5.5->5.7 problem. group by & order by

[Seungwon Park]

select * from (
select * from table_name order by col1, col2 desc
) as my_table_tmp group by col1;


I am not a specialist in mysql. I wandered to ask this question but, It was not easy to get the answer. Can anyone help me, I think this forum is filled with specialists so I hope good result here..
I want to execute above query. If column 1 is identical then I want to choose the one with biggest value in column 2. Upper query worked fine with mysql 5.5.
But In 5.7(now I am using), this query always gets me the least of column 2 with no regard to desc or asc option.. I changed desc to asc and the result was chosen.

How can I do "If column 1 is identical then I want to choose the one with biggest value in column 2."

cf)I made the only_full_group_by off.