Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
1656 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 1656 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72226852 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72225394 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #72225341 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C2×#93752 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #72216251 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #7623661 | — | 2 | 2 | no | — |
| 7 | #492533 | C4 | 1 | 2 | yes | — |
| 8 | #492532 | C4 | 1 | 2 | yes | — |
| 9 | #492531 | — | 2 | 2 | no | — |
| 10 | #492530 | — | 2 | 4 | no | — |
| 11 | #491465 | C22 | 1 | 1 | yes | characteristic |
| 12 | #490484 | — | 2 | 2 | no | — |
| 13 | #488869 | — | 2 | 2 | no | — |
| 14 | C2×#12046 | C22 | 1 | 2 | yes | — |
| 15 | #152283 | — | 2 | 2 | no | — |
| 16 | C2×#7459 | C22 | 1 | 2 | yes | complemented |
| 17 | #141812 | — | 2 | 2 | no | — |
| 18 | #135781 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C2×#7052 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #94365 | — | 2 | 2 | no | — |
| 21 | #93868 | — | 2 | 2 | no | — |
| 22 | #93752 | — | 2 | 4 | no | — |
| 23 | #62635 | — | 4 | 2 | no | — |
| 24 | #61105 | — | 2 | 2 | no | — |
| 25 | #33860 | — | 2 | 4 | no | — |
| 26 | #33859 | — | 4 | 4 | no | — |
| 27 | #33858 | — | 2 | 4 | no | — |
| 28 | #33857 | — | 4 | 4 | no | — |
| 29 | #33856 | — | 2 | 8 | no | — |
| 30 | #33713 | — | 2 | 2 | no | — |
| 31 | #33617 | — | 4 | 2 | no | — |
| 32 | #33594 | — | 2 | 4 | no | — |
| 33 | #33538 | — | 4 | 4 | no | — |
| 34 | C2×#2178 | D4 | 1 | 2 | yes | — |
| 35 | C2×#2170 | — | 2 | 2 | no | — |
| 36 | #19603 | D4 | 1 | 2 | yes | — |
| 37 | C2×#1422 | — | 2 | 2 | no | — |
| 38 | #13625 | — | 4 | 2 | no | — |
| 39 | #12909 | — | 2 | 2 | no | — |
| 40 | #12518 | — | 2 | 2 | no | — |
| 41 | #12517 | D4 | 1 | 2 | yes | — |
| 42 | #12516 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | #12515 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | #12438 | — | 2 | 8 | no | — |
| 45 | #12437 | — | 2 | 4 | no | — |
| 46 | #12436 | — | 2 | 4 | no | — |
| 47 | #12313 | — | 2 | 4 | no | — |
| 48 | #12312 | — | 2 | 4 | no | — |
| 49 | #12311 | — | 2 | 4 | no | — |
| 50 | #12310 | — | 2 | 4 | no | — |
| 51 | #12046 | — | 2 | 2 | no | — |
| 52 | #12046 | — | 2 | 2 | no | — |
| 53 | #12046 | C2×C4 | 1 | 4 | yes | — |
| 54 | #12046 | D4 | 1 | 4 | yes | — |
| 55 | C2×#1373 | D4 | 1 | 2 | yes | — |
| 56 | #11920 | — | 2 | 2 | no | — |
| 57 | #11671 | — | 4 | 4 | no | — |
| 58 | C2×#1335 | — | 2 | 2 | no | — |
| 59 | C2×C8×C16 | — | 2 | 1 | no | — |
| 60 | C2×C8×C16 | C23 | 1 | 1 | yes | characteristic |
| 61 | #8823 | — | 2 | 1 | no | — |
| 62 | #7476 | — | 4 | 2 | no | — |
| 63 | #7459 | — | 2 | 2 | no | — |
| 64 | #7459 | — | 2 | 2 | no | — |
| 65 | #7052 | — | 2 | 2 | no | — |
| 66 | #3584 | — | 4 | 4 | no | — |
| 67 | #3417 | — | 4 | 4 | no | — |
| 68 | #3417 | — | 8 | 2 | no | — |
| 69 | #3416 | — | 4 | 8 | no | — |
| 70 | #3416 | — | 8 | 4 | no | — |
| 71 | #3415 | — | 4 | 4 | no | — |
| 72 | #3415 | — | 8 | 2 | no | — |
| 73 | #3414 | — | 4 | 4 | no | — |
| 74 | #3414 | — | 8 | 4 | no | — |
| 75 | C2×#508 | — | 4 | 2 | no | — |
| 76 | C2×#508 | — | 4 | 2 | no | — |
| 77 | C2×#508 | — | 8 | 4 | no | — |
| 78 | C2×#508 | D8 | 1 | 2 | yes | — |
| 79 | C2×#504 | — | 4 | 2 | no | — |
| 80 | #3293 | — | 2 | 4 | no | — |
| 81 | #3292 | — | 2 | 4 | no | — |
| 82 | #3291 | — | 8 | 2 | no | — |
| 83 | #3290 | — | 4 | 8 | no | — |
| 84 | #3169 | — | 4 | 2 | no | — |
| 85 | #3147 | — | 2 | 2 | no | — |
| 86 | #3067 | — | 4 | 4 | no | — |
| 87 | #3018 | — | 8 | 2 | no | — |
| 88 | C2×#443 | — | 2 | 2 | no | — |
| 89 | C2×M64 | — | 4 | 2 | no | — |
| 90 | #2249 | — | 4 | 2 | no | — |
| 91 | #2249 | — | 4 | 2 | no | — |
| 92 | #2248 | — | 2 | 4 | no | — |
| 93 | #2247 | — | 2 | 2 | no | — |
| 94 | #2246 | — | 2 | 2 | no | — |
| 95 | #2223 | — | 4 | 8 | no | — |
| 96 | #2222 | — | 4 | 4 | no | — |
| 97 | #2221 | — | 4 | 4 | no | — |
| 98 | #2214 | — | 2 | 8 | no | — |
| 99 | #2213 | — | 2 | 8 | no | — |
| 100 | #2212 | — | 4 | 8 | no | — |
| 101 | #2195 | — | 4 | 8 | no | — |
| 102 | #2194 | — | 4 | 8 | no | — |
| 103 | #2193 | — | 4 | 8 | no | — |
| 104 | #2192 | — | 4 | 8 | no | — |
| 105 | #2178 | — | 2 | 2 | no | — |
| 106 | #2178 | — | 2 | 2 | no | — |
| 107 | #2178 | C22⋊C4 | 1 | 4 | yes | — |
| 108 | #2178 | SD16 | 1 | 4 | yes | — |
| 109 | #2170 | — | 2 | 4 | no | — |
| 110 | #2170 | — | 2 | 4 | no | — |
| 111 | #2170 | — | 4 | 2 | no | — |
| 112 | #2170 | — | 4 | 2 | no | — |
| 113 | C2×#368 | — | 4 | 2 | no | — |
| 114 | C2×#368 | — | 4 | 2 | no | — |
| 115 | C2×#368 | D8 | 1 | 2 | yes | — |
| 116 | C2×#364 | — | 2 | 2 | no | — |
| 117 | #2148 | — | 4 | 4 | no | — |
| 118 | C2×#359 | — | 2 | 2 | no | — |
| 119 | C2×#350 | — | 4 | 2 | no | — |
| 120 | C2×C4×C16 | — | 2 | 2 | no | — |
| 121 | C2×C4×C16 | C2×D4 | 1 | 2 | yes | — |
| 122 | #1848 | — | 4 | 1 | no | — |
| 123 | #1713 | C22⋊C4 | 1 | 2 | yes | — |
| 124 | #1712 | C22⋊C4 | 1 | 2 | yes | — |
| 125 | #1709 | — | 2 | 2 | no | — |
| 126 | #1706 | — | 4 | 2 | no | — |
| 127 | #1567 | — | 4 | 2 | no | — |
| 128 | C2×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | #1422 | — | 4 | 2 | no | — |
| 130 | #1422 | — | 4 | 2 | no | — |
| 131 | #1420 | — | 8 | 2 | no | — |
| 132 | #1419 | — | 8 | 2 | no | — |
| 133 | #1373 | — | 2 | 2 | no | — |
| 134 | #1373 | C22⋊C4 | 1 | 4 | yes | — |
| 135 | #1358 | — | 2 | 4 | no | — |
| 136 | #1357 | — | 2 | 4 | no | — |
| 137 | #1335 | — | 2 | 4 | no | — |
| 138 | #1335 | — | 2 | 4 | no | — |
| 139 | #1331 | — | 8 | 8 | no | — |
| 140 | C8×C16 | — | 4 | 1 | no | — |
| 141 | C8×C16 | — | 4 | 1 | no | — |
| 142 | C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 143 | C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | C8×C16 | C2×D4 | 1 | 2 | yes | — |
| 145 | #585 | — | 8 | 2 | no | — |
| 146 | #578 | — | 4 | 8 | no | — |
| 147 | #578 | — | 8 | 4 | no | — |
| 148 | #577 | — | 8 | 8 | no | — |
| 149 | #577 | — | 16 | 4 | no | — |
| 150 | #576 | — | 4 | 8 | no | — |
| 151 | #576 | — | 8 | 4 | no | — |
| 152 | #575 | — | 8 | 4 | no | — |
| 153 | #575 | — | 16 | 4 | no | — |
| 154 | C2×#135 | — | 2 | 2 | no | — |
| 155 | C2×#135 | — | 4 | 4 | no | — |
| 156 | C2×#135 | — | 8 | 8 | no | — |
| 157 | C2×#131 | — | 4 | 2 | no | — |
| 158 | #532 | — | 4 | 2 | no | — |
| 159 | #510 | — | 4 | 8 | no | — |
| 160 | #510 | — | 8 | 8 | no | — |
| 161 | #510 | — | 8 | 8 | no | — |
| 162 | #510 | — | 8 | 4 | no | — |
| 163 | #509 | — | 4 | 8 | no | — |
| 164 | #509 | — | 8 | 8 | no | — |
| 165 | #509 | — | 8 | 8 | no | — |
| 166 | #509 | — | 8 | 4 | no | — |
| 167 | #508 | — | 2 | 2 | no | — |
| 168 | #508 | — | 2 | 2 | no | — |
| 169 | #508 | — | 8 | 8 | no | — |
| 170 | #508 | — | 8 | 8 | no | — |
| 171 | #508 | — | 8 | 4 | no | — |
| 172 | #508 | — | 8 | 4 | no | — |
| 173 | #508 | — | 8 | 2 | no | — |
| 174 | #508 | — | 8 | 2 | no | — |
| 175 | #508 | — | 8 | 2 | no | — |
| 176 | #508 | — | 8 | 2 | no | — |
| 177 | #508 | — | 16 | 2 | no | — |
| 178 | #508 | — | 16 | 2 | no | — |
| 179 | #508 | #102 | 1 | 4 | yes | — |
| 180 | #508 | SD32 | 1 | 4 | yes | — |
| 181 | C2×Q32 | — | 4 | 2 | no | — |
| 182 | C2×Q32 | — | 4 | 2 | no | — |
| 183 | C2×Q32 | — | 8 | 4 | no | — |
| 184 | C2×Q32 | D16 | 1 | 2 | yes | — |
| 185 | C2×SD32 | — | 2 | 2 | no | — |
| 186 | C2×SD32 | — | 4 | 4 | no | — |
| 187 | C2×SD32 | — | 4 | 4 | no | — |
| 188 | C2×SD32 | — | 8 | 8 | no | — |
| 189 | C2×D16 | — | 4 | 2 | no | — |
| 190 | C2×D16 | — | 4 | 2 | no | — |
| 191 | C2×D16 | — | 8 | 4 | no | — |
| 192 | C2×D16 | D16 | 1 | 2 | yes | — |
| 193 | #504 | — | 4 | 4 | no | — |
| 194 | #504 | — | 4 | 4 | no | — |
| 195 | #504 | — | 8 | 2 | no | — |
| 196 | #504 | — | 8 | 2 | no | — |
| 197 | C2×M32 | — | 4 | 2 | no | — |
| 198 | C2×M32 | — | 8 | 2 | no | — |
| 199 | C22×C16 | — | 4 | 2 | no | — |
| 200 | C22×C16 | — | 8 | 2 | no | — |
| 201 | C22×C16 | C2×D8 | 1 | 2 | yes | — |
| 202 | C22×C16 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 203 | #500 | — | 4 | 2 | no | — |
| 204 | #495 | — | 4 | 4 | no | — |
| 205 | #494 | — | 2 | 2 | no | — |
| 206 | #493 | — | 2 | 2 | no | — |
| 207 | #493 | — | 4 | 2 | no | — |
| 208 | #492 | — | 4 | 2 | no | — |
| 209 | #486 | — | 8 | 2 | no | — |
| 210 | #473 | — | 4 | 8 | no | — |
| 211 | #472 | — | 4 | 8 | no | — |
| 212 | #471 | — | 8 | 8 | no | — |
| 213 | #466 | — | 8 | 4 | no | — |
| 214 | #456 | — | 8 | 4 | no | — |
| 215 | #455 | — | 8 | 4 | no | — |
| 216 | #454 | — | 8 | 4 | no | — |
| 217 | #453 | — | 8 | 4 | no | — |
| 218 | #443 | — | 2 | 4 | no | — |
| 219 | #443 | — | 2 | 4 | no | — |
| 220 | #443 | — | 4 | 2 | no | — |
| 221 | #443 | — | 4 | 2 | no | — |
| 222 | C4×D8 | — | 8 | 4 | no | — |
| 223 | C2×#108 | — | 2 | 2 | no | — |
| 224 | C2×#108 | — | 8 | 2 | no | — |
| 225 | #423 | — | 8 | 1 | no | — |
| 226 | C2×#104 | — | 4 | 2 | no | — |
| 227 | #413 | — | 8 | 2 | no | — |
| 228 | C2×C4×C8 | — | 2 | 1 | no | — |
| 229 | C2×C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 230 | M64 | — | 8 | 2 | no | — |
| 231 | M64 | — | 8 | 2 | no | — |
| 232 | C2×C32 | — | 8 | 2 | no | — |
| 233 | #368 | — | 2 | 2 | no | — |
| 234 | #368 | — | 8 | 2 | no | — |
| 235 | #368 | — | 8 | 2 | no | — |
| 236 | #368 | — | 16 | 2 | no | — |
| 237 | #368 | #102 | 1 | 4 | yes | — |
| 238 | #364 | — | 2 | 4 | no | — |
| 239 | #364 | — | 4 | 2 | no | — |
| 240 | #362 | — | 4 | 8 | no | — |
| 241 | #361 | — | 4 | 8 | no | — |
| 242 | #359 | — | 2 | 4 | no | — |
| 243 | #359 | — | 2 | 4 | no | — |
| 244 | #350 | — | 4 | 4 | no | — |
| 245 | #350 | — | 4 | 4 | no | — |
| 246 | C4×C16 | — | 2 | 4 | no | — |
| 247 | C4×C16 | — | 4 | 2 | no | — |
| 248 | C4×C16 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 249 | C4×C16 | #120 | 1 | 2 | yes | — |
| 250 | C4×C16 | C2×SD16 | 1 | 2 | yes | — |
| 251 | C4×C16 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 252 | #335 | — | 8 | 4 | no | — |
| 253 | C82 | — | 2 | 1 | no | — |
| 254 | C82 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 255 | C82 | #120 | 1 | 1 | yes | characteristic |
| 256 | 2−1+4 | — | 8 | 4 | no | — |
| 257 | 2−1+4 | — | 16 | 4 | no | — |
| 258 | H(5,𝔽2) | — | 8 | 4 | no | — |
| 259 | H(5,𝔽2) | — | 16 | 4 | no | — |
| 260 | H(5,𝔽2) | — | 32 | 2 | no | — |
| 261 | C2×#41 | — | 4 | 2 | no | — |
| 262 | C2×#41 | — | 8 | 2 | no | — |
| 263 | C2×#41 | — | 16 | 8 | no | — |
| 264 | C2×#41 | — | 32 | 2 | no | — |
| 265 | #137 | — | 8 | 8 | no | — |
| 266 | #137 | — | 16 | 8 | no | — |
| 267 | #137 | — | 16 | 8 | no | — |
| 268 | #137 | — | 16 | 4 | no | — |
| 269 | AGL(1,ℤ/8) | — | 8 | 8 | no | — |
| 270 | AGL(1,ℤ/8) | — | 16 | 8 | no | — |
| 271 | AGL(1,ℤ/8) | — | 16 | 8 | no | — |
| 272 | AGL(1,ℤ/8) | — | 16 | 4 | no | — |
| 273 | #135 | — | 2 | 4 | no | — |
| 274 | #135 | — | 2 | 4 | no | — |
| 275 | #135 | — | 4 | 2 | no | — |
| 276 | #135 | — | 4 | 2 | no | — |
| 277 | #135 | — | 8 | 8 | no | — |
| 278 | #135 | — | 8 | 8 | no | — |
| 279 | #135 | — | 8 | 4 | no | — |
| 280 | #135 | — | 8 | 4 | no | — |
| 281 | #135 | — | 8 | 4 | no | — |
| 282 | #135 | — | 8 | 4 | no | — |
| 283 | #135 | — | 16 | 8 | no | — |
| 284 | #135 | — | 16 | 8 | no | — |
| 285 | C2×Q16 | — | 2 | 2 | no | — |
| 286 | C2×Q16 | — | 4 | 4 | no | — |
| 287 | C2×Q16 | — | 8 | 8 | no | — |
| 288 | C2×SD16 | — | 4 | 2 | no | — |
| 289 | C2×SD16 | — | 8 | 4 | no | — |
| 290 | C2×SD16 | — | 16 | 8 | no | — |
| 291 | C2×D8 | — | 2 | 2 | no | — |
| 292 | C2×D8 | — | 4 | 4 | no | — |
| 293 | C2×D8 | — | 8 | 4 | no | — |
| 294 | C2×D8 | — | 8 | 8 | no | — |
| 295 | #131 | — | 4 | 4 | no | — |
| 296 | #131 | — | 4 | 4 | no | — |
| 297 | #131 | — | 8 | 2 | no | — |
| 298 | #131 | — | 8 | 2 | no | — |
| 299 | C2×M16 | — | 4 | 2 | no | — |
| 300 | C2×M16 | — | 8 | 2 | no | — |
| 301 | C2×M16 | — | 16 | 1 | no | — |
| 302 | C22×C8 | — | 2 | 2 | no | — |
| 303 | C22×C8 | — | 8 | 2 | no | — |
| 304 | C22×C8 | #447 | 1 | 2 | yes | — |
| 305 | C4⋊Q8 | — | 4 | 2 | no | — |
| 306 | #127 | — | 4 | 2 | no | — |
| 307 | #124 | — | 8 | 2 | no | — |
| 308 | #121 | — | 16 | 2 | no | — |
| 309 | C4×D4 | — | 16 | 2 | no | — |
| 310 | C2×C42 | #453 | 1 | 1 | yes | characteristic |
| 311 | Q32 | — | 2 | 2 | no | — |
| 312 | Q32 | — | 8 | 8 | no | — |
| 313 | Q32 | — | 8 | 2 | no | — |
| 314 | Q32 | — | 8 | 2 | no | — |
| 315 | Q32 | — | 16 | 2 | no | — |
| 316 | Q32 | #357 | 1 | 4 | yes | — |
| 317 | SD32 | — | 2 | 4 | no | — |
| 318 | SD32 | — | 2 | 4 | no | — |
| 319 | SD32 | — | 8 | 8 | no | — |
| 320 | SD32 | — | 8 | 8 | no | — |
| 321 | SD32 | — | 8 | 4 | no | — |
| 322 | SD32 | — | 8 | 4 | no | — |
| 323 | SD32 | — | 16 | 4 | no | — |
| 324 | D16 | — | 2 | 2 | no | — |
| 325 | D16 | — | 8 | 8 | no | — |
| 326 | D16 | — | 8 | 2 | no | — |
| 327 | D16 | — | 8 | 2 | no | — |
| 328 | D16 | — | 16 | 2 | no | — |
| 329 | D16 | #357 | 1 | 4 | yes | — |
| 330 | M32 | — | 4 | 4 | no | — |
| 331 | M32 | — | 8 | 2 | no | — |
| 332 | M32 | — | 8 | 4 | no | — |
| 333 | M32 | — | 8 | 4 | no | — |
| 334 | C2×C16 | — | 2 | 2 | no | — |
| 335 | C2×C16 | — | 2 | 2 | no | — |
| 336 | C2×C16 | — | 4 | 4 | no | — |
| 337 | C2×C16 | — | 8 | 4 | no | — |
| 338 | C2×C16 | — | 8 | 2 | no | — |
| 339 | C2×C16 | — | 8 | 4 | no | — |
| 340 | C2×C16 | — | 8 | 4 | no | — |
| 341 | C2×C16 | C2×#102 | 1 | 2 | yes | — |
| 342 | C2×C16 | #418 | 1 | 2 | yes | — |
| 343 | C2×C16 | #447 | 1 | 2 | yes | — |
| 344 | C2×C16 | #450 | 1 | 2 | yes | — |
| 345 | C2×C16 | C2×D16 | 1 | 2 | yes | — |
| 346 | C2×C16 | C2×SD32 | 1 | 2 | yes | — |
| 347 | C2×C16 | #509 | 1 | 2 | yes | — |
| 348 | C2×C16 | #509 | 1 | 2 | yes | — |
| 349 | #108 | — | 2 | 4 | no | — |
| 350 | #108 | — | 4 | 2 | no | — |
| 351 | #108 | — | 16 | 2 | no | — |
| 352 | #108 | — | 16 | 2 | no | — |
| 353 | #107 | — | 8 | 4 | no | — |
| 354 | C4⋊C8 | — | 16 | 2 | no | — |
| 355 | #104 | — | 4 | 4 | no | — |
| 356 | #104 | — | 4 | 4 | no | — |
| 357 | #102 | — | 16 | 4 | no | — |
| 358 | #101 | — | 8 | 4 | no | — |
| 359 | #100 | — | 8 | 4 | no | — |
| 360 | C4×C8 | — | 2 | 2 | no | — |
| 361 | C4×C8 | — | 2 | 1 | no | — |
| 362 | C4×C8 | — | 2 | 1 | no | — |
| 363 | C4×C8 | #379 | 1 | 1 | yes | characteristic |
| 364 | C4×C8 | #450 | 1 | 2 | yes | — |
| 365 | C4×C8 | #455 | 1 | 1 | yes | characteristic |
| 366 | C32 | — | 16 | 2 | no | — |
| 367 | #41 | — | 4 | 4 | no | — |
| 368 | #41 | — | 4 | 4 | no | — |
| 369 | #41 | — | 8 | 2 | no | — |
| 370 | #41 | — | 8 | 2 | no | — |
| 371 | #41 | — | 16 | 8 | no | — |
| 372 | #41 | — | 16 | 8 | no | — |
| 373 | #41 | — | 16 | 4 | no | — |
| 374 | #41 | — | 16 | 4 | no | — |
| 375 | #41 | — | 32 | 4 | no | — |
| 376 | #41 | — | 32 | 8 | no | — |
| 377 | #41 | — | 32 | 4 | no | — |
| 378 | #41 | — | 32 | 4 | no | — |
| 379 | C2×Q8 | — | 4 | 2 | no | — |
| 380 | C2×Q8 | — | 8 | 2 | no | — |
| 381 | C2×Q8 | — | 16 | 8 | no | — |
| 382 | C2×Q8 | — | 32 | 2 | no | — |
| 383 | C2×D4 | — | 4 | 2 | no | — |
| 384 | C2×D4 | — | 8 | 2 | no | — |
| 385 | C2×D4 | — | 8 | 2 | no | — |
| 386 | C2×D4 | — | 16 | 2 | no | — |
| 387 | C2×D4 | — | 16 | 8 | no | — |
| 388 | C2×D4 | — | 16 | 2 | no | — |
| 389 | C2×D4 | — | 32 | 4 | no | — |
| 390 | C2×D4 | — | 32 | 2 | no | — |
| 391 | C2×D4 | — | 32 | 8 | no | — |
| 392 | C22×C4 | — | 2 | 1 | no | — |
| 393 | C22×C4 | — | 8 | 2 | no | — |
| 394 | C22×C4 | — | 16 | 2 | no | — |
| 395 | C22×C4 | — | 32 | 4 | no | — |
| 396 | C22×C4 | #1619 | 1 | 1 | yes | characteristic |
| 397 | Q16 | — | 2 | 4 | no | — |
| 398 | Q16 | — | 4 | 2 | no | — |
| 399 | Q16 | — | 8 | 4 | no | — |
| 400 | Q16 | — | 8 | 4 | no | — |
| 401 | Q16 | — | 16 | 8 | no | — |
| 402 | SD16 | — | 4 | 4 | no | — |
| 403 | SD16 | — | 4 | 4 | no | — |
| 404 | SD16 | — | 16 | 8 | no | — |
| 405 | SD16 | — | 16 | 8 | no | — |
| 406 | SD16 | — | 16 | 4 | no | — |
| 407 | SD16 | — | 16 | 4 | no | — |
| 408 | D8 | — | 2 | 4 | no | — |
| 409 | D8 | — | 4 | 2 | no | — |
| 410 | D8 | — | 8 | 4 | no | — |
| 411 | D8 | — | 8 | 4 | no | — |
| 412 | D8 | — | 16 | 8 | no | — |
| 413 | D8 | — | 16 | 8 | no | — |
| 414 | M16 | — | 4 | 4 | no | — |
| 415 | M16 | — | 8 | 2 | no | — |
| 416 | M16 | — | 8 | 4 | no | — |
| 417 | M16 | — | 8 | 4 | no | — |
| 418 | M16 | — | 32 | 2 | no | — |
| 419 | C2×C8 | — | 2 | 2 | no | — |
| 420 | C2×C8 | — | 2 | 2 | no | — |
| 421 | C2×C8 | — | 4 | 4 | no | — |
| 422 | C2×C8 | — | 8 | 2 | no | — |
| 423 | C2×C8 | — | 8 | 4 | no | — |
| 424 | C2×C8 | — | 8 | 4 | no | — |
| 425 | C2×C8 | — | 32 | 1 | no | — |
| 426 | C2×C8 | #1639 | 1 | 2 | yes | — |
| 427 | C2×C8 | #1786 | 1 | 2 | yes | — |
| 428 | C2×C8 | #2184 | 1 | 2 | yes | — |
| 429 | C2×C8 | #2187 | 1 | 2 | yes | — |
| 430 | C2×C8 | #2192 | 1 | 2 | yes | — |
| 431 | C2×C8 | #2194 | 1 | 2 | yes | — |
| 432 | C4⋊C4 | — | 16 | 2 | no | — |
| 433 | C22⋊C4 | — | 32 | 2 | no | — |
| 434 | C42 | — | 2 | 1 | no | — |
| 435 | C42 | #1629 | 1 | 1 | yes | characteristic |
| 436 | C42 | #1792 | 1 | 1 | yes | characteristic |
| 437 | C16 | — | 2 | 2 | no | — |
| 438 | C16 | — | 2 | 2 | no | — |
| 439 | C16 | — | 8 | 4 | no | — |
| 440 | C16 | — | 8 | 4 | no | — |
| 441 | C16 | C2×#357 | 1 | 2 | yes | — |
| 442 | C16 | #2140 | 1 | 2 | yes | — |
| 443 | C16 | #2184 | 1 | 2 | yes | — |
| 444 | C16 | #2187 | 1 | 2 | yes | — |
| 445 | C23 | — | 8 | 2 | no | — |
| 446 | C23 | — | 16 | 2 | no | — |
| 447 | C23 | — | 32 | 4 | no | — |
| 448 | C23 | #12312 | 1 | 1 | yes | characteristic |
| 449 | Q8 | — | 4 | 4 | no | — |
| 450 | Q8 | — | 8 | 2 | no | — |
| 451 | Q8 | — | 16 | 4 | no | — |
| 452 | Q8 | — | 32 | 4 | no | — |
| 453 | D4 | — | 4 | 4 | no | — |
| 454 | D4 | — | 8 | 4 | no | — |
| 455 | D4 | — | 8 | 4 | no | — |
| 456 | D4 | — | 8 | 2 | no | — |
| 457 | D4 | — | 16 | 4 | no | — |
| 458 | D4 | — | 32 | 4 | no | — |
| 459 | D4 | — | 32 | 8 | no | — |
| 460 | D4 | — | 32 | 4 | no | — |
| 461 | D4 | — | 32 | 4 | no | — |
| 462 | C2×C4 | — | 2 | 1 | no | — |
| 463 | C2×C4 | — | 2 | 1 | no | — |
| 464 | C2×C4 | — | 4 | 2 | no | — |
| 465 | C2×C4 | — | 8 | 2 | no | — |
| 466 | C2×C4 | — | 8 | 4 | no | — |
| 467 | C2×C4 | — | 8 | 4 | no | — |
| 468 | C2×C4 | — | 16 | 2 | no | — |
| 469 | C2×C4 | — | 32 | 4 | no | — |
| 470 | C2×C4 | — | 32 | 8 | no | — |
| 471 | C2×C4 | — | 32 | 2 | no | — |
| 472 | C2×C4 | — | 32 | 2 | no | — |
| 473 | C2×C4 | #8443 | 1 | 1 | yes | characteristic |
| 474 | C2×C4 | #12310 | 1 | 1 | yes | characteristic |
| 475 | C2×C4 | #12316 | 1 | 2 | yes | — |
| 476 | C2×C4 | #12320 | 1 | 2 | yes | — |
| 477 | C8 | — | 2 | 4 | no | — |
| 478 | C8 | — | 4 | 2 | no | — |
| 479 | C8 | — | 8 | 4 | no | — |
| 480 | C8 | — | 64 | 1 | no | — |
| 481 | C8 | #12368 | 1 | 2 | yes | — |
| 482 | C8 | #12372 | 1 | 2 | yes | — |
| 483 | C8 | #12731 | 1 | 2 | yes | — |
| 484 | C8 | #12748 | 1 | 2 | yes | — |
| 485 | C22 | — | 4 | 1 | no | — |
| 486 | C22 | — | 8 | 4 | no | — |
| 487 | C22 | — | 32 | 2 | no | — |
| 488 | C22 | — | 32 | 2 | no | — |
| 489 | C22 | — | 64 | 2 | no | — |
| 490 | C22 | — | 128 | 4 | no | — |
| 491 | C22 | #123295 | 1 | 2 | yes | — |
| 492 | C22 | #131832 | 1 | 1 | yes | characteristic |
| 493 | C4 | — | 2 | 2 | no | — |
| 494 | C4 | — | 4 | 1 | no | — |
| 495 | C4 | — | 8 | 4 | no | — |
| 496 | C4 | — | 32 | 2 | no | — |
| 497 | C4 | #123275 | 1 | 1 | yes | characteristic |
| 498 | C4 | #123285 | 1 | 1 | yes | characteristic |
| 499 | C4 | #131848 | 1 | 2 | yes | — |
| 500 | C2 | — | 2 | 1 | no | — |
| 501 | C2 | — | 2 | 2 | no | — |
| 502 | C2 | — | 16 | 4 | no | — |
| 503 | C2 | — | 64 | 2 | no | — |
| 504 | C2 | #72225182 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #123285 |
| commutator | C8×C16 | C22×C4 |
| Frattini, cosocle | C2×C8×C16 | C23 |
| socle | C2 | #72225182 |
| prime radical | #72225394 | C2 |
| LCS | G ▷ C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×C8×C16 ◁ G | |
| LECS | G ▷ C2×C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72226852 | C2 | semidirect |
| 3. #72225341 | C2 | semidirect |
| 4. C2×#93752 | C2 | semidirect |
| 5. #72216251 | C2 | semidirect |
| 16. C2×#7459 | C22 | semidirect |
| 18. #135781 | C22 | semidirect |
| 19. C2×#7052 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72226852 | 2 |
| #72225394 | 2 |
| #72225341 | 2 |
| C2×#93752 | 2 |
| #72216251 | 2 |