Subgroups — C₂²×Q₈×Dic₆₁ #21458995

Order 7808.

1664 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×Dic₆₁	C₂	1	24	yes	maximal, direct product factor
2	C₂²×C₄⋊Dic₆₁	C₂	1	3	yes	maximal
3	C₂²×C₄×Dic₆₁	C₂	1	3	yes	maximal
4	C₂³×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂³×Dic₆₁	C₂²	1	3	yes	—
6	C₂³×Dic₆₁	C₂²	1	1	yes	characteristic
7	Q₈×Dic₆₁	C₂²	1	64	yes	direct product factor
8	C₂×C₄⋊Dic₆₁	C₂²	1	36	yes	—
9	C₂×C₄×Dic₆₁	C₂²	1	36	yes	—
10	C₂²×Q₈×C₆₁	C₄	1	16	yes	complemented
11	C₂²×Q₈×C₆₁	C₂²	1	12	yes	—
12	C₂³×C₄×C₆₁	C₂²	1	3	yes	—
13	C₂⁴×C₆₁	C₂³	1	1	yes	characteristic
14	C₂×Q₈×C₆₁	C₂×C₄	1	96	yes	complemented
15	C₂×Q₈×C₆₁	C₂³	1	16	yes	—
16	C₂²×C₄×C₆₁	C₂×C₄	1	24	yes	—
17	C₂²×C₄×C₆₁	C₂³	1	18	yes	—
18	C₂²×Dic₆₁	—	2	12	no	—
19	C₂²×Dic₆₁	Q₈	1	8	yes	direct product factor
20	C₂²×Dic₆₁	C₂³	1	18	yes	—
21	C₂²×Dic₆₁	C₂³	1	6	yes	—
22	C₄⋊Dic₆₁	C₂³	1	48	yes	—
23	C₄×Dic₆₁	C₂³	1	48	yes	—
24	C₂³×C₆₁	C₂²×C₄	1	4	yes	—
25	C₂³×C₆₁	C₂×Q₈	1	4	yes	—
26	C₂³×C₆₁	#41	1	4	yes	—
27	C₂³×C₆₁	C₂⁴	1	3	yes	—
28	Q₈×C₆₁	C₂²×C₄	1	64	yes	complemented
29	C₂×C₄×C₆₁	C₂²×C₄	1	72	yes	—
30	C₂×C₄×C₆₁	C₂⁴	1	12	yes	—
31	C₂×Dic₆₁	—	2	36	no	—
32	C₂×Dic₆₁	C₂×Q₈	1	24	yes	direct product factor
33	C₂×Dic₆₁	C₂⁴	1	12	yes	—
34	C₂×Dic₆₁	C₂⁴	1	4	yes	—
35	C₂²×C₆₁	C₄×Q₈	1	16	yes	complemented
36	C₂²×C₆₁	C₂³×C₄	1	6	yes	—
37	C₂²×C₆₁	C₂²×Q₈	1	6	yes	—
38	C₂²×C₆₁	C₂×#41	1	6	yes	—
39	C₂²×C₆₁	C₂⁵	1	1	yes	characteristic
40	C₄×C₆₁	C₂³×C₄	1	24	yes	—
41	Dic₆₁	—	2	12	no	—
42	Dic₆₁	C₂²×Q₈	1	8	yes	direct product factor
43	C₂²×C₄×Q₈	—	61	1	no	maximal, Sylow
44	C₂×C₆₁	C₂×C₄×Q₈	1	12	yes	complemented
45	C₂×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
46	C₂×C₆₁	C₂³×Q₈	1	1	yes	characteristic
47	C₂×C₆₁	C₂²×#41	1	1	yes	characteristic
48	C₂³×Q₈	D₆₁	1	1	yes	characteristic
49	C₂×C₄×Q₈	—	61	24	no	—
50	C₂²×C₄⋊C₄	—	61	3	no	—
51	C₂²×C₄²	—	61	3	no	—
52	C₆₁	C₂²×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
53	C₂²×Q₈	Dic₆₁	1	16	yes	direct product factor
54	C₂²×Q₈	C₂×D₆₁	1	12	yes	—
55	C₂³×C₄	—	61	1	no	—
56	C₂³×C₄	—	61	3	no	—
57	C₂³×C₄	C₂×D₆₁	1	3	yes	—
58	C₄×Q₈	—	61	64	no	—
59	C₂×C₄⋊C₄	—	61	36	no	—
60	C₂×C₄²	—	61	36	no	—
61	C₂⁴	C₂²×D₆₁	1	1	yes	characteristic
62	C₂×Q₈	C₂×Dic₆₁	1	96	yes	direct product factor
63	C₂×Q₈	C₂²×D₆₁	1	16	yes	—
64	C₂²×C₄	—	61	8	no	—
65	C₂²×C₄	—	61	6	no	—
66	C₂²×C₄	—	61	18	no	—
67	C₂²×C₄	—	122	12	no	—
68	C₂²×C₄	C₂×Dic₆₁	1	24	yes	—
69	C₂²×C₄	C₂²×D₆₁	1	18	yes	—
70	C₄⋊C₄	—	61	48	no	—
71	C₄²	—	61	48	no	—
72	C₂³	Q₈×D₆₁	1	4	yes	—
73	C₂³	#11758226	1	4	yes	—
74	C₂³	C₂²×Dic₆₁	1	4	yes	—
75	C₂³	C₂³×D₆₁	1	3	yes	—
76	Q₈	C₂²×Dic₆₁	1	64	yes	direct product factor
77	C₂×C₄	—	61	24	no	—
78	C₂×C₄	—	61	4	no	—
79	C₂×C₄	—	61	12	no	—
80	C₂×C₄	—	122	36	no	—
81	C₂×C₄	C₂²×Dic₆₁	1	72	yes	—
82	C₂×C₄	C₂³×D₆₁	1	12	yes	—
83	C₂²	Q₈×Dic₆₁	1	16	yes	direct product factor
84	C₂²	C₂³×Dic₆₁	1	6	yes	—
85	C₂²	C₂×Q₈×D₆₁	1	6	yes	—
86	C₂²	C₂×#11758226	1	6	yes	—
87	C₂²	C₂⁴×D₆₁	1	1	yes	characteristic
88	C₄	—	61	8	no	—
89	C₄	—	122	12	no	—
90	C₄	C₂³×Dic₆₁	1	24	yes	—
91	C₂	C₂×Q₈×Dic₆₁	1	12	yes	direct product factor
92	C₂	C₂⁴×Dic₆₁	1	1	yes	characteristic
93	C₂	C₂²×Q₈×D₆₁	1	1	yes	characteristic
94	C₂	C₂²×#11758226	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂²×D₆₁
commutator	C₂×C₆₁	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₆₁
Fitting	C₂³×Q₈×C₆₁	C₂
socle	C₂⁴×C₆₁	C₂³
hypercenter	C₂³×Q₈	D₆₁
hypocenter	C₆₁	C₂²×C₄×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. C₂×Q₈×Dic₆₁	C₂	direct (N × H)
7. Q₈×Dic₆₁	C₂²	direct (N × H)
10. C₂²×Q₈×C₆₁	C₄	semidirect
14. C₂×Q₈×C₆₁	C₂×C₄	semidirect
19. C₂²×Dic₆₁	Q₈	direct (N × H)
28. Q₈×C₆₁	C₂²×C₄	semidirect
32. C₂×Dic₆₁	C₂×Q₈	direct (N × H)
35. C₂²×C₆₁	C₄×Q₈	semidirect
42. Dic₆₁	C₂²×Q₈	direct (N × H)
44. C₂×C₆₁	C₂×C₄×Q₈	semidirect
52. C₆₁	C₂²×C₄×Q₈	semidirect
53. C₂²×Q₈	Dic₆₁	direct (N × H)
62. C₂×Q₈	C₂×Dic₆₁	direct (N × H)
76. Q₈	C₂²×Dic₆₁	direct (N × H)
83. C₂²	Q₈×Dic₆₁	direct (N × H)
91. C₂	C₂×Q₈×Dic₆₁	direct (N × H)

Subgroups — C22×Q8×Dic61 #21458995

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×Q₈×Dic₆₁ #21458995