Subgroups — C₁₇×#11763982 #32915499

Order 18564.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#10587716	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₇×#261	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₇×#63270	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×C₁₇×D₁₃	C₂×C₃	1	1	yes	characteristic
5	C₁₇×AGL(1,𝔽₁₃)	—	7	1	no	maximal, Hall
6	C₇×C₁₃×C₁₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₄×C₁₇×ΓL(1,𝔽₈)	—	13	1	no	maximal, Hall
8	C₁₇×D₁₃⋊C₃	—	7	1	no	—
9	#11763982	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₇×#261	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₇×ΓL(1,𝔽₈)	—	13	1	no	—
12	C₁₇×C₁₃⋊C₃	—	7	1	no	Hall
13	#10587716	C₂×C₁₇	1	1	yes	characteristic
14	C₄×C₇×C₁₇	—	13	1	no	Hall
15	C₁₇×D₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
16	C₇×#261	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
17	C₁₇×ΓL(1,𝔽₈)	—	13	1	no	Hall
18	#63270	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
19	C₂×C₇×C₁₇	—	13	1	no	—
20	C₁₃×C₁₇	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
21	C₃×C₄×C₁₇	—	91	1	no	Hall
22	C₇×D₁₃	C₂×C₃×C₁₇	1	1	yes	characteristic
23	AGL(1,𝔽₁₃)	—	7	1	no	Hall
24	C₇×C₁₇	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₁₇	—	91	1	no	—
26	C₇×C₁₃	C₃×C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
27	C₄×ΓL(1,𝔽₈)	—	13	1	no	Hall
28	D₁₃⋊C₃	—	7	1	no	—
29	C₄×C₁₇	—	13	1	no	Hall
30	#261	C₁₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
31	C₃×C₁₇	—	91	1	no	Hall
32	C₂×ΓL(1,𝔽₈)	—	13	1	no	—
33	C₁₃⋊C₃	—	7	1	no	Hall
34	C₂×C₁₇	—	13	1	no	—
35	C₄×C₇	—	13	1	no	Hall
36	D₁₃	C₂×C₁₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
37	ΓL(1,𝔽₈)	—	13	1	no	Hall
38	C₁₇	#11763982	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×C₇	—	13	1	no	—
40	C₁₃	C₄×C₁₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₄	—	91	1	no	Hall
42	C₇	C₁₇×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	91	1	no	—
44	C₄	—	13	1	no	Sylow
45	C₃	—	91	1	no	Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇	#11763982
commutator, hypocenter	C₇×C₁₃	C₃×C₄×C₁₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₁₇	C₃×C₄
prime radical	C₁₇×#10587716	C₂
cosocle	C₇×D₁₃	C₂×C₃×C₁₇
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
2. C₇×C₁₇×#261	C₃	semidirect
3. C₁₇×#63270	C₄	semidirect
6. C₇×C₁₃×C₁₇	C₃×C₄	semidirect
9. #11763982	C₁₇	direct (N × H)
10. C₁₇×#261	ΓL(1,𝔽₈)	semidirect
16. C₇×#261	C₃×C₁₇	semidirect
18. #63270	C₄×C₁₇	semidirect
20. C₁₃×C₁₇	C₄×ΓL(1,𝔽₈)	semidirect
24. C₇×C₁₇	AGL(1,𝔽₁₃)	semidirect
26. C₇×C₁₃	C₃×C₄×C₁₇	semidirect
30. #261	C₁₇×ΓL(1,𝔽₈)	semidirect
38. C₁₇	#11763982	direct (N × H)
40. C₁₃	C₄×C₁₇×ΓL(1,𝔽₈)	semidirect
42. C₇	C₁₇×AGL(1,𝔽₁₃)	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#10587716	2
C₇×C₁₇×#261	3
C₁₇×AGL(1,𝔽₁₃)	7
C₄×C₁₇×ΓL(1,𝔽₈)	13
#11763982	17

Subgroups — C17×#11763982 #32915499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#11763982 #32915499