Subgroups — #21454096

Order 7808.

3422 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519746	C₂	1	7	yes	maximal, complemented
2	#16839618	C₂	1	7	yes	maximal, complemented
3	C₂⁶×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₂²⋊D₆₁	C₂²	1	7	yes	complemented
5	#14519746	—	2	28	no	—
6	C₂×C₂²⋊Dic₆₁	C₂²	1	21	yes	complemented
7	C₂⁵×C₆₁	—	2	28	no	—
8	C₂⁵×C₆₁	C₂²	1	7	yes	—
9	C₂⁴×C₆₁	—	2	224	no	—
10	C₂⁴×C₆₁	—	2	84	no	—
11	C₂⁴×C₆₁	D₄	1	28	yes	complemented
12	C₂⁴×C₆₁	C₂³	1	7	yes	—
13	C₂³×D₆₁	C₂³	1	1	yes	characteristic, complemented
14	C₂×C₂²⋊D₆₁	—	2	42	no	—
15	C₂²×Dic₆₁	C₂³	1	7	yes	complemented
16	C₂²⋊Dic₆₁	—	2	42	no	—
17	C₂³×C₆₁	—	2	256	no	—
18	C₂³×C₆₁	—	2	224	no	—
19	C₂³×C₆₁	—	2	168	no	—
20	C₂³×C₆₁	—	2	28	no	—
21	C₂³×C₆₁	C₂×D₄	1	42	yes	—
22	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
23	C₂²×D₆₁	—	2	7	no	—
24	C₂²⋊D₆₁	—	4	28	no	—
25	C₂×Dic₆₁	—	2	21	no	—
26	C₂²×C₆₁	—	2	224	no	—
27	C₂²×C₆₁	—	2	84	no	—
28	C₂²×C₆₁	#120	1	28	yes	complemented
29	C₂²×C₆₁	C₂²×D₄	1	7	yes	—
30	C₂×D₆₁	—	4	7	no	—
31	Dic₆₁	—	4	7	no	—
32	#2846	—	61	1	no	maximal, Sylow
33	C₂×C₆₁	—	2	28	no	—
34	C₂×C₆₁	C₂×#120	1	7	yes	—
35	D₆₁	—	8	1	no	—
36	C₂⁶	D₆₁	1	1	yes	characteristic, complemented
37	C₂×#120	—	61	7	no	—
38	#379	—	61	7	no	—
39	C₆₁	#2846	1	1	yes	characteristic, complemented, Sylow
40	C₂⁵	—	2	28	no	—
41	C₂⁵	C₂×D₆₁	1	7	yes	—
42	C₂²×D₄	—	61	7	no	—
43	#120	—	122	28	no	—
44	C₂×C₂²⋊C₄	—	61	21	no	—
45	C₂⁴	—	2	224	no	—
46	C₂⁴	—	2	84	no	—
47	C₂⁴	—	61	1	no	—
48	C₂⁴	C₂²⋊D₆₁	1	28	yes	complemented
49	C₂⁴	C₂²×D₆₁	1	7	yes	—
50	C₂×D₄	—	122	42	no	—
51	C₂²×C₄	—	61	7	no	—
52	C₂²⋊C₄	—	122	42	no	—
53	C₂³	—	2	256	no	—
54	C₂³	—	2	224	no	—
55	C₂³	—	2	28	no	—
56	C₂³	—	2	168	no	—
57	C₂³	—	122	7	no	—
58	C₂³	C₂×C₂²⋊D₆₁	1	42	yes	—
59	C₂³	C₂³×D₆₁	1	1	yes	characteristic
60	D₄	—	244	28	no	—
61	C₂×C₄	—	122	21	no	—
62	C₂²	—	2	224	no	—
63	C₂²	—	2	84	no	—
64	C₂²	—	244	7	no	—
65	C₂²	#14519746	1	28	yes	complemented
66	C₂²	C₂²×C₂²⋊D₆₁	1	7	yes	—
67	C₄	—	244	7	no	—
68	C₂	—	2	28	no	—
69	C₂	—	488	1	no	—
70	C₂	C₂×#14519746	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₆₁
commutator, socle	C₂³×C₆₁	C₂⁴
Fitting	C₂⁶×C₆₁	C₂
hypercenter	C₂⁶	D₆₁
hypocenter	C₆₁	#2846
LCS	G ▷ C₂³×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂⁶

Complements

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

N	H ≅ G/N	type
1. C₂×#14519746	C₂	semidirect
2. #16839618	C₂	semidirect
3. C₂⁶×C₆₁	C₂	semidirect
4. C₂²×C₂²⋊D₆₁	C₂²	semidirect
6. C₂×C₂²⋊Dic₆₁	C₂²	semidirect
11. C₂⁴×C₆₁	D₄	semidirect
13. C₂³×D₆₁	C₂³	semidirect
15. C₂²×Dic₆₁	C₂³	semidirect
28. C₂²×C₆₁	#120	semidirect
36. C₂⁶	D₆₁	semidirect
39. C₆₁	#2846	semidirect
48. C₂⁴	C₂²⋊D₆₁	semidirect
65. C₂²	#14519746	semidirect