Finite Group Databasebeta

← C₂⁴×D₃ #1023

Subgroups — C₂⁴×D₃ #1023

Order 96.

748 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₃	C₂	1	30	yes	maximal, direct product factor
3	C₂⁵	—	3	1	no	maximal, Sylow
4	C₂³×C₃	C₂²	1	15	yes	complemented
5	C₂²×D₃	C₂²	1	140	yes	direct product factor
6	C₂⁴	—	3	30	no	—
7	C₂⁴	D₃	1	1	yes	characteristic, direct product factor
8	C₂²×C₃	C₂³	1	35	yes	complemented
9	C₂×D₃	C₂³	1	120	yes	direct product factor
10	C₂³	—	3	140	no	—
11	C₂³	C₂×D₃	1	15	yes	direct product factor
12	C₂×C₃	C₂⁴	1	15	yes	complemented
13	D₃	C₂⁴	1	16	yes	direct product factor
14	C₂²	—	3	120	no	—
15	C₂²	C₂²×D₃	1	35	yes	direct product factor
16	C₃	C₂⁵	1	1	yes	characteristic, complemented, Sylow
17	C₂	—	3	16	no	—
18	C₂	C₂³×D₃	1	15	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁴	D₃
commutator, cosocle, hypocenter	C₃	C₂⁵
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃	C₂	semidirect
2. C₂³×D₃	C₂	direct (N × H)
4. C₂³×C₃	C₂²	semidirect
5. C₂²×D₃	C₂²	direct (N × H)
7. C₂⁴	D₃	direct (N × H)
8. C₂²×C₃	C₂³	semidirect
9. C₂×D₃	C₂³	direct (N × H)
11. C₂³	C₂×D₃	direct (N × H)
12. C₂×C₃	C₂⁴	semidirect
13. D₃	C₂⁴	direct (N × H)
15. C₂²	C₂²×D₃	direct (N × H)
16. C₃	C₂⁵	semidirect
18. C₂	C₂³×D₃	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×C₃	2
C₂³×D₃	2
C₂⁵	3