Subgroups — C₁₇×C₃⋊D₃×D₁₇ #23780918

Order 10404.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₃⋊D₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₁₇×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₇×D₁₇	—	3	4	no	maximal
5	C₃²×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₇×D₁₇	D₃	1	4	yes	complemented
7	D₃×C₁₇²	—	3	4	no	—
8	C₁₇×D₅₁	—	3	4	no	—
9	C₂×C₁₇×D₁₇	—	9	1	no	Hall
10	C₃×C₁₇²	C₂×D₃	1	4	yes	complemented
11	C₂×C₁₇×C₃⋊D₃	—	17	1	no	maximal
12	C₃⋊D₃×D₁₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor
13	C₂×C₁₇²	—	9	1	no	—
14	C₁₇×D₁₇	—	9	1	no	—
15	C₁₇×D₁₇	C₃⋊D₃	1	1	yes	characteristic, direct product factor
16	C₂×C₃²×C₁₇	—	17	1	no	—
17	C₃⋊D₅₁	C₂×C₁₇	1	1	yes	characteristic, complemented
18	C₁₇×C₃⋊D₃	—	2	8	no	—
19	C₁₇×C₃⋊D₃	—	17	1	no	—
20	C₁₇×C₃⋊D₃	D₁₇	1	1	yes	characteristic, direct product factor
21	C₁₇×C₃⋊D₃	C₂×C₁₇	1	1	yes	characteristic, complemented
22	C₃²×D₁₇	C₂×C₁₇	1	1	yes	characteristic, complemented
23	C₁₇²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₃×C₁₇	—	51	4	no	—
25	D₃×D₁₇	—	3	4	no	—
26	C₃²×C₁₇	—	2	8	no	—
27	C₃²×C₁₇	C₂×D₁₇	1	1	yes	characteristic, complemented
28	C₃²×C₁₇	C₂²×C₁₇	1	1	yes	characteristic, complemented
29	C₂×C₃×C₁₇	—	17	4	no	—
30	D₅₁	—	3	4	no	—
31	C₃×D₁₇	D₃×C₁₇	1	4	yes	complemented
32	D₃×C₁₇	—	3	4	no	—
33	D₃×C₁₇	—	3	4	no	—
34	D₃×C₁₇	—	6	32	no	—
35	D₃×C₁₇	—	51	4	no	—
36	C₂²×C₁₇	—	153	1	no	—
37	C₂×D₁₇	—	9	1	no	—
38	C₃×C₁₇	—	2	32	no	—
39	C₃×C₁₇	D₃×D₁₇	1	4	yes	complemented
40	C₃×C₁₇	C₂×D₃×C₁₇	1	4	yes	complemented
41	C₂×C₃⋊D₃	—	17	1	no	Hall
42	C₂×C₁₇	—	9	1	no	—
43	C₂×C₁₇	—	9	1	no	—
44	C₂×C₁₇	—	17	1	no	—
45	C₂×C₁₇	—	18	8	no	—
46	C₂×C₁₇	—	153	1	no	—
47	D₁₇	—	9	1	no	—
48	D₁₇	C₁₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor
49	C₂×C₃²	—	17	1	no	—
50	C₃⋊D₃	—	17	1	no	—
51	C₃⋊D₃	C₁₇×D₁₇	1	1	yes	characteristic, direct product factor
52	C₁₇	—	2	8	no	—
53	C₁₇	C₃⋊D₃×D₁₇	1	1	yes	characteristic, direct product factor
54	C₁₇	C₂×C₁₇×C₃⋊D₃	1	1	yes	characteristic, complemented
55	C₂×D₃	—	51	4	no	—
56	C₃²	C₂×C₁₇×D₁₇	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	—	17	4	no	—
58	D₃	—	3	4	no	—
59	D₃	—	51	4	no	—
60	C₂²	—	153	1	no	Sylow
61	C₃	D₃×C₁₇×D₁₇	1	4	yes	complemented
62	C₂	—	9	1	no	—
63	C₂	—	17	1	no	—
64	C₂	—	153	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇	C₃⋊D₃×D₁₇
commutator, cosocle, hypocenter	C₃²×C₁₇	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇²	C₂²
LCS	G ▷ C₃²×C₁₇
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₃⋊D₅₁	C₂	semidirect
2. C₁₇²×C₃⋊D₃	C₂	semidirect
3. C₃²×C₁₇×D₁₇	C₂	semidirect
5. C₃²×C₁₇²	C₂²	semidirect
6. C₃×C₁₇×D₁₇	D₃	semidirect
10. C₃×C₁₇²	C₂×D₃	semidirect
12. C₃⋊D₃×D₁₇	C₁₇	direct (N × H)
15. C₁₇×D₁₇	C₃⋊D₃	direct (N × H)
17. C₃⋊D₅₁	C₂×C₁₇	semidirect
20. C₁₇×C₃⋊D₃	D₁₇	direct (N × H)
21. C₁₇×C₃⋊D₃	C₂×C₁₇	semidirect
22. C₃²×D₁₇	C₂×C₁₇	semidirect
23. C₁₇²	C₂×C₃⋊D₃	semidirect
27. C₃²×C₁₇	C₂×D₁₇	semidirect
28. C₃²×C₁₇	C₂²×C₁₇	semidirect
31. C₃×D₁₇	D₃×C₁₇	semidirect
39. C₃×C₁₇	D₃×D₁₇	semidirect
40. C₃×C₁₇	C₂×D₃×C₁₇	semidirect
48. D₁₇	C₁₇×C₃⋊D₃	direct (N × H)
51. C₃⋊D₃	C₁₇×D₁₇	direct (N × H)
53. C₁₇	C₃⋊D₃×D₁₇	direct (N × H)
54. C₁₇	C₂×C₁₇×C₃⋊D₃	semidirect
56. C₃²	C₂×C₁₇×D₁₇	semidirect
61. C₃	D₃×C₁₇×D₁₇	semidirect

Subgroups — C17×C3⋊D3×D17 #23780918

Conjugacy classes of subgroups

Complements

Subgroups — C₁₇×C₃⋊D₃×D₁₇ #23780918