  We present the results of a high resolution (0.27 arcsec/px) near-infrared H
band (1.65 micron) imaging survey of a complete sample of 20 flat spectrum
radio quasars (FSRQ) extracted from the 2Jy catalogue of radio sources. The
observed objects are intrinsically luminous with median M(B) = -25.5. The
median redshift of the objects in the sample is z = 0.65. At this redshift, the
H band observations probe the old stellar population of the hosts at rest frame
wavelength of 1 micron. We are able to detect the host galaxy clearly for six
(30 %) FSRQs and marginally for six (30 %) other FSRQs, while the object
remains unresolved for eight (40 %) cases. We find the galaxies hosting FSRQs
to be very luminous (M(H) = -27). Compared with the typical galaxy luminosity
L* (M*(H) = -25) they appear 2 mag brighter, although the undetected hosts may
reduce this difference. They are also at least as bright as, and probably by 1
mag brighter than, the brightest cluster galaxies (M(H) = -26). The
luminosities of the FSRQ hosts are intermediate between host galaxies of low
redshift radio-loud quasars and BL Lac objects (M(H) = -26), and the hosts of
high redshift radio-loud quasars (M(H) = -29), in good agreement with current
unified models for radio-loud AGN, taking into account stellar evolution in the
elliptical host galaxies. Finally, we find an indicative trend between the host
and nuclear luminosity for the most luminous FSRQs, supporting the suggestion
based on studies of lower redshift AGN, that there is a minimum host galaxy
luminosity which increases linearly with the quasar luminosity.
