Genomes undergo changes in organization as a result of gene duplications, chromosomal rearrangements and local mutations, among other mechanisms. In contrast to prokaryotes, in which genes of a common function are often organized in operons and reside contiguously along the genome, most eukaryotes show much weaker clustering of genes by function, except for few concrete functional groups. We set out to check systematically if there is a relation between gene function and gene organization in the human genome. We test this question for three types of functional groups: pairs of interacting proteins, complexes and pathways. We find a significant concentration of functional groups both in terms of their distance within the same chromosome and in terms of their dispersal over several chromosomes. Moreover, using Hi-C contact map of the tendency of chromosomal segments to appear close in the 3D space of the nucleus, we show that members of the same functional group that reside on distinct chromosomes tend to co-localize in space. The result holds for all three types of functional groups that we tested. Hence, the human genome shows substantial concentration of functional groups within chromosomes and across chromosomes in space.