I’m not at all an expert on Islamism, but by my limited understanding, al-Qaeda, insofar as they base themselves on the writings of Sayyid Qutb, are in a certain sense anarchists.
In a converse sense, however, they are the precise opposites of anarchists. How so?
(note that this is specifically al-Qaeda, in whatever sense it exists, that I’m speaking of, not any of the more successful and mainstream groups like Hamas or the Iranian government)
Anarchism could be defined either more broadly, as, 1, “opposition to authority and hierarchy in general”, or more narrowly, as, 2, “rejection of states” (compare socialism as “support for economic equality” vs. “rejection of private property”).
The typical anarchist would accept point 1., and therefore accept point 2. on that basis. What (at least one reading of) al-Qaeda’s ideology does is to invert this: they vigourously reject 1., and therefore accept 2. on that basis.