Theoretical constraints on the scalar potential of the compact 341 model with three quadruplets scalar fields are discussed. It is shown that in order to ensure the good behavior of the potential and the viability of the model, the criteria, such as copositivity, minimization, perturbative unitarity, perturbativity of the scalar couplings and no ghost scalar bosons (scalar bosons masses positivity), are imposed and bounds on the scalar couplings are obtained. Moreover, the existence of the Landau pole in the model imposes stringent limits.