Subgroups — #37548640

Order 23168.

80 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	#26042120	C₂	1	1	yes	maximal, characteristic
3	#26041054	C₂	1	1	yes	maximal, characteristic
4	C₂×#15668452	C₄	1	2	yes	—
5	C₄×#13089685	C₄	1	1	yes	characteristic
6	C₄×#13089685	C₄	1	1	yes	characteristic
7	C₂×#15668424	C₄	1	1	yes	characteristic
8	C₈×Dic₁₈₁	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₁₈₁	C₄	1	1	yes	characteristic
10	C₂×#13089685	—	2	1	no	—
11	C₂×#13089685	—	2	1	no	—
12	#15668452	C₈	1	4	yes	complemented
13	C₂×#13089678	C₂×C₄	1	1	yes	characteristic
14	C₄×Dic₁₈₁	C₂×C₄	1	1	yes	characteristic
15	#15668424	—	2	1	no	—
16	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
17	C₁₆×C₁₈₁	—	2	1	no	—
18	#13089685	—	4	1	no	—
19	#13089685	—	4	1	no	—
20	C₂×Dic₁₈₁	M₁₆	1	1	yes	characteristic
21	C₂×Dic₁₈₁	M₁₆	1	1	yes	characteristic
22	#13089678	C₂×C₈	1	2	yes	—
23	C₂×C₄×C₁₈₁	C₄²	1	1	yes	characteristic
24	C₈×C₁₈₁	M₁₆	1	1	yes	characteristic
25	C₈×C₁₈₁	M₁₆	1	1	yes	characteristic
26	C₂²×C₁₈₁	#97	1	1	yes	characteristic
27	C₄×C₁₈₁	C₄×C₈	1	1	yes	characteristic
28	C₄×C₁₈₁	#97	1	1	yes	characteristic
29	Dic₁₈₁	—	2	1	no	—
30	Dic₁₈₁	—	2	1	no	—
31	C₂×C₁₈₁	#322	1	1	yes	characteristic
32	C₂×C₁₈₁	#347	1	1	yes	characteristic
33	C₂×C₁₈₁	#347	1	1	yes	characteristic
34	C₁₈₁	#1313	1	1	yes	characteristic, complemented, Sylow
35	#1313	—	181	1	no	maximal, Sylow
36	#346	—	181	1	no	—
37	#346	—	181	1	no	—
38	#322	—	181	1	no	—
39	C₂×C₁₆	—	181	1	no	—
40	C₂×C₁₆	—	181	2	no	—
41	C₂×C₁₆	#10624382	1	1	yes	characteristic
42	C₄×C₈	—	181	1	no	—
43	C₄×C₈	—	181	1	no	—
44	C₄×C₈	—	181	1	no	—
45	C₂×C₈	—	362	1	no	—
46	C₂×C₈	—	362	1	no	—
47	C₂×C₈	—	181	1	no	—
48	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
49	C₄²	—	181	1	no	—
50	C₁₆	—	2	1	no	—
51	C₁₆	—	362	1	no	—
52	C₁₆	—	181	4	no	—
53	C₂×C₄	—	181	1	no	—
54	C₂×C₄	—	181	1	no	—
55	C₂×C₄	C₄×#10624382	1	1	yes	characteristic
56	C₈	—	181	2	no	—
57	C₈	—	724	1	no	—
58	C₈	—	724	1	no	—
59	C₈	#15668458	1	1	yes	characteristic
60	C₈	#15668459	1	1	yes	characteristic
61	C₂²	#19153870	1	1	yes	characteristic
62	C₄	—	362	1	no	—
63	C₄	—	362	1	no	—
64	C₄	C₈×#10624382	1	1	yes	characteristic
65	C₄	#19153871	1	1	yes	characteristic
66	C₂	#13089685⋊C₈	1	1	yes	characteristic
67	C₂	#26042169	1	1	yes	characteristic
68	C₂	#26042170	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#10624382
commutator	C₄×C₁₈₁	C₄×C₈
Frattini	C₂×C₈	C₂×#10624382
Fitting	C₂×C₁₆×C₁₈₁	C₄
socle, prime radical	C₂²×C₁₈₁	#97
cosocle	C₈×Dic₁₈₁	C₂²
hypercenter	C₂×C₁₆	#10624382
hypocenter	C₁₈₁	#1313
LCS	G ▷ C₄×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
12. #15668452	C₈	semidirect
34. C₁₈₁	#1313	semidirect

Maximal subgroups

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

subgroup	index
#26042168	2
#26042120	2
#26041054	2
#1313	181