Subgroups — C₃×C₄₃×D₁₂₃ #44540637

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	C₄₃×D₁₂₃	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₄₃×D₄₁	—	3	1	no	maximal
4	C₃×C₄₁×C₄₃	—	2	1	no	—
5	C₃×C₄₁×C₄₃	D₃	1	1	yes	characteristic, complemented
6	C₃×C₄₁×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₄₃×D₄₁	—	3	1	no	Hall
8	C₄₁×C₄₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	C₃×D₃×C₄₃	—	41	1	no	maximal, Hall
10	C₃×D₁₂₃	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃²×C₄₃	D₄₁	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₄₁	C₂×C₄₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₄₃	—	123	1	no	—
14	D₃×C₄₃	—	41	1	no	—
15	D₁₂₃	C₃×C₄₃	1	1	yes	characteristic, direct product factor
16	C₃×D₄₁	—	3	1	no	—
17	C₃×C₄₃	—	2	1	no	—
18	C₃×C₄₃	C₃×D₄₁	1	1	yes	characteristic, complemented
19	C₃×C₄₃	D₁₂₃	1	1	yes	characteristic, direct product factor
20	C₃×C₄₁	—	2	1	no	—
21	C₃×C₄₁	D₃×C₄₃	1	1	yes	characteristic, complemented
22	C₃×C₄₁	C₂×C₃×C₄₃	1	1	yes	characteristic, complemented
23	C₂×C₄₃	—	123	1	no	Hall
24	D₄₁	—	3	1	no	Hall
25	C₄₃	C₃×D₁₂₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₄₁	C₃×D₃×C₄₃	1	1	yes	characteristic, complemented, Sylow
27	C₃×D₃	—	41	1	no	Hall
28	C₃²	C₄₃×D₄₁	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	123	1	no	—
30	D₃	—	41	1	no	—
31	C₃	—	2	1	no	—
32	C₃	C₃×C₄₃×D₄₁	1	1	yes	characteristic, complemented
33	C₃	C₄₃×D₁₂₃	1	1	yes	characteristic, direct product factor
34	C₂	—	123	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₄₃	D₁₂₃
commutator, cosocle, hypocenter	C₃×C₄₁	C₂×C₃×C₄₃
Frattini	C₁	G
Fitting, socle	C₃²×C₄₁×C₄₃	C₂
LCS	G ▷ C₃×C₄₁
UCS	C₁ ◁ C₃×C₄₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₄₁×C₄₃	C₂	semidirect
2. C₄₃×D₁₂₃	C₃	direct (N × H)
5. C₃×C₄₁×C₄₃	D₃	semidirect
6. C₃×C₄₁×C₄₃	C₂×C₃	semidirect
8. C₄₁×C₄₃	C₃×D₃	semidirect
10. C₃×D₁₂₃	C₄₃	direct (N × H)
11. C₃²×C₄₃	D₄₁	semidirect
12. C₃²×C₄₁	C₂×C₄₃	semidirect
15. D₁₂₃	C₃×C₄₃	direct (N × H)
18. C₃×C₄₃	C₃×D₄₁	semidirect
19. C₃×C₄₃	D₁₂₃	direct (N × H)
21. C₃×C₄₁	D₃×C₄₃	semidirect
22. C₃×C₄₁	C₂×C₃×C₄₃	semidirect
25. C₄₃	C₃×D₁₂₃	direct (N × H)
26. C₄₁	C₃×D₃×C₄₃	semidirect
28. C₃²	C₄₃×D₄₁	semidirect
32. C₃	C₃×C₄₃×D₄₁	semidirect
33. C₃	C₄₃×D₁₂₃	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
C₄₃×D₁₂₃	3
C₃×C₄₃×D₄₁	3
C₃×D₃×C₄₃	41
C₃×D₁₂₃	43

Subgroups — C3×C43×D123 #44540637

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₃×D₁₂₃ #44540637