Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1094 conjugacy classes of subgroups.
The subgroup lattice has 369 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #41×D16 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #512789 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #483475 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #150160 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #150138 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #150124 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #150064 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | D8×#41 | — | 2 | 1 | no | — |
| 9 | #33958 | C4 | 1 | 1 | yes | characteristic |
| 10 | Q8×D16 | C4 | 1 | 1 | yes | characteristic |
| 11 | #33925 | — | 2 | 1 | no | — |
| 12 | #33901 | C4 | 1 | 3 | yes | — |
| 13 | #33861 | — | 2 | 3 | no | — |
| 14 | D4×D16 | C4 | 1 | 3 | yes | — |
| 15 | #33733 | C22 | 1 | 3 | yes | — |
| 16 | #33660 | — | 2 | 3 | no | — |
| 17 | C16×#41 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C4×D16 | C22 | 1 | 3 | yes | — |
| 19 | #17837 | — | 2 | 1 | no | — |
| 20 | Q8×C32 | — | 2 | 1 | no | — |
| 21 | #13646 | — | 2 | 3 | no | — |
| 22 | #13640 | C22 | 1 | 3 | yes | complemented |
| 23 | C4×M64 | C22 | 1 | 3 | yes | complemented |
| 24 | #12036 | — | 2 | 3 | no | — |
| 25 | #12023 | C22 | 1 | 3 | yes | complemented |
| 26 | #12008 | C22 | 1 | 3 | yes | complemented |
| 27 | #7385 | C22 | 1 | 1 | yes | characteristic |
| 28 | #7385 | C22 | 1 | 3 | yes | — |
| 29 | #7385 | C22 | 1 | 3 | yes | complemented |
| 30 | #7385 | C22 | 1 | 3 | yes | complemented |
| 31 | #7385 | C22 | 1 | 6 | yes | complemented |
| 32 | D4×#41 | — | 4 | 1 | no | — |
| 33 | C22×D16 | C2×C4 | 1 | 3 | yes | — |
| 34 | #3391 | — | 2 | 1 | no | — |
| 35 | Q8×D8 | — | 2 | 1 | no | — |
| 36 | #3358 | — | 4 | 1 | no | — |
| 37 | #3334 | — | 2 | 3 | no | — |
| 38 | #3294 | — | 4 | 3 | no | — |
| 39 | D4×D8 | — | 2 | 3 | no | — |
| 40 | #3169 | — | 2 | 3 | no | — |
| 41 | #3100 | — | 4 | 3 | no | — |
| 42 | #2991 | — | 4 | 1 | no | — |
| 43 | C8×#41 | D4 | 1 | 1 | yes | characteristic |
| 44 | C2×C4×D8 | — | 2 | 3 | no | — |
| 45 | C2×M64 | — | 2 | 3 | no | — |
| 46 | #2252 | C2×C4 | 1 | 3 | yes | — |
| 47 | #2246 | C2×C4 | 1 | 3 | yes | — |
| 48 | #2240 | — | 2 | 3 | no | — |
| 49 | #2232 | — | 2 | 6 | no | — |
| 50 | #2224 | — | 2 | 3 | no | — |
| 51 | #2224 | — | 2 | 3 | no | — |
| 52 | #2215 | — | 2 | 3 | no | — |
| 53 | #2215 | C2×C4 | 1 | 6 | yes | — |
| 54 | #2206 | — | 2 | 3 | no | — |
| 55 | #2206 | — | 2 | 3 | no | — |
| 56 | #2184 | — | 2 | 6 | no | — |
| 57 | Q8×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | Q8×C16 | D4 | 1 | 1 | yes | characteristic |
| 59 | C4×D16 | — | 2 | 3 | no | — |
| 60 | C4×D16 | — | 2 | 3 | no | — |
| 61 | C4×D16 | — | 2 | 3 | no | — |
| 62 | C4×D16 | C2×C4 | 1 | 3 | yes | — |
| 63 | C4×D16 | C2×C4 | 1 | 3 | yes | — |
| 64 | C4×D16 | C23 | 1 | 1 | yes | characteristic |
| 65 | C4×D16 | C23 | 1 | 3 | yes | — |
| 66 | D4×C16 | C2×C4 | 1 | 3 | yes | — |
| 67 | D4×C16 | D4 | 1 | 3 | yes | — |
| 68 | #2162 | D4 | 1 | 3 | yes | — |
| 69 | C2×#366 | C2×C4 | 1 | 3 | yes | — |
| 70 | C2×#357 | — | 2 | 3 | no | — |
| 71 | C2×C4×C16 | C23 | 1 | 3 | yes | — |
| 72 | #1574 | — | 4 | 3 | no | — |
| 73 | #1567 | — | 2 | 3 | no | — |
| 74 | #1564 | — | 2 | 3 | no | — |
| 75 | C4⋊C32 | — | 2 | 3 | no | — |
| 76 | C22⋊C32 | — | 2 | 3 | no | — |
| 77 | #1397 | C23 | 1 | 3 | yes | — |
| 78 | #1397 | C23 | 1 | 1 | yes | characteristic |
| 79 | C4×C32 | — | 2 | 3 | no | — |
| 80 | #1372 | — | 2 | 3 | no | — |
| 81 | #1372 | C23 | 1 | 1 | yes | characteristic |
| 82 | #1372 | C23 | 1 | 3 | yes | — |
| 83 | #1371 | — | 2 | 3 | no | — |
| 84 | C22×#41 | — | 8 | 1 | no | — |
| 85 | C22×D8 | — | 2 | 3 | no | — |
| 86 | #550 | — | 4 | 1 | no | — |
| 87 | D4×Q8 | — | 4 | 1 | no | — |
| 88 | #548 | — | 8 | 1 | no | — |
| 89 | #547 | — | 4 | 3 | no | — |
| 90 | #546 | — | 8 | 3 | no | — |
| 91 | D42 | — | 4 | 3 | no | — |
| 92 | #532 | — | 4 | 3 | no | — |
| 93 | #525 | — | 8 | 3 | no | — |
| 94 | C4×#41 | D8 | 1 | 1 | yes | characteristic |
| 95 | C2×C4×D4 | — | 4 | 3 | no | — |
| 96 | C2×D16 | — | 2 | 6 | no | — |
| 97 | C2×D16 | — | 2 | 3 | no | — |
| 98 | C2×D16 | — | 2 | 3 | no | — |
| 99 | C2×D16 | — | 4 | 3 | no | — |
| 100 | C2×D16 | C22×C4 | 1 | 3 | yes | — |
| 101 | C2×D16 | C22×C4 | 1 | 1 | yes | characteristic |
| 102 | C22×C16 | C22×C4 | 1 | 3 | yes | — |
| 103 | C22×C16 | C2×D4 | 1 | 3 | yes | — |
| 104 | #500 | — | 2 | 3 | no | — |
| 105 | #493 | — | 2 | 3 | no | — |
| 106 | #486 | — | 4 | 3 | no | — |
| 107 | #480 | — | 4 | 6 | no | — |
| 108 | #474 | — | 4 | 3 | no | — |
| 109 | #474 | — | 4 | 3 | no | — |
| 110 | #466 | — | 2 | 6 | no | — |
| 111 | #466 | — | 4 | 3 | no | — |
| 112 | #459 | — | 4 | 3 | no | — |
| 113 | #459 | — | 4 | 3 | no | — |
| 114 | #447 | — | 4 | 6 | no | — |
| 115 | C8×Q8 | — | 8 | 1 | no | — |
| 116 | C8×Q8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 117 | C8×Q8 | SD16 | 1 | 1 | yes | characteristic |
| 118 | C4×D8 | — | 2 | 3 | no | — |
| 119 | C4×D8 | — | 2 | 3 | no | — |
| 120 | C4×D8 | — | 2 | 3 | no | — |
| 121 | C4×D8 | — | 2 | 1 | no | — |
| 122 | C4×D8 | — | 4 | 3 | no | — |
| 123 | C4×D8 | — | 4 | 3 | no | — |
| 124 | C4×D8 | — | 4 | 3 | no | — |
| 125 | #436 | — | 8 | 3 | no | — |
| 126 | C8×D4 | C22⋊C4 | 1 | 3 | yes | — |
| 127 | C8×D4 | SD16 | 1 | 3 | yes | — |
| 128 | #431 | — | 4 | 3 | no | — |
| 129 | #431 | D8 | 1 | 3 | yes | — |
| 130 | C2×#107 | — | 2 | 3 | no | — |
| 131 | #423 | — | 4 | 3 | no | — |
| 132 | C2×#102 | — | 4 | 3 | no | — |
| 133 | C2×C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 134 | M64 | — | 4 | 6 | no | — |
| 135 | C2×C32 | — | 2 | 1 | no | — |
| 136 | C2×C32 | — | 2 | 3 | no | — |
| 137 | #366 | — | 2 | 3 | no | — |
| 138 | #366 | — | 2 | 3 | no | — |
| 139 | #366 | C22×C4 | 1 | 1 | yes | characteristic |
| 140 | #366 | C22×C4 | 1 | 3 | yes | — |
| 141 | C4⋊C16 | C22⋊C4 | 1 | 3 | yes | — |
| 142 | C4⋊C16 | C22⋊C4 | 1 | 3 | yes | — |
| 143 | #357 | — | 2 | 3 | no | — |
| 144 | #357 | — | 2 | 3 | no | — |
| 145 | #357 | — | 2 | 6 | no | — |
| 146 | #357 | — | 2 | 1 | no | — |
| 147 | #357 | — | 2 | 3 | no | — |
| 148 | C22⋊C16 | C22⋊C4 | 1 | 6 | yes | — |
| 149 | C4×C16 | C22×C4 | 1 | 3 | yes | — |
| 150 | C4×C16 | C2×D4 | 1 | 3 | yes | — |
| 151 | C4×C16 | C2×D4 | 1 | 3 | yes | — |
| 152 | C4×C16 | C24 | 1 | 1 | yes | characteristic |
| 153 | #335 | — | 2 | 1 | no | — |
| 154 | #335 | — | 2 | 3 | no | — |
| 155 | #335 | — | 4 | 3 | no | — |
| 156 | #334 | — | 4 | 3 | no | — |
| 157 | C2×#41 | — | 8 | 1 | no | — |
| 158 | C2×#41 | — | 8 | 3 | no | — |
| 159 | C2×#41 | — | 8 | 3 | no | — |
| 160 | C2×#41 | — | 16 | 8 | no | — |
| 161 | C2×#41 | SD32 | 1 | 1 | yes | characteristic |
| 162 | C22×Q8 | — | 8 | 1 | no | — |
| 163 | C22×D4 | — | 4 | 3 | no | — |
| 164 | C22×D4 | — | 8 | 3 | no | — |
| 165 | C23×C4 | — | 8 | 3 | no | — |
| 166 | C2×D8 | — | 2 | 1 | no | — |
| 167 | C2×D8 | — | 2 | 3 | no | — |
| 168 | C2×D8 | — | 4 | 6 | no | — |
| 169 | C2×D8 | — | 4 | 3 | no | — |
| 170 | C2×D8 | — | 4 | 3 | no | — |
| 171 | C2×D8 | — | 8 | 3 | no | — |
| 172 | C2×M16 | — | 8 | 3 | no | — |
| 173 | C22×C8 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 174 | C22×C8 | C2×SD16 | 1 | 3 | yes | — |
| 175 | C4⋊Q8 | — | 4 | 3 | no | — |
| 176 | #127 | — | 4 | 3 | no | — |
| 177 | #124 | — | 8 | 3 | no | — |
| 178 | #123 | — | 8 | 6 | no | — |
| 179 | C22⋊Q8 | — | 8 | 3 | no | — |
| 180 | C22⋊Q8 | — | 8 | 3 | no | — |
| 181 | #121 | — | 4 | 6 | no | — |
| 182 | #121 | — | 8 | 3 | no | — |
| 183 | #121 | — | 8 | 3 | no | — |
| 184 | #121 | — | 8 | 3 | no | — |
| 185 | #120 | — | 8 | 6 | no | — |
| 186 | C4×Q8 | #102 | 1 | 1 | yes | characteristic |
| 187 | C4×Q8 | D16 | 1 | 1 | yes | characteristic |
| 188 | C4×D4 | — | 4 | 1 | no | — |
| 189 | C4×D4 | — | 4 | 3 | no | — |
| 190 | C4×D4 | — | 4 | 3 | no | — |
| 191 | C4×D4 | — | 4 | 3 | no | — |
| 192 | C4×D4 | — | 8 | 3 | no | — |
| 193 | C4×D4 | — | 8 | 3 | no | — |
| 194 | C4×D4 | — | 8 | 3 | no | — |
| 195 | C4×D4 | #102 | 1 | 3 | yes | — |
| 196 | C4×D4 | D16 | 1 | 3 | yes | — |
| 197 | #117 | SD32 | 1 | 3 | yes | — |
| 198 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 199 | C2×C22⋊C4 | — | 8 | 3 | no | — |
| 200 | C2×C42 | C2×D8 | 1 | 3 | yes | — |
| 201 | D16 | — | 2 | 3 | no | — |
| 202 | D16 | — | 2 | 1 | no | — |
| 203 | D16 | — | 2 | 3 | no | — |
| 204 | D16 | — | 4 | 6 | no | — |
| 205 | D16 | — | 8 | 3 | no | — |
| 206 | D16 | #131 | 1 | 2 | yes | — |
| 207 | C2×C16 | — | 2 | 3 | no | — |
| 208 | C2×C16 | — | 2 | 3 | no | — |
| 209 | C2×C16 | — | 4 | 3 | no | — |
| 210 | C2×C16 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 211 | C2×C16 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 212 | C2×C16 | C23×C4 | 1 | 1 | yes | characteristic |
| 213 | C2×C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 214 | #107 | — | 2 | 1 | no | — |
| 215 | #107 | — | 2 | 3 | no | — |
| 216 | #107 | — | 4 | 3 | no | — |
| 217 | #107 | — | 4 | 3 | no | — |
| 218 | C4⋊C8 | — | 4 | 1 | no | — |
| 219 | C4⋊C8 | — | 4 | 3 | no | — |
| 220 | C4⋊C8 | — | 8 | 3 | no | — |
| 221 | C4⋊C8 | #102 | 1 | 3 | yes | — |
| 222 | C4⋊C8 | #102 | 1 | 3 | yes | — |
| 223 | #102 | — | 4 | 1 | no | — |
| 224 | #102 | — | 4 | 3 | no | — |
| 225 | #102 | — | 4 | 3 | no | — |
| 226 | #102 | — | 4 | 3 | no | — |
| 227 | #102 | — | 4 | 6 | no | — |
| 228 | C22⋊C8 | — | 8 | 3 | no | — |
| 229 | C22⋊C8 | #102 | 1 | 6 | yes | — |
| 230 | C4×C8 | — | 8 | 3 | no | — |
| 231 | C4×C8 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 232 | C4×C8 | C2×D8 | 1 | 3 | yes | — |
| 233 | C4×C8 | C2×SD16 | 1 | 3 | yes | — |
| 234 | C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 235 | C32 | — | 2 | 2 | no | — |
| 236 | C32 | — | 4 | 3 | no | — |
| 237 | C24 | — | 8 | 3 | no | — |
| 238 | #41 | — | 2 | 4 | no | — |
| 239 | #41 | — | 16 | 12 | no | — |
| 240 | #41 | — | 16 | 12 | no | — |
| 241 | #41 | — | 16 | 4 | no | — |
| 242 | C2×Q8 | — | 8 | 3 | no | — |
| 243 | C2×Q8 | — | 16 | 4 | no | — |
| 244 | C2×Q8 | #357 | 1 | 1 | yes | characteristic |
| 245 | C2×D4 | — | 4 | 1 | no | — |
| 246 | C2×D4 | — | 4 | 3 | no | — |
| 247 | C2×D4 | — | 8 | 6 | no | — |
| 248 | C2×D4 | — | 8 | 6 | no | — |
| 249 | C2×D4 | — | 8 | 3 | no | — |
| 250 | C2×D4 | — | 8 | 3 | no | — |
| 251 | C2×D4 | — | 8 | 3 | no | — |
| 252 | C2×D4 | — | 16 | 3 | no | — |
| 253 | C2×D4 | — | 16 | 12 | no | — |
| 254 | C2×D4 | #357 | 1 | 3 | yes | — |
| 255 | C22×C4 | — | 8 | 3 | no | — |
| 256 | C22×C4 | — | 8 | 1 | no | — |
| 257 | C22×C4 | — | 8 | 3 | no | — |
| 258 | C22×C4 | — | 8 | 3 | no | — |
| 259 | C22×C4 | — | 8 | 3 | no | — |
| 260 | C22×C4 | — | 16 | 12 | no | — |
| 261 | C22×C4 | C2×#102 | 1 | 3 | yes | — |
| 262 | C22×C4 | C2×D16 | 1 | 3 | yes | — |
| 263 | C22×C4 | C2×SD32 | 1 | 3 | yes | — |
| 264 | D8 | — | 2 | 2 | no | — |
| 265 | D8 | — | 4 | 3 | no | — |
| 266 | D8 | — | 4 | 1 | no | — |
| 267 | D8 | — | 4 | 3 | no | — |
| 268 | D8 | — | 8 | 6 | no | — |
| 269 | D8 | — | 16 | 3 | no | — |
| 270 | M16 | — | 32 | 3 | no | — |
| 271 | C2×C8 | — | 2 | 3 | no | — |
| 272 | C2×C8 | — | 2 | 3 | no | — |
| 273 | C2×C8 | — | 4 | 3 | no | — |
| 274 | C2×C8 | — | 8 | 1 | no | — |
| 275 | C2×C8 | — | 8 | 3 | no | — |
| 276 | C2×C8 | C2×#102 | 1 | 3 | yes | — |
| 277 | C2×C8 | C2×#102 | 1 | 3 | yes | — |
| 278 | C2×C8 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 279 | C2×C8 | C22×SD16 | 1 | 1 | yes | characteristic |
| 280 | C4⋊C4 | — | 4 | 1 | no | — |
| 281 | C4⋊C4 | — | 4 | 3 | no | — |
| 282 | C4⋊C4 | — | 8 | 3 | no | — |
| 283 | C4⋊C4 | — | 8 | 3 | no | — |
| 284 | C4⋊C4 | #357 | 1 | 3 | yes | — |
| 285 | C4⋊C4 | #357 | 1 | 3 | yes | — |
| 286 | C22⋊C4 | — | 8 | 1 | no | — |
| 287 | C22⋊C4 | — | 8 | 3 | no | — |
| 288 | C22⋊C4 | — | 8 | 3 | no | — |
| 289 | C22⋊C4 | — | 8 | 3 | no | — |
| 290 | C22⋊C4 | — | 8 | 6 | no | — |
| 291 | C22⋊C4 | #357 | 1 | 6 | yes | — |
| 292 | C42 | C2×#102 | 1 | 3 | yes | — |
| 293 | C42 | C2×D16 | 1 | 3 | yes | — |
| 294 | C42 | C2×SD32 | 1 | 3 | yes | — |
| 295 | C42 | C22×D8 | 1 | 1 | yes | characteristic |
| 296 | C16 | — | 2 | 3 | no | — |
| 297 | C16 | — | 2 | 1 | no | — |
| 298 | C16 | — | 2 | 3 | no | — |
| 299 | C16 | C2×#131 | 1 | 1 | yes | characteristic |
| 300 | C16 | #568 | 1 | 1 | yes | characteristic |
| 301 | C23 | — | 8 | 1 | no | — |
| 302 | C23 | — | 8 | 3 | no | — |
| 303 | C23 | — | 16 | 6 | no | — |
| 304 | C23 | — | 16 | 6 | no | — |
| 305 | C23 | — | 32 | 3 | no | — |
| 306 | C23 | C2×#357 | 1 | 3 | yes | — |
| 307 | Q8 | — | 16 | 6 | no | — |
| 308 | Q8 | #1419 | 1 | 4 | yes | — |
| 309 | D4 | — | 2 | 6 | no | — |
| 310 | D4 | — | 4 | 2 | no | — |
| 311 | D4 | — | 8 | 3 | no | — |
| 312 | D4 | — | 8 | 1 | no | — |
| 313 | D4 | — | 8 | 3 | no | — |
| 314 | D4 | — | 16 | 6 | no | — |
| 315 | D4 | — | 16 | 12 | no | — |
| 316 | D4 | — | 16 | 6 | no | — |
| 317 | D4 | — | 32 | 3 | no | — |
| 318 | C2×C4 | — | 2 | 6 | no | — |
| 319 | C2×C4 | — | 2 | 3 | no | — |
| 320 | C2×C4 | — | 2 | 3 | no | — |
| 321 | C2×C4 | — | 4 | 3 | no | — |
| 322 | C2×C4 | — | 8 | 1 | no | — |
| 323 | C2×C4 | — | 8 | 3 | no | — |
| 324 | C2×C4 | — | 16 | 2 | no | — |
| 325 | C2×C4 | — | 16 | 6 | no | — |
| 326 | C2×C4 | — | 16 | 6 | no | — |
| 327 | C2×C4 | — | 16 | 6 | no | — |
| 328 | C2×C4 | — | 16 | 6 | no | — |
| 329 | C2×C4 | C2×#357 | 1 | 3 | yes | — |
| 330 | C2×C4 | C2×#357 | 1 | 3 | yes | — |
| 331 | C2×C4 | C2×#357 | 1 | 3 | yes | — |
| 332 | C2×C4 | C22×#102 | 1 | 1 | yes | characteristic |
| 333 | C2×C4 | C22×D16 | 1 | 1 | yes | characteristic |
| 334 | C2×C4 | C22×SD32 | 1 | 1 | yes | characteristic |
| 335 | C8 | — | 2 | 3 | no | — |
| 336 | C8 | — | 2 | 1 | no | — |
| 337 | C8 | — | 2 | 3 | no | — |
| 338 | C8 | — | 16 | 1 | no | — |
| 339 | C8 | — | 16 | 3 | no | — |
| 340 | C8 | #2880 | 1 | 1 | yes | characteristic |
| 341 | C8 | #2901 | 1 | 1 | yes | characteristic |
| 342 | C22 | — | 2 | 3 | no | — |
| 343 | C22 | — | 2 | 3 | no | — |
| 344 | C22 | — | 2 | 3 | no | — |
| 345 | C22 | — | 8 | 2 | no | — |
| 346 | C22 | — | 16 | 1 | no | — |
| 347 | C22 | — | 16 | 1 | no | — |
| 348 | C22 | — | 16 | 3 | no | — |
| 349 | C22 | — | 16 | 3 | no | — |
| 350 | C22 | — | 16 | 3 | no | — |
| 351 | C22 | — | 32 | 12 | no | — |
| 352 | C22 | C22×#357 | 1 | 1 | yes | characteristic |
| 353 | C4 | — | 2 | 3 | no | — |
| 354 | C4 | — | 2 | 1 | no | — |
| 355 | C4 | — | 2 | 3 | no | — |
| 356 | C4 | — | 2 | 1 | no | — |
| 357 | C4 | — | 16 | 1 | no | — |
| 358 | C4 | — | 16 | 3 | no | — |
| 359 | C4 | C2×#1419 | 1 | 6 | yes | — |
| 360 | C4 | #17507 | 1 | 1 | yes | characteristic |
| 361 | C4 | #33385 | 1 | 1 | yes | characteristic |
| 362 | C2 | — | 4 | 3 | no | — |
| 363 | C2 | — | 16 | 2 | no | — |
| 364 | C2 | — | 32 | 3 | no | — |
| 365 | C2 | #481395 | 1 | 1 | yes | characteristic |
| 366 | C2 | #512698 | 1 | 1 | yes | characteristic |
| 367 | C2 | C22×#1419 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×#357 |
| commutator | C2×C16 | C23×C4 |
| Frattini, cosocle | C4×C16 | C24 |
| prime radical | #41×D16 | C2 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×#41 ◁ C8×#41 ◁ C16×#41 ◁ G | |
| LECS | G ▷ C4×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #512789 | C2 | semidirect |
| 3. #483475 | C2 | semidirect |
| 4. #150160 | C2 | semidirect |
| 5. #150138 | C2 | semidirect |
| 6. #150124 | C2 | semidirect |
| 7. #150064 | C2 | semidirect |
| 22. #13640 | C22 | semidirect |
| 23. C4×M64 | C22 | semidirect |
| 25. #12023 | C22 | semidirect |
| 26. #12008 | C22 | semidirect |
| 29. #7385 | C22 | semidirect |
| 30. #7385 | C22 | semidirect |
| 31. #7385 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D16 | 2 |
| #512789 | 2 |
| #483475 | 2 |
| #150160 | 2 |
| #150138 | 2 |
| #150124 | 2 |
| #150064 | 2 |