Subgroups — D₃²×C₁₇² #23780925

Order 10404.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃×C₁₇²	C₂	1	2	yes	maximal, complemented
3	C₂×D₃×C₁₇²	—	3	2	no	maximal
4	C₃²×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₇²	—	3	2	no	—
6	D₃×C₁₇²	—	3	2	no	—
7	D₃×C₁₇²	—	6	1	no	—
8	D₃×C₁₇²	D₃	1	2	yes	direct product factor
9	C₂²×C₁₇²	—	9	1	no	Hall
10	C₃×C₁₇²	—	2	1	no	—
11	C₃×C₁₇²	C₂×D₃	1	2	yes	complemented
12	D₃²×C₁₇	C₁₇	1	18	yes	maximal, direct product factor
13	C₂×C₁₇²	—	3	2	no	—
14	C₂×C₁₇²	—	9	1	no	—
15	C₁₇×C₃⋊D₃	C₂×C₁₇	1	18	yes	complemented
16	C₃×D₃×C₁₇	C₂×C₁₇	1	36	yes	complemented
17	C₁₇²	D₃²	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×D₃×C₁₇	—	3	36	no	—
19	C₃²×C₁₇	C₂²×C₁₇	1	18	yes	complemented
20	C₂×C₃×C₁₇	—	3	36	no	—
21	D₃×C₁₇	—	3	36	no	—
22	D₃×C₁₇	—	6	18	no	—
23	D₃×C₁₇	D₃×C₁₇	1	36	yes	direct product factor
24	C₂²×C₁₇	—	9	18	no	—
25	C₃×C₁₇	—	2	18	no	—
26	C₃×C₁₇	C₂×D₃×C₁₇	1	36	yes	complemented
27	D₃²	C₁₇²	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₁₇	—	3	36	no	—
29	C₂×C₁₇	—	9	18	no	—
30	C₃⋊D₃	C₂×C₁₇²	1	1	yes	characteristic, complemented
31	C₃×D₃	C₂×C₁₇²	1	2	yes	complemented
32	C₁₇	D₃²×C₁₇	1	18	yes	direct product factor
33	C₂×D₃	—	3	2	no	—
34	C₃²	C₂²×C₁₇²	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃	—	3	2	no	—
36	D₃	—	3	2	no	—
37	D₃	—	6	1	no	—
38	D₃	D₃×C₁₇²	1	2	yes	direct product factor
39	C₂²	—	9	1	no	Sylow
40	C₃	—	2	1	no	—
41	C₃	C₂×D₃×C₁₇²	1	2	yes	complemented
42	C₂	—	3	2	no	—
43	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇²	D₃²
commutator, cosocle, hypocenter	C₃²	C₂²×C₁₇²
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇²	C₂²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₁₇²

Complements

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

N	H ≅ G/N	type
1. C₁₇²×C₃⋊D₃	C₂	semidirect
2. C₃×D₃×C₁₇²	C₂	semidirect
4. C₃²×C₁₇²	C₂²	semidirect
8. D₃×C₁₇²	D₃	direct (N × H)
11. C₃×C₁₇²	C₂×D₃	semidirect
12. D₃²×C₁₇	C₁₇	direct (N × H)
15. C₁₇×C₃⋊D₃	C₂×C₁₇	semidirect
16. C₃×D₃×C₁₇	C₂×C₁₇	semidirect
17. C₁₇²	D₃²	direct (N × H)
19. C₃²×C₁₇	C₂²×C₁₇	semidirect
23. D₃×C₁₇	D₃×C₁₇	direct (N × H)
26. C₃×C₁₇	C₂×D₃×C₁₇	semidirect
27. D₃²	C₁₇²	direct (N × H)
30. C₃⋊D₃	C₂×C₁₇²	semidirect
31. C₃×D₃	C₂×C₁₇²	semidirect
32. C₁₇	D₃²×C₁₇	direct (N × H)
34. C₃²	C₂²×C₁₇²	semidirect
38. D₃	D₃×C₁₇²	direct (N × H)
41. C₃	C₂×D₃×C₁₇²	semidirect

Subgroups — D32×C172 #23780925

Conjugacy classes of subgroups

Complements

Subgroups — D₃²×C₁₇² #23780925