Subgroups — #21460937

Order 7808.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840694	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14519827	C₂	1	1	yes	maximal, characteristic, complemented
3	#16840180	C₂	1	1	yes	maximal, characteristic
4	#14519827	—	2	1	no	—
5	#14519827	—	2	1	no	—
6	#14519783	C₄	1	1	yes	characteristic
7	#14519716	—	2	1	no	—
8	C₂×#11758185	C₂²	1	1	yes	characteristic
9	C₁₆×D₆₁	—	2	1	no	—
10	M₃₂×C₆₁	C₄	1	1	yes	characteristic
11	#11758222	C₈	1	1	yes	characteristic
12	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
13	#11758194	C₈	1	1	yes	characteristic
14	#11758189	—	2	1	no	—
15	C₈×D₆₁	—	2	1	no	—
16	C₁₆×C₆₁	—	2	1	no	—
17	#11758185	D₄	1	1	yes	characteristic
18	#11758185	D₄	1	1	yes	characteristic
19	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
20	C₂²⋊D₆₁	—	2	1	no	—
21	D₂₄₄	C₁₆	1	1	yes	characteristic
22	C₄×D₆₁	—	2	1	no	—
23	Dic₁₂₂	C₁₆	1	1	yes	characteristic
24	C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₆₁	M₁₆	1	1	yes	characteristic
26	#92418	—	2	1	no	—
27	C₂²×C₆₁	M₃₂	1	1	yes	characteristic
28	C₂×D₆₁	—	2	1	no	—
29	C₄×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
30	C₄×C₆₁	C₂×C₁₆	1	1	yes	characteristic
31	Dic₆₁	—	2	1	no	—
32	#1401	—	61	1	no	maximal, Sylow
33	C₂×C₆₁	—	2	1	no	—
34	C₂×C₆₁	C₂²⋊C₁₆	1	1	yes	characteristic
35	D₆₁	—	4	1	no	—
36	#504	—	61	1	no	—
37	M₆₄	—	61	1	no	—
38	C₂×C₃₂	—	61	1	no	—
39	C₆₁	#1401	1	1	yes	characteristic, complemented, Sylow
40	#131	—	61	1	no	—
41	M₃₂	—	122	1	no	—
42	M₃₂	#6923	1	1	yes	characteristic
43	C₂×C₁₆	—	61	1	no	—
44	C₂×C₁₆	—	122	1	no	—
45	C₃₂	—	122	1	no	—
46	C₃₂	—	122	1	no	—
47	#41	—	61	1	no	—
48	M₁₆	—	61	1	no	—
49	M₁₆	—	122	1	no	—
50	C₂×C₈	—	122	1	no	—
51	C₂×C₈	C₂×#6923	1	1	yes	characteristic
52	C₁₆	—	2	1	no	—
53	C₁₆	—	61	1	no	—
54	C₁₆	—	61	1	no	—
55	Q₈	—	61	1	no	—
56	D₄	—	61	1	no	—
57	D₄	—	122	1	no	—
58	C₂×C₄	—	122	1	no	—
59	C₂×C₄	D₆₁⋊C₈	1	1	yes	characteristic
60	C₈	—	122	1	no	—
61	C₈	#11758213	1	1	yes	characteristic
62	C₈	C₂²⋊#6923	1	1	yes	characteristic
63	C₂²	—	122	1	no	—
64	C₂²	#14519852	1	1	yes	characteristic
65	C₄	—	122	1	no	—
66	C₄	#14519834	1	1	yes	characteristic
67	C₄	D₆₁⋊C₁₆	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	244	1	no	—
70	C₂	#16840657	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#6923
commutator	C₄×C₆₁	C₂×C₁₆
Frattini	C₂×C₈	C₂×#6923
Fitting	M₃₂×C₆₁	C₄
socle	C₂×C₆₁	C₂²⋊C₁₆
hypercenter	M₃₂	#6923
hypocenter	C₆₁	#1401
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
1. #16840694	C₂	semidirect
2. C₂×#14519827	C₂	semidirect
39. C₆₁	#1401	semidirect