Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
2454 conjugacy classes of subgroups.
The subgroup lattice has 712 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61111 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #61108 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #60472 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #30871 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #30497 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #28498 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #25806 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #25448 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #25198 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #24810 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #24423 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #24287 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #23893 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #23042 | C2 | 1 | 2 | yes | maximal, complemented |
| 15 | #21477 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #3586 | C22 | 1 | 4 | yes | — |
| 17 | #3586 | C22 | 1 | 4 | yes | complemented |
| 18 | #3584 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C2×#578 | C22 | 1 | 2 | yes | — |
| 20 | #3573 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #3293 | — | 2 | 4 | no | — |
| 22 | #3293 | — | 2 | 4 | no | — |
| 23 | #3291 | — | 2 | 4 | no | — |
| 24 | #3290 | — | 2 | 4 | no | — |
| 25 | #3289 | — | 2 | 8 | no | — |
| 26 | #3289 | — | 2 | 4 | no | — |
| 27 | #3289 | — | 2 | 4 | no | — |
| 28 | #3156 | C22 | 1 | 2 | yes | complemented |
| 29 | #3152 | C22 | 1 | 2 | yes | — |
| 30 | C2×#494 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #3069 | — | 2 | 8 | no | — |
| 32 | #3069 | C22 | 1 | 4 | yes | — |
| 33 | #3069 | C22 | 1 | 4 | yes | complemented |
| 34 | #3069 | C22 | 1 | 4 | yes | complemented |
| 35 | #3069 | C22 | 1 | 4 | yes | complemented |
| 36 | #3069 | C22 | 1 | 4 | yes | complemented |
| 37 | #3067 | — | 2 | 4 | no | — |
| 38 | #3067 | C22 | 1 | 2 | yes | — |
| 39 | #3067 | C22 | 1 | 2 | yes | — |
| 40 | C2×#473 | — | 2 | 4 | no | — |
| 41 | C2×#473 | C22 | 1 | 2 | yes | complemented |
| 42 | C2×#473 | C22 | 1 | 2 | yes | complemented |
| 43 | C2×#473 | C22 | 1 | 2 | yes | complemented |
| 44 | #3022 | C22 | 1 | 4 | yes | complemented |
| 45 | #3020 | C22 | 1 | 4 | yes | — |
| 46 | #3018 | C22 | 1 | 2 | yes | — |
| 47 | #3018 | C22 | 1 | 1 | yes | characteristic |
| 48 | C2×#456 | C22 | 1 | 4 | yes | complemented |
| 49 | #3011 | C22 | 1 | 4 | yes | complemented |
| 50 | #2957 | C22 | 1 | 2 | yes | complemented |
| 51 | #2956 | C22 | 1 | 4 | yes | complemented |
| 52 | #2955 | C22 | 1 | 2 | yes | — |
| 53 | #2931 | C22 | 1 | 1 | yes | characteristic |
| 54 | #2916 | C22 | 1 | 2 | yes | complemented |
| 55 | #2889 | C22 | 1 | 4 | yes | complemented |
| 56 | #2070 | C22 | 1 | 4 | yes | complemented |
| 57 | #2050 | C22 | 1 | 2 | yes | complemented |
| 58 | #2049 | C22 | 1 | 4 | yes | complemented |
| 59 | #2049 | C22 | 1 | 4 | yes | complemented |
| 60 | #2020 | C22 | 1 | 2 | yes | complemented |
| 61 | #2020 | C22 | 1 | 2 | yes | complemented |
| 62 | #2020 | C22 | 1 | 4 | yes | complemented |
| 63 | #2017 | C22 | 1 | 2 | yes | — |
| 64 | #2009 | C22 | 1 | 4 | yes | complemented |
| 65 | #2005 | C22 | 1 | 4 | yes | complemented |
| 66 | #1979 | C22 | 1 | 2 | yes | complemented |
| 67 | #1974 | C22 | 1 | 2 | yes | complemented |
| 68 | #1966 | C22 | 1 | 2 | yes | complemented |
| 69 | #1953 | C22 | 1 | 2 | yes | complemented |
| 70 | #1932 | C22 | 1 | 4 | yes | complemented |
| 71 | #1915 | C22 | 1 | 4 | yes | complemented |
| 72 | #1902 | C22 | 1 | 4 | yes | complemented |
| 73 | #1884 | C22 | 1 | 1 | yes | characteristic |
| 74 | #1881 | C22 | 1 | 2 | yes | — |
| 75 | #1881 | C22 | 1 | 4 | yes | complemented |
| 76 | #1861 | C22 | 1 | 2 | yes | complemented |
| 77 | #1858 | C22 | 1 | 4 | yes | complemented |
| 78 | #1858 | C22 | 1 | 1 | yes | characteristic, complemented |
| 79 | #1813 | C22 | 1 | 1 | yes | characteristic, complemented |
| 80 | #1794 | C22 | 1 | 1 | yes | characteristic, complemented |
| 81 | #1791 | C22 | 1 | 2 | yes | complemented |
| 82 | C4×#108 | C22 | 1 | 1 | yes | characteristic, complemented |
| 83 | #1764 | C22 | 1 | 2 | yes | complemented |
| 84 | #1757 | C22 | 1 | 1 | yes | characteristic, complemented |
| 85 | #585 | C23 | 1 | 1 | yes | characteristic |
| 86 | #585 | C23 | 1 | 2 | yes | — |
| 87 | C2×2−1+4 | C23 | 1 | 4 | yes | — |
| 88 | #578 | — | 2 | 8 | no | — |
| 89 | #578 | — | 2 | 8 | no | — |
| 90 | #578 | — | 2 | 8 | no | — |
| 91 | #578 | — | 2 | 2 | no | — |
| 92 | #578 | — | 2 | 4 | no | — |
| 93 | #578 | — | 2 | 4 | no | — |
| 94 | #578 | — | 4 | 2 | no | — |
| 95 | #578 | — | 4 | 2 | no | — |
| 96 | #578 | — | 4 | 4 | no | — |
| 97 | #577 | — | 2 | 8 | no | — |
| 98 | #577 | — | 2 | 8 | no | — |
| 99 | #577 | — | 2 | 8 | no | — |
| 100 | #577 | — | 2 | 4 | no | — |
| 101 | #577 | — | 4 | 4 | no | — |
| 102 | #576 | — | 2 | 2 | no | — |
| 103 | #575 | — | 2 | 8 | no | — |
| 104 | #575 | — | 4 | 1 | no | — |
| 105 | #575 | — | 4 | 4 | no | — |
| 106 | #575 | C23 | 1 | 2 | yes | — |
| 107 | #575 | C23 | 1 | 4 | yes | — |
| 108 | #575 | C23 | 1 | 2 | yes | — |
| 109 | #575 | C23 | 1 | 4 | yes | — |
| 110 | C2×#137 | — | 2 | 4 | no | — |
| 111 | C2×#137 | — | 2 | 8 | no | — |
| 112 | C2×#137 | — | 4 | 4 | no | — |
| 113 | C2×#137 | C23 | 1 | 4 | yes | — |
| 114 | C2×#137 | C23 | 1 | 4 | yes | — |
| 115 | C2×#137 | C23 | 1 | 4 | yes | — |
| 116 | C2×#137 | C23 | 1 | 4 | yes | — |
| 117 | C2×#137 | C23 | 1 | 4 | yes | — |
| 118 | C2×#135 | — | 2 | 2 | no | — |
| 119 | C2×#135 | — | 4 | 1 | no | — |
| 120 | C2×#135 | C23 | 1 | 2 | yes | — |
| 121 | C22×Q16 | — | 2 | 2 | no | — |
| 122 | C22×Q16 | C23 | 1 | 2 | yes | — |
| 123 | C22×Q16 | C23 | 1 | 2 | yes | — |
| 124 | #568 | — | 2 | 4 | no | — |
| 125 | #568 | — | 4 | 1 | no | — |
| 126 | #568 | C23 | 1 | 4 | yes | — |
| 127 | #568 | C23 | 1 | 2 | yes | — |
| 128 | #568 | C23 | 1 | 4 | yes | — |
| 129 | #568 | C23 | 1 | 1 | yes | characteristic |
| 130 | C2×#131 | — | 2 | 4 | no | — |
| 131 | C2×#131 | — | 4 | 1 | no | — |
| 132 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 133 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 134 | C2×#131 | C23 | 1 | 2 | yes | — |
| 135 | #536 | C23 | 1 | 4 | yes | — |
| 136 | #532 | C23 | 1 | 1 | yes | characteristic |
| 137 | C2×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 138 | #497 | — | 2 | 4 | no | — |
| 139 | #497 | — | 2 | 2 | no | — |
| 140 | #497 | — | 2 | 2 | no | — |
| 141 | #495 | — | 2 | 2 | no | — |
| 142 | #494 | — | 2 | 2 | no | — |
| 143 | #494 | — | 2 | 2 | no | — |
| 144 | #494 | — | 4 | 1 | no | — |
| 145 | #494 | — | 4 | 1 | no | — |
| 146 | #492 | — | 2 | 2 | no | — |
| 147 | #473 | — | 2 | 8 | no | — |
| 148 | #473 | — | 2 | 8 | no | — |
| 149 | #473 | — | 2 | 2 | no | — |
| 150 | #473 | — | 2 | 4 | no | — |
| 151 | #473 | — | 2 | 4 | no | — |
| 152 | #473 | — | 2 | 4 | no | — |
| 153 | #473 | — | 2 | 4 | no | — |
| 154 | #473 | — | 2 | 4 | no | — |
| 155 | #473 | — | 2 | 4 | no | — |
| 156 | #473 | — | 2 | 8 | no | — |
| 157 | #473 | — | 2 | 8 | no | — |
| 158 | #473 | — | 2 | 8 | no | — |
| 159 | #473 | D4 | 1 | 4 | yes | complemented |
| 160 | #472 | — | 2 | 2 | no | — |
| 161 | #472 | D4 | 1 | 4 | yes | complemented |
| 162 | #471 | — | 2 | 8 | no | — |
| 163 | #471 | — | 2 | 8 | no | — |
| 164 | #471 | — | 2 | 4 | no | — |
| 165 | #471 | — | 2 | 8 | no | — |
| 166 | #471 | — | 2 | 8 | no | — |
| 167 | #471 | — | 2 | 8 | no | — |
| 168 | #471 | D4 | 1 | 8 | yes | complemented |
| 169 | #456 | — | 2 | 8 | no | — |
| 170 | #456 | — | 2 | 2 | no | — |
| 171 | #456 | — | 2 | 8 | no | — |
| 172 | #456 | — | 2 | 8 | no | — |
| 173 | #456 | — | 2 | 8 | no | — |
| 174 | #456 | D4 | 1 | 2 | yes | — |
| 175 | #455 | — | 2 | 2 | no | — |
| 176 | #455 | — | 2 | 8 | no | — |
| 177 | #455 | D4 | 1 | 2 | yes | — |
| 178 | #454 | — | 2 | 8 | no | — |
| 179 | #454 | — | 2 | 2 | no | — |
| 180 | #454 | D4 | 1 | 2 | yes | — |
| 181 | #453 | — | 2 | 2 | no | — |
| 182 | #453 | D4 | 1 | 2 | yes | — |
| 183 | #452 | — | 4 | 4 | no | — |
| 184 | #451 | — | 4 | 4 | no | — |
| 185 | #444 | — | 2 | 4 | no | — |
| 186 | #444 | — | 2 | 4 | no | — |
| 187 | #444 | — | 2 | 8 | no | — |
| 188 | #443 | — | 2 | 4 | no | — |
| 189 | #443 | — | 2 | 4 | no | — |
| 190 | #443 | — | 2 | 8 | no | — |
| 191 | #436 | — | 4 | 1 | no | — |
| 192 | C8×D4 | — | 4 | 1 | no | — |
| 193 | #430 | — | 2 | 4 | no | — |
| 194 | #430 | C23 | 1 | 4 | yes | — |
| 195 | #430 | C23 | 1 | 4 | yes | — |
| 196 | #430 | C23 | 1 | 2 | yes | — |
| 197 | C2×#108 | — | 2 | 4 | no | — |
| 198 | C2×#108 | C23 | 1 | 2 | yes | — |
| 199 | C2×#108 | C23 | 1 | 2 | yes | — |
| 200 | #423 | C23 | 1 | 1 | yes | characteristic |
| 201 | #421 | C23 | 1 | 2 | yes | — |
| 202 | #421 | C23 | 1 | 4 | yes | — |
| 203 | #421 | C23 | 1 | 2 | yes | — |
| 204 | C2×#104 | C23 | 1 | 4 | yes | — |
| 205 | C2×#104 | C23 | 1 | 2 | yes | — |
| 206 | #419 | C23 | 1 | 4 | yes | — |
| 207 | #416 | C23 | 1 | 2 | yes | — |
| 208 | #413 | — | 2 | 8 | no | — |
| 209 | #413 | C23 | 1 | 2 | yes | — |
| 210 | #413 | C23 | 1 | 4 | yes | — |
| 211 | #413 | C23 | 1 | 4 | yes | — |
| 212 | #413 | C23 | 1 | 1 | yes | characteristic |
| 213 | C2×#101 | — | 2 | 8 | no | — |
| 214 | C2×#101 | C23 | 1 | 4 | yes | — |
| 215 | C2×#101 | C23 | 1 | 4 | yes | — |
| 216 | C2×#101 | C23 | 1 | 4 | yes | — |
| 217 | C2×#101 | C23 | 1 | 4 | yes | — |
| 218 | #410 | C23 | 1 | 1 | yes | characteristic |
| 219 | #408 | C23 | 1 | 1 | yes | characteristic |
| 220 | #408 | C23 | 1 | 4 | yes | — |
| 221 | #408 | C23 | 1 | 1 | yes | characteristic |
| 222 | #405 | C23 | 1 | 2 | yes | — |
| 223 | C4×M16 | C23 | 1 | 2 | yes | — |
| 224 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 225 | #344 | C23 | 1 | 2 | yes | — |
| 226 | #344 | C23 | 1 | 4 | yes | — |
| 227 | #341 | C23 | 1 | 2 | yes | — |
| 228 | #341 | C23 | 1 | 2 | yes | — |
| 229 | #339 | C23 | 1 | 2 | yes | — |
| 230 | #338 | C23 | 1 | 2 | yes | — |
| 231 | 2−1+4 | — | 2 | 2 | no | — |
| 232 | 2−1+4 | — | 2 | 8 | no | — |
| 233 | 2−1+4 | — | 2 | 8 | no | — |
| 234 | 2−1+4 | — | 2 | 4 | no | — |
| 235 | 2−1+4 | — | 2 | 2 | no | — |
| 236 | 2−1+4 | — | 4 | 4 | no | — |
| 237 | 2−1+4 | — | 4 | 4 | no | — |
| 238 | 2−1+4 | C2×D4 | 1 | 2 | yes | — |
| 239 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 240 | H(5,𝔽2) | — | 2 | 4 | no | — |
| 241 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 242 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 243 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 244 | H(5,𝔽2) | C2×D4 | 1 | 2 | yes | — |
| 245 | C2×#41 | — | 2 | 4 | no | — |
| 246 | C2×#41 | — | 2 | 4 | no | — |
| 247 | C2×#41 | — | 2 | 4 | no | — |
| 248 | C2×#41 | — | 4 | 4 | no | — |
| 249 | C2×#41 | — | 4 | 1 | no | — |
| 250 | C2×#41 | — | 4 | 2 | no | — |
| 251 | C2×#41 | — | 4 | 4 | no | — |
| 252 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 253 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 254 | C2×#41 | C24 | 1 | 4 | yes | — |
| 255 | C2×#41 | C24 | 1 | 2 | yes | — |
| 256 | C22×Q8 | — | 2 | 4 | no | — |
| 257 | C22×Q8 | — | 2 | 4 | no | — |
| 258 | C22×Q8 | C24 | 1 | 4 | yes | — |
| 259 | #137 | — | 2 | 2 | no | — |
| 260 | #137 | — | 2 | 4 | no | — |
| 261 | #137 | — | 2 | 8 | no | — |
| 262 | #137 | — | 2 | 8 | no | — |
| 263 | #137 | — | 2 | 4 | no | — |
| 264 | #137 | — | 2 | 4 | no | — |
| 265 | #137 | — | 2 | 4 | no | — |
| 266 | #137 | — | 2 | 8 | no | — |
| 267 | #137 | — | 2 | 8 | no | — |
| 268 | #137 | — | 2 | 8 | no | — |
| 269 | #137 | — | 2 | 8 | no | — |
| 270 | #137 | — | 4 | 8 | no | — |
| 271 | #137 | — | 4 | 8 | no | — |
| 272 | #137 | — | 4 | 4 | no | — |
| 273 | #137 | — | 4 | 4 | no | — |
| 274 | #137 | — | 4 | 4 | no | — |
| 275 | #137 | — | 4 | 4 | no | — |
| 276 | #137 | — | 4 | 8 | no | — |
| 277 | #137 | — | 4 | 8 | no | — |
| 278 | #137 | — | 4 | 8 | no | — |
| 279 | #137 | — | 4 | 4 | no | — |
| 280 | #137 | — | 4 | 8 | no | — |
| 281 | #137 | — | 4 | 8 | no | — |
| 282 | #137 | — | 4 | 8 | no | — |
| 283 | #137 | C2×D4 | 1 | 8 | yes | — |
| 284 | #137 | C2×D4 | 1 | 4 | yes | — |
| 285 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 286 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 287 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 288 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 289 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 290 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 291 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 292 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 293 | AGL(1,ℤ/8) | C2×D4 | 1 | 8 | yes | — |
| 294 | AGL(1,ℤ/8) | C2×D4 | 1 | 4 | yes | — |
| 295 | #135 | — | 2 | 4 | no | — |
| 296 | #135 | — | 2 | 8 | no | — |
| 297 | #135 | — | 2 | 2 | no | — |
| 298 | #135 | — | 2 | 2 | no | — |
| 299 | #135 | — | 2 | 2 | no | — |
| 300 | #135 | — | 2 | 2 | no | — |
| 301 | #135 | — | 4 | 4 | no | — |
| 302 | #135 | — | 4 | 4 | no | — |
| 303 | #135 | — | 4 | 2 | no | — |
| 304 | #135 | — | 4 | 4 | no | — |
| 305 | #135 | — | 4 | 8 | no | — |
| 306 | #135 | — | 4 | 8 | no | — |
| 307 | #135 | — | 4 | 2 | no | — |
| 308 | #135 | — | 4 | 8 | no | — |
| 309 | #135 | — | 4 | 2 | no | — |
| 310 | #135 | — | 4 | 8 | no | — |
| 311 | C2×Q16 | — | 2 | 4 | no | — |
| 312 | C2×Q16 | — | 2 | 4 | no | — |
| 313 | C2×Q16 | — | 2 | 4 | no | — |
| 314 | C2×Q16 | — | 2 | 4 | no | — |
| 315 | C2×Q16 | — | 2 | 4 | no | — |
| 316 | C2×Q16 | — | 2 | 2 | no | — |
| 317 | C2×Q16 | — | 2 | 2 | no | — |
| 318 | C2×Q16 | — | 2 | 2 | no | — |
| 319 | C2×Q16 | — | 2 | 2 | no | — |
| 320 | C2×Q16 | — | 2 | 2 | no | — |
| 321 | C2×Q16 | — | 2 | 2 | no | — |
| 322 | C2×Q16 | — | 4 | 4 | no | — |
| 323 | C2×Q16 | — | 4 | 4 | no | — |
| 324 | C2×Q16 | — | 4 | 4 | no | — |
| 325 | C2×Q16 | — | 4 | 2 | no | — |
| 326 | C2×Q16 | — | 4 | 1 | no | — |
| 327 | C2×Q16 | — | 4 | 8 | no | — |
| 328 | C2×Q16 | — | 4 | 8 | no | — |
| 329 | C2×Q16 | C2×D4 | 1 | 2 | yes | — |
| 330 | C2×SD16 | — | 2 | 4 | no | — |
| 331 | C2×SD16 | — | 2 | 4 | no | — |
| 332 | C2×SD16 | — | 2 | 4 | no | — |
| 333 | C2×SD16 | — | 2 | 4 | no | — |
| 334 | C2×SD16 | — | 2 | 4 | no | — |
| 335 | C2×SD16 | — | 4 | 2 | no | — |
| 336 | C2×SD16 | — | 4 | 8 | no | — |
| 337 | C2×SD16 | — | 4 | 8 | no | — |
| 338 | C2×SD16 | C2×D4 | 1 | 4 | yes | — |
| 339 | C2×D8 | — | 4 | 1 | no | — |
| 340 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 341 | #131 | — | 2 | 2 | no | — |
| 342 | #131 | — | 2 | 2 | no | — |
| 343 | #131 | — | 2 | 4 | no | — |
| 344 | #131 | — | 2 | 8 | no | — |
| 345 | #131 | — | 2 | 4 | no | — |
| 346 | #131 | — | 2 | 8 | no | — |
| 347 | #131 | — | 2 | 8 | no | — |
| 348 | #131 | — | 2 | 2 | no | — |
| 349 | #131 | — | 2 | 2 | no | — |
| 350 | #131 | — | 2 | 2 | no | — |
| 351 | #131 | — | 2 | 2 | no | — |
| 352 | #131 | — | 4 | 2 | no | — |
| 353 | #131 | — | 4 | 2 | no | — |
| 354 | #131 | — | 4 | 4 | no | — |
| 355 | #131 | — | 4 | 4 | no | — |
| 356 | #131 | — | 4 | 2 | no | — |
| 357 | #131 | C2×D4 | 1 | 4 | yes | — |
| 358 | #131 | C2×D4 | 1 | 4 | yes | — |
| 359 | C2×M16 | — | 2 | 2 | no | — |
| 360 | C2×M16 | — | 2 | 1 | no | — |
| 361 | C2×M16 | — | 2 | 1 | no | — |
| 362 | C2×M16 | — | 2 | 4 | no | — |
| 363 | C2×M16 | — | 2 | 8 | no | — |
| 364 | C2×M16 | — | 4 | 4 | no | — |
| 365 | C2×M16 | — | 4 | 1 | no | — |
| 366 | C2×M16 | — | 4 | 4 | no | — |
| 367 | C2×M16 | — | 4 | 2 | no | — |
| 368 | C2×M16 | C24 | 1 | 1 | yes | characteristic |
| 369 | C2×M16 | C24 | 1 | 1 | yes | characteristic |
| 370 | C2×M16 | C24 | 1 | 4 | yes | — |
| 371 | C2×M16 | C24 | 1 | 2 | yes | — |
| 372 | C2×M16 | C24 | 1 | 4 | yes | — |
| 373 | C2×M16 | C24 | 1 | 2 | yes | — |
| 374 | C22×C8 | — | 2 | 2 | no | — |
| 375 | C22×C8 | — | 2 | 1 | no | — |
| 376 | C22×C8 | — | 2 | 1 | no | — |
| 377 | C22×C8 | — | 4 | 2 | no | — |
| 378 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 379 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 380 | C4⋊Q8 | — | 2 | 4 | no | — |
| 381 | C4⋊Q8 | — | 2 | 2 | no | — |
| 382 | C4⋊Q8 | — | 2 | 2 | no | — |
| 383 | C4⋊Q8 | — | 4 | 2 | no | — |
| 384 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 385 | #127 | C2×D4 | 1 | 1 | yes | characteristic |
| 386 | #124 | — | 2 | 4 | no | — |
| 387 | #124 | C2×D4 | 1 | 1 | yes | characteristic |
| 388 | #124 | C2×D4 | 1 | 1 | yes | characteristic |
| 389 | #123 | — | 4 | 4 | no | — |
| 390 | C22⋊Q8 | — | 4 | 4 | no | — |
| 391 | #121 | — | 4 | 1 | no | — |
| 392 | C4×D4 | — | 4 | 1 | no | — |
| 393 | #117 | C24 | 1 | 2 | yes | — |
| 394 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 395 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 396 | #108 | — | 2 | 8 | no | — |
| 397 | #108 | — | 2 | 8 | no | — |
| 398 | #108 | — | 2 | 4 | no | — |
| 399 | #108 | — | 2 | 2 | no | — |
| 400 | #108 | — | 2 | 2 | no | — |
| 401 | #108 | C2×D4 | 1 | 4 | yes | — |
| 402 | #108 | C2×D4 | 1 | 4 | yes | — |
| 403 | C4⋊C8 | — | 4 | 1 | no | — |
| 404 | #104 | — | 2 | 4 | no | — |
| 405 | #104 | — | 2 | 8 | no | — |
| 406 | #104 | — | 2 | 4 | no | — |
| 407 | #104 | — | 2 | 4 | no | — |
| 408 | #104 | — | 2 | 4 | no | — |
| 409 | #104 | C2×D4 | 1 | 4 | yes | — |
| 410 | #104 | C2×D4 | 1 | 4 | yes | — |
| 411 | #103 | — | 2 | 2 | no | — |
| 412 | #103 | — | 4 | 4 | no | — |
| 413 | #102 | — | 2 | 2 | no | — |
| 414 | #101 | — | 2 | 4 | no | — |
| 415 | #101 | — | 2 | 2 | no | — |
| 416 | #101 | — | 2 | 8 | no | — |
| 417 | #101 | — | 2 | 8 | no | — |
| 418 | #101 | — | 2 | 8 | no | — |
| 419 | #101 | — | 2 | 8 | no | — |
| 420 | #101 | C2×D4 | 1 | 8 | yes | — |
| 421 | #101 | C2×D4 | 1 | 2 | yes | — |
| 422 | #100 | — | 2 | 4 | no | — |
| 423 | #100 | — | 2 | 2 | no | — |
| 424 | #100 | C2×D4 | 1 | 8 | yes | — |
| 425 | #100 | C2×D4 | 1 | 2 | yes | — |
| 426 | #99 | — | 4 | 1 | no | — |
| 427 | C22⋊C8 | — | 4 | 1 | no | — |
| 428 | C22⋊C8 | — | 4 | 1 | no | — |
| 429 | C22⋊C8 | — | 4 | 4 | no | — |
| 430 | #97 | — | 2 | 2 | no | — |
| 431 | #97 | — | 2 | 2 | no | — |
| 432 | C4×C8 | — | 2 | 2 | no | — |
| 433 | C4×C8 | — | 2 | 1 | no | — |
| 434 | C4×C8 | — | 2 | 1 | no | — |
| 435 | C4×C8 | — | 2 | 2 | no | — |
| 436 | #41 | — | 2 | 2 | no | — |
| 437 | #41 | — | 2 | 2 | no | — |
| 438 | #41 | — | 2 | 4 | no | — |
| 439 | #41 | — | 2 | 4 | no | — |
| 440 | #41 | — | 2 | 4 | no | — |
| 441 | #41 | — | 2 | 4 | no | — |
| 442 | #41 | — | 2 | 2 | no | — |
| 443 | #41 | — | 2 | 2 | no | — |
| 444 | #41 | — | 2 | 4 | no | — |
| 445 | #41 | — | 2 | 2 | no | — |
| 446 | #41 | — | 2 | 4 | no | — |
| 447 | #41 | — | 2 | 2 | no | — |
| 448 | #41 | — | 4 | 2 | no | — |
| 449 | #41 | — | 4 | 2 | no | — |
| 450 | #41 | — | 4 | 4 | no | — |
| 451 | #41 | — | 4 | 8 | no | — |
| 452 | #41 | — | 4 | 8 | no | — |
| 453 | #41 | — | 4 | 2 | no | — |
| 454 | #41 | — | 4 | 4 | no | — |
| 455 | #41 | — | 4 | 4 | no | — |
| 456 | #41 | — | 4 | 4 | no | — |
| 457 | #41 | — | 4 | 8 | no | — |
| 458 | #41 | — | 8 | 4 | no | — |
| 459 | #41 | — | 8 | 2 | no | — |
| 460 | #41 | — | 8 | 2 | no | — |
| 461 | #41 | — | 8 | 8 | no | — |
| 462 | #41 | — | 8 | 8 | no | — |
| 463 | #41 | — | 8 | 4 | no | — |
| 464 | #41 | C22×D4 | 1 | 4 | yes | — |
| 465 | #41 | C22×D4 | 1 | 4 | yes | — |
| 466 | C2×Q8 | — | 2 | 4 | no | — |
| 467 | C2×Q8 | — | 2 | 4 | no | — |
| 468 | C2×Q8 | — | 2 | 4 | no | — |
| 469 | C2×Q8 | — | 2 | 4 | no | — |
| 470 | C2×Q8 | — | 2 | 4 | no | — |
| 471 | C2×Q8 | — | 2 | 4 | no | — |
| 472 | C2×Q8 | — | 2 | 4 | no | — |
| 473 | C2×Q8 | — | 4 | 4 | no | — |
| 474 | C2×Q8 | — | 4 | 8 | no | — |
| 475 | C2×Q8 | — | 4 | 8 | no | — |
| 476 | C2×Q8 | — | 4 | 1 | no | — |
| 477 | C2×Q8 | — | 4 | 2 | no | — |
| 478 | C2×Q8 | — | 4 | 4 | no | — |
| 479 | C2×Q8 | — | 4 | 8 | no | — |
| 480 | C2×Q8 | — | 8 | 4 | no | — |
| 481 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 482 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 483 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 484 | C2×Q8 | H(5,𝔽2) | 1 | 2 | yes | — |
| 485 | C2×D4 | — | 2 | 2 | no | — |
| 486 | C2×D4 | — | 2 | 4 | no | — |
| 487 | C2×D4 | — | 2 | 1 | no | — |
| 488 | C2×D4 | — | 2 | 1 | no | — |
| 489 | C2×D4 | — | 2 | 4 | no | — |
| 490 | C2×D4 | — | 4 | 1 | no | — |
| 491 | C2×D4 | — | 4 | 2 | no | — |
| 492 | C2×D4 | — | 4 | 1 | no | — |
| 493 | C2×D4 | — | 4 | 2 | no | — |
| 494 | C2×D4 | — | 4 | 4 | no | — |
| 495 | C2×D4 | — | 4 | 4 | no | — |
| 496 | C2×D4 | — | 4 | 4 | no | — |
| 497 | C2×D4 | — | 8 | 4 | no | — |
| 498 | C2×D4 | — | 8 | 2 | no | — |
| 499 | C2×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 500 | C2×D4 | C22×D4 | 1 | 4 | yes | — |
| 501 | C2×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 502 | C2×D4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 503 | C22×C4 | — | 2 | 2 | no | — |
| 504 | C22×C4 | — | 2 | 1 | no | — |
| 505 | C22×C4 | — | 2 | 1 | no | — |
| 506 | C22×C4 | — | 2 | 1 | no | — |
| 507 | C22×C4 | — | 2 | 4 | no | — |
| 508 | C22×C4 | — | 2 | 4 | no | — |
| 509 | C22×C4 | — | 4 | 2 | no | — |
| 510 | C22×C4 | — | 4 | 4 | no | — |
| 511 | C22×C4 | — | 4 | 4 | no | — |
| 512 | C22×C4 | — | 8 | 2 | no | — |
| 513 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 514 | Q16 | — | 2 | 8 | no | — |
| 515 | Q16 | — | 2 | 4 | no | — |
| 516 | Q16 | — | 2 | 2 | no | — |
| 517 | Q16 | — | 2 | 2 | no | — |
| 518 | Q16 | — | 4 | 8 | no | — |
| 519 | Q16 | — | 4 | 8 | no | — |
| 520 | Q16 | — | 4 | 8 | no | — |
| 521 | Q16 | — | 4 | 8 | no | — |
| 522 | Q16 | — | 4 | 4 | no | — |
| 523 | Q16 | — | 4 | 2 | no | — |
| 524 | Q16 | — | 4 | 8 | no | — |
| 525 | Q16 | — | 4 | 2 | no | — |
| 526 | Q16 | — | 4 | 2 | no | — |
| 527 | Q16 | — | 4 | 2 | no | — |
| 528 | Q16 | — | 4 | 2 | no | — |
| 529 | Q16 | — | 8 | 4 | no | — |
| 530 | SD16 | — | 2 | 4 | no | — |
| 531 | SD16 | — | 2 | 8 | no | — |
| 532 | SD16 | — | 2 | 8 | no | — |
| 533 | SD16 | — | 2 | 4 | no | — |
| 534 | SD16 | — | 2 | 4 | no | — |
| 535 | SD16 | — | 2 | 4 | no | — |
| 536 | SD16 | — | 4 | 8 | no | — |
| 537 | SD16 | — | 4 | 8 | no | — |
| 538 | SD16 | — | 4 | 8 | no | — |
| 539 | SD16 | — | 4 | 8 | no | — |
| 540 | SD16 | — | 4 | 4 | no | — |
| 541 | SD16 | — | 4 | 4 | no | — |
| 542 | SD16 | — | 4 | 4 | no | — |
| 543 | SD16 | — | 4 | 8 | no | — |
| 544 | D8 | — | 2 | 8 | no | — |
| 545 | D8 | — | 2 | 4 | no | — |
| 546 | D8 | — | 2 | 2 | no | — |
| 547 | D8 | — | 2 | 2 | no | — |
| 548 | D8 | — | 4 | 2 | no | — |
| 549 | D8 | — | 4 | 4 | no | — |
| 550 | M16 | — | 2 | 2 | no | — |
| 551 | M16 | — | 2 | 2 | no | — |
| 552 | M16 | — | 2 | 4 | no | — |
| 553 | M16 | — | 2 | 4 | no | — |
| 554 | M16 | — | 2 | 4 | no | — |
| 555 | M16 | — | 2 | 2 | no | — |
| 556 | M16 | — | 2 | 4 | no | — |
| 557 | M16 | — | 2 | 4 | no | — |
| 558 | M16 | — | 2 | 2 | no | — |
| 559 | M16 | — | 4 | 2 | no | — |
| 560 | M16 | — | 4 | 8 | no | — |
| 561 | M16 | — | 4 | 4 | no | — |
| 562 | M16 | — | 4 | 8 | no | — |
| 563 | M16 | — | 4 | 2 | no | — |
| 564 | M16 | — | 4 | 2 | no | — |
| 565 | M16 | C22×D4 | 1 | 4 | yes | — |
| 566 | M16 | C22×D4 | 1 | 8 | yes | — |
| 567 | M16 | C22×D4 | 1 | 4 | yes | — |
| 568 | C2×C8 | — | 2 | 2 | no | — |
| 569 | C2×C8 | — | 2 | 4 | no | — |
| 570 | C2×C8 | — | 2 | 2 | no | — |
| 571 | C2×C8 | — | 2 | 4 | no | — |
| 572 | C2×C8 | — | 2 | 4 | no | — |
| 573 | C2×C8 | — | 2 | 1 | no | — |
| 574 | C2×C8 | — | 2 | 2 | no | — |
| 575 | C2×C8 | — | 2 | 4 | no | — |
| 576 | C2×C8 | — | 2 | 1 | no | — |
| 577 | C2×C8 | — | 2 | 1 | no | — |
| 578 | C2×C8 | — | 4 | 2 | no | — |
| 579 | C2×C8 | — | 4 | 8 | no | — |
| 580 | C2×C8 | — | 4 | 4 | no | — |
| 581 | C2×C8 | — | 4 | 8 | no | — |
| 582 | C2×C8 | — | 4 | 1 | no | — |
| 583 | C2×C8 | — | 4 | 1 | no | — |
| 584 | C2×C8 | — | 4 | 1 | no | — |
| 585 | C2×C8 | — | 4 | 1 | no | — |
| 586 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 587 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 588 | C2×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 589 | C2×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 590 | C4⋊C4 | — | 2 | 2 | no | — |
| 591 | C4⋊C4 | — | 4 | 1 | no | — |
| 592 | C4⋊C4 | — | 8 | 2 | no | — |
| 593 | C4⋊C4 | — | 8 | 2 | no | — |
| 594 | C4⋊C4 | — | 8 | 4 | no | — |
| 595 | C22⋊C4 | — | 2 | 2 | no | — |
| 596 | C22⋊C4 | — | 4 | 1 | no | — |
| 597 | C22⋊C4 | — | 4 | 1 | no | — |
| 598 | C22⋊C4 | — | 8 | 4 | no | — |
| 599 | C42 | — | 2 | 1 | no | — |
| 600 | C42 | — | 2 | 2 | no | — |
| 601 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 602 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 603 | C23 | — | 2 | 2 | no | — |
| 604 | C23 | — | 2 | 4 | no | — |
| 605 | C23 | — | 2 | 1 | no | — |
| 606 | C23 | — | 2 | 1 | no | — |
| 607 | C23 | — | 4 | 2 | no | — |
| 608 | C23 | — | 8 | 2 | no | — |
| 609 | C23 | #585 | 1 | 1 | yes | characteristic |
| 610 | Q8 | — | 2 | 2 | no | — |
| 611 | Q8 | — | 2 | 4 | no | — |
| 612 | Q8 | — | 2 | 4 | no | — |
| 613 | Q8 | — | 2 | 2 | no | — |
| 614 | Q8 | — | 2 | 2 | no | — |
| 615 | Q8 | — | 4 | 2 | no | — |
| 616 | Q8 | — | 4 | 4 | no | — |
| 617 | Q8 | — | 4 | 4 | no | — |
| 618 | Q8 | — | 4 | 4 | no | — |
| 619 | Q8 | — | 4 | 4 | no | — |
| 620 | Q8 | — | 8 | 8 | no | — |
| 621 | Q8 | — | 8 | 2 | no | — |
| 622 | Q8 | D42 | 1 | 4 | yes | — |
| 623 | D4 | — | 2 | 4 | no | — |
| 624 | D4 | — | 2 | 4 | no | — |
| 625 | D4 | — | 2 | 4 | no | — |
| 626 | D4 | — | 2 | 4 | no | — |
| 627 | D4 | — | 2 | 2 | no | — |
| 628 | D4 | — | 2 | 2 | no | — |
| 629 | D4 | — | 2 | 2 | no | — |
| 630 | D4 | — | 4 | 4 | no | — |
| 631 | D4 | — | 4 | 2 | no | — |
| 632 | D4 | — | 4 | 2 | no | — |
| 633 | D4 | — | 4 | 2 | no | — |
| 634 | D4 | — | 4 | 4 | no | — |
| 635 | D4 | — | 4 | 4 | no | — |
| 636 | D4 | — | 8 | 2 | no | — |
| 637 | D4 | — | 8 | 2 | no | — |
| 638 | D4 | — | 8 | 4 | no | — |
| 639 | D4 | — | 8 | 8 | no | — |
| 640 | D4 | D42 | 1 | 4 | yes | — |
| 641 | C2×C4 | — | 2 | 2 | no | — |
| 642 | C2×C4 | — | 2 | 1 | no | — |
| 643 | C2×C4 | — | 2 | 4 | no | — |
| 644 | C2×C4 | — | 2 | 4 | no | — |
| 645 | C2×C4 | — | 2 | 4 | no | — |
| 646 | C2×C4 | — | 2 | 1 | no | — |
| 647 | C2×C4 | — | 2 | 1 | no | — |
| 648 | C2×C4 | — | 2 | 1 | no | — |
| 649 | C2×C4 | — | 4 | 2 | no | — |
| 650 | C2×C4 | — | 4 | 4 | no | — |
| 651 | C2×C4 | — | 4 | 2 | no | — |
| 652 | C2×C4 | — | 4 | 1 | no | — |
| 653 | C2×C4 | — | 4 | 1 | no | — |
| 654 | C2×C4 | — | 4 | 4 | no | — |
| 655 | C2×C4 | — | 4 | 1 | no | — |
| 656 | C2×C4 | — | 4 | 4 | no | — |
| 657 | C2×C4 | — | 4 | 1 | no | — |
| 658 | C2×C4 | — | 4 | 2 | no | — |
| 659 | C2×C4 | — | 4 | 4 | no | — |
| 660 | C2×C4 | — | 4 | 4 | no | — |
| 661 | C2×C4 | — | 4 | 4 | no | — |
| 662 | C2×C4 | — | 8 | 8 | no | — |
| 663 | C2×C4 | — | 8 | 4 | no | — |
| 664 | C2×C4 | — | 8 | 2 | no | — |
| 665 | C2×C4 | — | 8 | 8 | no | — |
| 666 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 667 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 668 | C2×C4 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 669 | C2×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 670 | C8 | — | 2 | 4 | no | — |
| 671 | C8 | — | 2 | 4 | no | — |
| 672 | C8 | — | 2 | 8 | no | — |
| 673 | C8 | — | 4 | 1 | no | — |
| 674 | C8 | — | 4 | 1 | no | — |
| 675 | C8 | — | 4 | 4 | no | — |
| 676 | C8 | — | 4 | 1 | no | — |
| 677 | C8 | D42 | 1 | 1 | yes | characteristic |
| 678 | C8 | D42 | 1 | 2 | yes | — |
| 679 | C8 | D42 | 1 | 1 | yes | characteristic |
| 680 | C22 | — | 2 | 4 | no | — |
| 681 | C22 | — | 4 | 1 | no | — |
| 682 | C22 | — | 4 | 1 | no | — |
| 683 | C22 | — | 4 | 4 | no | — |
| 684 | C22 | — | 4 | 1 | no | — |
| 685 | C22 | — | 8 | 2 | no | — |
| 686 | C22 | — | 8 | 1 | no | — |
| 687 | C22 | — | 8 | 1 | no | — |
| 688 | C22 | — | 8 | 4 | no | — |
| 689 | C22 | — | 16 | 2 | no | — |
| 690 | C22 | — | 32 | 2 | no | — |
| 691 | C22 | #3488 | 1 | 2 | yes | — |
| 692 | C22 | #3496 | 1 | 1 | yes | characteristic |
| 693 | C4 | — | 2 | 2 | no | — |
| 694 | C4 | — | 2 | 4 | no | — |
| 695 | C4 | — | 4 | 1 | no | — |
| 696 | C4 | — | 4 | 1 | no | — |
| 697 | C4 | — | 4 | 1 | no | — |
| 698 | C4 | — | 4 | 4 | no | — |
| 699 | C4 | — | 8 | 2 | no | — |
| 700 | C4 | — | 8 | 4 | no | — |
| 701 | C4 | C2×D42 | 1 | 2 | yes | — |
| 702 | C4 | C2×D42 | 1 | 1 | yes | characteristic |
| 703 | C4 | #3537 | 1 | 1 | yes | characteristic |
| 704 | C2 | — | 2 | 1 | no | — |
| 705 | C2 | — | 2 | 2 | no | — |
| 706 | C2 | — | 4 | 4 | no | — |
| 707 | C2 | — | 8 | 1 | no | — |
| 708 | C2 | — | 8 | 4 | no | — |
| 709 | C2 | — | 8 | 1 | no | — |
| 710 | C2 | #58997 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #58997 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #61111 | C2 | semidirect |
| 2. #61108 | C2 | semidirect |
| 3. #60472 | C2 | semidirect |
| 4. #30871 | C2 | semidirect |
| 5. #30497 | C2 | semidirect |
| 6. #28498 | C2 | semidirect |
| 7. #25806 | C2 | semidirect |
| 8. #25448 | C2 | semidirect |
| 9. #25198 | C2 | semidirect |
| 10. #24810 | C2 | semidirect |
| 11. #24423 | C2 | semidirect |
| 12. #24287 | C2 | semidirect |
| 13. #23893 | C2 | semidirect |
| 14. #23042 | C2 | semidirect |
| 15. #21477 | C2 | semidirect |
| 17. #3586 | C22 | semidirect |
| 18. #3584 | C22 | semidirect |
| 20. #3573 | C22 | semidirect |
| 28. #3156 | C22 | semidirect |
| 30. C2×#494 | C22 | semidirect |
| 33. #3069 | C22 | semidirect |
| 34. #3069 | C22 | semidirect |
| 35. #3069 | C22 | semidirect |
| 36. #3069 | C22 | semidirect |
| 41. C2×#473 | C22 | semidirect |
| 42. C2×#473 | C22 | semidirect |
| 43. C2×#473 | C22 | semidirect |
| 44. #3022 | C22 | semidirect |
| 48. C2×#456 | C22 | semidirect |
| 49. #3011 | C22 | semidirect |
| 50. #2957 | C22 | semidirect |
| 51. #2956 | C22 | semidirect |
| 54. #2916 | C22 | semidirect |
| 55. #2889 | C22 | semidirect |
| 56. #2070 | C22 | semidirect |
| 57. #2050 | C22 | semidirect |
| 58. #2049 | C22 | semidirect |
| 59. #2049 | C22 | semidirect |
| 60. #2020 | C22 | semidirect |
| 61. #2020 | C22 | semidirect |
| 62. #2020 | C22 | semidirect |
| 64. #2009 | C22 | semidirect |
| 65. #2005 | C22 | semidirect |
| 66. #1979 | C22 | semidirect |
| 67. #1974 | C22 | semidirect |
| 68. #1966 | C22 | semidirect |
| 69. #1953 | C22 | semidirect |
| 70. #1932 | C22 | semidirect |
| 71. #1915 | C22 | semidirect |
| 72. #1902 | C22 | semidirect |
| 75. #1881 | C22 | semidirect |
| 76. #1861 | C22 | semidirect |
| 77. #1858 | C22 | semidirect |
| 78. #1858 | C22 | semidirect |
| 79. #1813 | C22 | semidirect |
| 80. #1794 | C22 | semidirect |
| 81. #1791 | C22 | semidirect |
| 82. C4×#108 | C22 | semidirect |
| 83. #1764 | C22 | semidirect |
| 84. #1757 | C22 | semidirect |
| 159. #473 | D4 | semidirect |
| 161. #472 | D4 | semidirect |
| 168. #471 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61111 | 2 |
| #61108 | 2 |
| #60472 | 2 |
| #30871 | 2 |
| #30497 | 2 |
| #28498 | 2 |
| #25806 | 2 |
| #25448 | 2 |
| #25198 | 2 |
| #24810 | 2 |
| #24423 | 2 |
| #24287 | 2 |
| #23893 | 2 |
| #23042 | 2 |
| #21477 | 2 |