Subgroups — D₃×C₁₇×C₇⋊D₇ #23756251

Order 9996.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₃⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₇²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₇×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₇×C₇⋊D₇	—	3	1	no	maximal, Hall
5	C₃×C₇²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₇²×C₁₇	—	3	1	no	—
7	C₁₇×C₇⋊D₇	—	3	1	no	—
8	C₁₇×C₇⋊D₇	D₃	1	1	yes	characteristic, direct product factor
9	D₃×D₇×C₁₇	—	7	8	no	maximal
10	C₇²×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₁₇×D₂₁	—	7	8	no	—
12	D₃×C₇×C₁₇	D₇	1	8	yes	complemented
13	C₃×D₇×C₁₇	—	7	8	no	—
14	D₃×C₇⋊D₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×D₇×C₁₇	—	21	8	no	—
16	C₃×C₇×C₁₇	C₂×D₇	1	8	yes	complemented
17	C₃⋊(C₇⋊D₇)	C₂×C₁₇	1	1	yes	characteristic, complemented
18	D₃×C₇²	C₂×C₁₇	1	1	yes	characteristic, complemented
19	C₃×C₇⋊D₇	C₂×C₁₇	1	1	yes	characteristic, complemented
20	C₂×C₇×C₁₇	—	3	8	no	—
21	D₇×C₁₇	—	7	8	no	—
22	D₇×C₁₇	—	21	8	no	—
23	C₂×D₃×C₁₇	—	49	1	no	Hall
24	C₂×C₇⋊D₇	—	3	1	no	Hall
25	C₃×C₇²	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
26	C₇×C₁₇	D₃×D₇	1	8	yes	complemented
27	C₂×C₃×C₁₇	—	49	1	no	—
28	D₃×C₁₇	—	49	1	no	—
29	D₃×C₁₇	C₇⋊D₇	1	1	yes	characteristic, direct product factor
30	C₂×C₇²	—	3	1	no	—
31	C₇⋊D₇	—	3	1	no	—
32	C₇⋊D₇	D₃×C₁₇	1	1	yes	characteristic, direct product factor
33	D₃×D₇	—	7	8	no	—
34	C₂²×C₁₇	—	147	1	no	Hall
35	C₃×C₁₇	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
36	C₇²	C₂×D₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
37	D₂₁	—	7	8	no	—
38	C₃×D₇	—	7	8	no	—
39	D₃×C₇	D₇×C₁₇	1	8	yes	complemented
40	C₂×C₁₇	—	3	1	no	—
41	C₂×C₁₇	—	49	1	no	—
42	C₂×C₁₇	—	147	1	no	—
43	C₂×D₇	—	21	8	no	—
44	C₃×C₇	C₂×D₇×C₁₇	1	8	yes	complemented
45	C₁₇	D₃×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
46	C₂×C₇	—	3	8	no	—
47	D₇	—	7	8	no	—
48	D₇	—	21	8	no	—
49	C₂×D₃	—	49	1	no	Hall
50	C₇	D₃×D₇×C₁₇	1	8	yes	complemented
51	C₂×C₃	—	49	1	no	—
52	D₃	—	49	1	no	—
53	D₃	C₁₇×C₇⋊D₇	1	1	yes	characteristic, direct product factor
54	C₂²	—	147	1	no	Sylow
55	C₃	C₂×C₁₇×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	3	1	no	—
57	C₂	—	49	1	no	—
58	C₂	—	147	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇	D₃×C₇⋊D₇
commutator, cosocle, hypocenter	C₃×C₇²	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₇	C₂²
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₃⋊(C₇⋊D₇)	C₂	semidirect
2. D₃×C₇²×C₁₇	C₂	semidirect
3. C₃×C₁₇×C₇⋊D₇	C₂	semidirect
5. C₃×C₇²×C₁₇	C₂²	semidirect
8. C₁₇×C₇⋊D₇	D₃	direct (N × H)
10. C₇²×C₁₇	C₂×D₃	semidirect
12. D₃×C₇×C₁₇	D₇	semidirect
14. D₃×C₇⋊D₇	C₁₇	direct (N × H)
16. C₃×C₇×C₁₇	C₂×D₇	semidirect
17. C₃⋊(C₇⋊D₇)	C₂×C₁₇	semidirect
18. D₃×C₇²	C₂×C₁₇	semidirect
19. C₃×C₇⋊D₇	C₂×C₁₇	semidirect
25. C₃×C₇²	C₂²×C₁₇	semidirect
26. C₇×C₁₇	D₃×D₇	semidirect
29. D₃×C₁₇	C₇⋊D₇	direct (N × H)
32. C₇⋊D₇	D₃×C₁₇	direct (N × H)
35. C₃×C₁₇	C₂×C₇⋊D₇	semidirect
36. C₇²	C₂×D₃×C₁₇	semidirect
39. D₃×C₇	D₇×C₁₇	semidirect
44. C₃×C₇	C₂×D₇×C₁₇	semidirect
45. C₁₇	D₃×C₇⋊D₇	direct (N × H)
50. C₇	D₃×D₇×C₁₇	semidirect
53. D₃	C₁₇×C₇⋊D₇	direct (N × H)
55. C₃	C₂×C₁₇×C₇⋊D₇	semidirect

Subgroups — D3×C17×C7⋊D7 #23756251

Conjugacy classes of subgroups

Complements

Subgroups — D₃×C₁₇×C₇⋊D₇ #23756251