Finite Group Databasebeta

← C₃²×C₁₁²×C₂₃ #38736749

Subgroups — C₃²×C₁₁²×C₂₃ #38736749

Order 25047.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁²×C₂₃	C₃	1	4	yes	maximal, direct product factor
2	C₁₁²×C₂₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
3	C₃²×C₁₁×C₂₃	C₁₁	1	12	yes	maximal, direct product factor
4	C₃²×C₁₁²	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₁×C₂₃	C₃×C₁₁	1	48	yes	direct product factor
6	C₃×C₁₁²	C₃×C₂₃	1	4	yes	direct product factor
7	C₁₁×C₂₃	C₃²×C₁₁	1	12	yes	direct product factor
8	C₃²×C₂₃	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
9	C₁₁²	C₃²×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
10	C₃²×C₁₁	C₁₁×C₂₃	1	12	yes	direct product factor
11	C₃×C₂₃	C₃×C₁₁²	1	4	yes	direct product factor
12	C₃×C₁₁	C₃×C₁₁×C₂₃	1	48	yes	direct product factor
13	C₂₃	C₃²×C₁₁²	1	1	yes	characteristic, direct product factor, Sylow
14	C₁₁	C₃²×C₁₁×C₂₃	1	12	yes	direct product factor
15	C₃²	C₁₁²×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₃	C₃×C₁₁²×C₂₃	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×C₁₁²×C₂₃	C₃	direct (N × H)
2. C₁₁²×C₂₃	C₃²	direct (N × H)
3. C₃²×C₁₁×C₂₃	C₁₁	direct (N × H)
4. C₃²×C₁₁²	C₂₃	direct (N × H)
5. C₃×C₁₁×C₂₃	C₃×C₁₁	direct (N × H)
6. C₃×C₁₁²	C₃×C₂₃	direct (N × H)
7. C₁₁×C₂₃	C₃²×C₁₁	direct (N × H)
8. C₃²×C₂₃	C₁₁²	direct (N × H)
9. C₁₁²	C₃²×C₂₃	direct (N × H)
10. C₃²×C₁₁	C₁₁×C₂₃	direct (N × H)
11. C₃×C₂₃	C₃×C₁₁²	direct (N × H)
12. C₃×C₁₁	C₃×C₁₁×C₂₃	direct (N × H)
13. C₂₃	C₃²×C₁₁²	direct (N × H)
14. C₁₁	C₃²×C₁₁×C₂₃	direct (N × H)
15. C₃²	C₁₁²×C₂₃	direct (N × H)
16. C₃	C₃×C₁₁²×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
C₃×C₁₁²×C₂₃	3
C₃²×C₁₁×C₂₃	11
C₃²×C₁₁²	23