Finite Group Databasebeta

← C₉×C₁₁₉₃ #24924378

Subgroups — C₉×C₁₁₉₃ #24924378

Order 10737.

6 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁₉₃	C₃	1	1	yes	maximal, characteristic
2	C₁₁₉₃	C₉	1	1	yes	characteristic, direct product factor, Sylow
3	C₉	C₁₁₉₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₃	C₃×C₁₁₉₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₁₁₉₃
socle, prime radical	C₃×C₁₁₉₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁₉₃	C₉	direct (N × H)
3. C₉	C₁₁₉₃	direct (N × H)