Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
4782 conjugacy classes of subgroups.
The subgroup lattice has 656 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×#67043 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#10623282 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13082285 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13077934 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #13077904 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #13077870 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #13077853 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #13077838 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | C2×#10622351 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #13077150 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C11×#2880 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C22×C11×#41 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#67043 | — | 2 | 3 | no | — |
| 14 | C2×#67043 | — | 2 | 1 | no | — |
| 15 | C2×#67043 | — | 2 | 16 | no | — |
| 16 | C2×#67043 | C22 | 1 | 2 | yes | — |
| 17 | C2×#67043 | C22 | 1 | 6 | yes | complemented |
| 18 | C2×#67042 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C22×Q8×D11 | — | 2 | 1 | no | — |
| 20 | C22×#4341 | — | 2 | 3 | no | — |
| 21 | C22×#4339 | C22 | 1 | 3 | yes | complemented |
| 22 | C23×Dic22 | C22 | 1 | 3 | yes | complemented |
| 23 | C2×C11×#131 | C22 | 1 | 2 | yes | complemented |
| 24 | #10623365 | — | 2 | 1 | no | — |
| 25 | #10623364 | C22 | 1 | 3 | yes | complemented |
| 26 | #10623361 | C22 | 1 | 3 | yes | complemented |
| 27 | #10623360 | — | 2 | 3 | no | — |
| 28 | #10623358 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #10623348 | — | 2 | 1 | no | — |
| 30 | D4×C22⋊D11 | — | 2 | 3 | no | — |
| 31 | #10623322 | C22 | 1 | 3 | yes | — |
| 32 | C2×#66983 | C22 | 1 | 3 | yes | — |
| 33 | #10623282 | — | 2 | 16 | no | — |
| 34 | C2×#66962 | C22 | 1 | 6 | yes | complemented |
| 35 | C2×#66961 | C22 | 1 | 6 | yes | complemented |
| 36 | C2×#66957 | C22 | 1 | 6 | yes | complemented |
| 37 | C22×#4314 | C22 | 1 | 6 | yes | complemented |
| 38 | C11×#408 | C22 | 1 | 6 | yes | complemented |
| 39 | C11×#407 | C22 | 1 | 3 | yes | complemented |
| 40 | C2×C11×C22⋊C8 | C22 | 1 | 3 | yes | complemented |
| 41 | #10622746 | C22 | 1 | 6 | yes | complemented |
| 42 | #10622733 | C22 | 1 | 6 | yes | complemented |
| 43 | #10622726 | C22 | 1 | 6 | yes | complemented |
| 44 | C2×#66880 | C22 | 1 | 6 | yes | complemented |
| 45 | #10622352 | C22 | 1 | 3 | yes | complemented |
| 46 | #10622352 | C22 | 1 | 6 | yes | complemented |
| 47 | #10622351 | C22 | 1 | 3 | yes | complemented |
| 48 | #10622351 | C22 | 1 | 6 | yes | complemented |
| 49 | #10622351 | C22 | 1 | 12 | yes | complemented |
| 50 | #10622351 | C22 | 1 | 6 | yes | complemented |
| 51 | #10622347 | C22 | 1 | 6 | yes | complemented |
| 52 | #10622347 | C22 | 1 | 12 | yes | complemented |
| 53 | #10622346 | C22 | 1 | 6 | yes | complemented |
| 54 | #10622345 | C22 | 1 | 3 | yes | complemented |
| 55 | #10622344 | C22 | 1 | 1 | yes | characteristic, complemented |
| 56 | C2×C11×#41 | — | 2 | 8 | no | — |
| 57 | C2×C11×#41 | D4 | 1 | 3 | yes | — |
| 58 | C2×C11×#41 | D4 | 1 | 1 | yes | characteristic |
| 59 | C2×C11×#41 | C23 | 1 | 3 | yes | — |
| 60 | C2×C11×#41 | C23 | 1 | 1 | yes | characteristic |
| 61 | C22×Q8×C11 | D4 | 1 | 1 | yes | characteristic |
| 62 | C22×D4×C11 | D4 | 1 | 3 | yes | — |
| 63 | C23×C4×C11 | C23 | 1 | 3 | yes | — |
| 64 | C22×C22⋊D11 | — | 2 | 3 | no | — |
| 65 | C22×C22⋊D11 | — | 2 | 3 | no | — |
| 66 | C23×Dic11 | — | 2 | 3 | no | — |
| 67 | #67043 | — | 2 | 16 | no | — |
| 68 | #67043 | — | 2 | 48 | no | — |
| 69 | #67043 | — | 2 | 8 | no | — |
| 70 | #67043 | — | 2 | 24 | no | — |
| 71 | #67043 | — | 2 | 24 | no | — |
| 72 | #67043 | D4 | 1 | 16 | yes | complemented |
| 73 | #67042 | — | 2 | 8 | no | — |
| 74 | C2×#4343 | — | 2 | 1 | no | — |
| 75 | C2×Q8×D11 | — | 2 | 16 | no | — |
| 76 | C2×Q8×D11 | — | 2 | 2 | no | — |
| 77 | C2×Q8×D11 | — | 2 | 6 | no | — |
| 78 | C2×#4341 | — | 2 | 48 | no | — |
| 79 | C2×#4341 | — | 2 | 6 | no | — |
| 80 | C2×#4341 | — | 2 | 12 | no | — |
| 81 | C2×#4341 | — | 2 | 6 | no | — |
| 82 | C2×D4×D11 | — | 2 | 3 | no | — |
| 83 | C2×#4339 | — | 2 | 3 | no | — |
| 84 | C2×#4339 | — | 2 | 3 | no | — |
| 85 | C2×#4339 | — | 2 | 24 | no | — |
| 86 | C2×#4339 | C23 | 1 | 3 | yes | — |
| 87 | C2×#4339 | C23 | 1 | 6 | yes | — |
| 88 | C2×#4339 | C23 | 1 | 6 | yes | — |
| 89 | C22×D44 | C23 | 1 | 3 | yes | — |
| 90 | C22×D44 | C23 | 1 | 1 | yes | characteristic |
| 91 | C22×C4×D11 | — | 2 | 3 | no | — |
| 92 | C22×Dic22 | — | 2 | 3 | no | — |
| 93 | C22×Dic22 | — | 2 | 3 | no | — |
| 94 | C22×Dic22 | — | 2 | 3 | no | — |
| 95 | C22×Dic22 | — | 2 | 24 | no | — |
| 96 | C22×Dic22 | C23 | 1 | 3 | yes | — |
| 97 | C22×Dic22 | C23 | 1 | 6 | yes | — |
| 98 | C22×Dic22 | C23 | 1 | 6 | yes | — |
| 99 | C11×#131 | — | 2 | 8 | no | — |
| 100 | C2×C11×M16 | C23 | 1 | 6 | yes | — |
| 101 | C22×C8×C11 | C23 | 1 | 6 | yes | — |
| 102 | #67006 | — | 2 | 3 | no | — |
| 103 | #67000 | — | 2 | 3 | no | — |
| 104 | #66999 | — | 2 | 3 | no | — |
| 105 | Q8×Dic11 | — | 2 | 1 | no | — |
| 106 | #66993 | — | 2 | 3 | no | — |
| 107 | #66992 | — | 2 | 6 | no | — |
| 108 | #66991 | — | 2 | 3 | no | — |
| 109 | #66990 | — | 2 | 6 | no | — |
| 110 | D4×Dic11 | — | 2 | 3 | no | — |
| 111 | #66983 | — | 2 | 3 | no | — |
| 112 | #66983 | — | 2 | 3 | no | — |
| 113 | #66983 | C23 | 1 | 3 | yes | — |
| 114 | #66983 | C23 | 1 | 6 | yes | — |
| 115 | #66983 | C23 | 1 | 3 | yes | — |
| 116 | #66982 | — | 2 | 3 | no | — |
| 117 | C4×C22⋊D11 | — | 2 | 3 | no | — |
| 118 | C4×C22⋊D11 | — | 2 | 3 | no | — |
| 119 | C2×(C2×D11)⋊C4 | — | 2 | 3 | no | — |
| 120 | #66979 | C23 | 1 | 3 | yes | — |
| 121 | C2×C4⋊Dic11 | C23 | 1 | 3 | yes | — |
| 122 | #66977 | C23 | 1 | 1 | yes | characteristic |
| 123 | #66977 | C23 | 1 | 3 | yes | — |
| 124 | #66962 | — | 2 | 24 | no | — |
| 125 | #66961 | — | 2 | 24 | no | — |
| 126 | C2×Dic44 | C23 | 1 | 6 | yes | — |
| 127 | #66957 | — | 2 | 24 | no | — |
| 128 | C2×D88 | C23 | 1 | 6 | yes | — |
| 129 | C2×#4314 | — | 2 | 24 | no | — |
| 130 | C2×#4314 | C23 | 1 | 6 | yes | — |
| 131 | C2×#4314 | C23 | 1 | 12 | yes | — |
| 132 | C2×#4314 | C23 | 1 | 2 | yes | — |
| 133 | C11×C22⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 134 | C11×C22⋊C8 | C23 | 1 | 3 | yes | — |
| 135 | C11×C22⋊C8 | C23 | 1 | 6 | yes | — |
| 136 | C11×C22⋊C8 | C23 | 1 | 6 | yes | — |
| 137 | #66885 | C23 | 1 | 2 | yes | — |
| 138 | #66885 | C23 | 1 | 6 | yes | — |
| 139 | #66880 | C23 | 1 | 6 | yes | — |
| 140 | #66880 | C23 | 1 | 6 | yes | — |
| 141 | #66880 | C23 | 1 | 12 | yes | — |
| 142 | #60374 | — | 11 | 1 | no | maximal, Sylow |
| 143 | C24×C11 | C2×D4 | 1 | 3 | yes | — |
| 144 | C23×D11 | — | 2 | 1 | no | — |
| 145 | C23×D11 | — | 2 | 3 | no | — |
| 146 | C11×#41 | — | 2 | 4 | no | — |
| 147 | C11×#41 | — | 2 | 12 | no | — |
| 148 | C11×#41 | — | 2 | 12 | no | — |
| 149 | C11×#41 | C2×D4 | 1 | 8 | yes | — |
| 150 | C2×Q8×C11 | — | 2 | 4 | no | — |
| 151 | C2×Q8×C11 | C2×D4 | 1 | 3 | yes | — |
| 152 | C2×Q8×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 153 | C2×D4×C11 | — | 2 | 12 | no | — |
| 154 | C2×D4×C11 | C2×D4 | 1 | 6 | yes | — |
| 155 | C2×D4×C11 | C2×D4 | 1 | 3 | yes | — |
| 156 | C2×D4×C11 | C2×D4 | 1 | 3 | yes | — |
| 157 | C22×C4×C11 | — | 2 | 12 | no | — |
| 158 | C22×C4×C11 | C2×D4 | 1 | 3 | yes | — |
| 159 | C22×C4×C11 | C2×D4 | 1 | 3 | yes | — |
| 160 | C22×C4×C11 | C2×D4 | 1 | 3 | yes | — |
| 161 | C22×C4×C11 | C24 | 1 | 1 | yes | characteristic |
| 162 | C22×C4×C11 | C24 | 1 | 3 | yes | — |
| 163 | C22×C4×C11 | C24 | 1 | 3 | yes | — |
| 164 | C2×C22⋊D11 | — | 2 | 24 | no | — |
| 165 | C2×C22⋊D11 | — | 2 | 6 | no | — |
| 166 | C2×C22⋊D11 | — | 2 | 6 | no | — |
| 167 | C2×C22⋊D11 | — | 2 | 3 | no | — |
| 168 | C2×C22⋊D11 | — | 2 | 3 | no | — |
| 169 | C2×C22⋊D11 | — | 2 | 3 | no | — |
| 170 | C2×C22⋊D11 | — | 2 | 6 | no | — |
| 171 | C2×C22⋊D11 | — | 8 | 6 | no | — |
| 172 | C22×Dic11 | — | 2 | 24 | no | — |
| 173 | C22×Dic11 | — | 2 | 3 | no | — |
| 174 | C22×Dic11 | — | 2 | 6 | no | — |
| 175 | C22×Dic11 | — | 2 | 6 | no | — |
| 176 | C22×Dic11 | — | 2 | 3 | no | — |
| 177 | #4343 | — | 4 | 4 | no | — |
| 178 | Q8×D11 | — | 2 | 48 | no | — |
| 179 | Q8×D11 | — | 2 | 16 | no | — |
| 180 | #4341 | — | 2 | 96 | no | — |
| 181 | #4341 | — | 2 | 48 | no | — |
| 182 | #4341 | — | 2 | 48 | no | — |
| 183 | D4×D11 | — | 4 | 12 | no | — |
| 184 | #4339 | — | 2 | 24 | no | — |
| 185 | #4339 | — | 2 | 24 | no | — |
| 186 | #4339 | — | 2 | 12 | no | — |
| 187 | #4339 | — | 2 | 12 | no | — |
| 188 | #4339 | — | 2 | 12 | no | — |
| 189 | #4339 | — | 2 | 12 | no | — |
| 190 | #4339 | C2×D4 | 1 | 24 | yes | complemented |
| 191 | C2×D44 | — | 2 | 4 | no | — |
| 192 | C2×D44 | — | 2 | 1 | no | — |
| 193 | C2×D44 | — | 2 | 3 | no | — |
| 194 | C2×D44 | — | 2 | 12 | no | — |
| 195 | C2×D44 | C24 | 1 | 3 | yes | — |
| 196 | C2×D44 | C24 | 1 | 2 | yes | — |
| 197 | C2×C4×D11 | — | 2 | 24 | no | — |
| 198 | C2×C4×D11 | — | 2 | 6 | no | — |
| 199 | C2×C4×D11 | — | 2 | 6 | no | — |
| 200 | C2×C4×D11 | — | 2 | 3 | no | — |
| 201 | C2×Dic22 | — | 2 | 24 | no | — |
| 202 | C2×Dic22 | — | 2 | 24 | no | — |
| 203 | C2×Dic22 | — | 2 | 24 | no | — |
| 204 | C2×Dic22 | — | 2 | 12 | no | — |
| 205 | C2×Dic22 | — | 2 | 24 | no | — |
| 206 | C2×Dic22 | — | 2 | 3 | no | — |
| 207 | C2×Dic22 | — | 2 | 6 | no | — |
| 208 | C2×Dic22 | — | 2 | 6 | no | — |
| 209 | C2×Dic22 | — | 2 | 12 | no | — |
| 210 | C2×Dic22 | C2×D4 | 1 | 24 | yes | complemented |
| 211 | C2×Dic22 | C24 | 1 | 1 | yes | characteristic |
| 212 | C2×Dic22 | C24 | 1 | 6 | yes | — |
| 213 | C11×M16 | — | 2 | 12 | no | — |
| 214 | C2×C8×C11 | — | 2 | 12 | no | — |
| 215 | C2×C8×C11 | C24 | 1 | 2 | yes | — |
| 216 | C2×C8×C11 | C24 | 1 | 6 | yes | — |
| 217 | C22⋊Dic11 | — | 2 | 1 | no | — |
| 218 | C22⋊Dic11 | — | 2 | 3 | no | — |
| 219 | C22⋊Dic11 | — | 2 | 3 | no | — |
| 220 | (C2×D11)⋊C4 | — | 2 | 3 | no | — |
| 221 | (C2×D11)⋊C4 | — | 2 | 6 | no | — |
| 222 | (C2×D11)⋊C4 | — | 2 | 3 | no | — |
| 223 | C4⋊Dic11 | — | 2 | 3 | no | — |
| 224 | C4⋊Dic11 | C24 | 1 | 3 | yes | — |
| 225 | C4⋊Dic11 | C24 | 1 | 1 | yes | characteristic |
| 226 | Dic11⋊C4 | — | 2 | 1 | no | — |
| 227 | Dic11⋊C4 | — | 2 | 3 | no | — |
| 228 | C4×Dic11 | — | 2 | 3 | no | — |
| 229 | Dic44 | — | 2 | 12 | no | — |
| 230 | D88 | — | 2 | 12 | no | — |
| 231 | #4314 | — | 2 | 4 | no | — |
| 232 | #4314 | — | 2 | 12 | no | — |
| 233 | #4314 | — | 2 | 24 | no | — |
| 234 | C22×2−1+4 | — | 11 | 1 | no | — |
| 235 | C2×#577 | — | 11 | 2 | no | — |
| 236 | #3488 | — | 11 | 1 | no | — |
| 237 | #3013 | — | 11 | 6 | no | — |
| 238 | #3010 | — | 11 | 6 | no | — |
| 239 | #3006 | — | 11 | 3 | no | — |
| 240 | #3004 | — | 11 | 3 | no | — |
| 241 | #3002 | — | 11 | 3 | no | — |
| 242 | C2×#448 | — | 11 | 3 | no | — |
| 243 | #2898 | — | 11 | 2 | no | — |
| 244 | #2880 | D11 | 1 | 1 | yes | characteristic, complemented |
| 245 | C23×C11 | — | 2 | 6 | no | — |
| 246 | C23×C11 | — | 2 | 6 | no | — |
| 247 | C23×C11 | — | 4 | 3 | no | — |
| 248 | C23×C11 | C22×D4 | 1 | 3 | yes | — |
| 249 | C23×C11 | C22×D4 | 1 | 3 | yes | — |
| 250 | C23×C11 | C22×D4 | 1 | 1 | yes | characteristic |
| 251 | C22×D11 | — | 2 | 4 | no | — |
| 252 | C22×D11 | — | 2 | 2 | no | — |
| 253 | C22×D11 | — | 2 | 3 | no | — |
| 254 | C22×D11 | — | 4 | 2 | no | — |
| 255 | C22×D11 | — | 4 | 2 | no | — |
| 256 | C22×D11 | — | 4 | 6 | no | — |
| 257 | C22×D11 | — | 8 | 3 | no | — |
| 258 | C22×D11 | — | 8 | 3 | no | — |
| 259 | Q8×C11 | — | 2 | 6 | no | — |
| 260 | Q8×C11 | #120 | 1 | 4 | yes | — |
| 261 | D4×C11 | — | 2 | 12 | no | — |
| 262 | D4×C11 | — | 2 | 6 | no | — |
| 263 | D4×C11 | #120 | 1 | 12 | yes | — |
| 264 | C2×C4×C11 | — | 2 | 6 | no | — |
| 265 | C2×C4×C11 | — | 2 | 6 | no | — |
| 266 | C2×C4×C11 | — | 2 | 6 | no | — |
| 267 | C2×C4×C11 | — | 2 | 2 | no | — |
| 268 | C2×C4×C11 | — | 2 | 6 | no | — |
| 269 | C2×C4×C11 | C22×D4 | 1 | 1 | yes | characteristic |
| 270 | C2×C4×C11 | C22×D4 | 1 | 3 | yes | — |
| 271 | C2×C4×C11 | C22×D4 | 1 | 3 | yes | — |
| 272 | C2×C4×C11 | C22×D4 | 1 | 12 | yes | — |
| 273 | C2×C4×C11 | C25 | 1 | 1 | yes | characteristic |
| 274 | C22⋊D11 | — | 2 | 24 | no | — |
| 275 | C22⋊D11 | — | 2 | 24 | no | — |
| 276 | C22⋊D11 | — | 4 | 6 | no | — |
| 277 | C22⋊D11 | — | 4 | 6 | no | — |
| 278 | C22⋊D11 | — | 8 | 3 | no | — |
| 279 | C22⋊D11 | — | 8 | 6 | no | — |
| 280 | C2×Dic11 | — | 2 | 12 | no | — |
| 281 | C2×Dic11 | — | 2 | 24 | no | — |
| 282 | C2×Dic11 | — | 2 | 24 | no | — |
| 283 | C2×Dic11 | — | 2 | 6 | no | — |
| 284 | C2×Dic11 | — | 2 | 1 | no | — |
| 285 | C2×Dic11 | — | 2 | 3 | no | — |
| 286 | C2×Dic11 | — | 2 | 1 | no | — |
| 287 | C2×Dic11 | — | 8 | 3 | no | — |
| 288 | D44 | — | 2 | 4 | no | — |
| 289 | D44 | — | 2 | 2 | no | — |
| 290 | D44 | — | 2 | 6 | no | — |
| 291 | D44 | — | 4 | 6 | no | — |
| 292 | D44 | C22×D4 | 1 | 4 | yes | — |
| 293 | C4×D11 | — | 2 | 24 | no | — |
| 294 | C4×D11 | — | 2 | 24 | no | — |
| 295 | C4×D11 | — | 4 | 6 | no | — |
| 296 | Dic22 | — | 2 | 12 | no | — |
| 297 | Dic22 | — | 2 | 24 | no | — |
| 298 | Dic22 | — | 2 | 24 | no | — |
| 299 | Dic22 | — | 2 | 6 | no | — |
| 300 | Dic22 | — | 2 | 2 | no | — |
| 301 | Dic22 | C22×D4 | 1 | 12 | yes | — |
| 302 | C8×C11 | — | 2 | 2 | no | — |
| 303 | C8×C11 | — | 2 | 6 | no | — |
| 304 | C2×2−1+4 | — | 11 | 2 | no | — |
| 305 | C2×2−1+4 | — | 11 | 6 | no | — |
| 306 | C2×2−1+4 | — | 22 | 16 | no | — |
| 307 | C2×2−1+4 | — | 22 | 3 | no | — |
| 308 | C2×2−1+4 | — | 22 | 1 | no | — |
| 309 | C2×H(5,𝔽2) | — | 11 | 1 | no | — |
| 310 | C22×#41 | — | 11 | 3 | no | — |
| 311 | C22×#41 | — | 22 | 3 | no | — |
| 312 | C22×#41 | C2×D11 | 1 | 1 | yes | characteristic |
| 313 | C23×Q8 | — | 11 | 3 | no | — |
| 314 | C23×Q8 | — | 22 | 1 | no | — |
| 315 | #577 | — | 22 | 16 | no | — |
| 316 | C2×#137 | — | 11 | 6 | no | — |
| 317 | C2×AGL(1,ℤ/8) | — | 11 | 6 | no | — |
| 318 | C2×#135 | — | 11 | 6 | no | — |
| 319 | C22×SD16 | — | 11 | 6 | no | — |
| 320 | C2×#131 | C2×D11 | 1 | 2 | yes | complemented |
| 321 | #550 | — | 22 | 1 | no | — |
| 322 | #548 | — | 22 | 1 | no | — |
| 323 | #546 | — | 22 | 3 | no | — |
| 324 | D42 | — | 22 | 3 | no | — |
| 325 | #537 | — | 11 | 3 | no | — |
| 326 | #535 | — | 11 | 3 | no | — |
| 327 | #525 | — | 11 | 3 | no | — |
| 328 | C2×#121 | — | 11 | 3 | no | — |
| 329 | #520 | — | 11 | 1 | no | — |
| 330 | #452 | — | 11 | 6 | no | — |
| 331 | #451 | — | 11 | 3 | no | — |
| 332 | #451 | — | 11 | 6 | no | — |
| 333 | #450 | — | 11 | 1 | no | — |
| 334 | #449 | — | 11 | 6 | no | — |
| 335 | #449 | — | 11 | 12 | no | — |
| 336 | #448 | — | 11 | 3 | no | — |
| 337 | #448 | — | 11 | 6 | no | — |
| 338 | #448 | — | 11 | 12 | no | — |
| 339 | #448 | — | 11 | 6 | no | — |
| 340 | #447 | — | 11 | 3 | no | — |
| 341 | #419 | — | 11 | 6 | no | — |
| 342 | #417 | — | 11 | 6 | no | — |
| 343 | #416 | — | 11 | 6 | no | — |
| 344 | C2×#103 | — | 11 | 6 | no | — |
| 345 | #408 | C2×D11 | 1 | 6 | yes | complemented |
| 346 | #407 | C2×D11 | 1 | 3 | yes | complemented |
| 347 | C2×C22⋊C8 | C2×D11 | 1 | 3 | yes | complemented |
| 348 | C22×C11 | — | 2 | 1 | no | — |
| 349 | C22×C11 | — | 2 | 3 | no | — |
| 350 | C22×C11 | — | 2 | 1 | no | — |
| 351 | C22×C11 | — | 2 | 3 | no | — |
| 352 | C22×C11 | — | 2 | 3 | no | — |
| 353 | C22×C11 | — | 2 | 3 | no | — |
| 354 | C22×C11 | — | 2 | 3 | no | — |
| 355 | C22×C11 | — | 4 | 12 | no | — |
| 356 | C22×C11 | C2×#120 | 1 | 6 | yes | — |
| 357 | C22×C11 | #577 | 1 | 2 | yes | complemented |
| 358 | C22×C11 | C23×D4 | 1 | 1 | yes | characteristic |
| 359 | C2×D11 | — | 2 | 4 | no | — |
| 360 | C2×D11 | — | 4 | 8 | no | — |
| 361 | C2×D11 | — | 4 | 2 | no | — |
| 362 | C2×D11 | — | 4 | 2 | no | — |
| 363 | C2×D11 | — | 4 | 3 | no | — |
| 364 | C2×D11 | — | 4 | 3 | no | — |
| 365 | C2×D11 | — | 4 | 3 | no | — |
| 366 | C2×D11 | — | 16 | 6 | no | — |
| 367 | C4×C11 | — | 2 | 1 | no | — |
| 368 | C4×C11 | — | 2 | 3 | no | — |
| 369 | C4×C11 | C2×#120 | 1 | 6 | yes | — |
| 370 | C4×C11 | C23×D4 | 1 | 2 | yes | — |
| 371 | Dic11 | — | 2 | 12 | no | — |
| 372 | Dic11 | — | 4 | 1 | no | — |
| 373 | Dic11 | — | 4 | 1 | no | — |
| 374 | Dic11 | — | 4 | 3 | no | — |
| 375 | 2−1+4 | — | 11 | 16 | no | — |
| 376 | 2−1+4 | — | 22 | 24 | no | — |
| 377 | 2−1+4 | — | 22 | 24 | no | — |
| 378 | 2−1+4 | — | 22 | 48 | no | — |
| 379 | 2−1+4 | — | 22 | 16 | no | — |
| 380 | 2−1+4 | — | 22 | 8 | no | — |
| 381 | H(5,𝔽2) | — | 22 | 8 | no | — |
| 382 | C2×#41 | — | 2 | 8 | no | — |
| 383 | C2×#41 | — | 11 | 6 | no | — |
| 384 | C2×#41 | — | 11 | 3 | no | — |
| 385 | C2×#41 | — | 11 | 6 | no | — |
| 386 | C2×#41 | — | 22 | 24 | no | — |
| 387 | C2×#41 | — | 22 | 48 | no | — |
| 388 | C2×#41 | — | 22 | 1 | no | — |
| 389 | C2×#41 | — | 22 | 12 | no | — |
| 390 | C2×#41 | — | 22 | 6 | no | — |
| 391 | C2×#41 | — | 22 | 6 | no | — |
| 392 | C2×#41 | — | 22 | 3 | no | — |
| 393 | C2×#41 | — | 22 | 3 | no | — |
| 394 | C2×#41 | D44 | 1 | 3 | yes | — |
| 395 | C2×#41 | D44 | 1 | 1 | yes | characteristic |
| 396 | C2×#41 | C22×D11 | 1 | 3 | yes | — |
| 397 | C2×#41 | C22×D11 | 1 | 1 | yes | characteristic |
| 398 | C22×Q8 | — | 11 | 6 | no | — |
| 399 | C22×Q8 | — | 11 | 3 | no | — |
| 400 | C22×Q8 | — | 11 | 6 | no | — |
| 401 | C22×Q8 | — | 22 | 24 | no | — |
| 402 | C22×Q8 | — | 22 | 16 | no | — |
| 403 | C22×Q8 | — | 22 | 6 | no | — |
| 404 | C22×Q8 | — | 22 | 2 | no | — |
| 405 | C22×Q8 | — | 22 | 3 | no | — |
| 406 | C22×Q8 | — | 22 | 3 | no | — |
| 407 | C22×Q8 | — | 22 | 3 | no | — |
| 408 | C22×Q8 | D44 | 1 | 1 | yes | characteristic |
| 409 | C22×D4 | — | 11 | 3 | no | — |
| 410 | C22×D4 | — | 11 | 1 | no | — |
| 411 | C22×D4 | — | 22 | 3 | no | — |
| 412 | C22×D4 | — | 22 | 3 | no | — |
| 413 | C22×D4 | — | 22 | 3 | no | — |
| 414 | C22×D4 | D44 | 1 | 3 | yes | — |
| 415 | C23×C4 | — | 22 | 3 | no | — |
| 416 | C23×C4 | — | 22 | 3 | no | — |
| 417 | C23×C4 | C22×D11 | 1 | 3 | yes | — |
| 418 | #137 | — | 22 | 24 | no | — |
| 419 | AGL(1,ℤ/8) | — | 22 | 24 | no | — |
| 420 | #135 | — | 22 | 24 | no | — |
| 421 | C2×Q16 | — | 11 | 6 | no | — |
| 422 | C2×SD16 | — | 11 | 6 | no | — |
| 423 | C2×SD16 | — | 11 | 12 | no | — |
| 424 | C2×SD16 | — | 11 | 2 | no | — |
| 425 | C2×SD16 | — | 22 | 24 | no | — |
| 426 | C2×D8 | — | 11 | 6 | no | — |
| 427 | #131 | — | 2 | 8 | no | — |
| 428 | C2×M16 | C22×D11 | 1 | 6 | yes | — |
| 429 | C22×C8 | C22×D11 | 1 | 6 | yes | — |
| 430 | #127 | — | 22 | 3 | no | — |
| 431 | #124 | — | 22 | 3 | no | — |
| 432 | #123 | — | 22 | 3 | no | — |
| 433 | C22⋊Q8 | — | 11 | 1 | no | — |
| 434 | C22⋊Q8 | — | 11 | 3 | no | — |
| 435 | C22⋊Q8 | — | 22 | 3 | no | — |
| 436 | #121 | — | 11 | 3 | no | — |
| 437 | #121 | — | 11 | 6 | no | — |
| 438 | #121 | — | 11 | 3 | no | — |
| 439 | #121 | — | 22 | 6 | no | — |
| 440 | #121 | — | 22 | 3 | no | — |
| 441 | #121 | — | 22 | 3 | no | — |
| 442 | #121 | — | 22 | 3 | no | — |
| 443 | #120 | — | 22 | 3 | no | — |
| 444 | #120 | — | 22 | 6 | no | — |
| 445 | C4×Q8 | — | 22 | 1 | no | — |
| 446 | C4×D4 | — | 22 | 3 | no | — |
| 447 | C4×D4 | — | 22 | 3 | no | — |
| 448 | C4×D4 | — | 22 | 3 | no | — |
| 449 | #117 | — | 11 | 3 | no | — |
| 450 | C2×C4⋊C4 | — | 11 | 3 | no | — |
| 451 | C2×C22⋊C4 | — | 22 | 3 | no | — |
| 452 | #103 | — | 11 | 6 | no | — |
| 453 | #103 | — | 11 | 12 | no | — |
| 454 | #103 | — | 11 | 6 | no | — |
| 455 | #102 | — | 11 | 2 | no | — |
| 456 | #102 | — | 11 | 6 | no | — |
| 457 | C22⋊C8 | C22×D11 | 1 | 1 | yes | characteristic |
| 458 | C22⋊C8 | C22×D11 | 1 | 3 | yes | — |
| 459 | C22⋊C8 | C22×D11 | 1 | 6 | yes | — |
| 460 | C22⋊C8 | C22×D11 | 1 | 6 | yes | — |
| 461 | C2×C11 | — | 2 | 2 | no | — |
| 462 | C2×C11 | — | 2 | 6 | no | — |
| 463 | C2×C11 | — | 4 | 3 | no | — |
| 464 | C2×C11 | C22×#120 | 1 | 1 | yes | characteristic |
| 465 | C2×C11 | C2×#577 | 1 | 1 | yes | characteristic |
| 466 | C2×C11 | #3586 | 1 | 1 | yes | characteristic |
| 467 | D11 | — | 4 | 4 | no | — |
| 468 | D11 | — | 8 | 3 | no | — |
| 469 | C24 | — | 22 | 1 | no | — |
| 470 | C24 | — | 22 | 3 | no | — |
| 471 | C24 | C2×D44 | 1 | 3 | yes | — |
| 472 | #41 | — | 2 | 4 | no | — |
| 473 | #41 | — | 2 | 12 | no | — |
| 474 | #41 | — | 2 | 12 | no | — |
| 475 | #41 | — | 11 | 24 | no | — |
| 476 | #41 | — | 22 | 12 | no | — |
| 477 | #41 | — | 22 | 12 | no | — |
| 478 | #41 | — | 22 | 24 | no | — |
| 479 | #41 | — | 22 | 24 | no | — |
| 480 | #41 | — | 22 | 96 | no | — |
| 481 | #41 | — | 22 | 48 | no | — |
| 482 | #41 | — | 22 | 48 | no | — |
| 483 | #41 | — | 22 | 12 | no | — |
| 484 | #41 | — | 22 | 12 | no | — |
| 485 | #41 | — | 44 | 4 | no | — |
| 486 | #41 | D4×D11 | 1 | 8 | yes | — |
| 487 | C2×Q8 | — | 2 | 4 | no | — |
| 488 | C2×Q8 | — | 11 | 24 | no | — |
| 489 | C2×Q8 | — | 11 | 6 | no | — |
| 490 | C2×Q8 | — | 11 | 1 | no | — |
| 491 | C2×Q8 | — | 22 | 12 | no | — |
| 492 | C2×Q8 | — | 22 | 24 | no | — |
| 493 | C2×Q8 | — | 22 | 24 | no | — |
| 494 | C2×Q8 | — | 22 | 24 | no | — |
| 495 | C2×Q8 | — | 22 | 24 | no | — |
| 496 | C2×Q8 | — | 22 | 48 | no | — |
| 497 | C2×Q8 | — | 22 | 16 | no | — |
| 498 | C2×Q8 | — | 22 | 6 | no | — |
| 499 | C2×Q8 | — | 22 | 3 | no | — |
| 500 | C2×Q8 | — | 22 | 6 | no | — |
| 501 | C2×Q8 | — | 22 | 12 | no | — |
| 502 | C2×Q8 | C2×D44 | 1 | 3 | yes | — |
| 503 | C2×Q8 | C2×D44 | 1 | 1 | yes | characteristic |
| 504 | C2×D4 | — | 2 | 12 | no | — |
| 505 | C2×D4 | — | 11 | 2 | no | — |
| 506 | C2×D4 | — | 11 | 3 | no | — |
| 507 | C2×D4 | — | 22 | 4 | no | — |
| 508 | C2×D4 | — | 22 | 24 | no | — |
| 509 | C2×D4 | — | 22 | 6 | no | — |
| 510 | C2×D4 | — | 22 | 6 | no | — |
| 511 | C2×D4 | — | 22 | 3 | no | — |
| 512 | C2×D4 | — | 22 | 3 | no | — |
| 513 | C2×D4 | — | 22 | 3 | no | — |
| 514 | C2×D4 | — | 22 | 6 | no | — |
| 515 | C2×D4 | — | 22 | 1 | no | — |
| 516 | C2×D4 | — | 22 | 3 | no | — |
| 517 | C2×D4 | — | 22 | 12 | no | — |
| 518 | C2×D4 | — | 44 | 12 | no | — |
| 519 | C2×D4 | — | 88 | 6 | no | — |
| 520 | C2×D4 | C2×D44 | 1 | 6 | yes | — |
| 521 | C2×D4 | C2×D44 | 1 | 3 | yes | — |
| 522 | C2×D4 | C2×D44 | 1 | 3 | yes | — |
| 523 | C22×C4 | — | 2 | 12 | no | — |
| 524 | C22×C4 | — | 22 | 24 | no | — |
| 525 | C22×C4 | — | 22 | 24 | no | — |
| 526 | C22×C4 | — | 22 | 3 | no | — |
| 527 | C22×C4 | — | 22 | 6 | no | — |
| 528 | C22×C4 | — | 22 | 6 | no | — |
| 529 | C22×C4 | — | 22 | 6 | no | — |
| 530 | C22×C4 | — | 22 | 6 | no | — |
| 531 | C22×C4 | — | 22 | 3 | no | — |
| 532 | C22×C4 | — | 22 | 3 | no | — |
| 533 | C22×C4 | C2×D44 | 1 | 3 | yes | — |
| 534 | C22×C4 | C2×D44 | 1 | 3 | yes | — |
| 535 | C22×C4 | C2×D44 | 1 | 3 | yes | — |
| 536 | C22×C4 | C23×D11 | 1 | 1 | yes | characteristic |
| 537 | C22×C4 | C23×D11 | 1 | 3 | yes | — |
| 538 | C22×C4 | C23×D11 | 1 | 3 | yes | — |
| 539 | Q16 | — | 22 | 12 | no | — |
| 540 | SD16 | — | 22 | 4 | no | — |
| 541 | SD16 | — | 22 | 12 | no | — |
| 542 | SD16 | — | 22 | 24 | no | — |
| 543 | D8 | — | 22 | 12 | no | — |
| 544 | M16 | — | 2 | 12 | no | — |
| 545 | C2×C8 | — | 2 | 12 | no | — |
| 546 | C2×C8 | C23×D11 | 1 | 2 | yes | — |
| 547 | C2×C8 | C23×D11 | 1 | 6 | yes | — |
| 548 | C4⋊C4 | — | 11 | 3 | no | — |
| 549 | C4⋊C4 | — | 11 | 1 | no | — |
| 550 | C4⋊C4 | — | 22 | 3 | no | — |
| 551 | C4⋊C4 | — | 22 | 1 | no | — |
| 552 | C4⋊C4 | — | 22 | 3 | no | — |
| 553 | C22⋊C4 | — | 22 | 3 | no | — |
| 554 | C22⋊C4 | — | 22 | 1 | no | — |
| 555 | C22⋊C4 | — | 22 | 3 | no | — |
| 556 | C22⋊C4 | — | 22 | 3 | no | — |
| 557 | C22⋊C4 | — | 22 | 6 | no | — |
| 558 | C22⋊C4 | — | 22 | 3 | no | — |
| 559 | C42 | — | 22 | 3 | no | — |
| 560 | C11 | #60374 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 561 | C23 | — | 2 | 6 | no | — |
| 562 | C23 | — | 2 | 6 | no | — |
| 563 | C23 | — | 4 | 3 | no | — |
| 564 | C23 | — | 22 | 4 | no | — |
| 565 | C23 | — | 22 | 2 | no | — |
| 566 | C23 | — | 22 | 3 | no | — |
| 567 | C23 | — | 44 | 2 | no | — |
| 568 | C23 | — | 44 | 2 | no | — |
| 569 | C23 | — | 44 | 6 | no | — |
| 570 | C23 | — | 88 | 3 | no | — |
| 571 | C23 | — | 88 | 3 | no | — |
| 572 | C23 | C22×D44 | 1 | 3 | yes | — |
| 573 | C23 | C22×D44 | 1 | 3 | yes | — |
| 574 | C23 | C22×D44 | 1 | 1 | yes | characteristic |
| 575 | Q8 | — | 2 | 6 | no | — |
| 576 | Q8 | — | 11 | 12 | no | — |
| 577 | Q8 | — | 22 | 12 | no | — |
| 578 | Q8 | — | 22 | 24 | no | — |
| 579 | Q8 | — | 22 | 24 | no | — |
| 580 | Q8 | — | 22 | 6 | no | — |
| 581 | Q8 | — | 22 | 2 | no | — |
| 582 | Q8 | #66935 | 1 | 4 | yes | — |
| 583 | D4 | — | 2 | 12 | no | — |
| 584 | D4 | — | 2 | 6 | no | — |
| 585 | D4 | — | 11 | 4 | no | — |
| 586 | D4 | — | 22 | 4 | no | — |
| 587 | D4 | — | 22 | 24 | no | — |
| 588 | D4 | — | 22 | 24 | no | — |
| 589 | D4 | — | 22 | 2 | no | — |
| 590 | D4 | — | 22 | 6 | no | — |
| 591 | D4 | — | 44 | 6 | no | — |
| 592 | D4 | — | 44 | 6 | no | — |
| 593 | D4 | — | 44 | 6 | no | — |
| 594 | D4 | — | 88 | 6 | no | — |
| 595 | D4 | — | 88 | 3 | no | — |
| 596 | D4 | #66935 | 1 | 12 | yes | — |
| 597 | C2×C4 | — | 2 | 6 | no | — |
| 598 | C2×C4 | — | 2 | 6 | no | — |
| 599 | C2×C4 | — | 2 | 6 | no | — |
| 600 | C2×C4 | — | 2 | 2 | no | — |
| 601 | C2×C4 | — | 2 | 6 | no | — |
| 602 | C2×C4 | — | 22 | 24 | no | — |
| 603 | C2×C4 | — | 22 | 12 | no | — |
| 604 | C2×C4 | — | 22 | 24 | no | — |
| 605 | C2×C4 | — | 22 | 24 | no | — |
| 606 | C2×C4 | — | 22 | 6 | no | — |
| 607 | C2×C4 | — | 22 | 24 | no | — |
| 608 | C2×C4 | — | 22 | 1 | no | — |
| 609 | C2×C4 | — | 22 | 3 | no | — |
| 610 | C2×C4 | — | 22 | 1 | no | — |
| 611 | C2×C4 | — | 44 | 6 | no | — |
| 612 | C2×C4 | — | 88 | 3 | no | — |
| 613 | C2×C4 | C22×D44 | 1 | 3 | yes | — |
| 614 | C2×C4 | C22×D44 | 1 | 1 | yes | characteristic |
| 615 | C2×C4 | C22×D44 | 1 | 3 | yes | — |
| 616 | C2×C4 | C2×D4×D11 | 1 | 12 | yes | — |
| 617 | C2×C4 | C24×D11 | 1 | 1 | yes | characteristic |
| 618 | C8 | — | 2 | 2 | no | — |
| 619 | C8 | — | 2 | 6 | no | — |
| 620 | C22 | — | 2 | 1 | no | — |
| 621 | C22 | — | 2 | 3 | no | — |
| 622 | C22 | — | 2 | 1 | no | — |
| 623 | C22 | — | 2 | 3 | no | — |
| 624 | C22 | — | 2 | 3 | no | — |
| 625 | C22 | — | 2 | 3 | no | — |
| 626 | C22 | — | 2 | 3 | no | — |
| 627 | C22 | — | 4 | 12 | no | — |
| 628 | C22 | — | 22 | 4 | no | — |
| 629 | C22 | — | 44 | 8 | no | — |
| 630 | C22 | — | 44 | 2 | no | — |
| 631 | C22 | — | 44 | 2 | no | — |
| 632 | C22 | — | 44 | 3 | no | — |
| 633 | C22 | — | 44 | 3 | no | — |
| 634 | C22 | — | 44 | 3 | no | — |
| 635 | C22 | — | 176 | 6 | no | — |
| 636 | C22 | C2×#66935 | 1 | 6 | yes | — |
| 637 | C22 | #10623282 | 1 | 2 | yes | complemented |
| 638 | C22 | C23×D44 | 1 | 1 | yes | characteristic |
| 639 | C4 | — | 2 | 1 | no | — |
| 640 | C4 | — | 2 | 3 | no | — |
| 641 | C4 | — | 22 | 12 | no | — |
| 642 | C4 | — | 44 | 1 | no | — |
| 643 | C4 | — | 44 | 1 | no | — |
| 644 | C4 | — | 44 | 3 | no | — |
| 645 | C4 | C2×#66935 | 1 | 6 | yes | — |
| 646 | C4 | C22×D4×D11 | 1 | 2 | yes | — |
| 647 | C2 | — | 2 | 2 | no | — |
| 648 | C2 | — | 2 | 6 | no | — |
| 649 | C2 | — | 4 | 3 | no | — |
| 650 | C2 | — | 44 | 4 | no | — |
| 651 | C2 | — | 88 | 3 | no | — |
| 652 | C2 | C22×#66935 | 1 | 1 | yes | characteristic |
| 653 | C2 | C2×#10623282 | 1 | 1 | yes | characteristic |
| 654 | C2 | #13083404 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#67043 | C2 | semidirect |
| 2. C2×#10623282 | C2 | semidirect |
| 3. #13082285 | C2 | semidirect |
| 4. #13077934 | C2 | semidirect |
| 5. #13077904 | C2 | semidirect |
| 6. #13077870 | C2 | semidirect |
| 7. #13077853 | C2 | semidirect |
| 8. #13077838 | C2 | semidirect |
| 9. C2×#10622351 | C2 | semidirect |
| 10. #13077150 | C2 | semidirect |
| 11. C11×#2880 | C2 | semidirect |
| 17. C2×#67043 | C22 | semidirect |
| 18. C2×#67042 | C22 | semidirect |
| 21. C22×#4339 | C22 | semidirect |
| 22. C23×Dic22 | C22 | semidirect |
| 23. C2×C11×#131 | C22 | semidirect |
| 25. #10623364 | C22 | semidirect |
| 26. #10623361 | C22 | semidirect |
| 28. #10623358 | C22 | semidirect |
| 34. C2×#66962 | C22 | semidirect |
| 35. C2×#66961 | C22 | semidirect |
| 36. C2×#66957 | C22 | semidirect |
| 37. C22×#4314 | C22 | semidirect |
| 38. C11×#408 | C22 | semidirect |
| 39. C11×#407 | C22 | semidirect |
| 40. C2×C11×C22⋊C8 | C22 | semidirect |
| 41. #10622746 | C22 | semidirect |
| 42. #10622733 | C22 | semidirect |
| 43. #10622726 | C22 | semidirect |
| 44. C2×#66880 | C22 | semidirect |
| 45. #10622352 | C22 | semidirect |
| 46. #10622352 | C22 | semidirect |
| 47. #10622351 | C22 | semidirect |
| 48. #10622351 | C22 | semidirect |
| 49. #10622351 | C22 | semidirect |
| 50. #10622351 | C22 | semidirect |
| 51. #10622347 | C22 | semidirect |
| 52. #10622347 | C22 | semidirect |
| 53. #10622346 | C22 | semidirect |
| 54. #10622345 | C22 | semidirect |
| 55. #10622344 | C22 | semidirect |
| 72. #67043 | D4 | semidirect |
| 190. #4339 | C2×D4 | semidirect |
| 210. C2×Dic22 | C2×D4 | semidirect |
| 244. #2880 | D11 | semidirect |
| 320. C2×#131 | C2×D11 | semidirect |
| 345. #408 | C2×D11 | semidirect |
| 346. #407 | C2×D11 | semidirect |
| 347. C2×C22⋊C8 | C2×D11 | semidirect |
| 357. C22×C11 | #577 | semidirect |
| 560. C11 | #60374 | semidirect |
| 637. C22 | #10623282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67043 | 2 |
| C2×#10623282 | 2 |
| #13082285 | 2 |
| #13077934 | 2 |
| #13077904 | 2 |
| #13077870 | 2 |
| #13077853 | 2 |
| #13077838 | 2 |
| C2×#10622351 | 2 |
| #13077150 | 2 |
| C11×#2880 | 2 |
| #60374 | 11 |