Subgroups — D₃×C₃⋊(C₁₇⋊D₁₇) #23780928

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	1	yes	maximal, characteristic, complemented
2	C₃×C₃⋊(C₁₇⋊D₁₇)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃×C₁₇²	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃⋊(C₁₇⋊D₁₇)	—	3	1	no	maximal
5	D₃×C₁₇⋊D₁₇	—	3	1	no	maximal
6	C₃²×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₇²	—	3	1	no	—
8	C₃×C₁₇⋊D₁₇	—	3	1	no	—
9	D₃×C₁₇²	D₃	1	1	yes	characteristic, complemented
10	C₃⋊(C₁₇⋊D₁₇)	—	3	1	no	—
11	C₃⋊(C₁₇⋊D₁₇)	—	3	1	no	—
12	C₃⋊(C₁₇⋊D₁₇)	—	6	1	no	—
13	C₃⋊(C₁₇⋊D₁₇)	D₃	1	1	yes	characteristic, direct product factor
14	C₂×C₁₇⋊D₁₇	—	9	1	no	Hall
15	C₃×C₁₇²	—	2	1	no	—
16	C₃×C₁₇²	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₇²	C₂×D₃	1	1	yes	characteristic, complemented
18	D₃×D₅₁	—	17	18	no	maximal
19	C₂×C₁₇²	—	3	1	no	—
20	C₁₇⋊D₁₇	—	3	1	no	—
21	C₁₇⋊D₁₇	—	9	1	no	—
22	C₃⋊D₅₁	—	17	18	no	—
23	C₃×D₅₁	—	17	18	no	—
24	C₃×D₃×C₁₇	D₁₇	1	18	yes	complemented
25	C₁₇²	D₃²	1	1	yes	characteristic, complemented, Sylow
26	C₂×D₅₁	—	51	18	no	—
27	D₃×D₁₇	—	51	18	no	—
28	C₃²×C₁₇	C₂×D₁₇	1	18	yes	complemented
29	C₂×C₃×C₁₇	—	3	18	no	—
30	D₅₁	—	17	18	no	—
31	D₅₁	—	51	18	no	—
32	D₅₁	—	51	18	no	—
33	D₅₁	—	102	18	no	—
34	C₃×D₁₇	—	51	18	no	—
35	D₃×C₁₇	D₅₁	1	18	yes	complemented
36	C₂×D₁₇	—	153	18	no	—
37	C₃×C₁₇	—	2	18	no	—
38	C₃×C₁₇	D₃×D₁₇	1	18	yes	complemented
39	C₃×C₁₇	C₂×D₅₁	1	18	yes	complemented
40	D₃²	—	289	1	no	Hall
41	C₂×C₁₇	—	3	18	no	—
42	D₁₇	—	51	18	no	—
43	D₁₇	—	153	18	no	—
44	C₃⋊D₃	—	289	1	no	—
45	C₃×D₃	—	289	1	no	—
46	C₃×D₃	C₁₇⋊D₁₇	1	1	yes	characteristic, complemented
47	C₁₇	D₃×D₅₁	1	18	yes	complemented
48	C₂×D₃	—	867	1	no	—
49	C₂×D₃	—	867	1	no	—
50	C₃²	C₂×C₁₇⋊D₁₇	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	3	1	no	—
52	C₂×C₃	—	867	1	no	—
53	D₃	—	289	1	no	—
54	D₃	—	867	1	no	—
55	D₃	—	867	1	no	—
56	D₃	—	1734	1	no	—
57	D₃	C₃⋊(C₁₇⋊D₁₇)	1	1	yes	characteristic, direct product factor
58	C₂²	—	2601	1	no	Sylow
59	C₃	—	2	1	no	—
60	C₃	D₃×C₁₇⋊D₁₇	1	1	yes	characteristic, complemented
61	C₃	C₂×C₃⋊(C₁₇⋊D₁₇)	1	1	yes	characteristic, complemented
62	C₂	—	3	1	no	—
63	C₂	—	2601	1	no	—
64	C₂	—	867	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₃⋊(C₁₇⋊D₁₇))	C₂	semidirect
2. C₃×C₃⋊(C₁₇⋊D₁₇)	C₂	semidirect
3. C₃×D₃×C₁₇²	C₂	semidirect
6. C₃²×C₁₇²	C₂²	semidirect
9. D₃×C₁₇²	D₃	semidirect
13. C₃⋊(C₁₇⋊D₁₇)	D₃	direct (N × H)
16. C₃×C₁₇²	C₂×D₃	semidirect
17. C₃×C₁₇²	C₂×D₃	semidirect
24. C₃×D₃×C₁₇	D₁₇	semidirect
25. C₁₇²	D₃²	semidirect
28. C₃²×C₁₇	C₂×D₁₇	semidirect
35. D₃×C₁₇	D₅₁	semidirect
38. C₃×C₁₇	D₃×D₁₇	semidirect
39. C₃×C₁₇	C₂×D₅₁	semidirect
46. C₃×D₃	C₁₇⋊D₁₇	semidirect
47. C₁₇	D₃×D₅₁	semidirect
50. C₃²	C₂×C₁₇⋊D₁₇	semidirect
57. D₃	C₃⋊(C₁₇⋊D₁₇)	direct (N × H)
60. C₃	D₃×C₁₇⋊D₁₇	semidirect
61. C₃	C₂×C₃⋊(C₁₇⋊D₁₇)	semidirect

Subgroups — D3×C3⋊(C17⋊D17) #23780928

Conjugacy classes of subgroups

Complements

Subgroups — D₃×C₃⋊(C₁₇⋊D₁₇) #23780928