Subgroups — #37574396

Order 24448.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈×Dic₁₉₁	C₂	1	2	yes	maximal, complemented
2	#27132491	C₂	1	1	yes	maximal, characteristic, complemented
3	#27132464	C₂	1	2	yes	maximal, complemented
4	#27132438	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₆×C₁₉₁	C₂	1	1	yes	maximal, characteristic
6	D₄×Dic₁₉₁	—	2	2	no	—
7	C₂×C₁₉₁⋊C₁₆	C₂²	1	1	yes	characteristic
8	#20259256	C₂²	1	2	yes	—
9	#20259243	—	2	2	no	—
10	C₈×Dic₁₉₁	C₂²	1	1	yes	characteristic
11	C₂×D₈×C₁₉₁	C₂²	1	2	yes	—
12	D₁₆×C₁₉₁	C₄	1	4	yes	complemented
13	C₂×C₁₆×C₁₉₁	C₂²	1	1	yes	characteristic
14	C₂²×Dic₁₉₁	—	4	2	no	—
15	C₂×C₁₉₁⋊C₈	D₄	1	1	yes	characteristic
16	C₄⋊Dic₁₉₁	—	2	2	no	—
17	C₂²⋊Dic₁₉₁	—	4	2	no	—
18	C₄×Dic₁₉₁	D₄	1	1	yes	characteristic
19	C₁₉₁⋊C₁₆	—	2	1	no	—
20	C₂×D₄×C₁₉₁	—	2	2	no	—
21	D₈×C₁₉₁	—	2	2	no	—
22	D₈×C₁₉₁	C₂×C₄	1	4	yes	complemented
23	C₂×C₈×C₁₉₁	C₂³	1	1	yes	characteristic
24	C₁₆×C₁₉₁	C₂×C₄	1	2	yes	complemented
25	C₂×Dic₁₉₁	—	4	2	no	—
26	C₂×Dic₁₉₁	—	8	4	no	—
27	C₂×Dic₁₉₁	D₈	1	2	yes	—
28	C₁₉₁⋊C₈	—	2	1	no	—
29	C₂³×C₁₉₁	—	4	2	no	—
30	D₄×C₁₉₁	—	2	4	no	—
31	D₄×C₁₉₁	—	4	2	no	—
32	C₂×C₄×C₁₉₁	C₂×D₄	1	1	yes	characteristic
33	C₈×C₁₉₁	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₁₉₁	#41	1	1	yes	characteristic
35	C₂²×C₁₉₁	—	4	4	no	—
36	C₂²×C₁₉₁	—	8	2	no	—
37	C₂²×C₁₉₁	—	8	2	no	—
38	C₂²×C₁₉₁	C₂×D₈	1	1	yes	characteristic
39	C₄×C₁₉₁	C₄×D₄	1	1	yes	characteristic
40	C₄×C₁₉₁	#135	1	1	yes	characteristic
41	Dic₁₉₁	—	2	2	no	—
42	Dic₁₉₁	—	8	2	no	—
43	C₂×C₁₉₁	—	8	4	no	—
44	C₂×C₁₉₁	C₄×D₈	1	1	yes	characteristic
45	C₂×C₁₉₁	#509	1	2	yes	—
46	C₁₉₁	#2177	1	1	yes	characteristic, complemented, Sylow
47	#2177	—	191	1	no	maximal, Sylow
48	C₂×D₁₆	D₁₉₁	1	1	yes	characteristic
49	C₄×D₈	—	191	2	no	—
50	#367	—	191	1	no	—
51	#357	—	191	2	no	—
52	#346	—	191	1	no	—
53	C₂×D₈	C₂×D₁₉₁	1	2	yes	—
54	C₄×D₄	—	382	2	no	—
55	D₁₆	Dic₁₉₁	1	4	yes	complemented
56	C₂×C₁₆	—	191	1	no	—
57	C₂×C₁₆	C₂×D₁₉₁	1	1	yes	characteristic
58	#107	—	191	2	no	—
59	#102	—	382	2	no	—
60	C₄×C₈	—	191	1	no	—
61	C₂×D₄	—	2	2	no	—
62	C₂²×C₄	—	764	2	no	—
63	D₈	—	2	2	no	—
64	D₈	C₂×Dic₁₉₁	1	4	yes	complemented
65	C₂×C₈	—	191	1	no	—
66	C₂×C₈	C₂²×D₁₉₁	1	1	yes	characteristic
67	C₄⋊C₄	—	382	2	no	—
68	C₂²⋊C₄	—	764	2	no	—
69	C₄²	—	191	1	no	—
70	C₁₆	—	382	1	no	—
71	C₁₆	C₂×Dic₁₉₁	1	2	yes	complemented
72	C₂³	—	4	2	no	—
73	D₄	—	2	4	no	—
74	D₄	—	4	2	no	—
75	C₂×C₄	—	191	2	no	—
76	C₂×C₄	—	1528	4	no	—
77	C₂×C₄	—	764	2	no	—
78	C₂×C₄	D₄×D₁₉₁	1	1	yes	characteristic
79	C₈	—	382	1	no	—
80	C₈	C₂²×Dic₁₉₁	1	1	yes	characteristic
81	C₈	#15690286	1	1	yes	characteristic
82	C₂²	—	4	4	no	—
83	C₂²	—	8	2	no	—
84	C₂²	—	8	2	no	—
85	C₂²	D₈×D₁₉₁	1	1	yes	characteristic
86	C₄	—	382	2	no	—
87	C₄	—	1528	2	no	—
88	C₄	D₄×Dic₁₉₁	1	1	yes	characteristic
89	C₄	#20259341	1	1	yes	characteristic
90	C₂	—	8	4	no	—
91	C₂	D₈×Dic₁₉₁	1	1	yes	characteristic
92	C₂	#27133097	1	2	yes	—

	subgroup	G/H
center	C₂²	D₈×D₁₉₁
commutator	C₈×C₁₉₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₉₁
Fitting, prime radical	C₂×D₁₆×C₁₉₁	C₂
socle	C₂²×C₁₉₁	C₂×D₈
cosocle	C₂×C₈×C₁₉₁	C₂³
hypercenter	C₂×D₁₆	D₁₉₁
hypocenter	C₁₉₁	#2177
LCS	G ▷ C₈×C₁₉₁ ▷ C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

Complements

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

N	H ≅ G/N	type
1. D₈×Dic₁₉₁	C₂	semidirect
2. #27132491	C₂	semidirect
3. #27132464	C₂	semidirect
4. #27132438	C₂	semidirect
12. D₁₆×C₁₉₁	C₄	semidirect
22. D₈×C₁₉₁	C₂×C₄	semidirect
24. C₁₆×C₁₉₁	C₂×C₄	semidirect
46. C₁₉₁	#2177	semidirect
55. D₁₆	Dic₁₉₁	semidirect
64. D₈	C₂×Dic₁₉₁	semidirect
71. C₁₆	C₂×Dic₁₉₁	semidirect

Maximal subgroups

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

subgroup	index
D₈×Dic₁₉₁	2
#27132491	2
#27132464	2
#27132438	2
C₂×D₁₆×C₁₉₁	2
#2177	191