Subgroups — C₂×C₄₃×D₁₈₃ #44538398

Order 31476.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×D₁₈₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₄₃×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×D₆₁	—	3	1	no	maximal, Hall
4	C₃×C₄₃×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₄₃×C₆₁	D₃	1	1	yes	characteristic, complemented
6	C₄₃×D₆₁	—	3	2	no	—
7	C₄₃×C₆₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₁₈₃	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×D₃×C₄₃	—	61	1	no	maximal, Hall
10	C₂×C₃×C₆₁	C₂×C₄₃	1	1	yes	characteristic, complemented
11	D₁₈₃	C₂×C₄₃	1	2	yes	direct product factor
12	C₂×C₃×C₄₃	D₆₁	1	1	yes	characteristic, complemented
13	D₃×C₄₃	—	61	2	no	—
14	C₂×D₆₁	—	3	1	no	Hall
15	C₃×C₆₁	C₂²×C₄₃	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₄₃	—	183	1	no	Hall
17	C₃×C₄₃	C₂×D₆₁	1	1	yes	characteristic, complemented, Hall
18	C₂×C₆₁	D₃×C₄₃	1	1	yes	characteristic, complemented
19	D₆₁	—	3	2	no	—
20	C₂×C₄₃	—	183	2	no	—
21	C₂×C₄₃	D₁₈₃	1	1	yes	characteristic, direct product factor
22	C₆₁	C₂×D₃×C₄₃	1	1	yes	characteristic, complemented, Sylow
23	C₄₃	C₂×D₁₈₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×D₃	—	61	1	no	Hall
25	C₂×C₃	C₄₃×D₆₁	1	1	yes	characteristic, complemented
26	D₃	—	61	2	no	—
27	C₂²	—	183	1	no	Sylow
28	C₃	C₂×C₄₃×D₆₁	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	183	2	no	—
30	C₂	C₄₃×D₁₈₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₄₃	D₁₈₃
commutator, cosocle, hypocenter	C₃×C₆₁	C₂²×C₄₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₄₃×C₆₁	C₂
LCS	G ▷ C₃×C₆₁
UCS	C₁ ◁ C₂×C₄₃

Complements

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

N	H ≅ G/N	type
1. C₄₃×D₁₈₃	C₂	direct (N × H)
2. C₂×C₃×C₄₃×C₆₁	C₂	semidirect
4. C₃×C₄₃×C₆₁	C₂²	semidirect
5. C₂×C₄₃×C₆₁	D₃	semidirect
7. C₄₃×C₆₁	C₂×D₃	semidirect
8. C₂×D₁₈₃	C₄₃	direct (N × H)
10. C₂×C₃×C₆₁	C₂×C₄₃	semidirect
11. D₁₈₃	C₂×C₄₃	direct (N × H)
12. C₂×C₃×C₄₃	D₆₁	semidirect
15. C₃×C₆₁	C₂²×C₄₃	semidirect
17. C₃×C₄₃	C₂×D₆₁	semidirect
18. C₂×C₆₁	D₃×C₄₃	semidirect
21. C₂×C₄₃	D₁₈₃	direct (N × H)
22. C₆₁	C₂×D₃×C₄₃	semidirect
23. C₄₃	C₂×D₁₈₃	direct (N × H)
25. C₂×C₃	C₄₃×D₆₁	semidirect
28. C₃	C₂×C₄₃×D₆₁	semidirect
30. C₂	C₄₃×D₁₈₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×D₁₈₃	2
C₂×C₃×C₄₃×C₆₁	2
C₂×C₄₃×D₆₁	3
C₂×D₁₈₃	43
C₂×D₃×C₄₃	61

Subgroups — C2×C43×D183 #44538398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×D₁₈₃ #44538398