Subgroups — C₁₇×C₃₁×D₂₁ #36348992

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	D₇×C₁₇×C₃₁	—	3	1	no	maximal, Hall
3	C₇×C₁₇×C₃₁	D₃	1	1	yes	characteristic, complemented, Hall
4	D₃×C₁₇×C₃₁	—	7	1	no	maximal, Hall
5	C₃×C₁₇×C₃₁	D₇	1	1	yes	characteristic, complemented, Hall
6	C₃₁×D₂₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₇×C₃₁	—	21	1	no	Hall
8	C₁₇×D₂₁	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₇×C₃₁	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
10	C₁₇×C₃₁	D₂₁	1	1	yes	characteristic, direct product factor, Hall
11	D₇×C₃₁	—	3	1	no	Hall
12	C₃×C₇×C₁₇	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
13	D₇×C₁₇	—	3	1	no	Hall
14	C₇×C₃₁	D₃×C₁₇	1	1	yes	characteristic, complemented, Hall
15	D₃×C₃₁	—	7	1	no	Hall
16	C₇×C₁₇	D₃×C₃₁	1	1	yes	characteristic, complemented, Hall
17	D₃×C₁₇	—	7	1	no	Hall
18	C₃×C₃₁	D₇×C₁₇	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃₁	—	21	1	no	Hall
20	C₃×C₁₇	D₇×C₃₁	1	1	yes	characteristic, complemented, Hall
21	D₂₁	C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₁₇	—	21	1	no	Hall
23	C₃₁	C₁₇×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
24	C₃×C₇	C₂×C₁₇×C₃₁	1	1	yes	characteristic, complemented, Hall
25	C₁₇	C₃₁×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
26	D₇	—	3	1	no	Hall
27	C₇	D₃×C₁₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
28	D₃	—	7	1	no	Hall
29	C₃	D₇×C₁₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇×C₃₁	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₁₇×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₇×C₃₁	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₁₇×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₇×C₃₁	C₂	semidirect
3. C₇×C₁₇×C₃₁	D₃	semidirect
5. C₃×C₁₇×C₃₁	D₇	semidirect
6. C₃₁×D₂₁	C₁₇	direct (N × H)
8. C₁₇×D₂₁	C₃₁	direct (N × H)
9. C₃×C₇×C₃₁	C₂×C₁₇	semidirect
10. C₁₇×C₃₁	D₂₁	direct (N × H)
12. C₃×C₇×C₁₇	C₂×C₃₁	semidirect
14. C₇×C₃₁	D₃×C₁₇	semidirect
16. C₇×C₁₇	D₃×C₃₁	semidirect
18. C₃×C₃₁	D₇×C₁₇	semidirect
20. C₃×C₁₇	D₇×C₃₁	semidirect
21. D₂₁	C₁₇×C₃₁	direct (N × H)
23. C₃₁	C₁₇×D₂₁	direct (N × H)
24. C₃×C₇	C₂×C₁₇×C₃₁	semidirect
25. C₁₇	C₃₁×D₂₁	direct (N × H)
27. C₇	D₃×C₁₇×C₃₁	semidirect
29. C₃	D₇×C₁₇×C₃₁	semidirect

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
D₇×C₁₇×C₃₁	3
D₃×C₁₇×C₃₁	7
C₃₁×D₂₁	17
C₁₇×D₂₁	31

Subgroups — C17×C31×D21 #36348992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×C₃₁×D₂₁ #36348992