  In materials, certain approximated symmetry operations can exist in a
lower-order approximation of the effective model but are good enough to
influence the physical responses of the system, and these approximated
symmetries were recently dubbed "quasi-symmetries" \cite{guo_arxiv_2021}. In
this work, we reveal a hierarchy structure of the quasi-symmetries and the
corresponding nodal structures that they enforce via two different approaches
of the perturbation expansions for the effective model in the chiral crystal
material CoSi. In the first approach, we treat the spin-independent linear
momentum (k) term as the zero-order Hamiltonian. Its energy bands are four-fold
degenerate due to an SU(2)$\times$SU(2) quasi-symmetry. We next consider both
the k-independent spin-orbit coupling (SOC) and full quadratic-k terms as the
perturbation terms and find that the first-order perturbation leads to a model
described by a self-commuting "stabilizer code" Hamiltonian with a U(1)
quasi-symmetry that can protect nodal planes. In the second approach, we treat
the SOC-free linear-k term and k-independent SOC term as the zero-order. They
exhibit an SU(2) quasi-symmetry, which can be reduced to U(1) quasi-symmetry by
a choice of quadratic terms. Correspondingly, a two-fold degeneracy for all the
bands due to the SU(2) quasi-symmetry is reduced to two-fold nodal planes that
are protected by the U(1) quasi-symmetry. For both approaches, including
higher-order perturbation will break the U(1) quasi-symmetry and induce a small
gap $\sim$ 1 meV for the nodal planes. These quasi-symmetry protected near
degeneracies play an essential role in understanding recent quantum oscillation
experiments in CoSi.
