Subgroups — #21460933

Order 7808.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519827	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₆×D₆₁	C₂	1	1	yes	maximal, characteristic
3	#14519827	—	2	2	no	—
4	C₂×C₈×D₆₁	C₄	1	1	yes	characteristic
5	C₂×#11758185	C₂²	1	1	yes	characteristic
6	C₁₆×D₆₁	—	2	2	no	—
7	C₂×C₁₆×C₆₁	C₄	1	1	yes	characteristic
8	C₂×C₄×D₆₁	C₈	1	1	yes	characteristic
9	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
10	C₂×#92418	C₈	1	1	yes	characteristic
11	C₈×D₆₁	—	2	1	no	—
12	C₈×D₆₁	—	2	1	no	—
13	C₁₆×C₆₁	—	2	1	no	—
14	#11758185	D₄	1	2	yes	—
15	C₂²×D₆₁	C₁₆	1	1	yes	characteristic
16	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
17	C₂×Dic₆₁	C₁₆	1	1	yes	characteristic
18	C₄×D₆₁	—	2	1	no	—
19	C₄×D₆₁	—	2	1	no	—
20	C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₈×C₆₁	M₁₆	1	1	yes	characteristic
22	#92418	—	2	1	no	—
23	C₂²×C₆₁	C₂×C₁₆	1	1	yes	characteristic
24	C₂×D₆₁	—	2	1	no	—
25	C₂×D₆₁	—	2	1	no	—
26	C₂×D₆₁	C₃₂	1	2	yes	complemented
27	C₄×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
28	C₄×C₆₁	M₃₂	1	1	yes	characteristic
29	Dic₆₁	—	2	1	no	—
30	C₂²⋊C₃₂	—	61	1	no	maximal, Sylow
31	C₂×C₆₁	C₂²⋊C₁₆	1	1	yes	characteristic
32	C₂×C₆₁	C₂×C₃₂	1	1	yes	characteristic
33	C₂×C₆₁	M₆₄	1	1	yes	characteristic
34	D₆₁	—	2	2	no	—
35	C₂²×C₁₆	—	61	1	no	—
36	C₂×C₃₂	—	61	2	no	—
37	C₆₁	C₂²⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₈	—	61	1	no	—
39	C₂×C₁₆	—	61	1	no	—
40	C₂×C₁₆	—	122	2	no	—
41	C₂×C₁₆	#6923	1	1	yes	characteristic
42	C₃₂	—	122	2	no	—
43	C₂²×C₄	—	61	1	no	—
44	C₂×C₈	—	61	1	no	—
45	C₂×C₈	—	122	1	no	—
46	C₂×C₈	—	122	1	no	—
47	C₂×C₈	C₂×#6923	1	1	yes	characteristic
48	C₁₆	—	2	1	no	—
49	C₁₆	—	61	2	no	—
50	C₂³	—	61	1	no	—
51	C₂×C₄	—	61	1	no	—
52	C₂×C₄	—	122	1	no	—
53	C₂×C₄	—	122	1	no	—
54	C₂×C₄	D₆₁⋊C₈	1	1	yes	characteristic
55	C₈	—	122	1	no	—
56	C₈	#11758213	1	1	yes	characteristic
57	C₈	C₂²⋊#6923	1	1	yes	characteristic
58	C₂²	—	61	2	no	—
59	C₂²	—	122	1	no	—
60	C₂²	—	122	1	no	—
61	C₂²	D₆₁⋊C₁₆	1	1	yes	characteristic
62	C₄	—	122	1	no	—
63	C₄	#14519834	1	1	yes	characteristic
64	C₄	#14519852	1	1	yes	characteristic
65	C₂	—	122	2	no	—
66	C₂	#16840657	1	1	yes	characteristic
67	C₂	D₆₁⋊C₃₂	1	1	yes	characteristic
68	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	C₂²⋊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
1. C₂×#14519827	C₂	semidirect
26. C₂×D₆₁	C₃₂	semidirect
37. C₆₁	C₂²⋊C₃₂	semidirect