← #29835356
Subgroups — #29835356
Order 15616.
570 conjugacy classes of subgroups.
The subgroup lattice has 372 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #21456358 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #21448064 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #21448055 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #21448050 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #21448046 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #21447539 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #21447531 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #21447526 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | C2×#16839566 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #21447416 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C61×#3156 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #16840390 | — | 2 | 1 | no | — |
| 13 | C2×#14519717 | C22 | 1 | 1 | yes | characteristic |
| 14 | C22×#11758185 | C22 | 1 | 1 | yes | characteristic |
| 15 | #16840171 | — | 2 | 2 | no | — |
| 16 | #16840167 | C22 | 1 | 2 | yes | — |
| 17 | #16840164 | C22 | 1 | 2 | yes | — |
| 18 | #16839804 | — | 2 | 1 | no | — |
| 19 | #16839800 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#14519711 | C22 | 1 | 1 | yes | characteristic |
| 21 | #16839566 | C22 | 1 | 2 | yes | — |
| 22 | #16839566 | C22 | 1 | 2 | yes | — |
| 23 | #16839566 | C22 | 1 | 1 | yes | characteristic |
| 24 | #16839566 | C22 | 1 | 1 | yes | characteristic |
| 25 | #16839566 | C22 | 1 | 2 | yes | — |
| 26 | #16839566 | C22 | 1 | 2 | yes | — |
| 27 | #16839566 | C22 | 1 | 2 | yes | — |
| 28 | #16839563 | C22 | 1 | 1 | yes | characteristic |
| 29 | #16839563 | C22 | 1 | 1 | yes | characteristic |
| 30 | #16839563 | C22 | 1 | 2 | yes | — |
| 31 | #16839538 | C22 | 1 | 2 | yes | — |
| 32 | C4×#11758185 | C22 | 1 | 2 | yes | — |
| 33 | C2×#137×C61 | — | 2 | 1 | no | — |
| 34 | C2×#135×C61 | C22 | 1 | 1 | yes | characteristic |
| 35 | C22×Q16×C61 | C22 | 1 | 1 | yes | characteristic |
| 36 | C61×#536 | — | 2 | 1 | no | — |
| 37 | C61×#497 | — | 2 | 2 | no | — |
| 38 | C61×#495 | C22 | 1 | 2 | yes | — |
| 39 | C61×#494 | C22 | 1 | 2 | yes | — |
| 40 | C61×#405 | C22 | 1 | 1 | yes | characteristic |
| 41 | #14519777 | — | 2 | 2 | no | — |
| 42 | #14519776 | — | 4 | 1 | no | — |
| 43 | #14519769 | — | 2 | 2 | no | — |
| 44 | #14519768 | — | 4 | 1 | no | — |
| 45 | #14519754 | — | 4 | 2 | no | — |
| 46 | #14519736 | — | 2 | 1 | no | — |
| 47 | C2×C4⋊Dic61 | — | 2 | 1 | no | — |
| 48 | #14519717 | — | 2 | 2 | no | — |
| 49 | C2×#11758185 | — | 2 | 2 | no | — |
| 50 | C2×#11758185 | C23 | 1 | 1 | yes | characteristic |
| 51 | C2×#11758185 | C23 | 1 | 2 | yes | — |
| 52 | C2×#11758185 | C23 | 1 | 1 | yes | characteristic |
| 53 | #14519711 | — | 2 | 1 | no | — |
| 54 | #14519711 | — | 2 | 2 | no | — |
| 55 | #14519711 | C23 | 1 | 2 | yes | — |
| 56 | #14519711 | C23 | 1 | 1 | yes | characteristic |
| 57 | #14519711 | C23 | 1 | 1 | yes | characteristic |
| 58 | #14519709 | — | 2 | 1 | no | — |
| 59 | #14519709 | — | 2 | 2 | no | — |
| 60 | C2×#41×C61 | — | 2 | 1 | no | — |
| 61 | C22×Q8×C61 | — | 2 | 1 | no | — |
| 62 | #137×C61 | — | 4 | 4 | no | — |
| 63 | #135×C61 | — | 2 | 2 | no | — |
| 64 | #135×C61 | — | 2 | 2 | no | — |
| 65 | C2×Q16×C61 | — | 2 | 1 | no | — |
| 66 | C2×Q16×C61 | — | 2 | 2 | no | — |
| 67 | C2×Q16×C61 | — | 2 | 2 | no | — |
| 68 | C2×Q16×C61 | — | 2 | 2 | no | — |
| 69 | C2×Q16×C61 | C23 | 1 | 2 | yes | — |
| 70 | C2×Q16×C61 | C23 | 1 | 1 | yes | characteristic |
| 71 | C2×SD16×C61 | — | 2 | 1 | no | — |
| 72 | C2×SD16×C61 | — | 2 | 2 | no | — |
| 73 | C2×D8×C61 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×M16×C61 | D4 | 1 | 1 | yes | characteristic |
| 75 | C22×C8×C61 | C23 | 1 | 1 | yes | characteristic |
| 76 | C4⋊Q8×C61 | — | 2 | 2 | no | — |
| 77 | #124×C61 | — | 2 | 2 | no | — |
| 78 | #123×C61 | — | 4 | 2 | no | — |
| 79 | C22⋊Q8×C61 | — | 4 | 1 | no | — |
| 80 | C22⋊Q8×C61 | — | 4 | 1 | no | — |
| 81 | #117×C61 | D4 | 1 | 1 | yes | characteristic |
| 82 | #97×C61 | D4 | 1 | 2 | yes | — |
| 83 | C4×C8×C61 | C23 | 1 | 2 | yes | — |
| 84 | #41×C61 | — | 4 | 2 | no | — |
| 85 | #41×C61 | — | 4 | 2 | no | — |
| 86 | C2×Q8×C61 | — | 2 | 2 | no | — |
| 87 | C2×Q8×C61 | — | 2 | 1 | no | — |
| 88 | C2×Q8×C61 | — | 4 | 1 | no | — |
| 89 | C2×Q8×C61 | — | 4 | 2 | no | — |
| 90 | C2×Q8×C61 | — | 4 | 2 | no | — |
| 91 | C2×D4×C61 | — | 2 | 1 | no | — |
| 92 | C2×D4×C61 | — | 4 | 1 | no | — |
| 93 | C22×C4×C61 | — | 4 | 1 | no | — |
| 94 | C22×C4×C61 | — | 4 | 1 | no | — |
| 95 | C22×C4×C61 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C22×Dic61 | — | 4 | 1 | no | — |
| 97 | C2×Dic122 | — | 4 | 2 | no | — |
| 98 | Q16×C61 | — | 2 | 2 | no | — |
| 99 | Q16×C61 | — | 2 | 2 | no | — |
| 100 | Q16×C61 | — | 2 | 1 | no | — |
| 101 | Q16×C61 | — | 2 | 1 | no | — |
| 102 | Q16×C61 | — | 4 | 2 | no | — |
| 103 | Q16×C61 | — | 4 | 4 | no | — |
| 104 | SD16×C61 | — | 4 | 2 | no | — |
| 105 | SD16×C61 | — | 4 | 4 | no | — |
| 106 | D8×C61 | — | 2 | 1 | no | — |
| 107 | D8×C61 | — | 2 | 1 | no | — |
| 108 | M16×C61 | SD16 | 1 | 4 | yes | — |
| 109 | C2×C8×C61 | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | C2×C8×C61 | C2×D4 | 1 | 2 | yes | — |
| 111 | C2×C8×C61 | #41 | 1 | 2 | yes | — |
| 112 | C2×C8×C61 | #41 | 1 | 2 | yes | — |
| 113 | C2×C8×C61 | C24 | 1 | 1 | yes | characteristic |
| 114 | C4⋊C4×C61 | — | 4 | 2 | no | — |
| 115 | C4⋊C4×C61 | — | 4 | 2 | no | — |
| 116 | C4⋊C4×C61 | D8 | 1 | 1 | yes | characteristic |
| 117 | C4⋊C4×C61 | D8 | 1 | 1 | yes | characteristic |
| 118 | C22⋊C4×C61 | — | 4 | 2 | no | — |
| 119 | C22⋊C4×C61 | — | 4 | 2 | no | — |
| 120 | C22⋊C4×C61 | D8 | 1 | 2 | yes | — |
| 121 | C42×C61 | C2×D4 | 1 | 2 | yes | — |
| 122 | C22⋊Dic61 | — | 4 | 1 | no | — |
| 123 | C4⋊Dic61 | — | 2 | 1 | no | — |
| 124 | C4⋊Dic61 | — | 2 | 2 | no | — |
| 125 | C4⋊Dic61 | — | 2 | 1 | no | — |
| 126 | C4⋊Dic61 | — | 4 | 1 | no | — |
| 127 | C4⋊Dic61 | — | 4 | 2 | no | — |
| 128 | #11758196 | — | 4 | 2 | no | — |
| 129 | #11758196 | — | 4 | 2 | no | — |
| 130 | C4×Dic61 | — | 4 | 1 | no | — |
| 131 | #11758185 | — | 2 | 1 | no | — |
| 132 | #11758185 | — | 2 | 1 | no | — |
| 133 | #11758185 | — | 2 | 2 | no | — |
| 134 | C23×C61 | — | 4 | 1 | no | — |
| 135 | C23×C61 | C2×D8 | 1 | 1 | yes | characteristic |
| 136 | Q8×C61 | — | 4 | 1 | no | — |
| 137 | Q8×C61 | — | 4 | 2 | no | — |
| 138 | Q8×C61 | — | 4 | 2 | no | — |
| 139 | Q8×C61 | — | 4 | 1 | no | — |
| 140 | Q8×C61 | — | 8 | 2 | no | — |
| 141 | D4×C61 | — | 4 | 1 | no | — |
| 142 | D4×C61 | — | 4 | 1 | no | — |
| 143 | D4×C61 | — | 8 | 2 | no | — |
| 144 | C2×C4×C61 | — | 4 | 2 | no | — |
| 145 | C2×C4×C61 | — | 4 | 1 | no | — |
| 146 | C2×C4×C61 | — | 8 | 2 | no | — |
| 147 | C2×C4×C61 | — | 8 | 2 | no | — |
| 148 | C2×C4×C61 | #124 | 1 | 2 | yes | — |
| 149 | C2×C4×C61 | C2×D8 | 1 | 2 | yes | — |
| 150 | C2×C4×C61 | C2×D8 | 1 | 2 | yes | — |
| 151 | C2×C4×C61 | C2×D8 | 1 | 1 | yes | characteristic |
| 152 | C2×C4×C61 | C2×SD16 | 1 | 2 | yes | — |
| 153 | C2×C4×C61 | C22×D4 | 1 | 1 | yes | characteristic |
| 154 | C2×Dic61 | — | 4 | 1 | no | — |
| 155 | C2×Dic61 | — | 4 | 1 | no | — |
| 156 | C2×Dic61 | — | 4 | 2 | no | — |
| 157 | C2×Dic61 | — | 16 | 1 | no | — |
| 158 | Dic122 | — | 16 | 2 | no | — |
| 159 | C8×C61 | #124 | 1 | 2 | yes | — |
| 160 | C8×C61 | C2×SD16 | 1 | 4 | yes | — |
| 161 | C8×C61 | C2×#41 | 1 | 1 | yes | characteristic |
| 162 | C8×C61 | C2×#41 | 1 | 1 | yes | characteristic |
| 163 | #33703 | — | 61 | 1 | no | maximal, Sylow |
| 164 | C22×C61 | — | 2 | 1 | no | — |
| 165 | C22×C61 | — | 2 | 1 | no | — |
| 166 | C22×C61 | — | 8 | 1 | no | — |
| 167 | C22×C61 | — | 8 | 1 | no | — |
| 168 | C22×C61 | — | 8 | 1 | no | — |
| 169 | C22×C61 | #486 | 1 | 2 | yes | — |
| 170 | C22×C61 | C22×D8 | 1 | 1 | yes | characteristic |
| 171 | C4×C61 | — | 2 | 2 | no | — |
| 172 | C4×C61 | — | 2 | 2 | no | — |
| 173 | C4×C61 | — | 8 | 1 | no | — |
| 174 | C4×C61 | — | 8 | 2 | no | — |
| 175 | C4×C61 | #486 | 1 | 2 | yes | — |
| 176 | C4×C61 | C2×#124 | 1 | 1 | yes | characteristic |
| 177 | C4×C61 | C22×SD16 | 1 | 1 | yes | characteristic |
| 178 | Dic61 | — | 8 | 1 | no | — |
| 179 | Dic61 | — | 8 | 2 | no | — |
| 180 | Dic61 | — | 8 | 1 | no | — |
| 181 | #3164 | — | 61 | 1 | no | — |
| 182 | #3156 | D61 | 1 | 1 | yes | characteristic |
| 183 | #2245 | — | 61 | 2 | no | — |
| 184 | #2243 | — | 61 | 2 | no | — |
| 185 | #2242 | — | 61 | 2 | no | — |
| 186 | #2241 | — | 61 | 2 | no | — |
| 187 | #2141 | — | 61 | 1 | no | — |
| 188 | #2139 | — | 61 | 1 | no | — |
| 189 | #2138 | — | 61 | 1 | no | — |
| 190 | C2×#358 | — | 61 | 1 | no | — |
| 191 | #2108 | — | 61 | 1 | no | — |
| 192 | C2×C61 | — | 2 | 2 | no | — |
| 193 | C2×C61 | — | 16 | 1 | no | — |
| 194 | C2×C61 | C2×#486 | 1 | 1 | yes | characteristic |
| 195 | C2×C61 | #3416 | 1 | 1 | yes | characteristic |
| 196 | C2×C61 | #3417 | 1 | 1 | yes | characteristic |
| 197 | C2×#137 | — | 2 | 1 | no | — |
| 198 | C2×#135 | C2×D61 | 1 | 1 | yes | characteristic |
| 199 | C22×Q16 | C2×D61 | 1 | 1 | yes | characteristic |
| 200 | #544 | — | 122 | 1 | no | — |
| 201 | #536 | — | 2 | 1 | no | — |
| 202 | C2×M32 | — | 61 | 1 | no | — |
| 203 | C22×C16 | — | 61 | 1 | no | — |
| 204 | #501 | — | 122 | 2 | no | — |
| 205 | #500 | — | 61 | 2 | no | — |
| 206 | #499 | — | 61 | 2 | no | — |
| 207 | #497 | — | 2 | 2 | no | — |
| 208 | #495 | C2×D61 | 1 | 2 | yes | — |
| 209 | #494 | C2×D61 | 1 | 2 | yes | — |
| 210 | #428 | — | 122 | 1 | no | — |
| 211 | #427 | — | 61 | 1 | no | — |
| 212 | C2×#107 | — | 61 | 1 | no | — |
| 213 | #405 | C2×D61 | 1 | 1 | yes | characteristic |
| 214 | #358 | — | 61 | 2 | no | — |
| 215 | #358 | — | 61 | 2 | no | — |
| 216 | #358 | — | 61 | 1 | no | — |
| 217 | #358 | — | 61 | 1 | no | — |
| 218 | #358 | — | 61 | 2 | no | — |
| 219 | #358 | — | 61 | 2 | no | — |
| 220 | #358 | — | 61 | 2 | no | — |
| 221 | #357 | — | 61 | 1 | no | — |
| 222 | #357 | — | 61 | 1 | no | — |
| 223 | #357 | — | 61 | 2 | no | — |
| 224 | #346 | — | 61 | 2 | no | — |
| 225 | C4×C16 | — | 61 | 2 | no | — |
| 226 | C61 | #33703 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 227 | C2×#41 | — | 2 | 1 | no | — |
| 228 | C22×Q8 | — | 2 | 1 | no | — |
| 229 | #137 | — | 4 | 4 | no | — |
| 230 | #135 | — | 2 | 2 | no | — |
| 231 | #135 | — | 2 | 2 | no | — |
| 232 | C2×Q16 | — | 2 | 2 | no | — |
| 233 | C2×Q16 | — | 2 | 2 | no | — |
| 234 | C2×Q16 | — | 2 | 1 | no | — |
| 235 | C2×Q16 | — | 2 | 2 | no | — |
| 236 | C2×Q16 | C22×D61 | 1 | 2 | yes | — |
| 237 | C2×Q16 | C22×D61 | 1 | 1 | yes | characteristic |
| 238 | C2×SD16 | — | 2 | 1 | no | — |
| 239 | C2×SD16 | — | 2 | 2 | no | — |
| 240 | C2×D8 | C22×D61 | 1 | 1 | yes | characteristic |
| 241 | C2×M16 | C22⋊D61 | 1 | 1 | yes | characteristic |
| 242 | C22×C8 | C22×D61 | 1 | 1 | yes | characteristic |
| 243 | C4⋊Q8 | — | 2 | 2 | no | — |
| 244 | C4⋊Q8 | — | 122 | 2 | no | — |
| 245 | C4⋊Q8 | — | 244 | 1 | no | — |
| 246 | #125 | — | 122 | 2 | no | — |
| 247 | #125 | — | 244 | 1 | no | — |
| 248 | #124 | — | 2 | 2 | no | — |
| 249 | #123 | — | 4 | 2 | no | — |
| 250 | C22⋊Q8 | — | 4 | 1 | no | — |
| 251 | C22⋊Q8 | — | 4 | 1 | no | — |
| 252 | C22⋊Q8 | — | 244 | 2 | no | — |
| 253 | #117 | — | 122 | 1 | no | — |
| 254 | #117 | C22⋊D61 | 1 | 1 | yes | characteristic |
| 255 | C2×C4⋊C4 | — | 122 | 1 | no | — |
| 256 | M32 | — | 122 | 2 | no | — |
| 257 | C2×C16 | — | 61 | 1 | no | — |
| 258 | C2×C16 | — | 61 | 2 | no | — |
| 259 | C2×C16 | — | 61 | 1 | no | — |
| 260 | C2×C16 | — | 122 | 2 | no | — |
| 261 | #107 | — | 61 | 2 | no | — |
| 262 | #107 | — | 61 | 1 | no | — |
| 263 | #107 | — | 61 | 1 | no | — |
| 264 | #107 | — | 122 | 1 | no | — |
| 265 | #107 | — | 122 | 2 | no | — |
| 266 | #106 | — | 122 | 1 | no | — |
| 267 | #106 | — | 122 | 2 | no | — |
| 268 | #97 | C22⋊D61 | 1 | 2 | yes | — |
| 269 | C4×C8 | C22×D61 | 1 | 2 | yes | — |
| 270 | #41 | — | 4 | 2 | no | — |
| 271 | #41 | — | 4 | 2 | no | — |
| 272 | C2×Q8 | — | 2 | 2 | no | — |
| 273 | C2×Q8 | — | 2 | 1 | no | — |
| 274 | C2×Q8 | — | 4 | 1 | no | — |
| 275 | C2×Q8 | — | 4 | 2 | no | — |
| 276 | C2×Q8 | — | 4 | 2 | no | — |
| 277 | C2×Q8 | — | 244 | 2 | no | — |
| 278 | C2×D4 | — | 2 | 1 | no | — |
| 279 | C2×D4 | — | 4 | 1 | no | — |
| 280 | C22×C4 | — | 4 | 1 | no | — |
| 281 | C22×C4 | — | 4 | 1 | no | — |
| 282 | C22×C4 | — | 244 | 1 | no | — |
| 283 | C22×C4 | C2×C22⋊D61 | 1 | 1 | yes | characteristic |
| 284 | Q16 | — | 2 | 2 | no | — |
| 285 | Q16 | — | 2 | 2 | no | — |
| 286 | Q16 | — | 2 | 1 | no | — |
| 287 | Q16 | — | 2 | 1 | no | — |
| 288 | Q16 | — | 4 | 2 | no | — |
| 289 | Q16 | — | 4 | 4 | no | — |
| 290 | SD16 | — | 4 | 2 | no | — |
| 291 | SD16 | — | 4 | 4 | no | — |
| 292 | D8 | — | 2 | 1 | no | — |
| 293 | D8 | — | 2 | 1 | no | — |
| 294 | M16 | #11758200 | 1 | 4 | yes | — |
| 295 | C2×C8 | #11758224 | 1 | 2 | yes | — |
| 296 | C2×C8 | #11758224 | 1 | 2 | yes | — |
| 297 | C2×C8 | C2×C22⋊D61 | 1 | 1 | yes | characteristic |
| 298 | C2×C8 | C2×C22⋊D61 | 1 | 2 | yes | — |
| 299 | C2×C8 | C23×D61 | 1 | 1 | yes | characteristic |
| 300 | C4⋊C4 | — | 4 | 2 | no | — |
| 301 | C4⋊C4 | — | 4 | 2 | no | — |
| 302 | C4⋊C4 | — | 122 | 1 | no | — |
| 303 | C4⋊C4 | — | 122 | 2 | no | — |
| 304 | C4⋊C4 | — | 122 | 1 | no | — |
| 305 | C4⋊C4 | — | 244 | 1 | no | — |
| 306 | C4⋊C4 | — | 244 | 2 | no | — |
| 307 | C4⋊C4 | — | 244 | 2 | no | — |
| 308 | C4⋊C4 | — | 244 | 2 | no | — |
| 309 | C4⋊C4 | #11758199 | 1 | 1 | yes | characteristic |
| 310 | C4⋊C4 | #11758199 | 1 | 1 | yes | characteristic |
| 311 | C22⋊C4 | — | 4 | 2 | no | — |
| 312 | C22⋊C4 | — | 4 | 2 | no | — |
| 313 | C22⋊C4 | — | 244 | 1 | no | — |
| 314 | C22⋊C4 | #11758199 | 1 | 2 | yes | — |
| 315 | C42 | — | 244 | 1 | no | — |
| 316 | C42 | C2×C22⋊D61 | 1 | 2 | yes | — |
| 317 | C16 | — | 122 | 1 | no | — |
| 318 | C16 | — | 122 | 1 | no | — |
| 319 | C16 | — | 122 | 2 | no | — |
| 320 | C23 | — | 4 | 1 | no | — |
| 321 | C23 | C2×#11758199 | 1 | 1 | yes | characteristic |
| 322 | Q8 | — | 4 | 1 | no | — |
| 323 | Q8 | — | 4 | 2 | no | — |
| 324 | Q8 | — | 4 | 2 | no | — |
| 325 | Q8 | — | 4 | 1 | no | — |
| 326 | Q8 | — | 8 | 2 | no | — |
| 327 | Q8 | — | 976 | 2 | no | — |
| 328 | D4 | — | 4 | 1 | no | — |
| 329 | D4 | — | 4 | 1 | no | — |
| 330 | D4 | — | 8 | 2 | no | — |
| 331 | C2×C4 | — | 4 | 2 | no | — |
| 332 | C2×C4 | — | 4 | 1 | no | — |
| 333 | C2×C4 | — | 8 | 2 | no | — |
| 334 | C2×C4 | — | 8 | 2 | no | — |
| 335 | C2×C4 | — | 976 | 1 | no | — |
| 336 | C2×C4 | — | 244 | 1 | no | — |
| 337 | C2×C4 | — | 244 | 1 | no | — |
| 338 | C2×C4 | — | 244 | 2 | no | — |
| 339 | C2×C4 | #14519764 | 1 | 2 | yes | — |
| 340 | C2×C4 | C2×#11758199 | 1 | 2 | yes | — |
| 341 | C2×C4 | C2×#11758199 | 1 | 2 | yes | — |
| 342 | C2×C4 | C2×#11758199 | 1 | 1 | yes | characteristic |
| 343 | C2×C4 | C2×#11758200 | 1 | 2 | yes | — |
| 344 | C2×C4 | C22×C22⋊D61 | 1 | 1 | yes | characteristic |
| 345 | C8 | #14519764 | 1 | 2 | yes | — |
| 346 | C8 | C2×#11758200 | 1 | 4 | yes | — |
| 347 | C8 | C2×#11758224 | 1 | 1 | yes | characteristic |
| 348 | C8 | C2×#11758224 | 1 | 1 | yes | characteristic |
| 349 | C22 | — | 2 | 1 | no | — |
| 350 | C22 | — | 2 | 1 | no | — |
| 351 | C22 | — | 8 | 1 | no | — |
| 352 | C22 | — | 8 | 1 | no | — |
| 353 | C22 | — | 8 | 1 | no | — |
| 354 | C22 | #16840108 | 1 | 2 | yes | — |
| 355 | C22 | C22×#11758199 | 1 | 1 | yes | characteristic |
| 356 | C4 | — | 2 | 2 | no | — |
| 357 | C4 | — | 2 | 2 | no | — |
| 358 | C4 | — | 8 | 1 | no | — |
| 359 | C4 | — | 8 | 2 | no | — |
| 360 | C4 | — | 488 | 2 | no | — |
| 361 | C4 | — | 488 | 1 | no | — |
| 362 | C4 | — | 488 | 1 | no | — |
| 363 | C4 | #16840108 | 1 | 2 | yes | — |
| 364 | C4 | C2×#14519764 | 1 | 1 | yes | characteristic |
| 365 | C4 | C22×#11758200 | 1 | 1 | yes | characteristic |
| 366 | C2 | — | 2 | 2 | no | — |
| 367 | C2 | — | 16 | 1 | no | — |
| 368 | C2 | C2×#16840108 | 1 | 1 | yes | characteristic |
| 369 | C2 | #21458963 | 1 | 1 | yes | characteristic |
| 370 | C2 | #21458970 | 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