Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1203 conjugacy classes of subgroups.
The subgroup lattice has 688 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #7624863 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #512843 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #500852 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #151298 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #151297 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #151187 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #150883 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #149671 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #62635 | C22 | 1 | 1 | yes | characteristic |
| 10 | #62332 | — | 2 | 1 | no | — |
| 11 | #33981 | — | 2 | 2 | no | — |
| 12 | #33902 | — | 2 | 2 | no | — |
| 13 | #33899 | — | 2 | 2 | no | — |
| 14 | #33898 | — | 2 | 2 | no | — |
| 15 | #33850 | — | 2 | 2 | no | — |
| 16 | #33821 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #33819 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #33770 | — | 2 | 1 | no | — |
| 19 | #33770 | C22 | 1 | 2 | yes | complemented |
| 20 | #33736 | — | 2 | 1 | no | — |
| 21 | #33617 | — | 2 | 1 | no | — |
| 22 | #33611 | — | 2 | 1 | no | — |
| 23 | #33611 | C22 | 1 | 2 | yes | — |
| 24 | #33434 | C22 | 1 | 1 | yes | characteristic |
| 25 | #24287 | — | 2 | 1 | no | — |
| 26 | #13668 | — | 2 | 2 | no | — |
| 27 | #13668 | C22 | 1 | 4 | yes | — |
| 28 | #13667 | — | 2 | 2 | no | — |
| 29 | #13667 | C22 | 1 | 4 | yes | — |
| 30 | C2×#1418 | — | 2 | 2 | no | — |
| 31 | #13556 | C22 | 1 | 2 | yes | — |
| 32 | #13444 | C22 | 1 | 2 | yes | — |
| 33 | #13312 | C22 | 1 | 2 | yes | — |
| 34 | #13241 | — | 2 | 1 | no | — |
| 35 | #12840 | C22 | 1 | 1 | yes | characteristic |
| 36 | #12746 | — | 2 | 1 | no | — |
| 37 | #7425 | C22 | 1 | 4 | yes | complemented |
| 38 | #7424 | C22 | 1 | 4 | yes | complemented |
| 39 | #7364 | C22 | 1 | 2 | yes | complemented |
| 40 | #7337 | C22 | 1 | 2 | yes | complemented |
| 41 | #3584 | — | 2 | 1 | no | — |
| 42 | #3548 | — | 4 | 1 | no | — |
| 43 | #3417 | — | 4 | 1 | no | — |
| 44 | #3416 | — | 4 | 2 | no | — |
| 45 | #3415 | — | 4 | 1 | no | — |
| 46 | #3414 | — | 2 | 2 | no | — |
| 47 | #3414 | C23 | 1 | 2 | yes | — |
| 48 | C2×#508 | — | 2 | 1 | no | — |
| 49 | C2×#508 | — | 2 | 1 | no | — |
| 50 | C2×#508 | — | 2 | 2 | no | — |
| 51 | C2×#508 | D4 | 1 | 2 | yes | — |
| 52 | C2×#504 | D4 | 1 | 1 | yes | characteristic |
| 53 | C2×#504 | C23 | 1 | 1 | yes | characteristic |
| 54 | #3338 | — | 2 | 2 | no | — |
| 55 | #3334 | — | 2 | 2 | no | — |
| 56 | #3333 | — | 4 | 2 | no | — |
| 57 | #3330 | — | 4 | 2 | no | — |
| 58 | #3287 | — | 2 | 2 | no | — |
| 59 | #3283 | — | 2 | 2 | no | — |
| 60 | #3254 | — | 4 | 1 | no | — |
| 61 | #3203 | — | 4 | 1 | no | — |
| 62 | #3203 | — | 4 | 1 | no | — |
| 63 | #3170 | — | 2 | 1 | no | — |
| 64 | #3169 | — | 2 | 1 | no | — |
| 65 | #3067 | — | 2 | 2 | no | — |
| 66 | #3061 | — | 2 | 2 | no | — |
| 67 | #3061 | — | 2 | 2 | no | — |
| 68 | #3018 | — | 4 | 1 | no | — |
| 69 | #2931 | D4 | 1 | 1 | yes | characteristic |
| 70 | #2264 | — | 2 | 4 | no | — |
| 71 | #2264 | — | 4 | 2 | no | — |
| 72 | #2263 | — | 2 | 4 | no | — |
| 73 | #2263 | — | 4 | 2 | no | — |
| 74 | #2262 | — | 4 | 4 | no | — |
| 75 | C2×M64 | — | 2 | 2 | no | — |
| 76 | #2254 | — | 2 | 1 | no | — |
| 77 | #2248 | — | 2 | 1 | no | — |
| 78 | #2241 | — | 2 | 1 | no | — |
| 79 | #2240 | — | 2 | 1 | no | — |
| 80 | #2235 | — | 2 | 2 | no | — |
| 81 | #2235 | — | 2 | 2 | no | — |
| 82 | #2233 | — | 2 | 2 | no | — |
| 83 | #2233 | — | 2 | 2 | no | — |
| 84 | #2226 | — | 2 | 2 | no | — |
| 85 | #2225 | — | 2 | 2 | no | — |
| 86 | #2223 | — | 4 | 2 | no | — |
| 87 | #2222 | — | 4 | 1 | no | — |
| 88 | #2221 | — | 4 | 1 | no | — |
| 89 | #2219 | — | 2 | 1 | no | — |
| 90 | #2219 | — | 2 | 1 | no | — |
| 91 | #2219 | D4 | 1 | 2 | yes | — |
| 92 | #2219 | C23 | 1 | 2 | yes | — |
| 93 | #2218 | — | 2 | 1 | no | — |
| 94 | #2218 | — | 2 | 1 | no | — |
| 95 | #2218 | D4 | 1 | 2 | yes | — |
| 96 | #2218 | C23 | 1 | 2 | yes | — |
| 97 | #2217 | — | 2 | 2 | no | — |
| 98 | #2217 | — | 2 | 2 | no | — |
| 99 | #2217 | — | 2 | 2 | no | — |
| 100 | #2217 | — | 2 | 2 | no | — |
| 101 | #2209 | — | 2 | 2 | no | — |
| 102 | #2206 | — | 2 | 2 | no | — |
| 103 | #2189 | — | 2 | 2 | no | — |
| 104 | #2189 | — | 2 | 2 | no | — |
| 105 | #2186 | — | 2 | 2 | no | — |
| 106 | #2186 | — | 2 | 2 | no | — |
| 107 | C4×SD32 | — | 2 | 2 | no | — |
| 108 | C4×SD32 | — | 2 | 2 | no | — |
| 109 | #2169 | — | 2 | 2 | no | — |
| 110 | D4×C16 | — | 2 | 2 | no | — |
| 111 | C2×#368 | — | 2 | 1 | no | — |
| 112 | C2×#367 | — | 2 | 1 | no | — |
| 113 | C2×#367 | D4 | 1 | 2 | yes | — |
| 114 | #2150 | C23 | 1 | 1 | yes | characteristic |
| 115 | #2148 | — | 2 | 2 | no | — |
| 116 | C2×#359 | — | 2 | 2 | no | — |
| 117 | #2139 | — | 2 | 2 | no | — |
| 118 | #2139 | — | 2 | 2 | no | — |
| 119 | #2113 | D4 | 1 | 1 | yes | characteristic |
| 120 | #2113 | C23 | 1 | 1 | yes | characteristic |
| 121 | C2×C4×C16 | D4 | 1 | 1 | yes | characteristic |
| 122 | #2050 | — | 4 | 1 | no | — |
| 123 | #2017 | — | 4 | 1 | no | — |
| 124 | #1974 | — | 2 | 2 | no | — |
| 125 | #1813 | — | 2 | 1 | no | — |
| 126 | #1791 | — | 4 | 1 | no | — |
| 127 | #1418 | — | 2 | 4 | no | — |
| 128 | #1418 | — | 2 | 4 | no | — |
| 129 | #1400 | — | 2 | 2 | no | — |
| 130 | #1400 | C23 | 1 | 4 | yes | — |
| 131 | #1385 | C23 | 1 | 2 | yes | — |
| 132 | #585 | — | 4 | 1 | no | — |
| 133 | #578 | — | 4 | 2 | no | — |
| 134 | #577 | — | 8 | 2 | no | — |
| 135 | #576 | — | 4 | 2 | no | — |
| 136 | #575 | — | 4 | 2 | no | — |
| 137 | #575 | — | 4 | 1 | no | — |
| 138 | #575 | — | 4 | 2 | no | — |
| 139 | C2×#135 | — | 2 | 2 | no | — |
| 140 | C2×#135 | — | 2 | 2 | no | — |
| 141 | C2×#135 | — | 2 | 2 | no | — |
| 142 | C2×#135 | — | 4 | 2 | no | — |
| 143 | C2×#131 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | C2×#131 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | #562 | — | 8 | 1 | no | — |
| 146 | #562 | — | 8 | 1 | no | — |
| 147 | #554 | — | 4 | 2 | no | — |
| 148 | #554 | — | 8 | 1 | no | — |
| 149 | #550 | — | 4 | 2 | no | — |
| 150 | #550 | — | 8 | 1 | no | — |
| 151 | #547 | — | 4 | 2 | no | — |
| 152 | #547 | — | 4 | 2 | no | — |
| 153 | #540 | — | 8 | 2 | no | — |
| 154 | #537 | — | 4 | 2 | no | — |
| 155 | #537 | — | 4 | 2 | no | — |
| 156 | #537 | — | 8 | 2 | no | — |
| 157 | #533 | — | 4 | 1 | no | — |
| 158 | #532 | — | 4 | 1 | no | — |
| 159 | #532 | D8 | 1 | 1 | yes | characteristic |
| 160 | #510 | — | 4 | 2 | no | — |
| 161 | #510 | — | 4 | 4 | no | — |
| 162 | #509 | — | 4 | 2 | no | — |
| 163 | #509 | — | 4 | 4 | no | — |
| 164 | #508 | — | 2 | 4 | no | — |
| 165 | #508 | — | 2 | 4 | no | — |
| 166 | #508 | — | 4 | 1 | no | — |
| 167 | #508 | — | 4 | 2 | no | — |
| 168 | #508 | — | 4 | 1 | no | — |
| 169 | #508 | — | 4 | 2 | no | — |
| 170 | #508 | — | 4 | 2 | no | — |
| 171 | #508 | — | 4 | 1 | no | — |
| 172 | #508 | — | 4 | 1 | no | — |
| 173 | #508 | — | 8 | 1 | no | — |
| 174 | #508 | — | 8 | 1 | no | — |
| 175 | C2×Q32 | — | 2 | 2 | no | — |
| 176 | C2×Q32 | — | 2 | 1 | no | — |
| 177 | C2×Q32 | — | 2 | 1 | no | — |
| 178 | C2×Q32 | C2×D4 | 1 | 2 | yes | — |
| 179 | C2×SD32 | — | 2 | 2 | no | — |
| 180 | C2×SD32 | — | 2 | 2 | no | — |
| 181 | C2×SD32 | — | 2 | 2 | no | — |
| 182 | C2×SD32 | — | 4 | 2 | no | — |
| 183 | C2×D16 | — | 2 | 2 | no | — |
| 184 | C2×D16 | — | 2 | 1 | no | — |
| 185 | C2×D16 | — | 2 | 1 | no | — |
| 186 | C2×D16 | C2×D4 | 1 | 2 | yes | — |
| 187 | #504 | — | 4 | 1 | no | — |
| 188 | #504 | — | 4 | 1 | no | — |
| 189 | #504 | — | 4 | 1 | no | — |
| 190 | #504 | — | 4 | 1 | no | — |
| 191 | C2×M32 | — | 2 | 1 | no | — |
| 192 | C2×M32 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C2×M32 | C2×D4 | 1 | 2 | yes | — |
| 194 | C2×M32 | C24 | 1 | 1 | yes | characteristic |
| 195 | C22×C16 | — | 2 | 1 | no | — |
| 196 | C22×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 197 | C22×C16 | C2×D4 | 1 | 2 | yes | — |
| 198 | C22×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 199 | #500 | — | 2 | 1 | no | — |
| 200 | #500 | — | 2 | 1 | no | — |
| 201 | #494 | — | 2 | 1 | no | — |
| 202 | #493 | — | 2 | 1 | no | — |
| 203 | #487 | — | 4 | 1 | no | — |
| 204 | #486 | — | 4 | 1 | no | — |
| 205 | #484 | — | 4 | 2 | no | — |
| 206 | #484 | — | 4 | 2 | no | — |
| 207 | #480 | — | 4 | 2 | no | — |
| 208 | #480 | — | 4 | 2 | no | — |
| 209 | #477 | — | 4 | 2 | no | — |
| 210 | #474 | — | 4 | 2 | no | — |
| 211 | #473 | — | 4 | 2 | no | — |
| 212 | #472 | — | 4 | 2 | no | — |
| 213 | #471 | — | 8 | 2 | no | — |
| 214 | #468 | — | 4 | 2 | no | — |
| 215 | #468 | — | 4 | 2 | no | — |
| 216 | #468 | — | 4 | 2 | no | — |
| 217 | #468 | — | 4 | 2 | no | — |
| 218 | #467 | — | 2 | 2 | no | — |
| 219 | #467 | — | 2 | 2 | no | — |
| 220 | #467 | — | 2 | 2 | no | — |
| 221 | #467 | — | 4 | 1 | no | — |
| 222 | #466 | — | 2 | 2 | no | — |
| 223 | #466 | — | 2 | 2 | no | — |
| 224 | #466 | — | 2 | 2 | no | — |
| 225 | #466 | — | 4 | 1 | no | — |
| 226 | #461 | — | 4 | 2 | no | — |
| 227 | #460 | — | 4 | 2 | no | — |
| 228 | #456 | — | 8 | 1 | no | — |
| 229 | #455 | — | 8 | 1 | no | — |
| 230 | #454 | — | 8 | 1 | no | — |
| 231 | #453 | — | 8 | 1 | no | — |
| 232 | #452 | — | 4 | 2 | no | — |
| 233 | #452 | — | 4 | 2 | no | — |
| 234 | #449 | — | 4 | 2 | no | — |
| 235 | #449 | — | 4 | 2 | no | — |
| 236 | C4×Q16 | — | 2 | 2 | no | — |
| 237 | C4×Q16 | — | 4 | 1 | no | — |
| 238 | C4×D8 | — | 2 | 2 | no | — |
| 239 | C4×D8 | — | 4 | 1 | no | — |
| 240 | #436 | — | 2 | 2 | no | — |
| 241 | C8×D4 | — | 2 | 2 | no | — |
| 242 | C2×#108 | — | 2 | 2 | no | — |
| 243 | C2×#107 | — | 2 | 2 | no | — |
| 244 | C2×#107 | — | 2 | 2 | no | — |
| 245 | #423 | D8 | 1 | 1 | yes | characteristic |
| 246 | C2×#104 | — | 4 | 2 | no | — |
| 247 | #417 | — | 4 | 2 | no | — |
| 248 | #417 | — | 4 | 2 | no | — |
| 249 | #413 | — | 4 | 1 | no | — |
| 250 | #413 | — | 4 | 2 | no | — |
| 251 | #408 | — | 4 | 2 | no | — |
| 252 | #408 | D8 | 1 | 1 | yes | characteristic |
| 253 | #408 | D8 | 1 | 1 | yes | characteristic |
| 254 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 255 | Q64 | — | 4 | 4 | no | — |
| 256 | SD64 | — | 4 | 4 | no | — |
| 257 | SD64 | — | 4 | 4 | no | — |
| 258 | D32 | — | 4 | 4 | no | — |
| 259 | M64 | — | 2 | 4 | no | — |
| 260 | M64 | — | 4 | 2 | no | — |
| 261 | C2×C32 | — | 4 | 2 | no | — |
| 262 | #368 | — | 4 | 1 | no | — |
| 263 | #368 | — | 4 | 1 | no | — |
| 264 | #367 | — | 2 | 1 | no | — |
| 265 | #367 | — | 2 | 1 | no | — |
| 266 | #367 | — | 2 | 2 | no | — |
| 267 | #367 | — | 2 | 2 | no | — |
| 268 | #367 | C2×D4 | 1 | 2 | yes | — |
| 269 | #367 | C2×D4 | 1 | 2 | yes | — |
| 270 | C4⋊C16 | — | 2 | 2 | no | — |
| 271 | #362 | — | 4 | 2 | no | — |
| 272 | #361 | — | 4 | 2 | no | — |
| 273 | #359 | — | 8 | 2 | no | — |
| 274 | #358 | — | 2 | 2 | no | — |
| 275 | #358 | — | 2 | 2 | no | — |
| 276 | #358 | — | 2 | 2 | no | — |
| 277 | #358 | — | 2 | 2 | no | — |
| 278 | #357 | — | 2 | 2 | no | — |
| 279 | #357 | — | 2 | 2 | no | — |
| 280 | #357 | — | 2 | 2 | no | — |
| 281 | #357 | — | 2 | 2 | no | — |
| 282 | C22⋊C16 | — | 2 | 2 | no | — |
| 283 | C22⋊C16 | — | 2 | 2 | no | — |
| 284 | C4×C16 | — | 2 | 1 | no | — |
| 285 | C4×C16 | — | 2 | 1 | no | — |
| 286 | #338 | — | 4 | 1 | no | — |
| 287 | 2−1+4 | — | 8 | 2 | no | — |
| 288 | 2−1+4 | — | 8 | 1 | no | — |
| 289 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 290 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 291 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 292 | C2×#41 | — | 4 | 2 | no | — |
| 293 | C2×#41 | — | 4 | 2 | no | — |
| 294 | C2×#41 | — | 4 | 2 | no | — |
| 295 | C2×#41 | — | 8 | 1 | no | — |
| 296 | C2×#41 | — | 8 | 2 | no | — |
| 297 | C2×#41 | — | 8 | 2 | no | — |
| 298 | C2×#41 | — | 16 | 2 | no | — |
| 299 | C2×#41 | C2×D8 | 1 | 1 | yes | characteristic |
| 300 | C2×#41 | C2×D8 | 1 | 1 | yes | characteristic |
| 301 | #137 | — | 8 | 4 | no | — |
| 302 | #137 | — | 8 | 2 | no | — |
| 303 | #137 | — | 8 | 2 | no | — |
| 304 | #137 | — | 8 | 2 | no | — |
| 305 | AGL(1,ℤ/8) | — | 8 | 4 | no | — |
| 306 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 307 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 308 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 309 | #135 | — | 4 | 2 | no | — |
| 310 | #135 | — | 4 | 2 | no | — |
| 311 | #135 | — | 4 | 4 | no | — |
| 312 | #135 | — | 4 | 2 | no | — |
| 313 | #135 | — | 4 | 2 | no | — |
| 314 | #135 | — | 8 | 2 | no | — |
| 315 | #135 | — | 8 | 2 | no | — |
| 316 | #135 | — | 8 | 2 | no | — |
| 317 | #135 | — | 8 | 2 | no | — |
| 318 | #135 | — | 8 | 2 | no | — |
| 319 | #135 | — | 8 | 2 | no | — |
| 320 | #135 | — | 16 | 2 | no | — |
| 321 | C2×Q16 | — | 2 | 2 | no | — |
| 322 | C2×Q16 | — | 2 | 2 | no | — |
| 323 | C2×Q16 | — | 4 | 2 | no | — |
| 324 | C2×Q16 | — | 4 | 1 | no | — |
| 325 | C2×SD16 | — | 4 | 2 | no | — |
| 326 | C2×SD16 | — | 4 | 2 | no | — |
| 327 | C2×SD16 | — | 4 | 2 | no | — |
| 328 | C2×SD16 | — | 8 | 2 | no | — |
| 329 | C2×D8 | — | 2 | 2 | no | — |
| 330 | C2×D8 | — | 2 | 2 | no | — |
| 331 | C2×D8 | — | 4 | 2 | no | — |
| 332 | C2×D8 | — | 4 | 1 | no | — |
| 333 | #131 | — | 4 | 1 | no | — |
| 334 | #131 | — | 4 | 1 | no | — |
| 335 | #131 | — | 4 | 1 | no | — |
| 336 | #131 | — | 4 | 1 | no | — |
| 337 | C2×M16 | — | 2 | 1 | no | — |
| 338 | C2×M16 | — | 4 | 2 | no | — |
| 339 | C2×M16 | C2×D8 | 1 | 1 | yes | characteristic |
| 340 | C2×M16 | C2×D8 | 1 | 1 | yes | characteristic |
| 341 | C2×M16 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 342 | C22×C8 | — | 2 | 1 | no | — |
| 343 | C22×C8 | #120 | 1 | 2 | yes | — |
| 344 | C22×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 345 | C22×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 346 | C4⋊Q8 | — | 4 | 1 | no | — |
| 347 | C4⋊Q8 | — | 4 | 1 | no | — |
| 348 | C4⋊Q8 | — | 4 | 1 | no | — |
| 349 | C4⋊Q8 | D16 | 1 | 1 | yes | characteristic |
| 350 | #127 | — | 4 | 1 | no | — |
| 351 | #127 | — | 8 | 2 | no | — |
| 352 | #127 | D16 | 1 | 1 | yes | characteristic |
| 353 | #125 | — | 8 | 2 | no | — |
| 354 | #125 | — | 8 | 1 | no | — |
| 355 | #124 | — | 8 | 1 | no | — |
| 356 | #124 | D16 | 1 | 1 | yes | characteristic |
| 357 | #124 | D16 | 1 | 1 | yes | characteristic |
| 358 | #123 | — | 8 | 2 | no | — |
| 359 | #123 | — | 8 | 2 | no | — |
| 360 | #123 | — | 8 | 2 | no | — |
| 361 | #123 | — | 8 | 2 | no | — |
| 362 | C22⋊Q8 | — | 4 | 2 | no | — |
| 363 | C22⋊Q8 | — | 4 | 2 | no | — |
| 364 | C22⋊Q8 | — | 4 | 2 | no | — |
| 365 | C22⋊Q8 | — | 8 | 2 | no | — |
| 366 | C22⋊Q8 | — | 8 | 2 | no | — |
| 367 | C22⋊Q8 | — | 8 | 2 | no | — |
| 368 | C22⋊Q8 | — | 8 | 1 | no | — |
| 369 | C22⋊Q8 | — | 8 | 2 | no | — |
| 370 | C22⋊Q8 | — | 8 | 2 | no | — |
| 371 | #121 | — | 2 | 2 | no | — |
| 372 | #121 | — | 4 | 2 | no | — |
| 373 | #121 | — | 4 | 2 | no | — |
| 374 | #121 | — | 4 | 2 | no | — |
| 375 | #121 | — | 8 | 2 | no | — |
| 376 | #121 | — | 8 | 2 | no | — |
| 377 | #121 | — | 8 | 1 | no | — |
| 378 | #121 | — | 8 | 2 | no | — |
| 379 | #121 | — | 8 | 2 | no | — |
| 380 | #121 | — | 8 | 2 | no | — |
| 381 | #121 | — | 8 | 2 | no | — |
| 382 | #121 | — | 8 | 2 | no | — |
| 383 | #121 | — | 8 | 2 | no | — |
| 384 | #121 | — | 8 | 2 | no | — |
| 385 | C4×Q8 | — | 4 | 2 | no | — |
| 386 | C4×Q8 | — | 8 | 1 | no | — |
| 387 | C4×D4 | — | 2 | 2 | no | — |
| 388 | C4×D4 | — | 4 | 2 | no | — |
| 389 | C4×D4 | — | 8 | 2 | no | — |
| 390 | C4×D4 | — | 8 | 2 | no | — |
| 391 | C4×D4 | — | 8 | 1 | no | — |
| 392 | #117 | — | 8 | 1 | no | — |
| 393 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 394 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 395 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 396 | C2×C42 | C2×D8 | 1 | 1 | yes | characteristic |
| 397 | Q32 | — | 2 | 4 | no | — |
| 398 | Q32 | — | 4 | 2 | no | — |
| 399 | Q32 | — | 4 | 1 | no | — |
| 400 | Q32 | — | 4 | 1 | no | — |
| 401 | Q32 | — | 8 | 1 | no | — |
| 402 | SD32 | — | 4 | 2 | no | — |
| 403 | SD32 | — | 4 | 4 | no | — |
| 404 | SD32 | — | 4 | 2 | no | — |
| 405 | SD32 | — | 4 | 2 | no | — |
| 406 | SD32 | — | 4 | 2 | no | — |
| 407 | SD32 | — | 8 | 2 | no | — |
| 408 | D16 | — | 2 | 4 | no | — |
| 409 | D16 | — | 4 | 2 | no | — |
| 410 | D16 | — | 4 | 1 | no | — |
| 411 | D16 | — | 4 | 1 | no | — |
| 412 | D16 | — | 8 | 1 | no | — |
| 413 | M32 | — | 4 | 2 | no | — |
| 414 | M32 | — | 4 | 1 | no | — |
| 415 | M32 | — | 4 | 1 | no | — |
| 416 | M32 | — | 8 | 1 | no | — |
| 417 | C2×C16 | — | 2 | 1 | no | — |
| 418 | C2×C16 | — | 2 | 1 | no | — |
| 419 | C2×C16 | — | 2 | 2 | no | — |
| 420 | C2×C16 | — | 2 | 2 | no | — |
| 421 | C2×C16 | — | 2 | 1 | no | — |
| 422 | C2×C16 | — | 2 | 1 | no | — |
| 423 | C2×C16 | — | 4 | 1 | no | — |
| 424 | C2×C16 | — | 4 | 1 | no | — |
| 425 | C2×C16 | — | 4 | 1 | no | — |
| 426 | C2×C16 | #120 | 1 | 1 | yes | characteristic |
| 427 | C2×C16 | #120 | 1 | 1 | yes | characteristic |
| 428 | C2×C16 | C22×D4 | 1 | 2 | yes | — |
| 429 | #108 | — | 4 | 2 | no | — |
| 430 | #108 | — | 4 | 2 | no | — |
| 431 | #107 | — | 2 | 2 | no | — |
| 432 | #107 | — | 2 | 2 | no | — |
| 433 | #107 | — | 4 | 2 | no | — |
| 434 | #107 | — | 4 | 1 | no | — |
| 435 | #107 | — | 4 | 1 | no | — |
| 436 | #107 | — | 4 | 2 | no | — |
| 437 | C4⋊C8 | — | 2 | 2 | no | — |
| 438 | #104 | — | 8 | 2 | no | — |
| 439 | #104 | — | 8 | 2 | no | — |
| 440 | #103 | — | 4 | 2 | no | — |
| 441 | #103 | — | 4 | 2 | no | — |
| 442 | #103 | — | 4 | 2 | no | — |
| 443 | #103 | — | 4 | 2 | no | — |
| 444 | #102 | — | 4 | 2 | no | — |
| 445 | #102 | — | 4 | 2 | no | — |
| 446 | #102 | — | 4 | 2 | no | — |
| 447 | #102 | — | 4 | 2 | no | — |
| 448 | #101 | — | 8 | 2 | no | — |
| 449 | #101 | — | 8 | 1 | no | — |
| 450 | #100 | — | 8 | 2 | no | — |
| 451 | #100 | — | 8 | 1 | no | — |
| 452 | C22⋊C8 | — | 2 | 2 | no | — |
| 453 | C22⋊C8 | — | 2 | 2 | no | — |
| 454 | C22⋊C8 | — | 16 | 2 | no | — |
| 455 | C4×C8 | — | 2 | 1 | no | — |
| 456 | C4×C8 | — | 2 | 1 | no | — |
| 457 | C32 | — | 4 | 4 | no | — |
| 458 | #41 | — | 4 | 1 | no | — |
| 459 | #41 | — | 4 | 1 | no | — |
| 460 | #41 | — | 4 | 1 | no | — |
| 461 | #41 | — | 4 | 1 | no | — |
| 462 | #41 | — | 8 | 2 | no | — |
| 463 | #41 | — | 8 | 4 | no | — |
| 464 | #41 | — | 8 | 2 | no | — |
| 465 | #41 | — | 8 | 2 | no | — |
| 466 | #41 | — | 8 | 2 | no | — |
| 467 | #41 | — | 16 | 2 | no | — |
| 468 | #41 | — | 16 | 2 | no | — |
| 469 | #41 | — | 16 | 2 | no | — |
| 470 | #41 | — | 16 | 2 | no | — |
| 471 | #41 | — | 16 | 2 | no | — |
| 472 | #41 | — | 16 | 4 | no | — |
| 473 | #41 | — | 16 | 2 | no | — |
| 474 | #41 | — | 16 | 2 | no | — |
| 475 | #41 | — | 16 | 2 | no | — |
| 476 | #41 | — | 32 | 2 | no | — |
| 477 | #41 | — | 32 | 4 | no | — |
| 478 | C2×Q8 | — | 4 | 2 | no | — |
| 479 | C2×Q8 | — | 4 | 2 | no | — |
| 480 | C2×Q8 | — | 8 | 1 | no | — |
| 481 | C2×Q8 | — | 8 | 1 | no | — |
| 482 | C2×Q8 | — | 8 | 2 | no | — |
| 483 | C2×Q8 | — | 16 | 2 | no | — |
| 484 | C2×Q8 | C2×D16 | 1 | 1 | yes | characteristic |
| 485 | C2×Q8 | C2×D16 | 1 | 1 | yes | characteristic |
| 486 | C2×D4 | — | 2 | 2 | no | — |
| 487 | C2×D4 | — | 2 | 1 | no | — |
| 488 | C2×D4 | — | 4 | 2 | no | — |
| 489 | C2×D4 | — | 4 | 2 | no | — |
| 490 | C2×D4 | — | 8 | 2 | no | — |
| 491 | C2×D4 | — | 8 | 1 | no | — |
| 492 | C2×D4 | — | 8 | 1 | no | — |
| 493 | C2×D4 | — | 8 | 2 | no | — |
| 494 | C2×D4 | — | 8 | 2 | no | — |
| 495 | C2×D4 | — | 8 | 2 | no | — |
| 496 | C2×D4 | — | 8 | 2 | no | — |
| 497 | C2×D4 | — | 8 | 2 | no | — |
| 498 | C2×D4 | — | 8 | 2 | no | — |
| 499 | C2×D4 | — | 16 | 2 | no | — |
| 500 | C2×D4 | — | 16 | 4 | no | — |
| 501 | C2×D4 | — | 16 | 2 | no | — |
| 502 | C2×D4 | C2×D16 | 1 | 1 | yes | characteristic |
| 503 | C2×D4 | C2×D16 | 1 | 1 | yes | characteristic |
| 504 | C2×D4 | #509 | 1 | 2 | yes | — |
| 505 | C22×C4 | — | 2 | 1 | no | — |
| 506 | C22×C4 | — | 2 | 1 | no | — |
| 507 | C22×C4 | — | 8 | 2 | no | — |
| 508 | C22×C4 | — | 8 | 2 | no | — |
| 509 | C22×C4 | — | 8 | 2 | no | — |
| 510 | C22×C4 | — | 8 | 2 | no | — |
| 511 | C22×C4 | — | 8 | 2 | no | — |
| 512 | C22×C4 | — | 8 | 2 | no | — |
| 513 | C22×C4 | — | 16 | 2 | no | — |
| 514 | C22×C4 | #447 | 1 | 2 | yes | — |
| 515 | C22×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 516 | Q16 | — | 4 | 2 | no | — |
| 517 | Q16 | — | 4 | 2 | no | — |
| 518 | Q16 | — | 4 | 2 | no | — |
| 519 | Q16 | — | 4 | 2 | no | — |
| 520 | Q16 | — | 8 | 2 | no | — |
| 521 | Q16 | — | 16 | 1 | no | — |
| 522 | Q16 | — | 16 | 2 | no | — |
| 523 | SD16 | — | 8 | 2 | no | — |
| 524 | SD16 | — | 8 | 4 | no | — |
| 525 | SD16 | — | 8 | 2 | no | — |
| 526 | SD16 | — | 16 | 2 | no | — |
| 527 | SD16 | — | 16 | 2 | no | — |
| 528 | SD16 | — | 16 | 2 | no | — |
| 529 | SD16 | — | 16 | 2 | no | — |
| 530 | D8 | — | 4 | 2 | no | — |
| 531 | D8 | — | 4 | 2 | no | — |
| 532 | D8 | — | 4 | 2 | no | — |
| 533 | D8 | — | 4 | 2 | no | — |
| 534 | D8 | — | 8 | 2 | no | — |
| 535 | D8 | — | 16 | 1 | no | — |
| 536 | D8 | — | 16 | 2 | no | — |
| 537 | M16 | — | 4 | 1 | no | — |
| 538 | M16 | — | 4 | 2 | no | — |
| 539 | M16 | — | 4 | 1 | no | — |
| 540 | M16 | — | 8 | 1 | no | — |
| 541 | M16 | — | 8 | 2 | no | — |
| 542 | M16 | — | 8 | 2 | no | — |
| 543 | C2×C8 | — | 2 | 1 | no | — |
| 544 | C2×C8 | — | 2 | 2 | no | — |
| 545 | C2×C8 | — | 2 | 1 | no | — |
| 546 | C2×C8 | — | 2 | 2 | no | — |
| 547 | C2×C8 | — | 2 | 1 | no | — |
| 548 | C2×C8 | — | 2 | 1 | no | — |
| 549 | C2×C8 | — | 4 | 1 | no | — |
| 550 | C2×C8 | — | 4 | 1 | no | — |
| 551 | C2×C8 | — | 4 | 1 | no | — |
| 552 | C2×C8 | — | 8 | 2 | no | — |
| 553 | C2×C8 | #447 | 1 | 2 | yes | — |
| 554 | C2×C8 | C2×#120 | 1 | 1 | yes | characteristic |
| 555 | C2×C8 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 556 | C4⋊C4 | — | 2 | 2 | no | — |
| 557 | C4⋊C4 | — | 4 | 2 | no | — |
| 558 | C4⋊C4 | — | 4 | 2 | no | — |
| 559 | C4⋊C4 | — | 8 | 2 | no | — |
| 560 | C4⋊C4 | — | 8 | 1 | no | — |
| 561 | C4⋊C4 | — | 8 | 2 | no | — |
| 562 | C4⋊C4 | — | 8 | 1 | no | — |
| 563 | C4⋊C4 | — | 8 | 1 | no | — |
| 564 | C4⋊C4 | — | 8 | 1 | no | — |
| 565 | C4⋊C4 | — | 8 | 2 | no | — |
| 566 | C4⋊C4 | — | 8 | 2 | no | — |
| 567 | C4⋊C4 | — | 8 | 2 | no | — |
| 568 | C4⋊C4 | — | 8 | 2 | no | — |
| 569 | C22⋊C4 | — | 2 | 2 | no | — |
| 570 | C22⋊C4 | — | 2 | 2 | no | — |
| 571 | C22⋊C4 | — | 8 | 2 | no | — |
| 572 | C22⋊C4 | — | 8 | 2 | no | — |
| 573 | C22⋊C4 | — | 8 | 2 | no | — |
| 574 | C22⋊C4 | — | 8 | 2 | no | — |
| 575 | C22⋊C4 | — | 8 | 2 | no | — |
| 576 | C22⋊C4 | — | 8 | 2 | no | — |
| 577 | C22⋊C4 | — | 8 | 2 | no | — |
| 578 | C42 | — | 2 | 1 | no | — |
| 579 | C42 | — | 8 | 2 | no | — |
| 580 | C42 | C2×D16 | 1 | 1 | yes | characteristic |
| 581 | C42 | C2×D16 | 1 | 1 | yes | characteristic |
| 582 | C16 | — | 2 | 2 | no | — |
| 583 | C16 | — | 2 | 1 | no | — |
| 584 | C16 | — | 4 | 1 | no | — |
| 585 | C16 | — | 4 | 1 | no | — |
| 586 | C16 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 587 | C16 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 588 | C23 | — | 2 | 1 | no | — |
| 589 | C23 | — | 8 | 2 | no | — |
| 590 | C23 | — | 8 | 2 | no | — |
| 591 | C23 | — | 16 | 2 | no | — |
| 592 | C23 | #2184 | 1 | 2 | yes | — |
| 593 | C23 | C2×#509 | 1 | 1 | yes | characteristic |
| 594 | Q8 | — | 4 | 1 | no | — |
| 595 | Q8 | — | 4 | 1 | no | — |
| 596 | Q8 | — | 8 | 2 | no | — |
| 597 | Q8 | — | 8 | 2 | no | — |
| 598 | Q8 | — | 8 | 2 | no | — |
| 599 | Q8 | — | 8 | 2 | no | — |
| 600 | Q8 | — | 16 | 2 | no | — |
| 601 | Q8 | — | 16 | 2 | no | — |
| 602 | Q8 | — | 32 | 1 | no | — |
| 603 | D4 | — | 4 | 1 | no | — |
| 604 | D4 | — | 4 | 2 | no | — |
| 605 | D4 | — | 4 | 1 | no | — |
| 606 | D4 | — | 4 | 4 | no | — |
| 607 | D4 | — | 8 | 2 | no | — |
| 608 | D4 | — | 8 | 1 | no | — |
| 609 | D4 | — | 8 | 2 | no | — |
| 610 | D4 | — | 8 | 2 | no | — |
| 611 | D4 | — | 8 | 2 | no | — |
| 612 | D4 | — | 16 | 2 | no | — |
| 613 | D4 | — | 16 | 2 | no | — |
| 614 | D4 | — | 16 | 2 | no | — |
| 615 | D4 | — | 16 | 4 | no | — |
| 616 | D4 | — | 16 | 2 | no | — |
| 617 | D4 | — | 32 | 1 | no | — |
| 618 | D4 | — | 32 | 2 | no | — |
| 619 | D4 | — | 32 | 2 | no | — |
| 620 | D4 | — | 32 | 2 | no | — |
| 621 | D4 | — | 32 | 2 | no | — |
| 622 | D4 | — | 32 | 2 | no | — |
| 623 | C2×C4 | — | 2 | 1 | no | — |
| 624 | C2×C4 | — | 2 | 1 | no | — |
| 625 | C2×C4 | — | 2 | 2 | no | — |
| 626 | C2×C4 | — | 2 | 1 | no | — |
| 627 | C2×C4 | — | 2 | 2 | no | — |
| 628 | C2×C4 | — | 2 | 1 | no | — |
| 629 | C2×C4 | — | 2 | 1 | no | — |
| 630 | C2×C4 | — | 4 | 2 | no | — |
| 631 | C2×C4 | — | 4 | 1 | no | — |
| 632 | C2×C4 | — | 4 | 1 | no | — |
| 633 | C2×C4 | — | 8 | 2 | no | — |
| 634 | C2×C4 | — | 8 | 2 | no | — |
| 635 | C2×C4 | — | 8 | 2 | no | — |
| 636 | C2×C4 | — | 8 | 2 | no | — |
| 637 | C2×C4 | — | 16 | 2 | no | — |
| 638 | C2×C4 | — | 16 | 4 | no | — |
| 639 | C2×C4 | — | 16 | 4 | no | — |
| 640 | C2×C4 | — | 16 | 2 | no | — |
| 641 | C2×C4 | — | 16 | 2 | no | — |
| 642 | C2×C4 | — | 32 | 2 | no | — |
| 643 | C2×C4 | — | 32 | 2 | no | — |
| 644 | C2×C4 | — | 32 | 2 | no | — |
| 645 | C2×C4 | — | 32 | 2 | no | — |
| 646 | C2×C4 | #2184 | 1 | 2 | yes | — |
| 647 | C2×C4 | C2×#447 | 1 | 1 | yes | characteristic |
| 648 | C2×C4 | C22×D16 | 1 | 1 | yes | characteristic |
| 649 | C8 | — | 2 | 1 | no | — |
| 650 | C8 | — | 2 | 2 | no | — |
| 651 | C8 | — | 4 | 1 | no | — |
| 652 | C8 | — | 4 | 1 | no | — |
| 653 | C8 | — | 16 | 2 | no | — |
| 654 | C8 | #3021 | 1 | 1 | yes | characteristic |
| 655 | C8 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 656 | C22 | — | 2 | 1 | no | — |
| 657 | C22 | — | 2 | 2 | no | — |
| 658 | C22 | — | 4 | 1 | no | — |
| 659 | C22 | — | 4 | 2 | no | — |
| 660 | C22 | — | 4 | 2 | no | — |
| 661 | C22 | — | 4 | 1 | no | — |
| 662 | C22 | — | 16 | 2 | no | — |
| 663 | C22 | — | 16 | 2 | no | — |
| 664 | C22 | — | 16 | 2 | no | — |
| 665 | C22 | — | 16 | 2 | no | — |
| 666 | C22 | — | 32 | 2 | no | — |
| 667 | C22 | — | 64 | 2 | no | — |
| 668 | C22 | C2×#2184 | 1 | 1 | yes | characteristic |
| 669 | C4 | — | 2 | 2 | no | — |
| 670 | C4 | — | 2 | 1 | no | — |
| 671 | C4 | — | 2 | 2 | no | — |
| 672 | C4 | — | 4 | 1 | no | — |
| 673 | C4 | — | 4 | 1 | no | — |
| 674 | C4 | — | 16 | 2 | no | — |
| 675 | C4 | — | 16 | 2 | no | — |
| 676 | C4 | — | 16 | 2 | no | — |
| 677 | C4 | — | 16 | 2 | no | — |
| 678 | C4 | #18194 | 1 | 1 | yes | characteristic |
| 679 | C4 | #33531 | 1 | 1 | yes | characteristic |
| 680 | C2 | — | 2 | 1 | no | — |
| 681 | C2 | — | 4 | 1 | no | — |
| 682 | C2 | — | 4 | 2 | no | — |
| 683 | C2 | — | 8 | 1 | no | — |
| 684 | C2 | — | 32 | 2 | no | — |
| 685 | C2 | — | 32 | 2 | no | — |
| 686 | 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. #7624863 | C2 | semidirect |
| 2. #512843 | C2 | semidirect |
| 3. #500852 | C2 | semidirect |
| 4. #151298 | C2 | semidirect |
| 5. #151297 | C2 | semidirect |
| 6. #151187 | C2 | semidirect |
| 7. #150883 | C2 | semidirect |
| 8. #149671 | C2 | semidirect |
| 16. #33821 | C22 | semidirect |
| 17. #33819 | C22 | semidirect |
| 19. #33770 | C22 | semidirect |
| 37. #7425 | C22 | semidirect |
| 38. #7424 | C22 | semidirect |
| 39. #7364 | C22 | semidirect |
| 40. #7337 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #7624863 | 2 |
| #512843 | 2 |
| #500852 | 2 |
| #151298 | 2 |
| #151297 | 2 |
| #151187 | 2 |
| #150883 | 2 |
| #149671 | 2 |