Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
2056 conjugacy classes of subgroups.
The subgroup lattice has 421 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#3416 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #60648 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C4×#576 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #33590 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #33586 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #33583 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #33580 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #33579 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | C2×#2208 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #33398 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #33382 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×#578 | — | 2 | 1 | no | — |
| 13 | C2×#578 | C22 | 1 | 2 | yes | — |
| 14 | C2×#576 | C22 | 1 | 1 | yes | characteristic |
| 15 | #3499 | — | 2 | 1 | no | — |
| 16 | C4×H(5,𝔽2) | — | 2 | 1 | no | — |
| 17 | #3416 | — | 2 | 16 | no | — |
| 18 | C2×#510 | C22 | 1 | 6 | yes | — |
| 19 | C2×#509 | C22 | 1 | 6 | yes | — |
| 20 | C2×#508 | C22 | 1 | 6 | yes | — |
| 21 | C22×SD32 | C22 | 1 | 6 | yes | — |
| 22 | C2×#504 | C22 | 1 | 2 | yes | — |
| 23 | #3156 | — | 2 | 3 | no | — |
| 24 | #3156 | C22 | 1 | 6 | yes | complemented |
| 25 | #3152 | — | 2 | 3 | no | — |
| 26 | #3147 | C22 | 1 | 3 | yes | complemented |
| 27 | C2×#494 | C22 | 1 | 3 | yes | complemented |
| 28 | #2951 | C22 | 1 | 3 | yes | — |
| 29 | #2948 | C22 | 1 | 3 | yes | — |
| 30 | #2946 | — | 2 | 3 | no | — |
| 31 | C4×AGL(1,ℤ/8) | — | 2 | 3 | no | — |
| 32 | C4×#135 | C22 | 1 | 3 | yes | — |
| 33 | C2×C4×D8 | C22 | 1 | 3 | yes | — |
| 34 | #2913 | C22 | 1 | 1 | yes | characteristic |
| 35 | #2897 | — | 2 | 1 | no | — |
| 36 | C4×#131 | C22 | 1 | 1 | yes | characteristic |
| 37 | #2211 | C22 | 1 | 6 | yes | complemented |
| 38 | #2210 | C22 | 1 | 6 | yes | complemented |
| 39 | #2210 | C22 | 1 | 12 | yes | complemented |
| 40 | #2209 | C22 | 1 | 3 | yes | complemented |
| 41 | #2209 | C22 | 1 | 6 | yes | complemented |
| 42 | #2208 | C22 | 1 | 3 | yes | complemented |
| 43 | #2208 | C22 | 1 | 6 | yes | complemented |
| 44 | #2208 | C22 | 1 | 12 | yes | complemented |
| 45 | #2208 | C22 | 1 | 6 | yes | complemented |
| 46 | #2207 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | #2206 | C22 | 1 | 3 | yes | complemented |
| 48 | #2151 | C22 | 1 | 6 | yes | complemented |
| 49 | #2150 | C22 | 1 | 3 | yes | complemented |
| 50 | C2×C4⋊C16 | C22 | 1 | 3 | yes | complemented |
| 51 | #2141 | C22 | 1 | 6 | yes | complemented |
| 52 | #2139 | C22 | 1 | 6 | yes | complemented |
| 53 | #2138 | C22 | 1 | 6 | yes | complemented |
| 54 | C2×#358 | C22 | 1 | 6 | yes | complemented |
| 55 | C2×2−1+4 | — | 2 | 2 | no | — |
| 56 | C2×H(5,𝔽2) | — | 2 | 1 | no | — |
| 57 | #578 | — | 2 | 8 | no | — |
| 58 | #578 | — | 2 | 8 | no | — |
| 59 | #578 | — | 4 | 8 | no | — |
| 60 | #576 | — | 2 | 4 | no | — |
| 61 | #576 | D4 | 1 | 8 | yes | complemented |
| 62 | C2×#137 | — | 2 | 6 | no | — |
| 63 | C2×#137 | — | 2 | 6 | no | — |
| 64 | C2×AGL(1,ℤ/8) | — | 2 | 3 | no | — |
| 65 | C2×#135 | — | 2 | 3 | no | — |
| 66 | C2×#135 | C23 | 1 | 6 | yes | — |
| 67 | C2×#135 | C23 | 1 | 3 | yes | — |
| 68 | C22×Q16 | — | 2 | 3 | no | — |
| 69 | C22×Q16 | C23 | 1 | 6 | yes | — |
| 70 | C22×D8 | C23 | 1 | 3 | yes | — |
| 71 | C2×#131 | D4 | 1 | 1 | yes | characteristic |
| 72 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 73 | D4×Q8 | — | 4 | 1 | no | — |
| 74 | D4×Q8 | — | 4 | 1 | no | — |
| 75 | #547 | — | 4 | 3 | no | — |
| 76 | #547 | — | 4 | 3 | no | — |
| 77 | #536 | — | 2 | 6 | no | — |
| 78 | #532 | — | 2 | 3 | no | — |
| 79 | C2×C4⋊Q8 | — | 2 | 3 | no | — |
| 80 | #520 | — | 2 | 1 | no | — |
| 81 | #520 | — | 2 | 3 | no | — |
| 82 | #520 | — | 4 | 1 | no | — |
| 83 | #518 | — | 2 | 3 | no | — |
| 84 | #518 | — | 4 | 3 | no | — |
| 85 | C4×#41 | — | 2 | 3 | no | — |
| 86 | C4×#41 | — | 4 | 1 | no | — |
| 87 | C4×#41 | D4 | 1 | 1 | yes | characteristic |
| 88 | C2×C4×D4 | — | 2 | 3 | no | — |
| 89 | C2×C4×D4 | — | 4 | 3 | no | — |
| 90 | #510 | — | 2 | 24 | no | — |
| 91 | #509 | — | 2 | 24 | no | — |
| 92 | #508 | — | 2 | 24 | no | — |
| 93 | C2×Q32 | C23 | 1 | 6 | yes | — |
| 94 | C2×SD32 | — | 2 | 24 | no | — |
| 95 | C2×SD32 | C23 | 1 | 6 | yes | — |
| 96 | C2×SD32 | C23 | 1 | 12 | yes | — |
| 97 | C2×SD32 | C23 | 1 | 2 | yes | — |
| 98 | C2×D16 | C23 | 1 | 6 | yes | — |
| 99 | #504 | — | 2 | 8 | no | — |
| 100 | C2×M32 | C23 | 1 | 6 | yes | — |
| 101 | C22×C16 | C23 | 1 | 6 | yes | — |
| 102 | #497 | — | 2 | 12 | no | — |
| 103 | #495 | — | 2 | 3 | no | — |
| 104 | #495 | C23 | 1 | 6 | yes | — |
| 105 | #494 | — | 2 | 3 | no | — |
| 106 | #494 | — | 2 | 3 | no | — |
| 107 | #494 | C23 | 1 | 3 | yes | — |
| 108 | #494 | C23 | 1 | 6 | yes | — |
| 109 | #493 | C23 | 1 | 1 | yes | characteristic |
| 110 | #492 | — | 2 | 3 | no | — |
| 111 | #442 | — | 2 | 6 | no | — |
| 112 | #440 | — | 2 | 6 | no | — |
| 113 | C4×Q16 | C23 | 1 | 1 | yes | characteristic |
| 114 | C4×Q16 | C23 | 1 | 3 | yes | — |
| 115 | C4×SD16 | — | 2 | 3 | no | — |
| 116 | C4×SD16 | — | 2 | 3 | no | — |
| 117 | C4×D8 | — | 2 | 3 | no | — |
| 118 | C4×D8 | — | 2 | 3 | no | — |
| 119 | C4×D8 | C23 | 1 | 3 | yes | — |
| 120 | C4×D8 | C23 | 1 | 6 | yes | — |
| 121 | C4×D8 | C23 | 1 | 3 | yes | — |
| 122 | #428 | — | 2 | 3 | no | — |
| 123 | #427 | C23 | 1 | 3 | yes | — |
| 124 | C2×#107 | C23 | 1 | 3 | yes | — |
| 125 | #418 | — | 2 | 3 | no | — |
| 126 | #417 | — | 2 | 3 | no | — |
| 127 | #416 | — | 2 | 3 | no | — |
| 128 | C2×#102 | — | 2 | 3 | no | — |
| 129 | #405 | D4 | 1 | 3 | yes | — |
| 130 | #405 | C23 | 1 | 3 | yes | — |
| 131 | C4×M16 | D4 | 1 | 3 | yes | — |
| 132 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 133 | C4⋊C16 | C23 | 1 | 1 | yes | characteristic |
| 134 | C4⋊C16 | C23 | 1 | 3 | yes | — |
| 135 | C4⋊C16 | C23 | 1 | 6 | yes | — |
| 136 | C4⋊C16 | C23 | 1 | 6 | yes | — |
| 137 | #358 | C23 | 1 | 6 | yes | — |
| 138 | #358 | C23 | 1 | 12 | yes | — |
| 139 | #358 | C23 | 1 | 6 | yes | — |
| 140 | #357 | C23 | 1 | 2 | yes | — |
| 141 | #357 | C23 | 1 | 6 | yes | — |
| 142 | 2−1+4 | — | 4 | 8 | no | — |
| 143 | 2−1+4 | — | 4 | 8 | no | — |
| 144 | H(5,𝔽2) | — | 2 | 8 | no | — |
| 145 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 146 | C2×#41 | — | 2 | 3 | no | — |
| 147 | C2×#41 | — | 2 | 6 | no | — |
| 148 | C2×#41 | — | 4 | 1 | no | — |
| 149 | C2×#41 | — | 4 | 6 | no | — |
| 150 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 151 | C22×Q8 | — | 2 | 6 | no | — |
| 152 | C22×Q8 | — | 4 | 2 | no | — |
| 153 | C22×D4 | — | 2 | 3 | no | — |
| 154 | C22×D4 | — | 4 | 3 | no | — |
| 155 | C23×C4 | — | 4 | 3 | no | — |
| 156 | #137 | — | 4 | 24 | no | — |
| 157 | #137 | — | 4 | 24 | no | — |
| 158 | AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 159 | #135 | — | 2 | 12 | no | — |
| 160 | #135 | — | 2 | 6 | no | — |
| 161 | #135 | — | 2 | 12 | no | — |
| 162 | #135 | — | 4 | 12 | no | — |
| 163 | #135 | C2×D4 | 1 | 12 | yes | — |
| 164 | C2×Q16 | — | 2 | 12 | no | — |
| 165 | C2×Q16 | — | 2 | 3 | no | — |
| 166 | C2×Q16 | — | 2 | 6 | no | — |
| 167 | C2×Q16 | — | 2 | 6 | no | — |
| 168 | C2×Q16 | — | 2 | 12 | no | — |
| 169 | C2×Q16 | — | 4 | 12 | no | — |
| 170 | C2×Q16 | C24 | 1 | 6 | yes | — |
| 171 | C2×Q16 | C24 | 1 | 1 | yes | characteristic |
| 172 | C2×SD16 | — | 2 | 3 | no | — |
| 173 | C2×SD16 | — | 2 | 6 | no | — |
| 174 | C2×SD16 | — | 2 | 6 | no | — |
| 175 | C2×D8 | — | 2 | 3 | no | — |
| 176 | C2×D8 | — | 2 | 1 | no | — |
| 177 | C2×D8 | — | 2 | 6 | no | — |
| 178 | C2×D8 | C2×D4 | 1 | 12 | yes | — |
| 179 | C2×D8 | C24 | 1 | 2 | yes | — |
| 180 | C2×D8 | C24 | 1 | 3 | yes | — |
| 181 | #131 | — | 2 | 4 | no | — |
| 182 | #131 | C2×D4 | 1 | 4 | yes | — |
| 183 | #131 | #41 | 1 | 4 | yes | — |
| 184 | C2×M16 | C2×D4 | 1 | 3 | yes | — |
| 185 | C2×M16 | C2×D4 | 1 | 3 | yes | — |
| 186 | C22×C8 | C2×D4 | 1 | 3 | yes | — |
| 187 | C22×C8 | C24 | 1 | 3 | yes | — |
| 188 | C4⋊Q8 | — | 2 | 3 | no | — |
| 189 | C4⋊Q8 | — | 2 | 6 | no | — |
| 190 | C4⋊Q8 | — | 4 | 3 | no | — |
| 191 | C4⋊Q8 | — | 4 | 3 | no | — |
| 192 | #127 | — | 2 | 1 | no | — |
| 193 | #124 | — | 2 | 6 | no | — |
| 194 | #123 | — | 4 | 12 | no | — |
| 195 | C22⋊Q8 | — | 4 | 6 | no | — |
| 196 | C22⋊Q8 | — | 4 | 6 | no | — |
| 197 | #121 | — | 4 | 3 | no | — |
| 198 | #121 | — | 4 | 3 | no | — |
| 199 | C4×Q8 | — | 2 | 1 | no | — |
| 200 | C4×Q8 | — | 2 | 3 | no | — |
| 201 | C4×Q8 | — | 4 | 1 | no | — |
| 202 | C4×Q8 | D8 | 1 | 1 | yes | characteristic |
| 203 | C4×Q8 | D8 | 1 | 1 | yes | characteristic |
| 204 | C4×D4 | — | 2 | 3 | no | — |
| 205 | C4×D4 | — | 2 | 6 | no | — |
| 206 | C4×D4 | — | 2 | 3 | no | — |
| 207 | C4×D4 | — | 4 | 3 | no | — |
| 208 | C4×D4 | — | 4 | 3 | no | — |
| 209 | C4×D4 | — | 4 | 3 | no | — |
| 210 | C4×D4 | — | 4 | 3 | no | — |
| 211 | C4×D4 | — | 4 | 3 | no | — |
| 212 | C4×D4 | — | 4 | 6 | no | — |
| 213 | C4×D4 | — | 4 | 3 | no | — |
| 214 | C4×D4 | — | 4 | 3 | no | — |
| 215 | C4×D4 | — | 4 | 3 | no | — |
| 216 | C4×D4 | — | 4 | 3 | no | — |
| 217 | C4×D4 | D8 | 1 | 3 | yes | — |
| 218 | C4×D4 | D8 | 1 | 3 | yes | — |
| 219 | #117 | — | 2 | 3 | no | — |
| 220 | #117 | — | 4 | 3 | no | — |
| 221 | #117 | — | 4 | 3 | no | — |
| 222 | #117 | C2×D4 | 1 | 3 | yes | — |
| 223 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 224 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 225 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 226 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 227 | C2×C22⋊C4 | — | 4 | 3 | no | — |
| 228 | C2×C22⋊C4 | — | 4 | 6 | no | — |
| 229 | C2×C42 | — | 4 | 3 | no | — |
| 230 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 231 | Q32 | — | 2 | 12 | no | — |
| 232 | SD32 | — | 2 | 4 | no | — |
| 233 | SD32 | — | 2 | 12 | no | — |
| 234 | SD32 | — | 2 | 24 | no | — |
| 235 | D16 | — | 2 | 12 | no | — |
| 236 | M32 | — | 2 | 12 | no | — |
| 237 | C2×C16 | — | 2 | 12 | no | — |
| 238 | C2×C16 | C24 | 1 | 2 | yes | — |
| 239 | C2×C16 | C24 | 1 | 6 | yes | — |
| 240 | #107 | — | 2 | 3 | no | — |
| 241 | #107 | C24 | 1 | 3 | yes | — |
| 242 | #107 | C24 | 1 | 1 | yes | characteristic |
| 243 | #106 | — | 2 | 3 | no | — |
| 244 | #103 | — | 2 | 1 | no | — |
| 245 | #103 | — | 2 | 3 | no | — |
| 246 | #102 | — | 2 | 3 | no | — |
| 247 | #102 | — | 2 | 6 | no | — |
| 248 | #102 | — | 2 | 3 | no | — |
| 249 | #97 | C2×D4 | 1 | 6 | yes | — |
| 250 | C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 251 | C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 252 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 253 | C4×C8 | C24 | 1 | 3 | yes | — |
| 254 | C24 | — | 4 | 3 | no | — |
| 255 | #41 | — | 2 | 12 | no | — |
| 256 | #41 | — | 4 | 8 | no | — |
| 257 | #41 | — | 4 | 6 | no | — |
| 258 | #41 | — | 4 | 12 | no | — |
| 259 | #41 | — | 4 | 12 | no | — |
| 260 | #41 | — | 8 | 24 | no | — |
| 261 | #41 | #121 | 1 | 4 | yes | — |
| 262 | #41 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 263 | C2×Q8 | — | 2 | 1 | no | — |
| 264 | C2×Q8 | — | 2 | 6 | no | — |
| 265 | C2×Q8 | — | 4 | 6 | no | — |
| 266 | C2×Q8 | — | 4 | 12 | no | — |
| 267 | C2×Q8 | — | 4 | 12 | no | — |
| 268 | C2×Q8 | — | 8 | 8 | no | — |
| 269 | C2×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 270 | C2×D4 | — | 2 | 12 | no | — |
| 271 | C2×D4 | — | 2 | 3 | no | — |
| 272 | C2×D4 | — | 2 | 2 | no | — |
| 273 | C2×D4 | — | 4 | 3 | no | — |
| 274 | C2×D4 | — | 4 | 24 | no | — |
| 275 | C2×D4 | — | 4 | 6 | no | — |
| 276 | C2×D4 | — | 4 | 3 | no | — |
| 277 | C2×D4 | — | 4 | 1 | no | — |
| 278 | C2×D4 | — | 4 | 1 | no | — |
| 279 | C2×D4 | — | 4 | 6 | no | — |
| 280 | C2×D4 | C2×D8 | 1 | 3 | yes | — |
| 281 | C22×C4 | — | 4 | 3 | no | — |
| 282 | C22×C4 | — | 4 | 6 | no | — |
| 283 | C22×C4 | — | 4 | 3 | no | — |
| 284 | C22×C4 | — | 4 | 3 | no | — |
| 285 | C22×C4 | — | 4 | 6 | no | — |
| 286 | C22×C4 | — | 4 | 3 | no | — |
| 287 | C22×C4 | — | 4 | 6 | no | — |
| 288 | C22×C4 | — | 16 | 6 | no | — |
| 289 | C22×C4 | C2×D8 | 1 | 3 | yes | — |
| 290 | C22×C4 | C2×D8 | 1 | 3 | yes | — |
| 291 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 292 | Q16 | — | 2 | 6 | no | — |
| 293 | Q16 | — | 2 | 1 | no | — |
| 294 | Q16 | — | 2 | 6 | no | — |
| 295 | Q16 | — | 4 | 6 | no | — |
| 296 | Q16 | — | 4 | 12 | no | — |
| 297 | Q16 | — | 4 | 12 | no | — |
| 298 | Q16 | C22×D4 | 1 | 2 | yes | — |
| 299 | SD16 | — | 2 | 12 | no | — |
| 300 | SD16 | — | 4 | 12 | no | — |
| 301 | SD16 | — | 4 | 12 | no | — |
| 302 | D8 | — | 2 | 12 | no | — |
| 303 | D8 | — | 2 | 2 | no | — |
| 304 | D8 | — | 2 | 3 | no | — |
| 305 | D8 | — | 2 | 2 | no | — |
| 306 | D8 | — | 4 | 2 | no | — |
| 307 | D8 | C22×D4 | 1 | 6 | yes | — |
| 308 | M16 | — | 2 | 6 | no | — |
| 309 | M16 | #121 | 1 | 12 | yes | — |
| 310 | C2×C8 | — | 2 | 6 | no | — |
| 311 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 312 | C2×C8 | C22×D4 | 1 | 3 | yes | — |
| 313 | C2×C8 | C22×D4 | 1 | 3 | yes | — |
| 314 | C2×C8 | C22×D4 | 1 | 6 | yes | — |
| 315 | C2×C8 | C2×#41 | 1 | 6 | yes | — |
| 316 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 317 | C4⋊C4 | — | 2 | 1 | no | — |
| 318 | C4⋊C4 | — | 2 | 3 | no | — |
| 319 | C4⋊C4 | — | 4 | 3 | no | — |
| 320 | C4⋊C4 | — | 4 | 3 | no | — |
| 321 | C4⋊C4 | — | 4 | 3 | no | — |
| 322 | C4⋊C4 | — | 4 | 3 | no | — |
| 323 | C4⋊C4 | — | 4 | 6 | no | — |
| 324 | C4⋊C4 | — | 4 | 6 | no | — |
| 325 | C4⋊C4 | — | 4 | 1 | no | — |
| 326 | C4⋊C4 | C2×D8 | 1 | 3 | yes | — |
| 327 | C4⋊C4 | C2×D8 | 1 | 3 | yes | — |
| 328 | C22⋊C4 | — | 4 | 3 | no | — |
| 329 | C22⋊C4 | — | 4 | 3 | no | — |
| 330 | C22⋊C4 | — | 4 | 6 | no | — |
| 331 | C22⋊C4 | — | 4 | 3 | no | — |
| 332 | C22⋊C4 | — | 4 | 6 | no | — |
| 333 | C22⋊C4 | — | 4 | 6 | no | — |
| 334 | C22⋊C4 | C2×D8 | 1 | 6 | yes | — |
| 335 | C42 | — | 4 | 1 | no | — |
| 336 | C42 | — | 4 | 3 | no | — |
| 337 | C42 | — | 4 | 3 | no | — |
| 338 | C42 | C2×D8 | 1 | 3 | yes | — |
| 339 | C42 | C2×D8 | 1 | 3 | yes | — |
| 340 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 341 | C42 | C22×D4 | 1 | 3 | yes | — |
| 342 | C16 | — | 2 | 2 | no | — |
| 343 | C16 | — | 2 | 6 | no | — |
| 344 | C23 | — | 4 | 3 | no | — |
| 345 | C23 | — | 4 | 12 | no | — |
| 346 | C23 | — | 4 | 2 | no | — |
| 347 | C23 | — | 16 | 3 | no | — |
| 348 | C23 | — | 16 | 3 | no | — |
| 349 | C23 | C22×D8 | 1 | 3 | yes | — |
| 350 | Q8 | — | 2 | 2 | no | — |
| 351 | Q8 | — | 4 | 1 | no | — |
| 352 | Q8 | — | 4 | 6 | no | — |
| 353 | Q8 | — | 4 | 6 | no | — |
| 354 | Q8 | — | 8 | 12 | no | — |
| 355 | Q8 | #459 | 1 | 4 | yes | — |
| 356 | D4 | — | 2 | 6 | no | — |
| 357 | D4 | — | 4 | 12 | no | — |
| 358 | D4 | — | 4 | 2 | no | — |
| 359 | D4 | — | 4 | 12 | no | — |
| 360 | D4 | — | 4 | 3 | no | — |
| 361 | D4 | — | 4 | 2 | no | — |
| 362 | D4 | — | 8 | 2 | no | — |
| 363 | D4 | — | 8 | 12 | no | — |
| 364 | D4 | — | 8 | 2 | no | — |
| 365 | D4 | #459 | 1 | 12 | yes | — |
| 366 | C2×C4 | — | 2 | 6 | no | — |
| 367 | C2×C4 | — | 4 | 3 | no | — |
| 368 | C2×C4 | — | 4 | 1 | no | — |
| 369 | C2×C4 | — | 4 | 12 | no | — |
| 370 | C2×C4 | — | 4 | 1 | no | — |
| 371 | C2×C4 | — | 4 | 3 | no | — |
| 372 | C2×C4 | — | 4 | 6 | no | — |
| 373 | C2×C4 | — | 8 | 12 | no | — |
| 374 | C2×C4 | — | 8 | 6 | no | — |
| 375 | C2×C4 | — | 8 | 12 | no | — |
| 376 | C2×C4 | — | 16 | 3 | no | — |
| 377 | C2×C4 | — | 16 | 6 | no | — |
| 378 | C2×C4 | — | 16 | 3 | no | — |
| 379 | C2×C4 | C2×#121 | 1 | 6 | yes | — |
| 380 | C2×C4 | C22×D8 | 1 | 3 | yes | — |
| 381 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 382 | C2×C4 | C22×D8 | 1 | 3 | yes | — |
| 383 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 384 | C2×C4 | C22×D8 | 1 | 3 | yes | — |
| 385 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 386 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 387 | C8 | — | 2 | 1 | no | — |
| 388 | C8 | — | 2 | 3 | no | — |
| 389 | C8 | C2×#121 | 1 | 6 | yes | — |
| 390 | C8 | C23×D4 | 1 | 1 | yes | characteristic |
| 391 | C8 | C22×#41 | 1 | 1 | yes | characteristic |
| 392 | C22 | — | 2 | 3 | no | — |
| 393 | C22 | — | 2 | 3 | no | — |
| 394 | C22 | — | 4 | 6 | no | — |
| 395 | C22 | — | 8 | 3 | no | — |
| 396 | C22 | — | 8 | 3 | no | — |
| 397 | C22 | — | 8 | 2 | no | — |
| 398 | C22 | — | 8 | 2 | no | — |
| 399 | C22 | — | 8 | 2 | no | — |
| 400 | C22 | — | 16 | 12 | no | — |
| 401 | C22 | C2×#459 | 1 | 6 | yes | — |
| 402 | C22 | C23×D8 | 1 | 1 | yes | characteristic |
| 403 | C4 | — | 2 | 3 | no | — |
| 404 | C4 | — | 2 | 1 | no | — |
| 405 | C4 | — | 2 | 3 | no | — |
| 406 | C4 | — | 4 | 2 | no | — |
| 407 | C4 | — | 8 | 3 | no | — |
| 408 | C4 | — | 8 | 1 | no | — |
| 409 | C4 | — | 8 | 6 | no | — |
| 410 | C4 | C2×#459 | 1 | 6 | yes | — |
| 411 | C4 | #3416 | 1 | 2 | yes | complemented |
| 412 | C4 | C22×#121 | 1 | 1 | yes | characteristic |
| 413 | C4 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 414 | C2 | — | 2 | 6 | no | — |
| 415 | C2 | — | 8 | 6 | no | — |
| 416 | C2 | — | 16 | 2 | no | — |
| 417 | C2 | C22×#459 | 1 | 1 | yes | characteristic |
| 418 | C2 | C2×#3416 | 1 | 1 | yes | characteristic |
| 419 | C2 | #62637 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C23×D8 |
| commutator, Frattini, cosocle | C2×C8 | C25 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×#41 ◁ C4×#131 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#3416 | C2 | semidirect |
| 2. #60648 | C2 | semidirect |
| 3. C4×#576 | C2 | semidirect |
| 4. #33590 | C2 | semidirect |
| 5. #33586 | C2 | semidirect |
| 6. #33583 | C2 | semidirect |
| 7. #33580 | C2 | semidirect |
| 8. #33579 | C2 | semidirect |
| 9. C2×#2208 | C2 | semidirect |
| 10. #33398 | C2 | semidirect |
| 11. #33382 | C2 | semidirect |
| 24. #3156 | C22 | semidirect |
| 26. #3147 | C22 | semidirect |
| 27. C2×#494 | C22 | semidirect |
| 37. #2211 | C22 | semidirect |
| 38. #2210 | C22 | semidirect |
| 39. #2210 | C22 | semidirect |
| 40. #2209 | C22 | semidirect |
| 41. #2209 | C22 | semidirect |
| 42. #2208 | C22 | semidirect |
| 43. #2208 | C22 | semidirect |
| 44. #2208 | C22 | semidirect |
| 45. #2208 | C22 | semidirect |
| 46. #2207 | C22 | semidirect |
| 47. #2206 | C22 | semidirect |
| 48. #2151 | C22 | semidirect |
| 49. #2150 | C22 | semidirect |
| 50. C2×C4⋊C16 | C22 | semidirect |
| 51. #2141 | C22 | semidirect |
| 52. #2139 | C22 | semidirect |
| 53. #2138 | C22 | semidirect |
| 54. C2×#358 | C22 | semidirect |
| 61. #576 | D4 | semidirect |
| 411. C4 | #3416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3416 | 2 |
| #60648 | 2 |
| C4×#576 | 2 |
| #33590 | 2 |
| #33586 | 2 |
| #33583 | 2 |
| #33580 | 2 |
| #33579 | 2 |
| C2×#2208 | 2 |
| #33398 | 2 |
| #33382 | 2 |