<p>Shallow water waves are seen in atmospheric science, geophysical fluid dynamics and oceanography. In this paper, we study a (3+1)-dimensional generalized Hirota-Satsuma-Ito equation for the shallow water waves. Lie-symmetry generators and groups are presented by virtue of the Lie-symmetry analysis. We derive the optimal system of certain subalgebras via the optimal system analysis. According to that system, we obtain certain symmetry reductions. Power-series, <i>N</i>-soliton, <i>M</i>-breather and hyperbolic-tangent solutions are derived through those reductions, where <i>N</i> and <i>M</i> are the integers. Two- and three-solitons as well as one breather are graphically shown. Besides, we prove that the aforementioned equation is nonlinearly self-adjoint and obtain certain conservation laws based on the nonlinearly self-adjoint condition. Our results might help people understand some localized waves and symmetry for the shallow water waves.</p>