Finite Group Databasebeta

← C₁₁×C₂₃×C₈₁ #72198110

Subgroups — C₁₁×C₂₃×C₈₁ #72198110

Order 20493.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₂₃×C₂₇	C₃	1	1	yes	maximal, characteristic
2	C₉×C₁₁×C₂₃	C₉	1	1	yes	characteristic
3	C₂₃×C₈₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₁×C₈₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₁×C₂₃	C₂₇	1	1	yes	characteristic
6	C₂₃×C₂₇	C₃×C₁₁	1	1	yes	characteristic
7	C₁₁×C₂₇	C₃×C₂₃	1	1	yes	characteristic
8	C₁₁×C₂₃	C₈₁	1	1	yes	characteristic, direct product factor, Hall
9	C₉×C₂₃	C₉×C₁₁	1	1	yes	characteristic
10	C₉×C₁₁	C₉×C₂₃	1	1	yes	characteristic
11	C₈₁	C₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×C₂₃	C₁₁×C₂₇	1	1	yes	characteristic
13	C₃×C₁₁	C₂₃×C₂₇	1	1	yes	characteristic
14	C₂₇	C₃×C₁₁×C₂₃	1	1	yes	characteristic
15	C₂₃	C₁₁×C₈₁	1	1	yes	characteristic, direct product factor, Sylow
16	C₁₁	C₂₃×C₈₁	1	1	yes	characteristic, direct product factor, Sylow
17	C₉	C₉×C₁₁×C₂₃	1	1	yes	characteristic
18	C₃	C₁₁×C₂₃×C₂₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₇	C₃×C₁₁×C₂₃
socle, prime radical	C₃×C₁₁×C₂₃	C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₃×C₈₁	C₁₁	direct (N × H)
4. C₁₁×C₈₁	C₂₃	direct (N × H)
8. C₁₁×C₂₃	C₈₁	direct (N × H)
11. C₈₁	C₁₁×C₂₃	direct (N × H)
15. C₂₃	C₁₁×C₈₁	direct (N × H)
16. C₁₁	C₂₃×C₈₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₂₃×C₂₇	3
C₂₃×C₈₁	11
C₁₁×C₈₁	23