Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1557 conjugacy classes of subgroups.
The subgroup lattice has 395 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62472 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #60498 | C2 | 1 | 2 | yes | maximal |
| 3 | #60343 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #19453 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #19441 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #19297 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #19287 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #19158 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | C2×#1696 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #17826 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #17722 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #3503 | C22 | 1 | 2 | yes | — |
| 13 | C4×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 14 | Q8×Q16 | — | 2 | 1 | no | — |
| 15 | Q8×Q16 | — | 2 | 1 | no | — |
| 16 | #3338 | — | 2 | 3 | no | — |
| 17 | #3338 | — | 2 | 3 | no | — |
| 18 | #3230 | C22 | 1 | 6 | yes | — |
| 19 | #3170 | C22 | 1 | 3 | yes | — |
| 20 | C2×#500 | C22 | 1 | 3 | yes | — |
| 21 | #3083 | — | 2 | 6 | no | — |
| 22 | #3082 | — | 2 | 6 | no | — |
| 23 | #3079 | C22 | 1 | 6 | yes | — |
| 24 | #3078 | C22 | 1 | 6 | yes | — |
| 25 | #3076 | C22 | 1 | 6 | yes | — |
| 26 | C2×#477 | C22 | 1 | 6 | yes | — |
| 27 | #2990 | — | 2 | 3 | no | — |
| 28 | #2989 | C22 | 1 | 3 | yes | — |
| 29 | #2988 | C22 | 1 | 1 | yes | characteristic |
| 30 | #2984 | — | 2 | 1 | no | — |
| 31 | #2983 | C22 | 1 | 3 | yes | — |
| 32 | #2970 | — | 2 | 3 | no | — |
| 33 | #2965 | C22 | 1 | 3 | yes | — |
| 34 | C8×#41 | C22 | 1 | 1 | yes | characteristic |
| 35 | Q8×M16 | — | 2 | 1 | no | — |
| 36 | C2×#446 | C22 | 1 | 3 | yes | — |
| 37 | #2913 | — | 2 | 2 | no | — |
| 38 | #2906 | C22 | 1 | 2 | yes | — |
| 39 | #2898 | — | 2 | 2 | no | — |
| 40 | #1704 | C22 | 1 | 12 | yes | — |
| 41 | #1704 | C22 | 1 | 6 | yes | — |
| 42 | #1703 | C22 | 1 | 6 | yes | — |
| 43 | #1696 | C22 | 1 | 6 | yes | — |
| 44 | #1696 | C22 | 1 | 6 | yes | — |
| 45 | #1696 | C22 | 1 | 3 | yes | — |
| 46 | #1696 | C22 | 1 | 12 | yes | — |
| 47 | #1695 | C22 | 1 | 3 | yes | — |
| 48 | #1695 | C22 | 1 | 6 | yes | — |
| 49 | #1690 | C22 | 1 | 3 | yes | — |
| 50 | #1689 | C22 | 1 | 1 | yes | characteristic |
| 51 | #1570 | C22 | 1 | 6 | yes | — |
| 52 | #1566 | C22 | 1 | 3 | yes | — |
| 53 | C2×#334 | C22 | 1 | 3 | yes | — |
| 54 | #1550 | C22 | 1 | 6 | yes | — |
| 55 | #1548 | C22 | 1 | 6 | yes | — |
| 56 | #1542 | C22 | 1 | 6 | yes | — |
| 57 | C2×#333 | C22 | 1 | 6 | yes | — |
| 58 | C2×2−1+4 | D4 | 1 | 1 | yes | characteristic |
| 59 | C2×#131 | — | 2 | 2 | no | — |
| 60 | Q82 | — | 2 | 2 | no | — |
| 61 | #557 | — | 2 | 2 | no | — |
| 62 | #554 | — | 2 | 6 | no | — |
| 63 | D4×Q8 | — | 2 | 6 | no | — |
| 64 | #544 | — | 2 | 6 | no | — |
| 65 | #533 | C23 | 1 | 6 | yes | — |
| 66 | C2×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 67 | #520 | — | 2 | 3 | no | — |
| 68 | #520 | — | 2 | 2 | no | — |
| 69 | #520 | D4 | 1 | 3 | yes | — |
| 70 | #520 | D4 | 1 | 1 | yes | characteristic |
| 71 | #519 | — | 2 | 1 | no | — |
| 72 | #519 | D4 | 1 | 3 | yes | — |
| 73 | C4×#41 | — | 2 | 3 | no | — |
| 74 | C4×#41 | C23 | 1 | 3 | yes | — |
| 75 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 76 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 77 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 78 | #500 | — | 2 | 3 | no | — |
| 79 | #500 | — | 2 | 3 | no | — |
| 80 | #500 | C23 | 1 | 3 | yes | — |
| 81 | #500 | C23 | 1 | 6 | yes | — |
| 82 | #494 | C23 | 1 | 1 | yes | characteristic |
| 83 | #487 | C23 | 1 | 6 | yes | — |
| 84 | #484 | — | 2 | 12 | no | — |
| 85 | #479 | — | 2 | 6 | no | — |
| 86 | #479 | — | 2 | 12 | no | — |
| 87 | #478 | — | 2 | 6 | no | — |
| 88 | #477 | — | 2 | 12 | no | — |
| 89 | #477 | — | 2 | 6 | no | — |
| 90 | #477 | — | 2 | 6 | no | — |
| 91 | #477 | C23 | 1 | 6 | yes | — |
| 92 | #477 | C23 | 1 | 12 | yes | — |
| 93 | #476 | C23 | 1 | 6 | yes | — |
| 94 | #475 | — | 2 | 6 | no | — |
| 95 | #475 | C23 | 1 | 6 | yes | — |
| 96 | #474 | — | 2 | 6 | no | — |
| 97 | #474 | C23 | 1 | 2 | yes | — |
| 98 | #467 | — | 2 | 3 | no | — |
| 99 | #467 | — | 2 | 3 | no | — |
| 100 | #446 | — | 2 | 3 | no | — |
| 101 | #446 | — | 2 | 3 | no | — |
| 102 | #446 | — | 2 | 3 | no | — |
| 103 | #446 | — | 2 | 3 | no | — |
| 104 | #446 | C23 | 1 | 3 | yes | — |
| 105 | #446 | C23 | 1 | 6 | yes | — |
| 106 | #446 | C23 | 1 | 3 | yes | — |
| 107 | C8×Q8 | — | 2 | 1 | no | — |
| 108 | C8×Q8 | D4 | 1 | 1 | yes | characteristic |
| 109 | C8×Q8 | D4 | 1 | 1 | yes | characteristic |
| 110 | C4×Q16 | — | 2 | 3 | no | — |
| 111 | C4×Q16 | — | 2 | 3 | no | — |
| 112 | #436 | C23 | 1 | 1 | yes | characteristic |
| 113 | #436 | C23 | 1 | 3 | yes | — |
| 114 | #435 | — | 2 | 3 | no | — |
| 115 | #435 | — | 2 | 3 | no | — |
| 116 | #435 | — | 2 | 6 | no | — |
| 117 | C8×D4 | — | 2 | 3 | no | — |
| 118 | C8×D4 | D4 | 1 | 3 | yes | — |
| 119 | C8×D4 | D4 | 1 | 3 | yes | — |
| 120 | #432 | — | 2 | 3 | no | — |
| 121 | #432 | — | 2 | 6 | no | — |
| 122 | #431 | — | 2 | 3 | no | — |
| 123 | #431 | C23 | 1 | 3 | yes | — |
| 124 | #431 | C23 | 1 | 3 | yes | — |
| 125 | #428 | — | 2 | 6 | no | — |
| 126 | #428 | — | 2 | 6 | no | — |
| 127 | #427 | — | 2 | 6 | no | — |
| 128 | C2×#107 | — | 2 | 3 | no | — |
| 129 | C2×#107 | — | 2 | 3 | no | — |
| 130 | C2×#107 | — | 2 | 6 | no | — |
| 131 | #424 | — | 2 | 6 | no | — |
| 132 | #423 | — | 2 | 3 | no | — |
| 133 | #423 | C23 | 1 | 6 | yes | — |
| 134 | C2×C4⋊C8 | — | 2 | 3 | no | — |
| 135 | C2×C4⋊C8 | C23 | 1 | 6 | yes | — |
| 136 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 137 | #419 | — | 2 | 6 | no | — |
| 138 | #417 | — | 2 | 6 | no | — |
| 139 | #416 | — | 2 | 6 | no | — |
| 140 | C2×#103 | — | 2 | 6 | no | — |
| 141 | C4×M16 | — | 2 | 3 | no | — |
| 142 | C2×#97 | — | 2 | 3 | no | — |
| 143 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 144 | #334 | C23 | 1 | 1 | yes | characteristic |
| 145 | #334 | C23 | 1 | 3 | yes | — |
| 146 | #334 | C23 | 1 | 6 | yes | — |
| 147 | #334 | C23 | 1 | 6 | yes | — |
| 148 | #333 | C23 | 1 | 6 | yes | — |
| 149 | #333 | C23 | 1 | 12 | yes | — |
| 150 | #333 | C23 | 1 | 6 | yes | — |
| 151 | #332 | C23 | 1 | 2 | yes | — |
| 152 | #332 | C23 | 1 | 6 | yes | — |
| 153 | 2−1+4 | — | 2 | 8 | no | — |
| 154 | C2×#41 | — | 2 | 3 | no | — |
| 155 | C2×#41 | C2×D4 | 1 | 3 | yes | — |
| 156 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C22×Q8 | — | 2 | 1 | no | — |
| 158 | C22×Q8 | — | 2 | 6 | no | — |
| 159 | C22×Q8 | C2×D4 | 1 | 3 | yes | — |
| 160 | C2×Q16 | — | 2 | 1 | no | — |
| 161 | C2×Q16 | — | 2 | 1 | no | — |
| 162 | #131 | — | 4 | 8 | no | — |
| 163 | C2×M16 | — | 2 | 6 | no | — |
| 164 | C2×M16 | — | 2 | 1 | no | — |
| 165 | C2×M16 | — | 2 | 3 | no | — |
| 166 | C22×C8 | — | 2 | 6 | no | — |
| 167 | C22×C8 | — | 2 | 3 | no | — |
| 168 | C22×C8 | C2×D4 | 1 | 3 | yes | — |
| 169 | C22×C8 | C2×D4 | 1 | 3 | yes | — |
| 170 | C4⋊Q8 | — | 2 | 6 | no | — |
| 171 | C4⋊Q8 | — | 2 | 6 | no | — |
| 172 | C4⋊Q8 | — | 2 | 6 | no | — |
| 173 | C4⋊Q8 | — | 4 | 6 | no | — |
| 174 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 175 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 176 | #125 | — | 2 | 6 | no | — |
| 177 | #125 | — | 4 | 6 | no | — |
| 178 | C22⋊Q8 | — | 2 | 6 | no | — |
| 179 | C22⋊Q8 | — | 2 | 6 | no | — |
| 180 | C22⋊Q8 | — | 4 | 12 | no | — |
| 181 | C4×Q8 | — | 2 | 1 | no | — |
| 182 | C4×Q8 | — | 2 | 3 | no | — |
| 183 | C4×Q8 | — | 2 | 3 | no | — |
| 184 | C4×Q8 | — | 2 | 3 | no | — |
| 185 | C4×Q8 | — | 2 | 3 | no | — |
| 186 | C4×Q8 | — | 2 | 6 | no | — |
| 187 | C4×Q8 | — | 2 | 6 | no | — |
| 188 | C4×Q8 | — | 4 | 2 | no | — |
| 189 | C4×Q8 | C2×D4 | 1 | 6 | yes | — |
| 190 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 191 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C4×Q8 | #41 | 1 | 1 | yes | characteristic |
| 193 | C4×Q8 | C24 | 1 | 3 | yes | — |
| 194 | C4×D4 | — | 2 | 3 | no | — |
| 195 | C4×D4 | — | 2 | 3 | no | — |
| 196 | C4×D4 | — | 2 | 3 | no | — |
| 197 | C4×D4 | — | 2 | 6 | no | — |
| 198 | C4×D4 | — | 4 | 6 | no | — |
| 199 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 200 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 201 | C4×D4 | #41 | 1 | 3 | yes | — |
| 202 | C4×D4 | C24 | 1 | 1 | yes | characteristic |
| 203 | #117 | — | 2 | 3 | no | — |
| 204 | #117 | — | 2 | 6 | no | — |
| 205 | #117 | — | 2 | 3 | no | — |
| 206 | #117 | — | 2 | 6 | no | — |
| 207 | #117 | C2×D4 | 1 | 3 | yes | — |
| 208 | #117 | C2×D4 | 1 | 3 | yes | — |
| 209 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 210 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 211 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 212 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 213 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 214 | C2×C42 | — | 2 | 3 | no | — |
| 215 | C2×C42 | — | 2 | 3 | no | — |
| 216 | C2×C42 | C24 | 1 | 3 | yes | — |
| 217 | #107 | — | 2 | 3 | no | — |
| 218 | #107 | — | 2 | 3 | no | — |
| 219 | #107 | — | 2 | 6 | no | — |
| 220 | #107 | — | 2 | 6 | no | — |
| 221 | #107 | — | 2 | 6 | no | — |
| 222 | #107 | — | 2 | 12 | no | — |
| 223 | #107 | — | 2 | 2 | no | — |
| 224 | #106 | — | 2 | 6 | no | — |
| 225 | #106 | — | 2 | 6 | no | — |
| 226 | C4⋊C8 | — | 2 | 3 | no | — |
| 227 | C4⋊C8 | — | 2 | 6 | no | — |
| 228 | C4⋊C8 | — | 2 | 3 | no | — |
| 229 | C4⋊C8 | — | 2 | 3 | no | — |
| 230 | C4⋊C8 | — | 2 | 6 | no | — |
| 231 | C4⋊C8 | — | 2 | 6 | no | — |
| 232 | C4⋊C8 | C2×D4 | 1 | 3 | yes | — |
| 233 | C4⋊C8 | C2×D4 | 1 | 3 | yes | — |
| 234 | C4⋊C8 | C24 | 1 | 3 | yes | — |
| 235 | C4⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 236 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 237 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 238 | #103 | — | 2 | 6 | no | — |
| 239 | #103 | — | 2 | 12 | no | — |
| 240 | #103 | — | 2 | 6 | no | — |
| 241 | #103 | — | 2 | 6 | no | — |
| 242 | #103 | — | 2 | 6 | no | — |
| 243 | #102 | — | 2 | 2 | no | — |
| 244 | #102 | — | 2 | 6 | no | — |
| 245 | C22⋊C8 | — | 2 | 3 | no | — |
| 246 | C22⋊C8 | — | 2 | 1 | no | — |
| 247 | C22⋊C8 | — | 2 | 3 | no | — |
| 248 | C22⋊C8 | C2×D4 | 1 | 6 | yes | — |
| 249 | #97 | — | 2 | 3 | no | — |
| 250 | #97 | — | 2 | 6 | no | — |
| 251 | #97 | — | 2 | 3 | no | — |
| 252 | C4×C8 | — | 2 | 3 | no | — |
| 253 | C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 254 | C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 255 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 256 | C4×C8 | C24 | 1 | 3 | yes | — |
| 257 | #41 | — | 2 | 12 | no | — |
| 258 | #41 | — | 4 | 12 | no | — |
| 259 | #41 | #137 | 1 | 8 | yes | — |
| 260 | C2×Q8 | — | 2 | 3 | no | — |
| 261 | C2×Q8 | — | 2 | 12 | no | — |
| 262 | C2×Q8 | — | 2 | 2 | no | — |
| 263 | C2×Q8 | — | 2 | 6 | no | — |
| 264 | C2×Q8 | — | 4 | 4 | no | — |
| 265 | C2×Q8 | — | 4 | 6 | no | — |
| 266 | C2×Q8 | — | 16 | 6 | no | — |
| 267 | C2×Q8 | #121 | 1 | 1 | yes | characteristic |
| 268 | C2×Q8 | C22×D4 | 1 | 3 | yes | — |
| 269 | C2×D4 | — | 2 | 3 | no | — |
| 270 | C2×D4 | #121 | 1 | 3 | yes | — |
| 271 | C2×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 272 | C22×C4 | — | 2 | 3 | no | — |
| 273 | C22×C4 | — | 2 | 3 | no | — |
| 274 | C22×C4 | — | 2 | 3 | no | — |
| 275 | C22×C4 | — | 2 | 1 | no | — |
| 276 | C22×C4 | — | 2 | 3 | no | — |
| 277 | C22×C4 | — | 4 | 6 | no | — |
| 278 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 279 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 280 | C22×C4 | C2×#41 | 1 | 3 | yes | — |
| 281 | Q16 | — | 4 | 2 | no | — |
| 282 | Q16 | — | 4 | 2 | no | — |
| 283 | M16 | — | 4 | 12 | no | — |
| 284 | M16 | — | 4 | 2 | no | — |
| 285 | M16 | — | 8 | 3 | no | — |
| 286 | C2×C8 | — | 2 | 6 | no | — |
| 287 | C2×C8 | — | 2 | 1 | no | — |
| 288 | C2×C8 | — | 2 | 3 | no | — |
| 289 | C2×C8 | — | 2 | 6 | no | — |
| 290 | C2×C8 | — | 2 | 2 | no | — |
| 291 | C2×C8 | — | 4 | 3 | no | — |
| 292 | C2×C8 | — | 4 | 12 | no | — |
| 293 | C2×C8 | — | 8 | 3 | no | — |
| 294 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 295 | C2×C8 | C22×D4 | 1 | 3 | yes | — |
| 296 | C2×C8 | C22×D4 | 1 | 3 | yes | — |
| 297 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 298 | C4⋊C4 | — | 2 | 6 | no | — |
| 299 | C4⋊C4 | — | 2 | 3 | no | — |
| 300 | C4⋊C4 | — | 2 | 3 | no | — |
| 301 | C4⋊C4 | — | 2 | 3 | no | — |
| 302 | C4⋊C4 | — | 2 | 2 | no | — |
| 303 | C4⋊C4 | — | 2 | 6 | no | — |
| 304 | C4⋊C4 | — | 2 | 6 | no | — |
| 305 | C4⋊C4 | — | 2 | 2 | no | — |
| 306 | C4⋊C4 | — | 4 | 6 | no | — |
| 307 | C4⋊C4 | — | 4 | 6 | no | — |
| 308 | C4⋊C4 | — | 4 | 6 | no | — |
| 309 | C4⋊C4 | — | 4 | 6 | no | — |
| 310 | C4⋊C4 | #121 | 1 | 3 | yes | — |
| 311 | C4⋊C4 | #121 | 1 | 3 | yes | — |
| 312 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 313 | C4⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 314 | C22⋊C4 | — | 2 | 3 | no | — |
| 315 | C22⋊C4 | — | 2 | 3 | no | — |
| 316 | C22⋊C4 | — | 2 | 1 | no | — |
| 317 | C22⋊C4 | — | 4 | 6 | no | — |
| 318 | C22⋊C4 | #121 | 1 | 6 | yes | — |
| 319 | C42 | — | 2 | 3 | no | — |
| 320 | C42 | — | 2 | 6 | no | — |
| 321 | C42 | — | 2 | 3 | no | — |
| 322 | C42 | — | 2 | 3 | no | — |
| 323 | C42 | — | 4 | 6 | no | — |
| 324 | C42 | C22×D4 | 1 | 3 | yes | — |
| 325 | C42 | C22×D4 | 1 | 3 | yes | — |
| 326 | C42 | C2×#41 | 1 | 3 | yes | — |
| 327 | C42 | C25 | 1 | 1 | yes | characteristic |
| 328 | C23 | — | 2 | 1 | no | — |
| 329 | C23 | C2×#121 | 1 | 3 | yes | — |
| 330 | Q8 | — | 2 | 6 | no | — |
| 331 | Q8 | — | 4 | 6 | no | — |
| 332 | Q8 | — | 4 | 2 | no | — |
| 333 | Q8 | — | 4 | 2 | no | — |
| 334 | Q8 | — | 8 | 6 | no | — |
| 335 | Q8 | — | 16 | 6 | no | — |
| 336 | Q8 | #470 | 1 | 4 | yes | — |
| 337 | D4 | — | 2 | 2 | no | — |
| 338 | D4 | — | 4 | 6 | no | — |
| 339 | D4 | #470 | 1 | 12 | yes | — |
| 340 | C2×C4 | — | 2 | 3 | no | — |
| 341 | C2×C4 | — | 2 | 3 | no | — |
| 342 | C2×C4 | — | 2 | 1 | no | — |
| 343 | C2×C4 | — | 2 | 3 | no | — |
| 344 | C2×C4 | — | 2 | 3 | no | — |
| 345 | C2×C4 | — | 4 | 3 | no | — |
| 346 | C2×C4 | — | 4 | 6 | no | — |
| 347 | C2×C4 | — | 4 | 1 | no | — |
| 348 | C2×C4 | — | 4 | 6 | no | — |
| 349 | C2×C4 | — | 4 | 1 | no | — |
| 350 | C2×C4 | — | 4 | 2 | no | — |
| 351 | C2×C4 | — | 4 | 6 | no | — |
| 352 | C2×C4 | — | 8 | 3 | no | — |
| 353 | C2×C4 | — | 8 | 3 | no | — |
| 354 | C2×C4 | — | 16 | 6 | no | — |
| 355 | C2×C4 | C2×#121 | 1 | 3 | yes | — |
| 356 | C2×C4 | C2×#121 | 1 | 3 | yes | — |
| 357 | C2×C4 | C2×#121 | 1 | 3 | yes | — |
| 358 | C2×C4 | C2×#137 | 1 | 12 | yes | — |
| 359 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 360 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 361 | C2×C4 | C22×#41 | 1 | 1 | yes | characteristic |
| 362 | C8 | — | 2 | 1 | no | — |
| 363 | C8 | — | 2 | 3 | no | — |
| 364 | C8 | — | 2 | 3 | no | — |
| 365 | C8 | — | 4 | 3 | no | — |
| 366 | C8 | — | 4 | 2 | no | — |
| 367 | C8 | — | 4 | 6 | no | — |
| 368 | C8 | — | 4 | 1 | no | — |
| 369 | C8 | #578 | 1 | 2 | yes | — |
| 370 | C22 | — | 2 | 3 | no | — |
| 371 | C22 | — | 2 | 3 | no | — |
| 372 | C22 | — | 4 | 1 | no | — |
| 373 | C22 | — | 4 | 1 | no | — |
| 374 | C22 | — | 4 | 1 | no | — |
| 375 | C22 | C2×#470 | 1 | 6 | yes | — |
| 376 | C22 | C22×#121 | 1 | 1 | yes | characteristic |
| 377 | C4 | — | 2 | 3 | no | — |
| 378 | C4 | — | 2 | 1 | no | — |
| 379 | C4 | — | 2 | 3 | no | — |
| 380 | C4 | — | 4 | 1 | no | — |
| 381 | C4 | — | 4 | 3 | no | — |
| 382 | C4 | — | 4 | 3 | no | — |
| 383 | C4 | — | 8 | 2 | no | — |
| 384 | C4 | — | 8 | 6 | no | — |
| 385 | C4 | C2×#470 | 1 | 6 | yes | — |
| 386 | C4 | C22×#137 | 1 | 2 | yes | — |
| 387 | C4 | C2×#578 | 1 | 1 | yes | characteristic |
| 388 | C4 | #3586 | 1 | 1 | yes | characteristic |
| 389 | C2 | — | 2 | 6 | no | — |
| 390 | C2 | — | 8 | 1 | no | — |
| 391 | C2 | #60432 | 1 | 1 | yes | characteristic |
| 392 | C2 | C22×#470 | 1 | 1 | yes | characteristic |
| 393 | C2 | #60471 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×#121 |
| commutator, Frattini, cosocle | C42 | C25 |
| prime radical | C2×2−1+4 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×#41 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62472 | C2 | semidirect |
| 4. #19453 | C2 | semidirect |
| 5. #19441 | C2 | semidirect |
| 6. #19297 | C2 | semidirect |
| 7. #19287 | C2 | semidirect |
| 8. #19158 | C2 | semidirect |
| 9. C2×#1696 | C2 | semidirect |
| 10. #17826 | C2 | semidirect |
| 11. #17722 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62472 | 2 |
| #60498 | 2 |
| #60343 | 2 |
| #19453 | 2 |
| #19441 | 2 |
| #19297 | 2 |
| #19287 | 2 |
| #19158 | 2 |
| C2×#1696 | 2 |
| #17826 | 2 |
| #17722 | 2 |