Finite Group Databasebeta

← C₂³×C₁₁×C₂₃ #72182012

Subgroups — C₂³×C₁₁×C₂₃ #72182012

Order 2024.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×C₂₃	C₂	1	7	yes	maximal, direct product factor
2	C₂×C₁₁×C₂₃	C₂²	1	7	yes	direct product factor
3	C₁₁×C₂₃	C₂³	1	1	yes	characteristic, direct product factor, Hall
4	C₂³×C₂₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₂₃	C₂×C₁₁	1	7	yes	direct product factor
6	C₂³×C₁₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₂₃	C₂²×C₁₁	1	7	yes	direct product factor
8	C₂²×C₁₁	C₂×C₂₃	1	7	yes	direct product factor
9	C₂₃	C₂³×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₁₁	C₂²×C₂₃	1	7	yes	direct product factor
11	C₁₁	C₂³×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₂³	C₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₂²	C₂×C₁₁×C₂₃	1	7	yes	direct product factor
14	C₂	C₂²×C₁₁×C₂₃	1	7	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. C₂²×C₁₁×C₂₃	C₂	direct (N × H)
2. C₂×C₁₁×C₂₃	C₂²	direct (N × H)
3. C₁₁×C₂₃	C₂³	direct (N × H)
4. C₂³×C₂₃	C₁₁	direct (N × H)
5. C₂²×C₂₃	C₂×C₁₁	direct (N × H)
6. C₂³×C₁₁	C₂₃	direct (N × H)
7. C₂×C₂₃	C₂²×C₁₁	direct (N × H)
8. C₂²×C₁₁	C₂×C₂₃	direct (N × H)
9. C₂₃	C₂³×C₁₁	direct (N × H)
10. C₂×C₁₁	C₂²×C₂₃	direct (N × H)
11. C₁₁	C₂³×C₂₃	direct (N × H)
12. C₂³	C₁₁×C₂₃	direct (N × H)
13. C₂²	C₂×C₁₁×C₂₃	direct (N × H)
14. C₂	C₂²×C₁₁×C₂₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₁×C₂₃	2
C₂³×C₂₃	11
C₂³×C₁₁	23