Subgroups — #21460844

Order 7808.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840623	C₂	1	2	yes	maximal
2	#16839537	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#92420	—	2	2	no	—
4	C₂×#11758185	C₄	1	1	yes	characteristic
5	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₆₁	C₄	1	1	yes	characteristic
7	C₂×#92420	—	4	2	no	—
8	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
9	C₄×Dic₆₁	D₄	1	1	yes	characteristic
10	C₂×#92418	Q₈	1	1	yes	characteristic
11	C₁₆×C₆₁	C₈	1	2	yes	complemented
12	#11758185	—	2	1	no	—
13	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
14	C₂×Dic₆₁	SD₁₆	1	2	yes	—
15	#92420	—	8	2	no	—
16	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
17	C₈×C₆₁	M₁₆	1	1	yes	characteristic
18	#92418	—	2	1	no	—
19	C₂²×C₆₁	#106	1	1	yes	characteristic
20	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
21	C₄×C₆₁	#108	1	1	yes	characteristic
22	Dic₆₁	—	2	2	no	—
23	#1368	—	61	1	no	maximal, Sylow
24	C₂×C₆₁	#334	1	1	yes	characteristic
25	C₂×C₆₁	#365	1	2	yes	—
26	#346	—	61	1	no	—
27	#334	—	61	2	no	—
28	C₆₁	#1368	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₁₆	—	61	1	no	—
30	C₂×C₁₆	#6923	1	1	yes	characteristic
31	C₄⋊C₈	—	122	2	no	—
32	C₄×C₈	—	61	1	no	—
33	C₂×C₈	—	61	1	no	—
34	C₂×C₈	—	244	2	no	—
35	C₂×C₈	C₂×#6923	1	1	yes	characteristic
36	C₄²	—	61	1	no	—
37	C₁₆	—	122	1	no	—
38	C₁₆	#92420	1	2	yes	complemented
39	C₂×C₄	—	61	2	no	—
40	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
41	C₈	—	122	1	no	—
42	C₈	—	488	2	no	—
43	C₈	#11758213	1	1	yes	characteristic
44	C₈	C₂×#92420	1	1	yes	characteristic
45	C₂²	#14519845	1	1	yes	characteristic
46	C₄	—	122	2	no	—
47	C₄	C₄⋊#92420	1	1	yes	characteristic
48	C₄	#14519847	1	1	yes	characteristic
49	C₂	#16840623	1	1	yes	characteristic
50	C₂	#16840687	1	2	yes	—

	subgroup	G/H
center	C₂²	#14519845
commutator	C₈×C₆₁	C₂×C₈
Frattini	C₂×C₈	C₂×#6923
Fitting	C₂×C₁₆×C₆₁	C₄
socle	C₂²×C₆₁	#106
hypercenter	C₂×C₁₆	#6923
hypocenter	C₆₁	#1368
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
11. C₁₆×C₆₁	C₈	semidirect
28. C₆₁	#1368	semidirect
38. C₁₆	#92420	semidirect