Subgroups — C₂×D₃×C₇²×C₁₇ #23756277

Order 9996.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₇²×C₁₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₇²×C₁₇	—	3	1	no	maximal, Hall
4	C₃×C₇²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇²×C₁₇	—	3	2	no	—
6	C₂×C₇²×C₁₇	D₃	1	1	yes	characteristic, direct product factor
7	C₂×D₃×C₇×C₁₇	C₇	1	8	yes	maximal, direct product factor
8	C₇²×C₁₇	C₂×D₃	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃×C₇×C₁₇	C₂×C₇	1	8	yes	complemented
10	D₃×C₇×C₁₇	C₂×C₇	1	16	yes	direct product factor
11	C₂×D₃×C₇²	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₇×C₁₇	—	3	8	no	—
13	C₃×C₇×C₁₇	C₂²×C₇	1	8	yes	complemented
14	C₂×C₃×C₇²	C₂×C₁₇	1	1	yes	characteristic, complemented
15	D₃×C₇²	C₂×C₁₇	1	2	yes	direct product factor
16	C₂×C₇×C₁₇	—	3	16	no	—
17	C₂×C₇×C₁₇	D₃×C₇	1	8	yes	direct product factor
18	C₂×D₃×C₁₇	C₇²	1	1	yes	characteristic, direct product factor, Hall
19	C₂²×C₇²	—	3	1	no	Hall
20	C₃×C₇²	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
21	C₇×C₁₇	C₂×D₃×C₇	1	8	yes	direct product factor
22	C₂×C₃×C₁₇	C₂×C₇²	1	1	yes	characteristic, complemented
23	D₃×C₁₇	C₂×C₇²	1	2	yes	direct product factor
24	C₂×C₇²	—	3	2	no	—
25	C₂×C₇²	D₃×C₁₇	1	1	yes	characteristic, direct product factor
26	C₂×D₃×C₇	C₇×C₁₇	1	8	yes	direct product factor
27	C₂²×C₁₇	—	3	1	no	Hall
28	C₃×C₁₇	C₂²×C₇²	1	1	yes	characteristic, complemented, Hall
29	C₇²	C₂×D₃×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃×C₇	C₂×C₇×C₁₇	1	8	yes	complemented
31	D₃×C₇	C₂×C₇×C₁₇	1	16	yes	direct product factor
32	C₂×C₁₇	—	3	2	no	—
33	C₂×C₁₇	D₃×C₇²	1	1	yes	characteristic, direct product factor
34	C₂²×C₇	—	3	8	no	—
35	C₃×C₇	C₂²×C₇×C₁₇	1	8	yes	complemented
36	C₁₇	C₂×D₃×C₇²	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₇	—	3	16	no	—
38	C₂×C₇	D₃×C₇×C₁₇	1	8	yes	direct product factor
39	C₂×D₃	C₇²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
40	C₇	C₂×D₃×C₇×C₁₇	1	8	yes	direct product factor
41	C₂×C₃	C₂×C₇²×C₁₇	1	1	yes	characteristic, complemented
42	D₃	C₂×C₇²×C₁₇	1	2	yes	direct product factor
43	C₂²	—	3	1	no	Sylow
44	C₃	C₂²×C₇²×C₁₇	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	3	2	no	—
46	C₂	D₃×C₇²×C₁₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇²×C₁₇	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₇²×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇²×C₁₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₇²×C₁₇

Complements

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

N	H ≅ G/N	type
1. D₃×C₇²×C₁₇	C₂	direct (N × H)
2. C₂×C₃×C₇²×C₁₇	C₂	semidirect
4. C₃×C₇²×C₁₇	C₂²	semidirect
6. C₂×C₇²×C₁₇	D₃	direct (N × H)
7. C₂×D₃×C₇×C₁₇	C₇	direct (N × H)
8. C₇²×C₁₇	C₂×D₃	direct (N × H)
9. C₂×C₃×C₇×C₁₇	C₂×C₇	semidirect
10. D₃×C₇×C₁₇	C₂×C₇	direct (N × H)
11. C₂×D₃×C₇²	C₁₇	direct (N × H)
13. C₃×C₇×C₁₇	C₂²×C₇	semidirect
14. C₂×C₃×C₇²	C₂×C₁₇	semidirect
15. D₃×C₇²	C₂×C₁₇	direct (N × H)
17. C₂×C₇×C₁₇	D₃×C₇	direct (N × H)
18. C₂×D₃×C₁₇	C₇²	direct (N × H)
20. C₃×C₇²	C₂²×C₁₇	semidirect
21. C₇×C₁₇	C₂×D₃×C₇	direct (N × H)
22. C₂×C₃×C₁₇	C₂×C₇²	semidirect
23. D₃×C₁₇	C₂×C₇²	direct (N × H)
25. C₂×C₇²	D₃×C₁₇	direct (N × H)
26. C₂×D₃×C₇	C₇×C₁₇	direct (N × H)
28. C₃×C₁₇	C₂²×C₇²	semidirect
29. C₇²	C₂×D₃×C₁₇	direct (N × H)
30. C₂×C₃×C₇	C₂×C₇×C₁₇	semidirect
31. D₃×C₇	C₂×C₇×C₁₇	direct (N × H)
33. C₂×C₁₇	D₃×C₇²	direct (N × H)
35. C₃×C₇	C₂²×C₇×C₁₇	semidirect
36. C₁₇	C₂×D₃×C₇²	direct (N × H)
38. C₂×C₇	D₃×C₇×C₁₇	direct (N × H)
39. C₂×D₃	C₇²×C₁₇	direct (N × H)
40. C₇	C₂×D₃×C₇×C₁₇	direct (N × H)
41. C₂×C₃	C₂×C₇²×C₁₇	semidirect
42. D₃	C₂×C₇²×C₁₇	direct (N × H)
44. C₃	C₂²×C₇²×C₁₇	semidirect
46. C₂	D₃×C₇²×C₁₇	direct (N × H)

Subgroups — C2×D3×C72×C17 #23756277

Conjugacy classes of subgroups

Complements

Subgroups — C₂×D₃×C₇²×C₁₇ #23756277