Subgroups — #30594795

Order 15616.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21460931	C₂	1	1	yes	maximal, characteristic
2	#21460736	C₂	1	1	yes	maximal, characteristic
3	#21443954	C₂	1	1	yes	maximal, characteristic
4	#16840694	C₄	1	2	yes	—
5	#16840651	C₄	1	1	yes	characteristic
6	#16840603	C₄	1	1	yes	characteristic
7	#16839596	C₄	1	1	yes	characteristic
8	#16839537	C₂²	1	1	yes	characteristic
9	C₆₁×M₆₄	C₄	1	1	yes	characteristic
10	C₂×#11758187	—	2	1	no	—
11	C₄×#92420	—	2	1	no	—
12	#14519827	C₈	1	4	yes	complemented
13	C₂×#11758185	C₂×C₄	1	1	yes	characteristic
14	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
15	#14519683	—	2	1	no	—
16	C₂×C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₃₂×C₆₁	—	2	1	no	—
18	C₂×#92420	—	4	1	no	—
19	C₂×C₈×C₆₁	C₄²	1	1	yes	characteristic
20	C₄×Dic₆₁	M₁₆	1	1	yes	characteristic
21	C₂×#92418	M₁₆	1	1	yes	characteristic
22	#11758187	—	4	1	no	—
23	C₁₆×C₆₁	M₁₆	1	1	yes	characteristic
24	C₁₆×C₆₁	M₁₆	1	1	yes	characteristic
25	#11758185	C₂×C₈	1	2	yes	—
26	C₂×C₄×C₆₁	#97	1	1	yes	characteristic
27	C₂×Dic₆₁	—	2	1	no	—
28	#92420	—	8	1	no	—
29	C₈×C₆₁	C₄×C₈	1	1	yes	characteristic
30	C₈×C₆₁	#97	1	1	yes	characteristic
31	#92418	—	2	1	no	—
32	#7333	—	61	1	no	maximal, Sylow
33	C₂²×C₆₁	#347	1	1	yes	characteristic
34	C₄×C₆₁	#322	1	1	yes	characteristic
35	C₄×C₆₁	#347	1	1	yes	characteristic
36	Dic₆₁	—	4	1	no	—
37	#1398	—	61	1	no	—
38	#1398	—	61	1	no	—
39	#1313	—	61	1	no	—
40	C₂×C₆₁	—	2	1	no	—
41	C₂×C₆₁	#1313	1	1	yes	characteristic
42	M₆₄	—	61	2	no	—
43	M₆₄	—	61	1	no	—
44	M₆₄	#6923	1	1	yes	characteristic
45	#346	—	61	1	no	—
46	#346	—	61	1	no	—
47	#322	—	61	1	no	—
48	C₆₁	#7333	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₁₆	—	61	1	no	—
50	C₂×C₁₆	—	122	1	no	—
51	C₂×C₁₆	C₂×#6923	1	1	yes	characteristic
52	C₄×C₈	—	61	1	no	—
53	C₄×C₈	—	122	1	no	—
54	C₃₂	—	2	1	no	—
55	C₃₂	—	61	4	no	—
56	C₃₂	—	122	1	no	—
57	C₂×C₈	—	61	1	no	—
58	C₂×C₈	—	244	1	no	—
59	C₂×C₈	C₄×#6923	1	1	yes	characteristic
60	C₄²	—	61	1	no	—
61	C₁₆	—	61	2	no	—
62	C₁₆	—	244	1	no	—
63	C₁₆	#11758213	1	1	yes	characteristic
64	C₁₆	#11758217	1	1	yes	characteristic
65	C₂×C₄	—	122	1	no	—
66	C₂×C₄	#14519831	1	1	yes	characteristic
67	C₈	—	122	1	no	—
68	C₈	—	488	1	no	—
69	C₈	C₈×#6923	1	1	yes	characteristic
70	C₈	#14519832	1	1	yes	characteristic
71	C₂²	#16840652	1	1	yes	characteristic
72	C₄	—	244	1	no	—
73	C₄	#92420⋊C₈	1	1	yes	characteristic
74	C₄	#16840653	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	#21460738	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#92420⋊C₈
commutator	C₈×C₆₁	C₄×C₈
Frattini	C₂×C₁₆	C₂×#6923
Fitting	C₆₁×M₆₄	C₄
socle	C₂×C₆₁	#1313
prime radical	C₂²×C₆₁	#347
cosocle	#16839537	C₂²
hypercenter	M₆₄	#6923
hypocenter	C₆₁	#7333
LCS	G ▷ C₈×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
12. #14519827	C₈	semidirect
48. C₆₁	#7333	semidirect

Maximal subgroups

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

subgroup	index
#21460931	2
#21460736	2
#21443954	2
#7333	61