Finite Group Databasebeta

← C₃³×C₂₈₃⋊C₃ #37523976

Subgroups — C₃³×C₂₈₃⋊C₃ #37523976

Order 22923.

424 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₈₃⋊C₃	C₃	1	39	yes	maximal, direct product factor
2	C₃³×C₂₈₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₂₈₃	C₃²	1	13	yes	complemented
4	C₃×C₂₈₃⋊C₃	C₃²	1	117	yes	direct product factor
5	C₃×C₂₈₃	C₃³	1	13	yes	complemented
6	C₂₈₃⋊C₃	C₃³	1	27	yes	direct product factor
7	C₂₈₃	C₃⁴	1	1	yes	characteristic, complemented, Sylow
8	C₃⁴	—	283	1	no	maximal, Sylow
9	C₃³	—	283	39	no	—
10	C₃³	C₂₈₃⋊C₃	1	1	yes	characteristic, direct product factor
11	C₃²	—	283	117	no	—
12	C₃²	C₃×C₂₈₃⋊C₃	1	13	yes	direct product factor
13	C₃	—	283	27	no	—
14	C₃	C₃²×C₂₈₃⋊C₃	1	13	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₃³	C₂₈₃⋊C₃
commutator, cosocle, hypocenter	C₂₈₃	C₃⁴
Frattini	C₁	G
Fitting, socle	C₃³×C₂₈₃	C₃
LCS	G ▷ C₂₈₃
UCS	C₁ ◁ C₃³

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂₈₃⋊C₃	C₃	direct (N × H)
2. C₃³×C₂₈₃	C₃	semidirect
3. C₃²×C₂₈₃	C₃²	semidirect
4. C₃×C₂₈₃⋊C₃	C₃²	direct (N × H)
5. C₃×C₂₈₃	C₃³	semidirect
6. C₂₈₃⋊C₃	C₃³	direct (N × H)
7. C₂₈₃	C₃⁴	semidirect
10. C₃³	C₂₈₃⋊C₃	direct (N × H)
12. C₃²	C₃×C₂₈₃⋊C₃	direct (N × H)
14. C₃	C₃²×C₂₈₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₂₈₃⋊C₃	3
C₃³×C₂₈₃	3
C₃⁴	283