Subgroups — #21460936

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	#16840179	C₂	1	1	yes	maximal, characteristic
4	#14519827	—	2	1	no	—
5	#14519827	—	2	1	no	—
6	#14519717	—	2	1	no	—
7	#14519717	C₄	1	1	yes	characteristic
8	C₂×#11758185	—	2	1	no	—
9	C₂×#11758185	C₂²	1	1	yes	characteristic
10	#131×C₆₁	C₄	1	1	yes	characteristic
11	#41×C₆₁	C₈	1	1	yes	characteristic
12	M₁₆×C₆₁	—	2	1	no	—
13	M₁₆×C₆₁	C₈	1	1	yes	characteristic
14	C₂×C₈×C₆₁	—	2	1	no	—
15	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
16	#11758185	—	2	1	no	—
17	#11758185	D₄	1	1	yes	characteristic
18	#11758185	D₄	1	1	yes	characteristic
19	Q₈×C₆₁	C₁₆	1	1	yes	characteristic
20	D₄×C₆₁	—	2	1	no	—
21	D₄×C₆₁	C₁₆	1	1	yes	characteristic
22	C₂×C₄×C₆₁	—	2	1	no	—
23	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
24	C₈×C₆₁	—	2	1	no	—
25	C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₆₁	M₁₆	1	1	yes	characteristic
27	C₂²×C₆₁	—	2	1	no	—
28	C₂²×C₆₁	M₃₂	1	1	yes	characteristic
29	C₄×C₆₁	—	2	1	no	—
30	C₄×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
31	C₄×C₆₁	C₂×C₁₆	1	1	yes	characteristic
32	#1401	—	61	1	no	maximal, Sylow
33	C₂×C₆₁	—	2	1	no	—
34	C₂×C₆₁	—	4	1	no	—
35	C₂×C₆₁	C₂²⋊C₁₆	1	1	yes	characteristic
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	#6923	1	1	yes	characteristic
41	M₃₂	—	61	1	no	—
42	M₃₂	—	122	1	no	—
43	C₂×C₁₆	—	61	1	no	—
44	C₂×C₁₆	—	122	1	no	—
45	C₃₂	—	122	1	no	—
46	C₃₂	—	122	1	no	—
47	#41	#92420	1	1	yes	characteristic
48	M₁₆	—	2	1	no	—
49	M₁₆	#92420	1	1	yes	characteristic
50	C₂×C₈	—	2	1	no	—
51	C₂×C₈	C₂×#6923	1	1	yes	characteristic
52	C₁₆	—	61	1	no	—
53	C₁₆	—	61	1	no	—
54	C₁₆	—	122	1	no	—
55	Q₈	#11758187	1	1	yes	characteristic
56	D₄	—	2	1	no	—
57	D₄	#11758187	1	1	yes	characteristic
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	C₂×#92420	1	1	yes	characteristic
60	C₈	—	2	1	no	—
61	C₈	#11758217	1	1	yes	characteristic
62	C₈	C₂²⋊#6923	1	1	yes	characteristic
63	C₂²	—	2	1	no	—
64	C₂²	#14519851	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	C₂²⋊#92420	1	1	yes	characteristic
67	C₄	C₂×#11758187	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	4	1	no	—
70	C₂	C₂²⋊#11758187	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#6923
commutator	C₄×C₆₁	C₂×C₁₆
Frattini	C₂×C₈	C₂×#6923
Fitting	#131×C₆₁	C₄
socle	C₂×C₆₁	C₂²⋊C₁₆
hypercenter	#131	#6923
hypocenter	C₆₁	#1401
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #131

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