Subgroups — C₃×C₇×D₁₁×C₄₁ #34038812

Order 18942.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₁×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₁₁×C₄₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₁×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₁₁×C₄₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₇×C₄₁	—	11	1	no	maximal, Hall
6	C₃×C₁₁×C₄₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	D₁₁×C₄₁	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₇×C₄₁	D₁₁	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₇×C₄₁	—	11	1	no	Hall
10	C₃×C₇×D₁₁	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₁₁×C₄₁	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₄₁	C₃×D₁₁	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₄₁	—	11	1	no	Hall
14	C₃×C₇×C₁₁	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
15	C₇×D₁₁	C₃×C₄₁	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₄₁	C₇×D₁₁	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₄₁	—	11	1	no	Hall
18	C₇×C₁₁	C₂×C₃×C₄₁	1	1	yes	characteristic, complemented, Hall
19	C₃×D₁₁	C₇×C₄₁	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃×C₇	—	11	1	no	Hall
21	C₄₁	C₃×C₇×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₃×C₁₁	C₂×C₇×C₄₁	1	1	yes	characteristic, complemented, Hall
23	D₁₁	C₃×C₇×C₄₁	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₇	D₁₁×C₄₁	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₇	—	11	1	no	Hall
26	C₁₁	C₂×C₃×C₇×C₄₁	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₃×D₁₁×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	—	11	1	no	Hall
29	C₃	C₇×D₁₁×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇×C₄₁	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₃×C₇×C₄₁
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₄₁	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₃×C₇×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₁×C₄₁	C₂	semidirect
2. C₇×D₁₁×C₄₁	C₃	direct (N × H)
3. C₇×C₁₁×C₄₁	C₂×C₃	semidirect
4. C₃×D₁₁×C₄₁	C₇	direct (N × H)
6. C₃×C₁₁×C₄₁	C₂×C₇	semidirect
7. D₁₁×C₄₁	C₃×C₇	direct (N × H)
8. C₃×C₇×C₄₁	D₁₁	direct (N × H)
10. C₃×C₇×D₁₁	C₄₁	direct (N × H)
11. C₁₁×C₄₁	C₂×C₃×C₇	semidirect
12. C₇×C₄₁	C₃×D₁₁	direct (N × H)
14. C₃×C₇×C₁₁	C₂×C₄₁	semidirect
15. C₇×D₁₁	C₃×C₄₁	direct (N × H)
16. C₃×C₄₁	C₇×D₁₁	direct (N × H)
18. C₇×C₁₁	C₂×C₃×C₄₁	semidirect
19. C₃×D₁₁	C₇×C₄₁	direct (N × H)
21. C₄₁	C₃×C₇×D₁₁	direct (N × H)
22. C₃×C₁₁	C₂×C₇×C₄₁	semidirect
23. D₁₁	C₃×C₇×C₄₁	direct (N × H)
24. C₃×C₇	D₁₁×C₄₁	direct (N × H)
26. C₁₁	C₂×C₃×C₇×C₄₁	semidirect
27. C₇	C₃×D₁₁×C₄₁	direct (N × H)
29. C₃	C₇×D₁₁×C₄₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₁×C₄₁	2
C₇×D₁₁×C₄₁	3
C₃×D₁₁×C₄₁	7
C₂×C₃×C₇×C₄₁	11
C₃×C₇×D₁₁	41

Subgroups — C3×C7×D11×C41 #34038812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×D₁₁×C₄₁ #34038812