Subgroups — #30595979

Order 15616.

582 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14519831	C₂	1	3	yes	maximal
2	#21461013	C₂	1	3	yes	maximal
3	C₈²×D₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#14519831	C₄	1	12	yes	—
5	C₄×D₆₁⋊C₈	C₂²	1	3	yes	—
6	C₄²×#6923	C₂²	1	1	yes	characteristic
7	#16840603	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	#14519831	—	2	24	no	—
14	C₄×#92420	C₂×C₄	1	12	yes	—
15	C₂×C₈×D₆₁	C₂×C₄	1	6	yes	—
16	C₄²×D₆₁	C₂³	1	1	yes	characteristic
17	C₄×#92418	C₂×C₄	1	3	yes	—
18	C₈×Dic₆₁	C₂×C₄	1	6	yes	—
19	C₄×C₈×C₆₁	C₂×C₄	1	3	yes	—
20	C₂²×#6923	C₄²	1	4	yes	—
21	C₂×C₄×D₆₁	C₂²×C₄	1	3	yes	—
22	C₂×#92420	C₄²	1	12	yes	—
23	C₄×#6923	—	2	12	no	—
24	D₆₁⋊C₈	—	2	12	no	—
25	C₂×C₈×C₆₁	C₄²	1	6	yes	—
26	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
27	C₄×Dic₆₁	C₂²×C₄	1	3	yes	—
28	C₂×#92418	C₄²	1	6	yes	—
29	C₈×D₆₁	M₁₆	1	24	yes	—
30	C₂²×D₆₁	C₂×C₄²	1	1	yes	characteristic
31	C₂×#6923	—	2	12	no	—
32	C₂×C₄×C₆₁	C₂×C₄²	1	3	yes	—
33	C₂×Dic₆₁	C₂×C₄²	1	3	yes	—
34	C₄×D₆₁	C₂×M₁₆	1	12	yes	—
35	#92420	—	2	12	no	—
36	C₈×C₆₁	#97	1	12	yes	complemented
37	#92418	#97	1	12	yes	complemented
38	#7846	—	61	1	no	maximal, Sylow
39	C₂²×C₆₁	C₄³	1	1	yes	characteristic
40	C₂×D₆₁	C₄×M₁₆	1	6	yes	—
41	#6923	—	4	4	no	—
42	C₄×C₆₁	C₂×#97	1	6	yes	—
43	Dic₆₁	C₄×M₁₆	1	6	yes	—
44	C₄×#97	—	61	3	no	—
45	C₂×#322	—	61	3	no	—
46	C₂×C₈²	—	61	1	no	—
47	C₂×C₆₁	C₄×#97	1	3	yes	—
48	D₆₁	#1455	1	4	yes	—
49	C₂×#97	—	61	12	no	—
50	C₂×C₄×C₈	—	61	3	no	—
51	C₂×C₄×C₈	—	61	3	no	—
52	C₄³	—	61	1	no	—
53	#322	—	61	12	no	—
54	C₈²	—	61	3	no	—
55	C₈²	#6923	1	1	yes	characteristic, complemented
56	C₆₁	#7846	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₈	—	61	6	no	—
58	C₂²×C₈	—	61	6	no	—
59	C₂×C₄²	—	61	1	no	—
60	C₂×C₄²	—	61	6	no	—
61	#97	—	122	24	no	—
62	C₄×C₈	—	61	12	no	—
63	C₄×C₈	—	61	6	no	—
64	C₄×C₈	—	61	3	no	—
65	C₄×C₈	C₂×#6923	1	3	yes	—
66	C₂²×C₄	—	61	3	no	—
67	C₂²×C₄	—	61	4	no	—
68	C₂×C₈	—	61	6	no	—
69	C₂×C₈	—	61	24	no	—
70	C₂×C₈	—	61	12	no	—
71	C₂×C₈	—	122	12	no	—
72	C₂×C₈	C₄×#6923	1	6	yes	—
73	C₄²	—	61	3	no	—
74	C₄²	—	122	12	no	—
75	C₄²	C₂²×#6923	1	1	yes	characteristic
76	C₂³	—	61	1	no	—
77	C₂×C₄	—	61	3	no	—
78	C₂×C₄	—	61	12	no	—
79	C₂×C₄	—	122	12	no	—
80	C₂×C₄	C₂×C₄×#6923	1	3	yes	—
81	C₈	—	61	12	no	—
82	C₈	—	122	12	no	—
83	C₈	#14519831	1	12	yes	complemented
84	C₂²	—	61	6	no	—
85	C₂²	C₄²×#6923	1	1	yes	characteristic
86	C₄	—	61	6	no	—
87	C₄	—	244	4	no	—
88	C₄	C₂×#14519831	1	6	yes	—
89	C₂	—	61	4	no	—
90	C₂	C₄×#14519831	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	#7846
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. #16840603	C₄	semidirect
9. C₈×#92418	C₄	semidirect
10. C₈²×C₆₁	C₄	semidirect
36. C₈×C₆₁	#97	semidirect
37. #92418	#97	semidirect
55. C₈²	#6923	semidirect
56. C₆₁	#7846	semidirect
83. C₈	#14519831	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14519831	2
#21461013	2
C₈²×D₆₁	2
#7846	61