Subgroups — #21460847

Order 7808.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840684	C₂	1	2	yes	maximal
2	#16839537	C₂	1	1	yes	maximal, characteristic
3	#14519851	—	2	2	no	—
4	C₂×#11758185	C₄	1	1	yes	characteristic
5	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₆₁	C₄	1	1	yes	characteristic
7	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
8	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
9	C₂×#92418	D₄	1	1	yes	characteristic
10	#11758187	—	4	2	no	—
11	C₁₆×C₆₁	—	2	1	no	—
12	#11758185	C₈	1	2	yes	—
13	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
14	C₂×Dic₆₁	—	2	1	no	—
15	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
16	C₈×C₆₁	M₁₆	1	1	yes	characteristic
17	#92418	SD₁₆	1	2	yes	—
18	C₂²×C₆₁	#108	1	1	yes	characteristic
19	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
20	C₄×C₆₁	#106	1	1	yes	characteristic
21	Dic₆₁	—	4	1	no	—
22	#1369	—	61	1	no	maximal, Sylow
23	C₂×C₆₁	—	2	1	no	—
24	C₂×C₆₁	#334	1	1	yes	characteristic
25	#364	—	61	2	no	—
26	#346	—	61	1	no	—
27	C₆₁	#1369	1	1	yes	characteristic, complemented, Sylow
28	M₃₂	—	122	2	no	—
29	C₂×C₁₆	—	61	1	no	—
30	C₂×C₁₆	#6923	1	1	yes	characteristic
31	C₄×C₈	—	61	1	no	—
32	C₂×C₈	—	61	1	no	—
33	C₂×C₈	C₂×#6923	1	1	yes	characteristic
34	C₄²	—	61	1	no	—
35	C₁₆	—	2	1	no	—
36	C₁₆	—	61	2	no	—
37	C₁₆	—	244	2	no	—
38	C₂×C₄	—	122	1	no	—
39	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
40	C₈	—	61	2	no	—
41	C₈	D₆₁⋊C₈	1	1	yes	characteristic
42	C₈	#11758217	1	1	yes	characteristic
43	C₂²	#14519848	1	1	yes	characteristic
44	C₄	—	244	1	no	—
45	C₄	#14519844	1	1	yes	characteristic
46	C₄	#14519845	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#16840624	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14519845
commutator	C₈×C₆₁	C₂×C₈
Frattini	C₂×C₈	C₂×#6923
Fitting	C₂×C₁₆×C₆₁	C₄
socle	C₂×C₆₁	#334
hypercenter	C₂×C₁₆	#6923
hypocenter	C₆₁	#1369
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
27. C₆₁	#1369	semidirect