Subgroups — C₂²×C₇×C₁₇×C₃₇ #31798549

Order 17612.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₇×C₃₇	C₂	1	3	yes	maximal, direct product factor
2	C₇×C₁₇×C₃₇	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₁₇×C₃₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₁₇×C₃₇	C₂×C₇	1	3	yes	direct product factor
5	C₂²×C₇×C₃₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₇×C₃₇	C₂²×C₇	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₇×C₃₇	C₂×C₁₇	1	3	yes	direct product factor
8	C₂²×C₇×C₁₇	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₃₇	C₂²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₇×C₁₇	C₂×C₃₇	1	3	yes	direct product factor
11	C₂²×C₃₇	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
12	C₇×C₁₇	C₂²×C₃₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃₇	C₂×C₇×C₁₇	1	3	yes	direct product factor
14	C₂²×C₁₇	C₇×C₃₇	1	1	yes	characteristic, direct product factor, Hall
15	C₃₇	C₂²×C₇×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₁₇	C₂×C₇×C₃₇	1	3	yes	direct product factor
17	C₂²×C₇	C₁₇×C₃₇	1	1	yes	characteristic, direct product factor, Hall
18	C₁₇	C₂²×C₇×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₇	C₂×C₁₇×C₃₇	1	3	yes	direct product factor
20	C₇	C₂²×C₁₇×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²	C₇×C₁₇×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₇×C₁₇×C₃₇	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×C₇×C₁₇×C₃₇	C₂	direct (N × H)
2. C₇×C₁₇×C₃₇	C₂²	direct (N × H)
3. C₂²×C₁₇×C₃₇	C₇	direct (N × H)
4. C₂×C₁₇×C₃₇	C₂×C₇	direct (N × H)
5. C₂²×C₇×C₃₇	C₁₇	direct (N × H)
6. C₁₇×C₃₇	C₂²×C₇	direct (N × H)
7. C₂×C₇×C₃₇	C₂×C₁₇	direct (N × H)
8. C₂²×C₇×C₁₇	C₃₇	direct (N × H)
9. C₇×C₃₇	C₂²×C₁₇	direct (N × H)
10. C₂×C₇×C₁₇	C₂×C₃₇	direct (N × H)
11. C₂²×C₃₇	C₇×C₁₇	direct (N × H)
12. C₇×C₁₇	C₂²×C₃₇	direct (N × H)
13. C₂×C₃₇	C₂×C₇×C₁₇	direct (N × H)
14. C₂²×C₁₇	C₇×C₃₇	direct (N × H)
15. C₃₇	C₂²×C₇×C₁₇	direct (N × H)
16. C₂×C₁₇	C₂×C₇×C₃₇	direct (N × H)
17. C₂²×C₇	C₁₇×C₃₇	direct (N × H)
18. C₁₇	C₂²×C₇×C₃₇	direct (N × H)
19. C₂×C₇	C₂×C₁₇×C₃₇	direct (N × H)
20. C₇	C₂²×C₁₇×C₃₇	direct (N × H)
21. C₂²	C₇×C₁₇×C₃₇	direct (N × H)
22. C₂	C₂×C₇×C₁₇×C₃₇	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×C₇×C₁₇×C₃₇	2
C₂²×C₁₇×C₃₇	7
C₂²×C₇×C₃₇	17
C₂²×C₇×C₁₇	37

Subgroups — C22×C7×C17×C37 #31798549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇×C₁₇×C₃₇ #31798549