Subgroups — C₃×A₄×ΓL(1,𝔽₃₂) #19150112

Order 5580.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×ΓL(1,𝔽₃₂)	C₃	1	1	yes	maximal, characteristic, complemented
2	A₄×ΓL(1,𝔽₃₂)	C₃	1	3	yes	maximal, direct product factor
3	C₃²×ΓL(1,𝔽₃₂)	—	4	1	no	maximal, Hall
4	C₃×A₄×C₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₃×ΓL(1,𝔽₃₂)	—	3	1	no	—
6	C₂²×ΓL(1,𝔽₃₂)	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×ΓL(1,𝔽₃₂)	—	4	3	no	—
8	C₃×ΓL(1,𝔽₃₂)	A₄	1	1	yes	characteristic, direct product factor
9	C₂²×C₃×C₃₁	C₃×C₅	1	1	yes	characteristic, complemented
10	A₄×C₃₁	C₃×C₅	1	3	yes	complemented
11	C₂×ΓL(1,𝔽₃₂)	—	3	1	no	—
12	C₃²×C₃₁	—	4	1	no	Hall
13	C₂×C₃×C₃₁	—	3	1	no	—
14	C₃×C₅×A₄	—	31	1	no	maximal, Hall
15	ΓL(1,𝔽₃₂)	C₃×A₄	1	1	yes	characteristic, direct product factor, Hall
16	C₂²×C₃₁	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₃×C₃₁	—	4	3	no	—
18	C₃×C₃₁	C₅×A₄	1	1	yes	characteristic, complemented
19	C₂×C₃₁	—	3	1	no	—
20	C₂²×C₃×C₅	—	31	1	no	—
21	C₅×A₄	—	31	3	no	—
22	C₃²×C₅	—	124	1	no	Hall
23	C₃×A₄	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Hall
24	C₃₁	C₃×C₅×A₄	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃×C₅	—	93	1	no	—
26	C₂²×C₅	—	31	1	no	Hall
27	C₃×C₅	—	31	1	no	—
28	C₃×C₅	—	124	3	no	—
29	C₂²×C₃	C₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented
30	A₄	C₃×ΓL(1,𝔽₃₂)	1	3	yes	direct product factor
31	C₂×C₅	—	93	1	no	—
32	C₃²	—	4	1	no	Sylow
33	C₂×C₃	—	3	1	no	—
34	C₅	—	31	1	no	Sylow
35	C₂²	C₃²×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Sylow
36	C₃	—	4	3	no	—
37	C₃	A₄×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃	A₄×ΓL(1,𝔽₃₂)
commutator, hypocenter	C₂²×C₃₁	C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₃₁	C₃×C₅
LCS	G ▷ C₂²×C₃₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×ΓL(1,𝔽₃₂)	C₃	semidirect
2. A₄×ΓL(1,𝔽₃₂)	C₃	direct (N × H)
4. C₃×A₄×C₃₁	C₅	semidirect
6. C₂²×ΓL(1,𝔽₃₂)	C₃²	semidirect
8. C₃×ΓL(1,𝔽₃₂)	A₄	direct (N × H)
9. C₂²×C₃×C₃₁	C₃×C₅	semidirect
10. A₄×C₃₁	C₃×C₅	semidirect
15. ΓL(1,𝔽₃₂)	C₃×A₄	direct (N × H)
16. C₂²×C₃₁	C₃²×C₅	semidirect
18. C₃×C₃₁	C₅×A₄	semidirect
23. C₃×A₄	ΓL(1,𝔽₃₂)	direct (N × H)
24. C₃₁	C₃×C₅×A₄	semidirect
29. C₂²×C₃	C₃×ΓL(1,𝔽₃₂)	semidirect
30. A₄	C₃×ΓL(1,𝔽₃₂)	direct (N × H)
35. C₂²	C₃²×ΓL(1,𝔽₃₂)	semidirect
37. C₃	A₄×ΓL(1,𝔽₃₂)	direct (N × H)

Subgroups — C3×A4×ΓL(1,𝔽32) #19150112

Conjugacy classes of subgroups

Complements

Subgroups — C₃×A₄×ΓL(1,𝔽₃₂) #19150112