Subgroups — C₁₇×#13095531 #40996113

Order 26418.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#11715913	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₇×D₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₇×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₁₇×D₃₇⋊C₃	—	7	1	no	maximal, Hall
5	C₁₇×C₃₇⋊C₃	—	7	1	no	Hall
6	#13095531	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₇×D₃₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
8	#11715913	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₇×ΓL(1,𝔽₈)	—	37	1	no	maximal, Hall
10	C₁₇×C₃₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
11	C₇×D₃₇	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
12	C₁₇×ΓL(1,𝔽₈)	—	37	1	no	Hall
13	C₇×C₃₇	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇×C₁₇	—	37	1	no	Hall
15	D₃₇⋊C₃	—	7	1	no	Hall
16	C₇×C₁₇	D₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₃₇⋊C₃	—	7	1	no	Hall
18	C₂×C₃×C₁₇	—	259	1	no	Hall
19	D₃₇	C₁₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
20	C₃×C₁₇	—	259	1	no	Hall
21	C₂×ΓL(1,𝔽₈)	—	37	1	no	Hall
22	C₃₇	C₂×C₁₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₇	—	37	1	no	Hall
24	ΓL(1,𝔽₈)	—	37	1	no	Hall
25	C₁₇	#13095531	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₇	—	37	1	no	Hall
27	C₇	C₁₇×D₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	259	1	no	Hall
29	C₃	—	259	1	no	Sylow
30	C₂	—	37	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	#13095531
commutator, cosocle, hypocenter	C₇×C₃₇	C₂×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₇×C₃₇	C₂×C₃
LCS	G ▷ C₇×C₃₇
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×#11715913	C₂	semidirect
2. C₇×C₁₇×D₃₇	C₃	semidirect
3. C₇×C₁₇×C₃₇	C₂×C₃	semidirect
6. #13095531	C₁₇	direct (N × H)
7. C₁₇×D₃₇	ΓL(1,𝔽₈)	semidirect
8. #11715913	C₂×C₁₇	semidirect
10. C₁₇×C₃₇	C₂×ΓL(1,𝔽₈)	semidirect
11. C₇×D₃₇	C₃×C₁₇	semidirect
13. C₇×C₃₇	C₂×C₃×C₁₇	semidirect
16. C₇×C₁₇	D₃₇⋊C₃	semidirect
19. D₃₇	C₁₇×ΓL(1,𝔽₈)	semidirect
22. C₃₇	C₂×C₁₇×ΓL(1,𝔽₈)	semidirect
25. C₁₇	#13095531	direct (N × H)
27. C₇	C₁₇×D₃₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#11715913	2
C₇×C₁₇×D₃₇	3
C₁₇×D₃₇⋊C₃	7
#13095531	17
C₂×C₁₇×ΓL(1,𝔽₈)	37

Subgroups — C17×#13095531 #40996113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#13095531 #40996113