Subgroups — #37548682

Order 23168.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042168	C₂	1	1	yes	maximal, characteristic
2	#26042140	C₂	1	1	yes	maximal, characteristic
3	#26041373	C₂	1	1	yes	maximal, characteristic
4	C₂×#15668452	—	2	1	no	—
5	C₄⋊#13089685	—	2	1	no	—
6	C₂×Dic₇₂₄	C₄	1	1	yes	characteristic
7	#19153781	—	2	1	no	—
8	#19153739	—	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	—	2	2	no	—
13	C₂×Dic₃₆₂	—	2	1	no	—
14	Dic₇₂₄	—	2	1	no	—
15	Dic₇₂₄	C₈	1	2	yes	complemented
16	C₂×#13089678	D₄	1	1	yes	characteristic
17	#15668428	—	4	1	no	—
18	C₄×Dic₁₈₁	—	4	1	no	—
19	C₄×Dic₁₈₁	D₄	1	1	yes	characteristic
20	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
21	C₄⋊C₄×C₁₈₁	—	2	1	no	—
22	#13089685	—	8	1	no	—
23	Dic₃₆₂	—	2	2	no	—
24	Dic₃₆₂	—	4	1	no	—
25	C₂×Dic₁₈₁	—	4	1	no	—
26	C₂×Dic₁₈₁	D₈	1	1	yes	characteristic
27	C₂×Dic₁₈₁	SD₁₆	1	1	yes	characteristic
28	#13089678	—	2	1	no	—
29	C₂×C₄×C₁₈₁	—	4	1	no	—
30	C₂×C₄×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
31	C₈×C₁₈₁	C₂×C₈	1	1	yes	characteristic
32	C₈×C₁₈₁	M₁₆	1	1	yes	characteristic
33	C₂²×C₁₈₁	#102	1	1	yes	characteristic
34	C₄×C₁₈₁	—	8	1	no	—
35	C₄×C₁₈₁	C₂²⋊C₈	1	1	yes	characteristic
36	C₄×C₁₈₁	#104	1	1	yes	characteristic
37	Dic₁₈₁	—	2	1	no	—
38	Dic₁₈₁	—	2	1	no	—
39	Dic₁₈₁	—	4	2	no	—
40	C₂×C₁₈₁	D₄⋊C₈	1	1	yes	characteristic
41	C₂×C₁₈₁	#360	1	1	yes	characteristic
42	C₂×C₁₈₁	#362	1	1	yes	characteristic
43	C₁₈₁	#1334	1	1	yes	characteristic, complemented, Sylow
44	#1334	—	181	1	no	maximal, Sylow
45	C₄×Q₁₆	—	181	1	no	—
46	#346	—	181	1	no	—
47	#334	—	181	1	no	—
48	C₂×Q₁₆	—	181	1	no	—
49	C₄×Q₈	—	362	1	no	—
50	C₂×C₁₆	—	362	1	no	—
51	#107	#10624382	1	1	yes	characteristic
52	C₄⋊C₈	—	362	1	no	—
53	#103	—	362	1	no	—
54	C₄×C₈	—	181	1	no	—
55	C₂×Q₈	—	362	1	no	—
56	Q₁₆	—	362	1	no	—
57	Q₁₆	—	181	2	no	—
58	C₂×C₈	—	181	1	no	—
59	C₂×C₈	—	724	1	no	—
60	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
61	C₄⋊C₄	—	2	1	no	—
62	C₄⋊C₄	—	724	1	no	—
63	C₄²	—	181	1	no	—
64	C₄²	—	724	1	no	—
65	C₁₆	—	362	2	no	—
66	Q₈	—	362	2	no	—
67	Q₈	—	724	1	no	—
68	C₂×C₄	—	4	1	no	—
69	C₂×C₄	—	181	1	no	—
70	C₂×C₄	—	181	1	no	—
71	C₂×C₄	—	724	1	no	—
72	C₂×C₄	C₂²⋊#10624382	1	1	yes	characteristic
73	C₈	—	362	1	no	—
74	C₈	—	1448	1	no	—
75	C₈	D₁₈₁⋊C₈	1	1	yes	characteristic
76	C₈	#15668459	1	1	yes	characteristic
77	C₂²	#19153878	1	1	yes	characteristic
78	C₄	—	8	1	no	—
79	C₄	—	362	1	no	—
80	C₄	—	362	1	no	—
81	C₄	—	724	2	no	—
82	C₄	#19153873	1	1	yes	characteristic
83	C₄	#19153881	1	1	yes	characteristic
84	C₂	#26042127	1	1	yes	characteristic
85	C₂	#26042195	1	1	yes	characteristic
86	C₂	#26042198	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19153878
commutator	C₈×C₁₈₁	C₂×C₈
Frattini	C₂×C₈	C₂×#10624382
Fitting	#107×C₁₈₁	C₄
socle, prime radical	C₂²×C₁₈₁	#102
cosocle	C₈×Dic₁₈₁	C₂²
hypercenter	#107	#10624382
hypocenter	C₁₈₁	#1334
LCS	G ▷ C₈×C₁₈₁ ▷ 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
15. Dic₇₂₄	C₈	semidirect
43. C₁₈₁	#1334	semidirect

Maximal subgroups

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

subgroup	index
#26042168	2
#26042140	2
#26041373	2
#1334	181