Subgroups — ΓL(1,𝔽₃₂)×C₁₁⋊D₁₁ #49175992

Order 37510.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₁×C₁₁⋊D₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁²×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	D₁₁×ΓL(1,𝔽₃₂)	—	11	12	no	maximal
5	C₁₁×ΓL(1,𝔽₃₂)	D₁₁	1	12	yes	complemented
6	C₅×C₁₁⋊D₁₁	—	31	1	no	maximal, Hall
7	D₁₁×C₃₁	—	11	12	no	—
8	C₅×C₁₁²	—	31	1	no	Hall
9	C₁₁×C₃₁	C₅×D₁₁	1	12	yes	complemented
10	C₂×ΓL(1,𝔽₃₂)	—	121	1	no	Hall
11	C₁₁⋊D₁₁	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Hall
12	ΓL(1,𝔽₃₂)	C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor, Hall
13	C₁₁²	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Sylow
14	C₅×D₁₁	—	341	12	no	—
15	C₂×C₃₁	—	121	1	no	Hall
16	C₅×C₁₁	—	31	12	no	—
17	C₃₁	C₅×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
18	D₁₁	—	11	12	no	—
19	C₁₁	D₁₁×ΓL(1,𝔽₃₂)	1	12	yes	complemented
20	C₂×C₅	—	3751	1	no	Hall
21	C₅	—	31	1	no	Sylow
22	C₂	—	121	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁²×C₃₁	C₂×C₅
LCS	G ▷ C₁₁²×C₃₁
UCS	C₁

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

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