Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
7161 conjugacy classes of subgroups.
The subgroup lattice has 431 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62989 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #62988 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #62469 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #62243 | C2 | 1 | 9 | yes | maximal, complemented |
| 5 | #62099 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #62096 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #61697 | C2 | 1 | 9 | yes | maximal, complemented |
| 8 | #61695 | C2 | 1 | 9 | yes | maximal, complemented |
| 9 | SD16×#41 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | C2×#3335 | C2 | 1 | 9 | yes | maximal, complemented |
| 11 | C8×H(5,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#585 | — | 2 | 1 | no | — |
| 13 | #3504 | — | 2 | 6 | no | — |
| 14 | #3503 | C22 | 1 | 6 | yes | complemented |
| 15 | #3501 | — | 2 | 9 | no | — |
| 16 | #3501 | C22 | 1 | 9 | yes | complemented |
| 17 | #3499 | C22 | 1 | 6 | yes | — |
| 18 | #3496 | C22 | 1 | 9 | yes | — |
| 19 | #3489 | — | 2 | 6 | no | — |
| 20 | #3485 | — | 2 | 9 | no | — |
| 21 | Q8×#41 | C22 | 1 | 6 | yes | complemented |
| 22 | C2×#554 | C22 | 1 | 9 | yes | complemented |
| 23 | D4×#41 | C22 | 1 | 6 | yes | — |
| 24 | C2×#547 | C22 | 1 | 9 | yes | — |
| 25 | C4×H(5,𝔽2) | — | 2 | 1 | no | — |
| 26 | C4×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 27 | #3392 | C22 | 1 | 2 | yes | complemented |
| 28 | Q8×SD16 | C22 | 1 | 6 | yes | complemented |
| 29 | Q8×SD16 | C22 | 1 | 12 | yes | complemented |
| 30 | #3362 | C22 | 1 | 6 | yes | complemented |
| 31 | #3359 | C22 | 1 | 6 | yes | complemented |
| 32 | #3335 | C22 | 1 | 36 | yes | complemented |
| 33 | #3335 | C22 | 1 | 36 | yes | complemented |
| 34 | #3335 | C22 | 1 | 36 | yes | complemented |
| 35 | #3335 | C22 | 1 | 18 | yes | complemented |
| 36 | #3335 | C22 | 1 | 36 | yes | complemented |
| 37 | #3298 | C22 | 1 | 36 | yes | complemented |
| 38 | #3298 | C22 | 1 | 18 | yes | complemented |
| 39 | #3295 | C22 | 1 | 18 | yes | complemented |
| 40 | #3295 | C22 | 1 | 36 | yes | complemented |
| 41 | D4×SD16 | C22 | 1 | 18 | yes | complemented |
| 42 | #3246 | C22 | 1 | 18 | yes | complemented |
| 43 | #3229 | C22 | 1 | 18 | yes | complemented |
| 44 | #3227 | C22 | 1 | 18 | yes | complemented |
| 45 | #3187 | C22 | 1 | 36 | yes | complemented |
| 46 | #3167 | C22 | 1 | 18 | yes | complemented |
| 47 | C2×#498 | C22 | 1 | 9 | yes | complemented |
| 48 | #3103 | C22 | 1 | 18 | yes | complemented |
| 49 | #3101 | C22 | 1 | 18 | yes | complemented |
| 50 | C2×#481 | C22 | 1 | 18 | yes | complemented |
| 51 | C2×#483 | C22 | 1 | 18 | yes | complemented |
| 52 | C2×#475 | C22 | 1 | 9 | yes | complemented |
| 53 | C2×#476 | C22 | 1 | 9 | yes | complemented |
| 54 | C2×#465 | C22 | 1 | 18 | yes | complemented |
| 55 | #2988 | C22 | 1 | 6 | yes | complemented |
| 56 | #2972 | C22 | 1 | 9 | yes | complemented |
| 57 | C8×#41 | C22 | 1 | 6 | yes | complemented |
| 58 | C2×C4×SD16 | C22 | 1 | 9 | yes | complemented |
| 59 | C2×C8×D4 | C22 | 1 | 9 | yes | complemented |
| 60 | C22×#106 | C22 | 1 | 6 | yes | complemented |
| 61 | #585 | — | 4 | 16 | no | — |
| 62 | C2×2−1+4 | — | 2 | 6 | no | — |
| 63 | C2×H(5,𝔽2) | — | 2 | 9 | no | — |
| 64 | C2×H(5,𝔽2) | D4 | 1 | 1 | yes | characteristic |
| 65 | C22×#41 | — | 2 | 6 | no | — |
| 66 | C22×#41 | — | 2 | 9 | no | — |
| 67 | C22×SD16 | C23 | 1 | 9 | yes | — |
| 68 | C23×C8 | C23 | 1 | 6 | yes | — |
| 69 | Q82 | C23 | 1 | 6 | yes | — |
| 70 | #557 | — | 2 | 6 | no | — |
| 71 | #557 | — | 2 | 6 | no | — |
| 72 | #557 | C23 | 1 | 2 | yes | — |
| 73 | #554 | — | 2 | 36 | no | — |
| 74 | #554 | — | 2 | 18 | no | — |
| 75 | #554 | — | 2 | 36 | no | — |
| 76 | #554 | C23 | 1 | 18 | yes | — |
| 77 | #554 | C23 | 1 | 36 | yes | — |
| 78 | #550 | C23 | 1 | 2 | yes | — |
| 79 | D4×Q8 | — | 2 | 6 | no | — |
| 80 | D4×Q8 | — | 2 | 18 | no | — |
| 81 | D4×Q8 | C23 | 1 | 18 | yes | — |
| 82 | D4×Q8 | C23 | 1 | 6 | yes | — |
| 83 | #548 | — | 2 | 6 | no | — |
| 84 | #547 | — | 2 | 36 | no | — |
| 85 | #547 | — | 2 | 18 | no | — |
| 86 | #547 | C23 | 1 | 18 | yes | — |
| 87 | #547 | C23 | 1 | 36 | yes | — |
| 88 | #546 | — | 2 | 18 | no | — |
| 89 | #546 | — | 2 | 36 | no | — |
| 90 | D42 | C23 | 1 | 18 | yes | — |
| 91 | #544 | — | 2 | 18 | no | — |
| 92 | #544 | — | 2 | 9 | no | — |
| 93 | #543 | — | 2 | 18 | no | — |
| 94 | #537 | — | 2 | 9 | no | — |
| 95 | #536 | — | 2 | 18 | no | — |
| 96 | #534 | — | 2 | 18 | no | — |
| 97 | #533 | — | 2 | 18 | no | — |
| 98 | #533 | C23 | 1 | 18 | yes | — |
| 99 | #532 | C23 | 1 | 18 | yes | — |
| 100 | C2×C4⋊Q8 | C23 | 1 | 9 | yes | — |
| 101 | C2×C4⋊Q8 | C23 | 1 | 9 | yes | — |
| 102 | C2×#125 | — | 2 | 9 | no | — |
| 103 | #525 | — | 2 | 18 | no | — |
| 104 | C2×#123 | — | 2 | 18 | no | — |
| 105 | C2×C22⋊Q8 | — | 2 | 9 | no | — |
| 106 | C2×C22⋊Q8 | — | 2 | 18 | no | — |
| 107 | C2×C22⋊Q8 | C23 | 1 | 18 | yes | — |
| 108 | C2×#121 | C23 | 1 | 18 | yes | — |
| 109 | #520 | — | 2 | 6 | no | — |
| 110 | #520 | D4 | 1 | 6 | yes | — |
| 111 | #518 | — | 2 | 9 | no | — |
| 112 | #518 | D4 | 1 | 9 | yes | — |
| 113 | C4×#41 | — | 2 | 6 | no | — |
| 114 | C4×#41 | C23 | 1 | 6 | yes | — |
| 115 | C2×C4×Q8 | C23 | 1 | 9 | yes | — |
| 116 | C2×C4×D4 | — | 2 | 9 | no | — |
| 117 | C2×C4×D4 | C23 | 1 | 9 | yes | — |
| 118 | C2×C4×D4 | C23 | 1 | 9 | yes | — |
| 119 | C22×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 120 | C22×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 121 | #498 | C23 | 1 | 18 | yes | — |
| 122 | #498 | C23 | 1 | 36 | yes | — |
| 123 | #492 | C23 | 1 | 6 | yes | — |
| 124 | #487 | C23 | 1 | 18 | yes | — |
| 125 | #486 | C23 | 1 | 18 | yes | — |
| 126 | #483 | C23 | 1 | 36 | yes | — |
| 127 | #483 | C23 | 1 | 72 | yes | — |
| 128 | #481 | C23 | 1 | 36 | yes | — |
| 129 | #481 | C23 | 1 | 72 | yes | — |
| 130 | #476 | C23 | 1 | 18 | yes | — |
| 131 | #476 | C23 | 1 | 18 | yes | — |
| 132 | #476 | C23 | 1 | 36 | yes | — |
| 133 | #475 | C23 | 1 | 18 | yes | — |
| 134 | #475 | C23 | 1 | 36 | yes | — |
| 135 | #475 | C23 | 1 | 18 | yes | — |
| 136 | #465 | C23 | 1 | 36 | yes | — |
| 137 | #465 | C23 | 1 | 36 | yes | — |
| 138 | #465 | C23 | 1 | 72 | yes | — |
| 139 | #461 | C23 | 1 | 6 | yes | — |
| 140 | #461 | C23 | 1 | 18 | yes | — |
| 141 | #460 | C23 | 1 | 6 | yes | — |
| 142 | #460 | C23 | 1 | 18 | yes | — |
| 143 | #450 | C23 | 1 | 36 | yes | — |
| 144 | #448 | C23 | 1 | 36 | yes | — |
| 145 | C8×Q8 | C23 | 1 | 6 | yes | — |
| 146 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 147 | C4×SD16 | C23 | 1 | 6 | yes | — |
| 148 | C4×SD16 | C23 | 1 | 18 | yes | — |
| 149 | C4×SD16 | C23 | 1 | 18 | yes | — |
| 150 | C4×SD16 | C23 | 1 | 18 | yes | — |
| 151 | C4×SD16 | C23 | 1 | 36 | yes | — |
| 152 | C8×D4 | C23 | 1 | 18 | yes | — |
| 153 | C8×D4 | C23 | 1 | 36 | yes | — |
| 154 | C8×D4 | C23 | 1 | 18 | yes | — |
| 155 | #431 | C23 | 1 | 18 | yes | — |
| 156 | C2×#106 | C23 | 1 | 18 | yes | — |
| 157 | C2×#106 | C23 | 1 | 18 | yes | — |
| 158 | C2×#106 | C23 | 1 | 18 | yes | — |
| 159 | C2×#106 | C23 | 1 | 18 | yes | — |
| 160 | C2×#106 | C23 | 1 | 9 | yes | — |
| 161 | C2×C4⋊C8 | C23 | 1 | 9 | yes | — |
| 162 | C2×#103 | C23 | 1 | 18 | yes | — |
| 163 | C2×#103 | C23 | 1 | 9 | yes | — |
| 164 | C2×#102 | C23 | 1 | 9 | yes | — |
| 165 | C2×#102 | C23 | 1 | 18 | yes | — |
| 166 | C2×C22⋊C8 | C23 | 1 | 18 | yes | — |
| 167 | C2×C4×C8 | C23 | 1 | 9 | yes | — |
| 168 | 2−1+4 | — | 4 | 48 | no | — |
| 169 | H(5,𝔽2) | — | 4 | 72 | no | — |
| 170 | H(5,𝔽2) | SD16 | 1 | 16 | yes | complemented |
| 171 | C2×#41 | — | 2 | 2 | no | — |
| 172 | C2×#41 | — | 2 | 18 | no | — |
| 173 | C2×#41 | — | 2 | 36 | no | — |
| 174 | C2×#41 | — | 2 | 18 | no | — |
| 175 | C2×#41 | — | 4 | 48 | no | — |
| 176 | C2×#41 | — | 4 | 72 | no | — |
| 177 | C2×#41 | C2×D4 | 1 | 6 | yes | — |
| 178 | C22×Q8 | — | 2 | 6 | no | — |
| 179 | C22×Q8 | — | 2 | 9 | no | — |
| 180 | C22×Q8 | — | 2 | 9 | no | — |
| 181 | C22×Q8 | C24 | 1 | 9 | yes | — |
| 182 | C22×D4 | — | 2 | 18 | no | — |
| 183 | C22×D4 | — | 2 | 18 | no | — |
| 184 | C22×D4 | C2×D4 | 1 | 9 | yes | — |
| 185 | C22×D4 | C24 | 1 | 9 | yes | — |
| 186 | C23×C4 | — | 2 | 6 | no | — |
| 187 | C23×C4 | — | 2 | 6 | no | — |
| 188 | C23×C4 | — | 2 | 9 | no | — |
| 189 | C23×C4 | C24 | 1 | 6 | yes | — |
| 190 | C2×SD16 | — | 4 | 18 | no | — |
| 191 | C2×SD16 | C24 | 1 | 6 | yes | — |
| 192 | C2×SD16 | C24 | 1 | 18 | yes | — |
| 193 | C2×SD16 | C24 | 1 | 12 | yes | — |
| 194 | C22×C8 | — | 4 | 12 | no | — |
| 195 | C22×C8 | C24 | 1 | 9 | yes | — |
| 196 | C22×C8 | C24 | 1 | 18 | yes | — |
| 197 | C22×C8 | C24 | 1 | 9 | yes | — |
| 198 | C4⋊Q8 | — | 2 | 18 | no | — |
| 199 | C4⋊Q8 | — | 2 | 18 | no | — |
| 200 | C4⋊Q8 | — | 2 | 18 | no | — |
| 201 | C4⋊Q8 | — | 2 | 18 | no | — |
| 202 | C4⋊Q8 | C24 | 1 | 6 | yes | — |
| 203 | C4⋊Q8 | C24 | 1 | 18 | yes | — |
| 204 | C4⋊Q8 | C24 | 1 | 18 | yes | — |
| 205 | #127 | C24 | 1 | 6 | yes | — |
| 206 | #125 | — | 2 | 18 | no | — |
| 207 | #125 | — | 2 | 36 | no | — |
| 208 | #125 | — | 2 | 6 | no | — |
| 209 | #125 | — | 2 | 18 | no | — |
| 210 | #124 | — | 2 | 18 | no | — |
| 211 | #123 | — | 2 | 36 | no | — |
| 212 | #123 | — | 2 | 72 | no | — |
| 213 | C22⋊Q8 | — | 2 | 36 | no | — |
| 214 | C22⋊Q8 | — | 2 | 18 | no | — |
| 215 | C22⋊Q8 | — | 2 | 18 | no | — |
| 216 | C22⋊Q8 | — | 2 | 36 | no | — |
| 217 | C22⋊Q8 | — | 2 | 18 | no | — |
| 218 | C22⋊Q8 | — | 2 | 36 | no | — |
| 219 | C22⋊Q8 | — | 2 | 72 | no | — |
| 220 | C22⋊Q8 | — | 2 | 36 | no | — |
| 221 | C22⋊Q8 | C24 | 1 | 36 | yes | — |
| 222 | #121 | — | 2 | 36 | no | — |
| 223 | #121 | — | 2 | 18 | no | — |
| 224 | #121 | — | 2 | 6 | no | — |
| 225 | #121 | — | 2 | 18 | no | — |
| 226 | #121 | C24 | 1 | 36 | yes | — |
| 227 | #120 | — | 2 | 36 | no | — |
| 228 | C4×Q8 | — | 2 | 2 | no | — |
| 229 | C4×Q8 | — | 2 | 6 | no | — |
| 230 | C4×Q8 | — | 2 | 18 | no | — |
| 231 | C4×Q8 | — | 2 | 18 | no | — |
| 232 | C4×Q8 | C2×D4 | 1 | 6 | yes | — |
| 233 | C4×Q8 | C24 | 1 | 6 | yes | — |
| 234 | C4×Q8 | C24 | 1 | 18 | yes | — |
| 235 | C4×Q8 | C24 | 1 | 2 | yes | — |
| 236 | C4×D4 | — | 2 | 18 | no | — |
| 237 | C4×D4 | — | 2 | 36 | no | — |
| 238 | C4×D4 | — | 2 | 18 | no | — |
| 239 | C4×D4 | — | 2 | 18 | no | — |
| 240 | C4×D4 | — | 2 | 18 | no | — |
| 241 | C4×D4 | C2×D4 | 1 | 36 | yes | — |
| 242 | C4×D4 | C2×D4 | 1 | 18 | yes | — |
| 243 | C4×D4 | C24 | 1 | 6 | yes | — |
| 244 | C4×D4 | C24 | 1 | 18 | yes | — |
| 245 | C4×D4 | C24 | 1 | 18 | yes | — |
| 246 | #117 | — | 2 | 18 | no | — |
| 247 | #117 | C2×D4 | 1 | 18 | yes | — |
| 248 | C2×C4⋊C4 | — | 2 | 18 | no | — |
| 249 | C2×C4⋊C4 | — | 2 | 18 | no | — |
| 250 | C2×C4⋊C4 | — | 2 | 9 | no | — |
| 251 | C2×C4⋊C4 | — | 2 | 9 | no | — |
| 252 | C2×C4⋊C4 | — | 2 | 18 | no | — |
| 253 | C2×C4⋊C4 | — | 2 | 9 | no | — |
| 254 | C2×C4⋊C4 | C2×D4 | 1 | 9 | yes | — |
| 255 | C2×C4⋊C4 | C24 | 1 | 9 | yes | — |
| 256 | C2×C4⋊C4 | C24 | 1 | 9 | yes | — |
| 257 | C2×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 258 | C2×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 259 | C2×C22⋊C4 | — | 2 | 18 | no | — |
| 260 | C2×C22⋊C4 | — | 2 | 9 | no | — |
| 261 | C2×C22⋊C4 | — | 2 | 18 | no | — |
| 262 | C2×C22⋊C4 | C2×D4 | 1 | 18 | yes | — |
| 263 | C2×C42 | — | 2 | 9 | no | — |
| 264 | C2×C42 | C24 | 1 | 9 | yes | — |
| 265 | #106 | C24 | 1 | 1 | yes | characteristic |
| 266 | #106 | C24 | 1 | 9 | yes | — |
| 267 | #106 | C24 | 1 | 9 | yes | — |
| 268 | #106 | C24 | 1 | 9 | yes | — |
| 269 | #106 | C24 | 1 | 36 | yes | — |
| 270 | #106 | C24 | 1 | 36 | yes | — |
| 271 | C4⋊C8 | C24 | 1 | 18 | yes | — |
| 272 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 273 | #103 | C24 | 1 | 6 | yes | — |
| 274 | #103 | C24 | 1 | 36 | yes | — |
| 275 | #103 | C24 | 1 | 18 | yes | — |
| 276 | #102 | C24 | 1 | 6 | yes | — |
| 277 | #102 | C24 | 1 | 36 | yes | — |
| 278 | #102 | C24 | 1 | 18 | yes | — |
| 279 | C22⋊C8 | C24 | 1 | 36 | yes | — |
| 280 | C4×C8 | C24 | 1 | 6 | yes | — |
| 281 | C4×C8 | C24 | 1 | 18 | yes | — |
| 282 | C24 | — | 2 | 9 | no | — |
| 283 | C24 | C22×D4 | 1 | 6 | yes | — |
| 284 | #41 | — | 4 | 8 | no | — |
| 285 | #41 | — | 4 | 72 | no | — |
| 286 | #41 | — | 4 | 144 | no | — |
| 287 | #41 | — | 4 | 72 | no | — |
| 288 | #41 | C2×SD16 | 1 | 48 | yes | complemented |
| 289 | C2×Q8 | — | 2 | 18 | no | — |
| 290 | C2×Q8 | — | 2 | 9 | no | — |
| 291 | C2×Q8 | — | 2 | 18 | no | — |
| 292 | C2×Q8 | — | 4 | 9 | no | — |
| 293 | C2×Q8 | — | 4 | 9 | no | — |
| 294 | C2×Q8 | — | 4 | 24 | no | — |
| 295 | C2×Q8 | — | 4 | 36 | no | — |
| 296 | C2×Q8 | — | 16 | 9 | no | — |
| 297 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 298 | C2×Q8 | C25 | 1 | 6 | yes | — |
| 299 | C2×D4 | — | 2 | 36 | no | — |
| 300 | C2×D4 | — | 2 | 6 | no | — |
| 301 | C2×D4 | — | 2 | 6 | no | — |
| 302 | C2×D4 | — | 2 | 9 | no | — |
| 303 | C2×D4 | — | 4 | 9 | no | — |
| 304 | C2×D4 | — | 4 | 9 | no | — |
| 305 | C2×D4 | — | 4 | 72 | no | — |
| 306 | C2×D4 | — | 4 | 72 | no | — |
| 307 | C2×D4 | C2×SD16 | 1 | 72 | yes | complemented |
| 308 | C2×D4 | C22×D4 | 1 | 18 | yes | — |
| 309 | C2×D4 | C25 | 1 | 6 | yes | — |
| 310 | C22×C4 | — | 2 | 9 | no | — |
| 311 | C22×C4 | — | 2 | 18 | no | — |
| 312 | C22×C4 | — | 2 | 9 | no | — |
| 313 | C22×C4 | — | 2 | 9 | no | — |
| 314 | C22×C4 | — | 2 | 18 | no | — |
| 315 | C22×C4 | — | 2 | 6 | no | — |
| 316 | C22×C4 | — | 2 | 18 | no | — |
| 317 | C22×C4 | — | 4 | 6 | no | — |
| 318 | C22×C4 | — | 4 | 6 | no | — |
| 319 | C22×C4 | — | 4 | 24 | no | — |
| 320 | C22×C4 | — | 4 | 36 | no | — |
| 321 | C22×C4 | — | 16 | 6 | no | — |
| 322 | C22×C4 | C22×D4 | 1 | 9 | yes | — |
| 323 | C22×C4 | C22×D4 | 1 | 18 | yes | — |
| 324 | C22×C4 | C22×D4 | 1 | 9 | yes | — |
| 325 | C22×C4 | C25 | 1 | 9 | yes | — |
| 326 | SD16 | — | 2 | 12 | no | — |
| 327 | SD16 | — | 4 | 18 | no | — |
| 328 | SD16 | — | 4 | 12 | no | — |
| 329 | C2×C8 | — | 2 | 18 | no | — |
| 330 | C2×C8 | — | 4 | 18 | no | — |
| 331 | C2×C8 | — | 4 | 9 | no | — |
| 332 | C2×C8 | C25 | 1 | 6 | yes | — |
| 333 | C2×C8 | C25 | 1 | 9 | yes | — |
| 334 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 335 | C4⋊C4 | — | 2 | 9 | no | — |
| 336 | C4⋊C4 | — | 2 | 9 | no | — |
| 337 | C4⋊C4 | — | 2 | 6 | no | — |
| 338 | C4⋊C4 | — | 2 | 18 | no | — |
| 339 | C4⋊C4 | — | 2 | 18 | no | — |
| 340 | C4⋊C4 | — | 2 | 18 | no | — |
| 341 | C4⋊C4 | — | 2 | 18 | no | — |
| 342 | C4⋊C4 | — | 2 | 36 | no | — |
| 343 | C4⋊C4 | — | 2 | 18 | no | — |
| 344 | C4⋊C4 | — | 2 | 6 | no | — |
| 345 | C4⋊C4 | — | 2 | 6 | no | — |
| 346 | C4⋊C4 | C22×D4 | 1 | 18 | yes | — |
| 347 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 348 | C4⋊C4 | C25 | 1 | 1 | yes | characteristic |
| 349 | C4⋊C4 | C25 | 1 | 9 | yes | — |
| 350 | C4⋊C4 | C25 | 1 | 1 | yes | characteristic |
| 351 | C4⋊C4 | C25 | 1 | 9 | yes | — |
| 352 | C22⋊C4 | — | 2 | 36 | no | — |
| 353 | C22⋊C4 | — | 2 | 6 | no | — |
| 354 | C22⋊C4 | — | 2 | 36 | no | — |
| 355 | C22⋊C4 | — | 2 | 18 | no | — |
| 356 | C22⋊C4 | C22×D4 | 1 | 36 | yes | — |
| 357 | C42 | — | 2 | 6 | no | — |
| 358 | C42 | — | 2 | 18 | no | — |
| 359 | C42 | C22×D4 | 1 | 18 | yes | — |
| 360 | C42 | C25 | 1 | 6 | yes | — |
| 361 | C23 | — | 2 | 6 | no | — |
| 362 | C23 | — | 4 | 6 | no | — |
| 363 | C23 | — | 4 | 6 | no | — |
| 364 | C23 | — | 4 | 18 | no | — |
| 365 | C23 | — | 8 | 9 | no | — |
| 366 | C23 | — | 8 | 9 | no | — |
| 367 | C23 | C22×SD16 | 1 | 24 | yes | — |
| 368 | C23 | C23×D4 | 1 | 9 | yes | — |
| 369 | Q8 | — | 2 | 6 | no | — |
| 370 | Q8 | — | 2 | 6 | no | — |
| 371 | Q8 | — | 4 | 36 | no | — |
| 372 | Q8 | — | 8 | 9 | no | — |
| 373 | Q8 | — | 8 | 18 | no | — |
| 374 | Q8 | C22×SD16 | 1 | 8 | yes | — |
| 375 | D4 | — | 2 | 6 | no | — |
| 376 | D4 | — | 2 | 6 | no | — |
| 377 | D4 | — | 4 | 72 | no | — |
| 378 | D4 | — | 4 | 12 | no | — |
| 379 | D4 | — | 8 | 6 | no | — |
| 380 | D4 | — | 8 | 9 | no | — |
| 381 | D4 | C22×SD16 | 1 | 72 | yes | — |
| 382 | C2×C4 | — | 2 | 9 | no | — |
| 383 | C2×C4 | — | 2 | 9 | no | — |
| 384 | C2×C4 | — | 2 | 1 | no | — |
| 385 | C2×C4 | — | 2 | 6 | no | — |
| 386 | C2×C4 | — | 2 | 9 | no | — |
| 387 | C2×C4 | — | 2 | 1 | no | — |
| 388 | C2×C4 | — | 2 | 9 | no | — |
| 389 | C2×C4 | — | 4 | 18 | no | — |
| 390 | C2×C4 | — | 4 | 9 | no | — |
| 391 | C2×C4 | — | 4 | 18 | no | — |
| 392 | C2×C4 | — | 4 | 36 | no | — |
| 393 | C2×C4 | — | 4 | 12 | no | — |
| 394 | C2×C4 | — | 4 | 36 | no | — |
| 395 | C2×C4 | — | 8 | 9 | no | — |
| 396 | C2×C4 | — | 8 | 18 | no | — |
| 397 | C2×C4 | — | 8 | 9 | no | — |
| 398 | C2×C4 | C22×SD16 | 1 | 36 | yes | — |
| 399 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 400 | C2×C4 | C23×D4 | 1 | 9 | yes | — |
| 401 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 402 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 403 | C8 | — | 2 | 9 | no | — |
| 404 | C8 | — | 2 | 6 | no | — |
| 405 | C8 | #585 | 1 | 2 | yes | complemented |
| 406 | C22 | — | 2 | 9 | no | — |
| 407 | C22 | — | 2 | 9 | no | — |
| 408 | C22 | — | 4 | 24 | no | — |
| 409 | C22 | — | 4 | 6 | no | — |
| 410 | C22 | — | 4 | 6 | no | — |
| 411 | C22 | — | 4 | 6 | no | — |
| 412 | C22 | — | 16 | 18 | no | — |
| 413 | C22 | C23×SD16 | 1 | 18 | yes | — |
| 414 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 415 | C4 | — | 2 | 9 | no | — |
| 416 | C4 | — | 2 | 6 | no | — |
| 417 | C4 | — | 4 | 6 | no | — |
| 418 | C4 | — | 4 | 1 | no | — |
| 419 | C4 | — | 4 | 9 | no | — |
| 420 | C4 | — | 4 | 1 | no | — |
| 421 | C4 | — | 4 | 9 | no | — |
| 422 | C4 | C23×SD16 | 1 | 12 | yes | — |
| 423 | C4 | C2×#585 | 1 | 1 | yes | characteristic |
| 424 | C4 | 2−1+6 | 1 | 1 | yes | characteristic |
| 425 | C2 | — | 2 | 18 | no | — |
| 426 | C2 | — | 8 | 6 | no | — |
| 427 | C2 | #62988 | 1 | 1 | yes | characteristic |
| 428 | C2 | C24×SD16 | 1 | 1 | yes | characteristic |
| 429 | C2 | #63092 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| prime radical | #62988 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×H(5,𝔽2) ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62989 | C2 | semidirect |
| 3. #62469 | C2 | semidirect |
| 4. #62243 | C2 | semidirect |
| 5. #62099 | C2 | semidirect |
| 6. #62096 | C2 | semidirect |
| 7. #61697 | C2 | semidirect |
| 8. #61695 | C2 | semidirect |
| 9. SD16×#41 | C2 | semidirect |
| 10. C2×#3335 | C2 | semidirect |
| 11. C8×H(5,𝔽2) | C2 | semidirect |
| 14. #3503 | C22 | semidirect |
| 16. #3501 | C22 | semidirect |
| 21. Q8×#41 | C22 | semidirect |
| 22. C2×#554 | C22 | semidirect |
| 27. #3392 | C22 | semidirect |
| 28. Q8×SD16 | C22 | semidirect |
| 29. Q8×SD16 | C22 | semidirect |
| 30. #3362 | C22 | semidirect |
| 31. #3359 | C22 | semidirect |
| 32. #3335 | C22 | semidirect |
| 33. #3335 | C22 | semidirect |
| 34. #3335 | C22 | semidirect |
| 35. #3335 | C22 | semidirect |
| 36. #3335 | C22 | semidirect |
| 37. #3298 | C22 | semidirect |
| 38. #3298 | C22 | semidirect |
| 39. #3295 | C22 | semidirect |
| 40. #3295 | C22 | semidirect |
| 41. D4×SD16 | C22 | semidirect |
| 42. #3246 | C22 | semidirect |
| 43. #3229 | C22 | semidirect |
| 44. #3227 | C22 | semidirect |
| 45. #3187 | C22 | semidirect |
| 46. #3167 | C22 | semidirect |
| 47. C2×#498 | C22 | semidirect |
| 48. #3103 | C22 | semidirect |
| 49. #3101 | C22 | semidirect |
| 50. C2×#481 | C22 | semidirect |
| 51. C2×#483 | C22 | semidirect |
| 52. C2×#475 | C22 | semidirect |
| 53. C2×#476 | C22 | semidirect |
| 54. C2×#465 | C22 | semidirect |
| 55. #2988 | C22 | semidirect |
| 56. #2972 | C22 | semidirect |
| 57. C8×#41 | C22 | semidirect |
| 58. C2×C4×SD16 | C22 | semidirect |
| 59. C2×C8×D4 | C22 | semidirect |
| 60. C22×#106 | C22 | semidirect |
| 170. H(5,𝔽2) | SD16 | semidirect |
| 288. #41 | C2×SD16 | semidirect |
| 307. C2×D4 | C2×SD16 | semidirect |
| 405. C8 | #585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62989 | 2 |
| #62988 | 2 |
| #62469 | 2 |
| #62243 | 2 |
| #62099 | 2 |
| #62096 | 2 |
| #61697 | 2 |
| #61695 | 2 |
| SD16×#41 | 2 |
| C2×#3335 | 2 |
| C8×H(5,𝔽2) | 2 |