Subgroups — #37548875

Order 23168.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042212	C₂	1	1	yes	maximal, characteristic, complemented
2	#26042206	C₂	1	1	yes	maximal, characteristic, complemented
3	#26041712	C₂	1	1	yes	maximal, characteristic
4	#19153885	—	2	1	no	—
5	#19153866	—	2	1	no	—
6	#19153839	—	2	1	no	—
7	#19153759	—	2	1	no	—
8	D₂₈₉₆	C₄	1	1	yes	characteristic, complemented
9	C₁₆×D₁₈₁	C₂²	1	1	yes	characteristic
10	Q₃₂×C₁₈₁	C₄	1	1	yes	characteristic, complemented
11	C₄⋊#10624382	—	4	1	no	—
12	#15668450	—	4	1	no	—
13	#15668436	—	4	1	no	—
14	D₁₄₄₈	—	2	1	no	—
15	C₈×D₁₈₁	D₄	1	1	yes	characteristic
16	#15668424	D₄	1	1	yes	characteristic
17	Q₁₆×C₁₈₁	—	2	1	no	—
18	C₁₆×C₁₈₁	C₂×C₄	1	1	yes	characteristic
19	C₂×#10624382	—	8	1	no	—
20	D₇₂₄	—	4	1	no	—
21	D₇₂₄	—	8	1	no	—
22	C₄×D₁₈₁	—	8	1	no	—
23	C₄×D₁₈₁	D₈	1	1	yes	characteristic
24	#13089678	SD₁₆	1	1	yes	characteristic
25	Q₈×C₁₈₁	—	4	1	no	—
26	C₈×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×D₁₈₁	—	8	1	no	—
28	C₂×D₁₈₁	D₁₆	1	1	yes	characteristic
29	#10624382	—	16	1	no	—
30	C₄×C₁₈₁	—	8	1	no	—
31	C₄×C₁₈₁	#102	1	1	yes	characteristic
32	Dic₁₈₁	SD₃₂	1	1	yes	characteristic
33	C₂×C₁₈₁	#357	1	1	yes	characteristic
34	D₁₈₁	—	2	1	no	—
35	D₁₈₁	—	16	1	no	—
36	C₁₈₁	#1418	1	1	yes	characteristic, complemented, Sylow
37	#1418	—	181	1	no	maximal, Sylow
38	#508	—	181	1	no	—
39	M₆₄	—	181	1	no	—
40	#367	—	181	1	no	—
41	#135	—	362	1	no	—
42	Q₃₂	#10624382	1	1	yes	characteristic, complemented
43	SD₃₂	—	362	1	no	—
44	D₁₆	—	181	1	no	—
45	C₂×C₁₆	—	181	1	no	—
46	#107	—	362	1	no	—
47	C₃₂	—	362	1	no	—
48	#41	—	724	1	no	—
49	Q₁₆	—	2	1	no	—
50	SD₁₆	—	724	1	no	—
51	D₈	—	362	1	no	—
52	C₂×C₈	—	181	1	no	—
53	C₄⋊C₄	—	724	1	no	—
54	C₁₆	—	181	1	no	—
55	C₁₆	C₂×#10624382	1	1	yes	characteristic
56	Q₈	—	4	1	no	—
57	D₄	—	1448	1	no	—
58	D₄	—	724	1	no	—
59	C₂×C₄	—	1448	1	no	—
60	C₂×C₄	—	1448	1	no	—
61	C₂×C₄	—	181	1	no	—
62	C₈	—	181	1	no	—
63	C₈	C₂²⋊#10624382	1	1	yes	characteristic
64	C₂²	—	1448	1	no	—
65	C₂²	—	181	1	no	—
66	C₄	—	8	1	no	—
67	C₄	—	2896	1	no	—
68	C₄	—	181	1	no	—
69	C₄	#19153878	1	1	yes	characteristic
70	C₂	—	2896	1	no	—
71	C₂	—	362	1	no	—
72	C₂	#26042191	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26042191
commutator	C₁₆×C₁₈₁	C₂×C₄
Frattini	C₁₆	C₂×#10624382
Fitting	Q₃₂×C₁₈₁	C₄
socle	C₂×C₁₈₁	#357
prime radical	#26041712	C₂
cosocle	C₁₆×D₁₈₁	C₂²
hypercenter	Q₃₂	#10624382
hypocenter	C₁₈₁	#1418
LCS	G ▷ C₁₆×C₁₈₁ ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
1. #26042212	C₂	semidirect
2. #26042206	C₂	semidirect
8. D₂₈₉₆	C₄	semidirect
10. Q₃₂×C₁₈₁	C₄	semidirect
36. C₁₈₁	#1418	semidirect
42. Q₃₂	#10624382	semidirect

Maximal subgroups

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

subgroup	index
#26042212	2
#26042206	2
#26041712	2
#1418	181