Subgroups — C₂⁶×D₈ #72304942

Order 1024.

1193173 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×D₄	C₂	1	2	yes	maximal, complemented
2	C₂⁵×D₈	C₂	1	252	yes	maximal, direct product factor
3	C₂⁶×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁸	—	2	2	no	—
5	C₂⁵×D₄	—	2	126	no	—
6	C₂⁵×D₄	C₂²	1	252	yes	complemented
7	C₂⁶×C₄	C₂²	1	1	yes	characteristic
8	C₂⁴×D₈	C₂²	1	10416	yes	direct product factor
9	C₂⁵×C₈	C₂²	1	126	yes	complemented
10	C₂⁷	—	2	252	no	—
11	C₂⁷	—	4	128	no	—
12	C₂⁷	D₄	1	1	yes	characteristic
13	C₂⁴×D₄	—	2	7812	no	—
14	C₂⁴×D₄	C₂³	1	5208	yes	complemented
15	C₂⁵×C₄	D₄	1	63	yes	—
16	C₂⁵×C₄	C₂³	1	63	yes	—
17	C₂³×D₈	C₂³	1	89280	yes	direct product factor
18	C₂⁴×C₈	C₂³	1	2604	yes	complemented
19	C₂⁶	—	2	5208	no	—
20	C₂⁶	—	4	8064	no	—
21	C₂⁶	D₈	1	64	yes	direct product factor
22	C₂⁶	C₂×D₄	1	63	yes	—
23	C₂³×D₄	—	2	78120	no	—
24	C₂³×D₄	C₂⁴	1	22320	yes	complemented
25	C₂⁴×C₄	C₂×D₄	1	1953	yes	—
26	C₂⁴×C₄	C₂⁴	1	651	yes	—
27	C₂²×D₈	C₂⁴	1	166656	yes	direct product factor
28	C₂³×C₈	C₂⁴	1	11160	yes	complemented
29	C₂⁵	—	2	22320	no	—
30	C₂⁵	—	4	83328	no	—
31	C₂⁵	C₂×D₈	1	2016	yes	direct product factor
32	C₂⁵	C₂²×D₄	1	651	yes	—
33	C₂²×D₄	—	2	156240	no	—
34	C₂²×D₄	C₂⁵	1	20832	yes	complemented
35	C₂³×C₄	C₂²×D₄	1	9765	yes	—
36	C₂³×C₄	C₂⁵	1	1395	yes	—
37	C₂×D₈	C₂⁵	1	64512	yes	direct product factor
38	C₂²×C₈	C₂⁵	1	10416	yes	complemented
39	C₂⁴	—	2	20832	no	—
40	C₂⁴	—	4	178560	no	—
41	C₂⁴	C₂²×D₈	1	10416	yes	direct product factor
42	C₂⁴	C₂³×D₄	1	1395	yes	—
43	C₂×D₄	—	2	62496	no	—
44	C₂×D₄	C₂⁶	1	4032	yes	complemented
45	C₂²×C₄	C₂³×D₄	1	9765	yes	—
46	C₂²×C₄	C₂⁶	1	651	yes	—
47	D₈	C₂⁶	1	4096	yes	direct product factor
48	C₂×C₈	C₂⁶	1	2016	yes	complemented
49	C₂³	—	2	4032	no	—
50	C₂³	—	4	83328	no	—
51	C₂³	C₂³×D₈	1	11160	yes	direct product factor
52	C₂³	C₂⁴×D₄	1	651	yes	—
53	D₄	—	2	4032	no	—
54	D₄	C₂⁷	1	128	yes	complemented
55	C₂×C₄	C₂⁴×D₄	1	1953	yes	—
56	C₂×C₄	C₂⁷	1	63	yes	—
57	C₈	C₂⁷	1	64	yes	complemented
58	C₂²	—	2	128	no	—
59	C₂²	—	4	8064	no	—
60	C₂²	C₂⁴×D₈	1	2604	yes	direct product factor
61	C₂²	C₂⁵×D₄	1	63	yes	—
62	C₄	C₂⁵×D₄	1	63	yes	—
63	C₄	C₂⁸	1	1	yes	characteristic
64	C₂	—	4	128	no	—
65	C₂	C₂⁵×D₈	1	126	yes	direct product factor
66	C₂	C₂⁶×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁷	D₄
commutator, Frattini, cosocle	C₄	C₂⁸
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁷ ◁ C₂⁶×C₄ ◁ G
LECS	G ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂⁶×D₄	C₂	semidirect
2. C₂⁵×D₈	C₂	direct (N × H)
3. C₂⁶×C₈	C₂	semidirect
6. C₂⁵×D₄	C₂²	semidirect
8. C₂⁴×D₈	C₂²	direct (N × H)
9. C₂⁵×C₈	C₂²	semidirect
14. C₂⁴×D₄	C₂³	semidirect
17. C₂³×D₈	C₂³	direct (N × H)
18. C₂⁴×C₈	C₂³	semidirect
21. C₂⁶	D₈	direct (N × H)
24. C₂³×D₄	C₂⁴	semidirect
27. C₂²×D₈	C₂⁴	direct (N × H)
28. C₂³×C₈	C₂⁴	semidirect
31. C₂⁵	C₂×D₈	direct (N × H)
34. C₂²×D₄	C₂⁵	semidirect
37. C₂×D₈	C₂⁵	direct (N × H)
38. C₂²×C₈	C₂⁵	semidirect
41. C₂⁴	C₂²×D₈	direct (N × H)
44. C₂×D₄	C₂⁶	semidirect
47. D₈	C₂⁶	direct (N × H)
48. C₂×C₈	C₂⁶	semidirect
51. C₂³	C₂³×D₈	direct (N × H)
54. D₄	C₂⁷	semidirect
57. C₈	C₂⁷	semidirect
60. C₂²	C₂⁴×D₈	direct (N × H)
65. C₂	C₂⁵×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
C₂⁶×D₄	2
C₂⁵×D₈	2
C₂⁶×C₈	2

Subgroups — C26×D8 #72304942

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁶×D₈ #72304942