If we are talking Carboniferous, then, whatever it is (trilobite or not), it is not a Illaenus. Only trilobites belonging to Proetida survived into the Carboniferous. If it is a Carboniferous trilobite then the number of thorax-segments indicates that it belongs to Aulacopleuroidea.
It doesn't look like a trilobite to me. The pattern doesn't look quite right for it and I think the shape of the block overall and the markings are related, rather than being separate. I think fossil plant sounds more likely to me, but I will try and find out more from the experts when I'm back at the museum in the new year.