← #44564899
Subgroups — #44564899
Order 32128.
1024 conjugacy classes of subgroups.
The subgroup lattice has 402 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #30632441 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #30632435 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #30632393 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #30632390 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #30632385 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #30632338 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #30632338 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #30632317 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #30632293 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #30632285 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #30632284 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #30632268 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #30632237 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #30632221 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C2×#125×C251 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#16860810 | C22 | 1 | 2 | yes | — |
| 17 | C2×#16860810 | C22 | 1 | 4 | yes | — |
| 18 | #22548715 | C22 | 1 | 1 | yes | characteristic |
| 19 | #22548714 | C22 | 1 | 2 | yes | — |
| 20 | #22548714 | C22 | 1 | 4 | yes | — |
| 21 | #22548712 | C22 | 1 | 1 | yes | characteristic |
| 22 | #22548710 | C22 | 1 | 4 | yes | — |
| 23 | #22548710 | C22 | 1 | 4 | yes | — |
| 24 | #22548709 | C22 | 1 | 2 | yes | — |
| 25 | #22548707 | C22 | 1 | 1 | yes | characteristic |
| 26 | #22548706 | C22 | 1 | 2 | yes | — |
| 27 | #22548705 | C22 | 1 | 4 | yes | — |
| 28 | #22548703 | C22 | 1 | 1 | yes | characteristic |
| 29 | #22548703 | C22 | 1 | 2 | yes | — |
| 30 | #22548700 | C22 | 1 | 4 | yes | — |
| 31 | #22548700 | C22 | 1 | 4 | yes | — |
| 32 | #22548700 | C22 | 1 | 4 | yes | — |
| 33 | #22548700 | C22 | 1 | 4 | yes | — |
| 34 | #22548700 | C22 | 1 | 4 | yes | — |
| 35 | #22548698 | C22 | 1 | 2 | yes | — |
| 36 | #22548698 | C22 | 1 | 4 | yes | — |
| 37 | #22548695 | C22 | 1 | 4 | yes | — |
| 38 | #22548695 | C22 | 1 | 4 | yes | — |
| 39 | #22548694 | C22 | 1 | 1 | yes | characteristic |
| 40 | #22548693 | C22 | 1 | 4 | yes | — |
| 41 | #22548693 | C22 | 1 | 4 | yes | — |
| 42 | #22548693 | C22 | 1 | 4 | yes | — |
| 43 | #22548693 | C22 | 1 | 4 | yes | — |
| 44 | #22548690 | C22 | 1 | 4 | yes | — |
| 45 | #22548690 | C22 | 1 | 4 | yes | — |
| 46 | #22548690 | C22 | 1 | 2 | yes | — |
| 47 | #22548690 | C22 | 1 | 4 | yes | — |
| 48 | #22548690 | C22 | 1 | 2 | yes | — |
| 49 | #22548689 | C22 | 1 | 1 | yes | characteristic |
| 50 | #22548689 | C22 | 1 | 2 | yes | — |
| 51 | #22548689 | C22 | 1 | 2 | yes | — |
| 52 | #22548689 | C22 | 1 | 4 | yes | — |
| 53 | C4×Dic502 | C22 | 1 | 1 | yes | characteristic |
| 54 | C4×D1004 | C22 | 1 | 1 | yes | characteristic |
| 55 | C4×D1004 | C22 | 1 | 2 | yes | — |
| 56 | C4×D1004 | C22 | 1 | 2 | yes | — |
| 57 | #22548677 | C22 | 1 | 4 | yes | — |
| 58 | #22548677 | C22 | 1 | 2 | yes | — |
| 59 | #22548677 | C22 | 1 | 2 | yes | — |
| 60 | C4×C22⋊D251 | C22 | 1 | 2 | yes | — |
| 61 | C4×C22⋊D251 | C22 | 1 | 4 | yes | — |
| 62 | #22548673 | C22 | 1 | 2 | yes | — |
| 63 | #22548672 | C22 | 1 | 2 | yes | — |
| 64 | C4⋊C4×D251 | C22 | 1 | 4 | yes | — |
| 65 | C4⋊C4×D251 | C22 | 1 | 2 | yes | — |
| 66 | #125×C251 | C22 | 1 | 2 | yes | — |
| 67 | #125×C251 | C22 | 1 | 2 | yes | — |
| 68 | #125×C251 | C22 | 1 | 2 | yes | — |
| 69 | #125×C251 | C22 | 1 | 2 | yes | — |
| 70 | C2×C4⋊C4×C251 | C22 | 1 | 2 | yes | — |
| 71 | C2×C4⋊C4×C251 | C22 | 1 | 1 | yes | characteristic |
| 72 | C2×C4⋊C4×C251 | C22 | 1 | 2 | yes | — |
| 73 | C2×C4⋊C4×C251 | C22 | 1 | 1 | yes | characteristic |
| 74 | C2×C42×C251 | C22 | 1 | 1 | yes | characteristic |
| 75 | #16860810 | — | 4 | 4 | no | — |
| 76 | #16860810 | — | 4 | 8 | no | — |
| 77 | C2×Dic502 | C23 | 1 | 4 | yes | — |
| 78 | C2×Dic502 | C23 | 1 | 2 | yes | — |
| 79 | C2×Dic502 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×D1004 | C23 | 1 | 2 | yes | — |
| 81 | C2×D1004 | C23 | 1 | 4 | yes | — |
| 82 | C2×D1004 | C23 | 1 | 2 | yes | — |
| 83 | C2×D1004 | C23 | 1 | 4 | yes | — |
| 84 | C2×D1004 | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×D1004 | C23 | 1 | 2 | yes | — |
| 86 | C2×C22⋊D251 | C23 | 1 | 4 | yes | — |
| 87 | C2×C22⋊D251 | C23 | 1 | 2 | yes | — |
| 88 | C2×C4×D251 | C23 | 1 | 2 | yes | — |
| 89 | C2×C4×D251 | C23 | 1 | 4 | yes | — |
| 90 | C2×C4×D251 | C23 | 1 | 4 | yes | — |
| 91 | C2×C4×D251 | C23 | 1 | 4 | yes | — |
| 92 | C2×C4×D251 | C23 | 1 | 4 | yes | — |
| 93 | C4⋊Dic251 | C23 | 1 | 2 | yes | — |
| 94 | C4⋊Dic251 | C23 | 1 | 4 | yes | — |
| 95 | C4⋊Dic251 | C23 | 1 | 2 | yes | — |
| 96 | C4⋊Dic251 | C23 | 1 | 1 | yes | characteristic |
| 97 | C4⋊Dic251 | C23 | 1 | 1 | yes | characteristic |
| 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 | 2 | yes | — |
| 102 | Dic251⋊C4 | C23 | 1 | 2 | yes | — |
| 103 | Dic251⋊C4 | C23 | 1 | 4 | yes | — |
| 104 | Dic251⋊C4 | C23 | 1 | 2 | yes | — |
| 105 | C22⋊Dic251 | C23 | 1 | 2 | yes | — |
| 106 | (C2×D251)⋊C4 | C23 | 1 | 2 | yes | — |
| 107 | (C2×D251)⋊C4 | C23 | 1 | 2 | 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 | (C2×D251)⋊C4 | C23 | 1 | 4 | yes | — |
| 114 | (C2×D251)⋊C4 | C23 | 1 | 4 | yes | — |
| 115 | (C2×D251)⋊C4 | C23 | 1 | 4 | yes | — |
| 116 | (C2×D251)⋊C4 | C23 | 1 | 4 | yes | — |
| 117 | C4×Dic251 | C23 | 1 | 2 | yes | — |
| 118 | C4×Dic251 | C23 | 1 | 4 | yes | — |
| 119 | C22×C4×C251 | C23 | 1 | 1 | yes | characteristic |
| 120 | C22×C4×C251 | C23 | 1 | 2 | yes | — |
| 121 | C22×C4×C251 | C23 | 1 | 1 | yes | characteristic |
| 122 | C22×C4×C251 | C23 | 1 | 1 | yes | characteristic |
| 123 | C22×C4×C251 | C23 | 1 | 2 | yes | — |
| 124 | C4⋊C4×C251 | C23 | 1 | 2 | yes | — |
| 125 | C4⋊C4×C251 | C23 | 1 | 4 | yes | — |
| 126 | C4⋊C4×C251 | C23 | 1 | 2 | yes | — |
| 127 | C4⋊C4×C251 | C23 | 1 | 4 | yes | — |
| 128 | C4⋊C4×C251 | C23 | 1 | 4 | yes | — |
| 129 | C4⋊C4×C251 | C23 | 1 | 4 | yes | — |
| 130 | C4⋊C4×C251 | C23 | 1 | 2 | yes | — |
| 131 | C4⋊C4×C251 | C23 | 1 | 2 | yes | — |
| 132 | C42×C251 | C23 | 1 | 1 | yes | characteristic |
| 133 | C42×C251 | C23 | 1 | 1 | yes | characteristic |
| 134 | C42×C251 | C23 | 1 | 1 | yes | characteristic |
| 135 | C42×C251 | C23 | 1 | 1 | yes | characteristic |
| 136 | C22×D251 | C24 | 1 | 2 | yes | — |
| 137 | C22×D251 | C24 | 1 | 4 | yes | — |
| 138 | Dic502 | — | 4 | 1 | no | — |
| 139 | Dic502 | — | 4 | 4 | no | — |
| 140 | Dic502 | — | 4 | 2 | no | — |
| 141 | D1004 | — | 2 | 4 | no | — |
| 142 | D1004 | — | 4 | 4 | no | — |
| 143 | D1004 | — | 4 | 2 | no | — |
| 144 | D1004 | — | 4 | 1 | no | — |
| 145 | D1004 | — | 4 | 4 | no | — |
| 146 | D1004 | — | 4 | 2 | no | — |
| 147 | C22⋊D251 | — | 2 | 8 | no | — |
| 148 | C22⋊D251 | — | 2 | 4 | no | — |
| 149 | C2×Dic251 | C24 | 1 | 2 | yes | — |
| 150 | C2×Dic251 | C24 | 1 | 2 | yes | — |
| 151 | C2×Dic251 | C24 | 1 | 2 | yes | — |
| 152 | C2×Dic251 | C24 | 1 | 4 | yes | — |
| 153 | C4×D251 | — | 2 | 4 | no | — |
| 154 | C4×D251 | — | 4 | 4 | no | — |
| 155 | C4×D251 | — | 4 | 4 | no | — |
| 156 | C4×D251 | — | 4 | 4 | no | — |
| 157 | C4×D251 | — | 4 | 4 | no | — |
| 158 | C23×C251 | C24 | 1 | 1 | yes | characteristic |
| 159 | C2×C4×C251 | — | 2 | 2 | no | — |
| 160 | C2×C4×C251 | — | 2 | 4 | no | — |
| 161 | C2×C4×C251 | — | 2 | 2 | no | — |
| 162 | C2×C4×C251 | — | 4 | 2 | no | — |
| 163 | C2×C4×C251 | — | 4 | 1 | no | — |
| 164 | C2×C4×C251 | C24 | 1 | 1 | yes | characteristic |
| 165 | C2×C4×C251 | C24 | 1 | 1 | yes | characteristic |
| 166 | C2×C4×C251 | C24 | 1 | 1 | yes | characteristic |
| 167 | C2×C4×C251 | C24 | 1 | 1 | yes | characteristic |
| 168 | C2×C4×C251 | C24 | 1 | 1 | yes | characteristic |
| 169 | C2×C4×C251 | C24 | 1 | 4 | yes | — |
| 170 | C2×C4×C251 | C24 | 1 | 4 | yes | — |
| 171 | C2×C4×C251 | C24 | 1 | 1 | yes | characteristic |
| 172 | C22×C251 | — | 2 | 1 | no | — |
| 173 | C22×C251 | — | 2 | 1 | no | — |
| 174 | C22×C251 | H(5,𝔽2) | 1 | 2 | yes | — |
| 175 | C22×C251 | C25 | 1 | 1 | yes | characteristic |
| 176 | C2×D251 | — | 2 | 2 | no | — |
| 177 | C2×D251 | — | 2 | 4 | no | — |
| 178 | C2×D251 | — | 2 | 2 | no | — |
| 179 | C2×D251 | — | 2 | 4 | no | — |
| 180 | C2×D251 | — | 2 | 4 | no | — |
| 181 | C2×D251 | — | 2 | 2 | no | — |
| 182 | C4×C251 | — | 2 | 1 | no | — |
| 183 | C4×C251 | — | 2 | 4 | no | — |
| 184 | C4×C251 | — | 2 | 1 | no | — |
| 185 | C4×C251 | — | 2 | 1 | no | — |
| 186 | C4×C251 | — | 2 | 4 | no | — |
| 187 | C4×C251 | — | 2 | 1 | no | — |
| 188 | C4×C251 | — | 2 | 1 | no | — |
| 189 | C4×C251 | 2−1+4 | 1 | 2 | yes | — |
| 190 | Dic251 | — | 2 | 4 | no | — |
| 191 | Dic251 | — | 2 | 2 | no | — |
| 192 | Dic251 | — | 2 | 2 | no | — |
| 193 | Dic251 | — | 2 | 2 | no | — |
| 194 | C2×C251 | — | 2 | 2 | no | — |
| 195 | C2×C251 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 196 | C2×C251 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 197 | C2×C251 | #585 | 1 | 1 | yes | characteristic |
| 198 | D251 | — | 4 | 2 | no | — |
| 199 | D251 | — | 4 | 4 | no | — |
| 200 | C251 | #3559 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 201 | #3559 | — | 251 | 1 | no | maximal, Sylow |
| 202 | #563 | — | 251 | 2 | no | — |
| 203 | #562 | — | 251 | 2 | no | — |
| 204 | #554 | — | 251 | 2 | no | — |
| 205 | #553 | — | 251 | 2 | no | — |
| 206 | #553 | — | 251 | 2 | no | — |
| 207 | #547 | — | 251 | 4 | no | — |
| 208 | #547 | — | 251 | 2 | no | — |
| 209 | #544 | — | 251 | 2 | no | — |
| 210 | #540 | — | 251 | 2 | no | — |
| 211 | #539 | — | 251 | 4 | no | — |
| 212 | #539 | — | 251 | 2 | no | — |
| 213 | #537 | — | 251 | 2 | no | — |
| 214 | #532 | — | 251 | 1 | no | — |
| 215 | #529 | — | 251 | 1 | no | — |
| 216 | C2×#125 | D251 | 1 | 1 | yes | characteristic, complemented |
| 217 | C2×#41 | — | 251 | 2 | no | — |
| 218 | C2×#41 | — | 251 | 4 | no | — |
| 219 | C4⋊Q8 | — | 251 | 2 | no | — |
| 220 | C4⋊Q8 | — | 251 | 4 | no | — |
| 221 | C4⋊Q8 | — | 251 | 1 | no | — |
| 222 | #127 | — | 251 | 1 | no | — |
| 223 | #126 | — | 251 | 4 | no | — |
| 224 | #126 | — | 251 | 4 | no | — |
| 225 | #126 | — | 251 | 2 | no | — |
| 226 | #125 | — | 251 | 4 | no | — |
| 227 | #125 | — | 251 | 2 | no | — |
| 228 | #125 | — | 251 | 1 | no | — |
| 229 | #125 | C2×D251 | 1 | 2 | yes | — |
| 230 | #125 | C2×D251 | 1 | 2 | yes | — |
| 231 | #125 | C2×D251 | 1 | 2 | yes | — |
| 232 | #125 | C2×D251 | 1 | 2 | yes | — |
| 233 | #124 | — | 251 | 1 | no | — |
| 234 | #124 | — | 251 | 2 | no | — |
| 235 | #123 | — | 251 | 2 | no | — |
| 236 | #123 | — | 251 | 4 | no | — |
| 237 | #123 | — | 251 | 4 | no | — |
| 238 | #123 | — | 251 | 4 | no | — |
| 239 | #123 | — | 251 | 4 | no | — |
| 240 | #123 | — | 251 | 4 | no | — |
| 241 | #123 | — | 251 | 4 | no | — |
| 242 | C22⋊Q8 | — | 251 | 1 | no | — |
| 243 | C22⋊Q8 | — | 251 | 4 | no | — |
| 244 | C22⋊Q8 | — | 251 | 4 | no | — |
| 245 | C22⋊Q8 | — | 251 | 4 | no | — |
| 246 | C22⋊Q8 | — | 251 | 4 | no | — |
| 247 | C22⋊Q8 | — | 251 | 4 | no | — |
| 248 | C22⋊Q8 | — | 251 | 4 | no | — |
| 249 | #121 | — | 251 | 1 | no | — |
| 250 | #121 | — | 251 | 2 | no | — |
| 251 | #121 | — | 251 | 2 | no | — |
| 252 | #121 | — | 251 | 4 | no | — |
| 253 | #121 | — | 251 | 4 | no | — |
| 254 | #121 | — | 251 | 4 | no | — |
| 255 | #121 | — | 251 | 2 | no | — |
| 256 | #121 | — | 251 | 4 | no | — |
| 257 | #121 | — | 251 | 2 | no | — |
| 258 | C4×Q8 | — | 251 | 1 | no | — |
| 259 | C4×D4 | — | 251 | 2 | no | — |
| 260 | C4×D4 | — | 251 | 4 | no | — |
| 261 | C4×D4 | — | 251 | 4 | no | — |
| 262 | C4×D4 | — | 251 | 2 | no | — |
| 263 | C4×D4 | — | 251 | 2 | no | — |
| 264 | C4×D4 | — | 251 | 1 | no | — |
| 265 | C4×D4 | — | 251 | 2 | no | — |
| 266 | C4×D4 | — | 251 | 2 | no | — |
| 267 | #117 | — | 251 | 2 | no | — |
| 268 | #117 | — | 251 | 2 | no | — |
| 269 | C2×C4⋊C4 | — | 251 | 4 | no | — |
| 270 | C2×C4⋊C4 | — | 251 | 2 | no | — |
| 271 | C2×C4⋊C4 | C2×D251 | 1 | 2 | yes | — |
| 272 | C2×C4⋊C4 | C2×D251 | 1 | 1 | yes | characteristic |
| 273 | C2×C4⋊C4 | C2×D251 | 1 | 2 | yes | — |
| 274 | C2×C4⋊C4 | C2×D251 | 1 | 1 | yes | characteristic |
| 275 | C2×C42 | C2×D251 | 1 | 1 | yes | characteristic |
| 276 | #41 | — | 1004 | 4 | no | — |
| 277 | #41 | — | 1004 | 8 | no | — |
| 278 | C2×Q8 | — | 251 | 1 | no | — |
| 279 | C2×Q8 | — | 251 | 4 | no | — |
| 280 | C2×Q8 | — | 251 | 2 | no | — |
| 281 | C2×D4 | — | 251 | 2 | no | — |
| 282 | C2×D4 | — | 251 | 4 | no | — |
| 283 | C2×D4 | — | 251 | 4 | no | — |
| 284 | C2×D4 | — | 251 | 1 | no | — |
| 285 | C2×D4 | — | 251 | 2 | no | — |
| 286 | C2×D4 | — | 251 | 4 | no | — |
| 287 | C2×D4 | — | 251 | 2 | no | — |
| 288 | C2×D4 | — | 251 | 2 | no | — |
| 289 | C22×C4 | — | 251 | 4 | no | — |
| 290 | C22×C4 | — | 251 | 4 | no | — |
| 291 | C22×C4 | — | 251 | 4 | no | — |
| 292 | C22×C4 | — | 251 | 4 | no | — |
| 293 | C22×C4 | — | 251 | 2 | no | — |
| 294 | C22×C4 | C22×D251 | 1 | 1 | yes | characteristic |
| 295 | C22×C4 | C22×D251 | 1 | 1 | yes | characteristic |
| 296 | C22×C4 | C22×D251 | 1 | 2 | yes | — |
| 297 | C22×C4 | C22×D251 | 1 | 1 | yes | characteristic |
| 298 | C22×C4 | C22×D251 | 1 | 2 | yes | — |
| 299 | C4⋊C4 | — | 251 | 2 | no | — |
| 300 | C4⋊C4 | — | 251 | 2 | no | — |
| 301 | C4⋊C4 | — | 251 | 4 | no | — |
| 302 | C4⋊C4 | — | 251 | 4 | no | — |
| 303 | C4⋊C4 | — | 251 | 4 | no | — |
| 304 | C4⋊C4 | — | 251 | 2 | no | — |
| 305 | C4⋊C4 | — | 251 | 2 | no | — |
| 306 | C4⋊C4 | — | 251 | 4 | no | — |
| 307 | C4⋊C4 | — | 251 | 2 | no | — |
| 308 | C4⋊C4 | — | 251 | 2 | no | — |
| 309 | C4⋊C4 | — | 251 | 1 | no | — |
| 310 | C4⋊C4 | — | 251 | 1 | no | — |
| 311 | C4⋊C4 | C22×D251 | 1 | 2 | yes | — |
| 312 | C4⋊C4 | C22×D251 | 1 | 4 | yes | — |
| 313 | C4⋊C4 | C22×D251 | 1 | 2 | yes | — |
| 314 | C4⋊C4 | C22×D251 | 1 | 4 | yes | — |
| 315 | C4⋊C4 | C22×D251 | 1 | 4 | yes | — |
| 316 | C4⋊C4 | C22×D251 | 1 | 4 | yes | — |
| 317 | C4⋊C4 | C22×D251 | 1 | 2 | yes | — |
| 318 | C4⋊C4 | C22×D251 | 1 | 2 | yes | — |
| 319 | C22⋊C4 | — | 251 | 2 | no | — |
| 320 | C22⋊C4 | — | 251 | 2 | no | — |
| 321 | C22⋊C4 | — | 251 | 4 | no | — |
| 322 | C22⋊C4 | — | 251 | 2 | no | — |
| 323 | C22⋊C4 | — | 251 | 2 | no | — |
| 324 | C22⋊C4 | — | 251 | 4 | no | — |
| 325 | C22⋊C4 | — | 251 | 4 | no | — |
| 326 | C22⋊C4 | — | 251 | 4 | no | — |
| 327 | C22⋊C4 | — | 251 | 4 | no | — |
| 328 | C22⋊C4 | — | 251 | 4 | no | — |
| 329 | C22⋊C4 | — | 251 | 4 | no | — |
| 330 | C22⋊C4 | — | 251 | 2 | no | — |
| 331 | C42 | — | 251 | 2 | no | — |
| 332 | C42 | — | 251 | 4 | no | — |
| 333 | C42 | C22×D251 | 1 | 1 | yes | characteristic |
| 334 | C42 | C22×D251 | 1 | 1 | yes | characteristic |
| 335 | C42 | C22×D251 | 1 | 1 | yes | characteristic |
| 336 | C42 | C22×D251 | 1 | 1 | yes | characteristic |
| 337 | C23 | — | 251 | 2 | no | — |
| 338 | C23 | — | 251 | 4 | no | — |
| 339 | C23 | C23×D251 | 1 | 1 | yes | characteristic |
| 340 | Q8 | — | 1004 | 4 | no | — |
| 341 | Q8 | — | 1004 | 2 | no | — |
| 342 | Q8 | — | 1004 | 1 | no | — |
| 343 | D4 | — | 1004 | 4 | no | — |
| 344 | D4 | — | 1004 | 2 | no | — |
| 345 | D4 | — | 1004 | 4 | no | — |
| 346 | D4 | — | 1004 | 2 | no | — |
| 347 | D4 | — | 1004 | 1 | no | — |
| 348 | D4 | — | 502 | 4 | no | — |
| 349 | D4 | — | 502 | 8 | no | — |
| 350 | D4 | — | 502 | 4 | no | — |
| 351 | C2×C4 | — | 2 | 2 | no | — |
| 352 | C2×C4 | — | 2 | 4 | no | — |
| 353 | C2×C4 | — | 2 | 2 | no | — |
| 354 | C2×C4 | — | 4 | 2 | no | — |
| 355 | C2×C4 | — | 4 | 1 | no | — |
| 356 | C2×C4 | — | 1004 | 4 | no | — |
| 357 | C2×C4 | — | 1004 | 4 | no | — |
| 358 | C2×C4 | — | 1004 | 4 | no | — |
| 359 | C2×C4 | — | 1004 | 4 | no | — |
| 360 | C2×C4 | — | 502 | 4 | no | — |
| 361 | C2×C4 | — | 251 | 2 | no | — |
| 362 | C2×C4 | — | 251 | 2 | no | — |
| 363 | C2×C4 | — | 251 | 2 | no | — |
| 364 | C2×C4 | — | 251 | 4 | no | — |
| 365 | C2×C4 | C23×D251 | 1 | 4 | yes | — |
| 366 | C2×C4 | C23×D251 | 1 | 1 | yes | characteristic |
| 367 | C2×C4 | C23×D251 | 1 | 1 | yes | characteristic |
| 368 | C2×C4 | C23×D251 | 1 | 1 | yes | characteristic |
| 369 | C2×C4 | C23×D251 | 1 | 1 | yes | characteristic |
| 370 | C2×C4 | C23×D251 | 1 | 1 | yes | characteristic |
| 371 | C2×C4 | C23×D251 | 1 | 4 | yes | — |
| 372 | C2×C4 | C23×D251 | 1 | 1 | yes | characteristic |
| 373 | C22 | — | 2 | 1 | no | — |
| 374 | C22 | — | 2 | 1 | no | — |
| 375 | C22 | — | 502 | 2 | no | — |
| 376 | C22 | — | 502 | 4 | no | — |
| 377 | C22 | — | 502 | 2 | no | — |
| 378 | C22 | — | 502 | 4 | no | — |
| 379 | C22 | — | 502 | 4 | no | — |
| 380 | C22 | — | 502 | 2 | no | — |
| 381 | C22 | #22548761 | 1 | 2 | yes | — |
| 382 | C22 | C24×D251 | 1 | 1 | yes | characteristic |
| 383 | C4 | — | 2 | 1 | no | — |
| 384 | C4 | — | 2 | 4 | no | — |
| 385 | C4 | — | 2 | 1 | no | — |
| 386 | C4 | — | 2 | 1 | no | — |
| 387 | C4 | — | 2 | 4 | no | — |
| 388 | C4 | — | 2 | 1 | no | — |
| 389 | C4 | — | 2 | 1 | no | — |
| 390 | C4 | — | 502 | 4 | no | — |
| 391 | C4 | — | 502 | 2 | no | — |
| 392 | C4 | — | 502 | 2 | no | — |
| 393 | C4 | — | 502 | 2 | no | — |
| 394 | C4 | #22548763 | 1 | 2 | yes | — |
| 395 | C2 | — | 2 | 2 | no | — |
| 396 | C2 | — | 1004 | 2 | no | — |
| 397 | C2 | — | 1004 | 4 | no | — |
| 398 | C2 | C2×#22548761 | 1 | 1 | yes | characteristic |
| 399 | C2 | C2×#22548763 | 1 | 1 | yes | characteristic |
| 400 | C2 | #30632523 | 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