Subgroups — C₂×C₃×D₃×C₁₇² #23780947

Order 10404.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×C₁₇²	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₇²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₁₇²	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂²×C₃×C₁₇²	—	3	1	no	maximal
5	C₃²×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₁₇²	—	2	1	no	—
7	C₂×C₃×C₁₇²	—	3	2	no	—
8	C₂×C₃×C₁₇²	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₃×C₁₇²	C₂×C₃	1	1	yes	characteristic, complemented
10	D₃×C₁₇²	C₂×C₃	1	2	yes	direct product factor
11	C₂²×C₁₇²	—	3	1	no	Hall
12	C₃×C₁₇²	—	2	1	no	—
13	C₃×C₁₇²	C₂×D₃	1	1	yes	characteristic, direct product factor
14	C₃×C₁₇²	C₂²×C₃	1	1	yes	characteristic, complemented
15	C₂×C₃×D₃×C₁₇	C₁₇	1	18	yes	maximal, direct product factor
16	C₂×C₁₇²	—	3	2	no	—
17	C₂×C₁₇²	C₃×D₃	1	1	yes	characteristic, direct product factor
18	C₂×C₃²×C₁₇	C₂×C₁₇	1	18	yes	complemented
19	C₃×D₃×C₁₇	C₂×C₁₇	1	36	yes	direct product factor
20	C₁₇²	C₂×C₃×D₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²×C₃×C₁₇	—	3	18	no	—
22	C₂×D₃×C₁₇	C₃×C₁₇	1	18	yes	direct product factor
23	C₃²×C₁₇	C₂²×C₁₇	1	18	yes	complemented
24	C₂×C₃×C₁₇	—	2	18	no	—
25	C₂×C₃×C₁₇	—	3	36	no	—
26	C₂×C₃×C₁₇	D₃×C₁₇	1	18	yes	direct product factor
27	C₂×C₃×C₁₇	C₂×C₃×C₁₇	1	18	yes	complemented
28	D₃×C₁₇	C₂×C₃×C₁₇	1	36	yes	direct product factor
29	C₂²×C₁₇	—	3	18	no	—
30	C₃×C₁₇	—	2	18	no	—
31	C₃×C₁₇	C₂×D₃×C₁₇	1	18	yes	direct product factor
32	C₃×C₁₇	C₂²×C₃×C₁₇	1	18	yes	complemented
33	C₂×C₃×D₃	C₁₇²	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₁₇	—	3	36	no	—
35	C₂×C₁₇	C₃×D₃×C₁₇	1	18	yes	direct product factor
36	C₂×C₃²	C₂×C₁₇²	1	1	yes	characteristic, complemented
37	C₃×D₃	C₂×C₁₇²	1	2	yes	direct product factor
38	C₁₇	C₂×C₃×D₃×C₁₇	1	18	yes	direct product factor
39	C₂²×C₃	—	3	1	no	—
40	C₂×D₃	C₃×C₁₇²	1	1	yes	characteristic, direct product factor
41	C₃²	C₂²×C₁₇²	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃	—	2	1	no	—
43	C₂×C₃	—	3	2	no	—
44	C₂×C₃	D₃×C₁₇²	1	1	yes	characteristic, direct product factor
45	C₂×C₃	C₂×C₃×C₁₇²	1	1	yes	characteristic, complemented
46	D₃	C₂×C₃×C₁₇²	1	2	yes	direct product factor
47	C₂²	—	3	1	no	Sylow
48	C₃	—	2	1	no	—
49	C₃	C₂²×C₃×C₁₇²	1	1	yes	characteristic, complemented
50	C₃	C₂×D₃×C₁₇²	1	1	yes	characteristic, direct product factor
51	C₂	—	3	2	no	—
52	C₂	C₃×D₃×C₁₇²	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₇²	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₃×C₁₇²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₇²	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₁₇²

Complements

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

N	H ≅ G/N	type
1. C₃×D₃×C₁₇²	C₂	direct (N × H)
2. C₂×C₃²×C₁₇²	C₂	semidirect
3. C₂×D₃×C₁₇²	C₃	direct (N × H)
5. C₃²×C₁₇²	C₂²	semidirect
8. C₂×C₃×C₁₇²	D₃	direct (N × H)
9. C₂×C₃×C₁₇²	C₂×C₃	semidirect
10. D₃×C₁₇²	C₂×C₃	direct (N × H)
13. C₃×C₁₇²	C₂×D₃	direct (N × H)
14. C₃×C₁₇²	C₂²×C₃	semidirect
15. C₂×C₃×D₃×C₁₇	C₁₇	direct (N × H)
17. C₂×C₁₇²	C₃×D₃	direct (N × H)
18. C₂×C₃²×C₁₇	C₂×C₁₇	semidirect
19. C₃×D₃×C₁₇	C₂×C₁₇	direct (N × H)
20. C₁₇²	C₂×C₃×D₃	direct (N × H)
22. C₂×D₃×C₁₇	C₃×C₁₇	direct (N × H)
23. C₃²×C₁₇	C₂²×C₁₇	semidirect
26. C₂×C₃×C₁₇	D₃×C₁₇	direct (N × H)
27. C₂×C₃×C₁₇	C₂×C₃×C₁₇	semidirect
28. D₃×C₁₇	C₂×C₃×C₁₇	direct (N × H)
31. C₃×C₁₇	C₂×D₃×C₁₇	direct (N × H)
32. C₃×C₁₇	C₂²×C₃×C₁₇	semidirect
33. C₂×C₃×D₃	C₁₇²	direct (N × H)
35. C₂×C₁₇	C₃×D₃×C₁₇	direct (N × H)
36. C₂×C₃²	C₂×C₁₇²	semidirect
37. C₃×D₃	C₂×C₁₇²	direct (N × H)
38. C₁₇	C₂×C₃×D₃×C₁₇	direct (N × H)
40. C₂×D₃	C₃×C₁₇²	direct (N × H)
41. C₃²	C₂²×C₁₇²	semidirect
44. C₂×C₃	D₃×C₁₇²	direct (N × H)
45. C₂×C₃	C₂×C₃×C₁₇²	semidirect
46. D₃	C₂×C₃×C₁₇²	direct (N × H)
49. C₃	C₂²×C₃×C₁₇²	semidirect
50. C₃	C₂×D₃×C₁₇²	direct (N × H)
52. C₂	C₃×D₃×C₁₇²	direct (N × H)

Subgroups — C2×C3×D3×C172 #23780947

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×D₃×C₁₇² #23780947