Subgroups — #29601052

Order 15616.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21444030	C₂	1	3	yes	maximal, complemented
2	C₂×#16839481	C₂	1	3	yes	maximal, complemented
3	C₆₁×#2258	C₂	1	1	yes	maximal, characteristic
4	#16839481	C₂²	1	1	yes	characteristic
5	#16839481	C₂²	1	3	yes	—
6	C₆₁×#504	C₄	1	1	yes	characteristic
7	C₆₁×M₆₄	C₄	1	3	yes	—
8	C₂×C₃₂×C₆₁	C₂²	1	3	yes	—
9	#131×C₆₁	C₈	1	1	yes	characteristic
10	M₃₂×C₆₁	C₈	1	3	yes	—
11	C₂×C₁₆×C₆₁	C₂×C₄	1	3	yes	—
12	C₃₂×C₆₁	C₂×C₄	1	3	yes	—
13	C₃₂×C₆₁	C₂³	1	1	yes	characteristic
14	#41×C₆₁	C₁₆	1	1	yes	characteristic
15	M₁₆×C₆₁	C₁₆	1	3	yes	—
16	C₂×C₈×C₆₁	C₂×C₈	1	3	yes	—
17	C₁₆×C₆₁	C₂×C₈	1	3	yes	—
18	C₁₆×C₆₁	C₂²×C₄	1	1	yes	characteristic
19	Q₈×C₆₁	C₃₂	1	1	yes	characteristic
20	D₄×C₆₁	C₃₂	1	3	yes	—
21	C₂×C₄×C₆₁	C₂×C₁₆	1	3	yes	—
22	C₈×C₆₁	C₂×C₁₆	1	3	yes	—
23	C₈×C₆₁	C₂²×C₈	1	1	yes	characteristic
24	#13737	—	61	1	no	maximal, Sylow
25	C₂²×C₆₁	C₂×C₃₂	1	3	yes	—
26	C₄×C₆₁	C₂×C₃₂	1	3	yes	—
27	C₄×C₆₁	C₂²×C₁₆	1	1	yes	characteristic
28	#2258	D₆₁	1	1	yes	characteristic
29	M₁₂₈	—	61	3	no	—
30	C₂×C₆₄	—	61	3	no	—
31	C₂×C₆₁	—	2	3	no	—
32	C₂×C₆₁	C₂²×C₃₂	1	1	yes	characteristic
33	#504	Dic₆₁	1	1	yes	characteristic
34	M₆₄	Dic₆₁	1	3	yes	—
35	C₂×C₃₂	C₂×D₆₁	1	3	yes	—
36	C₆₄	—	61	1	no	—
37	C₆₄	—	61	3	no	—
38	C₆₁	#13737	1	1	yes	characteristic, complemented, Sylow
39	#131	#92418	1	1	yes	characteristic
40	M₃₂	#92418	1	3	yes	—
41	C₂×C₁₆	C₂×Dic₆₁	1	3	yes	—
42	C₃₂	C₂×Dic₆₁	1	3	yes	—
43	C₃₂	C₂²×D₆₁	1	1	yes	characteristic
44	#41	#11758185	1	1	yes	characteristic
45	M₁₆	#11758185	1	3	yes	—
46	C₂×C₈	C₂×#92418	1	3	yes	—
47	C₁₆	C₂×#92418	1	3	yes	—
48	C₁₆	C₂²×Dic₆₁	1	1	yes	characteristic
49	Q₈	#14519683	1	1	yes	characteristic
50	D₄	#14519683	1	3	yes	—
51	C₂×C₄	C₂×#11758185	1	3	yes	—
52	C₈	C₂×#11758185	1	3	yes	—
53	C₈	C₂²×#92418	1	1	yes	characteristic
54	C₂²	C₂×#14519683	1	3	yes	—
55	C₄	C₂×#14519683	1	3	yes	—
56	C₄	C₂²×#11758185	1	1	yes	characteristic
57	C₂	—	2	3	no	—
58	C₂	C₂²×#14519683	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃₂	C₂²×D₆₁
commutator, socle	C₂×C₆₁	C₂²×C₃₂
Fitting	C₆₁×#2258	C₂
prime radical	#41×C₆₁	C₁₆
cosocle	C₃₂×C₆₁	C₂³
hypercenter	#2258	D₆₁
hypocenter	C₆₁	#13737
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₃₂ ◁ #2258

Complements

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

N	H ≅ G/N	type
1. #21444030	C₂	semidirect
2. C₂×#16839481	C₂	semidirect
38. C₆₁	#13737	semidirect

Maximal subgroups

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

subgroup	index
#21444030	2
C₂×#16839481	2
C₆₁×#2258	2
#13737	61