Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
798 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 112 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 | #11714124 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #11711530 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11711496 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11711481 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | A4×#443 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #497275 | — | 3 | 1 | no | maximal, Sylow |
| 7 | A4×#135 | C4 | 1 | 1 | yes | characteristic |
| 8 | A4×#131 | C22 | 1 | 2 | yes | — |
| 9 | A4×#108 | C4 | 1 | 1 | yes | characteristic |
| 10 | A4×#104 | C4 | 1 | 2 | yes | — |
| 11 | C4×C8×A4 | C22 | 1 | 1 | yes | characteristic |
| 12 | #73104 | — | 2 | 2 | no | — |
| 13 | #73104 | C22 | 1 | 2 | yes | — |
| 14 | C2×A4⋊C16 | — | 2 | 2 | no | — |
| 15 | C2×A4⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×A4⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 17 | #70924 | — | 4 | 1 | no | maximal |
| 18 | C22×#443 | D3 | 1 | 1 | yes | characteristic |
| 19 | C2×#2171 | — | 3 | 1 | no | — |
| 20 | C2×#2171 | — | 3 | 1 | no | — |
| 21 | #33334 | — | 3 | 2 | no | — |
| 22 | #13196 | — | 3 | 1 | no | — |
| 23 | #13196 | — | 3 | 1 | no | — |
| 24 | #12980 | — | 3 | 2 | no | — |
| 25 | #12980 | — | 3 | 2 | no | — |
| 26 | #12788 | — | 3 | 1 | no | — |
| 27 | #12683 | — | 3 | 2 | no | — |
| 28 | #12599 | — | 3 | 1 | no | — |
| 29 | A4×#41 | C2×C4 | 1 | 2 | yes | — |
| 30 | A4×Q16 | C8 | 1 | 1 | yes | characteristic |
| 31 | A4×SD16 | C8 | 1 | 2 | yes | — |
| 32 | A4×D8 | C8 | 1 | 1 | yes | characteristic |
| 33 | A4×M16 | — | 2 | 2 | no | — |
| 34 | A4×M16 | C2×C4 | 1 | 2 | yes | — |
| 35 | C2×C8×A4 | — | 2 | 2 | no | — |
| 36 | C2×C8×A4 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | C2×C8×A4 | C23 | 1 | 1 | yes | characteristic |
| 38 | C42×A4 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | C3×#443 | — | 4 | 1 | no | — |
| 40 | #5140 | — | 4 | 2 | no | — |
| 41 | A4⋊C16 | — | 2 | 2 | no | — |
| 42 | A4⋊C16 | — | 2 | 1 | no | — |
| 43 | A4⋊C16 | D4 | 1 | 2 | yes | — |
| 44 | #4561 | — | 4 | 2 | no | — |
| 45 | #4463 | — | 4 | 1 | no | — |
| 46 | #4461 | — | 4 | 1 | no | — |
| 47 | C22×#135 | Dic3 | 1 | 1 | yes | characteristic |
| 48 | C22×#131 | C2×D3 | 1 | 2 | yes | — |
| 49 | C2×#504 | — | 3 | 2 | no | — |
| 50 | C2×#504 | — | 3 | 2 | no | — |
| 51 | C2×#443 | — | 3 | 1 | no | — |
| 52 | C2×#443 | — | 3 | 1 | no | — |
| 53 | C2×#443 | — | 3 | 2 | no | — |
| 54 | C2×#443 | — | 3 | 1 | no | — |
| 55 | C2×#443 | — | 3 | 1 | no | — |
| 56 | C2×#443 | — | 3 | 2 | no | — |
| 57 | C22×#108 | Dic3 | 1 | 1 | yes | characteristic |
| 58 | C22×#104 | Dic3 | 1 | 2 | yes | — |
| 59 | C22×C4×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 60 | #2171 | — | 6 | 1 | no | — |
| 61 | #2171 | — | 6 | 1 | no | — |
| 62 | #2171 | — | 6 | 2 | no | — |
| 63 | #2171 | — | 6 | 2 | no | — |
| 64 | #2171 | — | 6 | 1 | no | — |
| 65 | #2171 | — | 6 | 1 | no | — |
| 66 | C2×#364 | — | 3 | 1 | no | — |
| 67 | C2×#364 | — | 3 | 1 | no | — |
| 68 | C2×#350 | — | 3 | 2 | no | — |
| 69 | C2×#350 | — | 3 | 2 | no | — |
| 70 | C2×#350 | — | 3 | 2 | no | — |
| 71 | C2×#350 | — | 3 | 2 | no | — |
| 72 | #2113 | — | 3 | 2 | no | — |
| 73 | #2113 | — | 3 | 2 | no | — |
| 74 | #2113 | — | 6 | 2 | no | — |
| 75 | #2113 | — | 6 | 2 | no | — |
| 76 | #2112 | — | 3 | 2 | no | — |
| 77 | #2112 | — | 6 | 2 | no | — |
| 78 | C2×C22⋊C16 | — | 3 | 1 | no | — |
| 79 | C2×C22⋊C16 | — | 3 | 1 | no | — |
| 80 | C2×C22⋊C16 | — | 6 | 2 | no | — |
| 81 | C2×#346 | — | 3 | 1 | no | — |
| 82 | C2×#346 | — | 3 | 1 | no | — |
| 83 | #1376 | — | 3 | 2 | no | — |
| 84 | #1374 | — | 3 | 1 | no | — |
| 85 | #1374 | — | 3 | 1 | no | — |
| 86 | Q8×A4 | C2×C8 | 1 | 2 | yes | — |
| 87 | D4×A4 | — | 2 | 2 | no | — |
| 88 | D4×A4 | C2×C8 | 1 | 2 | yes | — |
| 89 | C2×C4×A4 | — | 2 | 2 | no | — |
| 90 | C2×C4×A4 | — | 2 | 1 | no | — |
| 91 | C2×C4×A4 | C22×C4 | 1 | 1 | yes | characteristic |
| 92 | C3×#135 | — | 4 | 1 | no | — |
| 93 | C3×#131 | — | 4 | 2 | no | — |
| 94 | C8×A4 | — | 2 | 2 | no | — |
| 95 | C8×A4 | C2×C8 | 1 | 1 | yes | characteristic |
| 96 | C8×A4 | C2×C8 | 1 | 1 | yes | characteristic |
| 97 | C8×A4 | C2×D4 | 1 | 1 | yes | characteristic |
| 98 | C8×A4 | #41 | 1 | 1 | yes | characteristic |
| 99 | C3×#108 | — | 4 | 1 | no | — |
| 100 | C3×#104 | — | 4 | 2 | no | — |
| 101 | C3×C4×C8 | — | 4 | 1 | no | — |
| 102 | #812 | — | 4 | 2 | no | — |
| 103 | #812 | — | 8 | 2 | no | — |
| 104 | C2×C3⋊C16 | — | 4 | 1 | no | — |
| 105 | C2×C3⋊C16 | — | 4 | 1 | no | — |
| 106 | C2×C3⋊C16 | — | 8 | 2 | no | — |
| 107 | C22×#41 | C2×Dic3 | 1 | 2 | yes | — |
| 108 | C2×#135 | — | 3 | 1 | no | — |
| 109 | C2×#135 | — | 3 | 1 | no | — |
| 110 | C2×#135 | — | 3 | 2 | no | — |
| 111 | C2×#135 | — | 3 | 1 | no | — |
| 112 | C2×#135 | — | 3 | 2 | no | — |
| 113 | C2×#135 | — | 3 | 1 | no | — |
| 114 | C22×Q16 | C3⋊C8 | 1 | 1 | yes | characteristic |
| 115 | C22×SD16 | C3⋊C8 | 1 | 2 | yes | — |
| 116 | C22×D8 | C3⋊C8 | 1 | 1 | yes | characteristic |
| 117 | C2×#131 | — | 3 | 2 | no | — |
| 118 | C2×#131 | — | 3 | 2 | no | — |
| 119 | C2×#131 | — | 3 | 2 | no | — |
| 120 | C2×#131 | — | 3 | 2 | no | — |
| 121 | C2×#131 | — | 6 | 2 | no | — |
| 122 | C2×#131 | — | 6 | 2 | no | — |
| 123 | C22×M16 | — | 2 | 2 | no | — |
| 124 | C22×M16 | C2×Dic3 | 1 | 2 | yes | — |
| 125 | C23×C8 | — | 2 | 2 | no | — |
| 126 | C23×C8 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 127 | C23×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 128 | C22×C42 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 129 | #504 | — | 6 | 2 | no | — |
| 130 | #504 | — | 6 | 2 | no | — |
| 131 | #504 | — | 6 | 2 | no | — |
| 132 | #504 | — | 6 | 2 | no | — |
| 133 | #504 | — | 12 | 2 | no | — |
| 134 | #504 | — | 12 | 2 | no | — |
| 135 | C2×M32 | — | 3 | 2 | no | — |
| 136 | C2×M32 | — | 3 | 2 | no | — |
| 137 | C2×M32 | — | 6 | 2 | no | — |
| 138 | C2×M32 | — | 6 | 2 | no | — |
| 139 | C22×C16 | — | 3 | 1 | no | — |
| 140 | C22×C16 | — | 3 | 1 | no | — |
| 141 | C22×C16 | — | 3 | 1 | no | — |
| 142 | C22×C16 | — | 3 | 1 | no | — |
| 143 | C22×C16 | — | 6 | 2 | no | — |
| 144 | C22×C16 | — | 6 | 2 | no | — |
| 145 | #443 | — | 3 | 1 | no | — |
| 146 | #443 | — | 3 | 2 | no | — |
| 147 | #443 | — | 3 | 1 | no | — |
| 148 | #443 | — | 3 | 2 | no | — |
| 149 | #443 | — | 3 | 1 | no | — |
| 150 | #443 | — | 6 | 1 | no | — |
| 151 | #443 | — | 6 | 1 | no | — |
| 152 | #443 | — | 6 | 1 | no | — |
| 153 | #443 | — | 6 | 2 | no | — |
| 154 | #443 | — | 6 | 2 | no | — |
| 155 | #443 | S4 | 1 | 1 | yes | characteristic |
| 156 | C2×#108 | — | 3 | 1 | no | — |
| 157 | C2×#108 | — | 3 | 2 | no | — |
| 158 | C2×#108 | — | 3 | 1 | no | — |
| 159 | C2×#104 | — | 3 | 2 | no | — |
| 160 | C2×#104 | — | 3 | 2 | no | — |
| 161 | C2×#104 | — | 3 | 2 | no | — |
| 162 | C2×#104 | — | 3 | 2 | no | — |
| 163 | C2×C4×C8 | — | 3 | 1 | no | — |
| 164 | C2×C4×C8 | — | 3 | 1 | no | — |
| 165 | C2×C4×C8 | — | 3 | 1 | no | — |
| 166 | C2×C4×C8 | — | 3 | 1 | no | — |
| 167 | #364 | — | 6 | 1 | no | — |
| 168 | #364 | — | 6 | 1 | no | — |
| 169 | #364 | — | 6 | 1 | no | — |
| 170 | #364 | — | 6 | 1 | no | — |
| 171 | #350 | — | 6 | 2 | no | — |
| 172 | #350 | — | 6 | 2 | no | — |
| 173 | #350 | — | 6 | 2 | no | — |
| 174 | #350 | — | 6 | 2 | no | — |
| 175 | #350 | — | 12 | 2 | no | — |
| 176 | #350 | — | 12 | 2 | no | — |
| 177 | C22⋊C16 | — | 3 | 2 | no | — |
| 178 | C22⋊C16 | — | 3 | 2 | no | — |
| 179 | C22⋊C16 | — | 6 | 2 | no | — |
| 180 | C22⋊C16 | — | 6 | 2 | no | — |
| 181 | C22⋊C16 | — | 6 | 2 | no | — |
| 182 | C22⋊C16 | — | 6 | 2 | no | — |
| 183 | C22⋊C16 | — | 6 | 1 | no | — |
| 184 | C22⋊C16 | — | 6 | 2 | no | — |
| 185 | C22⋊C16 | — | 6 | 2 | no | — |
| 186 | C22⋊C16 | — | 6 | 1 | no | — |
| 187 | #346 | — | 6 | 1 | no | — |
| 188 | #346 | — | 6 | 1 | no | — |
| 189 | #346 | — | 6 | 1 | no | — |
| 190 | #346 | — | 6 | 1 | no | — |
| 191 | C22×A4 | — | 2 | 2 | no | — |
| 192 | C22×A4 | #131 | 1 | 1 | yes | characteristic |
| 193 | C3×#41 | — | 4 | 2 | no | — |
| 194 | C4×A4 | — | 2 | 2 | no | — |
| 195 | C4×A4 | — | 4 | 1 | no | — |
| 196 | C4×A4 | C4×D4 | 1 | 1 | yes | characteristic |
| 197 | C4×A4 | C22×C8 | 1 | 1 | yes | characteristic |
| 198 | C3×Q16 | — | 4 | 1 | no | — |
| 199 | C3×SD16 | — | 4 | 2 | no | — |
| 200 | C3×D8 | — | 4 | 1 | no | — |
| 201 | C3×M16 | — | 4 | 2 | no | — |
| 202 | C3×M16 | — | 8 | 2 | no | — |
| 203 | C2×C3×C8 | — | 4 | 1 | no | — |
| 204 | C2×C3×C8 | — | 4 | 1 | no | — |
| 205 | C2×C3×C8 | — | 8 | 2 | no | — |
| 206 | C3×C42 | — | 4 | 1 | no | — |
| 207 | C3⋊C16 | — | 4 | 2 | no | — |
| 208 | C3⋊C16 | — | 8 | 1 | no | — |
| 209 | C3⋊C16 | — | 8 | 2 | no | — |
| 210 | C2×#41 | — | 3 | 2 | no | — |
| 211 | C2×#41 | — | 3 | 2 | no | — |
| 212 | C2×#41 | — | 3 | 2 | no | — |
| 213 | C2×#41 | — | 3 | 2 | no | — |
| 214 | C2×#41 | — | 6 | 2 | no | — |
| 215 | C2×#41 | — | 6 | 2 | no | — |
| 216 | C22×Q8 | C2×C3⋊C8 | 1 | 2 | yes | — |
| 217 | C22×D4 | — | 2 | 2 | no | — |
| 218 | C22×D4 | C2×C3⋊C8 | 1 | 2 | yes | — |
| 219 | C23×C4 | — | 2 | 2 | no | — |
| 220 | C23×C4 | — | 2 | 1 | no | — |
| 221 | C23×C4 | C22×Dic3 | 1 | 1 | yes | characteristic |
| 222 | #135 | — | 3 | 2 | no | — |
| 223 | #135 | — | 3 | 1 | no | — |
| 224 | #135 | — | 3 | 2 | no | — |
| 225 | #135 | — | 3 | 1 | no | — |
| 226 | #135 | — | 3 | 1 | no | — |
| 227 | #135 | — | 6 | 1 | no | — |
| 228 | #135 | — | 6 | 1 | no | — |
| 229 | #135 | — | 6 | 1 | no | — |
| 230 | #135 | — | 6 | 2 | no | — |
| 231 | #135 | — | 6 | 2 | no | — |
| 232 | #135 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 233 | C2×Q16 | — | 3 | 1 | no | — |
| 234 | C2×Q16 | — | 3 | 1 | no | — |
| 235 | C2×Q16 | — | 3 | 2 | no | — |
| 236 | C2×SD16 | — | 3 | 2 | no | — |
| 237 | C2×SD16 | — | 3 | 2 | no | — |
| 238 | C2×SD16 | — | 3 | 2 | no | — |
| 239 | C2×SD16 | — | 3 | 2 | no | — |
| 240 | C2×D8 | — | 3 | 1 | no | — |
| 241 | C2×D8 | — | 3 | 1 | no | — |
| 242 | C2×D8 | — | 3 | 2 | no | — |
| 243 | #131 | — | 3 | 2 | no | — |
| 244 | #131 | — | 3 | 2 | no | — |
| 245 | #131 | — | 3 | 2 | no | — |
| 246 | #131 | — | 6 | 2 | no | — |
| 247 | #131 | — | 6 | 2 | no | — |
| 248 | #131 | — | 6 | 2 | no | — |
| 249 | #131 | — | 6 | 2 | no | — |
| 250 | #131 | — | 6 | 2 | no | — |
| 251 | #131 | — | 12 | 2 | no | — |
| 252 | #131 | — | 12 | 2 | no | — |
| 253 | #131 | C2×S4 | 1 | 2 | yes | — |
| 254 | C2×M16 | — | 3 | 2 | no | — |
| 255 | C2×M16 | — | 3 | 2 | no | — |
| 256 | C2×M16 | — | 6 | 2 | no | — |
| 257 | C2×M16 | — | 6 | 2 | no | — |
| 258 | C2×M16 | — | 6 | 2 | no | — |
| 259 | C2×M16 | — | 6 | 2 | no | — |
| 260 | C2×M16 | — | 6 | 2 | no | — |
| 261 | C22×C8 | — | 2 | 2 | no | — |
| 262 | C22×C8 | — | 3 | 1 | no | — |
| 263 | C22×C8 | — | 3 | 1 | no | — |
| 264 | C22×C8 | — | 3 | 1 | no | — |
| 265 | C22×C8 | — | 3 | 1 | no | — |
| 266 | C22×C8 | — | 3 | 1 | no | — |
| 267 | C22×C8 | — | 3 | 1 | no | — |
| 268 | C22×C8 | — | 3 | 1 | no | — |
| 269 | C22×C8 | — | 3 | 1 | no | — |
| 270 | C22×C8 | — | 6 | 2 | no | — |
| 271 | C22×C8 | — | 6 | 2 | no | — |
| 272 | C22×C8 | — | 6 | 2 | no | — |
| 273 | C22×C8 | — | 6 | 2 | no | — |
| 274 | C22×C8 | C2×C3⋊C8 | 1 | 1 | yes | characteristic |
| 275 | C22×C8 | C2×C3⋊C8 | 1 | 1 | yes | characteristic |
| 276 | C22×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 277 | C22×C8 | #237 | 1 | 1 | yes | characteristic |
| 278 | C2×C42 | — | 3 | 1 | no | — |
| 279 | C2×C42 | — | 3 | 1 | no | — |
| 280 | C2×C42 | — | 6 | 1 | no | — |
| 281 | M32 | — | 6 | 2 | no | — |
| 282 | M32 | — | 6 | 2 | no | — |
| 283 | M32 | — | 6 | 2 | no | — |
| 284 | M32 | — | 6 | 2 | no | — |
| 285 | M32 | — | 12 | 2 | no | — |
| 286 | M32 | — | 12 | 2 | no | — |
| 287 | M32 | — | 12 | 2 | no | — |
| 288 | M32 | — | 12 | 2 | no | — |
| 289 | C2×C16 | — | 3 | 2 | no | — |
| 290 | C2×C16 | — | 3 | 2 | no | — |
| 291 | C2×C16 | — | 6 | 1 | no | — |
| 292 | C2×C16 | — | 6 | 1 | no | — |
| 293 | C2×C16 | — | 6 | 1 | no | — |
| 294 | C2×C16 | — | 6 | 1 | no | — |
| 295 | C2×C16 | — | 6 | 1 | no | — |
| 296 | C2×C16 | — | 6 | 2 | no | — |
| 297 | C2×C16 | — | 6 | 2 | no | — |
| 298 | C2×C16 | — | 6 | 1 | no | — |
| 299 | C2×C16 | — | 6 | 1 | no | — |
| 300 | C2×C16 | — | 6 | 1 | no | — |
| 301 | C2×C16 | — | 6 | 1 | no | — |
| 302 | C2×C16 | — | 6 | 1 | no | — |
| 303 | C2×C16 | — | 12 | 2 | no | — |
| 304 | C2×C16 | — | 12 | 2 | no | — |
| 305 | C2×C16 | — | 12 | 2 | no | — |
| 306 | C2×C16 | — | 12 | 2 | no | — |
| 307 | #108 | — | 3 | 2 | no | — |
| 308 | #108 | — | 3 | 1 | no | — |
| 309 | #108 | — | 6 | 1 | no | — |
| 310 | #108 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 311 | #104 | — | 3 | 2 | no | — |
| 312 | #104 | — | 3 | 2 | no | — |
| 313 | #104 | — | 3 | 2 | no | — |
| 314 | #104 | — | 6 | 2 | no | — |
| 315 | #104 | SL(2,ℤ/4) | 1 | 2 | yes | — |
| 316 | C4×C8 | — | 3 | 1 | no | — |
| 317 | C4×C8 | — | 3 | 1 | no | — |
| 318 | C4×C8 | — | 3 | 1 | no | — |
| 319 | C4×C8 | — | 6 | 1 | no | — |
| 320 | C4×C8 | C2×S4 | 1 | 1 | yes | characteristic |
| 321 | C2×A4 | — | 2 | 1 | no | — |
| 322 | C2×A4 | — | 4 | 2 | no | — |
| 323 | C2×A4 | C8×D4 | 1 | 1 | yes | characteristic |
| 324 | C3×Q8 | — | 4 | 2 | no | — |
| 325 | C3×D4 | — | 4 | 2 | no | — |
| 326 | C3×D4 | — | 8 | 2 | no | — |
| 327 | C2×C3×C4 | — | 4 | 1 | no | — |
| 328 | C2×C3×C4 | — | 8 | 2 | no | — |
| 329 | C2×C3×C4 | — | 8 | 1 | no | — |
| 330 | C3×C8 | — | 4 | 1 | no | — |
| 331 | C3×C8 | — | 4 | 1 | no | — |
| 332 | C3×C8 | — | 4 | 1 | no | — |
| 333 | C3×C8 | — | 4 | 1 | no | — |
| 334 | C3×C8 | — | 8 | 2 | no | — |
| 335 | C24 | — | 2 | 2 | no | — |
| 336 | C24 | #948 | 1 | 1 | yes | characteristic |
| 337 | #41 | — | 3 | 2 | no | — |
| 338 | #41 | — | 3 | 2 | no | — |
| 339 | #41 | — | 3 | 2 | no | — |
| 340 | #41 | — | 6 | 2 | no | — |
| 341 | #41 | — | 6 | 2 | no | — |
| 342 | #41 | — | 6 | 2 | no | — |
| 343 | #41 | — | 6 | 2 | no | — |
| 344 | #41 | — | 6 | 2 | no | — |
| 345 | #41 | — | 12 | 2 | no | — |
| 346 | #41 | — | 12 | 2 | no | — |
| 347 | #41 | C2×SL(2,ℤ/4) | 1 | 2 | yes | — |
| 348 | C2×Q8 | — | 3 | 2 | no | — |
| 349 | C2×Q8 | — | 3 | 2 | no | — |
| 350 | C2×Q8 | — | 6 | 2 | no | — |
| 351 | C2×D4 | — | 3 | 2 | no | — |
| 352 | C2×D4 | — | 3 | 2 | no | — |
| 353 | C2×D4 | — | 6 | 2 | no | — |
| 354 | C2×D4 | — | 6 | 2 | no | — |
| 355 | C2×D4 | — | 6 | 2 | no | — |
| 356 | C2×D4 | — | 6 | 2 | no | — |
| 357 | C2×D4 | — | 6 | 2 | no | — |
| 358 | C22×C4 | — | 2 | 2 | no | — |
| 359 | C22×C4 | — | 3 | 1 | no | — |
| 360 | C22×C4 | — | 3 | 1 | no | — |
| 361 | C22×C4 | — | 3 | 1 | no | — |
| 362 | C22×C4 | — | 3 | 1 | no | — |
| 363 | C22×C4 | — | 4 | 1 | no | — |
| 364 | C22×C4 | — | 6 | 2 | no | — |
| 365 | C22×C4 | — | 6 | 1 | no | — |
| 366 | C22×C4 | — | 6 | 2 | no | — |
| 367 | C22×C4 | — | 6 | 2 | no | — |
| 368 | C22×C4 | — | 6 | 2 | no | — |
| 369 | C22×C4 | — | 6 | 1 | no | — |
| 370 | C22×C4 | — | 12 | 1 | no | — |
| 371 | C22×C4 | C22×C3⋊C8 | 1 | 1 | yes | characteristic |
| 372 | C22×C4 | D4×Dic3 | 1 | 1 | yes | characteristic |
| 373 | Q16 | — | 3 | 2 | no | — |
| 374 | Q16 | — | 3 | 1 | no | — |
| 375 | Q16 | — | 6 | 1 | no | — |
| 376 | Q16 | A4⋊C8 | 1 | 1 | yes | characteristic |
| 377 | SD16 | — | 3 | 2 | no | — |
| 378 | SD16 | — | 3 | 2 | no | — |
| 379 | SD16 | — | 3 | 2 | no | — |
| 380 | SD16 | — | 6 | 2 | no | — |
| 381 | SD16 | A4⋊C8 | 1 | 2 | yes | — |
| 382 | D8 | — | 3 | 2 | no | — |
| 383 | D8 | — | 3 | 1 | no | — |
| 384 | D8 | — | 6 | 1 | no | — |
| 385 | D8 | A4⋊C8 | 1 | 1 | yes | characteristic |
| 386 | M16 | — | 2 | 2 | no | — |
| 387 | M16 | — | 3 | 2 | no | — |
| 388 | M16 | — | 6 | 2 | no | — |
| 389 | M16 | — | 6 | 2 | no | — |
| 390 | M16 | — | 6 | 2 | no | — |
| 391 | M16 | — | 6 | 2 | no | — |
| 392 | M16 | — | 6 | 2 | no | — |
| 393 | M16 | — | 12 | 2 | no | — |
| 394 | M16 | C2×SL(2,ℤ/4) | 1 | 2 | yes | — |
| 395 | C2×C8 | — | 2 | 2 | no | — |
| 396 | C2×C8 | — | 3 | 1 | no | — |
| 397 | C2×C8 | — | 3 | 1 | no | — |
| 398 | C2×C8 | — | 3 | 1 | no | — |
| 399 | C2×C8 | — | 3 | 1 | no | — |
| 400 | C2×C8 | — | 3 | 1 | no | — |
| 401 | C2×C8 | — | 3 | 1 | no | — |
| 402 | C2×C8 | — | 3 | 1 | no | — |
| 403 | C2×C8 | — | 3 | 1 | no | — |
| 404 | C2×C8 | — | 3 | 1 | no | — |
| 405 | C2×C8 | — | 3 | 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 | — | 6 | 2 | no | — |
| 411 | C2×C8 | — | 6 | 2 | no | — |
| 412 | C2×C8 | — | 6 | 1 | no | — |
| 413 | C2×C8 | — | 6 | 1 | no | — |
| 414 | C2×C8 | — | 6 | 2 | no | — |
| 415 | C2×C8 | — | 6 | 2 | no | — |
| 416 | C2×C8 | — | 6 | 2 | no | — |
| 417 | C2×C8 | — | 12 | 2 | no | — |
| 418 | C2×C8 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 419 | C2×C8 | C22×S4 | 1 | 1 | yes | characteristic |
| 420 | C42 | — | 3 | 1 | no | — |
| 421 | C42 | — | 6 | 1 | no | — |
| 422 | C42 | — | 6 | 1 | no | — |
| 423 | C42 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 424 | C16 | — | 6 | 2 | no | — |
| 425 | C16 | — | 6 | 2 | no | — |
| 426 | C16 | — | 12 | 1 | no | — |
| 427 | C16 | — | 12 | 2 | no | — |
| 428 | C16 | — | 12 | 2 | no | — |
| 429 | C16 | — | 12 | 1 | no | — |
| 430 | C22×C3 | — | 4 | 1 | no | — |
| 431 | C22×C3 | — | 8 | 2 | no | — |
| 432 | A4 | #2171 | 1 | 1 | yes | characteristic, complemented |
| 433 | C3×C4 | — | 4 | 1 | no | — |
| 434 | C3×C4 | — | 4 | 1 | no | — |
| 435 | C3×C4 | — | 8 | 2 | no | — |
| 436 | C3×C4 | — | 16 | 1 | no | — |
| 437 | C23 | — | 2 | 1 | no | — |
| 438 | C23 | — | 3 | 1 | no | — |
| 439 | C23 | — | 3 | 1 | no | — |
| 440 | C23 | — | 4 | 2 | no | — |
| 441 | C23 | — | 6 | 2 | no | — |
| 442 | C23 | — | 6 | 1 | no | — |
| 443 | C23 | — | 6 | 2 | no | — |
| 444 | C23 | — | 12 | 2 | no | — |
| 445 | C23 | D4×C3⋊C8 | 1 | 1 | yes | characteristic |
| 446 | Q8 | — | 3 | 2 | no | — |
| 447 | Q8 | — | 6 | 2 | no | — |
| 448 | Q8 | — | 6 | 2 | no | — |
| 449 | Q8 | C2×A4⋊C8 | 1 | 2 | yes | — |
| 450 | D4 | — | 2 | 2 | no | — |
| 451 | D4 | — | 3 | 2 | no | — |
| 452 | D4 | — | 6 | 2 | no | — |
| 453 | D4 | — | 6 | 2 | no | — |
| 454 | D4 | — | 6 | 2 | no | — |
| 455 | D4 | — | 6 | 2 | no | — |
| 456 | D4 | — | 6 | 2 | no | — |
| 457 | D4 | — | 12 | 2 | no | — |
| 458 | D4 | C2×A4⋊C8 | 1 | 2 | yes | — |
| 459 | C2×C4 | — | 2 | 2 | no | — |
| 460 | C2×C4 | — | 2 | 1 | no | — |
| 461 | C2×C4 | — | 3 | 1 | no | — |
| 462 | C2×C4 | — | 3 | 1 | no | — |
| 463 | C2×C4 | — | 3 | 1 | no | — |
| 464 | C2×C4 | — | 3 | 1 | no | — |
| 465 | C2×C4 | — | 3 | 1 | no | — |
| 466 | C2×C4 | — | 3 | 1 | no | — |
| 467 | C2×C4 | — | 3 | 1 | no | — |
| 468 | C2×C4 | — | 6 | 2 | no | — |
| 469 | C2×C4 | — | 6 | 2 | no | — |
| 470 | C2×C4 | — | 6 | 1 | no | — |
| 471 | C2×C4 | — | 6 | 2 | no | — |
| 472 | C2×C4 | — | 6 | 2 | no | — |
| 473 | C2×C4 | — | 6 | 2 | no | — |
| 474 | C2×C4 | — | 6 | 2 | no | — |
| 475 | C2×C4 | — | 6 | 1 | no | — |
| 476 | C2×C4 | — | 12 | 2 | no | — |
| 477 | C2×C4 | — | 12 | 1 | no | — |
| 478 | C2×C4 | — | 12 | 1 | no | — |
| 479 | C2×C4 | — | 12 | 1 | no | — |
| 480 | C2×C4 | C22×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 481 | C8 | — | 2 | 2 | no | — |
| 482 | C8 | — | 3 | 1 | no | — |
| 483 | C8 | — | 3 | 1 | no | — |
| 484 | C8 | — | 3 | 1 | no | — |
| 485 | C8 | — | 3 | 1 | no | — |
| 486 | C8 | — | 6 | 2 | no | — |
| 487 | C8 | C2×A4⋊C8 | 1 | 1 | yes | characteristic |
| 488 | C8 | C2×A4⋊C8 | 1 | 1 | yes | characteristic |
| 489 | C8 | D4×S4 | 1 | 1 | yes | characteristic |
| 490 | C8 | #5914 | 1 | 1 | yes | characteristic |
| 491 | C2×C3 | — | 4 | 1 | no | — |
| 492 | C2×C3 | — | 8 | 1 | no | — |
| 493 | C2×C3 | — | 16 | 2 | no | — |
| 494 | C22 | — | 2 | 2 | no | — |
| 495 | C22 | — | 3 | 1 | no | — |
| 496 | C22 | — | 3 | 1 | no | — |
| 497 | C22 | — | 3 | 1 | no | — |
| 498 | C22 | — | 6 | 1 | no | — |
| 499 | C22 | — | 6 | 1 | no | — |
| 500 | C22 | — | 6 | 1 | no | — |
| 501 | C22 | — | 6 | 1 | no | — |
| 502 | C22 | — | 6 | 2 | no | — |
| 503 | C22 | — | 12 | 2 | no | — |
| 504 | C22 | — | 12 | 2 | no | — |
| 505 | C22 | — | 12 | 2 | no | — |
| 506 | C22 | — | 12 | 2 | no | — |
| 507 | C22 | #70924 | 1 | 1 | yes | characteristic, complemented |
| 508 | C22 | #85511 | 1 | 1 | yes | characteristic |
| 509 | C4 | — | 2 | 2 | no | — |
| 510 | C4 | — | 3 | 1 | no | — |
| 511 | C4 | — | 3 | 1 | no | — |
| 512 | C4 | — | 4 | 1 | no | — |
| 513 | C4 | — | 6 | 2 | no | — |
| 514 | C4 | — | 12 | 1 | no | — |
| 515 | C4 | C22×A4⋊C8 | 1 | 1 | yes | characteristic |
| 516 | C4 | D4×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 517 | C3 | — | 4 | 1 | no | Sylow |
| 518 | C2 | — | 2 | 1 | no | — |
| 519 | C2 | — | 3 | 1 | no | — |
| 520 | C2 | — | 3 | 1 | no | — |
| 521 | C2 | — | 4 | 2 | no | — |
| 522 | C2 | — | 6 | 1 | no | — |
| 523 | C2 | — | 12 | 2 | no | — |
| 524 | C2 | D4×A4⋊C8 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11714124 | C2 | semidirect |
| 2. #11711530 | C2 | semidirect |
| 3. #11711496 | C2 | semidirect |
| 4. #11711481 | C2 | semidirect |
| 432. A4 | #2171 | semidirect |
| 507. C22 | #70924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11714124 | 2 |
| #11711530 | 2 |
| #11711496 | 2 |
| #11711481 | 2 |
| A4×#443 | 2 |
| #497275 | 3 |
| #70924 | 4 |