The nuclear modification factor $R_{\mathrm{AA}}$ and the azimuthal anisotropy coefficient $v_{2}$ of prompt and nonprompt (i.e. those from decays of b hadrons) ${\mathrm{J}}/\psi $ mesons, measured from PbPb and pp collisions at $\sqrt{{s_{{\text {NN}}}}} =2.76$ $,\mathrm{TeV}$ at the LHC, are reported. The results are presented in several event centrality intervals and several kinematic regions, for transverse momenta $p{\mathrm{T}} >6.5$ $,{\mathrm{GeV}}/{\mathrm{c}}$ and rapidity $|{y}|<2.4$ , extending down to $p_{\mathrm{T}} =3$ $,{\mathrm{GeV}}/{\mathrm{c}}$ in the $1.6<|{y}|<2.4$ range. The $v_{2}$ of prompt ${\mathrm{J}}/\psi $ is found to be nonzero, but with no strong dependence on centrality, rapidity, or $p_{\mathrm{T}}$ over the full kinematic range studied. The measured $v_{2}$ of nonprompt ${\mathrm{J}}/\psi $ is consistent with zero. The $R_{\mathrm{AA}}$ of prompt ${\mathrm{J}}/\psi $ exhibits a suppression that increases from peripheral to central collisions but does not vary strongly as a function of either y or $p_{\mathrm{T}}$ in the fiducial range. The nonprompt ${\mathrm{J}}/\psi $ $R_{\mathrm{AA}}$ shows a suppression which becomes stronger as rapidity or $p_{\mathrm{T}}$ increases. The $v_{2}$ and $R_{\mathrm{AA}}$ of open and hidden charm, and of open charm and beauty, are compared.