Subgroups — C₂³×Q₈×D₆₁ #21460613

Order 7808.

6264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Dic₁₂₂	C₂	1	3	yes	maximal, complemented
2	C₂²×Q₈×D₆₁	C₂	1	56	yes	maximal, direct product factor
3	C₂³×C₄×D₆₁	C₂	1	3	yes	maximal
4	C₂³×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁴×D₆₁	C₂²	1	1	yes	characteristic
6	C₂²×Dic₁₂₂	C₂²	1	84	yes	complemented
7	C₂×Q₈×D₆₁	C₂²	1	448	yes	direct product factor
8	C₂³×Dic₆₁	C₂²	1	3	yes	—
9	C₂²×C₄×D₆₁	C₂²	1	84	yes	—
10	C₂²×Q₈×C₆₁	C₂²	1	28	yes	complemented
11	C₂³×C₄×C₆₁	C₂²	1	3	yes	—
12	C₂⁴×C₆₁	C₂³	1	1	yes	characteristic
13	C₂³×D₆₁	Q₈	1	16	yes	direct product factor
14	C₂³×D₆₁	C₂³	1	14	yes	—
15	C₂×Q₈×C₆₁	C₂³	1	112	yes	complemented
16	C₂²×C₄×C₆₁	C₂³	1	42	yes	—
17	C₂²×Dic₆₁	C₂³	1	42	yes	—
18	Q₈×D₆₁	C₂³	1	512	yes	direct product factor
19	C₂×C₄×D₆₁	C₂³	1	336	yes	—
20	C₂×Dic₁₂₂	C₂³	1	336	yes	complemented
21	C₂³×C₆₁	C₂×Q₈	1	8	yes	complemented
22	C₂³×C₆₁	C₂⁴	1	7	yes	—
23	C₂²×D₆₁	C₂×Q₈	1	112	yes	direct product factor
24	C₂²×D₆₁	C₂⁴	1	28	yes	—
25	Q₈×C₆₁	C₂⁴	1	64	yes	complemented
26	C₂×C₄×C₆₁	C₂⁴	1	84	yes	—
27	C₂×Dic₆₁	C₂⁴	1	84	yes	—
28	C₄×D₆₁	C₂⁴	1	192	yes	—
29	Dic₁₂₂	C₂⁴	1	192	yes	complemented
30	C₂²×C₆₁	C₂²×Q₈	1	28	yes	complemented
31	C₂²×C₆₁	C₂⁵	1	7	yes	—
32	C₂×D₆₁	C₂²×Q₈	1	112	yes	direct product factor
33	C₂×D₆₁	C₂⁵	1	8	yes	—
34	C₄×C₆₁	C₂⁵	1	24	yes	—
35	Dic₆₁	C₂⁵	1	24	yes	—
36	C₂⁴×Q₈	—	61	1	no	maximal, Sylow
37	C₂×C₆₁	C₂³×Q₈	1	14	yes	complemented
38	C₂×C₆₁	C₂⁶	1	1	yes	characteristic
39	D₆₁	C₂³×Q₈	1	16	yes	direct product factor
40	C₂³×Q₈	—	61	56	no	—
41	C₂³×Q₈	—	61	3	no	—
42	C₂³×Q₈	D₆₁	1	1	yes	characteristic, direct product factor
43	C₂⁴×C₄	—	61	3	no	—
44	C₆₁	C₂⁴×Q₈	1	1	yes	characteristic, complemented, Sylow
45	C₂⁵	—	61	1	no	—
46	C₂²×Q₈	—	61	448	no	—
47	C₂²×Q₈	—	61	84	no	—
48	C₂²×Q₈	C₂×D₆₁	1	28	yes	direct product factor
49	C₂³×C₄	—	61	3	no	—
50	C₂³×C₄	—	61	84	no	—
51	C₂³×C₄	C₂×D₆₁	1	3	yes	—
52	C₂⁴	—	61	16	no	—
53	C₂⁴	—	61	14	no	—
54	C₂⁴	C₂²×D₆₁	1	1	yes	characteristic
55	C₂×Q₈	—	61	512	no	—
56	C₂×Q₈	—	61	336	no	—
57	C₂×Q₈	C₂²×D₆₁	1	112	yes	direct product factor
58	C₂²×C₄	—	61	42	no	—
59	C₂²×C₄	—	61	336	no	—
60	C₂²×C₄	C₂²×D₆₁	1	42	yes	—
61	C₂³	—	61	112	no	—
62	C₂³	—	61	28	no	—
63	C₂³	Q₈×D₆₁	1	8	yes	direct product factor
64	C₂³	C₂³×D₆₁	1	7	yes	—
65	Q₈	—	61	192	no	—
66	Q₈	C₂³×D₆₁	1	64	yes	direct product factor
67	C₂×C₄	—	61	84	no	—
68	C₂×C₄	—	61	192	no	—
69	C₂×C₄	C₂³×D₆₁	1	84	yes	—
70	C₂²	—	61	112	no	—
71	C₂²	—	61	8	no	—
72	C₂²	C₂×Q₈×D₆₁	1	28	yes	direct product factor
73	C₂²	C₂⁴×D₆₁	1	7	yes	—
74	C₄	—	61	24	no	—
75	C₄	C₂⁴×D₆₁	1	24	yes	—
76	C₂	—	61	16	no	—
77	C₂	C₂²×Q₈×D₆₁	1	14	yes	direct product factor
78	C₂	C₂⁵×D₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂²×D₆₁
commutator	C₂×C₆₁	C₂⁶
Frattini	C₂	C₂⁵×D₆₁
Fitting	C₂³×Q₈×C₆₁	C₂
socle	C₂⁴×C₆₁	C₂³
hypercenter	C₂³×Q₈	D₆₁
hypocenter	C₆₁	C₂⁴×Q₈
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂⁴ ◁ C₂³×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂³×Dic₁₂₂	C₂	semidirect
2. C₂²×Q₈×D₆₁	C₂	direct (N × H)
4. C₂³×Q₈×C₆₁	C₂	semidirect
6. C₂²×Dic₁₂₂	C₂²	semidirect
7. C₂×Q₈×D₆₁	C₂²	direct (N × H)
10. C₂²×Q₈×C₆₁	C₂²	semidirect
13. C₂³×D₆₁	Q₈	direct (N × H)
15. C₂×Q₈×C₆₁	C₂³	semidirect
18. Q₈×D₆₁	C₂³	direct (N × H)
20. C₂×Dic₁₂₂	C₂³	semidirect
21. C₂³×C₆₁	C₂×Q₈	semidirect
23. C₂²×D₆₁	C₂×Q₈	direct (N × H)
25. Q₈×C₆₁	C₂⁴	semidirect
29. Dic₁₂₂	C₂⁴	semidirect
30. C₂²×C₆₁	C₂²×Q₈	semidirect
32. C₂×D₆₁	C₂²×Q₈	direct (N × H)
37. C₂×C₆₁	C₂³×Q₈	semidirect
39. D₆₁	C₂³×Q₈	direct (N × H)
42. C₂³×Q₈	D₆₁	direct (N × H)
44. C₆₁	C₂⁴×Q₈	semidirect
48. C₂²×Q₈	C₂×D₆₁	direct (N × H)
57. C₂×Q₈	C₂²×D₆₁	direct (N × H)
63. C₂³	Q₈×D₆₁	direct (N × H)
66. Q₈	C₂³×D₆₁	direct (N × H)
72. C₂²	C₂×Q₈×D₆₁	direct (N × H)
77. C₂	C₂²×Q₈×D₆₁	direct (N × H)

Subgroups — C23×Q8×D61 #21460613

Conjugacy classes of subgroups

Complements

Subgroups — C₂³×Q₈×D₆₁ #21460613