Subgroups — #37570552

Order 24448.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27133028	C₂	1	1	yes	maximal, characteristic
2	#27132441	C₂	1	1	yes	maximal, characteristic, complemented
3	#347×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#20259319	C₄	1	1	yes	characteristic
5	#20259314	C₄	1	1	yes	characteristic
6	#20259262	—	2	1	no	—
7	#20259244	—	2	1	no	—
8	#20259244	—	2	1	no	—
9	M₃₂×C₁₉₁	—	2	1	no	—
10	#97×C₁₉₁	C₂²	1	1	yes	characteristic
11	C₂×D₇₆₄	—	2	1	no	—
12	C₂×D₇₆₄	—	4	1	no	—
13	C₄⋊Dic₁₉₁	—	2	1	no	—
14	Dic₁₉₁⋊C₄	—	4	1	no	—
15	C₁₉₁⋊C₁₆	—	2	2	no	—
16	C₂×C₈×C₁₉₁	D₄	1	1	yes	characteristic
17	C₂×C₈×C₁₉₁	D₄	1	1	yes	characteristic
18	C₄²×C₁₉₁	C₂×C₄	1	1	yes	characteristic
19	C₁₆×C₁₉₁	—	2	2	no	—
20	C₂²×D₁₉₁	—	4	1	no	—
21	D₇₆₄	—	4	1	no	—
22	D₇₆₄	—	4	1	no	—
23	D₇₆₄	—	8	2	no	—
24	C₂×Dic₁₉₁	—	4	1	no	—
25	C₂×C₄×C₁₉₁	—	2	1	no	—
26	C₂×C₄×C₁₉₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₈×C₁₉₁	—	2	1	no	—
28	C₈×C₁₉₁	—	2	1	no	—
29	C₂²×C₁₉₁	#100	1	1	yes	characteristic
30	C₂×D₁₉₁	—	8	2	no	—
31	C₂×D₁₉₁	—	8	1	no	—
32	C₄×C₁₉₁	—	4	1	no	—
33	C₄×C₁₉₁	#104	1	1	yes	characteristic
34	C₄×C₁₉₁	#104	1	1	yes	characteristic
35	Dic₁₉₁	—	8	1	no	—
36	C₂×C₁₉₁	—	2	1	no	—
37	C₂×C₁₉₁	#329	1	1	yes	characteristic
38	D₁₉₁	—	16	1	no	—
39	C₁₉₁	#1355	1	1	yes	characteristic, complemented, Sylow
40	#1355	—	191	1	no	maximal, Sylow
41	#490	—	191	1	no	—
42	#347	—	191	1	no	—
43	#347	D₁₉₁	1	1	yes	characteristic, complemented
44	#127	—	191	1	no	—
45	#125	—	191	1	no	—
46	M₃₂	—	2	1	no	—
47	M₃₂	—	382	1	no	—
48	#102	—	382	1	no	—
49	#102	—	382	1	no	—
50	#97	C₂×D₁₉₁	1	1	yes	characteristic
51	C₂×D₄	—	382	1	no	—
52	C₂×D₄	—	764	1	no	—
53	C₂×C₈	C₂²⋊D₁₉₁	1	1	yes	characteristic
54	C₂×C₈	D₇₆₄	1	1	yes	characteristic
55	C₄⋊C₄	—	382	1	no	—
56	C₄⋊C₄	—	764	1	no	—
57	C₄²	C₄×D₁₉₁	1	1	yes	characteristic
58	C₁₆	—	2	2	no	—
59	C₁₆	—	382	2	no	—
60	C₂³	—	764	1	no	—
61	D₄	—	1528	2	no	—
62	D₄	—	764	1	no	—
63	D₄	—	764	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	764	1	no	—
66	C₂×C₄	(C₂×D₁₉₁)⋊C₄	1	1	yes	characteristic
67	C₈	—	2	1	no	—
68	C₈	—	2	1	no	—
69	C₂²	—	1528	2	no	—
70	C₂²	—	1528	1	no	—
71	C₂²	#20259238	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	1528	1	no	—
74	C₄	#20259248	1	1	yes	characteristic
75	C₄	#20259250	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	3056	1	no	—
78	C₂	#27132402	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#27132402
commutator	C₄²×C₁₉₁	C₂×C₄
Frattini	#97	C₂×D₁₉₁
Fitting	#347×C₁₉₁	C₂
socle	C₂×C₁₉₁	#329
prime radical	#20259319	C₄
cosocle	#97×C₁₉₁	C₂²
hypercenter	#347	D₁₉₁
hypocenter	C₁₉₁	#1355
LCS	G ▷ C₄²×C₁₉₁ ▷ C₂×C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #347

Complements

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

N	H ≅ G/N	type
2. #27132441	C₂	semidirect
3. #347×C₁₉₁	C₂	semidirect
39. C₁₉₁	#1355	semidirect
43. #347	D₁₉₁	semidirect

Maximal subgroups

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

subgroup	index
#27133028	2
#27132441	2
#347×C₁₉₁	2
#1355	191