High-resolution imaging observations from the Hinode spacecraft in the Ca II H line are employed to study the dynamics of the chromosphere above a sunspot. We find that umbral flashes and other brightenings produced by the oscillation are extremely rich in fine structure, even beyond the resolving limit of our observations (0farcs22). The umbra is tremendously dynamic to the point that our time cadence of 20 s does not suffice to resolve the fast lateral (probably apparent) motion of the emission source. Some bright elements in our data set move with horizontal propagation speeds of 30 km s-1. We have detected filamentary structures inside the umbra (some of which have a horizontal extension of ~1500 km) which, to our best knowledge, had not been reported before. The power spectra of the intensity fluctuations reveal a few distinct areas with different properties within the umbra that seem to correspond with the umbral cores that form it. Inside each one of these areas the dominant frequencies of the oscillation are coherent, but they vary considerably from one core to another.