为什么只能读取一个带子键的cookie值？

我在App_Code中写了有关写入Cookies和读取cookies的类（pub.cs）    /// <summary>
    /// 写入带子键的cookies
    /// </summary>
    /// <param name="strkey"></param>
    ///<param name="strsubkey"></param>
    ///<param name="strvalue"></param>
    /// <returns></returns>
    public void  WriteSubCookies(string strkey,string strsubkey,string strvalue)
    {
        if ((strkey.Length)>=0&&(strsubkey.Length)>=0)
        {
            System.Web.HttpCookie newcookie=new HttpCookie(strkey);
            newcookie.Values[strsubkey]=strvalue;
            newcookie.Expires=DateTime.Now.AddDays(1);
            System.Web.HttpContext.Current.Response.AppendCookie(newcookie);
        }
    }
    /// <summary>
    /// 读取带子键的cookies
    /// </summary>
    /// <param name="strkey"></param>
    ///<param name="strsubkey"></param>
    /// <returns></returns>
    public void GetSubCookies(string strkey,string strsubkey)
    {
        if ((System.Web.HttpContext.Current.Request.Cookies[strkey]) != null)
        {
            string getsubcookiesresult;
            System.Web.HttpContext.Current.Response.Write(System.Web.HttpContext.Current.Server.HtmlEncode(System.Web.HttpContext.Current.Request.Cookies[strkey][strsubkey]));        }
        else
        {
            System.Web.HttpContext.Current.Response.Write("");
        }
        
    }但是读取的时候，只能读取最后写入的cookies
===================================================
测试：public partial class _Default : System.Web.UI.Page 
{
    protected void Page_Load(object sender, EventArgs e)
    {
     //protected HtmlGenericControl title;
      //  this.title.innerText=pub.city;
        pub mypub = new pub();
        mypub.WriteSubCookies("mypub","username","张晓初");
        mypub.WriteSubCookies("mypub", "userid", "20080001");
        mypub.GetSubCookies("mypub","username");
        mypub.GetSubCookies("mypub","userid");
    }
}
============
结果:
20080001 
("张晓初"并没有读出来，不知道是什么原因？)