  We study the reduced fidelity susceptibility $\chi_{r}$ for an $M$-body
subsystem of an $N$-body Lipkin-Meshkov-Glick model with $\tau=M/N$ fixed. The
reduced fidelity susceptibility can be viewed as the response of subsystem to a
certain parameter. In noncritical region, the inner correlation of the system
is weak, and $\chi_{r}$ behaves similar with the global fidelity susceptibility
$\chi_{g}$, the ratio $\eta=\chi_{r}/\chi_{g}$ depends on $\tau$ but not $N$.
However, at the critical point, the inner correlation tends to be divergent,
then we find $\chi_{r}$ approaches $\chi_{g}$ with the increasing the $N$, and
$\eta=1$ in the thermodynamic limit. The analytical predictions are perfect
agreement with the numerical results.
