  For the two-dimensional Navier--Stokes equations of isentropic
magnetohydrodynamics (MHD) with $\gamma$-law gas equation of state, $\gamma\ge
1$, and infinite electrical resistivity, we carry out a global analysis
categorizing all possible viscous shock profiles. Precisely, we show that the
phase portrait of the traveling-wave ODE generically consists of either two
rest points connected by a viscous Lax profile, or else four rest points, two
saddles and two nodes. In the latter configuration, which rest points are
connected by profiles depends on the ratio of viscosities, and can involve Lax,
overcompressive, or undercompressive shock profiles. For the monatomic and
diatomic cases $\gamma=5/3$ and $\gamma= 7/5$, with standard viscosity ratio
for a nonmagnetic gas, we find numerically that the the nodes are connected by
a family of overcompressive profiles bounded by Lax profiles connecting saddles
to nodes, with no undercompressive shocks occurring. We carry out a systematic
numerical Evans function analysis indicating that all of these two-dimensional
shock profiles are linearly and nonlinearly stable, both with respect to two-
and three-dimensional perturbations. For the same gas constants, but different
viscosity ratios, we investigate also cases for which undercompressive shocks
appear; these are seen numerically to be stable as well
