Subgroups — D₃×C₄₁×C₄₃⋊C₃ #44540628

Order 31734.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₁×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₄₁×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×C₄₃⋊C₃	—	3	1	no	maximal
4	C₃×C₄₁×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
5	C₄₁×C₄₃⋊C₃	—	2	1	no	—
6	C₄₁×C₄₃⋊C₃	D₃	1	1	yes	characteristic, direct product factor
7	C₂×C₄₁×C₄₃	—	3	1	no	Hall
8	C₄₁×C₄₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	D₃×C₄₃⋊C₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×D₃×C₄₁	—	43	1	no	maximal, Hall
11	C₃×C₄₃⋊C₃	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₄₁	—	43	1	no	Hall
13	D₃×C₄₃	C₃×C₄₁	1	1	yes	characteristic, complemented
14	C₂×C₄₃⋊C₃	—	3	1	no	—
15	C₂×C₃×C₄₁	—	129	1	no	—
16	D₃×C₄₁	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
17	C₃×C₄₃	C₂×C₃×C₄₁	1	1	yes	characteristic, complemented
18	C₄₃⋊C₃	—	2	1	no	—
19	C₄₃⋊C₃	D₃×C₄₁	1	1	yes	characteristic, direct product factor
20	C₃×C₄₁	—	43	1	no	—
21	C₃×C₄₁	—	86	1	no	—
22	C₃×C₄₁	C₂×C₄₃⋊C₃	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, complemented, Sylow
26	C₄₁	D₃×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₃×D₃	—	43	1	no	Hall
28	C₃²	—	43	1	no	Sylow
29	C₂×C₃	—	129	1	no	—
30	D₃	C₄₁×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
31	C₃	—	43	1	no	—
32	C₃	—	86	1	no	—
33	C₃	C₂×C₄₁×C₄₃⋊C₃	1	1	yes	characteristic, complemented
34	C₂	—	3	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₄₁×C₄₃⋊C₃	C₂	semidirect
2. D₃×C₄₁×C₄₃	C₃	semidirect
4. C₃×C₄₁×C₄₃	C₂×C₃	semidirect
6. C₄₁×C₄₃⋊C₃	D₃	direct (N × H)
8. C₄₁×C₄₃	C₃×D₃	semidirect
9. D₃×C₄₃⋊C₃	C₄₁	direct (N × H)
11. C₃×C₄₃⋊C₃	C₂×C₄₁	semidirect
13. D₃×C₄₃	C₃×C₄₁	semidirect
16. D₃×C₄₁	C₄₃⋊C₃	direct (N × H)
17. C₃×C₄₃	C₂×C₃×C₄₁	semidirect
19. C₄₃⋊C₃	D₃×C₄₁	direct (N × H)
22. C₃×C₄₁	C₂×C₄₃⋊C₃	semidirect
25. C₄₃	C₃×D₃×C₄₁	semidirect
26. C₄₁	D₃×C₄₃⋊C₃	direct (N × H)
30. D₃	C₄₁×C₄₃⋊C₃	direct (N × H)
33. C₃	C₂×C₄₁×C₄₃⋊C₃	semidirect

Maximal subgroups

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

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

Subgroups — D3×C41×C43⋊C3 #44540628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₄₁×C₄₃⋊C₃ #44540628