Subgroups — D₃₃×ΓL(1,𝔽₃₂) #23779461

Order 10230.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₁×ΓL(1,𝔽₃₂)	—	3	1	no	maximal, Hall
3	C₃₁×D₃₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₁×ΓL(1,𝔽₃₂)	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	D₃×ΓL(1,𝔽₃₂)	—	11	1	no	maximal, Hall
7	D₁₁×C₃₁	—	3	1	no	Hall
8	C₃×ΓL(1,𝔽₃₂)	D₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₃₁	C₅×D₃	1	1	yes	characteristic, complemented, Hall
10	C₅×D₃₃	—	31	1	no	maximal, Hall
11	C₂×ΓL(1,𝔽₃₂)	—	33	1	no	Hall
12	D₃×C₃₁	—	11	1	no	Hall
13	C₃×C₅×C₁₁	—	31	1	no	Hall
14	ΓL(1,𝔽₃₂)	D₃₃	1	1	yes	characteristic, direct product factor, Hall
15	C₅×D₁₁	—	93	1	no	Hall
16	C₃×C₃₁	C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
17	D₃₃	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃₁	—	33	1	no	Hall
19	C₅×C₁₁	—	31	1	no	Hall
20	C₃×C₁₁	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Hall
21	C₃₁	C₅×D₃₃	1	1	yes	characteristic, complemented, Sylow
22	C₅×D₃	—	341	1	no	Hall
23	D₁₁	—	3	1	no	Hall
24	C₃×C₅	—	31	1	no	Hall
25	C₁₁	D₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	1023	1	no	Hall
27	D₃	—	11	1	no	Hall
28	C₅	—	31	1	no	Sylow
29	C₃	D₁₁×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	33	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁×C₃₁	C₂×C₅
LCS	G ▷ C₃×C₁₁×C₃₁
UCS	C₁

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