  This paper presents symmetry classes of the Hartree-Fock (HF) solutions of
spin and orbital ordered states in a t_{2g} Hubbard model on a two-dimensional
square lattice. Using a group theoretical bifurcation theory of the Hartree
Fock equation, we obtained many types of broken symmetry solutions which
bifurcate from the normal state through one step transition in cases of
commensurate ordering vectors Q_0=(0,0), Q_1=(\pi,\pi), Q_2=(\pi,0) and
Q_3=(0,\pi). Each broken symmetry state is characterized by the presence of
local order parameters(LOP) at each lattice site: quadrupole moment
Q=(Q_2^2,Q_{12},Q_{23},Q_{31}), orbital angular momentum l=(l_1,l_2,l_3), spin
density s=(s^1,s^2,s^3), spin quadrupole moment Q^{\lambda}=(Q_2^{2\lambda},
Q_{12}^{\lambda},Q_{23}^{\lambda},Q_{31}^{\lambda}) and spin orbital angular
momentum l^{\lambda}=(l_1^{\lambda},l_2^{\lambda},l_3^{\lambda}) where
\lambda=1,2,3. We performed numerical calculations for some parameter sets.
Then we have found that many types of non-collinear magnetic orbital ordered
states having LOP:Q^{\lambda} and l^{\lambda} can be the ground state for these
parameter sets.
