You have to graduate high school or get a GED to enlist in the military, so that cuts out most of the lower and a good deal of the lower-middle classes.
You must be joking. The great majority of the lower class has a high school degree, and virtually all of the lower-middle class has a high school degree.
Those without a high school degree or GED are the 'underclass' - a significantly smaller portion of the working class. Getting a high school degree provides a person with almost no employability due to anti-employment economic policy which resulted in a terrible inadequacy of jobs.