Subgroups — D₈×D₆₉₁ #36348808

Order 22112.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×D₆₉₁	C₂	1	2	yes	maximal, complemented
2	D₅₅₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#26010851	C₂	1	2	yes	maximal, complemented
4	C₈×D₆₉₁	C₂	1	1	yes	maximal, characteristic, complemented
5	D₈×C₆₉₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₆₉₁	—	2	2	no	—
7	D₂₇₆₄	C₂²	1	2	yes	complemented
8	C₂²⋊D₆₉₁	—	2	2	no	—
9	C₄×D₆₉₁	C₂²	1	1	yes	characteristic
10	C₆₉₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
11	D₄×C₆₉₁	C₂²	1	2	yes	complemented
12	C₈×C₆₉₁	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₆₉₁	—	2	2	no	—
14	C₂×D₆₉₁	—	2	2	no	—
15	C₂×D₆₉₁	—	4	4	no	—
16	C₂×D₆₉₁	D₄	1	1	yes	characteristic
17	C₄×C₆₉₁	C₂³	1	1	yes	characteristic
18	Dic₆₉₁	D₄	1	1	yes	characteristic
19	C₂×C₆₉₁	—	4	2	no	—
20	C₂×C₆₉₁	C₂×D₄	1	1	yes	characteristic
21	D₆₉₁	—	4	2	no	—
22	D₆₉₁	D₈	1	2	yes	direct product factor
23	C₆₉₁	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₈	—	691	1	no	maximal, Sylow
25	C₂×D₄	—	691	2	no	—
26	D₈	—	691	2	no	—
27	D₈	—	691	1	no	—
28	D₈	D₆₉₁	1	1	yes	characteristic, direct product factor
29	C₂×C₈	—	691	1	no	—
30	C₂³	—	1382	2	no	—
31	D₄	—	1382	2	no	—
32	D₄	—	691	2	no	—
33	D₄	C₂×D₆₉₁	1	2	yes	complemented
34	C₂×C₄	—	691	1	no	—
35	C₈	—	691	1	no	—
36	C₈	C₂×D₆₉₁	1	1	yes	characteristic, complemented
37	C₂²	—	2	2	no	—
38	C₂²	—	1382	2	no	—
39	C₂²	—	691	1	no	—
40	C₂²	—	2764	4	no	—
41	C₄	—	691	1	no	—
42	C₄	C₂²×D₆₉₁	1	1	yes	characteristic
43	C₂	—	4	2	no	—
44	C₂	—	691	2	no	—
45	C₂	—	2764	2	no	—
46	C₂	D₄×D₆₉₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₆₉₁
commutator, cosocle	C₄×C₆₉₁	C₂³
Frattini	C₄	C₂²×D₆₉₁
Fitting	D₈×C₆₉₁	C₂
socle	C₂×C₆₉₁	C₂×D₄
hypercenter	D₈	D₆₉₁
hypocenter	C₆₉₁	C₂×D₈
LCS	G ▷ C₄×C₆₉₁ ▷ C₂×C₆₉₁ ▷ C₆₉₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. D₄×D₆₉₁	C₂	semidirect
2. D₅₅₂₈	C₂	semidirect
3. #26010851	C₂	semidirect
4. C₈×D₆₉₁	C₂	semidirect
5. D₈×C₆₉₁	C₂	semidirect
7. D₂₇₆₄	C₂²	semidirect
10. C₆₉₁⋊C₈	C₂²	semidirect
11. D₄×C₆₉₁	C₂²	semidirect
12. C₈×C₆₉₁	C₂²	semidirect
22. D₆₉₁	D₈	direct (N × H)
23. C₆₉₁	C₂×D₈	semidirect
28. D₈	D₆₉₁	direct (N × H)
33. D₄	C₂×D₆₉₁	semidirect
36. C₈	C₂×D₆₉₁	semidirect

Maximal subgroups

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

subgroup	index
D₄×D₆₉₁	2
D₅₅₂₈	2
#26010851	2
C₈×D₆₉₁	2
D₈×C₆₉₁	2
C₂×D₈	691

Subgroups — D8×D691 #36348808

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈×D₆₉₁ #36348808