Subgroups — C₂×C₃²×C₁₇×D₁₇ #23780949

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

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₁₇	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂²×C₃²×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₇²	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₃²×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₇×D₁₇	C₂	direct (N × H)
2. C₂×C₃²×C₁₇²	C₂	semidirect
3. C₂×C₃×C₁₇×D₁₇	C₃	direct (N × H)
4. C₃²×C₁₇²	C₂²	semidirect
5. C₂×C₃×C₁₇²	C₂×C₃	semidirect
6. C₃×C₁₇×D₁₇	C₂×C₃	direct (N × H)
7. C₂×C₁₇×D₁₇	C₃²	direct (N × H)
8. C₃×C₁₇²	C₂²×C₃	semidirect
10. C₂×C₃²×D₁₇	C₁₇	direct (N × H)
11. C₂×C₁₇²	C₂×C₃²	semidirect
12. C₁₇×D₁₇	C₂×C₃²	direct (N × H)
15. C₂×C₃²×C₁₇	D₁₇	direct (N × H)
16. C₂×C₃²×C₁₇	C₂×C₁₇	semidirect
17. C₃²×D₁₇	C₂×C₁₇	direct (N × H)
18. C₁₇²	C₂²×C₃²	semidirect
20. C₂×C₃×D₁₇	C₃×C₁₇	direct (N × H)
22. C₃²×C₁₇	C₂×D₁₇	direct (N × H)
23. C₃²×C₁₇	C₂²×C₁₇	semidirect
26. C₂×C₃×C₁₇	C₃×D₁₇	direct (N × H)
27. C₂×C₃×C₁₇	C₂×C₃×C₁₇	semidirect
28. C₃×D₁₇	C₂×C₃×C₁₇	direct (N × H)
30. C₂×D₁₇	C₃²×C₁₇	direct (N × H)
32. C₃×C₁₇	C₂×C₃×D₁₇	direct (N × H)
33. C₃×C₁₇	C₂²×C₃×C₁₇	semidirect
37. C₂×C₁₇	C₃²×D₁₇	direct (N × H)
38. C₂×C₁₇	C₂×C₃²×C₁₇	semidirect
39. D₁₇	C₂×C₃²×C₁₇	direct (N × H)
41. C₂×C₃²	C₁₇×D₁₇	direct (N × H)
43. C₁₇	C₂×C₃²×D₁₇	direct (N × H)
44. C₁₇	C₂²×C₃²×C₁₇	semidirect
46. C₃²	C₂×C₁₇×D₁₇	direct (N × H)
48. C₂×C₃	C₃×C₁₇×D₁₇	direct (N × H)
50. C₃	C₂×C₃×C₁₇×D₁₇	direct (N × H)
52. C₂	C₃²×C₁₇×D₁₇	direct (N × H)

Subgroups — C2×C32×C17×D17 #23780949

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃²×C₁₇×D₁₇ #23780949