Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
590 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 50 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 | #33568 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #33558 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #31072 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13569 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13565 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #8528 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #7502 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #3545 | C22 | 1 | 1 | yes | characteristic |
| 9 | #3026 | — | 2 | 1 | no | — |
| 10 | #3020 | — | 2 | 1 | no | — |
| 11 | C2×#454 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#455 | C22 | 1 | 1 | yes | characteristic |
| 13 | #3013 | — | 2 | 1 | no | — |
| 14 | #3012 | — | 2 | 1 | no | — |
| 15 | #2204 | — | 2 | 2 | no | — |
| 16 | #2203 | — | 2 | 1 | no | — |
| 17 | #2202 | — | 2 | 1 | no | — |
| 18 | #2201 | — | 2 | 1 | no | — |
| 19 | #2199 | — | 2 | 1 | no | — |
| 20 | #2197 | — | 2 | 2 | no | — |
| 21 | #2133 | — | 2 | 1 | no | — |
| 22 | C2×#355 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#354 | C22 | 1 | 1 | yes | characteristic |
| 24 | #2121 | — | 2 | 1 | no | — |
| 25 | #2052 | — | 2 | 1 | no | — |
| 26 | #2051 | — | 2 | 1 | no | — |
| 27 | #2040 | — | 2 | 1 | no | — |
| 28 | #1974 | — | 2 | 1 | no | — |
| 29 | #1958 | C22 | 1 | 1 | yes | characteristic |
| 30 | #1533 | C22 | 1 | 1 | yes | characteristic |
| 31 | #1512 | — | 2 | 1 | no | — |
| 32 | #1494 | — | 2 | 1 | no | — |
| 33 | #1404 | — | 2 | 2 | no | — |
| 34 | #1403 | — | 2 | 2 | no | — |
| 35 | C2×2−1+4 | D4 | 1 | 1 | yes | characteristic, complemented |
| 36 | C2×H(5,𝔽2) | D4 | 1 | 1 | yes | characteristic |
| 37 | #575 | — | 4 | 1 | no | — |
| 38 | C2×#137 | — | 2 | 1 | no | — |
| 39 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 40 | C2×#135 | — | 2 | 1 | no | — |
| 41 | #563 | D4 | 1 | 1 | yes | characteristic, complemented |
| 42 | #562 | — | 2 | 1 | no | — |
| 43 | H(3,𝔽4) | D4 | 1 | 1 | yes | characteristic, complemented |
| 44 | #555 | — | 2 | 1 | no | — |
| 45 | #551 | — | 2 | 1 | no | — |
| 46 | #551 | — | 4 | 1 | no | — |
| 47 | #546 | — | 4 | 1 | no | — |
| 48 | #542 | — | 4 | 1 | no | — |
| 49 | #538 | — | 4 | 1 | no | — |
| 50 | #537 | — | 2 | 1 | no | — |
| 51 | #536 | — | 2 | 1 | no | — |
| 52 | #534 | — | 2 | 1 | no | — |
| 53 | #534 | — | 4 | 1 | no | — |
| 54 | #529 | — | 2 | 1 | no | — |
| 55 | C2×#124 | C23 | 1 | 1 | yes | characteristic |
| 56 | #458 | — | 2 | 2 | no | — |
| 57 | #458 | — | 4 | 1 | no | — |
| 58 | B(4,𝔽2) | — | 2 | 2 | no | — |
| 59 | B(4,𝔽2) | — | 4 | 1 | no | — |
| 60 | #456 | — | 2 | 2 | no | — |
| 61 | #456 | — | 4 | 1 | no | — |
| 62 | #455 | — | 2 | 1 | no | — |
| 63 | #455 | — | 2 | 1 | no | — |
| 64 | #455 | — | 2 | 1 | no | — |
| 65 | #455 | — | 2 | 1 | no | — |
| 66 | #454 | — | 2 | 2 | no | — |
| 67 | #454 | — | 2 | 1 | no | — |
| 68 | #454 | — | 2 | 1 | no | — |
| 69 | #454 | — | 2 | 1 | no | — |
| 70 | #454 | — | 2 | 1 | no | — |
| 71 | #454 | — | 4 | 1 | no | — |
| 72 | #452 | — | 4 | 1 | no | — |
| 73 | #452 | — | 4 | 1 | no | — |
| 74 | #451 | — | 4 | 1 | no | — |
| 75 | #450 | — | 4 | 1 | no | — |
| 76 | #449 | — | 4 | 1 | no | — |
| 77 | #449 | — | 4 | 1 | no | — |
| 78 | #448 | — | 4 | 1 | no | — |
| 79 | #447 | — | 4 | 1 | no | — |
| 80 | #432 | — | 2 | 1 | no | — |
| 81 | C2×#108 | — | 2 | 1 | no | — |
| 82 | #421 | — | 4 | 1 | no | — |
| 83 | C2×#104 | — | 2 | 1 | no | — |
| 84 | C2×#104 | — | 2 | 1 | no | — |
| 85 | #417 | — | 2 | 1 | no | — |
| 86 | #417 | — | 2 | 1 | no | — |
| 87 | C2×#103 | — | 2 | 1 | no | — |
| 88 | C2×#102 | — | 2 | 1 | no | — |
| 89 | C2×#101 | — | 2 | 1 | no | — |
| 90 | C2×#101 | D4 | 1 | 1 | yes | characteristic, complemented |
| 91 | C2×#100 | D4 | 1 | 1 | yes | characteristic |
| 92 | C2×#99 | — | 2 | 1 | no | — |
| 93 | C2×#99 | — | 4 | 1 | no | — |
| 94 | #408 | — | 2 | 1 | no | — |
| 95 | #408 | — | 2 | 1 | no | — |
| 96 | C2×C4×C8 | D4 | 1 | 1 | yes | characteristic, complemented |
| 97 | #382 | D4 | 1 | 1 | yes | characteristic, complemented |
| 98 | #356 | — | 2 | 2 | no | — |
| 99 | #355 | — | 2 | 2 | no | — |
| 100 | #355 | — | 2 | 1 | no | — |
| 101 | #355 | D4 | 1 | 2 | yes | complemented |
| 102 | #354 | — | 2 | 1 | no | — |
| 103 | #354 | D4 | 1 | 2 | yes | complemented |
| 104 | #352 | — | 2 | 2 | no | — |
| 105 | AΣL(1,𝔽16) | — | 2 | 2 | no | — |
| 106 | #343 | — | 2 | 1 | no | — |
| 107 | #329 | — | 2 | 1 | no | — |
| 108 | #329 | — | 2 | 1 | no | — |
| 109 | #328 | — | 4 | 1 | no | — |
| 110 | #327 | — | 4 | 1 | no | — |
| 111 | Q8⋊C8 | — | 4 | 1 | no | — |
| 112 | D4⋊C8 | — | 4 | 1 | no | — |
| 113 | 2−1+4 | — | 2 | 1 | no | — |
| 114 | 2−1+4 | — | 2 | 1 | no | — |
| 115 | 2−1+4 | — | 4 | 1 | no | — |
| 116 | 2−1+4 | — | 8 | 1 | no | — |
| 117 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 118 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 119 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 120 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 121 | C2×#41 | — | 2 | 1 | no | — |
| 122 | C2×#41 | — | 2 | 1 | no | — |
| 123 | C2×#41 | — | 2 | 1 | no | — |
| 124 | C2×#41 | — | 4 | 1 | no | — |
| 125 | C2×#41 | — | 4 | 1 | no | — |
| 126 | C2×#41 | — | 4 | 1 | no | — |
| 127 | C22×Q8 | — | 4 | 1 | no | — |
| 128 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C22×D4 | — | 2 | 1 | no | — |
| 130 | C22×D4 | — | 4 | 1 | no | — |
| 131 | C22×D4 | — | 4 | 1 | no | — |
| 132 | C22×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | #137 | — | 4 | 2 | no | — |
| 134 | #137 | — | 4 | 1 | no | — |
| 135 | #137 | — | 4 | 1 | no | — |
| 136 | #137 | — | 8 | 1 | no | — |
| 137 | #137 | — | 8 | 1 | no | — |
| 138 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 139 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 140 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 141 | AGL(1,ℤ/8) | — | 8 | 1 | no | — |
| 142 | AGL(1,ℤ/8) | — | 8 | 1 | no | — |
| 143 | #135 | — | 8 | 1 | no | — |
| 144 | #135 | — | 8 | 1 | no | — |
| 145 | #135 | — | 8 | 2 | no | — |
| 146 | C2×Q16 | — | 2 | 1 | no | — |
| 147 | C2×Q16 | — | 4 | 1 | no | — |
| 148 | C2×SD16 | — | 2 | 1 | no | — |
| 149 | C2×SD16 | — | 2 | 1 | no | — |
| 150 | C2×SD16 | — | 4 | 1 | no | — |
| 151 | C2×SD16 | — | 4 | 1 | no | — |
| 152 | C2×D8 | — | 2 | 1 | no | — |
| 153 | C2×D8 | — | 4 | 1 | no | — |
| 154 | C2×M16 | — | 2 | 1 | no | — |
| 155 | C2×M16 | — | 2 | 1 | no | — |
| 156 | C2×M16 | — | 4 | 1 | no | — |
| 157 | C22×C8 | — | 2 | 1 | no | — |
| 158 | C4⋊Q8 | — | 2 | 1 | no | — |
| 159 | C4⋊Q8 | — | 2 | 1 | no | — |
| 160 | #126 | — | 4 | 1 | no | — |
| 161 | #126 | — | 4 | 1 | no | — |
| 162 | #126 | — | 4 | 1 | no | — |
| 163 | #125 | — | 2 | 1 | no | — |
| 164 | #124 | — | 2 | 1 | no | — |
| 165 | #124 | — | 2 | 1 | no | — |
| 166 | #124 | — | 2 | 1 | no | — |
| 167 | #124 | — | 4 | 1 | no | — |
| 168 | #124 | — | 4 | 1 | no | — |
| 169 | #124 | — | 4 | 1 | no | — |
| 170 | #124 | C2×D4 | 1 | 1 | yes | characteristic |
| 171 | #124 | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | #124 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | #124 | #41 | 1 | 1 | yes | characteristic |
| 174 | #123 | — | 2 | 1 | no | — |
| 175 | #123 | — | 2 | 1 | no | — |
| 176 | #123 | — | 4 | 1 | no | — |
| 177 | #123 | — | 4 | 1 | no | — |
| 178 | #123 | — | 4 | 1 | no | — |
| 179 | #123 | — | 4 | 1 | no | — |
| 180 | #123 | — | 4 | 1 | no | — |
| 181 | #123 | — | 4 | 2 | no | — |
| 182 | #123 | — | 8 | 1 | no | — |
| 183 | C22⋊Q8 | — | 2 | 1 | no | — |
| 184 | C22⋊Q8 | — | 4 | 1 | no | — |
| 185 | C22⋊Q8 | — | 4 | 1 | no | — |
| 186 | C22⋊Q8 | — | 4 | 1 | no | — |
| 187 | C22⋊Q8 | — | 4 | 1 | no | — |
| 188 | C22⋊Q8 | — | 4 | 1 | no | — |
| 189 | C22⋊Q8 | — | 4 | 1 | no | — |
| 190 | #121 | — | 2 | 1 | no | — |
| 191 | #121 | — | 4 | 1 | no | — |
| 192 | #121 | — | 4 | 1 | no | — |
| 193 | #121 | — | 4 | 1 | no | — |
| 194 | #121 | — | 4 | 1 | no | — |
| 195 | #121 | — | 4 | 1 | no | — |
| 196 | #121 | — | 4 | 1 | no | — |
| 197 | #121 | — | 8 | 1 | no | — |
| 198 | #121 | — | 8 | 2 | no | — |
| 199 | #120 | — | 2 | 1 | no | — |
| 200 | #120 | — | 2 | 1 | no | — |
| 201 | #120 | — | 4 | 1 | no | — |
| 202 | #120 | — | 4 | 1 | no | — |
| 203 | #120 | — | 4 | 2 | no | — |
| 204 | #120 | — | 8 | 1 | no | — |
| 205 | C4×Q8 | — | 2 | 1 | no | — |
| 206 | C4×D4 | — | 2 | 1 | no | — |
| 207 | C4×D4 | — | 4 | 1 | no | — |
| 208 | C4×D4 | — | 4 | 1 | no | — |
| 209 | C4×D4 | — | 4 | 1 | no | — |
| 210 | #117 | — | 2 | 1 | no | — |
| 211 | #117 | — | 4 | 1 | no | — |
| 212 | #117 | — | 4 | 1 | no | — |
| 213 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 214 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 215 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 216 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 217 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 218 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 219 | #108 | — | 8 | 1 | no | — |
| 220 | C4⋊C8 | — | 4 | 1 | no | — |
| 221 | #104 | — | 4 | 2 | no | — |
| 222 | #104 | — | 4 | 2 | no | — |
| 223 | #104 | — | 4 | 1 | no | — |
| 224 | #104 | — | 4 | 1 | no | — |
| 225 | #104 | — | 4 | 1 | no | — |
| 226 | #104 | — | 4 | 1 | no | — |
| 227 | #103 | — | 4 | 1 | no | — |
| 228 | #103 | — | 4 | 1 | no | — |
| 229 | #103 | — | 4 | 1 | no | — |
| 230 | #103 | — | 4 | 1 | no | — |
| 231 | #102 | — | 4 | 1 | no | — |
| 232 | #102 | — | 4 | 1 | no | — |
| 233 | #102 | — | 4 | 1 | no | — |
| 234 | #102 | — | 4 | 1 | no | — |
| 235 | #101 | — | 2 | 2 | no | — |
| 236 | #101 | — | 2 | 1 | no | — |
| 237 | #101 | — | 2 | 1 | no | — |
| 238 | #101 | — | 4 | 1 | no | — |
| 239 | #100 | — | 2 | 1 | no | — |
| 240 | #100 | — | 2 | 1 | no | — |
| 241 | #99 | — | 2 | 2 | no | — |
| 242 | #99 | — | 4 | 2 | no | — |
| 243 | #99 | — | 4 | 2 | no | — |
| 244 | #99 | — | 4 | 1 | no | — |
| 245 | C22⋊C8 | — | 4 | 1 | no | — |
| 246 | C22⋊C8 | — | 4 | 1 | no | — |
| 247 | C22⋊C8 | — | 4 | 1 | no | — |
| 248 | C22⋊C8 | — | 4 | 1 | no | — |
| 249 | C22⋊C8 | — | 4 | 1 | no | — |
| 250 | #97 | — | 4 | 1 | no | — |
| 251 | C4×C8 | — | 4 | 1 | no | — |
| 252 | #95 | — | 4 | 1 | no | — |
| 253 | C24 | — | 2 | 1 | no | — |
| 254 | C24 | — | 2 | 1 | no | — |
| 255 | C24 | — | 4 | 1 | no | — |
| 256 | #41 | — | 4 | 2 | no | — |
| 257 | #41 | — | 4 | 1 | no | — |
| 258 | #41 | — | 4 | 1 | no | — |
| 259 | #41 | — | 4 | 1 | no | — |
| 260 | #41 | — | 4 | 1 | no | — |
| 261 | #41 | — | 4 | 2 | no | — |
| 262 | #41 | — | 4 | 1 | no | — |
| 263 | #41 | — | 4 | 1 | no | — |
| 264 | #41 | — | 4 | 1 | no | — |
| 265 | #41 | — | 4 | 1 | no | — |
| 266 | #41 | — | 8 | 1 | no | — |
| 267 | #41 | — | 8 | 1 | no | — |
| 268 | #41 | — | 8 | 2 | no | — |
| 269 | #41 | — | 8 | 1 | no | — |
| 270 | #41 | — | 8 | 1 | no | — |
| 271 | #41 | — | 8 | 1 | no | — |
| 272 | #41 | — | 8 | 1 | no | — |
| 273 | #41 | — | 8 | 2 | no | — |
| 274 | #41 | — | 8 | 1 | no | — |
| 275 | #41 | — | 8 | 1 | no | — |
| 276 | C2×Q8 | — | 2 | 1 | no | — |
| 277 | C2×Q8 | — | 2 | 1 | no | — |
| 278 | C2×Q8 | — | 2 | 1 | no | — |
| 279 | C2×Q8 | — | 2 | 1 | no | — |
| 280 | C2×Q8 | — | 2 | 1 | no | — |
| 281 | C2×Q8 | — | 4 | 1 | no | — |
| 282 | C2×Q8 | — | 4 | 1 | no | — |
| 283 | C2×Q8 | — | 4 | 1 | no | — |
| 284 | C2×Q8 | — | 8 | 1 | no | — |
| 285 | C2×Q8 | — | 8 | 1 | no | — |
| 286 | C2×Q8 | — | 8 | 2 | no | — |
| 287 | C2×Q8 | #120 | 1 | 1 | yes | characteristic |
| 288 | C2×Q8 | #121 | 1 | 1 | yes | characteristic |
| 289 | C2×D4 | — | 2 | 1 | no | — |
| 290 | C2×D4 | — | 2 | 1 | no | — |
| 291 | C2×D4 | — | 2 | 1 | no | — |
| 292 | C2×D4 | — | 2 | 1 | no | — |
| 293 | C2×D4 | — | 2 | 1 | no | — |
| 294 | C2×D4 | — | 4 | 1 | no | — |
| 295 | C2×D4 | — | 4 | 1 | no | — |
| 296 | C2×D4 | — | 4 | 1 | no | — |
| 297 | C2×D4 | — | 4 | 2 | no | — |
| 298 | C2×D4 | — | 4 | 2 | no | — |
| 299 | C2×D4 | — | 4 | 1 | no | — |
| 300 | C2×D4 | — | 4 | 1 | no | — |
| 301 | C2×D4 | — | 4 | 1 | no | — |
| 302 | C2×D4 | — | 4 | 1 | no | — |
| 303 | C2×D4 | — | 4 | 1 | no | — |
| 304 | C2×D4 | — | 4 | 1 | no | — |
| 305 | C2×D4 | — | 8 | 1 | no | — |
| 306 | C2×D4 | — | 8 | 1 | no | — |
| 307 | C2×D4 | — | 8 | 1 | no | — |
| 308 | C2×D4 | — | 8 | 2 | no | — |
| 309 | C2×D4 | — | 8 | 1 | no | — |
| 310 | C2×D4 | — | 8 | 1 | no | — |
| 311 | C2×D4 | — | 8 | 1 | no | — |
| 312 | C2×D4 | — | 8 | 1 | no | — |
| 313 | C2×D4 | — | 8 | 1 | no | — |
| 314 | C2×D4 | — | 8 | 2 | no | — |
| 315 | C2×D4 | #120 | 1 | 1 | yes | characteristic |
| 316 | C2×D4 | #121 | 1 | 1 | yes | characteristic |
| 317 | C22×C4 | — | 2 | 1 | no | — |
| 318 | C22×C4 | — | 2 | 1 | no | — |
| 319 | C22×C4 | — | 2 | 1 | no | — |
| 320 | C22×C4 | — | 4 | 1 | no | — |
| 321 | C22×C4 | — | 4 | 1 | no | — |
| 322 | C22×C4 | — | 4 | 1 | no | — |
| 323 | C22×C4 | — | 4 | 1 | no | — |
| 324 | C22×C4 | — | 4 | 1 | no | — |
| 325 | C22×C4 | — | 4 | 1 | no | — |
| 326 | C22×C4 | — | 4 | 1 | no | — |
| 327 | C22×C4 | — | 8 | 1 | no | — |
| 328 | C22×C4 | — | 8 | 1 | no | — |
| 329 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 330 | Q16 | — | 8 | 1 | no | — |
| 331 | Q16 | — | 8 | 1 | no | — |
| 332 | Q16 | — | 8 | 1 | no | — |
| 333 | Q16 | — | 8 | 2 | no | — |
| 334 | SD16 | — | 8 | 1 | no | — |
| 335 | SD16 | — | 8 | 1 | no | — |
| 336 | SD16 | — | 8 | 1 | no | — |
| 337 | SD16 | — | 8 | 1 | no | — |
| 338 | SD16 | — | 8 | 1 | no | — |
| 339 | SD16 | — | 8 | 1 | no | — |
| 340 | SD16 | — | 8 | 2 | no | — |
| 341 | SD16 | — | 8 | 2 | no | — |
| 342 | D8 | — | 8 | 1 | no | — |
| 343 | D8 | — | 8 | 1 | no | — |
| 344 | D8 | — | 8 | 1 | no | — |
| 345 | D8 | — | 8 | 2 | no | — |
| 346 | M16 | — | 4 | 2 | no | — |
| 347 | M16 | — | 4 | 1 | no | — |
| 348 | M16 | — | 4 | 1 | no | — |
| 349 | M16 | — | 4 | 1 | no | — |
| 350 | M16 | — | 4 | 1 | no | — |
| 351 | M16 | — | 8 | 1 | no | — |
| 352 | C2×C8 | — | 2 | 1 | no | — |
| 353 | C2×C8 | — | 2 | 1 | no | — |
| 354 | C2×C8 | — | 4 | 1 | no | — |
| 355 | C2×C8 | — | 4 | 1 | no | — |
| 356 | C2×C8 | — | 4 | 1 | no | — |
| 357 | C2×C8 | — | 4 | 1 | no | — |
| 358 | C2×C8 | — | 8 | 1 | no | — |
| 359 | C2×C8 | — | 8 | 1 | no | — |
| 360 | C4⋊C4 | — | 2 | 1 | no | — |
| 361 | C4⋊C4 | — | 2 | 1 | no | — |
| 362 | C4⋊C4 | — | 4 | 1 | no | — |
| 363 | C4⋊C4 | — | 4 | 1 | no | — |
| 364 | C4⋊C4 | — | 4 | 1 | no | — |
| 365 | C4⋊C4 | — | 4 | 1 | no | — |
| 366 | C4⋊C4 | — | 4 | 1 | no | — |
| 367 | C4⋊C4 | — | 4 | 1 | no | — |
| 368 | C4⋊C4 | — | 4 | 1 | no | — |
| 369 | C4⋊C4 | — | 4 | 1 | no | — |
| 370 | C4⋊C4 | — | 4 | 1 | no | — |
| 371 | C4⋊C4 | — | 8 | 1 | no | — |
| 372 | C4⋊C4 | — | 8 | 2 | no | — |
| 373 | C22⋊C4 | — | 2 | 1 | no | — |
| 374 | C22⋊C4 | — | 2 | 1 | no | — |
| 375 | C22⋊C4 | — | 4 | 1 | no | — |
| 376 | C22⋊C4 | — | 4 | 1 | no | — |
| 377 | C22⋊C4 | — | 4 | 1 | no | — |
| 378 | C22⋊C4 | — | 4 | 1 | no | — |
| 379 | C22⋊C4 | — | 4 | 1 | no | — |
| 380 | C22⋊C4 | — | 4 | 1 | no | — |
| 381 | C22⋊C4 | — | 4 | 1 | no | — |
| 382 | C22⋊C4 | — | 4 | 1 | no | — |
| 383 | C22⋊C4 | — | 4 | 1 | no | — |
| 384 | C22⋊C4 | — | 4 | 1 | no | — |
| 385 | C22⋊C4 | — | 4 | 1 | no | — |
| 386 | C22⋊C4 | — | 4 | 1 | no | — |
| 387 | C22⋊C4 | — | 4 | 1 | no | — |
| 388 | C22⋊C4 | — | 4 | 2 | no | — |
| 389 | C22⋊C4 | — | 8 | 1 | no | — |
| 390 | C22⋊C4 | — | 8 | 1 | no | — |
| 391 | C22⋊C4 | — | 8 | 2 | no | — |
| 392 | C22⋊C4 | — | 8 | 1 | no | — |
| 393 | C22⋊C4 | — | 8 | 2 | no | — |
| 394 | C42 | — | 2 | 1 | no | — |
| 395 | C42 | — | 2 | 1 | no | — |
| 396 | C42 | — | 2 | 1 | no | — |
| 397 | C42 | — | 4 | 1 | no | — |
| 398 | C42 | #121 | 1 | 1 | yes | characteristic |
| 399 | C42 | #127 | 1 | 1 | yes | characteristic |
| 400 | C23 | — | 2 | 1 | no | — |
| 401 | C23 | — | 2 | 1 | no | — |
| 402 | C23 | — | 4 | 1 | no | — |
| 403 | C23 | — | 4 | 1 | no | — |
| 404 | C23 | — | 4 | 2 | no | — |
| 405 | C23 | — | 4 | 1 | no | — |
| 406 | C23 | — | 4 | 1 | no | — |
| 407 | C23 | — | 4 | 1 | no | — |
| 408 | C23 | — | 8 | 1 | no | — |
| 409 | C23 | — | 8 | 1 | no | — |
| 410 | C23 | — | 16 | 1 | no | — |
| 411 | C23 | — | 16 | 1 | no | — |
| 412 | C23 | — | 32 | 1 | no | — |
| 413 | C23 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 414 | Q8 | — | 4 | 1 | no | — |
| 415 | Q8 | — | 4 | 1 | no | — |
| 416 | Q8 | — | 4 | 1 | no | — |
| 417 | Q8 | — | 4 | 1 | no | — |
| 418 | Q8 | — | 4 | 1 | no | — |
| 419 | Q8 | — | 4 | 1 | no | — |
| 420 | Q8 | — | 4 | 2 | no | — |
| 421 | Q8 | — | 8 | 1 | no | — |
| 422 | Q8 | — | 8 | 1 | no | — |
| 423 | Q8 | — | 8 | 1 | no | — |
| 424 | Q8 | — | 8 | 1 | no | — |
| 425 | D4 | — | 4 | 1 | no | — |
| 426 | D4 | — | 4 | 1 | no | — |
| 427 | D4 | — | 4 | 1 | no | — |
| 428 | D4 | — | 4 | 1 | no | — |
| 429 | D4 | — | 4 | 1 | no | — |
| 430 | D4 | — | 4 | 1 | no | — |
| 431 | D4 | — | 4 | 2 | no | — |
| 432 | D4 | — | 8 | 1 | no | — |
| 433 | D4 | — | 8 | 1 | no | — |
| 434 | D4 | — | 8 | 1 | no | — |
| 435 | D4 | — | 8 | 1 | no | — |
| 436 | D4 | — | 8 | 2 | no | — |
| 437 | D4 | — | 8 | 2 | no | — |
| 438 | D4 | — | 8 | 1 | no | — |
| 439 | D4 | — | 8 | 1 | no | — |
| 440 | D4 | — | 8 | 1 | no | — |
| 441 | D4 | — | 8 | 1 | no | — |
| 442 | D4 | — | 8 | 1 | no | — |
| 443 | D4 | — | 8 | 1 | no | — |
| 444 | D4 | — | 16 | 1 | no | — |
| 445 | D4 | — | 16 | 1 | no | — |
| 446 | D4 | — | 16 | 1 | no | — |
| 447 | D4 | — | 32 | 1 | no | — |
| 448 | D4 | — | 32 | 2 | no | — |
| 449 | C2×C4 | — | 2 | 1 | no | — |
| 450 | C2×C4 | — | 2 | 1 | no | — |
| 451 | C2×C4 | — | 2 | 1 | no | — |
| 452 | C2×C4 | — | 2 | 1 | no | — |
| 453 | C2×C4 | — | 2 | 1 | no | — |
| 454 | C2×C4 | — | 2 | 1 | no | — |
| 455 | C2×C4 | — | 4 | 1 | no | — |
| 456 | C2×C4 | — | 4 | 1 | no | — |
| 457 | C2×C4 | — | 4 | 2 | no | — |
| 458 | C2×C4 | — | 4 | 1 | no | — |
| 459 | C2×C4 | — | 4 | 1 | no | — |
| 460 | C2×C4 | — | 4 | 1 | no | — |
| 461 | C2×C4 | — | 4 | 1 | no | — |
| 462 | C2×C4 | — | 4 | 1 | no | — |
| 463 | C2×C4 | — | 8 | 1 | no | — |
| 464 | C2×C4 | — | 8 | 1 | no | — |
| 465 | C2×C4 | — | 8 | 1 | no | — |
| 466 | C2×C4 | — | 8 | 1 | no | — |
| 467 | C2×C4 | — | 8 | 1 | no | — |
| 468 | C2×C4 | — | 8 | 2 | no | — |
| 469 | C2×C4 | — | 8 | 2 | no | — |
| 470 | C2×C4 | — | 8 | 1 | no | — |
| 471 | C2×C4 | — | 8 | 1 | no | — |
| 472 | C2×C4 | — | 8 | 2 | no | — |
| 473 | C2×C4 | — | 8 | 1 | no | — |
| 474 | C2×C4 | — | 16 | 1 | no | — |
| 475 | C2×C4 | — | 16 | 1 | no | — |
| 476 | C2×C4 | — | 16 | 1 | no | — |
| 477 | C2×C4 | — | 16 | 1 | no | — |
| 478 | C2×C4 | — | 32 | 1 | no | — |
| 479 | C2×C4 | #392 | 1 | 1 | yes | characteristic |
| 480 | C2×C4 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 481 | C8 | — | 4 | 1 | no | — |
| 482 | C8 | — | 4 | 1 | no | — |
| 483 | C8 | — | 8 | 1 | no | — |
| 484 | C8 | — | 8 | 1 | no | — |
| 485 | C8 | — | 8 | 2 | no | — |
| 486 | C8 | — | 16 | 1 | no | — |
| 487 | C22 | — | 4 | 1 | no | — |
| 488 | C22 | — | 4 | 1 | no | — |
| 489 | C22 | — | 4 | 1 | no | — |
| 490 | C22 | — | 8 | 1 | no | — |
| 491 | C22 | — | 8 | 1 | no | — |
| 492 | C22 | — | 8 | 1 | no | — |
| 493 | C22 | — | 8 | 1 | no | — |
| 494 | C22 | — | 8 | 1 | no | — |
| 495 | C22 | — | 8 | 1 | no | — |
| 496 | C22 | — | 8 | 1 | no | — |
| 497 | C22 | — | 8 | 1 | no | — |
| 498 | C22 | — | 8 | 1 | no | — |
| 499 | C22 | — | 8 | 1 | no | — |
| 500 | C22 | — | 8 | 1 | no | — |
| 501 | C22 | — | 16 | 1 | no | — |
| 502 | C22 | — | 16 | 1 | no | — |
| 503 | C22 | — | 16 | 2 | no | — |
| 504 | C22 | — | 16 | 2 | no | — |
| 505 | C22 | — | 32 | 1 | no | — |
| 506 | C22 | #2021 | 1 | 1 | yes | characteristic |
| 507 | C22 | #2196 | 1 | 1 | yes | characteristic |
| 508 | C22 | #2199 | 1 | 1 | yes | characteristic |
| 509 | C4 | — | 2 | 1 | no | — |
| 510 | C4 | — | 2 | 1 | no | — |
| 511 | C4 | — | 4 | 1 | no | — |
| 512 | C4 | — | 4 | 1 | no | — |
| 513 | C4 | — | 4 | 1 | no | — |
| 514 | C4 | — | 4 | 1 | no | — |
| 515 | C4 | — | 8 | 1 | no | — |
| 516 | C4 | — | 8 | 1 | no | — |
| 517 | C4 | — | 8 | 1 | no | — |
| 518 | C4 | — | 8 | 1 | no | — |
| 519 | C4 | — | 8 | 1 | no | — |
| 520 | C4 | — | 16 | 1 | no | — |
| 521 | C4 | — | 16 | 2 | no | — |
| 522 | C2 | — | 2 | 1 | no | — |
| 523 | C2 | — | 2 | 1 | no | — |
| 524 | C2 | — | 2 | 1 | no | — |
| 525 | C2 | — | 8 | 1 | no | — |
| 526 | C2 | — | 8 | 1 | no | — |
| 527 | C2 | — | 16 | 1 | no | — |
| 528 | C2 | — | 16 | 1 | no | — |
| 529 | C2 | — | 16 | 1 | no | — |
| 530 | C2 | #13343 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #13343 |
| commutator, Frattini, cosocle | C2×#124 | C23 |
| LCS | G ▷ C2×#124 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×#124 ◁ G | |
| LECS | G ▷ C2×#124 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #33568 | C2 | semidirect |
| 2. #33558 | C2 | semidirect |
| 3. #31072 | C2 | semidirect |
| 4. #13569 | C2 | semidirect |
| 5. #13565 | C2 | semidirect |
| 6. #8528 | C2 | semidirect |
| 7. #7502 | C2 | semidirect |
| 35. C2×2−1+4 | D4 | semidirect |
| 41. #563 | D4 | semidirect |
| 43. H(3,𝔽4) | D4 | semidirect |
| 90. C2×#101 | D4 | semidirect |
| 96. C2×C4×C8 | D4 | semidirect |
| 97. #382 | D4 | semidirect |
| 101. #355 | D4 | semidirect |
| 103. #354 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #33568 | 2 |
| #33558 | 2 |
| #31072 | 2 |
| #13569 | 2 |
| #13565 | 2 |
| #8528 | 2 |
| #7502 | 2 |