We present a study of the 3-dimensional environment for a sample of 386 galaxies in the Catalogue of Isolated Galaxies (CIG, Karachentseva 1973) using the Ninth Data Release of the Sloan Digital Sky Survey (SDSS-DR9). We aim to identify and quantify the effects of the satellite distribution around a sample of galaxies in the CIG, as well as the effects of the Large Scale Structure (LSS). To recover the physically bound galaxies we first focus on the satellites which are within the escape speed of each CIG galaxy. We also propose a more conservative method using the stacked Gaussian distribution of the velocity difference of the neighbours. The tidal strengths affecting the primary galaxy are estimated to quantify the effects of the local and LSS environments. We also define the projected number density parameter at the fifth nearest neighbour to characterise the LSS around the CIG galaxies. Out of the 386 CIG galaxies considered in this study, at least 340 (88% of the sample) have no physically linked satellite. Following the more conservative Gaussian distribution of physical satellites around the CIG galaxies leads to upper limits. Out of the 386 CIG galaxies, 327 (85% of the sample) have no physical companion within a projected distance of 0.3Mpc. The CIG galaxies are distributed following the LSS of the local Universe, although presenting a large heterogeneity in their degree of connection with it. When present around a CIG galaxy, the effect of physically bound galaxies largely dominates (usually by more than 90%) the tidal strengths generated by the LSS. The CIG samples a variety of environments, from galaxies with physical satellites to galaxies with no neighbours within 3Mpc. A clear segregation appears between early-type CIG galaxies with companions and isolated late-type CIG galaxies. Isolated galaxies are in general bluer, with likely younger stellar populations and rather high star formation with respect to older, redder CIG galaxies with companions. Reciprocally, the satellites are redder and with an older stellar populations around massive early-type CIG galaxies, while they have a younger stellar content around massive late-type CIG galaxies. This suggests that the CIG is composed of a heterogeneous population of galaxies, sampling from old to more recent, dynamical systems of galaxies. CIG galaxies with companions might have a mild tendency (0.3-0.4dex) to be more massive, and may indicate a higher frequency of having suffered a merger in the past.