Subgroups — #21443741

Order 7808.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839538	C₂	1	1	yes	maximal, characteristic
2	#16839483	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#346	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758185	C₄	1	2	yes	—
5	C₄×#92418	C₄	1	2	yes	—
6	C₂×C₁₆×C₆₁	C₄	1	2	yes	—
7	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
10	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
11	C₂×#92418	—	2	2	no	—
12	C₁₆×C₆₁	—	2	2	no	—
13	#11758185	C₈	1	4	yes	complemented
14	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
15	C₂×C₄×C₆₁	M₁₆	1	2	yes	—
16	C₈×C₆₁	C₂×C₈	1	2	yes	—
17	C₈×C₆₁	M₁₆	1	2	yes	—
18	#92418	—	4	2	no	—
19	C₂²×C₆₁	#97	1	1	yes	characteristic
20	C₄×C₆₁	—	2	2	no	—
21	C₄×C₆₁	C₄×C₈	1	1	yes	characteristic
22	C₄×C₆₁	#97	1	1	yes	characteristic
23	#1313	—	61	1	no	maximal, Sylow
24	C₂×C₆₁	#322	1	1	yes	characteristic
25	C₂×C₆₁	#347	1	2	yes	—
26	#346	—	61	1	no	—
27	#346	D₆₁	1	1	yes	characteristic
28	#322	—	61	1	no	—
29	C₆₁	#1313	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₁₆	—	61	2	no	—
31	C₂×C₁₆	Dic₆₁	1	2	yes	—
32	C₄×C₈	—	61	2	no	—
33	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
34	C₂×C₈	—	122	2	no	—
35	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
36	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
37	C₄²	C₄×D₆₁	1	1	yes	characteristic
38	C₁₆	—	2	2	no	—
39	C₁₆	—	61	4	no	—
40	C₂×C₄	#11758189	1	2	yes	—
41	C₂×C₄	C₄×Dic₆₁	1	1	yes	characteristic
42	C₈	—	244	2	no	—
43	C₈	C₈×D₆₁	1	2	yes	—
44	C₈	#11758194	1	2	yes	—
45	C₂²	#14519687	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₈×Dic₆₁	1	1	yes	characteristic
48	C₄	#14519688	1	1	yes	characteristic
49	C₂	#16839484	1	1	yes	characteristic
50	C₂	#16839539	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄×Dic₆₁
commutator	C₄×C₆₁	C₄×C₈
Frattini	C₄×C₈	C₂×D₆₁
Fitting	C₆₁×#346	C₂
socle	C₂²×C₆₁	#97
hypercenter	#346	D₆₁
hypocenter	C₆₁	#1313
LCS	G ▷ C₄×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ #346

Complements

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

N	H ≅ G/N	type
13. #11758185	C₈	semidirect
29. C₆₁	#1313	semidirect