Finite Group Databasebeta

← C₁₇⋊(D₂₈₃⋊C₃) #43274459

Subgroups — C₁₇⋊(D₂₈₃⋊C₃) #43274459

Order 28866.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₂₈₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₈₁₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₇×C₂₈₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	D₂₈₃⋊C₃	—	17	1	no	maximal, Hall
5	C₂₈₃⋊C₃	D₁₇	1	1	yes	characteristic, complemented, Hall
6	D₂₈₃	—	17	1	no	Hall
7	C₂₈₃	C₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
8	C₃×D₁₇	—	283	1	no	maximal, Hall
9	C₃×C₁₇	—	283	1	no	Hall
10	D₁₇	—	283	1	no	Hall
11	C₁₇	D₂₈₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	4811	1	no	Hall
13	C₃	—	283	1	no	Sylow
14	C₂	—	4811	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₇×C₂₈₃	C₂×C₃
LCS	G ▷ C₁₇×C₂₈₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₂₈₃⋊C₃	C₂	semidirect
2. D₄₈₁₁	C₃	semidirect
3. C₁₇×C₂₈₃	C₂×C₃	semidirect
5. C₂₈₃⋊C₃	D₁₇	semidirect
7. C₂₈₃	C₃×D₁₇	semidirect
11. C₁₇	D₂₈₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×C₂₈₃⋊C₃	2
D₄₈₁₁	3
D₂₈₃⋊C₃	17
C₃×D₁₇	283