System for fastening an insulating panel to a structure, wherein the system comprises at least one fastening element connectable to the insulating panel and a dowel associated with the fastening element, wherein the fastening element has an opening into which the dowel is insertable in order to dowel the fastening element and thus the associated insulating panel to the structure, wherein the fastening element has a preferably plate-like holding portion for flat connection to and/or holding of the insulating panel, characterised in that the dowel in the inserted state is secured or securable positively to the fastening element against rotation relative to the fastening element by means of an anti-rotation device arranged and/or formed between a conical receptacle, which the fastening element has for a dowel head of the dowel for axial abutment of the dowel in the installed state, and the dowel head, wherein the dowel head has a recess on the circumferential side in which an engagement portion of the fastening element engages or can engage as an anti-rotation device in the installed state, and/or in that the dowel has a dowel head which is more yielding in the axial direction than the fastening element, wherein the dowel head has a recess on the circumferential side which weakens the dowel head, and/or wherein the dowel head has a conically widening opening for receiving a screw head, which opening has a smaller opening angle to the longitudinal axis of the dowel than a conical receptacle to the longitudinal axis, the fastening element having the receptacle for the dowel head for axial abutment of the dowel in the installed state. wherein the system comprises at least one fastening element connectable to the insulating panel and a dowel associated with the fastening element, wherein the fastening element has an opening into which the dowel is insertable in order to dowel the fastening element and thus the associated insulating panel to the structure, wherein the fastening element has a preferably plate-like holding portion for flat connection to and/or holding of the insulating panel, characterised in that the dowel in the inserted state is secured or securable positively to the fastening element against rotation relative to the fastening element by means of an anti-rotation device arranged and/or formed between a conical receptacle, which the fastening element has for a dowel head of the dowel for axial abutment of the dowel in the installed state, and the dowel head, wherein the dowel head has a recess on the circumferential side in which an engagement portion of the fastening element engages or can engage as an anti-rotation device in the installed state, and/or in that the dowel has a dowel head which is more yielding in the axial direction than the fastening element, wherein the dowel head has a recess on the circumferential side which weakens the dowel head, and/or wherein the dowel head has a conically widening opening for receiving a screw head, which opening has a smaller opening angle to the longitudinal axis of the dowel than a conical receptacle to the longitudinal axis, the fastening element having the receptacle for the dowel head for axial abutment of the dowel in the installed state.