← #44564774
Subgroups — #44564774
Order 32128.
1002 conjugacy classes of subgroups.
The subgroup lattice has 410 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #30632440 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #30632436 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #30632421 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #30632417 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #30632408 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #30632405 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | Q8×C22⋊D251 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #30632350 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #30632305 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #30632301 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #30632260 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #30632258 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #30632239 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #30632233 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | #536×C251 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#16860810 | C22 | 1 | 1 | yes | characteristic |
| 17 | C22×Dic502 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×Q8×D251 | C22 | 1 | 2 | yes | — |
| 19 | #22548714 | C22 | 1 | 2 | yes | — |
| 20 | #22548714 | C22 | 1 | 4 | yes | — |
| 21 | #22548714 | C22 | 1 | 4 | yes | — |
| 22 | #22548713 | C22 | 1 | 1 | yes | characteristic |
| 23 | #22548713 | C22 | 1 | 2 | yes | — |
| 24 | #22548713 | C22 | 1 | 2 | yes | — |
| 25 | #22548713 | C22 | 1 | 4 | yes | — |
| 26 | #22548711 | C22 | 1 | 1 | yes | characteristic |
| 27 | #22548710 | C22 | 1 | 4 | yes | — |
| 28 | #22548709 | C22 | 1 | 4 | yes | — |
| 29 | #22548708 | C22 | 1 | 4 | yes | — |
| 30 | #22548708 | C22 | 1 | 4 | yes | — |
| 31 | #22548705 | C22 | 1 | 4 | yes | — |
| 32 | #22548704 | C22 | 1 | 1 | yes | characteristic |
| 33 | #22548702 | C22 | 1 | 1 | yes | characteristic |
| 34 | #22548702 | C22 | 1 | 2 | yes | — |
| 35 | #22548701 | C22 | 1 | 4 | yes | — |
| 36 | #22548701 | C22 | 1 | 4 | yes | — |
| 37 | #22548701 | C22 | 1 | 4 | yes | — |
| 38 | #22548700 | C22 | 1 | 4 | yes | — |
| 39 | #22548697 | C22 | 1 | 4 | yes | — |
| 40 | #22548696 | C22 | 1 | 2 | yes | — |
| 41 | #22548696 | C22 | 1 | 2 | yes | — |
| 42 | #22548695 | C22 | 1 | 2 | yes | — |
| 43 | #22548694 | C22 | 1 | 2 | yes | — |
| 44 | #22548694 | C22 | 1 | 2 | yes | — |
| 45 | #22548694 | C22 | 1 | 4 | yes | — |
| 46 | #22548693 | C22 | 1 | 4 | yes | — |
| 47 | #22548692 | C22 | 1 | 4 | yes | — |
| 48 | #22548692 | C22 | 1 | 4 | yes | — |
| 49 | #22548691 | C22 | 1 | 2 | yes | — |
| 50 | #22548691 | C22 | 1 | 4 | yes | — |
| 51 | #22548687 | C22 | 1 | 2 | yes | — |
| 52 | #22548687 | C22 | 1 | 2 | yes | — |
| 53 | Q8×Dic251 | C22 | 1 | 2 | yes | — |
| 54 | C4×Dic502 | C22 | 1 | 4 | yes | — |
| 55 | #22548680 | C22 | 1 | 2 | yes | — |
| 56 | #22548680 | C22 | 1 | 4 | yes | — |
| 57 | #22548680 | C22 | 1 | 4 | yes | — |
| 58 | C4×C22⋊D251 | C22 | 1 | 2 | yes | — |
| 59 | C4×C22⋊D251 | C22 | 1 | 2 | yes | — |
| 60 | C4×C22⋊D251 | C22 | 1 | 4 | yes | — |
| 61 | (C22⋊D251)⋊C4 | C22 | 1 | 4 | yes | — |
| 62 | #22548674 | C22 | 1 | 1 | yes | characteristic |
| 63 | #22548673 | C22 | 1 | 2 | yes | — |
| 64 | #22548671 | C22 | 1 | 4 | yes | — |
| 65 | C2×C4×Dic251 | C22 | 1 | 1 | yes | characteristic |
| 66 | C2×#41×C251 | C22 | 1 | 1 | yes | characteristic |
| 67 | C22×Q8×C251 | C22 | 1 | 1 | yes | characteristic |
| 68 | C4⋊Q8×C251 | C22 | 1 | 2 | yes | — |
| 69 | #124×C251 | C22 | 1 | 2 | yes | — |
| 70 | #123×C251 | C22 | 1 | 2 | yes | — |
| 71 | #123×C251 | C22 | 1 | 2 | yes | — |
| 72 | C22⋊Q8×C251 | C22 | 1 | 2 | yes | — |
| 73 | C22⋊Q8×C251 | C22 | 1 | 2 | yes | — |
| 74 | #117×C251 | C22 | 1 | 1 | yes | characteristic |
| 75 | #16860810 | — | 4 | 2 | no | — |
| 76 | C2×Dic502 | — | 4 | 2 | no | — |
| 77 | C2×Dic502 | C23 | 1 | 2 | yes | — |
| 78 | C2×Dic502 | C23 | 1 | 4 | yes | — |
| 79 | C2×Dic502 | C23 | 1 | 4 | yes | — |
| 80 | C2×Dic502 | C23 | 1 | 2 | yes | — |
| 81 | C2×Dic502 | C23 | 1 | 1 | yes | characteristic |
| 82 | Q8×D251 | — | 4 | 4 | no | — |
| 83 | C2×D1004 | C23 | 1 | 1 | yes | characteristic |
| 84 | C2×C22⋊D251 | C23 | 1 | 2 | yes | — |
| 85 | C2×C22⋊D251 | C23 | 1 | 2 | yes | — |
| 86 | C2×C22⋊D251 | C23 | 1 | 2 | yes | — |
| 87 | C22×Dic251 | C23 | 1 | 2 | yes | — |
| 88 | C22×Dic251 | C23 | 1 | 2 | yes | — |
| 89 | C2×C4×D251 | C23 | 1 | 2 | yes | — |
| 90 | C2×C4×D251 | C23 | 1 | 4 | yes | — |
| 91 | C4⋊Dic251 | C23 | 1 | 2 | yes | — |
| 92 | C4⋊Dic251 | C23 | 1 | 4 | yes | — |
| 93 | C4⋊Dic251 | C23 | 1 | 4 | yes | — |
| 94 | Dic251⋊C4 | C23 | 1 | 4 | yes | — |
| 95 | Dic251⋊C4 | C23 | 1 | 4 | yes | — |
| 96 | Dic251⋊C4 | C23 | 1 | 4 | yes | — |
| 97 | Dic251⋊C4 | C23 | 1 | 2 | yes | — |
| 98 | Dic251⋊C4 | C23 | 1 | 2 | yes | — |
| 99 | Dic251⋊C4 | C23 | 1 | 4 | yes | — |
| 100 | Dic251⋊C4 | C23 | 1 | 4 | yes | — |
| 101 | Dic251⋊C4 | C23 | 1 | 4 | yes | — |
| 102 | Dic251⋊C4 | C23 | 1 | 4 | yes | — |
| 103 | C22⋊Dic251 | C23 | 1 | 4 | yes | — |
| 104 | C22⋊Dic251 | C23 | 1 | 2 | yes | — |
| 105 | C22⋊Dic251 | C23 | 1 | 2 | yes | — |
| 106 | C22⋊Dic251 | C23 | 1 | 2 | yes | — |
| 107 | C22⋊Dic251 | C23 | 1 | 4 | yes | — |
| 108 | (C2×D251)⋊C4 | C23 | 1 | 4 | yes | — |
| 109 | (C2×D251)⋊C4 | C23 | 1 | 4 | yes | — |
| 110 | (C2×D251)⋊C4 | C23 | 1 | 2 | yes | — |
| 111 | (C2×D251)⋊C4 | C23 | 1 | 2 | yes | — |
| 112 | (C2×D251)⋊C4 | C23 | 1 | 4 | yes | — |
| 113 | C4×Dic251 | C23 | 1 | 2 | yes | — |
| 114 | C4×Dic251 | C23 | 1 | 1 | yes | characteristic |
| 115 | C4×Dic251 | C23 | 1 | 1 | yes | characteristic |
| 116 | C4×Dic251 | C23 | 1 | 4 | yes | — |
| 117 | C4×Dic251 | C23 | 1 | 4 | yes | — |
| 118 | C4×Dic251 | C23 | 1 | 4 | yes | — |
| 119 | C4×Dic251 | C23 | 1 | 2 | yes | — |
| 120 | #41×C251 | — | 4 | 2 | no | — |
| 121 | C2×Q8×C251 | — | 4 | 2 | no | — |
| 122 | C2×Q8×C251 | C23 | 1 | 2 | yes | — |
| 123 | C2×Q8×C251 | C23 | 1 | 2 | yes | — |
| 124 | C2×Q8×C251 | C23 | 1 | 1 | yes | characteristic |
| 125 | C2×D4×C251 | C23 | 1 | 1 | yes | characteristic |
| 126 | C2×D4×C251 | C23 | 1 | 1 | yes | characteristic |
| 127 | C2×D4×C251 | C23 | 1 | 1 | yes | characteristic |
| 128 | C22×C4×C251 | C23 | 1 | 1 | yes | characteristic |
| 129 | C22×C4×C251 | C23 | 1 | 1 | yes | characteristic |
| 130 | C22×C4×C251 | C23 | 1 | 1 | yes | characteristic |
| 131 | C22×C4×C251 | C23 | 1 | 2 | yes | — |
| 132 | C4⋊C4×C251 | C23 | 1 | 2 | yes | — |
| 133 | C4⋊C4×C251 | C23 | 1 | 4 | yes | — |
| 134 | C4⋊C4×C251 | C23 | 1 | 4 | yes | — |
| 135 | C22⋊C4×C251 | C23 | 1 | 2 | yes | — |
| 136 | C22⋊C4×C251 | C23 | 1 | 4 | yes | — |
| 137 | C22⋊C4×C251 | C23 | 1 | 4 | yes | — |
| 138 | C42×C251 | C23 | 1 | 2 | yes | — |
| 139 | C22×D251 | C24 | 1 | 2 | yes | — |
| 140 | Dic502 | — | 2 | 4 | no | — |
| 141 | Dic502 | — | 2 | 8 | no | — |
| 142 | Dic502 | — | 4 | 4 | no | — |
| 143 | Dic502 | — | 4 | 2 | no | — |
| 144 | Dic502 | — | 4 | 1 | no | — |
| 145 | D1004 | — | 4 | 1 | no | — |
| 146 | C22⋊D251 | — | 2 | 4 | no | — |
| 147 | C22⋊D251 | — | 2 | 4 | no | — |
| 148 | C22⋊D251 | — | 4 | 2 | no | — |
| 149 | C2×Dic251 | — | 2 | 4 | no | — |
| 150 | C2×Dic251 | — | 4 | 2 | no | — |
| 151 | C2×Dic251 | C24 | 1 | 4 | yes | — |
| 152 | C2×Dic251 | C24 | 1 | 2 | yes | — |
| 153 | C2×Dic251 | C24 | 1 | 2 | yes | — |
| 154 | C2×Dic251 | C24 | 1 | 4 | yes | — |
| 155 | C2×Dic251 | C24 | 1 | 2 | yes | — |
| 156 | C4×D251 | — | 2 | 4 | no | — |
| 157 | C4×D251 | — | 4 | 4 | no | — |
| 158 | C23×C251 | C24 | 1 | 1 | yes | characteristic |
| 159 | C23×C251 | C24 | 1 | 1 | yes | characteristic |
| 160 | C23×C251 | C24 | 1 | 1 | yes | characteristic |
| 161 | Q8×C251 | — | 2 | 4 | no | — |
| 162 | Q8×C251 | — | 4 | 2 | no | — |
| 163 | Q8×C251 | — | 4 | 1 | no | — |
| 164 | D4×C251 | — | 4 | 1 | no | — |
| 165 | D4×C251 | — | 4 | 1 | no | — |
| 166 | D4×C251 | — | 4 | 1 | no | — |
| 167 | C2×C4×C251 | — | 2 | 2 | no | — |
| 168 | C2×C4×C251 | — | 2 | 2 | no | — |
| 169 | C2×C4×C251 | — | 2 | 2 | no | — |
| 170 | C2×C4×C251 | — | 4 | 2 | no | — |
| 171 | C2×C4×C251 | C24 | 1 | 1 | yes | characteristic |
| 172 | C2×C4×C251 | C24 | 1 | 4 | yes | — |
| 173 | C2×C4×C251 | C24 | 1 | 4 | yes | — |
| 174 | C2×C4×C251 | C24 | 1 | 1 | yes | characteristic |
| 175 | C2×C4×C251 | C24 | 1 | 1 | yes | characteristic |
| 176 | C2×C4×C251 | C24 | 1 | 1 | yes | characteristic |
| 177 | C22×C251 | — | 2 | 1 | no | — |
| 178 | C22×C251 | — | 2 | 1 | no | — |
| 179 | C22×C251 | — | 2 | 1 | no | — |
| 180 | C22×C251 | — | 2 | 2 | no | — |
| 181 | C22×C251 | — | 2 | 2 | no | — |
| 182 | C22×C251 | — | 2 | 2 | no | — |
| 183 | C22×C251 | C25 | 1 | 1 | yes | characteristic |
| 184 | C2×D251 | — | 2 | 2 | no | — |
| 185 | C2×D251 | — | 2 | 2 | no | — |
| 186 | C2×D251 | — | 2 | 2 | no | — |
| 187 | C4×C251 | — | 2 | 1 | no | — |
| 188 | C4×C251 | — | 2 | 1 | no | — |
| 189 | C4×C251 | — | 2 | 1 | no | — |
| 190 | C4×C251 | — | 2 | 4 | no | — |
| 191 | C4×C251 | — | 2 | 4 | no | — |
| 192 | C4×C251 | H(5,𝔽2) | 1 | 2 | yes | — |
| 193 | Dic251 | — | 2 | 2 | no | — |
| 194 | Dic251 | — | 2 | 4 | no | — |
| 195 | Dic251 | — | 2 | 2 | no | — |
| 196 | Dic251 | — | 2 | 4 | no | — |
| 197 | Dic251 | 2−1+4 | 1 | 4 | yes | — |
| 198 | C2×C251 | — | 4 | 1 | no | — |
| 199 | C2×C251 | — | 4 | 1 | no | — |
| 200 | C2×C251 | — | 4 | 1 | no | — |
| 201 | C2×C251 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 202 | C2×C251 | C2×2−1+4 | 1 | 2 | yes | — |
| 203 | D251 | — | 4 | 2 | no | — |
| 204 | C251 | #3550 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 205 | #3550 | — | 251 | 1 | no | maximal, Sylow |
| 206 | #563 | — | 251 | 2 | no | — |
| 207 | #563 | — | 251 | 2 | no | — |
| 208 | #559 | — | 251 | 2 | no | — |
| 209 | Q82 | — | 251 | 2 | no | — |
| 210 | #556 | — | 251 | 2 | no | — |
| 211 | #556 | — | 251 | 2 | no | — |
| 212 | D4×Q8 | — | 251 | 2 | no | — |
| 213 | D4×Q8 | — | 251 | 2 | no | — |
| 214 | #542 | — | 251 | 4 | no | — |
| 215 | #542 | — | 251 | 4 | no | — |
| 216 | #536 | — | 251 | 1 | no | — |
| 217 | #536 | — | 251 | 2 | no | — |
| 218 | #536 | D251 | 1 | 1 | yes | characteristic, complemented |
| 219 | #533 | — | 251 | 2 | no | — |
| 220 | #532 | — | 251 | 1 | no | — |
| 221 | C2×#41 | — | 251 | 1 | no | — |
| 222 | C2×#41 | C2×D251 | 1 | 1 | yes | characteristic |
| 223 | C22×Q8 | — | 251 | 2 | no | — |
| 224 | C22×Q8 | — | 251 | 1 | no | — |
| 225 | C22×Q8 | C2×D251 | 1 | 1 | yes | characteristic |
| 226 | C4⋊Q8 | — | 251 | 1 | no | — |
| 227 | C4⋊Q8 | — | 251 | 2 | no | — |
| 228 | C4⋊Q8 | — | 251 | 2 | no | — |
| 229 | C4⋊Q8 | — | 251 | 4 | no | — |
| 230 | C4⋊Q8 | — | 251 | 2 | no | — |
| 231 | C4⋊Q8 | — | 251 | 4 | no | — |
| 232 | C4⋊Q8 | — | 251 | 4 | no | — |
| 233 | C4⋊Q8 | C2×D251 | 1 | 2 | yes | — |
| 234 | #127 | — | 251 | 1 | no | — |
| 235 | #126 | — | 251 | 4 | no | — |
| 236 | #126 | — | 251 | 4 | no | — |
| 237 | #126 | — | 251 | 4 | no | — |
| 238 | #126 | — | 251 | 4 | no | — |
| 239 | #125 | — | 251 | 4 | no | — |
| 240 | #124 | — | 251 | 1 | no | — |
| 241 | #124 | — | 251 | 1 | no | — |
| 242 | #124 | — | 251 | 2 | no | — |
| 243 | #124 | — | 251 | 4 | no | — |
| 244 | #124 | — | 251 | 4 | no | — |
| 245 | #124 | — | 251 | 4 | no | — |
| 246 | #124 | C2×D251 | 1 | 2 | yes | — |
| 247 | #123 | — | 251 | 2 | no | — |
| 248 | #123 | — | 251 | 2 | no | — |
| 249 | #123 | — | 251 | 4 | no | — |
| 250 | #123 | — | 251 | 4 | no | — |
| 251 | #123 | C2×D251 | 1 | 2 | yes | — |
| 252 | #123 | C2×D251 | 1 | 2 | yes | — |
| 253 | C22⋊Q8 | — | 251 | 2 | no | — |
| 254 | C22⋊Q8 | — | 251 | 4 | no | — |
| 255 | C22⋊Q8 | — | 251 | 2 | no | — |
| 256 | C22⋊Q8 | — | 251 | 2 | no | — |
| 257 | C22⋊Q8 | — | 251 | 4 | no | — |
| 258 | C22⋊Q8 | — | 251 | 2 | no | — |
| 259 | C22⋊Q8 | — | 251 | 4 | no | — |
| 260 | C22⋊Q8 | — | 251 | 4 | no | — |
| 261 | C22⋊Q8 | — | 251 | 4 | no | — |
| 262 | C22⋊Q8 | C2×D251 | 1 | 2 | yes | — |
| 263 | C22⋊Q8 | C2×D251 | 1 | 2 | yes | — |
| 264 | #121 | — | 251 | 2 | no | — |
| 265 | #121 | — | 251 | 2 | no | — |
| 266 | C4×Q8 | — | 251 | 2 | no | — |
| 267 | C4×Q8 | — | 251 | 2 | no | — |
| 268 | C4×Q8 | — | 251 | 4 | no | — |
| 269 | C4×Q8 | — | 251 | 4 | no | — |
| 270 | C4×Q8 | — | 251 | 4 | no | — |
| 271 | C4×D4 | — | 251 | 2 | no | — |
| 272 | C4×D4 | — | 251 | 2 | no | — |
| 273 | C4×D4 | — | 251 | 4 | no | — |
| 274 | C4×D4 | — | 251 | 4 | no | — |
| 275 | #117 | — | 251 | 1 | no | — |
| 276 | #117 | — | 251 | 2 | no | — |
| 277 | #117 | — | 251 | 4 | no | — |
| 278 | #117 | C2×D251 | 1 | 1 | yes | characteristic |
| 279 | C2×C42 | — | 251 | 1 | no | — |
| 280 | #41 | — | 4 | 2 | no | — |
| 281 | #41 | — | 1004 | 2 | no | — |
| 282 | C2×Q8 | — | 4 | 2 | no | — |
| 283 | C2×Q8 | — | 1004 | 2 | no | — |
| 284 | C2×Q8 | — | 1004 | 4 | no | — |
| 285 | C2×Q8 | — | 251 | 4 | no | — |
| 286 | C2×Q8 | — | 251 | 2 | no | — |
| 287 | C2×Q8 | — | 251 | 1 | no | — |
| 288 | C2×Q8 | — | 251 | 4 | no | — |
| 289 | C2×Q8 | — | 251 | 2 | no | — |
| 290 | C2×Q8 | C22×D251 | 1 | 2 | yes | — |
| 291 | C2×Q8 | C22×D251 | 1 | 2 | yes | — |
| 292 | C2×Q8 | C22×D251 | 1 | 1 | yes | characteristic |
| 293 | C2×D4 | — | 251 | 2 | no | — |
| 294 | C2×D4 | — | 251 | 2 | no | — |
| 295 | C2×D4 | — | 251 | 2 | no | — |
| 296 | C2×D4 | — | 251 | 1 | no | — |
| 297 | C2×D4 | C22×D251 | 1 | 1 | yes | characteristic |
| 298 | C2×D4 | C22×D251 | 1 | 1 | yes | characteristic |
| 299 | C2×D4 | C22×D251 | 1 | 1 | yes | characteristic |
| 300 | C22×C4 | — | 251 | 2 | no | — |
| 301 | C22×C4 | — | 251 | 4 | no | — |
| 302 | C22×C4 | — | 251 | 2 | no | — |
| 303 | C22×C4 | — | 251 | 2 | no | — |
| 304 | C22×C4 | C22×D251 | 1 | 1 | yes | characteristic |
| 305 | C22×C4 | C22×D251 | 1 | 1 | yes | characteristic |
| 306 | C22×C4 | C22×D251 | 1 | 1 | yes | characteristic |
| 307 | C22×C4 | C22×D251 | 1 | 2 | yes | — |
| 308 | C4⋊C4 | — | 251 | 2 | no | — |
| 309 | C4⋊C4 | — | 251 | 4 | no | — |
| 310 | C4⋊C4 | — | 251 | 4 | no | — |
| 311 | C4⋊C4 | — | 251 | 4 | no | — |
| 312 | C4⋊C4 | — | 251 | 2 | no | — |
| 313 | C4⋊C4 | — | 251 | 2 | no | — |
| 314 | C4⋊C4 | — | 251 | 4 | no | — |
| 315 | C4⋊C4 | — | 251 | 4 | no | — |
| 316 | C4⋊C4 | — | 251 | 4 | no | — |
| 317 | C4⋊C4 | — | 251 | 4 | no | — |
| 318 | C4⋊C4 | — | 251 | 4 | no | — |
| 319 | C4⋊C4 | — | 251 | 4 | no | — |
| 320 | C4⋊C4 | C22×D251 | 1 | 2 | yes | — |
| 321 | C4⋊C4 | C22×D251 | 1 | 4 | yes | — |
| 322 | C4⋊C4 | C22×D251 | 1 | 4 | yes | — |
| 323 | C22⋊C4 | — | 251 | 4 | no | — |
| 324 | C22⋊C4 | — | 251 | 2 | no | — |
| 325 | C22⋊C4 | — | 251 | 2 | no | — |
| 326 | C22⋊C4 | — | 251 | 2 | no | — |
| 327 | C22⋊C4 | — | 251 | 4 | no | — |
| 328 | C22⋊C4 | — | 251 | 4 | no | — |
| 329 | C22⋊C4 | — | 251 | 2 | no | — |
| 330 | C22⋊C4 | — | 251 | 2 | no | — |
| 331 | C22⋊C4 | — | 251 | 4 | no | — |
| 332 | C22⋊C4 | — | 251 | 4 | no | — |
| 333 | C22⋊C4 | C22×D251 | 1 | 4 | yes | — |
| 334 | C22⋊C4 | C22×D251 | 1 | 2 | yes | — |
| 335 | C22⋊C4 | C22×D251 | 1 | 4 | yes | — |
| 336 | C42 | — | 251 | 2 | no | — |
| 337 | C42 | — | 251 | 1 | no | — |
| 338 | C42 | — | 251 | 1 | no | — |
| 339 | C42 | — | 251 | 4 | no | — |
| 340 | C42 | — | 251 | 4 | no | — |
| 341 | C42 | — | 251 | 2 | no | — |
| 342 | C42 | — | 251 | 4 | no | — |
| 343 | C42 | C22×D251 | 1 | 2 | yes | — |
| 344 | C23 | — | 251 | 2 | no | — |
| 345 | C23 | C23×D251 | 1 | 1 | yes | characteristic |
| 346 | C23 | C23×D251 | 1 | 1 | yes | characteristic |
| 347 | C23 | C23×D251 | 1 | 1 | yes | characteristic |
| 348 | Q8 | — | 2 | 4 | no | — |
| 349 | Q8 | — | 4 | 2 | no | — |
| 350 | Q8 | — | 4 | 1 | no | — |
| 351 | Q8 | — | 1004 | 2 | no | — |
| 352 | Q8 | — | 1004 | 4 | no | — |
| 353 | Q8 | — | 1004 | 1 | no | — |
| 354 | Q8 | — | 502 | 8 | no | — |
| 355 | Q8 | — | 502 | 4 | no | — |
| 356 | D4 | — | 4 | 1 | no | — |
| 357 | D4 | — | 4 | 1 | no | — |
| 358 | D4 | — | 4 | 1 | no | — |
| 359 | D4 | — | 1004 | 1 | no | — |
| 360 | D4 | — | 1004 | 2 | no | — |
| 361 | D4 | — | 502 | 4 | no | — |
| 362 | D4 | — | 502 | 4 | no | — |
| 363 | C2×C4 | — | 2 | 2 | no | — |
| 364 | C2×C4 | — | 2 | 2 | no | — |
| 365 | C2×C4 | — | 2 | 2 | no | — |
| 366 | C2×C4 | — | 4 | 2 | no | — |
| 367 | C2×C4 | — | 1004 | 4 | no | — |
| 368 | C2×C4 | — | 1004 | 2 | no | — |
| 369 | C2×C4 | — | 502 | 4 | no | — |
| 370 | C2×C4 | — | 502 | 4 | no | — |
| 371 | C2×C4 | — | 251 | 4 | no | — |
| 372 | C2×C4 | — | 251 | 2 | no | — |
| 373 | C2×C4 | — | 251 | 2 | no | — |
| 374 | C2×C4 | — | 251 | 4 | no | — |
| 375 | C2×C4 | — | 251 | 2 | no | — |
| 376 | C2×C4 | C23×D251 | 1 | 4 | yes | — |
| 377 | C2×C4 | C23×D251 | 1 | 1 | yes | characteristic |
| 378 | C2×C4 | C23×D251 | 1 | 1 | yes | characteristic |
| 379 | C2×C4 | C23×D251 | 1 | 4 | yes | — |
| 380 | C2×C4 | C23×D251 | 1 | 1 | yes | characteristic |
| 381 | C2×C4 | C23×D251 | 1 | 1 | yes | characteristic |
| 382 | C22 | — | 2 | 1 | no | — |
| 383 | C22 | — | 2 | 1 | no | — |
| 384 | C22 | — | 2 | 1 | no | — |
| 385 | C22 | — | 2 | 2 | no | — |
| 386 | C22 | — | 2 | 2 | no | — |
| 387 | C22 | — | 2 | 2 | no | — |
| 388 | C22 | — | 502 | 2 | no | — |
| 389 | C22 | — | 502 | 2 | no | — |
| 390 | C22 | — | 502 | 2 | no | — |
| 391 | C22 | C24×D251 | 1 | 1 | yes | characteristic |
| 392 | C4 | — | 2 | 1 | no | — |
| 393 | C4 | — | 2 | 1 | no | — |
| 394 | C4 | — | 2 | 1 | no | — |
| 395 | C4 | — | 2 | 4 | no | — |
| 396 | C4 | — | 2 | 4 | no | — |
| 397 | C4 | — | 502 | 4 | no | — |
| 398 | C4 | — | 502 | 2 | no | — |
| 399 | C4 | — | 502 | 2 | no | — |
| 400 | C4 | — | 502 | 4 | no | — |
| 401 | C4 | — | 251 | 4 | no | — |
| 402 | C4 | #22548760 | 1 | 2 | yes | — |
| 403 | C2 | — | 4 | 1 | no | — |
| 404 | C2 | — | 4 | 1 | no | — |
| 405 | C2 | — | 4 | 1 | no | — |
| 406 | C2 | — | 1004 | 2 | no | — |
| 407 | C2 | C2×#22548760 | 1 | 1 | yes | characteristic |
| 408 | C2 | 2−1+4×D251 | 1 | 2 | yes | — |
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