Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
2690 conjugacy classes of subgroups.
The subgroup lattice has 432 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#3292 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #61051 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | C2×#3147 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #30485 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #28505 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #25804 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #25433 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #24280 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #23908 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #23201 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #21544 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×#576 | C22 | 1 | 4 | yes | — |
| 13 | C22×#135 | C22 | 1 | 4 | yes | complemented |
| 14 | #3485 | C22 | 1 | 4 | yes | complemented |
| 15 | C2×#532 | C22 | 1 | 2 | yes | complemented |
| 16 | #3292 | — | 2 | 8 | no | — |
| 17 | #3283 | — | 2 | 8 | no | — |
| 18 | #3280 | — | 2 | 8 | no | — |
| 19 | #3267 | — | 2 | 16 | no | — |
| 20 | #3156 | C22 | 1 | 4 | yes | — |
| 21 | #3147 | — | 2 | 8 | no | — |
| 22 | C2×#495 | C22 | 1 | 4 | yes | complemented |
| 23 | C2×#494 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C2×#493 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#492 | C22 | 1 | 2 | yes | complemented |
| 26 | C2×#473 | C22 | 1 | 4 | yes | complemented |
| 27 | C2×#472 | C22 | 1 | 4 | yes | — |
| 28 | #3059 | C22 | 1 | 4 | yes | complemented |
| 29 | #3050 | C22 | 1 | 2 | yes | — |
| 30 | #3042 | C22 | 1 | 8 | yes | complemented |
| 31 | C2×#455 | C22 | 1 | 4 | yes | complemented |
| 32 | C2×#453 | C22 | 1 | 4 | yes | — |
| 33 | #3009 | C22 | 1 | 8 | yes | complemented |
| 34 | #3005 | C22 | 1 | 8 | yes | complemented |
| 35 | C2×#443 | C22 | 1 | 2 | yes | — |
| 36 | #2948 | C22 | 1 | 4 | yes | complemented |
| 37 | #2929 | C22 | 1 | 4 | yes | complemented |
| 38 | C22×C4×C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #2046 | C22 | 1 | 8 | yes | complemented |
| 40 | #2019 | C22 | 1 | 8 | yes | complemented |
| 41 | #2005 | C22 | 1 | 8 | yes | complemented |
| 42 | #2003 | C22 | 1 | 8 | yes | complemented |
| 43 | #1979 | C22 | 1 | 4 | yes | complemented |
| 44 | #1978 | C22 | 1 | 4 | yes | complemented |
| 45 | #1974 | C22 | 1 | 2 | yes | — |
| 46 | #1945 | C22 | 1 | 2 | yes | complemented |
| 47 | #1937 | C22 | 1 | 4 | yes | complemented |
| 48 | #1896 | C22 | 1 | 4 | yes | complemented |
| 49 | #1887 | C22 | 1 | 4 | yes | complemented |
| 50 | #1885 | C22 | 1 | 4 | yes | complemented |
| 51 | #1810 | C22 | 1 | 2 | yes | complemented |
| 52 | #1785 | C22 | 1 | 4 | yes | complemented |
| 53 | #1772 | C22 | 1 | 2 | yes | complemented |
| 54 | #1764 | C22 | 1 | 4 | yes | complemented |
| 55 | C2×H(5,𝔽2) | C23 | 1 | 4 | yes | — |
| 56 | C22×#41 | C23 | 1 | 4 | yes | — |
| 57 | #576 | — | 2 | 16 | no | — |
| 58 | #576 | — | 4 | 8 | no | — |
| 59 | C2×#137 | C23 | 1 | 8 | yes | — |
| 60 | C2×AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 61 | C2×AGL(1,ℤ/8) | C23 | 1 | 8 | yes | — |
| 62 | C2×#135 | — | 2 | 4 | no | — |
| 63 | C2×#135 | — | 2 | 16 | no | — |
| 64 | C2×#135 | — | 2 | 8 | no | — |
| 65 | C2×#135 | — | 2 | 8 | no | — |
| 66 | C2×#135 | — | 4 | 8 | no | — |
| 67 | C2×#135 | C23 | 1 | 2 | yes | — |
| 68 | C22×Q16 | C23 | 1 | 4 | yes | — |
| 69 | C22×SD16 | C23 | 1 | 8 | yes | — |
| 70 | C22×D8 | — | 2 | 4 | no | — |
| 71 | C22×D8 | C23 | 1 | 4 | yes | — |
| 72 | C2×#131 | C23 | 1 | 4 | yes | — |
| 73 | C23×C8 | C23 | 1 | 2 | yes | — |
| 74 | #547 | — | 2 | 16 | no | — |
| 75 | #546 | — | 2 | 16 | no | — |
| 76 | #536 | C23 | 1 | 8 | yes | — |
| 77 | #534 | — | 4 | 4 | no | — |
| 78 | #532 | — | 2 | 8 | no | — |
| 79 | #532 | — | 4 | 4 | no | — |
| 80 | C2×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 81 | C2×#127 | C23 | 1 | 2 | yes | — |
| 82 | C2×#124 | C23 | 1 | 4 | yes | — |
| 83 | #525 | C23 | 1 | 4 | yes | — |
| 84 | C2×#123 | — | 4 | 4 | no | — |
| 85 | C2×#121 | — | 4 | 2 | no | — |
| 86 | #518 | C23 | 1 | 4 | yes | — |
| 87 | C2×C4×D4 | — | 4 | 2 | no | — |
| 88 | C22×C42 | C23 | 1 | 1 | yes | characteristic |
| 89 | #497 | — | 2 | 8 | no | — |
| 90 | #495 | — | 2 | 16 | no | — |
| 91 | #495 | — | 2 | 4 | no | — |
| 92 | #494 | — | 2 | 4 | no | — |
| 93 | #494 | — | 2 | 4 | no | — |
| 94 | #493 | D4 | 1 | 8 | yes | complemented |
| 95 | #492 | — | 2 | 8 | no | — |
| 96 | #473 | — | 4 | 8 | no | — |
| 97 | #472 | — | 2 | 16 | no | — |
| 98 | #470 | — | 2 | 8 | no | — |
| 99 | #467 | — | 2 | 8 | no | — |
| 100 | #467 | D4 | 1 | 4 | yes | complemented |
| 101 | #466 | D4 | 1 | 4 | yes | complemented |
| 102 | #465 | D4 | 1 | 8 | yes | complemented |
| 103 | #463 | — | 2 | 16 | no | — |
| 104 | #461 | — | 2 | 16 | no | — |
| 105 | #455 | — | 4 | 8 | no | — |
| 106 | #453 | — | 2 | 16 | no | — |
| 107 | #452 | — | 2 | 16 | no | — |
| 108 | #452 | — | 2 | 16 | no | — |
| 109 | #450 | — | 2 | 16 | no | — |
| 110 | #449 | — | 2 | 16 | no | — |
| 111 | #443 | — | 2 | 8 | no | — |
| 112 | #442 | — | 2 | 8 | no | — |
| 113 | C4×D8 | — | 2 | 8 | no | — |
| 114 | #435 | — | 2 | 8 | no | — |
| 115 | C8×D4 | — | 2 | 8 | no | — |
| 116 | C2×#108 | C23 | 1 | 2 | yes | — |
| 117 | C2×#108 | C23 | 1 | 2 | yes | — |
| 118 | #427 | C23 | 1 | 2 | yes | — |
| 119 | #424 | C23 | 1 | 4 | yes | — |
| 120 | C2×#104 | C23 | 1 | 4 | yes | — |
| 121 | C2×#104 | C23 | 1 | 4 | yes | — |
| 122 | #419 | C23 | 1 | 8 | yes | — |
| 123 | #418 | C23 | 1 | 8 | yes | — |
| 124 | #416 | C23 | 1 | 4 | yes | — |
| 125 | C2×#101 | C23 | 1 | 8 | yes | — |
| 126 | C2×#100 | C23 | 1 | 4 | yes | — |
| 127 | C2×#100 | C23 | 1 | 4 | yes | — |
| 128 | #408 | C23 | 1 | 4 | yes | — |
| 129 | #407 | C23 | 1 | 4 | yes | — |
| 130 | #405 | C23 | 1 | 4 | yes | — |
| 131 | C2×C4×C8 | — | 2 | 4 | no | — |
| 132 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 133 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 134 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 135 | #341 | C23 | 1 | 4 | yes | — |
| 136 | #339 | C23 | 1 | 4 | yes | — |
| 137 | #339 | C23 | 1 | 4 | yes | — |
| 138 | H(5,𝔽2) | — | 2 | 8 | no | — |
| 139 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 140 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 141 | C2×#41 | — | 2 | 8 | no | — |
| 142 | C2×#41 | — | 2 | 8 | no | — |
| 143 | C2×#41 | — | 2 | 16 | no | — |
| 144 | C2×#41 | — | 4 | 4 | no | — |
| 145 | C2×#41 | — | 4 | 8 | no | — |
| 146 | C2×#41 | C24 | 1 | 4 | yes | — |
| 147 | C22×Q8 | C24 | 1 | 4 | yes | — |
| 148 | C22×D4 | — | 2 | 8 | no | — |
| 149 | C22×D4 | — | 2 | 4 | no | — |
| 150 | C22×D4 | — | 4 | 2 | no | — |
| 151 | C22×D4 | — | 4 | 4 | no | — |
| 152 | C22×D4 | C24 | 1 | 4 | yes | — |
| 153 | C23×C4 | — | 2 | 1 | no | — |
| 154 | C23×C4 | — | 2 | 4 | no | — |
| 155 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 156 | #137 | — | 4 | 8 | no | — |
| 157 | #137 | — | 4 | 8 | no | — |
| 158 | AGL(1,ℤ/8) | — | 2 | 16 | no | — |
| 159 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 160 | AGL(1,ℤ/8) | — | 4 | 32 | no | — |
| 161 | #135 | — | 2 | 4 | no | — |
| 162 | #135 | — | 2 | 4 | no | — |
| 163 | #135 | — | 4 | 32 | no | — |
| 164 | #135 | — | 4 | 32 | no | — |
| 165 | #135 | — | 4 | 16 | no | — |
| 166 | C2×Q16 | — | 2 | 8 | no | — |
| 167 | C2×Q16 | — | 2 | 4 | no | — |
| 168 | C2×Q16 | — | 2 | 4 | no | — |
| 169 | C2×Q16 | — | 2 | 8 | no | — |
| 170 | C2×Q16 | — | 2 | 8 | no | — |
| 171 | C2×Q16 | C2×D4 | 1 | 2 | yes | — |
| 172 | C2×SD16 | — | 2 | 8 | no | — |
| 173 | C2×SD16 | — | 2 | 16 | no | — |
| 174 | C2×SD16 | — | 2 | 8 | no | — |
| 175 | C2×SD16 | — | 2 | 16 | no | — |
| 176 | C2×SD16 | — | 4 | 8 | no | — |
| 177 | C2×SD16 | C2×D4 | 1 | 4 | yes | — |
| 178 | C2×D8 | — | 2 | 8 | no | — |
| 179 | C2×D8 | — | 2 | 4 | no | — |
| 180 | C2×D8 | — | 2 | 4 | no | — |
| 181 | C2×D8 | — | 2 | 8 | no | — |
| 182 | C2×D8 | — | 4 | 16 | no | — |
| 183 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 184 | C2×D8 | C2×D4 | 1 | 16 | yes | — |
| 185 | #131 | — | 2 | 8 | no | — |
| 186 | #131 | — | 2 | 8 | no | — |
| 187 | C2×M16 | — | 2 | 4 | no | — |
| 188 | C2×M16 | C24 | 1 | 4 | yes | — |
| 189 | C2×M16 | C24 | 1 | 4 | yes | — |
| 190 | C22×C8 | — | 2 | 4 | no | — |
| 191 | C22×C8 | — | 2 | 4 | no | — |
| 192 | C22×C8 | — | 2 | 4 | no | — |
| 193 | C22×C8 | C2×D4 | 1 | 4 | yes | — |
| 194 | C22×C8 | C2×D4 | 1 | 4 | yes | — |
| 195 | C22×C8 | C24 | 1 | 2 | yes | — |
| 196 | C22×C8 | C24 | 1 | 2 | yes | — |
| 197 | C4⋊Q8 | — | 2 | 8 | no | — |
| 198 | C4⋊Q8 | — | 2 | 4 | no | — |
| 199 | C4⋊Q8 | — | 4 | 2 | no | — |
| 200 | #127 | — | 4 | 2 | no | — |
| 201 | #127 | C2×D4 | 1 | 8 | yes | — |
| 202 | #124 | — | 2 | 8 | no | — |
| 203 | #124 | — | 2 | 8 | no | — |
| 204 | #124 | — | 2 | 8 | no | — |
| 205 | #123 | — | 2 | 4 | no | — |
| 206 | #123 | — | 4 | 8 | no | — |
| 207 | #123 | — | 4 | 16 | no | — |
| 208 | #123 | — | 4 | 8 | no | — |
| 209 | C22⋊Q8 | — | 2 | 16 | no | — |
| 210 | C22⋊Q8 | C2×D4 | 1 | 8 | yes | — |
| 211 | #121 | — | 4 | 16 | no | — |
| 212 | #121 | — | 4 | 16 | no | — |
| 213 | #121 | C2×D4 | 1 | 8 | yes | — |
| 214 | #120 | — | 2 | 4 | no | — |
| 215 | #120 | — | 4 | 8 | no | — |
| 216 | C4×D4 | — | 2 | 8 | no | — |
| 217 | C4×D4 | — | 2 | 16 | no | — |
| 218 | C4×D4 | — | 4 | 16 | no | — |
| 219 | #117 | C24 | 1 | 4 | yes | — |
| 220 | C2×C4⋊C4 | — | 4 | 8 | no | — |
| 221 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 222 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 223 | C2×C22⋊C4 | — | 4 | 8 | no | — |
| 224 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 225 | C2×C42 | — | 2 | 1 | no | — |
| 226 | C2×C42 | — | 2 | 2 | no | — |
| 227 | C2×C42 | — | 2 | 2 | no | — |
| 228 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 229 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 230 | #108 | — | 2 | 4 | no | — |
| 231 | #108 | — | 2 | 4 | no | — |
| 232 | #107 | C2×D4 | 1 | 4 | yes | — |
| 233 | #106 | C2×D4 | 1 | 4 | yes | — |
| 234 | C4⋊C8 | — | 2 | 8 | no | — |
| 235 | #104 | — | 2 | 8 | no | — |
| 236 | #104 | — | 2 | 8 | no | — |
| 237 | #103 | — | 2 | 16 | no | — |
| 238 | #103 | C2×D4 | 1 | 8 | yes | — |
| 239 | #102 | — | 2 | 16 | no | — |
| 240 | #102 | C2×D4 | 1 | 8 | yes | — |
| 241 | #101 | — | 4 | 8 | no | — |
| 242 | #100 | — | 2 | 8 | no | — |
| 243 | #100 | — | 4 | 4 | no | — |
| 244 | C22⋊C8 | — | 2 | 8 | no | — |
| 245 | C22⋊C8 | — | 2 | 8 | no | — |
| 246 | #97 | — | 2 | 4 | no | — |
| 247 | C4×C8 | — | 2 | 4 | no | — |
| 248 | C4×C8 | — | 2 | 4 | no | — |
| 249 | C4×C8 | — | 2 | 2 | no | — |
| 250 | C4×C8 | C2×D4 | 1 | 4 | yes | — |
| 251 | C24 | — | 2 | 4 | no | — |
| 252 | C24 | — | 4 | 4 | no | — |
| 253 | C24 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 254 | #41 | — | 2 | 4 | no | — |
| 255 | #41 | — | 2 | 4 | no | — |
| 256 | #41 | — | 2 | 4 | no | — |
| 257 | #41 | — | 2 | 4 | no | — |
| 258 | #41 | — | 4 | 32 | no | — |
| 259 | #41 | — | 4 | 16 | no | — |
| 260 | #41 | — | 8 | 16 | no | — |
| 261 | #41 | — | 8 | 8 | no | — |
| 262 | C2×Q8 | — | 2 | 8 | no | — |
| 263 | C2×Q8 | — | 2 | 4 | no | — |
| 264 | C2×Q8 | — | 2 | 8 | no | — |
| 265 | C2×Q8 | — | 2 | 4 | no | — |
| 266 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 267 | C2×D4 | — | 2 | 4 | no | — |
| 268 | C2×D4 | — | 2 | 8 | no | — |
| 269 | C2×D4 | — | 2 | 8 | no | — |
| 270 | C2×D4 | — | 2 | 8 | no | — |
| 271 | C2×D4 | — | 2 | 4 | no | — |
| 272 | C2×D4 | — | 4 | 8 | no | — |
| 273 | C2×D4 | — | 4 | 8 | no | — |
| 274 | C2×D4 | — | 4 | 16 | no | — |
| 275 | C2×D4 | — | 4 | 8 | no | — |
| 276 | C2×D4 | — | 4 | 8 | no | — |
| 277 | C2×D4 | — | 8 | 8 | no | — |
| 278 | C2×D4 | — | 8 | 8 | no | — |
| 279 | C2×D4 | — | 8 | 4 | no | — |
| 280 | C2×D4 | — | 8 | 8 | no | — |
| 281 | C2×D4 | — | 8 | 8 | no | — |
| 282 | C2×D4 | C22×D4 | 1 | 8 | yes | — |
| 283 | C2×D4 | C22×D4 | 1 | 4 | yes | — |
| 284 | C22×C4 | — | 2 | 1 | no | — |
| 285 | C22×C4 | — | 2 | 1 | no | — |
| 286 | C22×C4 | — | 2 | 1 | no | — |
| 287 | C22×C4 | — | 2 | 2 | no | — |
| 288 | C22×C4 | — | 2 | 4 | no | — |
| 289 | C22×C4 | — | 2 | 1 | no | — |
| 290 | C22×C4 | — | 2 | 4 | no | — |
| 291 | C22×C4 | — | 2 | 4 | no | — |
| 292 | C22×C4 | — | 4 | 4 | no | — |
| 293 | C22×C4 | — | 4 | 8 | no | — |
| 294 | C22×C4 | — | 4 | 4 | no | — |
| 295 | C22×C4 | — | 4 | 8 | no | — |
| 296 | C22×C4 | — | 4 | 8 | no | — |
| 297 | C22×C4 | — | 8 | 4 | no | — |
| 298 | C22×C4 | C22×D4 | 1 | 4 | yes | — |
| 299 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 300 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 301 | Q16 | — | 2 | 4 | no | — |
| 302 | Q16 | — | 4 | 8 | no | — |
| 303 | Q16 | — | 4 | 8 | no | — |
| 304 | Q16 | — | 8 | 8 | no | — |
| 305 | SD16 | — | 2 | 8 | no | — |
| 306 | SD16 | — | 4 | 32 | no | — |
| 307 | SD16 | — | 4 | 16 | no | — |
| 308 | SD16 | — | 8 | 8 | no | — |
| 309 | D8 | — | 2 | 16 | no | — |
| 310 | D8 | — | 2 | 16 | no | — |
| 311 | D8 | — | 2 | 4 | no | — |
| 312 | D8 | — | 4 | 16 | no | — |
| 313 | M16 | — | 2 | 4 | no | — |
| 314 | M16 | — | 2 | 4 | no | — |
| 315 | M16 | — | 2 | 4 | no | — |
| 316 | M16 | — | 2 | 4 | no | — |
| 317 | M16 | — | 4 | 8 | no | — |
| 318 | C2×C8 | — | 2 | 2 | no | — |
| 319 | C2×C8 | — | 2 | 2 | no | — |
| 320 | C2×C8 | — | 2 | 8 | no | — |
| 321 | C2×C8 | — | 2 | 8 | no | — |
| 322 | C2×C8 | — | 2 | 4 | no | — |
| 323 | C2×C8 | — | 2 | 4 | no | — |
| 324 | C2×C8 | — | 4 | 8 | no | — |
| 325 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 326 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 327 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 328 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 329 | C2×C8 | H(5,𝔽2) | 1 | 4 | yes | — |
| 330 | C4⋊C4 | — | 2 | 8 | no | — |
| 331 | C4⋊C4 | — | 4 | 16 | no | — |
| 332 | C4⋊C4 | — | 4 | 8 | no | — |
| 333 | C4⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 334 | C22⋊C4 | — | 2 | 8 | no | — |
| 335 | C22⋊C4 | — | 2 | 4 | no | — |
| 336 | C22⋊C4 | — | 2 | 8 | no | — |
| 337 | C22⋊C4 | — | 4 | 8 | no | — |
| 338 | C22⋊C4 | — | 4 | 16 | no | — |
| 339 | C22⋊C4 | — | 4 | 16 | no | — |
| 340 | C42 | — | 2 | 4 | no | — |
| 341 | C42 | — | 2 | 1 | no | — |
| 342 | C42 | — | 2 | 4 | no | — |
| 343 | C42 | — | 2 | 1 | no | — |
| 344 | C42 | C22×D4 | 1 | 2 | yes | — |
| 345 | C42 | H(5,𝔽2) | 1 | 2 | yes | — |
| 346 | C23 | — | 2 | 1 | no | — |
| 347 | C23 | — | 2 | 1 | no | — |
| 348 | C23 | — | 2 | 4 | no | — |
| 349 | C23 | — | 2 | 8 | no | — |
| 350 | C23 | — | 4 | 2 | no | — |
| 351 | C23 | — | 4 | 4 | no | — |
| 352 | C23 | — | 4 | 4 | no | — |
| 353 | C23 | — | 8 | 8 | no | — |
| 354 | C23 | — | 8 | 8 | no | — |
| 355 | C23 | — | 16 | 8 | no | — |
| 356 | C23 | D42 | 1 | 2 | yes | — |
| 357 | C23 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 358 | Q8 | — | 2 | 4 | no | — |
| 359 | Q8 | — | 2 | 4 | no | — |
| 360 | Q8 | — | 4 | 8 | no | — |
| 361 | Q8 | — | 4 | 8 | no | — |
| 362 | D4 | — | 2 | 16 | no | — |
| 363 | D4 | — | 2 | 4 | no | — |
| 364 | D4 | — | 2 | 4 | no | — |
| 365 | D4 | — | 4 | 4 | no | — |
| 366 | D4 | — | 4 | 4 | no | — |
| 367 | D4 | — | 4 | 8 | no | — |
| 368 | D4 | — | 8 | 16 | no | — |
| 369 | D4 | — | 8 | 8 | no | — |
| 370 | D4 | — | 8 | 16 | no | — |
| 371 | D4 | — | 8 | 16 | no | — |
| 372 | C2×C4 | — | 2 | 4 | no | — |
| 373 | C2×C4 | — | 2 | 1 | no | — |
| 374 | C2×C4 | — | 2 | 2 | no | — |
| 375 | C2×C4 | — | 2 | 1 | no | — |
| 376 | C2×C4 | — | 2 | 4 | no | — |
| 377 | C2×C4 | — | 2 | 4 | no | — |
| 378 | C2×C4 | — | 2 | 8 | no | — |
| 379 | C2×C4 | — | 2 | 4 | no | — |
| 380 | C2×C4 | — | 2 | 2 | no | — |
| 381 | C2×C4 | — | 4 | 8 | no | — |
| 382 | C2×C4 | — | 4 | 2 | no | — |
| 383 | C2×C4 | — | 4 | 4 | no | — |
| 384 | C2×C4 | — | 4 | 4 | no | — |
| 385 | C2×C4 | — | 4 | 4 | no | — |
| 386 | C2×C4 | — | 4 | 4 | no | — |
| 387 | C2×C4 | — | 4 | 4 | no | — |
| 388 | C2×C4 | — | 8 | 16 | no | — |
| 389 | C2×C4 | — | 8 | 8 | no | — |
| 390 | C2×C4 | — | 16 | 8 | no | — |
| 391 | C2×C4 | D42 | 1 | 2 | yes | — |
| 392 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 393 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 394 | C2×C4 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 395 | C2×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 396 | C8 | — | 2 | 4 | no | — |
| 397 | C8 | — | 4 | 4 | no | — |
| 398 | C8 | — | 4 | 4 | no | — |
| 399 | C8 | D42 | 1 | 4 | yes | — |
| 400 | C8 | D42 | 1 | 4 | yes | — |
| 401 | C22 | — | 2 | 2 | no | — |
| 402 | C22 | — | 2 | 4 | no | — |
| 403 | C22 | — | 2 | 2 | no | — |
| 404 | C22 | — | 4 | 2 | no | — |
| 405 | C22 | — | 4 | 2 | no | — |
| 406 | C22 | — | 4 | 8 | no | — |
| 407 | C22 | — | 4 | 4 | no | — |
| 408 | C22 | — | 4 | 8 | no | — |
| 409 | C22 | — | 8 | 8 | no | — |
| 410 | C22 | — | 8 | 8 | no | — |
| 411 | C22 | — | 16 | 4 | no | — |
| 412 | C22 | — | 32 | 8 | no | — |
| 413 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 414 | C22 | #3484 | 1 | 1 | yes | characteristic |
| 415 | C22 | #3543 | 1 | 1 | yes | characteristic |
| 416 | C4 | — | 2 | 4 | no | — |
| 417 | C4 | — | 2 | 2 | no | — |
| 418 | C4 | — | 4 | 2 | no | — |
| 419 | C4 | — | 4 | 8 | no | — |
| 420 | C4 | — | 4 | 4 | no | — |
| 421 | C4 | — | 8 | 4 | no | — |
| 422 | C4 | C2×D42 | 1 | 2 | yes | — |
| 423 | C4 | #3498 | 1 | 2 | yes | — |
| 424 | C2 | — | 2 | 1 | no | — |
| 425 | C2 | — | 2 | 1 | no | — |
| 426 | C2 | — | 4 | 2 | no | — |
| 427 | C2 | — | 8 | 4 | no | — |
| 428 | C2 | — | 8 | 8 | no | — |
| 429 | C2 | #59126 | 1 | 1 | yes | characteristic |
| 430 | C2 | #61105 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#3292 | C2 | semidirect |
| 2. #61051 | C2 | semidirect |
| 3. C2×#3147 | C2 | semidirect |
| 4. #30485 | C2 | semidirect |
| 5. #28505 | C2 | semidirect |
| 6. #25804 | C2 | semidirect |
| 7. #25433 | C2 | semidirect |
| 8. #24280 | C2 | semidirect |
| 9. #23908 | C2 | semidirect |
| 10. #23201 | C2 | semidirect |
| 11. #21544 | C2 | semidirect |
| 13. C22×#135 | C22 | semidirect |
| 14. #3485 | C22 | semidirect |
| 15. C2×#532 | C22 | semidirect |
| 22. C2×#495 | C22 | semidirect |
| 23. C2×#494 | C22 | semidirect |
| 25. C2×#492 | C22 | semidirect |
| 26. C2×#473 | C22 | semidirect |
| 28. #3059 | C22 | semidirect |
| 30. #3042 | C22 | semidirect |
| 31. C2×#455 | C22 | semidirect |
| 33. #3009 | C22 | semidirect |
| 34. #3005 | C22 | semidirect |
| 36. #2948 | C22 | semidirect |
| 37. #2929 | C22 | semidirect |
| 38. C22×C4×C8 | C22 | semidirect |
| 39. #2046 | C22 | semidirect |
| 40. #2019 | C22 | semidirect |
| 41. #2005 | C22 | semidirect |
| 42. #2003 | C22 | semidirect |
| 43. #1979 | C22 | semidirect |
| 44. #1978 | C22 | semidirect |
| 46. #1945 | C22 | semidirect |
| 47. #1937 | C22 | semidirect |
| 48. #1896 | C22 | semidirect |
| 49. #1887 | C22 | semidirect |
| 50. #1885 | C22 | semidirect |
| 51. #1810 | C22 | semidirect |
| 52. #1785 | C22 | semidirect |
| 53. #1772 | C22 | semidirect |
| 54. #1764 | C22 | semidirect |
| 94. #493 | D4 | semidirect |
| 100. #467 | D4 | semidirect |
| 101. #466 | D4 | semidirect |
| 102. #465 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3292 | 2 |
| #61051 | 2 |
| C2×#3147 | 2 |
| #30485 | 2 |
| #28505 | 2 |
| #25804 | 2 |
| #25433 | 2 |
| #24280 | 2 |
| #23908 | 2 |
| #23201 | 2 |
| #21544 | 2 |