Subgroups — C₁₇×#10587720 #22604659

Order 9282.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#63270	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₇×C₁₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₇×C₁₃⋊C₃	—	7	1	no	maximal, Hall
5	C₁₇×AGL(1,𝔽₇)	—	13	1	no	maximal, Hall
6	C₁₇×C₁₃⋊C₃	—	7	1	no	Hall
7	#10587720	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₃×C₁₇	—	7	1	no	Hall
9	C₁₇×ΓL(1,𝔽₈)	—	13	1	no	Hall
10	#63270	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
11	D₇×C₁₇	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
12	C₁₃×C₁₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
13	C₁₃×D₇	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₇×C₁₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₁₇	—	91	1	no	Hall
16	C₇×C₁₃	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₃⋊C₃	—	7	1	no	Hall
18	C₃×C₁₇	—	91	1	no	Hall
19	AGL(1,𝔽₇)	—	13	1	no	Hall
20	C₁₃⋊C₃	—	7	1	no	Hall
21	C₂×C₁₇	—	7	1	no	Hall
22	C₂×C₁₃	—	7	1	no	Hall
23	ΓL(1,𝔽₈)	—	13	1	no	Hall
24	C₁₇	#10587720	1	1	yes	characteristic, direct product factor, Sylow
25	D₇	C₁₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
26	C₁₃	C₁₇×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₂×C₁₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	91	1	no	Hall
29	C₃	—	91	1	no	Sylow
30	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	#10587720
commutator, hypocenter	C₇×C₁₃	C₂×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₁₇	C₂×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×#63270	C₂	semidirect
2. C₁₃×D₇×C₁₇	C₃	semidirect
3. C₇×C₁₃×C₁₇	C₂×C₃	semidirect
7. #10587720	C₁₇	direct (N × H)
10. #63270	C₂×C₁₇	semidirect
11. D₇×C₁₇	C₁₃⋊C₃	semidirect
12. C₁₃×C₁₇	AGL(1,𝔽₇)	semidirect
13. C₁₃×D₇	C₃×C₁₇	semidirect
14. C₇×C₁₇	C₂×C₁₃⋊C₃	semidirect
16. C₇×C₁₃	C₂×C₃×C₁₇	semidirect
24. C₁₇	#10587720	direct (N × H)
25. D₇	C₁₇×C₁₃⋊C₃	semidirect
26. C₁₃	C₁₇×AGL(1,𝔽₇)	semidirect
27. C₇	C₂×C₁₇×C₁₃⋊C₃	semidirect

Subgroups — C17×#10587720 #22604659

Conjugacy classes of subgroups

Complements

Subgroups — C₁₇×#10587720 #22604659