Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
2456 conjugacy classes of subgroups.
The subgroup lattice has 419 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#3416 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C2×#3415 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #60649 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #60647 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #33722 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #33720 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #33719 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #33717 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #33716 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | C2×#2250 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #33326 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#578 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#577 | — | 2 | 1 | no | — |
| 14 | C2×#576 | — | 2 | 1 | no | — |
| 15 | C2×#576 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#576 | C22 | 1 | 2 | yes | — |
| 17 | #3500 | — | 2 | 1 | no | — |
| 18 | #3498 | — | 2 | 1 | no | — |
| 19 | #3416 | — | 2 | 16 | no | — |
| 20 | #3415 | — | 2 | 16 | no | — |
| 21 | C2×#510 | C22 | 1 | 6 | yes | complemented |
| 22 | C2×#509 | C22 | 1 | 6 | yes | complemented |
| 23 | C2×#509 | C22 | 1 | 6 | yes | complemented |
| 24 | C2×#509 | C22 | 1 | 6 | yes | complemented |
| 25 | C2×#508 | C22 | 1 | 6 | yes | complemented |
| 26 | C2×#508 | C22 | 1 | 6 | yes | complemented |
| 27 | C22×SD32 | C22 | 1 | 6 | yes | complemented |
| 28 | C22×D16 | C22 | 1 | 6 | yes | complemented |
| 29 | C2×#504 | C22 | 1 | 2 | yes | — |
| 30 | #3156 | C22 | 1 | 3 | yes | complemented |
| 31 | #3155 | — | 2 | 3 | no | — |
| 32 | #3155 | C22 | 1 | 3 | yes | complemented |
| 33 | #3155 | C22 | 1 | 6 | yes | complemented |
| 34 | #3154 | — | 2 | 3 | no | — |
| 35 | #3153 | — | 2 | 3 | no | — |
| 36 | #3151 | — | 2 | 3 | no | — |
| 37 | #3147 | C22 | 1 | 3 | yes | complemented |
| 38 | #3147 | C22 | 1 | 3 | yes | complemented |
| 39 | C2×#495 | C22 | 1 | 3 | yes | complemented |
| 40 | C2×#493 | C22 | 1 | 3 | yes | complemented |
| 41 | C4×#131 | C22 | 1 | 1 | yes | characteristic |
| 42 | #2251 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | #2251 | C22 | 1 | 3 | yes | complemented |
| 44 | #2251 | C22 | 1 | 6 | yes | complemented |
| 45 | #2250 | C22 | 1 | 3 | yes | complemented |
| 46 | #2250 | C22 | 1 | 6 | yes | complemented |
| 47 | #2250 | C22 | 1 | 12 | yes | complemented |
| 48 | #2250 | C22 | 1 | 3 | yes | complemented |
| 49 | #2250 | C22 | 1 | 6 | yes | complemented |
| 50 | #2249 | C22 | 1 | 12 | yes | complemented |
| 51 | #2248 | C22 | 1 | 6 | yes | complemented |
| 52 | #2246 | C22 | 1 | 6 | yes | complemented |
| 53 | #2108 | C22 | 1 | 6 | yes | complemented |
| 54 | C4×M32 | C22 | 1 | 3 | yes | complemented |
| 55 | C2×#346 | C22 | 1 | 3 | yes | complemented |
| 56 | C2×2−1+4 | — | 2 | 1 | no | — |
| 57 | C2×H(5,𝔽2) | — | 2 | 2 | no | — |
| 58 | C2×H(5,𝔽2) | — | 2 | 1 | no | — |
| 59 | #578 | — | 2 | 8 | no | — |
| 60 | #577 | — | 4 | 8 | no | — |
| 61 | #576 | — | 2 | 8 | no | — |
| 62 | #576 | — | 2 | 8 | no | — |
| 63 | #576 | — | 2 | 8 | no | — |
| 64 | #576 | — | 4 | 8 | no | — |
| 65 | C2×#137 | — | 2 | 3 | no | — |
| 66 | C2×#137 | — | 2 | 3 | no | — |
| 67 | C2×AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 68 | C2×AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 69 | C2×AGL(1,ℤ/8) | — | 2 | 3 | no | — |
| 70 | C2×AGL(1,ℤ/8) | — | 2 | 3 | no | — |
| 71 | C2×#135 | — | 2 | 3 | no | — |
| 72 | C2×#135 | — | 2 | 3 | no | — |
| 73 | C2×#135 | C23 | 1 | 3 | yes | — |
| 74 | C2×#135 | C23 | 1 | 6 | yes | — |
| 75 | C2×#135 | C23 | 1 | 3 | yes | — |
| 76 | C22×Q16 | C23 | 1 | 3 | yes | — |
| 77 | C22×SD16 | — | 2 | 3 | no | — |
| 78 | C22×D8 | — | 2 | 3 | no | — |
| 79 | C22×D8 | C23 | 1 | 6 | yes | — |
| 80 | C22×D8 | C23 | 1 | 3 | yes | — |
| 81 | C2×#131 | D4 | 1 | 1 | yes | characteristic |
| 82 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 83 | #550 | — | 4 | 2 | no | — |
| 84 | #548 | — | 4 | 2 | no | — |
| 85 | #546 | — | 4 | 6 | no | — |
| 86 | D42 | — | 4 | 6 | no | — |
| 87 | #536 | — | 2 | 3 | no | — |
| 88 | #535 | — | 2 | 3 | no | — |
| 89 | #535 | — | 2 | 6 | no | — |
| 90 | #532 | — | 2 | 3 | no | — |
| 91 | #532 | — | 2 | 3 | no | — |
| 92 | C2×#127 | — | 2 | 3 | no | — |
| 93 | C2×#124 | — | 2 | 3 | no | — |
| 94 | C4×#41 | D4 | 1 | 1 | yes | characteristic |
| 95 | #510 | — | 2 | 24 | no | — |
| 96 | #509 | — | 2 | 24 | no | — |
| 97 | #509 | — | 2 | 24 | no | — |
| 98 | #509 | — | 2 | 24 | no | — |
| 99 | #508 | — | 2 | 24 | no | — |
| 100 | #508 | — | 2 | 24 | no | — |
| 101 | C2×Q32 | C23 | 1 | 2 | yes | — |
| 102 | C2×Q32 | C23 | 1 | 6 | yes | — |
| 103 | C2×SD32 | — | 2 | 24 | no | — |
| 104 | C2×SD32 | C23 | 1 | 6 | yes | — |
| 105 | C2×SD32 | C23 | 1 | 12 | yes | — |
| 106 | C2×SD32 | C23 | 1 | 2 | yes | — |
| 107 | C2×SD32 | C23 | 1 | 6 | yes | — |
| 108 | C2×SD32 | C23 | 1 | 6 | yes | — |
| 109 | C2×D16 | — | 2 | 24 | no | — |
| 110 | C2×D16 | C23 | 1 | 6 | yes | — |
| 111 | C2×D16 | C23 | 1 | 12 | yes | — |
| 112 | C2×D16 | C23 | 1 | 6 | yes | — |
| 113 | #504 | D4 | 1 | 16 | yes | complemented |
| 114 | C2×M32 | C23 | 1 | 6 | yes | — |
| 115 | C22×C16 | C23 | 1 | 6 | yes | — |
| 116 | #497 | — | 2 | 6 | no | — |
| 117 | #496 | — | 2 | 12 | no | — |
| 118 | #496 | — | 2 | 6 | no | — |
| 119 | #495 | — | 2 | 3 | no | — |
| 120 | #495 | — | 2 | 3 | no | — |
| 121 | #495 | — | 2 | 3 | no | — |
| 122 | #495 | — | 2 | 3 | no | — |
| 123 | #495 | C23 | 1 | 3 | yes | — |
| 124 | #495 | C23 | 1 | 6 | yes | — |
| 125 | #495 | C23 | 1 | 1 | yes | characteristic |
| 126 | #495 | C23 | 1 | 6 | yes | — |
| 127 | #494 | C23 | 1 | 1 | yes | characteristic |
| 128 | #494 | C23 | 1 | 3 | yes | — |
| 129 | #493 | — | 2 | 3 | no | — |
| 130 | #493 | — | 2 | 3 | no | — |
| 131 | #493 | C23 | 1 | 3 | yes | — |
| 132 | #493 | C23 | 1 | 6 | yes | — |
| 133 | #493 | C23 | 1 | 3 | yes | — |
| 134 | #492 | — | 2 | 3 | no | — |
| 135 | #492 | — | 2 | 3 | no | — |
| 136 | #405 | D4 | 1 | 3 | yes | — |
| 137 | #405 | C23 | 1 | 3 | yes | — |
| 138 | C4×M16 | D4 | 1 | 3 | yes | — |
| 139 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 140 | #346 | C23 | 1 | 1 | yes | characteristic |
| 141 | #346 | C23 | 1 | 3 | yes | — |
| 142 | #346 | C23 | 1 | 6 | yes | — |
| 143 | C4×C16 | C23 | 1 | 6 | yes | — |
| 144 | 2−1+4 | — | 4 | 4 | no | — |
| 145 | 2−1+4 | — | 4 | 4 | no | — |
| 146 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 147 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 148 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 149 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 150 | C2×#41 | — | 2 | 6 | no | — |
| 151 | C2×#41 | — | 2 | 3 | no | — |
| 152 | C2×#41 | — | 2 | 3 | no | — |
| 153 | C2×#41 | — | 4 | 1 | no | — |
| 154 | C2×#41 | — | 4 | 2 | no | — |
| 155 | C2×#41 | — | 4 | 3 | no | — |
| 156 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C22×Q8 | — | 2 | 3 | no | — |
| 158 | C22×Q8 | — | 4 | 1 | no | — |
| 159 | C22×D4 | — | 2 | 3 | no | — |
| 160 | C22×D4 | — | 2 | 6 | no | — |
| 161 | C22×D4 | — | 4 | 6 | no | — |
| 162 | C22×D4 | — | 4 | 3 | no | — |
| 163 | C22×D4 | — | 4 | 6 | no | — |
| 164 | #137 | — | 4 | 12 | no | — |
| 165 | #137 | — | 4 | 12 | no | — |
| 166 | AGL(1,ℤ/8) | — | 4 | 24 | no | — |
| 167 | AGL(1,ℤ/8) | — | 4 | 12 | no | — |
| 168 | AGL(1,ℤ/8) | — | 4 | 24 | no | — |
| 169 | AGL(1,ℤ/8) | — | 4 | 12 | no | — |
| 170 | #135 | — | 2 | 12 | no | — |
| 171 | #135 | — | 2 | 12 | no | — |
| 172 | #135 | — | 2 | 12 | no | — |
| 173 | #135 | — | 2 | 12 | no | — |
| 174 | #135 | — | 4 | 12 | no | — |
| 175 | #135 | — | 4 | 12 | no | — |
| 176 | C2×Q16 | — | 2 | 12 | no | — |
| 177 | C2×Q16 | — | 2 | 3 | no | — |
| 178 | C2×Q16 | — | 2 | 1 | no | — |
| 179 | C2×Q16 | — | 2 | 3 | no | — |
| 180 | C2×Q16 | C24 | 1 | 3 | yes | — |
| 181 | C2×Q16 | C24 | 1 | 1 | yes | characteristic |
| 182 | C2×Q16 | C24 | 1 | 2 | yes | — |
| 183 | C2×SD16 | — | 2 | 3 | no | — |
| 184 | C2×SD16 | — | 2 | 6 | no | — |
| 185 | C2×SD16 | — | 2 | 1 | no | — |
| 186 | C2×SD16 | — | 2 | 6 | no | — |
| 187 | C2×SD16 | — | 2 | 6 | no | — |
| 188 | C2×SD16 | — | 2 | 3 | no | — |
| 189 | C2×SD16 | — | 2 | 3 | no | — |
| 190 | C2×SD16 | — | 4 | 12 | no | — |
| 191 | C2×D8 | — | 2 | 12 | no | — |
| 192 | C2×D8 | — | 2 | 12 | no | — |
| 193 | C2×D8 | — | 2 | 12 | no | — |
| 194 | C2×D8 | — | 2 | 3 | no | — |
| 195 | C2×D8 | — | 2 | 6 | no | — |
| 196 | C2×D8 | — | 2 | 6 | no | — |
| 197 | C2×D8 | — | 2 | 3 | no | — |
| 198 | C2×D8 | — | 2 | 3 | no | — |
| 199 | C2×D8 | — | 4 | 12 | no | — |
| 200 | C2×D8 | C24 | 1 | 6 | yes | — |
| 201 | C2×D8 | C24 | 1 | 3 | yes | — |
| 202 | C2×D8 | C24 | 1 | 1 | yes | characteristic |
| 203 | #131 | D8 | 1 | 8 | yes | — |
| 204 | #131 | C2×D4 | 1 | 8 | yes | — |
| 205 | C2×M16 | C2×D4 | 1 | 3 | yes | — |
| 206 | C2×M16 | C2×D4 | 1 | 3 | yes | — |
| 207 | C22×C8 | C2×D4 | 1 | 3 | yes | — |
| 208 | C22×C8 | C24 | 1 | 3 | yes | — |
| 209 | C4⋊Q8 | — | 2 | 1 | no | — |
| 210 | C4⋊Q8 | — | 2 | 3 | no | — |
| 211 | #127 | — | 2 | 3 | no | — |
| 212 | #127 | — | 2 | 6 | no | — |
| 213 | #127 | — | 2 | 3 | no | — |
| 214 | #127 | — | 4 | 6 | no | — |
| 215 | #124 | — | 2 | 3 | no | — |
| 216 | #124 | — | 2 | 6 | no | — |
| 217 | #124 | — | 2 | 1 | no | — |
| 218 | #124 | — | 2 | 6 | no | — |
| 219 | #124 | — | 4 | 6 | no | — |
| 220 | #123 | — | 4 | 6 | no | — |
| 221 | C22⋊Q8 | — | 4 | 6 | no | — |
| 222 | #121 | — | 4 | 6 | no | — |
| 223 | #121 | — | 4 | 6 | no | — |
| 224 | #121 | — | 4 | 12 | no | — |
| 225 | #121 | — | 4 | 6 | no | — |
| 226 | #120 | — | 4 | 12 | no | — |
| 227 | #120 | — | 4 | 6 | no | — |
| 228 | C4×Q8 | D8 | 1 | 2 | yes | — |
| 229 | C4×D4 | — | 4 | 6 | no | — |
| 230 | C4×D4 | — | 4 | 6 | no | — |
| 231 | C4×D4 | D8 | 1 | 6 | yes | — |
| 232 | #117 | C2×D4 | 1 | 3 | yes | — |
| 233 | C2×C22⋊C4 | — | 4 | 6 | no | — |
| 234 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 235 | Q32 | — | 2 | 4 | no | — |
| 236 | Q32 | — | 2 | 12 | no | — |
| 237 | SD32 | — | 2 | 12 | no | — |
| 238 | SD32 | — | 2 | 24 | no | — |
| 239 | SD32 | — | 2 | 4 | no | — |
| 240 | SD32 | — | 2 | 12 | no | — |
| 241 | SD32 | — | 2 | 12 | no | — |
| 242 | D16 | — | 2 | 12 | no | — |
| 243 | D16 | — | 2 | 24 | no | — |
| 244 | D16 | — | 2 | 12 | no | — |
| 245 | M32 | C2×D4 | 1 | 24 | yes | complemented |
| 246 | C2×C16 | C2×D4 | 1 | 24 | yes | complemented |
| 247 | C2×C16 | C24 | 1 | 6 | yes | — |
| 248 | C2×C16 | C24 | 1 | 2 | yes | — |
| 249 | #97 | C2×D4 | 1 | 6 | yes | — |
| 250 | C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 251 | C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 252 | C4×C8 | C24 | 1 | 3 | yes | — |
| 253 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 254 | C24 | — | 4 | 3 | no | — |
| 255 | C24 | — | 4 | 6 | no | — |
| 256 | #41 | — | 4 | 6 | no | — |
| 257 | #41 | — | 4 | 12 | no | — |
| 258 | #41 | — | 4 | 6 | no | — |
| 259 | #41 | — | 4 | 12 | no | — |
| 260 | #41 | — | 4 | 6 | no | — |
| 261 | #41 | — | 4 | 6 | no | — |
| 262 | #41 | — | 8 | 4 | no | — |
| 263 | #41 | — | 8 | 8 | no | — |
| 264 | #41 | — | 8 | 12 | no | — |
| 265 | #41 | #127 | 1 | 4 | yes | — |
| 266 | #41 | C2×D8 | 1 | 4 | yes | — |
| 267 | C2×Q8 | — | 2 | 2 | no | — |
| 268 | C2×Q8 | — | 2 | 3 | no | — |
| 269 | C2×Q8 | — | 2 | 1 | no | — |
| 270 | C2×Q8 | — | 4 | 3 | no | — |
| 271 | C2×Q8 | — | 4 | 6 | no | — |
| 272 | C2×Q8 | — | 4 | 6 | no | — |
| 273 | C2×Q8 | — | 8 | 4 | no | — |
| 274 | C2×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 275 | C2×D4 | — | 2 | 3 | no | — |
| 276 | C2×D4 | — | 2 | 6 | no | — |
| 277 | C2×D4 | — | 2 | 1 | no | — |
| 278 | C2×D4 | — | 4 | 6 | no | — |
| 279 | C2×D4 | — | 4 | 3 | no | — |
| 280 | C2×D4 | — | 4 | 3 | no | — |
| 281 | C2×D4 | — | 4 | 6 | no | — |
| 282 | C2×D4 | — | 4 | 12 | no | — |
| 283 | C2×D4 | — | 4 | 12 | no | — |
| 284 | C2×D4 | — | 4 | 6 | no | — |
| 285 | C2×D4 | — | 4 | 6 | no | — |
| 286 | C2×D4 | — | 4 | 3 | no | — |
| 287 | C2×D4 | — | 4 | 6 | no | — |
| 288 | C2×D4 | — | 4 | 6 | no | — |
| 289 | C2×D4 | — | 4 | 12 | no | — |
| 290 | C2×D4 | — | 8 | 24 | no | — |
| 291 | C2×D4 | — | 8 | 12 | no | — |
| 292 | C2×D4 | — | 16 | 12 | no | — |
| 293 | C2×D4 | C2×D8 | 1 | 3 | yes | — |
| 294 | C22×C4 | — | 4 | 3 | no | — |
| 295 | C22×C4 | — | 4 | 6 | no | — |
| 296 | C22×C4 | — | 4 | 3 | no | — |
| 297 | C22×C4 | — | 4 | 3 | no | — |
| 298 | C22×C4 | C2×D8 | 1 | 6 | yes | — |
| 299 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 300 | Q16 | — | 2 | 6 | no | — |
| 301 | Q16 | — | 2 | 2 | no | — |
| 302 | Q16 | — | 2 | 2 | no | — |
| 303 | Q16 | — | 2 | 2 | no | — |
| 304 | Q16 | — | 4 | 6 | no | — |
| 305 | Q16 | — | 4 | 2 | no | — |
| 306 | Q16 | — | 4 | 6 | no | — |
| 307 | SD16 | — | 4 | 12 | no | — |
| 308 | SD16 | — | 4 | 6 | no | — |
| 309 | SD16 | — | 4 | 6 | no | — |
| 310 | SD16 | — | 4 | 6 | no | — |
| 311 | SD16 | — | 4 | 12 | no | — |
| 312 | SD16 | — | 4 | 2 | no | — |
| 313 | SD16 | — | 4 | 12 | no | — |
| 314 | D8 | — | 2 | 6 | no | — |
| 315 | D8 | — | 2 | 6 | no | — |
| 316 | D8 | — | 2 | 2 | no | — |
| 317 | D8 | — | 2 | 6 | no | — |
| 318 | D8 | — | 4 | 6 | no | — |
| 319 | D8 | — | 4 | 12 | no | — |
| 320 | D8 | — | 4 | 6 | no | — |
| 321 | D8 | — | 4 | 12 | no | — |
| 322 | D8 | — | 4 | 6 | no | — |
| 323 | M16 | #127 | 1 | 12 | yes | — |
| 324 | M16 | C2×D8 | 1 | 12 | yes | — |
| 325 | C2×C8 | C2×D8 | 1 | 12 | yes | — |
| 326 | C2×C8 | C22×D4 | 1 | 3 | yes | — |
| 327 | C2×C8 | C22×D4 | 1 | 12 | yes | — |
| 328 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 329 | C2×C8 | C22×D4 | 1 | 3 | yes | — |
| 330 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 331 | C4⋊C4 | — | 4 | 2 | no | — |
| 332 | C4⋊C4 | — | 4 | 6 | no | — |
| 333 | C4⋊C4 | C2×D8 | 1 | 6 | yes | — |
| 334 | C22⋊C4 | — | 4 | 6 | no | — |
| 335 | C22⋊C4 | — | 4 | 12 | no | — |
| 336 | C22⋊C4 | — | 4 | 2 | no | — |
| 337 | C22⋊C4 | — | 4 | 12 | no | — |
| 338 | C22⋊C4 | C2×D8 | 1 | 6 | yes | — |
| 339 | C42 | C2×D8 | 1 | 6 | yes | — |
| 340 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 341 | C42 | C22×D4 | 1 | 3 | yes | — |
| 342 | C16 | C22×D4 | 1 | 4 | yes | — |
| 343 | C16 | C22×D4 | 1 | 12 | yes | — |
| 344 | C23 | — | 4 | 3 | no | — |
| 345 | C23 | — | 4 | 1 | no | — |
| 346 | C23 | — | 4 | 6 | no | — |
| 347 | C23 | — | 8 | 12 | no | — |
| 348 | C23 | — | 8 | 6 | no | — |
| 349 | C23 | — | 16 | 12 | no | — |
| 350 | C23 | — | 16 | 6 | no | — |
| 351 | C23 | C22×D8 | 1 | 3 | yes | — |
| 352 | Q8 | — | 4 | 1 | no | — |
| 353 | Q8 | — | 4 | 2 | no | — |
| 354 | Q8 | — | 4 | 3 | no | — |
| 355 | Q8 | — | 4 | 3 | no | — |
| 356 | Q8 | — | 4 | 2 | no | — |
| 357 | Q8 | — | 4 | 1 | no | — |
| 358 | Q8 | — | 8 | 6 | no | — |
| 359 | Q8 | #493 | 1 | 4 | yes | — |
| 360 | D4 | — | 4 | 3 | no | — |
| 361 | D4 | — | 4 | 6 | no | — |
| 362 | D4 | — | 4 | 1 | no | — |
| 363 | D4 | — | 4 | 6 | no | — |
| 364 | D4 | — | 4 | 1 | no | — |
| 365 | D4 | — | 4 | 3 | no | — |
| 366 | D4 | — | 8 | 12 | no | — |
| 367 | D4 | — | 8 | 12 | no | — |
| 368 | D4 | — | 8 | 6 | no | — |
| 369 | D4 | — | 8 | 6 | no | — |
| 370 | D4 | — | 8 | 12 | no | — |
| 371 | D4 | — | 8 | 6 | no | — |
| 372 | D4 | — | 16 | 6 | no | — |
| 373 | D4 | — | 16 | 12 | no | — |
| 374 | D4 | #493 | 1 | 12 | yes | — |
| 375 | C2×C4 | — | 4 | 6 | no | — |
| 376 | C2×C4 | — | 4 | 2 | no | — |
| 377 | C2×C4 | — | 4 | 3 | no | — |
| 378 | C2×C4 | — | 4 | 1 | no | — |
| 379 | C2×C4 | — | 8 | 6 | no | — |
| 380 | C2×C4 | — | 8 | 12 | no | — |
| 381 | C2×C4 | — | 8 | 6 | no | — |
| 382 | C2×C4 | — | 8 | 6 | no | — |
| 383 | C2×C4 | C2×#127 | 1 | 6 | yes | — |
| 384 | C2×C4 | C22×D8 | 1 | 2 | yes | — |
| 385 | C2×C4 | C22×D8 | 1 | 6 | yes | — |
| 386 | C2×C4 | C22×D8 | 1 | 3 | yes | — |
| 387 | C2×C4 | C22×D8 | 1 | 6 | yes | — |
| 388 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 389 | C8 | C2×#127 | 1 | 6 | yes | — |
| 390 | C8 | C22×D8 | 1 | 2 | yes | — |
| 391 | C8 | C22×D8 | 1 | 6 | yes | — |
| 392 | C8 | C23×D4 | 1 | 2 | yes | — |
| 393 | C22 | — | 2 | 6 | no | — |
| 394 | C22 | — | 8 | 12 | no | — |
| 395 | C22 | — | 8 | 2 | no | — |
| 396 | C22 | — | 8 | 6 | no | — |
| 397 | C22 | — | 8 | 1 | no | — |
| 398 | C22 | — | 8 | 6 | no | — |
| 399 | C22 | — | 8 | 3 | no | — |
| 400 | C22 | — | 32 | 12 | no | — |
| 401 | C22 | — | 32 | 6 | no | — |
| 402 | C22 | C2×#493 | 1 | 6 | yes | — |
| 403 | C22 | C23×D8 | 1 | 1 | yes | characteristic |
| 404 | C4 | — | 2 | 2 | no | — |
| 405 | C4 | — | 2 | 6 | no | — |
| 406 | C4 | — | 8 | 2 | no | — |
| 407 | C4 | — | 8 | 1 | no | — |
| 408 | C4 | — | 8 | 3 | no | — |
| 409 | C4 | C2×#493 | 1 | 6 | yes | — |
| 410 | C4 | C22×#127 | 1 | 1 | yes | characteristic |
| 411 | C4 | C23×D8 | 1 | 1 | yes | characteristic |
| 412 | C2 | — | 2 | 6 | no | — |
| 413 | C2 | — | 16 | 1 | no | — |
| 414 | C2 | — | 16 | 6 | no | — |
| 415 | C2 | — | 16 | 3 | no | — |
| 416 | C2 | C22×#493 | 1 | 1 | yes | characteristic |
| 417 | C2 | #62636 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C23×D8 |
| commutator, Frattini, cosocle | C2×C8 | C25 |
| 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 |
|---|---|---|
| 1. C2×#3416 | C2 | semidirect |
| 2. C2×#3415 | C2 | semidirect |
| 3. #60649 | C2 | semidirect |
| 4. #60647 | C2 | semidirect |
| 5. #33722 | C2 | semidirect |
| 6. #33720 | C2 | semidirect |
| 7. #33719 | C2 | semidirect |
| 8. #33717 | C2 | semidirect |
| 9. #33716 | C2 | semidirect |
| 10. C2×#2250 | C2 | semidirect |
| 11. #33326 | C2 | semidirect |
| 21. C2×#510 | C22 | semidirect |
| 22. C2×#509 | C22 | semidirect |
| 23. C2×#509 | C22 | semidirect |
| 24. C2×#509 | C22 | semidirect |
| 25. C2×#508 | C22 | semidirect |
| 26. C2×#508 | C22 | semidirect |
| 27. C22×SD32 | C22 | semidirect |
| 28. C22×D16 | C22 | semidirect |
| 30. #3156 | C22 | semidirect |
| 32. #3155 | C22 | semidirect |
| 33. #3155 | C22 | semidirect |
| 37. #3147 | C22 | semidirect |
| 38. #3147 | C22 | semidirect |
| 39. C2×#495 | C22 | semidirect |
| 40. C2×#493 | C22 | semidirect |
| 42. #2251 | C22 | semidirect |
| 43. #2251 | C22 | semidirect |
| 44. #2251 | C22 | semidirect |
| 45. #2250 | C22 | semidirect |
| 46. #2250 | C22 | semidirect |
| 47. #2250 | C22 | semidirect |
| 48. #2250 | C22 | semidirect |
| 49. #2250 | C22 | semidirect |
| 50. #2249 | C22 | semidirect |
| 51. #2248 | C22 | semidirect |
| 52. #2246 | C22 | semidirect |
| 53. #2108 | C22 | semidirect |
| 54. C4×M32 | C22 | semidirect |
| 55. C2×#346 | C22 | semidirect |
| 113. #504 | D4 | semidirect |
| 245. M32 | C2×D4 | semidirect |
| 246. C2×C16 | C2×D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3416 | 2 |
| C2×#3415 | 2 |
| #60649 | 2 |
| #60647 | 2 |
| #33722 | 2 |
| #33720 | 2 |
| #33719 | 2 |
| #33717 | 2 |
| #33716 | 2 |
| C2×#2250 | 2 |
| #33326 | 2 |