Subgroups — C₂⁴×D₈ #63077

Order 256.

7727 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄	C₂	1	2	yes	maximal, complemented
2	C₂³×D₈	C₂	1	60	yes	maximal, direct product factor
3	C₂⁴×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁶	—	2	2	no	—
5	C₂³×D₄	—	2	30	no	—
6	C₂³×D₄	C₂²	1	60	yes	complemented
7	C₂⁴×C₄	C₂²	1	1	yes	characteristic
8	C₂²×D₈	C₂²	1	560	yes	direct product factor
9	C₂³×C₈	C₂²	1	30	yes	complemented
10	C₂⁵	—	2	60	no	—
11	C₂⁵	—	4	32	no	—
12	C₂⁵	D₄	1	1	yes	characteristic
13	C₂²×D₄	—	2	420	no	—
14	C₂²×D₄	C₂³	1	280	yes	complemented
15	C₂³×C₄	D₄	1	15	yes	—
16	C₂³×C₄	C₂³	1	15	yes	—
17	C₂×D₈	C₂³	1	960	yes	direct product factor
18	C₂²×C₈	C₂³	1	140	yes	complemented
19	C₂⁴	—	2	280	no	—
20	C₂⁴	—	4	480	no	—
21	C₂⁴	D₈	1	16	yes	direct product factor
22	C₂⁴	C₂×D₄	1	15	yes	—
23	C₂×D₄	—	2	840	no	—
24	C₂×D₄	C₂⁴	1	240	yes	complemented
25	C₂²×C₄	C₂×D₄	1	105	yes	—
26	C₂²×C₄	C₂⁴	1	35	yes	—
27	D₈	C₂⁴	1	256	yes	direct product factor
28	C₂×C₈	C₂⁴	1	120	yes	complemented
29	C₂³	—	2	240	no	—
30	C₂³	—	4	1120	no	—
31	C₂³	C₂×D₈	1	120	yes	direct product factor
32	C₂³	C₂²×D₄	1	35	yes	—
33	D₄	—	2	240	no	—
34	D₄	C₂⁵	1	32	yes	complemented
35	C₂×C₄	C₂²×D₄	1	105	yes	—
36	C₂×C₄	C₂⁵	1	15	yes	—
37	C₈	C₂⁵	1	16	yes	complemented
38	C₂²	—	2	32	no	—
39	C₂²	—	4	480	no	—
40	C₂²	C₂²×D₈	1	140	yes	direct product factor
41	C₂²	C₂³×D₄	1	15	yes	—
42	C₄	C₂³×D₄	1	15	yes	—
43	C₄	C₂⁶	1	1	yes	characteristic
44	C₂	—	4	32	no	—
45	C₂	C₂³×D₈	1	30	yes	direct product factor
46	C₂	C₂⁴×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁵	D₄
commutator, Frattini, cosocle	C₄	C₂⁶
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁵ ◁ C₂⁴×C₄ ◁ G
LECS	G ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₄	C₂	semidirect
2. C₂³×D₈	C₂	direct (N × H)
3. C₂⁴×C₈	C₂	semidirect
6. C₂³×D₄	C₂²	semidirect
8. C₂²×D₈	C₂²	direct (N × H)
9. C₂³×C₈	C₂²	semidirect
14. C₂²×D₄	C₂³	semidirect
17. C₂×D₈	C₂³	direct (N × H)
18. C₂²×C₈	C₂³	semidirect
21. C₂⁴	D₈	direct (N × H)
24. C₂×D₄	C₂⁴	semidirect
27. D₈	C₂⁴	direct (N × H)
28. C₂×C₈	C₂⁴	semidirect
31. C₂³	C₂×D₈	direct (N × H)
34. D₄	C₂⁵	semidirect
37. C₈	C₂⁵	semidirect
40. C₂²	C₂²×D₈	direct (N × H)
45. C₂	C₂³×D₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₄	2
C₂³×D₈	2
C₂⁴×C₈	2

Subgroups — C24×D8 #63077

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×D₈ #63077