Subgroups — C₁₁×C₃⋊D₅₀₁ #45683405

Order 33066.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₁×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₅₀₁	—	3	4	no	maximal
3	C₃×C₁₁×C₁₆₇	D₃	1	4	yes	complemented
4	C₁₁×D₁₆₇	—	9	1	no	Hall
5	C₃⋊D₅₀₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₁₆₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
7	C₃²×C₁₆₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
8	D₅₀₁	—	3	4	no	—
9	C₃×C₁₆₇	D₃×C₁₁	1	4	yes	complemented
10	D₁₆₇	—	9	1	no	Hall
11	C₁₁×C₃⋊D₃	—	167	1	no	maximal, Hall
12	C₁₆₇	C₁₁×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
13	C₃²×C₁₁	D₁₆₇	1	1	yes	characteristic, complemented, Hall
14	D₃×C₁₁	—	501	4	no	—
15	C₃×C₁₁	D₅₀₁	1	4	yes	complemented
16	C₂×C₁₁	—	1503	1	no	Hall
17	C₃⋊D₃	—	167	1	no	Hall
18	C₁₁	C₃⋊D₅₀₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₃²	C₁₁×D₁₆₇	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	501	4	no	—
21	C₃	C₁₁×D₅₀₁	1	4	yes	complemented
22	C₂	—	1503	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	C₃⋊D₅₀₁
commutator, cosocle, hypocenter	C₃²×C₁₆₇	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₁₆₇	C₂
LCS	G ▷ C₃²×C₁₆₇
UCS	C₁ ◁ C₁₁

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.