look for several ways to suppress cLFV, at least under the experimental bound.

  --------------------- -------------------- ------- ---------- ----------
       Superfield              $S_4$          $Z_4$   U(1)$_L$   U(1)$_R$
        \[0.2em\]                                               
     \[-1.1em\] $L$          ${\bf 3}$          1        1          1
   \[0.4em\] $\bar{E}$      ${\bf 2+1}$         2        -1         0
      \[0.4em\] $N$          ${\bf 3}$          3        -1         0
    \[0.4em\] $\Phi$     ${\bf 3+3^\prime}$     1        0          0
    \[0.4em\] $\chi$       ${\bf 1+2+3}$        2        2          0
     \[0.4em\] $H_u$         ${\bf 1}$          0        0          1
     \[0.4em\] $H_d$         ${\bf 1}$          0        0          1
      \[0.4em\] $X$          ${\bf 1}$          0        0          2
        \[0.4em\]                                               
  --------------------- -------------------- ------- ---------- ----------

  : Charge assignments under $S_4 \times Z_4 \times {\rm U(1)}_L \times {\rm U(1)}_R $ for leptons, flavons, Higgs, and SUSY breaking spurions. []{data-label="table:charges"}

To make the PMNS matrix tri-bi maximal, we use $S_4$ discrete symmetry, since it is closely related to the permutation structure of Yukawa couplings. Other discrete symmetries, such as $A_4$, the even permutation of the $S_4$ could be used. The main difference is that the first and the second generation of the right-handed leptons belong to ${\bf 2}$ dimensional representation in $S_4$ while they correspond to different one dimensional representations, ${\bf 1^\prime}$, ${\bf 1^{\prime\prime}}$ in $A_4$. In [@He:2006dk; @He:2006qd; @He:2011gb; @BenTov:2012tg], the structure we use is obtained from $A_4$ symmetry and 