SELECT
  table1.CLASS_NAME AS CLASS,
  table1.PERSON_NAME AS PERSON,
  table2.MAX_AMT AS HOUSEHOLDS
FROM
  (
    SELECT
      PERSON_NAME,
      CLASS_NAME,
      AMT
    FROM
      HOUSEHOLD
    WHERE
      CLASS_CODE <> '01'
    AND
      PERSON_CODE > 1    
  ) AS table1
INNER JOIN
  (
    SELECT
      CLASS_NAME,
      MAX(AMT) AS MAX_AMT
    FROM
      HOUSEHOLD
    WHERE
      CLASS_CODE <> '01'
    AND
      PERSON_CODE > 1   
    GROUP BY
      CLASS_NAME
  ) AS table2
ON
  table1.CLASS_NAME = table2.CLASS_NAME
AND
  table1.AMT = table2.MAX_AMT
-- GROUP BY
--   CLASS
-- ORDER BY
--   CLASS