$_POST["subject] is not defined in your form. Your SUBJECT field is called EMAIL:
Change:
<div class="form-group">
<label for="subject">Subject<span class="help-required">*</span></label>
<input type="text" name="email" id="subject" class="form-control required" role="input" aria-required="true">
</div>
With:
<div class="form-group">
<label for="subject">Subject<span class="help-required">*</span></label>
<input type="text" name="subject" id="subject" class="form-control required" role="input" aria-required="true">
</div>