Subgroups — C₂×C₃×C₃⋊(C₁₇⋊D₁₇) #23780945

Order 10404.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃⋊(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	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×C₁₇⋊D₁₇	—	3	1	no	maximal
5	C₃²×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₁₇²	—	2	1	no	—
7	C₂×C₃×C₁₇²	D₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₁₇²	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×C₁₇⋊D₁₇	—	3	2	no	—
10	C₃⋊(C₁₇⋊D₁₇)	C₂×C₃	1	2	yes	direct product factor
11	C₂×C₁₇⋊D₁₇	—	3	1	no	Hall
12	C₃×C₁₇²	—	2	1	no	—
13	C₃×C₁₇²	C₂×D₃	1	1	yes	characteristic, complemented
14	C₃×C₁₇²	C₂²×C₃	1	1	yes	characteristic, complemented
15	C₂×C₃×D₅₁	—	17	18	no	maximal
16	C₂×C₁₇²	C₃×D₃	1	1	yes	characteristic, complemented
17	C₁₇⋊D₁₇	—	3	2	no	—
18	C₂×C₃²×C₁₇	D₁₇	1	18	yes	complemented
19	C₃×D₅₁	—	17	36	no	—
20	C₁₇²	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×D₅₁	—	17	18	no	—
22	C₂×C₃×D₁₇	—	51	18	no	—
23	C₃²×C₁₇	C₂×D₁₇	1	18	yes	complemented
24	C₂×C₃×C₁₇	—	2	18	no	—
25	C₂×C₃×C₁₇	C₃×D₁₇	1	18	yes	complemented
26	C₂×C₃×C₁₇	D₅₁	1	18	yes	complemented
27	D₅₁	—	17	36	no	—
28	C₃×D₁₇	—	51	36	no	—
29	C₂×D₁₇	—	51	18	no	—
30	C₃×C₁₇	—	2	18	no	—
31	C₃×C₁₇	C₂×C₃×D₁₇	1	18	yes	complemented
32	C₃×C₁₇	C₂×D₅₁	1	18	yes	complemented
33	C₂×C₃×D₃	—	289	1	no	Hall
34	C₂×C₁₇	C₃×D₅₁	1	18	yes	complemented
35	D₁₇	—	51	36	no	—
36	C₂×C₃²	C₁₇⋊D₁₇	1	1	yes	characteristic, complemented
37	C₃×D₃	—	289	2	no	—
38	C₁₇	C₂×C₃×D₅₁	1	18	yes	complemented
39	C₂²×C₃	—	867	1	no	—
40	C₂×D₃	—	289	1	no	—
41	C₃²	C₂×C₁₇⋊D₁₇	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃	—	2	1	no	—
43	C₂×C₃	—	867	2	no	—
44	C₂×C₃	C₃⋊(C₁₇⋊D₁₇)	1	1	yes	characteristic, direct product factor
45	C₂×C₃	C₃×C₁₇⋊D₁₇	1	1	yes	characteristic, complemented
46	D₃	—	289	2	no	—
47	C₂²	—	867	1	no	Sylow
48	C₃	—	2	1	no	—
49	C₃	C₂×C₃×C₁₇⋊D₁₇	1	1	yes	characteristic, complemented
50	C₃	C₂×C₃⋊(C₁₇⋊D₁₇)	1	1	yes	characteristic, direct product factor
51	C₂	—	867	2	no	—
52	C₂	C₃×C₃⋊(C₁₇⋊D₁₇)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₃⋊(C₁₇⋊D₁₇)
commutator, cosocle, hypocenter	C₃×C₁₇²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₇²	C₂
LCS	G ▷ C₃×C₁₇²
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₃⋊(C₁₇⋊D₁₇)	C₂	direct (N × H)
2. C₂×C₃²×C₁₇²	C₂	semidirect
3. C₂×C₃⋊(C₁₇⋊D₁₇)	C₃	direct (N × H)
5. C₃²×C₁₇²	C₂²	semidirect
7. C₂×C₃×C₁₇²	D₃	semidirect
8. C₂×C₃×C₁₇²	C₂×C₃	semidirect
10. C₃⋊(C₁₇⋊D₁₇)	C₂×C₃	direct (N × H)
13. C₃×C₁₇²	C₂×D₃	semidirect
14. C₃×C₁₇²	C₂²×C₃	semidirect
16. C₂×C₁₇²	C₃×D₃	semidirect
18. C₂×C₃²×C₁₇	D₁₇	semidirect
20. C₁₇²	C₂×C₃×D₃	semidirect
23. C₃²×C₁₇	C₂×D₁₇	semidirect
25. C₂×C₃×C₁₇	C₃×D₁₇	semidirect
26. C₂×C₃×C₁₇	D₅₁	semidirect
31. C₃×C₁₇	C₂×C₃×D₁₇	semidirect
32. C₃×C₁₇	C₂×D₅₁	semidirect
34. C₂×C₁₇	C₃×D₅₁	semidirect
36. C₂×C₃²	C₁₇⋊D₁₇	semidirect
38. C₁₇	C₂×C₃×D₅₁	semidirect
41. C₃²	C₂×C₁₇⋊D₁₇	semidirect
44. C₂×C₃	C₃⋊(C₁₇⋊D₁₇)	direct (N × H)
45. C₂×C₃	C₃×C₁₇⋊D₁₇	semidirect
49. C₃	C₂×C₃×C₁₇⋊D₁₇	semidirect
50. C₃	C₂×C₃⋊(C₁₇⋊D₁₇)	direct (N × H)
52. C₂	C₃×C₃⋊(C₁₇⋊D₁₇)	direct (N × H)

Subgroups — C2×C3×C3⋊(C17⋊D17) #23780945

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₃⋊(C₁₇⋊D₁₇) #23780945