Subgroups — C₁₇×C₃⋊D₂₃₁ #37555669

Order 23562.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×D₂₃₁	—	3	4	no	maximal
3	C₃×C₇×C₁₁×C₁₇	D₃	1	4	yes	complemented
4	C₁₇×C₃⋊D₃₃	—	7	1	no	maximal, Hall
5	C₁₇×D₇₇	—	9	1	no	Hall
6	C₁₇×C₃⋊D₂₁	—	11	1	no	maximal, Hall
7	C₃²×C₁₁×C₁₇	D₇	1	1	yes	characteristic, complemented, Hall
8	C₃⋊D₂₃₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₁₁×C₁₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
10	C₁₇×D₃₃	—	21	4	no	—
11	C₃²×C₇×C₁₇	D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₁₇×D₂₁	—	33	4	no	—
13	C₃²×C₇×C₁₁	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₁×C₁₇	D₂₁	1	4	yes	complemented
15	D₂₃₁	—	3	4	no	—
16	C₁₇×D₁₁	—	63	1	no	Hall
17	C₃×C₇×C₁₇	D₃₃	1	4	yes	complemented
18	C₁₇×C₃⋊D₃	—	77	1	no	Hall
19	D₇×C₁₇	—	99	1	no	Hall
20	C₃×C₇×C₁₁	D₃×C₁₇	1	4	yes	complemented
21	C₃⋊D₃₃	—	7	1	no	Hall
22	C₁₁×C₁₇	C₃⋊D₂₁	1	1	yes	characteristic, complemented, Hall
23	D₇₇	—	9	1	no	Hall
24	C₃²×C₁₇	D₇₇	1	1	yes	characteristic, complemented, Hall
25	C₃⋊D₂₁	—	11	1	no	Hall
26	C₇×C₁₇	C₃⋊D₃₃	1	1	yes	characteristic, complemented, Hall
27	D₃×C₁₇	—	231	4	no	—
28	C₃²×C₁₁	D₇×C₁₇	1	1	yes	characteristic, complemented, Hall
29	C₇×C₁₁	C₁₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
30	D₃₃	—	21	4	no	—
31	C₃²×C₇	C₁₇×D₁₁	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₇	D₂₃₁	1	4	yes	complemented
33	D₂₁	—	33	4	no	—
34	C₂×C₁₇	—	693	1	no	Hall
35	C₃×C₁₁	C₁₇×D₂₁	1	4	yes	complemented
36	D₁₁	—	63	1	no	Hall
37	C₃×C₇	C₁₇×D₃₃	1	4	yes	complemented
38	C₃⋊D₃	—	77	1	no	Hall
39	C₁₇	C₃⋊D₂₃₁	1	1	yes	characteristic, direct product factor, Sylow
40	D₇	—	99	1	no	Hall
41	C₁₁	C₁₇×C₃⋊D₂₁	1	1	yes	characteristic, complemented, Sylow
42	C₃²	C₁₇×D₇₇	1	1	yes	characteristic, complemented, Sylow
43	C₇	C₁₇×C₃⋊D₃₃	1	1	yes	characteristic, complemented, Sylow
44	D₃	—	231	4	no	—
45	C₃	C₁₇×D₂₃₁	1	4	yes	complemented
46	C₂	—	693	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	C₃⋊D₂₃₁
commutator, cosocle, hypocenter	C₃²×C₇×C₁₁	C₂×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁×C₁₇	C₂
LCS	G ▷ C₃²×C₇×C₁₁
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₁×C₁₇	C₂	semidirect
3. C₃×C₇×C₁₁×C₁₇	D₃	semidirect
7. C₃²×C₁₁×C₁₇	D₇	semidirect
8. C₃⋊D₂₃₁	C₁₇	direct (N × H)
9. C₇×C₁₁×C₁₇	C₃⋊D₃	semidirect
11. C₃²×C₇×C₁₇	D₁₁	semidirect
13. C₃²×C₇×C₁₁	C₂×C₁₇	semidirect
14. C₃×C₁₁×C₁₇	D₂₁	semidirect
17. C₃×C₇×C₁₇	D₃₃	semidirect
20. C₃×C₇×C₁₁	D₃×C₁₇	semidirect
22. C₁₁×C₁₇	C₃⋊D₂₁	semidirect
24. C₃²×C₁₇	D₇₇	semidirect
26. C₇×C₁₇	C₃⋊D₃₃	semidirect
28. C₃²×C₁₁	D₇×C₁₇	semidirect
29. C₇×C₁₁	C₁₇×C₃⋊D₃	semidirect
31. C₃²×C₇	C₁₇×D₁₁	semidirect
32. C₃×C₁₇	D₂₃₁	semidirect
35. C₃×C₁₁	C₁₇×D₂₁	semidirect
37. C₃×C₇	C₁₇×D₃₃	semidirect
39. C₁₇	C₃⋊D₂₃₁	direct (N × H)
41. C₁₁	C₁₇×C₃⋊D₂₁	semidirect
42. C₃²	C₁₇×D₇₇	semidirect
43. C₇	C₁₇×C₃⋊D₃₃	semidirect
45. C₃	C₁₇×D₂₃₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₇×C₁₁×C₁₇	2
C₁₇×D₂₃₁	3
C₁₇×C₃⋊D₃₃	7
C₁₇×C₃⋊D₂₁	11
C₃⋊D₂₃₁	17

Subgroups — C17×C3⋊D231 #37555669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×C₃⋊D₂₃₁ #37555669