Subgroups — #21461013

Order 7808.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₆₁⋊C₈	C₂	1	2	yes	maximal
2	#16840603	C₂	1	4	yes	maximal, complemented
3	C₄×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×D₆₁⋊C₈	C₄	1	4	yes	—
5	C₄×#92420	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	1	yes	characteristic
13	C₂×C₄×D₆₁	C₂×C₄	1	2	yes	—
14	C₂×#92420	C₂×C₄	1	8	yes	—
15	D₆₁⋊C₈	—	2	8	no	—
16	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
17	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
19	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
20	C₂×#92418	C₂×C₄	1	2	yes	—
21	C₈×D₆₁	C₈	1	8	yes	complemented
22	C₂²×D₆₁	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₆₁	C₄²	1	2	yes	—
24	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
25	C₂×Dic₆₁	C₄²	1	1	yes	characteristic
26	C₂×Dic₆₁	C₂²×C₄	1	2	yes	—
27	C₄×D₆₁	C₂×C₈	1	4	yes	—
28	C₄×D₆₁	M₁₆	1	8	yes	—
29	#92420	—	2	8	no	—
30	C₈×C₆₁	C₂×C₈	1	4	yes	complemented
31	#92418	C₂×C₈	1	4	yes	complemented
32	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
33	C₂×D₆₁	C₄×C₈	1	2	yes	—
34	C₂×D₆₁	#97	1	4	yes	—
35	C₄×C₆₁	#97	1	4	yes	—
36	C₄×C₆₁	C₂²×C₈	1	2	yes	—
37	Dic₆₁	C₄×C₈	1	2	yes	—
38	Dic₆₁	C₂×M₁₆	1	4	yes	—
39	C₂×#322	—	61	1	no	maximal, Sylow
40	C₂×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
41	C₂×C₆₁	C₂×#97	1	2	yes	—
42	D₆₁	#322	1	4	yes	complemented
43	C₂×C₄×C₈	—	61	2	no	—
44	C₂×C₄×C₈	—	61	1	no	—
45	#322	—	61	4	no	—
46	C₆₁	C₂×#322	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₈	—	61	2	no	—
48	C₂²×C₈	—	61	4	no	—
49	C₂×C₄²	—	61	1	no	—
50	C₄×C₈	—	61	4	no	—
51	C₄×C₈	—	61	4	no	—
52	C₄×C₈	—	61	2	no	—
53	C₄×C₈	—	61	1	no	—
54	C₄×C₈	#6923	1	1	yes	characteristic
55	C₂²×C₄	—	61	2	no	—
56	C₂²×C₄	—	61	1	no	—
57	C₂×C₈	—	61	2	no	—
58	C₂×C₈	—	61	8	no	—
59	C₂×C₈	—	61	8	no	—
60	C₂×C₈	—	122	8	no	—
61	C₂×C₈	C₂×#6923	1	2	yes	—
62	C₄²	—	61	2	no	—
63	C₄²	—	61	1	no	—
64	C₄²	C₂×#6923	1	1	yes	characteristic
65	C₂³	—	61	1	no	—
66	C₂×C₄	—	61	1	no	—
67	C₂×C₄	—	61	2	no	—
68	C₂×C₄	—	61	8	no	—
69	C₂×C₄	—	61	4	no	—
70	C₂×C₄	C₄×#6923	1	2	yes	—
71	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
72	C₈	—	61	4	no	—
73	C₈	—	122	8	no	—
74	C₈	D₆₁⋊C₈	1	4	yes	complemented
75	C₂²	—	61	2	no	—
76	C₂²	—	61	4	no	—
77	C₂²	C₂×C₄×#6923	1	1	yes	characteristic
78	C₄	—	61	2	no	—
79	C₄	—	61	4	no	—
80	C₄	#14519831	1	4	yes	—
81	C₄	C₂×D₆₁⋊C₈	1	2	yes	—
82	C₂	—	61	4	no	—
83	C₂	C₄×D₆₁⋊C₈	1	1	yes	characteristic
84	C₂	C₂×#14519831	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂×#6923
commutator	C₂×C₆₁	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₄×C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄²
hypercenter	C₄×C₈	#6923
hypocenter	C₆₁	C₂×#322
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #16840603	C₂	semidirect
21. C₈×D₆₁	C₈	semidirect
30. C₈×C₆₁	C₂×C₈	semidirect
31. #92418	C₂×C₈	semidirect
42. D₆₁	#322	semidirect
46. C₆₁	C₂×#322	semidirect
74. C₈	D₆₁⋊C₈	semidirect