Subgroups — #21460959

Order 7808.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840667	C₂	1	2	yes	maximal
2	#16840128	C₂	1	1	yes	maximal, characteristic
3	#14519836	—	2	2	no	—
4	#14519774	C₂²	1	1	yes	characteristic
5	#14519697	—	2	2	no	—
6	#14519688	C₄	1	1	yes	characteristic, complemented
7	#125×C₆₁	C₄	1	1	yes	characteristic, complemented
8	C₂×D₂₄₄	—	4	1	no	—
9	C₂×D₂₄₄	D₄	1	2	yes	—
10	C₂²⋊#6923	—	4	2	no	—
11	C₄⋊C₄×C₆₁	—	2	1	no	—
12	C₄⋊C₄×C₆₁	—	4	1	no	—
13	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
14	C₂×#92418	—	2	1	no	—
15	C₂²×D₆₁	—	2	2	no	—
16	C₂×#6923	—	8	2	no	—
17	C₂×C₄×C₆₁	—	2	1	no	—
18	C₂×C₄×C₆₁	—	4	1	no	—
19	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
20	D₂₄₄	—	4	2	no	—
21	D₂₄₄	—	8	2	no	—
22	#92418	—	4	1	no	—
23	C₂²×C₆₁	#99	1	1	yes	characteristic
24	C₂×D₆₁	—	4	2	no	—
25	C₂×D₆₁	—	8	2	no	—
26	#6923	—	16	2	no	—
27	C₄×C₆₁	—	2	1	no	—
28	C₄×C₆₁	—	4	1	no	—
29	C₄×C₆₁	—	8	1	no	—
30	#1412	—	61	1	no	maximal, Sylow
31	C₂×C₆₁	—	2	1	no	—
32	C₂×C₆₁	#354	1	1	yes	characteristic
33	D₆₁	—	8	2	no	—
34	#490	—	61	1	no	—
35	#353	—	61	2	no	—
36	C₆₁	#1412	1	1	yes	characteristic, complemented, Sylow
37	#127	—	61	1	no	—
38	#125	#6923	1	1	yes	characteristic, complemented
39	#102	—	122	2	no	—
40	#99	—	122	2	no	—
41	#97	—	61	1	no	—
42	C₂×D₄	—	61	2	no	—
43	C₂×D₄	—	244	1	no	—
44	C₂×C₈	—	122	1	no	—
45	C₄⋊C₄	—	2	1	no	—
46	C₄⋊C₄	—	4	1	no	—
47	C₂²⋊C₄	—	244	2	no	—
48	C₄²	C₂×#6923	1	1	yes	characteristic
49	C₂³	—	122	2	no	—
50	D₄	—	488	2	no	—
51	D₄	—	244	2	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	—	4	1	no	—
54	C₂×C₄	—	488	2	no	—
55	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
56	C₈	—	244	1	no	—
57	C₂²	—	488	2	no	—
58	C₂²	—	244	2	no	—
59	C₂²	#14519835	1	1	yes	characteristic
60	C₄	—	2	1	no	—
61	C₄	—	4	1	no	—
62	C₄	—	8	1	no	—
63	C₄	—	976	2	no	—
64	C₂	—	2	1	no	—
65	C₂	—	488	2	no	—
66	C₂	#16840668	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16840668
commutator	C₄²×C₆₁	C₂×C₄
Frattini	C₄²	C₂×#6923
Fitting	#125×C₆₁	C₄
socle	C₂×C₆₁	#354
hypercenter	#125	#6923
hypocenter	C₆₁	#1412
LCS	G ▷ C₄²×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
6. #14519688	C₄	semidirect
7. #125×C₆₁	C₄	semidirect
36. C₆₁	#1412	semidirect
38. #125	#6923	semidirect