  Higher-order optical harmonics entered the realm of nanostructured solids
being observed recently in optical gratings and metasurfaces with a
subwavelength thickness. Structuring materials at the subwavelength scale
allows for resonant enhancing of the efficiency of nonlinear processes and
reducing the size of high-harmonic sources. Here we report the observation of
up to a seventh harmonic generated from a single subwavelength resonator made
of AlGaAs material. This process is enabled by careful engineering of the
resonator geometry for supporting optical modes associated with a quasi-bound
state in the continuum in the mid-infrared spectral range at around
{\lambda}=3.7 {\mu}m pump wavelength. The resonator volume measures ~ 0.1
{\lambda}^3. The resonant modes are excited with an azimuthally polarized
tightly focused beam. We evaluate the contributions of perturbative and
non-perturbative nonlinearities to the harmonic generation process. Our work
proves the possibility to miniaturize solid-state sources of high harmonics to
the subwavelength volumes.
