Finite Group Databasebeta

← C₃²×C₁₀₃⋊C₁₇ #30628787

Subgroups — C₃²×C₁₀₃⋊C₁₇ #30628787

Order 15759.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₀₃⋊C₁₇	C₃	1	4	yes	maximal, direct product factor
2	C₁₀₃⋊C₁₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
3	C₃²×C₁₀₃	C₁₇	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃×C₁₀₃	C₃×C₁₇	1	4	yes	complemented
5	C₃²×C₁₇	—	103	1	no	maximal, Hall
6	C₁₀₃	C₃²×C₁₇	1	1	yes	characteristic, complemented, Sylow
7	C₃×C₁₇	—	103	4	no	—
8	C₁₇	—	103	1	no	Sylow
9	C₃²	C₁₀₃⋊C₁₇	1	1	yes	characteristic, direct product factor, Sylow
10	C₃	C₃×C₁₀₃⋊C₁₇	1	4	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₃²	C₁₀₃⋊C₁₇
commutator, cosocle, hypocenter	C₁₀₃	C₃²×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₀₃	C₁₇
LCS	G ▷ C₁₀₃
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₀₃⋊C₁₇	C₃	direct (N × H)
2. C₁₀₃⋊C₁₇	C₃²	direct (N × H)
3. C₃²×C₁₀₃	C₁₇	semidirect
4. C₃×C₁₀₃	C₃×C₁₇	semidirect
6. C₁₀₃	C₃²×C₁₇	semidirect
9. C₃²	C₁₀₃⋊C₁₇	direct (N × H)
10. C₃	C₃×C₁₀₃⋊C₁₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₀₃⋊C₁₇	3
C₃²×C₁₀₃	17
C₃²×C₁₇	103