Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
550 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 61 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 | A4×#1368 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72342686 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72342674 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #72225020 | — | 3 | 1 | no | maximal, Sylow |
| 5 | #11714191 | C4 | 1 | 1 | yes | characteristic |
| 6 | #11712861 | — | 2 | 1 | no | — |
| 7 | #11711655 | — | 2 | 1 | no | — |
| 8 | #11711600 | — | 2 | 1 | no | — |
| 9 | #11711538 | C4 | 1 | 1 | yes | characteristic |
| 10 | A4×#346 | C22 | 1 | 1 | yes | characteristic |
| 11 | A4×#334 | — | 2 | 1 | no | — |
| 12 | #10682654 | — | 4 | 1 | no | maximal |
| 13 | #495881 | — | 3 | 1 | no | — |
| 14 | C22×#1368 | D3 | 1 | 1 | yes | characteristic, complemented |
| 15 | #151891 | — | 3 | 1 | no | — |
| 16 | C2×#7389 | — | 3 | 1 | no | — |
| 17 | C2×#7389 | — | 3 | 1 | no | — |
| 18 | #94057 | — | 3 | 1 | no | — |
| 19 | #94057 | — | 3 | 1 | no | — |
| 20 | #85440 | — | 2 | 1 | no | — |
| 21 | #85437 | — | 4 | 1 | no | — |
| 22 | C2×A4×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 23 | C2×A4×C16 | D4 | 1 | 1 | yes | characteristic |
| 24 | A4×C4⋊C8 | — | 4 | 1 | no | — |
| 25 | C4×C8×A4 | D4 | 1 | 1 | yes | characteristic |
| 26 | #73105 | — | 2 | 1 | no | — |
| 27 | #73046 | — | 4 | 1 | no | — |
| 28 | #73037 | C8 | 1 | 1 | yes | characteristic, complemented |
| 29 | #73036 | — | 2 | 1 | no | — |
| 30 | #73035 | C8 | 1 | 1 | yes | characteristic, complemented |
| 31 | #69085 | — | 4 | 1 | no | — |
| 32 | A4⋊C32 | — | 2 | 2 | no | — |
| 33 | C3×#1368 | — | 4 | 1 | no | — |
| 34 | #67519 | — | 4 | 1 | no | — |
| 35 | #33600 | — | 3 | 1 | no | — |
| 36 | C2×#2179 | — | 3 | 1 | no | — |
| 37 | C22×#346 | C2×D3 | 1 | 1 | yes | characteristic |
| 38 | #21544 | — | 6 | 1 | no | — |
| 39 | C22×#334 | — | 2 | 1 | no | — |
| 40 | #13553 | — | 6 | 1 | no | — |
| 41 | C2×#1398 | — | 3 | 1 | no | — |
| 42 | C2×#1398 | — | 3 | 1 | no | — |
| 43 | #13242 | — | 3 | 1 | no | — |
| 44 | #13170 | — | 3 | 1 | no | — |
| 45 | #13152 | — | 6 | 1 | no | — |
| 46 | #13063 | — | 6 | 1 | no | — |
| 47 | #12837 | — | 3 | 1 | no | — |
| 48 | #12671 | — | 3 | 1 | no | — |
| 49 | #12642 | — | 6 | 1 | no | — |
| 50 | C2×#1368 | — | 3 | 1 | no | — |
| 51 | C2×#1368 | — | 3 | 1 | no | — |
| 52 | C2×#1368 | — | 6 | 1 | no | — |
| 53 | #7466 | — | 6 | 1 | no | — |
| 54 | #7389 | — | 6 | 2 | no | — |
| 55 | #7389 | — | 6 | 1 | no | — |
| 56 | #7389 | — | 6 | 1 | no | — |
| 57 | #5912 | — | 4 | 1 | no | — |
| 58 | C2×C8×A4 | — | 8 | 1 | no | — |
| 59 | C2×C8×A4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 60 | C2×C8×A4 | SD16 | 1 | 1 | yes | characteristic |
| 61 | C42×A4 | D8 | 1 | 1 | yes | characteristic |
| 62 | #5409 | — | 4 | 1 | no | — |
| 63 | #5402 | — | 2 | 1 | no | — |
| 64 | #5401 | — | 4 | 1 | no | — |
| 65 | #5400 | — | 8 | 1 | no | — |
| 66 | C8×S4 | — | 8 | 1 | no | — |
| 67 | #5398 | — | 2 | 1 | no | — |
| 68 | #4904 | — | 4 | 1 | no | — |
| 69 | #4700 | — | 8 | 1 | no | — |
| 70 | A4×C16 | — | 2 | 1 | no | — |
| 71 | A4×C16 | C2×C8 | 1 | 1 | yes | characteristic |
| 72 | A4×C16 | M16 | 1 | 1 | yes | characteristic |
| 73 | C3×#346 | — | 4 | 1 | no | — |
| 74 | C3×#334 | — | 8 | 1 | no | — |
| 75 | #4510 | — | 8 | 1 | no | — |
| 76 | #4506 | — | 4 | 1 | no | — |
| 77 | #4499 | — | 8 | 1 | no | — |
| 78 | C2×#508 | — | 3 | 1 | no | — |
| 79 | C23×C16 | C4×D3 | 1 | 1 | yes | characteristic |
| 80 | C23×C16 | D12 | 1 | 1 | yes | characteristic |
| 81 | #3050 | — | 6 | 1 | no | — |
| 82 | C2×#443 | — | 6 | 1 | no | — |
| 83 | #2929 | — | 12 | 1 | no | — |
| 84 | C22×C4⋊C8 | — | 4 | 1 | no | — |
| 85 | C22×C4×C8 | #67 | 1 | 1 | yes | characteristic |
| 86 | C2×M64 | — | 6 | 1 | no | — |
| 87 | C2×M64 | — | 6 | 1 | no | — |
| 88 | #2217 | — | 6 | 1 | no | — |
| 89 | #2217 | — | 6 | 1 | no | — |
| 90 | #2216 | — | 3 | 1 | no | — |
| 91 | #2216 | — | 3 | 1 | no | — |
| 92 | #2215 | — | 3 | 1 | no | — |
| 93 | #2215 | — | 3 | 1 | no | — |
| 94 | #2179 | — | 6 | 1 | no | — |
| 95 | #2179 | — | 6 | 1 | no | — |
| 96 | #2179 | — | 6 | 1 | no | — |
| 97 | #2179 | — | 6 | 1 | no | — |
| 98 | C2×#368 | — | 3 | 1 | no | — |
| 99 | C2×#368 | — | 3 | 1 | no | — |
| 100 | #2158 | — | 3 | 1 | no | — |
| 101 | C2×#359 | — | 6 | 1 | no | — |
| 102 | C2×#359 | — | 6 | 1 | no | — |
| 103 | #2138 | — | 6 | 1 | no | — |
| 104 | C2×#346 | — | 3 | 1 | no | — |
| 105 | C2×#346 | — | 3 | 1 | no | — |
| 106 | C2×#346 | — | 3 | 1 | no | — |
| 107 | C2×#346 | — | 3 | 1 | no | — |
| 108 | #1974 | — | 6 | 1 | no | — |
| 109 | #1945 | — | 6 | 1 | no | — |
| 110 | #1937 | — | 12 | 1 | no | — |
| 111 | #1896 | — | 12 | 1 | no | — |
| 112 | #1810 | — | 6 | 1 | no | — |
| 113 | #1772 | — | 6 | 1 | no | — |
| 114 | #1764 | — | 12 | 1 | no | — |
| 115 | C2×#334 | — | 6 | 1 | no | — |
| 116 | C2×#334 | — | 6 | 1 | no | — |
| 117 | C2×#334 | — | 12 | 1 | no | — |
| 118 | C22⋊C32 | — | 6 | 2 | no | — |
| 119 | C22⋊C32 | — | 6 | 2 | no | — |
| 120 | #1398 | — | 6 | 1 | no | — |
| 121 | #1398 | — | 6 | 1 | no | — |
| 122 | #1398 | — | 6 | 1 | no | — |
| 123 | #1398 | — | 6 | 1 | no | — |
| 124 | #1382 | — | 6 | 1 | no | — |
| 125 | #1382 | — | 6 | 1 | no | — |
| 126 | #1381 | — | 6 | 1 | no | — |
| 127 | #1368 | — | 3 | 2 | no | — |
| 128 | #1368 | — | 3 | 1 | no | — |
| 129 | #1368 | — | 6 | 1 | no | — |
| 130 | #1368 | S4 | 1 | 1 | yes | characteristic, complemented |
| 131 | C2×C4×A4 | — | 2 | 1 | no | — |
| 132 | C2×C4×A4 | #102 | 1 | 1 | yes | characteristic |
| 133 | GL(2,ℤ/4) | — | 8 | 1 | no | — |
| 134 | C4⋊S4 | — | 4 | 1 | no | — |
| 135 | C4×S4 | — | 8 | 1 | no | — |
| 136 | A4⋊Q8 | — | 4 | 1 | no | — |
| 137 | #904 | — | 8 | 1 | no | — |
| 138 | #901 | — | 16 | 1 | no | — |
| 139 | C8×A4 | — | 2 | 1 | no | — |
| 140 | C8×A4 | — | 16 | 1 | no | — |
| 141 | C8×A4 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 142 | C8×A4 | #104 | 1 | 1 | yes | characteristic |
| 143 | A4⋊C8 | — | 8 | 1 | no | — |
| 144 | C2×C3×C16 | — | 4 | 1 | no | — |
| 145 | C2×C3×C16 | — | 4 | 1 | no | — |
| 146 | C3×C4⋊C8 | — | 16 | 1 | no | — |
| 147 | C3×C4×C8 | — | 4 | 1 | no | — |
| 148 | #819 | — | 8 | 1 | no | — |
| 149 | #805 | — | 16 | 1 | no | — |
| 150 | Dic24 | — | 4 | 1 | no | — |
| 151 | #800 | — | 8 | 1 | no | — |
| 152 | D48 | — | 4 | 1 | no | — |
| 153 | C3⋊C32 | — | 8 | 2 | no | — |
| 154 | C2×#135 | — | 6 | 1 | no | — |
| 155 | C2×#131 | — | 12 | 1 | no | — |
| 156 | C23×C8 | — | 8 | 1 | no | — |
| 157 | C23×C8 | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 158 | C23×C8 | #215 | 1 | 1 | yes | characteristic |
| 159 | #525 | — | 12 | 1 | no | — |
| 160 | C22×C42 | #213 | 1 | 1 | yes | characteristic |
| 161 | #508 | — | 6 | 1 | no | — |
| 162 | #508 | — | 6 | 1 | no | — |
| 163 | #508 | — | 6 | 1 | no | — |
| 164 | #508 | — | 6 | 1 | no | — |
| 165 | C2×Q32 | — | 3 | 1 | no | — |
| 166 | C2×SD32 | — | 6 | 1 | no | — |
| 167 | C2×D16 | — | 3 | 1 | no | — |
| 168 | C22×C16 | — | 2 | 1 | no | — |
| 169 | C22×C16 | — | 3 | 1 | no | — |
| 170 | C22×C16 | — | 3 | 1 | no | — |
| 171 | C22×C16 | — | 3 | 1 | no | — |
| 172 | C22×C16 | — | 3 | 1 | no | — |
| 173 | C22×C16 | — | 3 | 1 | no | — |
| 174 | C22×C16 | — | 3 | 1 | no | — |
| 175 | C22×C16 | — | 6 | 1 | no | — |
| 176 | C22×C16 | D3×C8 | 1 | 1 | yes | characteristic |
| 177 | C22×C16 | ΓL(1,𝔽25) | 1 | 1 | yes | characteristic |
| 178 | #467 | — | 6 | 1 | no | — |
| 179 | #467 | — | 6 | 1 | no | — |
| 180 | #466 | — | 6 | 1 | no | — |
| 181 | #466 | — | 6 | 1 | no | — |
| 182 | #465 | — | 12 | 1 | no | — |
| 183 | #465 | — | 12 | 1 | no | — |
| 184 | #443 | — | 12 | 1 | no | — |
| 185 | #443 | — | 12 | 1 | no | — |
| 186 | #443 | — | 12 | 1 | no | — |
| 187 | #443 | — | 12 | 1 | no | — |
| 188 | #435 | — | 24 | 1 | no | — |
| 189 | #435 | — | 24 | 1 | no | — |
| 190 | C8×D4 | — | 24 | 1 | no | — |
| 191 | C8×D4 | — | 24 | 1 | no | — |
| 192 | C2×#108 | — | 6 | 1 | no | — |
| 193 | C2×#108 | — | 6 | 1 | no | — |
| 194 | #427 | — | 6 | 1 | no | — |
| 195 | #424 | — | 12 | 1 | no | — |
| 196 | C2×C4⋊C8 | — | 12 | 1 | no | — |
| 197 | C2×C4⋊C8 | — | 12 | 1 | no | — |
| 198 | C2×C4⋊C8 | — | 24 | 1 | no | — |
| 199 | C2×#104 | — | 12 | 1 | no | — |
| 200 | C2×#104 | — | 12 | 1 | no | — |
| 201 | #416 | — | 12 | 1 | no | — |
| 202 | #408 | — | 12 | 1 | no | — |
| 203 | #407 | — | 12 | 1 | no | — |
| 204 | #405 | — | 12 | 1 | no | — |
| 205 | C2×C4×C8 | — | 3 | 1 | no | — |
| 206 | C2×C4×C8 | — | 3 | 1 | no | — |
| 207 | C2×C4×C8 | — | 3 | 1 | no | — |
| 208 | C2×C4×C8 | — | 3 | 1 | no | — |
| 209 | M64 | — | 12 | 1 | no | — |
| 210 | M64 | — | 12 | 1 | no | — |
| 211 | M64 | — | 12 | 1 | no | — |
| 212 | M64 | — | 12 | 1 | no | — |
| 213 | C2×C32 | — | 6 | 2 | no | — |
| 214 | C2×C32 | — | 6 | 2 | no | — |
| 215 | #368 | — | 6 | 1 | no | — |
| 216 | #368 | — | 6 | 1 | no | — |
| 217 | #368 | — | 6 | 1 | no | — |
| 218 | #368 | — | 6 | 1 | no | — |
| 219 | #367 | — | 6 | 1 | no | — |
| 220 | #366 | — | 3 | 1 | no | — |
| 221 | #366 | — | 3 | 1 | no | — |
| 222 | #359 | — | 12 | 1 | no | — |
| 223 | #359 | — | 12 | 2 | no | — |
| 224 | #359 | — | 12 | 1 | no | — |
| 225 | #358 | — | 6 | 1 | no | — |
| 226 | #358 | — | 6 | 1 | no | — |
| 227 | #357 | — | 6 | 1 | no | — |
| 228 | #357 | — | 6 | 1 | no | — |
| 229 | #346 | — | 3 | 1 | no | — |
| 230 | #346 | — | 3 | 1 | no | — |
| 231 | #346 | — | 3 | 1 | no | — |
| 232 | #346 | — | 6 | 1 | no | — |
| 233 | #346 | C2×S4 | 1 | 1 | yes | characteristic |
| 234 | #341 | — | 12 | 1 | no | — |
| 235 | #339 | — | 12 | 1 | no | — |
| 236 | #339 | — | 12 | 1 | no | — |
| 237 | #334 | — | 2 | 1 | no | — |
| 238 | #334 | — | 6 | 1 | no | — |
| 239 | #334 | — | 12 | 1 | no | — |
| 240 | #334 | — | 12 | 1 | no | — |
| 241 | C22×A4 | #360 | 1 | 1 | yes | characteristic |
| 242 | C2×S4 | — | 8 | 1 | no | — |
| 243 | #235 | — | 16 | 1 | no | — |
| 244 | C4×A4 | — | 4 | 1 | no | — |
| 245 | C4×A4 | D4⋊C8 | 1 | 1 | yes | characteristic |
| 246 | C4×A4 | #361 | 1 | 1 | yes | characteristic |
| 247 | SL(2,ℤ/4) | — | 8 | 1 | no | — |
| 248 | C2×C3×C8 | — | 4 | 1 | no | — |
| 249 | C2×C3×C8 | — | 4 | 1 | no | — |
| 250 | C2×C3×C8 | — | 32 | 1 | no | — |
| 251 | C3×C42 | — | 4 | 1 | no | — |
| 252 | #208 | — | 16 | 1 | no | — |
| 253 | Dic12 | — | 8 | 1 | no | — |
| 254 | D24 | — | 8 | 1 | no | — |
| 255 | #204 | — | 16 | 1 | no | — |
| 256 | ΓL(1,𝔽25) | — | 32 | 1 | no | — |
| 257 | D3×C8 | — | 32 | 1 | no | — |
| 258 | C3×C16 | — | 4 | 1 | no | — |
| 259 | C3×C16 | — | 4 | 1 | no | — |
| 260 | C3×C16 | — | 8 | 1 | no | — |
| 261 | C2×#41 | — | 12 | 1 | no | — |
| 262 | C23×C4 | — | 2 | 1 | no | — |
| 263 | C23×C4 | #809 | 1 | 1 | yes | characteristic |
| 264 | #135 | — | 12 | 1 | no | — |
| 265 | #135 | — | 12 | 1 | no | — |
| 266 | #135 | — | 12 | 1 | no | — |
| 267 | #135 | — | 12 | 1 | no | — |
| 268 | C2×Q16 | — | 6 | 1 | no | — |
| 269 | C2×SD16 | — | 12 | 1 | no | — |
| 270 | C2×D8 | — | 6 | 1 | no | — |
| 271 | #131 | — | 24 | 1 | no | — |
| 272 | #131 | — | 24 | 1 | no | — |
| 273 | #131 | — | 24 | 1 | no | — |
| 274 | #131 | — | 24 | 1 | no | — |
| 275 | C2×M16 | — | 12 | 1 | no | — |
| 276 | C2×M16 | — | 12 | 1 | no | — |
| 277 | C2×M16 | — | 24 | 1 | no | — |
| 278 | C22×C8 | — | 2 | 1 | no | — |
| 279 | C22×C8 | — | 3 | 1 | no | — |
| 280 | C22×C8 | — | 3 | 1 | no | — |
| 281 | C22×C8 | — | 3 | 1 | no | — |
| 282 | C22×C8 | — | 3 | 1 | no | — |
| 283 | C22×C8 | — | 3 | 1 | no | — |
| 284 | C22×C8 | — | 3 | 1 | no | — |
| 285 | C22×C8 | — | 6 | 1 | no | — |
| 286 | C22×C8 | — | 16 | 1 | no | — |
| 287 | C22×C8 | — | 24 | 1 | no | — |
| 288 | C22×C8 | — | 24 | 1 | no | — |
| 289 | C22×C8 | — | 24 | 1 | no | — |
| 290 | C22×C8 | — | 48 | 1 | no | — |
| 291 | C22×C8 | (C2×D3)⋊C8 | 1 | 1 | yes | characteristic |
| 292 | C22×C8 | #825 | 1 | 1 | yes | characteristic |
| 293 | #123 | — | 24 | 1 | no | — |
| 294 | C22⋊Q8 | — | 12 | 1 | no | — |
| 295 | C22⋊Q8 | — | 12 | 1 | no | — |
| 296 | #121 | — | 12 | 1 | no | — |
| 297 | #121 | — | 12 | 1 | no | — |
| 298 | #120 | — | 24 | 1 | no | — |
| 299 | C4×D4 | — | 24 | 1 | no | — |
| 300 | C4×D4 | — | 24 | 1 | no | — |
| 301 | #117 | — | 12 | 1 | no | — |
| 302 | C2×C42 | — | 3 | 1 | no | — |
| 303 | C2×C42 | — | 3 | 1 | no | — |
| 304 | C2×C42 | — | 6 | 1 | no | — |
| 305 | Q32 | — | 6 | 1 | no | — |
| 306 | Q32 | — | 6 | 1 | no | — |
| 307 | SD32 | — | 12 | 1 | no | — |
| 308 | SD32 | — | 12 | 1 | no | — |
| 309 | D16 | — | 6 | 1 | no | — |
| 310 | D16 | — | 6 | 1 | no | — |
| 311 | C2×C16 | — | 3 | 1 | no | — |
| 312 | C2×C16 | — | 3 | 1 | no | — |
| 313 | C2×C16 | — | 3 | 1 | no | — |
| 314 | C2×C16 | — | 3 | 1 | no | — |
| 315 | C2×C16 | — | 3 | 1 | no | — |
| 316 | C2×C16 | — | 3 | 1 | no | — |
| 317 | C2×C16 | — | 3 | 1 | no | — |
| 318 | C2×C16 | — | 3 | 1 | no | — |
| 319 | C2×C16 | — | 6 | 1 | no | — |
| 320 | C2×C16 | — | 6 | 1 | no | — |
| 321 | C2×C16 | — | 6 | 1 | no | — |
| 322 | C2×C16 | — | 6 | 1 | no | — |
| 323 | C2×C16 | — | 6 | 1 | no | — |
| 324 | C2×C16 | C4×S4 | 1 | 1 | yes | characteristic |
| 325 | C2×C16 | C4⋊S4 | 1 | 1 | yes | characteristic |
| 326 | #108 | — | 12 | 1 | no | — |
| 327 | #108 | — | 12 | 1 | no | — |
| 328 | #108 | — | 12 | 1 | no | — |
| 329 | #108 | — | 12 | 1 | no | — |
| 330 | #107 | — | 6 | 1 | no | — |
| 331 | #107 | — | 6 | 1 | no | — |
| 332 | #106 | — | 12 | 1 | no | — |
| 333 | C4⋊C8 | — | 4 | 1 | no | — |
| 334 | C4⋊C8 | — | 12 | 1 | no | — |
| 335 | C4⋊C8 | — | 24 | 1 | no | — |
| 336 | C4⋊C8 | — | 24 | 1 | no | — |
| 337 | C4⋊C8 | — | 24 | 1 | no | — |
| 338 | C4⋊C8 | — | 24 | 1 | no | — |
| 339 | #104 | — | 24 | 2 | no | — |
| 340 | #104 | — | 24 | 1 | no | — |
| 341 | #104 | — | 24 | 1 | no | — |
| 342 | #103 | — | 12 | 1 | no | — |
| 343 | #103 | — | 12 | 1 | no | — |
| 344 | #102 | — | 12 | 1 | no | — |
| 345 | #102 | — | 12 | 1 | no | — |
| 346 | C22⋊C8 | — | 24 | 1 | no | — |
| 347 | C22⋊C8 | — | 24 | 1 | no | — |
| 348 | C22⋊C8 | — | 24 | 1 | no | — |
| 349 | C22⋊C8 | — | 24 | 1 | no | — |
| 350 | #97 | — | 24 | 1 | no | — |
| 351 | C4×C8 | — | 3 | 1 | no | — |
| 352 | C4×C8 | — | 3 | 1 | no | — |
| 353 | C4×C8 | — | 3 | 1 | no | — |
| 354 | C4×C8 | — | 6 | 1 | no | — |
| 355 | C4×C8 | — | 24 | 1 | no | — |
| 356 | C4×C8 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 357 | C32 | — | 12 | 2 | no | — |
| 358 | C32 | — | 12 | 2 | no | — |
| 359 | C2×A4 | — | 2 | 1 | no | — |
| 360 | C2×A4 | #1333 | 1 | 1 | yes | characteristic |
| 361 | S4 | — | 16 | 1 | no | — |
| 362 | C2×C3×C4 | — | 4 | 1 | no | — |
| 363 | C2×C3×C4 | — | 8 | 1 | no | — |
| 364 | #67 | — | 32 | 1 | no | — |
| 365 | D12 | — | 16 | 1 | no | — |
| 366 | C4×D3 | — | 32 | 1 | no | — |
| 367 | Dic6 | — | 16 | 1 | no | — |
| 368 | C3×C8 | — | 4 | 1 | no | — |
| 369 | C3×C8 | — | 4 | 1 | no | — |
| 370 | C3×C8 | — | 8 | 1 | no | — |
| 371 | C3×C8 | — | 64 | 1 | no | — |
| 372 | C3⋊C8 | — | 32 | 1 | no | — |
| 373 | C24 | #4488 | 1 | 1 | yes | characteristic |
| 374 | #41 | — | 24 | 1 | no | — |
| 375 | #41 | — | 24 | 1 | no | — |
| 376 | #41 | — | 24 | 1 | no | — |
| 377 | #41 | — | 24 | 1 | no | — |
| 378 | C2×Q8 | — | 12 | 1 | no | — |
| 379 | C2×D4 | — | 12 | 1 | no | — |
| 380 | C2×D4 | — | 24 | 1 | no | — |
| 381 | C2×D4 | — | 24 | 1 | no | — |
| 382 | C2×D4 | — | 24 | 1 | no | — |
| 383 | C22×C4 | — | 3 | 1 | no | — |
| 384 | C22×C4 | — | 3 | 1 | no | — |
| 385 | C22×C4 | — | 3 | 1 | no | — |
| 386 | C22×C4 | — | 3 | 1 | no | — |
| 387 | C22×C4 | — | 4 | 1 | no | — |
| 388 | C22×C4 | — | 6 | 1 | no | — |
| 389 | C22×C4 | — | 6 | 1 | no | — |
| 390 | C22×C4 | — | 12 | 1 | no | — |
| 391 | C22×C4 | — | 24 | 1 | no | — |
| 392 | C22×C4 | #4483 | 1 | 1 | yes | characteristic |
| 393 | C22×C4 | #4495 | 1 | 1 | yes | characteristic |
| 394 | Q16 | — | 12 | 1 | no | — |
| 395 | Q16 | — | 12 | 1 | no | — |
| 396 | SD16 | — | 24 | 1 | no | — |
| 397 | SD16 | — | 24 | 1 | no | — |
| 398 | D8 | — | 12 | 1 | no | — |
| 399 | D8 | — | 12 | 1 | no | — |
| 400 | M16 | — | 24 | 1 | no | — |
| 401 | M16 | — | 24 | 1 | no | — |
| 402 | M16 | — | 24 | 1 | no | — |
| 403 | M16 | — | 24 | 1 | no | — |
| 404 | M16 | — | 48 | 1 | no | — |
| 405 | M16 | — | 48 | 1 | no | — |
| 406 | C2×C8 | — | 3 | 1 | no | — |
| 407 | C2×C8 | — | 3 | 1 | no | — |
| 408 | C2×C8 | — | 3 | 1 | no | — |
| 409 | C2×C8 | — | 3 | 1 | no | — |
| 410 | C2×C8 | — | 3 | 1 | no | — |
| 411 | C2×C8 | — | 3 | 1 | no | — |
| 412 | C2×C8 | — | 3 | 1 | no | — |
| 413 | C2×C8 | — | 3 | 1 | no | — |
| 414 | C2×C8 | — | 6 | 1 | no | — |
| 415 | C2×C8 | — | 6 | 1 | no | — |
| 416 | C2×C8 | — | 6 | 1 | no | — |
| 417 | C2×C8 | — | 6 | 1 | no | — |
| 418 | C2×C8 | — | 6 | 1 | no | — |
| 419 | C2×C8 | — | 8 | 1 | no | — |
| 420 | C2×C8 | — | 24 | 1 | no | — |
| 421 | C2×C8 | — | 24 | 1 | no | — |
| 422 | C2×C8 | — | 24 | 1 | no | — |
| 423 | C2×C8 | — | 48 | 1 | no | — |
| 424 | C2×C8 | — | 48 | 1 | no | — |
| 425 | C2×C8 | — | 48 | 1 | no | — |
| 426 | C2×C8 | — | 48 | 1 | no | — |
| 427 | C2×C8 | — | 48 | 1 | no | — |
| 428 | C2×C8 | — | 48 | 1 | no | — |
| 429 | C2×C8 | (C2×S4)⋊C4 | 1 | 1 | yes | characteristic |
| 430 | C2×C8 | #5417 | 1 | 1 | yes | characteristic |
| 431 | C4⋊C4 | — | 12 | 1 | no | — |
| 432 | C4⋊C4 | — | 12 | 1 | no | — |
| 433 | C4⋊C4 | — | 24 | 1 | no | — |
| 434 | C4⋊C4 | — | 24 | 1 | no | — |
| 435 | C22⋊C4 | — | 24 | 1 | no | — |
| 436 | C22⋊C4 | — | 24 | 1 | no | — |
| 437 | C22⋊C4 | — | 24 | 1 | no | — |
| 438 | C22⋊C4 | — | 24 | 1 | no | — |
| 439 | C22⋊C4 | — | 24 | 1 | no | — |
| 440 | C42 | — | 3 | 2 | no | — |
| 441 | C42 | — | 3 | 1 | no | — |
| 442 | C42 | — | 6 | 1 | no | — |
| 443 | C42 | — | 24 | 1 | no | — |
| 444 | C42 | #5415 | 1 | 1 | yes | characteristic |
| 445 | C16 | — | 2 | 1 | no | — |
| 446 | C16 | — | 3 | 1 | no | — |
| 447 | C16 | — | 3 | 1 | no | — |
| 448 | C16 | — | 6 | 1 | no | — |
| 449 | C16 | C8×S4 | 1 | 1 | yes | characteristic |
| 450 | C16 | #5400 | 1 | 1 | yes | characteristic |
| 451 | C22×C3 | — | 4 | 1 | no | — |
| 452 | C2×D3 | — | 32 | 1 | no | — |
| 453 | A4 | #7389 | 1 | 1 | yes | characteristic, complemented |
| 454 | C3×C4 | — | 4 | 1 | no | — |
| 455 | C3×C4 | — | 4 | 1 | no | — |
| 456 | C3×C4 | — | 16 | 1 | no | — |
| 457 | Dic3 | — | 32 | 1 | no | — |
| 458 | C23 | — | 2 | 1 | no | — |
| 459 | C23 | — | 3 | 1 | no | — |
| 460 | C23 | — | 3 | 1 | no | — |
| 461 | C23 | — | 6 | 1 | no | — |
| 462 | C23 | — | 24 | 1 | no | — |
| 463 | C23 | #67465 | 1 | 1 | yes | characteristic |
| 464 | Q8 | — | 24 | 1 | no | — |
| 465 | Q8 | — | 24 | 1 | no | — |
| 466 | D4 | — | 24 | 1 | no | — |
| 467 | D4 | — | 24 | 1 | no | — |
| 468 | D4 | — | 48 | 1 | no | — |
| 469 | D4 | — | 48 | 2 | no | — |
| 470 | D4 | — | 48 | 1 | no | — |
| 471 | D4 | — | 48 | 1 | no | — |
| 472 | D4 | — | 48 | 1 | no | — |
| 473 | C2×C4 | — | 2 | 1 | no | — |
| 474 | C2×C4 | — | 3 | 1 | no | — |
| 475 | C2×C4 | — | 3 | 1 | no | — |
| 476 | C2×C4 | — | 3 | 1 | no | — |
| 477 | C2×C4 | — | 3 | 1 | no | — |
| 478 | C2×C4 | — | 3 | 1 | no | — |
| 479 | C2×C4 | — | 3 | 1 | no | — |
| 480 | C2×C4 | — | 3 | 1 | no | — |
| 481 | C2×C4 | — | 6 | 1 | no | — |
| 482 | C2×C4 | — | 6 | 1 | no | — |
| 483 | C2×C4 | — | 12 | 1 | no | — |
| 484 | C2×C4 | — | 12 | 1 | no | — |
| 485 | C2×C4 | — | 12 | 1 | no | — |
| 486 | C2×C4 | — | 12 | 1 | no | — |
| 487 | C2×C4 | — | 24 | 1 | no | — |
| 488 | C2×C4 | — | 24 | 1 | no | — |
| 489 | C2×C4 | — | 24 | 1 | no | — |
| 490 | C2×C4 | — | 48 | 1 | no | — |
| 491 | C2×C4 | — | 48 | 1 | no | — |
| 492 | C2×C4 | #73053 | 1 | 1 | yes | characteristic |
| 493 | C8 | — | 2 | 1 | no | — |
| 494 | C8 | — | 3 | 1 | no | — |
| 495 | C8 | — | 3 | 1 | no | — |
| 496 | C8 | — | 6 | 1 | no | — |
| 497 | C8 | — | 16 | 1 | no | — |
| 498 | C8 | — | 48 | 1 | no | — |
| 499 | C8 | — | 48 | 1 | no | — |
| 500 | C8 | — | 48 | 1 | no | — |
| 501 | C8 | (C2×S4)⋊C8 | 1 | 1 | yes | characteristic |
| 502 | C8 | #73117 | 1 | 1 | yes | characteristic |
| 503 | C2×C3 | — | 4 | 1 | no | — |
| 504 | C2×C3 | — | 8 | 1 | no | — |
| 505 | D3 | — | 64 | 1 | no | — |
| 506 | C22 | — | 3 | 1 | no | — |
| 507 | C22 | — | 3 | 1 | no | — |
| 508 | C22 | — | 3 | 2 | no | — |
| 509 | C22 | — | 3 | 1 | no | — |
| 510 | C22 | — | 6 | 1 | no | — |
| 511 | C22 | — | 6 | 1 | no | — |
| 512 | C22 | — | 6 | 1 | no | — |
| 513 | C22 | — | 48 | 1 | no | — |
| 514 | C22 | — | 48 | 1 | no | — |
| 515 | C22 | — | 48 | 1 | no | — |
| 516 | C22 | #10682654 | 1 | 1 | yes | characteristic, complemented |
| 517 | C22 | #11711572 | 1 | 1 | yes | characteristic |
| 518 | C4 | — | 3 | 1 | no | — |
| 519 | C4 | — | 3 | 1 | no | — |
| 520 | C4 | — | 4 | 1 | no | — |
| 521 | C4 | — | 12 | 1 | no | — |
| 522 | C4 | — | 48 | 1 | no | — |
| 523 | C4 | — | 48 | 1 | no | — |
| 524 | C4 | — | 48 | 1 | no | — |
| 525 | C4 | #11711105 | 1 | 1 | yes | characteristic |
| 526 | C4 | #11711574 | 1 | 1 | yes | characteristic |
| 527 | C3 | — | 4 | 1 | no | Sylow |
| 528 | C2 | — | 2 | 1 | no | — |
| 529 | C2 | — | 3 | 1 | no | — |
| 530 | C2 | — | 3 | 1 | no | — |
| 531 | C2 | — | 6 | 1 | no | — |
| 532 | C2 | — | 96 | 1 | no | — |
| 533 | C2 | #72342729 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. A4×#1368 | C2 | semidirect |
| 2. #72342686 | C2 | semidirect |
| 14. C22×#1368 | D3 | semidirect |
| 28. #73037 | C8 | semidirect |
| 30. #73035 | C8 | semidirect |
| 130. #1368 | S4 | semidirect |
| 453. A4 | #7389 | semidirect |
| 516. C22 | #10682654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#1368 | 2 |
| #72342686 | 2 |
| #72342674 | 2 |
| #72225020 | 3 |
| #10682654 | 4 |