Subgroups — #21448113

Order 7808.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839596	C₂	1	3	yes	maximal, complemented
2	C₂×#14519683	C₂	1	3	yes	maximal, complemented
3	C₆₁×#504	C₂	1	1	yes	maximal, characteristic
4	#14519683	C₂²	1	1	yes	characteristic
5	#14519683	C₂²	1	3	yes	—
6	#131×C₆₁	C₄	1	1	yes	characteristic
7	M₃₂×C₆₁	C₄	1	3	yes	—
8	C₂×C₁₆×C₆₁	C₂²	1	3	yes	—
9	#41×C₆₁	C₈	1	1	yes	characteristic
10	M₁₆×C₆₁	C₈	1	3	yes	—
11	C₂×C₈×C₆₁	C₂×C₄	1	3	yes	—
12	C₁₆×C₆₁	C₂×C₄	1	3	yes	—
13	C₁₆×C₆₁	C₂³	1	1	yes	characteristic
14	Q₈×C₆₁	C₁₆	1	1	yes	characteristic
15	D₄×C₆₁	C₁₆	1	3	yes	—
16	C₂×C₄×C₆₁	C₂×C₈	1	3	yes	—
17	C₈×C₆₁	C₂×C₈	1	3	yes	—
18	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
19	C₂²×C₆₁	C₂×C₁₆	1	3	yes	—
20	C₄×C₆₁	C₂×C₁₆	1	3	yes	—
21	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
22	#2258	—	61	1	no	maximal, Sylow
23	C₂×C₆₁	—	2	3	no	—
24	C₂×C₆₁	C₂²×C₁₆	1	1	yes	characteristic
25	#504	D₆₁	1	1	yes	characteristic
26	M₆₄	—	61	3	no	—
27	C₂×C₃₂	—	61	3	no	—
28	C₆₁	#2258	1	1	yes	characteristic, complemented, Sylow
29	#131	Dic₆₁	1	1	yes	characteristic
30	M₃₂	Dic₆₁	1	3	yes	—
31	C₂×C₁₆	C₂×D₆₁	1	3	yes	—
32	C₃₂	—	61	1	no	—
33	C₃₂	—	61	3	no	—
34	#41	#92418	1	1	yes	characteristic
35	M₁₆	#92418	1	3	yes	—
36	C₂×C₈	C₂×Dic₆₁	1	3	yes	—
37	C₁₆	C₂×Dic₆₁	1	3	yes	—
38	C₁₆	C₂²×D₆₁	1	1	yes	characteristic
39	Q₈	#11758185	1	1	yes	characteristic
40	D₄	#11758185	1	3	yes	—
41	C₂×C₄	C₂×#92418	1	3	yes	—
42	C₈	C₂×#92418	1	3	yes	—
43	C₈	C₂²×Dic₆₁	1	1	yes	characteristic
44	C₂²	C₂×#11758185	1	3	yes	—
45	C₄	C₂×#11758185	1	3	yes	—
46	C₄	C₂²×#92418	1	1	yes	characteristic
47	C₂	—	2	3	no	—
48	C₂	C₂²×#11758185	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₁₆	C₂²×D₆₁
commutator, socle	C₂×C₆₁	C₂²×C₁₆
Fitting	C₆₁×#504	C₂
hypercenter	#504	D₆₁
hypocenter	C₆₁	#2258
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₁₆ ◁ #504

Complements

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

N	H ≅ G/N	type
1. #16839596	C₂	semidirect
2. C₂×#14519683	C₂	semidirect
28. C₆₁	#2258	semidirect