Subgroups — #37572134

Order 24448.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27133040	C₂	1	1	yes	maximal, characteristic, complemented
2	#27133039	C₂	1	4	yes	maximal, complemented
3	C₈×C₁₉₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#493×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₅₂₈	—	2	2	no	—
6	C₂×#15690272	—	2	8	no	—
7	#20259319	C₂²	1	2	yes	—
8	C₄×C₁₉₁⋊C₈	C₂²	1	2	yes	—
9	C₂×D₈×C₁₉₁	—	2	2	no	—
10	#127×C₁₉₁	C₂²	1	2	yes	—
11	C₄×C₈×C₁₉₁	C₂²	1	1	yes	characteristic
12	C₂×D₇₆₄	—	2	4	no	—
13	C₂×D₇₆₄	—	2	2	no	—
14	D₁₅₂₈	—	4	4	no	—
15	#15690272	—	4	16	no	—
16	C₂×C₁₉₁⋊C₈	D₄	1	4	yes	—
17	C₂×D₄×C₁₉₁	—	2	4	no	—
18	C₂×D₄×C₁₉₁	—	2	2	no	—
19	D₈×C₁₉₁	—	4	4	no	—
20	C₂×C₈×C₁₉₁	D₄	1	2	yes	—
21	C₄²×C₁₉₁	C₂³	1	1	yes	characteristic
22	C₂²×D₁₉₁	—	4	2	no	—
23	D₇₆₄	—	4	8	no	—
24	D₇₆₄	—	4	4	no	—
25	C₁₉₁⋊C₈	D₈	1	8	yes	complemented
26	C₂³×C₁₉₁	—	4	2	no	—
27	D₄×C₁₉₁	—	4	4	no	—
28	D₄×C₁₉₁	—	4	8	no	—
29	C₂×C₄×C₁₉₁	C₂×D₄	1	2	yes	—
30	C₂×C₄×C₁₉₁	C₂×D₄	1	1	yes	characteristic
31	C₈×C₁₉₁	D₈	1	4	yes	complemented
32	C₂²×C₁₉₁	—	8	4	no	—
33	C₂²×C₁₉₁	—	8	2	no	—
34	C₂²×C₁₉₁	#127	1	1	yes	characteristic
35	C₂×D₁₉₁	—	8	4	no	—
36	C₂×D₁₉₁	—	8	2	no	—
37	C₄×C₁₉₁	C₂×D₈	1	4	yes	—
38	C₄×C₁₉₁	C₂×D₈	1	2	yes	—
39	C₂×C₁₉₁	—	16	2	no	—
40	C₂×C₁₉₁	#493	1	2	yes	—
41	C₂×C₁₉₁	#493	1	1	yes	characteristic
42	D₁₉₁	—	16	2	no	—
43	C₁₉₁	#1712	1	1	yes	characteristic, complemented, Sylow
44	#1712	—	191	1	no	maximal, Sylow
45	#493	—	191	4	no	—
46	#493	—	191	1	no	—
47	#493	D₁₉₁	1	1	yes	characteristic, complemented
48	C₈²	—	191	1	no	—
49	C₂×D₈	—	2	2	no	—
50	C₂×D₈	—	382	8	no	—
51	C₂×D₈	—	382	2	no	—
52	#127	—	191	2	no	—
53	#127	C₂×D₁₉₁	1	2	yes	—
54	C₄×C₈	—	191	2	no	—
55	C₄×C₈	C₂×D₁₉₁	1	1	yes	characteristic
56	C₂×D₄	—	2	4	no	—
57	C₂×D₄	—	2	2	no	—
58	C₂×D₄	—	382	4	no	—
59	C₂×D₄	—	382	2	no	—
60	D₈	—	4	4	no	—
61	D₈	—	764	16	no	—
62	D₈	—	764	4	no	—
63	C₂×C₈	—	191	4	no	—
64	C₂×C₈	C₂²⋊D₁₉₁	1	2	yes	—
65	C₄²	C₂²×D₁₉₁	1	1	yes	characteristic
66	C₂³	—	4	2	no	—
67	C₂³	—	764	2	no	—
68	D₄	—	4	8	no	—
69	D₄	—	4	4	no	—
70	D₄	—	764	8	no	—
71	D₄	—	764	4	no	—
72	C₂×C₄	D₄×D₁₉₁	1	2	yes	—
73	C₂×C₄	C₂×C₂²⋊D₁₉₁	1	1	yes	characteristic
74	C₈	—	191	8	no	—
75	C₈	#15690272	1	4	yes	complemented
76	C₂²	—	8	4	no	—
77	C₂²	—	8	2	no	—
78	C₂²	—	1528	4	no	—
79	C₂²	—	1528	2	no	—
80	C₂²	#20259318	1	1	yes	characteristic
81	C₄	D₈×D₁₉₁	1	4	yes	—
82	C₄	C₂×#15690272	1	2	yes	—
83	C₂	—	16	2	no	—
84	C₂	—	3056	2	no	—
85	C₂	#27133038	1	2	yes	—
86	C₂	#27133039	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#20259318
commutator, cosocle	C₄²×C₁₉₁	C₂³
Frattini	C₄²	C₂²×D₁₉₁
Fitting	#493×C₁₉₁	C₂
socle	C₂²×C₁₉₁	#127
hypercenter	#493	D₁₉₁
hypocenter	C₁₉₁	#1712
LCS	G ▷ C₄²×C₁₉₁ ▷ C₂²×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

Complements

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

N	H ≅ G/N	type
1. #27133040	C₂	semidirect
2. #27133039	C₂	semidirect
3. C₈×C₁₉₁⋊C₈	C₂	semidirect
4. #493×C₁₉₁	C₂	semidirect
25. C₁₉₁⋊C₈	D₈	semidirect
31. C₈×C₁₉₁	D₈	semidirect
43. C₁₉₁	#1712	semidirect
47. #493	D₁₉₁	semidirect
75. C₈	#15690272	semidirect

Maximal subgroups

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

subgroup	index
#27133040	2
#27133039	2
C₈×C₁₉₁⋊C₈	2
#493×C₁₉₁	2
#1712	191