Subgroups — #21460935

Order 7808.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840694	C₂	1	2	yes	maximal, complemented
2	C₂×#14519716	C₂	1	1	yes	maximal, characteristic
3	#14519827	—	2	2	no	—
4	C₂×C₈×D₆₁	C₄	1	1	yes	characteristic
5	#14519716	—	2	2	no	—
6	C₂×#11758185	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₆₁	C₄	1	1	yes	characteristic
8	C₂×C₄×D₆₁	C₈	1	1	yes	characteristic
9	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
10	C₂×#92418	C₈	1	1	yes	characteristic
11	C₈×D₆₁	—	2	1	no	—
12	C₈×D₆₁	—	2	1	no	—
13	C₁₆×C₆₁	—	2	1	no	—
14	#11758185	D₄	1	2	yes	—
15	C₂²×D₆₁	C₁₆	1	1	yes	characteristic
16	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
17	C₂×Dic₆₁	C₁₆	1	1	yes	characteristic
18	C₄×D₆₁	—	2	1	no	—
19	C₄×D₆₁	—	2	1	no	—
20	C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₈×C₆₁	M₁₆	1	1	yes	characteristic
22	#92418	—	2	1	no	—
23	C₂²×C₆₁	C₂×C₁₆	1	1	yes	characteristic
24	C₂×D₆₁	—	2	1	no	—
25	C₂×D₆₁	—	4	1	no	—
26	C₄×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
27	C₄×C₆₁	M₃₂	1	1	yes	characteristic
28	Dic₆₁	—	2	1	no	—
29	#1400	—	61	1	no	maximal, Sylow
30	C₂×C₆₁	—	2	1	no	—
31	C₂×C₆₁	C₂²⋊C₁₆	1	1	yes	characteristic
32	D₆₁	—	4	1	no	—
33	C₂×M₃₂	—	61	1	no	—
34	M₆₄	—	61	2	no	—
35	C₆₁	#1400	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₈	—	61	1	no	—
37	M₃₂	—	122	2	no	—
38	C₂×C₁₆	—	61	1	no	—
39	C₂×C₁₆	#6923	1	1	yes	characteristic
40	C₃₂	—	122	2	no	—
41	C₂²×C₄	—	61	1	no	—
42	C₂×C₈	—	61	1	no	—
43	C₂×C₈	—	122	1	no	—
44	C₂×C₈	—	122	1	no	—
45	C₂×C₈	C₂×#6923	1	1	yes	characteristic
46	C₁₆	—	2	1	no	—
47	C₁₆	—	61	2	no	—
48	C₂³	—	61	1	no	—
49	C₂×C₄	—	61	1	no	—
50	C₂×C₄	—	122	1	no	—
51	C₂×C₄	—	122	1	no	—
52	C₂×C₄	D₆₁⋊C₈	1	1	yes	characteristic
53	C₈	—	122	1	no	—
54	C₈	#11758213	1	1	yes	characteristic
55	C₈	C₂²⋊#6923	1	1	yes	characteristic
56	C₂²	—	122	1	no	—
57	C₂²	—	244	1	no	—
58	C₂²	D₆₁⋊C₁₆	1	1	yes	characteristic
59	C₄	—	122	1	no	—
60	C₄	#14519834	1	1	yes	characteristic
61	C₄	#14519852	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	244	1	no	—
64	C₂	#16840657	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#6923
commutator	C₂²×C₆₁	C₂×C₁₆
Frattini	C₂×C₈	C₂×#6923
Fitting	C₂×C₁₆×C₆₁	C₄
socle	C₂×C₆₁	C₂²⋊C₁₆
hypercenter	C₂×C₁₆	#6923
hypocenter	C₆₁	#1400
LCS	G ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. #16840694	C₂	semidirect
35. C₆₁	#1400	semidirect