Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1996 conjugacy classes of subgroups.
The subgroup lattice has 650 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13082400 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13082243 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | Q8×#4325 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13081252 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13081251 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13081210 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #13081208 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #13080945 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #13080940 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #13079996 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #13079745 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #13078674 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #13078426 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | #13077747 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | Q8×C11×SD16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#67040 | — | 2 | 1 | no | — |
| 17 | Q82×C11 | C22 | 1 | 1 | yes | characteristic |
| 18 | D4×Q8×C11 | C22 | 1 | 1 | yes | characteristic |
| 19 | Q8×C22⋊D11 | — | 2 | 1 | no | — |
| 20 | #10623265 | — | 2 | 3 | no | — |
| 21 | #10623265 | C22 | 1 | 3 | yes | — |
| 22 | #10623257 | C22 | 1 | 3 | yes | — |
| 23 | #10623256 | — | 2 | 3 | no | — |
| 24 | #10623256 | C22 | 1 | 3 | yes | — |
| 25 | D11×C4⋊Q8 | C22 | 1 | 3 | yes | — |
| 26 | #10623162 | — | 2 | 3 | no | — |
| 27 | #10623159 | — | 2 | 3 | no | — |
| 28 | #10623108 | — | 2 | 1 | no | — |
| 29 | #10623108 | C22 | 1 | 3 | yes | — |
| 30 | #10623108 | C22 | 1 | 1 | yes | characteristic |
| 31 | Q8×D44 | C22 | 1 | 1 | yes | characteristic |
| 32 | C4×#4343 | — | 2 | 1 | no | — |
| 33 | C4×#4343 | C22 | 1 | 3 | yes | — |
| 34 | C4×#4343 | C22 | 1 | 1 | yes | characteristic |
| 35 | #10623082 | C22 | 1 | 3 | yes | — |
| 36 | #10623079 | C22 | 1 | 3 | yes | — |
| 37 | C11×#498 | C22 | 1 | 3 | yes | — |
| 38 | C11×#476 | C22 | 1 | 3 | yes | — |
| 39 | C11×#475 | C22 | 1 | 3 | yes | — |
| 40 | C8×Q8×C11 | C22 | 1 | 1 | yes | characteristic |
| 41 | C4×C11×SD16 | C22 | 1 | 3 | yes | — |
| 42 | #10622785 | C22 | 1 | 3 | yes | — |
| 43 | #10622776 | C22 | 1 | 1 | yes | characteristic |
| 44 | #10622701 | C22 | 1 | 3 | yes | — |
| 45 | #10622700 | C22 | 1 | 3 | yes | — |
| 46 | #10622697 | C22 | 1 | 3 | yes | — |
| 47 | #10622692 | C22 | 1 | 3 | yes | — |
| 48 | C4×#4325 | C22 | 1 | 3 | yes | — |
| 49 | Q8×C11⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 50 | #10622633 | C22 | 1 | 3 | yes | — |
| 51 | #10622628 | C22 | 1 | 3 | yes | — |
| 52 | C4×#4323 | C22 | 1 | 3 | yes | — |
| 53 | #10622483 | C22 | 1 | 3 | yes | — |
| 54 | #10622483 | C22 | 1 | 6 | yes | — |
| 55 | #10622479 | C22 | 1 | 3 | yes | — |
| 56 | #10622478 | C22 | 1 | 6 | yes | — |
| 57 | #10622476 | C22 | 1 | 6 | yes | — |
| 58 | #10622476 | C22 | 1 | 6 | yes | — |
| 59 | #10622474 | C22 | 1 | 6 | yes | — |
| 60 | #10622459 | C22 | 1 | 3 | yes | — |
| 61 | #10622456 | C22 | 1 | 3 | yes | — |
| 62 | #10622451 | C22 | 1 | 3 | yes | — |
| 63 | #10622450 | C22 | 1 | 3 | yes | — |
| 64 | #10622424 | C22 | 1 | 3 | yes | — |
| 65 | #10622416 | C22 | 1 | 6 | yes | — |
| 66 | #10622407 | C22 | 1 | 3 | yes | — |
| 67 | #10622399 | C22 | 1 | 3 | yes | — |
| 68 | #10622397 | C22 | 1 | 3 | yes | — |
| 69 | #10622395 | C22 | 1 | 6 | yes | — |
| 70 | #10622307 | C22 | 1 | 3 | yes | — |
| 71 | C4×D88 | C22 | 1 | 3 | yes | — |
| 72 | #10622301 | C22 | 1 | 3 | yes | — |
| 73 | #10622298 | C22 | 1 | 3 | yes | — |
| 74 | C22×Q8×C11 | — | 2 | 1 | no | — |
| 75 | #67040 | — | 4 | 8 | no | — |
| 76 | C2×#4343 | — | 2 | 1 | no | — |
| 77 | C2×#4343 | — | 2 | 3 | no | — |
| 78 | C2×#4343 | — | 2 | 3 | no | — |
| 79 | C2×#4343 | D4 | 1 | 1 | yes | characteristic |
| 80 | C2×#4343 | C23 | 1 | 3 | yes | — |
| 81 | C2×Q8×D11 | — | 2 | 1 | no | — |
| 82 | C2×Q8×D11 | — | 2 | 3 | no | — |
| 83 | C2×#4339 | — | 2 | 3 | no | — |
| 84 | C2×#4339 | — | 2 | 3 | no | — |
| 85 | C2×C11×SD16 | C23 | 1 | 1 | yes | characteristic |
| 86 | C11×C4⋊Q8 | — | 2 | 3 | no | — |
| 87 | C11×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 88 | C11×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 89 | C11×C22⋊Q8 | — | 2 | 3 | no | — |
| 90 | C4×Q8×C11 | — | 2 | 1 | no | — |
| 91 | C4×Q8×C11 | C23 | 1 | 3 | yes | — |
| 92 | C4×Q8×C11 | C23 | 1 | 1 | yes | characteristic |
| 93 | C4×D4×C11 | C23 | 1 | 3 | yes | — |
| 94 | #67000 | — | 2 | 6 | no | — |
| 95 | #67000 | — | 2 | 3 | no | — |
| 96 | #66999 | — | 2 | 3 | no | — |
| 97 | Q8×Dic11 | D4 | 1 | 1 | yes | characteristic |
| 98 | Q8×Dic11 | C23 | 1 | 1 | yes | characteristic |
| 99 | #66997 | — | 2 | 3 | no | — |
| 100 | C2×#4325 | C23 | 1 | 1 | yes | characteristic |
| 101 | #66993 | C23 | 1 | 1 | yes | characteristic |
| 102 | #66991 | C23 | 1 | 3 | yes | — |
| 103 | C2×#4323 | C23 | 1 | 3 | yes | — |
| 104 | C4×C22⋊D11 | — | 2 | 3 | no | — |
| 105 | #66977 | — | 2 | 3 | no | — |
| 106 | C2×D88 | C23 | 1 | 3 | yes | — |
| 107 | C2×#4313 | C23 | 1 | 6 | yes | — |
| 108 | #66950 | — | 2 | 3 | no | — |
| 109 | #66948 | — | 2 | 3 | no | — |
| 110 | #66948 | — | 2 | 3 | no | — |
| 111 | #66948 | — | 2 | 3 | no | — |
| 112 | #66948 | — | 2 | 6 | no | — |
| 113 | #66948 | C23 | 1 | 6 | yes | — |
| 114 | #66948 | C23 | 1 | 3 | yes | — |
| 115 | #66947 | — | 2 | 6 | no | — |
| 116 | #66946 | — | 2 | 3 | no | — |
| 117 | #66946 | — | 2 | 3 | no | — |
| 118 | #66946 | D4 | 1 | 3 | yes | — |
| 119 | #66946 | C23 | 1 | 3 | yes | — |
| 120 | #66945 | — | 2 | 3 | no | — |
| 121 | #66945 | — | 2 | 3 | no | — |
| 122 | #66945 | D4 | 1 | 3 | yes | — |
| 123 | #66945 | C23 | 1 | 3 | yes | — |
| 124 | C4⋊C4×D11 | — | 2 | 3 | no | — |
| 125 | C4⋊C4×D11 | C23 | 1 | 6 | yes | — |
| 126 | #66941 | — | 2 | 3 | no | — |
| 127 | #66941 | C23 | 1 | 3 | yes | — |
| 128 | #66938 | — | 2 | 3 | no | — |
| 129 | #66937 | — | 2 | 3 | no | — |
| 130 | #66936 | — | 2 | 6 | no | — |
| 131 | #66927 | — | 2 | 3 | no | — |
| 132 | #66927 | C23 | 1 | 3 | yes | — |
| 133 | C4×D44 | — | 2 | 3 | no | — |
| 134 | C4×D44 | — | 2 | 3 | no | — |
| 135 | C4×D44 | C23 | 1 | 3 | yes | — |
| 136 | C4×D44 | C23 | 1 | 3 | yes | — |
| 137 | C4×D44 | C23 | 1 | 3 | yes | — |
| 138 | C42×D11 | — | 2 | 3 | no | — |
| 139 | C42×D11 | C23 | 1 | 3 | yes | — |
| 140 | #66922 | C23 | 1 | 3 | yes | — |
| 141 | C11×#106 | C23 | 1 | 3 | yes | — |
| 142 | C11×#106 | C23 | 1 | 6 | yes | — |
| 143 | C11×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 144 | C11×#103 | C23 | 1 | 3 | yes | — |
| 145 | C11×#102 | C23 | 1 | 3 | yes | — |
| 146 | C4×C8×C11 | C23 | 1 | 3 | yes | — |
| 147 | #66899 | C23 | 1 | 3 | yes | — |
| 148 | #66896 | C23 | 1 | 1 | yes | characteristic |
| 149 | #66885 | C23 | 1 | 3 | yes | — |
| 150 | #66885 | C23 | 1 | 6 | yes | — |
| 151 | #66885 | C23 | 1 | 1 | yes | characteristic |
| 152 | (C2×D11)⋊C8 | C23 | 1 | 3 | yes | — |
| 153 | (C2×D11)⋊C8 | C23 | 1 | 3 | yes | — |
| 154 | #66882 | C23 | 1 | 3 | yes | — |
| 155 | Dic11⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 156 | Dic11⋊C8 | C23 | 1 | 3 | yes | — |
| 157 | #66873 | C23 | 1 | 3 | yes | — |
| 158 | #66873 | C23 | 1 | 6 | yes | — |
| 159 | #66873 | C23 | 1 | 3 | yes | — |
| 160 | #66872 | C23 | 1 | 6 | yes | — |
| 161 | #66872 | C23 | 1 | 3 | yes | — |
| 162 | #66871 | C23 | 1 | 3 | yes | — |
| 163 | C4⋊(C11⋊C8) | C23 | 1 | 3 | yes | — |
| 164 | C4×C11⋊C8 | C23 | 1 | 3 | yes | — |
| 165 | #62150 | — | 11 | 1 | no | maximal, Sylow |
| 166 | C2×Q8×C11 | — | 2 | 3 | no | — |
| 167 | C2×Q8×C11 | — | 2 | 3 | no | — |
| 168 | C2×Q8×C11 | — | 4 | 4 | no | — |
| 169 | C2×Q8×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C2×Q8×C11 | C24 | 1 | 1 | yes | characteristic |
| 171 | C2×D4×C11 | C24 | 1 | 1 | yes | characteristic |
| 172 | C22×C4×C11 | — | 2 | 3 | no | — |
| 173 | C2×C22⋊D11 | — | 2 | 1 | no | — |
| 174 | C2×C22⋊D11 | — | 2 | 1 | no | — |
| 175 | C2×C22⋊D11 | — | 2 | 3 | no | — |
| 176 | #4343 | — | 2 | 4 | no | — |
| 177 | #4343 | — | 2 | 6 | no | — |
| 178 | #4343 | — | 4 | 3 | no | — |
| 179 | #4343 | — | 4 | 12 | no | — |
| 180 | #4343 | — | 4 | 4 | no | — |
| 181 | #4343 | — | 8 | 6 | no | — |
| 182 | Q8×D11 | — | 4 | 12 | no | — |
| 183 | Q8×D11 | — | 4 | 4 | no | — |
| 184 | #4339 | — | 4 | 12 | no | — |
| 185 | #4339 | — | 4 | 12 | no | — |
| 186 | C2×D44 | — | 2 | 3 | no | — |
| 187 | C2×D44 | — | 2 | 3 | no | — |
| 188 | C2×D44 | — | 2 | 6 | no | — |
| 189 | C2×D44 | — | 2 | 3 | no | — |
| 190 | C2×D44 | — | 2 | 3 | no | — |
| 191 | C2×D44 | C2×D4 | 1 | 3 | yes | — |
| 192 | C2×D44 | C24 | 1 | 3 | yes | — |
| 193 | C2×D44 | C24 | 1 | 1 | yes | characteristic |
| 194 | C2×C4×D11 | — | 2 | 3 | no | — |
| 195 | C2×C4×D11 | — | 2 | 3 | no | — |
| 196 | C2×C4×D11 | — | 2 | 6 | no | — |
| 197 | C2×C4×D11 | — | 2 | 3 | no | — |
| 198 | C2×C4×D11 | — | 2 | 3 | no | — |
| 199 | C2×C4×D11 | C2×D4 | 1 | 3 | yes | — |
| 200 | C2×C4×D11 | C2×D4 | 1 | 3 | yes | — |
| 201 | C2×C4×D11 | C24 | 1 | 3 | yes | — |
| 202 | C2×Dic22 | — | 2 | 3 | no | — |
| 203 | C2×Dic22 | — | 2 | 3 | no | — |
| 204 | C11×SD16 | — | 2 | 2 | no | — |
| 205 | C2×C8×C11 | C24 | 1 | 3 | yes | — |
| 206 | C2×C8×C11 | C24 | 1 | 1 | yes | characteristic |
| 207 | C11×C4⋊C4 | — | 2 | 3 | no | — |
| 208 | C11×C4⋊C4 | — | 2 | 3 | no | — |
| 209 | C11×C4⋊C4 | — | 2 | 3 | no | — |
| 210 | C11×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 211 | C11×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 212 | C11×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 213 | C11×C22⋊C4 | — | 2 | 3 | no | — |
| 214 | C42×C11 | — | 2 | 3 | no | — |
| 215 | C42×C11 | C24 | 1 | 3 | yes | — |
| 216 | C22⋊Dic11 | — | 2 | 3 | no | — |
| 217 | #4325 | — | 2 | 2 | no | — |
| 218 | #4323 | — | 4 | 3 | no | — |
| 219 | (C2×D11)⋊C4 | — | 2 | 6 | no | — |
| 220 | (C2×D11)⋊C4 | — | 2 | 3 | no | — |
| 221 | (C2×D11)⋊C4 | — | 2 | 3 | no | — |
| 222 | (C2×D11)⋊C4 | — | 2 | 3 | no | — |
| 223 | (C2×D11)⋊C4 | — | 2 | 3 | no | — |
| 224 | (C2×D11)⋊C4 | — | 2 | 3 | no | — |
| 225 | (C2×D11)⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 226 | C4⋊Dic11 | — | 2 | 1 | no | — |
| 227 | C4⋊Dic11 | — | 2 | 3 | no | — |
| 228 | C4⋊Dic11 | C2×D4 | 1 | 3 | yes | — |
| 229 | C4⋊Dic11 | C24 | 1 | 1 | yes | characteristic |
| 230 | C4⋊Dic11 | C24 | 1 | 3 | yes | — |
| 231 | Dic11⋊C4 | — | 2 | 6 | no | — |
| 232 | Dic11⋊C4 | — | 2 | 3 | no | — |
| 233 | C4×Dic11 | — | 2 | 1 | no | — |
| 234 | C4×Dic11 | — | 2 | 3 | no | — |
| 235 | C4×Dic11 | C2×D4 | 1 | 3 | yes | — |
| 236 | C4×Dic11 | C2×D4 | 1 | 3 | yes | — |
| 237 | C4×Dic11 | C24 | 1 | 1 | yes | characteristic |
| 238 | C2×C11⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 239 | C2×C11⋊C8 | C24 | 1 | 3 | yes | — |
| 240 | D88 | — | 4 | 3 | no | — |
| 241 | #4313 | — | 4 | 6 | no | — |
| 242 | #3499 | — | 11 | 1 | no | — |
| 243 | #3483 | — | 11 | 1 | no | — |
| 244 | Q8×SD16 | — | 11 | 1 | no | — |
| 245 | Q8×SD16 | D11 | 1 | 1 | yes | characteristic, complemented |
| 246 | #3358 | — | 11 | 1 | no | — |
| 247 | #3358 | — | 11 | 1 | no | — |
| 248 | #3354 | — | 11 | 3 | no | — |
| 249 | #3354 | — | 11 | 3 | no | — |
| 250 | #3332 | — | 11 | 3 | no | — |
| 251 | #3332 | — | 11 | 3 | no | — |
| 252 | #3253 | — | 11 | 3 | no | — |
| 253 | #3227 | — | 11 | 3 | no | — |
| 254 | #3106 | — | 11 | 3 | no | — |
| 255 | #3079 | — | 11 | 3 | no | — |
| 256 | #2991 | — | 11 | 1 | no | — |
| 257 | C23×C11 | — | 2 | 1 | no | — |
| 258 | C22×D11 | — | 2 | 1 | no | — |
| 259 | C22×D11 | — | 2 | 3 | no | — |
| 260 | C22×D11 | C22×D4 | 1 | 3 | yes | — |
| 261 | Q8×C11 | — | 2 | 1 | no | — |
| 262 | Q8×C11 | — | 4 | 6 | no | — |
| 263 | Q8×C11 | — | 8 | 3 | no | — |
| 264 | Q8×C11 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 265 | Q8×C11 | 2−1+4 | 1 | 2 | yes | complemented |
| 266 | D4×C11 | — | 2 | 1 | no | — |
| 267 | D4×C11 | — | 2 | 1 | no | — |
| 268 | C2×C4×C11 | — | 2 | 1 | no | — |
| 269 | C2×C4×C11 | — | 2 | 3 | no | — |
| 270 | C2×C4×C11 | — | 2 | 3 | no | — |
| 271 | C2×C4×C11 | — | 4 | 6 | no | — |
| 272 | C2×C4×C11 | C22×D4 | 1 | 3 | yes | — |
| 273 | C2×C4×C11 | C22×D4 | 1 | 3 | yes | — |
| 274 | C2×C4×C11 | C25 | 1 | 1 | yes | characteristic |
| 275 | C22⋊D11 | — | 4 | 2 | no | — |
| 276 | C22⋊D11 | — | 4 | 6 | no | — |
| 277 | C22⋊D11 | — | 4 | 2 | no | — |
| 278 | C2×Dic11 | — | 2 | 1 | no | — |
| 279 | C2×Dic11 | — | 2 | 3 | no | — |
| 280 | C2×Dic11 | C22×D4 | 1 | 3 | yes | — |
| 281 | C2×Dic11 | C22×D4 | 1 | 1 | yes | characteristic |
| 282 | C2×Dic11 | C22×D4 | 1 | 1 | yes | characteristic |
| 283 | D44 | — | 2 | 6 | no | — |
| 284 | D44 | — | 2 | 1 | no | — |
| 285 | D44 | — | 2 | 3 | no | — |
| 286 | D44 | — | 2 | 1 | no | — |
| 287 | D44 | — | 2 | 3 | no | — |
| 288 | D44 | — | 4 | 6 | no | — |
| 289 | D44 | — | 4 | 6 | no | — |
| 290 | D44 | — | 4 | 6 | no | — |
| 291 | D44 | — | 8 | 3 | no | — |
| 292 | D44 | — | 8 | 6 | no | — |
| 293 | C4×D11 | — | 2 | 6 | no | — |
| 294 | C4×D11 | — | 2 | 3 | no | — |
| 295 | C4×D11 | — | 2 | 3 | no | — |
| 296 | C4×D11 | — | 2 | 6 | no | — |
| 297 | C4×D11 | — | 4 | 6 | no | — |
| 298 | C4×D11 | — | 4 | 12 | no | — |
| 299 | C4×D11 | — | 4 | 6 | no | — |
| 300 | C4×D11 | — | 4 | 6 | no | — |
| 301 | C4×D11 | — | 4 | 6 | no | — |
| 302 | Dic22 | — | 4 | 6 | no | — |
| 303 | Dic22 | — | 4 | 6 | no | — |
| 304 | C8×C11 | — | 2 | 1 | no | — |
| 305 | C8×C11 | — | 2 | 3 | no | — |
| 306 | C11⋊C8 | — | 2 | 1 | no | — |
| 307 | C11⋊C8 | — | 2 | 3 | no | — |
| 308 | C2×2−1+4 | — | 22 | 1 | no | — |
| 309 | Q82 | C2×D11 | 1 | 1 | yes | characteristic |
| 310 | #555 | — | 11 | 3 | no | — |
| 311 | #555 | — | 22 | 3 | no | — |
| 312 | #550 | — | 11 | 1 | no | — |
| 313 | #550 | — | 11 | 3 | no | — |
| 314 | #550 | — | 22 | 1 | no | — |
| 315 | D4×Q8 | — | 11 | 1 | no | — |
| 316 | D4×Q8 | — | 22 | 1 | no | — |
| 317 | D4×Q8 | C2×D11 | 1 | 1 | yes | characteristic |
| 318 | #547 | — | 11 | 3 | no | — |
| 319 | #547 | — | 11 | 3 | no | — |
| 320 | #547 | — | 22 | 3 | no | — |
| 321 | #536 | — | 22 | 3 | no | — |
| 322 | #532 | — | 11 | 3 | no | — |
| 323 | #532 | — | 11 | 3 | no | — |
| 324 | #532 | — | 22 | 3 | no | — |
| 325 | C2×C4⋊Q8 | — | 11 | 3 | no | — |
| 326 | C4×#41 | — | 11 | 1 | no | — |
| 327 | C4×#41 | — | 11 | 3 | no | — |
| 328 | C4×#41 | — | 22 | 1 | no | — |
| 329 | #498 | — | 11 | 3 | no | — |
| 330 | #498 | C2×D11 | 1 | 3 | yes | — |
| 331 | #486 | — | 11 | 3 | no | — |
| 332 | #486 | — | 11 | 3 | no | — |
| 333 | #482 | — | 11 | 3 | no | — |
| 334 | #482 | — | 11 | 3 | no | — |
| 335 | #481 | — | 11 | 6 | no | — |
| 336 | #481 | — | 11 | 6 | no | — |
| 337 | #477 | — | 11 | 3 | no | — |
| 338 | #476 | — | 11 | 3 | no | — |
| 339 | #476 | — | 11 | 6 | no | — |
| 340 | #476 | — | 11 | 3 | no | — |
| 341 | #476 | C2×D11 | 1 | 3 | yes | — |
| 342 | #475 | — | 11 | 3 | no | — |
| 343 | #475 | C2×D11 | 1 | 3 | yes | — |
| 344 | #474 | — | 11 | 3 | no | — |
| 345 | #474 | — | 11 | 3 | no | — |
| 346 | #469 | — | 11 | 6 | no | — |
| 347 | #469 | — | 11 | 6 | no | — |
| 348 | #460 | — | 11 | 1 | no | — |
| 349 | #459 | — | 11 | 3 | no | — |
| 350 | #459 | — | 11 | 3 | no | — |
| 351 | #459 | — | 11 | 3 | no | — |
| 352 | #449 | — | 11 | 3 | no | — |
| 353 | #449 | — | 11 | 3 | no | — |
| 354 | C8×Q8 | — | 11 | 1 | no | — |
| 355 | C8×Q8 | C2×D11 | 1 | 1 | yes | characteristic |
| 356 | C4×SD16 | — | 11 | 3 | no | — |
| 357 | C4×SD16 | C2×D11 | 1 | 3 | yes | — |
| 358 | C4×D8 | — | 11 | 3 | no | — |
| 359 | C4×D8 | — | 11 | 3 | no | — |
| 360 | #436 | — | 11 | 3 | no | — |
| 361 | #436 | — | 11 | 3 | no | — |
| 362 | #431 | — | 11 | 3 | no | — |
| 363 | #428 | — | 11 | 6 | no | — |
| 364 | #423 | — | 11 | 3 | no | — |
| 365 | #417 | — | 11 | 6 | no | — |
| 366 | C22×C11 | — | 4 | 1 | no | — |
| 367 | C22×C11 | — | 4 | 1 | no | — |
| 368 | C22×C11 | — | 4 | 1 | no | — |
| 369 | C22×C11 | C23×D4 | 1 | 1 | yes | characteristic |
| 370 | C2×D11 | — | 2 | 3 | no | — |
| 371 | C2×D11 | — | 2 | 3 | no | — |
| 372 | C2×D11 | — | 2 | 3 | no | — |
| 373 | C2×D11 | — | 4 | 3 | no | — |
| 374 | C2×D11 | — | 4 | 1 | no | — |
| 375 | C2×D11 | — | 4 | 1 | no | — |
| 376 | C2×D11 | — | 4 | 3 | no | — |
| 377 | C2×D11 | — | 4 | 3 | no | — |
| 378 | C2×D11 | — | 4 | 1 | no | — |
| 379 | C4×C11 | — | 2 | 2 | no | — |
| 380 | C4×C11 | — | 2 | 3 | no | — |
| 381 | C4×C11 | — | 4 | 3 | no | — |
| 382 | C4×C11 | — | 4 | 3 | no | — |
| 383 | C4×C11 | C2×AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 384 | C4×C11 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 385 | C4×C11 | #585 | 1 | 1 | yes | characteristic |
| 386 | Dic11 | — | 2 | 3 | no | — |
| 387 | Dic11 | — | 2 | 1 | no | — |
| 388 | Dic11 | — | 4 | 3 | no | — |
| 389 | Dic11 | — | 4 | 1 | no | — |
| 390 | Dic11 | #577 | 1 | 2 | yes | — |
| 391 | 2−1+4 | — | 44 | 8 | no | — |
| 392 | C2×#41 | — | 11 | 1 | no | — |
| 393 | C2×#41 | — | 11 | 3 | no | — |
| 394 | C2×#41 | — | 22 | 3 | no | — |
| 395 | C2×#41 | — | 22 | 3 | no | — |
| 396 | C2×#41 | — | 22 | 3 | no | — |
| 397 | C2×#41 | — | 22 | 3 | no | — |
| 398 | C2×#41 | — | 22 | 1 | no | — |
| 399 | C22×Q8 | — | 2 | 1 | no | — |
| 400 | C22×Q8 | — | 22 | 3 | no | — |
| 401 | C22×Q8 | — | 22 | 1 | no | — |
| 402 | C2×SD16 | — | 11 | 1 | no | — |
| 403 | C2×SD16 | C22×D11 | 1 | 1 | yes | characteristic |
| 404 | C2×D8 | — | 11 | 3 | no | — |
| 405 | C2×D8 | — | 11 | 3 | no | — |
| 406 | C2×M16 | — | 11 | 6 | no | — |
| 407 | C4⋊Q8 | — | 2 | 3 | no | — |
| 408 | C4⋊Q8 | — | 11 | 3 | no | — |
| 409 | C4⋊Q8 | — | 11 | 3 | no | — |
| 410 | C4⋊Q8 | — | 22 | 3 | no | — |
| 411 | C4⋊Q8 | — | 22 | 3 | no | — |
| 412 | C4⋊Q8 | C22×D11 | 1 | 3 | yes | — |
| 413 | C4⋊Q8 | C22×D11 | 1 | 3 | yes | — |
| 414 | #127 | — | 11 | 1 | no | — |
| 415 | #127 | — | 11 | 3 | no | — |
| 416 | #127 | — | 22 | 3 | no | — |
| 417 | #124 | — | 22 | 3 | no | — |
| 418 | #124 | — | 22 | 3 | no | — |
| 419 | #124 | — | 22 | 6 | no | — |
| 420 | #123 | — | 22 | 6 | no | — |
| 421 | #123 | — | 22 | 6 | no | — |
| 422 | C22⋊Q8 | — | 2 | 3 | no | — |
| 423 | C22⋊Q8 | — | 22 | 3 | no | — |
| 424 | C22⋊Q8 | — | 22 | 3 | no | — |
| 425 | C22⋊Q8 | — | 22 | 3 | no | — |
| 426 | #121 | — | 11 | 3 | no | — |
| 427 | #121 | — | 11 | 3 | no | — |
| 428 | #121 | — | 11 | 6 | no | — |
| 429 | #121 | — | 22 | 3 | no | — |
| 430 | #121 | — | 22 | 6 | no | — |
| 431 | #121 | — | 22 | 3 | no | — |
| 432 | #121 | — | 22 | 3 | no | — |
| 433 | #121 | — | 22 | 3 | no | — |
| 434 | C4×Q8 | — | 2 | 1 | no | — |
| 435 | C4×Q8 | — | 11 | 1 | no | — |
| 436 | C4×Q8 | — | 11 | 1 | no | — |
| 437 | C4×Q8 | C22×D11 | 1 | 3 | yes | — |
| 438 | C4×Q8 | C22×D11 | 1 | 1 | yes | characteristic |
| 439 | C4×D4 | — | 11 | 3 | no | — |
| 440 | C4×D4 | — | 11 | 3 | no | — |
| 441 | C4×D4 | — | 11 | 3 | no | — |
| 442 | C4×D4 | — | 11 | 3 | no | — |
| 443 | C4×D4 | — | 11 | 3 | no | — |
| 444 | C4×D4 | — | 22 | 3 | no | — |
| 445 | C4×D4 | — | 22 | 3 | no | — |
| 446 | C4×D4 | — | 22 | 3 | no | — |
| 447 | C4×D4 | — | 22 | 3 | no | — |
| 448 | C4×D4 | — | 22 | 3 | no | — |
| 449 | C4×D4 | C22×D11 | 1 | 3 | yes | — |
| 450 | #117 | — | 11 | 3 | no | — |
| 451 | #117 | — | 11 | 3 | no | — |
| 452 | #117 | — | 22 | 3 | no | — |
| 453 | #117 | — | 22 | 3 | no | — |
| 454 | C2×C4⋊C4 | — | 11 | 6 | no | — |
| 455 | C2×C4⋊C4 | — | 22 | 3 | no | — |
| 456 | C2×C42 | — | 11 | 3 | no | — |
| 457 | C2×C42 | — | 22 | 3 | no | — |
| 458 | #107 | — | 11 | 3 | no | — |
| 459 | #107 | — | 11 | 3 | no | — |
| 460 | #106 | — | 11 | 6 | no | — |
| 461 | #106 | — | 11 | 3 | no | — |
| 462 | #106 | C22×D11 | 1 | 6 | yes | — |
| 463 | #106 | C22×D11 | 1 | 3 | yes | — |
| 464 | C4⋊C8 | — | 11 | 3 | no | — |
| 465 | C4⋊C8 | — | 11 | 1 | no | — |
| 466 | C4⋊C8 | — | 11 | 3 | no | — |
| 467 | C4⋊C8 | C22×D11 | 1 | 3 | yes | — |
| 468 | #103 | — | 11 | 3 | no | — |
| 469 | #103 | C22×D11 | 1 | 3 | yes | — |
| 470 | #102 | — | 11 | 1 | no | — |
| 471 | #102 | — | 11 | 6 | no | — |
| 472 | #102 | — | 11 | 1 | no | — |
| 473 | #102 | — | 11 | 3 | no | — |
| 474 | #102 | — | 11 | 6 | no | — |
| 475 | #102 | — | 11 | 3 | no | — |
| 476 | #102 | — | 11 | 3 | no | — |
| 477 | #102 | C22×D11 | 1 | 3 | yes | — |
| 478 | C22⋊C8 | — | 11 | 3 | no | — |
| 479 | C22⋊C8 | — | 11 | 3 | no | — |
| 480 | C4×C8 | — | 11 | 3 | no | — |
| 481 | C4×C8 | C22×D11 | 1 | 3 | yes | — |
| 482 | C2×C11 | — | 8 | 1 | no | — |
| 483 | C2×C11 | #3489 | 1 | 1 | yes | characteristic |
| 484 | C2×C11 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 485 | C2×C11 | C2×#577 | 1 | 1 | yes | characteristic |
| 486 | D11 | — | 4 | 3 | no | — |
| 487 | D11 | — | 8 | 3 | no | — |
| 488 | D11 | — | 8 | 1 | no | — |
| 489 | #41 | — | 22 | 4 | no | — |
| 490 | #41 | — | 22 | 6 | no | — |
| 491 | #41 | — | 44 | 12 | no | — |
| 492 | #41 | — | 44 | 12 | no | — |
| 493 | #41 | — | 44 | 3 | no | — |
| 494 | #41 | — | 44 | 12 | no | — |
| 495 | #41 | — | 44 | 4 | no | — |
| 496 | #41 | — | 88 | 6 | no | — |
| 497 | C2×Q8 | — | 2 | 3 | no | — |
| 498 | C2×Q8 | — | 2 | 3 | no | — |
| 499 | C2×Q8 | — | 4 | 4 | no | — |
| 500 | C2×Q8 | — | 22 | 3 | no | — |
| 501 | C2×Q8 | — | 22 | 3 | no | — |
| 502 | C2×Q8 | — | 44 | 12 | no | — |
| 503 | C2×Q8 | — | 44 | 4 | no | — |
| 504 | C2×Q8 | D4×D11 | 1 | 1 | yes | characteristic |
| 505 | C2×Q8 | C23×D11 | 1 | 1 | yes | characteristic |
| 506 | C2×D4 | — | 11 | 3 | no | — |
| 507 | C2×D4 | — | 11 | 3 | no | — |
| 508 | C2×D4 | — | 11 | 1 | no | — |
| 509 | C2×D4 | — | 22 | 3 | no | — |
| 510 | C2×D4 | — | 22 | 3 | no | — |
| 511 | C2×D4 | — | 22 | 6 | no | — |
| 512 | C2×D4 | — | 22 | 1 | no | — |
| 513 | C2×D4 | — | 22 | 1 | no | — |
| 514 | C2×D4 | — | 22 | 3 | no | — |
| 515 | C2×D4 | — | 22 | 3 | no | — |
| 516 | C2×D4 | — | 22 | 3 | no | — |
| 517 | C2×D4 | C23×D11 | 1 | 1 | yes | characteristic |
| 518 | C22×C4 | — | 2 | 3 | no | — |
| 519 | C22×C4 | — | 11 | 3 | no | — |
| 520 | C22×C4 | — | 11 | 3 | no | — |
| 521 | C22×C4 | — | 11 | 3 | no | — |
| 522 | C22×C4 | — | 22 | 3 | no | — |
| 523 | C22×C4 | — | 22 | 3 | no | — |
| 524 | C22×C4 | — | 22 | 6 | no | — |
| 525 | C22×C4 | — | 22 | 3 | no | — |
| 526 | C22×C4 | — | 22 | 3 | no | — |
| 527 | SD16 | — | 2 | 2 | no | — |
| 528 | SD16 | — | 22 | 2 | no | — |
| 529 | D8 | — | 44 | 3 | no | — |
| 530 | D8 | — | 44 | 3 | no | — |
| 531 | M16 | — | 44 | 6 | no | — |
| 532 | C2×C8 | — | 11 | 1 | no | — |
| 533 | C2×C8 | — | 11 | 3 | no | — |
| 534 | C2×C8 | C23×D11 | 1 | 1 | yes | characteristic |
| 535 | C2×C8 | C23×D11 | 1 | 3 | yes | — |
| 536 | C4⋊C4 | — | 2 | 3 | no | — |
| 537 | C4⋊C4 | — | 2 | 3 | no | — |
| 538 | C4⋊C4 | — | 2 | 3 | no | — |
| 539 | C4⋊C4 | — | 11 | 3 | no | — |
| 540 | C4⋊C4 | — | 11 | 3 | no | — |
| 541 | C4⋊C4 | — | 11 | 1 | no | — |
| 542 | C4⋊C4 | — | 22 | 6 | no | — |
| 543 | C4⋊C4 | — | 22 | 3 | no | — |
| 544 | C4⋊C4 | — | 22 | 1 | no | — |
| 545 | C4⋊C4 | — | 22 | 3 | no | — |
| 546 | C4⋊C4 | D4×D11 | 1 | 3 | yes | — |
| 547 | C4⋊C4 | C23×D11 | 1 | 3 | yes | — |
| 548 | C4⋊C4 | C23×D11 | 1 | 3 | yes | — |
| 549 | C22⋊C4 | — | 2 | 3 | no | — |
| 550 | C22⋊C4 | — | 11 | 6 | no | — |
| 551 | C22⋊C4 | — | 22 | 3 | no | — |
| 552 | C22⋊C4 | — | 22 | 6 | no | — |
| 553 | C22⋊C4 | — | 22 | 3 | no | — |
| 554 | C22⋊C4 | — | 22 | 3 | no | — |
| 555 | C22⋊C4 | — | 22 | 3 | no | — |
| 556 | C22⋊C4 | — | 22 | 3 | no | — |
| 557 | C22⋊C4 | — | 22 | 3 | no | — |
| 558 | C42 | — | 2 | 3 | no | — |
| 559 | C42 | — | 11 | 3 | no | — |
| 560 | C42 | — | 11 | 3 | no | — |
| 561 | C42 | — | 11 | 1 | no | — |
| 562 | C42 | — | 22 | 1 | no | — |
| 563 | C42 | — | 22 | 3 | no | — |
| 564 | C42 | C23×D11 | 1 | 3 | yes | — |
| 565 | C11 | #62150 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 566 | C23 | — | 2 | 1 | no | — |
| 567 | C23 | — | 11 | 3 | no | — |
| 568 | C23 | — | 22 | 1 | no | — |
| 569 | C23 | — | 22 | 3 | no | — |
| 570 | Q8 | — | 2 | 1 | no | — |
| 571 | Q8 | — | 4 | 6 | no | — |
| 572 | Q8 | — | 8 | 3 | no | — |
| 573 | Q8 | — | 44 | 6 | no | — |
| 574 | Q8 | — | 44 | 6 | no | — |
| 575 | Q8 | #66967 | 1 | 4 | yes | — |
| 576 | Q8 | #67040 | 1 | 2 | yes | complemented |
| 577 | D4 | — | 2 | 1 | no | — |
| 578 | D4 | — | 2 | 1 | no | — |
| 579 | D4 | — | 22 | 6 | no | — |
| 580 | D4 | — | 22 | 1 | no | — |
| 581 | D4 | — | 22 | 3 | no | — |
| 582 | D4 | — | 22 | 1 | no | — |
| 583 | D4 | — | 22 | 3 | no | — |
| 584 | D4 | — | 44 | 6 | no | — |
| 585 | D4 | — | 44 | 6 | no | — |
| 586 | D4 | — | 44 | 2 | no | — |
| 587 | D4 | — | 44 | 2 | no | — |
| 588 | D4 | — | 44 | 6 | no | — |
| 589 | D4 | — | 44 | 6 | no | — |
| 590 | D4 | — | 88 | 3 | no | — |
| 591 | D4 | — | 88 | 6 | no | — |
| 592 | C2×C4 | — | 2 | 1 | no | — |
| 593 | C2×C4 | — | 2 | 3 | no | — |
| 594 | C2×C4 | — | 2 | 3 | no | — |
| 595 | C2×C4 | — | 4 | 6 | no | — |
| 596 | C2×C4 | — | 11 | 1 | no | — |
| 597 | C2×C4 | — | 11 | 1 | no | — |
| 598 | C2×C4 | — | 11 | 3 | no | — |
| 599 | C2×C4 | — | 22 | 6 | no | — |
| 600 | C2×C4 | — | 22 | 6 | no | — |
| 601 | C2×C4 | — | 22 | 3 | no | — |
| 602 | C2×C4 | — | 22 | 3 | no | — |
| 603 | C2×C4 | — | 22 | 1 | no | — |
| 604 | C2×C4 | — | 22 | 3 | no | — |
| 605 | C2×C4 | — | 44 | 6 | no | — |
| 606 | C2×C4 | — | 44 | 6 | no | — |
| 607 | C2×C4 | — | 44 | 12 | no | — |
| 608 | C2×C4 | — | 44 | 6 | no | — |
| 609 | C2×C4 | — | 44 | 6 | no | — |
| 610 | C2×C4 | C2×D4×D11 | 1 | 3 | yes | — |
| 611 | C2×C4 | C2×D4×D11 | 1 | 3 | yes | — |
| 612 | C2×C4 | C24×D11 | 1 | 1 | yes | characteristic |
| 613 | C8 | — | 2 | 1 | no | — |
| 614 | C8 | — | 2 | 3 | no | — |
| 615 | C8 | — | 22 | 1 | no | — |
| 616 | C8 | — | 22 | 3 | no | — |
| 617 | C22 | — | 4 | 1 | no | — |
| 618 | C22 | — | 4 | 1 | no | — |
| 619 | C22 | — | 4 | 1 | no | — |
| 620 | C22 | — | 22 | 3 | no | — |
| 621 | C22 | — | 22 | 3 | no | — |
| 622 | C22 | — | 22 | 3 | no | — |
| 623 | C22 | — | 44 | 3 | no | — |
| 624 | C22 | — | 44 | 1 | no | — |
| 625 | C22 | — | 44 | 1 | no | — |
| 626 | C22 | — | 44 | 3 | no | — |
| 627 | C22 | — | 44 | 3 | no | — |
| 628 | C22 | — | 44 | 1 | no | — |
| 629 | C22 | C22×D4×D11 | 1 | 1 | yes | characteristic |
| 630 | C4 | — | 2 | 2 | no | — |
| 631 | C4 | — | 2 | 3 | no | — |
| 632 | C4 | — | 4 | 3 | no | — |
| 633 | C4 | — | 4 | 3 | no | — |
| 634 | C4 | — | 11 | 2 | no | — |
| 635 | C4 | — | 22 | 3 | no | — |
| 636 | C4 | — | 22 | 1 | no | — |
| 637 | C4 | — | 44 | 3 | no | — |
| 638 | C4 | — | 44 | 1 | no | — |
| 639 | C4 | C2×#66967 | 1 | 6 | yes | — |
| 640 | C4 | C2×#67040 | 1 | 1 | yes | characteristic |
| 641 | C4 | #10623457 | 1 | 1 | yes | characteristic |
| 642 | C2 | — | 8 | 1 | no | — |
| 643 | C2 | — | 44 | 3 | no | — |
| 644 | C2 | — | 88 | 3 | no | — |
| 645 | C2 | — | 88 | 1 | no | — |
| 646 | C2 | #13082293 | 1 | 1 | yes | characteristic |
| 647 | C2 | C22×#66967 | 1 | 1 | yes | characteristic |
| 648 | C2 | D11×#577 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13082400 | C2 | semidirect |
| 2. #13082243 | C2 | semidirect |
| 3. Q8×#4325 | C2 | semidirect |
| 4. #13081252 | C2 | semidirect |
| 5. #13081251 | C2 | semidirect |
| 6. #13081210 | C2 | semidirect |
| 7. #13081208 | C2 | semidirect |
| 8. #13080945 | C2 | semidirect |
| 9. #13080940 | C2 | semidirect |
| 10. #13079996 | C2 | semidirect |
| 11. #13079745 | C2 | semidirect |
| 12. #13078674 | C2 | semidirect |
| 13. #13078426 | C2 | semidirect |
| 14. #13077747 | C2 | semidirect |
| 15. Q8×C11×SD16 | C2 | semidirect |
| 245. Q8×SD16 | D11 | semidirect |
| 265. Q8×C11 | 2−1+4 | semidirect |
| 565. C11 | #62150 | semidirect |
| 576. Q8 | #67040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13082400 | 2 |
| #13082243 | 2 |
| Q8×#4325 | 2 |
| #13081252 | 2 |
| #13081251 | 2 |
| #13081210 | 2 |
| #13081208 | 2 |
| #13080945 | 2 |
| #13080940 | 2 |
| #13079996 | 2 |
| #13079745 | 2 |
| #13078674 | 2 |
| #13078426 | 2 |
| #13077747 | 2 |
| Q8×C11×SD16 | 2 |
| #62150 | 11 |