There are one square, one octagon, and one apeirogon on each vertex.
The dual of this tiling represents the fundamental domains of [∞,4], (*∞42) symmetry.
There are 15 small index subgroups constructed from [∞,4] by mirror removal and alternation.
In these images fundamental domains are alternately colored black and white, and mirrors exist on the boundaries between colors.
A larger subgroup is constructed as [∞,4*], index 8, as [∞,4+], (4*∞) with gyration points removed, becomes (*∞∞∞∞) or (*∞4), and another [∞*,4], index ∞ as [∞+,4], (∞*2) with gyration points removed as (*2∞).