  The scalar potentials of the non-semi-simple CSO(p,8-p)(p=7,6,5) gaugings of
N=8 supergravity are studied for critical points. The CSO(7,1) gauging has no
G_2-invariant critical points, the CSO(6,2) gauging has three new
SU(3)-invariant AdS critical points and the CSO(5,3) gauging has no
SO(5)-invariant critical points. The scalar potential of CSO(6,2) gauging in
four dimensions we discovered provides the SU(3) invariant scalar potential of
five dimensional SO(6) gauged supergravity. The nontrivial effective scalar
potential can be written in terms of the superpotential which can be read off
from A_1 tensor of the theory. We discuss first-order domain wall solutions by
analyzing the supergravity scalar-gravity action and using some algebraic
relations in a complex eigenvalue of A_1 tensor. We examine domain wall
solutions of G_2 sectors of noncompact SO(7,1) and CSO(7,1) gaugings and SU(3)
sectors of SO(6,2) and CSO(6,2) gaugings. They share common features with each
sector of compact SO(8) gauged N=8 supergravity in four dimensions. We analyze
the scalar potentials of the CSO(p,q,8-p-q) gauged supergravity we have found
before. The CSO(p,6-p,2) gauge theory in four dimensions can be reduced from
the SO(p,6-p) gauge theory in five dimensions. Moreover, the SO(p,5-p) gauge
theory in seven dimensions reduces to CSO(p,5-p,3) gauge theory in four
dimensions. Similarly, CSO(p,q-p,8-q) gauge theories in four dimensions are
related to SO(p,q-p)(q=2,3,4,7) gauge theories in other dimensions.
