The formation of clusters with crystal-like order in two dimensions is studied using Monte Carlo simulations. We find that the necessary conditions to induce the formation of clusters of one component is to add a second component that has a larger size and that has a long-range soft repulsive interaction with its own kind but not with the other one. The clusters of the small particles are found to be surrounded by a network of quasi-one-dimensional arrangements of the larger particles. The degree of order of the clusters is found to depend on the concentration of the larger particles. The findings explain recent experimental observations on lipid-poloxamer mixtures and they provide guidelines for how to form ordered clusters of nanoparticles in two dimensions.