The quaternary germanides RE4Mn2InGe4 (RE = La-Nd, Sm, Gd-Tm, Lu) have been prepared by arc-melting reactions of the elements and annealing at 800 degrees C and represent the second example of the RE4M2InGe4 series previously known only for M = Ni. Single-crystal X-ray diffraction studies conducted on the earlier RE members of RE4Mn2InGe4 confirmed that they adopt the monoclinic Ho4Ni2InGe4-type structure [space group C2/m, a = 16.646(2)-15.9808(9) angstrom, b = 4.4190(6)-4.2363(2) angstrom, c = 7.4834(10)-7.1590(4) angstrom, beta = 106.893(2)-106.304(1)degrees in the progression of RE from La to Gd]. The covalent framework contains Mn-centered tetrahedra and Ge-2 dimers that build up [Mn2Ge4] layers, which are held weakly together by four-coordinate In atoms and outline tunnels filled by the RE atoms. This bonding picture is supported by band-structure calculations. An alternative description based on Ge-centered trigonal prisms reveals that RE4Mn2InGe4 is closely related to RE2InGe2. The electrical resistivity behavior of Pr4Mn2InGe4 is similar to that of Pr2InGe2.