This solution guarantees that each 'sublist' that does appear will appear only once, and that you will get the longest lines. You may find, however, that some 'sublist's will not show up at all.

use warnings;
use strict;

my %data;
my %uniq;
my @final;

while (<DATA>) {
    $data{$_}=()=$_=~m/\s+\b/g;
}
OUTER:
foreach my $keys (sort {$data{$b} <=> $data{$a}} keys %data) {
    my @list=split(/\s+/,$keys);
    foreach (@list) {
        if (exists $uniq{$_}) {
            next OUTER;
        }
    }
    $uniq{$_}++ foreach (@list);
    push @final, $keys;
}

print @final;

__DATA__
mylist_12 sublist153  sublist_34 sublist_123 sublist_345 sublist_245
mylist_1  sublist_153  sublist_87  sublist_876  sublist_78
mylist_6  sublist_8
mylist_2  sublist_12  sublist_34  sublist_09
mylist_3  sublist_87  sublist_09
mylist_7  sublist_8  sublist_9
mylist_9  sublist_56
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