Finite Group Databasebeta

← C₃×C₁₇×C₂₁₁ #24924461

Subgroups — C₃×C₁₇×C₂₁₁ #24924461

Order 10761.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₂₁₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₂₁₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₁₁	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
4	C₃×C₁₇	C₂₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₇	C₃×C₂₁₁	1	1	yes	characteristic, direct product factor, Sylow
6	C₃	C₁₇×C₂₁₁	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₂₁₁	C₃	direct (N × H)
2. C₃×C₂₁₁	C₁₇	direct (N × H)
3. C₂₁₁	C₃×C₁₇	direct (N × H)
4. C₃×C₁₇	C₂₁₁	direct (N × H)
5. C₁₇	C₃×C₂₁₁	direct (N × H)
6. C₃	C₁₇×C₂₁₁	direct (N × H)