Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
1000 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 138 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 | #72226852 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72225406 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72225344 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72216534 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #72216236 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #498569 | — | 2 | 2 | no | — |
| 7 | #491485 | — | 2 | 2 | no | — |
| 8 | #491465 | C22 | 1 | 1 | yes | characteristic |
| 9 | #491465 | C22 | 1 | 1 | yes | characteristic |
| 10 | #152996 | — | 2 | 2 | no | — |
| 11 | C2×#7459 | C22 | 1 | 2 | yes | — |
| 12 | #150947 | — | 2 | 2 | no | — |
| 13 | #141262 | — | 2 | 2 | no | — |
| 14 | #137550 | — | 2 | 2 | no | — |
| 15 | #129142 | C22 | 1 | 2 | yes | — |
| 16 | #123406 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | #123406 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | #123405 | — | 2 | 2 | no | — |
| 19 | #123404 | C4 | 1 | 1 | yes | characteristic, complemented |
| 20 | #123403 | C4 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×C162 | C22 | 1 | 1 | yes | characteristic |
| 22 | #93868 | — | 2 | 2 | no | — |
| 23 | #33733 | — | 4 | 4 | no | — |
| 24 | #33713 | — | 2 | 2 | no | — |
| 25 | #33713 | — | 2 | 2 | no | — |
| 26 | #33465 | — | 4 | 2 | no | — |
| 27 | #23196 | — | 2 | 2 | no | — |
| 28 | #19603 | — | 2 | 1 | no | — |
| 29 | #19603 | D4 | 1 | 2 | yes | — |
| 30 | C2×#1422 | — | 2 | 2 | no | — |
| 31 | #13622 | — | 4 | 2 | no | — |
| 32 | #13620 | — | 4 | 2 | no | — |
| 33 | #13259 | — | 2 | 4 | no | — |
| 34 | #13243 | — | 4 | 2 | no | — |
| 35 | #13016 | — | 4 | 4 | no | — |
| 36 | #12670 | D4 | 1 | 2 | yes | — |
| 37 | #12664 | — | 2 | 2 | no | — |
| 38 | #12521 | — | 2 | 2 | no | — |
| 39 | #12518 | — | 2 | 2 | no | — |
| 40 | #12518 | — | 2 | 2 | no | — |
| 41 | #12517 | — | 2 | 1 | no | — |
| 42 | #12517 | D4 | 1 | 2 | yes | — |
| 43 | #12516 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | #12516 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | #12515 | — | 2 | 2 | no | — |
| 46 | #12515 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | #12515 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | #12509 | — | 2 | 2 | no | — |
| 49 | #12509 | — | 2 | 2 | no | — |
| 50 | #12503 | — | 4 | 4 | no | — |
| 51 | C2×#1373 | D4 | 1 | 2 | yes | — |
| 52 | #11922 | — | 2 | 2 | no | — |
| 53 | C2×C8×C16 | — | 2 | 1 | no | — |
| 54 | C2×C8×C16 | C23 | 1 | 1 | yes | characteristic |
| 55 | #7459 | — | 2 | 2 | no | — |
| 56 | #7459 | — | 2 | 2 | no | — |
| 57 | #7447 | — | 4 | 4 | no | — |
| 58 | #7179 | — | 2 | 2 | no | — |
| 59 | C162 | — | 2 | 1 | no | — |
| 60 | C162 | C2×C4 | 1 | 1 | yes | characteristic |
| 61 | C162 | C2×C4 | 1 | 1 | yes | characteristic |
| 62 | C2×#508 | — | 4 | 2 | no | — |
| 63 | C2×#508 | — | 4 | 2 | no | — |
| 64 | C2×#508 | — | 4 | 2 | no | — |
| 65 | C2×#508 | — | 4 | 2 | no | — |
| 66 | #3169 | — | 4 | 2 | no | — |
| 67 | #3169 | — | 4 | 2 | no | — |
| 68 | #3147 | — | 2 | 2 | no | — |
| 69 | #3147 | — | 4 | 1 | no | — |
| 70 | #2957 | — | 4 | 4 | no | — |
| 71 | C2×M64 | — | 4 | 2 | no | — |
| 72 | #2252 | — | 4 | 4 | no | — |
| 73 | #2249 | — | 4 | 2 | no | — |
| 74 | #2249 | — | 4 | 2 | no | — |
| 75 | #2249 | — | 4 | 2 | no | — |
| 76 | #2249 | — | 4 | 2 | no | — |
| 77 | #2248 | — | 2 | 4 | no | — |
| 78 | #2248 | — | 4 | 2 | no | — |
| 79 | #2247 | — | 2 | 2 | no | — |
| 80 | #2247 | — | 2 | 2 | no | — |
| 81 | #2246 | — | 2 | 2 | no | — |
| 82 | #2246 | — | 2 | 2 | no | — |
| 83 | #2246 | — | 4 | 4 | no | — |
| 84 | #2240 | — | 4 | 4 | no | — |
| 85 | #2240 | — | 4 | 4 | no | — |
| 86 | #2215 | — | 8 | 8 | no | — |
| 87 | #2179 | — | 8 | 4 | no | — |
| 88 | #2178 | — | 8 | 4 | no | — |
| 89 | C4×D16 | — | 8 | 8 | no | — |
| 90 | C2×#368 | D8 | 1 | 2 | yes | — |
| 91 | #2158 | D8 | 1 | 2 | yes | — |
| 92 | C2×#364 | — | 2 | 2 | no | — |
| 93 | #2145 | — | 4 | 4 | no | — |
| 94 | #2143 | — | 4 | 4 | no | — |
| 95 | #2108 | — | 4 | 2 | no | — |
| 96 | C2×C4×C16 | — | 2 | 2 | no | — |
| 97 | C2×C4×C16 | C2×D4 | 1 | 2 | yes | — |
| 98 | #1976 | — | 4 | 4 | no | — |
| 99 | #1884 | — | 8 | 2 | no | — |
| 100 | #1772 | — | 2 | 2 | no | — |
| 101 | #1713 | — | 2 | 1 | no | — |
| 102 | #1713 | C22⋊C4 | 1 | 2 | yes | — |
| 103 | #1712 | — | 2 | 1 | no | — |
| 104 | #1712 | C22⋊C4 | 1 | 2 | yes | — |
| 105 | #1709 | — | 2 | 2 | no | — |
| 106 | #1709 | — | 4 | 1 | no | — |
| 107 | #1706 | — | 4 | 2 | no | — |
| 108 | #1706 | — | 4 | 2 | no | — |
| 109 | C2×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | #1422 | — | 4 | 2 | no | — |
| 111 | #1422 | — | 4 | 2 | no | — |
| 112 | #1418 | — | 8 | 4 | no | — |
| 113 | #1417 | — | 8 | 4 | no | — |
| 114 | #1382 | — | 2 | 2 | no | — |
| 115 | #1379 | — | 4 | 2 | no | — |
| 116 | #1373 | — | 2 | 2 | no | — |
| 117 | #1373 | — | 2 | 2 | no | — |
| 118 | #1359 | — | 8 | 2 | no | — |
| 119 | C8×C16 | — | 2 | 2 | no | — |
| 120 | C8×C16 | — | 2 | 1 | no | — |
| 121 | C8×C16 | — | 2 | 1 | no | — |
| 122 | C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 123 | C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C8×C16 | #41 | 1 | 2 | yes | — |
| 125 | C2×#135 | — | 4 | 4 | no | — |
| 126 | C2×#135 | — | 8 | 2 | no | — |
| 127 | #568 | — | 8 | 2 | no | — |
| 128 | #532 | — | 4 | 2 | no | — |
| 129 | #532 | — | 8 | 1 | no | — |
| 130 | #508 | — | 8 | 2 | no | — |
| 131 | #508 | — | 8 | 2 | no | — |
| 132 | #508 | — | 8 | 2 | no | — |
| 133 | #508 | — | 8 | 2 | no | — |
| 134 | #508 | — | 8 | 2 | no | — |
| 135 | #508 | — | 8 | 2 | no | — |
| 136 | #508 | — | 8 | 2 | no | — |
| 137 | #508 | — | 8 | 2 | no | — |
| 138 | #508 | — | 16 | 2 | no | — |
| 139 | #508 | — | 16 | 2 | no | — |
| 140 | #508 | — | 16 | 2 | no | — |
| 141 | #508 | — | 16 | 2 | no | — |
| 142 | C2×Q32 | — | 4 | 2 | no | — |
| 143 | C2×Q32 | — | 4 | 2 | no | — |
| 144 | C2×Q32 | — | 4 | 2 | no | — |
| 145 | C2×Q32 | — | 4 | 2 | no | — |
| 146 | C2×SD32 | — | 4 | 4 | no | — |
| 147 | C2×SD32 | — | 4 | 4 | no | — |
| 148 | C2×SD32 | — | 8 | 2 | no | — |
| 149 | C2×SD32 | — | 8 | 2 | no | — |
| 150 | C2×D16 | — | 4 | 2 | no | — |
| 151 | C2×D16 | — | 4 | 2 | no | — |
| 152 | C2×D16 | — | 4 | 2 | no | — |
| 153 | C2×D16 | — | 4 | 2 | no | — |
| 154 | C2×D16 | — | 8 | 8 | no | — |
| 155 | C2×M32 | — | 4 | 2 | no | — |
| 156 | C22×C16 | — | 2 | 4 | no | — |
| 157 | C22×C16 | C2×D8 | 1 | 2 | yes | — |
| 158 | C22×C16 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 159 | #500 | — | 4 | 2 | no | — |
| 160 | #500 | — | 4 | 2 | no | — |
| 161 | #495 | — | 4 | 4 | no | — |
| 162 | #495 | — | 8 | 2 | no | — |
| 163 | #494 | — | 2 | 2 | no | — |
| 164 | #494 | — | 4 | 1 | no | — |
| 165 | #493 | — | 2 | 2 | no | — |
| 166 | #493 | — | 4 | 2 | no | — |
| 167 | #493 | — | 4 | 2 | no | — |
| 168 | #493 | — | 4 | 1 | no | — |
| 169 | #492 | — | 4 | 2 | no | — |
| 170 | #492 | — | 8 | 1 | no | — |
| 171 | #486 | — | 8 | 2 | no | — |
| 172 | #486 | — | 8 | 2 | no | — |
| 173 | #466 | — | 8 | 4 | no | — |
| 174 | #466 | — | 8 | 4 | no | — |
| 175 | #444 | — | 16 | 4 | no | — |
| 176 | #443 | — | 8 | 8 | no | — |
| 177 | C4×D8 | — | 8 | 4 | no | — |
| 178 | C4×D8 | — | 8 | 4 | no | — |
| 179 | C2×#108 | — | 2 | 2 | no | — |
| 180 | #427 | — | 2 | 2 | no | — |
| 181 | #421 | — | 8 | 4 | no | — |
| 182 | #410 | — | 8 | 2 | no | — |
| 183 | #405 | — | 4 | 2 | no | — |
| 184 | C2×C4×C8 | — | 2 | 1 | no | — |
| 185 | C2×C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 186 | M64 | — | 8 | 2 | no | — |
| 187 | M64 | — | 8 | 2 | no | — |
| 188 | C2×C32 | — | 8 | 2 | no | — |
| 189 | #368 | — | 2 | 2 | no | — |
| 190 | #368 | D16 | 1 | 4 | yes | complemented |
| 191 | #367 | — | 2 | 2 | no | — |
| 192 | #366 | — | 2 | 2 | no | — |
| 193 | #366 | — | 8 | 8 | no | — |
| 194 | #364 | — | 4 | 2 | no | — |
| 195 | #364 | — | 4 | 2 | no | — |
| 196 | #360 | — | 16 | 4 | no | — |
| 197 | #359 | — | 8 | 8 | no | — |
| 198 | #357 | — | 8 | 8 | no | — |
| 199 | #357 | — | 8 | 8 | no | — |
| 200 | #346 | — | 8 | 2 | no | — |
| 201 | C4×C16 | — | 2 | 2 | no | — |
| 202 | C4×C16 | — | 2 | 2 | no | — |
| 203 | C4×C16 | — | 2 | 4 | no | — |
| 204 | C4×C16 | — | 8 | 2 | no | — |
| 205 | C4×C16 | C4×D4 | 1 | 2 | yes | — |
| 206 | C4×C16 | #121 | 1 | 2 | yes | — |
| 207 | C4×C16 | #135 | 1 | 2 | yes | — |
| 208 | C4×C16 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 209 | #339 | — | 4 | 2 | no | — |
| 210 | C82 | — | 2 | 1 | no | — |
| 211 | C82 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 212 | C82 | #123 | 1 | 1 | yes | characteristic |
| 213 | C2×#41 | — | 8 | 2 | no | — |
| 214 | C2×#41 | — | 16 | 1 | no | — |
| 215 | #135 | — | 8 | 4 | no | — |
| 216 | #135 | — | 8 | 4 | no | — |
| 217 | #135 | — | 8 | 4 | no | — |
| 218 | #135 | — | 8 | 4 | no | — |
| 219 | #135 | — | 16 | 2 | no | — |
| 220 | #135 | — | 16 | 2 | no | — |
| 221 | #135 | — | 16 | 2 | no | — |
| 222 | #135 | — | 16 | 2 | no | — |
| 223 | C2×Q16 | — | 4 | 4 | no | — |
| 224 | C2×Q16 | — | 8 | 2 | no | — |
| 225 | C2×SD16 | — | 8 | 4 | no | — |
| 226 | C2×SD16 | — | 16 | 2 | no | — |
| 227 | C2×D8 | — | 4 | 4 | no | — |
| 228 | C2×D8 | — | 8 | 4 | no | — |
| 229 | C2×D8 | — | 8 | 4 | no | — |
| 230 | C2×D8 | — | 8 | 2 | no | — |
| 231 | #131 | — | 16 | 8 | no | — |
| 232 | C2×M16 | — | 4 | 2 | no | — |
| 233 | C2×M16 | — | 32 | 2 | no | — |
| 234 | C22×C8 | — | 2 | 2 | no | — |
| 235 | C22×C8 | #447 | 1 | 2 | yes | — |
| 236 | C4⋊Q8 | — | 4 | 2 | no | — |
| 237 | C4⋊Q8 | — | 8 | 1 | no | — |
| 238 | #127 | — | 4 | 2 | no | — |
| 239 | #127 | — | 8 | 1 | no | — |
| 240 | #124 | — | 8 | 2 | no | — |
| 241 | #124 | — | 16 | 1 | no | — |
| 242 | #121 | — | 16 | 2 | no | — |
| 243 | #121 | — | 16 | 2 | no | — |
| 244 | C4×D4 | — | 16 | 2 | no | — |
| 245 | C4×D4 | — | 16 | 2 | no | — |
| 246 | #117 | — | 4 | 2 | no | — |
| 247 | C2×C42 | #453 | 1 | 1 | yes | characteristic |
| 248 | Q32 | — | 8 | 2 | no | — |
| 249 | Q32 | — | 8 | 2 | no | — |
| 250 | Q32 | — | 8 | 2 | no | — |
| 251 | Q32 | — | 8 | 2 | no | — |
| 252 | Q32 | — | 16 | 2 | no | — |
| 253 | Q32 | — | 16 | 2 | no | — |
| 254 | SD32 | — | 8 | 4 | no | — |
| 255 | SD32 | — | 8 | 4 | no | — |
| 256 | SD32 | — | 16 | 4 | no | — |
| 257 | SD32 | — | 16 | 4 | no | — |
| 258 | SD32 | — | 16 | 2 | no | — |
| 259 | SD32 | — | 16 | 2 | no | — |
| 260 | D16 | — | 8 | 2 | no | — |
| 261 | D16 | — | 8 | 2 | no | — |
| 262 | D16 | — | 8 | 2 | no | — |
| 263 | D16 | — | 8 | 2 | no | — |
| 264 | D16 | — | 16 | 2 | no | — |
| 265 | D16 | — | 16 | 2 | no | — |
| 266 | D16 | — | 16 | 16 | no | — |
| 267 | M32 | — | 8 | 2 | no | — |
| 268 | M32 | — | 8 | 2 | no | — |
| 269 | C2×C16 | — | 2 | 4 | no | — |
| 270 | C2×C16 | — | 2 | 2 | no | — |
| 271 | C2×C16 | — | 2 | 2 | no | — |
| 272 | C2×C16 | — | 2 | 4 | no | — |
| 273 | C2×C16 | — | 4 | 8 | no | — |
| 274 | C2×C16 | — | 8 | 2 | no | — |
| 275 | C2×C16 | C4×D8 | 1 | 2 | yes | — |
| 276 | C2×C16 | #442 | 1 | 2 | yes | — |
| 277 | C2×C16 | #459 | 1 | 2 | yes | — |
| 278 | C2×C16 | #463 | 1 | 2 | yes | — |
| 279 | C2×C16 | C2×D16 | 1 | 2 | yes | — |
| 280 | C2×C16 | #508 | 1 | 2 | yes | — |
| 281 | C2×C16 | #509 | 1 | 2 | yes | — |
| 282 | C2×C16 | #509 | 1 | 2 | yes | — |
| 283 | #108 | — | 2 | 4 | no | — |
| 284 | #108 | — | 4 | 2 | no | — |
| 285 | #107 | — | 4 | 2 | no | — |
| 286 | #107 | — | 8 | 4 | no | — |
| 287 | #107 | — | 8 | 4 | no | — |
| 288 | #106 | — | 4 | 2 | no | — |
| 289 | #104 | — | 16 | 8 | no | — |
| 290 | #102 | — | 16 | 4 | no | — |
| 291 | #102 | — | 16 | 4 | no | — |
| 292 | #99 | — | 32 | 2 | no | — |
| 293 | #97 | — | 8 | 2 | no | — |
| 294 | C4×C8 | — | 2 | 2 | no | — |
| 295 | C4×C8 | — | 2 | 1 | no | — |
| 296 | C4×C8 | — | 2 | 1 | no | — |
| 297 | C4×C8 | — | 8 | 2 | no | — |
| 298 | C4×C8 | #386 | 1 | 1 | yes | characteristic |
| 299 | C4×C8 | #449 | 1 | 2 | yes | — |
| 300 | C4×C8 | #453 | 1 | 1 | yes | characteristic |
| 301 | C32 | — | 16 | 2 | no | — |
| 302 | #41 | — | 16 | 4 | no | — |
| 303 | #41 | — | 16 | 4 | no | — |
| 304 | #41 | — | 32 | 2 | no | — |
| 305 | #41 | — | 32 | 2 | no | — |
| 306 | C2×Q8 | — | 8 | 2 | no | — |
| 307 | C2×Q8 | — | 16 | 1 | no | — |
| 308 | C2×D4 | — | 8 | 2 | no | — |
| 309 | C2×D4 | — | 16 | 2 | no | — |
| 310 | C2×D4 | — | 16 | 2 | no | — |
| 311 | C2×D4 | — | 16 | 2 | no | — |
| 312 | C2×D4 | — | 16 | 1 | no | — |
| 313 | C2×D4 | — | 32 | 1 | no | — |
| 314 | C22×C4 | — | 2 | 1 | no | — |
| 315 | C22×C4 | — | 16 | 2 | no | — |
| 316 | C22×C4 | — | 32 | 1 | no | — |
| 317 | C22×C4 | #1619 | 1 | 1 | yes | characteristic |
| 318 | Q16 | — | 8 | 4 | no | — |
| 319 | Q16 | — | 8 | 4 | no | — |
| 320 | Q16 | — | 16 | 2 | no | — |
| 321 | Q16 | — | 16 | 2 | no | — |
| 322 | SD16 | — | 16 | 4 | no | — |
| 323 | SD16 | — | 16 | 4 | no | — |
| 324 | SD16 | — | 32 | 2 | no | — |
| 325 | SD16 | — | 32 | 2 | no | — |
| 326 | D8 | — | 8 | 4 | no | — |
| 327 | D8 | — | 8 | 4 | no | — |
| 328 | D8 | — | 16 | 8 | no | — |
| 329 | D8 | — | 16 | 8 | no | — |
| 330 | D8 | — | 16 | 2 | no | — |
| 331 | D8 | — | 16 | 2 | no | — |
| 332 | M16 | — | 4 | 4 | no | — |
| 333 | M16 | — | 8 | 2 | no | — |
| 334 | M16 | — | 32 | 4 | no | — |
| 335 | C2×C8 | — | 2 | 2 | no | — |
| 336 | C2×C8 | — | 2 | 2 | no | — |
| 337 | C2×C8 | — | 4 | 4 | no | — |
| 338 | C2×C8 | — | 8 | 2 | no | — |
| 339 | C2×C8 | — | 32 | 4 | no | — |
| 340 | C2×C8 | #1621 | 1 | 2 | yes | — |
| 341 | C2×C8 | #1879 | 1 | 2 | yes | — |
| 342 | C2×C8 | #2184 | 1 | 2 | yes | — |
| 343 | C2×C8 | #2186 | 1 | 2 | yes | — |
| 344 | C2×C8 | #2192 | 1 | 2 | yes | — |
| 345 | C2×C8 | #2192 | 1 | 2 | yes | — |
| 346 | C4⋊C4 | — | 8 | 2 | no | — |
| 347 | C4⋊C4 | — | 16 | 2 | no | — |
| 348 | C4⋊C4 | — | 16 | 2 | no | — |
| 349 | C22⋊C4 | — | 8 | 2 | no | — |
| 350 | C22⋊C4 | — | 32 | 2 | no | — |
| 351 | C22⋊C4 | — | 32 | 2 | no | — |
| 352 | C42 | — | 2 | 1 | no | — |
| 353 | C42 | — | 8 | 2 | no | — |
| 354 | C42 | #1620 | 1 | 1 | yes | characteristic |
| 355 | C42 | #1887 | 1 | 1 | yes | characteristic |
| 356 | C16 | — | 2 | 8 | no | — |
| 357 | C16 | — | 2 | 2 | no | — |
| 358 | C16 | — | 2 | 2 | no | — |
| 359 | C16 | — | 4 | 4 | no | — |
| 360 | C16 | — | 16 | 2 | no | — |
| 361 | C16 | C4×D16 | 1 | 2 | yes | — |
| 362 | C16 | #2177 | 1 | 2 | yes | — |
| 363 | C16 | #2206 | 1 | 2 | yes | — |
| 364 | C16 | #2210 | 1 | 2 | yes | — |
| 365 | C23 | — | 16 | 2 | no | — |
| 366 | C23 | — | 32 | 1 | no | — |
| 367 | C23 | #12310 | 1 | 1 | yes | characteristic |
| 368 | Q8 | — | 16 | 4 | no | — |
| 369 | Q8 | — | 32 | 2 | no | — |
| 370 | D4 | — | 16 | 4 | no | — |
| 371 | D4 | — | 32 | 4 | no | — |
| 372 | D4 | — | 32 | 4 | no | — |
| 373 | D4 | — | 32 | 4 | no | — |
| 374 | D4 | — | 32 | 2 | no | — |
| 375 | D4 | — | 64 | 2 | no | — |
| 376 | C2×C4 | — | 2 | 1 | no | — |
| 377 | C2×C4 | — | 2 | 1 | no | — |
| 378 | C2×C4 | — | 4 | 2 | no | — |
| 379 | C2×C4 | — | 16 | 2 | no | — |
| 380 | C2×C4 | — | 16 | 2 | no | — |
| 381 | C2×C4 | — | 32 | 2 | no | — |
| 382 | C2×C4 | — | 32 | 2 | no | — |
| 383 | C2×C4 | — | 32 | 1 | no | — |
| 384 | C2×C4 | — | 64 | 1 | no | — |
| 385 | C2×C4 | — | 64 | 1 | no | — |
| 386 | C2×C4 | #9061 | 1 | 1 | yes | characteristic |
| 387 | C2×C4 | #12310 | 1 | 1 | yes | characteristic |
| 388 | C2×C4 | #12316 | 1 | 2 | yes | — |
| 389 | C2×C4 | #12317 | 1 | 2 | yes | — |
| 390 | C8 | — | 2 | 4 | no | — |
| 391 | C8 | — | 4 | 2 | no | — |
| 392 | C8 | — | 8 | 4 | no | — |
| 393 | C8 | #12328 | 1 | 2 | yes | — |
| 394 | C8 | #12329 | 1 | 2 | yes | — |
| 395 | C8 | #13012 | 1 | 2 | yes | — |
| 396 | C8 | #13017 | 1 | 2 | yes | — |
| 397 | C22 | — | 4 | 1 | no | — |
| 398 | C22 | — | 32 | 2 | no | — |
| 399 | C22 | — | 64 | 2 | no | — |
| 400 | C22 | — | 64 | 2 | no | — |
| 401 | C22 | — | 64 | 1 | no | — |
| 402 | C22 | #123277 | 1 | 2 | yes | — |
| 403 | C22 | #137551 | 1 | 1 | yes | characteristic |
| 404 | C4 | — | 2 | 2 | no | — |
| 405 | C4 | — | 4 | 1 | no | — |
| 406 | C4 | — | 32 | 2 | no | — |
| 407 | C4 | — | 32 | 2 | no | — |
| 408 | C4 | — | 64 | 1 | no | — |
| 409 | C4 | #123275 | 1 | 1 | yes | characteristic |
| 410 | C4 | #123276 | 1 | 1 | yes | characteristic |
| 411 | C4 | #137536 | 1 | 2 | yes | — |
| 412 | C2 | — | 2 | 1 | no | — |
| 413 | C2 | — | 2 | 2 | no | — |
| 414 | C2 | — | 64 | 2 | no | — |
| 415 | C2 | — | 128 | 1 | no | — |
| 416 | C2 | #72225198 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #123275 |
| commutator | C8×C16 | C22×C4 |
| Frattini, cosocle | C2×C8×C16 | C23 |
| socle | C2 | #72225198 |
| prime radical | #72216236 | C2 |
| LCS | G ▷ C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×C8×C16 ◁ G | |
| LECS | G ▷ C2×C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72226852 | C2 | semidirect |
| 2. #72225406 | C2 | semidirect |
| 3. #72225344 | C2 | semidirect |
| 4. #72216534 | C2 | semidirect |
| 16. #123406 | C4 | semidirect |
| 17. #123406 | C4 | semidirect |
| 19. #123404 | C4 | semidirect |
| 20. #123403 | C4 | semidirect |
| 190. #368 | D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72226852 | 2 |
| #72225406 | 2 |
| #72225344 | 2 |
| #72216534 | 2 |
| #72216236 | 2 |