Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1198 conjugacy classes of subgroups.
The subgroup lattice has 414 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #60715 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #60666 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #33808 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #33803 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #33802 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #33732 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #33728 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #33705 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#2245 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #33651 | C2 | 1 | 4 | yes | maximal |
| 11 | #33632 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #33421 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #3509 | — | 2 | 1 | no | — |
| 14 | #3504 | — | 2 | 1 | no | — |
| 15 | #3185 | — | 2 | 2 | no | — |
| 16 | #3177 | — | 2 | 2 | no | — |
| 17 | #3177 | C22 | 1 | 4 | yes | — |
| 18 | #3170 | C22 | 1 | 4 | yes | — |
| 19 | #3166 | — | 2 | 1 | no | — |
| 20 | #3166 | — | 2 | 2 | no | — |
| 21 | #3164 | C22 | 1 | 4 | yes | — |
| 22 | #3164 | C22 | 1 | 2 | yes | — |
| 23 | #3163 | — | 2 | 2 | no | — |
| 24 | #3163 | — | 2 | 1 | no | — |
| 25 | #3160 | C22 | 1 | 2 | yes | — |
| 26 | #3160 | C22 | 1 | 1 | yes | characteristic |
| 27 | #3160 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×#499 | C22 | 1 | 2 | yes | — |
| 29 | C2×#499 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×#494 | C22 | 1 | 1 | yes | characteristic |
| 31 | #3139 | — | 2 | 1 | no | — |
| 32 | #3059 | — | 2 | 1 | no | — |
| 33 | #3059 | C22 | 1 | 2 | yes | — |
| 34 | #2950 | — | 2 | 1 | no | — |
| 35 | #2950 | C22 | 1 | 2 | yes | — |
| 36 | #2913 | C22 | 1 | 2 | yes | — |
| 37 | #2912 | — | 2 | 1 | no | — |
| 38 | C4×#131 | C22 | 1 | 1 | yes | characteristic |
| 39 | #2255 | C22 | 1 | 2 | yes | — |
| 40 | #2255 | C22 | 1 | 4 | yes | — |
| 41 | #2255 | C22 | 1 | 2 | yes | — |
| 42 | #2255 | C22 | 1 | 4 | yes | — |
| 43 | #2253 | C22 | 1 | 4 | yes | — |
| 44 | #2245 | C22 | 1 | 2 | yes | — |
| 45 | #2245 | C22 | 1 | 4 | yes | — |
| 46 | #2245 | C22 | 1 | 2 | yes | — |
| 47 | #2245 | C22 | 1 | 4 | yes | — |
| 48 | #2241 | C22 | 1 | 4 | yes | — |
| 49 | #2237 | C22 | 1 | 8 | yes | — |
| 50 | #2237 | C22 | 1 | 8 | yes | — |
| 51 | #2236 | C22 | 1 | 8 | yes | — |
| 52 | #2235 | C22 | 1 | 8 | yes | — |
| 53 | #2229 | C22 | 1 | 8 | yes | — |
| 54 | #2229 | C22 | 1 | 8 | yes | — |
| 55 | #2227 | C22 | 1 | 8 | yes | — |
| 56 | #2225 | C22 | 1 | 8 | yes | — |
| 57 | #2164 | C22 | 1 | 4 | yes | — |
| 58 | #2163 | C22 | 1 | 4 | yes | — |
| 59 | #2159 | C22 | 1 | 4 | yes | — |
| 60 | #2158 | C22 | 1 | 4 | yes | — |
| 61 | #2151 | C22 | 1 | 2 | yes | — |
| 62 | #2141 | C22 | 1 | 4 | yes | — |
| 63 | C2×#358 | C22 | 1 | 4 | yes | — |
| 64 | #2113 | C22 | 1 | 2 | yes | — |
| 65 | C4×M32 | C22 | 1 | 1 | yes | characteristic |
| 66 | C2×#346 | C22 | 1 | 1 | yes | characteristic |
| 67 | C22×Q16 | — | 2 | 1 | no | — |
| 68 | C22×Q16 | C23 | 1 | 2 | yes | — |
| 69 | C2×#131 | D4 | 1 | 1 | yes | characteristic |
| 70 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 71 | #557 | — | 4 | 2 | no | — |
| 72 | #557 | — | 4 | 2 | no | — |
| 73 | #556 | — | 4 | 2 | no | — |
| 74 | #554 | — | 4 | 4 | no | — |
| 75 | #554 | — | 4 | 2 | no | — |
| 76 | #552 | — | 4 | 4 | no | — |
| 77 | #544 | — | 2 | 2 | no | — |
| 78 | #544 | — | 2 | 4 | no | — |
| 79 | #541 | — | 2 | 4 | no | — |
| 80 | #536 | — | 2 | 2 | no | — |
| 81 | #533 | — | 2 | 1 | no | — |
| 82 | #533 | — | 2 | 1 | no | — |
| 83 | #533 | — | 2 | 2 | no | — |
| 84 | #533 | — | 2 | 4 | no | — |
| 85 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 86 | C2×#125 | — | 2 | 1 | no | — |
| 87 | C2×#125 | — | 2 | 2 | no | — |
| 88 | #520 | — | 2 | 2 | no | — |
| 89 | #519 | — | 2 | 2 | no | — |
| 90 | C4×#41 | D4 | 1 | 1 | yes | characteristic |
| 91 | C2×M32 | C23 | 1 | 2 | yes | — |
| 92 | C22×C16 | C23 | 1 | 2 | yes | — |
| 93 | #501 | — | 2 | 4 | no | — |
| 94 | #501 | — | 2 | 4 | no | — |
| 95 | #501 | — | 2 | 4 | no | — |
| 96 | #500 | C23 | 1 | 4 | yes | — |
| 97 | #500 | C23 | 1 | 2 | yes | — |
| 98 | #500 | C23 | 1 | 2 | yes | — |
| 99 | #499 | — | 2 | 2 | no | — |
| 100 | #499 | — | 2 | 1 | no | — |
| 101 | #499 | — | 2 | 2 | no | — |
| 102 | #499 | — | 2 | 1 | no | — |
| 103 | #499 | — | 2 | 2 | no | — |
| 104 | #499 | — | 2 | 1 | no | — |
| 105 | #499 | — | 2 | 1 | no | — |
| 106 | #499 | C23 | 1 | 1 | yes | characteristic |
| 107 | #499 | C23 | 1 | 2 | yes | — |
| 108 | #499 | C23 | 1 | 4 | yes | — |
| 109 | #499 | C23 | 1 | 2 | yes | — |
| 110 | #499 | C23 | 1 | 1 | yes | characteristic |
| 111 | #499 | C23 | 1 | 2 | yes | — |
| 112 | #498 | — | 2 | 2 | no | — |
| 113 | #498 | — | 2 | 1 | no | — |
| 114 | #498 | — | 2 | 1 | no | — |
| 115 | #494 | — | 2 | 1 | no | — |
| 116 | #494 | — | 2 | 1 | no | — |
| 117 | #494 | C23 | 1 | 2 | yes | — |
| 118 | #494 | C23 | 1 | 2 | yes | — |
| 119 | #491 | — | 2 | 4 | no | — |
| 120 | #487 | — | 2 | 4 | no | — |
| 121 | #470 | — | 2 | 4 | no | — |
| 122 | #470 | — | 2 | 4 | no | — |
| 123 | #467 | — | 2 | 4 | no | — |
| 124 | #467 | C23 | 1 | 8 | yes | — |
| 125 | #441 | — | 2 | 4 | no | — |
| 126 | #441 | — | 2 | 4 | no | — |
| 127 | C4×Q16 | — | 2 | 4 | no | — |
| 128 | C4×Q16 | C23 | 1 | 8 | yes | — |
| 129 | #428 | — | 2 | 2 | no | — |
| 130 | #428 | — | 2 | 4 | no | — |
| 131 | #428 | — | 2 | 2 | no | — |
| 132 | #428 | — | 2 | 4 | no | — |
| 133 | #427 | — | 2 | 2 | no | — |
| 134 | #427 | — | 2 | 1 | no | — |
| 135 | #427 | — | 2 | 1 | no | — |
| 136 | #427 | C23 | 1 | 2 | yes | — |
| 137 | #427 | C23 | 1 | 4 | yes | — |
| 138 | #427 | C23 | 1 | 2 | yes | — |
| 139 | C2×#107 | C23 | 1 | 2 | yes | — |
| 140 | C2×#107 | C23 | 1 | 4 | yes | — |
| 141 | C2×#106 | — | 2 | 2 | no | — |
| 142 | C2×#106 | — | 2 | 1 | no | — |
| 143 | #419 | — | 2 | 2 | no | — |
| 144 | #419 | — | 2 | 2 | no | — |
| 145 | #405 | D4 | 1 | 2 | yes | — |
| 146 | #405 | D4 | 1 | 1 | yes | characteristic |
| 147 | #405 | C23 | 1 | 1 | yes | characteristic |
| 148 | #405 | C23 | 1 | 2 | yes | — |
| 149 | C4×M16 | D4 | 1 | 1 | yes | characteristic |
| 150 | C4×M16 | D4 | 1 | 2 | yes | — |
| 151 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 152 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 153 | #367 | C23 | 1 | 4 | yes | — |
| 154 | #367 | C23 | 1 | 4 | yes | — |
| 155 | #367 | C23 | 1 | 8 | yes | — |
| 156 | #366 | C23 | 1 | 4 | yes | — |
| 157 | #366 | C23 | 1 | 4 | yes | — |
| 158 | #366 | C23 | 1 | 8 | yes | — |
| 159 | C4⋊C16 | C23 | 1 | 8 | yes | — |
| 160 | #358 | C23 | 1 | 8 | yes | — |
| 161 | #358 | C23 | 1 | 8 | yes | — |
| 162 | #358 | C23 | 1 | 8 | yes | — |
| 163 | #358 | C23 | 1 | 8 | yes | — |
| 164 | C22⋊C16 | C23 | 1 | 8 | yes | — |
| 165 | #346 | C23 | 1 | 2 | yes | — |
| 166 | #346 | C23 | 1 | 2 | yes | — |
| 167 | #346 | C23 | 1 | 2 | yes | — |
| 168 | C4×C16 | C23 | 1 | 2 | yes | — |
| 169 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C22×Q8 | — | 2 | 2 | no | — |
| 171 | C2×Q16 | — | 2 | 2 | no | — |
| 172 | C2×Q16 | — | 2 | 2 | no | — |
| 173 | C2×Q16 | — | 2 | 2 | no | — |
| 174 | C2×Q16 | — | 2 | 8 | no | — |
| 175 | C2×Q16 | — | 4 | 4 | no | — |
| 176 | C2×Q16 | C24 | 1 | 4 | yes | — |
| 177 | #131 | — | 2 | 4 | no | — |
| 178 | #131 | — | 2 | 4 | no | — |
| 179 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 180 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 181 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 183 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 184 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 185 | C22×C8 | C24 | 1 | 2 | yes | — |
| 186 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 187 | C4⋊Q8 | — | 2 | 2 | no | — |
| 188 | C4⋊Q8 | — | 2 | 4 | no | — |
| 189 | C4⋊Q8 | — | 2 | 2 | no | — |
| 190 | C4⋊Q8 | — | 2 | 2 | no | — |
| 191 | C4⋊Q8 | — | 2 | 2 | no | — |
| 192 | C4⋊Q8 | — | 4 | 2 | no | — |
| 193 | C4⋊Q8 | — | 4 | 2 | no | — |
| 194 | C4⋊Q8 | — | 4 | 4 | no | — |
| 195 | C4⋊Q8 | — | 4 | 2 | no | — |
| 196 | #126 | — | 4 | 8 | no | — |
| 197 | #125 | — | 2 | 2 | no | — |
| 198 | #125 | — | 2 | 1 | no | — |
| 199 | #125 | — | 2 | 4 | no | — |
| 200 | #125 | — | 2 | 2 | no | — |
| 201 | #125 | — | 2 | 1 | no | — |
| 202 | #125 | — | 2 | 2 | no | — |
| 203 | #125 | — | 4 | 8 | no | — |
| 204 | #125 | — | 4 | 2 | no | — |
| 205 | #125 | — | 4 | 4 | no | — |
| 206 | #125 | — | 4 | 4 | no | — |
| 207 | #125 | — | 4 | 2 | no | — |
| 208 | #125 | — | 4 | 4 | no | — |
| 209 | #124 | — | 4 | 2 | no | — |
| 210 | #123 | — | 4 | 4 | no | — |
| 211 | C22⋊Q8 | — | 2 | 8 | no | — |
| 212 | C22⋊Q8 | — | 4 | 2 | no | — |
| 213 | C22⋊Q8 | — | 4 | 4 | no | — |
| 214 | C22⋊Q8 | — | 4 | 2 | no | — |
| 215 | C22⋊Q8 | — | 4 | 4 | no | — |
| 216 | C22⋊Q8 | — | 4 | 4 | no | — |
| 217 | C22⋊Q8 | — | 4 | 4 | no | — |
| 218 | C22⋊Q8 | — | 4 | 4 | no | — |
| 219 | C4×Q8 | — | 2 | 8 | no | — |
| 220 | C4×Q8 | — | 4 | 2 | no | — |
| 221 | C4×Q8 | — | 4 | 4 | no | — |
| 222 | C4×Q8 | — | 4 | 4 | no | — |
| 223 | C4×Q8 | — | 4 | 4 | no | — |
| 224 | C4×Q8 | — | 4 | 2 | no | — |
| 225 | C4×Q8 | — | 4 | 2 | no | — |
| 226 | C4×Q8 | D8 | 1 | 2 | yes | — |
| 227 | C4×D4 | — | 4 | 4 | no | — |
| 228 | C4×D4 | — | 4 | 2 | no | — |
| 229 | C4×D4 | D8 | 1 | 4 | yes | — |
| 230 | C4×D4 | D8 | 1 | 2 | yes | — |
| 231 | #117 | — | 2 | 2 | no | — |
| 232 | #117 | — | 2 | 4 | no | — |
| 233 | #117 | — | 2 | 2 | no | — |
| 234 | #117 | — | 4 | 4 | no | — |
| 235 | #117 | — | 4 | 4 | no | — |
| 236 | #117 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | #117 | C2×D4 | 1 | 2 | yes | — |
| 238 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 239 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 240 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 241 | C2×C4⋊C4 | — | 4 | 4 | no | — |
| 242 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 243 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 244 | C2×C42 | C2×D4 | 1 | 2 | yes | — |
| 245 | M32 | — | 2 | 4 | no | — |
| 246 | C2×C16 | — | 2 | 4 | no | — |
| 247 | C2×C16 | C24 | 1 | 4 | yes | — |
| 248 | C2×C16 | C24 | 1 | 4 | yes | — |
| 249 | #107 | — | 2 | 4 | no | — |
| 250 | #107 | — | 2 | 2 | no | — |
| 251 | #107 | — | 2 | 4 | no | — |
| 252 | #107 | — | 2 | 2 | no | — |
| 253 | #107 | — | 2 | 2 | no | — |
| 254 | #107 | C24 | 1 | 4 | yes | — |
| 255 | #107 | C24 | 1 | 2 | yes | — |
| 256 | #107 | C24 | 1 | 2 | yes | — |
| 257 | #107 | C24 | 1 | 4 | yes | — |
| 258 | #106 | — | 2 | 1 | no | — |
| 259 | #106 | — | 2 | 2 | no | — |
| 260 | #106 | — | 2 | 4 | no | — |
| 261 | #106 | — | 2 | 2 | no | — |
| 262 | #106 | — | 2 | 1 | no | — |
| 263 | #106 | — | 2 | 2 | no | — |
| 264 | #106 | — | 2 | 4 | no | — |
| 265 | #106 | — | 2 | 2 | no | — |
| 266 | #106 | — | 2 | 2 | no | — |
| 267 | #103 | — | 2 | 8 | no | — |
| 268 | #103 | — | 2 | 8 | no | — |
| 269 | #97 | C2×D4 | 1 | 2 | yes | — |
| 270 | #97 | C2×D4 | 1 | 2 | yes | — |
| 271 | #97 | C2×D4 | 1 | 2 | yes | — |
| 272 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 273 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 274 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 275 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 276 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 277 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 278 | C4×C8 | C24 | 1 | 2 | yes | — |
| 279 | #41 | — | 2 | 2 | no | — |
| 280 | #41 | — | 2 | 2 | no | — |
| 281 | C2×Q8 | — | 2 | 4 | no | — |
| 282 | C2×Q8 | — | 4 | 2 | no | — |
| 283 | C2×Q8 | — | 4 | 2 | no | — |
| 284 | C2×Q8 | — | 4 | 4 | no | — |
| 285 | C2×Q8 | — | 4 | 2 | no | — |
| 286 | C2×Q8 | — | 4 | 4 | no | — |
| 287 | C2×Q8 | — | 4 | 4 | no | — |
| 288 | C2×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 289 | C2×D4 | C2×D8 | 1 | 2 | yes | — |
| 290 | C2×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 291 | C22×C4 | — | 4 | 2 | no | — |
| 292 | C22×C4 | — | 4 | 4 | no | — |
| 293 | C22×C4 | — | 4 | 2 | no | — |
| 294 | C22×C4 | C2×D8 | 1 | 2 | yes | — |
| 295 | C22×C4 | C2×D8 | 1 | 4 | yes | — |
| 296 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 297 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 298 | Q16 | — | 2 | 8 | no | — |
| 299 | Q16 | — | 4 | 4 | no | — |
| 300 | Q16 | — | 4 | 4 | no | — |
| 301 | Q16 | — | 4 | 4 | no | — |
| 302 | M16 | — | 2 | 2 | no | — |
| 303 | M16 | — | 2 | 2 | no | — |
| 304 | M16 | — | 2 | 4 | no | — |
| 305 | M16 | — | 2 | 4 | no | — |
| 306 | C2×C8 | — | 2 | 4 | no | — |
| 307 | C2×C8 | — | 2 | 4 | no | — |
| 308 | C2×C8 | #137 | 1 | 4 | yes | — |
| 309 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 310 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 311 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 312 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 313 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 314 | C2×C8 | 2−1+4 | 1 | 4 | yes | — |
| 315 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 316 | C4⋊C4 | — | 2 | 4 | no | — |
| 317 | C4⋊C4 | — | 2 | 2 | no | — |
| 318 | C4⋊C4 | — | 2 | 4 | no | — |
| 319 | C4⋊C4 | — | 2 | 2 | no | — |
| 320 | C4⋊C4 | — | 4 | 4 | no | — |
| 321 | C4⋊C4 | — | 4 | 2 | no | — |
| 322 | C4⋊C4 | — | 4 | 4 | no | — |
| 323 | C4⋊C4 | — | 4 | 2 | no | — |
| 324 | C4⋊C4 | — | 4 | 4 | no | — |
| 325 | C4⋊C4 | — | 4 | 4 | no | — |
| 326 | C4⋊C4 | — | 4 | 4 | no | — |
| 327 | C4⋊C4 | — | 4 | 4 | no | — |
| 328 | C4⋊C4 | — | 4 | 4 | no | — |
| 329 | C4⋊C4 | — | 4 | 2 | no | — |
| 330 | C4⋊C4 | — | 4 | 8 | no | — |
| 331 | C4⋊C4 | — | 4 | 2 | no | — |
| 332 | C4⋊C4 | — | 4 | 8 | no | — |
| 333 | C4⋊C4 | — | 4 | 4 | no | — |
| 334 | C4⋊C4 | — | 4 | 2 | no | — |
| 335 | C4⋊C4 | — | 4 | 4 | no | — |
| 336 | C4⋊C4 | C2×D8 | 1 | 2 | yes | — |
| 337 | C4⋊C4 | C2×D8 | 1 | 4 | yes | — |
| 338 | C22⋊C4 | — | 4 | 2 | no | — |
| 339 | C22⋊C4 | — | 4 | 4 | no | — |
| 340 | C22⋊C4 | — | 4 | 2 | no | — |
| 341 | C22⋊C4 | — | 4 | 8 | no | — |
| 342 | C22⋊C4 | C2×D8 | 1 | 2 | yes | — |
| 343 | C22⋊C4 | C2×D8 | 1 | 4 | yes | — |
| 344 | C42 | — | 4 | 4 | no | — |
| 345 | C42 | — | 4 | 2 | no | — |
| 346 | C42 | — | 4 | 2 | no | — |
| 347 | C42 | — | 4 | 8 | no | — |
| 348 | C42 | C2×D8 | 1 | 4 | yes | — |
| 349 | C42 | C2×D8 | 1 | 2 | yes | — |
| 350 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 351 | C42 | C22×D4 | 1 | 2 | yes | — |
| 352 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 353 | C16 | — | 2 | 4 | no | — |
| 354 | C16 | — | 2 | 4 | no | — |
| 355 | C23 | C22×D8 | 1 | 2 | yes | — |
| 356 | C23 | C22×D8 | 1 | 1 | yes | characteristic |
| 357 | Q8 | — | 2 | 2 | no | — |
| 358 | Q8 | — | 4 | 4 | no | — |
| 359 | Q8 | — | 4 | 4 | no | — |
| 360 | Q8 | — | 8 | 4 | no | — |
| 361 | Q8 | — | 8 | 4 | no | — |
| 362 | Q8 | — | 16 | 4 | no | — |
| 363 | Q8 | — | 16 | 2 | no | — |
| 364 | D4 | — | 2 | 4 | no | — |
| 365 | D4 | — | 2 | 2 | no | — |
| 366 | C2×C4 | — | 2 | 2 | no | — |
| 367 | C2×C4 | — | 2 | 2 | no | — |
| 368 | C2×C4 | — | 4 | 2 | no | — |
| 369 | C2×C4 | — | 4 | 4 | no | — |
| 370 | C2×C4 | — | 4 | 4 | no | — |
| 371 | C2×C4 | — | 4 | 2 | no | — |
| 372 | C2×C4 | — | 4 | 4 | no | — |
| 373 | C2×C4 | — | 4 | 4 | no | — |
| 374 | C2×C4 | — | 4 | 2 | no | — |
| 375 | C2×C4 | — | 8 | 4 | no | — |
| 376 | C2×C4 | — | 16 | 2 | no | — |
| 377 | C2×C4 | — | 16 | 4 | no | — |
| 378 | C2×C4 | #536 | 1 | 2 | yes | — |
| 379 | C2×C4 | C22×D8 | 1 | 2 | yes | — |
| 380 | C2×C4 | C22×D8 | 1 | 4 | yes | — |
| 381 | C2×C4 | C22×D8 | 1 | 2 | yes | — |
| 382 | C2×C4 | C22×D8 | 1 | 2 | yes | — |
| 383 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 384 | C2×C4 | C2×#137 | 1 | 2 | yes | — |
| 385 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 386 | C8 | — | 2 | 2 | no | — |
| 387 | C8 | — | 2 | 2 | no | — |
| 388 | C8 | #536 | 1 | 2 | yes | — |
| 389 | C8 | C2×#137 | 1 | 2 | yes | — |
| 390 | C8 | C2×#137 | 1 | 2 | yes | — |
| 391 | C8 | C2×2−1+4 | 1 | 2 | yes | — |
| 392 | C22 | — | 2 | 2 | no | — |
| 393 | C22 | — | 2 | 2 | no | — |
| 394 | C22 | — | 2 | 4 | no | — |
| 395 | C22 | #3226 | 1 | 2 | yes | — |
| 396 | C22 | C23×D8 | 1 | 1 | yes | characteristic |
| 397 | C4 | — | 2 | 2 | no | — |
| 398 | C4 | — | 2 | 2 | no | — |
| 399 | C4 | — | 2 | 4 | no | — |
| 400 | C4 | — | 2 | 2 | no | — |
| 401 | C4 | — | 8 | 4 | no | — |
| 402 | C4 | — | 8 | 4 | no | — |
| 403 | C4 | — | 8 | 2 | no | — |
| 404 | C4 | — | 8 | 4 | no | — |
| 405 | C4 | — | 8 | 2 | no | — |
| 406 | C4 | #3226 | 1 | 2 | yes | — |
| 407 | C4 | C2×#536 | 1 | 1 | yes | characteristic |
| 408 | C4 | C22×#137 | 1 | 1 | yes | characteristic |
| 409 | C2 | — | 2 | 2 | no | — |
| 410 | C2 | — | 4 | 2 | no | — |
| 411 | C2 | C2×#3226 | 1 | 1 | yes | characteristic |
| 412 | C2 | #62637 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C23×D8 |
| commutator, Frattini, cosocle | C2×C8 | C25 |
| prime radical | C2×#41 | C2×D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×#41 ◁ C4×#131 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #33808 | C2 | semidirect |
| 4. #33803 | C2 | semidirect |
| 5. #33802 | C2 | semidirect |
| 6. #33732 | C2 | semidirect |
| 7. #33728 | C2 | semidirect |
| 8. #33705 | C2 | semidirect |
| 9. C2×#2245 | C2 | semidirect |
| 11. #33632 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #60715 | 2 |
| #60666 | 2 |
| #33808 | 2 |
| #33803 | 2 |
| #33802 | 2 |
| #33732 | 2 |
| #33728 | 2 |
| #33705 | 2 |
| C2×#2245 | 2 |
| #33651 | 2 |
| #33632 | 2 |
| #33421 | 2 |