Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
640 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #83363 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #83355 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #78530 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C3×#1986 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #69487 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #69469 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #67668 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10194 | — | 3 | 1 | no | maximal, Sylow |
| 9 | C3×#533 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#908 | — | 2 | 2 | no | — |
| 11 | #5477 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#874 | C22 | 1 | 1 | yes | characteristic |
| 13 | C3×C4×M16 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×C4×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 15 | #5088 | — | 2 | 1 | no | — |
| 16 | #5085 | — | 2 | 1 | no | — |
| 17 | #5084 | — | 2 | 1 | no | — |
| 18 | #5083 | — | 2 | 1 | no | — |
| 19 | #5048 | — | 2 | 2 | no | — |
| 20 | #5046 | — | 2 | 2 | no | — |
| 21 | #5027 | — | 2 | 2 | no | — |
| 22 | #5027 | — | 2 | 1 | no | — |
| 23 | #5020 | — | 2 | 1 | no | — |
| 24 | C2×#809 | — | 2 | 2 | no | — |
| 25 | #4925 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×C4⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 27 | #4712 | — | 2 | 2 | no | — |
| 28 | #4695 | — | 2 | 1 | no | — |
| 29 | #4693 | — | 2 | 1 | no | — |
| 30 | C3×#339 | — | 2 | 2 | no | — |
| 31 | #4451 | — | 2 | 2 | no | — |
| 32 | #3246 | — | 3 | 1 | no | — |
| 33 | #3208 | — | 3 | 1 | no | — |
| 34 | #3151 | — | 3 | 1 | no | — |
| 35 | #1986 | D3 | 1 | 1 | yes | characteristic, complemented |
| 36 | #1982 | — | 3 | 1 | no | — |
| 37 | #1502 | — | 3 | 1 | no | — |
| 38 | #1283 | — | 3 | 1 | no | — |
| 39 | C2×#235 | — | 2 | 1 | no | — |
| 40 | C22×D12 | — | 2 | 1 | no | — |
| 41 | C22×D12 | — | 2 | 1 | no | — |
| 42 | C22×D12 | — | 2 | 1 | no | — |
| 43 | C2×C3×M16 | D4 | 1 | 2 | yes | — |
| 44 | C3×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 45 | C3×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 46 | C3×#125 | — | 2 | 1 | no | — |
| 47 | C3×C22⋊Q8 | — | 2 | 1 | no | — |
| 48 | C3×C22⋊Q8 | — | 2 | 1 | no | — |
| 49 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 50 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 51 | C3×#117 | — | 2 | 1 | no | — |
| 52 | C2×C3×C4⋊C4 | — | 2 | 1 | no | — |
| 53 | C2×C3×C42 | — | 2 | 1 | no | — |
| 54 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 55 | C2×#215 | — | 2 | 4 | no | — |
| 56 | C2×#215 | — | 2 | 2 | no | — |
| 57 | #930 | — | 2 | 1 | no | — |
| 58 | #930 | — | 2 | 1 | no | — |
| 59 | C22×C3⋊C8 | D4 | 1 | 2 | yes | — |
| 60 | #908 | — | 4 | 4 | no | — |
| 61 | #908 | — | 4 | 4 | no | — |
| 62 | C2×D24 | — | 2 | 4 | no | — |
| 63 | C2×#204 | — | 2 | 4 | no | — |
| 64 | #875 | — | 2 | 1 | no | — |
| 65 | #874 | — | 2 | 1 | no | — |
| 66 | #874 | — | 2 | 1 | no | — |
| 67 | #874 | — | 2 | 1 | no | — |
| 68 | #874 | D4 | 1 | 1 | yes | characteristic |
| 69 | #874 | D4 | 1 | 2 | yes | — |
| 70 | C4×D12 | — | 2 | 1 | no | — |
| 71 | C4×D12 | — | 2 | 1 | no | — |
| 72 | #869 | D4 | 1 | 1 | yes | characteristic |
| 73 | C3×#97 | — | 2 | 1 | no | — |
| 74 | C3×C4×C8 | — | 2 | 1 | no | — |
| 75 | C3×#95 | — | 2 | 1 | no | — |
| 76 | #835 | — | 2 | 2 | no | — |
| 77 | #830 | D4 | 1 | 2 | yes | — |
| 78 | #809 | — | 2 | 4 | no | — |
| 79 | #809 | — | 2 | 2 | no | — |
| 80 | #809 | — | 4 | 4 | no | — |
| 81 | #808 | — | 2 | 2 | no | — |
| 82 | C4⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 83 | C4⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 84 | C4⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 85 | C4×C3⋊C8 | — | 2 | 1 | no | — |
| 86 | C2×AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 87 | #533 | C2×D3 | 1 | 1 | yes | characteristic |
| 88 | #532 | — | 3 | 1 | no | — |
| 89 | C2×#127 | — | 3 | 1 | no | — |
| 90 | #496 | — | 6 | 2 | no | — |
| 91 | #493 | — | 6 | 1 | no | — |
| 92 | #492 | — | 6 | 1 | no | — |
| 93 | #492 | — | 6 | 1 | no | — |
| 94 | #486 | — | 6 | 1 | no | — |
| 95 | #476 | — | 6 | 1 | no | — |
| 96 | #475 | — | 6 | 1 | no | — |
| 97 | #465 | — | 6 | 2 | no | — |
| 98 | #461 | — | 6 | 1 | no | — |
| 99 | #460 | — | 6 | 2 | no | — |
| 100 | #460 | — | 6 | 1 | no | — |
| 101 | #450 | — | 6 | 2 | no | — |
| 102 | #431 | — | 3 | 1 | no | — |
| 103 | C2×C4⋊C8 | — | 3 | 1 | no | — |
| 104 | C2×#102 | — | 6 | 2 | no | — |
| 105 | C4×M16 | C2×D3 | 1 | 1 | yes | characteristic |
| 106 | C4×C4⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 107 | #339 | — | 2 | 2 | no | — |
| 108 | #327 | — | 6 | 2 | no | — |
| 109 | C23×D3 | — | 4 | 1 | no | — |
| 110 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 111 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 112 | C22×C3×C4 | — | 4 | 1 | no | — |
| 113 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C2×#67 | — | 4 | 1 | no | — |
| 117 | #235 | — | 4 | 2 | no | — |
| 118 | #235 | — | 4 | 2 | no | — |
| 119 | C2×D12 | — | 2 | 1 | no | — |
| 120 | C2×D12 | — | 2 | 2 | no | — |
| 121 | C2×D12 | — | 2 | 2 | no | — |
| 122 | C2×D12 | — | 2 | 1 | no | — |
| 123 | C2×D12 | — | 2 | 2 | no | — |
| 124 | C2×D12 | — | 2 | 1 | no | — |
| 125 | C2×D12 | — | 4 | 2 | no | — |
| 126 | C2×D12 | — | 4 | 2 | no | — |
| 127 | C2×D12 | — | 4 | 2 | no | — |
| 128 | C2×D12 | — | 4 | 2 | no | — |
| 129 | C2×D12 | — | 4 | 1 | no | — |
| 130 | C2×D12 | — | 4 | 1 | no | — |
| 131 | C2×D12 | — | 4 | 1 | no | — |
| 132 | C2×D12 | — | 8 | 2 | no | — |
| 133 | C2×C4×D3 | — | 4 | 1 | no | — |
| 134 | C2×Dic6 | — | 2 | 1 | no | — |
| 135 | C3×M16 | — | 2 | 2 | no | — |
| 136 | C3×M16 | SD16 | 1 | 4 | yes | complemented |
| 137 | C2×C3×C8 | — | 2 | 2 | no | — |
| 138 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 139 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 140 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 141 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 142 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 143 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 144 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 145 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 146 | C3×C22⋊C4 | — | 4 | 1 | no | — |
| 147 | C3×C42 | — | 4 | 1 | no | — |
| 148 | C3×C42 | — | 4 | 2 | no | — |
| 149 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 150 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 151 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 152 | C3×C42 | #41 | 1 | 1 | yes | characteristic |
| 153 | #215 | — | 8 | 4 | no | — |
| 154 | #215 | — | 8 | 2 | no | — |
| 155 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 156 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 157 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 158 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 159 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 160 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 161 | C2×C3⋊C8 | — | 4 | 2 | no | — |
| 162 | D24 | — | 4 | 8 | no | — |
| 163 | #204 | — | 4 | 8 | no | — |
| 164 | C2×#41 | — | 6 | 1 | no | — |
| 165 | C22×D4 | — | 6 | 1 | no | — |
| 166 | C22×D4 | — | 6 | 1 | no | — |
| 167 | C22×D4 | — | 6 | 1 | no | — |
| 168 | AGL(1,ℤ/8) | — | 12 | 4 | no | — |
| 169 | AGL(1,ℤ/8) | — | 12 | 4 | no | — |
| 170 | C2×SD16 | — | 6 | 4 | no | — |
| 171 | C2×SD16 | — | 6 | 4 | no | — |
| 172 | C2×SD16 | — | 6 | 2 | no | — |
| 173 | C2×D8 | — | 6 | 4 | no | — |
| 174 | C2×M16 | #67 | 1 | 2 | yes | — |
| 175 | C22×C8 | — | 3 | 2 | no | — |
| 176 | C4⋊Q8 | — | 3 | 1 | no | — |
| 177 | C4⋊Q8 | D12 | 1 | 1 | yes | characteristic |
| 178 | C4⋊Q8 | D12 | 1 | 1 | yes | characteristic |
| 179 | #127 | — | 3 | 2 | no | — |
| 180 | #127 | — | 3 | 1 | no | — |
| 181 | #127 | — | 6 | 1 | no | — |
| 182 | #127 | — | 6 | 1 | no | — |
| 183 | #127 | — | 6 | 1 | no | — |
| 184 | #125 | — | 2 | 1 | no | — |
| 185 | #124 | — | 6 | 1 | no | — |
| 186 | C22⋊Q8 | — | 2 | 1 | no | — |
| 187 | C22⋊Q8 | — | 2 | 1 | no | — |
| 188 | #121 | — | 6 | 1 | no | — |
| 189 | #121 | — | 6 | 1 | no | — |
| 190 | C4×Q8 | — | 2 | 1 | no | — |
| 191 | C4×Q8 | — | 2 | 1 | no | — |
| 192 | C4×D4 | — | 6 | 1 | no | — |
| 193 | C4×D4 | — | 6 | 1 | no | — |
| 194 | #117 | — | 2 | 1 | no | — |
| 195 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 196 | C2×C42 | — | 2 | 1 | no | — |
| 197 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 198 | #106 | — | 6 | 2 | no | — |
| 199 | C4⋊C8 | — | 6 | 1 | no | — |
| 200 | C4⋊C8 | — | 6 | 1 | no | — |
| 201 | C4⋊C8 | — | 6 | 1 | no | — |
| 202 | #103 | — | 6 | 2 | no | — |
| 203 | #102 | — | 6 | 4 | no | — |
| 204 | #102 | — | 6 | 2 | no | — |
| 205 | #102 | — | 12 | 4 | no | — |
| 206 | C22⋊C8 | — | 3 | 2 | no | — |
| 207 | #97 | — | 2 | 1 | no | — |
| 208 | C4×C8 | — | 2 | 1 | no | — |
| 209 | C4×C8 | — | 6 | 1 | no | — |
| 210 | #95 | — | 2 | 1 | no | — |
| 211 | C23×C3 | #127 | 1 | 1 | yes | characteristic |
| 212 | C22×D3 | — | 4 | 1 | no | — |
| 213 | C22×D3 | — | 4 | 2 | no | — |
| 214 | C22×D3 | — | 8 | 2 | no | — |
| 215 | C22×D3 | — | 8 | 2 | no | — |
| 216 | C22×D3 | — | 8 | 1 | no | — |
| 217 | C22×D3 | — | 8 | 1 | no | — |
| 218 | C3×Q8 | — | 4 | 2 | no | — |
| 219 | C3×Q8 | — | 4 | 1 | no | — |
| 220 | C3×Q8 | — | 4 | 1 | no | — |
| 221 | C2×C3×C4 | — | 2 | 1 | no | — |
| 222 | C2×C3×C4 | — | 2 | 1 | no | — |
| 223 | C2×C3×C4 | — | 4 | 1 | no | — |
| 224 | C2×C3×C4 | — | 4 | 2 | no | — |
| 225 | C2×C3×C4 | — | 4 | 1 | no | — |
| 226 | C2×C3×C4 | — | 4 | 1 | no | — |
| 227 | C2×C3×C4 | — | 8 | 1 | no | — |
| 228 | C2×C3×C4 | — | 8 | 1 | no | — |
| 229 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 230 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 231 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 232 | C2×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 233 | C2×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 234 | C2×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 235 | C2×C3×C4 | C2×SD16 | 1 | 2 | yes | — |
| 236 | C2×C3×C4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 237 | #67 | — | 8 | 1 | no | — |
| 238 | #67 | — | 8 | 1 | no | — |
| 239 | C2×Dic3 | — | 4 | 1 | no | — |
| 240 | D12 | — | 4 | 4 | no | — |
| 241 | D12 | — | 4 | 4 | no | — |
| 242 | D12 | — | 4 | 4 | no | — |
| 243 | D12 | — | 4 | 2 | no | — |
| 244 | D12 | — | 4 | 1 | no | — |
| 245 | D12 | — | 4 | 1 | no | — |
| 246 | D12 | — | 8 | 1 | no | — |
| 247 | D12 | — | 8 | 2 | no | — |
| 248 | D12 | — | 8 | 1 | no | — |
| 249 | D12 | — | 8 | 1 | no | — |
| 250 | D12 | — | 8 | 2 | no | — |
| 251 | C4×D3 | — | 8 | 2 | no | — |
| 252 | Dic6 | — | 4 | 2 | no | — |
| 253 | C3×C8 | — | 2 | 4 | no | — |
| 254 | C3⋊C8 | — | 4 | 2 | no | — |
| 255 | C3⋊C8 | — | 4 | 2 | no | — |
| 256 | C24 | — | 12 | 1 | no | — |
| 257 | #41 | — | 12 | 2 | no | — |
| 258 | #41 | — | 12 | 2 | no | — |
| 259 | C2×Q8 | — | 2 | 1 | no | — |
| 260 | C2×Q8 | — | 2 | 1 | no | — |
| 261 | C2×Q8 | — | 6 | 1 | no | — |
| 262 | C2×D4 | — | 6 | 1 | no | — |
| 263 | C2×D4 | — | 6 | 2 | no | — |
| 264 | C2×D4 | — | 6 | 2 | no | — |
| 265 | C2×D4 | — | 6 | 1 | no | — |
| 266 | C2×D4 | — | 6 | 1 | no | — |
| 267 | C2×D4 | — | 6 | 2 | no | — |
| 268 | C2×D4 | — | 12 | 2 | no | — |
| 269 | C2×D4 | — | 12 | 2 | no | — |
| 270 | C2×D4 | — | 12 | 1 | no | — |
| 271 | C2×D4 | — | 12 | 1 | no | — |
| 272 | C2×D4 | — | 12 | 1 | no | — |
| 273 | C2×D4 | — | 12 | 1 | no | — |
| 274 | C2×D4 | — | 12 | 2 | no | — |
| 275 | C2×D4 | — | 12 | 2 | no | — |
| 276 | C2×D4 | — | 24 | 2 | no | — |
| 277 | C22×C4 | — | 4 | 1 | no | — |
| 278 | C22×C4 | — | 12 | 1 | no | — |
| 279 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 280 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 281 | C22×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 282 | SD16 | — | 12 | 8 | no | — |
| 283 | SD16 | — | 24 | 4 | no | — |
| 284 | SD16 | — | 24 | 2 | no | — |
| 285 | D8 | — | 12 | 8 | no | — |
| 286 | M16 | — | 2 | 2 | no | — |
| 287 | M16 | #215 | 1 | 4 | yes | complemented |
| 288 | C2×C8 | — | 2 | 2 | no | — |
| 289 | C2×C8 | — | 6 | 2 | no | — |
| 290 | C2×C8 | — | 6 | 2 | no | — |
| 291 | C2×C8 | — | 12 | 2 | no | — |
| 292 | C4⋊C4 | — | 2 | 2 | no | — |
| 293 | C4⋊C4 | — | 2 | 1 | no | — |
| 294 | C4⋊C4 | — | 2 | 1 | no | — |
| 295 | C4⋊C4 | — | 2 | 1 | no | — |
| 296 | C4⋊C4 | — | 2 | 1 | no | — |
| 297 | C4⋊C4 | — | 4 | 1 | no | — |
| 298 | C4⋊C4 | — | 4 | 1 | no | — |
| 299 | C4⋊C4 | — | 4 | 1 | no | — |
| 300 | C4⋊C4 | — | 6 | 1 | no | — |
| 301 | C4⋊C4 | — | 6 | 1 | no | — |
| 302 | C22⋊C4 | — | 4 | 1 | no | — |
| 303 | C22⋊C4 | — | 12 | 1 | no | — |
| 304 | C22⋊C4 | — | 12 | 1 | no | — |
| 305 | C42 | — | 4 | 1 | no | — |
| 306 | C42 | — | 4 | 2 | no | — |
| 307 | C42 | C2×D12 | 1 | 1 | yes | characteristic |
| 308 | C42 | #235 | 1 | 1 | yes | characteristic |
| 309 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 310 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 311 | C22×C3 | — | 2 | 1 | no | — |
| 312 | C22×C3 | — | 2 | 1 | no | — |
| 313 | C22×C3 | #392 | 1 | 1 | yes | characteristic |
| 314 | C22×C3 | #492 | 1 | 1 | yes | characteristic |
| 315 | C22×C3 | #496 | 1 | 1 | yes | characteristic |
| 316 | C2×D3 | — | 8 | 2 | no | — |
| 317 | C2×D3 | — | 8 | 1 | no | — |
| 318 | C2×D3 | — | 8 | 2 | no | — |
| 319 | C2×D3 | — | 8 | 1 | no | — |
| 320 | C2×D3 | — | 8 | 1 | no | — |
| 321 | C2×D3 | — | 8 | 2 | no | — |
| 322 | C2×D3 | — | 16 | 2 | no | — |
| 323 | C2×D3 | — | 16 | 2 | no | — |
| 324 | C3×C4 | — | 2 | 1 | no | — |
| 325 | C3×C4 | — | 2 | 1 | no | — |
| 326 | C3×C4 | — | 2 | 1 | no | — |
| 327 | C3×C4 | — | 8 | 2 | no | — |
| 328 | C3×C4 | — | 8 | 1 | no | — |
| 329 | C3×C4 | — | 8 | 1 | no | — |
| 330 | C3×C4 | #450 | 1 | 2 | yes | — |
| 331 | C3×C4 | #453 | 1 | 1 | yes | characteristic |
| 332 | C3×C4 | #454 | 1 | 1 | yes | characteristic |
| 333 | C3×C4 | #460 | 1 | 2 | yes | — |
| 334 | Dic3 | — | 8 | 1 | no | — |
| 335 | C23 | — | 12 | 1 | no | — |
| 336 | C23 | — | 12 | 2 | no | — |
| 337 | C23 | — | 24 | 2 | no | — |
| 338 | C23 | — | 24 | 2 | no | — |
| 339 | C23 | — | 24 | 1 | no | — |
| 340 | C23 | — | 24 | 1 | no | — |
| 341 | C23 | #940 | 1 | 1 | yes | characteristic |
| 342 | Q8 | — | 4 | 2 | no | — |
| 343 | Q8 | — | 4 | 1 | no | — |
| 344 | Q8 | — | 4 | 1 | no | — |
| 345 | Q8 | — | 12 | 2 | no | — |
| 346 | D4 | — | 12 | 4 | no | — |
| 347 | D4 | — | 12 | 4 | no | — |
| 348 | D4 | — | 12 | 2 | no | — |
| 349 | D4 | — | 12 | 4 | no | — |
| 350 | D4 | — | 12 | 1 | no | — |
| 351 | D4 | — | 12 | 1 | no | — |
| 352 | D4 | — | 24 | 1 | no | — |
| 353 | D4 | — | 24 | 2 | no | — |
| 354 | D4 | — | 24 | 1 | no | — |
| 355 | D4 | — | 24 | 1 | no | — |
| 356 | D4 | — | 24 | 2 | no | — |
| 357 | D4 | — | 24 | 1 | no | — |
| 358 | D4 | — | 24 | 1 | no | — |
| 359 | C2×C4 | — | 2 | 1 | no | — |
| 360 | C2×C4 | — | 2 | 1 | no | — |
| 361 | C2×C4 | — | 4 | 1 | no | — |
| 362 | C2×C4 | — | 4 | 2 | no | — |
| 363 | C2×C4 | — | 4 | 1 | no | — |
| 364 | C2×C4 | — | 4 | 1 | no | — |
| 365 | C2×C4 | — | 8 | 1 | no | — |
| 366 | C2×C4 | — | 8 | 1 | no | — |
| 367 | C2×C4 | — | 12 | 1 | no | — |
| 368 | C2×C4 | — | 24 | 2 | no | — |
| 369 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 370 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 371 | C2×C4 | #884 | 1 | 1 | yes | characteristic |
| 372 | C2×C4 | #884 | 1 | 1 | yes | characteristic |
| 373 | C2×C4 | #930 | 1 | 1 | yes | characteristic |
| 374 | C2×C4 | #937 | 1 | 1 | yes | characteristic |
| 375 | C2×C4 | C2×#215 | 1 | 2 | yes | — |
| 376 | C2×C4 | #949 | 1 | 2 | yes | — |
| 377 | C8 | — | 2 | 4 | no | — |
| 378 | C8 | — | 12 | 2 | no | — |
| 379 | C8 | — | 12 | 2 | no | — |
| 380 | C2×C3 | — | 2 | 1 | no | — |
| 381 | C2×C3 | — | 2 | 1 | no | — |
| 382 | C2×C3 | #2006 | 1 | 1 | yes | characteristic |
| 383 | C2×C3 | #2008 | 1 | 1 | yes | characteristic |
| 384 | C2×C3 | #2014 | 1 | 1 | yes | characteristic |
| 385 | D3 | — | 16 | 1 | no | — |
| 386 | D3 | — | 16 | 2 | no | — |
| 387 | C22 | — | 2 | 1 | no | — |
| 388 | C22 | — | 2 | 1 | no | — |
| 389 | C22 | — | 24 | 2 | no | — |
| 390 | C22 | — | 24 | 1 | no | — |
| 391 | C22 | — | 24 | 1 | no | — |
| 392 | C22 | — | 24 | 2 | no | — |
| 393 | C22 | — | 24 | 2 | no | — |
| 394 | C22 | — | 24 | 1 | no | — |
| 395 | C22 | — | 48 | 2 | no | — |
| 396 | C22 | — | 48 | 2 | no | — |
| 397 | C22 | #4960 | 1 | 1 | yes | characteristic |
| 398 | C22 | #5058 | 1 | 1 | yes | characteristic |
| 399 | C22 | #5085 | 1 | 1 | yes | characteristic |
| 400 | C4 | — | 2 | 1 | no | — |
| 401 | C4 | — | 2 | 1 | no | — |
| 402 | C4 | — | 2 | 1 | no | — |
| 403 | C4 | — | 8 | 2 | no | — |
| 404 | C4 | — | 8 | 1 | no | — |
| 405 | C4 | — | 8 | 1 | no | — |
| 406 | C4 | — | 24 | 1 | no | — |
| 407 | C4 | #4822 | 1 | 1 | yes | characteristic |
| 408 | C4 | #4827 | 1 | 1 | yes | characteristic |
| 409 | C4 | #5027 | 1 | 2 | yes | — |
| 410 | C4 | #5046 | 1 | 2 | yes | — |
| 411 | C3 | #10194 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 412 | C2 | — | 2 | 1 | no | — |
| 413 | C2 | — | 2 | 1 | no | — |
| 414 | C2 | — | 48 | 2 | no | — |
| 415 | C2 | — | 48 | 1 | no | — |
| 416 | C2 | #69688 | 1 | 1 | yes | characteristic |
| 417 | C2 | #70392 | 1 | 1 | yes | characteristic |
| 418 | C2 | #70409 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #83363 | C2 | semidirect |
| 2. #83355 | C2 | semidirect |
| 4. C3×#1986 | C2 | semidirect |
| 5. #69487 | C2 | semidirect |
| 6. #69469 | C2 | semidirect |
| 7. #67668 | C2 | semidirect |
| 35. #1986 | D3 | semidirect |
| 136. C3×M16 | SD16 | semidirect |
| 287. M16 | #215 | semidirect |
| 411. C3 | #10194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83363 | 2 |
| #83355 | 2 |
| #78530 | 2 |
| C3×#1986 | 2 |
| #69487 | 2 |
| #69469 | 2 |
| #67668 | 2 |
| #10194 | 3 |