Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
404 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 53 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 | #21456730 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #21447770 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #21446922 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #21443814 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #21443810 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #21443756 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C61×#2190 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #16840560 | — | 2 | 1 | no | — |
| 9 | #16840341 | — | 2 | 1 | no | — |
| 10 | #16840202 | — | 2 | 1 | no | — |
| 11 | #16840094 | — | 2 | 1 | no | — |
| 12 | #16840079 | — | 2 | 1 | no | — |
| 13 | #16840020 | C22 | 1 | 1 | yes | characteristic |
| 14 | #16839989 | — | 2 | 1 | no | — |
| 15 | #16839925 | — | 2 | 1 | no | — |
| 16 | #16839904 | — | 2 | 1 | no | — |
| 17 | #16839730 | C22 | 1 | 1 | yes | characteristic |
| 18 | #16839729 | — | 2 | 1 | no | — |
| 19 | #16839572 | — | 2 | 1 | no | — |
| 20 | #16839544 | C22 | 1 | 1 | yes | characteristic |
| 21 | #16839520 | C22 | 1 | 1 | yes | characteristic |
| 22 | C61×#575 | C22 | 1 | 1 | yes | characteristic |
| 23 | C61×#509 | — | 2 | 1 | no | — |
| 24 | C61×#469 | C22 | 1 | 1 | yes | characteristic |
| 25 | C61×#360 | — | 2 | 1 | no | — |
| 26 | C61×#349 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#11758222 | D4 | 1 | 1 | yes | characteristic |
| 28 | C2×#11758224 | — | 2 | 1 | no | — |
| 29 | #14519808 | — | 4 | 1 | no | — |
| 30 | #14519807 | — | 4 | 1 | no | — |
| 31 | #14519803 | — | 4 | 1 | no | — |
| 32 | #14519802 | — | 4 | 1 | no | — |
| 33 | #14519797 | — | 4 | 2 | no | — |
| 34 | C2×Dic244 | D4 | 1 | 1 | yes | characteristic |
| 35 | C2×#11758200 | — | 2 | 1 | no | — |
| 36 | C2×#11758194 | — | 2 | 1 | no | — |
| 37 | C22×#92418 | D4 | 1 | 1 | yes | characteristic |
| 38 | #14519757 | — | 2 | 1 | no | — |
| 39 | #14519756 | — | 2 | 1 | no | — |
| 40 | #14519754 | — | 4 | 1 | no | — |
| 41 | #14519750 | — | 4 | 1 | no | — |
| 42 | #14519749 | — | 4 | 1 | no | — |
| 43 | #14519748 | — | 2 | 1 | no | — |
| 44 | #14519748 | — | 4 | 1 | no | — |
| 45 | C4⋊C4×D61 | — | 2 | 1 | no | — |
| 46 | #14519723 | — | 4 | 1 | no | — |
| 47 | #14519721 | — | 4 | 1 | no | — |
| 48 | #14519717 | — | 2 | 1 | no | — |
| 49 | #14519709 | D4 | 1 | 1 | yes | characteristic |
| 50 | #14519708 | — | 2 | 1 | no | — |
| 51 | #14519702 | — | 2 | 1 | no | — |
| 52 | #14519700 | — | 2 | 1 | no | — |
| 53 | #14519698 | — | 2 | 1 | no | — |
| 54 | C22⋊#92418 | — | 4 | 2 | no | — |
| 55 | #14519689 | — | 2 | 1 | no | — |
| 56 | #14519689 | — | 2 | 1 | no | — |
| 57 | C2×#41×C61 | — | 2 | 1 | no | — |
| 58 | #137×C61 | — | 4 | 1 | no | — |
| 59 | AGL(1,ℤ/8)×C61 | — | 4 | 1 | no | — |
| 60 | #135×C61 | — | 2 | 1 | no | — |
| 61 | #135×C61 | — | 2 | 1 | no | — |
| 62 | C2×D8×C61 | D4 | 1 | 1 | yes | characteristic |
| 63 | C2×M16×C61 | C23 | 1 | 1 | yes | characteristic |
| 64 | #121×C61 | — | 2 | 1 | no | — |
| 65 | SD32×C61 | — | 4 | 1 | no | — |
| 66 | D16×C61 | — | 4 | 1 | no | — |
| 67 | M32×C61 | — | 2 | 1 | no | — |
| 68 | #106×C61 | D4 | 1 | 1 | yes | characteristic |
| 69 | #102×C61 | — | 2 | 1 | no | — |
| 70 | #41×C61 | — | 4 | 1 | no | — |
| 71 | #41×C61 | — | 4 | 1 | no | — |
| 72 | #41×C61 | — | 4 | 1 | no | — |
| 73 | #41×C61 | — | 4 | 1 | no | — |
| 74 | C2×Q8×C61 | — | 2 | 1 | no | — |
| 75 | C2×D4×C61 | — | 2 | 1 | no | — |
| 76 | C2×D4×C61 | — | 2 | 1 | no | — |
| 77 | C2×D4×C61 | — | 4 | 1 | no | — |
| 78 | C2×D4×C61 | — | 4 | 1 | no | — |
| 79 | C22×C4×C61 | — | 4 | 1 | no | — |
| 80 | C22×C4×C61 | C2×D4 | 1 | 1 | yes | characteristic |
| 81 | C2×C22⋊D61 | — | 2 | 1 | no | — |
| 82 | C2×C22⋊D61 | — | 4 | 1 | no | — |
| 83 | C2×C22⋊D61 | — | 4 | 1 | no | — |
| 84 | C22×Dic61 | — | 4 | 1 | no | — |
| 85 | #11758224 | — | 8 | 1 | no | — |
| 86 | #11758224 | — | 8 | 1 | no | — |
| 87 | #11758222 | — | 4 | 1 | no | — |
| 88 | #11758222 | — | 4 | 1 | no | — |
| 89 | C2×D244 | D8 | 1 | 1 | yes | characteristic |
| 90 | C2×C4×D61 | — | 2 | 1 | no | — |
| 91 | C2×C4×D61 | — | 4 | 1 | no | — |
| 92 | C2×Dic122 | — | 2 | 1 | no | — |
| 93 | C2×Dic122 | D8 | 1 | 1 | yes | characteristic |
| 94 | Q16×C61 | — | 2 | 1 | no | — |
| 95 | Q16×C61 | — | 2 | 1 | no | — |
| 96 | SD16×C61 | — | 4 | 1 | no | — |
| 97 | SD16×C61 | — | 4 | 1 | no | — |
| 98 | D8×C61 | — | 2 | 1 | no | — |
| 99 | D8×C61 | — | 2 | 1 | no | — |
| 100 | D8×C61 | — | 4 | 1 | no | — |
| 101 | M16×C61 | — | 4 | 1 | no | — |
| 102 | C2×C8×C61 | C2×D4 | 1 | 1 | yes | characteristic |
| 103 | C2×C8×C61 | C2×D4 | 1 | 1 | yes | characteristic |
| 104 | C4⋊C4×C61 | — | 2 | 1 | no | — |
| 105 | C22⋊C4×C61 | — | 4 | 1 | no | — |
| 106 | C22⋊Dic61 | — | 4 | 1 | no | — |
| 107 | C22⋊Dic61 | — | 4 | 1 | no | — |
| 108 | #11758202 | — | 4 | 2 | no | — |
| 109 | #11758201 | — | 4 | 2 | no | — |
| 110 | #11758200 | — | 4 | 2 | no | — |
| 111 | #11758200 | — | 8 | 1 | no | — |
| 112 | #11758199 | — | 4 | 2 | no | — |
| 113 | #11758198 | — | 4 | 1 | no | — |
| 114 | C4⋊Dic61 | — | 2 | 1 | no | — |
| 115 | C4⋊Dic61 | — | 4 | 1 | no | — |
| 116 | #11758196 | — | 4 | 1 | no | — |
| 117 | #11758196 | — | 4 | 1 | no | — |
| 118 | #11758194 | — | 4 | 1 | no | — |
| 119 | #11758194 | — | 4 | 1 | no | — |
| 120 | C2×#92418 | — | 2 | 2 | no | — |
| 121 | C2×#92418 | — | 2 | 1 | no | — |
| 122 | C2×#92418 | — | 4 | 1 | no | — |
| 123 | Dic244 | — | 4 | 1 | no | — |
| 124 | C16×C61 | — | 4 | 1 | no | — |
| 125 | #11758185 | — | 4 | 1 | no | — |
| 126 | C23×C61 | — | 4 | 1 | no | — |
| 127 | C23×C61 | — | 4 | 1 | no | — |
| 128 | C23×C61 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 129 | C22×D61 | — | 2 | 1 | no | — |
| 130 | Q8×C61 | — | 4 | 1 | no | — |
| 131 | Q8×C61 | — | 4 | 1 | no | — |
| 132 | D4×C61 | — | 4 | 1 | no | — |
| 133 | D4×C61 | — | 4 | 1 | no | — |
| 134 | D4×C61 | — | 4 | 1 | no | — |
| 135 | D4×C61 | — | 4 | 1 | no | — |
| 136 | D4×C61 | — | 8 | 1 | no | — |
| 137 | D4×C61 | — | 8 | 1 | no | — |
| 138 | D4×C61 | — | 16 | 1 | no | — |
| 139 | C2×C4×C61 | — | 2 | 1 | no | — |
| 140 | C2×C4×C61 | — | 2 | 1 | no | — |
| 141 | C2×C4×C61 | — | 4 | 1 | no | — |
| 142 | C2×C4×C61 | — | 4 | 1 | no | — |
| 143 | C2×C4×C61 | — | 8 | 1 | no | — |
| 144 | C2×C4×C61 | — | 8 | 1 | no | — |
| 145 | C2×C4×C61 | #120 | 1 | 1 | yes | characteristic |
| 146 | C2×C4×C61 | C2×D8 | 1 | 1 | yes | characteristic |
| 147 | C22⋊D61 | — | 8 | 1 | no | — |
| 148 | C22⋊D61 | — | 8 | 2 | no | — |
| 149 | C22⋊D61 | — | 16 | 1 | no | — |
| 150 | C2×Dic61 | — | 2 | 1 | no | — |
| 151 | C2×Dic61 | — | 4 | 1 | no | — |
| 152 | C2×Dic61 | — | 4 | 1 | no | — |
| 153 | C2×Dic61 | — | 8 | 2 | no | — |
| 154 | D244 | — | 4 | 1 | no | — |
| 155 | C4×D61 | — | 4 | 1 | no | — |
| 156 | C4×D61 | — | 4 | 1 | no | — |
| 157 | C4×D61 | — | 16 | 1 | no | — |
| 158 | Dic122 | — | 4 | 1 | no | — |
| 159 | Dic122 | — | 4 | 1 | no | — |
| 160 | Dic122 | — | 4 | 1 | no | — |
| 161 | C8×C61 | — | 2 | 1 | no | — |
| 162 | C8×C61 | — | 2 | 1 | no | — |
| 163 | #92418 | — | 4 | 2 | no | — |
| 164 | #92418 | — | 4 | 1 | no | — |
| 165 | #12119 | — | 61 | 1 | no | maximal, Sylow |
| 166 | C22×C61 | — | 2 | 1 | no | — |
| 167 | C22×C61 | — | 4 | 1 | no | — |
| 168 | C22×C61 | — | 8 | 1 | no | — |
| 169 | C22×C61 | — | 8 | 1 | no | — |
| 170 | C22×C61 | — | 8 | 2 | no | — |
| 171 | C22×C61 | — | 8 | 1 | no | — |
| 172 | C22×C61 | — | 8 | 1 | no | — |
| 173 | C22×C61 | #447 | 1 | 1 | yes | characteristic |
| 174 | C2×D61 | — | 4 | 1 | no | — |
| 175 | C2×D61 | — | 4 | 1 | no | — |
| 176 | C2×D61 | — | 4 | 1 | no | — |
| 177 | C4×C61 | — | 2 | 1 | no | — |
| 178 | C4×C61 | — | 8 | 1 | no | — |
| 179 | C4×C61 | — | 8 | 1 | no | — |
| 180 | C4×C61 | #453 | 1 | 1 | yes | characteristic |
| 181 | C4×C61 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 182 | Dic61 | — | 4 | 1 | no | — |
| 183 | Dic61 | — | 8 | 1 | no | — |
| 184 | Dic61 | — | 8 | 1 | no | — |
| 185 | #3204 | — | 61 | 1 | no | — |
| 186 | #2191 | — | 61 | 1 | no | — |
| 187 | #2190 | D61 | 1 | 1 | yes | characteristic, complemented |
| 188 | #2017 | — | 61 | 1 | no | — |
| 189 | #1342 | — | 61 | 1 | no | — |
| 190 | #1341 | — | 61 | 1 | no | — |
| 191 | #1321 | — | 61 | 1 | no | — |
| 192 | C2×C61 | — | 2 | 1 | no | — |
| 193 | C2×C61 | — | 4 | 1 | no | — |
| 194 | C2×C61 | — | 16 | 1 | no | — |
| 195 | C2×C61 | — | 16 | 1 | no | — |
| 196 | C2×C61 | #1595 | 1 | 1 | yes | characteristic |
| 197 | D61 | — | 8 | 1 | no | — |
| 198 | #575 | — | 122 | 1 | no | — |
| 199 | #575 | C2×D61 | 1 | 1 | yes | characteristic |
| 200 | #537 | — | 122 | 1 | no | — |
| 201 | #510 | — | 122 | 1 | no | — |
| 202 | #509 | — | 2 | 1 | no | — |
| 203 | #483 | — | 122 | 1 | no | — |
| 204 | #481 | — | 122 | 1 | no | — |
| 205 | #470 | — | 61 | 1 | no | — |
| 206 | #469 | C2×D61 | 1 | 1 | yes | characteristic |
| 207 | #465 | — | 122 | 1 | no | — |
| 208 | #452 | — | 122 | 1 | no | — |
| 209 | #449 | — | 122 | 1 | no | — |
| 210 | #408 | — | 61 | 1 | no | — |
| 211 | #408 | — | 122 | 1 | no | — |
| 212 | #360 | — | 2 | 1 | no | — |
| 213 | #360 | — | 122 | 1 | no | — |
| 214 | #349 | — | 61 | 1 | no | — |
| 215 | #349 | C2×D61 | 1 | 1 | yes | characteristic |
| 216 | #338 | — | 61 | 1 | no | — |
| 217 | C61 | #12119 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 218 | C2×#41 | — | 2 | 1 | no | — |
| 219 | C2×#41 | — | 61 | 1 | no | — |
| 220 | C2×#41 | — | 122 | 1 | no | — |
| 221 | #137 | — | 4 | 1 | no | — |
| 222 | #137 | — | 244 | 1 | no | — |
| 223 | #137 | — | 244 | 1 | no | — |
| 224 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 225 | AGL(1,ℤ/8) | — | 244 | 1 | no | — |
| 226 | AGL(1,ℤ/8) | — | 244 | 1 | no | — |
| 227 | #135 | — | 2 | 1 | no | — |
| 228 | #135 | — | 2 | 1 | no | — |
| 229 | #135 | — | 244 | 2 | no | — |
| 230 | C2×Q16 | — | 61 | 1 | no | — |
| 231 | C2×SD16 | — | 122 | 1 | no | — |
| 232 | C2×D8 | C22⋊D61 | 1 | 1 | yes | characteristic |
| 233 | C2×M16 | — | 122 | 1 | no | — |
| 234 | C2×M16 | C22×D61 | 1 | 1 | yes | characteristic |
| 235 | C22×C8 | — | 61 | 1 | no | — |
| 236 | C22⋊Q8 | — | 122 | 1 | no | — |
| 237 | C22⋊Q8 | — | 122 | 1 | no | — |
| 238 | C22⋊Q8 | — | 244 | 1 | no | — |
| 239 | #121 | — | 2 | 1 | no | — |
| 240 | #121 | — | 122 | 1 | no | — |
| 241 | #121 | — | 244 | 1 | no | — |
| 242 | #121 | — | 244 | 1 | no | — |
| 243 | #121 | — | 244 | 1 | no | — |
| 244 | C2×C4⋊C4 | — | 122 | 1 | no | — |
| 245 | Q32 | — | 244 | 1 | no | — |
| 246 | SD32 | — | 4 | 1 | no | — |
| 247 | SD32 | — | 244 | 1 | no | — |
| 248 | D16 | — | 4 | 1 | no | — |
| 249 | M32 | — | 2 | 1 | no | — |
| 250 | M32 | — | 122 | 1 | no | — |
| 251 | #106 | — | 61 | 1 | no | — |
| 252 | #106 | — | 122 | 1 | no | — |
| 253 | #106 | C22⋊D61 | 1 | 1 | yes | characteristic |
| 254 | #103 | — | 122 | 1 | no | — |
| 255 | #103 | — | 122 | 1 | no | — |
| 256 | #102 | — | 2 | 1 | no | — |
| 257 | #102 | — | 122 | 1 | no | — |
| 258 | C22⋊C8 | — | 122 | 1 | no | — |
| 259 | C22⋊C8 | — | 122 | 1 | no | — |
| 260 | C22⋊C8 | — | 244 | 2 | no | — |
| 261 | #41 | — | 4 | 1 | no | — |
| 262 | #41 | — | 4 | 1 | no | — |
| 263 | #41 | — | 4 | 1 | no | — |
| 264 | #41 | — | 4 | 1 | no | — |
| 265 | #41 | — | 488 | 1 | no | — |
| 266 | #41 | — | 488 | 1 | no | — |
| 267 | #41 | — | 244 | 1 | no | — |
| 268 | #41 | — | 244 | 1 | no | — |
| 269 | C2×Q8 | — | 2 | 1 | no | — |
| 270 | C2×Q8 | — | 61 | 1 | no | — |
| 271 | C2×Q8 | — | 122 | 1 | no | — |
| 272 | C2×D4 | — | 2 | 1 | no | — |
| 273 | C2×D4 | — | 2 | 1 | no | — |
| 274 | C2×D4 | — | 4 | 1 | no | — |
| 275 | C2×D4 | — | 4 | 1 | no | — |
| 276 | C2×D4 | — | 61 | 1 | no | — |
| 277 | C2×D4 | — | 122 | 1 | no | — |
| 278 | C2×D4 | — | 244 | 1 | no | — |
| 279 | C2×D4 | — | 244 | 1 | no | — |
| 280 | C22×C4 | — | 4 | 1 | no | — |
| 281 | C22×C4 | — | 122 | 1 | no | — |
| 282 | C22×C4 | — | 244 | 1 | no | — |
| 283 | C22×C4 | — | 244 | 1 | no | — |
| 284 | C22×C4 | D4×D61 | 1 | 1 | yes | characteristic |
| 285 | Q16 | — | 2 | 1 | no | — |
| 286 | Q16 | — | 2 | 1 | no | — |
| 287 | Q16 | — | 244 | 1 | no | — |
| 288 | Q16 | — | 244 | 2 | no | — |
| 289 | SD16 | — | 4 | 1 | no | — |
| 290 | SD16 | — | 4 | 1 | no | — |
| 291 | SD16 | — | 488 | 1 | no | — |
| 292 | SD16 | — | 244 | 2 | no | — |
| 293 | SD16 | — | 244 | 2 | no | — |
| 294 | D8 | — | 2 | 1 | no | — |
| 295 | D8 | — | 2 | 1 | no | — |
| 296 | D8 | — | 4 | 1 | no | — |
| 297 | D8 | — | 244 | 2 | no | — |
| 298 | M16 | — | 4 | 1 | no | — |
| 299 | M16 | — | 244 | 1 | no | — |
| 300 | M16 | — | 244 | 1 | no | — |
| 301 | C2×C8 | — | 122 | 2 | no | — |
| 302 | C2×C8 | — | 122 | 1 | no | — |
| 303 | C2×C8 | — | 244 | 1 | no | — |
| 304 | C2×C8 | D4×D61 | 1 | 1 | yes | characteristic |
| 305 | C2×C8 | C2×C22⋊D61 | 1 | 1 | yes | characteristic |
| 306 | C4⋊C4 | — | 2 | 1 | no | — |
| 307 | C4⋊C4 | — | 122 | 1 | no | — |
| 308 | C4⋊C4 | — | 244 | 1 | no | — |
| 309 | C4⋊C4 | — | 244 | 1 | no | — |
| 310 | C4⋊C4 | — | 244 | 1 | no | — |
| 311 | C22⋊C4 | — | 4 | 1 | no | — |
| 312 | C22⋊C4 | — | 244 | 1 | no | — |
| 313 | C22⋊C4 | — | 244 | 1 | no | — |
| 314 | C22⋊C4 | — | 244 | 1 | no | — |
| 315 | C16 | — | 4 | 1 | no | — |
| 316 | C16 | — | 244 | 1 | no | — |
| 317 | C23 | — | 4 | 1 | no | — |
| 318 | C23 | — | 4 | 1 | no | — |
| 319 | C23 | — | 122 | 1 | no | — |
| 320 | C23 | #14519801 | 1 | 1 | yes | characteristic |
| 321 | Q8 | — | 4 | 1 | no | — |
| 322 | Q8 | — | 4 | 1 | no | — |
| 323 | Q8 | — | 244 | 1 | no | — |
| 324 | Q8 | — | 244 | 1 | no | — |
| 325 | Q8 | — | 244 | 1 | no | — |
| 326 | D4 | — | 4 | 1 | no | — |
| 327 | D4 | — | 4 | 1 | no | — |
| 328 | D4 | — | 4 | 1 | no | — |
| 329 | D4 | — | 4 | 1 | no | — |
| 330 | D4 | — | 8 | 1 | no | — |
| 331 | D4 | — | 8 | 1 | no | — |
| 332 | D4 | — | 16 | 1 | no | — |
| 333 | D4 | — | 976 | 1 | no | — |
| 334 | D4 | — | 488 | 2 | no | — |
| 335 | D4 | — | 488 | 1 | no | — |
| 336 | D4 | — | 244 | 1 | no | — |
| 337 | C2×C4 | — | 2 | 1 | no | — |
| 338 | C2×C4 | — | 2 | 1 | no | — |
| 339 | C2×C4 | — | 4 | 1 | no | — |
| 340 | C2×C4 | — | 4 | 1 | no | — |
| 341 | C2×C4 | — | 8 | 1 | no | — |
| 342 | C2×C4 | — | 8 | 1 | no | — |
| 343 | C2×C4 | — | 122 | 1 | no | — |
| 344 | C2×C4 | — | 976 | 1 | no | — |
| 345 | C2×C4 | — | 488 | 2 | no | — |
| 346 | C2×C4 | — | 244 | 1 | no | — |
| 347 | C2×C4 | — | 244 | 1 | no | — |
| 348 | C2×C4 | — | 244 | 1 | no | — |
| 349 | C2×C4 | — | 244 | 1 | no | — |
| 350 | C2×C4 | #14519745 | 1 | 1 | yes | characteristic |
| 351 | C2×C4 | D8×D61 | 1 | 1 | yes | characteristic |
| 352 | C8 | — | 2 | 1 | no | — |
| 353 | C8 | — | 2 | 1 | no | — |
| 354 | C8 | — | 244 | 2 | no | — |
| 355 | C8 | — | 244 | 1 | no | — |
| 356 | C22 | — | 2 | 1 | no | — |
| 357 | C22 | — | 4 | 1 | no | — |
| 358 | C22 | — | 8 | 1 | no | — |
| 359 | C22 | — | 8 | 1 | no | — |
| 360 | C22 | — | 8 | 2 | no | — |
| 361 | C22 | — | 8 | 1 | no | — |
| 362 | C22 | — | 8 | 1 | no | — |
| 363 | C22 | — | 244 | 1 | no | — |
| 364 | C22 | — | 244 | 1 | no | — |
| 365 | C22 | — | 244 | 1 | no | — |
| 366 | C22 | #16839894 | 1 | 1 | yes | characteristic |
| 367 | C4 | — | 2 | 1 | no | — |
| 368 | C4 | — | 8 | 1 | no | — |
| 369 | C4 | — | 8 | 1 | no | — |
| 370 | C4 | — | 488 | 1 | no | — |
| 371 | C4 | — | 488 | 1 | no | — |
| 372 | C4 | — | 244 | 1 | no | — |
| 373 | C4 | #16839928 | 1 | 1 | yes | characteristic |
| 374 | C4 | #16839948 | 1 | 1 | yes | characteristic |
| 375 | C2 | — | 2 | 1 | no | — |
| 376 | C2 | — | 4 | 1 | no | — |
| 377 | C2 | — | 16 | 1 | no | — |
| 378 | C2 | — | 16 | 1 | no | — |
| 379 | C2 | — | 488 | 1 | no | — |
| 380 | C2 | #21444735 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21456730 | C2 | semidirect |
| 2. #21447770 | C2 | semidirect |
| 3. #21446922 | C2 | semidirect |
| 4. #21443814 | C2 | semidirect |
| 5. #21443810 | C2 | semidirect |
| 6. #21443756 | C2 | semidirect |
| 7. C61×#2190 | C2 | semidirect |
| 187. #2190 | D61 | semidirect |
| 217. C61 | #12119 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456730 | 2 |
| #21447770 | 2 |
| #21446922 | 2 |
| #21443814 | 2 |
| #21443810 | 2 |
| #21443756 | 2 |
| C61×#2190 | 2 |
| #12119 | 61 |