Subgroups — C₁₁×C₃⋊D₃×C₁₁₃ #36375421

Order 22374.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₁×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₁₁×C₁₁₃	—	3	4	no	maximal
3	C₃×C₁₁×C₁₁₃	D₃	1	4	yes	complemented
4	C₂×C₁₁×C₁₁₃	—	9	1	no	Hall
5	C₃⋊D₃×C₁₁₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₁₁₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₁₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
8	D₃×C₁₁₃	—	3	4	no	—
9	C₃×C₁₁₃	D₃×C₁₁	1	4	yes	complemented
10	C₂×C₁₁₃	—	9	1	no	Hall
11	C₁₁×C₃⋊D₃	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₁₃	C₁₁×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₃²×C₁₁	C₂×C₁₁₃	1	1	yes	characteristic, complemented, Hall
14	D₃×C₁₁	—	3	4	no	—
15	C₃×C₁₁	D₃×C₁₁₃	1	4	yes	complemented
16	C₂×C₁₁	—	9	1	no	Hall
17	C₃⋊D₃	C₁₁×C₁₁₃	1	1	yes	characteristic, direct product factor, Hall
18	C₁₁	C₃⋊D₃×C₁₁₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₃²	C₂×C₁₁×C₁₁₃	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	3	4	no	—
21	C₃	D₃×C₁₁×C₁₁₃	1	4	yes	complemented
22	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₁₁₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₁₁×C₁₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₁₁₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₁₁×C₁₁₃

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.