Subgroups — C₁₇×(C₃⋊D₃)⋊D₁₇ #23780927

Order 10404.

184 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×C₁₇×D₅₁	C₂	1	2	yes	maximal, complemented
3	D₃×C₁₇×D₁₇	—	3	2	no	maximal
4	C₃²×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₇×D₁₇	—	3	2	no	—
6	D₃×C₁₇²	—	3	2	no	—
7	D₃×C₁₇²	—	6	1	no	—
8	C₁₇×D₅₁	D₃	1	2	yes	complemented
9	C₂×C₁₇×D₁₇	—	9	1	no	Hall
10	C₃×C₁₇²	—	2	1	no	—
11	C₃×C₁₇²	C₂×D₃	1	2	yes	complemented
12	(C₃⋊D₃)⋊D₁₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor
13	D₃²×C₁₇	—	17	1	no	maximal
14	C₂×C₁₇²	—	9	1	no	—
15	C₁₇×D₁₇	—	3	2	no	—
16	C₁₇×C₃⋊D₃	—	2	8	no	—
17	C₁₇×C₃⋊D₃	D₁₇	1	1	yes	characteristic, complemented
18	C₁₇×C₃⋊D₃	C₂×C₁₇	1	1	yes	characteristic, complemented
19	C₃×D₅₁	C₂×C₁₇	1	2	yes	complemented
20	C₃×D₃×C₁₇	—	17	2	no	—
21	C₁₇²	D₃²	1	1	yes	characteristic, complemented, Sylow
22	C₂×D₃×C₁₇	—	51	2	no	—
23	D₃×D₁₇	—	3	2	no	—
24	C₃²×C₁₇	—	2	8	no	—
25	C₃²×C₁₇	C₂×D₁₇	1	1	yes	characteristic, complemented
26	C₃²×C₁₇	C₂²×C₁₇	1	1	yes	characteristic, complemented
27	C₂×C₃×C₁₇	—	51	2	no	—
28	D₅₁	D₃×C₁₇	1	2	yes	complemented
29	C₃×D₁₇	—	3	2	no	—
30	D₃×C₁₇	—	3	2	no	—
31	D₃×C₁₇	—	3	2	no	—
32	D₃×C₁₇	—	6	16	no	—
33	D₃×C₁₇	—	6	1	no	—
34	D₃×C₁₇	—	6	1	no	—
35	D₃×C₁₇	—	6	16	no	—
36	D₃×C₁₇	—	17	2	no	—
37	C₂²×C₁₇	—	153	1	no	—
38	C₂×D₁₇	—	9	1	no	—
39	C₃×C₁₇	—	2	16	no	—
40	C₃×C₁₇	—	2	1	no	—
41	C₃×C₁₇	—	2	1	no	—
42	C₃×C₁₇	—	2	16	no	—
43	C₃×C₁₇	D₃×D₁₇	1	2	yes	complemented
44	C₃×C₁₇	C₂×D₃×C₁₇	1	2	yes	complemented
45	D₃²	—	17	1	no	Hall
46	C₂×C₁₇	—	9	1	no	—
47	C₂×C₁₇	—	9	1	no	—
48	C₂×C₁₇	—	18	8	no	—
49	C₂×C₁₇	—	51	2	no	—
50	D₁₇	—	3	2	no	—
51	C₃⋊D₃	C₁₇×D₁₇	1	1	yes	characteristic, complemented
52	C₃×D₃	—	17	2	no	—
53	C₁₇	—	2	8	no	—
54	C₁₇	D₃²×C₁₇	1	1	yes	characteristic, complemented
55	C₁₇	(C₃⋊D₃)⋊D₁₇	1	1	yes	characteristic, direct product factor
56	C₂×D₃	—	51	2	no	—
57	C₃²	C₂×C₁₇×D₁₇	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₃	—	51	2	no	—
59	D₃	—	3	2	no	—
60	D₃	—	6	1	no	—
61	D₃	—	17	2	no	—
62	C₂²	—	153	1	no	Sylow
63	C₃	—	2	1	no	—
64	C₃	D₃×C₁₇×D₁₇	1	2	yes	complemented
65	C₂	—	9	1	no	—
66	C₂	—	51	2	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. C₁₇²×C₃⋊D₃	C₂	semidirect
2. C₃×C₁₇×D₅₁	C₂	semidirect
4. C₃²×C₁₇²	C₂²	semidirect
8. C₁₇×D₅₁	D₃	semidirect
11. C₃×C₁₇²	C₂×D₃	semidirect
12. (C₃⋊D₃)⋊D₁₇	C₁₇	direct (N × H)
17. C₁₇×C₃⋊D₃	D₁₇	semidirect
18. C₁₇×C₃⋊D₃	C₂×C₁₇	semidirect
19. C₃×D₅₁	C₂×C₁₇	semidirect
21. C₁₇²	D₃²	semidirect
25. C₃²×C₁₇	C₂×D₁₇	semidirect
26. C₃²×C₁₇	C₂²×C₁₇	semidirect
28. D₅₁	D₃×C₁₇	semidirect
43. C₃×C₁₇	D₃×D₁₇	semidirect
44. C₃×C₁₇	C₂×D₃×C₁₇	semidirect
51. C₃⋊D₃	C₁₇×D₁₇	semidirect
54. C₁₇	D₃²×C₁₇	semidirect
55. C₁₇	(C₃⋊D₃)⋊D₁₇	direct (N × H)
57. C₃²	C₂×C₁₇×D₁₇	semidirect
64. C₃	D₃×C₁₇×D₁₇	semidirect

Subgroups — C17×(C3⋊D3)⋊D17 #23780927

Conjugacy classes of subgroups

Complements

Subgroups — C₁₇×(C₃⋊D₃)⋊D₁₇ #23780927