We analyse the central dark-matter (DM) content of ∼4500 massive (M★ ≳ 1010 M⊙), low-redshift (z < 0.1), early-type galaxies (ETGs), with high-quality ugrizY JHK photometry and optical spectroscopy from the Sloan Digital Sky Survey and the UKIRT Infrared Deep Sky Survey (UKIDSS). We estimate the ‘central’ fraction of DM within the K-band effective radius, Reff, using spherically symmetric isotropic galaxy models. We discuss the role of systematics in stellar mass estimates, dynamical modelling, and velocity dispersion anisotropy. The main results of the present work are the following: (1) DM fractions increase systematically with both structural parameters (i.e. Reff and Sérsic index, n) and mass proxies (central velocity dispersion, stellar and dynamical mass), as in previous studies, and decrease with central stellar density. (2) All correlations involving DM fractions are caused by two fundamental ones with galaxy effective radius and central velocity dispersion. These correlations are independent of each other, so that ETGs populate a central-DM plane (DMP), i.e. a correlation among fraction of total-to-stellar mass, effective radius, and velocity dispersion, whose scatter along the total-to-stellar mass axis amounts to ∼0.15 dex. (3) In general, under the assumption of an isothermal or a constant M/L profile for the total mass distribution, a Chabrier initial mass function (IMF) is favoured with respect to a bottom-heavier Salpeter IMF, as the latter produces negative (i.e. unphysical) DM fractions for more than 50 per cent of the galaxies in our sample. For a Chabrier IMF, the DM estimates agree with Λ cold dark matter toy-galaxy models based on contracted DM-halo density profiles. We also find agreement with predictions from hydrodynamical simulations. (4) The central DM content of ETGs does not depend significantly on the environment where galaxies reside, with group and field ETGs having similar DM trends.