Subgroups — #37548739

Order 23168.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042200	C₂	1	1	yes	maximal, characteristic
2	#26042143	C₂	1	1	yes	maximal, characteristic
3	#26041683	C₂	1	1	yes	maximal, characteristic
4	C₂×#15668452	—	2	1	no	—
5	C₄⋊#13089685	—	2	1	no	—
6	#19153815	—	2	1	no	—
7	#19153750	C₄	1	1	yes	characteristic
8	#19153749	—	2	1	no	—
9	C₈×Dic₁₈₁	C₂²	1	1	yes	characteristic
10	#107×C₁₈₁	C₄	1	1	yes	characteristic
11	C₂×#13089685	—	4	1	no	—
12	#15668452	—	4	1	no	—
13	C₂×Dic₃₆₂	—	4	1	no	—
14	C₂×#13089678	D₄	1	1	yes	characteristic
15	C₄⋊Dic₁₈₁	—	2	1	no	—
16	#15668428	—	4	1	no	—
17	C₄×Dic₁₈₁	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
19	C₄⋊C₄×C₁₈₁	—	2	1	no	—
20	#13089685	—	8	1	no	—
21	Dic₃₆₂	—	8	1	no	—
22	Dic₃₆₂	—	8	1	no	—
23	C₂×Dic₁₈₁	—	4	1	no	—
24	C₂×Dic₁₈₁	D₈	1	1	yes	characteristic
25	C₂×Dic₁₈₁	SD₁₆	1	1	yes	characteristic
26	#13089678	SD₁₆	1	1	yes	characteristic
27	#13089678	Q₁₆	1	1	yes	characteristic
28	C₂×C₄×C₁₈₁	—	4	1	no	—
29	C₂×C₄×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₈×C₁₈₁	—	2	1	no	—
31	C₂²×C₁₈₁	#102	1	1	yes	characteristic
32	C₄×C₁₈₁	—	8	1	no	—
33	C₄×C₁₈₁	#101	1	1	yes	characteristic
34	C₄×C₁₈₁	#103	1	1	yes	characteristic
35	Dic₁₈₁	—	2	1	no	—
36	Dic₁₈₁	—	8	1	no	—
37	Dic₁₈₁	D₁₆	1	1	yes	characteristic
38	Dic₁₈₁	SD₃₂	1	1	yes	characteristic
39	C₂×C₁₈₁	#332	1	1	yes	characteristic
40	C₂×C₁₈₁	#357	1	1	yes	characteristic
41	C₂×C₁₈₁	#362	1	1	yes	characteristic
42	C₁₈₁	#1364	1	1	yes	characteristic, complemented, Sylow
43	#1364	—	181	1	no	maximal, Sylow
44	#500	—	181	1	no	—
45	C₄⋊C₁₆	—	181	1	no	—
46	#335	—	181	1	no	—
47	C₄⋊Q₈	—	362	1	no	—
48	C₂×C₁₆	—	362	1	no	—
49	#107	—	362	1	no	—
50	#107	—	181	1	no	—
51	#107	#10624382	1	1	yes	characteristic
52	C₄⋊C₈	—	362	1	no	—
53	C₄×C₈	—	181	1	no	—
54	C₂×Q₈	—	724	1	no	—
55	C₂×C₈	—	181	1	no	—
56	C₂×C₈	—	724	1	no	—
57	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
58	C₄⋊C₄	—	2	1	no	—
59	C₄⋊C₄	—	362	1	no	—
60	C₄⋊C₄	—	724	1	no	—
61	C₄²	—	181	1	no	—
62	C₁₆	—	724	1	no	—
63	Q₈	—	1448	1	no	—
64	Q₈	—	1448	1	no	—
65	C₂×C₄	—	4	1	no	—
66	C₂×C₄	—	181	1	no	—
67	C₂×C₄	—	181	1	no	—
68	C₂×C₄	—	724	1	no	—
69	C₂×C₄	C₂²⋊#10624382	1	1	yes	characteristic
70	C₈	—	2	1	no	—
71	C₈	—	1448	1	no	—
72	C₈	—	181	1	no	—
73	C₈	—	181	1	no	—
74	C₂²	#19153878	1	1	yes	characteristic
75	C₄	—	8	1	no	—
76	C₄	—	362	1	no	—
77	C₄	—	1448	1	no	—
78	C₄	—	181	1	no	—
79	C₄	—	181	1	no	—
80	C₄	#19153877	1	1	yes	characteristic
81	C₄	#19153879	1	1	yes	characteristic
82	C₂	#26042138	1	1	yes	characteristic
83	C₂	#26042191	1	1	yes	characteristic
84	C₂	#26042198	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19153878
commutator	C₂×C₈×C₁₈₁	C₂×C₄
Frattini	C₂×C₈	C₂×#10624382
Fitting	#107×C₁₈₁	C₄
socle, prime radical	C₂²×C₁₈₁	#102
cosocle	C₈×Dic₁₈₁	C₂²
hypercenter	#107	#10624382
hypocenter	C₁₈₁	#1364
LCS	G ▷ C₂×C₈×C₁₈₁ ▷ C₂×C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
42. C₁₈₁	#1364	semidirect

Maximal subgroups

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

subgroup	index
#26042200	2
#26042143	2
#26041683	2
#1364	181