 8, $D_{193}:C_{32}$ x 4, $C_{772}:C_{16}$ x 4, $C_{193}:C_{64}$ x 4, $D_{193}:C_{32}$ x 2, $C_{193}:C_{64}$ x 2, $C_{32}\times D_{193}$, $C_{193}:C_{64}$, $C_{1544}.C_8$, $C_{1544}:C_8$, $D_{193}:C_{32}$, $C_{3088}:C_4$, $C_{12352}$

Order 9264: $C_{193}:C_{48}$ x 48, $C_3\times C_{193}:C_{16}$ x 16, $C_2\times C_{193}:C_{24}$ x 12, $C_{193}:C_{48}$ x 12, $C_{193}:C_{48}$ x 6, $C_3\times C_{193}:C_{16}$ x 4, $C_{1158}:C_8$ x 4, $C_{193}:(C_2\times C_{24})$ x 3, $C_8\times C_{193}:C_6$ x 3, $C_4\times C_{193}:C_{12}$ x 3, $C_{193}:C_{48}$ x 3, $C_{193}:C_{48}$ x 3, $C_{193}:C_{48}$ x 2, $C_{24}\times D_{193}$, $C_3\times C_{193}:C_{16}$, $C_{2316}:C_4$, $C_{9264}$, $D_{193}:C_{24}$

Order 6948: $C_{579}:C_{12}$ x 4, $C_{579}:C_{12}$, $C_{1158}:C_6$, $C_{2316}:C_3$

Order 6176: $C_{193}:C_{32}$ x 32, $C_{386}:C_{16}$ x 8, $C_{193}:C_{32}$ x 8, $C_{193}:C_{32}$ x 4, $D_{193}:C_{16}$ x 2, $C_{772}:C_8$ x 2, $C_{193}:C_{32}$ x 2, $C_{16}\times D_{193}$, $C_{193}:C_{32}$, $D_{193}:C_{16}$, $C_{1544}:C_4$, $C_{6176}$

Order 4632: $C_{193}:C_{24}$ x 24, $C_3\times C_{193}:C_8$ x 8, $C_{193}:C_{24}$ x 6, $C_{386}:C_{12}$ x 6, $C_{193}:C_{24}$ x 3, $C_4\times C_{193}:C_6$ x 3, $C_{1544}:C_3$ x 3, $C_3\times C_{193}:C_8$ x 2, $C_{1158}:C_4$ x 2, $C_3\times C_{193}:C_8$, $C_{12}\times D_{193}$, $C_{4632}$

Order 4096: $C_{64}^2$

Order 3474: $C_{579}:C_6$ x 2, $C_{1158}:C_3$

Order 3088: $C_{193}:C_{16}$ x 16, $C_{386}:C_8$ x 4, $C_{193}:C_{16}$ x 4, $C_{193}:C_{16}$ x 2, $D_{193}:C_8$, $C_{772}:C_4$, $C_8\times D_{193}$, $C_{193}:C_{16}$, $C_{3088}$

Order 2316: $C_{193}:C_{12}$ x 12, $C_{193}:C_{12}$ x 4, $C_{193}:C_{12}$ x 3, $C_{386}:C_6$ x 3, $C_{193}:C_{12}$ x 3, $C_3\times D_{386}$, $C_{193}:C_{12}$, $C_{2316}$

Order 1737: $C_{579}:C_3$

Order 1544: $C_{193}:C_8$ x 8, $C_{386}:C_4$ x 2, $C_{193}:C_8$ x 2, $C_4\times D_{193}$, $C_{193}:C_8$, $C_{1544}$

Order 1158: $C_{193}:C_6$ x 6, $C_{193}:C_6$ x 3, $C_3\times D_{193}$ x 2, $C_{1158}$

Order 772: $C_{193}:C_4$ x 4, $D_{386}$, $C_{772}$, $C_{193}:C_4$

Order 579: $C_{193}:C_3$ x 3, $C_{579}$

Order 386: $D_{193}$ x 2, $C_{386}$

Order 193: $C_{193}$

Order 192: $C_{192}$

Order 96: $C_{96}$

Order 64: $C_{64}$

Order 48: $C_{48}$

Order 32: $C_{32}$

Order 24: $C_{24}$

Order 16: $C_{16}$

Order 12: $C_{12}$

Order 9: $C_3^2$

Order 8: $C_8$

Order 6: $C_6$

Order 4: $C_4$

Order 3: $C_3$

Order 2: $C_2$

Order 1: $C_1$

Classes of subgroups up to automorphism

All subgroups of index up to 2 (order at least 3557376) are shown, as well as all normal subgroups of any index.

Order 7114752: $C_{193}:C_{192}^2$

Order 3557376: $C_{96}\times D_{193}.C_{96}$, $C_{192}\times C_{193}:C_{96}$

Order 2371584: $C_{192}\times C_{193}:C_{64}$, $C_{64}\times D_{193}.C_{96}$

Order 1778688: $C_3\times C_{386}.C_2.C_8^2.C_6.C_2$, $C_{9264}:C_{192}$, $C_{37056}.C_{48}$, $C_{18528}:C_{96}$

Order 1185792: $C_{18528}:C_{64}$, $C_{12352}.C_{96}$, $C_{12352}:C_{96}$, $C_{32}\times F_{193}$

Order 889344: $C_{18528}.C_{48}$, $C_{37056}.C_{24}$, $C_{9264}:C_{96}$, $C_{9264}.C_{96}$, $C_{18528}:C_{48}$, $C_{24}\times F_{193}$

Order 790528: $C_{12352}:C_{64}$

Order 592896: $C_{18528}:C_{32}$, $C_{12352}.C_{48}$, $C_{18528}.C_{32}$, $C_{12352}:C_{48}$, $C_{3088}:C_{192}$, $C_{6176}:C_{96}$, $C_{6176}.C_{96}$, $C_{16}\times F_{193}$

Order 444672: $C_{12}\times F_{193}$, $C_{18528}:C_{24}$, $C_{9264}:C_{48}$, $C_{9264}.C_{48}$, $C_{18528}.C_{24}$, $C_{4632}.C_{96}$, $C_{37056}.C_{12}$, $C_{9264}.C_{48}$, $C_{4632}:C_{96}$

Order 395264: $C_{12352}:C_{32}$, $C_{6176}:C_{64}$

Order 296448: $C_{18528}.C_{16}$, $C_{18528}:C_{16}$, $C_{3088}.C_{96}$, $C_{3088}.C_{96}$, $C_{6176}.C_{48}$, $C_{12352}:C_{24}$, $C_{3088}:C_{96}$, $C_{1544}:C_{192}$, $C_{12352}.C_{24}$, $C_{3088}:C_{96}$, $C_{6176}:C_{48}$, $C_8\times F_{193}$

Order 222336: $C_{18528}.C_{12}$, $C_{4632}.C_{48}$, $C_{9264}.C_{24}$, $C_{37056}.C_6$, $C_{9264}:C_{24}$, $C_{18528}:C_{12}$, $C_{2316}:C_{96}$, $C_{9264}.C_{24}$, $C_{2316}.C_{96}$, $C_{4632}.C_{48}$, $C_{4632}:C_{48}$, $C_6\times F_{193}$

Order 197632: $C_{12352}:C_{16}$, $C_{6176}:C_{32}$, $C_{3088}:C_{64}$, $C_{6176}.C_{32}$

Order 148224: $C_{3088}:C_{48}$, $C_{3088}.C_{48}$, $C_{3088}.C_{48}$, $C_{18528}.C_8$, $C_{2316}:C_{64}$, $C_{18528}:C_8$, $C_{12352}:C_{12}$, $C_{1544}.C_{96}$, $C_{6176}:C_{24}$, $C_{3088}.C_{48}$, $C_{6176}.C_{24}$, $C_{1544}:C_{96}$, $C_{12352}.C_{12}$, $C_{3088}.C_{48}$, $C_{1544}:C_{96}$, $C_4\times F_{193}$, $C_{1544}.C_{96}$, $C_{3088}:C_{48}$

Order 111168: $C_{1158}.C_{96}$, $C_{4632}.C_{24}$, $C_{9264}.C_{12}$, $C_{9264}:C_{12}$, $C_{4632}.C_{24}$, $C_{18528}.C_6$, $C_{579}:C_{192}$, $C_{579}:C_{192}$, $C_{4632}:C_{24}$, $C_{579}:C_{192}$, $C_{579}:C_{192}$, $C_{12352}:C_3^2$, $C_{2316}.C_{48}$, $C_{1158}:C_{96}$, $C_{2316}:C_{48}$, $C_3\times F_{193}$

Order 98816: $C_{6176}:C_{16}$, $C_{3088}.C_{32}$, $C_{6176}.C_{16}$, $C_{12352}:C_8$, $C_{3088}:C_{32}$, $C_{1544}:C_{64}$

Order 74112: $C_3\times C_{193}:(C_4\times C_{32})$, $C_3\times C_{193}:(C_2\times C_{64})$, $C_3\times C_{193}:(C_4\times C_{32})$, $C_{24}\times C_{193}:C_{16}$, $C_{18528}.C_4$, $D_{193}:C_{192}$, $D_{193}:C_{192}$, $C_{12352}.C_6$, $D_{193}:C_{192}$, $C_{12352}:C_6$, $D_{193}:C_{192}$, $C_{3088}:C_{24}$, $C_{18528}.C_4$, $D_{193}:C_{192}$, $C_{2316}:C_{32}$, $C_{1158}:C_{64}$, $C_{3088}:C_{24}$, $C_{3088}.C_{24}$, $C_{6176}:C_{12}$, $D_{193}:C_{192}$, $C_{772}:C_{96}$, $C_{1544}.C_{48}$, $C_{1544}:C_{48}$, $C_2\times F_{193}$

Order 55584: $C_{24}\times C_{193}:C_{12}$, $C_{96}\times C_{193}:C_3$, $C_3\times C_{193}:C_{96}$, $C_{9264}.C_6$, $C_{4632}.C_{12}$, $C_{2316}:C_{24}$, $C_{579}:C_{96}$, $C_{579}:C_{96}$, $C_{2316}.C_{24}$, $C_{579}:C_{96}$, $C_{579}:C_{96}$, $C_{1158}:C_{48}$

Order 49408: $C_{772}:C_{64}$, $C_{1544}.C_{32}$, $C_{1544}:C_{32}$, $C_{3088}.C_{16}$, $C_{3088}.C_{16}$, $C_{3088}:C_{16}$, $C_{6176}.C_8$, $C_{6176}:C_8$, $C_{12352}:C_4$

Order 37056: $C_{24}\times C_{193}:C_8$, $C_3\times C_{193}:(C_4\times C_{16})$, $C_3\times C_{193}:(C_2\times C_{32})$, $C_{48}\times C_{193}:C_4$, $C_3\times C_{193}:C_{64}$, $C_{96}\times D_{193}$, $C_3\times C_{193}:C_{64}$, $C_{772}.C_{48}$, $C_{2316}:C_{16}$, $D_{193}:C_{96}$, $C_{1158}:C_{32}$, $C_{193}:C_{192}$, $C_{37056}$, $D_{193}:C_{96}$, $C_{193}:C_{192}$, $C_{12352}:C_3$, $C_{193}:C_{192}$, $C_{3088}:C_{12}$, $C_{193}:C_{192}$, $C_{1544}:C_{24}$, $C_{193}:C_{192}$, $C_{193}:C_{192}$, $D_{193}:C_{96}$, $C_{386}:C_{96}$, $C_{193}:C_{192}$, $C_{1544}.C_{24}$, $C_{193}:C_{192}$, $D_{193}:C_{96}$, $C_{6176}:C_6$, $D_{193}:C_{96}$, $C_{772}:C_{48}$, $F_{193}$

Order 36864: $C_{192}^2$

Order 27792: $C_{12}\times C_{193}:C_{12}$, $C_{24}\times C_{193}:C_6$, $C_3\times C_{193}:C_{48}$, $C_{48}\times C_{193}:C_3$, $C_3\times C_{193}:(C_2\times C_{24})$, $C_3\times C_{193}:C_{48}$, $C_{579}:C_{48}$, $C_{1158}:C_{24}$, $C_{579}:C_{48}$

Order 24704: $C_{64}\times D_{193}$, $C_{386}:C_{64}$, $D_{193}:C_{64}$, $C_{772}:C_{32}$, $D_{193}:C_{64}$, $C_{1544}.C_{16}$, $C_{1544}:C_{16}$, $D_{193}:C_{64}$, $C_{3088}.C_8$, $C_{3088}:C_8$, $D_{193}:C_{64}$, $C_{6176}:C_4$

Order 18528: $C_3\times C_{193}:(C_2\times C_{16})$, $C_{32}\times C_{193}:C_3$, $C_3\times C_{193}:C_{32}$, $C_8\times C_{193}:C_{12}$, $C_{1544}:C_{12}$, $C_{48}\times D_{193}$, $C_{2316}:C_8$, $D_{193}:C_{48}$, $C_{3088}:C_6$, $C_{772}:C_{24}$, $D_{193}:C_{48}$, $C_{18528}$, $C_{193}:C_{96}$, $C_{1158}:C_{16}$, $C_{193}:C_{96}$, $C_{193}:C_{96}$, $C_{193}:C_{96}$, $C_{193}:C_{96}$, $C_{193}:C_{96}$, $D_{193}:C_{48}$, $C_{193}:C_{96}$, $C_{193}:C_{96}$, $C_{193}:C_{96}$, $C_{386}:C_{48}$

Order 13896: $C_3\times C_{193}:C_{24}$, $C_{12}\times C_{193}:C_6$, $C_3\times C_{193}:C_{24}$, $C_6\times C_{193}:C_{12}$, $C_{4632}:C_3$, $C_{579}:C_{24}$

Order 12352: $C_{32}\times D_{193}$, $C_{193}:C_{64}$, $C_{193}:C_{64}$, $C_{386}:C_{32}$, $C_{193}:C_{64}$, $D_{193}:C_{32}$, $C_{772}:C_{16}$, $C_{193}:C_{64}$, $D_{193}:C_{32}$, $C_{1544}.C_8$, $C_{1544}:C_8$, $C_{193}:C_{64}$, $D_{193}:C_{32}$, $C_{3088}:C_4$, $C_{193}:C_{64}$, $C_{12352}$

Order 9264: $C_{193}:(C_2\times C_{24})$, $C_{24}\times D_{193}$, $C_{193}:C_{48}$, $C_8\times C_{193}:C_6$, $C_3\times C_{193}:C_{16}$, $C_2\times C_{193}:C_{24}$, $C_4\times C_{193}:C_{12}$, $C_3\times C_{193}:C_{16}$, $C_3\times C_{193}:C_{16}$, $C_{2316}:C_4$, $C_{9264}$, $C_{193}:C_{48}$, $C_{1158}:C_8$, $C_{193}:C_{48}$, $D_{193}:C_{24}$, $C_{193}:C_{48}$, $C_{193}:C_{48}$, $C_{193}:C_{48}$

Order 6948: $C_{579}:C_{12}$, $C_{1158}:C_6$, $C_{2316}:C_3$, $C_{579}:C_{12}$

Order 6176: $C_{16}\times D_{193}$, $C_{193}:C_{32}$, $C_{193}:C_{32}$, $C_{386}:C_{16}$, $C_{193}:C_{32}$, $D_{193}:C_{16}$, $C_{772}:C_8$, $C_{193}:C_{32}$, $D_{193}:C_{16}$, $C_{1544}:C_4$, $C_{193}:C_{32}$, $C_{6176}$

Order 4632: $C_{193}:C_{24}$, $C_3\times C_{193}:C_8$, $C_4\times C_{193}:C_6$, $C_3\times C_{193}:C_8$, $C_3\times C_{193}:C_8$, $C_{12}\times D_{193}$, $C_{4632}$, $C_{1158}:C_4$, $C_{1544}:C_3$, $C_{193}:C_{24}$, $C_{193}:C_{24}$, $C_{386}:C_{12}$

Order 4096: $C_{64}^2$

Order 3474: $C_{1158}:C_3$, $C_{579}:C_6$

Order 3088: $C_{193}:C_{16}$, $C_{386}:C_8$, $C_{193}:C_{16}$, $D_{193}:C_8$, $C_{772}:C_4$, $C_{193}:C_{16}$, $C_8\times D_{193}$, $C_{193}:C_{16}$, $C_{3088}$

Order 2316: $C_3\times D_{386}$, $C_{193}:C_{12}$, $C_{193}:C_{12}$, $C_{386}:C_6$, $C_{193}:C_{12}$, $C_{193}:C_{12}$, $C_{193}:C_{12}$, $C_{2316}$

Order 1737: $C_{579}:C_3$

Order 1544: $C_4\times D_{193}$, $C_{193}:C_8$, $C_{193}:C_8$, $C_{386}:C_4$, $C_{193}:C_8$, $C_{1544}$

Order 1158: $C_{1158}$, $C_3\times D_{193}$, $C_{193}:C_6$, $C_{193}:C_6$

Order 772: $D_{386}$, $C_{193}:C_4$, $C_{772}$, $C_{193}:C_4$

Order 579: $C_{579}$, $C_{193}:C_3$

Order 386: $C_{386}$, $D_{193}$

Order 193: $C_{193}$

Order 192: $C_{192}$

Order 96: $C_{96}$

Order 64: $C_{64}$

Order 48: $C_{48}$

Order 32: $C_{32}$

Order 24: $C_{24}$

Order 16: $C_{16}$

Order 12: $C_{12}$

Order 9: $C_3^2$

Order 8: $C_8$

Order 6: $C_6$

Order 4: $C_4$

Order 3: $C_3$

Order 2: $C_2$

Order 1: $C_1$

Normal subgroups (quotient in parentheses)

Order 7114752: $C_{193}:C_{192}^2$ ($C_1$)

Order 3557376: $C_{96}\times D_{193}.C_{96}$ ($C_2$) x 2, $C_{192}\times C_{193}:C_{96}$ ($C_2$)

Order 2371584: $C_{64}\times D_{193}.C_{96}$ ($C_3$) x 3, $C_{192}\times C_{193}:C_{64}$ ($C_3$)

Order 1778688: $C_{9264}:C_{192}$ ($C_4$) x 4, $C_3\times C_{386}.C_2.C_8^2.C_6.C_2$ ($C_4$), $C_{37056}.C_{48}$ ($C_4$), $C_{18528}:C_{96}$ ($C_2^2$)

Order 1185792: $C_{32}\times F_{193}$ ($C_6$) x 6, $C_{12352}:C_{96}$ ($C_6$) x 3, $C_{18528}:C_{64}$ ($C_6$) x 2, $C_{12352}.C_{96}$ ($C_6$)

Order 889344: $C_{24}\times F_{193}$ ($C_8$) x 8, $C_{9264}:C_{96}$ ($C_2\times C_4$) x 2, $C_{9264}.C_{96}$ ($C_8$) x 2, $C_{18528}.C_{48}$ ($C_8$), $C_{37056}.C_{24}$ ($C_8$), $C_{18528}:C_{48}$ ($C_2\times C_4$)

Order 790528: $C_{12352}:C_{64}$ ($C_3^2$)

Order 592896: $C_{16}\times F_{193}$ ($C_{12}$) x 12, $C_{3088}:C_{192}$ ($C_{12}$) x 4, $C_{12352}:C_{48}$ ($C_{12}$) x 3, $C_{6176}:C_{96}$ ($C_2\times C_6$) x 3, $C_{6176}.C_{96}$ ($C_{12}$) x 3, $C_{18528}:C_{32}$ ($C_2\times C_6$), $C_{12352}.C_{48}$ ($C_{12}$), $C_{18528}.C_{32}$ ($C_{12}$)

Order 444672: $C_{12}\times F_{193}$ ($C_{16}$) x 16, $C_{4632}.C_{96}$ ($C_{16}$) x 4, $C_{4632}:C_{96}$ ($C_2\times C_8$) x 4, $C_{9264}.C_{48}$ ($C_{16}$) x 2, $C_{18528}:C_{24}$ ($C_2\times C_8$), $C_{9264}:C_{48}$ ($C_4^2$), $C_{18528}.C_{24}$ ($C_{16}$), $C_{37056}.C_{12}$ ($C_{16}$), $C_{9264}.C_{48}$ ($C_2\times C_8$)

Order 395264: $C_{6176}:C_{64}$ ($C_3\times C_6$) x 2, $C_{12352}:C_{32}$ ($C_3\times C_6$)

Order 296448: $C_8\times F_{193}$ ($C_{24}$) x 24, $C_{1544}:C_{192}$ ($C_{24}$) x 8, $C_{3088}.C_{96}$ ($C_{24}$) x 6, $C_{3088}:C_{96}$ ($C_2\times C_{12}$) x 6, $C_{6176}.C_{48}$ ($C_{24}$) x 3, $C_{12352}:C_{24}$ ($C_{24}$) x 3, $C_{6176}:C_{48}$ ($C_2\times C_{12}$) x 3, $C_{3088}.C_{96}$ ($C_{24}$) x 2, $C_{3088}:C_{96}$ ($C_2\times C_{12}$) x 2, $C_{18528}.C_{16}$ ($C_{24}$), $C_{18528}:C_{16}$ ($C_2\times C_{12}$), $C_{12352}.C_{24}$ ($C_{24}$)

Order 222336: $C_6\times F_{193}$ ($C_{32}$) x 32, $C_{2316}:C_{96}$ ($C_2\times C_{16}$) x 8, $C_{2316}.C_{96}$ ($C_{32}$) x 8, $C_{4632}.C_{48}$ ($C_{32}$) x 4, $C_{9264}.C_{24}$ ($C_{32}$) x 2, $C_{4632}.C_{48}$ ($C_2\times C_{16}$) x 2, $C_{4632}:C_{48}$ ($C_4\times C_8$) x 2, $C_{18528}.C_{12}$ ($C_{32}$), $C_{37056}.C_6$ ($C_{32}$), $C_{9264}:C_{24}$ ($C_4\times C_8$), $C_{18528}:C_{12}$ ($C_2\times C_{16}$), $C_{9264}.C_{24}$ ($C_2\times C_{16}$)

Order 197632: $C_{3088}:C_{64}$ ($C_3\times C_{12}$) x 4, $C_{12352}:C_{16}$ ($C_3\times C_{12}$), $C_{6176}:C_{32}$ ($C_6^2$), $C_{6176}.C_{32}$ ($C_3\times C_{12}$)

Order 148224: $C_4\times F_{193}$ ($C_{48}$) x 48, $C_{2316}:C_{64}$ ($C_{48}$) x 16, $C_{1544}:C_{96}$ ($C_2\times C_{24}$) x 12, $C_{1544}.C_{96}$ ($C_{48}$) x 12, $C_{3088}.C_{48}$ ($C_{48}$) x 6, $C_{1544}.C_{96}$ ($C_{48}$) x 4, $C_{1544}:C_{96}$ ($C_2\times C_{24}$) x 4, $C_{12352}:C_{12}$ ($C_{48}$) x 3, $C_{6176}:C_{24}$ ($C_2\times C_{24}$) x 3, $C_{6176}.C_{24}$ ($C_{48}$) x 3, $C_{3088}.C_{48}$ ($C_2\times C_{24}$) x 3, $C_{3088}:C_{48}$ ($C_4\times C_{12}$) x 3, $C_{3088}.C_{48}$ ($C_{48}$) x 2, $C_{3088}:C_{48}$ ($C_4\times C_{12}$), $C_{3088}.C_{48}$ ($C_2\times C_{24}$), $C_{18528}.C_8$ ($C_{48}$), $C_{18528}:C_8$ ($C_2\times C_{24}$), $C_{12352}.C_{12}$ ($C_{48}$)

Order 111168: $C_3\times F_{193}$ ($C_{64}$) x 64, $C_{579}:C_{192}$ ($C_{64}$) x 16, $C_{1158}:C_{96}$ ($C_2\times C_{32}$) x 16, $C_{579}:C_{192}$ ($C_{64}$) x 8, $C_{579}:C_{192}$ ($C_{64}$) x 4, $C_{2316}.C_{48}$ ($C_2\times C_{32}$) x 4, $C_{2316}:C_{48}$ ($C_4\times C_{16}$) x 4, $C_{4632}.C_{24}$ ($C_2\times C_{32}$) x 2, $C_{579}:C_{192}$ ($C_{64}$) x 2, $C_{1158}.C_{96}$ ($C_{64}$), $C_{9264}.C_{12}$ ($C_2\times C_{32}$), $C_{9264}:C_{12}$ ($C_4\times C_{16}$), $C_{4632}.C_{24}$ ($C_4\times C_{16}$), $C_{18528}.C_6$ ($C_2\times C_{32}$), $C_{4632}:C_{24}$ ($C_8^2$), $C_{12352}:C_3^2$ ($C_{64}$)

Order 98816: $C_{1544}:C_{64}$ ($C_3\times C_{24}$) x 8, $C_{3088}.C_{32}$ ($C_3\times C_{24}$) x 2, $C_{3088}:C_{32}$ ($C_6\times C_{12}$) x 2, $C_{6176}:C_{16}$ ($C_6\times C_{12}$), $C_{6176}.C_{16}$ ($C_3\times C_{24}$), $C_{12352}:C_8$ ($C_3\times C_{24}$)

Order 74112: $C_2\times F_{193}$ ($C_{96}$) x 96, $C_{1158}:C_{64}$ ($C_{96}$) x 32, $D_{193}:C_{192}$ ($C_{96}$) x 24, $C_{772}:C_{96}$ ($C_2\times C_{48}$) x 24, $D_{193}:C_{192}$ ($C_{96}$) x 12, $C_3\times C_{193}:(C_2\times C_{64})$ ($C_{96}$) x 8, $C_{2316}:C_{32}$ ($C_2\times C_{48}$) x 8, $D_{193}:C_{192}$ ($C_{96}$) x 6, $C_{1544}.C_{48}$ ($C_2\times C_{48}$) x 6, $C_{1544}:C_{48}$ ($C_4\times C_{24}$) x 6, $D_{193}:C_{192}$ ($C_{96}$) x 4, $D_{193}:C_{192}$ ($C_{96}$) x 3, $C_{12352}:C_6$ ($C_{96}$) x 3, $C_{3088}:C_{24}$ ($C_4\times C_{24}$) x 3, $C_{3088}.C_{24}$ ($C_2\times C_{48}$) x 3, $C_{6176}:C_{12}$ ($C_2\times C_{48}$) x 3, $C_3\times C_{193}:(C_4\times C_{32})$ ($C_2\times C_{48}$) x 2, $C_{24}\times C_{193}:C_{16}$ ($C_4\times C_{24}$) x 2, $D_{193}:C_{192}$ ($C_{96}$) x 2, $C_3\times C_{193}:(C_4\times C_{32})$ ($C_2\times C_{48}$), $C_{18528}.C_4$ ($C_{96}$), $C_{12352}.C_6$ ($C_{96}$), $C_{3088}:C_{24}$ ($C_4\times C_{24}$), $C_{18528}.C_4$ ($C_2\times C_{48}$)

Order 55584: $C_{579}:C_{96}$ ($C_2\times C_{64}$) x 32, $C_{579}:C_{96}$ ($C_2\times C_{64}$) x 8, $C_{1158}:C_{48}$ ($C_4\times C_{32}$) x 8, $C_{579}:C_{96}$ ($C_2\times C_{64}$) x 4, $C_{2316}:C_{24}$ ($C_8\times C_{16}$) x 2, $C_{579}:C_{96}$ ($C_2\times C_{64}$) x 2, $C_{2316}.C_{24}$ ($C_4\times C_{32}$) x 2, $C_{24}\times C_{193}:C_{12}$ ($C_8\times C_{16}$), $C_{96}\times C_{193}:C_3$ ($C_2\times C_{64}$), $C_3\times C_{193}:C_{96}$ ($C_2\times C_{64}$), $C_{9264}.C_6$ ($C_4\times C_{32}$), $C_{4632}.C_{12}$ ($C_4\times C_{32}$)

Order 49408: $C_{772}:C_{64}$ ($C_3\times C_{48}$) x 16, $C_{1544}.C_{32}$ ($C_3\times C_{48}$) x 4, $C_{1544}:C_{32}$ ($C_6\times C_{24}$) x 4, $C_{3088}.C_{16}$ ($C_3\times C_{48}$) x 2, $C_{3088}.C_{16}$ ($C_6\times C_{24}$), $C_{3088}:C_{16}$ ($C_{12}^2$), $C_{6176}.C_8$ ($C_3\times C_{48}$), $C_{6176}:C_8$ ($C_6\times C_{24}$), $C_{12352}:C_4$ ($C_3\times C_{48}$)

Order 37056: $F_{193}$ ($C_{192}$) x 192, $C_{193}:C_{192}$ ($C_{192}$) x 64, $C_{386}:C_{96}$ ($C_2\times C_{96}$) x 48, $C_{193}:C_{192}$ ($C_{192}$) x 48, $C_{193}:C_{192}$ ($C_{192}$) x 24, $C_{1158}:C_{32}$ ($C_2\times C_{96}$) x 16, $C_{193}:C_{192}$ ($C_{192}$) x 16, $C_{193}:C_{192}$ ($C_{192}$) x 12, $D_{193}:C_{96}$ ($C_2\times C_{96}$) x 12, $C_{772}:C_{48}$ ($C_4\times C_{48}$) x 12, $C_{193}:C_{192}$ ($C_{192}$) x 8, $C_{772}.C_{48}$ ($C_{192}$) x 6, $D_{193}:C_{96}$ ($C_2\times C_{96}$) x 6, $C_3\times C_{193}:C_{64}$ ($C_{192}$) x 4, $C_{2316}:C_{16}$ ($C_4\times C_{48}$) x 4, $D_{193}:C_{96}$ ($C_2\times C_{96}$) x 4, $C_{193}:C_{192}$ ($C_{192}$) x 3, $C_{12352}:C_3$ ($C_{192}$) x 3, $C_{3088}:C_{12}$ ($C_4\times C_{48}$) x 3, $C_{1544}:C_{24}$ ($C_8\times C_{24}$) x 3, $C_{1544}.C_{24}$ ($C_4\times C_{48}$) x 3, $C_{6176}:C_6$ ($C_2\times C_{96}$) x 3, $D_{193}:C_{96}$ ($C_2\times C_{96}$) x 3, $C_3\times C_{193}:C_{64}$ ($C_{192}$) x 2, $D_{193}:C_{96}$ ($C_2\times C_{96}$) x 2, $C_{24}\times C_{193}:C_8$ ($C_8\times C_{24}$), $C_3\times C_{193}:(C_4\times C_{16})$ ($C_4\times C_{48}$), $C_3\times C_{193}:(C_2\times C_{32})$ ($C_2\times C_{96}$), $C_{48}\times C_{193}:C_4$ ($C_4\times C_{48}$), $C_{96}\times D_{193}$ ($C_2\times C_{96}$), $C_{37056}$ ($C_{192}$), $C_{193}:C_{192}$ ($C_{192}$)

Order 27792: $C_{579}:C_{48}$ ($C_4\times C_{64}$) x 16, $C_{579}:C_{48}$ ($C_4\times C_{64}$) x 4, $C_{1158}:C_{24}$ ($C_8\times C_{32}$) x 4, $C_3\times C_{193}:C_{48}$ ($C_4\times C_{64}$) x 2, $C_{12}\times C_{193}:C_{12}$ ($C_{16}^2$), $C_{24}\times C_{193}:C_6$ ($C_8\times C_{32}$), $C_3\times C_{193}:C_{48}$ ($C_4\times C_{64}$), $C_{48}\times C_{193}:C_3$ ($C_4\times C_{64}$), $C_3\times C_{193}:(C_2\times C_{24})$ ($C_8\times C_{32}$)

Order 24704: $C_{386}:C_{64}$ ($C_3\times C_{96}$) x 32, $D_{193}:C_{64}$ ($C_3\times C_{96}$) x 8, $C_{772}:C_{32}$ ($C_6\times C_{48}$) x 8, $D_{193}:C_{64}$ ($C_3\times C_{96}$) x 4, $C_{1544}.C_{16}$ ($C_6\times C_{48}$) x 2, $C_{1544}:C_{16}$ ($C_{12}\times C_{24}$) x 2, $D_{193}:C_{64}$ ($C_3\times C_{96}$) x 2, $C_{64}\times D_{193}$ ($C_3\times C_{96}$), $C_{3088}.C_8$ ($C_6\times C_{48}$), $C_{3088}:C_8$ ($C_{12}\times C_{24}$), $D_{193}:C_{64}$ ($C_3\times C_{96}$), $C_{6176}:C_4$ ($C_6\times C_{48}$)

Order 18528: $C_{193}:C_{96}$ ($C_2\times C_{192}$) x 96, $C_{193}:C_{96}$ ($C_2\times C_{192}$) x 32, $C_{193}:C_{96}$ ($C_2\times C_{192}$) x 24, $C_{386}:C_{48}$ ($C_4\times C_{96}$) x 24, $C_{193}:C_{96}$ ($C_2\times C_{192}$) x 12, $C_3\times C_{193}:C_{32}$ ($C_2\times C_{192}$) x 8, $C_{1158}:C_{16}$ ($C_4\times C_{96}$) x 8, $C_{772}:C_{24}$ ($C_8\times C_{48}$) x 6, $C_{193}:C_{96}$ ($C_2\times C_{192}$) x 6, $D_{193}:C_{48}$ ($C_4\times C_{96}$) x 6, $C_{193}:C_{96}$ ($C_2\times C_{192}$) x 4, $C_{32}\times C_{193}:C_3$ ($C_2\times C_{192}$) x 3, $C_8\times C_{193}:C_{12}$ ($C_8\times C_{48}$) x 3, $C_{3088}:C_6$ ($C_4\times C_{96}$) x 3, $D_{193}:C_{48}$ ($C_4\times C_{96}$) x 3, $C_{193}:C_{96}$ ($C_2\times C_{192}$) x 3, $C_3\times C_{193}:(C_2\times C_{16})$ ($C_4\times C_{96}$) x 2, $C_{2316}:C_8$ ($C_8\times C_{48}$) x 2, $C_{193}:C_{96}$ ($C_2\times C_{192}$) x 2, $C_{1544}:C_{12}$ ($C_8\times C_{48}$), $C_{48}\times D_{193}$ ($C_4\times C_{96}$), $D_{193}:C_{48}$ ($C_4\times C_{96}$), $C_{18528}$ ($C_2\times C_{192}$), $C_{193}:C_{96}$ ($C_2\times C_{192}$)

Order 13896: $C_{579}:C_{24}$ ($C_8\times C_{64}$) x 8, $C_3\times C_{193}:C_{24}$ ($C_8\times C_{64}$) x 2, $C_6\times C_{193}:C_{12}$ ($C_{16}\times C_{32}$) x 2, $C_{12}\times C_{193}:C_6$ ($C_{16}\times C_{32}$), $C_3\times C_{193}:C_{24}$ ($C_8\times C_{64}$), $C_{4632}:C_3$ ($C_8\times C_{64}$)

Order 12352: $C_{193}:C_{64}$ ($C_3\times C_{192}$) x 64, $C_{386}:C_{32}$ ($C_6\times C_{96}$) x 16, $C_{193}:C_{64}$ ($C_3\times C_{192}$) x 16, $C_{193}:C_{64}$ ($C_3\times C_{192}$) x 8, $D_{193}:C_{32}$ ($C_6\times C_{96}$) x 4, $C_{772}:C_{16}$ ($C_{12}\times C_{48}$) x 4, $C_{193}:C_{64}$ ($C_3\times C_{192}$) x 4, $D_{193}:C_{32}$ ($C_6\times C_{96}$) x 2, $C_{193}:C_{64}$ ($C_3\times C_{192}$) x 2, $C_{32}\times D_{193}$ ($C_6\times C_{96}$), $C_{193}:C_{64}$ ($C_3\times C_{192}$), $C_{1544}.C_8$ ($C_{12}\times C_{48}$), $C_{1544}:C_8$ ($C_{24}^2$), $D_{193}:C_{32}$ ($C_6\times C_{96}$), $C_{3088}:C_4$ ($C_{12}\times C_{48}$), $C_{12352}$ ($C_3\times C_{192}$)

Order 9264: $C_{193}:C_{48}$ ($C_4\times C_{192}$) x 48, $C_3\times C_{193}:C_{16}$ ($C_4\times C_{192}$) x 16, $C_2\times C_{193}:C_{24}$ ($C_8\times C_{96}$) x 12, $C_{193}:C_{48}$ ($C_4\times C_{192}$) x 12, $C_{193}:C_{48}$ ($C_4\times C_{192}$) x 6, $C_3\times C_{193}:C_{16}$ ($C_4\times C_{192}$) x 4, $C_{1158}:C_8$ ($C_8\times C_{96}$) x 4, $C_{193}:(C_2\times C_{24})$ ($C_8\times C_{96}$) x 3, $C_8\times C_{193}:C_6$ ($C_8\times C_{96}$) x 3, $C_4\times C_{193}:C_{12}$ ($C_{16}\times C_{48}$) x 3, $C_{193}:C_{48}$ ($C_4\times C_{192}$) x 3, $C_{193}:C_{48}$ ($C_4\times C_{192}$) x 3, $C_{193}:C_{48}$ ($C_4\times C_{192}$) x 2, $C_{24}\times D_{193}$ ($C_8\times C_{96}$), $C_3\times C_{193}:C_{16}$ ($C_4\times C_{192}$), $C_{2316}:C_4$ ($C_{16}\times C_{48}$), $C_{9264}$ ($C_4\times C_{192}$), $D_{193}:C_{24}$ ($C_8\times C_{96}$)

Order 6948: $C_{579}:C_{12}$ ($C_{16}\times C_{64}$) x 4, $C_{579}:C_{12}$ ($C_{16}\times C_{64}$), $C_{1158}:C_6$ ($C_{32}^2$), $C_{2316}:C_3$ ($C_{16}\times C_{64}$)

Order 6176: $C_{193}:C_{32}$ ($C_6\times C_{192}$) x 32, $C_{386}:C_{16}$ ($C_{12}\times C_{96}$) x 8, $C_{193}:C_{32}$ ($C_6\times C_{192}$) x 8, $C_{193}:C_{32}$ ($C_6\times C_{192}$) x 4, $D_{193}:C_{16}$ ($C_{12}\times C_{96}$) x 2, $C_{772}:C_8$ ($C_{24}\times C_{48}$) x 2, $C_{193}:C_{32}$ ($C_6\times C_{192}$) x 2, $C_{16}\times D_{193}$ ($C_{12}\times C_{96}$), $C_{193}:C_{32}$ ($C_6\times C_{192}$), $D_{193}:C_{16}$ ($C_{12}\times C_{96}$), $C_{1544}:C_4$ ($C_{24}\times C_{48}$), $C_{6176}$ ($C_6\times C_{192}$)

Order 4632: $C_{193}:C_{24}$ ($C_8\times C_{192}$) x 24, $C_3\times C_{193}:C_8$ ($C_8\times C_{192}$) x 8, $C_{193}:C_{24}$ ($C_8\times C_{192}$) x 6, $C_{386}:C_{12}$ ($C_{16}\times C_{96}$) x 6, $C_{193}:C_{24}$ ($C_8\times C_{192}$) x 3, $C_4\times C_{193}:C_6$ ($C_{16}\times C_{96}$) x 3, $C_{1544}:C_3$ ($C_8\times C_{192}$) x 3, $C_3\times C_{193}:C_8$ ($C_8\times C_{192}$) x 2, $C_{1158}:C_4$ ($C_{16}\times C_{96}$) x 2, $C_3\times C_{193}:C_8$ ($C_8\times C_{192}$), $C_{12}\times D_{193}$ ($C_{16}\times C_{96}$), $C_{4632}$ ($C_8\times C_{192}$)

Order 3474: $C_{579}:C_6$ ($C_{32}\times C_{64}$) x 2, $C_{1158}:C_3$ ($C_{32}\times C_{64}$)

Order 3088: $C_{193}:C_{16}$ ($C_{12}\times C_{192}$) x 16, $C_{386}:C_8$ ($C_{24}\times C_{96}$) x 4, $C_{193}:C_{16}$ ($C_{12}\times C_{192}$) x 4, $C_{193}:C_{16}$ ($C_{12}\times C_{192}$) x 2, $D_{193}:C_8$ ($C_{24}\times C_{96}$), $C_{772}:C_4$ ($C_{48}^2$), $C_8\times D_{193}$ ($C_{24}\times C_{96}$), $C_{193}:C_{16}$ ($C_{12}\times C_{192}$), $C_{3088}$ ($C_{12}\times C_{192}$)

Order 2316: $C_{193}:C_{12}$ ($C_{16}\times C_{192}$) x 12, $C_{193}:C_{12}$ ($C_{16}\times C_{192}$) x 4, $C_{193}:C_{12}$ ($C_{16}\times C_{192}$) x 3, $C_{386}:C_6$ ($C_{32}\times C_{96}$) x 3, $C_{193}:C_{12}$ ($C_{16}\times C_{192}$) x 3, $C_3\times D_{386}$ ($C_{32}\times C_{96}$), $C_{193}:C_{12}$ ($C_{16}\times C_{192}$), $C_{2316}$ ($C_{16}\times C_{192}$)

Order 1737: $C_{579}:C_3$ ($C_{64}^2$)

Order 1544: $C_{193}:C_8$ ($C_{24}\times C_{192}$) x 8, $C_{386}:C_4$ ($C_{48}\times C_{96}$) x 2, $C_{193}:C_8$ ($C_{24}\times C_{192}$) x 2, $C_4\times D_{193}$ ($C_{48}\times C_{96}$), $C_{193}:C_8$ ($C_{24}\times C_{192}$), $C_{1544}$ ($C_{24}\times C_{192}$)

Order 1158: $C_{193}:C_6$ ($C_{32}\times C_{192}$) x 6, $C_{193}:C_6$ ($C_{32}\times C_{192}$) x 3, $C_3\times D_{193}$ ($C_{32}\times C_{192}$) x 2, $C_{1158}$ ($C_{32}\times C_{192}$)

Order 772: $C_{193}:C_4$ ($C_{48}\times C_{192}$) x 4, $D_{386}$ ($C_{96}^2$), $C_{772}$ ($C_{48}\times C_{192}$), $C_{193}:C_4$ ($C_{48}\times C_{192}$)

Order 579: $C_{193}:C_3$ ($C_{64}\times C_{192}$) x 3, $C_{579}$ ($C_{64}\times C_{192}$)

Order 386: $D_{193}$ ($C_{96}\times C_{192}$) x 2, $C_{386}$ ($C_{96}\times C_{192}$)

Order 193: $C_{193}$ ($C_{192}^2$)

Order 192: $C_{192}$ ($F_{193}$)

Order 96: $C_{96}$ ($C_2\times F_{193}$)

Order 64: $C_{64}$ ($C_3\times F_{193}$)

Order 48: $C_{48}$ ($C_4\times F_{193}$)

Order 32: $C_{32}$ ($C_6\times F_{193}$)

Order 24: $C_{24}$ ($C_8\times F_{193}$)

Order 16: $C_{16}$ ($C_{12}\times F_{193}$)

Order 12: $C_{12}$ ($C_{16}\times F_{193}$)

Order 8: $C_8$ ($C_{24}\times F_{193}$)

Order 6: $C_6$ ($C_{6176}.C_{192}$)

Order 4: $C_4$ ($C_{9264}.C_{192}$)

Order 3: $C_3$ ($C_{12352}.C_{192}$)

Order 2: $C_2$ ($C_{18528}.C_{192}$)

Order 1: $C_1$ ($C_{193}:C_{192}^2$)

Normal subgroups up to automorphism (quotient in parentheses)

Order 7114752: $C_{193}:C_{192}^2$ ($C_1$)

Order 3557376: $C_{96}\times D_{193}.C_{96}$ ($C_2$), $C_{192}\times C_{193}:C_{96}$ ($C_2$)

Order 2371584: $C_{192}\times C_{193}:C_{64}$ ($C_3$), $C_{64}\times D_{193}.C_{96}$ ($C_3$)

Order 1778688: $C_3\times C_{386}.C_2.C_8^2.C_6.C_2$ ($C_4$), $C_{9264}:C_{192}$ ($C_4$), $C_{37056}.C_{48}$ ($C_4$), $C_{18528}:C_{96}$ ($C_2^2$)

Order 1185792: $C_{18528}:C_{64}$ ($C_6$), $C_{12352}.C_{96}$ ($C_6$), $C_{12352}:C_{96}$ ($C_6$), $C_{32}\times F_{193}$ ($C_6$)

Order 889344: $C_{18528}.C_{48}$ ($C_8$), $C_{37056}.C_{24}$ ($C_8$), $C_{9264}:C_{96}$ ($C_2\times C_4$), $C_{9264}.C_{96}$ ($C_8$), $C_{18528}:C_{48}$ ($C_2\times C_4$), $C_{24}\times F_{193}$ ($C_8$)

Order 790528: $C_{12352}:C_{64}$ ($C_3^2$)

Order 592896: $C_{18528}:C_{32}$ ($C_2\times C_6$), $C_{12352}.C_{48}$ ($C_{12}$), $C_{18528}.C_{32}$ ($C_{12}$), $C_{12352}:C_{48}$ ($C_{12}$), $C_{3088}:C_{192}$ ($C_{12}$), $C_{6176}:C_{96}$ ($C_2\times C_6$), $C_{6176}.C_{96}$ ($C_{12}$), $C_{16}\times F_{193}$ ($C_{12}$)

Order 444672: $C_{12}\times F_{193}$ ($C_{16}$), $C_{18528}:C_{24}$ ($C_2\times C_8$), $C_{9264}:C_{48}$ ($C_4^2$), $C_{9264}.C_{48}$ ($C_{16}$), $C_{18528}.C_{24}$ ($C_{16}$), $C_{4632}.C_{96}$ ($C_{16}$), $C_{37056}.C_{12}$ ($C_{16}$), $C_{9264}.C_{48}$ ($C_2\times C_8$), $C_{4632}:C_{96}$ ($C_2\times C_8$)

Order 395264: $C_{12352}:C_{32}$ ($C_3\times C_6$), $C_{6176}:C_{64}$ ($C_3\times C_6$)

Order 296448: $C_{18528}.C_{16}$ ($C_{24}$), $C_{18528}:C_{16}$ ($C_2\times C_{12}$), $C_{3088}.C_{96}$ ($C_{24}$), $C_{3088}.C_{96}$ ($C_{24}$), $C_{6176}.C_{48}$ ($C_{24}$), $C_{12352}:C_{24}$ ($C_{24}$), $C_{3088}:C_{96}$ ($C_2\times C_{12}$), $C_{1544}:C_{192}$ ($C_{24}$), $C_{12352}.C_{24}$ ($C_{24}$), $C_{3088}:C_{96}$ ($C_2\times C_{12}$), $C_{6176}:C_{48}$ ($C_2\times C_{12}$), $C_8\times F_{193}$ ($C_{24}$)

Order 222336: $C_{18528}.C_{12}$ ($C_{32}$), $C_{4632}.C_{48}$ ($C_{32}$), $C_{9264}.C_{24}$ ($C_{32}$), $C_{37056}.C_6$ ($C_{32}$), $C_{9264}:C_{24}$ ($C_4\times C_8$), $C_{18528}:C_{12}$ ($C_2\times C_{16}$), $C_{2316}:C_{96}$ ($C_2\times C_{16}$), $C_{9264}.C_{24}$ ($C_2\times C_{16}$), $C_{2316}.C_{96}$ ($C_{32}$), $C_{4632}.C_{48}$ ($C_2\times C_{16}$), $C_{4632}:C_{48}$ ($C_4\times C_8$), $C_6\times F_{193}$ ($C_{32}$)

Order 197632: $C_{12352}:C_{16}$ ($C_3\times C_{12}$), $C_{6176}:C_{32}$ ($C_6^2$), $C_{3088}:C_{64}$ ($C_3\times C_{12}$), $C_{6176}.C_{32}$ ($C_3\times C_{12}$)

Order 148224: $C_{3088}:C_{48}$ ($C_4\times C_{12}$), $C_{3088}.C_{48}$ ($C_2\times C_{24}$), $C_{3088}.C_{48}$ ($C_{48}$), $C_{18528}.C_8$ ($C_{48}$), $C_{2316}:C_{64}$ ($C_{48}$), $C_{18528}:C_8$ ($C_2\times C_{24}$), $C_{12352}:C_{12}$ ($C_{48}$), $C_{1544}.C_{96}$ ($C_{48}$), $C_{6176}:C_{24}$ ($C_2\times C_{24}$), $C_{3088}.C_{48}$ ($C_{48}$), $C_{6176}.C_{24}$ ($C_{48}$), $C_{1544}:C_{96}$ ($C_2\times C_{24}$), $C_{12352}.C_{12}$ ($C_{48}$), $C_{3088}.C_{48}$ ($C_2\times C_{24}$), $C_{1544}:C_{96}$ ($C_2\times C_{24}$), $C_4\times F_{193}$ ($C_{48}$), $C_{1544}.C_{96}$ ($C_{48}$), $C_{3088}:C_{48}$ ($C_4\times C_{12}$)

Order 111168: $C_{1158}.C_{96}$ ($C_{64}$), $C_{4632}.C_{24}$ ($C_2\times C_{32}$), $C_{9264}.C_{12}$ ($C_2\times C_{32}$), $C_{9264}:C_{12}$ ($C_4\times C_{16}$), $C_{4632}.C_{24}$ ($C_4\times C_{16}$), $C_{18528}.C_6$ ($C_2\times C_{32}$), $C_{579}:C_{192}$ ($C_{64}$), $C_{579}:C_{192}$ ($C_{64}$), $C_{4632}:C_{24}$ ($C_8^2$), $C_{579}:C_{192}$ ($C_{64}$), $C_{579}:C_{192}$ ($C_{64}$), $C_{12352}:C_3^2$ ($C_{64}$), $C_{2316}.C_{48}$ ($C_2\times C_{32}$), $C_{1158}:C_{96}$ ($C_2\times C_{32}$), $C_{2316}:C_{48}$ ($C_4\times C_{16}$), $C_3\times F_{193}$ ($C_{64}$)

Order 98816: $C_{6176}:C_{16}$ ($C_6\times C_{12}$), $C_{3088}.C_{32}$ ($C_3\times C_{24}$), $C_{6176}.C_{16}$ ($C_3\times C_{24}$), $C_{12352}:C_8$ ($C_3\times C_{24}$), $C_{3088}:C_{32}$ ($C_6\times C_{12}$), $C_{1544}:C_{64}$ ($C_3\times C_{24}$)

Order 74112: $C_3\times C_{193}:(C_4\times C_{32})$ ($C_2\times C_{48}$), $C_3\times C_{193}:(C_2\times C_{64})$ ($C_{96}$), $C_3\times C_{193}:(C_4\times C_{32})$ ($C_2\times C_{48}$), $C_{24}\times C_{193}:C_{16}$ ($C_4\times C_{24}$), $C_{18528}.C_4$ ($C_{96}$), $D_{193}:C_{192}$ ($C_{96}$), $D_{193}:C_{192}$ ($C_{96}$), $C_{12352}.C_6$ ($C_{96}$), $D_{193}:C_{192}$ ($C_{96}$), $C_{12352}:C_6$ ($C_{96}$), $D_{193}:C_{192}$ ($C_{96}$), $C_{3088}:C_{24}$ ($C_4\times C_{24}$), $C_{18528}.C_4$ ($C_2\times C_{48}$), $D_{193}:C_{192}$ ($C_{96}$), $C_{2316}:C_{32}$ ($C_2\times C_{48}$), $C_{1158}:C_{64}$ ($C_{96}$), $C_{3088}:C_{24}$ ($C_4\times C_{24}$), $C_{3088}.C_{24}$ ($C_2\times C_{48}$), $C_{6176}:C_{12}$ ($C_2\times C_{48}$), $D_{193}:C_{192}$ ($C_{96}$), $C_{772}:C_{96}$ ($C_2\times C_{48}$), $C_{1544}.C_{48}$ ($C_2\times C_{48}$), $C_{1544}:C_{48}$ ($C_4\times C_{24}$), $C_2\times F_{193}$ ($C_{96}$)

Order 55584: $C_{24}\times C_{193}:C_{12}$ ($C_8\times C_{16}$), $C_{96}\times C_{193}:C_3$ ($C_2\times C_{64}$), $C_3\times C_{193}:C_{96}$ ($C_2\times C_{64}$), $C_{9264}.C_6$ ($C_4\times C_{32}$), $C_{4632}.C_{12}$ ($C_4\times C_{32}$), $C_{2316}:C_{24}$ ($C_8\times C_{16}$), $C_{579}:C_{96}$ ($C_2\times C_{64}$), $C_{579}:C_{96}$ ($C_2\times C_{64}$), $C_{2316}.C_{24}$ ($C_4\times C_{32}$), $C_{579}:C_{96}$ ($C_2\times C_{64}$), $C_{579}:C_{96}$ ($C_2\times C_{64}$), $C_{1158}:C_{48}$ ($C_4\times C_{32}$)

Order 49408: $C_{772}:C_{64}$ ($C_3\times C_{48}$), $C_{1544}.C_{32}$ ($C_3\times C_{48}$), $C_{1544}:C_{32}$ ($C_6\times C_{24}$), $C_{3088}.C_{16}$ ($C_3\times C_{48}$), $C_{3088}.C_{16}$ ($C_6\times C_{24}$), $C_{3088}:C_{16}$ ($C_{12}^2$), $C_{6176}.C_8$ ($C_3\times C_{48}$), $C_{6176}:C_8$ ($C_6\times C_{24}$), $C_{12352}:C_4$ ($C_3\times C_{48}$)

Order 37056: $C_{24}\times C_{193}:C_8$ ($C_8\times C_{24}$), $C_3\times C_{193}:(C_4\times C_{16})$ ($C_4\times C_{48}$), $C_3\times C_{193}:(C_2\times C_{32})$ ($C_2\times C_{96}$), $C_{48}\times C_{193}:C_4$ ($C_4\times C_{48}$), $C_3\times C_{193}:C_{64}$ ($C_{192}$), $C_{96}\times D_{193}$ ($C_2\times C_{96}$), $C_3\times C_{193}:C_{64}$ ($C_{192}$), $C_{772}.C_{48}$ ($C_{192}$), $C_{2316}:C_{16}$ ($C_4\times C_{48}$), $D_{193}:C_{96}$ ($C_2\times C_{96}$), $C_{1158}:C_{32}$ ($C_2\times C_{96}$), $C_{193}:C_{192}$ ($C_{192}$), $C_{37056}$ ($C_{192}$), $D_{193}:C_{96}$ ($C_2\times C_{96}$), $C_{193}:C_{192}$ ($C_{192}$), $C_{12352}:C_3$ ($C_{192}$), $C_{193}:C_{192}$ ($C_{192}$), $C_{3088}:C_{12}$ ($C_4\times C_{48}$), $C_{193}:C_{192}$ ($C_{192}$), $C_{1544}:C_{24}$ ($C_8\times C_{24}$), $C_{193}:C_{192}$ ($C_{192}$), $C_{193}:C_{192}$ ($C_{192}$), $D_{193}:C_{96}$ ($C_2\times C_{96}$), $C_{386}:C_{96}$ ($C_2\times C_{96}$), $C_{193}:C_{192}$ ($C_{192}$), $C_{1544}.C_{24}$ ($C_4\times C_{48}$), $C_{193}:C_{192}$ ($C_{192}$), $D_{193}:C_{96}$ ($C_2\times C_{96}$), $C_{6176}:C_6$ ($C_2\times C_{96}$), $D_{193}:C_{96}$ ($C_2\times C_{96}$), $C_{772}:C_{48}$ ($C_4\times C_{48}$), $F_{193}$ ($C_{192}$)

Order 27792: $C_{12}\times C_{193}:C_{12}$ ($C_{16}^2$), $C_{24}\times C_{193}:C_6$ ($C_8\times C_{32}$), $C_3\times C_{193}:C_{48}$ ($C_4\times C_{64}$), $C_{48}\times C_{193}:C_3$ ($C_4\times C_{64}$), $C_3\times C_{193}:(C_2\times C_{24})$ ($C_8\times C_{32}$), $C_3\times C_{193}:C_{48}$ ($C_4\times C_{64}$), $C_{579}:C_{48}$ ($C_4\times C_{64}$), $C_{1158}:C_{24}$ ($C_8\times C_{32}$), $C_{579}:C_{48}$ ($C_4\times C_{64}$)

Order 24704: $C_{64}\times D_{193}$ ($C_3\times C_{96}$), $C_{386}:C_{64}$ ($C_3\times C_{96}$), $D_{193}:C_{64}$ ($C_3\times C_{96}$), $C_{772}:C_{32}$ ($C_6\times C_{48}$), $D_{193}:C_{64}$ ($C_3\times C_{96}$), $C_{1544}.C_{16}$ ($C_6\times C_{48}$), $C_{1544}:C_{16}$ ($C_{12}\times C_{24}$), $D_{193}:C_{64}$ ($C_3\times C_{96}$), $C_{3088}.C_8$ ($C_6\times C_{48}$), $C_{3088}:C_8$ ($C_{12}\times C_{24}$), $D_{193}:C_{64}$ ($C_3\times C_{96}$), $C_{6176}:C_4$ ($C_6\times C_{48}$)

Order 18528: $C_3\times C_{193}:(C_2\times C_{16})$ ($C_4\times C_{96}$), $C_{32}\times C_{193}:C_3$ ($C_2\times C_{192}$), $C_3\times C_{193}:C_{32}$ ($C_2\times C_{192}$), $C_8\times C_{193}:C_{12}$ ($C_8\times C_{48}$), $C_{1544}:C_{12}$ ($C_8\times C_{48}$), $C_{48}\times D_{193}$ ($C_4\times C_{96}$), $C_{2316}:C_8$ ($C_8\times C_{48}$), $D_{193}:C_{48}$ ($C_4\times C_{96}$), $C_{3088}:C_6$ ($C_4\times C_{96}$), $C_{772}:C_{24}$ ($C_8\times C_{48}$), $D_{193}:C_{48}$ ($C_4\times C_{96}$), $C_{18528}$ ($C_2\times C_{192}$), $C_{193}:C_{96}$ ($C_2\times C_{192}$), $C_{1158}:C_{16}$ ($C_4\times C_{96}$), $C_{193}:C_{96}$ ($C_2\times C_{192}$), $C_{193}:C_{96}$ ($C_2\times C_{192}$), $C_{193}:C_{96}$ ($C_2\times C_{192}$), $C_{193}:C_{96}$ ($C_2\times C_{192}$), $C_{193}:C_{96}$ ($C_2\times C_{192}$), $D_{193}:C_{48}$ ($C_4\times C_{96}$), $C_{193}:C_{96}$ ($C_2\times C_{192}$), $C_{193}:C_{96}$ ($C_2\times C_{192}$), $C_{193}:C_{96}$ ($C_2\times C_{192}$), $C_{386}:C_{48}$ ($C_4\times C_{96}$)

Order 13896: $C_3\times C_{193}:C_{24}$ ($C_8\times C_{64}$), $C_{12}\times C_{193}:C_6$ ($C_{16}\times C_{32}$), $C_3\times C_{193}:C_{24}$ ($C_8\times C_{64}$), $C_6\times C_{193}:C_{12}$ ($C_{16}\times C_{32}$), $C_{4632}:C_3$ ($C_8\times C_{64}$), $C_{579}:C_{24}$ ($C_8\times C_{64}$)

Order 12352: $C_{32}\times D_{193}$ ($C_6\times C_{96}$), $C_{193}:C_{64}$ ($C_3\times C_{192}$), $C_{193}:C_{64}$ ($C_3\times C_{192}$), $C_{386}:C_{32}$ ($C_6\times C_{96}$), $C_{193}:C_{64}$ ($C_3\times C_{192}$), $D_{193}:C_{32}$ ($C_6\times C_{96}$), $C_{772}:C_{16}$ ($C_{12}\times C_{48}$), $C_{193}:C_{64}$ ($C_3\times C_{192}$), $D_{193}:C_{32}$ ($C_6\times C_{96}$), $C_{1544}.C_8$ ($C_{12}\times C_{48}$), $C_{1544}:C_8$ ($C_{24}^2$), $C_{193}:C_{64}$ ($C_3\times C_{192}$), $D_{193}:C_{32}$ ($C_6\times C_{96}$), $C_{3088}:C_4$ ($C_{12}\times C_{48}$), $C_{193}:C_{64}$ ($C_3\times C_{192}$), $C_{12352}$ ($C_3\times C_{192}$)

Order 9264: $C_{193}:(C_2\times C_{24})$ ($C_8\times C_{96}$), $C_{24}\times D_{193}$ ($C_8\times C_{96}$), $C_{193}:C_{48}$ ($C_4\times C_{192}$), $C_8\times C_{193}:C_6$ ($C_8\times C_{96}$), $C_3\times C_{193}:C_{16}$ ($C_4\times C_{192}$), $C_2\times C_{193}:C_{24}$ ($C_8\times C_{96}$), $C_4\times C_{193}:C_{12}$ ($C_{16}\times C_{48}$), $C_3\times C_{193}:C_{16}$ ($C_4\times C_{192}$), $C_3\times C_{193}:C_{16}$ ($C_4\times C_{192}$), $C_{2316}:C_4$ ($C_{16}\times C_{48}$), $C_{9264}$ ($C_4\times C_{192}$), $C_{193}:C_{48}$ ($C_4\times C_{192}$), $C_{1158}:C_8$ ($C_8\times C_{96}$), $C_{193}:C_{48}$ ($C_4\times C_{192}$), $D_{193}:C_{24}$ ($C_8\times C_{96}$), $C_{193}:C_{48}$ ($C_4\times C_{192}$), $C_{193}:C_{48}$ ($C_4\times C_{192}$), $C_{193}:C_{48}$ ($C_4\times C_{192}$)

Order 6948: $C_{579}:C_{12}$ ($C_{16}\times C_{64}$), $C_{1158}:C_6$ ($C_{32}^2$), $C_{2316}:C_3$ ($C_{16}\times C_{64}$), $C_{579}:C_{12}$ ($C_{16}\times C_{64}$)

Order 6176: $C_{16}\times D_{193}$ ($C_{12}\times C_{96}$), $C_{193}:C_{32}$ ($C_6\times C_{192}$), $C_{193}:C_{32}$ ($C_6\times C_{192}$), $C_{386}:C_{16}$ ($C_{12}\times C_{96}$), $C_{193}:C_{32}$ ($C_6\times C_{192}$), $D_{193}:C_{16}$ ($C_{12}\times C_{96}$), $C_{772}:C_8$ ($C_{24}\times C_{48}$), $C_{193}:C_{32}$ ($C_6\times C_{192}$), $D_{193}:C_{16}$ ($C_{12}\times C_{96}$), $C_{1544}:C_4$ ($C_{24}\times C_{48}$), $C_{193}:C_{32}$ ($C_6\times C_{192}$), $C_{6176}$ ($C_6\times C_{192}$)

Order 4632: $C_{193}:C_{24}$ ($C_8\times C_{192}$), $C_3\times C_{193}:C_8$ ($C_8\times C_{192}$), $C_4\times C_{193}:C_6$ ($C_{16}\times C_{96}$), $C_3\times C_{193}:C_8$ ($C_8\times C_{192}$), $C_3\times C_{193}:C_8$ ($C_8\times C_{192}$), $C_{12}\times D_{193}$ ($C_{16}\times C_{96}$), $C_{4632}$ ($C_8\times C_{192}$), $C_{1158}:C_4$ ($C_{16}\times C_{96}$), $C_{1544}:C_3$ ($C_8\times C_{192}$), $C_{193}:C_{24}$ ($C_8\times C_{192}$), $C_{193}:C_{24}$ ($C_8\times C_{192}$), $C_{386}:C_{12}$ ($C_{16}\times C_{96}$)

Order 3474: $C_{1158}:C_3$ ($C_{32}\times C_{64}$), $C_{579}:C_6$ ($C_{32}\times C_{64}$)

Order 3088: $C_{193}:C_{16}$ ($C_{12}\times C_{192}$), $C_{386}:C_8$ ($C_{24}\times C_{96}$), $C_{193}:C_{16}$ ($C_{12}\times C_{192}$), $D_{193}:C_8$ ($C_{24}\times C_{96}$), $C_{772}:C_4$ ($C_{48}^2$), $C_{193}:C_{16}$ ($C_{12}\times C_{192}$), $C_8\times D_{193}$ ($C_{24}\times C_{96}$), $C_{193}:C_{16}$ ($C_{12}\times C_{192}$), $C_{3088}$ ($C_{12}\times C_{192}$)

Order 2316: $C_3\times D_{386}$ ($C_{32}\times C_{96}$), $C_{193}:C_{12}$ ($C_{16}\times C_{192}$), $C_{193}:C_{12}$ ($C_{16}\times C_{192}$), $C_{386}:C_6$ ($C_{32}\times C_{96}$), $C_{193}:C_{12}$ ($C_{16}\times C_{192}$), $C_{193}:C_{12}$ ($C_{16}\times C_{192}$), $C_{193}:C_{12}$ ($C_{16}\times C_{192}$), $C_{2316}$ ($C_{16}\times C_{192}$)

Order 1737: $C_{579}:C_3$ ($C_{64}^2$)

Order 1544: $C_4\times D_{193}$ ($C_{48}\times C_{96}$), $C_{193}:C_8$ ($C_{24}\times C_{192}$), $C_{193}:C_8$ ($C_{24}\times C_{192}$), $C_{386}:C_4$ ($C_{48}\times C_{96}$), $C_{193}:C_8$ ($C_{24}\times C_{192}$), $C_{1544}$ ($C_{24}\times C_{192}$)

Order 1158: $C_{1158}$ ($C_{32}\times C_{192}$), $C_3\times D_{193}$ ($C_{32}\times C_{192}$), $C_{193}:C_6$ ($C_{32}\times C_{192}$), $C_{193}:C_6$ ($C_{32}\times C_{192}$)

Order 772: $D_{386}$ ($C_{96}^2$), $C_{193}:C_4$ ($C_{48}\times C_{192}$), $C_{772}$ ($C_{48}\times C_{192}$), $C_{193}:C_4$ ($C_{48}\times C_{192}$)

Order 579: $C_{579}$ ($C_{64}\times C_{192}$), $C_{193}:C_3$ ($C_{64}\times C_{192}$)

Order 386: $C_{386}$ ($C_{96}\times C_{192}$), $D_{193}$ ($C_{96}\times C_{192}$)

Order 193: $C_{193}$ ($C_{192}^2$)

Order 192: $C_{192}$ ($F_{193}$)

Order 96: $C_{96}$ ($C_2\times F_{193}$)

Order 64: $C_{64}$ ($C_3\times F_{193}$)

Order 48: $C_{48}$ ($C_4\times F_{193}$)

Order 32: $C_{32}$ ($C_6\times F_{193}$)

Order 24: $C_{24}$ ($C_8\times F_{193}$)

Order 16: $C_{16}$ ($C_{12}\times F_{193}$)

Order 12: $C_{12}$ ($C_{16}\times F_{193}$)

Order 8: $C_8$ ($C_{24}\times F_{193}$)

Order 6: $C_6$ ($C_{6176}.C_{192}$)

Order 4: $C_4$ ($C_{9264}.C_{192}$)

Order 3: $C_3$ ($C_{12352}.C_{192}$)

Order 2: $C_2$ ($C_{18528}.C_{192}$)

Order 1: $C_1$ ($C_{193}:C_{192}^2$)

Series

Derived series

$C_{193}:C_{192}^2$

$\rhd$

$C_{193}$

$\rhd$

$C_1$

Chief series

$C_{193}:C_{192}^2$

$\rhd$

$C_{192}\times C_{193}:C_{96}$

$\rhd$

$C_{37056}.C_{48}$

$\rhd$

$C_{37056}.C_{24}$

$\rhd$

$C_{37056}.C_{12}$

$\rhd$

$C_{37056}.C_6$

$\rhd$

$C_{12352}:C_3^2$

$\rhd$

$C_{37056}$

$\rhd$

$C_{18528}$

$\rhd$

$C_{9264}$

$\rhd$

$C_{4632}$

$\rhd$

$C_{2316}$

$\rhd$

$C_{1158}$

$\rhd$

$C_{579}$

$\rhd$

$C_{193}$

$\rhd$

$C_1$

Lower central series

$C_{193}:C_{192}^2$

$\rhd$

$C_{193}$

Upper central series

$C_1$

$\lhd$

$C_{192}$

Character theory

Complex character table

The $37056 \times 37056$ character table is not available for this group.

Rational character table

The $964 \times 964$ rational character table is not available for this group.