Subgroups — C₁₇×C₃⋊(C₃⋊(C₇⋊D₇)) #28418429

Order 14994.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×C₃⋊(C₇⋊D₇)	—	3	4	no	maximal
3	C₃×C₇²×C₁₇	D₃	1	4	yes	complemented
4	C₁₇×C₃⋊D₂₁	—	7	8	no	maximal
5	C₁₇×C₇⋊D₇	—	9	1	no	Hall
6	C₃²×C₇×C₁₇	D₇	1	8	yes	complemented
7	C₃⋊(C₃⋊(C₇⋊D₇))	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇²×C₁₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
9	C₁₇×D₂₁	—	21	32	no	—
10	C₃²×C₇²	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×C₁₇	D₂₁	1	32	yes	complemented
12	C₁₇×C₃⋊D₃	—	49	1	no	Hall
13	C₃⋊(C₇⋊D₇)	—	3	4	no	—
14	D₇×C₁₇	—	63	8	no	—
15	C₃²×C₁₇	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇²	D₃×C₁₇	1	4	yes	complemented
17	C₃⋊D₂₁	—	7	8	no	—
18	C₇×C₁₇	C₃⋊D₂₁	1	8	yes	complemented
19	D₃×C₁₇	—	147	4	no	—
20	C₇⋊D₇	—	9	1	no	Hall
21	C₃²×C₇	D₇×C₁₇	1	8	yes	complemented
22	C₃×C₁₇	C₃⋊(C₇⋊D₇)	1	4	yes	complemented
23	C₇²	C₁₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
24	D₂₁	—	21	32	no	—
25	C₂×C₁₇	—	441	1	no	Hall
26	C₃×C₇	C₁₇×D₂₁	1	32	yes	complemented
27	C₃⋊D₃	—	49	1	no	Hall
28	C₁₇	C₃⋊(C₃⋊(C₇⋊D₇))	1	1	yes	characteristic, direct product factor, Sylow
29	D₇	—	63	8	no	—
30	C₃²	C₁₇×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
31	C₇	C₁₇×C₃⋊D₂₁	1	8	yes	complemented
32	D₃	—	147	4	no	—
33	C₃	C₁₇×C₃⋊(C₇⋊D₇)	1	4	yes	complemented
34	C₂	—	441	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	C₃⋊(C₃⋊(C₇⋊D₇))
commutator, cosocle, hypocenter	C₃²×C₇²	C₂×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₇	C₂
LCS	G ▷ C₃²×C₇²
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇²×C₁₇	C₂	semidirect
3. C₃×C₇²×C₁₇	D₃	semidirect
6. C₃²×C₇×C₁₇	D₇	semidirect
7. C₃⋊(C₃⋊(C₇⋊D₇))	C₁₇	direct (N × H)
8. C₇²×C₁₇	C₃⋊D₃	semidirect
10. C₃²×C₇²	C₂×C₁₇	semidirect
11. C₃×C₇×C₁₇	D₂₁	semidirect
15. C₃²×C₁₇	C₇⋊D₇	semidirect
16. C₃×C₇²	D₃×C₁₇	semidirect
18. C₇×C₁₇	C₃⋊D₂₁	semidirect
21. C₃²×C₇	D₇×C₁₇	semidirect
22. C₃×C₁₇	C₃⋊(C₇⋊D₇)	semidirect
23. C₇²	C₁₇×C₃⋊D₃	semidirect
26. C₃×C₇	C₁₇×D₂₁	semidirect
28. C₁₇	C₃⋊(C₃⋊(C₇⋊D₇))	direct (N × H)
30. C₃²	C₁₇×C₇⋊D₇	semidirect
31. C₇	C₁₇×C₃⋊D₂₁	semidirect
33. C₃	C₁₇×C₃⋊(C₇⋊D₇)	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₇²×C₁₇	2
C₁₇×C₃⋊(C₇⋊D₇)	3
C₁₇×C₃⋊D₂₁	7
C₃⋊(C₃⋊(C₇⋊D₇))	17

Subgroups — C17×C3⋊(C3⋊(C7⋊D7)) #28418429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×C₃⋊(C₃⋊(C₇⋊D₇)) #28418429