A socket is provided for removing or installing a fastener having a hexagonally shaped portion. The socket includes a body having a longitudinal axis and opposing first and second ends. First surfaces define a tool-receiving portion at the first end. The tool-receiving portion is constructed and arranged to receive a portion of a tool. Second surfaces define a socket portion at the second end. The socket portion is constructed and arranged to receive and engage the portion of the fastener therein. Holding structure is associated with the socket portion and is constructed and arranged to non-magnetically hold the portion of the fastener in the socket portion so as to not fall out of the socket portion, either due to friction or vacuum, without providing torque to the fastener when the socket is rotated during installation or removal of the fastener.