Subgroups — #21460732

Order 7808.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11758187	C₂	1	2	yes	maximal
2	C₈×#92418	C₂	1	1	yes	maximal, characteristic
3	C₂×#11758187	C₄	1	4	yes	—
4	C₄×#92418	C₄	1	1	yes	characteristic
5	C₄×#92418	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic
7	C₂×C₈×C₆₁	C₈	1	2	yes	—
8	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
9	C₂×#92418	C₈	1	2	yes	—
10	C₂×#92418	C₂×C₄	1	2	yes	—
11	#11758187	—	2	4	no	—
12	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
13	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
14	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
15	C₈×C₆₁	C₁₆	1	4	yes	complemented
16	#92418	—	2	2	no	—
17	#92418	M₁₆	1	4	yes	—
18	C₂²×C₆₁	C₄×C₈	1	1	yes	characteristic
19	C₄×C₆₁	#97	1	2	yes	—
20	C₄×C₆₁	C₂×C₁₆	1	2	yes	—
21	C₄×C₆₁	M₃₂	1	2	yes	—
22	#1312	—	61	1	no	maximal, Sylow
23	C₂×C₆₁	#322	1	1	yes	characteristic
24	C₂×C₆₁	C₄×C₁₆	1	1	yes	characteristic
25	C₂×C₆₁	#346	1	1	yes	characteristic
26	C₄×C₁₆	—	61	2	no	—
27	C₈²	—	61	1	no	—
28	C₆₁	#1312	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₁₆	—	61	4	no	—
30	C₄×C₈	—	61	1	no	—
31	C₄×C₈	—	61	1	no	—
32	C₄×C₈	#6923	1	1	yes	characteristic
33	C₂×C₈	—	61	2	no	—
34	C₂×C₈	—	61	2	no	—
35	C₂×C₈	#92420	1	2	yes	—
36	C₄²	C₂×#6923	1	1	yes	characteristic
37	C₁₆	—	122	4	no	—
38	C₂×C₄	D₆₁⋊C₈	1	1	yes	characteristic
39	C₂×C₄	C₄×#6923	1	1	yes	characteristic
40	C₂×C₄	C₂×#92420	1	1	yes	characteristic
41	C₈	—	61	4	no	—
42	C₈	—	122	2	no	—
43	C₈	#11758187	1	4	yes	complemented
44	C₂²	C₄×#92420	1	1	yes	characteristic
45	C₄	#14519831	1	2	yes	—
46	C₄	C₂×#11758187	1	2	yes	—
47	C₄	#14519852	1	2	yes	—
48	C₂	#16840603	1	1	yes	characteristic
49	C₂	C₄×#11758187	1	1	yes	characteristic
50	C₂	#16840651	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂×#6923
commutator	C₂×C₆₁	C₄×C₁₆
Fitting	C₄×C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₄×C₈
hypercenter	C₄×C₈	#6923
hypocenter	C₆₁	#1312
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
15. C₈×C₆₁	C₁₆	semidirect
28. C₆₁	#1312	semidirect
43. C₈	#11758187	semidirect