A fastening clamp for fastening an elongated, rigid object, such as a support profile, a panel, such as a photovoltaic module, a component therefor or the like, to a substructure typically formed from a plurality of supports, comprising: - a clamping element (4, 4.1) with a clamping extension (33; 35, 35.1) intended for attachment to an object (30; 30.1, 30.2) to be fastened, - a connecting part with a connecting element for supporting the fastening clamp (1, 1.1) on an abutment of the support of the substructure, wherein the abutment points in the opposite direction of a contact surface provided by the profile support, on which the object to be fastened is to be placed, which connecting element has an abutment for engaging under the support for support on the abutment of the support, and the connecting part has a support section located adjacent to the lateral end of the support, which, when the fastening clamp (1, 1.1) is fastened to the support, acts against the object to be fastened (30; 30.1, 30.2) and/or a support leg of the clamping element (4, 4.1), and - a clamping device (5, 7) for clamping the clamping element (4, 4.1), which is supported on an object (30; 30.1, 30.2) to be fastened, relative to the connecting part, so that a clamping force can be applied via the clamping element (4, 4.1) to the object (30; 30.1, 30.2) to be fastened, which clamping device has a clamping means, the clamping axis of which, when the fastening clamp (1, 1.1) is fastened to the support, is guided past the lateral end of the support, wherein the abutment on the connecting part side is part of a hook-shaped connecting part for engaging behind a rear edge of the support, and the free end of such a hook-shaped connecting element forms the abutment for support on that inner side of the leg of the support which, with its outer side, provides the contact surface. - a clamping element (4, 4.1) with a clamping extension (33; 35, 35.1) intended for attachment to an object (30; 30.1, 30.2) to be fastened, - a connecting part with a connecting element for supporting the fastening clamp (1, 1.1) on an abutment of the support of the substructure, wherein the abutment points in the opposite direction of a contact surface provided by the profile support, on which the object to be fastened is to be placed, which connecting element has an abutment for engaging under the support for support on the abutment of the support, and the connecting part has a support section located adjacent to the lateral end of the support, which, when the fastening clamp (1, 1.1) is fastened to the support, acts against the object to be fastened (30; 30.1, 30.2) and/or a support leg of the clamping element (4, 4.1), and - a clamping device (5, 7) for clamping the clamping element (4, 4.1), which is supported on an object (30; 30.1, 30.2) to be fastened, relative to the connecting part, so that a clamping force can be applied via the clamping element (4, 4.1) to the object (30; 30.1, 30.2) to be fastened, which clamping device has a clamping means, the clamping axis of which, when the fastening clamp (1, 1.1) is fastened to the support, is guided past the lateral end of the support, wherein the abutment on the connecting part side is part of a hook-shaped connecting part for engaging behind a rear edge of the support, and the free end of such a hook-shaped connecting element forms the abutment for support on that inner side of the leg of the support which, with its outer side, provides the contact surface.