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The importance of hexagonal Lonsdaleite silicon-germanium has been growing lately due to its possible uses in optoelectronic devices. However, very little is known about defects in the hexagonal phases of group-IV semiconductors. We extend here an efficient constrained structure prediction algorithm designed for interface reconstructions to the study of point defect geometries. With this method we perform an exhaustive structure prediction study of the most energetically favorable intrinsic defects in Lonsdaleite silicon. We obtain among the lowest-energy structures the hexagonal counterparts of all known defects of cubic silicon, together with other often more complex geometries. Neutral vacancies, fourfold-coordinated, and Frenkel defects have comparable formation energies in both hexagonal and cubic phases, while some interstitial defects become considerably more stable in the hexagonal lattice. Furthermore, due to the reduced symmetry, formation energies can depend on the orientation of the defect with respect to the c axis. Finally, we calculate the density of states of the defective supercells to determine which defects lead to electronic states in the band gap, potentially affecting the performance of optoelectronic devices based on hexagonal group-IV crystals.