Finite Group Databasebeta

← C₂⁶×C₄ #63094

Subgroups — C₂⁶×C₄ #63094

Order 256.

55599 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁷	C₂	1	1	yes	maximal, characteristic
2	C₂⁵×C₄	C₂	1	126	yes	maximal, direct product factor
3	C₂⁶	C₄	1	64	yes	direct product factor
4	C₂⁶	C₂²	1	63	yes	—
5	C₂⁴×C₄	C₂²	1	2604	yes	direct product factor
6	C₂⁵	C₂×C₄	1	2016	yes	direct product factor
7	C₂⁵	C₂³	1	651	yes	—
8	C₂³×C₄	C₂³	1	11160	yes	direct product factor
9	C₂⁴	C₂²×C₄	1	10416	yes	direct product factor
10	C₂⁴	C₂⁴	1	1395	yes	—
11	C₂²×C₄	C₂⁴	1	10416	yes	direct product factor
12	C₂³	C₂³×C₄	1	11160	yes	direct product factor
13	C₂³	C₂⁵	1	651	yes	—
14	C₂×C₄	C₂⁵	1	2016	yes	direct product factor
15	C₂²	C₂⁴×C₄	1	2604	yes	direct product factor
16	C₂²	C₂⁶	1	63	yes	—
17	C₄	C₂⁶	1	64	yes	direct product factor
18	C₂	C₂⁵×C₄	1	126	yes	direct product factor
19	C₂	C₂⁷	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂⁵×C₄	C₂	direct (N × H)
3. C₂⁶	C₄	direct (N × H)
5. C₂⁴×C₄	C₂²	direct (N × H)
6. C₂⁵	C₂×C₄	direct (N × H)
8. C₂³×C₄	C₂³	direct (N × H)
9. C₂⁴	C₂²×C₄	direct (N × H)
11. C₂²×C₄	C₂⁴	direct (N × H)
12. C₂³	C₂³×C₄	direct (N × H)
14. C₂×C₄	C₂⁵	direct (N × H)
15. C₂²	C₂⁴×C₄	direct (N × H)
17. C₄	C₂⁶	direct (N × H)
18. C₂	C₂⁵×C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁷	2
C₂⁵×C₄	2