Subgroups — #21444025

Order 7808.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839592	C₂	1	1	yes	maximal, characteristic
2	#16839590	C₂	1	1	yes	maximal, characteristic
3	C₆₁×M₆₄	C₂	1	1	yes	maximal, characteristic
4	#14519713	—	2	1	no	—
5	#14519711	—	2	1	no	—
6	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
7	C₃₂×C₆₁	C₄	1	2	yes	complemented
8	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
9	C₄⋊Dic₆₁	—	4	1	no	—
10	#11758194	—	4	1	no	—
11	C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₆₁	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
14	C₂×Dic₆₁	—	8	1	no	—
15	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
16	C₈×C₆₁	Q₁₆	1	1	yes	characteristic
17	#92418	—	8	1	no	—
18	C₂²×C₆₁	SD₃₂	1	1	yes	characteristic
19	C₄×C₆₁	#107	1	1	yes	characteristic
20	C₄×C₆₁	SD₃₂	1	1	yes	characteristic
21	Dic₆₁	—	16	1	no	—
22	#1426	—	61	1	no	maximal, Sylow
23	C₂×C₆₁	—	2	1	no	—
24	C₂×C₆₁	#367	1	1	yes	characteristic
25	M₆₄	D₆₁	1	1	yes	characteristic
26	#368	—	61	1	no	—
27	#367	—	61	1	no	—
28	C₆₁	#1426	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
30	#108	—	122	1	no	—
31	#107	—	122	1	no	—
32	C₃₂	Dic₆₁	1	2	yes	complemented
33	M₁₆	—	244	1	no	—
34	C₂×C₈	D₂₄₄	1	1	yes	characteristic
35	C₄⋊C₄	—	244	1	no	—
36	C₁₆	Dic₁₂₂	1	1	yes	characteristic
37	C₁₆	C₂×Dic₆₁	1	1	yes	characteristic
38	C₂×C₄	—	488	1	no	—
39	C₂×C₄	D₄₈₈	1	1	yes	characteristic
40	C₈	—	488	1	no	—
41	C₈	Dic₂₄₄	1	1	yes	characteristic
42	C₈	C₄⋊Dic₆₁	1	1	yes	characteristic
43	C₂²	#14519722	1	1	yes	characteristic
44	C₄	—	976	1	no	—
45	C₄	#14519711	1	1	yes	characteristic
46	C₄	#14519722	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#16839590	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16839590
commutator	C₁₆×C₆₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₆₁
Fitting	C₆₁×M₆₄	C₂
socle	C₂×C₆₁	#367
hypercenter	M₆₄	D₆₁
hypocenter	C₆₁	#1426
LCS	G ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
7. C₃₂×C₆₁	C₄	semidirect
28. C₆₁	#1426	semidirect
32. C₃₂	Dic₆₁	semidirect