  It is shown that all four superintegrable quantum systems on the Euclidean
plane possess the same underlying hidden algebra $sl(3)$. The gauge-rotated
Hamiltonians, as well as their integrals of motion, once rewritten in
appropriate coordinates, preserve a flag of polynomials. This flag corresponds
to highest-weight finite-dimensional representations of the $sl(3)$-algebra,
realized by first order differential operators.
