Subgroups — #27135086

Order 12352.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15690530	C₂	1	1	yes	maximal, characteristic
2	#20259833	C₂	1	1	yes	maximal, characteristic
3	#107×C₁₉₃	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₁₉₃	—	2	1	no	—
5	#15690530	C₄	1	2	yes	complemented
6	C₂×C₈×C₁₉₃	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₁₉₃	—	2	1	no	—
8	C₂×Dic₁₉₃	—	4	1	no	—
9	C₂×C₄×C₁₉₃	—	4	1	no	—
10	C₂×C₄×C₁₉₃	D₄	1	1	yes	characteristic
11	C₈×C₁₉₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₉₃	Q₈	1	1	yes	characteristic
13	C₂²×C₁₉₃	D₈	1	1	yes	characteristic
14	C₄×C₁₉₃	—	8	1	no	—
15	C₄×C₁₉₃	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₁₉₃	Q₁₆	1	1	yes	characteristic
17	Dic₁₉₃	—	8	1	no	—
18	C₂×C₁₉₃	#107	1	1	yes	characteristic
19	C₂×C₁₉₃	SD₃₂	1	1	yes	characteristic
20	C₂×C₁₉₃	SD₃₂	1	1	yes	characteristic
21	C₁₉₃	#367	1	1	yes	characteristic, complemented, Sylow
22	#367	—	193	1	no	maximal, Sylow
23	C₂×C₁₆	—	193	1	no	—
24	#107	—	193	1	no	—
25	#107	D₁₉₃	1	1	yes	characteristic
26	C₂×C₈	C₂×D₁₉₃	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₄⋊C₄	—	386	1	no	—
29	C₁₆	—	193	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	772	1	no	—
32	C₂×C₄	C₂²⋊D₁₉₃	1	1	yes	characteristic
33	C₈	C₄×D₁₉₃	1	1	yes	characteristic
34	C₈	Dic₃₈₆	1	1	yes	characteristic
35	C₂²	#15690540	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	1544	1	no	—
38	C₄	#15690534	1	1	yes	characteristic
39	C₄	#15690545	1	1	yes	characteristic
40	C₂	#20259832	1	1	yes	characteristic
41	C₂	#20259842	1	1	yes	characteristic
42	C₂	#20259843	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15690540
commutator	C₈×C₁₉₃	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₉₃
Fitting	#107×C₁₉₃	C₂
socle, prime radical	C₂²×C₁₉₃	D₈
cosocle	C₂×C₈×C₁₉₃	C₂²
hypercenter	#107	D₁₉₃
hypocenter	C₁₉₃	#367
LCS	G ▷ C₈×C₁₉₃ ▷ C₄×C₁₉₃ ▷ C₂×C₁₉₃ ▷ C₁₉₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
5. #15690530	C₄	semidirect
21. C₁₉₃	#367	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#15690530	2
#20259833	2
#107×C₁₉₃	2
#367	193