Subgroups — C₃×C₁₇×D₂₁₇ #36348985

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	C₁₇×D₂₁₇	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	—	7	1	no	maximal, Hall
5	C₃×C₁₇×C₃₁	D₇	1	1	yes	characteristic, complemented, Hall
6	C₃×D₂₁₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₇×D₃₁	—	7	1	no	Hall
8	C₃×D₇×C₁₇	—	31	1	no	maximal, Hall
9	C₃×C₇×C₃₁	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
10	C₁₇×C₃₁	C₃×D₇	1	1	yes	characteristic, complemented, Hall
11	D₂₁₇	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₇×C₁₇	D₃₁	1	1	yes	characteristic, complemented, Hall
13	D₇×C₁₇	—	31	1	no	Hall
14	C₇×C₃₁	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
15	C₃×D₃₁	—	7	1	no	Hall
16	C₇×C₁₇	C₃×D₃₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₇	—	217	1	no	Hall
18	C₃×C₃₁	D₇×C₁₇	1	1	yes	characteristic, complemented, Hall
19	D₃₁	—	7	1	no	Hall
20	C₃×C₁₇	D₂₁₇	1	1	yes	characteristic, direct product factor, Hall
21	C₃×D₇	—	31	1	no	Hall
22	C₂×C₁₇	—	217	1	no	Hall
23	C₃₁	C₃×D₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₇	C₁₇×D₃₁	1	1	yes	characteristic, complemented, Hall
25	C₁₇	C₃×D₂₁₇	1	1	yes	characteristic, direct product factor, Sylow
26	D₇	—	31	1	no	Hall
27	C₇	C₃×C₁₇×D₃₁	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	217	1	no	Hall
29	C₃	C₁₇×D₂₁₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	217	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₇	D₂₁₇
commutator, cosocle, hypocenter	C₇×C₃₁	C₂×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₇×C₃₁	C₂
LCS	G ▷ C₇×C₃₁
UCS	C₁ ◁ C₃×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. C₁₇×D₂₁₇	C₃	direct (N × H)
3. C₇×C₁₇×C₃₁	C₂×C₃	semidirect
5. C₃×C₁₇×C₃₁	D₇	semidirect
6. C₃×D₂₁₇	C₁₇	direct (N × H)
9. C₃×C₇×C₃₁	C₂×C₁₇	semidirect
10. C₁₇×C₃₁	C₃×D₇	semidirect
11. D₂₁₇	C₃×C₁₇	direct (N × H)
12. C₃×C₇×C₁₇	D₃₁	semidirect
14. C₇×C₃₁	C₂×C₃×C₁₇	semidirect
16. C₇×C₁₇	C₃×D₃₁	semidirect
18. C₃×C₃₁	D₇×C₁₇	semidirect
20. C₃×C₁₇	D₂₁₇	direct (N × H)
23. C₃₁	C₃×D₇×C₁₇	semidirect
24. C₃×C₇	C₁₇×D₃₁	semidirect
25. C₁₇	C₃×D₂₁₇	direct (N × H)
27. C₇	C₃×C₁₇×D₃₁	semidirect
29. C₃	C₁₇×D₂₁₇	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
C₁₇×D₂₁₇	3
C₃×C₁₇×D₃₁	7
C₃×D₂₁₇	17
C₃×D₇×C₁₇	31

Subgroups — C3×C17×D217 #36348985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₇×D₂₁₇ #36348985