Does this demonstrate what you're after?

#!/bin/perl5

use strict;
use warnings;

my %hash=(); 
%hash=(
  "M01.001"           => 0,
  "M01.001.111"       => 0,
  "M01.001.111.111"   => 0,
  "M01.002"           => 0,
  "M01.002.003"       => 0
);

my %HoA;

for my $k ( keys %hash ){
  $k =~ /(M\d{2}\.\d{3})/;
  my $parent = $1;
  push @{$HoA{$parent}}, $k
}

foreach my $parent ( sort keys %HoA ) {
  print "$parent\n";
  foreach my $i ( 0 .. $#{$HoA{$parent}} ) {
    my $child = $HoA{$parent}[$i];
    next if $parent eq $child;
    print "\t$child\n";
  }
  print "\n";
 }
[download]

Produces...

M01.001
  M01.001.111
  M01.001.111.111

M01.002
  M01.002.003
[download]

How complex is the hierarchy? Would any 'children' have 'children' too?

The second loop came from perldsc. I think what you need is in there somewhere.