Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1009 conjugacy classes of subgroups.
The subgroup lattice has 358 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #3538 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #3486 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #3312 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #3300 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | D4×Q16 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #3270 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #3223 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #3202 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #3190 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #3127 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #3011 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×#451 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #2977 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C2×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 15 | C23×Q8 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#137 | C22 | 1 | 2 | yes | complemented |
| 17 | C22×Q16 | C22 | 1 | 4 | yes | — |
| 18 | C22×Q16 | C22 | 1 | 2 | yes | complemented |
| 19 | #563 | — | 2 | 2 | no | — |
| 20 | #552 | C22 | 1 | 4 | yes | — |
| 21 | #551 | — | 2 | 2 | no | — |
| 22 | D4×Q8 | — | 2 | 2 | no | — |
| 23 | D4×Q8 | C22 | 1 | 4 | yes | — |
| 24 | D4×Q8 | C22 | 1 | 4 | yes | — |
| 25 | #548 | — | 2 | 2 | no | — |
| 26 | #548 | C22 | 1 | 4 | yes | — |
| 27 | #544 | — | 2 | 2 | no | — |
| 28 | #541 | C22 | 1 | 2 | yes | — |
| 29 | #539 | — | 2 | 2 | no | — |
| 30 | #536 | — | 2 | 2 | no | — |
| 31 | #536 | C22 | 1 | 1 | yes | characteristic |
| 32 | #536 | C22 | 1 | 1 | yes | characteristic |
| 33 | #536 | C22 | 1 | 2 | yes | — |
| 34 | #525 | — | 2 | 2 | no | — |
| 35 | #525 | C22 | 1 | 1 | yes | characteristic |
| 36 | #525 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×C22⋊Q8 | C22 | 1 | 2 | yes | — |
| 38 | #519 | C22 | 1 | 1 | yes | characteristic |
| 39 | #497 | C22 | 1 | 2 | yes | complemented |
| 40 | #494 | C22 | 1 | 2 | yes | complemented |
| 41 | #491 | C22 | 1 | 2 | yes | complemented |
| 42 | #488 | C22 | 1 | 2 | yes | complemented |
| 43 | #485 | C22 | 1 | 4 | yes | — |
| 44 | #485 | C22 | 1 | 4 | yes | complemented |
| 45 | #483 | C22 | 1 | 2 | yes | — |
| 46 | #480 | C22 | 1 | 2 | yes | — |
| 47 | #479 | C22 | 1 | 4 | yes | complemented |
| 48 | #470 | C22 | 1 | 4 | yes | complemented |
| 49 | #467 | C22 | 1 | 4 | yes | — |
| 50 | #467 | C22 | 1 | 4 | yes | complemented |
| 51 | #465 | C22 | 1 | 4 | yes | — |
| 52 | #464 | C22 | 1 | 4 | yes | complemented |
| 53 | #462 | C22 | 1 | 4 | yes | complemented |
| 54 | #462 | C22 | 1 | 4 | yes | complemented |
| 55 | #452 | C22 | 1 | 4 | yes | — |
| 56 | #452 | C22 | 1 | 4 | yes | complemented |
| 57 | #451 | C22 | 1 | 4 | yes | — |
| 58 | #451 | C22 | 1 | 2 | yes | — |
| 59 | #451 | C22 | 1 | 4 | yes | — |
| 60 | #451 | C22 | 1 | 4 | yes | — |
| 61 | #451 | C22 | 1 | 4 | yes | — |
| 62 | #451 | C22 | 1 | 4 | yes | complemented |
| 63 | #451 | C22 | 1 | 4 | yes | complemented |
| 64 | #448 | C22 | 1 | 2 | yes | — |
| 65 | #441 | C22 | 1 | 4 | yes | complemented |
| 66 | C4×Q16 | C22 | 1 | 4 | yes | complemented |
| 67 | #435 | C22 | 1 | 4 | yes | — |
| 68 | C8×D4 | C22 | 1 | 4 | yes | — |
| 69 | #433 | C22 | 1 | 2 | yes | — |
| 70 | #419 | C22 | 1 | 2 | yes | complemented |
| 71 | #416 | C22 | 1 | 2 | yes | complemented |
| 72 | C2×#103 | C22 | 1 | 4 | yes | — |
| 73 | #408 | C22 | 1 | 2 | yes | — |
| 74 | C2×C22⋊C8 | C22 | 1 | 2 | yes | — |
| 75 | 2−1+4 | — | 4 | 4 | no | — |
| 76 | C2×#41 | — | 2 | 2 | no | — |
| 77 | C2×#41 | — | 2 | 1 | no | — |
| 78 | C2×#41 | C23 | 1 | 2 | yes | — |
| 79 | C2×#41 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×#41 | C23 | 1 | 1 | yes | characteristic |
| 81 | C22×Q8 | — | 2 | 1 | no | — |
| 82 | C22×Q8 | — | 2 | 1 | no | — |
| 83 | C22×Q8 | — | 2 | 2 | no | — |
| 84 | C22×Q8 | — | 4 | 4 | no | — |
| 85 | C22×Q8 | C23 | 1 | 1 | yes | characteristic |
| 86 | C22×Q8 | C23 | 1 | 4 | yes | — |
| 87 | C22×Q8 | C23 | 1 | 2 | yes | — |
| 88 | C22×Q8 | C23 | 1 | 2 | yes | — |
| 89 | C22×Q8 | C23 | 1 | 1 | yes | characteristic |
| 90 | C22×Q8 | C23 | 1 | 2 | yes | — |
| 91 | C23×C4 | — | 2 | 1 | no | — |
| 92 | C23×C4 | C23 | 1 | 1 | yes | characteristic |
| 93 | #137 | — | 4 | 4 | no | — |
| 94 | C2×Q16 | — | 4 | 8 | no | — |
| 95 | C2×Q16 | — | 4 | 4 | no | — |
| 96 | C2×Q16 | C23 | 1 | 4 | yes | — |
| 97 | C2×Q16 | C23 | 1 | 4 | yes | — |
| 98 | C2×Q16 | C23 | 1 | 4 | yes | — |
| 99 | C2×Q16 | C23 | 1 | 4 | yes | — |
| 100 | C2×Q16 | C23 | 1 | 4 | yes | — |
| 101 | C2×SD16 | C23 | 1 | 4 | yes | — |
| 102 | C2×M16 | C23 | 1 | 2 | yes | — |
| 103 | C22×C8 | C23 | 1 | 4 | yes | — |
| 104 | C22×C8 | C23 | 1 | 2 | yes | — |
| 105 | C4⋊Q8 | — | 2 | 2 | no | — |
| 106 | C4⋊Q8 | — | 2 | 1 | no | — |
| 107 | C4⋊Q8 | — | 2 | 4 | no | — |
| 108 | C4⋊Q8 | — | 2 | 4 | no | — |
| 109 | C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 110 | C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 111 | #126 | — | 2 | 4 | no | — |
| 112 | #126 | — | 2 | 4 | no | — |
| 113 | #125 | — | 2 | 4 | no | — |
| 114 | #125 | — | 2 | 4 | no | — |
| 115 | #125 | C23 | 1 | 2 | yes | — |
| 116 | #124 | — | 2 | 1 | no | — |
| 117 | #124 | — | 2 | 2 | no | — |
| 118 | #124 | — | 2 | 4 | no | — |
| 119 | #124 | C23 | 1 | 2 | yes | — |
| 120 | #123 | — | 2 | 2 | no | — |
| 121 | #123 | — | 2 | 2 | no | — |
| 122 | #123 | — | 2 | 2 | no | — |
| 123 | #123 | — | 2 | 4 | no | — |
| 124 | #123 | — | 2 | 1 | no | — |
| 125 | #123 | — | 2 | 2 | no | — |
| 126 | #123 | D4 | 1 | 2 | yes | — |
| 127 | C22⋊Q8 | — | 2 | 2 | no | — |
| 128 | C22⋊Q8 | — | 2 | 2 | no | — |
| 129 | C22⋊Q8 | — | 2 | 4 | no | — |
| 130 | C22⋊Q8 | — | 2 | 2 | no | — |
| 131 | C22⋊Q8 | — | 2 | 4 | no | — |
| 132 | C22⋊Q8 | — | 2 | 4 | no | — |
| 133 | C22⋊Q8 | — | 2 | 4 | no | — |
| 134 | C22⋊Q8 | — | 2 | 4 | no | — |
| 135 | C22⋊Q8 | D4 | 1 | 2 | yes | — |
| 136 | C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 137 | C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 138 | C22⋊Q8 | C23 | 1 | 2 | yes | — |
| 139 | C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 140 | C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 141 | #121 | — | 2 | 4 | no | — |
| 142 | #121 | D4 | 1 | 2 | yes | — |
| 143 | #121 | C23 | 1 | 2 | yes | — |
| 144 | #120 | — | 2 | 1 | no | — |
| 145 | #120 | D4 | 1 | 2 | yes | — |
| 146 | C4×Q8 | — | 2 | 2 | no | — |
| 147 | C4×Q8 | C23 | 1 | 4 | yes | — |
| 148 | C4×Q8 | C23 | 1 | 4 | yes | — |
| 149 | C4×D4 | — | 2 | 4 | no | — |
| 150 | C4×D4 | — | 2 | 4 | no | — |
| 151 | C4×D4 | — | 2 | 2 | no | — |
| 152 | C4×D4 | — | 2 | 4 | no | — |
| 153 | C4×D4 | C23 | 1 | 4 | yes | — |
| 154 | #117 | — | 2 | 2 | no | — |
| 155 | #117 | — | 2 | 4 | no | — |
| 156 | #117 | C23 | 1 | 1 | yes | characteristic |
| 157 | #117 | C23 | 1 | 2 | yes | — |
| 158 | #117 | C23 | 1 | 1 | yes | characteristic |
| 159 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 160 | C2×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 161 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 162 | #107 | C23 | 1 | 4 | yes | — |
| 163 | #106 | C23 | 1 | 4 | yes | — |
| 164 | C4⋊C8 | C23 | 1 | 4 | yes | — |
| 165 | #103 | C23 | 1 | 4 | yes | — |
| 166 | #103 | C23 | 1 | 4 | yes | — |
| 167 | #103 | C23 | 1 | 4 | yes | — |
| 168 | #103 | C23 | 1 | 4 | yes | — |
| 169 | #103 | C23 | 1 | 4 | yes | — |
| 170 | #103 | C23 | 1 | 4 | yes | — |
| 171 | #103 | C23 | 1 | 4 | yes | — |
| 172 | #102 | C23 | 1 | 4 | yes | — |
| 173 | C22⋊C8 | C23 | 1 | 4 | yes | — |
| 174 | C22⋊C8 | C23 | 1 | 2 | yes | — |
| 175 | C22⋊C8 | C23 | 1 | 2 | yes | — |
| 176 | C22⋊C8 | C23 | 1 | 4 | yes | — |
| 177 | #97 | C23 | 1 | 2 | yes | — |
| 178 | C4×C8 | C23 | 1 | 2 | yes | — |
| 179 | C24 | C2×D4 | 1 | 1 | yes | characteristic |
| 180 | #41 | — | 2 | 4 | no | — |
| 181 | #41 | — | 4 | 2 | no | — |
| 182 | #41 | — | 4 | 2 | no | — |
| 183 | #41 | — | 4 | 2 | no | — |
| 184 | #41 | — | 4 | 8 | no | — |
| 185 | #41 | — | 4 | 4 | no | — |
| 186 | C2×Q8 | — | 2 | 4 | no | — |
| 187 | C2×Q8 | — | 2 | 1 | no | — |
| 188 | C2×Q8 | — | 2 | 4 | no | — |
| 189 | C2×Q8 | — | 2 | 1 | no | — |
| 190 | C2×Q8 | — | 2 | 2 | no | — |
| 191 | C2×Q8 | — | 2 | 2 | no | — |
| 192 | C2×Q8 | — | 2 | 2 | no | — |
| 193 | C2×Q8 | — | 2 | 8 | no | — |
| 194 | C2×Q8 | — | 2 | 4 | no | — |
| 195 | C2×Q8 | — | 4 | 4 | no | — |
| 196 | C2×Q8 | — | 4 | 2 | no | — |
| 197 | C2×Q8 | — | 4 | 2 | no | — |
| 198 | C2×Q8 | — | 4 | 4 | no | — |
| 199 | C2×Q8 | — | 4 | 4 | no | — |
| 200 | C2×Q8 | — | 4 | 2 | no | — |
| 201 | C2×Q8 | — | 4 | 2 | no | — |
| 202 | C2×Q8 | — | 4 | 8 | no | — |
| 203 | C2×Q8 | — | 4 | 4 | no | — |
| 204 | C2×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 205 | C2×Q8 | C24 | 1 | 2 | yes | — |
| 206 | C2×Q8 | C24 | 1 | 1 | yes | characteristic |
| 207 | C2×Q8 | C24 | 1 | 4 | yes | — |
| 208 | C2×Q8 | C24 | 1 | 2 | yes | — |
| 209 | C2×D4 | — | 2 | 2 | no | — |
| 210 | C2×D4 | — | 2 | 1 | no | — |
| 211 | C2×D4 | — | 2 | 2 | no | — |
| 212 | C2×D4 | C2×D4 | 1 | 4 | yes | — |
| 213 | C2×D4 | C2×D4 | 1 | 2 | yes | — |
| 214 | C2×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 215 | C2×D4 | C24 | 1 | 1 | yes | characteristic |
| 216 | C22×C4 | — | 2 | 1 | no | — |
| 217 | C22×C4 | — | 2 | 2 | no | — |
| 218 | C22×C4 | — | 2 | 4 | no | — |
| 219 | C22×C4 | — | 2 | 2 | no | — |
| 220 | C22×C4 | — | 2 | 1 | no | — |
| 221 | C22×C4 | — | 2 | 2 | no | — |
| 222 | C22×C4 | — | 2 | 2 | no | — |
| 223 | C22×C4 | — | 2 | 2 | no | — |
| 224 | C22×C4 | — | 2 | 1 | no | — |
| 225 | C22×C4 | — | 4 | 2 | no | — |
| 226 | C22×C4 | — | 4 | 4 | no | — |
| 227 | C22×C4 | C2×D4 | 1 | 2 | yes | — |
| 228 | C22×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 229 | C22×C4 | C24 | 1 | 1 | yes | characteristic |
| 230 | C22×C4 | C24 | 1 | 2 | yes | — |
| 231 | C22×C4 | C24 | 1 | 2 | yes | — |
| 232 | Q16 | — | 2 | 8 | no | — |
| 233 | Q16 | — | 2 | 8 | no | — |
| 234 | Q16 | — | 4 | 4 | no | — |
| 235 | Q16 | — | 4 | 4 | no | — |
| 236 | Q16 | — | 4 | 4 | no | — |
| 237 | SD16 | — | 4 | 4 | no | — |
| 238 | M16 | — | 4 | 2 | no | — |
| 239 | C2×C8 | — | 4 | 2 | no | — |
| 240 | C2×C8 | — | 4 | 4 | no | — |
| 241 | C2×C8 | C24 | 1 | 4 | yes | — |
| 242 | C2×C8 | C24 | 1 | 4 | yes | — |
| 243 | C4⋊C4 | — | 2 | 4 | no | — |
| 244 | C4⋊C4 | — | 2 | 4 | no | — |
| 245 | C4⋊C4 | — | 2 | 2 | no | — |
| 246 | C4⋊C4 | — | 2 | 4 | no | — |
| 247 | C4⋊C4 | — | 2 | 4 | no | — |
| 248 | C4⋊C4 | — | 2 | 4 | no | — |
| 249 | C4⋊C4 | — | 2 | 4 | no | — |
| 250 | C4⋊C4 | — | 2 | 4 | no | — |
| 251 | C4⋊C4 | — | 2 | 2 | no | — |
| 252 | C4⋊C4 | — | 2 | 4 | no | — |
| 253 | C4⋊C4 | — | 2 | 4 | no | — |
| 254 | C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 255 | C4⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 256 | C4⋊C4 | C24 | 1 | 4 | yes | — |
| 257 | C4⋊C4 | C24 | 1 | 2 | yes | — |
| 258 | C22⋊C4 | — | 2 | 4 | no | — |
| 259 | C22⋊C4 | — | 2 | 4 | no | — |
| 260 | C22⋊C4 | — | 2 | 1 | no | — |
| 261 | C22⋊C4 | — | 2 | 2 | no | — |
| 262 | C22⋊C4 | — | 2 | 2 | no | — |
| 263 | C22⋊C4 | — | 2 | 4 | no | — |
| 264 | C22⋊C4 | — | 2 | 4 | no | — |
| 265 | C22⋊C4 | — | 2 | 4 | no | — |
| 266 | C22⋊C4 | — | 2 | 2 | no | — |
| 267 | C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 268 | C22⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 269 | C22⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 270 | C42 | — | 2 | 2 | no | — |
| 271 | C42 | — | 2 | 4 | no | — |
| 272 | C42 | — | 2 | 4 | no | — |
| 273 | C42 | — | 2 | 1 | no | — |
| 274 | C42 | C24 | 1 | 2 | yes | — |
| 275 | C23 | — | 2 | 4 | no | — |
| 276 | C23 | — | 2 | 1 | no | — |
| 277 | C23 | — | 4 | 1 | no | — |
| 278 | C23 | C22×D4 | 1 | 1 | yes | characteristic |
| 279 | C23 | C22×D4 | 1 | 2 | yes | — |
| 280 | C23 | C22×D4 | 1 | 2 | yes | — |
| 281 | Q8 | — | 2 | 4 | no | — |
| 282 | Q8 | — | 2 | 2 | no | — |
| 283 | Q8 | — | 2 | 4 | no | — |
| 284 | Q8 | — | 2 | 4 | no | — |
| 285 | Q8 | — | 2 | 4 | no | — |
| 286 | Q8 | — | 2 | 2 | no | — |
| 287 | Q8 | — | 4 | 1 | no | — |
| 288 | Q8 | — | 4 | 8 | no | — |
| 289 | Q8 | — | 4 | 4 | no | — |
| 290 | Q8 | — | 4 | 2 | no | — |
| 291 | Q8 | — | 8 | 2 | no | — |
| 292 | Q8 | — | 8 | 2 | no | — |
| 293 | Q8 | H(5,𝔽2) | 1 | 4 | yes | — |
| 294 | D4 | — | 2 | 8 | no | — |
| 295 | D4 | — | 2 | 2 | no | — |
| 296 | D4 | — | 4 | 1 | no | — |
| 297 | D4 | — | 4 | 2 | no | — |
| 298 | D4 | — | 4 | 4 | no | — |
| 299 | D4 | — | 4 | 2 | no | — |
| 300 | D4 | — | 4 | 4 | no | — |
| 301 | C2×C4 | — | 2 | 4 | no | — |
| 302 | C2×C4 | — | 2 | 2 | no | — |
| 303 | C2×C4 | — | 2 | 4 | no | — |
| 304 | C2×C4 | — | 2 | 2 | no | — |
| 305 | C2×C4 | — | 2 | 2 | no | — |
| 306 | C2×C4 | — | 2 | 2 | no | — |
| 307 | C2×C4 | — | 2 | 2 | no | — |
| 308 | C2×C4 | — | 2 | 4 | no | — |
| 309 | C2×C4 | — | 2 | 4 | no | — |
| 310 | C2×C4 | — | 2 | 2 | no | — |
| 311 | C2×C4 | — | 2 | 1 | no | — |
| 312 | C2×C4 | — | 4 | 2 | no | — |
| 313 | C2×C4 | — | 4 | 1 | no | — |
| 314 | C2×C4 | — | 4 | 4 | no | — |
| 315 | C2×C4 | — | 4 | 8 | no | — |
| 316 | C2×C4 | — | 4 | 4 | no | — |
| 317 | C2×C4 | — | 4 | 2 | no | — |
| 318 | C2×C4 | — | 4 | 2 | no | — |
| 319 | C2×C4 | — | 4 | 4 | no | — |
| 320 | C2×C4 | — | 8 | 2 | no | — |
| 321 | C2×C4 | — | 8 | 2 | no | — |
| 322 | C2×C4 | C22×D4 | 1 | 4 | yes | — |
| 323 | C2×C4 | C22×D4 | 1 | 2 | yes | — |
| 324 | C2×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 325 | C2×C4 | C22×D4 | 1 | 2 | yes | — |
| 326 | C2×C4 | C25 | 1 | 1 | yes | characteristic |
| 327 | C8 | — | 2 | 4 | no | — |
| 328 | C8 | — | 2 | 4 | no | — |
| 329 | C22 | — | 2 | 2 | no | — |
| 330 | C22 | — | 2 | 2 | no | — |
| 331 | C22 | — | 2 | 1 | no | — |
| 332 | C22 | — | 2 | 2 | no | — |
| 333 | C22 | — | 2 | 4 | no | — |
| 334 | C22 | — | 2 | 2 | no | — |
| 335 | C22 | — | 4 | 4 | no | — |
| 336 | C22 | — | 4 | 1 | no | — |
| 337 | C22 | — | 4 | 2 | no | — |
| 338 | C22 | #578 | 1 | 4 | yes | — |
| 339 | C22 | C23×D4 | 1 | 1 | yes | characteristic |
| 340 | C4 | — | 2 | 4 | no | — |
| 341 | C4 | — | 2 | 1 | no | — |
| 342 | C4 | — | 2 | 2 | no | — |
| 343 | C4 | — | 2 | 2 | no | — |
| 344 | C4 | — | 2 | 4 | no | — |
| 345 | C4 | — | 4 | 1 | no | — |
| 346 | C4 | — | 4 | 2 | no | — |
| 347 | C4 | — | 4 | 4 | no | — |
| 348 | C4 | — | 4 | 4 | no | — |
| 349 | C4 | — | 4 | 2 | no | — |
| 350 | C4 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 351 | C2 | — | 2 | 4 | no | — |
| 352 | C2 | — | 4 | 2 | no | — |
| 353 | C2 | — | 4 | 1 | no | — |
| 354 | C2 | — | 8 | 1 | no | — |
| 355 | C2 | #3484 | 1 | 1 | yes | characteristic |
| 356 | C2 | C2×#578 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25 |
| prime radical | #3486 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ #525 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3538 | C2 | semidirect |
| 3. #3312 | C2 | semidirect |
| 4. #3300 | C2 | semidirect |
| 5. D4×Q16 | C2 | semidirect |
| 6. #3270 | C2 | semidirect |
| 7. #3223 | C2 | semidirect |
| 8. #3202 | C2 | semidirect |
| 9. #3190 | C2 | semidirect |
| 10. #3127 | C2 | semidirect |
| 11. #3011 | C2 | semidirect |
| 12. C2×#451 | C2 | semidirect |
| 13. #2977 | C2 | semidirect |
| 16. C2×#137 | C22 | semidirect |
| 18. C22×Q16 | C22 | semidirect |
| 39. #497 | C22 | semidirect |
| 40. #494 | C22 | semidirect |
| 41. #491 | C22 | semidirect |
| 42. #488 | C22 | semidirect |
| 44. #485 | C22 | semidirect |
| 47. #479 | C22 | semidirect |
| 48. #470 | C22 | semidirect |
| 50. #467 | C22 | semidirect |
| 52. #464 | C22 | semidirect |
| 53. #462 | C22 | semidirect |
| 54. #462 | C22 | semidirect |
| 56. #452 | C22 | semidirect |
| 62. #451 | C22 | semidirect |
| 63. #451 | C22 | semidirect |
| 65. #441 | C22 | semidirect |
| 66. C4×Q16 | C22 | semidirect |
| 70. #419 | C22 | semidirect |
| 71. #416 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3538 | 2 |
| #3486 | 2 |
| #3312 | 2 |
| #3300 | 2 |
| D4×Q16 | 2 |
| #3270 | 2 |
| #3223 | 2 |
| #3202 | 2 |
| #3190 | 2 |
| #3127 | 2 |
| #3011 | 2 |
| C2×#451 | 2 |
| #2977 | 2 |