Subgroups — #21460985

Order 7808.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840691	C₂	1	1	yes	maximal, characteristic
2	#16840689	C₂	1	1	yes	maximal, characteristic
3	#16839595	C₂	1	1	yes	maximal, characteristic
4	#14519848	—	2	1	no	—
5	#14519846	—	2	1	no	—
6	C₁₆×D₆₁	C₂²	1	1	yes	characteristic
7	#14519683	C₄	1	1	yes	characteristic, complemented
8	C₃₂×C₆₁	C₄	1	1	yes	characteristic, complemented
9	C₄⋊#6923	—	4	1	no	—
10	#11758213	—	4	1	no	—
11	C₈×D₆₁	D₄	1	1	yes	characteristic
12	C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
13	#11758185	Q₈	1	1	yes	characteristic
14	C₂×#6923	—	8	1	no	—
15	C₄×D₆₁	D₈	1	1	yes	characteristic
16	#92420	—	8	1	no	—
17	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
18	#92418	Q₁₆	1	1	yes	characteristic
19	C₂×D₆₁	SD₃₂	1	1	yes	characteristic
20	#6923	—	16	1	no	—
21	C₄×C₆₁	#107	1	1	yes	characteristic
22	Dic₆₁	SD₃₂	1	1	yes	characteristic
23	#1426	—	61	1	no	maximal, Sylow
24	C₂×C₆₁	#367	1	1	yes	characteristic
25	D₆₁	—	2	1	no	—
26	M₆₄	—	61	1	no	—
27	#368	—	61	1	no	—
28	#367	—	61	1	no	—
29	C₆₁	#1426	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₁₆	—	61	1	no	—
31	#108	—	122	1	no	—
32	#107	—	122	1	no	—
33	C₃₂	—	61	1	no	—
34	C₃₂	#6923	1	1	yes	characteristic, complemented
35	M₁₆	—	244	1	no	—
36	C₂×C₈	—	61	1	no	—
37	C₄⋊C₄	—	244	1	no	—
38	C₁₆	—	61	1	no	—
39	C₁₆	C₂×#6923	1	1	yes	characteristic
40	C₂×C₄	—	61	1	no	—
41	C₂×C₄	—	488	1	no	—
42	C₈	—	61	1	no	—
43	C₈	—	488	1	no	—
44	C₈	C₄⋊#6923	1	1	yes	characteristic
45	C₂²	—	61	1	no	—
46	C₄	—	61	1	no	—
47	C₄	—	976	1	no	—
48	C₄	#14519846	1	1	yes	characteristic
49	C₂	—	122	1	no	—
50	C₂	#16840689	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16840689
commutator	C₁₆×C₆₁	C₂×C₄
Frattini	C₁₆	C₂×#6923
Fitting	C₃₂×C₆₁	C₄
socle	C₂×C₆₁	#367
hypercenter	C₃₂	#6923
hypocenter	C₆₁	#1426
LCS	G ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
7. #14519683	C₄	semidirect
8. C₃₂×C₆₁	C₄	semidirect
29. C₆₁	#1426	semidirect
34. C₃₂	#6923	semidirect