  Cosmography is an ideal tool to investigate the cosmic expansion history of
the Universe in a model-independent way. The equations of motion in modified
theories of gravity are usually very complicated; cosmography may select
practical models without imposing arbitrary choices a priori. We use the
model-independent way to derive $f(z)$ and its derivatives up to fourth order
in terms of measurable cosmographic parameters. We then fit those functions
into the luminosity distance directly. We perform the MCMC analysis by
considering three different sets of cosmographic functions. Using the largest
supernovae Ia Pantheon sample, we derive the constraints on the Hubble constant
$H_0$ and the cosmographic functions, and find that the former two terms in
Taylor expansion of luminosity distance work dominantly in $f(Q)$ gravity.
