Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
684 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 83 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 | #83357 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #83336 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #73431 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C3×#1506 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #70818 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #70804 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #67615 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10096 | — | 3 | 1 | no | maximal, Sylow |
| 9 | C3×#533 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#875 | — | 2 | 1 | no | — |
| 11 | C2×#875 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#874 | — | 2 | 1 | no | — |
| 13 | C2×#874 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×#432 | C22 | 1 | 1 | yes | characteristic |
| 15 | C3×#376 | C22 | 1 | 1 | yes | characteristic |
| 16 | #5089 | — | 2 | 1 | no | — |
| 17 | #5088 | — | 2 | 1 | no | — |
| 18 | #5088 | — | 2 | 1 | no | — |
| 19 | #5086 | — | 2 | 1 | no | — |
| 20 | #5067 | — | 2 | 2 | no | — |
| 21 | #5050 | — | 2 | 1 | no | — |
| 22 | #5046 | — | 2 | 1 | no | — |
| 23 | #5028 | — | 2 | 2 | no | — |
| 24 | #5001 | — | 2 | 2 | no | — |
| 25 | #4926 | C22 | 1 | 1 | yes | characteristic |
| 26 | C4×#208 | C22 | 1 | 1 | yes | characteristic |
| 27 | #4671 | — | 2 | 2 | no | — |
| 28 | #4671 | — | 2 | 2 | no | — |
| 29 | C3×#328 | — | 2 | 2 | no | — |
| 30 | #4485 | — | 2 | 2 | no | — |
| 31 | #4464 | — | 2 | 2 | no | — |
| 32 | #3215 | — | 3 | 1 | no | — |
| 33 | #3138 | — | 3 | 1 | no | — |
| 34 | #2657 | — | 3 | 1 | no | — |
| 35 | #1555 | — | 3 | 1 | no | — |
| 36 | #1527 | — | 3 | 1 | no | — |
| 37 | #1506 | D3 | 1 | 1 | yes | characteristic, complemented |
| 38 | #1300 | — | 3 | 1 | no | — |
| 39 | C22×D12 | — | 2 | 1 | no | — |
| 40 | C22×D12 | — | 2 | 4 | no | — |
| 41 | C22×D12 | — | 2 | 1 | no | — |
| 42 | C22×D12 | D4 | 1 | 2 | yes | — |
| 43 | C22×D12 | D4 | 1 | 1 | yes | characteristic |
| 44 | C22×Dic6 | D4 | 1 | 1 | yes | characteristic |
| 45 | C3×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic, complemented |
| 46 | C3×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic, complemented |
| 47 | C3×#125 | — | 2 | 1 | no | — |
| 48 | C3×C22⋊Q8 | — | 2 | 1 | no | — |
| 49 | C3×C22⋊Q8 | — | 2 | 1 | no | — |
| 50 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 51 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 52 | C3×#117 | — | 2 | 1 | no | — |
| 53 | C2×C3×C42 | — | 2 | 1 | no | — |
| 54 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 55 | C2×#216 | — | 2 | 2 | no | — |
| 56 | C2×#215 | — | 2 | 2 | no | — |
| 57 | C2×(C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 58 | C2×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 59 | C2×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 60 | C2×#208 | — | 2 | 1 | no | — |
| 61 | #875 | — | 2 | 1 | no | — |
| 62 | #875 | — | 2 | 1 | no | — |
| 63 | #875 | — | 2 | 1 | no | — |
| 64 | #875 | — | 2 | 1 | no | — |
| 65 | #875 | — | 4 | 4 | no | — |
| 66 | #874 | — | 2 | 1 | no | — |
| 67 | #874 | — | 2 | 1 | no | — |
| 68 | #874 | — | 2 | 1 | no | — |
| 69 | #874 | — | 2 | 1 | no | — |
| 70 | #874 | — | 4 | 4 | no | — |
| 71 | C3×C4⋊C8 | — | 2 | 1 | no | — |
| 72 | C3×C22⋊C8 | — | 2 | 1 | no | — |
| 73 | C3×#97 | — | 2 | 1 | no | — |
| 74 | C3×#95 | — | 2 | 1 | no | — |
| 75 | C3×#95 | D4 | 1 | 2 | yes | — |
| 76 | #830 | — | 2 | 1 | no | — |
| 77 | #810 | — | 2 | 2 | no | — |
| 78 | #809 | — | 2 | 4 | no | — |
| 79 | #809 | — | 2 | 4 | no | — |
| 80 | #809 | — | 2 | 2 | no | — |
| 81 | C4⋊(C3⋊C8) | D4 | 1 | 2 | yes | complemented |
| 82 | #803 | — | 2 | 1 | no | — |
| 83 | #803 | D4 | 1 | 2 | yes | complemented |
| 84 | C4×C3⋊C8 | — | 2 | 1 | no | — |
| 85 | #533 | C2×D3 | 1 | 1 | yes | characteristic |
| 86 | C2×#127 | — | 3 | 1 | no | — |
| 87 | C2×#127 | — | 6 | 1 | no | — |
| 88 | C2×#124 | — | 3 | 1 | no | — |
| 89 | C2×#124 | — | 6 | 1 | no | — |
| 90 | #497 | — | 6 | 1 | no | — |
| 91 | #490 | — | 6 | 2 | no | — |
| 92 | #489 | — | 6 | 1 | no | — |
| 93 | #486 | — | 6 | 1 | no | — |
| 94 | #486 | — | 6 | 1 | no | — |
| 95 | #464 | — | 6 | 2 | no | — |
| 96 | #451 | — | 6 | 1 | no | — |
| 97 | #450 | — | 6 | 1 | no | — |
| 98 | #432 | — | 3 | 1 | no | — |
| 99 | #432 | C2×D3 | 1 | 1 | yes | characteristic |
| 100 | #418 | — | 6 | 2 | no | — |
| 101 | C4×M16 | — | 3 | 1 | no | — |
| 102 | #392 | — | 6 | 2 | no | — |
| 103 | #392 | — | 6 | 2 | no | — |
| 104 | #376 | C2×D3 | 1 | 1 | yes | characteristic |
| 105 | #331 | — | 6 | 2 | no | — |
| 106 | #329 | — | 6 | 2 | no | — |
| 107 | #328 | — | 2 | 2 | no | — |
| 108 | C23×D3 | — | 2 | 2 | no | — |
| 109 | C23×D3 | — | 2 | 1 | no | — |
| 110 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 111 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 112 | C22×C3×C4 | — | 2 | 2 | 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 | C22×Dic3 | — | 2 | 1 | no | — |
| 117 | C2×D12 | — | 2 | 2 | no | — |
| 118 | C2×D12 | — | 2 | 1 | no | — |
| 119 | C2×D12 | — | 2 | 2 | no | — |
| 120 | C2×D12 | — | 2 | 1 | no | — |
| 121 | C2×D12 | — | 4 | 4 | no | — |
| 122 | C2×D12 | — | 4 | 2 | no | — |
| 123 | C2×D12 | — | 4 | 2 | no | — |
| 124 | C2×D12 | — | 4 | 8 | no | — |
| 125 | C2×D12 | — | 4 | 2 | no | — |
| 126 | C2×D12 | — | 4 | 1 | no | — |
| 127 | C2×D12 | — | 4 | 1 | no | — |
| 128 | C2×D12 | — | 4 | 1 | no | — |
| 129 | C2×D12 | — | 4 | 1 | no | — |
| 130 | C2×D12 | — | 8 | 2 | no | — |
| 131 | C2×D12 | — | 8 | 4 | no | — |
| 132 | C2×D12 | — | 8 | 4 | no | — |
| 133 | C2×Dic6 | — | 2 | 1 | no | — |
| 134 | C2×Dic6 | — | 2 | 1 | no | — |
| 135 | C2×Dic6 | — | 4 | 2 | no | — |
| 136 | C2×C3×C8 | — | 4 | 1 | no | — |
| 137 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 138 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 139 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 140 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 141 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 142 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 143 | C3×C22⋊C4 | — | 4 | 1 | no | — |
| 144 | C3×C42 | — | 2 | 4 | no | — |
| 145 | C3×C42 | — | 4 | 1 | no | — |
| 146 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 147 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 149 | C3×C42 | #41 | 1 | 1 | yes | characteristic |
| 150 | #216 | — | 8 | 2 | no | — |
| 151 | #215 | — | 8 | 2 | no | — |
| 152 | (C2×D3)⋊C4 | — | 4 | 8 | no | — |
| 153 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 154 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 155 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 156 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 157 | #208 | — | 4 | 2 | no | — |
| 158 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 159 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 160 | C22×Q8 | — | 3 | 1 | no | — |
| 161 | C22×D4 | — | 3 | 1 | no | — |
| 162 | C22×D4 | — | 3 | 2 | no | — |
| 163 | C22×D4 | — | 6 | 4 | no | — |
| 164 | C22×D4 | — | 6 | 1 | no | — |
| 165 | C22×D4 | — | 6 | 1 | no | — |
| 166 | C2×Q16 | — | 6 | 2 | no | — |
| 167 | C2×SD16 | — | 6 | 2 | no | — |
| 168 | C2×M16 | — | 6 | 1 | no | — |
| 169 | C4⋊Q8 | D12 | 1 | 1 | yes | characteristic, complemented |
| 170 | C4⋊Q8 | D12 | 1 | 1 | yes | characteristic, complemented |
| 171 | #127 | — | 6 | 1 | no | — |
| 172 | #127 | — | 6 | 1 | no | — |
| 173 | #127 | — | 6 | 1 | no | — |
| 174 | #127 | — | 6 | 1 | no | — |
| 175 | #127 | — | 12 | 4 | no | — |
| 176 | #125 | — | 2 | 1 | no | — |
| 177 | #124 | — | 6 | 1 | no | — |
| 178 | #124 | — | 6 | 1 | no | — |
| 179 | #124 | — | 6 | 1 | no | — |
| 180 | #124 | — | 6 | 1 | no | — |
| 181 | #124 | — | 12 | 4 | no | — |
| 182 | C22⋊Q8 | — | 2 | 1 | no | — |
| 183 | C22⋊Q8 | — | 2 | 1 | no | — |
| 184 | C4×Q8 | — | 2 | 1 | no | — |
| 185 | C4×Q8 | — | 2 | 1 | no | — |
| 186 | #117 | — | 2 | 1 | no | — |
| 187 | C2×C22⋊C4 | — | 6 | 4 | no | — |
| 188 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 189 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 190 | C2×C42 | — | 2 | 1 | no | — |
| 191 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 192 | C4⋊C8 | — | 2 | 1 | no | — |
| 193 | C4⋊C8 | — | 3 | 2 | no | — |
| 194 | #103 | — | 6 | 2 | no | — |
| 195 | #102 | — | 6 | 4 | no | — |
| 196 | #102 | — | 6 | 4 | no | — |
| 197 | #102 | — | 6 | 2 | no | — |
| 198 | C22⋊C8 | — | 2 | 1 | no | — |
| 199 | C22⋊C8 | — | 6 | 1 | no | — |
| 200 | #97 | — | 2 | 1 | no | — |
| 201 | #97 | — | 3 | 2 | no | — |
| 202 | #97 | — | 6 | 1 | no | — |
| 203 | C4×C8 | — | 6 | 1 | no | — |
| 204 | #95 | — | 2 | 1 | no | — |
| 205 | #95 | #67 | 1 | 2 | yes | — |
| 206 | C23×C3 | #120 | 1 | 1 | yes | characteristic |
| 207 | C22×D3 | — | 4 | 2 | no | — |
| 208 | C22×D3 | — | 4 | 2 | no | — |
| 209 | C22×D3 | — | 4 | 2 | no | — |
| 210 | C22×D3 | — | 4 | 2 | no | — |
| 211 | C22×D3 | — | 4 | 4 | no | — |
| 212 | C22×D3 | — | 4 | 1 | no | — |
| 213 | C22×D3 | — | 4 | 2 | no | — |
| 214 | C22×D3 | — | 4 | 4 | no | — |
| 215 | C22×D3 | — | 4 | 2 | no | — |
| 216 | C3×Q8 | — | 4 | 2 | no | — |
| 217 | C3×Q8 | — | 8 | 1 | no | — |
| 218 | C2×C3×C4 | — | 2 | 2 | no | — |
| 219 | C2×C3×C4 | — | 2 | 2 | no | — |
| 220 | C2×C3×C4 | — | 2 | 4 | no | — |
| 221 | C2×C3×C4 | — | 4 | 1 | no | — |
| 222 | C2×C3×C4 | — | 4 | 2 | no | — |
| 223 | C2×C3×C4 | — | 4 | 2 | no | — |
| 224 | C2×C3×C4 | — | 4 | 1 | no | — |
| 225 | C2×C3×C4 | — | 4 | 1 | no | — |
| 226 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 227 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 228 | C2×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 229 | C2×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 230 | C2×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 231 | C2×C3×C4 | #127 | 1 | 1 | yes | characteristic |
| 232 | C2×Dic3 | — | 4 | 2 | no | — |
| 233 | C2×Dic3 | — | 4 | 1 | no | — |
| 234 | D12 | — | 4 | 4 | no | — |
| 235 | D12 | — | 4 | 2 | no | — |
| 236 | D12 | — | 8 | 1 | no | — |
| 237 | D12 | — | 8 | 2 | no | — |
| 238 | D12 | — | 8 | 2 | no | — |
| 239 | D12 | — | 8 | 2 | no | — |
| 240 | D12 | — | 8 | 2 | no | — |
| 241 | D12 | — | 8 | 16 | no | — |
| 242 | D12 | — | 8 | 2 | no | — |
| 243 | Dic6 | — | 4 | 2 | no | — |
| 244 | Dic6 | — | 8 | 1 | no | — |
| 245 | C3×C8 | — | 8 | 1 | no | — |
| 246 | C3⋊C8 | — | 4 | 2 | no | — |
| 247 | C3⋊C8 | — | 4 | 2 | no | — |
| 248 | C24 | — | 6 | 2 | no | — |
| 249 | C24 | — | 6 | 1 | no | — |
| 250 | C2×Q8 | — | 2 | 1 | no | — |
| 251 | C2×Q8 | — | 2 | 1 | no | — |
| 252 | C2×Q8 | — | 6 | 1 | no | — |
| 253 | C2×Q8 | — | 6 | 1 | no | — |
| 254 | C2×Q8 | — | 12 | 2 | no | — |
| 255 | C2×D4 | — | 6 | 2 | no | — |
| 256 | C2×D4 | — | 6 | 1 | no | — |
| 257 | C2×D4 | — | 6 | 1 | no | — |
| 258 | C2×D4 | — | 6 | 2 | no | — |
| 259 | C2×D4 | — | 12 | 4 | no | — |
| 260 | C2×D4 | — | 12 | 2 | no | — |
| 261 | C2×D4 | — | 12 | 2 | no | — |
| 262 | C2×D4 | — | 12 | 2 | no | — |
| 263 | C2×D4 | — | 12 | 8 | no | — |
| 264 | C2×D4 | — | 12 | 1 | no | — |
| 265 | C2×D4 | — | 12 | 1 | no | — |
| 266 | C2×D4 | — | 12 | 1 | no | — |
| 267 | C2×D4 | — | 12 | 1 | no | — |
| 268 | C2×D4 | — | 24 | 2 | no | — |
| 269 | C2×D4 | — | 24 | 4 | no | — |
| 270 | C2×D4 | — | 24 | 4 | no | — |
| 271 | C22×C4 | — | 2 | 2 | no | — |
| 272 | C22×C4 | — | 6 | 1 | no | — |
| 273 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 274 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 275 | C22×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 276 | Q16 | — | 24 | 2 | no | — |
| 277 | SD16 | — | 24 | 2 | no | — |
| 278 | M16 | — | 12 | 2 | no | — |
| 279 | C2×C8 | — | 4 | 1 | no | — |
| 280 | C2×C8 | — | 6 | 2 | no | — |
| 281 | C2×C8 | — | 6 | 2 | no | — |
| 282 | C4⋊C4 | — | 2 | 1 | no | — |
| 283 | C4⋊C4 | — | 2 | 1 | no | — |
| 284 | C4⋊C4 | — | 2 | 1 | no | — |
| 285 | C4⋊C4 | — | 2 | 1 | no | — |
| 286 | C4⋊C4 | — | 4 | 1 | no | — |
| 287 | C4⋊C4 | — | 4 | 1 | no | — |
| 288 | C22⋊C4 | — | 4 | 1 | no | — |
| 289 | C22⋊C4 | — | 12 | 8 | no | — |
| 290 | C22⋊C4 | — | 12 | 1 | no | — |
| 291 | C22⋊C4 | — | 12 | 1 | no | — |
| 292 | C22⋊C4 | — | 12 | 1 | no | — |
| 293 | C22⋊C4 | — | 12 | 1 | no | — |
| 294 | C42 | — | 2 | 4 | no | — |
| 295 | C42 | — | 4 | 1 | no | — |
| 296 | C42 | C2×D12 | 1 | 1 | yes | characteristic |
| 297 | C42 | #235 | 1 | 1 | yes | characteristic |
| 298 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 299 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 300 | C22×C3 | — | 2 | 1 | no | — |
| 301 | C22×C3 | — | 2 | 1 | no | — |
| 302 | C22×C3 | #392 | 1 | 1 | yes | characteristic |
| 303 | C22×C3 | #455 | 1 | 2 | yes | — |
| 304 | C2×D3 | — | 8 | 4 | no | — |
| 305 | C2×D3 | — | 8 | 4 | no | — |
| 306 | C2×D3 | — | 8 | 4 | no | — |
| 307 | C2×D3 | — | 8 | 1 | no | — |
| 308 | C2×D3 | — | 8 | 2 | no | — |
| 309 | C2×D3 | — | 8 | 2 | no | — |
| 310 | C2×D3 | — | 8 | 1 | no | — |
| 311 | C2×D3 | — | 8 | 2 | no | — |
| 312 | C2×D3 | — | 8 | 1 | no | — |
| 313 | C3×C4 | — | 2 | 1 | no | — |
| 314 | C3×C4 | — | 2 | 1 | no | — |
| 315 | C3×C4 | — | 2 | 1 | no | — |
| 316 | C3×C4 | — | 2 | 1 | no | — |
| 317 | C3×C4 | — | 2 | 1 | no | — |
| 318 | C3×C4 | — | 4 | 4 | no | — |
| 319 | C3×C4 | — | 8 | 1 | no | — |
| 320 | C3×C4 | — | 8 | 1 | no | — |
| 321 | C3×C4 | #453 | 1 | 2 | yes | — |
| 322 | Dic3 | — | 8 | 1 | no | — |
| 323 | C23 | — | 12 | 2 | no | — |
| 324 | C23 | — | 12 | 2 | no | — |
| 325 | C23 | — | 12 | 2 | no | — |
| 326 | C23 | — | 12 | 2 | no | — |
| 327 | C23 | — | 12 | 4 | no | — |
| 328 | C23 | — | 12 | 4 | no | — |
| 329 | C23 | — | 12 | 2 | no | — |
| 330 | C23 | — | 12 | 1 | no | — |
| 331 | C23 | — | 12 | 2 | no | — |
| 332 | C23 | #937 | 1 | 1 | yes | characteristic |
| 333 | Q8 | — | 4 | 2 | no | — |
| 334 | Q8 | — | 8 | 1 | no | — |
| 335 | Q8 | — | 12 | 2 | no | — |
| 336 | Q8 | — | 24 | 1 | no | — |
| 337 | D4 | — | 12 | 4 | no | — |
| 338 | D4 | — | 12 | 2 | no | — |
| 339 | D4 | — | 24 | 2 | no | — |
| 340 | D4 | — | 24 | 1 | no | — |
| 341 | D4 | — | 24 | 2 | no | — |
| 342 | D4 | — | 24 | 2 | no | — |
| 343 | D4 | — | 24 | 2 | no | — |
| 344 | D4 | — | 24 | 16 | no | — |
| 345 | D4 | — | 24 | 2 | no | — |
| 346 | C2×C4 | — | 2 | 2 | no | — |
| 347 | C2×C4 | — | 2 | 2 | no | — |
| 348 | C2×C4 | — | 2 | 4 | no | — |
| 349 | C2×C4 | — | 4 | 1 | no | — |
| 350 | C2×C4 | — | 4 | 2 | no | — |
| 351 | C2×C4 | — | 4 | 2 | no | — |
| 352 | C2×C4 | — | 4 | 1 | no | — |
| 353 | C2×C4 | — | 4 | 1 | no | — |
| 354 | C2×C4 | — | 12 | 2 | no | — |
| 355 | C2×C4 | — | 12 | 1 | no | — |
| 356 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 357 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 358 | C2×C4 | #884 | 1 | 1 | yes | characteristic |
| 359 | C2×C4 | #884 | 1 | 1 | yes | characteristic |
| 360 | C2×C4 | #930 | 1 | 1 | yes | characteristic |
| 361 | C2×C4 | #940 | 1 | 1 | yes | characteristic |
| 362 | C8 | — | 8 | 1 | no | — |
| 363 | C8 | — | 12 | 2 | no | — |
| 364 | C8 | — | 12 | 2 | no | — |
| 365 | C2×C3 | — | 2 | 2 | no | — |
| 366 | C2×C3 | #2002 | 1 | 1 | yes | characteristic |
| 367 | C2×C3 | #2004 | 1 | 1 | yes | characteristic |
| 368 | C2×C3 | #2008 | 1 | 1 | yes | characteristic |
| 369 | D3 | — | 16 | 1 | no | — |
| 370 | D3 | — | 16 | 2 | no | — |
| 371 | C22 | — | 2 | 1 | no | — |
| 372 | C22 | — | 2 | 1 | no | — |
| 373 | C22 | — | 24 | 4 | no | — |
| 374 | C22 | — | 24 | 4 | no | — |
| 375 | C22 | — | 24 | 4 | no | — |
| 376 | C22 | — | 24 | 2 | no | — |
| 377 | C22 | — | 24 | 1 | no | — |
| 378 | C22 | — | 24 | 2 | no | — |
| 379 | C22 | — | 24 | 1 | no | — |
| 380 | C22 | — | 24 | 1 | no | — |
| 381 | C22 | — | 24 | 2 | no | — |
| 382 | C22 | #4960 | 1 | 1 | yes | characteristic |
| 383 | C22 | #5202 | 1 | 2 | yes | — |
| 384 | C4 | — | 2 | 1 | no | — |
| 385 | C4 | — | 2 | 1 | no | — |
| 386 | C4 | — | 2 | 1 | no | — |
| 387 | C4 | — | 2 | 1 | no | — |
| 388 | C4 | — | 2 | 1 | no | — |
| 389 | C4 | — | 4 | 4 | no | — |
| 390 | C4 | — | 8 | 1 | no | — |
| 391 | C4 | — | 8 | 1 | no | — |
| 392 | C4 | — | 24 | 1 | no | — |
| 393 | C4 | #4822 | 1 | 2 | yes | — |
| 394 | C3 | #10096 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 395 | C2 | — | 2 | 2 | no | — |
| 396 | C2 | — | 48 | 1 | no | — |
| 397 | C2 | — | 48 | 2 | no | — |
| 398 | C2 | #70050 | 1 | 1 | yes | characteristic |
| 399 | C2 | #70344 | 1 | 1 | yes | characteristic |
| 400 | C2 | #70385 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #83357 | C2 | semidirect |
| 2. #83336 | C2 | semidirect |
| 4. C3×#1506 | C2 | semidirect |
| 5. #70818 | C2 | semidirect |
| 6. #70804 | C2 | semidirect |
| 7. #67615 | C2 | semidirect |
| 37. #1506 | D3 | semidirect |
| 45. C3×C4⋊Q8 | D4 | semidirect |
| 46. C3×C4⋊Q8 | D4 | semidirect |
| 81. C4⋊(C3⋊C8) | D4 | semidirect |
| 83. #803 | D4 | semidirect |
| 169. C4⋊Q8 | D12 | semidirect |
| 170. C4⋊Q8 | D12 | semidirect |
| 394. C3 | #10096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83357 | 2 |
| #83336 | 2 |
| #73431 | 2 |
| C3×#1506 | 2 |
| #70818 | 2 |
| #70804 | 2 |
| #67615 | 2 |
| #10096 | 3 |