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Elements of the group are displayed as permutations of degree 16.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $C_2^8.S_4$ | 1A | $1$ | $1$ | $C_2^8.S_4$ | 1A | 1A | $()$ |
| $C_2^8.S_4$ | 2A | $2$ | $1$ | $C_2^8.S_4$ | 1A | 2A | $(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)$ |
| $C_2^8.S_4$ | 2B | $2$ | $1$ | $C_2^8.S_4$ | 1A | 2B | $(1,4)(2,3)(5,8)(6,7)(9,11)(10,12)(13,16)(14,15)$ |
| $C_2^8.S_4$ | 2C | $2$ | $1$ | $C_2^8.S_4$ | 1A | 2C | $(1,3)(2,4)(5,7)(6,8)(9,12)(10,11)(13,15)(14,16)$ |
| $C_2^8.S_4$ | 2D | $2$ | $4$ | $C_2^6:S_4$ | 1A | 2D | $(13,16)(14,15)$ |
| $C_2^8.S_4$ | 2E | $2$ | $4$ | $C_2^6:S_4$ | 1A | 2E | $(5,7)(6,8)$ |
| $C_2^8.S_4$ | 2F | $2$ | $4$ | $C_2^6:S_4$ | 1A | 2F | $(1,4)(2,3)(5,8)(6,7)(9,12)(10,11)(13,16)(14,15)$ |
| $C_2^8.S_4$ | 2G | $2$ | $4$ | $C_2^6:S_4$ | 1A | 2G | $(1,4)(2,3)(9,11)(10,12)(13,16)(14,15)$ |
| $C_2^8.S_4$ | 2H | $2$ | $4$ | $C_2^6:S_4$ | 1A | 2H | $(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)$ |
| $C_2^8.S_4$ | 2I | $2$ | $4$ | $C_2^6:S_4$ | 1A | 2I | $(1,3)(2,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)$ |
| $C_2^8.S_4$ | 2J | $2$ | $4$ | $C_2^6:S_4$ | 1A | 2J | $(1,4)(2,3)(5,8)(6,7)(9,10)(11,12)(13,16)(14,15)$ |
| $C_2^8.S_4$ | 2K | $2$ | $4$ | $C_2^6:S_4$ | 1A | 2K | $(13,14)(15,16)$ |
| $C_2^8.S_4$ | 2L | $2$ | $4$ | $C_2^6:S_4$ | 1A | 2L | $(5,7)(6,8)(9,12)(10,11)(13,15)(14,16)$ |
| $C_2^8.S_4$ | 2M | $2$ | $4$ | $C_2^6:S_4$ | 1A | 2M | $(1,3)(2,4)(5,7)(6,8)(9,12)(10,11)(13,14)(15,16)$ |
| $C_2^8.S_4$ | 2N | $2$ | $4$ | $C_2^6:S_4$ | 1A | 2N | $(1,2)(3,4)(5,6)(7,8)(9,11)(10,12)(13,14)(15,16)$ |
| $C_2^8.S_4$ | 2O | $2$ | $4$ | $C_2^6:S_4$ | 1A | 2O | $(1,3)(2,4)(5,7)(6,8)(9,12)(10,11)(13,16)(14,15)$ |
| $C_2^8.S_4$ | 2P | $2$ | $6$ | $(C_2^2\wr C_2)^2$ | 1A | 2P | $(9,10)(11,12)(13,14)(15,16)$ |
| $C_2^8.S_4$ | 2Q | $2$ | $6$ | $(C_2^2\wr C_2)^2$ | 1A | 2Q | $(9,11)(10,12)(13,16)(14,15)$ |
| $C_2^8.S_4$ | 2R | $2$ | $6$ | $(C_2^2\wr C_2)^2$ | 1A | 2R | $(9,12)(10,11)(13,15)(14,16)$ |
| $C_2^8.S_4$ | 2S | $2$ | $6$ | $(C_2^2\wr C_2)^2$ | 1A | 2S | $(1,4)(2,3)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)$ |
| $C_2^8.S_4$ | 2T | $2$ | $6$ | $(C_2^2\wr C_2)^2$ | 1A | 2T | $(1,4)(2,3)(5,6)(7,8)(9,11)(10,12)(13,14)(15,16)$ |
| $C_2^8.S_4$ | 2U | $2$ | $6$ | $(C_2^2\wr C_2)^2$ | 1A | 2U | $(1,2)(3,4)(5,7)(6,8)(9,10)(11,12)(13,15)(14,16)$ |
| $C_2^8.S_4$ | 2V | $2$ | $12$ | $C_2^6:D_4$ | 1A | 2V | $(9,10)(11,12)(13,15)(14,16)$ |
| $C_2^8.S_4$ | 2W | $2$ | $12$ | $C_2^6:D_4$ | 1A | 2W | $(9,10)(11,12)(13,16)(14,15)$ |
| $C_2^8.S_4$ | 2X | $2$ | $12$ | $C_2^6:D_4$ | 1A | 2X | $(9,11)(10,12)(13,15)(14,16)$ |
| $C_2^8.S_4$ | 2Y | $2$ | $12$ | $C_2^6:D_4$ | 1A | 2Y | $(5,6)(7,8)(9,10)(11,12)(13,15)(14,16)$ |
| $C_2^8.S_4$ | 2Z | $2$ | $12$ | $C_2^6:D_4$ | 1A | 2Z | $(5,6)(7,8)(9,10)(11,12)(13,16)(14,15)$ |
| $C_2^8.S_4$ | 2AA | $2$ | $12$ | $C_2^6:D_4$ | 1A | 2AA | $(5,6)(7,8)(9,11)(10,12)(13,16)(14,15)$ |
| $C_2^8.S_4$ | 2AB | $2$ | $12$ | $C_2^6:D_4$ | 1A | 2AB | $(5,6)(7,8)(9,12)(10,11)(13,15)(14,16)$ |
| $C_2^8.S_4$ | 2AC | $2$ | $12$ | $C_2^6:D_4$ | 1A | 2AC | $(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)$ |
| $C_2^8.S_4$ | 2AD | $2$ | $12$ | $C_2^6:D_4$ | 1A | 2AD | $(5,7)(6,8)(9,11)(10,12)(13,16)(14,15)$ |
| $C_2^8.S_4$ | 2AE | $2$ | $12$ | $C_2^6:D_4$ | 1A | 2AE | $(1,2)(3,4)(5,6)(7,8)(9,11)(10,12)(13,15)(14,16)$ |
| $C_2^8.S_4$ | 2AF | $2$ | $12$ | $C_2^6:D_4$ | 1A | 2AF | $(1,2)(3,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)$ |
| $C_2^8.S_4$ | 2AG | $2$ | $12$ | $C_2^6:D_4$ | 1A | 2AG | $(1,2)(3,4)(5,7)(6,8)(9,11)(10,12)(13,16)(14,15)$ |
| $C_2^8.S_4$ | 2AH | $2$ | $24$ | $C_2^5:D_4$ | 1A | 2AH | $(9,13)(10,14)(11,16)(12,15)$ |
| $C_2^8.S_4$ | 2AI | $2$ | $24$ | $C_2^8$ | 1A | 2AI | $(5,6)(7,8)(9,11)(10,12)(13,15)(14,16)$ |
| $C_2^8.S_4$ | 2AJ | $2$ | $24$ | $C_2^5:D_4$ | 1A | 2AJ | $(1,2)(3,4)(5,6)(7,8)(9,13)(10,14)(11,16)(12,15)$ |
| $C_2^8.S_4$ | 2AK | $2$ | $24$ | $C_2^5:D_4$ | 1A | 2AK | $(1,3)(2,4)(5,7)(6,8)(9,13)(10,14)(11,16)(12,15)$ |
| $C_2^8.S_4$ | 2AL | $2$ | $24$ | $C_2^5:D_4$ | 1A | 2AL | $(1,4)(2,3)(5,8)(6,7)(9,13)(10,14)(11,16)(12,15)$ |
| $C_2^8.S_4$ | 2AM | $2$ | $48$ | $C_2^7$ | 1A | 2AM | $(5,6)(7,8)(9,13)(10,14)(11,16)(12,15)$ |
| $C_2^8.S_4$ | 2AN | $2$ | $48$ | $C_2^7$ | 1A | 2AN | $(5,7)(6,8)(9,13)(10,14)(11,16)(12,15)$ |
| $C_2^8.S_4$ | 2AO | $2$ | $48$ | $C_2^7$ | 1A | 2AO | $(5,8)(6,7)(9,13)(10,14)(11,16)(12,15)$ |
| $C_2^8.S_4$ | 2AP | $2$ | $48$ | $C_2^7$ | 1A | 2AP | $(1,2)(3,4)(5,7)(6,8)(9,13)(10,14)(11,16)(12,15)$ |
| $C_2^8.S_4$ | 2AQ | $2$ | $48$ | $C_2^7$ | 1A | 2AQ | $(1,2)(3,4)(5,8)(6,7)(9,13)(10,14)(11,16)(12,15)$ |
| $C_2^8.S_4$ | 2AR | $2$ | $48$ | $C_2^7$ | 1A | 2AR | $(1,3)(2,4)(5,8)(6,7)(9,13)(10,14)(11,16)(12,15)$ |
| $C_2^8.S_4$ | 2AS | $2$ | $48$ | $C_2^3\wr C_2$ | 1A | 2AS | $(1,11)(2,12)(3,10)(4,9)(5,14)(6,13)(7,16)(8,15)$ |
| $C_2^8.S_4$ | 3A | $3$ | $128$ | $C_2^3\times C_6$ | 3A | 1A | $(1,5,11)(2,6,12)(3,7,10)(4,8,9)$ |
| $C_2^8.S_4$ | 4A | $4$ | $24$ | $C_2^3.C_2^5$ | 2P | 4A | $(9,13,10,14)(11,16,12,15)$ |
| $C_2^8.S_4$ | 4B | $4$ | $24$ | $C_2^3.C_2^5$ | 2Q | 4B | $(9,13,11,16)(10,14,12,15)$ |
| $C_2^8.S_4$ | 4C | $4$ | $24$ | $C_2^3.C_2^5$ | 2R | 4C | $(9,13,12,15)(10,14,11,16)$ |