push @{ $config->{groups}->{$last_group} }, $line;

##</code><code>##

use Data::Dumper;

my $last_group = "group_z";
my $line = "a line";

my $config = {          # a hash...
    groups => {         # ...of a hash...
        group_z => [    # ...of a list
            2, 3, "Peter", "Pan",
        ],
    },
};

push @{ $config->{groups}->{$last_group} }, $line;

print Dumper $config;

##</code><code>##

$VAR1 = {
          'groups' => {
                        'group_z' => [
                                       2,
                                       3,
                                       'Peter',
                                       'Pan',
                                       'a line'
                                     ]
                      }
        };