Subgroups — #21444102

Order 7808.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839815	C₂	1	2	yes	maximal
2	#16839483	C₂	1	2	yes	maximal, complemented
3	C₈×#92418	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₈×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₄⋊#92418	C₄	1	4	yes	—
6	C₂²⋊#92418	C₄	1	4	yes	—
7	C₄×#92418	C₂²	1	4	yes	—
8	C₂²×C₈×C₆₁	C₄	1	2	yes	—
9	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₆₁	C₄	1	2	yes	—
11	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₆₁	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₆₁	C₈	1	8	yes	complemented
16	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
18	C₄²×C₆₁	C₂×C₄	1	2	yes	—
19	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₆₁	C₂³	1	1	yes	characteristic
21	C₂×#92418	C₂×C₄	1	8	yes	—
22	C₂³×C₆₁	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₆₁	—	2	4	no	—
24	C₂×C₄×C₆₁	C₄²	1	2	yes	—
25	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₆₁	C₂×C₈	1	4	yes	—
27	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₆₁	C₂²×C₄	1	2	yes	—
29	C₈×C₆₁	C₂×C₈	1	4	yes	—
30	C₈×C₆₁	C₂×C₈	1	4	yes	—
31	#92418	—	2	8	no	—
32	C₂²×C₆₁	—	2	2	no	—
33	C₂²×C₆₁	C₄×C₈	1	2	yes	—
34	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
35	C₄×C₆₁	—	2	2	no	—
36	C₄×C₆₁	C₄×C₈	1	2	yes	—
37	C₄×C₆₁	C₂²×C₈	1	2	yes	—
38	C₄×C₆₁	#131	1	4	yes	—
39	#1450	—	61	1	no	maximal, Sylow
40	C₂×C₆₁	—	2	2	no	—
41	C₂×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
42	C₂×C₆₁	#405	1	2	yes	—
43	#431	—	61	2	no	—
44	C₂×C₄×C₈	D₆₁	1	1	yes	characteristic
45	#322	—	61	2	no	—
46	C₈²	—	61	2	no	—
47	C₆₁	#1450	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₈	Dic₆₁	1	2	yes	—
49	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
50	C₄⋊C₈	—	61	4	no	—
51	C₂²⋊C₈	—	61	4	no	—
52	C₄×C₈	—	61	4	no	—
53	C₄×C₈	Dic₆₁	1	2	yes	—
54	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
55	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
56	C₂²×C₄	C₄×D₆₁	1	2	yes	—
57	C₂²×C₄	C₂×Dic₆₁	1	1	yes	characteristic
58	C₂×C₈	—	61	8	no	—
59	C₂×C₈	#92418	1	8	yes	complemented
60	C₂×C₈	C₂×Dic₆₁	1	2	yes	—
61	C₂×C₈	C₂×Dic₆₁	1	2	yes	—
62	C₄²	C₄×D₆₁	1	2	yes	—
63	C₄²	C₂×Dic₆₁	1	1	yes	characteristic
64	C₄²	C₂²×D₆₁	1	1	yes	characteristic
65	C₂³	C₄×Dic₆₁	1	1	yes	characteristic
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	C₂×#92418	1	4	yes	—
68	C₂×C₄	C₄×Dic₆₁	1	2	yes	—
69	C₂×C₄	C₄×Dic₆₁	1	1	yes	characteristic
70	C₂×C₄	C₂×C₄×D₆₁	1	2	yes	—
71	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
72	C₈	—	122	8	no	—
73	C₈	C₂×#92418	1	4	yes	—
74	C₈	C₂×#92418	1	4	yes	—
75	C₂²	—	2	2	no	—
76	C₂²	C₄×#92418	1	2	yes	—
77	C₂²	C₂×C₄×Dic₆₁	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	C₄×#92418	1	2	yes	—
80	C₄	C₂²×#92418	1	2	yes	—
81	C₄	#14519783	1	4	yes	—
82	C₂	—	2	2	no	—
83	C₂	C₂×C₄×#92418	1	1	yes	characteristic
84	C₂	#16839717	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂×D₆₁
commutator	C₂×C₆₁	C₂×C₄×C₈
Frattini	C₄²	C₂²×D₆₁
Fitting	C₂×C₄×C₈×C₆₁	C₂
socle	C₂²×C₆₁	C₂×C₄²
hypercenter	C₂×C₄×C₈	D₆₁
hypocenter	C₆₁	#1450
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #16839483	C₂	semidirect
3. C₈×#92418	C₂	semidirect
15. C₂×C₈×C₆₁	C₈	semidirect
47. C₆₁	#1450	semidirect
59. C₂×C₈	#92418	semidirect