Switchable tapper for a valve train of an internal combustion engine

The invention relates to a switchable tappet (1) for a valve train of an internal combustion engine, with a housing (3), which has a ring-like cam stop bottom (2) and from the outer edge (4) of which a skirt(5) protrudes and from the inner wall (6) of which a hollow cylindrical shoulder (7) with a borehole (8) protrudes, in which an inner part (9), which can be moved axially relative to housing (3), extends, wherein, in a borehole (11) of the inner part (9), coupling means (12) are applied which, for a complete valve lift, can be brought sectionally into engagement with a dog surface (13) of the housing (3), wherein an inner part (9) is produced essentially as a thin-walled tube section, which is open at both ends and bridged by a transverse bridge (15) with the borehole (11), wherein, ascoupling means (12), only a piston, secured against rotating, is provided, which can be located in the coupling direction over at least one compression spring (17) and, in the uncoupling direction, over hydraulic means, which