Why are my DF for denominator so large? Reporting mixed model output

I've never used linear mixed effects models before, so I'm new to reporting the results. Following a paper that used the exact same procedures as mine (pre and post test of this specific task), I'm following their R code as well.

Mod5 <- lmer(rt ~ group * session * trialtype + (1 | subject),
data = data)

> anova(Mod5)
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF  DenDF  F value    Pr(>F)
group                      3566    1783     2  87.01   1.0340   0.35989
session                   30588   30588     1 608.02  17.7378 2.919e-05 ***
trialtype               3004359 1001453     3 608.02 580.7413 < 2.2e-16 ***
group:session             13907    6953     2 608.02   4.0322   0.01821 *
group:trialtype            6066    1011     6 608.02   0.5863   0.74142
session:trialtype         11775    3925     3 608.02   2.2761   0.07870 .
group:session:trialtype    6154    1026     6 608.02   0.5948   0.73463


I realize this is quite a complicated model because of the 3-way interaction, but I made predictions about it.

So, following the paper I'm modeling my model off of, they used the Kenward-Rogers adjustments to get DF. They sent me their code, so I used the same.

KR <- Anova(Mod5, type = 3, test.statistic = "F")
KR

> KR
Analysis of Deviance Table (Type III Wald F tests with Kenward-Roger df)

Response: rt
F Df Df.res  Pr(>F)
(Intercept)             593.5579  1 172.14 < 2e-16 ***
group                     0.9310  2 172.14 0.39612
session                   2.8249  1 608.00 0.09332 .
trialtype                91.5038  3 608.00 < 2e-16 ***
group:session             0.2686  2 608.00 0.76454
group:trialtype           0.7431  6 608.00 0.61509
session:trialtype         1.2301  3 608.00 0.29791
group:session:trialtype   0.5948  6 608.02 0.73463


I don't understand where the DenDF/Df.res are coming from.

3 groups, 30 participants per group, and each participant has 8 observations (4 are pre-test and 4 are post-test, which is what the trialtype is). There is only 1 observation missing from one participant.