Subgroups — C₂×C₁₇×D₁₁×C₄₁ #44501541

Order 30668.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×D₁₁×C₄₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁×C₁₇×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₁₇×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂²×C₁₇×C₄₁	—	11	1	no	maximal, Hall
5	C₂×D₁₁×C₄₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₁₇×C₄₁	—	11	2	no	—
7	C₂×C₁₇×C₄₁	D₁₁	1	1	yes	characteristic, direct product factor
8	C₂×C₁₁×C₄₁	C₂×C₁₇	1	1	yes	characteristic, complemented
9	D₁₁×C₄₁	C₂×C₁₇	1	2	yes	direct product factor
10	C₂×C₁₇×D₁₁	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₁₇×C₄₁	C₂×D₁₁	1	1	yes	characteristic, direct product factor, Hall
12	C₁₁×C₄₁	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₁×C₁₇	C₂×C₄₁	1	1	yes	characteristic, complemented
14	C₁₇×D₁₁	C₂×C₄₁	1	2	yes	direct product factor
15	C₁₁×C₁₇	C₂²×C₄₁	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₄₁	—	11	1	no	Hall
17	C₂×C₄₁	—	11	2	no	—
18	C₂×C₄₁	C₁₇×D₁₁	1	1	yes	characteristic, direct product factor
19	C₂²×C₁₇	—	11	1	no	Hall
20	C₂×D₁₁	C₁₇×C₄₁	1	1	yes	characteristic, direct product factor, Hall
21	C₄₁	C₂×C₁₇×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂×C₁₇	—	11	2	no	—
23	C₂×C₁₇	D₁₁×C₄₁	1	1	yes	characteristic, direct product factor
24	C₂×C₁₁	C₂×C₁₇×C₄₁	1	1	yes	characteristic, complemented
25	D₁₁	C₂×C₁₇×C₄₁	1	2	yes	direct product factor
26	C₁₇	C₂×D₁₁×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₁₁	C₂²×C₁₇×C₄₁	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	11	1	no	Sylow
29	C₂	—	11	2	no	—
30	C₂	C₁₇×D₁₁×C₄₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇×C₄₁	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂²×C₁₇×C₄₁
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₁₇×C₄₁	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₁₇×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₁₇×D₁₁×C₄₁	C₂	direct (N × H)
2. C₂×C₁₁×C₁₇×C₄₁	C₂	semidirect
3. C₁₁×C₁₇×C₄₁	C₂²	semidirect
5. C₂×D₁₁×C₄₁	C₁₇	direct (N × H)
7. C₂×C₁₇×C₄₁	D₁₁	direct (N × H)
8. C₂×C₁₁×C₄₁	C₂×C₁₇	semidirect
9. D₁₁×C₄₁	C₂×C₁₇	direct (N × H)
10. C₂×C₁₇×D₁₁	C₄₁	direct (N × H)
11. C₁₇×C₄₁	C₂×D₁₁	direct (N × H)
12. C₁₁×C₄₁	C₂²×C₁₇	semidirect
13. C₂×C₁₁×C₁₇	C₂×C₄₁	semidirect
14. C₁₇×D₁₁	C₂×C₄₁	direct (N × H)
15. C₁₁×C₁₇	C₂²×C₄₁	semidirect
18. C₂×C₄₁	C₁₇×D₁₁	direct (N × H)
20. C₂×D₁₁	C₁₇×C₄₁	direct (N × H)
21. C₄₁	C₂×C₁₇×D₁₁	direct (N × H)
23. C₂×C₁₇	D₁₁×C₄₁	direct (N × H)
24. C₂×C₁₁	C₂×C₁₇×C₄₁	semidirect
25. D₁₁	C₂×C₁₇×C₄₁	direct (N × H)
26. C₁₇	C₂×D₁₁×C₄₁	direct (N × H)
27. C₁₁	C₂²×C₁₇×C₄₁	semidirect
30. C₂	C₁₇×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
C₁₇×D₁₁×C₄₁	2
C₂×C₁₁×C₁₇×C₄₁	2
C₂²×C₁₇×C₄₁	11
C₂×D₁₁×C₄₁	17
C₂×C₁₇×D₁₁	41

Subgroups — C2×C17×D11×C41 #44501541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×D₁₁×C₄₁ #44501541