Subgroups — C₂²×C₁₁×C₁₇×C₄₃ #44565486

Order 32164.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₁₇×C₄₃	C₂	1	3	yes	maximal, direct product factor
2	C₁₁×C₁₇×C₄₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₁₇×C₄₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₁₁×C₄₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₇×C₄₃	C₂×C₁₁	1	3	yes	direct product factor
6	C₂×C₁₁×C₄₃	C₂×C₁₇	1	3	yes	direct product factor
7	C₂²×C₁₁×C₁₇	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×C₄₃	C₂²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
9	C₁₁×C₄₃	C₂²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₁×C₁₇	C₂×C₄₃	1	3	yes	direct product factor
11	C₁₁×C₁₇	C₂²×C₄₃	1	1	yes	characteristic, direct product factor, Hall
12	C₂²×C₄₃	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₄₃	C₂×C₁₁×C₁₇	1	3	yes	direct product factor
14	C₂²×C₁₇	C₁₁×C₄₃	1	1	yes	characteristic, direct product factor, Hall
15	C₂²×C₁₁	C₁₇×C₄₃	1	1	yes	characteristic, direct product factor, Hall
16	C₄₃	C₂²×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₁₇	C₂×C₁₁×C₄₃	1	3	yes	direct product factor
18	C₂×C₁₁	C₂×C₁₇×C₄₃	1	3	yes	direct product factor
19	C₁₇	C₂²×C₁₁×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₁₁	C₂²×C₁₇×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²	C₁₁×C₁₇×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₁₁×C₁₇×C₄₃	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×C₁₇×C₄₃	C₂	direct (N × H)
2. C₁₁×C₁₇×C₄₃	C₂²	direct (N × H)
3. C₂²×C₁₇×C₄₃	C₁₁	direct (N × H)
4. C₂²×C₁₁×C₄₃	C₁₇	direct (N × H)
5. C₂×C₁₇×C₄₃	C₂×C₁₁	direct (N × H)
6. C₂×C₁₁×C₄₃	C₂×C₁₇	direct (N × H)
7. C₂²×C₁₁×C₁₇	C₄₃	direct (N × H)
8. C₁₇×C₄₃	C₂²×C₁₁	direct (N × H)
9. C₁₁×C₄₃	C₂²×C₁₇	direct (N × H)
10. C₂×C₁₁×C₁₇	C₂×C₄₃	direct (N × H)
11. C₁₁×C₁₇	C₂²×C₄₃	direct (N × H)
12. C₂²×C₄₃	C₁₁×C₁₇	direct (N × H)
13. C₂×C₄₃	C₂×C₁₁×C₁₇	direct (N × H)
14. C₂²×C₁₇	C₁₁×C₄₃	direct (N × H)
15. C₂²×C₁₁	C₁₇×C₄₃	direct (N × H)
16. C₄₃	C₂²×C₁₁×C₁₇	direct (N × H)
17. C₂×C₁₇	C₂×C₁₁×C₄₃	direct (N × H)
18. C₂×C₁₁	C₂×C₁₇×C₄₃	direct (N × H)
19. C₁₇	C₂²×C₁₁×C₄₃	direct (N × H)
20. C₁₁	C₂²×C₁₇×C₄₃	direct (N × H)
21. C₂²	C₁₁×C₁₇×C₄₃	direct (N × H)
22. C₂	C₂×C₁₁×C₁₇×C₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×C₁₇×C₄₃	2
C₂²×C₁₇×C₄₃	11
C₂²×C₁₁×C₄₃	17
C₂²×C₁₁×C₁₇	43

Subgroups — C22×C11×C17×C43 #44565486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×C₁₇×C₄₃ #44565486