Reading a sequence of characters and dynamically splitting into multiple arrays
First obvious thing: Why do you do the almost same thing twice?

for (char c : chars) {
    if (Character.isUpperCase(c)) {
        characterList.add(c);
    } else if (Character.isLowerCase(c)) {
        characterList.add(c);
    } else if (Character.isDigit(c)) {
        characterList.add(c);
    }
}


...and...

for (Character character : characterList) {
    if (Character.isUpperCase(character)) {
        uppercaseStringBuilder.append(character);
    } else if (Character.isLowerCase(character)) {
        lowercaseStringBuilder.append(character);
    } else if (Character.isDigit(character)) {
        numericStringBuilder.append(character);
    }
}


You are going through an array, check if you want the character and add it to a list. Then you go through that list and make the same check again to put the character in different lists / StringBuilders. You can simply remove the last of these loops and add the characters directly from the array to the stringbuilders.

Also your output would be pretty much the same if you simple wrote, for example...

System.out.println(uppercaseStringBuilder.toString());


I guess, with Java8, your problem could be solved nicely (or not so nicely, since char primitives are a little bit tricky there) via Streams.