Subgroups — #37570515

Order 24448.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27132921	C₂	1	1	yes	maximal, characteristic
2	C₁₉₁⋊#338	C₂	1	1	yes	maximal, characteristic
3	#349×C₁₉₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₆₄	C₄	1	1	yes	characteristic
5	C₂×#15690271	—	2	1	no	—
6	#20259301	—	2	1	no	—
7	#20259254	C₄	1	1	yes	characteristic
8	#20259247	—	2	1	no	—
9	C₂×M₁₆×C₁₉₁	C₂²	1	1	yes	characteristic
10	M₃₂×C₁₉₁	—	2	1	no	—
11	C₂×Dic₃₈₂	—	2	1	no	—
12	Dic₇₆₄	—	4	1	no	—
13	#15690271	—	4	1	no	—
14	#15690271	—	4	1	no	—
15	C₂×C₁₉₁⋊C₈	—	2	2	no	—
16	C₄⋊Dic₁₉₁	—	2	1	no	—
17	Dic₁₉₁⋊C₄	—	4	1	no	—
18	C₂²⋊Dic₁₉₁	—	4	1	no	—
19	C₂²×C₄×C₁₉₁	D₄	1	1	yes	characteristic
20	M₁₆×C₁₉₁	—	4	1	no	—
21	C₂×C₈×C₁₉₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₁₉₁	D₄	1	1	yes	characteristic
23	C₁₆×C₁₉₁	—	4	1	no	—
24	Dic₃₈₂	—	4	1	no	—
25	Dic₃₈₂	—	4	1	no	—
26	C₂×Dic₁₉₁	—	4	1	no	—
27	C₂×Dic₁₉₁	—	4	1	no	—
28	C₁₉₁⋊C₈	—	4	2	no	—
29	C₂³×C₁₉₁	SD₁₆	1	1	yes	characteristic
30	C₂×C₄×C₁₉₁	—	2	1	no	—
31	C₂×C₄×C₁₉₁	—	2	1	no	—
32	C₂×C₄×C₁₉₁	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₉₁	D₈	1	1	yes	characteristic
34	C₈×C₁₉₁	—	2	1	no	—
35	C₈×C₁₉₁	—	2	1	no	—
36	C₂²×C₁₉₁	—	2	1	no	—
37	C₂²×C₁₉₁	—	4	1	no	—
38	C₂²×C₁₉₁	#102	1	1	yes	characteristic
39	C₄×C₁₉₁	—	2	1	no	—
40	C₄×C₁₉₁	#99	1	1	yes	characteristic
41	C₄×C₁₉₁	#104	1	1	yes	characteristic
42	Dic₁₉₁	—	8	1	no	—
43	Dic₁₉₁	—	8	1	no	—
44	C₂×C₁₉₁	—	2	1	no	—
45	C₂×C₁₉₁	—	4	1	no	—
46	C₂×C₁₉₁	#327	1	1	yes	characteristic
47	C₁₉₁	#1342	1	1	yes	characteristic, complemented, Sylow
48	#1342	—	191	1	no	maximal, Sylow
49	#470	—	191	1	no	—
50	#349	D₁₉₁	1	1	yes	characteristic
51	#338	—	191	1	no	—
52	C₂×Q₁₆	—	191	1	no	—
53	C₂×M₁₆	—	382	1	no	—
54	C₂×M₁₆	C₂×D₁₉₁	1	1	yes	characteristic
55	C₂²⋊Q₈	—	382	1	no	—
56	M₃₂	—	2	1	no	—
57	#106	—	191	1	no	—
58	#103	—	382	1	no	—
59	C₂×Q₈	—	382	1	no	—
60	C₂²×C₄	D₇₆₄	1	1	yes	characteristic
61	Q₁₆	—	764	1	no	—
62	M₁₆	—	4	1	no	—
63	M₁₆	—	764	1	no	—
64	M₁₆	—	764	1	no	—
65	C₂×C₈	—	382	2	no	—
66	C₂×C₈	C₄×D₁₉₁	1	1	yes	characteristic
67	C₂×C₈	C₂²⋊D₁₉₁	1	1	yes	characteristic
68	C₄⋊C₄	—	382	1	no	—
69	C₄⋊C₄	—	764	1	no	—
70	C₂²⋊C₄	—	764	1	no	—
71	C₁₆	—	4	1	no	—
72	C₂³	#15690276	1	1	yes	characteristic
73	Q₈	—	764	1	no	—
74	Q₈	—	764	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	764	1	no	—
78	C₂×C₄	—	764	1	no	—
79	C₂×C₄	(C₂×D₁₉₁)⋊C₄	1	1	yes	characteristic
80	C₂×C₄	D₁₅₂₈	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	2	1	no	—
83	C₈	—	764	2	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#20259244	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	1528	1	no	—
89	C₄	—	1528	1	no	—
90	C₄	#20259236	1	1	yes	characteristic
91	C₄	#20259248	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	4	1	no	—
94	C₂	#27132398	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#27132398
commutator	C₂×C₈×C₁₉₁	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₁₉₁
Fitting	#349×C₁₉₁	C₂
socle	C₂×C₁₉₁	#327
prime radical	C₂³×C₁₉₁	SD₁₆
cosocle	C₂×M₁₆×C₁₉₁	C₂²
hypercenter	#349	D₁₉₁
hypocenter	C₁₉₁	#1342
LCS	G ▷ C₂×C₈×C₁₉₁ ▷ C₂×C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

Complements

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

N	H ≅ G/N	type
47. C₁₉₁	#1342	semidirect

Maximal subgroups

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

subgroup	index
#27132921	2
C₁₉₁⋊#338	2
#349×C₁₉₁	2
#1342	191