Subgroups — #21460934

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×#14519717	C₂	1	1	yes	maximal, characteristic
3	#14519827	—	2	2	no	—
4	#14519717	—	2	2	no	—
5	C₂×#11758185	C₄	1	1	yes	characteristic
6	C₂×#11758185	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₆₁	C₄	1	1	yes	characteristic
8	C₂²×C₄×C₆₁	C₈	1	1	yes	characteristic
9	C₂×C₈×C₆₁	—	2	1	no	—
10	C₂×C₈×C₆₁	—	2	1	no	—
11	C₂×C₈×C₆₁	C₈	1	1	yes	characteristic
12	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
13	#11758185	—	2	1	no	—
14	#11758185	D₄	1	2	yes	—
15	C₂³×C₆₁	C₁₆	1	1	yes	characteristic
16	C₂×C₄×C₆₁	—	2	1	no	—
17	C₂×C₄×C₆₁	—	2	1	no	—
18	C₂×C₄×C₆₁	C₁₆	1	1	yes	characteristic
19	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
20	C₈×C₆₁	—	2	1	no	—
21	C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₆₁	M₁₆	1	1	yes	characteristic
23	C₂²×C₆₁	—	2	1	no	—
24	C₂²×C₆₁	—	4	1	no	—
25	C₂²×C₆₁	C₂×C₁₆	1	1	yes	characteristic
26	C₄×C₆₁	—	2	1	no	—
27	C₄×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
28	C₄×C₆₁	M₃₂	1	1	yes	characteristic
29	#1400	—	61	1	no	maximal, Sylow
30	C₂×C₆₁	—	2	1	no	—
31	C₂×C₆₁	—	4	1	no	—
32	C₂×C₆₁	C₂²⋊C₁₆	1	1	yes	characteristic
33	C₂×M₃₂	—	61	1	no	—
34	M₆₄	—	61	2	no	—
35	C₆₁	#1400	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₈	#6923	1	1	yes	characteristic
37	M₃₂	—	122	2	no	—
38	C₂×C₁₆	—	61	1	no	—
39	C₂×C₁₆	—	61	1	no	—
40	C₃₂	—	122	2	no	—
41	C₂²×C₄	#92420	1	1	yes	characteristic
42	C₂×C₈	—	2	1	no	—
43	C₂×C₈	—	2	1	no	—
44	C₂×C₈	#92420	1	1	yes	characteristic
45	C₂×C₈	C₂×#6923	1	1	yes	characteristic
46	C₁₆	—	61	2	no	—
47	C₁₆	—	122	1	no	—
48	C₂³	#11758187	1	1	yes	characteristic
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	#11758187	1	1	yes	characteristic
52	C₂×C₄	C₂×#92420	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	#11758217	1	1	yes	characteristic
55	C₈	C₂²⋊#6923	1	1	yes	characteristic
56	C₂²	—	2	1	no	—
57	C₂²	—	4	1	no	—
58	C₂²	C₂×#11758187	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	C₂²⋊#92420	1	1	yes	characteristic
61	C₄	#14519851	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	4	1	no	—
64	C₂	C₂²⋊#11758187	1	1	yes	characteristic

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

Complements

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

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