Probably rather inefficient, but it might do.

#! /usr/bin/perl

my %DEF = (
  I   => [qw( P Pl P.P P.Pl Pl.P Pl.Pl P.P.P P.P.Pl P.Pl.P P.Pl.Pl Pl.
+P.P Pl.P.Pl Pl.Pl.P Pl.Pl.Pl )],
  II  => [qw( E P.E Pl.E P.P.E P.Pl.E Pl.P.E Pl.Pl.E )],
  III => [qw( E.P E.Pl P.E.P P.E.Pl Pl.E.P Pl.E.Pl E.P.P E.P.Pl E.Pl.P
+ E.Pl.Pl )],
  IV  => [qw( E.E P.E.E Pl.E.E E.P.E E.Pl.E E.E.P E.E.Pl E.E.E )]
);
my @rank = map @$_, @DEF{qw(I II III IV)};
my %rank = map {$rank[$_-1] => $_} 1..@rank;
my @group = map {($_) x @{$DEF{$_}}} qw(I II III IV);
my %group = map {$rank[$_-1] => $group[$_-1]."_".$_} 1..@group;
sub rank { $rank{$a->[2]} <=> $rank{$b->[2]} }

my %T;

sub oh { map values %$_, @_ }
sub ab {
  my ($b, $a) = @_;
  [$b->[0], $a->[1], qq($a->[2].$b->[2]), qq($b->[3]<-$a->[3])]
}
sub xtend {
  my $a = shift;
  map {ab $_, $a} oh @{$T{$a->[0]}}{@_}
}
sub ins { $T{$_[3] //= $_[1]}{$_[2]}{$_[0]} = \@_ }

ins split /,\s*/ for <DATA>;
ins @$_ for map {xtend $_, qw(P E Pl)} (oh oh oh \%T);
ins @$_ for map {xtend $_, qw(P E Pl)} (oh oh oh \%T);

for (sort {rank} grep {$_->[1] eq 'Q'} (oh oh oh \%T)) {
  printf "%-4s: %20s,  %-8s %6s\n",
      $_->[0], qq($_->[0]<-$_->[3]), $_->[2], $group{$_->[2]};
}

__DATA__
M7,     Q,      P,
M7,     M28,    E,
M28,    M6,     E,
M6,     Q,      Pl,
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