Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
2884 conjugacy classes of subgroups.
The subgroup lattice has 514 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #7623665 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #492532 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #492531 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #492528 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #491469 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #490485 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #488869 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C2×#12310 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #483512 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #62636 | — | 2 | 4 | no | — |
| 11 | #61105 | C22 | 1 | 2 | yes | complemented |
| 12 | C2×#3292 | C22 | 1 | 2 | yes | complemented |
| 13 | #33858 | C22 | 1 | 16 | yes | complemented |
| 14 | #33856 | C22 | 1 | 16 | yes | complemented |
| 15 | #33854 | — | 2 | 16 | no | — |
| 16 | #33717 | C22 | 1 | 4 | yes | complemented |
| 17 | #33618 | — | 2 | 4 | no | — |
| 18 | #33594 | C22 | 1 | 4 | yes | complemented |
| 19 | C2×#2213 | C22 | 1 | 4 | yes | complemented |
| 20 | #33541 | — | 2 | 4 | no | — |
| 21 | #33539 | — | 2 | 4 | no | — |
| 22 | #33463 | C22 | 1 | 2 | yes | — |
| 23 | #33443 | C22 | 1 | 4 | yes | complemented |
| 24 | #19603 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C2×#1712 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #12519 | C22 | 1 | 4 | yes | complemented |
| 27 | #12517 | C22 | 1 | 2 | yes | complemented |
| 28 | #12515 | C22 | 1 | 2 | yes | complemented |
| 29 | #12438 | C22 | 1 | 16 | yes | complemented |
| 30 | #12436 | C22 | 1 | 16 | yes | complemented |
| 31 | #12313 | C22 | 1 | 4 | yes | complemented |
| 32 | #12312 | C22 | 1 | 4 | yes | complemented |
| 33 | #12311 | C22 | 1 | 4 | yes | complemented |
| 34 | #12310 | C22 | 1 | 8 | yes | complemented |
| 35 | #12310 | C22 | 1 | 8 | yes | complemented |
| 36 | #12310 | C22 | 1 | 4 | yes | complemented |
| 37 | #12047 | C22 | 1 | 8 | yes | complemented |
| 38 | #12046 | C22 | 1 | 8 | yes | complemented |
| 39 | #12011 | C22 | 1 | 2 | yes | complemented |
| 40 | #11920 | C22 | 1 | 2 | yes | complemented |
| 41 | C2×#1357 | C22 | 1 | 2 | yes | complemented |
| 42 | C2×#1335 | C22 | 1 | 4 | yes | complemented |
| 43 | C8×M32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | #3584 | — | 2 | 4 | no | — |
| 45 | C2×#576 | — | 2 | 4 | no | — |
| 46 | #3416 | — | 2 | 16 | no | — |
| 47 | #3416 | — | 4 | 8 | no | — |
| 48 | #3415 | — | 2 | 16 | no | — |
| 49 | #3415 | — | 4 | 8 | no | — |
| 50 | #3414 | — | 2 | 4 | no | — |
| 51 | #3414 | — | 4 | 8 | no | — |
| 52 | #3414 | D4 | 1 | 2 | yes | — |
| 53 | C2×#509 | — | 2 | 4 | no | — |
| 54 | C2×#509 | — | 2 | 4 | no | — |
| 55 | C2×#509 | — | 2 | 4 | no | — |
| 56 | C2×#509 | — | 4 | 8 | no | — |
| 57 | #3407 | — | 2 | 4 | no | — |
| 58 | #3293 | C23 | 1 | 4 | yes | — |
| 59 | #3292 | — | 2 | 8 | no | — |
| 60 | #3292 | — | 4 | 2 | no | — |
| 61 | #3292 | C23 | 1 | 4 | yes | — |
| 62 | #3292 | C23 | 1 | 8 | yes | complemented |
| 63 | #3291 | — | 4 | 2 | no | — |
| 64 | #3290 | — | 2 | 8 | no | — |
| 65 | #3169 | — | 4 | 1 | no | — |
| 66 | #3147 | C23 | 1 | 2 | yes | — |
| 67 | C2×#493 | — | 4 | 1 | no | — |
| 68 | C2×#493 | C23 | 1 | 2 | yes | — |
| 69 | #3067 | — | 2 | 4 | no | — |
| 70 | C2×#472 | — | 2 | 4 | no | — |
| 71 | #3018 | — | 4 | 2 | no | — |
| 72 | C2×#453 | — | 4 | 2 | no | — |
| 73 | C2×#443 | C23 | 1 | 4 | yes | — |
| 74 | #2250 | — | 2 | 8 | no | — |
| 75 | #2248 | C23 | 1 | 8 | yes | complemented |
| 76 | #2246 | C23 | 1 | 8 | yes | complemented |
| 77 | #2223 | — | 2 | 16 | no | — |
| 78 | #2221 | — | 2 | 16 | no | — |
| 79 | #2214 | C23 | 1 | 8 | yes | complemented |
| 80 | #2213 | — | 2 | 8 | no | — |
| 81 | #2213 | C23 | 1 | 16 | yes | — |
| 82 | #2213 | C23 | 1 | 8 | yes | complemented |
| 83 | #2212 | — | 2 | 8 | no | — |
| 84 | #2194 | — | 2 | 16 | no | — |
| 85 | #2193 | — | 2 | 16 | no | — |
| 86 | #2192 | — | 2 | 16 | no | — |
| 87 | #2192 | — | 2 | 16 | no | — |
| 88 | #2179 | D4 | 1 | 8 | yes | — |
| 89 | #2178 | C23 | 1 | 8 | yes | — |
| 90 | #2171 | — | 2 | 8 | no | — |
| 91 | #2170 | C23 | 1 | 16 | yes | complemented |
| 92 | #2161 | D4 | 1 | 2 | yes | — |
| 93 | C2×#364 | C23 | 1 | 4 | yes | — |
| 94 | #2148 | — | 2 | 4 | no | — |
| 95 | C2×#361 | — | 2 | 4 | no | — |
| 96 | #2143 | D4 | 1 | 4 | yes | — |
| 97 | #2117 | — | 2 | 4 | no | — |
| 98 | C4×M32 | C23 | 1 | 2 | yes | — |
| 99 | #1713 | C23 | 1 | 1 | yes | characteristic, complemented |
| 100 | #1712 | — | 4 | 1 | no | — |
| 101 | #1712 | C23 | 1 | 2 | yes | — |
| 102 | #1712 | C23 | 1 | 2 | yes | — |
| 103 | #1712 | C23 | 1 | 1 | yes | characteristic, complemented |
| 104 | #1709 | C23 | 1 | 2 | yes | complemented |
| 105 | #1706 | — | 4 | 1 | no | — |
| 106 | C2×C82 | C23 | 1 | 1 | yes | characteristic |
| 107 | #1373 | C23 | 1 | 8 | yes | complemented |
| 108 | #1358 | C23 | 1 | 4 | yes | complemented |
| 109 | #1357 | C23 | 1 | 8 | yes | complemented |
| 110 | #1357 | C23 | 1 | 4 | yes | complemented |
| 111 | #1335 | C23 | 1 | 8 | yes | complemented |
| 112 | #1335 | C23 | 1 | 8 | yes | complemented |
| 113 | #1311 | C23 | 1 | 2 | yes | complemented |
| 114 | C8×C16 | C23 | 1 | 2 | yes | complemented |
| 115 | #585 | — | 4 | 2 | no | — |
| 116 | C2×H(5,𝔽2) | — | 4 | 2 | no | — |
| 117 | #578 | — | 2 | 8 | no | — |
| 118 | #578 | — | 4 | 4 | no | — |
| 119 | #577 | — | 4 | 8 | no | — |
| 120 | #577 | — | 8 | 4 | no | — |
| 121 | #576 | — | 2 | 8 | no | — |
| 122 | #576 | — | 2 | 16 | no | — |
| 123 | #576 | — | 4 | 8 | no | — |
| 124 | #576 | — | 4 | 8 | no | — |
| 125 | #576 | — | 4 | 4 | no | — |
| 126 | #576 | — | 8 | 4 | no | — |
| 127 | #575 | — | 4 | 4 | no | — |
| 128 | #575 | — | 8 | 4 | no | — |
| 129 | C2×AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 130 | C2×AGL(1,ℤ/8) | — | 8 | 4 | no | — |
| 131 | C2×#135 | — | 2 | 4 | no | — |
| 132 | C2×#135 | — | 4 | 8 | no | — |
| 133 | C2×#135 | — | 4 | 4 | no | — |
| 134 | C2×#135 | C2×D4 | 1 | 4 | yes | — |
| 135 | C22×D8 | — | 2 | 4 | no | — |
| 136 | C22×D8 | — | 4 | 4 | no | — |
| 137 | C22×D8 | — | 8 | 2 | no | — |
| 138 | C2×#131 | — | 2 | 4 | no | — |
| 139 | #532 | — | 2 | 2 | no | — |
| 140 | C2×#127 | — | 2 | 2 | no | — |
| 141 | #510 | — | 2 | 8 | no | — |
| 142 | #510 | — | 4 | 4 | no | — |
| 143 | #510 | — | 4 | 16 | no | — |
| 144 | #510 | D8 | 1 | 8 | yes | complemented |
| 145 | #509 | — | 2 | 16 | no | — |
| 146 | #509 | — | 2 | 8 | no | — |
| 147 | #509 | — | 4 | 8 | no | — |
| 148 | #509 | — | 4 | 4 | no | — |
| 149 | #509 | — | 4 | 16 | no | — |
| 150 | #509 | — | 4 | 16 | no | — |
| 151 | #509 | — | 4 | 16 | no | — |
| 152 | #509 | — | 4 | 8 | no | — |
| 153 | #509 | — | 4 | 8 | no | — |
| 154 | #509 | — | 8 | 4 | no | — |
| 155 | #509 | — | 8 | 4 | no | — |
| 156 | #509 | D8 | 1 | 8 | yes | complemented |
| 157 | #508 | — | 4 | 8 | no | — |
| 158 | #508 | — | 4 | 16 | no | — |
| 159 | #508 | — | 4 | 16 | no | — |
| 160 | #508 | C2×D4 | 1 | 8 | yes | — |
| 161 | C2×SD32 | — | 2 | 8 | no | — |
| 162 | C2×SD32 | — | 2 | 8 | no | — |
| 163 | C2×SD32 | — | 4 | 4 | no | — |
| 164 | C2×SD32 | — | 4 | 16 | no | — |
| 165 | C2×D16 | — | 2 | 8 | no | — |
| 166 | C2×D16 | — | 2 | 8 | no | — |
| 167 | C2×D16 | — | 4 | 4 | no | — |
| 168 | C2×D16 | — | 4 | 16 | no | — |
| 169 | #504 | — | 2 | 16 | no | — |
| 170 | #504 | — | 4 | 8 | no | — |
| 171 | C2×M32 | — | 2 | 4 | no | — |
| 172 | C2×M32 | — | 4 | 8 | no | — |
| 173 | C2×M32 | C2×D4 | 1 | 2 | yes | — |
| 174 | C2×M32 | C2×D4 | 1 | 2 | yes | — |
| 175 | #500 | — | 4 | 1 | no | — |
| 176 | #495 | — | 2 | 4 | no | — |
| 177 | #494 | C24 | 1 | 2 | yes | — |
| 178 | #493 | — | 2 | 4 | no | — |
| 179 | #493 | — | 2 | 2 | no | — |
| 180 | #493 | — | 4 | 2 | no | — |
| 181 | #493 | — | 4 | 2 | no | — |
| 182 | #493 | — | 4 | 1 | no | — |
| 183 | #493 | — | 8 | 2 | no | — |
| 184 | #493 | C24 | 1 | 4 | yes | — |
| 185 | #493 | C24 | 1 | 2 | yes | — |
| 186 | #492 | — | 2 | 2 | no | — |
| 187 | #486 | — | 4 | 2 | no | — |
| 188 | #473 | — | 2 | 8 | no | — |
| 189 | #472 | — | 2 | 8 | no | — |
| 190 | #472 | — | 2 | 16 | no | — |
| 191 | #472 | — | 4 | 8 | no | — |
| 192 | #471 | — | 4 | 8 | no | — |
| 193 | #466 | — | 8 | 2 | no | — |
| 194 | #456 | — | 4 | 4 | no | — |
| 195 | #455 | — | 4 | 4 | no | — |
| 196 | #454 | — | 4 | 4 | no | — |
| 197 | #453 | — | 4 | 8 | no | — |
| 198 | #453 | — | 4 | 4 | no | — |
| 199 | #453 | — | 4 | 8 | no | — |
| 200 | #443 | — | 2 | 4 | no | — |
| 201 | #443 | — | 2 | 4 | no | — |
| 202 | #443 | C2×D4 | 1 | 8 | yes | — |
| 203 | #443 | C24 | 1 | 8 | yes | — |
| 204 | C4×D8 | — | 8 | 2 | no | — |
| 205 | C2×#108 | C2×D4 | 1 | 4 | yes | — |
| 206 | C2×#104 | — | 2 | 4 | no | — |
| 207 | #413 | — | 4 | 2 | no | — |
| 208 | C2×#100 | — | 4 | 2 | no | — |
| 209 | C2×C4×C8 | — | 2 | 1 | no | — |
| 210 | C2×C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 211 | #368 | C2×D4 | 1 | 8 | yes | — |
| 212 | #364 | — | 2 | 4 | no | — |
| 213 | #364 | C24 | 1 | 8 | yes | — |
| 214 | #362 | — | 2 | 8 | no | — |
| 215 | #361 | — | 2 | 16 | no | — |
| 216 | #361 | — | 2 | 8 | no | — |
| 217 | #359 | C2×D4 | 1 | 16 | yes | — |
| 218 | #350 | — | 2 | 16 | no | — |
| 219 | #346 | C2×D4 | 1 | 4 | yes | — |
| 220 | C4×C16 | C24 | 1 | 4 | yes | — |
| 221 | C82 | — | 2 | 1 | no | — |
| 222 | C82 | C24 | 1 | 1 | yes | characteristic |
| 223 | C82 | C24 | 1 | 1 | yes | characteristic |
| 224 | 2−1+4 | — | 4 | 4 | no | — |
| 225 | 2−1+4 | — | 8 | 4 | no | — |
| 226 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 227 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 228 | H(5,𝔽2) | — | 8 | 4 | no | — |
| 229 | H(5,𝔽2) | — | 8 | 8 | no | — |
| 230 | H(5,𝔽2) | — | 16 | 2 | no | — |
| 231 | H(5,𝔽2) | — | 16 | 2 | no | — |
| 232 | C2×#41 | — | 2 | 4 | no | — |
| 233 | C2×#41 | — | 4 | 2 | no | — |
| 234 | C2×#41 | — | 8 | 4 | no | — |
| 235 | C2×#41 | — | 8 | 8 | no | — |
| 236 | C2×#41 | — | 16 | 2 | no | — |
| 237 | C22×D4 | — | 4 | 2 | no | — |
| 238 | C22×D4 | — | 8 | 2 | no | — |
| 239 | C22×D4 | — | 8 | 4 | no | — |
| 240 | C22×D4 | — | 16 | 2 | no | — |
| 241 | #137 | — | 4 | 8 | no | — |
| 242 | #137 | — | 8 | 8 | no | — |
| 243 | #137 | — | 8 | 8 | no | — |
| 244 | #137 | — | 8 | 4 | no | — |
| 245 | AGL(1,ℤ/8) | — | 4 | 16 | no | — |
| 246 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 247 | AGL(1,ℤ/8) | — | 8 | 8 | no | — |
| 248 | AGL(1,ℤ/8) | — | 8 | 16 | no | — |
| 249 | AGL(1,ℤ/8) | — | 8 | 8 | no | — |
| 250 | AGL(1,ℤ/8) | — | 8 | 16 | no | — |
| 251 | AGL(1,ℤ/8) | — | 8 | 4 | no | — |
| 252 | AGL(1,ℤ/8) | — | 8 | 8 | no | — |
| 253 | #135 | — | 2 | 4 | no | — |
| 254 | #135 | — | 2 | 4 | no | — |
| 255 | #135 | — | 4 | 16 | no | — |
| 256 | #135 | — | 4 | 8 | no | — |
| 257 | #135 | — | 4 | 8 | no | — |
| 258 | #135 | — | 4 | 4 | no | — |
| 259 | #135 | — | 4 | 4 | no | — |
| 260 | #135 | — | 4 | 4 | no | — |
| 261 | #135 | — | 4 | 4 | no | — |
| 262 | #135 | — | 8 | 8 | no | — |
| 263 | #135 | — | 8 | 8 | no | — |
| 264 | #135 | — | 8 | 8 | no | — |
| 265 | #135 | C2×D8 | 1 | 8 | yes | — |
| 266 | #135 | C22×D4 | 1 | 8 | yes | — |
| 267 | C2×Q16 | — | 2 | 4 | no | — |
| 268 | C2×Q16 | — | 4 | 8 | no | — |
| 269 | C2×Q16 | C2×D8 | 1 | 4 | yes | — |
| 270 | C2×SD16 | — | 2 | 4 | no | — |
| 271 | C2×SD16 | — | 4 | 4 | no | — |
| 272 | C2×SD16 | — | 8 | 8 | no | — |
| 273 | C2×SD16 | — | 8 | 4 | no | — |
| 274 | C2×D8 | — | 2 | 8 | no | — |
| 275 | C2×D8 | — | 2 | 4 | no | — |
| 276 | C2×D8 | — | 4 | 16 | no | — |
| 277 | C2×D8 | — | 4 | 8 | no | — |
| 278 | C2×D8 | — | 4 | 4 | no | — |
| 279 | C2×D8 | — | 4 | 4 | no | — |
| 280 | C2×D8 | — | 4 | 4 | no | — |
| 281 | C2×D8 | — | 4 | 4 | no | — |
| 282 | C2×D8 | — | 4 | 4 | no | — |
| 283 | C2×D8 | — | 8 | 4 | no | — |
| 284 | C2×D8 | — | 8 | 4 | no | — |
| 285 | C2×D8 | — | 8 | 2 | no | — |
| 286 | C2×D8 | — | 8 | 8 | no | — |
| 287 | C2×D8 | — | 8 | 4 | no | — |
| 288 | C2×D8 | — | 16 | 8 | no | — |
| 289 | C2×D8 | C2×D8 | 1 | 4 | yes | — |
| 290 | #131 | — | 2 | 8 | no | — |
| 291 | #131 | — | 2 | 8 | no | — |
| 292 | #131 | — | 4 | 4 | no | — |
| 293 | #131 | — | 4 | 4 | no | — |
| 294 | C2×M16 | — | 2 | 4 | no | — |
| 295 | C2×M16 | — | 4 | 4 | no | — |
| 296 | C22×C8 | — | 2 | 2 | no | — |
| 297 | C22×C8 | — | 4 | 4 | no | — |
| 298 | C22×C8 | C22×D4 | 1 | 2 | yes | — |
| 299 | C4⋊Q8 | — | 2 | 2 | no | — |
| 300 | #127 | — | 2 | 4 | no | — |
| 301 | #127 | — | 2 | 2 | no | — |
| 302 | #127 | — | 4 | 2 | no | — |
| 303 | #127 | — | 8 | 2 | no | — |
| 304 | #124 | — | 4 | 2 | no | — |
| 305 | #121 | — | 8 | 2 | no | — |
| 306 | C4×D4 | — | 8 | 2 | no | — |
| 307 | C2×C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 308 | Q32 | — | 4 | 8 | no | — |
| 309 | Q32 | C2×D8 | 1 | 8 | yes | complemented |
| 310 | SD32 | — | 4 | 16 | no | — |
| 311 | SD32 | — | 4 | 8 | no | — |
| 312 | SD32 | — | 4 | 8 | no | — |
| 313 | SD32 | — | 4 | 16 | no | — |
| 314 | SD32 | — | 8 | 8 | no | — |
| 315 | SD32 | C2×D8 | 1 | 16 | yes | complemented |
| 316 | D16 | — | 4 | 8 | no | — |
| 317 | D16 | — | 4 | 16 | no | — |
| 318 | D16 | — | 4 | 16 | no | — |
| 319 | D16 | — | 8 | 8 | no | — |
| 320 | D16 | C2×D8 | 1 | 8 | yes | complemented |
| 321 | M32 | — | 2 | 4 | no | — |
| 322 | M32 | — | 2 | 8 | no | — |
| 323 | M32 | — | 4 | 4 | no | — |
| 324 | M32 | — | 4 | 16 | no | — |
| 325 | M32 | C2×D8 | 1 | 8 | yes | — |
| 326 | C2×C16 | — | 4 | 4 | no | — |
| 327 | C2×C16 | — | 4 | 16 | no | — |
| 328 | C2×C16 | C22×D4 | 1 | 4 | yes | — |
| 329 | C2×C16 | C22×D4 | 1 | 4 | yes | — |
| 330 | #108 | — | 2 | 4 | no | — |
| 331 | #108 | C22×D4 | 1 | 8 | yes | — |
| 332 | #107 | — | 8 | 2 | no | — |
| 333 | #104 | — | 2 | 8 | no | — |
| 334 | #104 | — | 2 | 8 | no | — |
| 335 | #102 | — | 8 | 4 | no | — |
| 336 | #101 | — | 4 | 4 | no | — |
| 337 | #100 | — | 4 | 8 | no | — |
| 338 | #100 | — | 4 | 4 | no | — |
| 339 | C4×C8 | — | 2 | 2 | no | — |
| 340 | C4×C8 | — | 2 | 1 | no | — |
| 341 | C4×C8 | — | 2 | 1 | no | — |
| 342 | C4×C8 | C22×D4 | 1 | 2 | yes | — |
| 343 | C4×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 344 | C4×C8 | C25 | 1 | 1 | yes | characteristic |
| 345 | C24 | — | 8 | 2 | no | — |
| 346 | C24 | — | 16 | 2 | no | — |
| 347 | #41 | — | 2 | 8 | no | — |
| 348 | #41 | — | 2 | 8 | no | — |
| 349 | #41 | — | 4 | 4 | no | — |
| 350 | #41 | — | 4 | 4 | no | — |
| 351 | #41 | — | 8 | 8 | no | — |
| 352 | #41 | — | 8 | 16 | no | — |
| 353 | #41 | — | 8 | 8 | no | — |
| 354 | #41 | — | 8 | 4 | no | — |
| 355 | #41 | — | 8 | 4 | no | — |
| 356 | #41 | — | 16 | 4 | no | — |
| 357 | #41 | — | 16 | 8 | no | — |
| 358 | #41 | — | 16 | 8 | no | — |
| 359 | #41 | — | 16 | 4 | no | — |
| 360 | #41 | — | 16 | 4 | no | — |
| 361 | C2×Q8 | — | 2 | 4 | no | — |
| 362 | C2×Q8 | — | 4 | 2 | no | — |
| 363 | C2×Q8 | — | 8 | 8 | no | — |
| 364 | C2×Q8 | — | 16 | 2 | no | — |
| 365 | C2×D4 | — | 2 | 4 | no | — |
| 366 | C2×D4 | — | 4 | 4 | no | — |
| 367 | C2×D4 | — | 4 | 2 | no | — |
| 368 | C2×D4 | — | 4 | 4 | no | — |
| 369 | C2×D4 | — | 8 | 2 | no | — |
| 370 | C2×D4 | — | 8 | 4 | no | — |
| 371 | C2×D4 | — | 8 | 16 | no | — |
| 372 | C2×D4 | — | 8 | 8 | no | — |
| 373 | C2×D4 | — | 8 | 2 | no | — |
| 374 | C2×D4 | — | 8 | 4 | no | — |
| 375 | C2×D4 | — | 8 | 4 | no | — |
| 376 | C2×D4 | — | 8 | 2 | no | — |
| 377 | C2×D4 | — | 16 | 2 | no | — |
| 378 | C2×D4 | — | 16 | 8 | no | — |
| 379 | C2×D4 | — | 16 | 4 | no | — |
| 380 | C2×D4 | — | 16 | 8 | no | — |
| 381 | C2×D4 | — | 16 | 8 | no | — |
| 382 | C2×D4 | — | 16 | 4 | no | — |
| 383 | C2×D4 | — | 16 | 8 | no | — |
| 384 | C2×D4 | — | 16 | 2 | no | — |
| 385 | C2×D4 | — | 16 | 8 | no | — |
| 386 | C22×C4 | — | 2 | 1 | no | — |
| 387 | C22×C4 | — | 4 | 4 | no | — |
| 388 | C22×C4 | — | 8 | 2 | no | — |
| 389 | C22×C4 | — | 16 | 2 | no | — |
| 390 | C22×C4 | — | 16 | 4 | no | — |
| 391 | C22×C4 | D42 | 1 | 1 | yes | characteristic |
| 392 | Q16 | — | 2 | 4 | no | — |
| 393 | Q16 | — | 4 | 4 | no | — |
| 394 | Q16 | — | 4 | 4 | no | — |
| 395 | Q16 | — | 8 | 8 | no | — |
| 396 | Q16 | C22×D8 | 1 | 8 | yes | — |
| 397 | SD16 | — | 2 | 8 | no | — |
| 398 | SD16 | — | 2 | 8 | no | — |
| 399 | SD16 | — | 8 | 8 | no | — |
| 400 | SD16 | — | 8 | 16 | no | — |
| 401 | SD16 | — | 8 | 8 | no | — |
| 402 | SD16 | — | 8 | 4 | no | — |
| 403 | SD16 | — | 8 | 4 | no | — |
| 404 | D8 | — | 2 | 4 | no | — |
| 405 | D8 | — | 4 | 4 | no | — |
| 406 | D8 | — | 4 | 8 | no | — |
| 407 | D8 | — | 4 | 4 | no | — |
| 408 | D8 | — | 4 | 8 | no | — |
| 409 | D8 | — | 8 | 16 | no | — |
| 410 | D8 | — | 8 | 8 | no | — |
| 411 | D8 | — | 8 | 4 | no | — |
| 412 | D8 | — | 8 | 4 | no | — |
| 413 | D8 | — | 16 | 4 | no | — |
| 414 | D8 | — | 16 | 8 | no | — |
| 415 | D8 | — | 16 | 8 | no | — |
| 416 | D8 | C22×D8 | 1 | 8 | yes | — |
| 417 | M16 | — | 2 | 8 | no | — |
| 418 | M16 | — | 4 | 4 | no | — |
| 419 | M16 | — | 4 | 8 | no | — |
| 420 | M16 | — | 4 | 8 | no | — |
| 421 | C2×C8 | — | 2 | 2 | no | — |
| 422 | C2×C8 | — | 2 | 2 | no | — |
| 423 | C2×C8 | — | 4 | 4 | no | — |
| 424 | C2×C8 | — | 4 | 4 | no | — |
| 425 | C2×C8 | — | 4 | 8 | no | — |
| 426 | C2×C8 | — | 4 | 8 | no | — |
| 427 | C2×C8 | D42 | 1 | 2 | yes | — |
| 428 | C2×C8 | C22×D8 | 1 | 4 | yes | — |
| 429 | C2×C8 | #576 | 1 | 4 | yes | — |
| 430 | C2×C8 | C23×D4 | 1 | 2 | yes | — |
| 431 | C4⋊C4 | — | 8 | 2 | no | — |
| 432 | C22⋊C4 | — | 16 | 2 | no | — |
| 433 | C42 | — | 2 | 1 | no | — |
| 434 | C42 | D42 | 1 | 1 | yes | characteristic |
| 435 | C42 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 436 | C16 | — | 2 | 4 | no | — |
| 437 | C16 | — | 4 | 8 | no | — |
| 438 | C16 | C22×D8 | 1 | 8 | yes | — |
| 439 | C23 | — | 4 | 4 | no | — |
| 440 | C23 | — | 8 | 2 | no | — |
| 441 | C23 | — | 8 | 4 | no | — |
| 442 | C23 | — | 16 | 4 | no | — |
| 443 | C23 | — | 16 | 8 | no | — |
| 444 | C23 | — | 16 | 2 | no | — |
| 445 | C23 | — | 16 | 2 | no | — |
| 446 | C23 | — | 32 | 4 | no | — |
| 447 | C23 | — | 64 | 4 | no | — |
| 448 | C23 | #3292 | 1 | 1 | yes | characteristic |
| 449 | Q8 | — | 2 | 8 | no | — |
| 450 | Q8 | — | 4 | 4 | no | — |
| 451 | Q8 | — | 8 | 4 | no | — |
| 452 | Q8 | — | 16 | 4 | no | — |
| 453 | D4 | — | 2 | 8 | no | — |
| 454 | D4 | — | 4 | 8 | no | — |
| 455 | D4 | — | 4 | 8 | no | — |
| 456 | D4 | — | 4 | 4 | no | — |
| 457 | D4 | — | 8 | 8 | no | — |
| 458 | D4 | — | 8 | 4 | no | — |
| 459 | D4 | — | 16 | 8 | no | — |
| 460 | D4 | — | 16 | 4 | no | — |
| 461 | D4 | — | 16 | 16 | no | — |
| 462 | D4 | — | 16 | 8 | no | — |
| 463 | D4 | — | 16 | 4 | no | — |
| 464 | D4 | — | 16 | 4 | no | — |
| 465 | D4 | — | 16 | 4 | no | — |
| 466 | D4 | — | 32 | 4 | no | — |
| 467 | C2×C4 | — | 2 | 1 | no | — |
| 468 | C2×C4 | — | 2 | 1 | no | — |
| 469 | C2×C4 | — | 4 | 2 | no | — |
| 470 | C2×C4 | — | 4 | 4 | no | — |
| 471 | C2×C4 | — | 4 | 8 | no | — |
| 472 | C2×C4 | — | 4 | 8 | no | — |
| 473 | C2×C4 | — | 8 | 2 | no | — |
| 474 | C2×C4 | — | 16 | 8 | no | — |
| 475 | C2×C4 | — | 16 | 4 | no | — |
| 476 | C2×C4 | — | 16 | 8 | no | — |
| 477 | C2×C4 | — | 16 | 2 | no | — |
| 478 | C2×C4 | — | 16 | 2 | no | — |
| 479 | C2×C4 | D4×D8 | 1 | 4 | yes | — |
| 480 | C2×C4 | #3292 | 1 | 1 | yes | characteristic |
| 481 | C2×C4 | C2×D42 | 1 | 1 | yes | characteristic |
| 482 | C8 | — | 2 | 4 | no | — |
| 483 | C8 | — | 4 | 2 | no | — |
| 484 | C8 | — | 4 | 8 | no | — |
| 485 | C8 | D4×D8 | 1 | 4 | yes | — |
| 486 | C8 | C23×D8 | 1 | 2 | yes | — |
| 487 | C8 | C2×#576 | 1 | 2 | yes | — |
| 488 | C22 | — | 4 | 1 | no | — |
| 489 | C22 | — | 4 | 8 | no | — |
| 490 | C22 | — | 16 | 4 | no | — |
| 491 | C22 | — | 16 | 2 | no | — |
| 492 | C22 | — | 16 | 4 | no | — |
| 493 | C22 | — | 32 | 4 | no | — |
| 494 | C22 | — | 32 | 2 | no | — |
| 495 | C22 | — | 32 | 4 | no | — |
| 496 | C22 | — | 64 | 2 | no | — |
| 497 | C22 | — | 64 | 4 | no | — |
| 498 | C22 | — | 64 | 8 | no | — |
| 499 | C22 | D82 | 1 | 2 | yes | — |
| 500 | C22 | C2×#3292 | 1 | 1 | yes | characteristic |
| 501 | C4 | — | 2 | 2 | no | — |
| 502 | C4 | — | 4 | 1 | no | — |
| 503 | C4 | — | 4 | 8 | no | — |
| 504 | C4 | — | 16 | 2 | no | — |
| 505 | C4 | D82 | 1 | 2 | yes | — |
| 506 | C4 | C2×D4×D8 | 1 | 2 | yes | — |
| 507 | C2 | — | 2 | 1 | no | — |
| 508 | C2 | — | 2 | 2 | no | — |
| 509 | C2 | — | 8 | 8 | no | — |
| 510 | C2 | — | 32 | 4 | no | — |
| 511 | C2 | — | 32 | 2 | no | — |
| 512 | C2 | C2×D82 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C2×D82 |
| commutator, Frattini, cosocle | C4×C8 | C25 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ C2×C4×C8 ◁ 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. #7623665 | C2 | semidirect |
| 2. #492532 | C2 | semidirect |
| 3. #492531 | C2 | semidirect |
| 4. #492528 | C2 | semidirect |
| 5. #491469 | C2 | semidirect |
| 6. #490485 | C2 | semidirect |
| 7. #488869 | C2 | semidirect |
| 8. C2×#12310 | C2 | semidirect |
| 9. #483512 | C2 | semidirect |
| 11. #61105 | C22 | semidirect |
| 12. C2×#3292 | C22 | semidirect |
| 13. #33858 | C22 | semidirect |
| 14. #33856 | C22 | semidirect |
| 16. #33717 | C22 | semidirect |
| 18. #33594 | C22 | semidirect |
| 19. C2×#2213 | C22 | semidirect |
| 23. #33443 | C22 | semidirect |
| 24. #19603 | C22 | semidirect |
| 25. C2×#1712 | C22 | semidirect |
| 26. #12519 | C22 | semidirect |
| 27. #12517 | C22 | semidirect |
| 28. #12515 | C22 | semidirect |
| 29. #12438 | C22 | semidirect |
| 30. #12436 | C22 | semidirect |
| 31. #12313 | C22 | semidirect |
| 32. #12312 | C22 | semidirect |
| 33. #12311 | C22 | semidirect |
| 34. #12310 | C22 | semidirect |
| 35. #12310 | C22 | semidirect |
| 36. #12310 | C22 | semidirect |
| 37. #12047 | C22 | semidirect |
| 38. #12046 | C22 | semidirect |
| 39. #12011 | C22 | semidirect |
| 40. #11920 | C22 | semidirect |
| 41. C2×#1357 | C22 | semidirect |
| 42. C2×#1335 | C22 | semidirect |
| 43. C8×M32 | C22 | semidirect |
| 62. #3292 | C23 | semidirect |
| 75. #2248 | C23 | semidirect |
| 76. #2246 | C23 | semidirect |
| 79. #2214 | C23 | semidirect |
| 82. #2213 | C23 | semidirect |
| 91. #2170 | C23 | semidirect |
| 99. #1713 | C23 | semidirect |
| 103. #1712 | C23 | semidirect |
| 104. #1709 | C23 | semidirect |
| 107. #1373 | C23 | semidirect |
| 108. #1358 | C23 | semidirect |
| 109. #1357 | C23 | semidirect |
| 110. #1357 | C23 | semidirect |
| 111. #1335 | C23 | semidirect |
| 112. #1335 | C23 | semidirect |
| 113. #1311 | C23 | semidirect |
| 114. C8×C16 | C23 | semidirect |
| 144. #510 | D8 | semidirect |
| 156. #509 | D8 | semidirect |
| 309. Q32 | C2×D8 | semidirect |
| 315. SD32 | C2×D8 | semidirect |
| 320. D16 | C2×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #7623665 | 2 |
| #492532 | 2 |
| #492531 | 2 |
| #492528 | 2 |
| #491469 | 2 |
| #490485 | 2 |
| #488869 | 2 |
| C2×#12310 | 2 |
| #483512 | 2 |