Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
7952 conjugacy classes of subgroups.
The subgroup lattice has 632 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#3498 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#3550 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #61662 | C2 | 1 | 32 | yes | maximal, direct product factor |
| 4 | C2×#3324 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | C2×#3304 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | C2×D4×SD16 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | C2×#3278 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | C2×#3208 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C2×#3200 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | C2×#3107 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C2×#3009 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | C2×#2979 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C22×H(5,𝔽2) | C22 | 1 | 2 | yes | — |
| 14 | C22×#137 | C22 | 1 | 4 | yes | complemented |
| 15 | C23×SD16 | C22 | 1 | 4 | yes | complemented |
| 16 | #3550 | — | 2 | 8 | no | — |
| 17 | #3550 | C22 | 1 | 16 | yes | complemented |
| 18 | C2×#563 | — | 2 | 2 | no | — |
| 19 | #3498 | — | 2 | 8 | no | — |
| 20 | #3498 | C22 | 1 | 16 | yes | — |
| 21 | C2×#559 | — | 2 | 1 | no | — |
| 22 | C2×Q82 | — | 2 | 1 | no | — |
| 23 | C2×#556 | C22 | 1 | 4 | yes | complemented |
| 24 | C2×#550 | C22 | 1 | 4 | yes | — |
| 25 | C2×D4×Q8 | C22 | 1 | 4 | yes | complemented |
| 26 | C2×D42 | — | 2 | 4 | no | — |
| 27 | C2×D42 | C22 | 1 | 4 | yes | — |
| 28 | C2×#542 | — | 2 | 4 | no | — |
| 29 | C2×#536 | C22 | 1 | 4 | yes | complemented |
| 30 | C2×#535 | — | 2 | 2 | no | — |
| 31 | C2×#535 | C22 | 1 | 2 | yes | — |
| 32 | C2×#533 | C22 | 1 | 2 | yes | complemented |
| 33 | C2×#532 | — | 2 | 1 | no | — |
| 34 | C2×#532 | C22 | 1 | 1 | yes | characteristic |
| 35 | C22×#127 | — | 2 | 1 | no | — |
| 36 | C22×#127 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×C4×#41 | C22 | 1 | 1 | yes | characteristic |
| 38 | #3324 | C22 | 1 | 64 | yes | complemented |
| 39 | #3304 | C22 | 1 | 64 | yes | complemented |
| 40 | D4×SD16 | C22 | 1 | 64 | yes | complemented |
| 41 | #3278 | C22 | 1 | 64 | yes | complemented |
| 42 | #3208 | C22 | 1 | 32 | yes | complemented |
| 43 | #3200 | C22 | 1 | 64 | yes | complemented |
| 44 | C2×#492 | C22 | 1 | 4 | yes | complemented |
| 45 | C2×#486 | C22 | 1 | 4 | yes | complemented |
| 46 | #3107 | C22 | 1 | 32 | yes | complemented |
| 47 | C2×#485 | C22 | 1 | 4 | yes | complemented |
| 48 | C2×#482 | C22 | 1 | 8 | yes | complemented |
| 49 | C2×#475 | C22 | 1 | 2 | yes | complemented |
| 50 | C2×#474 | C22 | 1 | 2 | yes | complemented |
| 51 | C2×#468 | C22 | 1 | 8 | yes | complemented |
| 52 | C2×#465 | C22 | 1 | 8 | yes | complemented |
| 53 | C2×#462 | C22 | 1 | 2 | yes | complemented |
| 54 | C2×#460 | C22 | 1 | 4 | yes | complemented |
| 55 | C2×#460 | C22 | 1 | 4 | yes | complemented |
| 56 | C2×#461 | C22 | 1 | 2 | yes | complemented |
| 57 | #3009 | C22 | 1 | 64 | yes | complemented |
| 58 | C2×#452 | C22 | 1 | 4 | yes | — |
| 59 | C2×#452 | C22 | 1 | 8 | yes | complemented |
| 60 | C2×#448 | C22 | 1 | 8 | yes | complemented |
| 61 | C2×#450 | C22 | 1 | 8 | yes | complemented |
| 62 | C2×#450 | C22 | 1 | 8 | yes | complemented |
| 63 | #2979 | C22 | 1 | 16 | yes | complemented |
| 64 | C2×C4×Q16 | C22 | 1 | 4 | yes | complemented |
| 65 | C2×C4×SD16 | C22 | 1 | 4 | yes | complemented |
| 66 | C2×#436 | C22 | 1 | 4 | yes | complemented |
| 67 | C2×C8×D4 | C22 | 1 | 4 | yes | complemented |
| 68 | C2×#431 | C22 | 1 | 2 | yes | complemented |
| 69 | C2×#418 | C22 | 1 | 4 | yes | complemented |
| 70 | C2×#416 | C22 | 1 | 4 | yes | complemented |
| 71 | C2×#408 | C22 | 1 | 4 | yes | complemented |
| 72 | C2×H(5,𝔽2) | — | 2 | 8 | no | — |
| 73 | C2×H(5,𝔽2) | — | 4 | 8 | no | — |
| 74 | C2×H(5,𝔽2) | — | 4 | 8 | no | — |
| 75 | C2×H(5,𝔽2) | C23 | 1 | 16 | yes | — |
| 76 | C22×#41 | — | 2 | 2 | no | — |
| 77 | C22×#41 | C23 | 1 | 1 | yes | characteristic |
| 78 | C22×#41 | C23 | 1 | 4 | yes | — |
| 79 | C22×#41 | C23 | 1 | 2 | yes | — |
| 80 | C23×Q8 | C23 | 1 | 4 | yes | — |
| 81 | C23×D4 | — | 2 | 2 | no | — |
| 82 | C23×D4 | — | 2 | 4 | no | — |
| 83 | C23×D4 | — | 2 | 4 | no | — |
| 84 | C23×D4 | — | 2 | 2 | no | — |
| 85 | C23×D4 | C23 | 1 | 4 | yes | — |
| 86 | C23×D4 | C23 | 1 | 2 | yes | — |
| 87 | C2×#137 | — | 4 | 16 | no | — |
| 88 | C2×#137 | C23 | 1 | 32 | yes | complemented |
| 89 | C22×Q16 | C23 | 1 | 4 | yes | — |
| 90 | C22×SD16 | — | 4 | 16 | no | — |
| 91 | C22×SD16 | C23 | 1 | 4 | yes | — |
| 92 | C22×SD16 | C23 | 1 | 8 | yes | — |
| 93 | C22×SD16 | C23 | 1 | 8 | yes | — |
| 94 | C22×SD16 | C23 | 1 | 32 | yes | complemented |
| 95 | C22×M16 | C23 | 1 | 4 | yes | — |
| 96 | C23×C8 | C23 | 1 | 4 | yes | — |
| 97 | #563 | — | 2 | 32 | no | — |
| 98 | #559 | — | 2 | 16 | no | — |
| 99 | Q82 | — | 2 | 16 | no | — |
| 100 | #556 | — | 2 | 16 | no | — |
| 101 | #556 | C23 | 1 | 32 | yes | complemented |
| 102 | #550 | — | 2 | 16 | no | — |
| 103 | #550 | C23 | 1 | 32 | yes | — |
| 104 | D4×Q8 | — | 2 | 16 | no | — |
| 105 | D4×Q8 | C23 | 1 | 32 | yes | complemented |
| 106 | D42 | — | 2 | 64 | no | — |
| 107 | D42 | — | 2 | 16 | no | — |
| 108 | D42 | C23 | 1 | 32 | yes | — |
| 109 | #542 | — | 2 | 64 | no | — |
| 110 | #536 | — | 2 | 16 | no | — |
| 111 | #536 | C23 | 1 | 32 | yes | complemented |
| 112 | #535 | — | 2 | 8 | no | — |
| 113 | #535 | — | 2 | 32 | no | — |
| 114 | #535 | C23 | 1 | 16 | yes | — |
| 115 | #533 | — | 2 | 8 | no | — |
| 116 | #533 | C23 | 1 | 16 | yes | complemented |
| 117 | #532 | — | 2 | 16 | no | — |
| 118 | #532 | D4 | 1 | 8 | yes | — |
| 119 | #532 | C23 | 1 | 8 | yes | — |
| 120 | C2×C4⋊Q8 | — | 2 | 4 | no | — |
| 121 | C2×C4⋊Q8 | — | 2 | 4 | no | — |
| 122 | C2×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 123 | C2×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 124 | C2×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 125 | C2×#127 | — | 2 | 2 | no | — |
| 126 | C2×#127 | — | 2 | 4 | no | — |
| 127 | C2×#127 | — | 2 | 16 | no | — |
| 128 | C2×#127 | — | 2 | 1 | no | — |
| 129 | C2×#127 | — | 2 | 1 | no | — |
| 130 | C2×#127 | — | 2 | 4 | no | — |
| 131 | C2×#127 | D4 | 1 | 1 | yes | characteristic |
| 132 | C2×#127 | C23 | 1 | 4 | yes | — |
| 133 | C2×#127 | C23 | 1 | 8 | yes | — |
| 134 | C2×#126 | — | 2 | 8 | no | — |
| 135 | C2×#125 | — | 2 | 2 | no | — |
| 136 | C2×#124 | — | 2 | 2 | no | — |
| 137 | C2×#124 | — | 2 | 4 | no | — |
| 138 | C2×#124 | — | 2 | 4 | no | — |
| 139 | C2×#124 | D4 | 1 | 2 | yes | — |
| 140 | C2×#123 | — | 2 | 4 | no | — |
| 141 | C2×#123 | — | 2 | 4 | no | — |
| 142 | C2×C22⋊Q8 | — | 2 | 2 | no | — |
| 143 | C2×C22⋊Q8 | — | 2 | 8 | no | — |
| 144 | C2×C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 145 | C2×C22⋊Q8 | C23 | 1 | 8 | yes | — |
| 146 | C2×#121 | — | 2 | 4 | no | — |
| 147 | C2×#121 | — | 2 | 8 | no | — |
| 148 | C2×#121 | D4 | 1 | 4 | yes | — |
| 149 | C2×#121 | C23 | 1 | 8 | yes | — |
| 150 | C2×#120 | — | 2 | 4 | no | — |
| 151 | C2×#120 | — | 2 | 8 | no | — |
| 152 | C4×#41 | — | 2 | 4 | no | — |
| 153 | C4×#41 | C23 | 1 | 8 | yes | — |
| 154 | C2×C4×Q8 | — | 2 | 4 | no | — |
| 155 | C2×C4×Q8 | — | 2 | 2 | no | — |
| 156 | C2×C4×Q8 | C23 | 1 | 2 | yes | — |
| 157 | C2×C4×Q8 | C23 | 1 | 4 | yes | — |
| 158 | C2×C4×D4 | — | 2 | 4 | no | — |
| 159 | C2×C4×D4 | — | 2 | 2 | no | — |
| 160 | C2×C4×D4 | — | 2 | 4 | no | — |
| 161 | C2×C4×D4 | C23 | 1 | 2 | yes | — |
| 162 | C2×C4×D4 | C23 | 1 | 4 | yes | — |
| 163 | C2×#117 | — | 2 | 2 | no | — |
| 164 | C2×#117 | — | 2 | 1 | no | — |
| 165 | C2×#117 | C23 | 1 | 4 | yes | — |
| 166 | C2×#117 | C23 | 1 | 1 | yes | characteristic |
| 167 | C22×C42 | — | 2 | 1 | no | — |
| 168 | C22×C42 | C23 | 1 | 1 | yes | characteristic |
| 169 | #492 | C23 | 1 | 32 | yes | complemented |
| 170 | #486 | C23 | 1 | 32 | yes | complemented |
| 171 | #485 | C23 | 1 | 32 | yes | complemented |
| 172 | #482 | C23 | 1 | 64 | yes | complemented |
| 173 | #475 | C23 | 1 | 16 | yes | complemented |
| 174 | #474 | C23 | 1 | 16 | yes | complemented |
| 175 | #468 | C23 | 1 | 64 | yes | complemented |
| 176 | #465 | C23 | 1 | 64 | yes | complemented |
| 177 | #462 | C23 | 1 | 16 | yes | complemented |
| 178 | #461 | C23 | 1 | 16 | yes | complemented |
| 179 | #460 | C23 | 1 | 32 | yes | complemented |
| 180 | #460 | C23 | 1 | 32 | yes | complemented |
| 181 | #452 | C23 | 1 | 32 | yes | — |
| 182 | #452 | C23 | 1 | 64 | yes | complemented |
| 183 | #450 | C23 | 1 | 64 | yes | complemented |
| 184 | #450 | C23 | 1 | 64 | yes | complemented |
| 185 | #448 | C23 | 1 | 64 | yes | complemented |
| 186 | C4×Q16 | C23 | 1 | 32 | yes | complemented |
| 187 | C4×SD16 | C23 | 1 | 32 | yes | complemented |
| 188 | #436 | C23 | 1 | 32 | yes | complemented |
| 189 | C8×D4 | C23 | 1 | 32 | yes | complemented |
| 190 | #431 | C23 | 1 | 16 | yes | complemented |
| 191 | C2×#107 | C23 | 1 | 4 | yes | — |
| 192 | C2×#106 | C23 | 1 | 4 | yes | — |
| 193 | C2×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 194 | C2×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 195 | #418 | C23 | 1 | 32 | yes | complemented |
| 196 | #416 | C23 | 1 | 32 | yes | complemented |
| 197 | C2×#103 | C23 | 1 | 4 | yes | — |
| 198 | C2×#103 | C23 | 1 | 4 | yes | — |
| 199 | C2×#103 | C23 | 1 | 4 | yes | — |
| 200 | C2×#102 | C23 | 1 | 8 | yes | — |
| 201 | C2×#102 | C23 | 1 | 8 | yes | — |
| 202 | C2×#102 | C23 | 1 | 4 | yes | — |
| 203 | #408 | C23 | 1 | 32 | yes | complemented |
| 204 | C2×C22⋊C8 | C23 | 1 | 8 | yes | — |
| 205 | C2×C22⋊C8 | C23 | 1 | 4 | yes | — |
| 206 | C2×C4×C8 | C23 | 1 | 4 | yes | — |
| 207 | C25 | — | 2 | 4 | no | — |
| 208 | C25 | — | 2 | 2 | no | — |
| 209 | H(5,𝔽2) | — | 4 | 32 | no | — |
| 210 | H(5,𝔽2) | — | 4 | 32 | no | — |
| 211 | H(5,𝔽2) | — | 4 | 64 | no | — |
| 212 | C2×#41 | — | 2 | 16 | no | — |
| 213 | C2×#41 | — | 2 | 4 | no | — |
| 214 | C2×#41 | — | 2 | 4 | no | — |
| 215 | C2×#41 | — | 2 | 2 | no | — |
| 216 | C2×#41 | — | 2 | 8 | no | — |
| 217 | C2×#41 | — | 2 | 16 | no | — |
| 218 | C2×#41 | — | 4 | 4 | no | — |
| 219 | C2×#41 | — | 4 | 4 | no | — |
| 220 | C2×#41 | — | 4 | 8 | no | — |
| 221 | C2×#41 | — | 4 | 16 | no | — |
| 222 | C2×#41 | C2×D4 | 1 | 8 | yes | — |
| 223 | C2×#41 | C24 | 1 | 4 | yes | — |
| 224 | C2×#41 | C24 | 1 | 16 | yes | — |
| 225 | C2×#41 | C24 | 1 | 8 | yes | — |
| 226 | C22×Q8 | — | 2 | 2 | no | — |
| 227 | C22×Q8 | — | 2 | 4 | no | — |
| 228 | C22×Q8 | — | 2 | 8 | no | — |
| 229 | C22×Q8 | — | 4 | 8 | no | — |
| 230 | C22×Q8 | — | 4 | 8 | no | — |
| 231 | C22×Q8 | C2×D4 | 1 | 2 | yes | — |
| 232 | C22×Q8 | C24 | 1 | 4 | yes | — |
| 233 | C22×Q8 | C24 | 1 | 1 | yes | characteristic |
| 234 | C22×Q8 | C24 | 1 | 16 | yes | — |
| 235 | C22×D4 | — | 2 | 1 | no | — |
| 236 | C22×D4 | — | 2 | 16 | no | — |
| 237 | C22×D4 | — | 2 | 4 | no | — |
| 238 | C22×D4 | — | 2 | 8 | no | — |
| 239 | C22×D4 | — | 2 | 16 | no | — |
| 240 | C22×D4 | — | 2 | 32 | no | — |
| 241 | C22×D4 | — | 2 | 32 | no | — |
| 242 | C22×D4 | — | 2 | 4 | no | — |
| 243 | C22×D4 | — | 2 | 4 | no | — |
| 244 | C22×D4 | — | 2 | 2 | no | — |
| 245 | C22×D4 | — | 2 | 4 | no | — |
| 246 | C22×D4 | — | 2 | 8 | no | — |
| 247 | C22×D4 | — | 2 | 4 | no | — |
| 248 | C22×D4 | — | 2 | 16 | no | — |
| 249 | C22×D4 | — | 4 | 8 | no | — |
| 250 | C22×D4 | — | 4 | 4 | no | — |
| 251 | C22×D4 | — | 4 | 4 | no | — |
| 252 | C22×D4 | — | 4 | 16 | no | — |
| 253 | C22×D4 | — | 4 | 32 | no | — |
| 254 | C22×D4 | — | 8 | 8 | no | — |
| 255 | C22×D4 | — | 8 | 16 | no | — |
| 256 | C22×D4 | C2×D4 | 1 | 4 | yes | — |
| 257 | C22×D4 | C2×D4 | 1 | 4 | yes | — |
| 258 | C22×D4 | C2×D4 | 1 | 2 | yes | — |
| 259 | C22×D4 | C24 | 1 | 4 | yes | — |
| 260 | C22×D4 | C24 | 1 | 16 | yes | — |
| 261 | C22×D4 | C24 | 1 | 1 | yes | characteristic |
| 262 | C22×D4 | C24 | 1 | 8 | yes | — |
| 263 | C23×C4 | — | 2 | 1 | no | — |
| 264 | C23×C4 | — | 2 | 4 | no | — |
| 265 | C23×C4 | — | 2 | 4 | no | — |
| 266 | C23×C4 | — | 2 | 2 | no | — |
| 267 | C23×C4 | C2×D4 | 1 | 2 | yes | — |
| 268 | C23×C4 | C24 | 1 | 4 | yes | — |
| 269 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 270 | #137 | — | 4 | 64 | no | — |
| 271 | C2×Q16 | — | 2 | 16 | no | — |
| 272 | C2×Q16 | C24 | 1 | 16 | yes | — |
| 273 | C2×SD16 | — | 2 | 16 | no | — |
| 274 | C2×SD16 | — | 4 | 16 | no | — |
| 275 | C2×SD16 | — | 4 | 16 | no | — |
| 276 | C2×SD16 | — | 4 | 64 | no | — |
| 277 | C2×SD16 | C24 | 1 | 16 | yes | — |
| 278 | C2×SD16 | C24 | 1 | 32 | yes | — |
| 279 | C2×SD16 | C24 | 1 | 32 | yes | — |
| 280 | C2×M16 | — | 4 | 8 | no | — |
| 281 | C2×M16 | C24 | 1 | 16 | yes | — |
| 282 | C22×C8 | — | 4 | 8 | no | — |
| 283 | C22×C8 | C24 | 1 | 4 | yes | — |
| 284 | C22×C8 | C24 | 1 | 4 | yes | — |
| 285 | C22×C8 | C24 | 1 | 16 | yes | — |
| 286 | C4⋊Q8 | — | 2 | 32 | no | — |
| 287 | C4⋊Q8 | — | 2 | 32 | no | — |
| 288 | C4⋊Q8 | — | 2 | 4 | no | — |
| 289 | C4⋊Q8 | — | 2 | 4 | no | — |
| 290 | C4⋊Q8 | C2×D4 | 1 | 8 | yes | — |
| 291 | C4⋊Q8 | C24 | 1 | 8 | yes | — |
| 292 | C4⋊Q8 | C24 | 1 | 8 | yes | — |
| 293 | #127 | — | 2 | 16 | no | — |
| 294 | #127 | — | 2 | 32 | no | — |
| 295 | #127 | — | 2 | 8 | no | — |
| 296 | #127 | — | 2 | 8 | no | — |
| 297 | #127 | — | 2 | 8 | no | — |
| 298 | #127 | C2×D4 | 1 | 8 | yes | — |
| 299 | #127 | C24 | 1 | 16 | yes | — |
| 300 | #126 | — | 2 | 64 | no | — |
| 301 | #125 | — | 2 | 16 | no | — |
| 302 | #124 | — | 2 | 16 | no | — |
| 303 | #124 | — | 2 | 32 | no | — |
| 304 | #124 | — | 2 | 32 | no | — |
| 305 | #124 | C2×D4 | 1 | 16 | yes | — |
| 306 | #123 | — | 2 | 32 | no | — |
| 307 | #123 | — | 2 | 32 | no | — |
| 308 | C22⋊Q8 | — | 2 | 16 | no | — |
| 309 | C22⋊Q8 | — | 2 | 8 | no | — |
| 310 | C22⋊Q8 | — | 2 | 16 | no | — |
| 311 | C22⋊Q8 | — | 2 | 64 | no | — |
| 312 | C22⋊Q8 | C24 | 1 | 16 | yes | — |
| 313 | C22⋊Q8 | C24 | 1 | 32 | yes | — |
| 314 | #121 | — | 2 | 16 | no | — |
| 315 | #121 | — | 2 | 32 | no | — |
| 316 | #121 | — | 2 | 64 | no | — |
| 317 | #121 | C2×D4 | 1 | 32 | yes | — |
| 318 | #121 | C24 | 1 | 32 | yes | — |
| 319 | #120 | — | 2 | 32 | no | — |
| 320 | #120 | — | 2 | 64 | no | — |
| 321 | C4×Q8 | — | 2 | 32 | no | — |
| 322 | C4×Q8 | — | 2 | 16 | no | — |
| 323 | C4×Q8 | — | 2 | 4 | no | — |
| 324 | C4×Q8 | — | 2 | 8 | no | — |
| 325 | C4×Q8 | C24 | 1 | 8 | yes | — |
| 326 | C4×Q8 | C24 | 1 | 16 | yes | — |
| 327 | C4×D4 | — | 2 | 32 | no | — |
| 328 | C4×D4 | — | 2 | 16 | no | — |
| 329 | C4×D4 | — | 2 | 32 | no | — |
| 330 | C4×D4 | — | 2 | 4 | no | — |
| 331 | C4×D4 | C2×D4 | 1 | 16 | yes | — |
| 332 | C4×D4 | C24 | 1 | 8 | yes | — |
| 333 | C4×D4 | C24 | 1 | 16 | yes | — |
| 334 | #117 | — | 2 | 16 | no | — |
| 335 | #117 | — | 2 | 2 | no | — |
| 336 | #117 | — | 2 | 8 | no | — |
| 337 | #117 | — | 2 | 8 | no | — |
| 338 | #117 | C24 | 1 | 4 | yes | — |
| 339 | #117 | C24 | 1 | 16 | yes | — |
| 340 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 341 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 342 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 343 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 344 | C2×C4⋊C4 | — | 2 | 8 | no | — |
| 345 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 346 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 347 | C2×C4⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 348 | C2×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 349 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 350 | C2×C22⋊C4 | — | 2 | 4 | no | — |
| 351 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 352 | C2×C22⋊C4 | — | 2 | 4 | no | — |
| 353 | C2×C22⋊C4 | — | 2 | 8 | no | — |
| 354 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 355 | C2×C22⋊C4 | — | 2 | 8 | no | — |
| 356 | C2×C22⋊C4 | C2×D4 | 1 | 8 | yes | — |
| 357 | C2×C42 | — | 2 | 1 | no | — |
| 358 | C2×C42 | — | 2 | 4 | no | — |
| 359 | C2×C42 | — | 2 | 4 | no | — |
| 360 | C2×C42 | — | 2 | 2 | no | — |
| 361 | C2×C42 | — | 2 | 8 | no | — |
| 362 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 363 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 364 | C2×C42 | C2×D4 | 1 | 4 | yes | — |
| 365 | C2×C42 | C24 | 1 | 2 | yes | — |
| 366 | C2×C42 | C24 | 1 | 4 | yes | — |
| 367 | #107 | C24 | 1 | 16 | yes | — |
| 368 | #106 | C24 | 1 | 16 | yes | — |
| 369 | C4⋊C8 | C24 | 1 | 8 | yes | — |
| 370 | C4⋊C8 | C24 | 1 | 8 | yes | — |
| 371 | #103 | C24 | 1 | 16 | yes | — |
| 372 | #103 | C24 | 1 | 16 | yes | — |
| 373 | #103 | C24 | 1 | 16 | yes | — |
| 374 | #102 | C24 | 1 | 32 | yes | — |
| 375 | #102 | C24 | 1 | 16 | yes | — |
| 376 | #102 | C24 | 1 | 32 | yes | — |
| 377 | C22⋊C8 | C24 | 1 | 16 | yes | — |
| 378 | C22⋊C8 | C24 | 1 | 32 | yes | — |
| 379 | C4×C8 | C24 | 1 | 16 | yes | — |
| 380 | C24 | — | 2 | 1 | no | — |
| 381 | C24 | — | 2 | 4 | no | — |
| 382 | C24 | — | 2 | 16 | no | — |
| 383 | C24 | — | 2 | 8 | no | — |
| 384 | C24 | — | 4 | 16 | no | — |
| 385 | C24 | — | 4 | 8 | no | — |
| 386 | C24 | — | 8 | 8 | no | — |
| 387 | C24 | — | 8 | 16 | no | — |
| 388 | C24 | C22×D4 | 1 | 1 | yes | characteristic |
| 389 | C24 | C22×D4 | 1 | 4 | yes | — |
| 390 | #41 | — | 2 | 16 | no | — |
| 391 | #41 | — | 2 | 8 | no | — |
| 392 | #41 | — | 2 | 8 | no | — |
| 393 | #41 | — | 2 | 32 | no | — |
| 394 | #41 | — | 4 | 16 | no | — |
| 395 | #41 | — | 4 | 8 | no | — |
| 396 | #41 | — | 4 | 8 | no | — |
| 397 | #41 | — | 4 | 16 | no | — |
| 398 | #41 | — | 4 | 32 | no | — |
| 399 | #41 | — | 4 | 64 | no | — |
| 400 | C2×Q8 | — | 2 | 1 | no | — |
| 401 | C2×Q8 | — | 2 | 8 | no | — |
| 402 | C2×Q8 | — | 2 | 4 | no | — |
| 403 | C2×Q8 | — | 2 | 16 | no | — |
| 404 | C2×Q8 | — | 2 | 2 | no | — |
| 405 | C2×Q8 | — | 2 | 8 | no | — |
| 406 | C2×Q8 | — | 2 | 8 | no | — |
| 407 | C2×Q8 | — | 4 | 4 | no | — |
| 408 | C2×Q8 | — | 4 | 16 | no | — |
| 409 | C2×Q8 | — | 4 | 16 | no | — |
| 410 | C2×Q8 | — | 4 | 8 | no | — |
| 411 | C2×Q8 | — | 8 | 8 | no | — |
| 412 | C2×Q8 | — | 8 | 16 | no | — |
| 413 | C2×Q8 | C22×D4 | 1 | 8 | yes | — |
| 414 | C2×Q8 | H(5,𝔽2) | 1 | 4 | yes | — |
| 415 | C2×Q8 | C25 | 1 | 8 | yes | — |
| 416 | C2×Q8 | C25 | 1 | 2 | yes | — |
| 417 | C2×D4 | — | 2 | 8 | no | — |
| 418 | C2×D4 | — | 2 | 4 | no | — |
| 419 | C2×D4 | — | 2 | 32 | no | — |
| 420 | C2×D4 | — | 2 | 16 | no | — |
| 421 | C2×D4 | — | 2 | 32 | no | — |
| 422 | C2×D4 | — | 2 | 16 | no | — |
| 423 | C2×D4 | — | 2 | 1 | no | — |
| 424 | C2×D4 | — | 2 | 16 | no | — |
| 425 | C2×D4 | — | 2 | 16 | no | — |
| 426 | C2×D4 | — | 2 | 4 | no | — |
| 427 | C2×D4 | — | 2 | 8 | no | — |
| 428 | C2×D4 | — | 2 | 16 | no | — |
| 429 | C2×D4 | — | 2 | 2 | no | — |
| 430 | C2×D4 | — | 2 | 8 | no | — |
| 431 | C2×D4 | — | 2 | 8 | no | — |
| 432 | C2×D4 | — | 4 | 16 | no | — |
| 433 | C2×D4 | — | 4 | 8 | no | — |
| 434 | C2×D4 | — | 4 | 8 | no | — |
| 435 | C2×D4 | — | 4 | 32 | no | — |
| 436 | C2×D4 | — | 4 | 4 | no | — |
| 437 | C2×D4 | — | 4 | 8 | no | — |
| 438 | C2×D4 | — | 4 | 16 | no | — |
| 439 | C2×D4 | — | 4 | 16 | no | — |
| 440 | C2×D4 | — | 4 | 8 | no | — |
| 441 | C2×D4 | — | 4 | 64 | no | — |
| 442 | C2×D4 | — | 4 | 16 | no | — |
| 443 | C2×D4 | — | 4 | 128 | no | — |
| 444 | C2×D4 | — | 4 | 16 | no | — |
| 445 | C2×D4 | — | 8 | 32 | no | — |
| 446 | C2×D4 | — | 8 | 8 | no | — |
| 447 | C2×D4 | — | 8 | 64 | no | — |
| 448 | C2×D4 | — | 8 | 16 | no | — |
| 449 | C2×D4 | C22×D4 | 1 | 16 | yes | — |
| 450 | C2×D4 | C22×D4 | 1 | 16 | yes | — |
| 451 | C2×D4 | C22×D4 | 1 | 8 | yes | — |
| 452 | C2×D4 | H(5,𝔽2) | 1 | 4 | yes | — |
| 453 | C2×D4 | C25 | 1 | 8 | yes | — |
| 454 | C2×D4 | C25 | 1 | 2 | yes | — |
| 455 | C22×C4 | — | 2 | 8 | no | — |
| 456 | C22×C4 | — | 2 | 1 | no | — |
| 457 | C22×C4 | — | 2 | 8 | no | — |
| 458 | C22×C4 | — | 2 | 4 | no | — |
| 459 | C22×C4 | — | 2 | 8 | no | — |
| 460 | C22×C4 | — | 2 | 8 | no | — |
| 461 | C22×C4 | — | 2 | 2 | no | — |
| 462 | C22×C4 | — | 2 | 2 | no | — |
| 463 | C22×C4 | — | 2 | 4 | no | — |
| 464 | C22×C4 | — | 2 | 2 | no | — |
| 465 | C22×C4 | — | 2 | 4 | no | — |
| 466 | C22×C4 | — | 2 | 16 | no | — |
| 467 | C22×C4 | — | 2 | 8 | no | — |
| 468 | C22×C4 | — | 2 | 16 | no | — |
| 469 | C22×C4 | — | 4 | 16 | no | — |
| 470 | C22×C4 | — | 4 | 8 | no | — |
| 471 | C22×C4 | — | 8 | 8 | no | — |
| 472 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 473 | C22×C4 | C22×D4 | 1 | 8 | yes | — |
| 474 | C22×C4 | C22×D4 | 1 | 8 | yes | — |
| 475 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 476 | C22×C4 | C22×D4 | 1 | 4 | yes | — |
| 477 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 478 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 479 | C22×C4 | C25 | 1 | 2 | yes | — |
| 480 | C22×C4 | C25 | 1 | 8 | yes | — |
| 481 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 482 | Q16 | — | 2 | 32 | no | — |
| 483 | SD16 | — | 2 | 32 | no | — |
| 484 | SD16 | — | 4 | 32 | no | — |
| 485 | SD16 | — | 4 | 32 | no | — |
| 486 | M16 | — | 4 | 16 | no | — |
| 487 | C2×C8 | — | 2 | 8 | no | — |
| 488 | C2×C8 | — | 2 | 8 | no | — |
| 489 | C2×C8 | — | 4 | 16 | no | — |
| 490 | C2×C8 | C25 | 1 | 8 | yes | — |
| 491 | C2×C8 | C25 | 1 | 8 | yes | — |
| 492 | C4⋊C4 | — | 2 | 8 | no | — |
| 493 | C4⋊C4 | — | 2 | 8 | no | — |
| 494 | C4⋊C4 | — | 2 | 8 | no | — |
| 495 | C4⋊C4 | — | 2 | 8 | no | — |
| 496 | C4⋊C4 | — | 2 | 32 | no | — |
| 497 | C4⋊C4 | — | 2 | 16 | no | — |
| 498 | C4⋊C4 | — | 2 | 16 | no | — |
| 499 | C4⋊C4 | — | 2 | 4 | no | — |
| 500 | C4⋊C4 | — | 2 | 2 | no | — |
| 501 | C4⋊C4 | C22×D4 | 1 | 16 | yes | — |
| 502 | C4⋊C4 | C25 | 1 | 8 | yes | — |
| 503 | C4⋊C4 | C25 | 1 | 4 | yes | — |
| 504 | C22⋊C4 | — | 2 | 16 | no | — |
| 505 | C22⋊C4 | — | 2 | 4 | no | — |
| 506 | C22⋊C4 | — | 2 | 16 | no | — |
| 507 | C22⋊C4 | — | 2 | 32 | no | — |
| 508 | C22⋊C4 | — | 2 | 8 | no | — |
| 509 | C22⋊C4 | — | 2 | 32 | no | — |
| 510 | C22⋊C4 | C22×D4 | 1 | 32 | yes | — |
| 511 | C42 | — | 2 | 4 | no | — |
| 512 | C42 | — | 2 | 8 | no | — |
| 513 | C42 | — | 2 | 16 | no | — |
| 514 | C42 | — | 2 | 16 | no | — |
| 515 | C42 | C22×D4 | 1 | 4 | yes | — |
| 516 | C42 | C22×D4 | 1 | 4 | yes | — |
| 517 | C42 | C22×D4 | 1 | 4 | yes | — |
| 518 | C42 | C25 | 1 | 4 | yes | — |
| 519 | C23 | — | 2 | 2 | no | — |
| 520 | C23 | — | 2 | 8 | no | — |
| 521 | C23 | — | 2 | 2 | no | — |
| 522 | C23 | — | 2 | 4 | no | — |
| 523 | C23 | — | 2 | 4 | no | — |
| 524 | C23 | — | 2 | 16 | no | — |
| 525 | C23 | — | 2 | 8 | no | — |
| 526 | C23 | — | 4 | 32 | no | — |
| 527 | C23 | — | 4 | 16 | no | — |
| 528 | C23 | — | 4 | 4 | no | — |
| 529 | C23 | — | 4 | 8 | no | — |
| 530 | C23 | — | 4 | 16 | no | — |
| 531 | C23 | — | 8 | 16 | no | — |
| 532 | C23 | — | 8 | 32 | no | — |
| 533 | C23 | — | 16 | 32 | no | — |
| 534 | C23 | — | 16 | 16 | no | — |
| 535 | C23 | C23×D4 | 1 | 2 | yes | — |
| 536 | C23 | C23×D4 | 1 | 8 | yes | — |
| 537 | C23 | C23×D4 | 1 | 1 | yes | characteristic |
| 538 | Q8 | — | 2 | 2 | no | — |
| 539 | Q8 | — | 2 | 4 | no | — |
| 540 | Q8 | — | 2 | 8 | no | — |
| 541 | Q8 | — | 2 | 8 | no | — |
| 542 | Q8 | — | 4 | 8 | no | — |
| 543 | Q8 | — | 4 | 8 | no | — |
| 544 | Q8 | — | 4 | 16 | no | — |
| 545 | Q8 | — | 8 | 16 | no | — |
| 546 | Q8 | C2×H(5,𝔽2) | 1 | 4 | yes | — |
| 547 | D4 | — | 2 | 16 | no | — |
| 548 | D4 | — | 2 | 2 | no | — |
| 549 | D4 | — | 2 | 8 | no | — |
| 550 | D4 | — | 2 | 8 | no | — |
| 551 | D4 | — | 2 | 4 | no | — |
| 552 | D4 | — | 2 | 32 | no | — |
| 553 | D4 | — | 4 | 8 | no | — |
| 554 | D4 | — | 4 | 16 | no | — |
| 555 | D4 | — | 4 | 32 | no | — |
| 556 | D4 | — | 4 | 32 | no | — |
| 557 | D4 | — | 4 | 16 | no | — |
| 558 | D4 | — | 4 | 8 | no | — |
| 559 | D4 | — | 4 | 32 | no | — |
| 560 | D4 | — | 8 | 16 | no | — |
| 561 | D4 | — | 8 | 32 | no | — |
| 562 | D4 | C2×H(5,𝔽2) | 1 | 4 | yes | — |
| 563 | C2×C4 | — | 2 | 16 | no | — |
| 564 | C2×C4 | — | 2 | 2 | no | — |
| 565 | C2×C4 | — | 2 | 2 | no | — |
| 566 | C2×C4 | — | 2 | 4 | no | — |
| 567 | C2×C4 | — | 2 | 8 | no | — |
| 568 | C2×C4 | — | 2 | 4 | no | — |
| 569 | C2×C4 | — | 2 | 8 | no | — |
| 570 | C2×C4 | — | 2 | 8 | no | — |
| 571 | C2×C4 | — | 2 | 2 | no | — |
| 572 | C2×C4 | — | 2 | 2 | no | — |
| 573 | C2×C4 | — | 2 | 4 | no | — |
| 574 | C2×C4 | — | 2 | 16 | no | — |
| 575 | C2×C4 | — | 2 | 16 | no | — |
| 576 | C2×C4 | — | 2 | 8 | no | — |
| 577 | C2×C4 | — | 2 | 4 | no | — |
| 578 | C2×C4 | — | 2 | 8 | no | — |
| 579 | C2×C4 | — | 4 | 32 | no | — |
| 580 | C2×C4 | — | 4 | 8 | no | — |
| 581 | C2×C4 | — | 4 | 4 | no | — |
| 582 | C2×C4 | — | 4 | 8 | no | — |
| 583 | C2×C4 | — | 4 | 16 | no | — |
| 584 | C2×C4 | — | 8 | 16 | no | — |
| 585 | C2×C4 | #577 | 1 | 8 | yes | — |
| 586 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 587 | C2×C4 | C23×D4 | 1 | 8 | yes | — |
| 588 | C2×C4 | C23×D4 | 1 | 4 | yes | — |
| 589 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 590 | C2×C4 | C23×D4 | 1 | 4 | yes | — |
| 591 | C2×C4 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 592 | C2×C4 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 593 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 594 | C8 | — | 2 | 8 | no | — |
| 595 | C8 | — | 2 | 8 | no | — |
| 596 | C22 | — | 2 | 8 | no | — |
| 597 | C22 | — | 2 | 2 | no | — |
| 598 | C22 | — | 2 | 4 | no | — |
| 599 | C22 | — | 2 | 4 | no | — |
| 600 | C22 | — | 2 | 16 | no | — |
| 601 | C22 | — | 4 | 4 | no | — |
| 602 | C22 | — | 4 | 16 | no | — |
| 603 | C22 | — | 4 | 4 | no | — |
| 604 | C22 | — | 4 | 8 | no | — |
| 605 | C22 | — | 4 | 8 | no | — |
| 606 | C22 | — | 4 | 16 | no | — |
| 607 | C22 | — | 8 | 16 | no | — |
| 608 | C22 | — | 16 | 32 | no | — |
| 609 | C22 | — | 16 | 16 | no | — |
| 610 | C22 | #3484 | 1 | 2 | yes | — |
| 611 | C22 | C2×#577 | 1 | 4 | yes | — |
| 612 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 613 | C4 | — | 2 | 2 | no | — |
| 614 | C4 | — | 2 | 4 | no | — |
| 615 | C4 | — | 2 | 8 | no | — |
| 616 | C4 | — | 2 | 4 | no | — |
| 617 | C4 | — | 4 | 8 | no | — |
| 618 | C4 | — | 4 | 4 | no | — |
| 619 | C4 | — | 4 | 8 | no | — |
| 620 | C4 | #3484 | 1 | 2 | yes | — |
| 621 | C4 | C2×#577 | 1 | 8 | yes | — |
| 622 | C4 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 623 | C4 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 624 | C2 | — | 4 | 8 | no | — |
| 625 | C2 | — | 4 | 2 | no | — |
| 626 | C2 | — | 4 | 4 | no | — |
| 627 | C2 | — | 8 | 8 | no | — |
| 628 | C2 | #61662 | 1 | 4 | yes | direct product factor |
| 629 | C2 | C2×#3484 | 1 | 1 | yes | characteristic |
| 630 | C2 | C22×#577 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| prime radical | C2×#3498 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C2×#532 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#3550 | C2 | semidirect |
| 3. #61662 | C2 | direct (N × H) |
| 4. C2×#3324 | C2 | semidirect |
| 5. C2×#3304 | C2 | semidirect |
| 6. C2×D4×SD16 | C2 | semidirect |
| 7. C2×#3278 | C2 | semidirect |
| 8. C2×#3208 | C2 | semidirect |
| 9. C2×#3200 | C2 | semidirect |
| 10. C2×#3107 | C2 | semidirect |
| 11. C2×#3009 | C2 | semidirect |
| 12. C2×#2979 | C2 | semidirect |
| 14. C22×#137 | C22 | semidirect |
| 15. C23×SD16 | C22 | semidirect |
| 17. #3550 | C22 | semidirect |
| 23. C2×#556 | C22 | semidirect |
| 25. C2×D4×Q8 | C22 | semidirect |
| 29. C2×#536 | C22 | semidirect |
| 32. C2×#533 | C22 | semidirect |
| 38. #3324 | C22 | semidirect |
| 39. #3304 | C22 | semidirect |
| 40. D4×SD16 | C22 | semidirect |
| 41. #3278 | C22 | semidirect |
| 42. #3208 | C22 | semidirect |
| 43. #3200 | C22 | semidirect |
| 44. C2×#492 | C22 | semidirect |
| 45. C2×#486 | C22 | semidirect |
| 46. #3107 | C22 | semidirect |
| 47. C2×#485 | C22 | semidirect |
| 48. C2×#482 | C22 | semidirect |
| 49. C2×#475 | C22 | semidirect |
| 50. C2×#474 | C22 | semidirect |
| 51. C2×#468 | C22 | semidirect |
| 52. C2×#465 | C22 | semidirect |
| 53. C2×#462 | C22 | semidirect |
| 54. C2×#460 | C22 | semidirect |
| 55. C2×#460 | C22 | semidirect |
| 56. C2×#461 | C22 | semidirect |
| 57. #3009 | C22 | semidirect |
| 59. C2×#452 | C22 | semidirect |
| 60. C2×#448 | C22 | semidirect |
| 61. C2×#450 | C22 | semidirect |
| 62. C2×#450 | C22 | semidirect |
| 63. #2979 | C22 | semidirect |
| 64. C2×C4×Q16 | C22 | semidirect |
| 65. C2×C4×SD16 | C22 | semidirect |
| 66. C2×#436 | C22 | semidirect |
| 67. C2×C8×D4 | C22 | semidirect |
| 68. C2×#431 | C22 | semidirect |
| 69. C2×#418 | C22 | semidirect |
| 70. C2×#416 | C22 | semidirect |
| 71. C2×#408 | C22 | semidirect |
| 88. C2×#137 | C23 | semidirect |
| 94. C22×SD16 | C23 | semidirect |
| 101. #556 | C23 | semidirect |
| 105. D4×Q8 | C23 | semidirect |
| 111. #536 | C23 | semidirect |
| 116. #533 | C23 | semidirect |
| 169. #492 | C23 | semidirect |
| 170. #486 | C23 | semidirect |
| 171. #485 | C23 | semidirect |
| 172. #482 | C23 | semidirect |
| 173. #475 | C23 | semidirect |
| 174. #474 | C23 | semidirect |
| 175. #468 | C23 | semidirect |
| 176. #465 | C23 | semidirect |
| 177. #462 | C23 | semidirect |
| 178. #461 | C23 | semidirect |
| 179. #460 | C23 | semidirect |
| 180. #460 | C23 | semidirect |
| 182. #452 | C23 | semidirect |
| 183. #450 | C23 | semidirect |
| 184. #450 | C23 | semidirect |
| 185. #448 | C23 | semidirect |
| 186. C4×Q16 | C23 | semidirect |
| 187. C4×SD16 | C23 | semidirect |
| 188. #436 | C23 | semidirect |
| 189. C8×D4 | C23 | semidirect |
| 190. #431 | C23 | semidirect |
| 195. #418 | C23 | semidirect |
| 196. #416 | C23 | semidirect |
| 203. #408 | C23 | semidirect |
| 628. C2 | #61662 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3498 | 2 |
| C2×#3550 | 2 |
| #61662 | 2 |
| C2×#3324 | 2 |
| C2×#3304 | 2 |
| C2×D4×SD16 | 2 |
| C2×#3278 | 2 |
| C2×#3208 | 2 |
| C2×#3200 | 2 |
| C2×#3107 | 2 |
| C2×#3009 | 2 |
| C2×#2979 | 2 |