You don't need a correlated subquery:

sqlite> select * from tbl;
c1          c2        
----------  ----------
1           a         
1           a         
1           b         
1           a         
2           b         
2           c         
2           a         
3           c         
3           c         
sqlite> select c1, max(cnt12) from
   ...>   (select c1, count(*) cnt12 from tbl
   ...>    group by c1, c2)
   ...> group by c1;
c1          max(cnt12)
----------  ----------
1           3         
2           1         
3           2         


Regards

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