[R] Error message in lmer

[Gang Chen]

I'm trying to run a simple one-way ANCOVA with the lmer function in R  
package lme4, but have encountered some conceptual problem. The data  
file MyData.txt is like this:

Group Subj Cov Resp
A       1   3.90   4.05
A	 2   4.05	4.25
A	 3   4.25	3.60
A	 4   3.60	4.20
A	 5   4.20	4.05
A	 6   4.05	3.85
B	 7   3.85	4.15
B	 8   4.15	4.60
B	 9   4.60	4.15
B	 10  4.15	4.40
B	 11  4.40	3.35
B	 12  3.35	3.80
B	 13  3.80   3.90

Since I would like to treat subject (Subj) as a random factor, my one- 
way ANCOVA (with covariate, Cov) is:

TestData=read.table("MyData.txt", header=T);
m1 <- lmer(Resp ~ Group * Cov + (1 | Subj), TestData)

but I got the following error message:

Error in lmerFactorList(formula, mf, fltype) :
         number of levels in grouping factor(s) 'Subj' is too large

Do I have some misconception about the model?

Thank you very much.

Gang