The dual of this tiling represents the fundamental domains of *443 symmetry.
It only has one subgroup 443, replacing mirrors with gyration points.
From a Wythoff construction there are ten hyperbolic uniform tilings that can be based from the regular octagonal tiling.
It can also be generated from the (4 3 3) hyperbolic tilings: This hyperbolic tiling is topologically related as a part of sequence of uniform truncated polyhedra with vertex configurations (n.6.6), and [n,3] Coxeter group symmetry.
This hyperbolic geometry-related article is a stub.