Subgroups — C₃²×D₁₇² #23780908

Order 10404.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇⋊D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×C₁₇×D₁₇	C₂	1	2	yes	maximal, complemented
3	C₃×D₁₇²	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₇×D₁₇	C₂×C₃	1	8	yes	complemented
6	C₃×C₁₇⋊D₁₇	C₂×C₃	1	4	yes	complemented
7	D₁₇²	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₁₇²	C₂²×C₃	1	4	yes	complemented
9	C₂×C₃²×D₁₇	—	17	2	no	maximal
10	C₁₇⋊D₁₇	C₂×C₃²	1	1	yes	characteristic, complemented
11	C₁₇×D₁₇	C₂×C₃²	1	2	yes	complemented
12	C₂×C₃²×C₁₇	—	17	2	no	—
13	C₃²×D₁₇	—	17	2	no	—
14	C₃²×D₁₇	—	34	8	no	—
15	C₃²×D₁₇	D₁₇	1	2	yes	direct product factor
16	C₁₇²	C₂²×C₃²	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃×D₁₇	—	17	8	no	—
18	C₃²×C₁₇	—	2	8	no	—
19	C₃²×C₁₇	C₂×D₁₇	1	2	yes	complemented
20	C₂×C₃×C₁₇	—	17	8	no	—
21	C₃×D₁₇	—	17	8	no	—
22	C₃×D₁₇	—	34	32	no	—
23	C₃×D₁₇	C₃×D₁₇	1	8	yes	direct product factor
24	C₂×D₁₇	—	17	2	no	—
25	C₃×C₁₇	—	2	32	no	—
26	C₃×C₁₇	C₂×C₃×D₁₇	1	8	yes	complemented
27	C₂²×C₃²	—	289	1	no	Hall
28	C₂×C₁₇	—	17	2	no	—
29	D₁₇	—	17	2	no	—
30	D₁₇	—	34	8	no	—
31	D₁₇	C₃²×D₁₇	1	2	yes	direct product factor
32	C₂×C₃²	—	17	2	no	—
33	C₂×C₃²	—	289	1	no	—
34	C₁₇	—	2	8	no	—
35	C₁₇	C₂×C₃²×D₁₇	1	2	yes	complemented
36	C₂²×C₃	—	289	4	no	—
37	C₃²	D₁₇²	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₃	—	17	8	no	—
39	C₂×C₃	—	289	4	no	—
40	C₂²	—	289	1	no	Sylow
41	C₃	C₃×D₁₇²	1	4	yes	direct product factor
42	C₂	—	17	2	no	—
43	C₂	—	289	1	no	—

	subgroup	G/H
center, hypercenter	C₃²	D₁₇²
commutator, cosocle, hypocenter	C₁₇²	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇²	C₂²
LCS	G ▷ C₁₇²
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₇⋊D₁₇	C₂	semidirect
2. C₃²×C₁₇×D₁₇	C₂	semidirect
3. C₃×D₁₇²	C₃	direct (N × H)
4. C₃²×C₁₇²	C₂²	semidirect
5. C₃×C₁₇×D₁₇	C₂×C₃	semidirect
6. C₃×C₁₇⋊D₁₇	C₂×C₃	semidirect
7. D₁₇²	C₃²	direct (N × H)
8. C₃×C₁₇²	C₂²×C₃	semidirect
10. C₁₇⋊D₁₇	C₂×C₃²	semidirect
11. C₁₇×D₁₇	C₂×C₃²	semidirect
15. C₃²×D₁₇	D₁₇	direct (N × H)
16. C₁₇²	C₂²×C₃²	semidirect
19. C₃²×C₁₇	C₂×D₁₇	semidirect
23. C₃×D₁₇	C₃×D₁₇	direct (N × H)
26. C₃×C₁₇	C₂×C₃×D₁₇	semidirect
31. D₁₇	C₃²×D₁₇	direct (N × H)
35. C₁₇	C₂×C₃²×D₁₇	semidirect
37. C₃²	D₁₇²	direct (N × H)
41. C₃	C₃×D₁₇²	direct (N × H)

Subgroups — C32×D172 #23780908

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×D₁₇² #23780908