Subgroups — #21461033

Order 7808.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840780	C₂	1	2	yes	maximal
2	#92420⋊C₈	C₂	1	4	yes	maximal, complemented
3	C₄×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
4	#14519844	C₄	1	4	yes	—
5	#14519834	C₄	1	4	yes	—
6	C₄×#92420	C₂²	1	4	yes	—
7	C₂×C₈×D₆₁	C₄	1	2	yes	—
8	C₄²×D₆₁	C₂²	1	1	yes	characteristic
9	C₄×#92418	C₄	1	1	yes	characteristic
10	C₈×Dic₆₁	C₂²	1	2	yes	—
11	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic
12	C₂×C₄×D₆₁	C₂×C₄	1	2	yes	—
13	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
14	C₂×#92420	C₂×C₄	1	8	yes	—
15	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
16	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
18	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
19	C₂×#92418	C₂×C₄	1	2	yes	—
20	C₈×D₆₁	—	2	4	no	—
21	C₂²×D₆₁	C₄²	1	1	yes	characteristic
22	C₂×C₄×C₆₁	C₄²	1	2	yes	—
23	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
24	C₂×Dic₆₁	C₄²	1	1	yes	characteristic
25	C₂×Dic₆₁	C₂²×C₄	1	2	yes	—
26	C₄×D₆₁	—	2	4	no	—
27	C₄×D₆₁	M₁₆	1	4	yes	—
28	#92420	—	2	8	no	—
29	C₈×C₆₁	—	2	2	no	—
30	#92418	—	2	2	no	—
31	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
32	C₂×D₆₁	—	2	2	no	—
33	C₂×D₆₁	#97	1	2	yes	—
34	C₄×C₆₁	—	2	2	no	—
35	C₄×C₆₁	C₂×M₁₆	1	2	yes	—
36	Dic₆₁	#97	1	2	yes	—
37	Dic₆₁	#131	1	4	yes	—
38	#1452	—	61	1	no	maximal, Sylow
39	C₂×C₆₁	C₂×#97	1	1	yes	characteristic
40	C₂×C₆₁	#405	1	2	yes	—
41	D₆₁	—	2	2	no	—
42	#431	—	61	2	no	—
43	C₂×C₄×C₈	—	61	1	no	—
44	#322	—	61	4	no	—
45	C₆₁	#1452	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₈	—	61	2	no	—
47	C₂×C₄²	—	61	1	no	—
48	C₄⋊C₈	—	61	4	no	—
49	C₂²⋊C₈	—	61	4	no	—
50	C₄×C₈	—	61	4	no	—
51	C₄×C₈	—	61	2	no	—
52	C₄×C₈	—	61	1	no	—
53	C₄×C₈	#6923	1	1	yes	characteristic
54	C₂²×C₄	—	61	1	no	—
55	C₂²×C₄	—	61	2	no	—
56	C₂×C₈	—	61	8	no	—
57	C₂×C₈	—	61	2	no	—
58	C₂×C₈	—	122	4	no	—
59	C₂×C₈	C₂×#6923	1	2	yes	—
60	C₄²	—	61	2	no	—
61	C₄²	—	61	1	no	—
62	C₄²	C₂×#6923	1	1	yes	characteristic
63	C₂³	—	61	1	no	—
64	C₂×C₄	—	61	1	no	—
65	C₂×C₄	—	61	2	no	—
66	C₂×C₄	—	61	4	no	—
67	C₂×C₄	—	122	4	no	—
68	C₂×C₄	C₄×#6923	1	2	yes	—
69	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
70	C₈	—	2	2	no	—
71	C₈	—	122	8	no	—
72	C₈	—	122	2	no	—
73	C₂²	—	61	2	no	—
74	C₂²	—	122	2	no	—
75	C₂²	C₂×C₄×#6923	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	61	2	no	—
78	C₄	—	61	4	no	—
79	C₄	D₆₁⋊M₁₆	1	2	yes	—
80	C₂	—	122	2	no	—
81	C₂	#16840721	1	1	yes	characteristic
82	C₂	#16840725	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#6923
commutator, socle	C₂²×C₆₁	C₂×C₄²
Fitting	C₄×C₈×C₆₁	C₄
hypercenter	C₄×C₈	#6923
hypocenter	C₆₁	#1452
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #92420⋊C₈	C₂	semidirect
45. C₆₁	#1452	semidirect