Subgroups — C₂³×C₄⋊Dic₆₁ #21458980

Order 7808.

2488 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Dic₆₁	C₂	1	2	yes	maximal
2	C₂²×C₄⋊Dic₆₁	C₂	1	28	yes	maximal, direct product factor
3	C₂⁴×C₄×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₆₁	—	2	16	no	—
5	C₂³×Dic₆₁	C₂²	1	28	yes	—
6	C₂×C₄⋊Dic₆₁	C₂²	1	112	yes	direct product factor
7	C₂⁵×C₆₁	C₂²	1	1	yes	characteristic
8	C₂³×C₄×C₆₁	C₄	1	16	yes	complemented
9	C₂³×C₄×C₆₁	C₂²	1	14	yes	—
10	C₂⁴×C₆₁	C₂×C₄	1	8	yes	—
11	C₂⁴×C₆₁	D₄	1	8	yes	—
12	C₂⁴×C₆₁	Q₈	1	8	yes	—
13	C₂⁴×C₆₁	C₂³	1	7	yes	—
14	C₂²×C₄×C₆₁	C₂×C₄	1	112	yes	complemented
15	C₂²×C₄×C₆₁	C₂³	1	28	yes	—
16	C₂²×Dic₆₁	—	2	112	no	—
17	C₂²×Dic₆₁	C₂³	1	56	yes	—
18	C₄⋊Dic₆₁	C₂³	1	64	yes	direct product factor
19	C₂³×C₆₁	C₄⋊C₄	1	64	yes	complemented
20	C₂³×C₆₁	C₂²×C₄	1	28	yes	—
21	C₂³×C₆₁	C₂×D₄	1	28	yes	—
22	C₂³×C₆₁	C₂×Q₈	1	28	yes	—
23	C₂³×C₆₁	C₂⁴	1	7	yes	—
24	C₂×C₄×C₆₁	C₂²×C₄	1	112	yes	complemented
25	C₂×C₄×C₆₁	C₂⁴	1	8	yes	—
26	C₂×Dic₆₁	—	2	112	no	—
27	C₂×Dic₆₁	C₂⁴	1	16	yes	—
28	C₂²×C₆₁	C₂×C₄⋊C₄	1	112	yes	complemented
29	C₂²×C₆₁	C₂³×C₄	1	14	yes	—
30	C₂²×C₆₁	C₂²×D₄	1	14	yes	—
31	C₂²×C₆₁	C₂²×Q₈	1	14	yes	—
32	C₂²×C₆₁	C₂⁵	1	1	yes	characteristic
33	C₄×C₆₁	C₂³×C₄	1	16	yes	complemented
34	Dic₆₁	—	2	16	no	—
35	C₂³×C₄⋊C₄	—	61	1	no	maximal, Sylow
36	C₂×C₆₁	C₂²×C₄⋊C₄	1	28	yes	complemented
37	C₂×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
38	C₂×C₆₁	C₂³×D₄	1	1	yes	characteristic
39	C₂×C₆₁	C₂³×Q₈	1	1	yes	characteristic
40	C₂⁴×C₄	—	61	2	no	—
41	C₂⁴×C₄	D₆₁	1	1	yes	characteristic
42	C₂²×C₄⋊C₄	—	61	28	no	—
43	C₆₁	C₂³×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
44	C₂⁵	C₂×D₆₁	1	1	yes	characteristic
45	C₂³×C₄	—	61	28	no	—
46	C₂³×C₄	—	122	16	no	—
47	C₂³×C₄	Dic₆₁	1	16	yes	complemented
48	C₂³×C₄	C₂×D₆₁	1	14	yes	—
49	C₂×C₄⋊C₄	—	61	112	no	—
50	C₂⁴	Dic₁₂₂	1	8	yes	—
51	C₂⁴	D₂₄₄	1	8	yes	—
52	C₂⁴	C₂×Dic₆₁	1	8	yes	—
53	C₂⁴	C₂²×D₆₁	1	7	yes	—
54	C₂²×C₄	—	61	56	no	—
55	C₂²×C₄	—	122	112	no	—
56	C₂²×C₄	C₂×Dic₆₁	1	112	yes	complemented
57	C₂²×C₄	C₂²×D₆₁	1	28	yes	—
58	C₄⋊C₄	—	61	64	no	—
59	C₂³	C₄⋊Dic₆₁	1	64	yes	direct product factor
60	C₂³	C₂×Dic₁₂₂	1	28	yes	—
61	C₂³	C₂×D₂₄₄	1	28	yes	—
62	C₂³	C₂²×Dic₆₁	1	28	yes	—
63	C₂³	C₂³×D₆₁	1	7	yes	—
64	C₂×C₄	—	61	16	no	—
65	C₂×C₄	—	122	112	no	—
66	C₂×C₄	C₂²×Dic₆₁	1	112	yes	complemented
67	C₂×C₄	C₂³×D₆₁	1	8	yes	—
68	C₂²	C₂×C₄⋊Dic₆₁	1	112	yes	direct product factor
69	C₂²	C₂³×Dic₆₁	1	14	yes	—
70	C₂²	C₂²×D₂₄₄	1	14	yes	—
71	C₂²	C₂²×Dic₁₂₂	1	14	yes	—
72	C₂²	C₂⁴×D₆₁	1	1	yes	characteristic
73	C₄	—	122	16	no	—
74	C₄	C₂³×Dic₆₁	1	16	yes	complemented
75	C₂	C₂²×C₄⋊Dic₆₁	1	28	yes	direct product factor
76	C₂	C₂⁴×Dic₆₁	1	1	yes	characteristic
77	C₂	C₂³×D₂₄₄	1	1	yes	characteristic
78	C₂	C₂³×Dic₁₂₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁵	C₂×D₆₁
commutator	C₂×C₆₁	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₆₁
Fitting	C₂⁴×C₄×C₆₁	C₂
socle	C₂⁵×C₆₁	C₂²
hypercenter	C₂⁴×C₄	D₆₁
hypocenter	C₆₁	C₂³×C₄⋊C₄
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂⁵ ◁ C₂⁴×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄⋊Dic₆₁	C₂	direct (N × H)
6. C₂×C₄⋊Dic₆₁	C₂²	direct (N × H)
8. C₂³×C₄×C₆₁	C₄	semidirect
14. C₂²×C₄×C₆₁	C₂×C₄	semidirect
18. C₄⋊Dic₆₁	C₂³	direct (N × H)
19. C₂³×C₆₁	C₄⋊C₄	semidirect
24. C₂×C₄×C₆₁	C₂²×C₄	semidirect
28. C₂²×C₆₁	C₂×C₄⋊C₄	semidirect
33. C₄×C₆₁	C₂³×C₄	semidirect
36. C₂×C₆₁	C₂²×C₄⋊C₄	semidirect
43. C₆₁	C₂³×C₄⋊C₄	semidirect
47. C₂³×C₄	Dic₆₁	semidirect
56. C₂²×C₄	C₂×Dic₆₁	semidirect
59. C₂³	C₄⋊Dic₆₁	direct (N × H)
66. C₂×C₄	C₂²×Dic₆₁	semidirect
68. C₂²	C₂×C₄⋊Dic₆₁	direct (N × H)
74. C₄	C₂³×Dic₆₁	semidirect
75. C₂	C₂²×C₄⋊Dic₆₁	direct (N × H)

Subgroups — C23×C4⋊Dic61 #21458980

Conjugacy classes of subgroups

Complements

Subgroups — C₂³×C₄⋊Dic₆₁ #21458980