Subgroups — C₂×C₁₇×#10587717 #32915549

Order 18564.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#10587717	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₇×#63271	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×C₁₇×D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₇×#63271	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×C₁₇×D₁₃	C₂×C₃	1	2	yes	complemented
6	C₂×C₇×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₁₇×D₁₃⋊C₃	—	7	1	no	maximal, Hall
8	C₇×C₁₃×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂²×C₁₇×ΓL(1,𝔽₈)	—	13	1	no	maximal, Hall
10	C₂×C₁₇×C₁₃⋊C₃	—	7	1	no	—
11	C₁₇×D₁₃⋊C₃	—	7	2	no	—
12	C₂×#10587717	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₁₇×D₁₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₇×ΓL(1,𝔽₈)	—	13	2	no	—
15	C₂×C₁₇×ΓL(1,𝔽₈)	—	13	1	no	—
16	C₁₇×C₁₃⋊C₃	—	7	1	no	Hall
17	C₂×#63271	C₂×C₁₇	1	1	yes	characteristic, complemented
18	#10587717	C₂×C₁₇	1	2	yes	direct product factor
19	C₂²×C₇×C₁₇	—	13	1	no	Hall
20	C₂×C₁₃×C₁₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
21	C₁₇×D₁₃	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
22	C₂×C₇×D₁₃	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
23	C₁₇×ΓL(1,𝔽₈)	—	13	1	no	Hall
24	#63271	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
25	C₂×C₇×C₁₇	—	13	2	no	—
26	C₂×C₇×C₁₇	D₁₃⋊C₃	1	1	yes	characteristic, complemented
27	C₁₃×C₁₇	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₃×C₁₇	—	91	1	no	Hall
29	C₂×C₇×C₁₃	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
30	C₇×D₁₃	C₂×C₃×C₁₇	1	2	yes	complemented
31	C₂×D₁₃⋊C₃	—	7	1	no	Hall
32	C₇×C₁₇	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₁₇	—	91	2	no	—
34	C₂×C₃×C₁₇	—	91	1	no	—
35	C₇×C₁₃	C₂²×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
36	C₂²×ΓL(1,𝔽₈)	—	13	1	no	Hall
37	C₂×C₁₃⋊C₃	—	7	1	no	—
38	D₁₃⋊C₃	—	7	2	no	—
39	C₂²×C₁₇	—	13	1	no	Hall
40	C₂×D₁₃	C₁₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
41	C₃×C₁₇	—	91	1	no	Hall
42	C₂×ΓL(1,𝔽₈)	—	13	2	no	—
43	C₂×ΓL(1,𝔽₈)	—	13	1	no	—
44	C₁₃⋊C₃	—	7	1	no	Hall
45	C₂×C₁₇	—	13	2	no	—
46	C₂×C₁₇	#10587717	1	1	yes	characteristic, direct product factor
47	C₂²×C₇	—	13	1	no	Hall
48	C₂×C₁₃	C₂×C₁₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
49	D₁₃	C₂×C₁₇×ΓL(1,𝔽₈)	1	2	yes	complemented
50	ΓL(1,𝔽₈)	—	13	1	no	Hall
51	C₁₇	C₂×#10587717	1	1	yes	characteristic, direct product factor, Sylow
52	C₂×C₇	—	13	2	no	—
53	C₂×C₇	C₁₇×D₁₃⋊C₃	1	1	yes	characteristic, complemented
54	C₁₃	C₂²×C₁₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₃	—	91	1	no	Hall
56	C₇	C₂×C₁₇×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	—	91	2	no	—
58	C₂×C₃	—	91	1	no	—
59	C₂²	—	13	1	no	Sylow
60	C₃	—	91	1	no	Sylow
61	C₂	—	13	2	no	—
62	C₂	C₁₇×#10587717	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇	#10587717
commutator, cosocle, hypocenter	C₇×C₁₃	C₂²×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₃×C₁₇	C₂×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×#10587717	C₂	direct (N × H)
2. C₂×C₁₇×#63271	C₂	semidirect
3. C₂×C₇×C₁₇×D₁₃	C₃	semidirect
4. C₁₇×#63271	C₂²	semidirect
5. C₇×C₁₇×D₁₃	C₂×C₃	semidirect
6. C₂×C₇×C₁₃×C₁₇	C₂×C₃	semidirect
8. C₇×C₁₃×C₁₇	C₂²×C₃	semidirect
12. C₂×#10587717	C₁₇	direct (N × H)
13. C₂×C₁₇×D₁₃	ΓL(1,𝔽₈)	semidirect
17. C₂×#63271	C₂×C₁₇	semidirect
18. #10587717	C₂×C₁₇	direct (N × H)
20. C₂×C₁₃×C₁₇	C₂×ΓL(1,𝔽₈)	semidirect
21. C₁₇×D₁₃	C₂×ΓL(1,𝔽₈)	semidirect
22. C₂×C₇×D₁₃	C₃×C₁₇	semidirect
24. #63271	C₂²×C₁₇	semidirect
26. C₂×C₇×C₁₇	D₁₃⋊C₃	semidirect
27. C₁₃×C₁₇	C₂²×ΓL(1,𝔽₈)	semidirect
29. C₂×C₇×C₁₃	C₂×C₃×C₁₇	semidirect
30. C₇×D₁₃	C₂×C₃×C₁₇	semidirect
32. C₇×C₁₇	C₂×D₁₃⋊C₃	semidirect
35. C₇×C₁₃	C₂²×C₃×C₁₇	semidirect
40. C₂×D₁₃	C₁₇×ΓL(1,𝔽₈)	semidirect
46. C₂×C₁₇	#10587717	direct (N × H)
48. C₂×C₁₃	C₂×C₁₇×ΓL(1,𝔽₈)	semidirect
49. D₁₃	C₂×C₁₇×ΓL(1,𝔽₈)	semidirect
51. C₁₇	C₂×#10587717	direct (N × H)
53. C₂×C₇	C₁₇×D₁₃⋊C₃	semidirect
54. C₁₃	C₂²×C₁₇×ΓL(1,𝔽₈)	semidirect
56. C₇	C₂×C₁₇×D₁₃⋊C₃	semidirect
62. C₂	C₁₇×#10587717	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×#10587717	2
C₂×C₁₇×#63271	2
C₂×C₇×C₁₇×D₁₃	3
C₂×C₁₇×D₁₃⋊C₃	7
C₂²×C₁₇×ΓL(1,𝔽₈)	13
C₂×#10587717	17

Subgroups — C2×C17×#10587717 #32915549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×#10587717 #32915549