  We present magnetization studies as a function of time, temperature and
magnetic field for $H$ $\parallel$ c-axis, in a hole-doped pnictide
superconductor, La$_{0.34}$Na$_{0.66}$Fe$_2$As$_2$, with, $T_c$ $\approx$ 27 K.
The obtained vortex phase-diagram shows that the magnetic irreversibility line
is very close to the mean-field superconducting transition line, similar to the
low $T_c$ superconductors, evidencing a strong pinning behavior. The
irreversibility line does not follow a power law behavior with ($T_c$-$T$),
however, it is well described using an expression developed in the literature
considering the effect of disorder in the system. The critical current density
estimated using the Bean's critical-state model is found to be of the order of
10$^5$ A/cm$^2$ below 12 K in the limit of zero magnetic field. A plot of the
normalized pinning force density as a function of the reduced magnetic field at
different temperatures shows a good scaling and the analysis suggests that the
vortex pinning is due to normal point like pinning centers. The temperature
dependence of the critical current density suggests that the pinning due to the
variation in charge carrier mean free path alone is not sufficient to explain
the experimental data. Magnetic relaxation rate as a function of temperature
and magnetic field is also studied.
