Subgroups — C₃×D₃×C₄₁×C₄₃ #44540635

Order 31734.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄₁×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₄₁×C₄₃	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₂×C₃×C₄₁×C₄₃	—	3	1	no	maximal
4	C₃×C₄₁×C₄₃	—	2	1	no	—
5	C₃×C₄₁×C₄₃	D₃	1	1	yes	characteristic, direct product factor
6	C₃×C₄₁×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₄₁×C₄₃	—	3	1	no	Hall
8	C₄₁×C₄₃	C₃×D₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃×D₃×C₄₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×D₃×C₄₁	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃²×C₄₃	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₄₁	C₂×C₄₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₄₃	—	3	1	no	—
14	D₃×C₄₃	C₃×C₄₁	1	1	yes	characteristic, direct product factor
15	C₂×C₃×C₄₁	—	3	1	no	—
16	D₃×C₄₁	C₃×C₄₃	1	1	yes	characteristic, direct product factor
17	C₃×C₄₃	—	2	1	no	—
18	C₃×C₄₃	D₃×C₄₁	1	1	yes	characteristic, direct product factor
19	C₃×C₄₃	C₂×C₃×C₄₁	1	1	yes	characteristic, complemented
20	C₃×C₄₁	—	2	1	no	—
21	C₃×C₄₁	D₃×C₄₃	1	1	yes	characteristic, direct product factor
22	C₃×C₄₁	C₂×C₃×C₄₃	1	1	yes	characteristic, complemented
23	C₂×C₄₃	—	3	1	no	Hall
24	C₂×C₄₁	—	3	1	no	Hall
25	C₄₃	C₃×D₃×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
26	C₄₁	C₃×D₃×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₃×D₃	C₄₁×C₄₃	1	1	yes	characteristic, direct product factor, Hall
28	C₃²	C₂×C₄₁×C₄₃	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	3	1	no	—
30	D₃	C₃×C₄₁×C₄₃	1	1	yes	characteristic, direct product factor
31	C₃	—	2	1	no	—
32	C₃	C₂×C₃×C₄₁×C₄₃	1	1	yes	characteristic, complemented
33	C₃	D₃×C₄₁×C₄₃	1	1	yes	characteristic, direct product factor
34	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₄₁×C₄₃	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₃×C₄₁×C₄₃
Frattini	C₁	G
Fitting, socle	C₃²×C₄₁×C₄₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₃×C₄₁×C₄₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₄₁×C₄₃	C₂	semidirect
2. D₃×C₄₁×C₄₃	C₃	direct (N × H)
5. C₃×C₄₁×C₄₃	D₃	direct (N × H)
6. C₃×C₄₁×C₄₃	C₂×C₃	semidirect
8. C₄₁×C₄₃	C₃×D₃	direct (N × H)
9. C₃×D₃×C₄₃	C₄₁	direct (N × H)
10. C₃×D₃×C₄₁	C₄₃	direct (N × H)
11. C₃²×C₄₃	C₂×C₄₁	semidirect
12. C₃²×C₄₁	C₂×C₄₃	semidirect
14. D₃×C₄₃	C₃×C₄₁	direct (N × H)
16. D₃×C₄₁	C₃×C₄₃	direct (N × H)
18. C₃×C₄₃	D₃×C₄₁	direct (N × H)
19. C₃×C₄₃	C₂×C₃×C₄₁	semidirect
21. C₃×C₄₁	D₃×C₄₃	direct (N × H)
22. C₃×C₄₁	C₂×C₃×C₄₃	semidirect
25. C₄₃	C₃×D₃×C₄₁	direct (N × H)
26. C₄₁	C₃×D₃×C₄₃	direct (N × H)
27. C₃×D₃	C₄₁×C₄₃	direct (N × H)
28. C₃²	C₂×C₄₁×C₄₃	semidirect
30. D₃	C₃×C₄₁×C₄₃	direct (N × H)
32. C₃	C₂×C₃×C₄₁×C₄₃	semidirect
33. C₃	D₃×C₄₁×C₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₄₁×C₄₃	2
D₃×C₄₁×C₄₃	3
C₂×C₃×C₄₁×C₄₃	3
C₃×D₃×C₄₃	41
C₃×D₃×C₄₁	43

Subgroups — C3×D3×C41×C43 #44540635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×C₄₁×C₄₃ #44540635