Subgroups — C₃×C₇×C₁₇×#261 #32915560

Order 18564.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₃×C₇×C₁₇	#261
commutator, hypocenter	C₁₃	C₃×C₄×C₇×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₁₇	C₄
prime radical	C₃×C₇×C₁₇×D₁₃	C₂
cosocle	D₁₃	C₂×C₃×C₇×C₁₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₇×C₁₇

Complements

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

N	H ≅ G/N	type
2. C₇×C₁₇×#261	C₃	direct (N × H)
3. C₃×C₇×C₁₃×C₁₇	C₄	semidirect
5. C₃×C₁₇×#261	C₇	direct (N × H)
6. C₇×C₁₃×C₁₇	C₃×C₄	semidirect
9. C₃×C₇×#261	C₁₇	direct (N × H)
10. C₁₇×#261	C₃×C₇	direct (N × H)
12. C₃×C₁₃×C₁₇	C₄×C₇	semidirect
16. C₇×#261	C₃×C₁₇	direct (N × H)
17. C₃×C₇×C₁₇	#261	direct (N × H)
18. C₃×C₇×C₁₃	C₄×C₁₇	semidirect
20. C₁₃×C₁₇	C₃×C₄×C₇	semidirect
23. C₃×#261	C₇×C₁₇	direct (N × H)
24. C₇×C₁₇	C₃×#261	direct (N × H)
26. C₇×C₁₃	C₃×C₄×C₁₇	semidirect
30. #261	C₃×C₇×C₁₇	direct (N × H)
31. C₃×C₁₇	C₇×#261	direct (N × H)
33. C₃×C₁₃	C₄×C₇×C₁₇	semidirect
37. C₃×C₇	C₁₇×#261	direct (N × H)
38. C₁₇	C₃×C₇×#261	direct (N × H)
40. C₁₃	C₃×C₄×C₇×C₁₇	semidirect
42. C₇	C₃×C₁₇×#261	direct (N × H)
45. C₃	C₇×C₁₇×#261	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₇×D₁₃	2
C₇×C₁₇×#261	3
C₃×C₁₇×#261	7
C₃×C₄×C₇×C₁₇	13
C₃×C₇×#261	17

Subgroups — C3×C7×C17×#261 #32915560

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×C₁₇×#261 #32915560