| Subgroup index | 1 | 2 | 4 | |||
|---|---|---|---|---|---|---|
| Diagram | 
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| Coxeter | [4,4] | [1+,4,4] | [4,4,1+] | [4,1+,4] | [4,1+,4,1+] | [1+,4,4,1+] |
| Orbifold | (*442) | (*2222) | (2*22) | (*2222) | ||
| Diagram | 
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| Coxeter | [4,4+] | [4+,4] | [(4,4,2+)] | [1+,4,1+,4] | [4+,4+] | |
| Orbifold | (4*2) | (2*22) | (22×) | |||
| Rotational subgroups | ||||||
| Index | 2 | 4 | 8 | |||
| Diagram | 
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| Coxeter | [4,4]+ | [1+,4,4+] | [4+,4,1+] | [(4,1+,4,2+)] | [1+,4,1+,4,1+] = [(4+,4+,2+)] | |
| Orbifold | (442) | (2222) | ||||
