  We compute the velocity dispersion profile, \sigmav(r_p), for satellites of
host galaxies in the Two Degree Field Galaxy Redshift Survey (2dFGRS) and in
the Lambda-CDM GIF simulation. We find 1345 hosts in the 2dFGRS with
luminosities in the range 0.5 L* < L < 5.5 L*, for which a total of 2475
satellite galaxies is obtained. The magnitudes of the galaxies in the GIF
simulation are converted to the b_J band pass, and hosts and satellites are
selected in the same manner as in the 2dFGRS. Of order 1200 hosts and 4100
satellites are found in the simulation. Overall, there is excellent agreement
between \sigmav(r_p) for the satellites in the 2dFGRS and the GIF simulation.
On large scales, \sigmav(r_p) decreases with projected radius, in good
agreement with the expectations of a CDM universe. Further, there is a marked
dependence of \sigmav(r_p) on both the host spectral type and the host
luminosity. In particular, \sigmav(r_p) has a substantially higher amplitude
and steeper slope for satellites of early-type hosts than it does for
satellites of late-type hosts. In addition, both the amplitude and slope of
\sigmav(r_p) increase with host luminosity. The velocity dispersion of
satellites located within small projected radii (r_p < 120 kpc) is only
marginally consistent with the local B-band Tully-Fisher relation, and is
fitted best by a relationship of the form \sigma_v \propto L^{0.45 \pm 0.10}.
