Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
690 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #21458064 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #21458061 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #21445424 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #21445351 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #21445350 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #21444966 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #21444871 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #21444701 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C61×#1619 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #16840477 | C22 | 1 | 2 | yes | — |
| 11 | #16840397 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #16840142 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | #16840108 | C22 | 1 | 2 | yes | complemented |
| 14 | #16840108 | C22 | 1 | 2 | yes | complemented |
| 15 | #16840085 | — | 2 | 2 | no | — |
| 16 | #16840083 | — | 2 | 2 | no | — |
| 17 | #16840053 | C22 | 1 | 2 | yes | complemented |
| 18 | #16840052 | C22 | 1 | 2 | yes | complemented |
| 19 | #16840013 | — | 2 | 2 | no | — |
| 20 | #16840012 | — | 2 | 2 | no | — |
| 21 | #16839954 | C22 | 1 | 2 | yes | — |
| 22 | #16839896 | — | 2 | 2 | no | — |
| 23 | #16839894 | — | 2 | 2 | no | — |
| 24 | C4×#11758199 | C22 | 1 | 2 | yes | — |
| 25 | #16839840 | C22 | 1 | 2 | yes | complemented |
| 26 | #16839839 | C22 | 1 | 2 | yes | complemented |
| 27 | #16839767 | — | 2 | 2 | no | — |
| 28 | #16839765 | — | 2 | 2 | no | — |
| 29 | #16839514 | C22 | 1 | 2 | yes | complemented |
| 30 | #16839510 | C22 | 1 | 2 | yes | complemented |
| 31 | #16839506 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #16839491 | C22 | 1 | 2 | yes | complemented |
| 33 | C8×#92418 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | D42×C61 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | C61×#493 | C22 | 1 | 1 | yes | characteristic |
| 36 | C61×#459 | C22 | 1 | 2 | yes | — |
| 37 | C61×#331 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | C61×D4⋊C8 | C22 | 1 | 2 | yes | complemented |
| 39 | C2×D4×D61 | — | 2 | 2 | no | — |
| 40 | C2×Dic244 | — | 4 | 1 | no | — |
| 41 | C2×#11758199 | — | 2 | 2 | no | — |
| 42 | C2×#11758199 | D4 | 1 | 2 | yes | — |
| 43 | C2×#11758194 | — | 2 | 2 | no | — |
| 44 | C2×#11758189 | — | 2 | 2 | no | — |
| 45 | #14519777 | C23 | 1 | 2 | yes | — |
| 46 | #14519763 | — | 4 | 2 | no | — |
| 47 | #14519751 | — | 2 | 2 | no | — |
| 48 | #14519748 | — | 2 | 2 | no | — |
| 49 | #14519748 | — | 2 | 2 | no | — |
| 50 | #14519745 | — | 4 | 1 | no | — |
| 51 | C4×D244 | C23 | 1 | 2 | yes | — |
| 52 | #14519736 | — | 2 | 2 | no | — |
| 53 | #14519735 | — | 2 | 2 | no | — |
| 54 | #14519710 | D4 | 1 | 2 | yes | — |
| 55 | #14519709 | — | 2 | 2 | no | — |
| 56 | #14519708 | — | 2 | 2 | no | — |
| 57 | C4⋊#92418 | C23 | 1 | 2 | yes | — |
| 58 | #14519699 | — | 2 | 2 | no | — |
| 59 | #14519698 | — | 2 | 2 | no | — |
| 60 | #14519698 | — | 2 | 2 | no | — |
| 61 | #14519698 | — | 2 | 2 | no | — |
| 62 | #14519698 | — | 2 | 2 | no | — |
| 63 | #14519698 | — | 2 | 2 | no | — |
| 64 | #14519698 | — | 2 | 2 | no | — |
| 65 | #14519698 | D4 | 1 | 2 | yes | — |
| 66 | #14519697 | D4 | 1 | 2 | yes | — |
| 67 | C22⋊#92418 | — | 2 | 2 | no | — |
| 68 | #14519689 | — | 2 | 2 | no | — |
| 69 | C4×#92418 | C23 | 1 | 2 | yes | — |
| 70 | C22×D4×C61 | — | 2 | 2 | no | — |
| 71 | C2×D8×C61 | — | 2 | 2 | no | — |
| 72 | C2×D8×C61 | — | 4 | 1 | no | — |
| 73 | #127×C61 | C23 | 1 | 1 | yes | characteristic |
| 74 | #127×C61 | C23 | 1 | 1 | yes | characteristic |
| 75 | #121×C61 | — | 2 | 2 | no | — |
| 76 | #120×C61 | — | 4 | 1 | no | — |
| 77 | C4×D4×C61 | C23 | 1 | 2 | yes | — |
| 78 | C4⋊C8×C61 | C23 | 1 | 2 | yes | — |
| 79 | #102×C61 | — | 2 | 2 | no | — |
| 80 | C4×C8×C61 | C23 | 1 | 1 | yes | characteristic |
| 81 | C24×C61 | — | 4 | 1 | no | — |
| 82 | C23×D61 | — | 4 | 1 | no | — |
| 83 | C2×D4×C61 | — | 2 | 2 | no | — |
| 84 | C2×D4×C61 | — | 2 | 2 | no | — |
| 85 | C2×D4×C61 | — | 2 | 1 | no | — |
| 86 | C2×D4×C61 | — | 2 | 1 | no | — |
| 87 | C2×D4×C61 | — | 4 | 2 | no | — |
| 88 | C2×D4×C61 | — | 4 | 4 | no | — |
| 89 | C2×D4×C61 | — | 8 | 2 | no | — |
| 90 | C2×D4×C61 | C2×D4 | 1 | 2 | yes | — |
| 91 | C22×C4×C61 | — | 2 | 2 | no | — |
| 92 | C2×C22⋊D61 | — | 4 | 2 | no | — |
| 93 | C2×C22⋊D61 | — | 4 | 2 | no | — |
| 94 | D4×D61 | — | 4 | 4 | no | — |
| 95 | D4×D61 | — | 8 | 2 | no | — |
| 96 | C2×D244 | C2×D4 | 1 | 2 | yes | — |
| 97 | C2×C4×D61 | — | 2 | 2 | no | — |
| 98 | C2×Dic122 | — | 2 | 2 | no | — |
| 99 | D8×C61 | — | 8 | 2 | no | — |
| 100 | D8×C61 | — | 8 | 2 | no | — |
| 101 | C2×C8×C61 | — | 2 | 1 | no | — |
| 102 | C2×C8×C61 | — | 2 | 2 | no | — |
| 103 | C4⋊C4×C61 | C2×D4 | 1 | 2 | yes | — |
| 104 | C22⋊C4×C61 | — | 2 | 2 | no | — |
| 105 | C22⋊C4×C61 | — | 4 | 1 | no | — |
| 106 | C42×C61 | C24 | 1 | 1 | yes | characteristic |
| 107 | C22⋊Dic61 | — | 4 | 1 | no | — |
| 108 | C22⋊Dic61 | — | 4 | 2 | no | — |
| 109 | #11758199 | — | 4 | 2 | no | — |
| 110 | #11758199 | — | 8 | 2 | no | — |
| 111 | #11758198 | — | 2 | 2 | no | — |
| 112 | #11758198 | — | 4 | 2 | no | — |
| 113 | C4⋊Dic61 | — | 2 | 2 | no | — |
| 114 | C4⋊Dic61 | — | 2 | 2 | no | — |
| 115 | C4⋊Dic61 | C2×D4 | 1 | 2 | yes | — |
| 116 | C4×Dic61 | — | 4 | 2 | no | — |
| 117 | #11758194 | — | 8 | 2 | no | — |
| 118 | C2×#92418 | — | 2 | 2 | no | — |
| 119 | C2×#92418 | C2×D4 | 1 | 2 | yes | — |
| 120 | C2×#92418 | C2×D4 | 1 | 2 | yes | — |
| 121 | Dic244 | — | 8 | 2 | no | — |
| 122 | #11758189 | — | 8 | 2 | no | — |
| 123 | C23×C61 | — | 2 | 2 | no | — |
| 124 | C23×C61 | — | 4 | 1 | no | — |
| 125 | C23×C61 | — | 4 | 1 | no | — |
| 126 | C23×C61 | — | 8 | 4 | no | — |
| 127 | C23×C61 | — | 16 | 1 | no | — |
| 128 | C22×D61 | — | 2 | 2 | no | — |
| 129 | C22×D61 | — | 8 | 4 | no | — |
| 130 | C22×D61 | — | 16 | 1 | no | — |
| 131 | D4×C61 | — | 2 | 2 | no | — |
| 132 | D4×C61 | — | 2 | 2 | no | — |
| 133 | D4×C61 | — | 4 | 2 | no | — |
| 134 | D4×C61 | — | 4 | 2 | no | — |
| 135 | D4×C61 | — | 4 | 2 | no | — |
| 136 | D4×C61 | — | 4 | 2 | no | — |
| 137 | D4×C61 | — | 8 | 1 | no | — |
| 138 | D4×C61 | — | 8 | 1 | no | — |
| 139 | D4×C61 | — | 8 | 4 | no | — |
| 140 | C2×C4×C61 | — | 2 | 2 | no | — |
| 141 | C2×C4×C61 | — | 4 | 2 | no | — |
| 142 | C2×C4×C61 | — | 4 | 2 | no | — |
| 143 | C2×C4×C61 | C22×D4 | 1 | 2 | yes | — |
| 144 | C2×C4×C61 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 145 | C22⋊D61 | — | 8 | 4 | no | — |
| 146 | C22⋊D61 | — | 16 | 2 | no | — |
| 147 | C2×Dic61 | — | 2 | 2 | no | — |
| 148 | C2×Dic61 | — | 4 | 2 | no | — |
| 149 | D244 | — | 2 | 2 | no | — |
| 150 | D244 | — | 2 | 2 | no | — |
| 151 | C4×D61 | — | 4 | 2 | no | — |
| 152 | C4×D61 | — | 4 | 2 | no | — |
| 153 | Dic122 | — | 8 | 2 | no | — |
| 154 | C8×C61 | — | 2 | 2 | no | — |
| 155 | C8×C61 | — | 4 | 2 | no | — |
| 156 | #92418 | — | 2 | 2 | no | — |
| 157 | #92418 | — | 2 | 2 | no | — |
| 158 | #92418 | — | 4 | 2 | no | — |
| 159 | #20302 | — | 61 | 1 | no | maximal, Sylow |
| 160 | C22×C61 | — | 4 | 2 | no | — |
| 161 | C22×C61 | — | 4 | 2 | no | — |
| 162 | C22×C61 | — | 4 | 2 | no | — |
| 163 | C22×C61 | — | 8 | 2 | no | — |
| 164 | C22×C61 | — | 8 | 2 | no | — |
| 165 | C22×C61 | — | 8 | 1 | no | — |
| 166 | C22×C61 | — | 8 | 1 | no | — |
| 167 | C22×C61 | — | 16 | 4 | no | — |
| 168 | C22×C61 | D42 | 1 | 1 | yes | characteristic |
| 169 | C2×D61 | — | 4 | 2 | no | — |
| 170 | C2×D61 | — | 4 | 2 | no | — |
| 171 | C2×D61 | — | 4 | 2 | no | — |
| 172 | C2×D61 | — | 16 | 4 | no | — |
| 173 | C4×C61 | — | 2 | 1 | no | — |
| 174 | C4×C61 | — | 4 | 2 | no | — |
| 175 | C4×C61 | #575 | 1 | 2 | yes | — |
| 176 | C4×C61 | #576 | 1 | 2 | yes | — |
| 177 | Dic61 | — | 4 | 2 | no | — |
| 178 | Dic61 | — | 8 | 2 | no | — |
| 179 | #3325 | — | 61 | 2 | no | — |
| 180 | #3325 | — | 61 | 2 | no | — |
| 181 | #1709 | — | 61 | 1 | no | — |
| 182 | #1697 | — | 61 | 2 | no | — |
| 183 | #1697 | — | 61 | 2 | no | — |
| 184 | #1634 | — | 61 | 2 | no | — |
| 185 | #1619 | — | 61 | 1 | no | — |
| 186 | #1619 | D61 | 1 | 1 | yes | characteristic, complemented |
| 187 | #1589 | — | 61 | 2 | no | — |
| 188 | C2×C61 | — | 8 | 2 | no | — |
| 189 | C2×C61 | — | 16 | 1 | no | — |
| 190 | C2×C61 | — | 16 | 1 | no | — |
| 191 | C2×C61 | #3273 | 1 | 2 | yes | — |
| 192 | C2×C61 | #3292 | 1 | 1 | yes | characteristic |
| 193 | D61 | — | 8 | 2 | no | — |
| 194 | #555 | — | 61 | 2 | no | — |
| 195 | D42 | — | 61 | 1 | no | — |
| 196 | D42 | C2×D61 | 1 | 1 | yes | characteristic, complemented |
| 197 | #494 | — | 61 | 1 | no | — |
| 198 | #493 | C2×D61 | 1 | 1 | yes | characteristic |
| 199 | #486 | — | 61 | 2 | no | — |
| 200 | #486 | — | 61 | 2 | no | — |
| 201 | #482 | — | 122 | 2 | no | — |
| 202 | #482 | — | 122 | 2 | no | — |
| 203 | #476 | — | 61 | 2 | no | — |
| 204 | #476 | — | 61 | 2 | no | — |
| 205 | #469 | — | 122 | 2 | no | — |
| 206 | #469 | — | 122 | 2 | no | — |
| 207 | #459 | — | 61 | 2 | no | — |
| 208 | #459 | C2×D61 | 1 | 2 | yes | — |
| 209 | #447 | — | 122 | 2 | no | — |
| 210 | #447 | — | 122 | 2 | no | — |
| 211 | C4×D8 | — | 61 | 2 | no | — |
| 212 | #436 | — | 61 | 2 | no | — |
| 213 | #436 | — | 61 | 2 | no | — |
| 214 | #418 | — | 122 | 2 | no | — |
| 215 | #418 | — | 122 | 2 | no | — |
| 216 | #335 | — | 61 | 2 | no | — |
| 217 | #333 | — | 61 | 2 | no | — |
| 218 | #331 | — | 61 | 1 | no | — |
| 219 | #331 | C2×D61 | 1 | 1 | yes | characteristic, complemented |
| 220 | D4⋊C8 | — | 61 | 2 | no | — |
| 221 | D4⋊C8 | C2×D61 | 1 | 2 | yes | complemented |
| 222 | C82 | — | 61 | 1 | no | — |
| 223 | C61 | #20302 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 224 | C22×D4 | — | 2 | 2 | no | — |
| 225 | C22×D4 | — | 122 | 2 | no | — |
| 226 | C2×Q16 | — | 244 | 1 | no | — |
| 227 | C2×D8 | — | 2 | 2 | no | — |
| 228 | C2×D8 | — | 4 | 1 | no | — |
| 229 | C2×D8 | — | 61 | 2 | no | — |
| 230 | C2×D8 | — | 122 | 2 | no | — |
| 231 | C2×M16 | — | 122 | 2 | no | — |
| 232 | C2×M16 | — | 122 | 2 | no | — |
| 233 | C4⋊Q8 | — | 61 | 2 | no | — |
| 234 | #127 | C22×D61 | 1 | 1 | yes | characteristic |
| 235 | #127 | C22×D61 | 1 | 1 | yes | characteristic |
| 236 | #124 | — | 244 | 2 | no | — |
| 237 | #121 | — | 2 | 2 | no | — |
| 238 | #121 | — | 122 | 2 | no | — |
| 239 | #121 | — | 122 | 2 | no | — |
| 240 | #121 | — | 122 | 2 | no | — |
| 241 | #120 | — | 4 | 1 | no | — |
| 242 | #120 | — | 244 | 1 | no | — |
| 243 | C4×D4 | — | 61 | 2 | no | — |
| 244 | C4×D4 | C22×D61 | 1 | 2 | yes | — |
| 245 | #117 | — | 122 | 2 | no | — |
| 246 | #117 | — | 122 | 2 | no | — |
| 247 | #107 | — | 61 | 2 | no | — |
| 248 | #106 | — | 122 | 2 | no | — |
| 249 | #106 | — | 122 | 2 | no | — |
| 250 | C4⋊C8 | — | 61 | 2 | no | — |
| 251 | C4⋊C8 | C22×D61 | 1 | 2 | yes | — |
| 252 | #102 | — | 2 | 2 | no | — |
| 253 | #102 | — | 61 | 2 | no | — |
| 254 | #102 | — | 61 | 2 | no | — |
| 255 | #102 | — | 122 | 2 | no | — |
| 256 | #102 | — | 122 | 2 | no | — |
| 257 | #102 | — | 122 | 2 | no | — |
| 258 | #102 | — | 122 | 2 | no | — |
| 259 | #102 | — | 122 | 2 | no | — |
| 260 | #102 | — | 122 | 2 | no | — |
| 261 | #102 | — | 122 | 2 | no | — |
| 262 | C22⋊C8 | — | 122 | 2 | no | — |
| 263 | C22⋊C8 | — | 122 | 2 | no | — |
| 264 | C4×C8 | — | 61 | 2 | no | — |
| 265 | C4×C8 | C22×D61 | 1 | 1 | yes | characteristic |
| 266 | C24 | — | 4 | 1 | no | — |
| 267 | C24 | — | 244 | 1 | no | — |
| 268 | C2×Q8 | — | 122 | 2 | no | — |
| 269 | C2×D4 | — | 2 | 2 | no | — |
| 270 | C2×D4 | — | 2 | 2 | no | — |
| 271 | C2×D4 | — | 2 | 1 | no | — |
| 272 | C2×D4 | — | 2 | 1 | no | — |
| 273 | C2×D4 | — | 4 | 2 | no | — |
| 274 | C2×D4 | — | 4 | 4 | no | — |
| 275 | C2×D4 | — | 8 | 2 | no | — |
| 276 | C2×D4 | — | 61 | 2 | no | — |
| 277 | C2×D4 | — | 488 | 2 | no | — |
| 278 | C2×D4 | — | 244 | 2 | no | — |
| 279 | C2×D4 | — | 244 | 4 | no | — |
| 280 | C2×D4 | — | 244 | 2 | no | — |
| 281 | C2×D4 | D4×D61 | 1 | 2 | yes | — |
| 282 | C22×C4 | — | 2 | 2 | no | — |
| 283 | C22×C4 | — | 122 | 2 | no | — |
| 284 | Q16 | — | 488 | 2 | no | — |
| 285 | D8 | — | 8 | 2 | no | — |
| 286 | D8 | — | 8 | 2 | no | — |
| 287 | D8 | — | 488 | 2 | no | — |
| 288 | D8 | — | 244 | 2 | no | — |
| 289 | M16 | — | 488 | 2 | no | — |
| 290 | M16 | — | 488 | 2 | no | — |
| 291 | C2×C8 | — | 2 | 1 | no | — |
| 292 | C2×C8 | — | 2 | 2 | no | — |
| 293 | C2×C8 | — | 61 | 2 | no | — |
| 294 | C2×C8 | — | 61 | 2 | no | — |
| 295 | C2×C8 | — | 122 | 2 | no | — |
| 296 | C4⋊C4 | — | 61 | 2 | no | — |
| 297 | C4⋊C4 | — | 122 | 2 | no | — |
| 298 | C4⋊C4 | — | 122 | 2 | no | — |
| 299 | C4⋊C4 | D4×D61 | 1 | 2 | yes | — |
| 300 | C22⋊C4 | — | 2 | 2 | no | — |
| 301 | C22⋊C4 | — | 4 | 1 | no | — |
| 302 | C22⋊C4 | — | 122 | 2 | no | — |
| 303 | C22⋊C4 | — | 244 | 2 | no | — |
| 304 | C22⋊C4 | — | 244 | 1 | no | — |
| 305 | C22⋊C4 | — | 244 | 2 | no | — |
| 306 | C42 | — | 244 | 2 | no | — |
| 307 | C42 | C23×D61 | 1 | 1 | yes | characteristic |
| 308 | C23 | — | 2 | 2 | no | — |
| 309 | C23 | — | 4 | 1 | no | — |
| 310 | C23 | — | 4 | 1 | no | — |
| 311 | C23 | — | 8 | 4 | no | — |
| 312 | C23 | — | 16 | 1 | no | — |
| 313 | C23 | — | 122 | 2 | no | — |
| 314 | C23 | — | 976 | 1 | no | — |
| 315 | C23 | — | 488 | 4 | no | — |
| 316 | Q8 | — | 488 | 2 | no | — |
| 317 | D4 | — | 2 | 2 | no | — |
| 318 | D4 | — | 2 | 2 | no | — |
| 319 | D4 | — | 4 | 2 | no | — |
| 320 | D4 | — | 4 | 2 | no | — |
| 321 | D4 | — | 4 | 2 | no | — |
| 322 | D4 | — | 4 | 2 | no | — |
| 323 | D4 | — | 8 | 1 | no | — |
| 324 | D4 | — | 8 | 1 | no | — |
| 325 | D4 | — | 8 | 4 | no | — |
| 326 | D4 | — | 122 | 2 | no | — |
| 327 | D4 | — | 122 | 2 | no | — |
| 328 | D4 | — | 976 | 2 | no | — |
| 329 | D4 | — | 488 | 4 | no | — |
| 330 | C2×C4 | — | 2 | 2 | no | — |
| 331 | C2×C4 | — | 4 | 2 | no | — |
| 332 | C2×C4 | — | 4 | 2 | no | — |
| 333 | C2×C4 | — | 122 | 2 | no | — |
| 334 | C2×C4 | — | 244 | 2 | no | — |
| 335 | C2×C4 | — | 244 | 2 | no | — |
| 336 | C2×C4 | — | 244 | 2 | no | — |
| 337 | C2×C4 | C2×D4×D61 | 1 | 2 | yes | — |
| 338 | C2×C4 | #14519822 | 1 | 1 | yes | characteristic |
| 339 | C8 | — | 2 | 2 | no | — |
| 340 | C8 | — | 4 | 2 | no | — |
| 341 | C8 | — | 122 | 2 | no | — |
| 342 | C8 | — | 122 | 2 | no | — |
| 343 | C8 | — | 244 | 2 | no | — |
| 344 | C22 | — | 4 | 2 | no | — |
| 345 | C22 | — | 4 | 2 | no | — |
| 346 | C22 | — | 4 | 2 | no | — |
| 347 | C22 | — | 8 | 2 | no | — |
| 348 | C22 | — | 8 | 2 | no | — |
| 349 | C22 | — | 8 | 1 | no | — |
| 350 | C22 | — | 8 | 1 | no | — |
| 351 | C22 | — | 16 | 4 | no | — |
| 352 | C22 | — | 976 | 4 | no | — |
| 353 | C22 | — | 244 | 2 | no | — |
| 354 | C22 | — | 244 | 2 | no | — |
| 355 | C22 | — | 244 | 2 | no | — |
| 356 | C22 | #16840394 | 1 | 1 | yes | characteristic |
| 357 | C4 | — | 2 | 1 | no | — |
| 358 | C4 | — | 4 | 2 | no | — |
| 359 | C4 | — | 488 | 2 | no | — |
| 360 | C4 | — | 244 | 2 | no | — |
| 361 | C4 | #16840558 | 1 | 2 | yes | — |
| 362 | C4 | #16840563 | 1 | 2 | yes | — |
| 363 | C2 | — | 8 | 2 | no | — |
| 364 | C2 | — | 16 | 1 | no | — |
| 365 | C2 | — | 16 | 1 | no | — |
| 366 | C2 | — | 488 | 2 | no | — |
| 367 | C2 | #21457430 | 1 | 2 | yes | — |
| 368 | C2 | #21457615 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21458064 | C2 | semidirect |
| 2. #21458061 | C2 | semidirect |
| 3. #21445424 | C2 | semidirect |
| 4. #21445351 | C2 | semidirect |
| 5. #21445350 | C2 | semidirect |
| 6. #21444966 | C2 | semidirect |
| 7. #21444871 | C2 | semidirect |
| 8. #21444701 | C2 | semidirect |
| 9. C61×#1619 | C2 | semidirect |
| 11. #16840397 | C22 | semidirect |
| 12. #16840142 | C22 | semidirect |
| 13. #16840108 | C22 | semidirect |
| 14. #16840108 | C22 | semidirect |
| 17. #16840053 | C22 | semidirect |
| 18. #16840052 | C22 | semidirect |
| 25. #16839840 | C22 | semidirect |
| 26. #16839839 | C22 | semidirect |
| 29. #16839514 | C22 | semidirect |
| 30. #16839510 | C22 | semidirect |
| 31. #16839506 | C22 | semidirect |
| 32. #16839491 | C22 | semidirect |
| 33. C8×#92418 | C22 | semidirect |
| 34. D42×C61 | C22 | semidirect |
| 37. C61×#331 | C22 | semidirect |
| 38. C61×D4⋊C8 | C22 | semidirect |
| 186. #1619 | D61 | semidirect |
| 196. D42 | C2×D61 | semidirect |
| 219. #331 | C2×D61 | semidirect |
| 221. D4⋊C8 | C2×D61 | semidirect |
| 223. C61 | #20302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458064 | 2 |
| #21458061 | 2 |
| #21445424 | 2 |
| #21445351 | 2 |
| #21445350 | 2 |
| #21444966 | 2 |
| #21444871 | 2 |
| #21444701 | 2 |
| C61×#1619 | 2 |
| #20302 | 61 |