Subgroups — C₁₇×C₃⋊(D₃₁⋊C₃) #23748677

Order 9486.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×D₃₁⋊C₃	—	3	1	no	maximal
3	C₁₇×D₉₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₇×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₇×C₃₁⋊C₃	—	2	1	no	—
6	C₁₇×C₃₁⋊C₃	D₃	1	1	yes	characteristic, complemented
7	C₁₇×D₃₁	—	3	1	no	Hall
8	C₃⋊(D₃₁⋊C₃)	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₇×C₃₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃×D₃×C₁₇	—	31	1	no	maximal, Hall
11	C₃×C₃₁⋊C₃	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
12	D₉₃	C₃×C₁₇	1	1	yes	characteristic, complemented
13	D₃₁⋊C₃	—	3	1	no	—
14	C₃²×C₁₇	—	31	1	no	Hall
15	C₂×C₃×C₁₇	—	93	1	no	—
16	D₃×C₁₇	—	31	1	no	—
17	C₃×C₃₁	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
18	C₃₁⋊C₃	—	2	1	no	—
19	C₃₁⋊C₃	D₃×C₁₇	1	1	yes	characteristic, complemented
20	D₃₁	—	3	1	no	Hall
21	C₃×C₁₇	—	31	1	no	—
22	C₃×C₁₇	—	62	1	no	—
23	C₃×C₁₇	D₃₁⋊C₃	1	1	yes	characteristic, complemented
24	C₂×C₁₇	—	93	1	no	Hall
25	C₃₁	C₃×D₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
26	C₃×D₃	—	31	1	no	Hall
27	C₁₇	C₃⋊(D₃₁⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
28	C₃²	—	31	1	no	Sylow
29	C₂×C₃	—	93	1	no	—
30	D₃	—	31	1	no	—
31	C₃	—	31	1	no	—
32	C₃	—	62	1	no	—
33	C₃	C₁₇×D₃₁⋊C₃	1	1	yes	characteristic, complemented
34	C₂	—	93	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	C₃⋊(D₃₁⋊C₃)
commutator, cosocle, hypocenter	C₃×C₃₁	C₂×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₇×C₃₁	C₂×C₃
LCS	G ▷ C₃×C₃₁
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₇×C₃₁⋊C₃	C₂	semidirect
3. C₁₇×D₉₃	C₃	semidirect
4. C₃×C₁₇×C₃₁	C₂×C₃	semidirect
6. C₁₇×C₃₁⋊C₃	D₃	semidirect
8. C₃⋊(D₃₁⋊C₃)	C₁₇	direct (N × H)
9. C₁₇×C₃₁	C₃×D₃	semidirect
11. C₃×C₃₁⋊C₃	C₂×C₁₇	semidirect
12. D₉₃	C₃×C₁₇	semidirect
17. C₃×C₃₁	C₂×C₃×C₁₇	semidirect
19. C₃₁⋊C₃	D₃×C₁₇	semidirect
23. C₃×C₁₇	D₃₁⋊C₃	semidirect
25. C₃₁	C₃×D₃×C₁₇	semidirect
27. C₁₇	C₃⋊(D₃₁⋊C₃)	direct (N × H)
33. C₃	C₁₇×D₃₁⋊C₃	semidirect

Subgroups — C17×C3⋊(D31⋊C3) #23748677

Conjugacy classes of subgroups

Complements

Subgroups — C₁₇×C₃⋊(D₃₁⋊C₃) #23748677