Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
439 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 439 conjugacy classes of subgroups — too many to draw. Only its 52 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 | #11712861 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11710984 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | A4×#364 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #136600 | — | 3 | 1 | no | maximal, Sylow |
| 5 | #85440 | C4 | 1 | 1 | yes | characteristic |
| 6 | #85437 | — | 2 | 1 | no | — |
| 7 | A4×M32 | — | 2 | 1 | no | — |
| 8 | C4×C8×A4 | C22 | 1 | 1 | yes | characteristic |
| 9 | #73105 | C4 | 1 | 1 | yes | characteristic |
| 10 | #73046 | — | 2 | 1 | no | — |
| 11 | C4×A4⋊C8 | — | 2 | 1 | no | — |
| 12 | #67569 | — | 4 | 1 | no | maximal |
| 13 | C22×#364 | D3 | 1 | 1 | yes | characteristic, complemented |
| 14 | #21544 | — | 3 | 1 | no | — |
| 15 | C2×#1336 | — | 3 | 1 | no | — |
| 16 | C2×#1336 | — | 3 | 1 | no | — |
| 17 | #8144 | — | 3 | 1 | no | — |
| 18 | #7182 | — | 3 | 1 | no | — |
| 19 | #7182 | — | 3 | 1 | no | — |
| 20 | #5912 | — | 2 | 1 | no | — |
| 21 | C2×C8×A4 | C2×C4 | 1 | 1 | yes | characteristic |
| 22 | C2×C8×A4 | D4 | 1 | 1 | yes | characteristic |
| 23 | C42×A4 | D4 | 1 | 1 | yes | characteristic |
| 24 | #5409 | — | 2 | 1 | no | — |
| 25 | C2×A4⋊C8 | — | 2 | 2 | no | — |
| 26 | #5402 | C8 | 1 | 1 | yes | characteristic, complemented |
| 27 | #5401 | — | 2 | 1 | no | — |
| 28 | #5400 | — | 4 | 1 | no | — |
| 29 | C8×S4 | — | 4 | 1 | no | — |
| 30 | #5398 | C8 | 1 | 1 | yes | characteristic, complemented |
| 31 | #4700 | — | 4 | 1 | no | — |
| 32 | A4×C16 | — | 4 | 1 | no | — |
| 33 | C3×#364 | — | 4 | 1 | no | — |
| 34 | #4455 | — | 4 | 1 | no | — |
| 35 | C22×M32 | — | 2 | 1 | no | — |
| 36 | #3050 | — | 3 | 1 | no | — |
| 37 | C2×#443 | — | 3 | 1 | no | — |
| 38 | #2929 | — | 6 | 1 | no | — |
| 39 | C22×C4×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 40 | C2×#364 | — | 3 | 1 | no | — |
| 41 | C2×#364 | — | 3 | 1 | no | — |
| 42 | C2×#364 | — | 6 | 1 | no | — |
| 43 | #1974 | — | 3 | 1 | no | — |
| 44 | #1945 | — | 3 | 1 | no | — |
| 45 | #1937 | — | 6 | 1 | no | — |
| 46 | #1896 | — | 6 | 1 | no | — |
| 47 | #1810 | — | 3 | 1 | no | — |
| 48 | #1772 | — | 3 | 1 | no | — |
| 49 | #1764 | — | 6 | 1 | no | — |
| 50 | C4×C22⋊C8 | — | 6 | 1 | no | — |
| 51 | C2×#322 | — | 3 | 1 | no | — |
| 52 | C2×#322 | — | 3 | 1 | no | — |
| 53 | #1336 | — | 6 | 2 | no | — |
| 54 | #1336 | — | 6 | 1 | no | — |
| 55 | #1336 | — | 6 | 1 | no | — |
| 56 | #1273 | — | 6 | 1 | no | — |
| 57 | C2×C4×A4 | — | 2 | 1 | no | — |
| 58 | C2×C4×A4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 59 | GL(2,ℤ/4) | — | 4 | 1 | no | — |
| 60 | C4⋊S4 | — | 2 | 1 | no | — |
| 61 | C4×S4 | — | 4 | 1 | no | — |
| 62 | A4⋊Q8 | — | 2 | 1 | no | — |
| 63 | #904 | — | 4 | 1 | no | — |
| 64 | #901 | — | 8 | 1 | no | — |
| 65 | C8×A4 | C2×C8 | 1 | 1 | yes | characteristic |
| 66 | C8×A4 | M16 | 1 | 1 | yes | characteristic |
| 67 | C8×A4 | D8 | 1 | 1 | yes | characteristic |
| 68 | C8×A4 | SD16 | 1 | 1 | yes | characteristic |
| 69 | A4⋊C8 | — | 4 | 2 | no | — |
| 70 | A4⋊C8 | — | 4 | 1 | no | — |
| 71 | C3×M32 | — | 8 | 1 | no | — |
| 72 | C3×C4×C8 | — | 4 | 1 | no | — |
| 73 | #819 | — | 4 | 1 | no | — |
| 74 | #805 | — | 8 | 1 | no | — |
| 75 | C4×C3⋊C8 | — | 8 | 1 | no | — |
| 76 | C2×#135 | — | 3 | 1 | no | — |
| 77 | C2×#131 | — | 6 | 1 | no | — |
| 78 | C23×C8 | C4×D3 | 1 | 1 | yes | characteristic |
| 79 | C23×C8 | #67 | 1 | 1 | yes | characteristic |
| 80 | #525 | — | 6 | 1 | no | — |
| 81 | C22×C42 | D12 | 1 | 1 | yes | characteristic |
| 82 | C2×M32 | — | 6 | 1 | no | — |
| 83 | C2×M32 | — | 6 | 1 | no | — |
| 84 | C2×M32 | — | 12 | 1 | no | — |
| 85 | C22×C16 | — | 4 | 1 | no | — |
| 86 | #467 | — | 3 | 1 | no | — |
| 87 | #467 | — | 3 | 1 | no | — |
| 88 | #466 | — | 3 | 1 | no | — |
| 89 | #466 | — | 3 | 1 | no | — |
| 90 | #465 | — | 6 | 1 | no | — |
| 91 | #465 | — | 6 | 1 | no | — |
| 92 | #443 | — | 6 | 1 | no | — |
| 93 | #443 | — | 6 | 1 | no | — |
| 94 | #443 | — | 6 | 1 | no | — |
| 95 | #443 | — | 6 | 1 | no | — |
| 96 | #435 | — | 12 | 1 | no | — |
| 97 | #435 | — | 12 | 1 | no | — |
| 98 | C8×D4 | — | 12 | 1 | no | — |
| 99 | C8×D4 | — | 12 | 1 | no | — |
| 100 | C2×#108 | — | 3 | 1 | no | — |
| 101 | C2×#108 | — | 3 | 1 | no | — |
| 102 | #427 | — | 3 | 1 | no | — |
| 103 | #424 | — | 6 | 1 | no | — |
| 104 | C2×#104 | — | 6 | 1 | no | — |
| 105 | C2×#104 | — | 6 | 1 | no | — |
| 106 | #416 | — | 6 | 1 | no | — |
| 107 | #408 | — | 6 | 1 | no | — |
| 108 | #407 | — | 6 | 1 | no | — |
| 109 | C2×C22⋊C8 | — | 6 | 2 | no | — |
| 110 | #405 | — | 6 | 1 | no | — |
| 111 | C2×C4×C8 | — | 3 | 1 | no | — |
| 112 | C2×C4×C8 | — | 3 | 1 | no | — |
| 113 | C2×C4×C8 | — | 3 | 1 | no | — |
| 114 | C2×C4×C8 | — | 3 | 1 | no | — |
| 115 | C2×C4×C8 | — | 6 | 1 | no | — |
| 116 | C2×C4×C8 | — | 6 | 1 | no | — |
| 117 | #364 | — | 3 | 2 | no | — |
| 118 | #364 | — | 3 | 1 | no | — |
| 119 | #364 | — | 6 | 1 | no | — |
| 120 | #364 | S4 | 1 | 1 | yes | characteristic, complemented |
| 121 | #341 | — | 6 | 1 | no | — |
| 122 | #339 | — | 6 | 1 | no | — |
| 123 | #339 | — | 6 | 1 | no | — |
| 124 | #336 | — | 6 | 2 | no | — |
| 125 | #322 | — | 6 | 1 | no | — |
| 126 | #322 | — | 6 | 1 | no | — |
| 127 | #322 | — | 6 | 1 | no | — |
| 128 | #322 | — | 6 | 1 | no | — |
| 129 | C22×A4 | #104 | 1 | 1 | yes | characteristic |
| 130 | C2×S4 | — | 4 | 1 | no | — |
| 131 | #235 | — | 8 | 1 | no | — |
| 132 | C4×A4 | — | 2 | 2 | no | — |
| 133 | C4×A4 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 134 | C4×A4 | #102 | 1 | 1 | yes | characteristic |
| 135 | SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 136 | C2×C3×C8 | — | 4 | 1 | no | — |
| 137 | C2×C3×C8 | — | 4 | 1 | no | — |
| 138 | C3×C42 | — | 4 | 1 | no | — |
| 139 | #208 | — | 8 | 1 | no | — |
| 140 | C2×C3⋊C8 | — | 8 | 2 | no | — |
| 141 | Dic12 | — | 4 | 1 | no | — |
| 142 | D24 | — | 4 | 1 | no | — |
| 143 | #204 | — | 8 | 1 | no | — |
| 144 | ΓL(1,𝔽25) | — | 16 | 1 | no | — |
| 145 | D3×C8 | — | 16 | 1 | no | — |
| 146 | C3×C16 | — | 16 | 1 | no | — |
| 147 | C2×#41 | — | 6 | 1 | no | — |
| 148 | C23×C4 | — | 2 | 1 | no | — |
| 149 | C23×C4 | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 150 | #135 | — | 6 | 1 | no | — |
| 151 | #135 | — | 6 | 1 | no | — |
| 152 | #135 | — | 6 | 1 | no | — |
| 153 | #135 | — | 6 | 1 | no | — |
| 154 | C2×Q16 | — | 3 | 1 | no | — |
| 155 | C2×SD16 | — | 6 | 1 | no | — |
| 156 | C2×D8 | — | 3 | 1 | no | — |
| 157 | #131 | — | 12 | 1 | no | — |
| 158 | #131 | — | 12 | 1 | no | — |
| 159 | #131 | — | 12 | 1 | no | — |
| 160 | #131 | — | 12 | 1 | no | — |
| 161 | C2×M16 | — | 6 | 1 | no | — |
| 162 | C2×M16 | — | 6 | 1 | no | — |
| 163 | C2×M16 | — | 12 | 1 | no | — |
| 164 | C22×C8 | — | 3 | 1 | no | — |
| 165 | C22×C8 | — | 3 | 1 | no | — |
| 166 | C22×C8 | — | 3 | 1 | no | — |
| 167 | C22×C8 | — | 3 | 1 | no | — |
| 168 | C22×C8 | — | 3 | 1 | no | — |
| 169 | C22×C8 | — | 3 | 1 | no | — |
| 170 | C22×C8 | — | 3 | 1 | no | — |
| 171 | C22×C8 | — | 3 | 1 | no | — |
| 172 | C22×C8 | — | 6 | 2 | no | — |
| 173 | C22×C8 | — | 6 | 2 | no | — |
| 174 | C22×C8 | — | 12 | 1 | no | — |
| 175 | C22×C8 | D3×C8 | 1 | 1 | yes | characteristic |
| 176 | C22×C8 | ΓL(1,𝔽25) | 1 | 1 | yes | characteristic |
| 177 | C22×C8 | #213 | 1 | 1 | yes | characteristic |
| 178 | C22×C8 | #215 | 1 | 1 | yes | characteristic |
| 179 | #123 | — | 12 | 1 | no | — |
| 180 | C22⋊Q8 | — | 6 | 1 | no | — |
| 181 | C22⋊Q8 | — | 6 | 1 | no | — |
| 182 | #121 | — | 6 | 1 | no | — |
| 183 | #121 | — | 6 | 1 | no | — |
| 184 | #120 | — | 12 | 1 | no | — |
| 185 | C4×D4 | — | 12 | 1 | no | — |
| 186 | C4×D4 | — | 12 | 1 | no | — |
| 187 | #117 | — | 6 | 1 | no | — |
| 188 | C2×C42 | — | 3 | 1 | no | — |
| 189 | C2×C42 | — | 3 | 1 | no | — |
| 190 | C2×C42 | — | 6 | 1 | no | — |
| 191 | M32 | — | 2 | 1 | no | — |
| 192 | M32 | — | 6 | 1 | no | — |
| 193 | M32 | — | 12 | 1 | no | — |
| 194 | M32 | — | 12 | 1 | no | — |
| 195 | C2×C16 | — | 12 | 1 | no | — |
| 196 | C2×C16 | — | 12 | 1 | no | — |
| 197 | #108 | — | 6 | 1 | no | — |
| 198 | #108 | — | 6 | 1 | no | — |
| 199 | #108 | — | 6 | 1 | no | — |
| 200 | #108 | — | 6 | 1 | no | — |
| 201 | #107 | — | 3 | 1 | no | — |
| 202 | #107 | — | 3 | 1 | no | — |
| 203 | #106 | — | 6 | 1 | no | — |
| 204 | C4⋊C8 | — | 12 | 1 | no | — |
| 205 | C4⋊C8 | — | 12 | 1 | no | — |
| 206 | #104 | — | 12 | 1 | no | — |
| 207 | #104 | — | 12 | 2 | no | — |
| 208 | #104 | — | 12 | 1 | no | — |
| 209 | #103 | — | 6 | 1 | no | — |
| 210 | #103 | — | 6 | 1 | no | — |
| 211 | #102 | — | 6 | 1 | no | — |
| 212 | #102 | — | 6 | 1 | no | — |
| 213 | C22⋊C8 | — | 12 | 1 | no | — |
| 214 | C22⋊C8 | — | 12 | 1 | no | — |
| 215 | C22⋊C8 | — | 12 | 2 | no | — |
| 216 | C22⋊C8 | — | 12 | 1 | no | — |
| 217 | C22⋊C8 | — | 12 | 2 | no | — |
| 218 | C22⋊C8 | — | 12 | 1 | no | — |
| 219 | #97 | — | 12 | 1 | no | — |
| 220 | C4×C8 | — | 3 | 1 | no | — |
| 221 | C4×C8 | — | 3 | 1 | no | — |
| 222 | C4×C8 | — | 3 | 1 | no | — |
| 223 | C4×C8 | — | 6 | 1 | no | — |
| 224 | C4×C8 | — | 12 | 1 | no | — |
| 225 | C4×C8 | — | 12 | 1 | no | — |
| 226 | C4×C8 | — | 12 | 1 | no | — |
| 227 | C4×C8 | — | 12 | 1 | no | — |
| 228 | C4×C8 | — | 12 | 1 | no | — |
| 229 | C4×C8 | C2×S4 | 1 | 1 | yes | characteristic |
| 230 | C2×A4 | — | 2 | 1 | no | — |
| 231 | C2×A4 | D4⋊C8 | 1 | 1 | yes | characteristic |
| 232 | S4 | — | 8 | 1 | no | — |
| 233 | C2×C3×C4 | — | 4 | 1 | no | — |
| 234 | C2×C3×C4 | — | 8 | 1 | no | — |
| 235 | #67 | — | 16 | 1 | no | — |
| 236 | D12 | — | 8 | 1 | no | — |
| 237 | C4×D3 | — | 16 | 1 | no | — |
| 238 | Dic6 | — | 8 | 1 | no | — |
| 239 | C3×C8 | — | 4 | 1 | no | — |
| 240 | C3×C8 | — | 4 | 1 | no | — |
| 241 | C3×C8 | — | 4 | 1 | no | — |
| 242 | C3×C8 | — | 4 | 1 | no | — |
| 243 | C3⋊C8 | — | 16 | 1 | no | — |
| 244 | C3⋊C8 | — | 16 | 2 | no | — |
| 245 | C24 | #825 | 1 | 1 | yes | characteristic |
| 246 | #41 | — | 12 | 1 | no | — |
| 247 | #41 | — | 12 | 1 | no | — |
| 248 | #41 | — | 12 | 1 | no | — |
| 249 | #41 | — | 12 | 1 | no | — |
| 250 | C2×Q8 | — | 6 | 1 | no | — |
| 251 | C2×D4 | — | 6 | 1 | no | — |
| 252 | C2×D4 | — | 12 | 1 | no | — |
| 253 | C2×D4 | — | 12 | 1 | no | — |
| 254 | C2×D4 | — | 12 | 1 | no | — |
| 255 | C22×C4 | — | 2 | 2 | no | — |
| 256 | C22×C4 | — | 3 | 1 | no | — |
| 257 | C22×C4 | — | 3 | 1 | no | — |
| 258 | C22×C4 | — | 3 | 1 | no | — |
| 259 | C22×C4 | — | 3 | 1 | no | — |
| 260 | C22×C4 | — | 6 | 1 | no | — |
| 261 | C22×C4 | — | 6 | 1 | no | — |
| 262 | C22×C4 | — | 6 | 2 | no | — |
| 263 | C22×C4 | — | 12 | 1 | no | — |
| 264 | C22×C4 | #809 | 1 | 1 | yes | characteristic |
| 265 | C22×C4 | (C2×D3)⋊C8 | 1 | 1 | yes | characteristic |
| 266 | Q16 | — | 6 | 1 | no | — |
| 267 | Q16 | — | 6 | 1 | no | — |
| 268 | SD16 | — | 12 | 1 | no | — |
| 269 | SD16 | — | 12 | 1 | no | — |
| 270 | D8 | — | 6 | 1 | no | — |
| 271 | D8 | — | 6 | 1 | no | — |
| 272 | M16 | — | 12 | 1 | no | — |
| 273 | M16 | — | 12 | 1 | no | — |
| 274 | M16 | — | 12 | 1 | no | — |
| 275 | M16 | — | 12 | 1 | no | — |
| 276 | M16 | — | 24 | 1 | no | — |
| 277 | M16 | — | 24 | 1 | no | — |
| 278 | C2×C8 | — | 3 | 1 | no | — |
| 279 | C2×C8 | — | 3 | 1 | no | — |
| 280 | C2×C8 | — | 3 | 1 | no | — |
| 281 | C2×C8 | — | 3 | 1 | no | — |
| 282 | C2×C8 | — | 3 | 1 | no | — |
| 283 | C2×C8 | — | 3 | 1 | no | — |
| 284 | C2×C8 | — | 3 | 1 | no | — |
| 285 | C2×C8 | — | 3 | 1 | no | — |
| 286 | C2×C8 | — | 3 | 1 | no | — |
| 287 | C2×C8 | — | 3 | 1 | no | — |
| 288 | C2×C8 | — | 3 | 1 | no | — |
| 289 | C2×C8 | — | 3 | 1 | no | — |
| 290 | C2×C8 | — | 3 | 1 | no | — |
| 291 | C2×C8 | — | 3 | 1 | no | — |
| 292 | C2×C8 | — | 6 | 1 | no | — |
| 293 | C2×C8 | — | 6 | 1 | no | — |
| 294 | C2×C8 | — | 12 | 2 | no | — |
| 295 | C2×C8 | — | 12 | 1 | no | — |
| 296 | C2×C8 | — | 12 | 1 | no | — |
| 297 | C2×C8 | — | 12 | 2 | no | — |
| 298 | C2×C8 | — | 12 | 2 | no | — |
| 299 | C2×C8 | — | 12 | 2 | no | — |
| 300 | C2×C8 | — | 12 | 2 | no | — |
| 301 | C2×C8 | — | 12 | 2 | no | — |
| 302 | C2×C8 | — | 24 | 1 | no | — |
| 303 | C2×C8 | — | 24 | 1 | no | — |
| 304 | C2×C8 | C4×S4 | 1 | 1 | yes | characteristic |
| 305 | C2×C8 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 306 | C4⋊C4 | — | 6 | 1 | no | — |
| 307 | C4⋊C4 | — | 6 | 1 | no | — |
| 308 | C4⋊C4 | — | 12 | 1 | no | — |
| 309 | C4⋊C4 | — | 12 | 1 | no | — |
| 310 | C22⋊C4 | — | 12 | 1 | no | — |
| 311 | C22⋊C4 | — | 12 | 1 | no | — |
| 312 | C22⋊C4 | — | 12 | 1 | no | — |
| 313 | C22⋊C4 | — | 12 | 1 | no | — |
| 314 | C22⋊C4 | — | 12 | 1 | no | — |
| 315 | C42 | — | 3 | 1 | no | — |
| 316 | C42 | — | 6 | 1 | no | — |
| 317 | C42 | — | 6 | 1 | no | — |
| 318 | C42 | — | 12 | 1 | no | — |
| 319 | C42 | C4⋊S4 | 1 | 1 | yes | characteristic |
| 320 | C16 | — | 4 | 1 | no | — |
| 321 | C16 | — | 12 | 1 | no | — |
| 322 | C22×C3 | — | 4 | 1 | no | — |
| 323 | C2×D3 | — | 16 | 1 | no | — |
| 324 | A4 | #1336 | 1 | 1 | yes | characteristic, complemented |
| 325 | C3×C4 | — | 4 | 1 | no | — |
| 326 | C3×C4 | — | 4 | 1 | no | — |
| 327 | C3×C4 | — | 8 | 2 | no | — |
| 328 | Dic3 | — | 16 | 1 | no | — |
| 329 | C23 | — | 2 | 1 | no | — |
| 330 | C23 | — | 3 | 1 | no | — |
| 331 | C23 | — | 3 | 1 | no | — |
| 332 | C23 | — | 6 | 1 | no | — |
| 333 | C23 | — | 12 | 1 | no | — |
| 334 | C23 | #4483 | 1 | 1 | yes | characteristic |
| 335 | Q8 | — | 12 | 1 | no | — |
| 336 | Q8 | — | 12 | 1 | no | — |
| 337 | D4 | — | 12 | 1 | no | — |
| 338 | D4 | — | 12 | 1 | no | — |
| 339 | D4 | — | 24 | 1 | no | — |
| 340 | D4 | — | 24 | 1 | no | — |
| 341 | D4 | — | 24 | 2 | no | — |
| 342 | D4 | — | 24 | 1 | no | — |
| 343 | D4 | — | 24 | 1 | no | — |
| 344 | C2×C4 | — | 2 | 1 | no | — |
| 345 | C2×C4 | — | 3 | 1 | no | — |
| 346 | C2×C4 | — | 3 | 1 | no | — |
| 347 | C2×C4 | — | 3 | 1 | no | — |
| 348 | C2×C4 | — | 3 | 1 | no | — |
| 349 | C2×C4 | — | 3 | 1 | no | — |
| 350 | C2×C4 | — | 3 | 1 | no | — |
| 351 | C2×C4 | — | 3 | 1 | no | — |
| 352 | C2×C4 | — | 6 | 2 | no | — |
| 353 | C2×C4 | — | 6 | 2 | no | — |
| 354 | C2×C4 | — | 6 | 1 | no | — |
| 355 | C2×C4 | — | 6 | 1 | no | — |
| 356 | C2×C4 | — | 6 | 2 | no | — |
| 357 | C2×C4 | — | 12 | 1 | no | — |
| 358 | C2×C4 | — | 12 | 1 | no | — |
| 359 | C2×C4 | — | 12 | 1 | no | — |
| 360 | C2×C4 | — | 12 | 1 | no | — |
| 361 | C2×C4 | — | 24 | 1 | no | — |
| 362 | C2×C4 | — | 24 | 1 | no | — |
| 363 | C2×C4 | (C2×S4)⋊C4 | 1 | 1 | yes | characteristic |
| 364 | C8 | — | 3 | 1 | no | — |
| 365 | C8 | — | 3 | 1 | no | — |
| 366 | C8 | — | 3 | 1 | no | — |
| 367 | C8 | — | 3 | 1 | no | — |
| 368 | C8 | — | 24 | 2 | no | — |
| 369 | C8 | — | 24 | 1 | no | — |
| 370 | C8 | — | 24 | 2 | no | — |
| 371 | C8 | — | 24 | 1 | no | — |
| 372 | C8 | C8×S4 | 1 | 1 | yes | characteristic |
| 373 | C8 | #5400 | 1 | 1 | yes | characteristic |
| 374 | C8 | #5415 | 1 | 1 | yes | characteristic |
| 375 | C8 | #5417 | 1 | 1 | yes | characteristic |
| 376 | C2×C3 | — | 4 | 1 | no | — |
| 377 | C2×C3 | — | 8 | 1 | no | — |
| 378 | D3 | — | 32 | 1 | no | — |
| 379 | C22 | — | 3 | 1 | no | — |
| 380 | C22 | — | 3 | 1 | no | — |
| 381 | C22 | — | 3 | 1 | no | — |
| 382 | C22 | — | 6 | 1 | no | — |
| 383 | C22 | — | 6 | 1 | no | — |
| 384 | C22 | — | 6 | 1 | no | — |
| 385 | C22 | — | 6 | 1 | no | — |
| 386 | C22 | — | 24 | 1 | no | — |
| 387 | C22 | — | 24 | 1 | no | — |
| 388 | C22 | — | 24 | 1 | no | — |
| 389 | C22 | #67569 | 1 | 1 | yes | characteristic, complemented |
| 390 | C22 | #73117 | 1 | 1 | yes | characteristic |
| 391 | C4 | — | 2 | 2 | no | — |
| 392 | C4 | — | 3 | 1 | no | — |
| 393 | C4 | — | 3 | 1 | no | — |
| 394 | C4 | — | 6 | 2 | no | — |
| 395 | C4 | — | 24 | 1 | no | — |
| 396 | C4 | — | 24 | 1 | no | — |
| 397 | C4 | — | 24 | 1 | no | — |
| 398 | C4 | #73053 | 1 | 1 | yes | characteristic |
| 399 | C4 | (C2×S4)⋊C8 | 1 | 1 | yes | characteristic |
| 400 | C3 | — | 4 | 1 | no | Sylow |
| 401 | C2 | — | 2 | 1 | no | — |
| 402 | C2 | — | 3 | 1 | no | — |
| 403 | C2 | — | 3 | 1 | no | — |
| 404 | C2 | — | 6 | 1 | no | — |
| 405 | C2 | — | 48 | 1 | no | — |
| 406 | C2 | #11711105 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11710984 | C2 | semidirect |
| 3. A4×#364 | C2 | semidirect |
| 13. C22×#364 | D3 | semidirect |
| 26. #5402 | C8 | semidirect |
| 30. #5398 | C8 | semidirect |
| 120. #364 | S4 | semidirect |
| 324. A4 | #1336 | semidirect |
| 389. C22 | #67569 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11712861 | 2 |
| #11710984 | 2 |
| A4×#364 | 2 |
| #136600 | 3 |
| #67569 | 4 |