Subgroups — C₂×C₃×D₁₁×C₂₈₁ #49150607

Order 37092.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₁×C₂₈₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₁×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₁×C₂₈₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₁×C₂₈₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₁×C₂₈₁	C₂×C₃	1	1	yes	characteristic, complemented
6	D₁₁×C₂₈₁	C₂×C₃	1	2	yes	direct product factor
7	C₂²×C₃×C₂₈₁	—	11	1	no	maximal, Hall
8	C₁₁×C₂₈₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₂₈₁	—	11	2	no	—
10	C₂×C₃×C₂₈₁	D₁₁	1	1	yes	characteristic, direct product factor
11	C₂²×C₂₈₁	—	11	1	no	Hall
12	C₃×C₂₈₁	C₂×D₁₁	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₂₈₁	—	11	2	no	—
14	C₂×C₂₈₁	C₃×D₁₁	1	1	yes	characteristic, direct product factor
15	C₂₈₁	C₂×C₃×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₃×D₁₁	C₂₈₁	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₁₁	C₂×C₂₈₁	1	1	yes	characteristic, complemented
18	C₃×D₁₁	C₂×C₂₈₁	1	2	yes	direct product factor
19	C₂×D₁₁	C₃×C₂₈₁	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₁₁	C₂²×C₂₈₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₁	C₂×C₃×C₂₈₁	1	1	yes	characteristic, complemented
22	D₁₁	C₂×C₃×C₂₈₁	1	2	yes	direct product factor
23	C₂²×C₃	—	11	1	no	Hall
24	C₁₁	C₂²×C₃×C₂₈₁	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃	—	11	2	no	—
26	C₂×C₃	D₁₁×C₂₈₁	1	1	yes	characteristic, direct product factor
27	C₂²	—	11	1	no	Sylow
28	C₃	C₂×D₁₁×C₂₈₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	11	2	no	—
30	C₂	C₃×D₁₁×C₂₈₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₈₁	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂²×C₃×C₂₈₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₁×C₂₈₁	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₃×C₂₈₁

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₁×C₂₈₁	C₂	direct (N × H)
2. C₂×C₃×C₁₁×C₂₈₁	C₂	semidirect
3. C₂×D₁₁×C₂₈₁	C₃	direct (N × H)
4. C₃×C₁₁×C₂₈₁	C₂²	semidirect
5. C₂×C₁₁×C₂₈₁	C₂×C₃	semidirect
6. D₁₁×C₂₈₁	C₂×C₃	direct (N × H)
8. C₁₁×C₂₈₁	C₂²×C₃	semidirect
10. C₂×C₃×C₂₈₁	D₁₁	direct (N × H)
12. C₃×C₂₈₁	C₂×D₁₁	direct (N × H)
14. C₂×C₂₈₁	C₃×D₁₁	direct (N × H)
15. C₂₈₁	C₂×C₃×D₁₁	direct (N × H)
16. C₂×C₃×D₁₁	C₂₈₁	direct (N × H)
17. C₂×C₃×C₁₁	C₂×C₂₈₁	semidirect
18. C₃×D₁₁	C₂×C₂₈₁	direct (N × H)
19. C₂×D₁₁	C₃×C₂₈₁	direct (N × H)
20. C₃×C₁₁	C₂²×C₂₈₁	semidirect
21. C₂×C₁₁	C₂×C₃×C₂₈₁	semidirect
22. D₁₁	C₂×C₃×C₂₈₁	direct (N × H)
24. C₁₁	C₂²×C₃×C₂₈₁	semidirect
26. C₂×C₃	D₁₁×C₂₈₁	direct (N × H)
28. C₃	C₂×D₁₁×C₂₈₁	direct (N × H)
30. C₂	C₃×D₁₁×C₂₈₁	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×D₁₁×C₂₈₁	2
C₂×C₃×C₁₁×C₂₈₁	2
C₂×D₁₁×C₂₈₁	3
C₂²×C₃×C₂₈₁	11
C₂×C₃×D₁₁	281

Subgroups — C2×C3×D11×C281 #49150607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₁₁×C₂₈₁ #49150607