Subgroups — D₈×D₆₆₁ #35232542

Order 21152.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×D₆₆₁	C₂	1	2	yes	maximal, complemented
2	D₅₂₈₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#24902357	C₂	1	2	yes	maximal, complemented
4	C₈×D₆₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	D₈×C₆₆₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₆₆₁	—	2	2	no	—
7	D₂₆₄₄	C₂²	1	2	yes	complemented
8	C₂²⋊D₆₆₁	—	2	2	no	—
9	C₄×D₆₆₁	C₂²	1	1	yes	characteristic
10	#19126971	C₂²	1	1	yes	characteristic, complemented
11	D₄×C₆₆₁	C₂²	1	2	yes	complemented
12	C₈×C₆₆₁	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₆₆₁	—	2	2	no	—
14	C₂×D₆₆₁	—	2	2	no	—
15	C₂×D₆₆₁	—	4	4	no	—
16	C₂×D₆₆₁	D₄	1	1	yes	characteristic
17	C₄×C₆₆₁	C₂³	1	1	yes	characteristic
18	Dic₆₆₁	D₄	1	1	yes	characteristic
19	C₂×C₆₆₁	—	4	2	no	—
20	C₂×C₆₆₁	C₂×D₄	1	1	yes	characteristic
21	D₆₆₁	—	4	2	no	—
22	D₆₆₁	D₈	1	2	yes	direct product factor
23	C₆₆₁	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₈	—	661	1	no	maximal, Sylow
25	C₂×D₄	—	661	2	no	—
26	D₈	—	661	2	no	—
27	D₈	—	661	1	no	—
28	D₈	D₆₆₁	1	1	yes	characteristic, direct product factor
29	C₂×C₈	—	661	1	no	—
30	C₂³	—	1322	2	no	—
31	D₄	—	1322	2	no	—
32	D₄	—	661	2	no	—
33	D₄	C₂×D₆₆₁	1	2	yes	complemented
34	C₂×C₄	—	661	1	no	—
35	C₈	—	661	1	no	—
36	C₈	C₂×D₆₆₁	1	1	yes	characteristic, complemented
37	C₂²	—	2	2	no	—
38	C₂²	—	1322	2	no	—
39	C₂²	—	2644	4	no	—
40	C₂²	—	661	1	no	—
41	C₄	—	661	1	no	—
42	C₄	C₂²×D₆₆₁	1	1	yes	characteristic
43	C₂	—	4	2	no	—
44	C₂	—	2644	2	no	—
45	C₂	—	661	2	no	—
46	C₂	D₄×D₆₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₆₆₁
commutator, cosocle	C₄×C₆₆₁	C₂³
Frattini	C₄	C₂²×D₆₆₁
Fitting	D₈×C₆₆₁	C₂
socle	C₂×C₆₆₁	C₂×D₄
hypercenter	D₈	D₆₆₁
hypocenter	C₆₆₁	C₂×D₈
LCS	G ▷ C₄×C₆₆₁ ▷ C₂×C₆₆₁ ▷ C₆₆₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. D₄×D₆₆₁	C₂	semidirect
2. D₅₂₈₈	C₂	semidirect
3. #24902357	C₂	semidirect
4. C₈×D₆₆₁	C₂	semidirect
5. D₈×C₆₆₁	C₂	semidirect
7. D₂₆₄₄	C₂²	semidirect
10. #19126971	C₂²	semidirect
11. D₄×C₆₆₁	C₂²	semidirect
12. C₈×C₆₆₁	C₂²	semidirect
22. D₆₆₁	D₈	direct (N × H)
23. C₆₆₁	C₂×D₈	semidirect
28. D₈	D₆₆₁	direct (N × H)
33. D₄	C₂×D₆₆₁	semidirect
36. C₈	C₂×D₆₆₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₄×D₆₆₁	2
D₅₂₈₈	2
#24902357	2
C₈×D₆₆₁	2
D₈×C₆₆₁	2
C₂×D₈	661

Subgroups — D8×D661 #35232542

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈×D₆₆₁ #35232542