Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
518 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 60 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 | #11711530 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11710984 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | A4×#443 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #129509 | — | 3 | 1 | no | maximal, Sylow |
| 5 | A4×#135 | C4 | 1 | 1 | yes | characteristic |
| 6 | A4×#131 | — | 2 | 1 | no | — |
| 7 | A4×#108 | C4 | 1 | 1 | yes | characteristic |
| 8 | A4×#104 | — | 2 | 1 | no | — |
| 9 | C4×C8×A4 | C22 | 1 | 1 | yes | characteristic |
| 10 | #73104 | — | 2 | 1 | no | — |
| 11 | C4×A4⋊C8 | — | 2 | 1 | no | — |
| 12 | #67767 | — | 4 | 1 | no | maximal |
| 13 | C22×#443 | D3 | 1 | 1 | yes | characteristic |
| 14 | #12788 | — | 3 | 1 | no | — |
| 15 | C2×#1336 | — | 3 | 1 | no | — |
| 16 | C2×#1336 | — | 3 | 1 | no | — |
| 17 | C2×#1336 | — | 3 | 1 | no | — |
| 18 | C2×#1336 | — | 3 | 1 | no | — |
| 19 | #8144 | — | 3 | 1 | no | — |
| 20 | A4×#41 | — | 2 | 1 | no | — |
| 21 | A4×Q16 | C8 | 1 | 1 | yes | characteristic, complemented |
| 22 | A4×SD16 | — | 2 | 1 | no | — |
| 23 | A4×D8 | C8 | 1 | 1 | yes | characteristic, complemented |
| 24 | A4×M16 | — | 2 | 1 | no | — |
| 25 | A4×M16 | — | 4 | 1 | no | — |
| 26 | C2×C8×A4 | — | 4 | 1 | no | — |
| 27 | C2×C8×A4 | C2×C4 | 1 | 1 | yes | characteristic |
| 28 | C2×C8×A4 | D4 | 1 | 1 | yes | characteristic |
| 29 | C42×A4 | D4 | 1 | 1 | yes | characteristic |
| 30 | C2×A4⋊C8 | — | 2 | 2 | no | — |
| 31 | C3×#443 | — | 4 | 1 | no | — |
| 32 | A4⋊C16 | — | 4 | 1 | no | — |
| 33 | #4463 | — | 4 | 1 | no | — |
| 34 | #4455 | — | 4 | 1 | no | — |
| 35 | C22×#135 | Dic3 | 1 | 1 | yes | characteristic |
| 36 | C22×#131 | — | 2 | 1 | no | — |
| 37 | C2×#443 | — | 3 | 1 | no | — |
| 38 | C2×#443 | — | 3 | 1 | no | — |
| 39 | C2×#443 | — | 3 | 1 | no | — |
| 40 | C2×#443 | — | 3 | 1 | no | — |
| 41 | C2×#443 | — | 6 | 1 | no | — |
| 42 | C2×#443 | — | 6 | 1 | no | — |
| 43 | C22×#108 | Dic3 | 1 | 1 | yes | characteristic |
| 44 | C22×#104 | — | 2 | 1 | no | — |
| 45 | C22×C4×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 46 | C2×#364 | — | 3 | 1 | no | — |
| 47 | C2×#364 | — | 3 | 1 | no | — |
| 48 | #2112 | — | 6 | 1 | no | — |
| 49 | C4×C22⋊C8 | — | 6 | 1 | no | — |
| 50 | C2×#322 | — | 3 | 1 | no | — |
| 51 | C2×#322 | — | 3 | 1 | no | — |
| 52 | #1376 | — | 6 | 1 | no | — |
| 53 | #1336 | — | 6 | 2 | no | — |
| 54 | #1336 | — | 6 | 2 | no | — |
| 55 | #1336 | — | 6 | 1 | no | — |
| 56 | #1336 | — | 6 | 1 | no | — |
| 57 | #1336 | — | 6 | 1 | no | — |
| 58 | #1336 | — | 6 | 1 | no | — |
| 59 | #1273 | — | 6 | 1 | no | — |
| 60 | Q8×A4 | — | 2 | 1 | no | — |
| 61 | D4×A4 | — | 2 | 1 | no | — |
| 62 | D4×A4 | — | 4 | 1 | no | — |
| 63 | C2×C4×A4 | — | 2 | 1 | no | — |
| 64 | C2×C4×A4 | — | 4 | 1 | no | — |
| 65 | C2×C4×A4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 66 | C3×#135 | — | 4 | 1 | no | — |
| 67 | C3×#131 | — | 8 | 1 | no | — |
| 68 | C8×A4 | — | 4 | 1 | no | — |
| 69 | C8×A4 | C2×C8 | 1 | 1 | yes | characteristic |
| 70 | C8×A4 | M16 | 1 | 1 | yes | characteristic |
| 71 | C8×A4 | D8 | 1 | 1 | yes | characteristic |
| 72 | C8×A4 | SD16 | 1 | 1 | yes | characteristic |
| 73 | A4⋊C8 | — | 4 | 2 | no | — |
| 74 | C3×#108 | — | 4 | 1 | no | — |
| 75 | C3×#104 | — | 8 | 1 | no | — |
| 76 | C3×C4×C8 | — | 4 | 1 | no | — |
| 77 | #812 | — | 8 | 1 | no | — |
| 78 | C4×C3⋊C8 | — | 8 | 1 | no | — |
| 79 | C22×#41 | — | 2 | 1 | no | — |
| 80 | C2×#135 | — | 3 | 1 | no | — |
| 81 | C2×#135 | — | 3 | 1 | no | — |
| 82 | C2×#135 | — | 3 | 1 | no | — |
| 83 | C2×#135 | — | 3 | 1 | no | — |
| 84 | C2×#135 | — | 6 | 1 | no | — |
| 85 | C2×#135 | — | 6 | 1 | no | — |
| 86 | C22×Q16 | C3⋊C8 | 1 | 1 | yes | characteristic, complemented |
| 87 | C22×SD16 | — | 2 | 1 | no | — |
| 88 | C22×D8 | C3⋊C8 | 1 | 1 | yes | characteristic, complemented |
| 89 | C2×#131 | — | 6 | 1 | no | — |
| 90 | C2×#131 | — | 6 | 1 | no | — |
| 91 | C2×#131 | — | 6 | 1 | no | — |
| 92 | C2×#131 | — | 6 | 1 | no | — |
| 93 | C2×#131 | — | 12 | 1 | no | — |
| 94 | C2×#131 | — | 12 | 1 | no | — |
| 95 | C22×M16 | — | 2 | 1 | no | — |
| 96 | C22×M16 | — | 4 | 1 | no | — |
| 97 | C23×C8 | — | 4 | 1 | no | — |
| 98 | C23×C8 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 99 | C23×C8 | #67 | 1 | 1 | yes | characteristic |
| 100 | C22×C42 | #67 | 1 | 1 | yes | characteristic |
| 101 | C2×M32 | — | 6 | 1 | no | — |
| 102 | C2×M32 | — | 6 | 1 | no | — |
| 103 | #443 | — | 3 | 2 | no | — |
| 104 | #443 | — | 3 | 2 | no | — |
| 105 | #443 | — | 3 | 1 | no | — |
| 106 | #443 | — | 3 | 1 | no | — |
| 107 | #443 | — | 3 | 1 | no | — |
| 108 | #443 | — | 6 | 1 | no | — |
| 109 | #443 | — | 6 | 1 | no | — |
| 110 | #443 | — | 6 | 1 | no | — |
| 111 | #443 | — | 6 | 2 | no | — |
| 112 | #443 | — | 6 | 2 | no | — |
| 113 | #443 | S4 | 1 | 1 | yes | characteristic |
| 114 | C2×#108 | — | 3 | 1 | no | — |
| 115 | C2×#108 | — | 3 | 1 | no | — |
| 116 | C2×#108 | — | 6 | 1 | no | — |
| 117 | C2×#104 | — | 6 | 1 | no | — |
| 118 | C2×#104 | — | 6 | 1 | no | — |
| 119 | C2×#104 | — | 6 | 1 | no | — |
| 120 | C2×#104 | — | 6 | 1 | no | — |
| 121 | C2×C22⋊C8 | — | 6 | 2 | no | — |
| 122 | C2×C4×C8 | — | 3 | 1 | no | — |
| 123 | C2×C4×C8 | — | 3 | 1 | no | — |
| 124 | C2×C4×C8 | — | 3 | 1 | no | — |
| 125 | C2×C4×C8 | — | 3 | 1 | no | — |
| 126 | C2×C4×C8 | — | 6 | 1 | no | — |
| 127 | C2×C4×C8 | — | 6 | 1 | no | — |
| 128 | #364 | — | 6 | 1 | no | — |
| 129 | #364 | — | 6 | 1 | no | — |
| 130 | #364 | — | 6 | 1 | no | — |
| 131 | #364 | — | 6 | 1 | no | — |
| 132 | C22⋊C16 | — | 12 | 1 | no | — |
| 133 | C22⋊C16 | — | 12 | 1 | no | — |
| 134 | #336 | — | 6 | 2 | no | — |
| 135 | #322 | — | 6 | 1 | no | — |
| 136 | #322 | — | 6 | 1 | no | — |
| 137 | #322 | — | 6 | 1 | no | — |
| 138 | #322 | — | 6 | 1 | no | — |
| 139 | C22×A4 | — | 4 | 1 | no | — |
| 140 | C22×A4 | #104 | 1 | 1 | yes | characteristic |
| 141 | C3×#41 | — | 8 | 1 | no | — |
| 142 | C4×A4 | — | 2 | 2 | no | — |
| 143 | C4×A4 | — | 4 | 1 | no | — |
| 144 | C4×A4 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 145 | C4×A4 | #102 | 1 | 1 | yes | characteristic |
| 146 | C3×Q16 | — | 4 | 1 | no | — |
| 147 | C3×SD16 | — | 8 | 1 | no | — |
| 148 | C3×D8 | — | 4 | 1 | no | — |
| 149 | C3×M16 | — | 8 | 1 | no | — |
| 150 | C3×M16 | — | 16 | 1 | no | — |
| 151 | C2×C3×C8 | — | 4 | 1 | no | — |
| 152 | C2×C3×C8 | — | 4 | 1 | no | — |
| 153 | C2×C3×C8 | — | 16 | 1 | no | — |
| 154 | C3×C42 | — | 4 | 1 | no | — |
| 155 | C2×C3⋊C8 | — | 8 | 2 | no | — |
| 156 | C3⋊C16 | — | 16 | 1 | no | — |
| 157 | C2×#41 | — | 6 | 1 | no | — |
| 158 | C2×#41 | — | 6 | 1 | no | — |
| 159 | C2×#41 | — | 6 | 1 | no | — |
| 160 | C2×#41 | — | 6 | 1 | no | — |
| 161 | C2×#41 | — | 12 | 1 | no | — |
| 162 | C2×#41 | — | 12 | 1 | no | — |
| 163 | C22×Q8 | — | 2 | 1 | no | — |
| 164 | C22×D4 | — | 2 | 1 | no | — |
| 165 | C22×D4 | — | 4 | 1 | no | — |
| 166 | C23×C4 | — | 2 | 1 | no | — |
| 167 | C23×C4 | — | 4 | 1 | no | — |
| 168 | C23×C4 | #217 | 1 | 1 | yes | characteristic |
| 169 | #135 | — | 3 | 2 | no | — |
| 170 | #135 | — | 3 | 2 | no | — |
| 171 | #135 | — | 3 | 1 | no | — |
| 172 | #135 | — | 3 | 1 | no | — |
| 173 | #135 | — | 3 | 1 | no | — |
| 174 | #135 | — | 6 | 1 | no | — |
| 175 | #135 | — | 6 | 1 | no | — |
| 176 | #135 | — | 6 | 1 | no | — |
| 177 | #135 | — | 6 | 2 | no | — |
| 178 | #135 | — | 6 | 2 | no | — |
| 179 | #135 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 180 | C2×Q16 | — | 3 | 1 | no | — |
| 181 | C2×Q16 | — | 3 | 1 | no | — |
| 182 | C2×Q16 | — | 6 | 1 | no | — |
| 183 | C2×SD16 | — | 6 | 1 | no | — |
| 184 | C2×SD16 | — | 6 | 1 | no | — |
| 185 | C2×SD16 | — | 6 | 1 | no | — |
| 186 | C2×SD16 | — | 6 | 1 | no | — |
| 187 | C2×D8 | — | 3 | 1 | no | — |
| 188 | C2×D8 | — | 3 | 1 | no | — |
| 189 | C2×D8 | — | 6 | 1 | no | — |
| 190 | #131 | — | 2 | 1 | no | — |
| 191 | #131 | — | 6 | 1 | no | — |
| 192 | #131 | — | 6 | 1 | no | — |
| 193 | #131 | — | 6 | 2 | no | — |
| 194 | #131 | — | 6 | 1 | no | — |
| 195 | #131 | — | 12 | 1 | no | — |
| 196 | #131 | — | 12 | 1 | no | — |
| 197 | #131 | — | 12 | 1 | no | — |
| 198 | #131 | — | 12 | 1 | no | — |
| 199 | #131 | — | 12 | 2 | no | — |
| 200 | #131 | — | 12 | 2 | no | — |
| 201 | C2×M16 | — | 6 | 1 | no | — |
| 202 | C2×M16 | — | 6 | 1 | no | — |
| 203 | C2×M16 | — | 12 | 1 | no | — |
| 204 | C2×M16 | — | 12 | 1 | no | — |
| 205 | C2×M16 | — | 12 | 1 | no | — |
| 206 | C2×M16 | — | 12 | 1 | no | — |
| 207 | C2×M16 | — | 12 | 1 | no | — |
| 208 | C22×C8 | — | 3 | 1 | no | — |
| 209 | C22×C8 | — | 3 | 1 | no | — |
| 210 | C22×C8 | — | 3 | 1 | no | — |
| 211 | C22×C8 | — | 3 | 1 | no | — |
| 212 | C22×C8 | — | 3 | 1 | no | — |
| 213 | C22×C8 | — | 3 | 1 | no | — |
| 214 | C22×C8 | — | 3 | 1 | no | — |
| 215 | C22×C8 | — | 3 | 1 | no | — |
| 216 | C22×C8 | — | 4 | 1 | no | — |
| 217 | C22×C8 | — | 6 | 2 | no | — |
| 218 | C22×C8 | — | 6 | 2 | no | — |
| 219 | C22×C8 | — | 12 | 1 | no | — |
| 220 | C22×C8 | — | 12 | 1 | no | — |
| 221 | C22×C8 | — | 12 | 1 | no | — |
| 222 | C22×C8 | — | 12 | 1 | no | — |
| 223 | C22×C8 | C2×C3⋊C8 | 1 | 1 | yes | characteristic |
| 224 | C22×C8 | #208 | 1 | 1 | yes | characteristic |
| 225 | C22×C8 | #213 | 1 | 1 | yes | characteristic |
| 226 | C22×C8 | #214 | 1 | 1 | yes | characteristic |
| 227 | C2×C42 | — | 3 | 1 | no | — |
| 228 | C2×C42 | — | 3 | 1 | no | — |
| 229 | C2×C42 | — | 6 | 1 | no | — |
| 230 | M32 | — | 12 | 1 | no | — |
| 231 | M32 | — | 12 | 1 | no | — |
| 232 | M32 | — | 12 | 1 | no | — |
| 233 | M32 | — | 12 | 1 | no | — |
| 234 | C2×C16 | — | 12 | 1 | no | — |
| 235 | C2×C16 | — | 12 | 1 | no | — |
| 236 | #108 | — | 3 | 2 | no | — |
| 237 | #108 | — | 3 | 1 | no | — |
| 238 | #108 | — | 6 | 1 | no | — |
| 239 | #108 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 240 | #104 | — | 2 | 1 | no | — |
| 241 | #104 | — | 6 | 1 | no | — |
| 242 | #104 | — | 6 | 1 | no | — |
| 243 | #104 | — | 6 | 2 | no | — |
| 244 | #104 | — | 6 | 1 | no | — |
| 245 | C22⋊C8 | — | 12 | 2 | no | — |
| 246 | C22⋊C8 | — | 12 | 2 | no | — |
| 247 | C4×C8 | — | 3 | 1 | no | — |
| 248 | C4×C8 | — | 3 | 1 | no | — |
| 249 | C4×C8 | — | 3 | 1 | no | — |
| 250 | C4×C8 | — | 6 | 1 | no | — |
| 251 | C4×C8 | — | 12 | 1 | no | — |
| 252 | C4×C8 | — | 12 | 1 | no | — |
| 253 | C4×C8 | — | 12 | 1 | no | — |
| 254 | C4×C8 | — | 12 | 1 | no | — |
| 255 | C4×C8 | C2×S4 | 1 | 1 | yes | characteristic |
| 256 | C2×A4 | — | 2 | 1 | no | — |
| 257 | C2×A4 | — | 8 | 1 | no | — |
| 258 | C2×A4 | D4⋊C8 | 1 | 1 | yes | characteristic |
| 259 | C3×Q8 | — | 8 | 1 | no | — |
| 260 | C3×D4 | — | 8 | 1 | no | — |
| 261 | C3×D4 | — | 16 | 1 | no | — |
| 262 | C2×C3×C4 | — | 4 | 1 | no | — |
| 263 | C2×C3×C4 | — | 8 | 1 | no | — |
| 264 | C2×C3×C4 | — | 16 | 1 | no | — |
| 265 | C3×C8 | — | 4 | 1 | no | — |
| 266 | C3×C8 | — | 4 | 1 | no | — |
| 267 | C3×C8 | — | 4 | 1 | no | — |
| 268 | C3×C8 | — | 4 | 1 | no | — |
| 269 | C3×C8 | — | 16 | 1 | no | — |
| 270 | C3⋊C8 | — | 16 | 2 | no | — |
| 271 | C24 | — | 4 | 1 | no | — |
| 272 | C24 | #837 | 1 | 1 | yes | characteristic |
| 273 | #41 | — | 2 | 1 | no | — |
| 274 | #41 | — | 6 | 1 | no | — |
| 275 | #41 | — | 6 | 1 | no | — |
| 276 | #41 | — | 6 | 2 | no | — |
| 277 | #41 | — | 6 | 1 | no | — |
| 278 | #41 | — | 12 | 1 | no | — |
| 279 | #41 | — | 12 | 1 | no | — |
| 280 | #41 | — | 12 | 1 | no | — |
| 281 | #41 | — | 12 | 1 | no | — |
| 282 | #41 | — | 12 | 2 | no | — |
| 283 | #41 | — | 12 | 2 | no | — |
| 284 | C2×Q8 | — | 6 | 1 | no | — |
| 285 | C2×Q8 | — | 6 | 1 | no | — |
| 286 | C2×Q8 | — | 12 | 1 | no | — |
| 287 | C2×D4 | — | 6 | 1 | no | — |
| 288 | C2×D4 | — | 6 | 1 | no | — |
| 289 | C2×D4 | — | 12 | 1 | no | — |
| 290 | C2×D4 | — | 12 | 1 | no | — |
| 291 | C2×D4 | — | 12 | 1 | no | — |
| 292 | C2×D4 | — | 12 | 1 | no | — |
| 293 | C2×D4 | — | 12 | 1 | no | — |
| 294 | C22×C4 | — | 2 | 2 | no | — |
| 295 | C22×C4 | — | 3 | 1 | no | — |
| 296 | C22×C4 | — | 3 | 1 | no | — |
| 297 | C22×C4 | — | 3 | 1 | no | — |
| 298 | C22×C4 | — | 3 | 1 | no | — |
| 299 | C22×C4 | — | 4 | 1 | no | — |
| 300 | C22×C4 | — | 6 | 1 | no | — |
| 301 | C22×C4 | — | 6 | 1 | no | — |
| 302 | C22×C4 | — | 6 | 2 | no | — |
| 303 | C22×C4 | — | 12 | 1 | no | — |
| 304 | C22×C4 | — | 12 | 1 | no | — |
| 305 | C22×C4 | — | 12 | 1 | no | — |
| 306 | C22×C4 | — | 12 | 1 | no | — |
| 307 | C22×C4 | #830 | 1 | 1 | yes | characteristic |
| 308 | C22×C4 | #832 | 1 | 1 | yes | characteristic |
| 309 | Q16 | — | 3 | 2 | no | — |
| 310 | Q16 | — | 3 | 1 | no | — |
| 311 | Q16 | — | 6 | 1 | no | — |
| 312 | Q16 | A4⋊C8 | 1 | 1 | yes | characteristic, complemented |
| 313 | SD16 | — | 2 | 1 | no | — |
| 314 | SD16 | — | 6 | 1 | no | — |
| 315 | SD16 | — | 6 | 1 | no | — |
| 316 | SD16 | — | 6 | 2 | no | — |
| 317 | SD16 | — | 6 | 1 | no | — |
| 318 | D8 | — | 3 | 2 | no | — |
| 319 | D8 | — | 3 | 1 | no | — |
| 320 | D8 | — | 6 | 1 | no | — |
| 321 | D8 | A4⋊C8 | 1 | 1 | yes | characteristic, complemented |
| 322 | M16 | — | 2 | 1 | no | — |
| 323 | M16 | — | 4 | 1 | no | — |
| 324 | M16 | — | 6 | 1 | no | — |
| 325 | M16 | — | 12 | 1 | no | — |
| 326 | M16 | — | 12 | 1 | no | — |
| 327 | M16 | — | 12 | 2 | no | — |
| 328 | M16 | — | 12 | 1 | no | — |
| 329 | M16 | — | 12 | 1 | no | — |
| 330 | M16 | — | 12 | 1 | no | — |
| 331 | C2×C8 | — | 3 | 1 | no | — |
| 332 | C2×C8 | — | 3 | 1 | no | — |
| 333 | C2×C8 | — | 3 | 1 | no | — |
| 334 | C2×C8 | — | 3 | 1 | no | — |
| 335 | C2×C8 | — | 3 | 1 | no | — |
| 336 | C2×C8 | — | 3 | 1 | no | — |
| 337 | C2×C8 | — | 3 | 1 | no | — |
| 338 | C2×C8 | — | 3 | 1 | no | — |
| 339 | C2×C8 | — | 3 | 1 | no | — |
| 340 | C2×C8 | — | 3 | 1 | no | — |
| 341 | C2×C8 | — | 3 | 1 | no | — |
| 342 | C2×C8 | — | 3 | 1 | no | — |
| 343 | C2×C8 | — | 3 | 1 | no | — |
| 344 | C2×C8 | — | 3 | 1 | no | — |
| 345 | C2×C8 | — | 4 | 1 | no | — |
| 346 | C2×C8 | — | 6 | 1 | no | — |
| 347 | C2×C8 | — | 6 | 1 | no | — |
| 348 | C2×C8 | — | 12 | 1 | no | — |
| 349 | C2×C8 | — | 12 | 1 | no | — |
| 350 | C2×C8 | — | 12 | 2 | no | — |
| 351 | C2×C8 | — | 12 | 1 | no | — |
| 352 | C2×C8 | — | 12 | 1 | no | — |
| 353 | C2×C8 | — | 12 | 1 | no | — |
| 354 | C2×C8 | — | 12 | 2 | no | — |
| 355 | C2×C8 | — | 12 | 2 | no | — |
| 356 | C2×C8 | — | 12 | 2 | no | — |
| 357 | C2×C8 | — | 12 | 2 | no | — |
| 358 | C2×C8 | — | 12 | 2 | no | — |
| 359 | C2×C8 | — | 12 | 2 | no | — |
| 360 | C2×C8 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 361 | C2×C8 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 362 | C42 | — | 3 | 1 | no | — |
| 363 | C42 | — | 6 | 1 | no | — |
| 364 | C42 | — | 6 | 1 | no | — |
| 365 | C42 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 366 | C16 | — | 24 | 1 | no | — |
| 367 | C16 | — | 24 | 1 | no | — |
| 368 | C22×C3 | — | 4 | 1 | no | — |
| 369 | C22×C3 | — | 16 | 1 | no | — |
| 370 | A4 | #1336 | 1 | 1 | yes | characteristic, complemented |
| 371 | C3×C4 | — | 4 | 1 | no | — |
| 372 | C3×C4 | — | 4 | 1 | no | — |
| 373 | C3×C4 | — | 8 | 2 | no | — |
| 374 | C3×C4 | — | 16 | 1 | no | — |
| 375 | C23 | — | 2 | 1 | no | — |
| 376 | C23 | — | 3 | 1 | no | — |
| 377 | C23 | — | 3 | 1 | no | — |
| 378 | C23 | — | 6 | 1 | no | — |
| 379 | C23 | — | 8 | 1 | no | — |
| 380 | C23 | — | 12 | 1 | no | — |
| 381 | C23 | — | 12 | 1 | no | — |
| 382 | C23 | — | 24 | 1 | no | — |
| 383 | C23 | D4⋊(C3⋊C8) | 1 | 1 | yes | characteristic |
| 384 | Q8 | — | 2 | 1 | no | — |
| 385 | Q8 | — | 6 | 1 | no | — |
| 386 | Q8 | — | 12 | 1 | no | — |
| 387 | Q8 | — | 12 | 1 | no | — |
| 388 | D4 | — | 2 | 1 | no | — |
| 389 | D4 | — | 4 | 1 | no | — |
| 390 | D4 | — | 6 | 1 | no | — |
| 391 | D4 | — | 12 | 1 | no | — |
| 392 | D4 | — | 12 | 1 | no | — |
| 393 | D4 | — | 12 | 1 | no | — |
| 394 | D4 | — | 12 | 1 | no | — |
| 395 | D4 | — | 12 | 2 | no | — |
| 396 | D4 | — | 12 | 1 | no | — |
| 397 | C2×C4 | — | 2 | 1 | no | — |
| 398 | C2×C4 | — | 3 | 1 | no | — |
| 399 | C2×C4 | — | 3 | 1 | no | — |
| 400 | C2×C4 | — | 3 | 1 | no | — |
| 401 | C2×C4 | — | 3 | 1 | no | — |
| 402 | C2×C4 | — | 3 | 1 | no | — |
| 403 | C2×C4 | — | 3 | 1 | no | — |
| 404 | C2×C4 | — | 3 | 1 | no | — |
| 405 | C2×C4 | — | 4 | 1 | no | — |
| 406 | C2×C4 | — | 6 | 2 | no | — |
| 407 | C2×C4 | — | 6 | 2 | no | — |
| 408 | C2×C4 | — | 6 | 1 | no | — |
| 409 | C2×C4 | — | 6 | 1 | no | — |
| 410 | C2×C4 | — | 6 | 2 | no | — |
| 411 | C2×C4 | — | 12 | 1 | no | — |
| 412 | C2×C4 | — | 12 | 1 | no | — |
| 413 | C2×C4 | — | 12 | 2 | no | — |
| 414 | C2×C4 | — | 12 | 1 | no | — |
| 415 | C2×C4 | — | 12 | 1 | no | — |
| 416 | C2×C4 | — | 12 | 1 | no | — |
| 417 | C2×C4 | — | 12 | 1 | no | — |
| 418 | C2×C4 | #5432 | 1 | 1 | yes | characteristic |
| 419 | C8 | — | 3 | 1 | no | — |
| 420 | C8 | — | 3 | 1 | no | — |
| 421 | C8 | — | 3 | 1 | no | — |
| 422 | C8 | — | 3 | 1 | no | — |
| 423 | C8 | — | 4 | 1 | no | — |
| 424 | C8 | — | 12 | 1 | no | — |
| 425 | C8 | — | 24 | 2 | no | — |
| 426 | C8 | — | 24 | 2 | no | — |
| 427 | C8 | C2×A4⋊C8 | 1 | 1 | yes | characteristic |
| 428 | C8 | #5409 | 1 | 1 | yes | characteristic |
| 429 | C8 | #5414 | 1 | 1 | yes | characteristic |
| 430 | C8 | #5415 | 1 | 1 | yes | characteristic |
| 431 | C2×C3 | — | 4 | 1 | no | — |
| 432 | C2×C3 | — | 8 | 1 | no | — |
| 433 | C2×C3 | — | 32 | 1 | no | — |
| 434 | C22 | — | 3 | 1 | no | — |
| 435 | C22 | — | 3 | 1 | no | — |
| 436 | C22 | — | 3 | 1 | no | — |
| 437 | C22 | — | 4 | 1 | no | — |
| 438 | C22 | — | 6 | 1 | no | — |
| 439 | C22 | — | 6 | 1 | no | — |
| 440 | C22 | — | 6 | 1 | no | — |
| 441 | C22 | — | 6 | 1 | no | — |
| 442 | C22 | — | 12 | 1 | no | — |
| 443 | C22 | — | 24 | 1 | no | — |
| 444 | C22 | — | 24 | 1 | no | — |
| 445 | C22 | — | 24 | 1 | no | — |
| 446 | C22 | — | 24 | 1 | no | — |
| 447 | C22 | #67767 | 1 | 1 | yes | characteristic, complemented |
| 448 | C22 | #73150 | 1 | 1 | yes | characteristic |
| 449 | C4 | — | 2 | 2 | no | — |
| 450 | C4 | — | 3 | 1 | no | — |
| 451 | C4 | — | 3 | 1 | no | — |
| 452 | C4 | — | 4 | 1 | no | — |
| 453 | C4 | — | 6 | 2 | no | — |
| 454 | C4 | — | 12 | 1 | no | — |
| 455 | C4 | #73141 | 1 | 1 | yes | characteristic |
| 456 | C4 | #73144 | 1 | 1 | yes | characteristic |
| 457 | C3 | — | 4 | 1 | no | Sylow |
| 458 | C2 | — | 2 | 1 | no | — |
| 459 | C2 | — | 3 | 1 | no | — |
| 460 | C2 | — | 3 | 1 | no | — |
| 461 | C2 | — | 6 | 1 | no | — |
| 462 | C2 | — | 8 | 1 | no | — |
| 463 | C2 | — | 24 | 1 | no | — |
| 464 | C2 | D4⋊(A4⋊C8) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11711530 | C2 | semidirect |
| 2. #11710984 | C2 | semidirect |
| 21. A4×Q16 | C8 | semidirect |
| 23. A4×D8 | C8 | semidirect |
| 86. C22×Q16 | C3⋊C8 | semidirect |
| 88. C22×D8 | C3⋊C8 | semidirect |
| 312. Q16 | A4⋊C8 | semidirect |
| 321. D8 | A4⋊C8 | semidirect |
| 370. A4 | #1336 | semidirect |
| 447. C22 | #67767 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11711530 | 2 |
| #11710984 | 2 |
| A4×#443 | 2 |
| #129509 | 3 |
| #67767 | 4 |