Subgroups — C₂⁶×D₄ #10587006

Order 512.

805186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁸	C₂	1	2	yes	maximal, complemented
2	C₂⁵×D₄	C₂	1	252	yes	maximal, direct product factor
3	C₂⁶×C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁷	—	2	128	no	—
5	C₂⁷	C₂²	1	1	yes	characteristic
6	C₂⁷	C₂²	1	252	yes	complemented
7	C₂⁴×D₄	C₂²	1	10416	yes	direct product factor
8	C₂⁵×C₄	C₂²	1	126	yes	complemented
9	C₂⁶	—	2	8064	no	—
10	C₂⁶	D₄	1	64	yes	direct product factor
11	C₂⁶	C₂³	1	63	yes	—
12	C₂⁶	C₂³	1	5208	yes	complemented
13	C₂³×D₄	C₂³	1	89280	yes	direct product factor
14	C₂⁴×C₄	C₂³	1	2604	yes	complemented
15	C₂⁵	—	2	83328	no	—
16	C₂⁵	C₂×D₄	1	2016	yes	direct product factor
17	C₂⁵	C₂⁴	1	651	yes	—
18	C₂⁵	C₂⁴	1	22320	yes	complemented
19	C₂²×D₄	C₂⁴	1	166656	yes	direct product factor
20	C₂³×C₄	C₂⁴	1	11160	yes	complemented
21	C₂⁴	—	2	178560	no	—
22	C₂⁴	C₂²×D₄	1	10416	yes	direct product factor
23	C₂⁴	C₂⁵	1	1395	yes	—
24	C₂⁴	C₂⁵	1	20832	yes	complemented
25	C₂×D₄	C₂⁵	1	64512	yes	direct product factor
26	C₂²×C₄	C₂⁵	1	10416	yes	complemented
27	C₂³	—	2	83328	no	—
28	C₂³	C₂³×D₄	1	11160	yes	direct product factor
29	C₂³	C₂⁶	1	651	yes	—
30	C₂³	C₂⁶	1	4032	yes	complemented
31	D₄	C₂⁶	1	4096	yes	direct product factor
32	C₂×C₄	C₂⁶	1	2016	yes	complemented
33	C₂²	—	2	8064	no	—
34	C₂²	C₂⁴×D₄	1	2604	yes	direct product factor
35	C₂²	C₂⁷	1	63	yes	—
36	C₂²	C₂⁷	1	128	yes	complemented
37	C₄	C₂⁷	1	64	yes	complemented
38	C₂	—	2	128	no	—
39	C₂	C₂⁵×D₄	1	126	yes	direct product factor
40	C₂	C₂⁸	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁷	C₂²
commutator, Frattini, cosocle	C₂	C₂⁸
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁷ ◁ G
LECS	G ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂⁸	C₂	semidirect
2. C₂⁵×D₄	C₂	direct (N × H)
3. C₂⁶×C₄	C₂	semidirect
6. C₂⁷	C₂²	semidirect
7. C₂⁴×D₄	C₂²	direct (N × H)
8. C₂⁵×C₄	C₂²	semidirect
10. C₂⁶	D₄	direct (N × H)
12. C₂⁶	C₂³	semidirect
13. C₂³×D₄	C₂³	direct (N × H)
14. C₂⁴×C₄	C₂³	semidirect
16. C₂⁵	C₂×D₄	direct (N × H)
18. C₂⁵	C₂⁴	semidirect
19. C₂²×D₄	C₂⁴	direct (N × H)
20. C₂³×C₄	C₂⁴	semidirect
22. C₂⁴	C₂²×D₄	direct (N × H)
24. C₂⁴	C₂⁵	semidirect
25. C₂×D₄	C₂⁵	direct (N × H)
26. C₂²×C₄	C₂⁵	semidirect
28. C₂³	C₂³×D₄	direct (N × H)
30. C₂³	C₂⁶	semidirect
31. D₄	C₂⁶	direct (N × H)
32. C₂×C₄	C₂⁶	semidirect
34. C₂²	C₂⁴×D₄	direct (N × H)
36. C₂²	C₂⁷	semidirect
37. C₄	C₂⁷	semidirect
39. C₂	C₂⁵×D₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁸	2
C₂⁵×D₄	2
C₂⁶×C₄	2

Subgroups — C26×D4 #10587006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁶×D₄ #10587006