Subgroups — C₂×C₁₁×C₁₃×D₄₃ #37589710

Order 24596.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₃×D₄₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁×C₁₃×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₁₃×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃×D₄₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₁×D₄₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₁₃×C₄₃	C₂×C₁₁	1	1	yes	characteristic, complemented
7	C₁₃×D₄₃	C₂×C₁₁	1	2	yes	direct product factor
8	C₂×C₁₁×C₄₃	C₂×C₁₃	1	1	yes	characteristic, complemented
9	C₁₁×D₄₃	C₂×C₁₃	1	2	yes	direct product factor
10	C₂²×C₁₁×C₁₃	—	43	1	no	maximal, Hall
11	C₁₃×C₄₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₁₁×C₄₃	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₁×C₁₃	—	43	2	no	—
14	C₂×C₁₁×C₁₃	D₄₃	1	1	yes	characteristic, direct product factor
15	C₂×D₄₃	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
16	C₁₁×C₁₃	C₂×D₄₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₄₃	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented
18	D₄₃	C₂×C₁₁×C₁₃	1	2	yes	direct product factor
19	C₂²×C₁₃	—	43	1	no	Hall
20	C₂²×C₁₁	—	43	1	no	Hall
21	C₄₃	C₂²×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₁₃	—	43	2	no	—
23	C₂×C₁₃	C₁₁×D₄₃	1	1	yes	characteristic, direct product factor
24	C₂×C₁₁	—	43	2	no	—
25	C₂×C₁₁	C₁₃×D₄₃	1	1	yes	characteristic, direct product factor
26	C₁₃	C₂×C₁₁×D₄₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₁₁	C₂×C₁₃×D₄₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	43	1	no	Sylow
29	C₂	—	43	2	no	—
30	C₂	C₁₁×C₁₃×D₄₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁×C₁₃	D₄₃
commutator, cosocle, hypocenter	C₄₃	C₂²×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₁₃×C₄₃	C₂
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₂×C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₃×D₄₃	C₂	direct (N × H)
2. C₂×C₁₁×C₁₃×C₄₃	C₂	semidirect
3. C₁₁×C₁₃×C₄₃	C₂²	semidirect
4. C₂×C₁₃×D₄₃	C₁₁	direct (N × H)
5. C₂×C₁₁×D₄₃	C₁₃	direct (N × H)
6. C₂×C₁₃×C₄₃	C₂×C₁₁	semidirect
7. C₁₃×D₄₃	C₂×C₁₁	direct (N × H)
8. C₂×C₁₁×C₄₃	C₂×C₁₃	semidirect
9. C₁₁×D₄₃	C₂×C₁₃	direct (N × H)
11. C₁₃×C₄₃	C₂²×C₁₁	semidirect
12. C₁₁×C₄₃	C₂²×C₁₃	semidirect
14. C₂×C₁₁×C₁₃	D₄₃	direct (N × H)
15. C₂×D₄₃	C₁₁×C₁₃	direct (N × H)
16. C₁₁×C₁₃	C₂×D₄₃	direct (N × H)
17. C₂×C₄₃	C₂×C₁₁×C₁₃	semidirect
18. D₄₃	C₂×C₁₁×C₁₃	direct (N × H)
21. C₄₃	C₂²×C₁₁×C₁₃	semidirect
23. C₂×C₁₃	C₁₁×D₄₃	direct (N × H)
25. C₂×C₁₁	C₁₃×D₄₃	direct (N × H)
26. C₁₃	C₂×C₁₁×D₄₃	direct (N × H)
27. C₁₁	C₂×C₁₃×D₄₃	direct (N × H)
30. C₂	C₁₁×C₁₃×D₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₁₃×D₄₃	2
C₂×C₁₁×C₁₃×C₄₃	2
C₂×C₁₃×D₄₃	11
C₂×C₁₁×D₄₃	13
C₂²×C₁₁×C₁₃	43

Subgroups — C2×C11×C13×D43 #37589710

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×C₁₃×D₄₃ #37589710