use List::Util qw( min );

my %grouped_maxes;
while (<DATA>) {
    chomp;
    my ($hash, $amount, $end) = split /_/;
    push @{ $grouped_maxes{$hash} }, $amount
        if defined($end) && $end eq 'max';
}

for my $hash (keys %grouped_maxes) {
    print("$hash: ", min( @{ $grouped_maxes{$hash} } ), "\n");
}

__DATA__
111aaa222ccc324567fed54333221235_1.04
111aaa222ccc324567fed54333221235_1.05_max
111aaa222ccc324567fed54333221235_0.98_min
111aaa222ccc324567fed54333221235_1.02_max
111aaa222ccc324567fed54333221235_0.21
777aaa222ccc324567fed54333221235_1.04
777aaa222ccc324567fed54333221235_1.07_min
777aaa222ccc324567fed54333221235_1.04_max
888aaa222ccc324567fed54333221235_0.21