symmetries={Symmetric[All],Symmetric[{1,2}],{{2,3,4,1},-1},Antisymmetric[{1,2}],{Symmetric[{1,2}],Antisymmetric[{3,4}]},{Antisymmetric[{1,2}],Antisymmetric[{3,4}],{Cycles[{{1,3},{2,4}}],1}},Antisymmetric[All]};

labels=Column/@{{"Complete ","Symmetry"},{"Symmetric ","in 1 pair"},{"Anticyclic","Symmetry"},{"Antisymmetric ","in 1 pair"},{"1 Symmetric and  ","1 Antisymmetric Pair"},{"Riemann","Symmetry"},{"Complete","Antisymmetry "}};

Manipulate[MatrixPlot@ArrayFlatten@Normal@Block[{c=1},SymmetrizedArray[_:>c++,ConstantArray[dimension,4],symmetry]],{{symmetry,Symmetric[All]},Thread[symmetries->labels] , ControlType->SetterBar}, {{dimension,5},Range[2,8],ControlType->SetterBar}]