  The $so(2,1)$ analysis for the bound state sector of the hypergeometric
Natanzon potentials (HNP) is extended to the scattering sector by considering
the continuous series of the $so(2,1)$ algebra. As a result a complete
algebraic treatment of the HNP by means of the $so(2,1)$ algebra is achieved.
  In the bound state sector we discuss a set of satellite potentials which
arises from the action of the $so(2,1)$ generators. It is shown that the set of
new potentials are not related to the one obtained by means of SUSYQM or of the
potential algebra approach using the $so(2,2)$ algebra.
