Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
7812 conjugacy classes of subgroups.
The subgroup lattice has 377 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#3502 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#3497 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #36049 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #35948 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #35910 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #35854 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #35180 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #35158 | C2 | 1 | 12 | yes | maximal, complemented |
| 9 | #34637 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | #34257 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | C2×#2276 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C22×2−1+4 | C22 | 1 | 2 | yes | — |
| 13 | #3502 | — | 2 | 16 | no | — |
| 14 | #3497 | — | 2 | 16 | no | — |
| 15 | C2×Q82 | C22 | 1 | 4 | yes | — |
| 16 | C2×#557 | C22 | 1 | 4 | yes | — |
| 17 | C2×#557 | C22 | 1 | 8 | yes | — |
| 18 | C2×#550 | C22 | 1 | 4 | yes | — |
| 19 | C2×D4×Q8 | C22 | 1 | 4 | yes | — |
| 20 | C2×#548 | C22 | 1 | 8 | yes | — |
| 21 | C2×#544 | C22 | 1 | 6 | yes | — |
| 22 | C2×#537 | C22 | 1 | 6 | yes | — |
| 23 | C2×#533 | C22 | 1 | 6 | yes | — |
| 24 | C2×#532 | C22 | 1 | 6 | yes | — |
| 25 | C2×#519 | C22 | 1 | 2 | yes | — |
| 26 | C22×C4×Q8 | C22 | 1 | 2 | yes | — |
| 27 | C22×C4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 28 | #2850 | C22 | 1 | 24 | yes | — |
| 29 | #2642 | C22 | 1 | 12 | yes | — |
| 30 | #2641 | C22 | 1 | 12 | yes | — |
| 31 | #2640 | C22 | 1 | 12 | yes | — |
| 32 | #2640 | C22 | 1 | 12 | yes | — |
| 33 | #2639 | C22 | 1 | 4 | yes | — |
| 34 | #2639 | C22 | 1 | 24 | yes | — |
| 35 | #2639 | C22 | 1 | 12 | yes | — |
| 36 | #2592 | C22 | 1 | 24 | yes | — |
| 37 | #2568 | C22 | 1 | 12 | yes | — |
| 38 | #2563 | C22 | 1 | 12 | yes | — |
| 39 | #2562 | C22 | 1 | 24 | yes | — |
| 40 | #2548 | C22 | 1 | 12 | yes | — |
| 41 | #2547 | C22 | 1 | 12 | yes | — |
| 42 | #2492 | C22 | 1 | 48 | yes | — |
| 43 | #2491 | C22 | 1 | 48 | yes | — |
| 44 | #2490 | C22 | 1 | 48 | yes | — |
| 45 | #2489 | C22 | 1 | 48 | yes | — |
| 46 | #2398 | C22 | 1 | 24 | yes | — |
| 47 | #2398 | C22 | 1 | 24 | yes | — |
| 48 | #2341 | C22 | 1 | 16 | yes | — |
| 49 | #2341 | C22 | 1 | 16 | yes | — |
| 50 | Q8×C22⋊C4 | C22 | 1 | 16 | yes | — |
| 51 | Q8×C22⋊C4 | C22 | 1 | 16 | yes | — |
| 52 | #2311 | C22 | 1 | 24 | yes | — |
| 53 | #2297 | C22 | 1 | 24 | yes | — |
| 54 | #2276 | C22 | 1 | 8 | yes | — |
| 55 | #2276 | C22 | 1 | 8 | yes | — |
| 56 | C2×C4×C4⋊C4 | C22 | 1 | 6 | yes | — |
| 57 | C2×C4×C4⋊C4 | C22 | 1 | 3 | yes | — |
| 58 | C2×#376 | C22 | 1 | 3 | yes | — |
| 59 | C2×2−1+4 | — | 2 | 16 | no | — |
| 60 | C2×2−1+4 | — | 2 | 32 | no | — |
| 61 | C22×#41 | C23 | 1 | 12 | yes | — |
| 62 | C22×#41 | C23 | 1 | 8 | yes | — |
| 63 | C23×Q8 | C23 | 1 | 8 | yes | — |
| 64 | C23×Q8 | C23 | 1 | 1 | yes | characteristic |
| 65 | Q82 | — | 2 | 32 | no | — |
| 66 | #557 | — | 2 | 32 | no | — |
| 67 | #557 | — | 2 | 64 | no | — |
| 68 | #550 | — | 2 | 32 | no | — |
| 69 | D4×Q8 | — | 2 | 32 | no | — |
| 70 | #548 | — | 2 | 64 | no | — |
| 71 | #544 | — | 2 | 48 | no | — |
| 72 | #537 | — | 2 | 48 | no | — |
| 73 | #533 | — | 2 | 48 | no | — |
| 74 | #532 | — | 2 | 48 | no | — |
| 75 | C2×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 76 | C2×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 77 | C2×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 78 | C2×C4⋊Q8 | C23 | 1 | 24 | yes | — |
| 79 | C2×#127 | C23 | 1 | 6 | yes | — |
| 80 | C2×#125 | C23 | 1 | 12 | yes | — |
| 81 | C2×#125 | C23 | 1 | 24 | yes | — |
| 82 | C2×#124 | C23 | 1 | 12 | yes | — |
| 83 | C2×#124 | C23 | 1 | 24 | yes | — |
| 84 | C2×C22⋊Q8 | C23 | 1 | 12 | yes | — |
| 85 | C2×C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 86 | C2×C22⋊Q8 | C23 | 1 | 24 | yes | — |
| 87 | C2×#121 | C23 | 1 | 12 | yes | — |
| 88 | C2×#121 | C23 | 1 | 4 | yes | — |
| 89 | C2×#121 | C23 | 1 | 24 | yes | — |
| 90 | #519 | — | 2 | 16 | no | — |
| 91 | C2×C4×Q8 | — | 2 | 16 | no | — |
| 92 | C2×C4×Q8 | D4 | 1 | 16 | yes | — |
| 93 | C2×C4×Q8 | C23 | 1 | 12 | yes | — |
| 94 | C2×C4×Q8 | C23 | 1 | 12 | yes | — |
| 95 | C2×C4×Q8 | C23 | 1 | 16 | yes | — |
| 96 | C2×C4×Q8 | C23 | 1 | 8 | yes | — |
| 97 | C2×C4×Q8 | C23 | 1 | 8 | yes | — |
| 98 | C2×C4×Q8 | C23 | 1 | 4 | yes | — |
| 99 | C2×C4×Q8 | C23 | 1 | 4 | yes | — |
| 100 | C2×C4×D4 | C23 | 1 | 12 | yes | — |
| 101 | C2×C4×D4 | C23 | 1 | 12 | yes | — |
| 102 | C2×#117 | C23 | 1 | 12 | yes | — |
| 103 | C22×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 104 | C22×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 105 | C22×C42 | C23 | 1 | 6 | yes | — |
| 106 | C22×C42 | C23 | 1 | 6 | yes | — |
| 107 | C22×C42 | C23 | 1 | 3 | yes | — |
| 108 | #400 | C23 | 1 | 24 | yes | — |
| 109 | #400 | C23 | 1 | 8 | yes | — |
| 110 | #400 | C23 | 1 | 48 | yes | — |
| 111 | #397 | C23 | 1 | 24 | yes | — |
| 112 | #397 | C23 | 1 | 8 | yes | — |
| 113 | #397 | C23 | 1 | 48 | yes | — |
| 114 | #394 | C23 | 1 | 24 | yes | — |
| 115 | #394 | C23 | 1 | 8 | yes | — |
| 116 | #394 | C23 | 1 | 48 | yes | — |
| 117 | #393 | C23 | 1 | 24 | yes | — |
| 118 | #393 | C23 | 1 | 8 | yes | — |
| 119 | #393 | C23 | 1 | 48 | yes | — |
| 120 | #391 | C23 | 1 | 48 | yes | — |
| 121 | #391 | C23 | 1 | 24 | yes | — |
| 122 | #391 | C23 | 1 | 24 | yes | — |
| 123 | #391 | C23 | 1 | 24 | yes | — |
| 124 | #390 | C23 | 1 | 24 | yes | — |
| 125 | #390 | C23 | 1 | 48 | yes | — |
| 126 | #390 | C23 | 1 | 24 | yes | — |
| 127 | #390 | C23 | 1 | 24 | yes | — |
| 128 | #388 | C23 | 1 | 96 | yes | — |
| 129 | #386 | C23 | 1 | 48 | yes | — |
| 130 | #386 | C23 | 1 | 16 | yes | — |
| 131 | #382 | C23 | 1 | 24 | yes | — |
| 132 | #380 | C23 | 1 | 48 | yes | — |
| 133 | #380 | C23 | 1 | 48 | yes | — |
| 134 | C4×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 135 | C4×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 136 | C4×C4⋊C4 | C23 | 1 | 48 | yes | — |
| 137 | C4×C22⋊C4 | C23 | 1 | 48 | yes | — |
| 138 | C4×C22⋊C4 | C23 | 1 | 48 | yes | — |
| 139 | #376 | C23 | 1 | 12 | yes | — |
| 140 | #376 | C23 | 1 | 12 | yes | — |
| 141 | C2×#95 | C23 | 1 | 1 | yes | characteristic |
| 142 | C2×#95 | C23 | 1 | 3 | yes | — |
| 143 | C2×#95 | C23 | 1 | 6 | yes | — |
| 144 | 2−1+4 | — | 4 | 128 | no | — |
| 145 | C2×#41 | — | 2 | 32 | no | — |
| 146 | C2×#41 | — | 2 | 64 | no | — |
| 147 | C2×#41 | — | 2 | 48 | no | — |
| 148 | C2×#41 | — | 2 | 96 | no | — |
| 149 | C22×Q8 | — | 2 | 32 | no | — |
| 150 | C22×Q8 | — | 2 | 64 | no | — |
| 151 | C22×Q8 | C2×D4 | 1 | 8 | yes | — |
| 152 | C22×Q8 | #41 | 1 | 16 | yes | — |
| 153 | C22×Q8 | C24 | 1 | 12 | yes | — |
| 154 | C22×Q8 | C24 | 1 | 4 | yes | — |
| 155 | C22×Q8 | C24 | 1 | 12 | yes | — |
| 156 | C22×Q8 | C24 | 1 | 4 | yes | — |
| 157 | C22×D4 | C24 | 1 | 8 | yes | — |
| 158 | C22×D4 | C24 | 1 | 12 | yes | — |
| 159 | C22×D4 | C24 | 1 | 4 | yes | — |
| 160 | C22×D4 | C24 | 1 | 12 | yes | — |
| 161 | C23×C4 | C24 | 1 | 24 | yes | — |
| 162 | C23×C4 | C24 | 1 | 6 | yes | — |
| 163 | C23×C4 | C24 | 1 | 2 | yes | — |
| 164 | C23×C4 | C24 | 1 | 3 | yes | — |
| 165 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 166 | C23×C4 | C24 | 1 | 3 | yes | — |
| 167 | C4⋊Q8 | — | 2 | 96 | no | — |
| 168 | C4⋊Q8 | — | 2 | 24 | no | — |
| 169 | C4⋊Q8 | — | 2 | 24 | no | — |
| 170 | C4⋊Q8 | — | 2 | 24 | no | — |
| 171 | #127 | — | 2 | 24 | no | — |
| 172 | #125 | — | 2 | 96 | no | — |
| 173 | #125 | — | 2 | 48 | no | — |
| 174 | #124 | — | 2 | 48 | no | — |
| 175 | #124 | — | 8 | 24 | no | — |
| 176 | C22⋊Q8 | — | 2 | 16 | no | — |
| 177 | C22⋊Q8 | — | 2 | 48 | no | — |
| 178 | C22⋊Q8 | — | 2 | 96 | no | — |
| 179 | #121 | — | 2 | 16 | no | — |
| 180 | #121 | — | 2 | 48 | no | — |
| 181 | #121 | — | 2 | 96 | no | — |
| 182 | C4×Q8 | — | 2 | 32 | no | — |
| 183 | C4×Q8 | — | 2 | 32 | no | — |
| 184 | C4×Q8 | — | 2 | 64 | no | — |
| 185 | C4×Q8 | — | 2 | 48 | no | — |
| 186 | C4×Q8 | — | 2 | 48 | no | — |
| 187 | C4×Q8 | C2×D4 | 1 | 32 | yes | — |
| 188 | C4×Q8 | C2×D4 | 1 | 32 | yes | — |
| 189 | C4×D4 | — | 2 | 48 | no | — |
| 190 | C4×D4 | — | 2 | 48 | no | — |
| 191 | #117 | — | 2 | 48 | no | — |
| 192 | C2×C4⋊C4 | — | 2 | 24 | no | — |
| 193 | C2×C4⋊C4 | C2×D4 | 1 | 24 | yes | — |
| 194 | C2×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 195 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 196 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 197 | C2×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 198 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 199 | C2×C4⋊C4 | C24 | 1 | 8 | yes | — |
| 200 | C2×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 201 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 202 | C2×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 203 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 204 | C2×C22⋊C4 | C24 | 1 | 8 | yes | — |
| 205 | C2×C22⋊C4 | C24 | 1 | 8 | yes | — |
| 206 | C2×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 207 | C2×C22⋊C4 | C24 | 1 | 48 | yes | — |
| 208 | C2×C22⋊C4 | C24 | 1 | 16 | yes | — |
| 209 | C2×C22⋊C4 | C24 | 1 | 16 | yes | — |
| 210 | C2×C22⋊C4 | C24 | 1 | 48 | yes | — |
| 211 | C2×C42 | — | 2 | 24 | no | — |
| 212 | C2×C42 | — | 8 | 6 | no | — |
| 213 | C2×C42 | C2×D4 | 1 | 24 | yes | — |
| 214 | C2×C42 | C24 | 1 | 24 | yes | — |
| 215 | C2×C42 | C24 | 1 | 24 | yes | — |
| 216 | C2×C42 | C24 | 1 | 24 | yes | — |
| 217 | C2×C42 | C24 | 1 | 6 | yes | — |
| 218 | C2×C42 | C24 | 1 | 6 | yes | — |
| 219 | #95 | C24 | 1 | 2 | yes | — |
| 220 | #95 | C24 | 1 | 2 | yes | — |
| 221 | #95 | C24 | 1 | 6 | yes | — |
| 222 | #95 | C24 | 1 | 24 | yes | — |
| 223 | #95 | C24 | 1 | 6 | yes | — |
| 224 | #95 | C24 | 1 | 16 | yes | — |
| 225 | #95 | C24 | 1 | 16 | yes | — |
| 226 | #95 | C24 | 1 | 48 | yes | — |
| 227 | #95 | C24 | 1 | 48 | yes | — |
| 228 | C24 | C25 | 1 | 8 | yes | — |
| 229 | C24 | C25 | 1 | 1 | yes | characteristic |
| 230 | #41 | — | 4 | 128 | no | — |
| 231 | #41 | — | 4 | 192 | no | — |
| 232 | C2×Q8 | — | 2 | 8 | no | — |
| 233 | C2×Q8 | — | 2 | 24 | no | — |
| 234 | C2×Q8 | — | 2 | 24 | no | — |
| 235 | C2×Q8 | — | 2 | 48 | no | — |
| 236 | C2×Q8 | — | 4 | 8 | no | — |
| 237 | C2×Q8 | — | 4 | 12 | no | — |
| 238 | C2×Q8 | — | 4 | 12 | no | — |
| 239 | C2×Q8 | — | 4 | 128 | no | — |
| 240 | C2×Q8 | #124 | 1 | 64 | yes | complemented |
| 241 | C2×Q8 | C22×D4 | 1 | 16 | yes | — |
| 242 | C2×Q8 | C2×#41 | 1 | 32 | yes | — |
| 243 | C2×D4 | — | 2 | 16 | no | — |
| 244 | C2×D4 | — | 2 | 32 | no | — |
| 245 | C2×D4 | — | 2 | 8 | no | — |
| 246 | C2×D4 | — | 2 | 24 | no | — |
| 247 | C2×D4 | — | 2 | 24 | no | — |
| 248 | C2×D4 | — | 2 | 48 | no | — |
| 249 | C2×D4 | — | 4 | 8 | no | — |
| 250 | C2×D4 | — | 4 | 12 | no | — |
| 251 | C2×D4 | — | 4 | 12 | no | — |
| 252 | C22×C4 | — | 2 | 4 | no | — |
| 253 | C22×C4 | — | 2 | 12 | no | — |
| 254 | C22×C4 | — | 2 | 48 | no | — |
| 255 | C22×C4 | — | 2 | 96 | no | — |
| 256 | C22×C4 | — | 4 | 3 | no | — |
| 257 | C22×C4 | — | 4 | 6 | no | — |
| 258 | C22×C4 | — | 4 | 2 | no | — |
| 259 | C22×C4 | — | 4 | 3 | no | — |
| 260 | C22×C4 | — | 4 | 6 | no | — |
| 261 | C22×C4 | — | 4 | 2 | no | — |
| 262 | C22×C4 | — | 4 | 2 | no | — |
| 263 | C22×C4 | C22×D4 | 1 | 4 | yes | — |
| 264 | C22×C4 | C22×D4 | 1 | 12 | yes | — |
| 265 | C22×C4 | C22×D4 | 1 | 12 | yes | — |
| 266 | C22×C4 | C2×#41 | 1 | 24 | yes | — |
| 267 | C22×C4 | C25 | 1 | 4 | yes | — |
| 268 | C22×C4 | C25 | 1 | 8 | yes | — |
| 269 | C22×C4 | C25 | 1 | 12 | yes | — |
| 270 | C22×C4 | C25 | 1 | 8 | yes | — |
| 271 | C22×C4 | C25 | 1 | 8 | yes | — |
| 272 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 273 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 274 | C22×C4 | C25 | 1 | 6 | yes | — |
| 275 | C22×C4 | C25 | 1 | 6 | yes | — |
| 276 | C4⋊C4 | — | 2 | 24 | no | — |
| 277 | C4⋊C4 | — | 2 | 24 | no | — |
| 278 | C4⋊C4 | — | 2 | 8 | no | — |
| 279 | C4⋊C4 | — | 2 | 24 | no | — |
| 280 | C4⋊C4 | — | 2 | 16 | no | — |
| 281 | C4⋊C4 | — | 2 | 8 | no | — |
| 282 | C4⋊C4 | — | 2 | 24 | no | — |
| 283 | C4⋊C4 | — | 2 | 48 | no | — |
| 284 | C4⋊C4 | — | 2 | 48 | no | — |
| 285 | C4⋊C4 | C22×D4 | 1 | 48 | yes | — |
| 286 | C22⋊C4 | — | 2 | 16 | no | — |
| 287 | C22⋊C4 | — | 2 | 16 | no | — |
| 288 | C22⋊C4 | — | 2 | 48 | no | — |
| 289 | C22⋊C4 | — | 4 | 16 | no | — |
| 290 | C22⋊C4 | — | 4 | 48 | no | — |
| 291 | C22⋊C4 | — | 4 | 16 | no | — |
| 292 | C22⋊C4 | — | 4 | 48 | no | — |
| 293 | C42 | — | 2 | 48 | no | — |
| 294 | C42 | — | 2 | 48 | no | — |
| 295 | C42 | — | 4 | 24 | no | — |
| 296 | C42 | C22×D4 | 1 | 24 | yes | — |
| 297 | C42 | C22×D4 | 1 | 24 | yes | — |
| 298 | C23 | — | 2 | 1 | no | — |
| 299 | C23 | — | 2 | 2 | no | — |
| 300 | C23 | — | 2 | 1 | no | — |
| 301 | C23 | — | 2 | 8 | no | — |
| 302 | C23 | — | 2 | 16 | no | — |
| 303 | C23 | — | 2 | 8 | no | — |
| 304 | C23 | — | 2 | 16 | no | — |
| 305 | C23 | — | 2 | 8 | no | — |
| 306 | C23 | C23×D4 | 1 | 2 | yes | — |
| 307 | C23 | C22×#41 | 1 | 4 | yes | — |
| 308 | C23 | C26 | 1 | 1 | yes | characteristic |
| 309 | Q8 | — | 4 | 16 | no | — |
| 310 | Q8 | — | 4 | 48 | no | — |
| 311 | Q8 | — | 8 | 24 | no | — |
| 312 | Q8 | C2×#124 | 1 | 64 | yes | — |
| 313 | D4 | — | 4 | 16 | no | — |
| 314 | D4 | — | 4 | 32 | no | — |
| 315 | D4 | — | 4 | 48 | no | — |
| 316 | D4 | — | 8 | 24 | no | — |
| 317 | C2×C4 | — | 2 | 6 | no | — |
| 318 | C2×C4 | — | 2 | 2 | no | — |
| 319 | C2×C4 | — | 2 | 6 | no | — |
| 320 | C2×C4 | — | 2 | 2 | no | — |
| 321 | C2×C4 | — | 2 | 8 | no | — |
| 322 | C2×C4 | — | 2 | 8 | no | — |
| 323 | C2×C4 | — | 2 | 8 | no | — |
| 324 | C2×C4 | — | 2 | 4 | no | — |
| 325 | C2×C4 | — | 2 | 12 | no | — |
| 326 | C2×C4 | — | 2 | 16 | no | — |
| 327 | C2×C4 | — | 2 | 12 | no | — |
| 328 | C2×C4 | — | 2 | 8 | no | — |
| 329 | C2×C4 | — | 2 | 4 | no | — |
| 330 | C2×C4 | — | 2 | 4 | no | — |
| 331 | C2×C4 | — | 2 | 12 | no | — |
| 332 | C2×C4 | — | 2 | 16 | no | — |
| 333 | C2×C4 | — | 2 | 8 | no | — |
| 334 | C2×C4 | — | 4 | 4 | no | — |
| 335 | C2×C4 | — | 4 | 12 | no | — |
| 336 | C2×C4 | — | 4 | 8 | no | — |
| 337 | C2×C4 | — | 4 | 24 | no | — |
| 338 | C2×C4 | — | 4 | 96 | no | — |
| 339 | C2×C4 | C2×#124 | 1 | 48 | yes | — |
| 340 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 341 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 342 | C2×C4 | C23×D4 | 1 | 12 | yes | — |
| 343 | C2×C4 | C23×D4 | 1 | 12 | yes | — |
| 344 | C2×C4 | C22×#41 | 1 | 24 | yes | — |
| 345 | C22 | — | 2 | 2 | no | — |
| 346 | C22 | — | 2 | 4 | no | — |
| 347 | C22 | — | 2 | 4 | no | — |
| 348 | C22 | — | 2 | 2 | no | — |
| 349 | C22 | — | 4 | 8 | no | — |
| 350 | C22 | — | 4 | 16 | no | — |
| 351 | C22 | — | 4 | 16 | no | — |
| 352 | C22 | — | 4 | 8 | no | — |
| 353 | C22 | — | 4 | 8 | no | — |
| 354 | C22 | C22×#124 | 1 | 4 | yes | — |
| 355 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 356 | C22 | C23×#41 | 1 | 2 | yes | — |
| 357 | C22 | H(7,𝔽2) | 1 | 1 | yes | characteristic |
| 358 | C22 | 2−1+6 | 1 | 2 | yes | — |
| 359 | C22 | 2−1+6 | 1 | 1 | yes | characteristic |
| 360 | C4 | — | 2 | 2 | no | — |
| 361 | C4 | — | 2 | 2 | no | — |
| 362 | C4 | — | 2 | 12 | no | — |
| 363 | C4 | — | 4 | 8 | no | — |
| 364 | C4 | — | 4 | 4 | no | — |
| 365 | C4 | — | 4 | 12 | no | — |
| 366 | C4 | — | 4 | 8 | no | — |
| 367 | C4 | — | 4 | 8 | no | — |
| 368 | C4 | C22×#124 | 1 | 24 | yes | — |
| 369 | C2 | — | 2 | 4 | no | — |
| 370 | C2 | — | 8 | 8 | no | — |
| 371 | C2 | C23×#124 | 1 | 1 | yes | characteristic |
| 372 | C2 | #62848 | 1 | 1 | yes | characteristic |
| 373 | C2 | #62850 | 1 | 2 | yes | — |
| 374 | C2 | #62851 | 1 | 2 | yes | — |
| 375 | C2 | #62853 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C23 | C26 |
| prime radical | C2×#3497 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#3502 | C2 | semidirect |
| 3. #36049 | C2 | semidirect |
| 4. #35948 | C2 | semidirect |
| 5. #35910 | C2 | semidirect |
| 6. #35854 | C2 | semidirect |
| 7. #35180 | C2 | semidirect |
| 8. #35158 | C2 | semidirect |
| 9. #34637 | C2 | semidirect |
| 10. #34257 | C2 | semidirect |
| 11. C2×#2276 | C2 | semidirect |
| 240. C2×Q8 | #124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3502 | 2 |
| C2×#3497 | 2 |
| #36049 | 2 |
| #35948 | 2 |
| #35910 | 2 |
| #35854 | 2 |
| #35180 | 2 |
| #35158 | 2 |
| #34637 | 2 |
| #34257 | 2 |
| C2×#2276 | 2 |