Something about "bathroom groups" tells me you might want to send the lav waste through the wall over to the shower, and tie in there as a wet vent. Or send the shower drain over towards the lav to pick up a wet vent behind the toilet. Either way, this replaces the vent you now have drawn for the shower. You won't need to roll the Wyeup 45 degrees as you have shown for the shower vent. This eliminates the early venting for the WC and that is fine as WC's don't need venting as early in the pipe as you have it drawn. The reason to combine the lav drain and the shower drain is so the WC becomes the last fixture in the chain, downstream of these two.
In your latest drawing you have shown a larger pipe size for the washer drain. This is not good. Go back to the 2" pipe diameter. When pipes are sized too wide, they don't carry stuff well, and you get more sedimentation, not less. Washers work well on 1.5" pipe (in Canada they have the same washers and only 1.5" pipe), so upsizing to 2" is already enough. Going to 2.5" (rare) is one more size up. Going to 3" is another size bigger. It's now too big. Go back to 2".
Your drawing shows the vent built with SanTees and going to a wall. I don't get it. I also saw that you put a 3" vent at the washer. Wow, talk about overkill.
The last clean out creates a little dead end at the curve. I would do the curve with a 1/8 (135 degree) bend and put a clean out a foot ahead of it, rolled partway up.
Based on what I've written so far, I might route the drains in the basement differently. Like maybe with the WC entering in the center of a double Wye.
Since I'm not a plumber, change nothing until someone else confirms some of what I just wrote here.
