Subgroups — C₃×C₇×C₁₇×D₃₁ #36348981

Order 22134.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₇×D₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₇×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₇×D₃₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₇×C₃₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₃×C₇×D₃₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₇×D₃₁	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃×C₇×C₁₇	—	31	1	no	maximal, Hall
9	C₃×C₇×C₃₁	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
10	C₁₇×C₃₁	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
11	C₇×D₃₁	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₇×C₁₇	D₃₁	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₇×C₁₇	—	31	1	no	Hall
14	C₇×C₃₁	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
15	C₃×D₃₁	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
16	C₇×C₁₇	C₃×D₃₁	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₁₇	—	31	1	no	Hall
18	C₃×C₃₁	C₂×C₇×C₁₇	1	1	yes	characteristic, complemented, Hall
19	D₃₁	C₃×C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₁₇	C₇×D₃₁	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃×C₇	—	31	1	no	Hall
22	C₂×C₁₇	—	31	1	no	Hall
23	C₃₁	C₂×C₃×C₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₇	C₁₇×D₃₁	1	1	yes	characteristic, direct product factor, Hall
25	C₁₇	C₃×C₇×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₇	—	31	1	no	Hall
27	C₇	C₃×C₁₇×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	—	31	1	no	Hall
29	C₃	C₇×C₁₇×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇×C₁₇	D₃₁
commutator, cosocle, hypocenter	C₃₁	C₂×C₃×C₇×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₇×C₃₁	C₂
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₃×C₇×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₇×C₃₁	C₂	semidirect
2. C₇×C₁₇×D₃₁	C₃	direct (N × H)
3. C₇×C₁₇×C₃₁	C₂×C₃	semidirect
4. C₃×C₁₇×D₃₁	C₇	direct (N × H)
5. C₃×C₁₇×C₃₁	C₂×C₇	semidirect
6. C₃×C₇×D₃₁	C₁₇	direct (N × H)
7. C₁₇×D₃₁	C₃×C₇	direct (N × H)
9. C₃×C₇×C₃₁	C₂×C₁₇	semidirect
10. C₁₇×C₃₁	C₂×C₃×C₇	semidirect
11. C₇×D₃₁	C₃×C₁₇	direct (N × H)
12. C₃×C₇×C₁₇	D₃₁	direct (N × H)
14. C₇×C₃₁	C₂×C₃×C₁₇	semidirect
15. C₃×D₃₁	C₇×C₁₇	direct (N × H)
16. C₇×C₁₇	C₃×D₃₁	direct (N × H)
18. C₃×C₃₁	C₂×C₇×C₁₇	semidirect
19. D₃₁	C₃×C₇×C₁₇	direct (N × H)
20. C₃×C₁₇	C₇×D₃₁	direct (N × H)
23. C₃₁	C₂×C₃×C₇×C₁₇	semidirect
24. C₃×C₇	C₁₇×D₃₁	direct (N × H)
25. C₁₇	C₃×C₇×D₃₁	direct (N × H)
27. C₇	C₃×C₁₇×D₃₁	direct (N × H)
29. C₃	C₇×C₁₇×D₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₇×C₃₁	2
C₇×C₁₇×D₃₁	3
C₃×C₁₇×D₃₁	7
C₃×C₇×D₃₁	17
C₂×C₃×C₇×C₁₇	31

Subgroups — C3×C7×C17×D31 #36348981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×C₁₇×D₃₁ #36348981