Finite Group Databasebeta

← C₂⁴×D₁₁ #67052

Subgroups — C₂⁴×D₁₁ #67052

Order 352.

748 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₁₁	C₂	1	30	yes	maximal, direct product factor
3	C₂³×C₁₁	C₂²	1	15	yes	complemented
4	C₂²×D₁₁	C₂²	1	140	yes	direct product factor
5	C₂²×C₁₁	C₂³	1	35	yes	complemented
6	C₂×D₁₁	C₂³	1	120	yes	direct product factor
7	C₂⁵	—	11	1	no	maximal, Sylow
8	C₂×C₁₁	C₂⁴	1	15	yes	complemented
9	D₁₁	C₂⁴	1	16	yes	direct product factor
10	C₂⁴	—	11	30	no	—
11	C₂⁴	D₁₁	1	1	yes	characteristic, direct product factor
12	C₁₁	C₂⁵	1	1	yes	characteristic, complemented, Sylow
13	C₂³	—	11	140	no	—
14	C₂³	C₂×D₁₁	1	15	yes	direct product factor
15	C₂²	—	11	120	no	—
16	C₂²	C₂²×D₁₁	1	35	yes	direct product factor
17	C₂	—	11	16	no	—
18	C₂	C₂³×D₁₁	1	15	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁴	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂⁵
Frattini	C₁	G
Fitting, socle	C₂⁴×C₁₁	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₁₁	C₂	semidirect
2. C₂³×D₁₁	C₂	direct (N × H)
3. C₂³×C₁₁	C₂²	semidirect
4. C₂²×D₁₁	C₂²	direct (N × H)
5. C₂²×C₁₁	C₂³	semidirect
6. C₂×D₁₁	C₂³	direct (N × H)
8. C₂×C₁₁	C₂⁴	semidirect
9. D₁₁	C₂⁴	direct (N × H)
11. C₂⁴	D₁₁	direct (N × H)
12. C₁₁	C₂⁵	semidirect
14. C₂³	C₂×D₁₁	direct (N × H)
16. C₂²	C₂²×D₁₁	direct (N × H)
18. C₂	C₂³×D₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₁₁	2
C₂³×D₁₁	2
C₂⁵	11