Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
624 conjugacy classes of subgroups.
The subgroup lattice has 392 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #28762 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #23180 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #19662 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #19235 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #19205 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #10503 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10205 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #9742 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #9607 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #9271 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #8256 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #3246 | C22 | 1 | 2 | yes | — |
| 13 | #3226 | C22 | 1 | 2 | yes | — |
| 14 | #3226 | C22 | 1 | 2 | yes | — |
| 15 | #3147 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#494 | C22 | 1 | 1 | yes | characteristic |
| 17 | #3139 | C22 | 1 | 2 | yes | — |
| 18 | #2960 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#444 | — | 2 | 1 | no | — |
| 20 | #2935 | C22 | 1 | 2 | yes | — |
| 21 | #2047 | — | 2 | 2 | no | — |
| 22 | #1988 | C22 | 1 | 2 | yes | — |
| 23 | #1980 | C22 | 1 | 2 | yes | — |
| 24 | #1979 | — | 2 | 1 | no | — |
| 25 | #1979 | — | 2 | 1 | no | — |
| 26 | #1975 | — | 2 | 1 | no | — |
| 27 | #1966 | C22 | 1 | 2 | yes | — |
| 28 | #1876 | — | 2 | 2 | no | — |
| 29 | C4×#108 | C22 | 1 | 1 | yes | characteristic |
| 30 | #1770 | C22 | 1 | 1 | yes | characteristic |
| 31 | #1722 | — | 2 | 2 | no | — |
| 32 | #1713 | — | 2 | 1 | no | — |
| 33 | #1709 | — | 2 | 1 | no | — |
| 34 | #1703 | — | 2 | 2 | no | — |
| 35 | #1699 | — | 2 | 2 | no | — |
| 36 | #1690 | — | 2 | 1 | no | — |
| 37 | #1688 | — | 2 | 1 | no | — |
| 38 | #1683 | — | 2 | 2 | no | — |
| 39 | #1679 | — | 2 | 2 | no | — |
| 40 | #1666 | — | 2 | 2 | no | — |
| 41 | #1565 | C22 | 1 | 2 | yes | — |
| 42 | C2×#334 | C22 | 1 | 1 | yes | characteristic |
| 43 | #1547 | C22 | 1 | 2 | yes | — |
| 44 | #1542 | C22 | 1 | 1 | yes | characteristic |
| 45 | C2×#332 | C22 | 1 | 2 | yes | — |
| 46 | #1503 | C22 | 1 | 1 | yes | characteristic |
| 47 | #1450 | C22 | 1 | 1 | yes | characteristic |
| 48 | #1303 | C22 | 1 | 1 | yes | characteristic |
| 49 | #1301 | C22 | 1 | 1 | yes | characteristic |
| 50 | #1283 | C22 | 1 | 2 | yes | — |
| 51 | C2×#135 | — | 2 | 1 | no | — |
| 52 | C2×#135 | — | 2 | 1 | no | — |
| 53 | C22×Q16 | — | 2 | 1 | no | — |
| 54 | C22×Q16 | — | 2 | 1 | no | — |
| 55 | C2×#131 | — | 2 | 2 | no | — |
| 56 | #533 | C23 | 1 | 1 | yes | characteristic |
| 57 | #532 | C23 | 1 | 2 | yes | — |
| 58 | C2×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 59 | #500 | — | 2 | 2 | no | — |
| 60 | #500 | — | 2 | 2 | no | — |
| 61 | #495 | — | 2 | 1 | no | — |
| 62 | #495 | — | 2 | 1 | no | — |
| 63 | #494 | — | 2 | 1 | no | — |
| 64 | #494 | — | 2 | 1 | no | — |
| 65 | #494 | — | 2 | 1 | no | — |
| 66 | #494 | — | 2 | 1 | no | — |
| 67 | #494 | D4 | 1 | 1 | yes | characteristic |
| 68 | #493 | D4 | 1 | 1 | yes | characteristic |
| 69 | #492 | D4 | 1 | 2 | yes | — |
| 70 | #491 | — | 4 | 2 | no | — |
| 71 | #487 | — | 2 | 2 | no | — |
| 72 | #487 | — | 2 | 2 | no | — |
| 73 | #486 | — | 2 | 2 | no | — |
| 74 | #486 | — | 2 | 2 | no | — |
| 75 | #480 | — | 2 | 4 | no | — |
| 76 | #480 | — | 4 | 2 | no | — |
| 77 | #476 | — | 2 | 2 | no | — |
| 78 | #475 | — | 2 | 2 | no | — |
| 79 | #474 | — | 2 | 2 | no | — |
| 80 | #474 | — | 2 | 2 | no | — |
| 81 | #474 | — | 4 | 2 | no | — |
| 82 | #465 | — | 4 | 2 | no | — |
| 83 | #461 | — | 2 | 2 | no | — |
| 84 | #460 | — | 2 | 2 | no | — |
| 85 | #446 | — | 2 | 1 | no | — |
| 86 | #446 | — | 2 | 1 | no | — |
| 87 | C8×Q8 | — | 2 | 1 | no | — |
| 88 | C8×Q8 | — | 2 | 1 | no | — |
| 89 | #444 | — | 4 | 4 | no | — |
| 90 | #436 | — | 2 | 2 | no | — |
| 91 | #435 | — | 4 | 2 | no | — |
| 92 | C8×D4 | — | 2 | 2 | no | — |
| 93 | #431 | C23 | 1 | 1 | yes | characteristic |
| 94 | #431 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×#108 | D4 | 1 | 1 | yes | characteristic |
| 96 | C2×#108 | D4 | 1 | 1 | yes | characteristic |
| 97 | #424 | — | 2 | 1 | no | — |
| 98 | #423 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 100 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 101 | C2×#104 | — | 2 | 2 | no | — |
| 102 | C2×#104 | — | 2 | 2 | no | — |
| 103 | #419 | — | 2 | 2 | no | — |
| 104 | #419 | — | 2 | 2 | no | — |
| 105 | C2×#101 | — | 2 | 2 | no | — |
| 106 | C2×#101 | — | 2 | 2 | no | — |
| 107 | #408 | — | 2 | 2 | no | — |
| 108 | #405 | — | 2 | 1 | no | — |
| 109 | C4×M16 | C23 | 1 | 2 | yes | — |
| 110 | C2×#97 | — | 2 | 1 | no | — |
| 111 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 112 | C4×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 113 | #341 | D4 | 1 | 2 | yes | — |
| 114 | #340 | — | 4 | 2 | no | — |
| 115 | #336 | — | 2 | 1 | no | — |
| 116 | #335 | — | 2 | 2 | no | — |
| 117 | #334 | — | 2 | 2 | no | — |
| 118 | #334 | — | 2 | 1 | no | — |
| 119 | #334 | — | 2 | 1 | no | — |
| 120 | #333 | D4 | 1 | 2 | yes | — |
| 121 | #332 | — | 2 | 2 | no | — |
| 122 | #332 | — | 2 | 2 | no | — |
| 123 | #332 | — | 2 | 2 | no | — |
| 124 | #332 | D4 | 1 | 2 | yes | — |
| 125 | #331 | — | 2 | 2 | no | — |
| 126 | #328 | — | 2 | 2 | no | — |
| 127 | #322 | — | 2 | 1 | no | — |
| 128 | C82 | — | 2 | 1 | no | — |
| 129 | C2×#41 | — | 2 | 2 | no | — |
| 130 | C22×Q8 | — | 2 | 2 | no | — |
| 131 | #135 | — | 4 | 2 | no | — |
| 132 | #135 | — | 4 | 2 | no | — |
| 133 | #135 | — | 8 | 1 | no | — |
| 134 | #135 | — | 8 | 1 | no | — |
| 135 | C2×Q16 | — | 2 | 1 | no | — |
| 136 | C2×Q16 | — | 2 | 1 | no | — |
| 137 | C2×Q16 | — | 4 | 1 | no | — |
| 138 | C2×Q16 | — | 4 | 1 | no | — |
| 139 | C2×Q16 | — | 4 | 1 | no | — |
| 140 | C2×Q16 | — | 4 | 1 | no | — |
| 141 | C2×Q16 | — | 4 | 2 | no | — |
| 142 | C2×Q16 | — | 4 | 2 | no | — |
| 143 | C2×Q16 | — | 8 | 1 | no | — |
| 144 | C2×Q16 | — | 8 | 1 | no | — |
| 145 | C2×SD16 | — | 2 | 2 | no | — |
| 146 | C2×SD16 | — | 2 | 2 | no | — |
| 147 | C2×SD16 | — | 4 | 2 | no | — |
| 148 | C2×D8 | — | 2 | 1 | no | — |
| 149 | C2×D8 | — | 2 | 1 | no | — |
| 150 | #131 | — | 4 | 4 | no | — |
| 151 | #131 | — | 8 | 2 | no | — |
| 152 | C2×M16 | — | 2 | 1 | no | — |
| 153 | C2×M16 | — | 4 | 2 | no | — |
| 154 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 155 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 156 | C22×C8 | — | 2 | 1 | no | — |
| 157 | C22×C8 | — | 2 | 2 | no | — |
| 158 | C22×C8 | — | 4 | 2 | no | — |
| 159 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 160 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | C4⋊Q8 | — | 2 | 2 | no | — |
| 162 | C4⋊Q8 | — | 2 | 2 | no | — |
| 163 | C4⋊Q8 | — | 2 | 2 | no | — |
| 164 | C4⋊Q8 | — | 2 | 2 | no | — |
| 165 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 166 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | #127 | C2×D4 | 1 | 2 | yes | — |
| 169 | #125 | — | 2 | 1 | no | — |
| 170 | #124 | — | 2 | 2 | no | — |
| 171 | C22⋊Q8 | — | 2 | 1 | no | — |
| 172 | C22⋊Q8 | — | 2 | 1 | no | — |
| 173 | #121 | — | 2 | 2 | no | — |
| 174 | #121 | — | 2 | 2 | no | — |
| 175 | C4×Q8 | — | 2 | 1 | no | — |
| 176 | C4×Q8 | — | 2 | 1 | no | — |
| 177 | C4×D4 | — | 2 | 2 | no | — |
| 178 | C4×D4 | — | 2 | 2 | no | — |
| 179 | #117 | — | 2 | 1 | no | — |
| 180 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 181 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 182 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 183 | C2×C42 | — | 2 | 1 | no | — |
| 184 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 185 | #108 | — | 2 | 2 | no | — |
| 186 | #108 | — | 2 | 2 | no | — |
| 187 | #107 | — | 4 | 2 | no | — |
| 188 | #107 | — | 4 | 2 | no | — |
| 189 | #107 | — | 4 | 4 | no | — |
| 190 | #106 | — | 4 | 2 | no | — |
| 191 | C4⋊C8 | — | 2 | 1 | no | — |
| 192 | C4⋊C8 | — | 2 | 2 | no | — |
| 193 | C4⋊C8 | — | 2 | 2 | no | — |
| 194 | C4⋊C8 | — | 2 | 1 | no | — |
| 195 | C4⋊C8 | — | 2 | 1 | no | — |
| 196 | C4⋊C8 | — | 2 | 1 | no | — |
| 197 | C4⋊C8 | — | 4 | 1 | no | — |
| 198 | C4⋊C8 | — | 4 | 1 | no | — |
| 199 | C4⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 200 | C4⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 201 | #104 | — | 4 | 4 | no | — |
| 202 | #104 | — | 8 | 2 | no | — |
| 203 | #103 | — | 4 | 2 | no | — |
| 204 | #103 | — | 4 | 2 | no | — |
| 205 | #103 | — | 4 | 2 | no | — |
| 206 | #103 | — | 4 | 2 | no | — |
| 207 | #103 | — | 4 | 2 | no | — |
| 208 | #102 | — | 4 | 2 | no | — |
| 209 | #102 | — | 4 | 2 | no | — |
| 210 | #102 | — | 4 | 2 | no | — |
| 211 | #102 | — | 4 | 4 | no | — |
| 212 | #101 | — | 8 | 2 | no | — |
| 213 | #101 | — | 8 | 2 | no | — |
| 214 | C22⋊C8 | — | 2 | 1 | no | — |
| 215 | C22⋊C8 | — | 4 | 2 | no | — |
| 216 | C22⋊C8 | — | 4 | 2 | no | — |
| 217 | C22⋊C8 | #41 | 1 | 2 | yes | — |
| 218 | #97 | — | 2 | 2 | no | — |
| 219 | #97 | — | 4 | 1 | no | — |
| 220 | #97 | — | 4 | 2 | no | — |
| 221 | C4×C8 | — | 2 | 1 | no | — |
| 222 | C4×C8 | — | 2 | 1 | no | — |
| 223 | C4×C8 | — | 2 | 2 | no | — |
| 224 | C4×C8 | — | 4 | 1 | no | — |
| 225 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 226 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 227 | C4×C8 | #41 | 1 | 1 | yes | characteristic |
| 228 | C4×C8 | #41 | 1 | 1 | yes | characteristic |
| 229 | #95 | — | 2 | 1 | no | — |
| 230 | #41 | — | 4 | 2 | no | — |
| 231 | #41 | — | 4 | 2 | no | — |
| 232 | #41 | — | 4 | 2 | no | — |
| 233 | #41 | — | 4 | 2 | no | — |
| 234 | C2×Q8 | — | 2 | 2 | no | — |
| 235 | C2×Q8 | — | 2 | 1 | no | — |
| 236 | C2×Q8 | — | 2 | 1 | no | — |
| 237 | C2×Q8 | — | 4 | 2 | no | — |
| 238 | C2×Q8 | — | 4 | 2 | no | — |
| 239 | C2×Q8 | — | 4 | 2 | no | — |
| 240 | C2×Q8 | — | 4 | 2 | no | — |
| 241 | C2×Q8 | — | 4 | 2 | no | — |
| 242 | C2×Q8 | — | 4 | 2 | no | — |
| 243 | C2×D4 | — | 2 | 2 | no | — |
| 244 | C2×D4 | — | 2 | 2 | no | — |
| 245 | C2×D4 | — | 2 | 2 | no | — |
| 246 | C2×D4 | — | 4 | 2 | no | — |
| 247 | C22×C4 | — | 4 | 2 | no | — |
| 248 | C22×C4 | — | 4 | 1 | no | — |
| 249 | C22×C4 | — | 4 | 2 | no | — |
| 250 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 251 | C22×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 252 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 253 | Q16 | — | 4 | 2 | no | — |
| 254 | Q16 | — | 8 | 1 | no | — |
| 255 | Q16 | — | 8 | 2 | no | — |
| 256 | Q16 | — | 8 | 2 | no | — |
| 257 | Q16 | — | 8 | 2 | no | — |
| 258 | Q16 | — | 8 | 2 | no | — |
| 259 | SD16 | — | 4 | 4 | no | — |
| 260 | SD16 | — | 8 | 2 | no | — |
| 261 | SD16 | — | 16 | 2 | no | — |
| 262 | D8 | — | 4 | 2 | no | — |
| 263 | D8 | — | 8 | 1 | no | — |
| 264 | M16 | — | 2 | 2 | no | — |
| 265 | M16 | — | 2 | 2 | no | — |
| 266 | M16 | — | 2 | 2 | no | — |
| 267 | M16 | — | 2 | 2 | no | — |
| 268 | M16 | — | 4 | 1 | no | — |
| 269 | M16 | — | 4 | 1 | no | — |
| 270 | M16 | — | 8 | 4 | no | — |
| 271 | C2×C8 | — | 2 | 1 | no | — |
| 272 | C2×C8 | — | 2 | 1 | no | — |
| 273 | C2×C8 | — | 2 | 2 | no | — |
| 274 | C2×C8 | — | 2 | 2 | no | — |
| 275 | C2×C8 | — | 2 | 2 | no | — |
| 276 | C2×C8 | — | 2 | 2 | no | — |
| 277 | C2×C8 | — | 2 | 2 | no | — |
| 278 | C2×C8 | — | 4 | 1 | no | — |
| 279 | C2×C8 | — | 4 | 1 | no | — |
| 280 | C2×C8 | — | 4 | 1 | no | — |
| 281 | C2×C8 | — | 4 | 2 | no | — |
| 282 | C2×C8 | — | 8 | 4 | no | — |
| 283 | C2×C8 | — | 8 | 2 | no | — |
| 284 | C2×C8 | #121 | 1 | 1 | yes | characteristic |
| 285 | C2×C8 | #121 | 1 | 1 | yes | characteristic |
| 286 | C2×C8 | #121 | 1 | 1 | yes | characteristic |
| 287 | C2×C8 | #121 | 1 | 1 | yes | characteristic |
| 288 | C2×C8 | #135 | 1 | 2 | yes | — |
| 289 | C2×C8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 290 | C4⋊C4 | — | 2 | 1 | no | — |
| 291 | C4⋊C4 | — | 2 | 1 | no | — |
| 292 | C4⋊C4 | — | 2 | 1 | no | — |
| 293 | C4⋊C4 | — | 2 | 1 | no | — |
| 294 | C4⋊C4 | — | 2 | 2 | no | — |
| 295 | C4⋊C4 | — | 2 | 2 | no | — |
| 296 | C4⋊C4 | — | 4 | 2 | no | — |
| 297 | C4⋊C4 | — | 4 | 1 | no | — |
| 298 | C4⋊C4 | — | 4 | 1 | no | — |
| 299 | C4⋊C4 | — | 4 | 2 | no | — |
| 300 | C4⋊C4 | — | 4 | 2 | no | — |
| 301 | C4⋊C4 | — | 4 | 2 | no | — |
| 302 | C4⋊C4 | — | 4 | 2 | no | — |
| 303 | C22⋊C4 | — | 4 | 1 | no | — |
| 304 | C22⋊C4 | — | 4 | 2 | no | — |
| 305 | C22⋊C4 | — | 4 | 2 | no | — |
| 306 | C42 | — | 4 | 1 | no | — |
| 307 | C42 | — | 4 | 1 | no | — |
| 308 | C42 | — | 4 | 1 | no | — |
| 309 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 310 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 311 | C42 | C2×#41 | 1 | 1 | yes | characteristic |
| 312 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 313 | C23 | — | 4 | 2 | no | — |
| 314 | C23 | #550 | 1 | 1 | yes | characteristic |
| 315 | Q8 | — | 4 | 2 | no | — |
| 316 | Q8 | — | 4 | 2 | no | — |
| 317 | Q8 | — | 4 | 2 | no | — |
| 318 | Q8 | — | 8 | 1 | no | — |
| 319 | Q8 | — | 8 | 2 | no | — |
| 320 | Q8 | — | 8 | 2 | no | — |
| 321 | Q8 | — | 8 | 2 | no | — |
| 322 | Q8 | — | 8 | 2 | no | — |
| 323 | D4 | — | 4 | 2 | no | — |
| 324 | D4 | — | 4 | 2 | no | — |
| 325 | D4 | — | 4 | 2 | no | — |
| 326 | D4 | — | 4 | 2 | no | — |
| 327 | D4 | — | 8 | 2 | no | — |
| 328 | D4 | — | 8 | 2 | no | — |
| 329 | D4 | — | 8 | 2 | no | — |
| 330 | C2×C4 | — | 2 | 2 | no | — |
| 331 | C2×C4 | — | 4 | 1 | no | — |
| 332 | C2×C4 | — | 4 | 1 | no | — |
| 333 | C2×C4 | — | 4 | 1 | no | — |
| 334 | C2×C4 | — | 4 | 2 | no | — |
| 335 | C2×C4 | — | 8 | 2 | no | — |
| 336 | C2×C4 | — | 8 | 2 | no | — |
| 337 | C2×C4 | — | 8 | 1 | no | — |
| 338 | C2×C4 | — | 8 | 1 | no | — |
| 339 | C2×C4 | — | 8 | 2 | no | — |
| 340 | C2×C4 | — | 8 | 1 | no | — |
| 341 | C2×C4 | — | 8 | 2 | no | — |
| 342 | C2×C4 | — | 8 | 2 | no | — |
| 343 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 344 | C2×C4 | #532 | 1 | 1 | yes | characteristic |
| 345 | C2×C4 | #540 | 1 | 1 | yes | characteristic |
| 346 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 347 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 348 | C2×C4 | #546 | 1 | 1 | yes | characteristic |
| 349 | C2×C4 | C2×#135 | 1 | 1 | yes | characteristic |
| 350 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 351 | C2×C4 | #576 | 1 | 1 | yes | characteristic |
| 352 | C2×C4 | #576 | 1 | 1 | yes | characteristic |
| 353 | C8 | — | 2 | 1 | no | — |
| 354 | C8 | — | 2 | 1 | no | — |
| 355 | C8 | — | 4 | 2 | no | — |
| 356 | C8 | — | 4 | 2 | no | — |
| 357 | C8 | — | 4 | 2 | no | — |
| 358 | C8 | — | 4 | 2 | no | — |
| 359 | C8 | — | 4 | 2 | no | — |
| 360 | C8 | — | 8 | 2 | no | — |
| 361 | C8 | — | 8 | 1 | no | — |
| 362 | C8 | #463 | 1 | 2 | yes | — |
| 363 | C8 | #463 | 1 | 2 | yes | — |
| 364 | C22 | — | 2 | 1 | no | — |
| 365 | C22 | — | 2 | 1 | no | — |
| 366 | C22 | — | 8 | 2 | no | — |
| 367 | C22 | — | 8 | 2 | no | — |
| 368 | C22 | — | 8 | 2 | no | — |
| 369 | C22 | #2428 | 1 | 1 | yes | characteristic |
| 370 | C22 | #3396 | 1 | 1 | yes | characteristic |
| 371 | C22 | #3399 | 1 | 1 | yes | characteristic |
| 372 | C4 | — | 2 | 1 | no | — |
| 373 | C4 | — | 2 | 1 | no | — |
| 374 | C4 | — | 2 | 1 | no | — |
| 375 | C4 | — | 8 | 2 | no | — |
| 376 | C4 | — | 8 | 1 | no | — |
| 377 | C4 | — | 8 | 1 | no | — |
| 378 | C4 | — | 16 | 1 | no | — |
| 379 | C4 | — | 16 | 2 | no | — |
| 380 | C4 | C2×#463 | 1 | 1 | yes | characteristic |
| 381 | C4 | #3041 | 1 | 1 | yes | characteristic |
| 382 | C4 | #3274 | 1 | 1 | yes | characteristic |
| 383 | C4 | #3287 | 1 | 1 | yes | characteristic |
| 384 | C4 | #3289 | 1 | 2 | yes | — |
| 385 | C2 | — | 2 | 1 | no | — |
| 386 | C2 | — | 2 | 1 | no | — |
| 387 | C2 | — | 16 | 2 | no | — |
| 388 | C2 | #25371 | 1 | 1 | yes | characteristic |
| 389 | C2 | #25445 | 1 | 1 | yes | characteristic |
| 390 | C2 | #25448 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #2428 |
| commutator, Frattini, cosocle | C2×C42 | C24 |
| prime radical | #3147 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28762 | C2 | semidirect |
| 4. #19235 | C2 | semidirect |
| 6. #10503 | C2 | semidirect |
| 7. #10205 | C2 | semidirect |
| 8. #9742 | C2 | semidirect |
| 9. #9607 | C2 | semidirect |
| 10. #9271 | C2 | semidirect |
| 11. #8256 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28762 | 2 |
| #23180 | 2 |
| #19662 | 2 |
| #19235 | 2 |
| #19205 | 2 |
| #10503 | 2 |
| #10205 | 2 |
| #9742 | 2 |
| #9607 | 2 |
| #9271 | 2 |
| #8256 | 2 |