Subgroups — #16840163

Order 3904.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14519768	C₂	1	2	yes	maximal
2	#14519711	C₂	1	1	yes	maximal, characteristic
3	#14519708	C₂	1	2	yes	maximal
4	C₈×Dic₆₁	C₂	1	1	yes	maximal, characteristic
5	#107×C₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×C₈×C₆₁	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
8	C₄⋊Dic₆₁	—	2	2	no	—
9	C₄⋊Dic₆₁	C₂²	1	2	yes	—
10	#11758196	—	2	2	no	—
11	C₄×Dic₆₁	C₂²	1	1	yes	characteristic
12	C₂×#92418	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₆₁	—	2	2	no	—
14	C₂×C₄×C₆₁	C₂³	1	1	yes	characteristic
15	C₂×Dic₆₁	—	2	2	no	—
16	C₂×Dic₆₁	D₄	1	1	yes	characteristic
17	C₂×Dic₆₁	D₄	1	1	yes	characteristic
18	C₈×C₆₁	Q₈	1	2	yes	—
19	#92418	Q₈	1	2	yes	—
20	C₂²×C₆₁	C₂×D₄	1	1	yes	characteristic
21	C₄×C₆₁	—	4	2	no	—
22	C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
24	Dic₆₁	—	2	1	no	—
25	Dic₆₁	—	2	1	no	—
26	Dic₆₁	—	4	2	no	—
27	C₂×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
28	C₂×C₆₁	#135	1	1	yes	characteristic
29	C₂×C₆₁	#135	1	1	yes	characteristic
30	#499	—	61	1	no	maximal, Sylow
31	C₆₁	#499	1	1	yes	characteristic, complemented, Sylow
32	#125	—	61	2	no	—
33	#107	—	61	1	no	—
34	#107	D₆₁	1	1	yes	characteristic
35	#106	—	61	2	no	—
36	C₄×C₈	—	61	1	no	—
37	C₂×C₈	—	61	1	no	—
38	C₂×C₈	C₂×D₆₁	1	1	yes	characteristic
39	C₄⋊C₄	—	61	2	no	—
40	C₄⋊C₄	—	122	2	no	—
41	C₄⋊C₄	—	122	2	no	—
42	C₄⋊C₄	C₂×D₆₁	1	2	yes	—
43	C₄²	—	61	1	no	—
44	C₂×C₄	—	2	2	no	—
45	C₂×C₄	—	61	1	no	—
46	C₂×C₄	—	61	1	no	—
47	C₂×C₄	—	122	2	no	—
48	C₂×C₄	C₂²×D₆₁	1	1	yes	characteristic
49	C₈	—	61	2	no	—
50	C₈	Dic₁₂₂	1	2	yes	—
51	C₂²	D₄×D₆₁	1	1	yes	characteristic
52	C₄	—	4	2	no	—
53	C₄	—	122	1	no	—
54	C₄	—	122	1	no	—
55	C₄	—	244	2	no	—
56	C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
57	C₄	Q₈×D₆₁	1	1	yes	characteristic
58	C₂	#14519776	1	1	yes	characteristic
59	C₂	#14519796	1	1	yes	characteristic
60	C₂	#14519800	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₆₁
commutator, cosocle	C₂×C₄×C₆₁	C₂³
Frattini	C₂×C₄	C₂²×D₆₁
Fitting	#107×C₆₁	C₂
socle, prime radical	C₂²×C₆₁	C₂×D₄
hypercenter	#107	D₆₁
hypocenter	C₆₁	#499
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
31. C₆₁	#499	semidirect

Maximal subgroups

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

subgroup	index
#14519768	2
#14519711	2
#14519708	2
C₈×Dic₆₁	2
#107×C₆₁	2
#499	61