Subgroups — C₂×C₁₇×C₃⋊D₅₁ #23780943

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	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₇²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×D₅₁	—	3	4	no	maximal
4	C₃²×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₇²	D₃	1	4	yes	complemented
6	C₁₇×D₅₁	—	3	8	no	—
7	C₂×C₁₇×D₁₇	—	9	1	no	Hall
8	C₃×C₁₇²	C₂×D₃	1	4	yes	complemented
9	C₂×C₃⋊D₅₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₁₇×C₃⋊D₃	—	17	1	no	maximal
11	C₂×C₁₇²	C₃⋊D₃	1	1	yes	characteristic, complemented
12	C₁₇×D₁₇	—	9	2	no	—
13	C₂×C₃²×C₁₇	—	2	8	no	—
14	C₂×C₃²×C₁₇	D₁₇	1	1	yes	characteristic, complemented
15	C₂×C₃²×C₁₇	C₂×C₁₇	1	1	yes	characteristic, complemented
16	C₃⋊D₅₁	C₂×C₁₇	1	2	yes	direct product factor
17	C₁₇×C₃⋊D₃	—	17	2	no	—
18	C₁₇²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×D₅₁	—	3	4	no	—
20	C₂×D₃×C₁₇	—	51	4	no	—
21	C₃²×C₁₇	—	2	8	no	—
22	C₃²×C₁₇	C₂×D₁₇	1	1	yes	characteristic, complemented
23	C₃²×C₁₇	C₂²×C₁₇	1	1	yes	characteristic, complemented
24	C₂×C₃×C₁₇	—	2	32	no	—
25	C₂×C₃×C₁₇	D₃×C₁₇	1	4	yes	complemented
26	C₂×C₃×C₁₇	D₅₁	1	4	yes	complemented
27	D₅₁	—	3	8	no	—
28	D₃×C₁₇	—	51	8	no	—
29	C₂²×C₁₇	—	153	1	no	—
30	C₂×D₁₇	—	9	1	no	—
31	C₃×C₁₇	—	2	32	no	—
32	C₃×C₁₇	C₂×D₃×C₁₇	1	4	yes	complemented
33	C₃×C₁₇	C₂×D₅₁	1	4	yes	complemented
34	C₂×C₃⋊D₃	—	17	1	no	Hall
35	C₂×C₁₇	—	2	8	no	—
36	C₂×C₁₇	—	153	2	no	—
37	C₂×C₁₇	C₁₇×C₃⋊D₃	1	1	yes	characteristic, complemented
38	C₂×C₁₇	C₃⋊D₅₁	1	1	yes	characteristic, direct product factor
39	D₁₇	—	9	2	no	—
40	C₂×C₃²	C₁₇×D₁₇	1	1	yes	characteristic, complemented
41	C₃⋊D₃	—	17	2	no	—
42	C₁₇	—	2	8	no	—
43	C₁₇	C₂×C₁₇×C₃⋊D₃	1	1	yes	characteristic, complemented
44	C₁₇	C₂×C₃⋊D₅₁	1	1	yes	characteristic, direct product factor
45	C₂×D₃	—	51	4	no	—
46	C₃²	C₂×C₁₇×D₁₇	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	C₁₇×D₅₁	1	4	yes	complemented
48	D₃	—	51	8	no	—
49	C₂²	—	153	1	no	Sylow
50	C₃	C₂×C₁₇×D₅₁	1	4	yes	complemented
51	C₂	—	153	2	no	—
52	C₂	C₁₇×C₃⋊D₅₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇	C₃⋊D₅₁
commutator, cosocle, hypocenter	C₃²×C₁₇	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₇²	C₂
LCS	G ▷ C₃²×C₁₇
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₃⋊D₅₁	C₂	direct (N × H)
2. C₂×C₃²×C₁₇²	C₂	semidirect
4. C₃²×C₁₇²	C₂²	semidirect
5. C₂×C₃×C₁₇²	D₃	semidirect
8. C₃×C₁₇²	C₂×D₃	semidirect
9. C₂×C₃⋊D₅₁	C₁₇	direct (N × H)
11. C₂×C₁₇²	C₃⋊D₃	semidirect
14. C₂×C₃²×C₁₇	D₁₇	semidirect
15. C₂×C₃²×C₁₇	C₂×C₁₇	semidirect
16. C₃⋊D₅₁	C₂×C₁₇	direct (N × H)
18. C₁₇²	C₂×C₃⋊D₃	semidirect
22. C₃²×C₁₇	C₂×D₁₇	semidirect
23. C₃²×C₁₇	C₂²×C₁₇	semidirect
25. C₂×C₃×C₁₇	D₃×C₁₇	semidirect
26. C₂×C₃×C₁₇	D₅₁	semidirect
32. C₃×C₁₇	C₂×D₃×C₁₇	semidirect
33. C₃×C₁₇	C₂×D₅₁	semidirect
37. C₂×C₁₇	C₁₇×C₃⋊D₃	semidirect
38. C₂×C₁₇	C₃⋊D₅₁	direct (N × H)
40. C₂×C₃²	C₁₇×D₁₇	semidirect
43. C₁₇	C₂×C₁₇×C₃⋊D₃	semidirect
44. C₁₇	C₂×C₃⋊D₅₁	direct (N × H)
46. C₃²	C₂×C₁₇×D₁₇	semidirect
47. C₂×C₃	C₁₇×D₅₁	semidirect
50. C₃	C₂×C₁₇×D₅₁	semidirect
52. C₂	C₁₇×C₃⋊D₅₁	direct (N × H)

Subgroups — C2×C17×C3⋊D51 #23780943

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₇×C₃⋊D₅₁ #23780943