<Select name='tag' classes={{root: 'thinger1', 'selectMenu': 'thinger2', 'MuiList': {root:  'thinger3'}}} onChange={this.handleChange} className={[classes.lightGreyBackground].join(' ')}>

<div>
        <TextField select name="first" value={1} fullWidth>
          <MenuItem value={1}>1</MenuItem>
          <MenuItem value={2}>2</MenuItem>
        </TextField>
      </div>