The coherent vortex extraction (CVE) decomposes each turbulent flow realization into two orthogonal components: a coherent and a random incoherent flow. They both contribute to all scales in the inertial range, but exhibit different statistical behaviour. The CVE decomposition is based on the nonlinear filtering of the vorticity field projected onto an orthonormal wavelet basis made of compactly supported functions. We decompose a 3D homogeneous isotropic turbulent flow at Taylor microscale Reynolds numbers R$_λ$ = 140 computed by a direct numerical simulation (DNS) at resolution N = 256$^3$. Only wavelet modes correspond to the coherent flow made of vortex tubes, which contributes to of the enstrophy. Another observation is that the coherent flow exhibits in the inertial range the same $k^{-5/3}$ slope in the energy spectrum and slope in the enstrophy spectrum as the total flow does. The remaining 96.3 %N wavelet modes correspond to a random residual flow which is structureless, quasi equipartition of energy and a Gaussian velocity probability distribution function (PDF). We also analyse and visualize the Lamb vector, its divergence and curl and study the contributions coming from the coherent and incoherent components of vorticity and the induced velocity.