Photoionization of the hydrogen molecule was studied using our previously developed semiclassical trajectory method. The focus was on the parameters of the field for which there are no other results, namely a short photo-pulse with photon energies from soft to hard x-rays and with intensities including superatomic values. We calculated photoionization probabilities for the single and double ionization of H2. In the superatomic field we observed the transient
from single-photon to multiphoton double photoionization, the inversion of single and double ionization probabilities, and distinct stabilization effect for the single photoionization. We also observed a specific behavior in the single photoionization probability dynamics with a dip in the middle of the pulse, which becomes extremely deep for a field approaching relativistic intensity. The agreement of our previous results with independent data on the helium atom in superatomic field is an important argument in favor of the efficiency of the used method. This allows us to hope that the probabilities of photoionization of a hydrogen molecule in an atomic and superatomic x-ray field obtained in this work are not only the first, but also quite reasonable results on the indicated process.