Subgroups — C₁₁×C₄₃×D₃₃ #44530221

Order 31218.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁²×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₁₁×C₄₃	—	3	1	no	maximal, Hall
3	C₁₁²×C₄₃	D₃	1	1	yes	characteristic, complemented, Hall
4	C₄₃×D₃₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor
5	D₃×C₁₁×C₄₃	—	11	1	no	maximal
6	C₃×C₁₁×C₄₃	—	2	5	no	—
7	C₃×C₁₁×C₄₃	D₁₁	1	1	yes	characteristic, complemented
8	C₃×C₁₁×C₄₃	C₂×C₁₁	1	1	yes	characteristic, complemented
9	C₂×C₁₁×C₄₃	—	33	1	no	—
10	D₁₁×C₄₃	—	3	1	no	—
11	C₁₁×D₃₃	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₁×C₄₃	—	2	5	no	—
13	C₁₁×C₄₃	D₃×C₁₁	1	1	yes	characteristic, complemented
14	C₁₁×C₄₃	D₃₃	1	1	yes	characteristic, direct product factor
15	C₃×C₁₁²	C₂×C₄₃	1	1	yes	characteristic, complemented, Hall
16	D₃×C₄₃	—	11	1	no	Hall
17	C₁₁×D₁₁	—	3	1	no	Hall
18	C₃×C₄₃	C₁₁×D₁₁	1	1	yes	characteristic, complemented, Hall
19	C₁₁²	D₃×C₄₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₄₃	—	33	1	no	Hall
21	D₃₃	C₁₁×C₄₃	1	1	yes	characteristic, direct product factor
22	D₃×C₁₁	—	11	1	no	—
23	C₄₃	C₁₁×D₃₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₃×C₁₁	—	2	5	no	—
25	C₃×C₁₁	D₁₁×C₄₃	1	1	yes	characteristic, complemented
26	C₃×C₁₁	C₂×C₁₁×C₄₃	1	1	yes	characteristic, complemented
27	C₂×C₁₁	—	33	1	no	—
28	D₁₁	—	3	1	no	—
29	C₁₁	—	2	5	no	—
30	C₁₁	D₃×C₁₁×C₄₃	1	1	yes	characteristic, complemented
31	C₁₁	C₄₃×D₃₃	1	1	yes	characteristic, direct product factor
32	D₃	—	11	1	no	Hall
33	C₃	C₁₁×D₁₁×C₄₃	1	1	yes	characteristic, complemented, Sylow
34	C₂	—	33	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₄₃	D₃₃
commutator, cosocle, hypocenter	C₃×C₁₁	C₂×C₁₁×C₄₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₁²×C₄₃	C₂
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₁₁×C₄₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁²×C₄₃	C₂	semidirect
3. C₁₁²×C₄₃	D₃	semidirect
4. C₄₃×D₃₃	C₁₁	direct (N × H)
7. C₃×C₁₁×C₄₃	D₁₁	semidirect
8. C₃×C₁₁×C₄₃	C₂×C₁₁	semidirect
11. C₁₁×D₃₃	C₄₃	direct (N × H)
13. C₁₁×C₄₃	D₃×C₁₁	semidirect
14. C₁₁×C₄₃	D₃₃	direct (N × H)
15. C₃×C₁₁²	C₂×C₄₃	semidirect
18. C₃×C₄₃	C₁₁×D₁₁	semidirect
19. C₁₁²	D₃×C₄₃	semidirect
21. D₃₃	C₁₁×C₄₃	direct (N × H)
23. C₄₃	C₁₁×D₃₃	direct (N × H)
25. C₃×C₁₁	D₁₁×C₄₃	semidirect
26. C₃×C₁₁	C₂×C₁₁×C₄₃	semidirect
30. C₁₁	D₃×C₁₁×C₄₃	semidirect
31. C₁₁	C₄₃×D₃₃	direct (N × H)
33. C₃	C₁₁×D₁₁×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₁²×C₄₃	2
C₁₁×D₁₁×C₄₃	3
C₄₃×D₃₃	11
D₃×C₁₁×C₄₃	11
C₁₁×D₃₃	43

Subgroups — C11×C43×D33 #44530221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₄₃×D₃₃ #44530221