Subgroups — C₂×C₃²×C₄₁×C₄₃ #44540623

Order 31734.

48 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, direct product factor, Hall
2	C₂×C₃×C₄₁×C₄₃	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₄₁×C₄₃	C₂×C₃	1	4	yes	direct product factor
4	C₂×C₄₁×C₄₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
5	C₄₁×C₄₃	C₂×C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₃²×C₄₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃²×C₄₁	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃²×C₄₃	C₂×C₄₁	1	1	yes	characteristic, direct product factor, Hall
9	C₃²×C₄₁	C₂×C₄₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₄₃	C₃×C₄₁	1	4	yes	direct product factor
11	C₂×C₃×C₄₁	C₃×C₄₃	1	4	yes	direct product factor
12	C₃×C₄₃	C₂×C₃×C₄₁	1	4	yes	direct product factor
13	C₃×C₄₁	C₂×C₃×C₄₃	1	4	yes	direct product factor
14	C₂×C₄₃	C₃²×C₄₁	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₄₁	C₃²×C₄₃	1	1	yes	characteristic, direct product factor, Hall
16	C₄₃	C₂×C₃²×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
17	C₄₁	C₂×C₃²×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₃²	C₄₁×C₄₃	1	1	yes	characteristic, direct product factor, Hall
19	C₃²	C₂×C₄₁×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	C₃×C₄₁×C₄₃	1	4	yes	direct product factor
21	C₃	C₂×C₃×C₄₁×C₄₃	1	4	yes	direct product factor
22	C₂	C₃²×C₄₁×C₄₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×C₄₁×C₄₃	C₂	direct (N × H)
2. C₂×C₃×C₄₁×C₄₃	C₃	direct (N × H)
3. C₃×C₄₁×C₄₃	C₂×C₃	direct (N × H)
4. C₂×C₄₁×C₄₃	C₃²	direct (N × H)
5. C₄₁×C₄₃	C₂×C₃²	direct (N × H)
6. C₂×C₃²×C₄₃	C₄₁	direct (N × H)
7. C₂×C₃²×C₄₁	C₄₃	direct (N × H)
8. C₃²×C₄₃	C₂×C₄₁	direct (N × H)
9. C₃²×C₄₁	C₂×C₄₃	direct (N × H)
10. C₂×C₃×C₄₃	C₃×C₄₁	direct (N × H)
11. C₂×C₃×C₄₁	C₃×C₄₃	direct (N × H)
12. C₃×C₄₃	C₂×C₃×C₄₁	direct (N × H)
13. C₃×C₄₁	C₂×C₃×C₄₃	direct (N × H)
14. C₂×C₄₃	C₃²×C₄₁	direct (N × H)
15. C₂×C₄₁	C₃²×C₄₃	direct (N × H)
16. C₄₃	C₂×C₃²×C₄₁	direct (N × H)
17. C₄₁	C₂×C₃²×C₄₃	direct (N × H)
18. C₂×C₃²	C₄₁×C₄₃	direct (N × H)
19. C₃²	C₂×C₄₁×C₄₃	direct (N × H)
20. C₂×C₃	C₃×C₄₁×C₄₃	direct (N × H)
21. C₃	C₂×C₃×C₄₁×C₄₃	direct (N × H)
22. C₂	C₃²×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
C₂×C₃×C₄₁×C₄₃	3
C₂×C₃²×C₄₃	41
C₂×C₃²×C₄₁	43

Subgroups — C2×C32×C41×C43 #44540623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₄₁×C₄₃ #44540623