Subgroups — #30594792

Order 15616.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21460930	C₂	1	1	yes	maximal, characteristic
2	#21460930	C₂	1	1	yes	maximal, characteristic
3	#21443740	C₂	1	1	yes	maximal, characteristic
4	#16840694	C₄	1	2	yes	—
5	#16840694	C₄	1	2	yes	—
6	#16839538	C₄	1	1	yes	characteristic
7	#16839538	C₂²	1	1	yes	characteristic
8	C₆₁×#322	C₄	1	1	yes	characteristic
9	#14519827	—	2	2	no	—
10	#14519827	C₈	1	4	yes	complemented
11	C₂×#11758185	—	2	1	no	—
12	C₂×#11758185	C₂×C₄	1	1	yes	characteristic
13	C₂×#11758185	C₂×C₄	1	1	yes	characteristic
14	C₄×C₈×C₆₁	—	2	1	no	—
15	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₆₁	—	4	1	no	—
17	C₂×C₈×C₆₁	C₄²	1	1	yes	characteristic
18	C₂×C₈×C₆₁	M₁₆	1	1	yes	characteristic
19	C₄²×C₆₁	M₁₆	1	1	yes	characteristic
20	#11758185	—	4	1	no	—
21	#11758185	C₂×C₈	1	2	yes	—
22	#11758185	M₁₆	1	2	yes	—
23	C₂×C₄×C₆₁	—	2	1	no	—
24	C₂×C₄×C₆₁	#97	1	1	yes	characteristic
25	C₈×C₆₁	—	2	1	no	—
26	C₈×C₆₁	—	8	1	no	—
27	C₈×C₆₁	C₄×C₈	1	1	yes	characteristic
28	C₈×C₆₁	#97	1	1	yes	characteristic
29	#7333	—	61	1	no	maximal, Sylow
30	C₂²×C₆₁	#347	1	1	yes	characteristic
31	C₄×C₆₁	—	4	1	no	—
32	C₄×C₆₁	#322	1	1	yes	characteristic
33	C₄×C₆₁	#347	1	1	yes	characteristic
34	#1398	—	61	1	no	—
35	#1398	—	61	1	no	—
36	#1313	—	61	1	no	—
37	C₂×C₆₁	—	2	1	no	—
38	C₂×C₆₁	#1313	1	1	yes	characteristic
39	M₆₄	—	61	2	no	—
40	M₆₄	—	61	2	no	—
41	#346	—	61	1	no	—
42	#346	—	61	1	no	—
43	#322	#6923	1	1	yes	characteristic
44	C₆₁	#7333	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₁₆	—	61	1	no	—
46	C₂×C₁₆	—	61	1	no	—
47	C₂×C₁₆	—	122	1	no	—
48	C₄×C₈	—	2	1	no	—
49	C₄×C₈	C₂×#6923	1	1	yes	characteristic
50	C₃₂	—	61	4	no	—
51	C₃₂	—	122	2	no	—
52	C₂×C₈	—	4	1	no	—
53	C₂×C₈	#11758213	1	1	yes	characteristic
54	C₂×C₈	C₄×#6923	1	1	yes	characteristic
55	C₄²	#11758217	1	1	yes	characteristic
56	C₁₆	—	61	2	no	—
57	C₁₆	—	61	2	no	—
58	C₁₆	—	244	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	#14519832	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	8	1	no	—
63	C₈	C₈×#6923	1	1	yes	characteristic
64	C₈	#14519831	1	1	yes	characteristic
65	C₂²	#16840654	1	1	yes	characteristic
66	C₄	—	4	1	no	—
67	C₄	#92420⋊C₈	1	1	yes	characteristic
68	C₄	#16840655	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	#21460737	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#92420⋊C₈
commutator	C₈×C₆₁	C₄×C₈
Frattini	C₄×C₈	C₂×#6923
Fitting	C₆₁×#322	C₄
socle	C₂×C₆₁	#1313
prime radical	C₂²×C₆₁	#347
cosocle	#16839538	C₂²
hypercenter	#322	#6923
hypocenter	C₆₁	#7333
LCS	G ▷ C₈×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₄×C₈ ◁ #322

Complements

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

N	H ≅ G/N	type
10. #14519827	C₈	semidirect
44. C₆₁	#7333	semidirect

Maximal subgroups

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

subgroup	index
#21460930	2
#21443740	2
#7333	61