Subgroups — D₈×D₇₆₉ #37589908

Order 24608.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×D₇₆₉	C₂	1	2	yes	maximal, complemented
2	D₆₁₅₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#27134366	C₂	1	2	yes	maximal, complemented
4	C₈×D₇₆₉	C₂	1	1	yes	maximal, characteristic, complemented
5	D₈×C₇₆₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₇₆₉	—	2	2	no	—
7	D₃₀₇₆	C₂²	1	2	yes	complemented
8	C₂²⋊D₇₆₉	—	2	2	no	—
9	C₄×D₇₆₉	C₂²	1	1	yes	characteristic
10	#20259670	C₂²	1	1	yes	characteristic, complemented
11	D₄×C₇₆₉	C₂²	1	2	yes	complemented
12	C₈×C₇₆₉	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₇₆₉	—	2	2	no	—
14	C₂×D₇₆₉	—	2	2	no	—
15	C₂×D₇₆₉	—	4	4	no	—
16	C₂×D₇₆₉	D₄	1	1	yes	characteristic
17	C₄×C₇₆₉	C₂³	1	1	yes	characteristic
18	Dic₇₆₉	D₄	1	1	yes	characteristic
19	C₂×C₇₆₉	—	4	2	no	—
20	C₂×C₇₆₉	C₂×D₄	1	1	yes	characteristic
21	D₇₆₉	—	4	2	no	—
22	D₇₆₉	D₈	1	2	yes	direct product factor
23	C₇₆₉	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₈	—	769	1	no	maximal, Sylow
25	C₂×D₄	—	769	2	no	—
26	D₈	—	769	2	no	—
27	D₈	—	769	1	no	—
28	D₈	D₇₆₉	1	1	yes	characteristic, direct product factor
29	C₂×C₈	—	769	1	no	—
30	C₂³	—	1538	2	no	—
31	D₄	—	769	2	no	—
32	D₄	—	1538	2	no	—
33	D₄	C₂×D₇₆₉	1	2	yes	complemented
34	C₂×C₄	—	769	1	no	—
35	C₈	—	769	1	no	—
36	C₈	C₂×D₇₆₉	1	1	yes	characteristic, complemented
37	C₂²	—	769	1	no	—
38	C₂²	—	2	2	no	—
39	C₂²	—	1538	2	no	—
40	C₂²	—	3076	4	no	—
41	C₄	—	769	1	no	—
42	C₄	C₂²×D₇₆₉	1	1	yes	characteristic
43	C₂	—	769	2	no	—
44	C₂	—	4	2	no	—
45	C₂	—	3076	2	no	—
46	C₂	D₄×D₇₆₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₇₆₉
commutator, cosocle	C₄×C₇₆₉	C₂³
Frattini	C₄	C₂²×D₇₆₉
Fitting	D₈×C₇₆₉	C₂
socle	C₂×C₇₆₉	C₂×D₄
hypercenter	D₈	D₇₆₉
hypocenter	C₇₆₉	C₂×D₈
LCS	G ▷ C₄×C₇₆₉ ▷ C₂×C₇₆₉ ▷ C₇₆₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. D₄×D₇₆₉	C₂	semidirect
2. D₆₁₅₂	C₂	semidirect
3. #27134366	C₂	semidirect
4. C₈×D₇₆₉	C₂	semidirect
5. D₈×C₇₆₉	C₂	semidirect
7. D₃₀₇₆	C₂²	semidirect
10. #20259670	C₂²	semidirect
11. D₄×C₇₆₉	C₂²	semidirect
12. C₈×C₇₆₉	C₂²	semidirect
22. D₇₆₉	D₈	direct (N × H)
23. C₇₆₉	C₂×D₈	semidirect
28. D₈	D₇₆₉	direct (N × H)
33. D₄	C₂×D₇₆₉	semidirect
36. C₈	C₂×D₇₆₉	semidirect

Maximal subgroups

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

subgroup	index
D₄×D₇₆₉	2
D₆₁₅₂	2
#27134366	2
C₈×D₇₆₉	2
D₈×C₇₆₉	2
C₂×D₈	769

Subgroups — D8×D769 #37589908

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈×D₇₆₉ #37589908