If I have a list that contains 16 sublist (enclosed in 2 curly

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If I have a list that contains 16 sublist (enclosed in 2 curly bracets),
L1 = {{{1, 1}, {1, 5}, {1, 8}}, {{2, 6}, {1, 10}, {0, 12}},
{{3, 2}, {1, 4}, {0, 15}}, {{1, 8}, {1, 14}, {2, 17}},
{{1, 2}, {2, 8}, {3, 12}}, {{2, 6}, {2, 11}, {2, 18}},
{{3, 6}, {1, 9}, {2,17}}, {{1, 8}, {3, 18}, {2, 19}} ... ...};

could I create a list from L1 that is made up of sublist 1, 2, 3, 4, 9, 10, 11,
12 and another that is made up of sublist 5, 6, 7, 8, 13, 14, 15, 16

I have had the idea of using Mod but don' t quite know how to
constuct it:

sub = 0;
sub++;
If[Mod[sub, 8, 1] < 4, Map[something?, L1], Map[something?,L1]]
 
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With the nested {} in your L1 it seems that you have a 3 dimensional "matrix." Is that what you really have? Or do you have some extra {} that are not really in your data?

If all those {} are actually present then is sublist 1 = {1, 1} or is it {{1, 1}, {1, 5}, {1, 8}}?

Perhaps showing what L2 and L3 should have as values given your L1 would be the most precise way of describing what you need.

If you can answer those questions then it will be possible to show you ways to do what you want.
 


Sorry, didn't make it very clear

sublist 1 = {{1, 1}, {1, 5}, {1, 8}}
sublist 2 = {{2, 6}, {1, 10}, {0, 12}} ...

so I want a new list that will be {sublist 1,sublist 2,sublist 3,sublist 4,sublist 9,sublist 10, sublist 11,sublist 12}
And another {sublist 5,sublist 6,sublist 7,sublist 8,sublist 13,sublist 14, sublist 15,sublist 16}
 


As long as Length[L1] is a multiple of 8

In[1]:=L1={{{1,1},{1,5},{1,8}},{{2,6},{1,10},{0,12}},{{3,2},{1,4},{0,15}},{{1,8},{1,14},{2,17}},
{{1,2},{2,8},{3,12}},{{2,6},{2,11},{2,18}},{{3,6},{1,9},{2,17}},{{1,8},{3,18},{2,19}}};

In[2]:=L2=L1[[Flatten[Table[8j+i,{j,0,(Length[L1]-8)/8},{i,1,4}]]]]

In[3]:=L3=L1[[Flatten[Table[8j+i+4,{j,0,(Length[L1]-8)/8},{i,1,4}]]]]