Never heard of them. How do they fit into the denominations?
The Coptic Orthodox broke off in the early centuries. I couldn't even tell you which one. Currently, they're headed by their own "Pope" (Patriarch), of which the present one is named Shenouda III. The Coptic Church (prior to the schism, obviously) was founded in the first century when St. Mark the Apostle arrived in Alexandria (Egypt).
For centuries, the Coptic Orthodox have been accused by both Catholics and the Eastern Orthodox Churches alike of being monophysites, but the current hierarchy of the Coptic Orthodox Church are calling this into dispute, saying that this has been a misnomer from the start. There was some mention that there has always been a misunderstanding of the diction. In all honesty, I haven't studied the matter in great depth, so I couldn't say much more on that.
Their monks still use the Coptic language (an ancient tongue that existed prior to Arabic), but my understanding is that Arabic now predominates in the liturgies. Again, you might want to check in on this matter.
Coptic Orthodox parishes were very rare in America as of 30 or so years ago. Then, more and more Coptic Christians immigrated, and the parishes began to grow. Many more were built. At the moment, only two major Coptic
Catholic parishes exist in America. Many hope that a similar phenomenon will occur with the Catholic parishes: a huge growth. Others, who have heard Coptic chant, are not so ready for such a growth.
Does that adequately answer your question?
Pinoy Monk