Finite Group Databasebeta

← C₉×C₁₁×C₁₀₉ #24925113

Subgroups — C₉×C₁₁×C₁₀₉ #24925113

Order 10791.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₁₀₉	C₃	1	1	yes	maximal, characteristic
2	C₁₁×C₁₀₉	C₉	1	1	yes	characteristic, direct product factor, Hall
3	C₉×C₁₀₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₀₉	C₃×C₁₁	1	1	yes	characteristic
5	C₁₀₉	C₉×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
6	C₉×C₁₁	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₁₁	C₃×C₁₀₉	1	1	yes	characteristic
8	C₁₁	C₉×C₁₀₉	1	1	yes	characteristic, direct product factor, Sylow
9	C₉	C₁₁×C₁₀₉	1	1	yes	characteristic, direct product factor, Sylow
10	C₃	C₃×C₁₁×C₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₁₁×C₁₀₉
socle, prime radical	C₃×C₁₁×C₁₀₉	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×C₁₀₉	C₉	direct (N × H)
3. C₉×C₁₀₉	C₁₁	direct (N × H)
5. C₁₀₉	C₉×C₁₁	direct (N × H)
6. C₉×C₁₁	C₁₀₉	direct (N × H)
8. C₁₁	C₉×C₁₀₉	direct (N × H)
9. C₉	C₁₁×C₁₀₉	direct (N × H)