Subgroups — C₂×C₁₇×C₃⋊(C₇⋊D₇) #23756273

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	2	yes	maximal, direct product factor
2	C₂×C₃×C₇²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×C₇⋊D₇	—	3	1	no	maximal, Hall
4	C₃×C₇²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇²×C₁₇	D₃	1	1	yes	characteristic, complemented
6	C₁₇×C₇⋊D₇	—	3	2	no	—
7	C₂×C₁₇×D₂₁	—	7	8	no	maximal
8	C₇²×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₇×C₁₇	D₇	1	8	yes	complemented
10	C₁₇×D₂₁	—	7	16	no	—
11	C₂×C₃⋊(C₇⋊D₇)	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×D₇×C₁₇	—	21	8	no	—
13	C₃×C₇×C₁₇	C₂×D₇	1	8	yes	complemented
14	C₂×C₃×C₇²	C₂×C₁₇	1	1	yes	characteristic, complemented
15	C₃⋊(C₇⋊D₇)	C₂×C₁₇	1	2	yes	direct product factor
16	C₂×C₇×C₁₇	D₂₁	1	8	yes	complemented
17	D₇×C₁₇	—	21	16	no	—
18	C₂×D₃×C₁₇	—	49	1	no	Hall
19	C₂×C₇⋊D₇	—	3	1	no	Hall
20	C₃×C₇²	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
21	C₇×C₁₇	C₂×D₂₁	1	8	yes	complemented
22	C₂×C₃×C₁₇	C₇⋊D₇	1	1	yes	characteristic, complemented
23	D₃×C₁₇	—	49	2	no	—
24	C₂×C₇²	D₃×C₁₇	1	1	yes	characteristic, complemented
25	C₇⋊D₇	—	3	2	no	—
26	C₂×D₂₁	—	7	8	no	—
27	C₂²×C₁₇	—	147	1	no	Hall
28	C₃×C₁₇	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
29	C₇²	C₂×D₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃×C₇	D₇×C₁₇	1	8	yes	complemented
31	D₂₁	—	7	16	no	—
32	C₂×C₁₇	—	147	2	no	—
33	C₂×C₁₇	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor
34	C₂×D₇	—	21	8	no	—
35	C₃×C₇	C₂×D₇×C₁₇	1	8	yes	complemented
36	C₁₇	C₂×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₇	C₁₇×D₂₁	1	8	yes	complemented
38	D₇	—	21	16	no	—
39	C₂×D₃	—	49	1	no	Hall
40	C₇	C₂×C₁₇×D₂₁	1	8	yes	complemented
41	C₂×C₃	C₁₇×C₇⋊D₇	1	1	yes	characteristic, complemented
42	D₃	—	49	2	no	—
43	C₂²	—	147	1	no	Sylow
44	C₃	C₂×C₁₇×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	147	2	no	—
46	C₂	C₁₇×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇	C₃⋊(C₇⋊D₇)
commutator, cosocle, hypocenter	C₃×C₇²	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇²×C₁₇	C₂
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₃⋊(C₇⋊D₇)	C₂	direct (N × H)
2. C₂×C₃×C₇²×C₁₇	C₂	semidirect
4. C₃×C₇²×C₁₇	C₂²	semidirect
5. C₂×C₇²×C₁₇	D₃	semidirect
8. C₇²×C₁₇	C₂×D₃	semidirect
9. C₂×C₃×C₇×C₁₇	D₇	semidirect
11. C₂×C₃⋊(C₇⋊D₇)	C₁₇	direct (N × H)
13. C₃×C₇×C₁₇	C₂×D₇	semidirect
14. C₂×C₃×C₇²	C₂×C₁₇	semidirect
15. C₃⋊(C₇⋊D₇)	C₂×C₁₇	direct (N × H)
16. C₂×C₇×C₁₇	D₂₁	semidirect
20. C₃×C₇²	C₂²×C₁₇	semidirect
21. C₇×C₁₇	C₂×D₂₁	semidirect
22. C₂×C₃×C₁₇	C₇⋊D₇	semidirect
24. C₂×C₇²	D₃×C₁₇	semidirect
28. C₃×C₁₇	C₂×C₇⋊D₇	semidirect
29. C₇²	C₂×D₃×C₁₇	semidirect
30. C₂×C₃×C₇	D₇×C₁₇	semidirect
33. C₂×C₁₇	C₃⋊(C₇⋊D₇)	direct (N × H)
35. C₃×C₇	C₂×D₇×C₁₇	semidirect
36. C₁₇	C₂×C₃⋊(C₇⋊D₇)	direct (N × H)
37. C₂×C₇	C₁₇×D₂₁	semidirect
40. C₇	C₂×C₁₇×D₂₁	semidirect
41. C₂×C₃	C₁₇×C₇⋊D₇	semidirect
44. C₃	C₂×C₁₇×C₇⋊D₇	semidirect
46. C₂	C₁₇×C₃⋊(C₇⋊D₇)	direct (N × H)

Subgroups — C2×C17×C3⋊(C7⋊D7) #23756273

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₇×C₃⋊(C₇⋊D₇) #23756273