Subgroups — #21445437

Order 7808.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840167	C₂	1	4	yes	maximal
2	#16840142	C₂	1	2	yes	maximal
3	C₈²×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₄₄	—	2	4	no	—
5	#14519777	C₂²	1	4	yes	—
6	#14519711	—	2	8	no	—
7	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₆₁	C₂²	1	2	yes	—
9	C₂×Dic₁₂₂	—	2	4	no	—
10	C₂×C₈×C₆₁	D₄	1	2	yes	—
11	C₂×C₈×C₆₁	D₄	1	4	yes	—
12	C₄²×C₆₁	C₂³	1	1	yes	characteristic
13	C₄⋊Dic₆₁	—	2	8	no	—
14	Dic₂₄₄	—	4	8	no	—
15	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
16	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
17	C₂×Dic₆₁	—	4	4	no	—
18	Dic₁₂₂	—	4	8	no	—
19	C₈×C₆₁	D₈	1	4	yes	—
20	C₈×C₆₁	Q₁₆	1	8	yes	complemented
21	C₂²×C₆₁	#127	1	1	yes	characteristic
22	C₄×C₆₁	C₂×D₈	1	2	yes	—
23	C₄×C₆₁	C₂×Q₁₆	1	4	yes	—
24	Dic₆₁	—	8	4	no	—
25	#1713	—	61	1	no	maximal, Sylow
26	C₂×C₆₁	#493	1	1	yes	characteristic
27	C₂×C₆₁	#494	1	2	yes	—
28	#500	—	61	4	no	—
29	#494	—	61	2	no	—
30	C₈²	D₆₁	1	1	yes	characteristic
31	C₆₁	#1713	1	1	yes	characteristic, complemented, Sylow
32	C₂×Q₁₆	—	122	4	no	—
33	C₄⋊Q₈	—	61	4	no	—
34	#107	—	122	8	no	—
35	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
36	C₄×C₈	C₂×D₆₁	1	2	yes	—
37	C₂×Q₈	—	122	4	no	—
38	Q₁₆	—	244	8	no	—
39	C₂×C₈	D₂₄₄	1	2	yes	—
40	C₂×C₈	D₂₄₄	1	4	yes	—
41	C₄⋊C₄	—	122	8	no	—
42	C₄²	C₂²×D₆₁	1	1	yes	characteristic
43	Q₈	—	244	8	no	—
44	C₂×C₄	—	244	4	no	—
45	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
46	C₂×C₄	C₂×D₂₄₄	1	2	yes	—
47	C₈	D₄₈₈	1	4	yes	—
48	C₈	Dic₂₄₄	1	8	yes	complemented
49	C₂²	#14519774	1	1	yes	characteristic
50	C₄	—	488	4	no	—
51	C₄	C₂×D₄₈₈	1	2	yes	—
52	C₄	C₂×Dic₂₄₄	1	4	yes	—
53	C₂	#16840139	1	1	yes	characteristic
54	C₂	#16840142	1	2	yes	—

	subgroup	G/H
center	C₂²	#14519774
commutator	C₄²×C₆₁	C₂³
Frattini	C₄²	C₂²×D₆₁
Fitting	C₈²×C₆₁	C₂
socle	C₂²×C₆₁	#127
hypercenter	C₈²	D₆₁
hypocenter	C₆₁	#1713
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
20. C₈×C₆₁	Q₁₆	semidirect
31. C₆₁	#1713	semidirect
48. C₈	Dic₂₄₄	semidirect