Subgroups — #21444016

Order 7808.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839596	C₂	1	1	yes	maximal, characteristic
2	C₁₆×Dic₆₁	C₂	1	1	yes	maximal, characteristic
3	C₆₁×M₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758185	C₄	1	1	yes	characteristic
5	C₈×Dic₆₁	C₄	1	1	yes	characteristic
6	#14519683	—	2	1	no	—
7	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
8	C₃₂×C₆₁	—	2	1	no	—
9	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
10	C₄×Dic₆₁	C₈	1	1	yes	characteristic
11	C₂×#92418	C₈	1	1	yes	characteristic
12	C₁₆×C₆₁	D₄	1	1	yes	characteristic
13	C₁₆×C₆₁	Q₈	1	1	yes	characteristic
14	#11758185	—	2	1	no	—
15	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
16	C₂×Dic₆₁	—	2	1	no	—
17	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₆₁	M₁₆	1	1	yes	characteristic
19	#92418	C₁₆	1	2	yes	—
20	C₂²×C₆₁	M₃₂	1	1	yes	characteristic
21	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₆₁	C₂×C₁₆	1	1	yes	characteristic
23	Dic₆₁	—	2	2	no	—
24	#1422	—	61	1	no	maximal, Sylow
25	C₂×C₆₁	—	2	1	no	—
26	C₂×C₆₁	C₄⋊C₁₆	1	1	yes	characteristic
27	M₆₄	—	61	1	no	—
28	M₆₄	D₆₁	1	1	yes	characteristic
29	C₄×C₁₆	—	61	1	no	—
30	C₆₁	#1422	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₁₆	—	61	1	no	—
32	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
33	C₄×C₈	—	61	1	no	—
34	C₃₂	—	2	1	no	—
35	C₃₂	—	122	1	no	—
36	C₂×C₈	—	61	1	no	—
37	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
38	C₄²	—	61	1	no	—
39	C₁₆	—	122	1	no	—
40	C₁₆	Dic₁₂₂	1	1	yes	characteristic
41	C₁₆	C₂²⋊D₆₁	1	1	yes	characteristic
42	C₂×C₄	—	122	1	no	—
43	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
44	C₈	—	61	2	no	—
45	C₈	#11758189	1	1	yes	characteristic
46	C₈	#11758196	1	1	yes	characteristic
47	C₂²	#14519716	1	1	yes	characteristic
48	C₄	—	122	2	no	—
49	C₄	#14519706	1	1	yes	characteristic
50	C₄	C₁₆×D₆₁	1	1	yes	characteristic
51	C₂	—	2	1	no	—
52	C₂	#16839580	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂²⋊D₆₁
commutator	C₄×C₆₁	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₆₁
Fitting	C₆₁×M₆₄	C₂
socle	C₂×C₆₁	C₄⋊C₁₆
hypercenter	M₆₄	D₆₁
hypocenter	C₆₁	#1422
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
30. C₆₁	#1422	semidirect