Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1069 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 1069 conjugacy classes of subgroups — too many to draw. Only its 136 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 | #60773 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #33530 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#2191 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #23434 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #12119 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #12118 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11688 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#1342 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11438 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#575 | — | 2 | 1 | no | — |
| 11 | C2×#575 | C22 | 1 | 1 | yes | characteristic |
| 12 | #3489 | — | 2 | 1 | no | — |
| 13 | #3414 | — | 2 | 1 | no | — |
| 14 | C2×#510 | — | 2 | 1 | no | — |
| 15 | #3204 | C22 | 1 | 2 | yes | complemented |
| 16 | #3202 | C22 | 1 | 2 | yes | complemented |
| 17 | #3201 | — | 2 | 2 | no | — |
| 18 | #3197 | — | 2 | 1 | no | — |
| 19 | #3196 | — | 2 | 2 | no | — |
| 20 | #3195 | — | 2 | 1 | no | — |
| 21 | #3099 | — | 2 | 1 | no | — |
| 22 | #3097 | — | 2 | 1 | no | — |
| 23 | #3056 | — | 2 | 1 | no | — |
| 24 | #3054 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#470 | C22 | 1 | 1 | yes | characteristic |
| 26 | #3013 | — | 2 | 1 | no | — |
| 27 | #3011 | — | 2 | 1 | no | — |
| 28 | #2879 | — | 2 | 1 | no | — |
| 29 | #2879 | C22 | 1 | 1 | yes | characteristic |
| 30 | #2191 | — | 2 | 2 | no | — |
| 31 | #2191 | — | 2 | 1 | no | — |
| 32 | #2191 | C22 | 1 | 2 | yes | complemented |
| 33 | #2191 | C22 | 1 | 4 | yes | complemented |
| 34 | #2190 | — | 2 | 1 | no | — |
| 35 | #2190 | C22 | 1 | 2 | yes | complemented |
| 36 | #2145 | — | 2 | 1 | no | — |
| 37 | C2×#360 | — | 2 | 1 | no | — |
| 38 | C2×#349 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#349 | C22 | 1 | 1 | yes | characteristic |
| 40 | #2017 | — | 2 | 2 | no | — |
| 41 | #2017 | C22 | 1 | 4 | yes | — |
| 42 | C2×#338 | C22 | 1 | 1 | yes | characteristic |
| 43 | #1342 | C22 | 1 | 2 | yes | complemented |
| 44 | #1342 | C22 | 1 | 4 | yes | complemented |
| 45 | #1341 | C22 | 1 | 2 | yes | complemented |
| 46 | #1321 | C22 | 1 | 4 | yes | complemented |
| 47 | C2×2−1+4 | — | 2 | 1 | no | — |
| 48 | C22×#41 | — | 2 | 1 | no | — |
| 49 | C22×#41 | D4 | 1 | 1 | yes | characteristic |
| 50 | #575 | — | 2 | 4 | no | — |
| 51 | #575 | — | 2 | 1 | no | — |
| 52 | #575 | — | 2 | 1 | no | — |
| 53 | #575 | — | 2 | 1 | no | — |
| 54 | #575 | — | 4 | 2 | no | — |
| 55 | #575 | — | 4 | 2 | no | — |
| 56 | #575 | — | 4 | 2 | no | — |
| 57 | #575 | — | 4 | 2 | no | — |
| 58 | #575 | C23 | 1 | 2 | yes | — |
| 59 | C2×#137 | — | 2 | 1 | no | — |
| 60 | C2×#137 | — | 4 | 1 | no | — |
| 61 | C2×#137 | — | 4 | 1 | no | — |
| 62 | C2×#137 | — | 4 | 1 | no | — |
| 63 | C2×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 64 | C2×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 65 | C2×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 66 | C2×#135 | — | 2 | 1 | no | — |
| 67 | C2×#135 | — | 2 | 1 | no | — |
| 68 | C2×#135 | — | 4 | 2 | no | — |
| 69 | C2×#135 | D4 | 1 | 1 | yes | characteristic |
| 70 | C22×Q16 | D4 | 1 | 1 | yes | characteristic |
| 71 | C22×M16 | — | 2 | 1 | no | — |
| 72 | C22×M16 | D4 | 1 | 1 | yes | characteristic |
| 73 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 74 | D4×Q8 | — | 4 | 1 | no | — |
| 75 | #548 | — | 4 | 1 | no | — |
| 76 | #547 | — | 4 | 1 | no | — |
| 77 | #547 | — | 4 | 2 | no | — |
| 78 | #546 | — | 4 | 2 | no | — |
| 79 | #546 | — | 4 | 1 | no | — |
| 80 | #537 | — | 2 | 1 | no | — |
| 81 | #537 | — | 2 | 2 | no | — |
| 82 | #536 | — | 2 | 1 | no | — |
| 83 | #536 | — | 2 | 2 | no | — |
| 84 | #525 | — | 2 | 2 | no | — |
| 85 | #525 | — | 2 | 1 | no | — |
| 86 | C2×C22⋊Q8 | — | 2 | 2 | no | — |
| 87 | C2×C22⋊Q8 | — | 2 | 1 | no | — |
| 88 | #520 | — | 2 | 1 | no | — |
| 89 | #510 | — | 2 | 4 | no | — |
| 90 | #510 | — | 2 | 2 | no | — |
| 91 | #510 | — | 4 | 1 | no | — |
| 92 | #510 | — | 4 | 2 | no | — |
| 93 | #509 | — | 2 | 2 | no | — |
| 94 | #509 | — | 4 | 1 | no | — |
| 95 | #508 | — | 4 | 2 | no | — |
| 96 | C2×Q32 | — | 4 | 1 | no | — |
| 97 | C2×SD32 | — | 4 | 1 | no | — |
| 98 | C2×M32 | — | 2 | 1 | no | — |
| 99 | C2×M32 | — | 2 | 1 | no | — |
| 100 | #485 | — | 2 | 2 | no | — |
| 101 | #485 | — | 2 | 2 | no | — |
| 102 | #485 | — | 2 | 2 | no | — |
| 103 | #484 | — | 2 | 2 | no | — |
| 104 | #483 | — | 2 | 2 | no | — |
| 105 | #483 | — | 2 | 2 | no | — |
| 106 | #482 | — | 2 | 2 | no | — |
| 107 | #481 | — | 2 | 2 | no | — |
| 108 | #470 | — | 2 | 2 | no | — |
| 109 | #470 | — | 2 | 1 | no | — |
| 110 | #470 | — | 2 | 1 | no | — |
| 111 | #470 | D4 | 1 | 1 | yes | characteristic |
| 112 | #470 | D4 | 1 | 2 | yes | — |
| 113 | #470 | C23 | 1 | 1 | yes | characteristic |
| 114 | #470 | C23 | 1 | 2 | yes | — |
| 115 | #469 | D4 | 1 | 1 | yes | characteristic |
| 116 | #469 | C23 | 1 | 1 | yes | characteristic |
| 117 | #468 | — | 2 | 2 | no | — |
| 118 | #468 | — | 2 | 1 | no | — |
| 119 | #468 | — | 2 | 1 | no | — |
| 120 | #467 | — | 2 | 2 | no | — |
| 121 | #465 | — | 2 | 2 | no | — |
| 122 | #452 | — | 2 | 2 | no | — |
| 123 | #452 | — | 2 | 2 | no | — |
| 124 | #452 | — | 2 | 2 | no | — |
| 125 | #451 | — | 2 | 2 | no | — |
| 126 | #451 | — | 2 | 2 | no | — |
| 127 | #451 | — | 2 | 2 | no | — |
| 128 | #449 | — | 2 | 2 | no | — |
| 129 | #448 | — | 2 | 2 | no | — |
| 130 | #428 | — | 2 | 1 | no | — |
| 131 | #427 | D4 | 1 | 1 | yes | characteristic |
| 132 | C2×#106 | D4 | 1 | 1 | yes | characteristic |
| 133 | #419 | — | 2 | 1 | no | — |
| 134 | #417 | — | 2 | 1 | no | — |
| 135 | #416 | — | 2 | 1 | no | — |
| 136 | C2×#103 | — | 2 | 1 | no | — |
| 137 | #408 | — | 2 | 1 | no | — |
| 138 | #408 | — | 2 | 1 | no | — |
| 139 | #408 | — | 2 | 4 | no | — |
| 140 | #408 | — | 4 | 2 | no | — |
| 141 | #408 | D4 | 1 | 2 | yes | — |
| 142 | #408 | C23 | 1 | 2 | yes | — |
| 143 | #407 | — | 2 | 1 | no | — |
| 144 | #407 | — | 2 | 1 | no | — |
| 145 | #407 | — | 4 | 2 | no | — |
| 146 | #360 | — | 2 | 4 | no | — |
| 147 | #360 | — | 2 | 2 | no | — |
| 148 | #360 | — | 2 | 2 | no | — |
| 149 | #349 | — | 2 | 1 | no | — |
| 150 | #349 | — | 2 | 1 | no | — |
| 151 | #349 | C23 | 1 | 2 | yes | — |
| 152 | #349 | C23 | 1 | 2 | yes | — |
| 153 | #338 | — | 2 | 1 | no | — |
| 154 | #338 | C23 | 1 | 2 | yes | — |
| 155 | 2−1+4 | — | 8 | 1 | no | — |
| 156 | 2−1+4 | — | 8 | 1 | no | — |
| 157 | 2−1+4 | — | 8 | 1 | no | — |
| 158 | 2−1+4 | — | 8 | 1 | no | — |
| 159 | C2×#41 | — | 2 | 1 | no | — |
| 160 | C2×#41 | — | 2 | 1 | no | — |
| 161 | C2×#41 | — | 2 | 2 | no | — |
| 162 | C2×#41 | — | 2 | 2 | no | — |
| 163 | C2×#41 | — | 2 | 1 | no | — |
| 164 | C2×#41 | — | 2 | 2 | no | — |
| 165 | C2×#41 | — | 4 | 1 | no | — |
| 166 | C2×#41 | — | 4 | 1 | no | — |
| 167 | C2×#41 | — | 4 | 1 | no | — |
| 168 | C2×#41 | — | 4 | 1 | no | — |
| 169 | C2×#41 | — | 4 | 1 | no | — |
| 170 | C2×#41 | — | 4 | 1 | no | — |
| 171 | C2×#41 | — | 4 | 1 | no | — |
| 172 | C2×#41 | — | 4 | 1 | no | — |
| 173 | C2×#41 | — | 4 | 1 | no | — |
| 174 | C2×#41 | — | 4 | 2 | no | — |
| 175 | C2×#41 | — | 4 | 1 | no | — |
| 176 | C2×#41 | — | 4 | 1 | no | — |
| 177 | C2×#41 | — | 4 | 1 | no | — |
| 178 | C2×#41 | — | 4 | 1 | no | — |
| 179 | C2×#41 | — | 4 | 1 | no | — |
| 180 | C2×#41 | — | 4 | 1 | no | — |
| 181 | C2×#41 | D8 | 1 | 2 | yes | — |
| 182 | C2×#41 | C2×D4 | 1 | 2 | yes | — |
| 183 | C22×Q8 | — | 2 | 1 | no | — |
| 184 | C22×Q8 | — | 2 | 2 | no | — |
| 185 | C22×Q8 | — | 2 | 1 | no | — |
| 186 | C22×Q8 | — | 4 | 1 | no | — |
| 187 | C22×Q8 | D8 | 1 | 1 | yes | characteristic |
| 188 | C22×D4 | — | 2 | 1 | no | — |
| 189 | C22×D4 | — | 2 | 1 | no | — |
| 190 | C22×D4 | — | 4 | 1 | no | — |
| 191 | C22×D4 | D8 | 1 | 1 | yes | characteristic |
| 192 | C23×C4 | — | 2 | 1 | no | — |
| 193 | C23×C4 | — | 4 | 1 | no | — |
| 194 | C23×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 195 | #137 | — | 4 | 2 | no | — |
| 196 | #137 | — | 4 | 2 | no | — |
| 197 | #137 | — | 4 | 2 | no | — |
| 198 | #137 | — | 4 | 2 | no | — |
| 199 | #137 | — | 4 | 4 | no | — |
| 200 | #137 | — | 4 | 4 | no | — |
| 201 | #137 | — | 4 | 4 | no | — |
| 202 | #137 | — | 4 | 4 | no | — |
| 203 | #137 | — | 8 | 1 | no | — |
| 204 | #137 | — | 8 | 1 | no | — |
| 205 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 206 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 207 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 208 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 209 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 210 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 211 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 212 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 213 | #135 | — | 2 | 2 | no | — |
| 214 | #135 | — | 2 | 2 | no | — |
| 215 | #135 | — | 2 | 2 | no | — |
| 216 | #135 | — | 2 | 2 | no | — |
| 217 | #135 | — | 4 | 1 | no | — |
| 218 | #135 | — | 4 | 1 | no | — |
| 219 | #135 | — | 4 | 8 | no | — |
| 220 | #135 | — | 4 | 1 | no | — |
| 221 | #135 | — | 4 | 1 | no | — |
| 222 | #135 | — | 4 | 8 | no | — |
| 223 | #135 | — | 4 | 1 | no | — |
| 224 | #135 | — | 4 | 1 | no | — |
| 225 | C2×Q16 | — | 2 | 1 | no | — |
| 226 | C2×Q16 | — | 2 | 1 | no | — |
| 227 | C2×Q16 | — | 2 | 2 | no | — |
| 228 | C2×Q16 | — | 2 | 1 | no | — |
| 229 | C2×Q16 | — | 4 | 1 | no | — |
| 230 | C2×Q16 | — | 4 | 1 | no | — |
| 231 | C2×Q16 | — | 4 | 2 | no | — |
| 232 | C2×Q16 | C2×D4 | 1 | 2 | yes | — |
| 233 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 234 | C2×SD16 | — | 2 | 2 | no | — |
| 235 | C2×SD16 | — | 2 | 1 | no | — |
| 236 | C2×SD16 | — | 4 | 1 | no | — |
| 237 | C2×SD16 | — | 4 | 1 | no | — |
| 238 | C2×SD16 | — | 4 | 2 | no | — |
| 239 | C2×SD16 | — | 4 | 2 | no | — |
| 240 | C2×D8 | — | 2 | 1 | no | — |
| 241 | C2×D8 | — | 2 | 1 | no | — |
| 242 | C2×D8 | — | 4 | 2 | no | — |
| 243 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 244 | C2×M16 | — | 2 | 2 | no | — |
| 245 | C2×M16 | — | 2 | 1 | no | — |
| 246 | C2×M16 | — | 2 | 2 | no | — |
| 247 | C2×M16 | — | 2 | 1 | no | — |
| 248 | C2×M16 | — | 4 | 1 | no | — |
| 249 | C2×M16 | — | 4 | 1 | no | — |
| 250 | C2×M16 | — | 4 | 1 | no | — |
| 251 | C2×M16 | — | 4 | 1 | no | — |
| 252 | C2×M16 | — | 4 | 1 | no | — |
| 253 | C2×M16 | — | 4 | 1 | no | — |
| 254 | C2×M16 | — | 4 | 1 | no | — |
| 255 | C2×M16 | — | 4 | 1 | no | — |
| 256 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 257 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 258 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 259 | C2×M16 | C24 | 1 | 1 | yes | characteristic |
| 260 | C22×C8 | — | 2 | 2 | no | — |
| 261 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 262 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 263 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 264 | C4⋊Q8 | — | 4 | 1 | no | — |
| 265 | C4⋊Q8 | — | 4 | 2 | no | — |
| 266 | #124 | — | 4 | 2 | no | — |
| 267 | #124 | — | 4 | 1 | no | — |
| 268 | #123 | — | 4 | 2 | no | — |
| 269 | #123 | — | 4 | 2 | no | — |
| 270 | #123 | — | 4 | 2 | no | — |
| 271 | #123 | — | 4 | 2 | no | — |
| 272 | #123 | — | 4 | 1 | no | — |
| 273 | C22⋊Q8 | — | 2 | 2 | no | — |
| 274 | C22⋊Q8 | — | 2 | 2 | no | — |
| 275 | C22⋊Q8 | — | 2 | 2 | no | — |
| 276 | C22⋊Q8 | — | 2 | 1 | no | — |
| 277 | C22⋊Q8 | — | 2 | 2 | no | — |
| 278 | C22⋊Q8 | — | 2 | 2 | no | — |
| 279 | C22⋊Q8 | — | 2 | 1 | no | — |
| 280 | C22⋊Q8 | — | 4 | 2 | no | — |
| 281 | C22⋊Q8 | — | 4 | 2 | no | — |
| 282 | C22⋊Q8 | — | 4 | 1 | no | — |
| 283 | C22⋊Q8 | — | 4 | 2 | no | — |
| 284 | C22⋊Q8 | — | 4 | 1 | no | — |
| 285 | C22⋊Q8 | — | 4 | 1 | no | — |
| 286 | #121 | — | 2 | 2 | no | — |
| 287 | #121 | — | 2 | 1 | no | — |
| 288 | #121 | — | 2 | 1 | no | — |
| 289 | #121 | — | 4 | 2 | no | — |
| 290 | #121 | — | 4 | 2 | no | — |
| 291 | #121 | — | 4 | 1 | no | — |
| 292 | #121 | — | 4 | 2 | no | — |
| 293 | #121 | — | 4 | 2 | no | — |
| 294 | #120 | — | 4 | 2 | no | — |
| 295 | #120 | — | 4 | 1 | no | — |
| 296 | C4×Q8 | — | 4 | 1 | no | — |
| 297 | C4×D4 | — | 4 | 2 | no | — |
| 298 | C4×D4 | — | 4 | 2 | no | — |
| 299 | C4×D4 | — | 4 | 2 | no | — |
| 300 | C4×D4 | — | 4 | 1 | no | — |
| 301 | C4×D4 | — | 4 | 1 | no | — |
| 302 | C4×D4 | — | 4 | 1 | no | — |
| 303 | #117 | — | 2 | 2 | no | — |
| 304 | #117 | — | 2 | 1 | no | — |
| 305 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 306 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 307 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 308 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 309 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 310 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 311 | Q32 | — | 4 | 4 | no | — |
| 312 | Q32 | — | 4 | 2 | no | — |
| 313 | SD32 | — | 4 | 4 | no | — |
| 314 | SD32 | — | 4 | 2 | no | — |
| 315 | SD32 | — | 4 | 2 | no | — |
| 316 | D16 | — | 4 | 2 | no | — |
| 317 | M32 | — | 2 | 2 | no | — |
| 318 | M32 | — | 2 | 2 | no | — |
| 319 | M32 | — | 4 | 1 | no | — |
| 320 | M32 | — | 4 | 1 | no | — |
| 321 | C2×C16 | — | 4 | 1 | no | — |
| 322 | C2×C16 | — | 4 | 1 | no | — |
| 323 | #107 | — | 2 | 2 | no | — |
| 324 | #107 | — | 2 | 1 | no | — |
| 325 | #106 | — | 2 | 2 | no | — |
| 326 | #106 | — | 2 | 1 | no | — |
| 327 | #106 | C2×D4 | 1 | 2 | yes | — |
| 328 | #106 | C2×D4 | 1 | 1 | yes | characteristic |
| 329 | #106 | C2×D4 | 1 | 1 | yes | characteristic |
| 330 | #103 | — | 2 | 2 | no | — |
| 331 | #103 | — | 2 | 2 | no | — |
| 332 | #103 | — | 2 | 2 | no | — |
| 333 | #103 | — | 2 | 2 | no | — |
| 334 | #103 | — | 2 | 1 | no | — |
| 335 | #103 | — | 2 | 2 | no | — |
| 336 | #103 | — | 2 | 1 | no | — |
| 337 | #102 | — | 2 | 2 | no | — |
| 338 | #102 | — | 2 | 1 | no | — |
| 339 | #102 | — | 2 | 1 | no | — |
| 340 | C22⋊C8 | — | 2 | 2 | no | — |
| 341 | C22⋊C8 | — | 2 | 2 | no | — |
| 342 | C22⋊C8 | — | 2 | 2 | no | — |
| 343 | C22⋊C8 | — | 2 | 2 | no | — |
| 344 | C22⋊C8 | — | 4 | 8 | no | — |
| 345 | C24 | — | 2 | 1 | no | — |
| 346 | C24 | — | 4 | 1 | no | — |
| 347 | C24 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 348 | #41 | — | 4 | 2 | no | — |
| 349 | #41 | — | 4 | 2 | no | — |
| 350 | #41 | — | 4 | 2 | no | — |
| 351 | #41 | — | 4 | 2 | no | — |
| 352 | #41 | — | 4 | 2 | no | — |
| 353 | #41 | — | 4 | 2 | no | — |
| 354 | #41 | — | 4 | 2 | no | — |
| 355 | #41 | — | 4 | 2 | no | — |
| 356 | #41 | — | 4 | 2 | no | — |
| 357 | #41 | — | 4 | 1 | no | — |
| 358 | #41 | — | 4 | 1 | no | — |
| 359 | #41 | — | 4 | 1 | no | — |
| 360 | #41 | — | 4 | 1 | no | — |
| 361 | #41 | — | 4 | 2 | no | — |
| 362 | #41 | — | 4 | 2 | no | — |
| 363 | #41 | — | 4 | 1 | no | — |
| 364 | #41 | — | 4 | 1 | no | — |
| 365 | #41 | — | 4 | 2 | no | — |
| 366 | #41 | — | 4 | 1 | no | — |
| 367 | #41 | — | 4 | 1 | no | — |
| 368 | #41 | — | 8 | 1 | no | — |
| 369 | #41 | — | 8 | 1 | no | — |
| 370 | #41 | — | 8 | 1 | no | — |
| 371 | #41 | — | 8 | 1 | no | — |
| 372 | #41 | — | 8 | 1 | no | — |
| 373 | #41 | — | 8 | 1 | no | — |
| 374 | #41 | — | 8 | 1 | no | — |
| 375 | #41 | — | 8 | 2 | no | — |
| 376 | #41 | — | 8 | 2 | no | — |
| 377 | #41 | — | 8 | 4 | no | — |
| 378 | #41 | — | 8 | 4 | no | — |
| 379 | #41 | — | 8 | 2 | no | — |
| 380 | #41 | — | 8 | 2 | no | — |
| 381 | #41 | — | 8 | 1 | no | — |
| 382 | #41 | — | 8 | 1 | no | — |
| 383 | #41 | — | 8 | 1 | no | — |
| 384 | C2×Q8 | — | 2 | 1 | no | — |
| 385 | C2×Q8 | — | 2 | 2 | no | — |
| 386 | C2×Q8 | — | 2 | 2 | no | — |
| 387 | C2×Q8 | — | 2 | 1 | no | — |
| 388 | C2×Q8 | — | 4 | 2 | no | — |
| 389 | C2×Q8 | — | 4 | 1 | no | — |
| 390 | C2×Q8 | — | 4 | 1 | no | — |
| 391 | C2×Q8 | — | 4 | 1 | no | — |
| 392 | C2×Q8 | — | 4 | 1 | no | — |
| 393 | C2×Q8 | — | 4 | 1 | no | — |
| 394 | C2×Q8 | — | 4 | 1 | no | — |
| 395 | C2×Q8 | — | 4 | 1 | no | — |
| 396 | C2×Q8 | — | 4 | 1 | no | — |
| 397 | C2×Q8 | — | 4 | 1 | no | — |
| 398 | C2×Q8 | — | 4 | 1 | no | — |
| 399 | C2×Q8 | — | 4 | 1 | no | — |
| 400 | C2×Q8 | — | 4 | 1 | no | — |
| 401 | C2×Q8 | — | 8 | 2 | no | — |
| 402 | C2×Q8 | — | 8 | 2 | no | — |
| 403 | C2×Q8 | — | 8 | 2 | no | — |
| 404 | C2×Q8 | — | 8 | 2 | no | — |
| 405 | C2×Q8 | C2×D8 | 1 | 2 | yes | — |
| 406 | C2×D4 | — | 2 | 2 | no | — |
| 407 | C2×D4 | — | 2 | 2 | no | — |
| 408 | C2×D4 | — | 2 | 2 | no | — |
| 409 | C2×D4 | — | 2 | 1 | no | — |
| 410 | C2×D4 | — | 2 | 1 | no | — |
| 411 | C2×D4 | — | 4 | 1 | no | — |
| 412 | C2×D4 | — | 4 | 1 | no | — |
| 413 | C2×D4 | — | 4 | 1 | no | — |
| 414 | C2×D4 | — | 4 | 1 | no | — |
| 415 | C2×D4 | — | 4 | 1 | no | — |
| 416 | C2×D4 | — | 4 | 1 | no | — |
| 417 | C2×D4 | — | 4 | 2 | no | — |
| 418 | C2×D4 | — | 4 | 2 | no | — |
| 419 | C2×D4 | — | 4 | 2 | no | — |
| 420 | C2×D4 | — | 4 | 1 | no | — |
| 421 | C2×D4 | — | 4 | 1 | no | — |
| 422 | C2×D4 | — | 4 | 2 | no | — |
| 423 | C2×D4 | — | 4 | 1 | no | — |
| 424 | C2×D4 | — | 4 | 1 | no | — |
| 425 | C2×D4 | — | 8 | 1 | no | — |
| 426 | C2×D4 | — | 8 | 1 | no | — |
| 427 | C2×D4 | — | 8 | 1 | no | — |
| 428 | C2×D4 | — | 8 | 1 | no | — |
| 429 | C2×D4 | — | 8 | 1 | no | — |
| 430 | C2×D4 | — | 8 | 1 | no | — |
| 431 | C2×D4 | C2×D8 | 1 | 2 | yes | — |
| 432 | C22×C4 | — | 2 | 1 | no | — |
| 433 | C22×C4 | — | 2 | 1 | no | — |
| 434 | C22×C4 | — | 2 | 1 | no | — |
| 435 | C22×C4 | — | 2 | 1 | no | — |
| 436 | C22×C4 | — | 2 | 1 | no | — |
| 437 | C22×C4 | — | 2 | 2 | no | — |
| 438 | C22×C4 | — | 2 | 2 | no | — |
| 439 | C22×C4 | — | 4 | 2 | no | — |
| 440 | C22×C4 | — | 4 | 2 | no | — |
| 441 | C22×C4 | — | 4 | 2 | no | — |
| 442 | C22×C4 | — | 4 | 2 | no | — |
| 443 | C22×C4 | — | 4 | 1 | no | — |
| 444 | C22×C4 | — | 4 | 1 | no | — |
| 445 | C22×C4 | — | 4 | 2 | no | — |
| 446 | C22×C4 | — | 4 | 1 | no | — |
| 447 | C22×C4 | — | 4 | 1 | no | — |
| 448 | C22×C4 | — | 8 | 1 | no | — |
| 449 | C22×C4 | — | 8 | 1 | no | — |
| 450 | C22×C4 | — | 8 | 1 | no | — |
| 451 | C22×C4 | — | 8 | 1 | no | — |
| 452 | C22×C4 | — | 8 | 1 | no | — |
| 453 | C22×C4 | — | 8 | 1 | no | — |
| 454 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 455 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 456 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 457 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 458 | C22×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 459 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 460 | Q16 | — | 2 | 2 | no | — |
| 461 | Q16 | — | 2 | 2 | no | — |
| 462 | Q16 | — | 4 | 2 | no | — |
| 463 | Q16 | — | 4 | 1 | no | — |
| 464 | Q16 | — | 4 | 1 | no | — |
| 465 | Q16 | — | 4 | 1 | no | — |
| 466 | Q16 | — | 4 | 8 | no | — |
| 467 | Q16 | — | 8 | 1 | no | — |
| 468 | Q16 | — | 8 | 2 | no | — |
| 469 | SD16 | — | 4 | 2 | no | — |
| 470 | SD16 | — | 4 | 2 | no | — |
| 471 | SD16 | — | 4 | 2 | no | — |
| 472 | SD16 | — | 4 | 2 | no | — |
| 473 | SD16 | — | 4 | 8 | no | — |
| 474 | SD16 | — | 4 | 8 | no | — |
| 475 | SD16 | — | 8 | 1 | no | — |
| 476 | SD16 | — | 8 | 2 | no | — |
| 477 | D8 | — | 2 | 2 | no | — |
| 478 | D8 | — | 2 | 2 | no | — |
| 479 | D8 | — | 4 | 1 | no | — |
| 480 | D8 | — | 4 | 1 | no | — |
| 481 | D8 | — | 4 | 1 | no | — |
| 482 | D8 | — | 4 | 8 | no | — |
| 483 | M16 | — | 4 | 1 | no | — |
| 484 | M16 | — | 4 | 1 | no | — |
| 485 | M16 | — | 4 | 1 | no | — |
| 486 | M16 | — | 4 | 1 | no | — |
| 487 | M16 | — | 4 | 2 | no | — |
| 488 | M16 | — | 4 | 2 | no | — |
| 489 | M16 | — | 4 | 2 | no | — |
| 490 | M16 | — | 4 | 2 | no | — |
| 491 | M16 | — | 4 | 1 | no | — |
| 492 | M16 | — | 4 | 1 | no | — |
| 493 | M16 | — | 8 | 1 | no | — |
| 494 | C2×C8 | — | 2 | 1 | no | — |
| 495 | C2×C8 | — | 2 | 1 | no | — |
| 496 | C2×C8 | — | 2 | 1 | no | — |
| 497 | C2×C8 | — | 2 | 1 | no | — |
| 498 | C2×C8 | — | 2 | 4 | no | — |
| 499 | C2×C8 | — | 2 | 2 | no | — |
| 500 | C2×C8 | — | 4 | 2 | no | — |
| 501 | C2×C8 | — | 4 | 2 | no | — |
| 502 | C2×C8 | — | 4 | 2 | no | — |
| 503 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 504 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 505 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 506 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 507 | C4⋊C4 | — | 2 | 2 | no | — |
| 508 | C4⋊C4 | — | 2 | 1 | no | — |
| 509 | C4⋊C4 | — | 2 | 1 | no | — |
| 510 | C4⋊C4 | — | 4 | 2 | no | — |
| 511 | C4⋊C4 | — | 4 | 2 | no | — |
| 512 | C4⋊C4 | — | 4 | 2 | no | — |
| 513 | C4⋊C4 | — | 4 | 2 | no | — |
| 514 | C4⋊C4 | — | 4 | 2 | no | — |
| 515 | C4⋊C4 | — | 4 | 1 | no | — |
| 516 | C4⋊C4 | — | 4 | 1 | no | — |
| 517 | C4⋊C4 | — | 4 | 1 | no | — |
| 518 | C4⋊C4 | — | 4 | 2 | no | — |
| 519 | C22⋊C4 | — | 4 | 2 | no | — |
| 520 | C22⋊C4 | — | 4 | 2 | no | — |
| 521 | C22⋊C4 | — | 4 | 2 | no | — |
| 522 | C22⋊C4 | — | 4 | 2 | no | — |
| 523 | C22⋊C4 | — | 4 | 2 | no | — |
| 524 | C22⋊C4 | — | 4 | 2 | no | — |
| 525 | C22⋊C4 | — | 4 | 1 | no | — |
| 526 | C22⋊C4 | — | 4 | 1 | no | — |
| 527 | C22⋊C4 | — | 4 | 2 | no | — |
| 528 | C22⋊C4 | — | 4 | 1 | no | — |
| 529 | C22⋊C4 | — | 4 | 1 | no | — |
| 530 | C22⋊C4 | — | 4 | 1 | no | — |
| 531 | C42 | — | 4 | 2 | no | — |
| 532 | C42 | — | 4 | 1 | no | — |
| 533 | C16 | — | 4 | 2 | no | — |
| 534 | C16 | — | 4 | 2 | no | — |
| 535 | C23 | — | 2 | 1 | no | — |
| 536 | C23 | — | 2 | 1 | no | — |
| 537 | C23 | — | 2 | 2 | no | — |
| 538 | C23 | — | 4 | 2 | no | — |
| 539 | C23 | — | 4 | 1 | no | — |
| 540 | C23 | — | 8 | 1 | no | — |
| 541 | C23 | — | 8 | 1 | no | — |
| 542 | C23 | — | 8 | 1 | no | — |
| 543 | C23 | — | 8 | 2 | no | — |
| 544 | C23 | — | 8 | 1 | no | — |
| 545 | C23 | — | 16 | 2 | no | — |
| 546 | C23 | #447 | 1 | 1 | yes | characteristic |
| 547 | C23 | #447 | 1 | 1 | yes | characteristic |
| 548 | C23 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 549 | Q8 | — | 4 | 2 | no | — |
| 550 | Q8 | — | 4 | 2 | no | — |
| 551 | Q8 | — | 4 | 1 | no | — |
| 552 | Q8 | — | 4 | 1 | no | — |
| 553 | Q8 | — | 4 | 2 | no | — |
| 554 | Q8 | — | 4 | 1 | no | — |
| 555 | Q8 | — | 4 | 2 | no | — |
| 556 | Q8 | — | 4 | 1 | no | — |
| 557 | Q8 | — | 4 | 2 | no | — |
| 558 | Q8 | — | 8 | 1 | no | — |
| 559 | Q8 | — | 8 | 4 | no | — |
| 560 | Q8 | — | 8 | 1 | no | — |
| 561 | Q8 | — | 8 | 1 | no | — |
| 562 | Q8 | — | 8 | 1 | no | — |
| 563 | D4 | — | 4 | 2 | no | — |
| 564 | D4 | — | 4 | 2 | no | — |
| 565 | D4 | — | 4 | 2 | no | — |
| 566 | D4 | — | 4 | 2 | no | — |
| 567 | D4 | — | 4 | 1 | no | — |
| 568 | D4 | — | 4 | 1 | no | — |
| 569 | D4 | — | 4 | 1 | no | — |
| 570 | D4 | — | 4 | 2 | no | — |
| 571 | D4 | — | 4 | 1 | no | — |
| 572 | D4 | — | 8 | 1 | no | — |
| 573 | D4 | — | 8 | 2 | no | — |
| 574 | D4 | — | 8 | 2 | no | — |
| 575 | D4 | — | 8 | 2 | no | — |
| 576 | D4 | — | 8 | 2 | no | — |
| 577 | D4 | — | 8 | 4 | no | — |
| 578 | D4 | — | 8 | 2 | no | — |
| 579 | D4 | — | 8 | 1 | no | — |
| 580 | D4 | — | 8 | 1 | no | — |
| 581 | D4 | — | 8 | 2 | no | — |
| 582 | D4 | — | 8 | 1 | no | — |
| 583 | D4 | — | 16 | 1 | no | — |
| 584 | D4 | — | 16 | 2 | no | — |
| 585 | C2×C4 | — | 2 | 1 | no | — |
| 586 | C2×C4 | — | 2 | 1 | no | — |
| 587 | C2×C4 | — | 2 | 1 | no | — |
| 588 | C2×C4 | — | 2 | 1 | no | — |
| 589 | C2×C4 | — | 2 | 1 | no | — |
| 590 | C2×C4 | — | 2 | 1 | no | — |
| 591 | C2×C4 | — | 2 | 1 | no | — |
| 592 | C2×C4 | — | 2 | 1 | no | — |
| 593 | C2×C4 | — | 2 | 1 | no | — |
| 594 | C2×C4 | — | 2 | 1 | no | — |
| 595 | C2×C4 | — | 2 | 2 | no | — |
| 596 | C2×C4 | — | 4 | 2 | no | — |
| 597 | C2×C4 | — | 4 | 2 | no | — |
| 598 | C2×C4 | — | 4 | 2 | no | — |
| 599 | C2×C4 | — | 4 | 1 | no | — |
| 600 | C2×C4 | — | 4 | 2 | no | — |
| 601 | C2×C4 | — | 4 | 1 | no | — |
| 602 | C2×C4 | — | 4 | 1 | no | — |
| 603 | C2×C4 | — | 4 | 2 | no | — |
| 604 | C2×C4 | — | 8 | 2 | no | — |
| 605 | C2×C4 | — | 8 | 2 | no | — |
| 606 | C2×C4 | — | 8 | 2 | no | — |
| 607 | C2×C4 | — | 8 | 1 | no | — |
| 608 | C2×C4 | — | 8 | 4 | no | — |
| 609 | C2×C4 | — | 8 | 1 | no | — |
| 610 | C2×C4 | — | 8 | 4 | no | — |
| 611 | C2×C4 | — | 8 | 1 | no | — |
| 612 | C2×C4 | — | 8 | 1 | no | — |
| 613 | C2×C4 | — | 8 | 1 | no | — |
| 614 | C2×C4 | — | 8 | 2 | no | — |
| 615 | C2×C4 | — | 8 | 1 | no | — |
| 616 | C2×C4 | — | 8 | 1 | no | — |
| 617 | C2×C4 | — | 8 | 2 | no | — |
| 618 | C2×C4 | — | 16 | 1 | no | — |
| 619 | C2×C4 | — | 16 | 2 | no | — |
| 620 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 621 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 622 | C2×C4 | #453 | 1 | 1 | yes | characteristic |
| 623 | C2×C4 | #453 | 1 | 1 | yes | characteristic |
| 624 | C2×C4 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 625 | C2×C4 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 626 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 627 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 628 | C8 | — | 2 | 1 | no | — |
| 629 | C8 | — | 2 | 1 | no | — |
| 630 | C8 | — | 2 | 1 | no | — |
| 631 | C8 | — | 2 | 1 | no | — |
| 632 | C8 | — | 4 | 4 | no | — |
| 633 | C8 | — | 4 | 2 | no | — |
| 634 | C22 | — | 2 | 1 | no | — |
| 635 | C22 | — | 2 | 1 | no | — |
| 636 | C22 | — | 4 | 1 | no | — |
| 637 | C22 | — | 4 | 1 | no | — |
| 638 | C22 | — | 4 | 1 | no | — |
| 639 | C22 | — | 4 | 2 | no | — |
| 640 | C22 | — | 4 | 2 | no | — |
| 641 | C22 | — | 4 | 2 | no | — |
| 642 | C22 | — | 8 | 1 | no | — |
| 643 | C22 | — | 8 | 1 | no | — |
| 644 | C22 | — | 8 | 1 | no | — |
| 645 | C22 | — | 8 | 1 | no | — |
| 646 | C22 | — | 8 | 4 | no | — |
| 647 | C22 | — | 8 | 1 | no | — |
| 648 | C22 | — | 8 | 2 | no | — |
| 649 | C22 | — | 16 | 2 | no | — |
| 650 | C22 | — | 16 | 2 | no | — |
| 651 | C22 | — | 16 | 2 | no | — |
| 652 | C22 | #1595 | 1 | 1 | yes | characteristic |
| 653 | C22 | #1595 | 1 | 1 | yes | characteristic |
| 654 | C22 | C2×#447 | 1 | 1 | yes | characteristic |
| 655 | C4 | — | 2 | 1 | no | — |
| 656 | C4 | — | 2 | 1 | no | — |
| 657 | C4 | — | 4 | 2 | no | — |
| 658 | C4 | — | 8 | 2 | no | — |
| 659 | C4 | — | 8 | 1 | no | — |
| 660 | C4 | — | 8 | 1 | no | — |
| 661 | C4 | — | 8 | 2 | no | — |
| 662 | C4 | — | 8 | 2 | no | — |
| 663 | C4 | — | 8 | 1 | no | — |
| 664 | C4 | #1595 | 1 | 1 | yes | characteristic |
| 665 | C4 | #1595 | 1 | 1 | yes | characteristic |
| 666 | C4 | C2×#453 | 1 | 1 | yes | characteristic |
| 667 | C4 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 668 | C2 | — | 2 | 1 | no | — |
| 669 | C2 | — | 2 | 1 | no | — |
| 670 | C2 | — | 2 | 1 | no | — |
| 671 | C2 | — | 4 | 1 | no | — |
| 672 | C2 | — | 4 | 1 | no | — |
| 673 | C2 | — | 8 | 2 | no | — |
| 674 | C2 | — | 16 | 1 | no | — |
| 675 | C2 | — | 16 | 2 | no | — |
| 676 | C2 | C2×#1595 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C2×#1595 |
| commutator, Frattini, cosocle | C2×M16 | C24 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ C22×M16 ◁ G | |
| LECS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #60773 | C2 | semidirect |
| 2. #33530 | C2 | semidirect |
| 3. C2×#2191 | C2 | semidirect |
| 4. #23434 | C2 | semidirect |
| 5. #12119 | C2 | semidirect |
| 6. #12118 | C2 | semidirect |
| 7. #11688 | C2 | semidirect |
| 8. C2×#1342 | C2 | semidirect |
| 9. #11438 | C2 | semidirect |
| 15. #3204 | C22 | semidirect |
| 16. #3202 | C22 | semidirect |
| 32. #2191 | C22 | semidirect |
| 33. #2191 | C22 | semidirect |
| 35. #2190 | C22 | semidirect |
| 43. #1342 | C22 | semidirect |
| 44. #1342 | C22 | semidirect |
| 45. #1341 | C22 | semidirect |
| 46. #1321 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #60773 | 2 |
| #33530 | 2 |
| C2×#2191 | 2 |
| #23434 | 2 |
| #12119 | 2 |
| #12118 | 2 |
| #11688 | 2 |
| C2×#1342 | 2 |
| #11438 | 2 |