Subgroups — #21448101

Order 7808.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840167	C₂	1	2	yes	maximal
2	#16839590	C₂	1	4	yes	maximal
3	C₄×C₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
4	#14519777	—	2	2	no	—
5	#14519711	—	2	2	no	—
6	#14519711	C₂²	1	4	yes	—
7	C₂×C₁₆×C₆₁	C₂²	1	2	yes	—
8	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₂₂	—	4	2	no	—
10	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
11	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
12	C₄²×C₆₁	D₄	1	1	yes	characteristic
13	C₄⋊Dic₆₁	—	2	4	no	—
14	C₄⋊Dic₆₁	—	4	2	no	—
15	C₁₆×C₆₁	Q₈	1	4	yes	complemented
16	C₂×C₄×C₆₁	D₈	1	2	yes	—
17	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
18	C₂×Dic₆₁	—	4	4	no	—
19	Dic₁₂₂	—	8	4	no	—
20	C₈×C₆₁	Q₁₆	1	2	yes	—
21	C₈×C₆₁	C₂×Q₈	1	2	yes	—
22	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
23	C₄×C₆₁	SD₃₂	1	4	yes	—
24	C₄×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
25	C₄×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
26	Dic₆₁	—	8	4	no	—
27	#2254	—	61	1	no	maximal, Sylow
28	C₂×C₆₁	#500	1	1	yes	characteristic
29	C₂×C₆₁	C₂×SD₃₂	1	2	yes	—
30	#500	—	61	2	no	—
31	#367	—	61	4	no	—
32	C₄×C₁₆	D₆₁	1	1	yes	characteristic
33	C₆₁	#2254	1	1	yes	characteristic, complemented, Sylow
34	C₄⋊Q₈	—	122	2	no	—
35	C₂×C₁₆	C₂×D₆₁	1	2	yes	—
36	#107	—	61	4	no	—
37	#107	—	122	2	no	—
38	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
39	C₂×Q₈	—	244	2	no	—
40	C₂×C₈	D₂₄₄	1	1	yes	characteristic
41	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
42	C₄⋊C₄	—	122	4	no	—
43	C₄⋊C₄	—	244	2	no	—
44	C₄²	D₂₄₄	1	1	yes	characteristic
45	C₁₆	Dic₁₂₂	1	4	yes	complemented
46	Q₈	—	488	4	no	—
47	C₂×C₄	—	244	4	no	—
48	C₂×C₄	D₄₈₈	1	2	yes	—
49	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
50	C₈	Dic₂₄₄	1	2	yes	—
51	C₈	C₂×Dic₁₂₂	1	2	yes	—
52	C₂²	C₂×D₄₈₈	1	1	yes	characteristic
53	C₄	—	488	4	no	—
54	C₄	#14519722	1	4	yes	—
55	C₄	#14519777	1	1	yes	characteristic
56	C₄	C₂×Dic₂₄₄	1	1	yes	characteristic
57	C₂	#16840167	1	1	yes	characteristic
58	C₂	C₂×#14519722	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₄₈₈
commutator	C₂×C₈×C₆₁	C₂³
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₄×C₁₆×C₆₁	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	C₄×C₁₆	D₆₁
hypocenter	C₆₁	#2254
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
15. C₁₆×C₆₁	Q₈	semidirect
33. C₆₁	#2254	semidirect
45. C₁₆	Dic₁₂₂	semidirect