Closed:Multifactor design with Genotype: Is it possible to group all?

Question

[anikng]

        Treat     Time
Sample1 Placebo    0h
Sample2 Placebo    0h
Sample3 Placebo    1h
Sample4 Placebo    1h
Sample7 Drug       0h
Sample8 Drug       0h
Sample9 Drug       1h
Sample10Drug       1h

For an experiment with above factors, I identified DEGs,

Group <- factor(paste(targets$Treat,targets$Time,sep="."))
cbind(targets,Group=Group)
design <- model.matrix(~0+Group)
colnames(design) <- levels(Group)
fit <- glmQLFit(y, design)
my.contrasts <- makeContrasts(
+ Drug.1vs0 = Drug.1h-Drug.0h,
+ Placebo.2vs0 = Placebo.2h-Placebo.0h,
+ levels=design)

qlf <- glmQLFTest(fit, contrast=my.contrasts[,"Drug.1vs0"])

But when new factor is added, for ex, Genotype,

         Treat Time Genotype
Sample1 Placebo 0h  a
Sample2 Placebo 0h  a
Sample3 Placebo 1h  a
Sample4 Placebo 1h  a
.
.

Sample4 Placebo 1h  c
Sample7 Drug    0h  c
Sample8 Drug    0h  c
Sample9 Drug    1h  c
Sample10Drug    1h  c

Can I combine the "Genotype" factor and follow the steps as above?

 Group <- factor(paste(targets$Treat,targets$Time,targets$Genotype,sep="."))

My aim is to extract genes that are induced at 1hr of drug treatment only for Genotype b (not a and c)