← #10574370
Subgroups — #10574370
Order 512.
6445 conjugacy classes of subgroups.
The subgroup lattice has 396 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #62686 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #60270 | C2 | 1 | 24 | yes | maximal, complemented |
| 3 | #60269 | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | #60268 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #60191 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #60143 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | C2×#2925 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #60099 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | C2×#568 | C22 | 1 | 6 | yes | — |
| 10 | #3461 | C4 | 1 | 6 | yes | — |
| 11 | #3461 | C4 | 1 | 6 | yes | — |
| 12 | #3460 | C4 | 1 | 6 | yes | — |
| 13 | #3460 | C4 | 1 | 6 | yes | — |
| 14 | #3459 | C4 | 1 | 4 | yes | — |
| 15 | #3459 | C4 | 1 | 4 | yes | — |
| 16 | #3458 | C22 | 1 | 1 | yes | characteristic |
| 17 | #3455 | C22 | 1 | 12 | yes | — |
| 18 | #3449 | C22 | 1 | 3 | yes | — |
| 19 | #3444 | C22 | 1 | 12 | yes | — |
| 20 | C2×C4×#41 | C22 | 1 | 3 | yes | — |
| 21 | #2995 | C22 | 1 | 48 | yes | complemented |
| 22 | #2994 | C22 | 1 | 48 | yes | complemented |
| 23 | #2993 | C22 | 1 | 48 | yes | complemented |
| 24 | #2992 | C22 | 1 | 48 | yes | complemented |
| 25 | #2991 | C22 | 1 | 8 | yes | complemented |
| 26 | #2990 | C22 | 1 | 24 | yes | complemented |
| 27 | #2989 | C22 | 1 | 24 | yes | complemented |
| 28 | #2988 | C22 | 1 | 8 | yes | complemented |
| 29 | #2961 | C22 | 1 | 24 | yes | complemented |
| 30 | #2960 | C22 | 1 | 24 | yes | complemented |
| 31 | #2933 | C22 | 1 | 48 | yes | complemented |
| 32 | #2933 | C22 | 1 | 48 | yes | complemented |
| 33 | #2932 | C22 | 1 | 24 | yes | — |
| 34 | #2931 | C22 | 1 | 24 | yes | — |
| 35 | #2925 | C22 | 1 | 12 | yes | complemented |
| 36 | #2925 | C22 | 1 | 12 | yes | complemented |
| 37 | #2925 | C22 | 1 | 24 | yes | complemented |
| 38 | C2×#433 | C22 | 1 | 12 | yes | complemented |
| 39 | C2×#432 | C22 | 1 | 6 | yes | complemented |
| 40 | C2×#431 | C22 | 1 | 6 | yes | complemented |
| 41 | #2906 | C22 | 1 | 24 | yes | complemented |
| 42 | #2906 | C22 | 1 | 24 | yes | complemented |
| 43 | #2905 | C22 | 1 | 6 | yes | — |
| 44 | #2905 | C22 | 1 | 12 | yes | complemented |
| 45 | C2×#423 | C22 | 1 | 3 | yes | — |
| 46 | C2×#423 | C22 | 1 | 12 | yes | complemented |
| 47 | C22×C4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 48 | C2×#408 | C22 | 1 | 6 | yes | — |
| 49 | C2×#405 | C22 | 1 | 6 | yes | — |
| 50 | C22×#41 | C23 | 1 | 3 | yes | — |
| 51 | #568 | — | 4 | 24 | no | — |
| 52 | C2×#131 | C23 | 1 | 48 | yes | — |
| 53 | C22×M16 | C23 | 1 | 6 | yes | — |
| 54 | C22×M16 | C23 | 1 | 24 | yes | — |
| 55 | C23×C8 | C23 | 1 | 2 | yes | — |
| 56 | #544 | C2×C4 | 1 | 6 | yes | — |
| 57 | #544 | C2×C4 | 1 | 6 | yes | — |
| 58 | #543 | C2×C4 | 1 | 4 | yes | — |
| 59 | #542 | C2×C4 | 1 | 24 | yes | — |
| 60 | #542 | C2×C4 | 1 | 24 | yes | — |
| 61 | #541 | C2×C4 | 1 | 24 | yes | — |
| 62 | #540 | C2×C4 | 1 | 24 | yes | — |
| 63 | #539 | C2×C4 | 1 | 24 | yes | — |
| 64 | #539 | C2×C4 | 1 | 24 | yes | — |
| 65 | #538 | C2×C4 | 1 | 24 | yes | — |
| 66 | #538 | C2×C4 | 1 | 24 | yes | — |
| 67 | #537 | C2×C4 | 1 | 6 | yes | — |
| 68 | #537 | C2×C4 | 1 | 6 | yes | — |
| 69 | #536 | C2×C4 | 1 | 12 | yes | — |
| 70 | #535 | C2×C4 | 1 | 12 | yes | — |
| 71 | #534 | C2×C4 | 1 | 12 | yes | — |
| 72 | #533 | C2×C4 | 1 | 12 | yes | — |
| 73 | #533 | C2×C4 | 1 | 12 | yes | — |
| 74 | #533 | C23 | 1 | 12 | yes | — |
| 75 | #532 | C2×C4 | 1 | 12 | yes | — |
| 76 | #532 | C2×C4 | 1 | 12 | yes | — |
| 77 | #532 | C23 | 1 | 12 | yes | — |
| 78 | #529 | C2×C4 | 1 | 24 | yes | — |
| 79 | #529 | C2×C4 | 1 | 24 | yes | — |
| 80 | #529 | C2×C4 | 1 | 24 | yes | — |
| 81 | #529 | C2×C4 | 1 | 24 | yes | — |
| 82 | #529 | C23 | 1 | 24 | yes | — |
| 83 | #529 | C23 | 1 | 24 | yes | — |
| 84 | #525 | C2×C4 | 1 | 24 | yes | — |
| 85 | #525 | C2×C4 | 1 | 24 | yes | — |
| 86 | #525 | C23 | 1 | 24 | yes | — |
| 87 | C4×#41 | C2×C4 | 1 | 12 | yes | — |
| 88 | C4×#41 | C2×C4 | 1 | 12 | yes | — |
| 89 | C4×#41 | C23 | 1 | 8 | yes | — |
| 90 | C4×#41 | C23 | 1 | 8 | yes | — |
| 91 | C4×#41 | C23 | 1 | 12 | yes | — |
| 92 | C4×#41 | C23 | 1 | 12 | yes | — |
| 93 | C2×C4×Q8 | C2×C4 | 1 | 3 | yes | — |
| 94 | C2×C4×Q8 | C2×C4 | 1 | 3 | yes | — |
| 95 | C2×C4×D4 | C2×C4 | 1 | 6 | yes | — |
| 96 | C2×C4×D4 | C2×C4 | 1 | 6 | yes | — |
| 97 | C2×C4×D4 | C2×C4 | 1 | 3 | yes | — |
| 98 | C2×C4×D4 | C2×C4 | 1 | 3 | yes | — |
| 99 | C2×#117 | C23 | 1 | 3 | yes | — |
| 100 | C2×#117 | C23 | 1 | 6 | yes | — |
| 101 | C22×C42 | C23 | 1 | 1 | yes | characteristic |
| 102 | C22×C42 | C23 | 1 | 6 | yes | — |
| 103 | #446 | C23 | 1 | 48 | yes | — |
| 104 | #446 | C23 | 1 | 48 | yes | — |
| 105 | C8×Q8 | C23 | 1 | 16 | yes | — |
| 106 | C8×Q8 | C23 | 1 | 16 | yes | — |
| 107 | #436 | C23 | 1 | 48 | yes | — |
| 108 | #436 | C23 | 1 | 48 | yes | — |
| 109 | #435 | C23 | 1 | 96 | yes | — |
| 110 | #435 | C23 | 1 | 96 | yes | — |
| 111 | C8×D4 | C23 | 1 | 48 | yes | — |
| 112 | C8×D4 | C23 | 1 | 48 | yes | — |
| 113 | #433 | C23 | 1 | 48 | yes | — |
| 114 | #433 | C23 | 1 | 48 | yes | — |
| 115 | #432 | C23 | 1 | 24 | yes | — |
| 116 | #432 | C23 | 1 | 24 | yes | — |
| 117 | #431 | C23 | 1 | 12 | yes | — |
| 118 | #431 | C23 | 1 | 12 | yes | — |
| 119 | #431 | C23 | 1 | 24 | yes | — |
| 120 | #424 | C23 | 1 | 48 | yes | — |
| 121 | #424 | C23 | 1 | 96 | yes | — |
| 122 | #423 | C23 | 1 | 12 | yes | — |
| 123 | #423 | C23 | 1 | 12 | yes | — |
| 124 | #423 | C23 | 1 | 24 | yes | — |
| 125 | #423 | C23 | 1 | 24 | yes | — |
| 126 | #423 | C23 | 1 | 24 | yes | — |
| 127 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 128 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 129 | C2×C4⋊C8 | C23 | 1 | 6 | yes | — |
| 130 | C2×C4⋊C8 | C23 | 1 | 6 | yes | — |
| 131 | C2×C4⋊C8 | C23 | 1 | 6 | yes | — |
| 132 | C2×C4⋊C8 | C23 | 1 | 24 | yes | — |
| 133 | C2×C4⋊C8 | C23 | 1 | 24 | yes | — |
| 134 | #408 | C23 | 1 | 24 | yes | — |
| 135 | #408 | C23 | 1 | 24 | yes | — |
| 136 | C2×C22⋊C8 | C23 | 1 | 12 | yes | — |
| 137 | C2×C22⋊C8 | C23 | 1 | 12 | yes | — |
| 138 | #405 | C23 | 1 | 24 | yes | — |
| 139 | #405 | C23 | 1 | 24 | yes | — |
| 140 | C2×#97 | C23 | 1 | 12 | yes | — |
| 141 | C2×C4×C8 | C23 | 1 | 12 | yes | — |
| 142 | C2×#41 | — | 2 | 12 | no | — |
| 143 | C2×#41 | — | 2 | 12 | no | — |
| 144 | C2×#41 | C22×C4 | 1 | 12 | yes | — |
| 145 | C2×#41 | C22×C4 | 1 | 8 | yes | — |
| 146 | C2×#41 | C22×C4 | 1 | 8 | yes | — |
| 147 | C2×#41 | C24 | 1 | 12 | yes | — |
| 148 | C22×Q8 | C22×C4 | 1 | 3 | yes | — |
| 149 | C22×D4 | C22×C4 | 1 | 6 | yes | — |
| 150 | C22×D4 | C22×C4 | 1 | 3 | yes | — |
| 151 | C23×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 152 | C23×C4 | C22×C4 | 1 | 6 | yes | — |
| 153 | C23×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 154 | C23×C4 | C22×C4 | 1 | 6 | yes | — |
| 155 | C23×C4 | C24 | 1 | 6 | yes | — |
| 156 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 157 | #131 | — | 4 | 96 | no | — |
| 158 | C2×M16 | — | 2 | 24 | no | — |
| 159 | C2×M16 | — | 4 | 48 | no | — |
| 160 | C2×M16 | C24 | 1 | 24 | yes | — |
| 161 | C2×M16 | C24 | 1 | 48 | yes | — |
| 162 | C22×C8 | — | 2 | 8 | no | — |
| 163 | C22×C8 | C24 | 1 | 6 | yes | — |
| 164 | C22×C8 | C24 | 1 | 6 | yes | — |
| 165 | C22×C8 | C24 | 1 | 12 | yes | — |
| 166 | C22×C8 | C24 | 1 | 48 | yes | — |
| 167 | C4⋊Q8 | C22×C4 | 1 | 12 | yes | — |
| 168 | C4⋊Q8 | C22×C4 | 1 | 12 | yes | — |
| 169 | C4⋊Q8 | C22×C4 | 1 | 12 | yes | — |
| 170 | #127 | C22×C4 | 1 | 12 | yes | — |
| 171 | #126 | C22×C4 | 1 | 48 | yes | — |
| 172 | #126 | C22×C4 | 1 | 48 | yes | — |
| 173 | #125 | C22×C4 | 1 | 24 | yes | — |
| 174 | #125 | C22×C4 | 1 | 24 | yes | — |
| 175 | #125 | C22×C4 | 1 | 24 | yes | — |
| 176 | #124 | C22×C4 | 1 | 24 | yes | — |
| 177 | #124 | C22×C4 | 1 | 24 | yes | — |
| 178 | #124 | C22×C4 | 1 | 24 | yes | — |
| 179 | #123 | C22×C4 | 1 | 48 | yes | — |
| 180 | #123 | C22×C4 | 1 | 48 | yes | — |
| 181 | #123 | C22×C4 | 1 | 48 | yes | — |
| 182 | C22⋊Q8 | C22×C4 | 1 | 24 | yes | — |
| 183 | C22⋊Q8 | C22×C4 | 1 | 24 | yes | — |
| 184 | C22⋊Q8 | C22×C4 | 1 | 24 | yes | — |
| 185 | C22⋊Q8 | C22×C4 | 1 | 24 | yes | — |
| 186 | C22⋊Q8 | C22×C4 | 1 | 24 | yes | — |
| 187 | C22⋊Q8 | C22×C4 | 1 | 24 | yes | — |
| 188 | #121 | C22×C4 | 1 | 24 | yes | — |
| 189 | #121 | C22×C4 | 1 | 24 | yes | — |
| 190 | #121 | C22×C4 | 1 | 24 | yes | — |
| 191 | #121 | C22×C4 | 1 | 24 | yes | — |
| 192 | #121 | C22×C4 | 1 | 24 | yes | — |
| 193 | #121 | C22×C4 | 1 | 24 | yes | — |
| 194 | #120 | C22×C4 | 1 | 48 | yes | — |
| 195 | C4×Q8 | C22×C4 | 1 | 12 | yes | — |
| 196 | C4×Q8 | C22×C4 | 1 | 12 | yes | — |
| 197 | C4×Q8 | C22×C4 | 1 | 12 | yes | — |
| 198 | C4×Q8 | C22×C4 | 1 | 12 | yes | — |
| 199 | C4×Q8 | C22×C4 | 1 | 8 | yes | — |
| 200 | C4×Q8 | C22×C4 | 1 | 8 | yes | — |
| 201 | C4×Q8 | C24 | 1 | 8 | yes | — |
| 202 | C4×Q8 | C24 | 1 | 8 | yes | — |
| 203 | C4×D4 | C22×C4 | 1 | 24 | yes | — |
| 204 | C4×D4 | C22×C4 | 1 | 24 | yes | — |
| 205 | C4×D4 | C22×C4 | 1 | 12 | yes | — |
| 206 | C4×D4 | C22×C4 | 1 | 12 | yes | — |
| 207 | C4×D4 | C22×C4 | 1 | 24 | yes | — |
| 208 | C4×D4 | C22×C4 | 1 | 24 | yes | — |
| 209 | C4×D4 | C22×C4 | 1 | 12 | yes | — |
| 210 | C4×D4 | C22×C4 | 1 | 12 | yes | — |
| 211 | C4×D4 | C22×C4 | 1 | 24 | yes | — |
| 212 | C4×D4 | C22×C4 | 1 | 24 | yes | — |
| 213 | C4×D4 | C24 | 1 | 24 | yes | — |
| 214 | C4×D4 | C24 | 1 | 24 | yes | — |
| 215 | #117 | C22×C4 | 1 | 12 | yes | — |
| 216 | #117 | C22×C4 | 1 | 24 | yes | — |
| 217 | #117 | C22×C4 | 1 | 24 | yes | — |
| 218 | #117 | C22×C4 | 1 | 24 | yes | — |
| 219 | #117 | C24 | 1 | 12 | yes | — |
| 220 | #117 | C24 | 1 | 24 | yes | — |
| 221 | C2×C4⋊C4 | C22×C4 | 1 | 3 | yes | — |
| 222 | C2×C4⋊C4 | C22×C4 | 1 | 3 | yes | — |
| 223 | C2×C4⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 224 | C2×C4⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 225 | C2×C22⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 226 | C2×C22⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 227 | C2×C22⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 228 | C2×C42 | C22×C4 | 1 | 3 | yes | — |
| 229 | C2×C42 | C22×C4 | 1 | 3 | yes | — |
| 230 | C2×C42 | C22×C4 | 1 | 6 | yes | — |
| 231 | C2×C42 | C22×C4 | 1 | 6 | yes | — |
| 232 | C2×C42 | C22×C4 | 1 | 12 | yes | — |
| 233 | C2×C42 | C22×C4 | 1 | 12 | yes | — |
| 234 | C2×C42 | C24 | 1 | 3 | yes | — |
| 235 | C2×C42 | C24 | 1 | 6 | yes | — |
| 236 | C2×C42 | C24 | 1 | 12 | yes | — |
| 237 | C2×C42 | C24 | 1 | 3 | yes | — |
| 238 | C2×C42 | C24 | 1 | 12 | yes | — |
| 239 | C4⋊C8 | C24 | 1 | 12 | yes | — |
| 240 | C4⋊C8 | C24 | 1 | 24 | yes | — |
| 241 | C4⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 242 | C4⋊C8 | C24 | 1 | 3 | yes | — |
| 243 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 244 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 245 | C4⋊C8 | C24 | 1 | 12 | yes | — |
| 246 | C4⋊C8 | C24 | 1 | 48 | yes | — |
| 247 | C4⋊C8 | C24 | 1 | 48 | yes | — |
| 248 | C22⋊C8 | C24 | 1 | 24 | yes | — |
| 249 | C22⋊C8 | C24 | 1 | 24 | yes | — |
| 250 | C22⋊C8 | C24 | 1 | 48 | yes | — |
| 251 | #97 | C24 | 1 | 48 | yes | — |
| 252 | C4×C8 | C24 | 1 | 24 | yes | — |
| 253 | C4×C8 | C24 | 1 | 24 | yes | — |
| 254 | C24 | C23×C4 | 1 | 6 | yes | — |
| 255 | C24 | C23×C4 | 1 | 1 | yes | characteristic |
| 256 | #41 | — | 2 | 48 | no | — |
| 257 | #41 | — | 2 | 24 | no | — |
| 258 | #41 | — | 2 | 24 | no | — |
| 259 | #41 | — | 4 | 16 | no | — |
| 260 | #41 | — | 8 | 8 | no | — |
| 261 | C2×Q8 | — | 2 | 12 | no | — |
| 262 | C2×Q8 | C23×C4 | 1 | 12 | yes | — |
| 263 | C2×Q8 | C23×C4 | 1 | 8 | yes | — |
| 264 | C2×Q8 | C23×C4 | 1 | 8 | yes | — |
| 265 | C2×D4 | — | 2 | 24 | no | — |
| 266 | C2×D4 | — | 2 | 12 | no | — |
| 267 | C2×D4 | C23×C4 | 1 | 24 | yes | — |
| 268 | C2×D4 | C23×C4 | 1 | 12 | yes | — |
| 269 | C2×D4 | C23×C4 | 1 | 24 | yes | — |
| 270 | C2×D4 | C23×C4 | 1 | 24 | yes | — |
| 271 | C22×C4 | — | 2 | 12 | no | — |
| 272 | C22×C4 | — | 2 | 12 | no | — |
| 273 | C22×C4 | — | 4 | 2 | no | — |
| 274 | C22×C4 | — | 4 | 12 | no | — |
| 275 | C22×C4 | — | 8 | 1 | no | — |
| 276 | C22×C4 | — | 8 | 6 | no | — |
| 277 | C22×C4 | C23×C4 | 1 | 3 | yes | — |
| 278 | C22×C4 | C23×C4 | 1 | 6 | yes | — |
| 279 | C22×C4 | C23×C4 | 1 | 12 | yes | — |
| 280 | C22×C4 | C23×C4 | 1 | 12 | yes | — |
| 281 | C22×C4 | C23×C4 | 1 | 3 | yes | — |
| 282 | C22×C4 | C23×C4 | 1 | 3 | yes | — |
| 283 | C22×C4 | C23×C4 | 1 | 3 | yes | — |
| 284 | C22×C4 | C23×C4 | 1 | 6 | yes | — |
| 285 | C22×C4 | C23×C4 | 1 | 6 | yes | — |
| 286 | C22×C4 | C23×C4 | 1 | 12 | yes | — |
| 287 | C22×C4 | C23×C4 | 1 | 12 | yes | — |
| 288 | C22×C4 | C23×C4 | 1 | 12 | yes | — |
| 289 | C22×C4 | C23×C4 | 1 | 3 | yes | — |
| 290 | C22×C4 | H(5,𝔽2) | 1 | 4 | yes | — |
| 291 | C22×C4 | 2−1+4 | 1 | 4 | yes | — |
| 292 | C22×C4 | C25 | 1 | 12 | yes | — |
| 293 | C22×C4 | C25 | 1 | 3 | yes | — |
| 294 | M16 | — | 2 | 48 | no | — |
| 295 | M16 | — | 4 | 48 | no | — |
| 296 | C2×C8 | — | 2 | 24 | no | — |
| 297 | C2×C8 | — | 2 | 12 | no | — |
| 298 | C2×C8 | — | 2 | 12 | no | — |
| 299 | C2×C8 | — | 4 | 48 | no | — |
| 300 | C2×C8 | C25 | 1 | 2 | yes | — |
| 301 | C2×C8 | C25 | 1 | 6 | yes | — |
| 302 | C2×C8 | C25 | 1 | 24 | yes | — |
| 303 | C4⋊C4 | C23×C4 | 1 | 12 | yes | — |
| 304 | C4⋊C4 | C23×C4 | 1 | 12 | yes | — |
| 305 | C4⋊C4 | C23×C4 | 1 | 24 | yes | — |
| 306 | C4⋊C4 | C23×C4 | 1 | 24 | yes | — |
| 307 | C4⋊C4 | C23×C4 | 1 | 24 | yes | — |
| 308 | C4⋊C4 | C23×C4 | 1 | 24 | yes | — |
| 309 | C4⋊C4 | C23×C4 | 1 | 24 | yes | — |
| 310 | C4⋊C4 | C23×C4 | 1 | 24 | yes | — |
| 311 | C22⋊C4 | C23×C4 | 1 | 24 | yes | — |
| 312 | C22⋊C4 | C23×C4 | 1 | 24 | yes | — |
| 313 | C22⋊C4 | C23×C4 | 1 | 24 | yes | — |
| 314 | C22⋊C4 | C23×C4 | 1 | 48 | yes | — |
| 315 | C22⋊C4 | C23×C4 | 1 | 48 | yes | — |
| 316 | C42 | C23×C4 | 1 | 3 | yes | — |
| 317 | C42 | C23×C4 | 1 | 3 | yes | — |
| 318 | C42 | C23×C4 | 1 | 12 | yes | — |
| 319 | C42 | C23×C4 | 1 | 6 | yes | — |
| 320 | C42 | C23×C4 | 1 | 12 | yes | — |
| 321 | C42 | C23×C4 | 1 | 12 | yes | — |
| 322 | C42 | C23×C4 | 1 | 12 | yes | — |
| 323 | C42 | C23×C4 | 1 | 12 | yes | — |
| 324 | C42 | C25 | 1 | 12 | yes | — |
| 325 | C42 | C25 | 1 | 1 | yes | characteristic |
| 326 | C42 | C25 | 1 | 3 | yes | — |
| 327 | C23 | — | 2 | 12 | no | — |
| 328 | C23 | — | 4 | 1 | no | — |
| 329 | C23 | — | 4 | 1 | no | — |
| 330 | C23 | — | 4 | 6 | no | — |
| 331 | C23 | — | 4 | 6 | no | — |
| 332 | C23 | #520 | 1 | 4 | yes | — |
| 333 | C23 | C24×C4 | 1 | 12 | yes | — |
| 334 | C23 | C24×C4 | 1 | 3 | yes | — |
| 335 | Q8 | — | 2 | 24 | no | — |
| 336 | Q8 | — | 4 | 8 | no | — |
| 337 | Q8 | — | 4 | 8 | no | — |
| 338 | D4 | — | 2 | 48 | no | — |
| 339 | D4 | — | 2 | 24 | no | — |
| 340 | D4 | — | 4 | 24 | no | — |
| 341 | D4 | — | 4 | 24 | no | — |
| 342 | C2×C4 | — | 2 | 12 | no | — |
| 343 | C2×C4 | — | 2 | 12 | no | — |
| 344 | C2×C4 | — | 2 | 12 | no | — |
| 345 | C2×C4 | — | 2 | 24 | no | — |
| 346 | C2×C4 | — | 2 | 6 | no | — |
| 347 | C2×C4 | — | 2 | 24 | no | — |
| 348 | C2×C4 | — | 4 | 3 | no | — |
| 349 | C2×C4 | — | 4 | 12 | no | — |
| 350 | C2×C4 | — | 4 | 6 | no | — |
| 351 | C2×C4 | — | 4 | 3 | no | — |
| 352 | C2×C4 | — | 4 | 3 | no | — |
| 353 | C2×C4 | — | 4 | 12 | no | — |
| 354 | C2×C4 | — | 4 | 6 | no | — |
| 355 | C2×C4 | — | 4 | 12 | no | — |
| 356 | C2×C4 | #520 | 1 | 12 | yes | — |
| 357 | C2×C4 | C24×C4 | 1 | 1 | yes | characteristic |
| 358 | C2×C4 | C24×C4 | 1 | 3 | yes | — |
| 359 | C2×C4 | C24×C4 | 1 | 3 | yes | — |
| 360 | C2×C4 | C24×C4 | 1 | 12 | yes | — |
| 361 | C2×C4 | C24×C4 | 1 | 12 | yes | — |
| 362 | C2×C4 | C24×C4 | 1 | 12 | yes | — |
| 363 | C2×C4 | C24×C4 | 1 | 3 | yes | — |
| 364 | C2×C4 | C24×C4 | 1 | 1 | yes | characteristic |
| 365 | C2×C4 | C2×H(5,𝔽2) | 1 | 6 | yes | — |
| 366 | C2×C4 | C2×2−1+4 | 1 | 6 | yes | — |
| 367 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 368 | C8 | — | 2 | 24 | no | — |
| 369 | C8 | — | 2 | 2 | no | — |
| 370 | C8 | — | 2 | 6 | no | — |
| 371 | C22 | — | 2 | 3 | no | — |
| 372 | C22 | — | 2 | 3 | no | — |
| 373 | C22 | — | 2 | 12 | no | — |
| 374 | C22 | — | 2 | 12 | no | — |
| 375 | C22 | — | 2 | 12 | no | — |
| 376 | C22 | — | 4 | 4 | no | — |
| 377 | C22 | — | 8 | 12 | no | — |
| 378 | C22 | C2×#520 | 1 | 6 | yes | — |
| 379 | C22 | C25×C4 | 1 | 1 | yes | characteristic |
| 380 | C4 | — | 2 | 3 | no | — |
| 381 | C4 | — | 2 | 12 | no | — |
| 382 | C4 | — | 2 | 1 | no | — |
| 383 | C4 | — | 2 | 3 | no | — |
| 384 | C4 | — | 2 | 12 | no | — |
| 385 | C4 | — | 2 | 12 | no | — |
| 386 | C4 | C2×#520 | 1 | 6 | yes | — |
| 387 | C4 | #3573 | 1 | 2 | yes | — |
| 388 | C4 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 389 | C4 | C22×2−1+4 | 1 | 1 | yes | characteristic |
| 390 | C2 | — | 2 | 6 | no | — |
| 391 | C2 | — | 4 | 12 | no | — |
| 392 | C2 | C22×#520 | 1 | 1 | yes | characteristic |
| 393 | C2 | C2×#3573 | 1 | 1 | yes | characteristic |
| 394 | C2 | #63076 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta