Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
782 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 133 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 | #505702 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #500850 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #153378 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #153351 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #153252 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #152886 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #152839 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #152513 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #152178 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #62635 | C22 | 1 | 1 | yes | characteristic |
| 11 | #33600 | C22 | 1 | 2 | yes | — |
| 12 | #33432 | C22 | 1 | 1 | yes | characteristic |
| 13 | C22×#367 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | #27675 | — | 2 | 1 | no | — |
| 15 | #24285 | — | 2 | 1 | no | — |
| 16 | #13638 | C22 | 1 | 2 | yes | complemented |
| 17 | #13630 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #13625 | C22 | 1 | 2 | yes | — |
| 19 | C2×#1418 | C22 | 1 | 2 | yes | — |
| 20 | C2×#1418 | C22 | 1 | 2 | yes | — |
| 21 | #13620 | C22 | 1 | 2 | yes | — |
| 22 | #13558 | C22 | 1 | 2 | yes | — |
| 23 | #13553 | C22 | 1 | 2 | yes | complemented |
| 24 | #13551 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #13518 | — | 2 | 1 | no | — |
| 26 | #13496 | — | 2 | 1 | no | — |
| 27 | #13447 | — | 2 | 1 | no | — |
| 28 | #13309 | — | 2 | 1 | no | — |
| 29 | #13243 | C22 | 1 | 2 | yes | — |
| 30 | #13172 | C22 | 1 | 2 | yes | complemented |
| 31 | #12871 | — | 2 | 1 | no | — |
| 32 | #12843 | C22 | 1 | 2 | yes | — |
| 33 | #12839 | C22 | 1 | 1 | yes | characteristic |
| 34 | #12837 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #12745 | — | 2 | 1 | no | — |
| 36 | #7480 | C22 | 1 | 2 | yes | complemented |
| 37 | #7477 | C22 | 1 | 2 | yes | complemented |
| 38 | #7477 | C22 | 1 | 2 | yes | complemented |
| 39 | #3584 | — | 2 | 1 | no | — |
| 40 | #3417 | — | 2 | 2 | no | — |
| 41 | #3416 | — | 4 | 2 | no | — |
| 42 | #3415 | — | 2 | 2 | no | — |
| 43 | #3414 | — | 2 | 1 | no | — |
| 44 | #3414 | — | 4 | 1 | no | — |
| 45 | C2×#508 | — | 4 | 1 | no | — |
| 46 | C2×#508 | C23 | 1 | 2 | yes | — |
| 47 | C2×#504 | C23 | 1 | 1 | yes | characteristic |
| 48 | C23×C16 | C23 | 1 | 1 | yes | characteristic |
| 49 | #3092 | — | 4 | 1 | no | — |
| 50 | #3050 | — | 2 | 2 | no | — |
| 51 | #3025 | — | 4 | 1 | no | — |
| 52 | #2929 | D4 | 1 | 1 | yes | characteristic |
| 53 | C22×#107 | — | 2 | 1 | no | — |
| 54 | C2×M64 | C23 | 1 | 2 | yes | — |
| 55 | C2×M64 | C23 | 1 | 2 | yes | — |
| 56 | #2217 | — | 4 | 2 | no | — |
| 57 | #2216 | — | 2 | 2 | no | — |
| 58 | #2215 | — | 2 | 2 | no | — |
| 59 | #2168 | — | 4 | 1 | no | — |
| 60 | D4×C16 | — | 4 | 1 | no | — |
| 61 | C2×#368 | C23 | 1 | 2 | yes | — |
| 62 | #2158 | C23 | 1 | 2 | yes | — |
| 63 | C2×#367 | — | 2 | 1 | no | — |
| 64 | C2×#367 | — | 4 | 1 | no | — |
| 65 | C2×#367 | — | 4 | 1 | no | — |
| 66 | C2×#367 | C23 | 1 | 2 | yes | — |
| 67 | #2151 | D4 | 1 | 1 | yes | characteristic |
| 68 | #2145 | — | 2 | 2 | no | — |
| 69 | #2138 | — | 2 | 2 | no | — |
| 70 | #2113 | D4 | 1 | 1 | yes | characteristic |
| 71 | #2112 | D4 | 1 | 1 | yes | characteristic |
| 72 | #2108 | C23 | 1 | 1 | yes | characteristic |
| 73 | #2089 | — | 4 | 1 | no | — |
| 74 | #2078 | — | 4 | 1 | no | — |
| 75 | #2053 | — | 4 | 1 | no | — |
| 76 | #2010 | — | 4 | 1 | no | — |
| 77 | #1976 | — | 2 | 2 | no | — |
| 78 | #1952 | — | 2 | 2 | no | — |
| 79 | #1821 | — | 4 | 1 | no | — |
| 80 | #1816 | — | 2 | 2 | no | — |
| 81 | #1812 | — | 2 | 1 | no | — |
| 82 | #1810 | — | 2 | 1 | no | — |
| 83 | #1794 | — | 4 | 1 | no | — |
| 84 | #1426 | — | 4 | 2 | no | — |
| 85 | #1422 | — | 4 | 1 | no | — |
| 86 | #1420 | — | 2 | 2 | no | — |
| 87 | #1419 | — | 2 | 2 | no | — |
| 88 | #1418 | — | 4 | 2 | no | — |
| 89 | #1418 | — | 4 | 2 | no | — |
| 90 | #1417 | — | 4 | 2 | no | — |
| 91 | #1401 | — | 4 | 2 | no | — |
| 92 | C22⋊C32 | — | 4 | 2 | no | — |
| 93 | #1398 | — | 4 | 1 | no | — |
| 94 | #1387 | — | 2 | 2 | no | — |
| 95 | #1387 | — | 2 | 2 | no | — |
| 96 | #1384 | — | 2 | 1 | no | — |
| 97 | #1381 | — | 2 | 1 | no | — |
| 98 | #585 | — | 4 | 1 | no | — |
| 99 | #578 | — | 4 | 2 | no | — |
| 100 | #577 | — | 8 | 2 | no | — |
| 101 | #576 | — | 4 | 2 | no | — |
| 102 | #575 | — | 4 | 2 | no | — |
| 103 | #575 | — | 4 | 1 | no | — |
| 104 | C2×#135 | — | 2 | 2 | no | — |
| 105 | C2×#135 | — | 4 | 2 | no | — |
| 106 | C2×#131 | C2×D4 | 1 | 1 | yes | characteristic |
| 107 | C23×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 108 | #525 | — | 4 | 2 | no | — |
| 109 | #525 | D8 | 1 | 1 | yes | characteristic |
| 110 | C22×C4⋊C4 | — | 4 | 1 | no | — |
| 111 | #510 | — | 4 | 2 | no | — |
| 112 | #510 | — | 4 | 4 | no | — |
| 113 | #509 | — | 4 | 2 | no | — |
| 114 | #509 | — | 4 | 4 | no | — |
| 115 | #508 | — | 2 | 2 | no | — |
| 116 | #508 | — | 2 | 2 | no | — |
| 117 | #508 | — | 2 | 2 | no | — |
| 118 | #508 | — | 2 | 2 | no | — |
| 119 | #508 | — | 4 | 2 | no | — |
| 120 | #508 | — | 4 | 2 | no | — |
| 121 | #508 | — | 4 | 2 | no | — |
| 122 | C2×Q32 | — | 4 | 1 | no | — |
| 123 | C2×Q32 | #41 | 1 | 2 | yes | — |
| 124 | C2×SD32 | — | 2 | 2 | no | — |
| 125 | C2×SD32 | — | 4 | 2 | no | — |
| 126 | C2×D16 | — | 4 | 1 | no | — |
| 127 | C2×D16 | #41 | 1 | 2 | yes | — |
| 128 | #504 | — | 2 | 2 | no | — |
| 129 | #504 | — | 2 | 2 | no | — |
| 130 | C2×M32 | — | 2 | 1 | no | — |
| 131 | C2×M32 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | C2×M32 | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | C22×C16 | — | 2 | 2 | no | — |
| 134 | C22×C16 | — | 2 | 1 | no | — |
| 135 | C22×C16 | — | 2 | 1 | no | — |
| 136 | C22×C16 | — | 2 | 2 | no | — |
| 137 | C22×C16 | — | 2 | 1 | no | — |
| 138 | C22×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C22×C16 | C24 | 1 | 1 | yes | characteristic |
| 140 | #484 | — | 8 | 1 | no | — |
| 141 | #483 | — | 8 | 1 | no | — |
| 142 | #481 | — | 8 | 1 | no | — |
| 143 | #480 | — | 8 | 1 | no | — |
| 144 | #467 | — | 4 | 2 | no | — |
| 145 | #466 | — | 4 | 2 | no | — |
| 146 | #465 | — | 8 | 2 | no | — |
| 147 | #458 | — | 8 | 2 | no | — |
| 148 | B(4,𝔽2) | — | 8 | 2 | no | — |
| 149 | #435 | — | 4 | 1 | no | — |
| 150 | C8×D4 | — | 4 | 1 | no | — |
| 151 | C2×#108 | — | 2 | 2 | no | — |
| 152 | #428 | — | 4 | 2 | no | — |
| 153 | #427 | — | 2 | 2 | no | — |
| 154 | C2×#107 | — | 2 | 2 | no | — |
| 155 | C2×#107 | — | 4 | 1 | no | — |
| 156 | C2×#107 | — | 4 | 1 | no | — |
| 157 | C2×#107 | — | 4 | 1 | no | — |
| 158 | C2×#107 | — | 4 | 1 | no | — |
| 159 | C2×#107 | — | 4 | 1 | no | — |
| 160 | #424 | D8 | 1 | 1 | yes | characteristic |
| 161 | #421 | — | 4 | 2 | no | — |
| 162 | #417 | — | 4 | 2 | no | — |
| 163 | #416 | — | 4 | 2 | no | — |
| 164 | #410 | — | 4 | 1 | no | — |
| 165 | #410 | — | 4 | 2 | no | — |
| 166 | #408 | D8 | 1 | 1 | yes | characteristic |
| 167 | #407 | — | 4 | 1 | no | — |
| 168 | #407 | D8 | 1 | 1 | yes | characteristic |
| 169 | #405 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | M64 | — | 2 | 2 | no | — |
| 171 | M64 | — | 2 | 2 | no | — |
| 172 | M64 | — | 2 | 2 | no | — |
| 173 | M64 | — | 2 | 2 | no | — |
| 174 | C2×C32 | — | 2 | 2 | no | — |
| 175 | C2×C32 | — | 2 | 2 | no | — |
| 176 | #368 | — | 2 | 2 | no | — |
| 177 | #368 | — | 2 | 2 | no | — |
| 178 | #367 | — | 2 | 2 | no | — |
| 179 | #367 | — | 2 | 2 | no | — |
| 180 | #367 | — | 2 | 2 | no | — |
| 181 | #367 | — | 4 | 2 | no | — |
| 182 | #366 | — | 2 | 2 | no | — |
| 183 | C4⋊C16 | — | 4 | 1 | no | — |
| 184 | #360 | — | 8 | 2 | no | — |
| 185 | #358 | — | 4 | 2 | no | — |
| 186 | #357 | — | 4 | 2 | no | — |
| 187 | C22⋊C16 | — | 4 | 1 | no | — |
| 188 | C22⋊C16 | — | 4 | 1 | no | — |
| 189 | #346 | — | 2 | 1 | no | — |
| 190 | C4×C16 | — | 2 | 1 | no | — |
| 191 | #343 | — | 4 | 2 | no | — |
| 192 | #343 | — | 4 | 2 | no | — |
| 193 | #341 | — | 4 | 1 | no | — |
| 194 | H(3,ℤ/4) | — | 4 | 1 | no | — |
| 195 | 2−1+4 | — | 8 | 2 | no | — |
| 196 | 2−1+4 | — | 8 | 1 | no | — |
| 197 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 198 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 199 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 200 | C2×#41 | — | 4 | 2 | no | — |
| 201 | C2×#41 | — | 8 | 2 | no | — |
| 202 | C2×#41 | — | 16 | 2 | no | — |
| 203 | C2×#41 | C2×D8 | 1 | 1 | yes | characteristic |
| 204 | C23×C4 | — | 8 | 1 | no | — |
| 205 | C23×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 206 | #137 | — | 8 | 2 | no | — |
| 207 | #137 | — | 8 | 4 | no | — |
| 208 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 209 | AGL(1,ℤ/8) | — | 8 | 4 | no | — |
| 210 | #135 | — | 4 | 4 | no | — |
| 211 | #135 | — | 4 | 2 | no | — |
| 212 | #135 | — | 4 | 2 | no | — |
| 213 | #135 | — | 4 | 2 | no | — |
| 214 | #135 | — | 4 | 2 | no | — |
| 215 | #135 | — | 8 | 2 | no | — |
| 216 | #135 | — | 8 | 2 | no | — |
| 217 | C2×Q16 | — | 2 | 2 | no | — |
| 218 | C2×Q16 | — | 4 | 2 | no | — |
| 219 | C2×SD16 | — | 4 | 2 | no | — |
| 220 | C2×SD16 | — | 8 | 2 | no | — |
| 221 | C2×D8 | — | 2 | 2 | no | — |
| 222 | C2×D8 | — | 4 | 2 | no | — |
| 223 | #131 | — | 2 | 2 | no | — |
| 224 | #131 | — | 2 | 2 | no | — |
| 225 | C2×M16 | — | 2 | 1 | no | — |
| 226 | C2×M16 | — | 4 | 2 | no | — |
| 227 | C2×M16 | C2×D8 | 1 | 1 | yes | characteristic |
| 228 | C2×M16 | C2×D8 | 1 | 1 | yes | characteristic |
| 229 | C22×C8 | — | 2 | 1 | no | — |
| 230 | C22×C8 | — | 2 | 1 | no | — |
| 231 | C22×C8 | — | 2 | 2 | no | — |
| 232 | C22×C8 | — | 2 | 1 | no | — |
| 233 | C22×C8 | — | 2 | 2 | no | — |
| 234 | C22×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 235 | C22×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 236 | #123 | — | 2 | 1 | no | — |
| 237 | #123 | — | 8 | 2 | no | — |
| 238 | C22⋊Q8 | — | 2 | 1 | no | — |
| 239 | C22⋊Q8 | — | 8 | 2 | no | — |
| 240 | #121 | — | 2 | 1 | no | — |
| 241 | #121 | — | 8 | 2 | no | — |
| 242 | #120 | — | 2 | 1 | no | — |
| 243 | #120 | — | 8 | 2 | no | — |
| 244 | C4×D4 | — | 4 | 1 | no | — |
| 245 | C4×D4 | — | 16 | 2 | no | — |
| 246 | #117 | — | 4 | 2 | no | — |
| 247 | #117 | C2×D8 | 1 | 1 | yes | characteristic |
| 248 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 249 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 250 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 251 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 252 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 253 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 254 | Q32 | — | 2 | 2 | no | — |
| 255 | Q32 | — | 2 | 2 | no | — |
| 256 | Q32 | — | 4 | 2 | no | — |
| 257 | SD32 | — | 4 | 4 | no | — |
| 258 | SD32 | — | 4 | 2 | no | — |
| 259 | SD32 | — | 4 | 2 | no | — |
| 260 | D16 | — | 2 | 2 | no | — |
| 261 | D16 | — | 2 | 2 | no | — |
| 262 | D16 | — | 4 | 2 | no | — |
| 263 | M32 | — | 2 | 2 | no | — |
| 264 | M32 | — | 2 | 2 | no | — |
| 265 | M32 | — | 4 | 2 | no | — |
| 266 | C2×C16 | — | 2 | 1 | no | — |
| 267 | C2×C16 | — | 2 | 1 | no | — |
| 268 | C2×C16 | — | 2 | 1 | no | — |
| 269 | C2×C16 | — | 2 | 2 | no | — |
| 270 | C2×C16 | — | 4 | 2 | no | — |
| 271 | C2×C16 | — | 4 | 1 | no | — |
| 272 | C2×C16 | — | 4 | 1 | no | — |
| 273 | C2×C16 | — | 4 | 1 | no | — |
| 274 | C2×C16 | — | 4 | 1 | no | — |
| 275 | C2×C16 | C2×#41 | 1 | 2 | yes | — |
| 276 | C2×C16 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 277 | C2×C16 | H(5,𝔽2) | 1 | 2 | yes | — |
| 278 | C2×C16 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 279 | #108 | — | 4 | 2 | no | — |
| 280 | #108 | — | 4 | 2 | no | — |
| 281 | #107 | — | 4 | 2 | no | — |
| 282 | #107 | — | 4 | 2 | no | — |
| 283 | #107 | — | 4 | 2 | no | — |
| 284 | #107 | — | 8 | 2 | no | — |
| 285 | #107 | — | 8 | 1 | no | — |
| 286 | #107 | — | 8 | 1 | no | — |
| 287 | #106 | — | 4 | 2 | no | — |
| 288 | #106 | — | 8 | 2 | no | — |
| 289 | C4⋊C8 | — | 4 | 1 | no | — |
| 290 | #104 | — | 16 | 2 | no | — |
| 291 | #103 | — | 8 | 2 | no | — |
| 292 | #103 | — | 8 | 2 | no | — |
| 293 | #102 | — | 8 | 2 | no | — |
| 294 | #102 | — | 8 | 2 | no | — |
| 295 | #99 | — | 8 | 4 | no | — |
| 296 | #99 | — | 8 | 2 | no | — |
| 297 | C22⋊C8 | — | 4 | 1 | no | — |
| 298 | C22⋊C8 | — | 4 | 1 | no | — |
| 299 | C22⋊C8 | — | 8 | 1 | no | — |
| 300 | C22⋊C8 | — | 8 | 1 | no | — |
| 301 | #97 | — | 2 | 1 | no | — |
| 302 | C4×C8 | — | 2 | 1 | no | — |
| 303 | C32 | — | 4 | 2 | no | — |
| 304 | C32 | — | 4 | 2 | no | — |
| 305 | C24 | #509 | 1 | 1 | yes | characteristic |
| 306 | #41 | — | 2 | 2 | no | — |
| 307 | #41 | — | 2 | 2 | no | — |
| 308 | #41 | — | 8 | 4 | no | — |
| 309 | #41 | — | 8 | 2 | no | — |
| 310 | #41 | — | 8 | 2 | no | — |
| 311 | #41 | — | 8 | 2 | no | — |
| 312 | #41 | — | 8 | 2 | no | — |
| 313 | #41 | — | 16 | 2 | no | — |
| 314 | #41 | — | 16 | 2 | no | — |
| 315 | #41 | — | 16 | 4 | no | — |
| 316 | #41 | — | 16 | 2 | no | — |
| 317 | #41 | — | 16 | 2 | no | — |
| 318 | C2×Q8 | — | 4 | 2 | no | — |
| 319 | C2×Q8 | — | 8 | 2 | no | — |
| 320 | C2×Q8 | — | 16 | 2 | no | — |
| 321 | C2×Q8 | #509 | 1 | 1 | yes | characteristic |
| 322 | C2×D4 | — | 2 | 1 | no | — |
| 323 | C2×D4 | — | 4 | 1 | no | — |
| 324 | C2×D4 | — | 4 | 2 | no | — |
| 325 | C2×D4 | — | 8 | 2 | no | — |
| 326 | C2×D4 | — | 8 | 2 | no | — |
| 327 | C2×D4 | — | 16 | 2 | no | — |
| 328 | C2×D4 | — | 16 | 4 | no | — |
| 329 | C2×D4 | — | 16 | 2 | no | — |
| 330 | C2×D4 | — | 16 | 2 | no | — |
| 331 | C2×D4 | #509 | 1 | 1 | yes | characteristic |
| 332 | C22×C4 | — | 2 | 1 | no | — |
| 333 | C22×C4 | — | 2 | 2 | no | — |
| 334 | C22×C4 | — | 2 | 1 | no | — |
| 335 | C22×C4 | — | 2 | 1 | no | — |
| 336 | C22×C4 | — | 2 | 2 | no | — |
| 337 | C22×C4 | — | 8 | 2 | no | — |
| 338 | C22×C4 | — | 8 | 2 | no | — |
| 339 | C22×C4 | — | 16 | 2 | no | — |
| 340 | C22×C4 | — | 16 | 1 | no | — |
| 341 | C22×C4 | — | 16 | 1 | no | — |
| 342 | C22×C4 | — | 32 | 2 | no | — |
| 343 | C22×C4 | #509 | 1 | 1 | yes | characteristic |
| 344 | C22×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 345 | Q16 | — | 4 | 2 | no | — |
| 346 | Q16 | — | 4 | 2 | no | — |
| 347 | Q16 | — | 8 | 2 | no | — |
| 348 | SD16 | — | 8 | 4 | no | — |
| 349 | SD16 | — | 8 | 2 | no | — |
| 350 | SD16 | — | 8 | 2 | no | — |
| 351 | D8 | — | 4 | 2 | no | — |
| 352 | D8 | — | 4 | 2 | no | — |
| 353 | D8 | — | 8 | 2 | no | — |
| 354 | M16 | — | 2 | 2 | no | — |
| 355 | M16 | — | 2 | 2 | no | — |
| 356 | M16 | — | 4 | 2 | no | — |
| 357 | M16 | — | 8 | 2 | no | — |
| 358 | M16 | — | 8 | 2 | no | — |
| 359 | C2×C8 | — | 2 | 1 | no | — |
| 360 | C2×C8 | — | 2 | 1 | no | — |
| 361 | C2×C8 | — | 2 | 1 | no | — |
| 362 | C2×C8 | — | 2 | 2 | no | — |
| 363 | C2×C8 | — | 4 | 1 | no | — |
| 364 | C2×C8 | — | 4 | 1 | no | — |
| 365 | C2×C8 | — | 4 | 1 | no | — |
| 366 | C2×C8 | — | 4 | 1 | no | — |
| 367 | C2×C8 | — | 4 | 2 | no | — |
| 368 | C2×C8 | — | 8 | 2 | no | — |
| 369 | C2×C8 | #534 | 1 | 1 | yes | characteristic |
| 370 | C2×C8 | #546 | 1 | 2 | yes | — |
| 371 | C2×C8 | #575 | 1 | 1 | yes | characteristic |
| 372 | C2×C8 | #577 | 1 | 2 | yes | — |
| 373 | C4⋊C4 | — | 2 | 1 | no | — |
| 374 | C4⋊C4 | — | 4 | 1 | no | — |
| 375 | C4⋊C4 | — | 8 | 2 | no | — |
| 376 | C4⋊C4 | — | 8 | 2 | no | — |
| 377 | C4⋊C4 | — | 8 | 2 | no | — |
| 378 | C4⋊C4 | — | 16 | 2 | no | — |
| 379 | C4⋊C4 | — | 16 | 1 | no | — |
| 380 | C4⋊C4 | — | 16 | 1 | no | — |
| 381 | C22⋊C4 | — | 2 | 1 | no | — |
| 382 | C22⋊C4 | — | 4 | 1 | no | — |
| 383 | C22⋊C4 | — | 4 | 1 | no | — |
| 384 | C22⋊C4 | — | 8 | 2 | no | — |
| 385 | C22⋊C4 | — | 16 | 2 | no | — |
| 386 | C22⋊C4 | — | 16 | 2 | no | — |
| 387 | C42 | — | 2 | 1 | no | — |
| 388 | C42 | — | 8 | 2 | no | — |
| 389 | C16 | — | 4 | 1 | no | — |
| 390 | C16 | — | 4 | 1 | no | — |
| 391 | C16 | — | 4 | 1 | no | — |
| 392 | C16 | #538 | 1 | 2 | yes | — |
| 393 | C16 | #551 | 1 | 1 | yes | characteristic |
| 394 | C16 | #560 | 1 | 1 | yes | characteristic |
| 395 | C23 | — | 2 | 2 | no | — |
| 396 | C23 | — | 2 | 1 | no | — |
| 397 | C23 | — | 2 | 1 | no | — |
| 398 | C23 | — | 4 | 2 | no | — |
| 399 | C23 | — | 8 | 2 | no | — |
| 400 | C23 | — | 16 | 2 | no | — |
| 401 | C23 | C2×#509 | 1 | 1 | yes | characteristic |
| 402 | Q8 | — | 2 | 2 | no | — |
| 403 | Q8 | — | 8 | 2 | no | — |
| 404 | Q8 | — | 8 | 2 | no | — |
| 405 | Q8 | — | 16 | 2 | no | — |
| 406 | D4 | — | 2 | 2 | no | — |
| 407 | D4 | — | 4 | 2 | no | — |
| 408 | D4 | — | 8 | 2 | no | — |
| 409 | D4 | — | 8 | 2 | no | — |
| 410 | D4 | — | 8 | 2 | no | — |
| 411 | D4 | — | 16 | 2 | no | — |
| 412 | D4 | — | 16 | 4 | no | — |
| 413 | D4 | — | 16 | 2 | no | — |
| 414 | D4 | — | 16 | 2 | no | — |
| 415 | D4 | — | 32 | 4 | no | — |
| 416 | C2×C4 | — | 2 | 2 | no | — |
| 417 | C2×C4 | — | 2 | 1 | no | — |
| 418 | C2×C4 | — | 2 | 1 | no | — |
| 419 | C2×C4 | — | 4 | 2 | no | — |
| 420 | C2×C4 | — | 4 | 1 | no | — |
| 421 | C2×C4 | — | 4 | 1 | no | — |
| 422 | C2×C4 | — | 4 | 1 | no | — |
| 423 | C2×C4 | — | 4 | 1 | no | — |
| 424 | C2×C4 | — | 4 | 1 | no | — |
| 425 | C2×C4 | — | 8 | 2 | no | — |
| 426 | C2×C4 | — | 16 | 4 | no | — |
| 427 | C2×C4 | — | 16 | 2 | no | — |
| 428 | C2×C4 | — | 16 | 2 | no | — |
| 429 | C2×C4 | — | 16 | 2 | no | — |
| 430 | C2×C4 | — | 16 | 2 | no | — |
| 431 | C2×C4 | — | 16 | 2 | no | — |
| 432 | C2×C4 | — | 32 | 2 | no | — |
| 433 | C2×C4 | — | 32 | 2 | no | — |
| 434 | C2×C4 | — | 32 | 2 | no | — |
| 435 | C2×C4 | #3186 | 1 | 1 | yes | characteristic |
| 436 | C2×C4 | #3294 | 1 | 2 | yes | — |
| 437 | C2×C4 | C2×#509 | 1 | 1 | yes | characteristic |
| 438 | C2×C4 | #3416 | 1 | 2 | yes | — |
| 439 | C8 | — | 4 | 1 | no | — |
| 440 | C8 | — | 4 | 1 | no | — |
| 441 | C8 | — | 4 | 1 | no | — |
| 442 | C8 | — | 16 | 2 | no | — |
| 443 | C8 | #2697 | 1 | 1 | yes | characteristic |
| 444 | C8 | #3200 | 1 | 1 | yes | characteristic |
| 445 | C8 | #3323 | 1 | 2 | yes | — |
| 446 | C22 | — | 2 | 2 | no | — |
| 447 | C22 | — | 2 | 4 | no | — |
| 448 | C22 | — | 4 | 1 | no | — |
| 449 | C22 | — | 4 | 1 | no | — |
| 450 | C22 | — | 4 | 2 | no | — |
| 451 | C22 | — | 4 | 1 | no | — |
| 452 | C22 | — | 4 | 1 | no | — |
| 453 | C22 | — | 8 | 1 | no | — |
| 454 | C22 | — | 16 | 2 | no | — |
| 455 | C22 | — | 32 | 2 | no | — |
| 456 | C22 | — | 64 | 2 | no | — |
| 457 | C22 | #33758 | 1 | 1 | yes | characteristic |
| 458 | C22 | #33877 | 1 | 2 | yes | — |
| 459 | C4 | — | 4 | 1 | no | — |
| 460 | C4 | — | 4 | 1 | no | — |
| 461 | C4 | — | 8 | 1 | no | — |
| 462 | C4 | — | 16 | 2 | no | — |
| 463 | C4 | — | 32 | 2 | no | — |
| 464 | C4 | — | 32 | 2 | no | — |
| 465 | C4 | #31666 | 1 | 1 | yes | characteristic |
| 466 | C4 | #33766 | 1 | 1 | yes | characteristic |
| 467 | C4 | #33873 | 1 | 2 | yes | — |
| 468 | C2 | — | 2 | 1 | no | — |
| 469 | C2 | — | 2 | 2 | no | — |
| 470 | C2 | — | 4 | 2 | no | — |
| 471 | C2 | — | 8 | 1 | no | — |
| 472 | C2 | — | 32 | 2 | no | — |
| 473 | C2 | #510507 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #510507 |
| commutator, Frattini, cosocle | C22×C16 | C24 |
| prime radical | #500850 | C2 |
| LCS | G ▷ C22×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #2929 ◁ #33432 ◁ G | |
| LECS | G ▷ C22×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #505702 | C2 | semidirect |
| 3. #153378 | C2 | semidirect |
| 4. #153351 | C2 | semidirect |
| 5. #153252 | C2 | semidirect |
| 6. #152886 | C2 | semidirect |
| 7. #152839 | C2 | semidirect |
| 8. #152513 | C2 | semidirect |
| 9. #152178 | C2 | semidirect |
| 13. C22×#367 | C22 | semidirect |
| 16. #13638 | C22 | semidirect |
| 17. #13630 | C22 | semidirect |
| 23. #13553 | C22 | semidirect |
| 24. #13551 | C22 | semidirect |
| 30. #13172 | C22 | semidirect |
| 34. #12837 | C22 | semidirect |
| 36. #7480 | C22 | semidirect |
| 37. #7477 | C22 | semidirect |
| 38. #7477 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #505702 | 2 |
| #500850 | 2 |
| #153378 | 2 |
| #153351 | 2 |
| #153252 | 2 |
| #152886 | 2 |
| #152839 | 2 |
| #152513 | 2 |
| #152178 | 2 |