Finite Group Databasebeta

← C₃²×C₂₃×C₈₃ #31769864

Subgroups — C₃²×C₂₃×C₈₃ #31769864

Order 17181.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₃×C₈₃	C₃	1	4	yes	maximal, direct product factor
2	C₂₃×C₈₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
3	C₃²×C₈₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₈₃	C₃×C₂₃	1	4	yes	direct product factor
5	C₃²×C₂₃	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₈₃	C₃²×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
7	C₃×C₂₃	C₃×C₈₃	1	4	yes	direct product factor
8	C₂₃	C₃²×C₈₃	1	1	yes	characteristic, direct product factor, Sylow
9	C₃²	C₂₃×C₈₃	1	1	yes	characteristic, direct product factor, Sylow
10	C₃	C₃×C₂₃×C₈₃	1	4	yes	direct product factor

	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. C₃×C₂₃×C₈₃	C₃	direct (N × H)
2. C₂₃×C₈₃	C₃²	direct (N × H)
3. C₃²×C₈₃	C₂₃	direct (N × H)
4. C₃×C₈₃	C₃×C₂₃	direct (N × H)
5. C₃²×C₂₃	C₈₃	direct (N × H)
6. C₈₃	C₃²×C₂₃	direct (N × H)
7. C₃×C₂₃	C₃×C₈₃	direct (N × H)
8. C₂₃	C₃²×C₈₃	direct (N × H)
9. C₃²	C₂₃×C₈₃	direct (N × H)
10. C₃	C₃×C₂₃×C₈₃	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×C₂₃×C₈₃	3
C₃²×C₈₃	23
C₃²×C₂₃	83