The largest Key Science Program of the RadioAstron space VLBI mission is a survey of active galactic nuclei (AGN). The main goal of the survey is to measure and study the brightness of AGN cores in order to better understand the physics of their emission while taking interstellar scattering into consideration. In this paper we present detection statistics for observations on ground-space baselines of a complete sample of radio-strong AGN at the wavelengths of 18, 6, and 1.3 cm. Two-thirds of them are indeed detected by RadioAstron and are found to contain extremely compact, tens to hundreds of μas structures within their cores.