optimising query with group by order by count

[mansup kulel]

Hi, I'm new here so please accept my apologies if i didn't make the post correctly.

Basically I'm trying to work with a table which has millions of records

and i need to perform the following query

the cat column is varchar(250) NOT NULL and has an index

SELECT `cat`, COUNT(`cat`) as total FROM `products` GROUP BY `SIC` HAVING `total` > 1 ORDER BY `total` DESC LIMIT 0, 200

it takes about 2. secs to execute and uses index, temporary table and filesort

and when i just execute the same query without ORDER BY it only take about 0.05 sec to execute as it only uses index

Could you please asist me on how can i optimise the query which will get about about 0.05 execution time and will not use filesort

Thank you very much for your time.