Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
717 conjugacy classes of subgroups.
The subgroup lattice has 434 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61373 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #33707 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #33579 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #19206 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #12359 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #12358 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #12355 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #12354 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C2×#1365 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11606 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11592 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #3503 | — | 2 | 1 | no | — |
| 13 | C2×#508 | — | 2 | 1 | no | — |
| 14 | #3386 | — | 2 | 2 | no | — |
| 15 | #3385 | — | 2 | 2 | no | — |
| 16 | #3383 | — | 2 | 1 | no | — |
| 17 | Q8×Q16 | C22 | 1 | 2 | yes | — |
| 18 | #3380 | C22 | 1 | 2 | yes | — |
| 19 | Q8×D8 | — | 2 | 1 | no | — |
| 20 | #3246 | — | 2 | 1 | no | — |
| 21 | #3164 | — | 2 | 1 | no | — |
| 22 | C2×#500 | C22 | 1 | 1 | yes | characteristic |
| 23 | #3147 | C22 | 1 | 1 | yes | characteristic |
| 24 | #3083 | — | 2 | 2 | no | — |
| 25 | #3079 | — | 2 | 1 | no | — |
| 26 | #2960 | C22 | 1 | 1 | yes | characteristic |
| 27 | #2951 | — | 2 | 1 | no | — |
| 28 | C4×#135 | C22 | 1 | 1 | yes | characteristic |
| 29 | #2243 | — | 2 | 2 | no | — |
| 30 | #2241 | C22 | 1 | 2 | yes | — |
| 31 | #2240 | C22 | 1 | 2 | yes | — |
| 32 | #2211 | — | 2 | 1 | no | — |
| 33 | #2210 | — | 2 | 1 | no | — |
| 34 | #2209 | C22 | 1 | 1 | yes | characteristic |
| 35 | #2208 | C22 | 1 | 1 | yes | characteristic |
| 36 | #2207 | C22 | 1 | 1 | yes | characteristic |
| 37 | #2206 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×C4⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 39 | #2139 | — | 2 | 2 | no | — |
| 40 | #2138 | — | 2 | 1 | no | — |
| 41 | C4×M32 | C22 | 1 | 1 | yes | characteristic |
| 42 | #1686 | — | 2 | 2 | no | — |
| 43 | #1670 | C22 | 1 | 2 | yes | — |
| 44 | #1668 | C22 | 1 | 2 | yes | — |
| 45 | C2×#335 | C22 | 1 | 1 | yes | characteristic |
| 46 | #1547 | — | 2 | 1 | no | — |
| 47 | #1365 | C22 | 1 | 2 | yes | — |
| 48 | #1365 | C22 | 1 | 2 | yes | — |
| 49 | Q8⋊C16 | C22 | 1 | 2 | yes | — |
| 50 | Q8⋊C16 | C22 | 1 | 2 | yes | — |
| 51 | #1332 | C22 | 1 | 2 | yes | — |
| 52 | #1331 | C22 | 1 | 2 | yes | — |
| 53 | C2×#135 | — | 2 | 1 | no | — |
| 54 | C2×#135 | — | 2 | 1 | no | — |
| 55 | C2×#135 | D4 | 1 | 1 | yes | characteristic |
| 56 | Q82 | — | 2 | 2 | no | — |
| 57 | #557 | — | 2 | 2 | no | — |
| 58 | #554 | — | 2 | 2 | no | — |
| 59 | #554 | — | 4 | 2 | no | — |
| 60 | D4×Q8 | — | 2 | 2 | no | — |
| 61 | D4×Q8 | — | 4 | 2 | no | — |
| 62 | #544 | — | 2 | 2 | no | — |
| 63 | #544 | — | 4 | 2 | no | — |
| 64 | #533 | — | 4 | 1 | no | — |
| 65 | #533 | D4 | 1 | 1 | yes | characteristic |
| 66 | #532 | — | 2 | 1 | no | — |
| 67 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 68 | C2×C4⋊Q8 | — | 4 | 1 | no | — |
| 69 | #520 | — | 2 | 2 | no | — |
| 70 | C4×#41 | — | 2 | 1 | no | — |
| 71 | #508 | — | 4 | 4 | no | — |
| 72 | C2×Q32 | — | 2 | 1 | no | — |
| 73 | C2×SD32 | — | 2 | 1 | no | — |
| 74 | C2×SD32 | — | 2 | 1 | no | — |
| 75 | C2×D16 | — | 2 | 1 | no | — |
| 76 | C2×M32 | — | 2 | 1 | no | — |
| 77 | C22×C16 | — | 2 | 1 | no | — |
| 78 | #501 | — | 2 | 4 | no | — |
| 79 | #500 | — | 2 | 2 | no | — |
| 80 | #500 | — | 2 | 1 | no | — |
| 81 | #500 | — | 2 | 1 | no | — |
| 82 | #500 | D4 | 1 | 2 | yes | — |
| 83 | #500 | C23 | 1 | 2 | yes | — |
| 84 | #499 | — | 2 | 2 | no | — |
| 85 | #495 | — | 2 | 1 | no | — |
| 86 | #495 | — | 2 | 1 | no | — |
| 87 | #494 | C23 | 1 | 1 | yes | characteristic |
| 88 | #493 | C23 | 1 | 1 | yes | characteristic |
| 89 | #492 | — | 2 | 1 | no | — |
| 90 | #479 | — | 2 | 4 | no | — |
| 91 | #478 | — | 2 | 4 | no | — |
| 92 | #477 | — | 2 | 4 | no | — |
| 93 | #477 | — | 2 | 2 | no | — |
| 94 | #476 | — | 2 | 2 | no | — |
| 95 | #476 | — | 4 | 1 | no | — |
| 96 | #475 | — | 2 | 2 | no | — |
| 97 | #475 | — | 2 | 2 | no | — |
| 98 | #474 | — | 2 | 2 | no | — |
| 99 | #474 | — | 2 | 4 | no | — |
| 100 | #465 | — | 4 | 2 | no | — |
| 101 | #461 | — | 4 | 1 | no | — |
| 102 | #460 | — | 2 | 2 | no | — |
| 103 | #446 | — | 2 | 1 | no | — |
| 104 | #446 | D4 | 1 | 2 | yes | — |
| 105 | C8×Q8 | — | 2 | 1 | no | — |
| 106 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 107 | #440 | — | 2 | 4 | no | — |
| 108 | C4×Q16 | — | 2 | 2 | no | — |
| 109 | C4×Q16 | D4 | 1 | 1 | yes | characteristic |
| 110 | C4×Q16 | C23 | 1 | 1 | yes | characteristic |
| 111 | C4×SD16 | — | 2 | 1 | no | — |
| 112 | C4×SD16 | — | 2 | 1 | no | — |
| 113 | C4×D8 | — | 2 | 2 | no | — |
| 114 | C4×D8 | D4 | 1 | 1 | yes | characteristic |
| 115 | C4×D8 | C23 | 1 | 1 | yes | characteristic |
| 116 | #428 | — | 2 | 2 | no | — |
| 117 | #427 | D4 | 1 | 1 | yes | characteristic |
| 118 | C2×#107 | — | 2 | 1 | no | — |
| 119 | C2×#107 | D4 | 1 | 2 | yes | — |
| 120 | #424 | — | 2 | 1 | no | — |
| 121 | #423 | D4 | 1 | 1 | yes | characteristic |
| 122 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 123 | #417 | — | 2 | 2 | no | — |
| 124 | #416 | — | 2 | 1 | no | — |
| 125 | #405 | — | 2 | 1 | no | — |
| 126 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 127 | C4⋊C16 | — | 2 | 1 | no | — |
| 128 | C4⋊C16 | C23 | 1 | 1 | yes | characteristic |
| 129 | C4⋊C16 | C23 | 1 | 1 | yes | characteristic |
| 130 | #358 | — | 2 | 1 | no | — |
| 131 | #358 | — | 2 | 1 | no | — |
| 132 | #358 | — | 2 | 4 | no | — |
| 133 | #357 | — | 2 | 1 | no | — |
| 134 | #357 | — | 2 | 1 | no | — |
| 135 | #357 | — | 2 | 4 | no | — |
| 136 | #346 | — | 2 | 1 | no | — |
| 137 | C4×C16 | C23 | 1 | 2 | yes | — |
| 138 | #335 | — | 2 | 1 | no | — |
| 139 | #335 | C23 | 1 | 2 | yes | — |
| 140 | #332 | — | 2 | 2 | no | — |
| 141 | #331 | — | 2 | 2 | no | — |
| 142 | C2×#41 | — | 2 | 1 | no | — |
| 143 | C2×#41 | — | 4 | 1 | no | — |
| 144 | C22×Q8 | — | 4 | 2 | no | — |
| 145 | C22×Q8 | — | 4 | 1 | no | — |
| 146 | #135 | — | 2 | 2 | no | — |
| 147 | #135 | — | 4 | 4 | no | — |
| 148 | #135 | — | 4 | 2 | no | — |
| 149 | #135 | — | 4 | 2 | no | — |
| 150 | #135 | SD16 | 1 | 4 | yes | complemented |
| 151 | C2×Q16 | — | 2 | 1 | no | — |
| 152 | C2×Q16 | — | 2 | 1 | no | — |
| 153 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C2×SD16 | — | 2 | 1 | no | — |
| 155 | C2×SD16 | — | 4 | 2 | no | — |
| 156 | C2×SD16 | — | 4 | 1 | no | — |
| 157 | C2×SD16 | — | 4 | 1 | no | — |
| 158 | C2×D8 | — | 2 | 1 | no | — |
| 159 | C2×D8 | — | 2 | 1 | no | — |
| 160 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | C2×M16 | — | 2 | 1 | no | — |
| 162 | C22×C8 | — | 4 | 1 | no | — |
| 163 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 165 | C4⋊Q8 | — | 2 | 4 | no | — |
| 166 | C4⋊Q8 | — | 2 | 2 | no | — |
| 167 | C4⋊Q8 | — | 2 | 2 | no | — |
| 168 | C4⋊Q8 | — | 2 | 1 | no | — |
| 169 | C4⋊Q8 | — | 4 | 2 | no | — |
| 170 | C4⋊Q8 | — | 4 | 4 | no | — |
| 171 | C4⋊Q8 | — | 4 | 2 | no | — |
| 172 | C4⋊Q8 | — | 4 | 2 | no | — |
| 173 | C4⋊Q8 | — | 4 | 1 | no | — |
| 174 | C4⋊Q8 | — | 4 | 1 | no | — |
| 175 | C4⋊Q8 | D8 | 1 | 1 | yes | characteristic |
| 176 | C4⋊Q8 | D8 | 1 | 1 | yes | characteristic |
| 177 | #127 | — | 2 | 1 | no | — |
| 178 | #125 | — | 2 | 4 | no | — |
| 179 | #125 | — | 2 | 1 | no | — |
| 180 | #125 | — | 4 | 2 | no | — |
| 181 | #125 | — | 4 | 4 | no | — |
| 182 | #124 | — | 4 | 1 | no | — |
| 183 | C22⋊Q8 | — | 2 | 1 | no | — |
| 184 | C22⋊Q8 | — | 4 | 4 | no | — |
| 185 | C22⋊Q8 | — | 4 | 2 | no | — |
| 186 | C22⋊Q8 | — | 4 | 4 | no | — |
| 187 | C22⋊Q8 | — | 4 | 4 | no | — |
| 188 | C22⋊Q8 | — | 4 | 2 | no | — |
| 189 | C22⋊Q8 | D8 | 1 | 2 | yes | — |
| 190 | #121 | — | 4 | 1 | no | — |
| 191 | #121 | — | 4 | 1 | no | — |
| 192 | C4×Q8 | — | 2 | 1 | no | — |
| 193 | C4×Q8 | — | 2 | 4 | no | — |
| 194 | C4×Q8 | — | 2 | 1 | no | — |
| 195 | C4×Q8 | — | 2 | 1 | no | — |
| 196 | C4×Q8 | — | 4 | 2 | no | — |
| 197 | C4×Q8 | — | 4 | 2 | no | — |
| 198 | C4×Q8 | C2×D4 | 1 | 2 | yes | — |
| 199 | C4×D4 | — | 2 | 4 | no | — |
| 200 | C4×D4 | — | 2 | 1 | no | — |
| 201 | C4×D4 | — | 2 | 1 | no | — |
| 202 | C4×D4 | — | 4 | 4 | no | — |
| 203 | C4×D4 | — | 4 | 1 | no | — |
| 204 | C4×D4 | — | 4 | 1 | no | — |
| 205 | C4×D4 | — | 4 | 1 | no | — |
| 206 | C4×D4 | — | 4 | 1 | no | — |
| 207 | #117 | — | 2 | 1 | no | — |
| 208 | #117 | — | 2 | 1 | no | — |
| 209 | #117 | — | 4 | 2 | no | — |
| 210 | #117 | — | 4 | 1 | no | — |
| 211 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 212 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 213 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 214 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 215 | C2×C42 | — | 4 | 1 | no | — |
| 216 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 217 | Q32 | — | 4 | 2 | no | — |
| 218 | SD32 | — | 4 | 2 | no | — |
| 219 | SD32 | — | 4 | 2 | no | — |
| 220 | D16 | — | 4 | 2 | no | — |
| 221 | M32 | — | 4 | 2 | no | — |
| 222 | C2×C16 | — | 2 | 2 | no | — |
| 223 | C2×C16 | — | 2 | 1 | no | — |
| 224 | C2×C16 | — | 2 | 1 | no | — |
| 225 | C2×C16 | — | 4 | 2 | no | — |
| 226 | #107 | — | 2 | 4 | no | — |
| 227 | #107 | — | 2 | 2 | no | — |
| 228 | #107 | — | 2 | 2 | no | — |
| 229 | #107 | — | 2 | 2 | no | — |
| 230 | #107 | C2×D4 | 1 | 4 | yes | — |
| 231 | #107 | C2×D4 | 1 | 1 | yes | characteristic |
| 232 | #107 | C2×D4 | 1 | 1 | yes | characteristic |
| 233 | #106 | — | 2 | 4 | no | — |
| 234 | #106 | — | 2 | 1 | no | — |
| 235 | #106 | — | 4 | 2 | no | — |
| 236 | C4⋊C8 | — | 2 | 2 | no | — |
| 237 | C4⋊C8 | — | 2 | 2 | no | — |
| 238 | C4⋊C8 | — | 2 | 1 | no | — |
| 239 | C4⋊C8 | — | 2 | 2 | no | — |
| 240 | C4⋊C8 | — | 4 | 1 | no | — |
| 241 | C4⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 242 | #103 | — | 2 | 4 | no | — |
| 243 | #103 | — | 2 | 1 | no | — |
| 244 | #103 | — | 2 | 1 | no | — |
| 245 | #103 | — | 4 | 2 | no | — |
| 246 | #102 | — | 2 | 4 | no | — |
| 247 | #102 | — | 2 | 1 | no | — |
| 248 | #102 | — | 2 | 1 | no | — |
| 249 | #102 | — | 4 | 2 | no | — |
| 250 | #97 | — | 2 | 2 | no | — |
| 251 | C4×C8 | — | 2 | 2 | no | — |
| 252 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 253 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 254 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 255 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 256 | #41 | — | 2 | 4 | no | — |
| 257 | #41 | — | 4 | 2 | no | — |
| 258 | #41 | — | 8 | 2 | no | — |
| 259 | #41 | — | 8 | 2 | no | — |
| 260 | C2×Q8 | — | 2 | 1 | no | — |
| 261 | C2×Q8 | — | 2 | 1 | no | — |
| 262 | C2×Q8 | — | 4 | 4 | no | — |
| 263 | C2×Q8 | — | 4 | 2 | no | — |
| 264 | C2×Q8 | — | 4 | 2 | no | — |
| 265 | C2×Q8 | — | 4 | 1 | no | — |
| 266 | C2×Q8 | — | 16 | 2 | no | — |
| 267 | C2×Q8 | — | 16 | 4 | no | — |
| 268 | C2×Q8 | C2×D8 | 1 | 2 | yes | — |
| 269 | C2×D4 | — | 2 | 1 | no | — |
| 270 | C2×D4 | — | 4 | 1 | no | — |
| 271 | C2×D4 | — | 4 | 1 | no | — |
| 272 | C2×D4 | — | 4 | 1 | no | — |
| 273 | C2×D4 | — | 4 | 1 | no | — |
| 274 | C2×D4 | — | 8 | 1 | no | — |
| 275 | C22×C4 | — | 4 | 4 | no | — |
| 276 | C22×C4 | — | 4 | 1 | no | — |
| 277 | C22×C4 | — | 4 | 2 | no | — |
| 278 | C22×C4 | — | 4 | 1 | no | — |
| 279 | C22×C4 | — | 4 | 1 | no | — |
| 280 | C22×C4 | — | 8 | 1 | no | — |
| 281 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 282 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 283 | C22×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 284 | Q16 | — | 2 | 1 | no | — |
| 285 | Q16 | — | 4 | 2 | no | — |
| 286 | Q16 | — | 4 | 1 | no | — |
| 287 | Q16 | — | 4 | 1 | no | — |
| 288 | Q16 | C2×SD16 | 1 | 2 | yes | — |
| 289 | SD16 | — | 2 | 4 | no | — |
| 290 | SD16 | — | 8 | 2 | no | — |
| 291 | SD16 | — | 8 | 2 | no | — |
| 292 | SD16 | — | 16 | 2 | no | — |
| 293 | D8 | — | 2 | 1 | no | — |
| 294 | D8 | — | 4 | 2 | no | — |
| 295 | D8 | — | 4 | 1 | no | — |
| 296 | D8 | — | 4 | 1 | no | — |
| 297 | D8 | C2×SD16 | 1 | 2 | yes | — |
| 298 | M16 | — | 4 | 2 | no | — |
| 299 | C2×C8 | — | 2 | 2 | no | — |
| 300 | C2×C8 | — | 2 | 2 | no | — |
| 301 | C2×C8 | — | 4 | 2 | no | — |
| 302 | C2×C8 | — | 16 | 1 | no | — |
| 303 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 304 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 305 | C2×C8 | C2×SD16 | 1 | 2 | yes | — |
| 306 | C2×C8 | #137 | 1 | 2 | yes | — |
| 307 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 308 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 309 | C4⋊C4 | — | 2 | 2 | no | — |
| 310 | C4⋊C4 | — | 2 | 1 | no | — |
| 311 | C4⋊C4 | — | 2 | 1 | no | — |
| 312 | C4⋊C4 | — | 2 | 1 | no | — |
| 313 | C4⋊C4 | — | 2 | 2 | no | — |
| 314 | C4⋊C4 | — | 2 | 1 | no | — |
| 315 | C4⋊C4 | — | 2 | 4 | no | — |
| 316 | C4⋊C4 | — | 2 | 1 | no | — |
| 317 | C4⋊C4 | — | 4 | 4 | no | — |
| 318 | C4⋊C4 | — | 4 | 4 | no | — |
| 319 | C4⋊C4 | — | 4 | 4 | no | — |
| 320 | C4⋊C4 | — | 4 | 4 | no | — |
| 321 | C4⋊C4 | — | 4 | 2 | no | — |
| 322 | C4⋊C4 | — | 4 | 1 | no | — |
| 323 | C4⋊C4 | — | 4 | 2 | no | — |
| 324 | C4⋊C4 | — | 4 | 2 | no | — |
| 325 | C4⋊C4 | — | 4 | 1 | no | — |
| 326 | C4⋊C4 | — | 4 | 1 | no | — |
| 327 | C4⋊C4 | — | 4 | 1 | no | — |
| 328 | C4⋊C4 | C2×D8 | 1 | 2 | yes | — |
| 329 | C22⋊C4 | — | 2 | 2 | no | — |
| 330 | C22⋊C4 | — | 4 | 4 | no | — |
| 331 | C22⋊C4 | — | 4 | 1 | no | — |
| 332 | C22⋊C4 | — | 4 | 1 | no | — |
| 333 | C22⋊C4 | — | 4 | 1 | no | — |
| 334 | C22⋊C4 | — | 8 | 1 | no | — |
| 335 | C22⋊C4 | — | 8 | 1 | no | — |
| 336 | C42 | — | 2 | 2 | no | — |
| 337 | C42 | — | 4 | 4 | no | — |
| 338 | C42 | — | 4 | 1 | no | — |
| 339 | C42 | — | 4 | 1 | no | — |
| 340 | C42 | — | 4 | 1 | no | — |
| 341 | C42 | #120 | 1 | 1 | yes | characteristic |
| 342 | C42 | C2×D8 | 1 | 1 | yes | characteristic |
| 343 | C42 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 344 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 345 | C16 | — | 4 | 2 | no | — |
| 346 | C16 | — | 4 | 1 | no | — |
| 347 | C16 | — | 4 | 1 | no | — |
| 348 | C23 | — | 4 | 1 | no | — |
| 349 | C23 | — | 8 | 1 | no | — |
| 350 | C23 | #447 | 1 | 1 | yes | characteristic |
| 351 | Q8 | — | 2 | 2 | no | — |
| 352 | Q8 | — | 2 | 2 | no | — |
| 353 | Q8 | — | 2 | 2 | no | — |
| 354 | Q8 | — | 4 | 2 | no | — |
| 355 | Q8 | — | 4 | 1 | no | — |
| 356 | Q8 | — | 8 | 4 | no | — |
| 357 | Q8 | — | 8 | 1 | no | — |
| 358 | Q8 | — | 8 | 1 | no | — |
| 359 | Q8 | — | 16 | 2 | no | — |
| 360 | Q8 | — | 16 | 4 | no | — |
| 361 | D4 | — | 2 | 2 | no | — |
| 362 | D4 | — | 4 | 4 | no | — |
| 363 | D4 | — | 4 | 1 | no | — |
| 364 | D4 | — | 8 | 1 | no | — |
| 365 | D4 | — | 8 | 1 | no | — |
| 366 | D4 | — | 8 | 1 | no | — |
| 367 | D4 | — | 8 | 1 | no | — |
| 368 | D4 | — | 16 | 1 | no | — |
| 369 | D4 | — | 16 | 2 | no | — |
| 370 | C2×C4 | — | 2 | 1 | no | — |
| 371 | C2×C4 | — | 2 | 1 | no | — |
| 372 | C2×C4 | — | 2 | 2 | no | — |
| 373 | C2×C4 | — | 2 | 2 | no | — |
| 374 | C2×C4 | — | 4 | 1 | no | — |
| 375 | C2×C4 | — | 4 | 1 | no | — |
| 376 | C2×C4 | — | 4 | 4 | no | — |
| 377 | C2×C4 | — | 4 | 1 | no | — |
| 378 | C2×C4 | — | 4 | 1 | no | — |
| 379 | C2×C4 | — | 4 | 4 | no | — |
| 380 | C2×C4 | — | 8 | 2 | no | — |
| 381 | C2×C4 | — | 8 | 1 | no | — |
| 382 | C2×C4 | — | 8 | 1 | no | — |
| 383 | C2×C4 | — | 8 | 1 | no | — |
| 384 | C2×C4 | — | 16 | 4 | no | — |
| 385 | C2×C4 | — | 16 | 2 | no | — |
| 386 | C2×C4 | — | 16 | 2 | no | — |
| 387 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 388 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 389 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 390 | C2×C4 | #448 | 1 | 2 | yes | — |
| 391 | C2×C4 | #454 | 1 | 2 | yes | — |
| 392 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 393 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 394 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 395 | C8 | — | 2 | 1 | no | — |
| 396 | C8 | — | 2 | 1 | no | — |
| 397 | C8 | — | 4 | 2 | no | — |
| 398 | C8 | — | 8 | 2 | no | — |
| 399 | C8 | #448 | 1 | 2 | yes | — |
| 400 | C8 | C22×SD16 | 1 | 1 | yes | characteristic |
| 401 | C8 | C2×#137 | 1 | 1 | yes | characteristic |
| 402 | C22 | — | 2 | 1 | no | — |
| 403 | C22 | — | 2 | 1 | no | — |
| 404 | C22 | — | 4 | 2 | no | — |
| 405 | C22 | — | 8 | 1 | no | — |
| 406 | C22 | — | 8 | 1 | no | — |
| 407 | C22 | — | 16 | 1 | no | — |
| 408 | C22 | — | 16 | 1 | no | — |
| 409 | C22 | — | 16 | 1 | no | — |
| 410 | C22 | #1627 | 1 | 2 | yes | — |
| 411 | C22 | C2×#447 | 1 | 1 | yes | characteristic |
| 412 | C4 | — | 2 | 1 | no | — |
| 413 | C4 | — | 2 | 1 | no | — |
| 414 | C4 | — | 2 | 1 | no | — |
| 415 | C4 | — | 4 | 2 | no | — |
| 416 | C4 | — | 4 | 2 | no | — |
| 417 | C4 | — | 4 | 2 | no | — |
| 418 | C4 | — | 8 | 1 | no | — |
| 419 | C4 | — | 8 | 4 | no | — |
| 420 | C4 | — | 8 | 1 | no | — |
| 421 | C4 | — | 16 | 1 | no | — |
| 422 | C4 | #1627 | 1 | 2 | yes | — |
| 423 | C4 | C2×#448 | 1 | 1 | yes | characteristic |
| 424 | C4 | C2×#454 | 1 | 1 | yes | characteristic |
| 425 | C4 | #3416 | 1 | 1 | yes | characteristic |
| 426 | C4 | #3417 | 1 | 1 | yes | characteristic |
| 427 | C2 | — | 2 | 2 | no | — |
| 428 | C2 | — | 8 | 2 | no | — |
| 429 | C2 | — | 32 | 1 | no | — |
| 430 | C2 | C2×#1627 | 1 | 1 | yes | characteristic |
| 431 | C2 | #33527 | 1 | 1 | yes | characteristic |
| 432 | C2 | #33539 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×#447 |
| commutator, Frattini, cosocle | C4×C8 | C24 |
| prime radical | #33579 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #2960 ◁ G | |
| LECS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #61373 | C2 | semidirect |
| 2. #33707 | C2 | semidirect |
| 4. #19206 | C2 | semidirect |
| 5. #12359 | C2 | semidirect |
| 6. #12358 | C2 | semidirect |
| 7. #12355 | C2 | semidirect |
| 8. #12354 | C2 | semidirect |
| 9. C2×#1365 | C2 | semidirect |
| 10. #11606 | C2 | semidirect |
| 11. #11592 | C2 | semidirect |
| 150. #135 | SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61373 | 2 |
| #33707 | 2 |
| #33579 | 2 |
| #19206 | 2 |
| #12359 | 2 |
| #12358 | 2 |
| #12355 | 2 |
| #12354 | 2 |
| C2×#1365 | 2 |
| #11606 | 2 |
| #11592 | 2 |