Finite Group Databasebeta

← C₂×C₂₃×C₂₃₃ #24924296

Subgroups — C₂×C₂₃×C₂₃₃ #24924296

Order 10718.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₂₃₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₂₃₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₃₃	C₂×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
4	C₂×C₂₃	C₂₃₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂₃	C₂×C₂₃₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	C₂₃×C₂₃₃	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. C₂₃×C₂₃₃	C₂	direct (N × H)
2. C₂×C₂₃₃	C₂₃	direct (N × H)
3. C₂₃₃	C₂×C₂₃	direct (N × H)
4. C₂×C₂₃	C₂₃₃	direct (N × H)
5. C₂₃	C₂×C₂₃₃	direct (N × H)
6. C₂	C₂₃×C₂₃₃	direct (N × H)