Subgroups — #21444022

Order 7808.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519683	C₂	1	1	yes	maximal, characteristic
2	#16839592	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#368	C₂	1	1	yes	maximal, characteristic
4	#14519713	—	2	1	no	—
5	#14519683	C₄	1	2	yes	—
6	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
7	#108×C₆₁	—	2	1	no	—
8	M₁₆×C₆₁	—	4	1	no	—
9	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
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	C₈×C₆₁	—	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	Q₃₂	1	1	yes	characteristic
19	C₄×C₆₁	#107	1	1	yes	characteristic
20	C₄×C₆₁	D₁₆	1	1	yes	characteristic
21	#1425	—	61	1	no	maximal, Sylow
22	C₂×C₆₁	—	2	1	no	—
23	C₂×C₆₁	#366	1	1	yes	characteristic
24	C₂×C₃₂	—	61	1	no	—
25	#368	—	61	1	no	—
26	#368	D₆₁	1	1	yes	characteristic
27	C₆₁	#1425	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
29	#108	—	2	1	no	—
30	#108	—	122	1	no	—
31	C₃₂	—	61	2	no	—
32	M₁₆	—	4	1	no	—
33	M₁₆	—	244	1	no	—
34	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
35	C₁₆	Dic₁₂₂	1	1	yes	characteristic
36	C₁₆	C₄×D₆₁	1	1	yes	characteristic
37	C₂×C₄	#11758199	1	1	yes	characteristic
38	C₈	—	8	1	no	—
39	C₈	—	488	1	no	—
40	C₈	#11758196	1	1	yes	characteristic
41	C₈	#11758202	1	1	yes	characteristic
42	C₂²	#14519723	1	1	yes	characteristic
43	C₄	#14519710	1	1	yes	characteristic
44	C₄	#14519718	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#16839587	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14519718
commutator	C₁₆×C₆₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₆₁
Fitting	C₆₁×#368	C₂
socle	C₂×C₆₁	#366
hypercenter	#368	D₆₁
hypocenter	C₆₁	#1425
LCS	G ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
27. C₆₁	#1425	semidirect