Flame bifurcations. extinction, and flammable regions of radiative counterflow premixed flames and the planar propagating flames are investigated numerically with general Lewis numbers. New insights and phenomena are presented by examining the interaction of radiation heat loss, Lewis number effect, and stretch. At a low Lewis number, the results show that for equivalence ratio lower than the standard flammability limit, radiation extinction limit and stretch extinction limit exist, respectively, at low and high stretch rates. For a higher equivalence ratio, this flame isola opens up and yields two stable flame branches, a normal flame branch, and a weak flame branch. A G-shaped curve showing the limits and flammable regions of these two flame regimes is obtained. The results show that the inferior limit of counterflow flame is lower than the standard limit. At unity Lewis number, the results show that, for equivalence ratio lower than the standard limit, there is also a flame isola with two distinct extinction limits at low and high stretch rates. For equivalence ratio larger than the standard limit, a new flame branch with flame standing far from the stagnation plane emerges on the low stretch rate side of the flame isola. This flame is related to the standard limit with the decrease of fuel concentration and merges with the flame isola when the fuel concentration is larger than a critical value. The extinction curve is also a G-shaped curve and the inferior limit is lower than the standard limit. At Lewis number larger than a critical value, for equivalence ratio near the standard limit, there is only the weakly stretched flame branch with a single stretch extinction limit. With an increase of fuel concentration, a weak flame isola emerges. As the fuel concentration further increases, this weak flame isola merges with the weakly stretched flame branch yielding three kinds of flame regimes. The resulting extinction curve is a K-shaped curve and the inferior limit is equal to the standard limit. The present results show that flame bifurcations and the existence of weak flames are physically intrinsic phenomena of radiative counterflow premixed flames. It is found that the normal flame and the weak flame can jump to each other at their limits. The obtained G and K-shaped curves show a clear relation between the counterflow flame and the planar propagating flame. The occurrence of G-K transition with the increase of Lewis number also gives a good explanation to the physics of the experimental results.