Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
7243 conjugacy classes of subgroups.
The subgroup lattice has 371 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #63004 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #63003 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #62413 | C2 | 1 | 10 | yes | maximal, complemented |
| 4 | #62357 | C2 | 1 | 5 | yes | maximal, complemented |
| 5 | #61951 | C2 | 1 | 10 | yes | maximal, complemented |
| 6 | #61948 | C2 | 1 | 10 | yes | maximal, complemented |
| 7 | #61883 | C2 | 1 | 5 | yes | maximal, complemented |
| 8 | #61881 | C2 | 1 | 5 | yes | maximal, complemented |
| 9 | SD16×#41 | C2 | 1 | 10 | yes | maximal, complemented |
| 10 | C2×#3392 | C2 | 1 | 5 | yes | maximal, complemented |
| 11 | C8×2−1+4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#585 | — | 2 | 1 | no | — |
| 13 | #3504 | — | 2 | 10 | no | — |
| 14 | #3503 | C22 | 1 | 10 | yes | complemented |
| 15 | #3502 | — | 2 | 5 | no | — |
| 16 | #3502 | C22 | 1 | 5 | yes | complemented |
| 17 | #3498 | C22 | 1 | 10 | yes | — |
| 18 | #3497 | C22 | 1 | 5 | yes | — |
| 19 | #3488 | — | 2 | 10 | no | — |
| 20 | #3487 | — | 2 | 5 | no | — |
| 21 | Q8×#41 | C22 | 1 | 10 | yes | complemented |
| 22 | C2×#557 | C22 | 1 | 5 | yes | complemented |
| 23 | D4×#41 | C22 | 1 | 10 | yes | — |
| 24 | C2×#550 | C22 | 1 | 5 | yes | — |
| 25 | C4×2−1+4 | — | 2 | 1 | no | — |
| 26 | C4×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 27 | #3392 | C22 | 1 | 20 | yes | complemented |
| 28 | #3392 | C22 | 1 | 20 | yes | complemented |
| 29 | #3392 | C22 | 1 | 20 | yes | complemented |
| 30 | #3392 | C22 | 1 | 20 | yes | complemented |
| 31 | #3392 | C22 | 1 | 10 | yes | complemented |
| 32 | Q8×SD16 | C22 | 1 | 10 | yes | complemented |
| 33 | #3362 | C22 | 1 | 20 | yes | complemented |
| 34 | #3362 | C22 | 1 | 10 | yes | complemented |
| 35 | #3359 | C22 | 1 | 20 | yes | complemented |
| 36 | #3359 | C22 | 1 | 10 | yes | complemented |
| 37 | #3335 | C22 | 1 | 10 | yes | complemented |
| 38 | #3298 | C22 | 1 | 30 | yes | complemented |
| 39 | #3295 | C22 | 1 | 30 | yes | complemented |
| 40 | D4×SD16 | C22 | 1 | 30 | yes | complemented |
| 41 | D4×SD16 | C22 | 1 | 60 | yes | complemented |
| 42 | #3246 | C22 | 1 | 30 | yes | complemented |
| 43 | #3208 | C22 | 1 | 30 | yes | complemented |
| 44 | #3206 | C22 | 1 | 30 | yes | complemented |
| 45 | #3167 | C22 | 1 | 30 | yes | complemented |
| 46 | C2×#492 | C22 | 1 | 15 | yes | complemented |
| 47 | #3103 | C22 | 1 | 30 | yes | complemented |
| 48 | #3101 | C22 | 1 | 30 | yes | complemented |
| 49 | C2×#460 | C22 | 1 | 15 | yes | complemented |
| 50 | C2×#461 | C22 | 1 | 15 | yes | complemented |
| 51 | #2988 | C22 | 1 | 10 | yes | complemented |
| 52 | #2982 | C22 | 1 | 5 | yes | complemented |
| 53 | C8×#41 | C22 | 1 | 10 | yes | complemented |
| 54 | C2×C8×Q8 | C22 | 1 | 5 | yes | complemented |
| 55 | C2×C4×SD16 | C22 | 1 | 15 | yes | complemented |
| 56 | #585 | — | 4 | 16 | no | — |
| 57 | C2×2−1+4 | — | 2 | 5 | no | — |
| 58 | C2×2−1+4 | D4 | 1 | 1 | yes | characteristic |
| 59 | C2×H(5,𝔽2) | — | 2 | 10 | no | — |
| 60 | C22×#41 | — | 2 | 10 | no | — |
| 61 | C22×#41 | — | 2 | 5 | no | — |
| 62 | C22×SD16 | C23 | 1 | 15 | yes | — |
| 63 | C22×SD16 | C23 | 1 | 30 | yes | — |
| 64 | Q82 | — | 2 | 10 | no | — |
| 65 | Q82 | C23 | 1 | 10 | yes | — |
| 66 | #557 | — | 2 | 20 | no | — |
| 67 | #557 | — | 2 | 10 | no | — |
| 68 | #557 | — | 2 | 20 | no | — |
| 69 | #557 | C23 | 1 | 10 | yes | — |
| 70 | #557 | C23 | 1 | 20 | yes | — |
| 71 | #554 | — | 2 | 30 | no | — |
| 72 | #554 | — | 2 | 30 | no | — |
| 73 | #554 | C23 | 1 | 10 | yes | — |
| 74 | #550 | — | 2 | 20 | no | — |
| 75 | #550 | — | 2 | 10 | no | — |
| 76 | #550 | C23 | 1 | 10 | yes | — |
| 77 | #550 | C23 | 1 | 20 | yes | — |
| 78 | D4×Q8 | C23 | 1 | 30 | yes | — |
| 79 | D4×Q8 | C23 | 1 | 10 | yes | — |
| 80 | #548 | — | 2 | 10 | no | — |
| 81 | #548 | — | 2 | 20 | no | — |
| 82 | #547 | C23 | 1 | 10 | yes | — |
| 83 | #546 | — | 2 | 30 | no | — |
| 84 | D42 | — | 2 | 30 | no | — |
| 85 | D42 | C23 | 1 | 30 | yes | — |
| 86 | #544 | — | 2 | 30 | no | — |
| 87 | #544 | — | 2 | 15 | no | — |
| 88 | #537 | — | 2 | 15 | no | — |
| 89 | #535 | — | 2 | 30 | no | — |
| 90 | #533 | — | 2 | 30 | no | — |
| 91 | #533 | C23 | 1 | 30 | yes | — |
| 92 | #532 | C23 | 1 | 30 | yes | — |
| 93 | C2×C4⋊Q8 | C23 | 1 | 15 | yes | — |
| 94 | C2×#127 | C23 | 1 | 15 | yes | — |
| 95 | C2×#125 | — | 2 | 15 | no | — |
| 96 | #525 | — | 2 | 30 | no | — |
| 97 | C2×#121 | — | 2 | 15 | no | — |
| 98 | #520 | — | 2 | 10 | no | — |
| 99 | #520 | D4 | 1 | 10 | yes | — |
| 100 | #519 | — | 2 | 5 | no | — |
| 101 | #519 | D4 | 1 | 5 | yes | — |
| 102 | C4×#41 | — | 2 | 10 | no | — |
| 103 | C4×#41 | C23 | 1 | 10 | yes | — |
| 104 | C2×C4×Q8 | — | 2 | 5 | no | — |
| 105 | C2×C4×Q8 | C23 | 1 | 15 | yes | — |
| 106 | C2×C4×Q8 | C23 | 1 | 5 | yes | — |
| 107 | C2×C4×D4 | C23 | 1 | 15 | yes | — |
| 108 | #498 | C23 | 1 | 10 | yes | — |
| 109 | #492 | C23 | 1 | 30 | yes | — |
| 110 | #492 | C23 | 1 | 60 | yes | — |
| 111 | #487 | C23 | 1 | 30 | yes | — |
| 112 | #486 | C23 | 1 | 30 | yes | — |
| 113 | #483 | C23 | 1 | 20 | yes | — |
| 114 | #481 | C23 | 1 | 20 | yes | — |
| 115 | #476 | C23 | 1 | 10 | yes | — |
| 116 | #476 | C23 | 1 | 30 | yes | — |
| 117 | #475 | C23 | 1 | 10 | yes | — |
| 118 | #475 | C23 | 1 | 30 | yes | — |
| 119 | #465 | C23 | 1 | 20 | yes | — |
| 120 | #465 | C23 | 1 | 60 | yes | — |
| 121 | #461 | C23 | 1 | 30 | yes | — |
| 122 | #461 | C23 | 1 | 30 | yes | — |
| 123 | #461 | C23 | 1 | 60 | yes | — |
| 124 | #460 | C23 | 1 | 30 | yes | — |
| 125 | #460 | C23 | 1 | 30 | yes | — |
| 126 | #460 | C23 | 1 | 60 | yes | — |
| 127 | #450 | C23 | 1 | 60 | yes | — |
| 128 | #448 | C23 | 1 | 60 | yes | — |
| 129 | C8×Q8 | C23 | 1 | 20 | yes | — |
| 130 | C8×Q8 | C23 | 1 | 10 | yes | — |
| 131 | C8×Q8 | C23 | 1 | 10 | yes | — |
| 132 | C4×SD16 | C23 | 1 | 10 | yes | — |
| 133 | C4×SD16 | C23 | 1 | 30 | yes | — |
| 134 | C4×SD16 | C23 | 1 | 60 | yes | — |
| 135 | C4×SD16 | C23 | 1 | 30 | yes | — |
| 136 | C4×SD16 | C23 | 1 | 30 | yes | — |
| 137 | C8×D4 | C23 | 1 | 10 | yes | — |
| 138 | C8×D4 | C23 | 1 | 30 | yes | — |
| 139 | #431 | C23 | 1 | 30 | yes | — |
| 140 | C2×#106 | C23 | 1 | 5 | yes | — |
| 141 | C2×C4⋊C8 | C23 | 1 | 15 | yes | — |
| 142 | C2×#103 | C23 | 1 | 15 | yes | — |
| 143 | C2×#102 | C23 | 1 | 15 | yes | — |
| 144 | C2×C4×C8 | C23 | 1 | 15 | yes | — |
| 145 | 2−1+4 | — | 4 | 40 | no | — |
| 146 | 2−1+4 | SD16 | 1 | 16 | yes | complemented |
| 147 | H(5,𝔽2) | — | 4 | 80 | no | — |
| 148 | C2×#41 | — | 2 | 10 | no | — |
| 149 | C2×#41 | — | 2 | 20 | no | — |
| 150 | C2×#41 | — | 2 | 10 | no | — |
| 151 | C2×#41 | — | 2 | 30 | no | — |
| 152 | C2×#41 | — | 4 | 80 | no | — |
| 153 | C2×#41 | — | 4 | 40 | no | — |
| 154 | C2×#41 | C2×D4 | 1 | 10 | yes | — |
| 155 | C22×Q8 | — | 2 | 10 | no | — |
| 156 | C22×Q8 | C2×D4 | 1 | 5 | yes | — |
| 157 | C22×Q8 | C24 | 1 | 15 | yes | — |
| 158 | C22×D4 | — | 2 | 30 | no | — |
| 159 | C22×D4 | — | 2 | 15 | no | — |
| 160 | C22×D4 | — | 2 | 15 | no | — |
| 161 | C22×D4 | C24 | 1 | 15 | yes | — |
| 162 | C23×C4 | — | 2 | 15 | no | — |
| 163 | C2×SD16 | — | 4 | 30 | no | — |
| 164 | C2×SD16 | — | 8 | 30 | no | — |
| 165 | C2×SD16 | C24 | 1 | 10 | yes | — |
| 166 | C2×SD16 | C24 | 1 | 60 | yes | — |
| 167 | C2×SD16 | C24 | 1 | 30 | yes | — |
| 168 | C22×C8 | C24 | 1 | 5 | yes | — |
| 169 | C22×C8 | C24 | 1 | 15 | yes | — |
| 170 | C4⋊Q8 | — | 2 | 30 | no | — |
| 171 | C4⋊Q8 | — | 2 | 30 | no | — |
| 172 | C4⋊Q8 | — | 2 | 30 | no | — |
| 173 | C4⋊Q8 | C24 | 1 | 30 | yes | — |
| 174 | C4⋊Q8 | C24 | 1 | 10 | yes | — |
| 175 | C4⋊Q8 | C24 | 1 | 10 | yes | — |
| 176 | #127 | — | 2 | 30 | no | — |
| 177 | #127 | C24 | 1 | 30 | yes | — |
| 178 | #125 | — | 2 | 30 | no | — |
| 179 | #125 | — | 2 | 60 | no | — |
| 180 | #125 | — | 2 | 10 | no | — |
| 181 | #125 | — | 2 | 30 | no | — |
| 182 | #124 | — | 2 | 30 | no | — |
| 183 | #123 | — | 2 | 20 | no | — |
| 184 | C22⋊Q8 | — | 2 | 30 | no | — |
| 185 | C22⋊Q8 | — | 2 | 10 | no | — |
| 186 | C22⋊Q8 | — | 2 | 30 | no | — |
| 187 | C22⋊Q8 | — | 2 | 20 | no | — |
| 188 | C22⋊Q8 | — | 2 | 60 | no | — |
| 189 | C22⋊Q8 | C24 | 1 | 20 | yes | — |
| 190 | #121 | — | 2 | 30 | no | — |
| 191 | #121 | — | 2 | 30 | no | — |
| 192 | #121 | — | 2 | 60 | no | — |
| 193 | #121 | — | 2 | 30 | no | — |
| 194 | #121 | C24 | 1 | 20 | yes | — |
| 195 | #120 | — | 2 | 60 | no | — |
| 196 | C4×Q8 | — | 2 | 10 | no | — |
| 197 | C4×Q8 | — | 2 | 20 | no | — |
| 198 | C4×Q8 | — | 2 | 10 | no | — |
| 199 | C4×Q8 | — | 2 | 30 | no | — |
| 200 | C4×Q8 | — | 2 | 30 | no | — |
| 201 | C4×Q8 | C2×D4 | 1 | 20 | yes | — |
| 202 | C4×Q8 | C2×D4 | 1 | 10 | yes | — |
| 203 | C4×Q8 | C24 | 1 | 10 | yes | — |
| 204 | C4×Q8 | C24 | 1 | 30 | yes | — |
| 205 | C4×Q8 | C24 | 1 | 10 | yes | — |
| 206 | C4×D4 | — | 2 | 10 | no | — |
| 207 | C4×D4 | — | 2 | 30 | no | — |
| 208 | C4×D4 | — | 2 | 30 | no | — |
| 209 | C4×D4 | — | 2 | 30 | no | — |
| 210 | C4×D4 | C2×D4 | 1 | 30 | yes | — |
| 211 | C4×D4 | C24 | 1 | 10 | yes | — |
| 212 | C4×D4 | C24 | 1 | 30 | yes | — |
| 213 | C4×D4 | C24 | 1 | 10 | yes | — |
| 214 | #117 | — | 2 | 30 | no | — |
| 215 | #117 | C2×D4 | 1 | 30 | yes | — |
| 216 | C2×C4⋊C4 | — | 2 | 15 | no | — |
| 217 | C2×C4⋊C4 | — | 2 | 15 | no | — |
| 218 | C2×C4⋊C4 | — | 2 | 15 | no | — |
| 219 | C2×C4⋊C4 | C2×D4 | 1 | 15 | yes | — |
| 220 | C2×C4⋊C4 | C24 | 1 | 5 | yes | — |
| 221 | C2×C4⋊C4 | C24 | 1 | 5 | yes | — |
| 222 | C2×C22⋊C4 | — | 2 | 15 | no | — |
| 223 | C2×C42 | — | 2 | 15 | no | — |
| 224 | C2×C42 | C24 | 1 | 15 | yes | — |
| 225 | #106 | C24 | 1 | 1 | yes | characteristic |
| 226 | #106 | C24 | 1 | 5 | yes | — |
| 227 | #106 | C24 | 1 | 5 | yes | — |
| 228 | #106 | C24 | 1 | 5 | yes | — |
| 229 | #106 | C24 | 1 | 20 | yes | — |
| 230 | C4⋊C8 | C24 | 1 | 30 | yes | — |
| 231 | C4⋊C8 | C24 | 1 | 10 | yes | — |
| 232 | #103 | C24 | 1 | 10 | yes | — |
| 233 | #103 | C24 | 1 | 30 | yes | — |
| 234 | #103 | C24 | 1 | 20 | yes | — |
| 235 | #102 | C24 | 1 | 10 | yes | — |
| 236 | #102 | C24 | 1 | 30 | yes | — |
| 237 | #102 | C24 | 1 | 20 | yes | — |
| 238 | C22⋊C8 | C24 | 1 | 20 | yes | — |
| 239 | C4×C8 | C24 | 1 | 10 | yes | — |
| 240 | C4×C8 | C24 | 1 | 30 | yes | — |
| 241 | C24 | — | 2 | 15 | no | — |
| 242 | #41 | — | 4 | 40 | no | — |
| 243 | #41 | — | 4 | 80 | no | — |
| 244 | #41 | — | 4 | 40 | no | — |
| 245 | #41 | — | 4 | 120 | no | — |
| 246 | #41 | C2×SD16 | 1 | 80 | yes | complemented |
| 247 | C2×Q8 | — | 2 | 10 | no | — |
| 248 | C2×Q8 | — | 2 | 10 | no | — |
| 249 | C2×Q8 | — | 2 | 15 | no | — |
| 250 | C2×Q8 | — | 4 | 15 | no | — |
| 251 | C2×Q8 | — | 4 | 15 | no | — |
| 252 | C2×Q8 | — | 4 | 40 | no | — |
| 253 | C2×Q8 | C2×SD16 | 1 | 40 | yes | complemented |
| 254 | C2×Q8 | C22×D4 | 1 | 10 | yes | — |
| 255 | C2×Q8 | C25 | 1 | 10 | yes | — |
| 256 | C2×D4 | — | 2 | 20 | no | — |
| 257 | C2×D4 | — | 2 | 30 | no | — |
| 258 | C2×D4 | — | 2 | 15 | no | — |
| 259 | C2×D4 | — | 2 | 30 | no | — |
| 260 | C2×D4 | — | 4 | 15 | no | — |
| 261 | C2×D4 | — | 4 | 15 | no | — |
| 262 | C2×D4 | — | 4 | 120 | no | — |
| 263 | C2×D4 | — | 4 | 60 | no | — |
| 264 | C2×D4 | — | 16 | 15 | no | — |
| 265 | C2×D4 | C22×D4 | 1 | 10 | yes | — |
| 266 | C2×D4 | C25 | 1 | 10 | yes | — |
| 267 | C22×C4 | — | 2 | 5 | no | — |
| 268 | C22×C4 | — | 2 | 5 | no | — |
| 269 | C22×C4 | — | 2 | 15 | no | — |
| 270 | C22×C4 | — | 2 | 10 | no | — |
| 271 | C22×C4 | — | 2 | 30 | no | — |
| 272 | C22×C4 | — | 4 | 60 | no | — |
| 273 | C22×C4 | C22×D4 | 1 | 15 | yes | — |
| 274 | C22×C4 | C22×D4 | 1 | 15 | yes | — |
| 275 | C22×C4 | C25 | 1 | 5 | yes | — |
| 276 | SD16 | — | 2 | 20 | no | — |
| 277 | SD16 | — | 4 | 30 | no | — |
| 278 | SD16 | — | 4 | 60 | no | — |
| 279 | C2×C8 | — | 2 | 10 | no | — |
| 280 | C2×C8 | — | 4 | 15 | no | — |
| 281 | C2×C8 | C25 | 1 | 5 | yes | — |
| 282 | C2×C8 | C25 | 1 | 10 | yes | — |
| 283 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 284 | C4⋊C4 | — | 2 | 10 | no | — |
| 285 | C4⋊C4 | — | 2 | 30 | no | — |
| 286 | C4⋊C4 | — | 2 | 30 | no | — |
| 287 | C4⋊C4 | — | 2 | 30 | no | — |
| 288 | C4⋊C4 | — | 2 | 5 | no | — |
| 289 | C4⋊C4 | — | 2 | 5 | no | — |
| 290 | C4⋊C4 | — | 2 | 10 | no | — |
| 291 | C4⋊C4 | — | 2 | 10 | no | — |
| 292 | C4⋊C4 | — | 2 | 20 | no | — |
| 293 | C4⋊C4 | C22×D4 | 1 | 30 | yes | — |
| 294 | C4⋊C4 | C22×D4 | 1 | 10 | yes | — |
| 295 | C4⋊C4 | C25 | 1 | 1 | yes | characteristic |
| 296 | C4⋊C4 | C25 | 1 | 5 | yes | — |
| 297 | C4⋊C4 | C25 | 1 | 1 | yes | characteristic |
| 298 | C4⋊C4 | C25 | 1 | 5 | yes | — |
| 299 | C22⋊C4 | — | 2 | 20 | no | — |
| 300 | C22⋊C4 | — | 2 | 10 | no | — |
| 301 | C22⋊C4 | — | 2 | 30 | no | — |
| 302 | C22⋊C4 | — | 2 | 20 | no | — |
| 303 | C22⋊C4 | C22×D4 | 1 | 20 | yes | — |
| 304 | C42 | — | 2 | 10 | no | — |
| 305 | C42 | — | 2 | 30 | no | — |
| 306 | C42 | C22×D4 | 1 | 30 | yes | — |
| 307 | C42 | C25 | 1 | 10 | yes | — |
| 308 | C23 | — | 2 | 10 | no | — |
| 309 | C23 | — | 4 | 30 | no | — |
| 310 | C23 | — | 8 | 15 | no | — |
| 311 | C23 | — | 8 | 15 | no | — |
| 312 | C23 | C23×D4 | 1 | 5 | yes | — |
| 313 | Q8 | — | 2 | 10 | no | — |
| 314 | Q8 | — | 2 | 10 | no | — |
| 315 | Q8 | — | 4 | 20 | no | — |
| 316 | Q8 | — | 8 | 10 | no | — |
| 317 | Q8 | — | 8 | 15 | no | — |
| 318 | Q8 | C22×SD16 | 1 | 40 | yes | — |
| 319 | D4 | — | 2 | 10 | no | — |
| 320 | D4 | — | 2 | 10 | no | — |
| 321 | D4 | — | 4 | 40 | no | — |
| 322 | D4 | — | 4 | 60 | no | — |
| 323 | D4 | — | 8 | 15 | no | — |
| 324 | D4 | — | 8 | 30 | no | — |
| 325 | D4 | C22×SD16 | 1 | 40 | yes | — |
| 326 | C2×C4 | — | 2 | 5 | no | — |
| 327 | C2×C4 | — | 2 | 5 | no | — |
| 328 | C2×C4 | — | 2 | 1 | no | — |
| 329 | C2×C4 | — | 2 | 5 | no | — |
| 330 | C2×C4 | — | 2 | 10 | no | — |
| 331 | C2×C4 | — | 2 | 1 | no | — |
| 332 | C2×C4 | — | 2 | 5 | no | — |
| 333 | C2×C4 | — | 4 | 15 | no | — |
| 334 | C2×C4 | — | 4 | 10 | no | — |
| 335 | C2×C4 | — | 4 | 20 | no | — |
| 336 | C2×C4 | — | 4 | 60 | no | — |
| 337 | C2×C4 | — | 8 | 5 | no | — |
| 338 | C2×C4 | — | 8 | 15 | no | — |
| 339 | C2×C4 | C22×SD16 | 1 | 60 | yes | — |
| 340 | C2×C4 | C23×D4 | 1 | 5 | yes | — |
| 341 | C2×C4 | C23×D4 | 1 | 10 | yes | — |
| 342 | C2×C4 | C23×D4 | 1 | 10 | yes | — |
| 343 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 344 | C8 | — | 2 | 5 | no | — |
| 345 | C8 | — | 2 | 10 | no | — |
| 346 | C8 | #585 | 1 | 2 | yes | complemented |
| 347 | C22 | — | 2 | 5 | no | — |
| 348 | C22 | — | 2 | 5 | no | — |
| 349 | C22 | — | 4 | 10 | no | — |
| 350 | C22 | — | 4 | 10 | no | — |
| 351 | C22 | — | 4 | 10 | no | — |
| 352 | C22 | — | 16 | 30 | no | — |
| 353 | C22 | C23×SD16 | 1 | 10 | yes | — |
| 354 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 355 | C4 | — | 2 | 5 | no | — |
| 356 | C4 | — | 2 | 10 | no | — |
| 357 | C4 | — | 4 | 10 | no | — |
| 358 | C4 | — | 4 | 1 | no | — |
| 359 | C4 | — | 4 | 5 | no | — |
| 360 | C4 | — | 4 | 1 | no | — |
| 361 | C4 | — | 4 | 5 | no | — |
| 362 | C4 | C23×SD16 | 1 | 20 | yes | — |
| 363 | C4 | C2×#585 | 1 | 1 | yes | characteristic |
| 364 | C4 | H(7,𝔽2) | 1 | 1 | yes | characteristic |
| 365 | C2 | — | 2 | 10 | no | — |
| 366 | C2 | — | 8 | 10 | no | — |
| 367 | C2 | #63003 | 1 | 1 | yes | characteristic |
| 368 | C2 | C24×SD16 | 1 | 1 | yes | characteristic |
| 369 | C2 | #63092 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| prime radical | #63003 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×2−1+4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #63004 | C2 | semidirect |
| 3. #62413 | C2 | semidirect |
| 4. #62357 | C2 | semidirect |
| 5. #61951 | C2 | semidirect |
| 6. #61948 | C2 | semidirect |
| 7. #61883 | C2 | semidirect |
| 8. #61881 | C2 | semidirect |
| 9. SD16×#41 | C2 | semidirect |
| 10. C2×#3392 | C2 | semidirect |
| 11. C8×2−1+4 | C2 | semidirect |
| 14. #3503 | C22 | semidirect |
| 16. #3502 | C22 | semidirect |
| 21. Q8×#41 | C22 | semidirect |
| 22. C2×#557 | C22 | semidirect |
| 27. #3392 | C22 | semidirect |
| 28. #3392 | C22 | semidirect |
| 29. #3392 | C22 | semidirect |
| 30. #3392 | C22 | semidirect |
| 31. #3392 | C22 | semidirect |
| 32. Q8×SD16 | C22 | semidirect |
| 33. #3362 | C22 | semidirect |
| 34. #3362 | C22 | semidirect |
| 35. #3359 | C22 | semidirect |
| 36. #3359 | C22 | semidirect |
| 37. #3335 | C22 | semidirect |
| 38. #3298 | C22 | semidirect |
| 39. #3295 | C22 | semidirect |
| 40. D4×SD16 | C22 | semidirect |
| 41. D4×SD16 | C22 | semidirect |
| 42. #3246 | C22 | semidirect |
| 43. #3208 | C22 | semidirect |
| 44. #3206 | C22 | semidirect |
| 45. #3167 | C22 | semidirect |
| 46. C2×#492 | C22 | semidirect |
| 47. #3103 | C22 | semidirect |
| 48. #3101 | C22 | semidirect |
| 49. C2×#460 | C22 | semidirect |
| 50. C2×#461 | C22 | semidirect |
| 51. #2988 | C22 | semidirect |
| 52. #2982 | C22 | semidirect |
| 53. C8×#41 | C22 | semidirect |
| 54. C2×C8×Q8 | C22 | semidirect |
| 55. C2×C4×SD16 | C22 | semidirect |
| 146. 2−1+4 | SD16 | semidirect |
| 246. #41 | C2×SD16 | semidirect |
| 253. C2×Q8 | C2×SD16 | semidirect |
| 346. C8 | #585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63004 | 2 |
| #63003 | 2 |
| #62413 | 2 |
| #62357 | 2 |
| #61951 | 2 |
| #61948 | 2 |
| #61883 | 2 |
| #61881 | 2 |
| SD16×#41 | 2 |
| C2×#3392 | 2 |
| C8×2−1+4 | 2 |