В более поздних версиях SQLite вы можете использовать оконные функции:
SELECT cc.*
FROM (SELECT company_id, car, COUNT(*) as cnt,
ROW_NUMBER() OVER (PARTITION BY company_id ORDER BY COUNT(*) DESC) as seqnum
FROM car_orders
GROUP by company_id, car
) cc
WHERE seqnum = 1;
В более ранних версиях это немного сложнее:
WITH cc as (
SELECT company_id, car, COUNT(*) as cnt
FROM car_orders
GROUP by company_id, car
)
SELECT cc.*
FROM cc
WHERE cc.cnt = (SELECT MAX(cc2.cnt)
FROM cc cc2
WHERE cc2.company_id = cc.company_id
);