Subgroups — C₃×C₄₁×D₄₃⋊C₃ #44540624

Order 31734.

48 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	C₄₁×D₄₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₄₁×D₄₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄₁×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
5	C₄₁×C₄₃⋊C₃	C₂×C₃	1	3	yes	complemented
6	C₄₁×D₄₃	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₄₁×C₄₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×D₄₃⋊C₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃²×C₄₁	—	43	1	no	maximal, Hall
10	C₃×C₄₃⋊C₃	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
11	C₃²×C₄₁	—	43	1	no	Hall
12	C₃×D₄₃	C₃×C₄₁	1	1	yes	characteristic, complemented
13	D₄₃⋊C₃	C₃×C₄₁	1	3	yes	direct product factor
14	C₂×C₃×C₄₁	—	43	3	no	—
15	C₂×C₃×C₄₁	—	43	1	no	—
16	C₃×C₄₃	C₂×C₃×C₄₁	1	1	yes	characteristic, complemented
17	C₄₃⋊C₃	C₂×C₃×C₄₁	1	3	yes	complemented
18	C₃×C₄₁	—	43	3	no	—
19	C₃×C₄₁	D₄₃⋊C₃	1	1	yes	characteristic, direct product factor
20	D₄₃	C₃²×C₄₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₄₁	—	43	1	no	Hall
22	C₄₃	C₂×C₃²×C₄₁	1	1	yes	characteristic, complemented, Sylow
23	C₄₁	C₃×D₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₃²	—	43	1	no	Hall
25	C₃²	—	43	1	no	Sylow
26	C₂×C₃	—	43	3	no	—
27	C₂×C₃	—	43	1	no	—
28	C₃	—	43	3	no	—
29	C₃	C₄₁×D₄₃⋊C₃	1	1	yes	characteristic, direct product factor
30	C₂	—	43	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₄₁	D₄₃⋊C₃
commutator, cosocle, hypocenter	C₄₃	C₂×C₃²×C₄₁
Frattini	C₁	G
Fitting, socle	C₃×C₄₁×C₄₃	C₂×C₃
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₃×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. C₄₁×D₄₃⋊C₃	C₃	direct (N × H)
3. C₃×C₄₁×D₄₃	C₃	semidirect
4. C₃×C₄₁×C₄₃	C₂×C₃	semidirect
5. C₄₁×C₄₃⋊C₃	C₂×C₃	semidirect
6. C₄₁×D₄₃	C₃²	semidirect
7. C₄₁×C₄₃	C₂×C₃²	semidirect
8. C₃×D₄₃⋊C₃	C₄₁	direct (N × H)
10. C₃×C₄₃⋊C₃	C₂×C₄₁	semidirect
12. C₃×D₄₃	C₃×C₄₁	semidirect
13. D₄₃⋊C₃	C₃×C₄₁	direct (N × H)
16. C₃×C₄₃	C₂×C₃×C₄₁	semidirect
17. C₄₃⋊C₃	C₂×C₃×C₄₁	semidirect
19. C₃×C₄₁	D₄₃⋊C₃	direct (N × H)
20. D₄₃	C₃²×C₄₁	semidirect
22. C₄₃	C₂×C₃²×C₄₁	semidirect
23. C₄₁	C₃×D₄₃⋊C₃	direct (N × H)
29. C₃	C₄₁×D₄₃⋊C₃	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×C₄₁×C₄₃⋊C₃	2
C₄₁×D₄₃⋊C₃	3
C₃×C₄₁×D₄₃	3
C₃×D₄₃⋊C₃	41
C₂×C₃²×C₄₁	43

Subgroups — C3×C41×D43⋊C3 #44540624

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₁×D₄₃⋊C₃ #44540624