Subgroups — #21460977

Order 7808.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519827	C₂	1	2	yes	maximal
2	C₁₆×Dic₆₁	C₂	1	1	yes	maximal, characteristic
3	#14519827	—	2	2	no	—
4	C₂×#11758185	C₂²	1	1	yes	characteristic
5	C₈×Dic₆₁	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₆₁	C₄	1	1	yes	characteristic
7	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
8	C₄×Dic₆₁	C₈	1	1	yes	characteristic
9	C₂×#92418	C₈	1	1	yes	characteristic
10	C₁₆×C₆₁	—	2	1	no	—
11	#11758185	D₄	1	1	yes	characteristic
12	#11758185	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
14	C₂×Dic₆₁	C₁₆	1	1	yes	characteristic
15	C₂×Dic₆₁	C₁₆	1	1	yes	characteristic
16	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₆₁	M₁₆	1	1	yes	characteristic
18	#92418	—	2	1	no	—
19	C₂²×C₆₁	C₂×C₁₆	1	1	yes	characteristic
20	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
21	C₄×C₆₁	M₃₂	1	1	yes	characteristic
22	Dic₆₁	—	2	1	no	—
23	Dic₆₁	C₃₂	1	2	yes	complemented
24	C₄⋊C₃₂	—	61	1	no	maximal, Sylow
25	C₂×C₆₁	C₄⋊C₁₆	1	1	yes	characteristic
26	C₂×C₆₁	C₂×C₃₂	1	1	yes	characteristic
27	C₂×C₆₁	M₆₄	1	1	yes	characteristic
28	C₂×C₃₂	—	61	2	no	—
29	C₄×C₁₆	—	61	1	no	—
30	C₆₁	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₁₆	—	61	1	no	—
32	C₂×C₁₆	#6923	1	1	yes	characteristic
33	C₄×C₈	—	61	1	no	—
34	C₃₂	—	122	2	no	—
35	C₂×C₈	—	61	1	no	—
36	C₂×C₈	C₂×#6923	1	1	yes	characteristic
37	C₄²	—	61	1	no	—
38	C₁₆	—	2	1	no	—
39	C₁₆	—	61	1	no	—
40	C₁₆	—	61	1	no	—
41	C₂×C₄	—	61	1	no	—
42	C₂×C₄	—	61	1	no	—
43	C₂×C₄	D₆₁⋊C₈	1	1	yes	characteristic
44	C₈	—	122	1	no	—
45	C₈	C₄⋊#6923	1	1	yes	characteristic
46	C₈	#11758217	1	1	yes	characteristic
47	C₂²	D₆₁⋊C₁₆	1	1	yes	characteristic
48	C₄	—	61	2	no	—
49	C₄	—	122	1	no	—
50	C₄	#14519844	1	1	yes	characteristic
51	C₄	#14519852	1	1	yes	characteristic
52	C₂	#16840683	1	1	yes	characteristic
53	C₂	D₆₁⋊C₃₂	1	1	yes	characteristic
54	C₂	#16840695	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#6923
commutator	C₂×C₆₁	C₂×C₃₂
Fitting	C₂×C₁₆×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₁₆
hypercenter	C₂×C₁₆	#6923
hypocenter	C₆₁	C₄⋊C₃₂
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
23. Dic₆₁	C₃₂	semidirect
30. C₆₁	C₄⋊C₃₂	semidirect