Subgroups — #21460822

Order 7808.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840654	C₂	1	2	yes	maximal, complemented
2	#16840128	C₂	1	1	yes	maximal, characteristic
3	#14519851	—	2	2	no	—
4	#14519774	C₄	1	1	yes	characteristic
5	#14519697	—	2	2	no	—
6	#14519688	C₂²	1	1	yes	characteristic
7	#125×C₆₁	C₄	1	1	yes	characteristic
8	C₂×D₂₄₄	—	2	1	no	—
9	C₂×D₂₄₄	—	4	1	no	—
10	C₄⋊C₄×C₆₁	—	2	1	no	—
11	C₄⋊C₄×C₆₁	—	4	1	no	—
12	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
13	C₂×#92418	D₄	1	2	yes	—
14	#11758187	—	2	4	no	—
15	C₂²×D₆₁	—	4	1	no	—
16	C₂×C₄×C₆₁	—	2	1	no	—
17	C₂×C₄×C₆₁	—	4	1	no	—
18	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
19	D₂₄₄	—	4	2	no	—
20	D₂₄₄	—	8	2	no	—
21	#92418	—	2	2	no	—
22	C₂²×C₆₁	#100	1	1	yes	characteristic
23	C₂×D₆₁	—	8	2	no	—
24	C₂×D₆₁	—	8	1	no	—
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	#329	1	1	yes	characteristic
31	D₆₁	—	16	1	no	—
32	#490	—	61	1	no	—
33	#347	—	61	2	no	—
34	C₆₁	#1355	1	1	yes	characteristic, complemented, Sylow
35	#127	—	61	1	no	—
36	#125	#6923	1	1	yes	characteristic
37	M₃₂	—	122	2	no	—
38	#102	—	122	2	no	—
39	#97	—	61	1	no	—
40	C₂×D₄	—	122	1	no	—
41	C₂×D₄	—	244	1	no	—
42	C₂×C₈	—	61	2	no	—
43	C₄⋊C₄	—	2	1	no	—
44	C₄⋊C₄	—	4	1	no	—
45	C₄²	C₂×#6923	1	1	yes	characteristic
46	C₁₆	—	122	4	no	—
47	C₂³	—	244	1	no	—
48	D₄	—	488	2	no	—
49	D₄	—	244	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	4	1	no	—
52	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
53	C₈	—	122	2	no	—
54	C₂²	—	488	2	no	—
55	C₂²	—	488	1	no	—
56	C₂²	#14519837	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	8	1	no	—
59	C₄	#14519842	1	2	yes	—
60	C₂	—	2	1	no	—
61	C₂	—	976	1	no	—
62	C₂	#16840618	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16840618
commutator	C₄²×C₆₁	C₂×C₄
Frattini	C₄²	C₂×#6923
Fitting	#125×C₆₁	C₄
socle	C₂×C₆₁	#329
hypercenter	#125	#6923
hypocenter	C₆₁	#1355
LCS	G ▷ C₄²×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
1. #16840654	C₂	semidirect
34. C₆₁	#1355	semidirect