In this present work, we report a structural and magnetic study of mixed Co58Pt42 clusters. A MgO, Nb, and Si matrix can be used to embed clusters, avoiding any magnetic interactions between particles. Transmission electron microscopy observations show that Co58Pt42 supported isolated clusters are about 2 nm in diameter and crystallized in the A1 fcc chemically disordered phase. Grazing incidence small-angle x-ray scattering (GISAXS) and grazing incidence wide-angle x-ray scattering (GIWAXS) reveal that buried clusters conserve these properties, interaction with matrix atoms being limited to their first atomic layers. Considering that 60% of particle atoms are located at surface, this interactions leads to a drastic change in magnetic properties that were investigated with conventional magnetometry and x-ray magnetic circular dichroism. Magnetization and blocking temperature are weaker for clusters embedded in Nb than in MgO, and totally vanish in silicon as silicides are formed. Magnetic volume of clusters embedded in MgO is close to the crystallized volume determined by GIWAXS experiments. Cluster can be seen as a pure ferromagnetic CoPt crystallized core surrounded by a cluster-matrix mixed shell. The outer shell plays a predominant role in magnetic properties, especially for clusters embedded in niobium that have a blocking temperature three times smaller than clusters embedded in MgO.