Finite Group Databasebeta

← C₂×C₃×C₁₀₉⋊C₃ #14520060

Subgroups — C₂×C₃×C₁₀₉⋊C₃ #14520060

Order 1962.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₀₉⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₁₀₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₀₉⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₁₀₉	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₀₉⋊C₃	C₂×C₃	1	3	yes	direct product factor
6	C₂×C₁₀₉	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₁₀₉	C₂×C₃²	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃²	—	109	1	no	maximal, Hall
9	C₃²	—	109	1	no	Sylow
10	C₂×C₃	—	109	3	no	—
11	C₂×C₃	C₁₀₉⋊C₃	1	1	yes	characteristic, direct product factor
12	C₃	—	109	3	no	—
13	C₃	C₂×C₁₀₉⋊C₃	1	1	yes	characteristic, direct product factor
14	C₂	C₃×C₁₀₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃	C₁₀₉⋊C₃
commutator, cosocle, hypocenter	C₁₀₉	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₀₉	C₃
LCS	G ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₀₉⋊C₃	C₂	direct (N × H)
2. C₂×C₃×C₁₀₉	C₃	semidirect
3. C₂×C₁₀₉⋊C₃	C₃	direct (N × H)
4. C₃×C₁₀₉	C₂×C₃	semidirect
5. C₁₀₉⋊C₃	C₂×C₃	direct (N × H)
6. C₂×C₁₀₉	C₃²	semidirect
7. C₁₀₉	C₂×C₃²	semidirect
11. C₂×C₃	C₁₀₉⋊C₃	direct (N × H)
13. C₃	C₂×C₁₀₉⋊C₃	direct (N × H)
14. C₂	C₃×C₁₀₉⋊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
C₃×C₁₀₉⋊C₃	2
C₂×C₃×C₁₀₉	3
C₂×C₁₀₉⋊C₃	3
C₂×C₃²	109