Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1239 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 1239 conjugacy classes of subgroups — too many to draw. Only its 151 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 | #7624857 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #512841 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #500852 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #151297 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #151185 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #150881 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #149671 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #62635 | C22 | 1 | 1 | yes | characteristic, complemented |
| 9 | #62328 | — | 2 | 1 | no | — |
| 10 | C2×#2263 | — | 2 | 2 | no | — |
| 11 | #33908 | — | 2 | 2 | no | — |
| 12 | #33892 | — | 2 | 4 | no | — |
| 13 | D4×D16 | — | 2 | 2 | no | — |
| 14 | #33819 | C22 | 1 | 2 | yes | complemented |
| 15 | #33765 | — | 2 | 1 | no | — |
| 16 | #33765 | C22 | 1 | 2 | yes | complemented |
| 17 | #33733 | — | 2 | 1 | no | — |
| 18 | #33617 | — | 2 | 1 | no | — |
| 19 | #33607 | — | 2 | 1 | no | — |
| 20 | #33607 | C22 | 1 | 2 | yes | — |
| 21 | #33434 | C22 | 1 | 1 | yes | characteristic |
| 22 | #24287 | — | 2 | 1 | no | — |
| 23 | #13667 | — | 2 | 4 | no | — |
| 24 | #13667 | C22 | 1 | 8 | yes | complemented |
| 25 | #13622 | — | 2 | 2 | no | — |
| 26 | #13556 | C22 | 1 | 2 | yes | complemented |
| 27 | #13444 | C22 | 1 | 2 | yes | complemented |
| 28 | #13312 | C22 | 1 | 2 | yes | complemented |
| 29 | #13241 | — | 2 | 1 | no | — |
| 30 | #12840 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #12746 | — | 2 | 1 | no | — |
| 32 | #7424 | C22 | 1 | 8 | yes | complemented |
| 33 | #7364 | C22 | 1 | 2 | yes | complemented |
| 34 | #7337 | C22 | 1 | 2 | yes | complemented |
| 35 | #3584 | — | 2 | 1 | no | — |
| 36 | #3549 | — | 4 | 1 | no | — |
| 37 | #3417 | — | 4 | 1 | no | — |
| 38 | #3416 | — | 4 | 2 | no | — |
| 39 | #3415 | — | 4 | 1 | no | — |
| 40 | #3414 | — | 2 | 2 | no | — |
| 41 | #3414 | C23 | 1 | 2 | yes | — |
| 42 | C2×#508 | — | 2 | 1 | no | — |
| 43 | C2×#508 | — | 2 | 2 | no | — |
| 44 | C22×D16 | — | 2 | 1 | no | — |
| 45 | C22×D16 | D4 | 1 | 2 | yes | — |
| 46 | C2×#504 | D4 | 1 | 1 | yes | characteristic |
| 47 | C2×#504 | C23 | 1 | 1 | yes | characteristic |
| 48 | #3341 | — | 2 | 4 | no | — |
| 49 | #3325 | — | 4 | 4 | no | — |
| 50 | D4×D8 | — | 2 | 4 | no | — |
| 51 | #3253 | — | 4 | 1 | no | — |
| 52 | #3199 | — | 4 | 1 | no | — |
| 53 | #3199 | — | 4 | 1 | no | — |
| 54 | #3169 | — | 2 | 2 | no | — |
| 55 | #3067 | — | 2 | 2 | no | — |
| 56 | #3058 | — | 2 | 2 | no | — |
| 57 | #3058 | — | 2 | 2 | no | — |
| 58 | #3018 | — | 4 | 1 | no | — |
| 59 | #2931 | D4 | 1 | 1 | yes | characteristic |
| 60 | #2263 | — | 2 | 8 | no | — |
| 61 | #2263 | — | 4 | 4 | no | — |
| 62 | C2×SD64 | — | 4 | 2 | no | — |
| 63 | C2×D32 | — | 4 | 2 | no | — |
| 64 | C2×M64 | — | 2 | 2 | no | — |
| 65 | #2252 | — | 2 | 1 | no | — |
| 66 | #2246 | — | 2 | 1 | no | — |
| 67 | #2240 | — | 2 | 2 | no | — |
| 68 | #2234 | — | 2 | 4 | no | — |
| 69 | #2234 | — | 2 | 4 | no | — |
| 70 | #2226 | — | 2 | 4 | no | — |
| 71 | #2223 | — | 4 | 2 | no | — |
| 72 | #2222 | — | 4 | 1 | no | — |
| 73 | #2221 | — | 4 | 1 | no | — |
| 74 | #2218 | — | 2 | 2 | no | — |
| 75 | #2218 | — | 2 | 2 | no | — |
| 76 | #2218 | D4 | 1 | 4 | yes | — |
| 77 | #2218 | C23 | 1 | 4 | yes | — |
| 78 | #2215 | — | 2 | 2 | no | — |
| 79 | #2215 | — | 2 | 2 | no | — |
| 80 | #2215 | — | 2 | 2 | no | — |
| 81 | #2215 | — | 2 | 2 | no | — |
| 82 | #2206 | — | 2 | 4 | no | — |
| 83 | #2184 | — | 2 | 4 | no | — |
| 84 | #2184 | — | 2 | 4 | no | — |
| 85 | C4×D16 | — | 2 | 2 | no | — |
| 86 | C4×D16 | — | 2 | 2 | no | — |
| 87 | #2169 | — | 2 | 2 | no | — |
| 88 | D4×C16 | — | 2 | 2 | no | — |
| 89 | C2×#368 | — | 2 | 1 | no | — |
| 90 | #2158 | — | 2 | 1 | no | — |
| 91 | #2158 | D4 | 1 | 2 | yes | — |
| 92 | #2150 | C23 | 1 | 1 | yes | characteristic |
| 93 | #2148 | — | 2 | 2 | no | — |
| 94 | C2×#359 | — | 2 | 2 | no | — |
| 95 | #2140 | — | 2 | 2 | no | — |
| 96 | #2140 | — | 2 | 2 | no | — |
| 97 | #2113 | D4 | 1 | 1 | yes | characteristic |
| 98 | #2113 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×C4×C16 | D4 | 1 | 1 | yes | characteristic |
| 100 | #2050 | — | 4 | 1 | no | — |
| 101 | #2017 | — | 4 | 1 | no | — |
| 102 | #1974 | — | 2 | 2 | no | — |
| 103 | #1813 | — | 2 | 1 | no | — |
| 104 | #1791 | — | 4 | 1 | no | — |
| 105 | #1418 | — | 2 | 8 | no | — |
| 106 | #1400 | — | 2 | 2 | no | — |
| 107 | #1400 | C23 | 1 | 4 | yes | — |
| 108 | #1385 | C23 | 1 | 2 | yes | — |
| 109 | #585 | — | 4 | 1 | no | — |
| 110 | #578 | — | 4 | 2 | no | — |
| 111 | #577 | — | 8 | 2 | no | — |
| 112 | #576 | — | 4 | 2 | no | — |
| 113 | #575 | — | 4 | 2 | no | — |
| 114 | #575 | — | 4 | 1 | no | — |
| 115 | #575 | — | 4 | 2 | no | — |
| 116 | C2×#135 | — | 2 | 2 | no | — |
| 117 | C2×#135 | — | 4 | 2 | no | — |
| 118 | C22×D8 | — | 2 | 2 | no | — |
| 119 | C22×D8 | — | 2 | 2 | no | — |
| 120 | C2×#131 | C2×D4 | 1 | 1 | yes | characteristic |
| 121 | C2×#131 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | H(3,𝔽4) | — | 8 | 1 | no | — |
| 123 | H(3,𝔽4) | — | 8 | 1 | no | — |
| 124 | #555 | — | 4 | 4 | no | — |
| 125 | #555 | — | 8 | 1 | no | — |
| 126 | D42 | — | 4 | 4 | no | — |
| 127 | D42 | — | 8 | 1 | no | — |
| 128 | #535 | — | 4 | 2 | no | — |
| 129 | #535 | — | 4 | 2 | no | — |
| 130 | #535 | — | 8 | 4 | no | — |
| 131 | #532 | — | 4 | 2 | no | — |
| 132 | #532 | D8 | 1 | 1 | yes | characteristic |
| 133 | #510 | — | 4 | 2 | no | — |
| 134 | #510 | — | 4 | 4 | no | — |
| 135 | #509 | — | 4 | 2 | no | — |
| 136 | #509 | — | 4 | 4 | no | — |
| 137 | #508 | — | 2 | 4 | no | — |
| 138 | #508 | — | 2 | 4 | no | — |
| 139 | #508 | — | 4 | 1 | no | — |
| 140 | #508 | — | 4 | 2 | no | — |
| 141 | #508 | — | 4 | 1 | no | — |
| 142 | #508 | — | 4 | 1 | no | — |
| 143 | #508 | — | 4 | 1 | no | — |
| 144 | C2×Q32 | — | 2 | 2 | no | — |
| 145 | C2×Q32 | — | 2 | 1 | no | — |
| 146 | C2×SD32 | — | 2 | 2 | no | — |
| 147 | C2×SD32 | — | 4 | 2 | no | — |
| 148 | C2×D16 | — | 2 | 2 | no | — |
| 149 | C2×D16 | — | 2 | 1 | no | — |
| 150 | C2×D16 | — | 2 | 2 | no | — |
| 151 | C2×D16 | — | 2 | 2 | no | — |
| 152 | C2×D16 | — | 2 | 2 | no | — |
| 153 | C2×D16 | — | 4 | 2 | no | — |
| 154 | C2×D16 | — | 4 | 2 | no | — |
| 155 | C2×D16 | — | 8 | 1 | no | — |
| 156 | C2×D16 | — | 8 | 1 | no | — |
| 157 | C2×D16 | C2×D4 | 1 | 4 | yes | — |
| 158 | #504 | — | 4 | 1 | no | — |
| 159 | #504 | — | 4 | 1 | no | — |
| 160 | #504 | — | 4 | 1 | no | — |
| 161 | #504 | — | 4 | 1 | no | — |
| 162 | C2×M32 | — | 2 | 1 | no | — |
| 163 | C2×M32 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C2×M32 | C2×D4 | 1 | 2 | yes | — |
| 165 | C2×M32 | C24 | 1 | 1 | yes | characteristic |
| 166 | C22×C16 | — | 2 | 1 | no | — |
| 167 | C22×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | C22×C16 | C2×D4 | 1 | 2 | yes | — |
| 169 | C22×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | #500 | — | 2 | 2 | no | — |
| 171 | #493 | — | 2 | 2 | no | — |
| 172 | #486 | — | 4 | 2 | no | — |
| 173 | #482 | — | 4 | 4 | no | — |
| 174 | #482 | — | 4 | 4 | no | — |
| 175 | #476 | — | 4 | 4 | no | — |
| 176 | #473 | — | 4 | 2 | no | — |
| 177 | #472 | — | 4 | 2 | no | — |
| 178 | #471 | — | 8 | 2 | no | — |
| 179 | #469 | — | 4 | 2 | no | — |
| 180 | #469 | — | 4 | 2 | no | — |
| 181 | #469 | — | 4 | 2 | no | — |
| 182 | #469 | — | 4 | 2 | no | — |
| 183 | #466 | — | 2 | 4 | no | — |
| 184 | #466 | — | 2 | 4 | no | — |
| 185 | #466 | — | 2 | 4 | no | — |
| 186 | #466 | — | 4 | 2 | no | — |
| 187 | #459 | — | 4 | 4 | no | — |
| 188 | #456 | — | 8 | 1 | no | — |
| 189 | #455 | — | 8 | 1 | no | — |
| 190 | #454 | — | 8 | 1 | no | — |
| 191 | #453 | — | 8 | 1 | no | — |
| 192 | #447 | — | 4 | 4 | no | — |
| 193 | #447 | — | 4 | 4 | no | — |
| 194 | C4×D8 | — | 2 | 4 | no | — |
| 195 | C4×D8 | — | 4 | 2 | no | — |
| 196 | #436 | — | 2 | 2 | no | — |
| 197 | C8×D4 | — | 2 | 2 | no | — |
| 198 | C2×#108 | — | 2 | 2 | no | — |
| 199 | #427 | — | 2 | 2 | no | — |
| 200 | #427 | — | 2 | 2 | no | — |
| 201 | #423 | D8 | 1 | 1 | yes | characteristic |
| 202 | C2×#104 | — | 4 | 2 | no | — |
| 203 | #418 | — | 4 | 2 | no | — |
| 204 | #418 | — | 4 | 2 | no | — |
| 205 | #413 | — | 4 | 1 | no | — |
| 206 | #413 | — | 4 | 2 | no | — |
| 207 | #408 | — | 4 | 2 | no | — |
| 208 | #408 | D8 | 1 | 1 | yes | characteristic |
| 209 | #408 | D8 | 1 | 1 | yes | characteristic |
| 210 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 211 | SD64 | — | 4 | 8 | no | — |
| 212 | D32 | — | 4 | 8 | no | — |
| 213 | M64 | — | 2 | 4 | no | — |
| 214 | M64 | — | 4 | 2 | no | — |
| 215 | C2×C32 | — | 4 | 2 | no | — |
| 216 | #368 | — | 4 | 1 | no | — |
| 217 | #368 | — | 4 | 1 | no | — |
| 218 | #367 | — | 2 | 2 | no | — |
| 219 | #367 | C2×D4 | 1 | 4 | yes | — |
| 220 | #366 | — | 2 | 2 | no | — |
| 221 | #366 | — | 2 | 2 | no | — |
| 222 | C4⋊C16 | — | 2 | 2 | no | — |
| 223 | #362 | — | 4 | 2 | no | — |
| 224 | #361 | — | 4 | 2 | no | — |
| 225 | #359 | — | 8 | 2 | no | — |
| 226 | #357 | — | 2 | 4 | no | — |
| 227 | #357 | — | 2 | 4 | no | — |
| 228 | #357 | — | 2 | 4 | no | — |
| 229 | #357 | — | 2 | 4 | no | — |
| 230 | C22⋊C16 | — | 2 | 2 | no | — |
| 231 | C22⋊C16 | — | 2 | 2 | no | — |
| 232 | C4×C16 | — | 2 | 1 | no | — |
| 233 | C4×C16 | — | 2 | 1 | no | — |
| 234 | #338 | — | 4 | 1 | no | — |
| 235 | 2−1+4 | — | 8 | 2 | no | — |
| 236 | 2−1+4 | — | 8 | 1 | no | — |
| 237 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 238 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 239 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 240 | C2×#41 | — | 4 | 2 | no | — |
| 241 | C2×#41 | — | 8 | 2 | no | — |
| 242 | C2×#41 | — | 8 | 2 | no | — |
| 243 | C2×#41 | — | 16 | 2 | no | — |
| 244 | C2×#41 | C2×D8 | 1 | 1 | yes | characteristic |
| 245 | C2×#41 | C2×D8 | 1 | 1 | yes | characteristic |
| 246 | C22×D4 | — | 4 | 2 | no | — |
| 247 | C22×D4 | — | 4 | 2 | no | — |
| 248 | C22×D4 | — | 8 | 4 | no | — |
| 249 | #137 | — | 8 | 4 | no | — |
| 250 | #137 | — | 8 | 2 | no | — |
| 251 | #137 | — | 8 | 2 | no | — |
| 252 | #137 | — | 8 | 2 | no | — |
| 253 | AGL(1,ℤ/8) | — | 8 | 4 | no | — |
| 254 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 255 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 256 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 257 | #135 | — | 4 | 2 | no | — |
| 258 | #135 | — | 4 | 2 | no | — |
| 259 | #135 | — | 4 | 4 | no | — |
| 260 | #135 | — | 4 | 2 | no | — |
| 261 | #135 | — | 4 | 2 | no | — |
| 262 | #135 | — | 8 | 2 | no | — |
| 263 | #135 | — | 8 | 2 | no | — |
| 264 | #135 | — | 16 | 2 | no | — |
| 265 | C2×Q16 | — | 2 | 2 | no | — |
| 266 | C2×Q16 | — | 4 | 2 | no | — |
| 267 | C2×SD16 | — | 4 | 2 | no | — |
| 268 | C2×SD16 | — | 8 | 2 | no | — |
| 269 | C2×D8 | — | 2 | 2 | no | — |
| 270 | C2×D8 | — | 2 | 4 | no | — |
| 271 | C2×D8 | — | 4 | 2 | no | — |
| 272 | C2×D8 | — | 4 | 2 | no | — |
| 273 | C2×D8 | — | 4 | 2 | no | — |
| 274 | C2×D8 | — | 4 | 2 | no | — |
| 275 | C2×D8 | — | 8 | 2 | no | — |
| 276 | C2×D8 | — | 8 | 2 | no | — |
| 277 | C2×D8 | — | 8 | 2 | no | — |
| 278 | C2×D8 | — | 8 | 2 | no | — |
| 279 | #131 | — | 4 | 1 | no | — |
| 280 | #131 | — | 4 | 1 | no | — |
| 281 | #131 | — | 4 | 1 | no | — |
| 282 | #131 | — | 4 | 1 | no | — |
| 283 | C2×M16 | — | 2 | 1 | no | — |
| 284 | C2×M16 | — | 4 | 2 | no | — |
| 285 | C2×M16 | C2×D8 | 1 | 1 | yes | characteristic |
| 286 | C2×M16 | C2×D8 | 1 | 1 | yes | characteristic |
| 287 | C2×M16 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 288 | C22×C8 | — | 2 | 1 | no | — |
| 289 | C22×C8 | #120 | 1 | 2 | yes | — |
| 290 | C22×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 291 | C22×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 292 | C4⋊Q8 | — | 4 | 2 | no | — |
| 293 | C4⋊Q8 | D16 | 1 | 1 | yes | characteristic |
| 294 | #127 | — | 4 | 2 | no | — |
| 295 | #127 | — | 8 | 2 | no | — |
| 296 | #127 | — | 8 | 2 | no | — |
| 297 | #127 | D16 | 1 | 1 | yes | characteristic |
| 298 | #124 | — | 8 | 4 | no | — |
| 299 | #124 | — | 8 | 4 | no | — |
| 300 | #124 | — | 8 | 2 | no | — |
| 301 | #124 | — | 8 | 2 | no | — |
| 302 | #124 | — | 8 | 2 | no | — |
| 303 | #124 | D16 | 1 | 1 | yes | characteristic |
| 304 | #124 | D16 | 1 | 1 | yes | characteristic |
| 305 | #121 | — | 2 | 2 | no | — |
| 306 | #121 | — | 4 | 4 | no | — |
| 307 | #121 | — | 4 | 4 | no | — |
| 308 | #121 | — | 4 | 4 | no | — |
| 309 | #121 | — | 8 | 4 | no | — |
| 310 | #121 | — | 8 | 2 | no | — |
| 311 | #121 | — | 8 | 4 | no | — |
| 312 | #120 | — | 8 | 4 | no | — |
| 313 | #120 | — | 8 | 4 | no | — |
| 314 | #120 | — | 8 | 2 | no | — |
| 315 | #120 | — | 8 | 2 | no | — |
| 316 | #120 | — | 8 | 2 | no | — |
| 317 | #120 | — | 8 | 2 | no | — |
| 318 | C4×D4 | — | 2 | 2 | no | — |
| 319 | C4×D4 | — | 4 | 4 | no | — |
| 320 | C4×D4 | — | 8 | 2 | no | — |
| 321 | #117 | — | 4 | 2 | no | — |
| 322 | #117 | — | 4 | 2 | no | — |
| 323 | #117 | — | 8 | 4 | no | — |
| 324 | C2×C42 | C2×D8 | 1 | 1 | yes | characteristic |
| 325 | Q32 | — | 2 | 4 | no | — |
| 326 | Q32 | — | 4 | 1 | no | — |
| 327 | Q32 | — | 4 | 1 | no | — |
| 328 | SD32 | — | 4 | 2 | no | — |
| 329 | SD32 | — | 4 | 4 | no | — |
| 330 | SD32 | — | 4 | 2 | no | — |
| 331 | D16 | — | 2 | 4 | no | — |
| 332 | D16 | — | 4 | 4 | no | — |
| 333 | D16 | — | 4 | 1 | no | — |
| 334 | D16 | — | 4 | 1 | no | — |
| 335 | D16 | — | 4 | 2 | no | — |
| 336 | D16 | — | 4 | 2 | no | — |
| 337 | D16 | — | 8 | 2 | no | — |
| 338 | D16 | — | 8 | 2 | no | — |
| 339 | M32 | — | 4 | 2 | no | — |
| 340 | M32 | — | 4 | 1 | no | — |
| 341 | M32 | — | 4 | 1 | no | — |
| 342 | M32 | — | 8 | 1 | no | — |
| 343 | C2×C16 | — | 2 | 1 | no | — |
| 344 | C2×C16 | — | 2 | 1 | no | — |
| 345 | C2×C16 | — | 2 | 2 | no | — |
| 346 | C2×C16 | — | 2 | 2 | no | — |
| 347 | C2×C16 | — | 2 | 1 | no | — |
| 348 | C2×C16 | — | 2 | 1 | no | — |
| 349 | C2×C16 | — | 4 | 1 | no | — |
| 350 | C2×C16 | — | 4 | 1 | no | — |
| 351 | C2×C16 | — | 4 | 1 | no | — |
| 352 | C2×C16 | #120 | 1 | 1 | yes | characteristic |
| 353 | C2×C16 | #120 | 1 | 1 | yes | characteristic |
| 354 | C2×C16 | C22×D4 | 1 | 2 | yes | — |
| 355 | #108 | — | 4 | 2 | no | — |
| 356 | #108 | — | 4 | 2 | no | — |
| 357 | #107 | — | 2 | 4 | no | — |
| 358 | #107 | — | 4 | 2 | no | — |
| 359 | #106 | — | 4 | 2 | no | — |
| 360 | #106 | — | 4 | 2 | no | — |
| 361 | C4⋊C8 | — | 2 | 2 | no | — |
| 362 | #104 | — | 8 | 2 | no | — |
| 363 | #104 | — | 8 | 2 | no | — |
| 364 | #102 | — | 4 | 4 | no | — |
| 365 | #102 | — | 4 | 4 | no | — |
| 366 | #102 | — | 4 | 4 | no | — |
| 367 | #102 | — | 4 | 4 | no | — |
| 368 | #101 | — | 8 | 2 | no | — |
| 369 | #101 | — | 8 | 1 | no | — |
| 370 | #100 | — | 8 | 2 | no | — |
| 371 | #100 | — | 8 | 1 | no | — |
| 372 | C22⋊C8 | — | 2 | 2 | no | — |
| 373 | C22⋊C8 | — | 2 | 2 | no | — |
| 374 | C22⋊C8 | — | 16 | 2 | no | — |
| 375 | C4×C8 | — | 2 | 1 | no | — |
| 376 | C4×C8 | — | 2 | 1 | no | — |
| 377 | C32 | — | 4 | 4 | no | — |
| 378 | C24 | — | 8 | 2 | no | — |
| 379 | C24 | — | 8 | 2 | no | — |
| 380 | #41 | — | 4 | 1 | no | — |
| 381 | #41 | — | 4 | 1 | no | — |
| 382 | #41 | — | 4 | 1 | no | — |
| 383 | #41 | — | 4 | 1 | no | — |
| 384 | #41 | — | 8 | 2 | no | — |
| 385 | #41 | — | 8 | 4 | no | — |
| 386 | #41 | — | 8 | 2 | no | — |
| 387 | #41 | — | 8 | 2 | no | — |
| 388 | #41 | — | 8 | 2 | no | — |
| 389 | #41 | — | 16 | 2 | no | — |
| 390 | #41 | — | 16 | 4 | no | — |
| 391 | #41 | — | 16 | 2 | no | — |
| 392 | #41 | — | 16 | 2 | no | — |
| 393 | #41 | — | 16 | 2 | no | — |
| 394 | #41 | — | 32 | 4 | no | — |
| 395 | C2×Q8 | — | 4 | 2 | no | — |
| 396 | C2×Q8 | — | 8 | 2 | no | — |
| 397 | C2×Q8 | — | 8 | 2 | no | — |
| 398 | C2×Q8 | — | 16 | 2 | no | — |
| 399 | C2×Q8 | C2×D16 | 1 | 1 | yes | characteristic |
| 400 | C2×Q8 | C2×D16 | 1 | 1 | yes | characteristic |
| 401 | C2×D4 | — | 2 | 2 | no | — |
| 402 | C2×D4 | — | 2 | 1 | no | — |
| 403 | C2×D4 | — | 4 | 2 | no | — |
| 404 | C2×D4 | — | 4 | 4 | no | — |
| 405 | C2×D4 | — | 8 | 2 | no | — |
| 406 | C2×D4 | — | 8 | 2 | no | — |
| 407 | C2×D4 | — | 8 | 2 | no | — |
| 408 | C2×D4 | — | 8 | 2 | no | — |
| 409 | C2×D4 | — | 8 | 2 | no | — |
| 410 | C2×D4 | — | 8 | 4 | no | — |
| 411 | C2×D4 | — | 8 | 4 | no | — |
| 412 | C2×D4 | — | 8 | 4 | no | — |
| 413 | C2×D4 | — | 8 | 2 | no | — |
| 414 | C2×D4 | — | 16 | 2 | no | — |
| 415 | C2×D4 | — | 16 | 2 | no | — |
| 416 | C2×D4 | — | 16 | 2 | no | — |
| 417 | C2×D4 | — | 16 | 2 | no | — |
| 418 | C2×D4 | — | 16 | 2 | no | — |
| 419 | C2×D4 | — | 16 | 4 | no | — |
| 420 | C2×D4 | — | 16 | 2 | no | — |
| 421 | C2×D4 | — | 32 | 8 | no | — |
| 422 | C2×D4 | C2×D16 | 1 | 1 | yes | characteristic |
| 423 | C2×D4 | C2×D16 | 1 | 1 | yes | characteristic |
| 424 | C2×D4 | #509 | 1 | 2 | yes | — |
| 425 | C22×C4 | — | 2 | 1 | no | — |
| 426 | C22×C4 | — | 2 | 1 | no | — |
| 427 | C22×C4 | — | 8 | 2 | no | — |
| 428 | C22×C4 | — | 8 | 4 | no | — |
| 429 | C22×C4 | — | 16 | 2 | no | — |
| 430 | C22×C4 | #447 | 1 | 2 | yes | — |
| 431 | C22×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 432 | Q16 | — | 4 | 2 | no | — |
| 433 | Q16 | — | 4 | 2 | no | — |
| 434 | Q16 | — | 8 | 2 | no | — |
| 435 | Q16 | — | 16 | 2 | no | — |
| 436 | SD16 | — | 8 | 2 | no | — |
| 437 | SD16 | — | 8 | 4 | no | — |
| 438 | SD16 | — | 8 | 2 | no | — |
| 439 | SD16 | — | 16 | 2 | no | — |
| 440 | SD16 | — | 16 | 2 | no | — |
| 441 | D8 | — | 4 | 2 | no | — |
| 442 | D8 | — | 4 | 4 | no | — |
| 443 | D8 | — | 4 | 2 | no | — |
| 444 | D8 | — | 4 | 4 | no | — |
| 445 | D8 | — | 8 | 2 | no | — |
| 446 | D8 | — | 16 | 2 | no | — |
| 447 | D8 | — | 16 | 2 | no | — |
| 448 | D8 | — | 16 | 2 | no | — |
| 449 | D8 | — | 16 | 2 | no | — |
| 450 | M16 | — | 4 | 1 | no | — |
| 451 | M16 | — | 4 | 2 | no | — |
| 452 | M16 | — | 4 | 1 | no | — |
| 453 | M16 | — | 8 | 1 | no | — |
| 454 | M16 | — | 8 | 2 | no | — |
| 455 | M16 | — | 8 | 2 | no | — |
| 456 | C2×C8 | — | 2 | 1 | no | — |
| 457 | C2×C8 | — | 2 | 2 | no | — |
| 458 | C2×C8 | — | 2 | 1 | no | — |
| 459 | C2×C8 | — | 2 | 2 | no | — |
| 460 | C2×C8 | — | 2 | 1 | no | — |
| 461 | C2×C8 | — | 2 | 1 | no | — |
| 462 | C2×C8 | — | 4 | 1 | no | — |
| 463 | C2×C8 | — | 4 | 1 | no | — |
| 464 | C2×C8 | — | 4 | 1 | no | — |
| 465 | C2×C8 | — | 8 | 2 | no | — |
| 466 | C2×C8 | #447 | 1 | 2 | yes | — |
| 467 | C2×C8 | C2×#120 | 1 | 1 | yes | characteristic |
| 468 | C2×C8 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 469 | C4⋊C4 | — | 2 | 2 | no | — |
| 470 | C4⋊C4 | — | 4 | 4 | no | — |
| 471 | C4⋊C4 | — | 8 | 2 | no | — |
| 472 | C22⋊C4 | — | 2 | 2 | no | — |
| 473 | C22⋊C4 | — | 2 | 2 | no | — |
| 474 | C22⋊C4 | — | 8 | 4 | no | — |
| 475 | C22⋊C4 | — | 8 | 4 | no | — |
| 476 | C22⋊C4 | — | 8 | 2 | no | — |
| 477 | C22⋊C4 | — | 8 | 2 | no | — |
| 478 | C22⋊C4 | — | 8 | 4 | no | — |
| 479 | C22⋊C4 | — | 8 | 4 | no | — |
| 480 | C42 | — | 2 | 1 | no | — |
| 481 | C42 | — | 8 | 2 | no | — |
| 482 | C42 | — | 8 | 2 | no | — |
| 483 | C42 | C2×D16 | 1 | 1 | yes | characteristic |
| 484 | C42 | C2×D16 | 1 | 1 | yes | characteristic |
| 485 | C16 | — | 2 | 2 | no | — |
| 486 | C16 | — | 2 | 1 | no | — |
| 487 | C16 | — | 4 | 1 | no | — |
| 488 | C16 | — | 4 | 1 | no | — |
| 489 | C16 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 490 | C16 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 491 | C23 | — | 2 | 1 | no | — |
| 492 | C23 | — | 8 | 2 | no | — |
| 493 | C23 | — | 8 | 4 | no | — |
| 494 | C23 | — | 16 | 2 | no | — |
| 495 | C23 | — | 32 | 2 | no | — |
| 496 | C23 | — | 32 | 2 | no | — |
| 497 | C23 | — | 32 | 4 | no | — |
| 498 | C23 | — | 32 | 4 | no | — |
| 499 | C23 | #2184 | 1 | 2 | yes | — |
| 500 | C23 | C2×#509 | 1 | 1 | yes | characteristic |
| 501 | Q8 | — | 4 | 1 | no | — |
| 502 | Q8 | — | 4 | 1 | no | — |
| 503 | Q8 | — | 8 | 2 | no | — |
| 504 | Q8 | — | 8 | 2 | no | — |
| 505 | Q8 | — | 16 | 2 | no | — |
| 506 | Q8 | — | 32 | 2 | no | — |
| 507 | D4 | — | 4 | 1 | no | — |
| 508 | D4 | — | 4 | 2 | no | — |
| 509 | D4 | — | 4 | 1 | no | — |
| 510 | D4 | — | 4 | 4 | no | — |
| 511 | D4 | — | 8 | 2 | no | — |
| 512 | D4 | — | 8 | 1 | no | — |
| 513 | D4 | — | 8 | 2 | no | — |
| 514 | D4 | — | 8 | 4 | no | — |
| 515 | D4 | — | 8 | 4 | no | — |
| 516 | D4 | — | 16 | 2 | no | — |
| 517 | D4 | — | 16 | 4 | no | — |
| 518 | D4 | — | 16 | 2 | no | — |
| 519 | D4 | — | 16 | 4 | no | — |
| 520 | D4 | — | 16 | 2 | no | — |
| 521 | D4 | — | 32 | 2 | no | — |
| 522 | D4 | — | 32 | 2 | no | — |
| 523 | D4 | — | 32 | 2 | no | — |
| 524 | D4 | — | 32 | 4 | no | — |
| 525 | D4 | — | 32 | 4 | no | — |
| 526 | D4 | — | 32 | 4 | no | — |
| 527 | C2×C4 | — | 2 | 1 | no | — |
| 528 | C2×C4 | — | 2 | 1 | no | — |
| 529 | C2×C4 | — | 2 | 2 | no | — |
| 530 | C2×C4 | — | 2 | 1 | no | — |
| 531 | C2×C4 | — | 2 | 2 | no | — |
| 532 | C2×C4 | — | 2 | 1 | no | — |
| 533 | C2×C4 | — | 2 | 1 | no | — |
| 534 | C2×C4 | — | 4 | 2 | no | — |
| 535 | C2×C4 | — | 4 | 1 | no | — |
| 536 | C2×C4 | — | 4 | 1 | no | — |
| 537 | C2×C4 | — | 8 | 2 | no | — |
| 538 | C2×C4 | — | 8 | 4 | no | — |
| 539 | C2×C4 | — | 16 | 2 | no | — |
| 540 | C2×C4 | — | 16 | 8 | no | — |
| 541 | C2×C4 | — | 16 | 4 | no | — |
| 542 | C2×C4 | — | 16 | 2 | no | — |
| 543 | C2×C4 | — | 16 | 2 | no | — |
| 544 | C2×C4 | #2184 | 1 | 2 | yes | — |
| 545 | C2×C4 | C2×#447 | 1 | 1 | yes | characteristic |
| 546 | C2×C4 | C22×D16 | 1 | 1 | yes | characteristic |
| 547 | C8 | — | 2 | 1 | no | — |
| 548 | C8 | — | 2 | 2 | no | — |
| 549 | C8 | — | 4 | 1 | no | — |
| 550 | C8 | — | 4 | 1 | no | — |
| 551 | C8 | — | 16 | 2 | no | — |
| 552 | C8 | #3021 | 1 | 1 | yes | characteristic |
| 553 | C8 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 554 | C22 | — | 2 | 1 | no | — |
| 555 | C22 | — | 2 | 2 | no | — |
| 556 | C22 | — | 4 | 1 | no | — |
| 557 | C22 | — | 4 | 2 | no | — |
| 558 | C22 | — | 4 | 2 | no | — |
| 559 | C22 | — | 4 | 1 | no | — |
| 560 | C22 | — | 16 | 4 | no | — |
| 561 | C22 | — | 16 | 4 | no | — |
| 562 | C22 | — | 16 | 2 | no | — |
| 563 | C22 | — | 16 | 4 | no | — |
| 564 | C22 | — | 32 | 2 | no | — |
| 565 | C22 | — | 64 | 2 | no | — |
| 566 | C22 | — | 64 | 4 | no | — |
| 567 | C22 | — | 64 | 4 | no | — |
| 568 | C22 | C2×#2184 | 1 | 1 | yes | characteristic |
| 569 | C4 | — | 2 | 2 | no | — |
| 570 | C4 | — | 2 | 1 | no | — |
| 571 | C4 | — | 2 | 2 | no | — |
| 572 | C4 | — | 4 | 1 | no | — |
| 573 | C4 | — | 4 | 1 | no | — |
| 574 | C4 | — | 16 | 4 | no | — |
| 575 | C4 | — | 16 | 2 | no | — |
| 576 | C4 | #18194 | 1 | 1 | yes | characteristic |
| 577 | C4 | #33531 | 1 | 1 | yes | characteristic |
| 578 | C2 | — | 2 | 1 | no | — |
| 579 | C2 | — | 4 | 1 | no | — |
| 580 | C2 | — | 4 | 2 | no | — |
| 581 | C2 | — | 8 | 1 | no | — |
| 582 | C2 | — | 32 | 4 | no | — |
| 583 | C2 | — | 32 | 2 | no | — |
| 584 | C2 | #486293 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #486293 |
| commutator, Frattini, cosocle | C2×M32 | C24 |
| LCS | G ▷ C2×M32 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×#131 ◁ #33434 ◁ G | |
| LECS | G ▷ C2×M32 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #7624857 | C2 | semidirect |
| 2. #512841 | C2 | semidirect |
| 3. #500852 | C2 | semidirect |
| 4. #151297 | C2 | semidirect |
| 5. #151185 | C2 | semidirect |
| 6. #150881 | C2 | semidirect |
| 7. #149671 | C2 | semidirect |
| 8. #62635 | C22 | semidirect |
| 14. #33819 | C22 | semidirect |
| 16. #33765 | C22 | semidirect |
| 24. #13667 | C22 | semidirect |
| 26. #13556 | C22 | semidirect |
| 27. #13444 | C22 | semidirect |
| 28. #13312 | C22 | semidirect |
| 30. #12840 | C22 | semidirect |
| 32. #7424 | C22 | semidirect |
| 33. #7364 | C22 | semidirect |
| 34. #7337 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #7624857 | 2 |
| #512841 | 2 |
| #500852 | 2 |
| #151297 | 2 |
| #151185 | 2 |
| #150881 | 2 |
| #149671 | 2 |