Subgroups — C₂⁶×A₄ #11710941

Order 768.

148483 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×A₄	C₂	1	63	yes	maximal, direct product factor
2	C₂⁸	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₂⁶×C₃	—	4	1	no	maximal
4	C₂⁴×A₄	C₂²	1	651	yes	direct product factor
5	C₂⁷	—	3	63	no	—
6	C₂⁷	—	3	1	no	—
7	C₂⁷	C₂×C₃	1	63	yes	complemented
8	C₂⁵×C₃	—	4	63	no	—
9	C₂³×A₄	C₂³	1	1395	yes	direct product factor
10	C₂⁶	—	3	1953	no	—
11	C₂⁶	—	3	1302	no	—
12	C₂⁶	—	3	63	no	—
13	C₂⁶	—	3	63	no	—
14	C₂⁶	A₄	1	1	yes	characteristic, direct product factor
15	C₂⁶	C₂²×C₃	1	651	yes	complemented
16	C₂⁴×C₃	—	4	651	no	—
17	C₂²×A₄	C₂⁴	1	651	yes	direct product factor
18	C₂⁵	—	3	9765	no	—
19	C₂⁵	—	3	19530	no	—
20	C₂⁵	—	3	1953	no	—
21	C₂⁵	—	3	651	no	—
22	C₂⁵	C₂×A₄	1	63	yes	direct product factor
23	C₂⁵	C₂³×C₃	1	1395	yes	complemented
24	C₂³×C₃	—	4	1395	no	—
25	C₂×A₄	C₂⁵	1	63	yes	direct product factor
26	C₂⁴	—	3	9765	no	—
27	C₂⁴	—	3	45570	no	—
28	C₂⁴	—	3	9765	no	—
29	C₂⁴	—	3	1395	no	—
30	C₂⁴	C₂²×A₄	1	651	yes	direct product factor
31	C₂⁴	C₂⁴×C₃	1	651	yes	complemented
32	C₂²×C₃	—	4	651	no	—
33	A₄	C₂⁶	1	1	yes	characteristic, direct product factor
34	C₂³	—	3	1953	no	—
35	C₂³	—	3	19530	no	—
36	C₂³	—	3	9765	no	—
37	C₂³	—	3	651	no	—
38	C₂³	C₂³×A₄	1	1395	yes	direct product factor
39	C₂³	C₂⁵×C₃	1	63	yes	complemented
40	C₂×C₃	—	4	63	no	—
41	C₂²	—	3	63	no	—
42	C₂²	—	3	1302	no	—
43	C₂²	—	3	1953	no	—
44	C₂²	—	3	63	no	—
45	C₂²	C₂⁴×A₄	1	651	yes	direct product factor
46	C₂²	C₂⁶×C₃	1	1	yes	characteristic, complemented
47	C₃	—	4	1	no	Sylow
48	C₂	—	3	63	no	—
49	C₂	—	3	1	no	—
50	C₂	C₂⁵×A₄	1	63	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁶	A₄
commutator, cosocle, hypocenter	C₂²	C₂⁶×C₃
Frattini	C₁	G
Fitting, socle	C₂⁸	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂⁶

Complements

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

N	H ≅ G/N	type
1. C₂⁵×A₄	C₂	direct (N × H)
2. C₂⁸	C₃	semidirect
4. C₂⁴×A₄	C₂²	direct (N × H)
7. C₂⁷	C₂×C₃	semidirect
9. C₂³×A₄	C₂³	direct (N × H)
14. C₂⁶	A₄	direct (N × H)
15. C₂⁶	C₂²×C₃	semidirect
17. C₂²×A₄	C₂⁴	direct (N × H)
22. C₂⁵	C₂×A₄	direct (N × H)
23. C₂⁵	C₂³×C₃	semidirect
25. C₂×A₄	C₂⁵	direct (N × H)
30. C₂⁴	C₂²×A₄	direct (N × H)
31. C₂⁴	C₂⁴×C₃	semidirect
33. A₄	C₂⁶	direct (N × H)
38. C₂³	C₂³×A₄	direct (N × H)
39. C₂³	C₂⁵×C₃	semidirect
45. C₂²	C₂⁴×A₄	direct (N × H)
46. C₂²	C₂⁶×C₃	semidirect
50. C₂	C₂⁵×A₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×A₄	2
C₂⁸	3
C₂⁶×C₃	4

Subgroups — C26×A4 #11710941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁶×A₄ #11710941