Subgroups — #21460929

Order 7808.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840695	C₂	1	1	yes	maximal, characteristic
2	#16840649	C₂	1	1	yes	maximal, characteristic
3	#16839595	C₂	1	1	yes	maximal, characteristic
4	D₆₁⋊C₁₆	C₄	1	1	yes	characteristic
5	C₈×#6923	C₄	1	1	yes	characteristic
6	#14519827	C₄	1	2	yes	complemented
7	C₁₆×D₆₁	C₂²	1	1	yes	characteristic
8	#14519683	C₄	1	1	yes	characteristic, complemented
9	C₃₂×C₆₁	C₄	1	1	yes	characteristic, complemented
10	C₄×#6923	C₈	1	1	yes	characteristic
11	D₆₁⋊C₈	C₈	1	1	yes	characteristic
12	C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
13	#11758187	C₈	1	2	yes	—
14	C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
15	#11758185	C₂×C₄	1	1	yes	characteristic
16	C₂×#6923	—	2	1	no	—
17	C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
18	#92420	—	2	1	no	—
19	C₈×C₆₁	C₄²	1	1	yes	characteristic
20	#92418	C₂×C₈	1	1	yes	characteristic
21	C₂×D₆₁	M₃₂	1	1	yes	characteristic
22	#6923	—	4	1	no	—
23	C₄×C₆₁	C₄×C₈	1	1	yes	characteristic
24	Dic₆₁	M₃₂	1	1	yes	characteristic
25	#1398	—	61	1	no	maximal, Sylow
26	C₂×C₆₁	#346	1	1	yes	characteristic
27	D₆₁	—	2	1	no	—
28	M₆₄	—	61	1	no	—
29	M₆₄	—	61	1	no	—
30	#346	—	61	1	no	—
31	C₆₁	#1398	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₁₆	—	61	1	no	—
33	C₂×C₁₆	—	61	1	no	—
34	C₄×C₈	—	61	1	no	—
35	C₃₂	—	61	2	no	—
36	C₃₂	—	61	1	no	—
37	C₃₂	#6923	1	1	yes	characteristic, complemented
38	C₂×C₈	—	61	1	no	—
39	C₂×C₈	—	61	1	no	—
40	C₄²	—	61	1	no	—
41	C₁₆	—	61	2	no	—
42	C₁₆	—	61	1	no	—
43	C₁₆	C₂×#6923	1	1	yes	characteristic
44	C₂×C₄	—	61	1	no	—
45	C₂×C₄	—	122	1	no	—
46	C₈	—	61	1	no	—
47	C₈	—	122	1	no	—
48	C₈	C₄×#6923	1	1	yes	characteristic
49	C₂²	—	61	1	no	—
50	C₄	—	61	1	no	—
51	C₄	—	244	1	no	—
52	C₄	C₈×#6923	1	1	yes	characteristic
53	C₂	—	122	1	no	—
54	C₂	#16840649	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×#6923
commutator	C₄×C₆₁	C₄×C₈
Frattini	C₁₆	C₂×#6923
Fitting	C₃₂×C₆₁	C₄
socle	C₂×C₆₁	#346
hypercenter	C₃₂	#6923
hypocenter	C₆₁	#1398
LCS	G ▷ C₄×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₈ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
6. #14519827	C₄	semidirect
8. #14519683	C₄	semidirect
9. C₃₂×C₆₁	C₄	semidirect
31. C₆₁	#1398	semidirect
37. C₃₂	#6923	semidirect