Subgroups — D₄₁×D₂₀₉ #46804651

Order 34276.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₅₆₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×D₂₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₁₉×D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×C₁₉×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₉×D₄₁	—	11	1	no	maximal, Hall
6	D₁₁×D₄₁	—	19	1	no	maximal, Hall
7	D₇₇₉	—	11	1	no	—
8	C₁₉×D₄₁	D₁₁	1	1	yes	characteristic, complemented
9	D₁₉×C₄₁	—	11	1	no	—
10	D₄₅₁	—	19	1	no	—
11	C₁₁×D₄₁	D₁₉	1	1	yes	characteristic, complemented
12	D₁₁×C₄₁	—	19	1	no	—
13	C₂×D₂₀₉	—	41	1	no	maximal, Hall
14	C₁₉×C₄₁	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₄₁	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₁×C₁₉	—	41	1	no	—
17	D₂₀₉	—	41	1	no	—
18	D₂₀₉	D₄₁	1	1	yes	characteristic, direct product factor
19	C₁₁×C₁₉	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
20	C₂×D₄₁	—	209	1	no	Hall
21	C₂×C₄₁	—	209	1	no	—
22	D₄₁	—	209	1	no	—
23	D₄₁	D₂₀₉	1	1	yes	characteristic, direct product factor
24	C₂×D₁₉	—	451	1	no	Hall
25	C₂×D₁₁	—	779	1	no	Hall
26	C₄₁	C₂×D₂₀₉	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₉	—	41	1	no	—
28	D₁₉	—	11	1	no	—
29	D₁₉	—	451	1	no	—
30	C₂×C₁₁	—	41	1	no	—
31	D₁₁	—	779	1	no	—
32	D₁₁	—	19	1	no	—
33	C₁₉	D₁₁×D₄₁	1	1	yes	characteristic, complemented, Sylow
34	C₁₁	D₁₉×D₄₁	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	8569	1	no	Sylow
36	C₂	—	41	1	no	—
37	C₂	—	8569	1	no	—
38	C₂	—	209	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. D₈₅₆₉	C₂	semidirect
2. C₄₁×D₂₀₉	C₂	semidirect
3. C₁₁×C₁₉×D₄₁	C₂	semidirect
4. C₁₁×C₁₉×C₄₁	C₂²	semidirect
8. C₁₉×D₄₁	D₁₁	semidirect
11. C₁₁×D₄₁	D₁₉	semidirect
14. C₁₉×C₄₁	C₂×D₁₁	semidirect
15. C₁₁×C₄₁	C₂×D₁₉	semidirect
18. D₂₀₉	D₄₁	direct (N × H)
19. C₁₁×C₁₉	C₂×D₄₁	semidirect
23. D₄₁	D₂₀₉	direct (N × H)
26. C₄₁	C₂×D₂₀₉	semidirect
33. C₁₉	D₁₁×D₄₁	semidirect
34. C₁₁	D₁₉×D₄₁	semidirect

Maximal subgroups

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

subgroup	index
D₈₅₆₉	2
C₄₁×D₂₀₉	2
C₁₁×C₁₉×D₄₁	2
D₁₉×D₄₁	11
D₁₁×D₄₁	19
C₂×D₂₀₉	41

Subgroups — D41×D209 #46804651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₁×D₂₀₉ #46804651