Subgroups — D₁₁×D₁₉×C₄₁ #46804652

Order 34276.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×D₂₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×D₁₁×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×D₁₉×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×C₁₉×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₉×C₄₁	—	11	1	no	maximal, Hall
6	C₂×D₁₁×C₄₁	—	19	1	no	maximal, Hall
7	C₂×C₁₉×C₄₁	—	11	1	no	—
8	D₁₉×C₄₁	—	11	1	no	—
9	D₁₉×C₄₁	D₁₁	1	1	yes	characteristic, direct product factor
10	C₂×C₁₁×C₄₁	—	19	1	no	—
11	D₁₁×C₄₁	—	19	1	no	—
12	D₁₁×C₄₁	D₁₉	1	1	yes	characteristic, direct product factor
13	D₁₁×D₁₉	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₁₉×C₄₁	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₄₁	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
16	D₂₀₉	C₂×C₄₁	1	1	yes	characteristic, complemented
17	C₁₁×D₁₉	C₂×C₄₁	1	1	yes	characteristic, complemented
18	C₁₉×D₁₁	C₂×C₄₁	1	1	yes	characteristic, complemented
19	C₁₁×C₁₉	C₂²×C₄₁	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₄₁	—	209	1	no	Hall
21	C₂×C₄₁	—	11	1	no	—
22	C₂×C₄₁	—	19	1	no	—
23	C₂×C₄₁	—	209	1	no	—
24	C₂×D₁₉	—	11	1	no	Hall
25	C₂×D₁₁	—	19	1	no	Hall
26	C₄₁	D₁₁×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₁₉	—	11	1	no	—
28	D₁₉	—	11	1	no	—
29	D₁₉	D₁₁×C₄₁	1	1	yes	characteristic, direct product factor
30	C₂×C₁₁	—	19	1	no	—
31	D₁₁	—	19	1	no	—
32	D₁₁	D₁₉×C₄₁	1	1	yes	characteristic, direct product factor
33	C₁₉	C₂×D₁₁×C₄₁	1	1	yes	characteristic, complemented, Sylow
34	C₁₁	C₂×D₁₉×C₄₁	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	209	1	no	Sylow
36	C₂	—	11	1	no	—
37	C₂	—	19	1	no	—
38	C₂	—	209	1	no	—

	subgroup	G/H
center, hypercenter	C₄₁	D₁₁×D₁₉
commutator, cosocle, hypocenter	C₁₁×C₁₉	C₂²×C₄₁
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₉×C₄₁	C₂²
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₄₁

Complements

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

N	H ≅ G/N	type
1. C₄₁×D₂₀₉	C₂	semidirect
2. C₁₉×D₁₁×C₄₁	C₂	semidirect
3. C₁₁×D₁₉×C₄₁	C₂	semidirect
4. C₁₁×C₁₉×C₄₁	C₂²	semidirect
9. D₁₉×C₄₁	D₁₁	direct (N × H)
12. D₁₁×C₄₁	D₁₉	direct (N × H)
13. D₁₁×D₁₉	C₄₁	direct (N × H)
14. C₁₉×C₄₁	C₂×D₁₁	semidirect
15. C₁₁×C₄₁	C₂×D₁₉	semidirect
16. D₂₀₉	C₂×C₄₁	semidirect
17. C₁₁×D₁₉	C₂×C₄₁	semidirect
18. C₁₉×D₁₁	C₂×C₄₁	semidirect
19. C₁₁×C₁₉	C₂²×C₄₁	semidirect
26. C₄₁	D₁₁×D₁₉	direct (N × H)
29. D₁₉	D₁₁×C₄₁	direct (N × H)
32. D₁₁	D₁₉×C₄₁	direct (N × H)
33. C₁₉	C₂×D₁₁×C₄₁	semidirect
34. C₁₁	C₂×D₁₉×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×D₂₀₉	2
C₁₉×D₁₁×C₄₁	2
C₁₁×D₁₉×C₄₁	2
C₂×D₁₉×C₄₁	11
C₂×D₁₁×C₄₁	19
D₁₁×D₁₉	41

Subgroups — D11×D19×C41 #46804652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×D₁₉×C₄₁ #46804652