Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
919 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 919 conjugacy classes of subgroups — too many to draw. Only its 123 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 | #3503⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #85431 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | Q8×#226 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #85424 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #85414 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #85365 | C2 | 1 | 2 | yes | maximal |
| 7 | #85363 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C4×#985 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #85337 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #61373 | — | 3 | 1 | no | maximal, Sylow |
| 11 | C2×#985 | C22 | 1 | 1 | yes | characteristic |
| 12 | #5728 | — | 4 | 1 | no | maximal |
| 13 | Q8×SL(2,𝔽3) | C22 | 1 | 2 | yes | — |
| 14 | #557⋊C3 | C22 | 1 | 2 | yes | — |
| 15 | #520⋊C3 | C22 | 1 | 2 | yes | — |
| 16 | C4×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 17 | #5426 | C22 | 1 | 2 | yes | — |
| 18 | #5424 | C22 | 1 | 1 | yes | characteristic |
| 19 | #5394 | C22 | 1 | 4 | yes | — |
| 20 | C4×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 21 | C4×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 22 | #5391 | C22 | 1 | 2 | yes | — |
| 23 | #5391 | C22 | 1 | 4 | yes | — |
| 24 | #5389 | C22 | 1 | 4 | yes | — |
| 25 | C4×#226 | C22 | 1 | 1 | yes | characteristic |
| 26 | C4×#226 | C22 | 1 | 1 | yes | characteristic |
| 27 | C4×#226 | C22 | 1 | 4 | yes | — |
| 28 | #5386 | C22 | 1 | 2 | yes | — |
| 29 | #3503 | — | 3 | 1 | no | — |
| 30 | #3503 | D3 | 1 | 1 | yes | characteristic, complemented |
| 31 | #3386 | — | 3 | 2 | no | — |
| 32 | #3386 | — | 3 | 2 | no | — |
| 33 | #3385 | — | 3 | 2 | no | — |
| 34 | #3385 | — | 3 | 2 | no | — |
| 35 | #3383 | — | 3 | 2 | no | — |
| 36 | Q8×Q16 | — | 3 | 2 | no | — |
| 37 | #3380 | — | 3 | 2 | no | — |
| 38 | Q8×D8 | — | 3 | 2 | no | — |
| 39 | #3164 | — | 3 | 2 | no | — |
| 40 | C2×#500 | — | 3 | 1 | no | — |
| 41 | #3083 | — | 3 | 2 | no | — |
| 42 | #3083 | — | 3 | 2 | no | — |
| 43 | #3079 | — | 3 | 1 | no | — |
| 44 | #3079 | — | 3 | 1 | no | — |
| 45 | #2960 | — | 3 | 1 | no | — |
| 46 | #2951 | — | 3 | 2 | no | — |
| 47 | C4×#135 | — | 3 | 1 | no | — |
| 48 | C2×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 49 | #985 | Q8 | 1 | 4 | yes | complemented |
| 50 | C2×GL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 51 | C2×#226 | C23 | 1 | 1 | yes | characteristic |
| 52 | C3×C4⋊Q8 | — | 4 | 1 | no | — |
| 53 | #946 | — | 4 | 2 | no | — |
| 54 | Q8×Dic3 | — | 4 | 2 | no | — |
| 55 | #897 | — | 4 | 2 | no | — |
| 56 | #892 | — | 4 | 2 | no | — |
| 57 | #890 | — | 4 | 2 | no | — |
| 58 | #887 | — | 4 | 2 | no | — |
| 59 | C42×D3 | — | 4 | 1 | no | — |
| 60 | #869 | — | 4 | 1 | no | — |
| 61 | C4×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 62 | C4×SL(2,𝔽3) | C23 | 1 | 4 | yes | — |
| 63 | C4×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 64 | #859 | C23 | 1 | 4 | yes | — |
| 65 | #859 | C23 | 1 | 1 | yes | characteristic |
| 66 | #859 | C23 | 1 | 1 | yes | characteristic |
| 67 | C2×#135 | — | 3 | 1 | no | — |
| 68 | Q82 | — | 3 | 2 | no | — |
| 69 | Q82 | C2×D3 | 1 | 2 | yes | — |
| 70 | #557 | — | 3 | 2 | no | — |
| 71 | #557 | C2×D3 | 1 | 2 | yes | — |
| 72 | #554 | — | 3 | 2 | no | — |
| 73 | #554 | — | 3 | 2 | no | — |
| 74 | #554 | — | 6 | 2 | no | — |
| 75 | D4×Q8 | — | 3 | 2 | no | — |
| 76 | D4×Q8 | — | 3 | 2 | no | — |
| 77 | D4×Q8 | — | 6 | 2 | no | — |
| 78 | #544 | — | 3 | 2 | no | — |
| 79 | #544 | — | 3 | 2 | no | — |
| 80 | #544 | — | 6 | 2 | no | — |
| 81 | #533 | — | 3 | 1 | no | — |
| 82 | #533 | — | 6 | 1 | no | — |
| 83 | C2×C4⋊Q8 | — | 3 | 1 | no | — |
| 84 | C2×C4⋊Q8 | — | 3 | 1 | no | — |
| 85 | C2×C4⋊Q8 | — | 6 | 1 | no | — |
| 86 | #520 | — | 3 | 2 | no | — |
| 87 | #520 | C2×D3 | 1 | 2 | yes | — |
| 88 | C4×#41 | — | 3 | 1 | no | — |
| 89 | C4×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 90 | #501 | — | 3 | 4 | no | — |
| 91 | #501 | — | 3 | 4 | no | — |
| 92 | #500 | — | 3 | 4 | no | — |
| 93 | #500 | — | 3 | 2 | no | — |
| 94 | #500 | — | 3 | 2 | no | — |
| 95 | #500 | — | 3 | 2 | no | — |
| 96 | #500 | — | 3 | 2 | no | — |
| 97 | #499 | — | 3 | 4 | no | — |
| 98 | #479 | — | 3 | 4 | no | — |
| 99 | #479 | — | 3 | 4 | no | — |
| 100 | #478 | — | 3 | 4 | no | — |
| 101 | #478 | — | 3 | 4 | no | — |
| 102 | #477 | — | 3 | 2 | no | — |
| 103 | #477 | — | 3 | 4 | no | — |
| 104 | #477 | — | 3 | 2 | no | — |
| 105 | #477 | — | 3 | 4 | no | — |
| 106 | #476 | — | 3 | 2 | no | — |
| 107 | #476 | — | 3 | 2 | no | — |
| 108 | #475 | — | 3 | 2 | no | — |
| 109 | #475 | — | 3 | 2 | no | — |
| 110 | #474 | — | 3 | 2 | no | — |
| 111 | #474 | — | 3 | 2 | no | — |
| 112 | #474 | — | 3 | 4 | no | — |
| 113 | #474 | — | 3 | 4 | no | — |
| 114 | #446 | — | 3 | 2 | no | — |
| 115 | #446 | — | 3 | 2 | no | — |
| 116 | C8×Q8 | — | 3 | 2 | no | — |
| 117 | C8×Q8 | — | 3 | 2 | no | — |
| 118 | #440 | — | 3 | 4 | no | — |
| 119 | #440 | — | 3 | 4 | no | — |
| 120 | C4×Q16 | — | 3 | 1 | no | — |
| 121 | C4×Q16 | — | 3 | 4 | no | — |
| 122 | C4×Q16 | — | 3 | 1 | no | — |
| 123 | C4×SD16 | — | 3 | 1 | no | — |
| 124 | C4×SD16 | — | 3 | 1 | no | — |
| 125 | C4×SD16 | — | 3 | 1 | no | — |
| 126 | C4×SD16 | — | 3 | 1 | no | — |
| 127 | C4×D8 | — | 3 | 1 | no | — |
| 128 | C4×D8 | — | 3 | 4 | no | — |
| 129 | C4×D8 | — | 3 | 1 | no | — |
| 130 | #428 | — | 3 | 2 | no | — |
| 131 | #428 | — | 3 | 2 | no | — |
| 132 | #427 | — | 3 | 1 | no | — |
| 133 | C2×#107 | — | 3 | 2 | no | — |
| 134 | C2×#107 | — | 3 | 2 | no | — |
| 135 | #424 | — | 3 | 2 | no | — |
| 136 | #423 | — | 3 | 1 | no | — |
| 137 | #417 | — | 3 | 2 | no | — |
| 138 | #417 | — | 3 | 2 | no | — |
| 139 | #416 | — | 3 | 1 | no | — |
| 140 | #416 | — | 3 | 1 | no | — |
| 141 | #405 | — | 3 | 2 | no | — |
| 142 | C2×C4×C8 | — | 3 | 1 | no | — |
| 143 | C2×C3×Q8 | — | 4 | 2 | no | — |
| 144 | C2×C4×D3 | — | 4 | 1 | no | — |
| 145 | C2×C4×D3 | — | 4 | 1 | no | — |
| 146 | C2×C4×D3 | — | 4 | 1 | no | — |
| 147 | C2×Dic6 | — | 4 | 2 | no | — |
| 148 | #41⋊C3 | C2×Q8 | 1 | 2 | yes | complemented |
| 149 | C2×SL(2,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 150 | GL(2,𝔽3) | C2×Q8 | 1 | 2 | yes | complemented |
| 151 | #226 | C2×Q8 | 1 | 2 | yes | complemented |
| 152 | C3×C4⋊C4 | — | 4 | 2 | no | — |
| 153 | C3×C4⋊C4 | — | 4 | 2 | no | — |
| 154 | C3×C42 | — | 4 | 1 | no | — |
| 155 | (C2×D3)⋊C4 | — | 4 | 4 | no | — |
| 156 | C4⋊Dic3 | — | 4 | 2 | no | — |
| 157 | C4⋊Dic3 | — | 4 | 4 | no | — |
| 158 | C4⋊Dic3 | — | 4 | 2 | no | — |
| 159 | Dic3⋊C4 | — | 4 | 4 | no | — |
| 160 | C4×Dic3 | — | 4 | 1 | no | — |
| 161 | C4×Dic3 | — | 4 | 1 | no | — |
| 162 | C4×Dic3 | — | 4 | 4 | no | — |
| 163 | C4×Dic3 | — | 4 | 1 | no | — |
| 164 | C2×#41 | — | 3 | 1 | no | — |
| 165 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 166 | C22×Q8 | — | 6 | 1 | no | — |
| 167 | C22×Q8 | — | 6 | 1 | no | — |
| 168 | C22×Q8 | — | 6 | 2 | no | — |
| 169 | #135 | — | 3 | 4 | no | — |
| 170 | #135 | — | 3 | 4 | no | — |
| 171 | C2×Q16 | — | 3 | 1 | no | — |
| 172 | C2×SD16 | — | 3 | 1 | no | — |
| 173 | C2×SD16 | — | 3 | 1 | no | — |
| 174 | C2×D8 | — | 3 | 1 | no | — |
| 175 | C2×M16 | — | 3 | 2 | no | — |
| 176 | C22×C8 | — | 3 | 1 | no | — |
| 177 | C22×C8 | — | 3 | 1 | no | — |
| 178 | C4⋊Q8 | — | 3 | 2 | no | — |
| 179 | C4⋊Q8 | — | 3 | 4 | no | — |
| 180 | C4⋊Q8 | — | 3 | 2 | no | — |
| 181 | C4⋊Q8 | — | 3 | 2 | no | — |
| 182 | C4⋊Q8 | — | 3 | 2 | no | — |
| 183 | C4⋊Q8 | — | 3 | 4 | no | — |
| 184 | C4⋊Q8 | — | 3 | 1 | no | — |
| 185 | C4⋊Q8 | — | 6 | 1 | no | — |
| 186 | C4⋊Q8 | — | 6 | 1 | no | — |
| 187 | C4⋊Q8 | — | 6 | 2 | no | — |
| 188 | C4⋊Q8 | — | 6 | 2 | no | — |
| 189 | C4⋊Q8 | — | 6 | 4 | no | — |
| 190 | C4⋊Q8 | — | 6 | 2 | no | — |
| 191 | C4⋊Q8 | — | 6 | 1 | no | — |
| 192 | C4⋊Q8 | S4 | 1 | 1 | yes | characteristic |
| 193 | #125 | — | 3 | 2 | no | — |
| 194 | #125 | — | 3 | 4 | no | — |
| 195 | #125 | — | 3 | 4 | no | — |
| 196 | #125 | — | 6 | 4 | no | — |
| 197 | #125 | — | 6 | 2 | no | — |
| 198 | C22⋊Q8 | — | 3 | 2 | no | — |
| 199 | C22⋊Q8 | — | 3 | 2 | no | — |
| 200 | C22⋊Q8 | — | 6 | 4 | no | — |
| 201 | C22⋊Q8 | — | 6 | 4 | no | — |
| 202 | C22⋊Q8 | — | 6 | 4 | no | — |
| 203 | C22⋊Q8 | — | 6 | 4 | no | — |
| 204 | C22⋊Q8 | — | 6 | 2 | no | — |
| 205 | C22⋊Q8 | — | 6 | 2 | no | — |
| 206 | C4×Q8 | — | 3 | 2 | no | — |
| 207 | C4×Q8 | — | 3 | 2 | no | — |
| 208 | C4×Q8 | — | 3 | 1 | no | — |
| 209 | C4×Q8 | — | 3 | 1 | no | — |
| 210 | C4×Q8 | — | 3 | 4 | no | — |
| 211 | C4×Q8 | — | 6 | 2 | no | — |
| 212 | C4×Q8 | — | 6 | 2 | no | — |
| 213 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 214 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 215 | C4×Q8 | C22×D3 | 1 | 4 | yes | — |
| 216 | C4×D4 | — | 3 | 4 | no | — |
| 217 | C4×D4 | — | 3 | 1 | no | — |
| 218 | C4×D4 | — | 3 | 1 | no | — |
| 219 | C4×D4 | — | 3 | 1 | no | — |
| 220 | C4×D4 | — | 3 | 1 | no | — |
| 221 | C4×D4 | — | 3 | 4 | no | — |
| 222 | C4×D4 | — | 6 | 4 | no | — |
| 223 | C4×D4 | — | 6 | 1 | no | — |
| 224 | C4×D4 | — | 6 | 1 | no | — |
| 225 | #117 | — | 3 | 2 | no | — |
| 226 | #117 | — | 3 | 1 | no | — |
| 227 | #117 | — | 3 | 1 | no | — |
| 228 | #117 | — | 6 | 1 | no | — |
| 229 | #117 | — | 6 | 2 | no | — |
| 230 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 231 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 232 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 233 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 234 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 235 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 236 | C2×C42 | — | 3 | 1 | no | — |
| 237 | C2×C42 | — | 6 | 1 | no | — |
| 238 | #107 | — | 3 | 4 | no | — |
| 239 | #107 | — | 3 | 4 | no | — |
| 240 | #107 | — | 3 | 4 | no | — |
| 241 | #107 | — | 3 | 4 | no | — |
| 242 | #107 | — | 3 | 1 | no | — |
| 243 | #107 | — | 3 | 1 | no | — |
| 244 | #107 | — | 3 | 4 | no | — |
| 245 | #107 | — | 3 | 4 | no | — |
| 246 | #106 | — | 3 | 1 | no | — |
| 247 | #106 | — | 3 | 1 | no | — |
| 248 | #106 | — | 3 | 4 | no | — |
| 249 | #106 | — | 3 | 4 | no | — |
| 250 | C4⋊C8 | — | 3 | 2 | no | — |
| 251 | C4⋊C8 | — | 3 | 2 | no | — |
| 252 | C4⋊C8 | — | 3 | 4 | no | — |
| 253 | C4⋊C8 | — | 3 | 4 | no | — |
| 254 | #103 | — | 3 | 1 | no | — |
| 255 | #103 | — | 3 | 1 | no | — |
| 256 | #103 | — | 3 | 4 | no | — |
| 257 | #103 | — | 3 | 1 | no | — |
| 258 | #103 | — | 3 | 1 | no | — |
| 259 | #103 | — | 3 | 4 | no | — |
| 260 | #102 | — | 3 | 1 | no | — |
| 261 | #102 | — | 3 | 1 | no | — |
| 262 | #102 | — | 3 | 1 | no | — |
| 263 | #102 | — | 3 | 1 | no | — |
| 264 | #102 | — | 3 | 4 | no | — |
| 265 | #102 | — | 3 | 4 | no | — |
| 266 | #97 | — | 3 | 4 | no | — |
| 267 | C4×C8 | — | 3 | 1 | no | — |
| 268 | C4×C8 | — | 3 | 1 | no | — |
| 269 | C4×C8 | — | 3 | 1 | no | — |
| 270 | C4×C8 | — | 3 | 1 | no | — |
| 271 | C4×C8 | — | 3 | 4 | no | — |
| 272 | C22×D3 | — | 4 | 1 | no | — |
| 273 | C3×Q8 | — | 8 | 4 | no | — |
| 274 | C2×C3×C4 | — | 4 | 1 | no | — |
| 275 | C2×C3×C4 | — | 4 | 1 | no | — |
| 276 | C2×C3×C4 | — | 4 | 1 | no | — |
| 277 | C2×C3×C4 | — | 4 | 4 | no | — |
| 278 | C2×Dic3 | — | 4 | 1 | no | — |
| 279 | C2×Dic3 | — | 4 | 1 | no | — |
| 280 | C2×Dic3 | — | 4 | 1 | no | — |
| 281 | C2×Dic3 | — | 4 | 4 | no | — |
| 282 | C4×D3 | — | 4 | 4 | no | — |
| 283 | C4×D3 | — | 8 | 2 | no | — |
| 284 | C4×D3 | — | 8 | 2 | no | — |
| 285 | Dic6 | — | 8 | 4 | no | — |
| 286 | SL(2,𝔽3) | C22×Q8 | 1 | 1 | yes | characteristic |
| 287 | #41 | — | 3 | 2 | no | — |
| 288 | #41 | — | 3 | 4 | no | — |
| 289 | #41 | — | 6 | 2 | no | — |
| 290 | #41 | D3×Q8 | 1 | 2 | yes | — |
| 291 | C2×Q8 | — | 3 | 2 | no | — |
| 292 | C2×Q8 | — | 3 | 1 | no | — |
| 293 | C2×Q8 | — | 6 | 2 | no | — |
| 294 | C2×Q8 | — | 6 | 2 | no | — |
| 295 | C2×Q8 | — | 6 | 4 | no | — |
| 296 | C2×Q8 | — | 6 | 2 | no | — |
| 297 | C2×Q8 | — | 24 | 2 | no | — |
| 298 | C2×Q8 | — | 24 | 2 | no | — |
| 299 | C2×Q8 | — | 24 | 4 | no | — |
| 300 | C2×Q8 | C2×S4 | 1 | 2 | yes | — |
| 301 | C2×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 302 | C2×D4 | — | 3 | 1 | no | — |
| 303 | C2×D4 | — | 3 | 1 | no | — |
| 304 | C2×D4 | — | 6 | 1 | no | — |
| 305 | C22×C4 | — | 3 | 1 | no | — |
| 306 | C22×C4 | — | 3 | 1 | no | — |
| 307 | C22×C4 | — | 3 | 1 | no | — |
| 308 | C22×C4 | — | 6 | 2 | no | — |
| 309 | C22×C4 | — | 6 | 4 | no | — |
| 310 | C22×C4 | — | 6 | 1 | no | — |
| 311 | C22×C4 | — | 6 | 2 | no | — |
| 312 | C22×C4 | — | 6 | 1 | no | — |
| 313 | C22×C4 | — | 6 | 1 | no | — |
| 314 | Q16 | — | 3 | 2 | no | — |
| 315 | Q16 | — | 3 | 2 | no | — |
| 316 | SD16 | — | 3 | 4 | no | — |
| 317 | SD16 | — | 3 | 2 | no | — |
| 318 | SD16 | — | 3 | 2 | no | — |
| 319 | D8 | — | 3 | 4 | no | — |
| 320 | M16 | — | 6 | 4 | no | — |
| 321 | C2×C8 | — | 3 | 1 | no | — |
| 322 | C2×C8 | — | 3 | 1 | no | — |
| 323 | C2×C8 | — | 3 | 4 | no | — |
| 324 | C2×C8 | — | 3 | 1 | no | — |
| 325 | C2×C8 | — | 3 | 1 | no | — |
| 326 | C2×C8 | — | 3 | 4 | no | — |
| 327 | C2×C8 | — | 6 | 2 | no | — |
| 328 | C4⋊C4 | — | 3 | 1 | no | — |
| 329 | C4⋊C4 | — | 3 | 4 | no | — |
| 330 | C4⋊C4 | — | 3 | 1 | no | — |
| 331 | C4⋊C4 | — | 3 | 2 | no | — |
| 332 | C4⋊C4 | — | 3 | 2 | no | — |
| 333 | C4⋊C4 | — | 3 | 4 | no | — |
| 334 | C4⋊C4 | — | 3 | 4 | no | — |
| 335 | C4⋊C4 | — | 3 | 1 | no | — |
| 336 | C4⋊C4 | — | 3 | 4 | no | — |
| 337 | C4⋊C4 | — | 3 | 1 | no | — |
| 338 | C4⋊C4 | — | 6 | 2 | no | — |
| 339 | C4⋊C4 | — | 6 | 4 | no | — |
| 340 | C4⋊C4 | — | 6 | 4 | no | — |
| 341 | C4⋊C4 | — | 6 | 2 | no | — |
| 342 | C4⋊C4 | — | 6 | 1 | no | — |
| 343 | C4⋊C4 | — | 6 | 1 | no | — |
| 344 | C4⋊C4 | — | 6 | 2 | no | — |
| 345 | C4⋊C4 | — | 6 | 2 | no | — |
| 346 | C4⋊C4 | — | 6 | 4 | no | — |
| 347 | C4⋊C4 | — | 6 | 4 | no | — |
| 348 | C4⋊C4 | C2×S4 | 1 | 2 | yes | — |
| 349 | C4⋊C4 | C2×S4 | 1 | 2 | yes | — |
| 350 | C22⋊C4 | — | 3 | 4 | no | — |
| 351 | C22⋊C4 | — | 6 | 1 | no | — |
| 352 | C22⋊C4 | — | 6 | 1 | no | — |
| 353 | C22⋊C4 | — | 6 | 1 | no | — |
| 354 | C22⋊C4 | — | 6 | 1 | no | — |
| 355 | C22⋊C4 | — | 6 | 4 | no | — |
| 356 | C42 | — | 3 | 1 | no | — |
| 357 | C42 | — | 3 | 1 | no | — |
| 358 | C42 | — | 3 | 4 | no | — |
| 359 | C42 | — | 3 | 1 | no | — |
| 360 | C42 | — | 6 | 1 | no | — |
| 361 | C42 | — | 6 | 1 | no | — |
| 362 | C42 | — | 6 | 1 | no | — |
| 363 | C42 | — | 6 | 4 | no | — |
| 364 | C42 | C2×S4 | 1 | 1 | yes | characteristic |
| 365 | C22×C3 | — | 4 | 1 | no | — |
| 366 | C2×D3 | — | 4 | 2 | no | — |
| 367 | C2×D3 | — | 8 | 1 | no | — |
| 368 | C2×D3 | — | 8 | 1 | no | — |
| 369 | C3×C4 | — | 4 | 2 | no | — |
| 370 | C3×C4 | — | 4 | 2 | no | — |
| 371 | C3×C4 | — | 4 | 2 | no | — |
| 372 | C3×C4 | — | 8 | 4 | no | — |
| 373 | Dic3 | — | 4 | 2 | no | — |
| 374 | Dic3 | — | 8 | 4 | no | — |
| 375 | Dic3 | — | 8 | 1 | no | — |
| 376 | Dic3 | — | 8 | 1 | no | — |
| 377 | C23 | — | 3 | 1 | no | — |
| 378 | C23 | — | 6 | 1 | no | — |
| 379 | Q8 | — | 2 | 4 | no | — |
| 380 | Q8 | — | 3 | 1 | no | — |
| 381 | Q8 | — | 3 | 2 | no | — |
| 382 | Q8 | — | 6 | 1 | no | — |
| 383 | Q8 | — | 6 | 4 | no | — |
| 384 | Q8 | — | 12 | 4 | no | — |
| 385 | Q8 | — | 24 | 2 | no | — |
| 386 | Q8 | — | 24 | 2 | no | — |
| 387 | Q8 | — | 24 | 4 | no | — |
| 388 | Q8 | C2×D3×Q8 | 1 | 1 | yes | characteristic |
| 389 | D4 | — | 3 | 2 | no | — |
| 390 | D4 | — | 3 | 2 | no | — |
| 391 | D4 | — | 6 | 1 | no | — |
| 392 | D4 | — | 6 | 1 | no | — |
| 393 | D4 | — | 6 | 4 | no | — |
| 394 | C2×C4 | — | 3 | 1 | no | — |
| 395 | C2×C4 | — | 3 | 2 | no | — |
| 396 | C2×C4 | — | 3 | 2 | no | — |
| 397 | C2×C4 | — | 3 | 1 | no | — |
| 398 | C2×C4 | — | 3 | 1 | no | — |
| 399 | C2×C4 | — | 3 | 4 | no | — |
| 400 | C2×C4 | — | 6 | 1 | no | — |
| 401 | C2×C4 | — | 6 | 4 | no | — |
| 402 | C2×C4 | — | 6 | 2 | no | — |
| 403 | C2×C4 | — | 6 | 2 | no | — |
| 404 | C2×C4 | — | 6 | 1 | no | — |
| 405 | C2×C4 | — | 6 | 1 | no | — |
| 406 | C2×C4 | — | 6 | 4 | no | — |
| 407 | C2×C4 | — | 12 | 2 | no | — |
| 408 | C2×C4 | — | 12 | 2 | no | — |
| 409 | C2×C4 | — | 24 | 2 | no | — |
| 410 | C2×C4 | — | 24 | 4 | no | — |
| 411 | C2×C4 | — | 24 | 2 | no | — |
| 412 | C2×C4 | C22×S4 | 1 | 4 | yes | — |
| 413 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 414 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 415 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 416 | C8 | — | 3 | 2 | no | — |
| 417 | C8 | — | 3 | 2 | no | — |
| 418 | C8 | — | 6 | 1 | no | — |
| 419 | C8 | — | 6 | 1 | no | — |
| 420 | C8 | — | 6 | 4 | no | — |
| 421 | C2×C3 | — | 4 | 1 | no | — |
| 422 | C2×C3 | — | 4 | 1 | no | — |
| 423 | C2×C3 | — | 4 | 1 | no | — |
| 424 | D3 | — | 8 | 2 | no | — |
| 425 | C22 | — | 3 | 2 | no | — |
| 426 | C22 | — | 6 | 1 | no | — |
| 427 | C22 | — | 6 | 1 | no | — |
| 428 | C22 | — | 6 | 2 | no | — |
| 429 | C22 | — | 12 | 1 | no | — |
| 430 | C22 | — | 12 | 1 | no | — |
| 431 | C22 | C23×S4 | 1 | 1 | yes | characteristic |
| 432 | C4 | — | 2 | 4 | no | — |
| 433 | C4 | — | 3 | 1 | no | — |
| 434 | C4 | — | 3 | 1 | no | — |
| 435 | C4 | — | 6 | 2 | no | — |
| 436 | C4 | — | 6 | 1 | no | — |
| 437 | C4 | — | 6 | 4 | no | — |
| 438 | C4 | — | 6 | 1 | no | — |
| 439 | C4 | — | 12 | 1 | no | — |
| 440 | C4 | — | 12 | 4 | no | — |
| 441 | C4 | — | 12 | 1 | no | — |
| 442 | C4 | Q8×S4 | 1 | 2 | yes | — |
| 443 | C4 | #5925 | 1 | 2 | yes | — |
| 444 | C4 | #5927 | 1 | 2 | yes | — |
| 445 | C3 | — | 4 | 1 | no | Sylow |
| 446 | C2 | — | 6 | 2 | no | — |
| 447 | C2 | — | 12 | 2 | no | — |
| 448 | C2 | C2×Q8×S4 | 1 | 1 | yes | characteristic |
| 449 | C2 | C2×#5925 | 1 | 1 | yes | characteristic |
| 450 | C2 | C2×#5927 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3503⋊C3 | C2 | semidirect |
| 2. #85431 | C2 | semidirect |
| 3. Q8×#226 | C2 | semidirect |
| 4. #85424 | C2 | semidirect |
| 5. #85414 | C2 | semidirect |
| 7. #85363 | C2 | semidirect |
| 9. #85337 | C2 | semidirect |
| 30. #3503 | D3 | semidirect |
| 49. #985 | Q8 | semidirect |
| 148. #41⋊C3 | C2×Q8 | semidirect |
| 150. GL(2,𝔽3) | C2×Q8 | semidirect |
| 151. #226 | C2×Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3503⋊C3 | 2 |
| #85431 | 2 |
| Q8×#226 | 2 |
| #85424 | 2 |
| #85414 | 2 |
| #85365 | 2 |
| #85363 | 2 |
| C4×#985 | 2 |
| #85337 | 2 |
| #61373 | 3 |
| #5728 | 4 |