Subgroups — #21460845

Order 7808.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840623	C₂	1	1	yes	maximal, characteristic
2	#16840623	C₂	1	1	yes	maximal, characteristic
3	#16839537	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#92420	—	2	1	no	—
5	C₄⋊#92420	—	2	1	no	—
6	C₂×#11758185	C₄	1	1	yes	characteristic
7	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₆₁	C₄	1	1	yes	characteristic
9	C₂×#92420	—	4	1	no	—
10	C₂×#92420	—	4	1	no	—
11	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
12	C₄×Dic₆₁	D₄	1	1	yes	characteristic
13	C₂×#92418	Q₈	1	1	yes	characteristic
14	C₁₆×C₆₁	—	2	1	no	—
15	#11758185	C₈	1	2	yes	complemented
16	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
17	C₂×Dic₆₁	SD₁₆	1	1	yes	characteristic
18	C₂×Dic₆₁	SD₁₆	1	1	yes	characteristic
19	#92420	—	8	1	no	—
20	#92420	—	8	1	no	—
21	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
22	C₈×C₆₁	M₁₆	1	1	yes	characteristic
23	#92418	—	2	1	no	—
24	C₂²×C₆₁	#106	1	1	yes	characteristic
25	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
26	C₄×C₆₁	#108	1	1	yes	characteristic
27	Dic₆₁	—	2	1	no	—
28	Dic₆₁	—	2	1	no	—
29	#1368	—	61	1	no	maximal, Sylow
30	C₂×C₆₁	#334	1	1	yes	characteristic
31	C₂×C₆₁	#365	1	1	yes	characteristic
32	C₂×C₆₁	#365	1	1	yes	characteristic
33	#346	—	61	1	no	—
34	#334	—	61	1	no	—
35	#334	—	61	1	no	—
36	C₆₁	#1368	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₁₆	—	61	1	no	—
38	C₂×C₁₆	#6923	1	1	yes	characteristic
39	C₄⋊C₈	—	122	1	no	—
40	C₄⋊C₈	—	122	1	no	—
41	C₄×C₈	—	61	1	no	—
42	C₂×C₈	—	61	1	no	—
43	C₂×C₈	—	244	1	no	—
44	C₂×C₈	—	244	1	no	—
45	C₂×C₈	C₂×#6923	1	1	yes	characteristic
46	C₄²	—	61	1	no	—
47	C₁₆	—	2	1	no	—
48	C₁₆	—	61	2	no	—
49	C₂×C₄	—	61	1	no	—
50	C₂×C₄	—	61	1	no	—
51	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
52	C₈	—	122	1	no	—
53	C₈	—	488	1	no	—
54	C₈	—	488	1	no	—
55	C₈	D₆₁⋊C₈	1	1	yes	characteristic
56	C₈	#11758217	1	1	yes	characteristic
57	C₂²	#14519845	1	1	yes	characteristic
58	C₄	—	122	1	no	—
59	C₄	—	122	1	no	—
60	C₄	#14519844	1	1	yes	characteristic
61	C₄	#14519848	1	1	yes	characteristic
62	C₂	#16840624	1	1	yes	characteristic
63	C₂	#16840686	1	1	yes	characteristic
64	C₂	#16840687	1	1	yes	characteristic

	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
15. #11758185	C₈	semidirect
36. C₆₁	#1368	semidirect