Subgroups — #37570497

Order 24448.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27132781	C₂	1	1	yes	maximal, characteristic
2	#27132484	C₂	1	1	yes	maximal, characteristic, complemented
3	#322×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#20259344	C₄	1	1	yes	characteristic
5	#20259328	—	2	1	no	—
6	#20259262	—	2	1	no	—
7	#20259258	C₄	1	1	yes	characteristic
8	#20259250	—	2	1	no	—
9	C₄×C₈×C₁₉₁	—	2	1	no	—
10	C₄×C₈×C₁₉₁	C₂²	1	1	yes	characteristic
11	#15690287	—	2	1	no	—
12	Dic₇₆₄	C₈	1	1	yes	characteristic, complemented
13	#15690276	—	2	1	no	—
14	D₁₅₂₈	C₈	1	1	yes	characteristic, complemented
15	#15690271	—	2	1	no	—
16	#15690270	—	4	1	no	—
17	C₈×D₁₉₁	—	4	1	no	—
18	C₁₉₁⋊C₁₆	—	4	1	no	—
19	C₂×C₈×C₁₉₁	—	2	2	no	—
20	C₂×C₈×C₁₉₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉₁	D₄	1	1	yes	characteristic
22	C₄²×C₁₉₁	D₄	1	1	yes	characteristic
23	Dic₃₈₂	—	2	1	no	—
24	D₇₆₄	—	2	1	no	—
25	C₂²⋊D₁₉₁	—	4	1	no	—
26	C₄×D₁₉₁	—	4	1	no	—
27	C₁₉₁⋊C₈	—	4	1	no	—
28	C₂×C₄×C₁₉₁	—	2	1	no	—
29	C₂×C₄×C₁₉₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₈×C₁₉₁	—	4	2	no	—
31	C₈×C₁₉₁	C₂×C₈	1	1	yes	characteristic
32	C₈×C₁₉₁	M₁₆	1	1	yes	characteristic
33	C₈×C₁₉₁	D₈	1	1	yes	characteristic
34	C₈×C₁₉₁	SD₁₆	1	1	yes	characteristic
35	C₂²×C₁₉₁	#104	1	1	yes	characteristic
36	C₂×D₁₉₁	—	4	1	no	—
37	C₄×C₁₉₁	—	2	2	no	—
38	C₄×C₁₉₁	C₂²⋊C₈	1	1	yes	characteristic
39	C₄×C₁₉₁	#102	1	1	yes	characteristic
40	Dic₁₉₁	—	4	1	no	—
41	C₂×C₁₉₁	—	2	1	no	—
42	C₂×C₁₉₁	D₄⋊C₈	1	1	yes	characteristic
43	D₁₉₁	—	8	1	no	—
44	C₁₉₁	#1336	1	1	yes	characteristic, complemented, Sylow
45	#1336	—	191	1	no	maximal, Sylow
46	#443	—	191	1	no	—
47	#364	—	191	1	no	—
48	#322	D₁₉₁	1	1	yes	characteristic, complemented
49	#135	—	191	1	no	—
50	#131	—	382	1	no	—
51	M₃₂	—	382	1	no	—
52	#108	—	191	1	no	—
53	#104	—	382	1	no	—
54	C₄×C₈	—	2	1	no	—
55	C₄×C₈	C₂×D₁₉₁	1	1	yes	characteristic
56	#41	—	382	1	no	—
57	Q₁₆	—	191	1	no	—
58	SD₁₆	—	382	1	no	—
59	D₈	—	191	1	no	—
60	M₁₆	—	382	1	no	—
61	M₁₆	—	764	1	no	—
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	764	1	no	—
64	C₂×C₈	C₄×D₁₉₁	1	1	yes	characteristic
65	C₂×C₈	D₇₆₄	1	1	yes	characteristic
66	C₄²	C₂²⋊D₁₉₁	1	1	yes	characteristic
67	C₁₆	—	764	1	no	—
68	Q₈	—	382	1	no	—
69	D₄	—	382	1	no	—
70	D₄	—	764	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	764	1	no	—
73	C₂×C₄	(C₂×D₁₉₁)⋊C₄	1	1	yes	characteristic
74	C₈	—	4	2	no	—
75	C₈	—	764	1	no	—
76	C₈	C₈×D₁₉₁	1	1	yes	characteristic
77	C₈	#15690270	1	1	yes	characteristic
78	C₈	D₁₅₂₈	1	1	yes	characteristic
79	C₈	#15690276	1	1	yes	characteristic
80	C₂²	—	764	1	no	—
81	C₂²	#20259250	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	764	1	no	—
84	C₄	(C₂×D₁₉₁)⋊C₈	1	1	yes	characteristic
85	C₄	#20259244	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	1528	1	no	—
88	C₂	#27132392	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#20259244
commutator	C₈×C₁₉₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₉₁
Fitting	#322×C₁₉₁	C₂
socle	C₂×C₁₉₁	D₄⋊C₈
prime radical	#20259344	C₄
cosocle	C₄×C₈×C₁₉₁	C₂²
hypercenter	#322	D₁₉₁
hypocenter	C₁₉₁	#1336
LCS	G ▷ C₈×C₁₉₁ ▷ C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #322

Complements

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

N	H ≅ G/N	type
2. #27132484	C₂	semidirect
3. #322×C₁₉₁	C₂	semidirect
12. Dic₇₆₄	C₈	semidirect
14. D₁₅₂₈	C₈	semidirect
44. C₁₉₁	#1336	semidirect
48. #322	D₁₉₁	semidirect

Maximal subgroups

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

subgroup	index
#27132781	2
#27132484	2
#322×C₁₉₁	2
#1336	191