Subgroups — #21443852

Order 7808.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839540	C₂	1	2	yes	maximal, complemented
2	C₆₁×#490	C₂	1	1	yes	maximal, characteristic
3	#14519717	—	2	2	no	—
4	#127×C₆₁	C₄	1	1	yes	characteristic
5	#125×C₆₁	C₄	1	1	yes	characteristic
6	#102×C₆₁	—	2	2	no	—
7	#97×C₆₁	C₂²	1	1	yes	characteristic
8	C₂×D₄×C₆₁	—	2	1	no	—
9	C₂×D₄×C₆₁	—	4	1	no	—
10	C₂×C₈×C₆₁	D₄	1	2	yes	—
11	C₄⋊C₄×C₆₁	—	2	1	no	—
12	C₄⋊C₄×C₆₁	—	4	1	no	—
13	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
14	#11758185	—	2	4	no	—
15	C₂³×C₆₁	—	4	1	no	—
16	D₄×C₆₁	—	4	2	no	—
17	D₄×C₆₁	—	8	2	no	—
18	C₂×C₄×C₆₁	—	2	1	no	—
19	C₂×C₄×C₆₁	—	4	1	no	—
20	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₈×C₆₁	—	2	2	no	—
22	C₂²×C₆₁	—	8	2	no	—
23	C₂²×C₆₁	—	8	1	no	—
24	C₂²×C₆₁	#100	1	1	yes	characteristic
25	C₄×C₆₁	—	4	1	no	—
26	C₄×C₆₁	—	8	1	no	—
27	C₄×C₆₁	#104	1	2	yes	—
28	#1355	—	61	1	no	maximal, Sylow
29	C₂×C₆₁	—	2	1	no	—
30	C₂×C₆₁	—	16	1	no	—
31	C₂×C₆₁	#329	1	1	yes	characteristic
32	#490	D₆₁	1	1	yes	characteristic
33	#347	—	61	2	no	—
34	C₆₁	#1355	1	1	yes	characteristic, complemented, Sylow
35	#127	Dic₆₁	1	1	yes	characteristic
36	#125	Dic₆₁	1	1	yes	characteristic
37	M₃₂	—	122	2	no	—
38	#102	—	2	2	no	—
39	#97	C₂×D₆₁	1	1	yes	characteristic
40	C₂×D₄	—	2	1	no	—
41	C₂×D₄	—	4	1	no	—
42	C₂×C₈	C₂²⋊D₆₁	1	2	yes	—
43	C₄⋊C₄	—	2	1	no	—
44	C₄⋊C₄	—	4	1	no	—
45	C₄²	C₂×Dic₆₁	1	1	yes	characteristic
46	C₁₆	—	122	4	no	—
47	C₂³	—	4	1	no	—
48	D₄	—	4	2	no	—
49	D₄	—	8	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	4	1	no	—
52	C₂×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
53	C₈	—	2	2	no	—
54	C₂²	—	8	2	no	—
55	C₂²	—	8	1	no	—
56	C₂²	#14519694	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	8	1	no	—
59	C₄	#14519704	1	2	yes	—
60	C₂	—	2	1	no	—
61	C₂	—	16	1	no	—
62	C₂	#16839502	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16839502
commutator	C₄²×C₆₁	C₂×C₄
Frattini	#97	C₂×D₆₁
Fitting	C₆₁×#490	C₂
socle	C₂×C₆₁	#329
hypercenter	#490	D₆₁
hypocenter	C₆₁	#1355
LCS	G ▷ C₄²×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #490

Complements

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

N	H ≅ G/N	type
1. #16839540	C₂	semidirect
34. C₆₁	#1355	semidirect