In this paper, we give a brief overview of generalized symmetries
from the point of view of the lattice regularization as a fully regularized framework.
At first, we illustrate the generalization of 't~Hooft anomaly matching
for higher-form symmetries.
Furthermore the main interest goes to the higher-group symmetry.
In particular, we find that the so-called $4$-group appears
in the lattice Yang--Mills theory under modification of instanton sum.