Subgroups — C₂⁶×SD₁₆ #72313891

Order 1024.

1012373 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁶×D₄	C₂	1	1	yes	maximal, characteristic
3	C₂⁵×SD₁₆	C₂	1	252	yes	maximal, direct product factor
4	C₂⁶×C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁸	—	2	1	no	—
6	C₂⁵×Q₈	—	2	63	no	—
7	C₂⁵×Q₈	C₂²	1	126	yes	complemented
8	C₂⁵×D₄	—	2	63	no	—
9	C₂⁵×D₄	C₂²	1	126	yes	—
10	C₂⁶×C₄	—	2	1	no	—
11	C₂⁶×C₄	C₂²	1	1	yes	characteristic
12	C₂⁴×SD₁₆	C₂²	1	10416	yes	direct product factor
13	C₂⁵×C₈	C₂²	1	126	yes	complemented
14	C₂⁷	—	2	126	no	—
15	C₂⁷	—	4	64	no	—
16	C₂⁷	D₄	1	1	yes	characteristic
17	C₂⁴×Q₈	—	2	3906	no	—
18	C₂⁴×Q₈	C₂³	1	2604	yes	complemented
19	C₂⁴×D₄	—	2	3906	no	—
20	C₂⁴×D₄	C₂³	1	2604	yes	—
21	C₂⁵×C₄	—	2	126	no	—
22	C₂⁵×C₄	D₄	1	63	yes	—
23	C₂⁵×C₄	C₂³	1	63	yes	—
24	C₂³×SD₁₆	C₂³	1	89280	yes	direct product factor
25	C₂⁴×C₈	C₂³	1	2604	yes	complemented
26	C₂⁶	—	2	2604	no	—
27	C₂⁶	—	4	4032	no	—
28	C₂⁶	SD₁₆	1	64	yes	direct product factor
29	C₂⁶	C₂×D₄	1	63	yes	—
30	C₂³×Q₈	—	2	39060	no	—
31	C₂³×Q₈	C₂⁴	1	11160	yes	complemented
32	C₂³×D₄	—	2	39060	no	—
33	C₂³×D₄	C₂⁴	1	11160	yes	—
34	C₂⁴×C₄	—	2	2604	no	—
35	C₂⁴×C₄	C₂×D₄	1	1953	yes	—
36	C₂⁴×C₄	C₂⁴	1	651	yes	—
37	C₂²×SD₁₆	C₂⁴	1	166656	yes	direct product factor
38	C₂³×C₈	C₂⁴	1	11160	yes	complemented
39	C₂⁵	—	2	11160	no	—
40	C₂⁵	—	4	41664	no	—
41	C₂⁵	C₂×SD₁₆	1	2016	yes	direct product factor
42	C₂⁵	C₂²×D₄	1	651	yes	—
43	C₂²×Q₈	—	2	78120	no	—
44	C₂²×Q₈	C₂⁵	1	10416	yes	complemented
45	C₂²×D₄	—	2	78120	no	—
46	C₂²×D₄	C₂⁵	1	10416	yes	—
47	C₂³×C₄	—	2	11160	no	—
48	C₂³×C₄	C₂²×D₄	1	9765	yes	—
49	C₂³×C₄	C₂⁵	1	1395	yes	—
50	C₂×SD₁₆	C₂⁵	1	64512	yes	direct product factor
51	C₂²×C₈	C₂⁵	1	10416	yes	complemented
52	C₂⁴	—	2	10416	no	—
53	C₂⁴	—	4	89280	no	—
54	C₂⁴	C₂²×SD₁₆	1	10416	yes	direct product factor
55	C₂⁴	C₂³×D₄	1	1395	yes	—
56	C₂×Q₈	—	2	31248	no	—
57	C₂×Q₈	C₂⁶	1	2016	yes	complemented
58	C₂×D₄	—	2	31248	no	—
59	C₂×D₄	C₂⁶	1	2016	yes	—
60	C₂²×C₄	—	2	10416	no	—
61	C₂²×C₄	C₂³×D₄	1	9765	yes	—
62	C₂²×C₄	C₂⁶	1	651	yes	—
63	SD₁₆	C₂⁶	1	4096	yes	direct product factor
64	C₂×C₈	C₂⁶	1	2016	yes	complemented
65	C₂³	—	2	2016	no	—
66	C₂³	—	4	41664	no	—
67	C₂³	C₂³×SD₁₆	1	11160	yes	direct product factor
68	C₂³	C₂⁴×D₄	1	651	yes	—
69	Q₈	—	2	2016	no	—
70	Q₈	C₂⁷	1	64	yes	complemented
71	D₄	—	2	2016	no	—
72	D₄	C₂⁷	1	64	yes	—
73	C₂×C₄	—	2	2016	no	—
74	C₂×C₄	C₂⁴×D₄	1	1953	yes	—
75	C₂×C₄	C₂⁷	1	63	yes	—
76	C₈	C₂⁷	1	64	yes	complemented
77	C₂²	—	2	64	no	—
78	C₂²	—	4	4032	no	—
79	C₂²	C₂⁴×SD₁₆	1	2604	yes	direct product factor
80	C₂²	C₂⁵×D₄	1	63	yes	—
81	C₄	—	2	64	no	—
82	C₄	C₂⁵×D₄	1	63	yes	—
83	C₄	C₂⁸	1	1	yes	characteristic
84	C₂	—	4	64	no	—
85	C₂	C₂⁵×SD₁₆	1	126	yes	direct product factor
86	C₂	C₂⁶×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁷	D₄
commutator, Frattini, cosocle	C₄	C₂⁸
prime radical	C₂⁶×D₄	C₂
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×Q₈	C₂	semidirect
3. C₂⁵×SD₁₆	C₂	direct (N × H)
4. C₂⁶×C₈	C₂	semidirect
7. C₂⁵×Q₈	C₂²	semidirect
12. C₂⁴×SD₁₆	C₂²	direct (N × H)
13. C₂⁵×C₈	C₂²	semidirect
18. C₂⁴×Q₈	C₂³	semidirect
24. C₂³×SD₁₆	C₂³	direct (N × H)
25. C₂⁴×C₈	C₂³	semidirect
28. C₂⁶	SD₁₆	direct (N × H)
31. C₂³×Q₈	C₂⁴	semidirect
37. C₂²×SD₁₆	C₂⁴	direct (N × H)
38. C₂³×C₈	C₂⁴	semidirect
41. C₂⁵	C₂×SD₁₆	direct (N × H)
44. C₂²×Q₈	C₂⁵	semidirect
50. C₂×SD₁₆	C₂⁵	direct (N × H)
51. C₂²×C₈	C₂⁵	semidirect
54. C₂⁴	C₂²×SD₁₆	direct (N × H)
57. C₂×Q₈	C₂⁶	semidirect
63. SD₁₆	C₂⁶	direct (N × H)
64. C₂×C₈	C₂⁶	semidirect
67. C₂³	C₂³×SD₁₆	direct (N × H)
70. Q₈	C₂⁷	semidirect
76. C₈	C₂⁷	semidirect
79. C₂²	C₂⁴×SD₁₆	direct (N × H)
85. C₂	C₂⁵×SD₁₆	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×Q₈	2
C₂⁶×D₄	2
C₂⁵×SD₁₆	2
C₂⁶×C₈	2

Subgroups — C26×SD16 #72313891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁶×SD₁₆ #72313891