Subgroups — #30595976

Order 15616.

486 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21461532	C₂	1	3	yes	maximal
2	#21461015	C₂	1	3	yes	maximal
3	C₈²×D₆₁	C₂	1	1	yes	maximal, characteristic
4	C₄×D₆₁⋊C₈	C₂²	1	3	yes	—
5	C₄²×#6923	C₂²	1	1	yes	characteristic
6	(C₂×#6923)⋊C₈	C₄	1	12	yes	—
7	#92420⋊C₈	C₄	1	12	yes	complemented
8	C₄×C₈×D₆₁	C₂²	1	3	yes	—
9	C₈×#92418	C₄	1	3	yes	complemented
10	C₈²×C₆₁	C₄	1	1	yes	characteristic, complemented
11	C₂×D₆₁⋊C₈	C₂×C₄	1	6	yes	—
12	C₂×C₄×#6923	C₂×C₄	1	6	yes	—
13	C₄×#92420	C₂×C₄	1	12	yes	—
14	C₂×C₈×D₆₁	C₂×C₄	1	6	yes	—
15	C₄²×D₆₁	C₂³	1	1	yes	characteristic
16	C₄×#92418	C₂×C₄	1	3	yes	—
17	C₈×Dic₆₁	C₂×C₄	1	6	yes	—
18	C₄×C₈×C₆₁	C₂×C₄	1	3	yes	—
19	C₂²×#6923	C₄²	1	4	yes	—
20	C₂×C₄×D₆₁	C₂²×C₄	1	3	yes	—
21	C₂×#92420	C₄²	1	12	yes	—
22	C₄×#6923	—	2	12	no	—
23	D₆₁⋊C₈	—	2	12	no	—
24	C₂×C₈×C₆₁	C₄²	1	6	yes	—
25	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
26	C₄×Dic₆₁	C₂²×C₄	1	3	yes	—
27	C₂×#92418	C₄²	1	6	yes	—
28	C₈×D₆₁	—	2	12	no	—
29	C₂²×D₆₁	C₂×C₄²	1	1	yes	characteristic
30	C₂×#6923	—	2	12	no	—
31	C₂×C₄×C₆₁	C₂×C₄²	1	3	yes	—
32	C₂×Dic₆₁	C₂×C₄²	1	3	yes	—
33	C₄×D₆₁	#131	1	12	yes	—
34	#92420	—	2	12	no	—
35	C₈×C₆₁	—	2	6	no	—
36	#92418	—	2	6	no	—
37	#7845	—	61	1	no	maximal, Sylow
38	C₂²×C₆₁	C₄³	1	1	yes	characteristic
39	C₂×D₆₁	#405	1	6	yes	—
40	#6923	—	4	4	no	—
41	C₄×C₆₁	#405	1	6	yes	—
42	Dic₆₁	#405	1	6	yes	—
43	#1744	—	61	3	no	—
44	C₂×#322	—	61	3	no	—
45	C₂×C₈²	—	61	1	no	—
46	C₂×C₆₁	#1726	1	3	yes	—
47	D₆₁	#1454	1	4	yes	—
48	C₂×C₄×C₈	—	61	3	no	—
49	C₂×C₄×C₈	—	61	3	no	—
50	C₄³	—	61	1	no	—
51	#336	—	61	12	no	—
52	#322	—	61	12	no	—
53	C₈²	—	61	3	no	—
54	C₈²	#6923	1	1	yes	characteristic, complemented
55	C₆₁	#7845	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₈	—	61	6	no	—
57	C₂²×C₈	—	61	6	no	—
58	C₂×C₄²	—	61	1	no	—
59	C₂×C₄²	—	61	6	no	—
60	C₄×C₈	—	61	12	no	—
61	C₄×C₈	—	61	6	no	—
62	C₄×C₈	—	61	3	no	—
63	C₄×C₈	C₂×#6923	1	3	yes	—
64	C₂²×C₄	—	61	3	no	—
65	C₂²×C₄	—	61	4	no	—
66	C₂×C₈	—	61	12	no	—
67	C₂×C₈	—	61	6	no	—
68	C₂×C₈	—	122	12	no	—
69	C₂×C₈	—	122	12	no	—
70	C₂×C₈	C₄×#6923	1	6	yes	—
71	C₄²	—	61	3	no	—
72	C₄²	—	122	12	no	—
73	C₄²	C₂²×#6923	1	1	yes	characteristic
74	C₂³	—	61	1	no	—
75	C₂×C₄	—	61	3	no	—
76	C₂×C₄	—	61	12	no	—
77	C₂×C₄	—	122	12	no	—
78	C₂×C₄	C₂×C₄×#6923	1	3	yes	—
79	C₈	—	2	6	no	—
80	C₈	—	122	12	no	—
81	C₈	—	122	6	no	—
82	C₂²	—	61	6	no	—
83	C₂²	C₄²×#6923	1	1	yes	characteristic
84	C₄	—	61	6	no	—
85	C₄	—	244	4	no	—
86	C₄	#16840725	1	6	yes	—
87	C₂	—	61	4	no	—
88	C₂	#21461475	1	3	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×#6923
commutator, socle	C₂²×C₆₁	C₄³
Fitting	C₈²×C₆₁	C₄
prime radical	C₂²×D₆₁	C₂×C₄²
cosocle	C₄²×D₆₁	C₂³
hypercenter	C₈²	#6923
hypocenter	C₆₁	#7845
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
7. #92420⋊C₈	C₄	semidirect
9. C₈×#92418	C₄	semidirect
10. C₈²×C₆₁	C₄	semidirect
54. C₈²	#6923	semidirect
55. C₆₁	#7845	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#21461532	2
#21461015	2
C₈²×D₆₁	2
#7845	61