AEGINRST has over 150 transposals, previously listed and discussed at length in Word Ways and Making the Alphabet Dance. What about the subsets of those letters? There are eight ways of selecting seven letters from AEGINRST, and all of them can be rearranged to form valid words. All are common and in Webster's Third.
Word Ways: Vol. 36
, Article 13.
Available at: http://digitalcommons.butler.edu/wordways/vol36/iss4/13