Subgroups — #21460730

Order 7808.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840648	C₂	1	1	yes	maximal, characteristic
2	C₈×#92420	C₂	1	1	yes	maximal, characteristic
3	C₁₆×Dic₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758187	C₄	1	2	yes	—
5	C₄×#92420	C₄	1	2	yes	—
6	C₂×#11758185	C₄	1	1	yes	characteristic
7	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₆₁	C₄	1	1	yes	characteristic
9	C₂×#92420	C₈	1	4	yes	—
10	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
11	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
12	C₂×#92418	C₂×C₄	1	1	yes	characteristic
13	#11758187	C₈	1	4	yes	complemented
14	C₁₆×C₆₁	C₈	1	2	yes	complemented
15	#11758185	C₈	1	2	yes	complemented
16	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
17	C₂×Dic₆₁	C₂×C₈	1	2	yes	—
18	#92420	—	2	4	no	—
19	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
20	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
21	#92418	C₂×C₈	1	2	yes	—
22	C₂²×C₆₁	C₄×C₈	1	1	yes	characteristic
23	C₄×C₆₁	C₄×C₈	1	1	yes	characteristic
24	C₄×C₆₁	C₄×C₈	1	1	yes	characteristic
25	Dic₆₁	M₃₂	1	4	yes	—
26	#1311	—	61	1	no	maximal, Sylow
27	C₂×C₆₁	C₈²	1	1	yes	characteristic
28	C₂×C₆₁	#346	1	2	yes	—
29	C₄×C₁₆	—	61	1	no	—
30	C₄×C₁₆	—	61	1	no	—
31	C₈²	—	61	1	no	—
32	C₆₁	#1311	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₁₆	—	61	2	no	—
34	C₂×C₁₆	—	61	1	no	—
35	C₂×C₁₆	#6923	1	1	yes	characteristic
36	C₄×C₈	—	61	2	no	—
37	C₄×C₈	—	61	1	no	—
38	C₂×C₈	—	61	1	no	—
39	C₂×C₈	—	61	4	no	—
40	C₂×C₈	C₂×#6923	1	1	yes	characteristic
41	C₄²	—	61	1	no	—
42	C₁₆	—	61	4	no	—
43	C₁₆	—	61	2	no	—
44	C₁₆	#92420	1	2	yes	complemented
45	C₂×C₄	—	61	2	no	—
46	C₂×C₄	C₄×#6923	1	1	yes	characteristic
47	C₈	—	61	2	no	—
48	C₈	—	122	4	no	—
49	C₈	D₆₁⋊C₈	1	1	yes	characteristic
50	C₈	C₂×#92420	1	1	yes	characteristic
51	C₂²	C₈×#6923	1	1	yes	characteristic
52	C₄	—	61	4	no	—
53	C₄	C₈×#6923	1	1	yes	characteristic
54	C₄	C₄×#92420	1	1	yes	characteristic
55	C₂	C₈×#92420	1	1	yes	characteristic
56	C₂	#16840649	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#6923
commutator	C₂×C₆₁	C₈²
Fitting	C₂×C₁₆×C₆₁	C₄
socle	C₂²×C₆₁	C₄×C₈
hypercenter	C₂×C₁₆	#6923
hypocenter	C₆₁	#1311
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
13. #11758187	C₈	semidirect
14. C₁₆×C₆₁	C₈	semidirect
15. #11758185	C₈	semidirect
32. C₆₁	#1311	semidirect
44. C₁₆	#92420	semidirect