Subgroups — #37548639

Order 23168.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042167	C₂	1	1	yes	maximal, characteristic
2	#26042167	C₂	1	1	yes	maximal, characteristic
3	#26041001	C₂	1	1	yes	maximal, characteristic
4	C₂×#15668452	C₄	1	2	yes	—
5	C₂×#15668452	C₄	1	2	yes	—
6	C₄×#13089678	C₄	1	1	yes	characteristic
7	C₄×#13089678	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₁₈₁	C₄	1	1	yes	characteristic
9	#15668452	—	2	2	no	—
10	#15668452	C₈	1	4	yes	complemented
11	C₂×#13089678	—	2	1	no	—
12	C₂×#13089678	C₂×C₄	1	1	yes	characteristic
13	C₂×#13089678	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₁₈₁	—	2	1	no	—
15	C₄²×C₁₈₁	C₂×C₄	1	1	yes	characteristic
16	#13089678	—	4	1	no	—
17	#13089678	C₂×C₈	1	2	yes	—
18	#13089678	M₁₆	1	2	yes	—
19	C₂×C₄×C₁₈₁	C₄²	1	1	yes	characteristic
20	C₂×C₄×C₁₈₁	M₁₆	1	1	yes	characteristic
21	C₂×C₄×C₁₈₁	M₁₆	1	1	yes	characteristic
22	C₈×C₁₈₁	—	4	1	no	—
23	C₂²×C₁₈₁	#97	1	1	yes	characteristic
24	C₄×C₁₈₁	—	2	1	no	—
25	C₄×C₁₈₁	—	2	1	no	—
26	C₄×C₁₈₁	C₄×C₈	1	1	yes	characteristic
27	C₄×C₁₈₁	#97	1	1	yes	characteristic
28	C₂×C₁₈₁	#322	1	1	yes	characteristic
29	C₂×C₁₈₁	#347	1	1	yes	characteristic
30	C₂×C₁₈₁	#347	1	1	yes	characteristic
31	C₁₈₁	#1313	1	1	yes	characteristic, complemented, Sylow
32	#1313	—	181	1	no	maximal, Sylow
33	#346	—	181	1	no	—
34	#346	—	181	1	no	—
35	#322	—	181	1	no	—
36	C₂×C₁₆	—	181	2	no	—
37	C₂×C₁₆	—	181	2	no	—
38	C₄×C₈	—	181	1	no	—
39	C₄×C₈	—	181	1	no	—
40	C₄×C₈	#10624382	1	1	yes	characteristic
41	C₂×C₈	—	2	1	no	—
42	C₂×C₈	—	362	1	no	—
43	C₂×C₈	—	181	1	no	—
44	C₂×C₈	—	181	1	no	—
45	C₄²	C₂×#10624382	1	1	yes	characteristic
46	C₁₆	—	362	2	no	—
47	C₁₆	—	181	4	no	—
48	C₂×C₄	C₄×#10624382	1	1	yes	characteristic
49	C₂×C₄	#15668458	1	1	yes	characteristic
50	C₂×C₄	#15668459	1	1	yes	characteristic
51	C₈	—	4	1	no	—
52	C₈	—	181	2	no	—
53	C₈	—	181	2	no	—
54	C₈	—	724	1	no	—
55	C₂²	#19153871	1	1	yes	characteristic
56	C₄	—	2	1	no	—
57	C₄	—	2	1	no	—
58	C₄	C₈×#10624382	1	1	yes	characteristic
59	C₄	#19153870	1	1	yes	characteristic
60	C₂	#13089685⋊C₈	1	1	yes	characteristic
61	C₂	#26042171	1	1	yes	characteristic
62	C₂	#26042172	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#10624382
commutator	C₄×C₁₈₁	C₄×C₈
Frattini	C₄²	C₂×#10624382
Fitting	C₄×C₈×C₁₈₁	C₄
socle, prime radical	C₂²×C₁₈₁	#97
cosocle	C₄×#13089678	C₂²
hypercenter	C₄×C₈	#10624382
hypocenter	C₁₈₁	#1313
LCS	G ▷ C₄×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
10. #15668452	C₈	semidirect
31. C₁₈₁	#1313	semidirect

Maximal subgroups

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

subgroup	index
#26042167	2
#26041001	2
#1313	181