Subgroups — D₈×D₄₅₇ #28410561

Order 14624.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×D₄₅₇	C₂	1	2	yes	maximal, complemented
2	D₃₆₅₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#20300726	C₂	1	2	yes	maximal, complemented
4	C₈×D₄₅₇	C₂	1	1	yes	maximal, characteristic, complemented
5	D₈×C₄₅₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₄₅₇	—	2	2	no	—
7	D₁₈₂₈	C₂²	1	2	yes	complemented
8	C₂²⋊D₄₅₇	—	2	2	no	—
9	C₄×D₄₅₇	C₂²	1	1	yes	characteristic
10	#16814532	C₂²	1	1	yes	characteristic, complemented
11	D₄×C₄₅₇	C₂²	1	2	yes	complemented
12	C₈×C₄₅₇	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₄₅₇	—	2	2	no	—
14	C₂×D₄₅₇	—	2	2	no	—
15	C₂×D₄₅₇	—	4	4	no	—
16	C₂×D₄₅₇	D₄	1	1	yes	characteristic
17	C₄×C₄₅₇	C₂³	1	1	yes	characteristic
18	Dic₄₅₇	D₄	1	1	yes	characteristic
19	C₂×C₄₅₇	—	4	2	no	—
20	C₂×C₄₅₇	C₂×D₄	1	1	yes	characteristic
21	D₄₅₇	—	4	2	no	—
22	D₄₅₇	D₈	1	2	yes	direct product factor
23	C₄₅₇	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₈	—	457	1	no	maximal, Sylow
25	C₂×D₄	—	457	2	no	—
26	D₈	—	457	2	no	—
27	D₈	—	457	1	no	—
28	D₈	D₄₅₇	1	1	yes	characteristic, direct product factor
29	C₂×C₈	—	457	1	no	—
30	C₂³	—	914	2	no	—
31	D₄	—	914	2	no	—
32	D₄	—	457	2	no	—
33	D₄	C₂×D₄₅₇	1	2	yes	complemented
34	C₂×C₄	—	457	1	no	—
35	C₈	—	457	1	no	—
36	C₈	C₂×D₄₅₇	1	1	yes	characteristic, complemented
37	C₂²	—	2	2	no	—
38	C₂²	—	1828	4	no	—
39	C₂²	—	914	2	no	—
40	C₂²	—	457	1	no	—
41	C₄	—	457	1	no	—
42	C₄	C₂²×D₄₅₇	1	1	yes	characteristic
43	C₂	—	4	2	no	—
44	C₂	—	1828	2	no	—
45	C₂	—	457	2	no	—
46	C₂	D₄×D₄₅₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₄₅₇
commutator, cosocle	C₄×C₄₅₇	C₂³
Frattini	C₄	C₂²×D₄₅₇
Fitting	D₈×C₄₅₇	C₂
socle	C₂×C₄₅₇	C₂×D₄
hypercenter	D₈	D₄₅₇
hypocenter	C₄₅₇	C₂×D₈
LCS	G ▷ C₄×C₄₅₇ ▷ C₂×C₄₅₇ ▷ C₄₅₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. D₄×D₄₅₇	C₂	semidirect
2. D₃₆₅₆	C₂	semidirect
3. #20300726	C₂	semidirect
4. C₈×D₄₅₇	C₂	semidirect
5. D₈×C₄₅₇	C₂	semidirect
7. D₁₈₂₈	C₂²	semidirect
10. #16814532	C₂²	semidirect
11. D₄×C₄₅₇	C₂²	semidirect
12. C₈×C₄₅₇	C₂²	semidirect
22. D₄₅₇	D₈	direct (N × H)
23. C₄₅₇	C₂×D₈	semidirect
28. D₈	D₄₅₇	direct (N × H)
33. D₄	C₂×D₄₅₇	semidirect
36. C₈	C₂×D₄₅₇	semidirect

Maximal subgroups

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

subgroup	index
D₄×D₄₅₇	2
D₃₆₅₆	2
#20300726	2
C₈×D₄₅₇	2
D₈×C₄₅₇	2
C₂×D₈	457

Subgroups — D8×D457 #28410561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈×D₄₅₇ #28410561