Subgroups — C₃⋊(ΓL(1,𝔽₃₂)⋊Dic₁₇) #44539269

Order 31620.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₇×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic
2	ΓL(1,𝔽₃₂)⋊Dic₁₇	—	3	1	no	maximal, Hall
3	C₃×C₁₇×ΓL(1,𝔽₃₂)	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₅₈₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₁₇×ΓL(1,𝔽₃₂)	D₃	1	1	yes	characteristic
6	C₂×C₃×C₁₇×C₃₁	C₂×C₅	1	1	yes	characteristic
7	C₁₇×ΓL(1,𝔽₃₂)	Dic₃	1	1	yes	characteristic, complemented, Hall
8	Dic₅₂₇	—	3	1	no	Hall
9	C₃⋊(Dic₃₁⋊C₅)	—	17	1	no	maximal, Hall
10	C₃×C₁₇×C₃₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₇×C₃₁	C₅×D₃	1	1	yes	characteristic
12	C₅×Dic₅₁	—	31	1	no	maximal, Hall
13	C₂×C₃×ΓL(1,𝔽₃₂)	D₁₇	1	1	yes	characteristic
14	Dic₃₁⋊C₅	—	51	1	no	Hall
15	C₁₇×C₃₁	C₅×Dic₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₅×C₁₇	—	31	1	no	—
17	C₃×ΓL(1,𝔽₃₂)	Dic₁₇	1	1	yes	characteristic, complemented, Hall
18	Dic₉₃	—	17	1	no	Hall
19	C₅×Dic₁₇	—	93	1	no	Hall
20	C₂×ΓL(1,𝔽₃₂)	D₅₁	1	1	yes	characteristic
21	C₃×C₅×C₁₇	—	31	1	no	Hall
22	Dic₅₁	—	31	1	no	Hall
23	C₂×C₃×C₃₁	C₅×D₁₇	1	1	yes	characteristic
24	C₂×C₅×C₁₇	—	31	1	no	—
25	ΓL(1,𝔽₃₂)	Dic₅₁	1	1	yes	characteristic, complemented, Hall
26	Dic₃₁	—	51	1	no	Hall
27	C₂×C₃×C₁₇	D₃₁⋊C₅	1	1	yes	characteristic
28	C₃×C₃₁	C₅×Dic₁₇	1	1	yes	characteristic, complemented, Hall
29	C₅×C₁₇	—	31	1	no	Hall
30	Dic₁₇	—	93	1	no	Hall
31	C₂×C₃₁	C₅×D₅₁	1	1	yes	characteristic
32	C₅×Dic₃	—	527	1	no	Hall
33	C₃×C₁₇	Dic₃₁⋊C₅	1	1	yes	characteristic, complemented, Hall
34	C₂×C₁₇	C₃⋊(D₃₁⋊C₅)	1	1	yes	characteristic
35	C₃₁	C₅×Dic₅₁	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₅	—	31	1	no	—
37	C₄×C₅	—	1581	1	no	Hall
38	C₁₇	C₃⋊(Dic₃₁⋊C₅)	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	—	31	1	no	Hall
40	Dic₃	—	527	1	no	Hall
41	C₂×C₅	—	31	1	no	—
42	C₂×C₃	C₁₇⋊(D₃₁⋊C₅)	1	1	yes	characteristic
43	C₅	—	31	1	no	Sylow
44	C₄	—	1581	1	no	Sylow
45	C₃	ΓL(1,𝔽₃₂)⋊Dic₁₇	1	1	yes	characteristic, complemented, Sylow
46	C₂	C₃⋊(C₁₇⋊(D₃₁⋊C₅))	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊(C₁₇⋊(D₃₁⋊C₅))
commutator, hypocenter	C₃×C₁₇×C₃₁	C₄×C₅
Fitting, socle, cosocle	C₂×C₃×C₁₇×C₃₁	C₂×C₅
prime radical	C₂×C₃×C₁₇×ΓL(1,𝔽₃₂)	C₂
LCS	G ▷ C₃×C₁₇×C₃₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₃×C₁₇×ΓL(1,𝔽₃₂)	C₄	semidirect
4. Dic₁₅₈₁	C₅	semidirect
7. C₁₇×ΓL(1,𝔽₃₂)	Dic₃	semidirect
10. C₃×C₁₇×C₃₁	C₄×C₅	semidirect
15. C₁₇×C₃₁	C₅×Dic₃	semidirect
17. C₃×ΓL(1,𝔽₃₂)	Dic₁₇	semidirect
25. ΓL(1,𝔽₃₂)	Dic₅₁	semidirect
28. C₃×C₃₁	C₅×Dic₁₇	semidirect
33. C₃×C₁₇	Dic₃₁⋊C₅	semidirect
35. C₃₁	C₅×Dic₅₁	semidirect
38. C₁₇	C₃⋊(Dic₃₁⋊C₅)	semidirect
45. C₃	ΓL(1,𝔽₃₂)⋊Dic₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₇×ΓL(1,𝔽₃₂)	2
ΓL(1,𝔽₃₂)⋊Dic₁₇	3
Dic₁₅₈₁	5
C₃⋊(Dic₃₁⋊C₅)	17
C₅×Dic₅₁	31

Subgroups — C3⋊(ΓL(1,𝔽32)⋊Dic17) #44539269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(ΓL(1,𝔽₃₂)⋊Dic₁₇) #44539269