Subgroups — C₆₁⋊#564 #16840517

Order 3904.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14519769	C₂	1	2	yes	maximal
2	#14519768	C₂	1	4	yes	maximal
3	#14519767	C₂	1	4	yes	maximal
4	#14519767	C₂	1	4	yes	maximal
5	#125×C₆₁	C₂	1	1	yes	maximal, characteristic
6	C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
7	C₄⋊C₄×C₆₁	C₂²	1	4	yes	—
8	C₄²×C₆₁	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₆₁	C₂²	1	2	yes	—
10	C₄⋊Dic₆₁	C₂²	1	4	yes	—
11	C₄⋊Dic₆₁	C₂²	1	2	yes	—
12	#11758196	C₂²	1	4	yes	—
13	#11758196	C₂²	1	4	yes	—
14	#11758196	C₂²	1	4	yes	—
15	#11758196	C₂²	1	4	yes	—
16	C₄×Dic₆₁	C₂²	1	4	yes	—
17	C₂×C₄×C₆₁	C₂³	1	4	yes	—
18	C₂×C₄×C₆₁	C₂³	1	1	yes	characteristic
19	C₂×C₄×C₆₁	C₂³	1	2	yes	—
20	C₂×Dic₆₁	C₂³	1	4	yes	—
21	C₂×Dic₆₁	C₂³	1	4	yes	—
22	C₂²×C₆₁	C₂⁴	1	1	yes	characteristic
23	C₄×C₆₁	—	2	4	no	—
24	C₄×C₆₁	—	2	2	no	—
25	C₄×C₆₁	—	2	1	no	—
26	Dic₆₁	—	2	4	no	—
27	Dic₆₁	—	2	4	no	—
28	C₂×C₆₁	2₋¹⁺⁴	1	2	yes	—
29	C₂×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
30	#564	—	61	1	no	maximal, Sylow
31	C₆₁	#564	1	1	yes	characteristic, complemented, Sylow
32	#125	—	61	4	no	—
33	#125	—	61	4	no	—
34	#125	—	61	4	no	—
35	#125	—	61	2	no	—
36	#125	D₆₁	1	1	yes	characteristic
37	C₄⋊C₄	—	61	4	no	—
38	C₄⋊C₄	—	61	4	no	—
39	C₄⋊C₄	—	61	4	no	—
40	C₄⋊C₄	—	61	4	no	—
41	C₄⋊C₄	—	61	4	no	—
42	C₄⋊C₄	—	61	2	no	—
43	C₄⋊C₄	—	61	2	no	—
44	C₄⋊C₄	C₂×D₆₁	1	2	yes	—
45	C₄⋊C₄	C₂×D₆₁	1	4	yes	—
46	C₄²	—	61	4	no	—
47	C₄²	C₂×D₆₁	1	1	yes	characteristic
48	C₂×C₄	—	61	4	no	—
49	C₂×C₄	—	61	4	no	—
50	C₂×C₄	C₂²×D₆₁	1	4	yes	—
51	C₂×C₄	C₂²×D₆₁	1	2	yes	—
52	C₂×C₄	C₂²×D₆₁	1	1	yes	characteristic
53	C₂²	C₂³×D₆₁	1	1	yes	characteristic
54	C₄	—	2	4	no	—
55	C₄	—	2	2	no	—
56	C₄	—	2	1	no	—
57	C₄	—	122	4	no	—
58	C₄	—	122	4	no	—
59	C₂	#14519824	1	2	yes	—
60	C₂	#14519825	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₆₁
commutator, socle, prime radical, cosocle	C₂²×C₆₁	C₂⁴
Fitting	#125×C₆₁	C₂
hypercenter	#125	D₆₁
hypocenter	C₆₁	#564
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
31. C₆₁	#564	semidirect

Maximal subgroups

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

subgroup	index
#14519769	2
#14519768	2
#14519767	2
#125×C₆₁	2
#564	61

Subgroups — C61⋊#564 #16840517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁⋊#564 #16840517