Subgroups — C₂×C₉×C₁₁×C₁₁₃ #36375405

Order 22374.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₁×C₁₁₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₁₁×C₁₁₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₁×C₁₁₃	C₂×C₃	1	1	yes	characteristic
4	C₂×C₁₁×C₁₁₃	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₉×C₁₁₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₁₁₃	C₂×C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₉×C₁₁₃	C₂×C₁₁	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃×C₁₁₃	C₃×C₁₁	1	1	yes	characteristic
9	C₃×C₁₁₃	C₂×C₃×C₁₁	1	1	yes	characteristic
10	C₂×C₁₁₃	C₉×C₁₁	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₉×C₁₁	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₁₃	C₂×C₉×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
13	C₉×C₁₁	C₂×C₁₁₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₁₁	C₃×C₁₁₃	1	1	yes	characteristic
15	C₃×C₁₁	C₂×C₃×C₁₁₃	1	1	yes	characteristic
16	C₂×C₁₁	C₉×C₁₁₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₉	C₁₁×C₁₁₃	1	1	yes	characteristic, direct product factor, Hall
18	C₁₁	C₂×C₉×C₁₁₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₉	C₂×C₁₁×C₁₁₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	C₃×C₁₁×C₁₁₃	1	1	yes	characteristic
21	C₃	C₂×C₃×C₁₁×C₁₁₃	1	1	yes	characteristic
22	C₂	C₉×C₁₁×C₁₁₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₁₁×C₁₁₃
socle, prime radical	C₂×C₃×C₁₁×C₁₁₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×C₁₁×C₁₁₃	C₂	direct (N × H)
4. C₂×C₁₁×C₁₁₃	C₉	direct (N × H)
5. C₂×C₉×C₁₁₃	C₁₁	direct (N × H)
6. C₁₁×C₁₁₃	C₂×C₉	direct (N × H)
7. C₉×C₁₁₃	C₂×C₁₁	direct (N × H)
10. C₂×C₁₁₃	C₉×C₁₁	direct (N × H)
11. C₂×C₉×C₁₁	C₁₁₃	direct (N × H)
12. C₁₁₃	C₂×C₉×C₁₁	direct (N × H)
13. C₉×C₁₁	C₂×C₁₁₃	direct (N × H)
16. C₂×C₁₁	C₉×C₁₁₃	direct (N × H)
17. C₂×C₉	C₁₁×C₁₁₃	direct (N × H)
18. C₁₁	C₂×C₉×C₁₁₃	direct (N × H)
19. C₉	C₂×C₁₁×C₁₁₃	direct (N × H)
22. C₂	C₉×C₁₁×C₁₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×C₁₁×C₁₁₃	2
C₂×C₃×C₁₁×C₁₁₃	3
C₂×C₉×C₁₁₃	11
C₂×C₉×C₁₁	113

Subgroups — C2×C9×C11×C113 #36375405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×C₁₁×C₁₁₃ #36375405