Most efficient way to search for unknown patterns in a string?

I am trying to find patterns that:

• occur more than once
• are more than 1 character long
• are not substrings of any other known pattern

without knowing any of the patterns that might occur.

For example:

• The string "the boy fell by the bell" would return 'ell', 'the b', 'y '.
• The string "the boy fell by the bell, the boy fell by the bell" would return 'the boy fell by the bell'.

Using double for-loops, it can be brute forced very inefficiently:

ArrayList<String> patternsList = new ArrayList<>();
int length = string.length();
for (int i = 0; i < length; i++) {
    int limit = (length - i) / 2;
    for (int j = limit; j >= 1; j--) {
        int candidateEndIndex = i + j;
        String candidate = string.substring(i, candidateEndIndex);

        if(candidate.length() <= 1) {
            continue;
        }

        if (string.substring(candidateEndIndex).contains(candidate)) {
            boolean notASubpattern = true;
            for (String pattern : patternsList) {
                if (pattern.contains(candidate)) {
                    notASubpattern = false;
                    break;
                }
            }

            if (notASubpattern) {
                patternsList.add(candidate);
            }
        }
    }
}

However, this is incredibly slow when searching large strings with tons of patterns.