  We study the evolution of substructure in the mass distribution with mass,
redshift and radius in a sample of simulated galaxy clusters. The sample,
containing $1226$ objects, spans the mass range $M_{200} = 10^{14} - 1.74
\times 10^{15} \ {\rm M_{\odot}} \ h^{-1}$ in six redshift bins from $z=0$ to
$z=1.179$. We consider three different diagnostics: 1) subhalos identified with
SUBFIND; 2) overdense regions localized by dividing the cluster into octants;
3) offset between the potential minimum and the center of mass. The octant
analysis is a new method that we introduce in this work. We find that none of
the diagnostics indicate a correlation between the mass of the cluster and the
fraction of substructures. On the other hand, all the diagnostics suggest an
evolution of substructures with redshift. For SUBFIND halos, the mass fraction
is constant with redshift at $R_{\mathrm{vir}}$, but shows a mild evolution at
$R_{200}$ and $R_{500}$. Also, the fraction of clusters with at least a subhalo
more massive than one thirtieth of the total mass is less than $20 \%$. Our new
method based on the octants returns a mass fraction in substructures which has
a strong evolution with redshift at all radii. The offsets also evolve strongly
with redshift. We also find a strong correlation for individual clusters
between the offset and the fraction of substructures identified with the octant
analysis. Our work puts strong constraints on the amount of substructures we
expect to find in galaxy clusters and on their evolution with redshift.
