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Elements of the group are displayed as permutations of degree 16.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $D_6^2:(C_2^2\times S_4)$ | 1A | $1$ | $1$ | $D_6^2:(C_2^2\times S_4)$ | 1A | 1A | $()$ |
| $D_6^2:(C_2^2\times S_4)$ | 2A | $2$ | $1$ | $D_6^2:(C_2^2\times S_4)$ | 1A | 2A | $(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2B | $2$ | $3$ | $(C_2^3\times S_3^2).C_2^4$ | 1A | 2B | $(1,6)(2,8)(3,7)(4,5)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2C | $2$ | $3$ | $(C_2^3\times S_3^2).C_2^4$ | 1A | 2C | $(1,3)(2,5)(4,8)(6,7)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2D | $2$ | $6$ | $C_2^4:D_6^2$ | 1A | 2D | $(12,13)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2E | $2$ | $6$ | $C_2^4:D_6^2$ | 1A | 2E | $(12,13)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2F | $2$ | $6$ | $D_6^2.C_2^4$ | 1A | 2F | $(2,4)(5,8)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2G | $2$ | $6$ | $D_6^2.C_2^4$ | 1A | 2G | $(1,3)(2,4)(5,8)(6,7)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2H | $2$ | $6$ | $D_6^2.C_2^4$ | 1A | 2H | $(1,3)(2,4)(5,8)(6,7)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2I | $2$ | $6$ | $D_6^2.C_2^4$ | 1A | 2I | $(2,5)(4,8)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2J | $2$ | $9$ | $C_2^7:D_6$ | 1A | 2J | $(9,12)(10,11)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2K | $2$ | $9$ | $C_2^7:D_6$ | 1A | 2K | $(10,11)(12,13)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2L | $2$ | $12$ | $D_6^2:D_4$ | 1A | 2L | $(4,8)(6,7)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2M | $2$ | $12$ | $D_6^2:D_4$ | 1A | 2M | $(4,8)(6,7)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2N | $2$ | $18$ | $C_2^6:D_6$ | 1A | 2N | $(2,4)(5,8)(12,13)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2O | $2$ | $18$ | $C_2^6:D_6$ | 1A | 2O | $(2,4)(5,8)(12,13)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2P | $2$ | $18$ | $C_2^6:D_6$ | 1A | 2P | $(2,4)(5,8)(11,14)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2Q | $2$ | $18$ | $C_2^6:D_6$ | 1A | 2Q | $(2,4)(5,8)(11,14)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2R | $2$ | $18$ | $C_2^6:D_6$ | 1A | 2R | $(1,3)(2,5)(4,8)(6,7)(12,13)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2S | $2$ | $18$ | $C_2^6:D_6$ | 1A | 2S | $(1,3)(2,5)(4,8)(6,7)(12,13)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2T | $2$ | $24$ | $C_2^2:D_6^2$ | 1A | 2T | $(1,2)(3,5)(4,7)(6,8)(9,14)(10,13)(11,12)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2U | $2$ | $24$ | $C_2^2:D_6^2$ | 1A | 2U | $(1,2)(3,5)(4,7)(6,8)(9,14)(10,13)(11,12)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2V | $2$ | $27$ | $C_2^6:D_4$ | 1A | 2V | $(1,3)(2,5)(4,8)(6,7)(11,14)(12,13)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2W | $2$ | $27$ | $C_2^6:D_4$ | 1A | 2W | $(1,6)(2,8)(3,7)(4,5)(9,12)(10,11)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2X | $2$ | $36$ | $D_6\times C_2^5$ | 1A | 2X | $(1,3)(2,4)(5,8)(6,7)(12,13)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2Y | $2$ | $36$ | $D_6\times C_2^5$ | 1A | 2Y | $(1,3)(2,4)(5,8)(6,7)(12,13)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2Z | $2$ | $54$ | not computed | 1A | 2Z | $(2,4)(5,8)(11,14)(12,13)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2AA | $2$ | $54$ | not computed | 1A | 2AA | $(2,4)(5,8)(11,14)(12,13)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2AB | $2$ | $54$ | not computed | 1A | 2AB | $(1,3)(2,4)(5,8)(6,7)(11,14)(12,13)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2AC | $2$ | $54$ | not computed | 1A | 2AC | $(1,6)(2,4)(3,7)(5,8)(9,12)(11,14)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2AD | $2$ | $72$ | not computed | 1A | 2AD | $(1,7)(5,8)(10,11)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2AE | $2$ | $72$ | not computed | 1A | 2AE | $(3,6)(5,8)(11,14)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2AF | $2$ | $72$ | not computed | 1A | 2AF | $(1,2)(3,4)(5,7)(6,8)(9,10)(11,12)(13,14)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2AG | $2$ | $72$ | not computed | 1A | 2AG | $(1,4)(2,6)(3,8)(5,7)(9,14)(10,12)(11,13)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2AH | $2$ | $108$ | not computed | 1A | 2AH | $(4,8)(6,7)(11,14)(12,13)$ |
| $D_6^2:(C_2^2\times S_4)$ | 2AI | $2$ | $108$ | not computed | 1A | 2AI | $(4,8)(6,7)(11,14)(12,13)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 3A | $3$ | $4$ | $C_3\times C_2^4.S_3^2.C_2$ | 3A | 1A | $(10,14,11)$ |
| $D_6^2:(C_2^2\times S_4)$ | 3B | $3$ | $4$ | $C_6\times C_2^4:S_3^2$ | 3B | 1A | $(9,13,12)(10,14,11)$ |
| $D_6^2:(C_2^2\times S_4)$ | 3C | $3$ | $32$ | $C_6\times \SOPlus(4,2)$ | 3C | 1A | $(3,7,6)(4,8,5)$ |
| $D_6^2:(C_2^2\times S_4)$ | 3D | $3$ | $128$ | not computed | 3D | 1A | $(1,7,6)(2,8,5)(10,14,11)$ |
| $D_6^2:(C_2^2\times S_4)$ | 3E | $3$ | $128$ | not computed | 3E | 1A | $(2,8,4)(3,7,6)(9,12,13)(10,11,14)$ |
| $D_6^2:(C_2^2\times S_4)$ | 4A | $4$ | $12$ | $D_6^2.C_2^3$ | 2B | 4A | $(1,7,6,3)(2,5,8,4)$ |
| $D_6^2:(C_2^2\times S_4)$ | 4B | $4$ | $12$ | $D_6^2.C_2^3$ | 2B | 4B | $(1,7,6,3)(2,5,8,4)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 4C | $4$ | $24$ | $C_4\times D_6^2$ | 2I | 4C | $(2,8,5,4)(6,7)$ |
| $D_6^2:(C_2^2\times S_4)$ | 4D | $4$ | $24$ | $C_4\times D_6^2$ | 2I | 4D | $(2,8,5,4)(6,7)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 4E | $4$ | $72$ | not computed | 2B | 4E | $(1,2,3,5)(4,6,8,7)(9,14)(10,12)(11,13)$ |
| $D_6^2:(C_2^2\times S_4)$ | 4F | $4$ | $72$ | not computed | 2J | 4F | $(1,4)(2,7)(3,8)(5,6)(9,11,12,10)(13,14)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 4G | $4$ | $72$ | not computed | 2I | 4G | $(1,7)(2,8,4,5)(9,12)(15,16)$ |
| $D_6^2:(C_2^2\times S_4)$ | 4H | $4$ | $72$ | not computed | 2B | 4H | $(1,2,7,4)(3,8,6,5)(9,14)(10,13)(11,12)$ |
| $D_6^2:(C_2^2\times S_4)$ | 4I | $4$ | $72$ | not computed | 2B | 4I | $(1,7,6,3)(2,5,8,4)(10,11)$ |