Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
678 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 109 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 | #13126146 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13125756 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13125288 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13115762 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13115755 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13113332 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C13×#1283 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#88162 | — | 2 | 2 | no | — |
| 9 | #11719182 | C22 | 1 | 1 | yes | characteristic |
| 10 | #11719182 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#88128 | C22 | 1 | 1 | yes | characteristic |
| 12 | C13×#431 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C13×C4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 14 | C4×C13×M16 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#88065 | — | 2 | 2 | no | — |
| 16 | #11718776 | — | 2 | 2 | no | — |
| 17 | C2×#88061 | — | 2 | 2 | no | — |
| 18 | C4×C4⋊Dic13 | C22 | 1 | 1 | yes | characteristic |
| 19 | #11718507 | — | 2 | 1 | no | — |
| 20 | #11718507 | — | 2 | 1 | no | — |
| 21 | #11718504 | — | 2 | 1 | no | — |
| 22 | #11718504 | — | 2 | 1 | no | — |
| 23 | #11718504 | — | 2 | 2 | no | — |
| 24 | #11718393 | — | 2 | 2 | no | — |
| 25 | #11718373 | — | 2 | 2 | no | — |
| 26 | #11718356 | — | 2 | 1 | no | — |
| 27 | #11718356 | — | 2 | 1 | no | — |
| 28 | #11718355 | — | 2 | 1 | no | — |
| 29 | #11718354 | — | 2 | 1 | no | — |
| 30 | #11718062 | — | 2 | 2 | no | — |
| 31 | C2×#6127 | — | 2 | 1 | no | — |
| 32 | C2×#6127 | — | 2 | 1 | no | — |
| 33 | C22×D52 | — | 2 | 1 | no | — |
| 34 | C22×D52 | — | 2 | 1 | no | — |
| 35 | C22×D52 | — | 2 | 1 | no | — |
| 36 | C2×C13×M16 | D4 | 1 | 2 | yes | — |
| 37 | C22×C8×C13 | D4 | 1 | 2 | yes | — |
| 38 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 39 | #88184 | — | 2 | 1 | no | — |
| 40 | #88184 | — | 2 | 1 | no | — |
| 41 | #88184 | — | 2 | 1 | no | — |
| 42 | #88184 | — | 2 | 1 | no | — |
| 43 | C2×C4⋊Dic13 | — | 2 | 1 | no | — |
| 44 | C2×C4×Dic13 | — | 2 | 1 | no | — |
| 45 | #88162 | — | 4 | 4 | no | — |
| 46 | #88162 | — | 4 | 4 | no | — |
| 47 | C2×D104 | — | 2 | 4 | no | — |
| 48 | C2×D104 | — | 2 | 2 | no | — |
| 49 | C2×D104 | — | 2 | 4 | no | — |
| 50 | C2×#6095 | — | 2 | 4 | no | — |
| 51 | #88129 | — | 2 | 1 | no | — |
| 52 | #88129 | — | 2 | 1 | no | — |
| 53 | #88128 | — | 2 | 1 | no | — |
| 54 | #88128 | — | 2 | 1 | no | — |
| 55 | #88128 | — | 2 | 1 | no | — |
| 56 | #88128 | D4 | 1 | 2 | yes | — |
| 57 | #88128 | D4 | 1 | 1 | yes | characteristic |
| 58 | #88128 | D4 | 1 | 1 | yes | characteristic |
| 59 | C4×D52 | — | 2 | 1 | no | — |
| 60 | C4×D52 | — | 2 | 1 | no | — |
| 61 | C4×D52 | — | 2 | 1 | no | — |
| 62 | C4×D52 | — | 2 | 1 | no | — |
| 63 | #88123 | D4 | 1 | 1 | yes | characteristic |
| 64 | #88123 | D4 | 1 | 1 | yes | characteristic |
| 65 | C13×C4⋊C8 | — | 2 | 1 | no | — |
| 66 | C13×C4⋊C8 | — | 2 | 1 | no | — |
| 67 | C13×C4⋊C8 | — | 2 | 1 | no | — |
| 68 | C13×C22⋊C8 | D4 | 1 | 2 | yes | — |
| 69 | C13×#97 | — | 2 | 1 | no | — |
| 70 | C4×C8×C13 | — | 2 | 1 | no | — |
| 71 | C4×C8×C13 | — | 2 | 1 | no | — |
| 72 | #88071 | — | 2 | 1 | no | — |
| 73 | #88065 | — | 4 | 4 | no | — |
| 74 | #88061 | — | 2 | 2 | no | — |
| 75 | #88061 | — | 2 | 2 | no | — |
| 76 | #88061 | — | 2 | 4 | no | — |
| 77 | #88061 | — | 4 | 4 | no | — |
| 78 | #88058 | — | 2 | 2 | no | — |
| 79 | #10192 | — | 13 | 1 | no | maximal, Sylow |
| 80 | C23×D13 | — | 4 | 1 | no | — |
| 81 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 82 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 83 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 84 | C2×C22⋊D13 | — | 4 | 1 | no | — |
| 85 | C2×C22⋊D13 | — | 4 | 1 | no | — |
| 86 | C22×Dic13 | — | 4 | 1 | no | — |
| 87 | #6127 | — | 4 | 2 | no | — |
| 88 | #6127 | — | 4 | 2 | no | — |
| 89 | #6127 | — | 4 | 2 | no | — |
| 90 | #6127 | — | 4 | 2 | no | — |
| 91 | C2×D52 | — | 2 | 1 | no | — |
| 92 | C2×D52 | — | 2 | 1 | no | — |
| 93 | C2×D52 | — | 2 | 1 | no | — |
| 94 | C2×D52 | — | 2 | 2 | no | — |
| 95 | C2×D52 | — | 2 | 2 | no | — |
| 96 | C2×D52 | — | 2 | 1 | no | — |
| 97 | C2×D52 | — | 2 | 2 | no | — |
| 98 | C2×D52 | — | 2 | 1 | no | — |
| 99 | C2×D52 | — | 2 | 1 | no | — |
| 100 | C2×D52 | — | 4 | 2 | no | — |
| 101 | C2×D52 | — | 4 | 2 | no | — |
| 102 | C2×D52 | — | 4 | 2 | no | — |
| 103 | C2×D52 | — | 4 | 2 | no | — |
| 104 | C2×D52 | — | 4 | 1 | no | — |
| 105 | C2×D52 | — | 4 | 1 | no | — |
| 106 | C2×D52 | — | 4 | 1 | no | — |
| 107 | C2×D52 | — | 8 | 2 | no | — |
| 108 | C2×C4×D13 | — | 4 | 1 | no | — |
| 109 | C2×C4×D13 | — | 4 | 1 | no | — |
| 110 | C2×Dic26 | — | 2 | 1 | no | — |
| 111 | C2×Dic26 | — | 2 | 1 | no | — |
| 112 | C13×M16 | — | 2 | 2 | no | — |
| 113 | C13×M16 | D8 | 1 | 4 | yes | complemented |
| 114 | C2×C8×C13 | — | 2 | 2 | no | — |
| 115 | C2×C8×C13 | — | 2 | 2 | no | — |
| 116 | C2×C8×C13 | — | 2 | 2 | no | — |
| 117 | C2×C8×C13 | — | 4 | 2 | no | — |
| 118 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 121 | C42×C13 | #41 | 1 | 1 | yes | characteristic |
| 122 | #6103 | — | 4 | 1 | no | — |
| 123 | #6103 | — | 4 | 1 | no | — |
| 124 | #6103 | — | 4 | 1 | no | — |
| 125 | #6103 | — | 4 | 1 | no | — |
| 126 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 127 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 128 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 129 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 130 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 131 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 132 | C4×Dic13 | — | 4 | 2 | no | — |
| 133 | D104 | — | 4 | 8 | no | — |
| 134 | D104 | — | 8 | 4 | no | — |
| 135 | D104 | — | 8 | 2 | no | — |
| 136 | #6095 | — | 4 | 8 | no | — |
| 137 | #3245 | — | 13 | 1 | no | — |
| 138 | #3205 | — | 13 | 1 | no | — |
| 139 | #3151 | — | 13 | 1 | no | — |
| 140 | #1982 | — | 13 | 1 | no | — |
| 141 | #1980 | — | 13 | 1 | no | — |
| 142 | #1502 | — | 13 | 1 | no | — |
| 143 | #1283 | D13 | 1 | 1 | yes | characteristic, complemented |
| 144 | C23×C13 | #127 | 1 | 1 | yes | characteristic |
| 145 | C22×D13 | — | 4 | 1 | no | — |
| 146 | C22×D13 | — | 4 | 1 | no | — |
| 147 | C22×D13 | — | 4 | 2 | no | — |
| 148 | C22×D13 | — | 8 | 2 | no | — |
| 149 | C22×D13 | — | 8 | 2 | no | — |
| 150 | C22×D13 | — | 8 | 1 | no | — |
| 151 | C22×D13 | — | 8 | 1 | no | — |
| 152 | C2×C4×C13 | — | 2 | 1 | no | — |
| 153 | C2×C4×C13 | — | 2 | 1 | no | — |
| 154 | C2×C4×C13 | — | 4 | 1 | no | — |
| 155 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 156 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 157 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 158 | C2×C4×C13 | #121 | 1 | 1 | yes | characteristic |
| 159 | C2×C4×C13 | #121 | 1 | 1 | yes | characteristic |
| 160 | C2×C4×C13 | #121 | 1 | 1 | yes | characteristic |
| 161 | C2×C4×C13 | C2×D8 | 1 | 2 | yes | — |
| 162 | C2×C4×C13 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 163 | C22⋊D13 | — | 8 | 1 | no | — |
| 164 | C22⋊D13 | — | 8 | 1 | no | — |
| 165 | C22⋊D13 | — | 8 | 1 | no | — |
| 166 | C22⋊D13 | — | 8 | 1 | no | — |
| 167 | C2×Dic13 | — | 4 | 2 | no | — |
| 168 | C2×Dic13 | — | 4 | 1 | no | — |
| 169 | C2×Dic13 | — | 4 | 1 | no | — |
| 170 | C2×Dic13 | — | 8 | 1 | no | — |
| 171 | C2×Dic13 | — | 8 | 1 | no | — |
| 172 | D52 | — | 4 | 2 | no | — |
| 173 | D52 | — | 4 | 4 | no | — |
| 174 | D52 | — | 4 | 4 | no | — |
| 175 | D52 | — | 4 | 4 | no | — |
| 176 | D52 | — | 4 | 2 | no | — |
| 177 | D52 | — | 4 | 1 | no | — |
| 178 | D52 | — | 4 | 1 | no | — |
| 179 | D52 | — | 4 | 1 | no | — |
| 180 | D52 | — | 4 | 1 | no | — |
| 181 | D52 | — | 4 | 2 | no | — |
| 182 | D52 | — | 8 | 2 | no | — |
| 183 | D52 | — | 8 | 1 | no | — |
| 184 | D52 | — | 8 | 1 | no | — |
| 185 | D52 | — | 8 | 1 | no | — |
| 186 | D52 | — | 8 | 2 | no | — |
| 187 | C4×D13 | — | 8 | 2 | no | — |
| 188 | C4×D13 | — | 8 | 2 | no | — |
| 189 | Dic26 | — | 4 | 2 | no | — |
| 190 | Dic26 | — | 4 | 2 | no | — |
| 191 | C8×C13 | — | 2 | 4 | no | — |
| 192 | C8×C13 | — | 4 | 2 | no | — |
| 193 | C8×C13 | — | 4 | 2 | no | — |
| 194 | C2×AGL(1,ℤ/8) | — | 26 | 2 | no | — |
| 195 | #532 | — | 13 | 1 | no | — |
| 196 | #532 | — | 13 | 1 | no | — |
| 197 | C2×#127 | — | 13 | 1 | no | — |
| 198 | #496 | — | 26 | 2 | no | — |
| 199 | #493 | — | 26 | 1 | no | — |
| 200 | #493 | — | 26 | 1 | no | — |
| 201 | #492 | — | 26 | 1 | no | — |
| 202 | #486 | — | 26 | 1 | no | — |
| 203 | #474 | — | 26 | 1 | no | — |
| 204 | #474 | — | 26 | 1 | no | — |
| 205 | #466 | — | 26 | 2 | no | — |
| 206 | #459 | — | 26 | 2 | no | — |
| 207 | #459 | — | 26 | 1 | no | — |
| 208 | #459 | — | 26 | 1 | no | — |
| 209 | #447 | — | 26 | 2 | no | — |
| 210 | #431 | C2×D13 | 1 | 1 | yes | characteristic |
| 211 | C2×C4⋊C8 | C2×D13 | 1 | 1 | yes | characteristic |
| 212 | C2×#104 | — | 26 | 2 | no | — |
| 213 | C2×#102 | — | 26 | 2 | no | — |
| 214 | C4×M16 | C2×D13 | 1 | 1 | yes | characteristic |
| 215 | C4×C4⋊C4 | — | 13 | 1 | no | — |
| 216 | #327 | — | 26 | 2 | no | — |
| 217 | C22×C13 | — | 2 | 1 | no | — |
| 218 | C22×C13 | — | 2 | 1 | no | — |
| 219 | C22×C13 | #392 | 1 | 1 | yes | characteristic |
| 220 | C22×C13 | #493 | 1 | 1 | yes | characteristic |
| 221 | C22×C13 | #496 | 1 | 1 | yes | characteristic |
| 222 | C2×D13 | — | 8 | 2 | no | — |
| 223 | C2×D13 | — | 8 | 1 | no | — |
| 224 | C2×D13 | — | 8 | 1 | no | — |
| 225 | C2×D13 | — | 8 | 2 | no | — |
| 226 | C2×D13 | — | 8 | 1 | no | — |
| 227 | C2×D13 | — | 8 | 1 | no | — |
| 228 | C2×D13 | — | 8 | 1 | no | — |
| 229 | C2×D13 | — | 8 | 1 | no | — |
| 230 | C2×D13 | — | 8 | 2 | no | — |
| 231 | C2×D13 | — | 16 | 2 | no | — |
| 232 | C2×D13 | — | 16 | 2 | no | — |
| 233 | C4×C13 | — | 2 | 1 | no | — |
| 234 | C4×C13 | — | 2 | 1 | no | — |
| 235 | C4×C13 | — | 2 | 1 | no | — |
| 236 | C4×C13 | #447 | 1 | 2 | yes | — |
| 237 | C4×C13 | #453 | 1 | 1 | yes | characteristic |
| 238 | C4×C13 | #454 | 1 | 1 | yes | characteristic |
| 239 | C4×C13 | #459 | 1 | 2 | yes | — |
| 240 | Dic13 | — | 8 | 2 | no | — |
| 241 | Dic13 | — | 8 | 1 | no | — |
| 242 | Dic13 | — | 8 | 1 | no | — |
| 243 | C2×#41 | — | 26 | 1 | no | — |
| 244 | C2×#41 | — | 26 | 1 | no | — |
| 245 | C22×D4 | — | 26 | 1 | no | — |
| 246 | C22×D4 | — | 26 | 1 | no | — |
| 247 | C22×D4 | — | 26 | 1 | no | — |
| 248 | AGL(1,ℤ/8) | — | 52 | 4 | no | — |
| 249 | AGL(1,ℤ/8) | — | 52 | 4 | no | — |
| 250 | C2×SD16 | — | 26 | 4 | no | — |
| 251 | C2×D8 | — | 26 | 4 | no | — |
| 252 | C2×D8 | — | 26 | 4 | no | — |
| 253 | C2×D8 | — | 26 | 2 | no | — |
| 254 | C2×M16 | D52 | 1 | 2 | yes | — |
| 255 | C22×C8 | D52 | 1 | 2 | yes | — |
| 256 | C4⋊Q8 | — | 13 | 1 | no | — |
| 257 | C4⋊Q8 | — | 13 | 1 | no | — |
| 258 | #127 | — | 13 | 2 | no | — |
| 259 | #127 | — | 13 | 1 | no | — |
| 260 | #127 | — | 13 | 1 | no | — |
| 261 | #127 | — | 26 | 1 | no | — |
| 262 | #127 | — | 26 | 1 | no | — |
| 263 | #127 | — | 26 | 1 | no | — |
| 264 | #124 | — | 26 | 1 | no | — |
| 265 | #124 | — | 26 | 1 | no | — |
| 266 | #121 | — | 26 | 1 | no | — |
| 267 | #121 | — | 26 | 1 | no | — |
| 268 | #121 | — | 26 | 1 | no | — |
| 269 | #121 | — | 26 | 1 | no | — |
| 270 | C4×D4 | — | 26 | 1 | no | — |
| 271 | C4×D4 | — | 26 | 1 | no | — |
| 272 | C4×D4 | — | 26 | 1 | no | — |
| 273 | C4×D4 | — | 26 | 1 | no | — |
| 274 | C2×C4⋊C4 | — | 26 | 1 | no | — |
| 275 | C2×C42 | — | 26 | 1 | no | — |
| 276 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 277 | #107 | — | 26 | 2 | no | — |
| 278 | C4⋊C8 | — | 2 | 1 | no | — |
| 279 | C4⋊C8 | — | 2 | 1 | no | — |
| 280 | C4⋊C8 | — | 2 | 1 | no | — |
| 281 | #104 | — | 52 | 4 | no | — |
| 282 | #102 | — | 26 | 4 | no | — |
| 283 | #102 | — | 26 | 2 | no | — |
| 284 | #102 | — | 26 | 2 | no | — |
| 285 | #102 | — | 52 | 4 | no | — |
| 286 | C22⋊C8 | D52 | 1 | 2 | yes | — |
| 287 | #97 | — | 2 | 1 | no | — |
| 288 | C4×C8 | — | 2 | 1 | no | — |
| 289 | C4×C8 | — | 2 | 1 | no | — |
| 290 | #95 | — | 26 | 1 | no | — |
| 291 | C2×C13 | — | 2 | 1 | no | — |
| 292 | C2×C13 | — | 2 | 1 | no | — |
| 293 | C2×C13 | #2006 | 1 | 1 | yes | characteristic |
| 294 | C2×C13 | #2008 | 1 | 1 | yes | characteristic |
| 295 | C2×C13 | #2011 | 1 | 1 | yes | characteristic |
| 296 | D13 | — | 16 | 1 | no | — |
| 297 | D13 | — | 16 | 1 | no | — |
| 298 | D13 | — | 16 | 2 | no | — |
| 299 | C24 | — | 52 | 1 | no | — |
| 300 | #41 | — | 52 | 2 | no | — |
| 301 | #41 | — | 52 | 2 | no | — |
| 302 | #41 | — | 52 | 2 | no | — |
| 303 | #41 | — | 52 | 2 | no | — |
| 304 | C2×Q8 | — | 26 | 1 | no | — |
| 305 | C2×Q8 | — | 26 | 1 | no | — |
| 306 | C2×D4 | — | 26 | 1 | no | — |
| 307 | C2×D4 | — | 26 | 1 | no | — |
| 308 | C2×D4 | — | 26 | 2 | no | — |
| 309 | C2×D4 | — | 26 | 1 | no | — |
| 310 | C2×D4 | — | 26 | 1 | no | — |
| 311 | C2×D4 | — | 26 | 2 | no | — |
| 312 | C2×D4 | — | 26 | 1 | no | — |
| 313 | C2×D4 | — | 26 | 2 | no | — |
| 314 | C2×D4 | — | 26 | 1 | no | — |
| 315 | C2×D4 | — | 52 | 2 | no | — |
| 316 | C2×D4 | — | 52 | 2 | no | — |
| 317 | C2×D4 | — | 52 | 1 | no | — |
| 318 | C2×D4 | — | 52 | 1 | no | — |
| 319 | C2×D4 | — | 52 | 1 | no | — |
| 320 | C2×D4 | — | 52 | 1 | no | — |
| 321 | C2×D4 | — | 52 | 1 | no | — |
| 322 | C2×D4 | — | 52 | 2 | no | — |
| 323 | C2×D4 | — | 52 | 2 | no | — |
| 324 | C2×D4 | — | 104 | 2 | no | — |
| 325 | C22×C4 | — | 52 | 1 | no | — |
| 326 | C22×C4 | — | 52 | 1 | no | — |
| 327 | C22×C4 | — | 52 | 1 | no | — |
| 328 | C22×C4 | C2×D52 | 1 | 1 | yes | characteristic |
| 329 | C22×C4 | C2×D52 | 1 | 1 | yes | characteristic |
| 330 | C22×C4 | C2×D52 | 1 | 1 | yes | characteristic |
| 331 | SD16 | — | 52 | 8 | no | — |
| 332 | D8 | — | 52 | 8 | no | — |
| 333 | D8 | — | 104 | 4 | no | — |
| 334 | D8 | — | 104 | 2 | no | — |
| 335 | M16 | — | 2 | 2 | no | — |
| 336 | M16 | D104 | 1 | 4 | yes | complemented |
| 337 | C2×C8 | — | 2 | 2 | no | — |
| 338 | C2×C8 | — | 2 | 2 | no | — |
| 339 | C2×C8 | — | 2 | 2 | no | — |
| 340 | C2×C8 | — | 4 | 2 | no | — |
| 341 | C4⋊C4 | — | 26 | 2 | no | — |
| 342 | C4⋊C4 | — | 26 | 1 | no | — |
| 343 | C4⋊C4 | — | 26 | 1 | no | — |
| 344 | C4⋊C4 | — | 26 | 1 | no | — |
| 345 | C4⋊C4 | — | 26 | 1 | no | — |
| 346 | C4⋊C4 | — | 52 | 1 | no | — |
| 347 | C22⋊C4 | — | 52 | 1 | no | — |
| 348 | C22⋊C4 | — | 52 | 1 | no | — |
| 349 | C22⋊C4 | — | 52 | 1 | no | — |
| 350 | C22⋊C4 | — | 52 | 1 | no | — |
| 351 | C42 | — | 52 | 2 | no | — |
| 352 | C42 | D4×D13 | 1 | 1 | yes | characteristic |
| 353 | C42 | D4×D13 | 1 | 1 | yes | characteristic |
| 354 | C42 | D4×D13 | 1 | 1 | yes | characteristic |
| 355 | C42 | #6131 | 1 | 1 | yes | characteristic |
| 356 | C13 | #10192 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 357 | C23 | — | 52 | 1 | no | — |
| 358 | C23 | — | 52 | 1 | no | — |
| 359 | C23 | — | 52 | 2 | no | — |
| 360 | C23 | — | 104 | 2 | no | — |
| 361 | C23 | — | 104 | 2 | no | — |
| 362 | C23 | — | 104 | 1 | no | — |
| 363 | C23 | — | 104 | 1 | no | — |
| 364 | C23 | #88128 | 1 | 1 | yes | characteristic |
| 365 | Q8 | — | 52 | 2 | no | — |
| 366 | Q8 | — | 52 | 2 | no | — |
| 367 | D4 | — | 52 | 2 | no | — |
| 368 | D4 | — | 52 | 4 | no | — |
| 369 | D4 | — | 52 | 4 | no | — |
| 370 | D4 | — | 52 | 1 | no | — |
| 371 | D4 | — | 52 | 1 | no | — |
| 372 | D4 | — | 52 | 1 | no | — |
| 373 | D4 | — | 52 | 1 | no | — |
| 374 | D4 | — | 52 | 2 | no | — |
| 375 | D4 | — | 52 | 2 | no | — |
| 376 | D4 | — | 52 | 4 | no | — |
| 377 | D4 | — | 104 | 1 | no | — |
| 378 | D4 | — | 104 | 2 | no | — |
| 379 | D4 | — | 104 | 1 | no | — |
| 380 | D4 | — | 104 | 1 | no | — |
| 381 | D4 | — | 104 | 1 | no | — |
| 382 | D4 | — | 104 | 1 | no | — |
| 383 | D4 | — | 104 | 1 | no | — |
| 384 | D4 | — | 104 | 1 | no | — |
| 385 | D4 | — | 104 | 2 | no | — |
| 386 | C2×C4 | — | 2 | 1 | no | — |
| 387 | C2×C4 | — | 2 | 1 | no | — |
| 388 | C2×C4 | — | 4 | 1 | no | — |
| 389 | C2×C4 | — | 52 | 2 | no | — |
| 390 | C2×C4 | — | 52 | 1 | no | — |
| 391 | C2×C4 | — | 52 | 1 | no | — |
| 392 | C2×C4 | — | 104 | 1 | no | — |
| 393 | C2×C4 | — | 104 | 1 | no | — |
| 394 | C2×C4 | — | 104 | 2 | no | — |
| 395 | C2×C4 | — | 104 | 2 | no | — |
| 396 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 397 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 398 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 399 | C2×C4 | #88149 | 1 | 1 | yes | characteristic |
| 400 | C2×C4 | #88149 | 1 | 1 | yes | characteristic |
| 401 | C2×C4 | #88149 | 1 | 1 | yes | characteristic |
| 402 | C2×C4 | C2×D104 | 1 | 2 | yes | — |
| 403 | C2×C4 | #88162 | 1 | 2 | yes | — |
| 404 | C8 | — | 2 | 4 | no | — |
| 405 | C8 | — | 4 | 2 | no | — |
| 406 | C8 | — | 4 | 2 | no | — |
| 407 | C22 | — | 2 | 1 | no | — |
| 408 | C22 | — | 2 | 1 | no | — |
| 409 | C22 | — | 104 | 1 | no | — |
| 410 | C22 | — | 104 | 1 | no | — |
| 411 | C22 | — | 104 | 2 | no | — |
| 412 | C22 | — | 104 | 2 | no | — |
| 413 | C22 | — | 104 | 1 | no | — |
| 414 | C22 | — | 104 | 1 | no | — |
| 415 | C22 | — | 104 | 2 | no | — |
| 416 | C22 | — | 104 | 1 | no | — |
| 417 | C22 | — | 104 | 1 | no | — |
| 418 | C22 | — | 208 | 2 | no | — |
| 419 | C22 | — | 208 | 2 | no | — |
| 420 | C22 | #11718332 | 1 | 1 | yes | characteristic |
| 421 | C22 | #11718356 | 1 | 1 | yes | characteristic |
| 422 | C22 | #11718373 | 1 | 1 | yes | characteristic |
| 423 | C4 | — | 2 | 1 | no | — |
| 424 | C4 | — | 2 | 1 | no | — |
| 425 | C4 | — | 2 | 1 | no | — |
| 426 | C4 | — | 104 | 2 | no | — |
| 427 | C4 | — | 104 | 1 | no | — |
| 428 | C4 | — | 104 | 1 | no | — |
| 429 | C4 | #11718393 | 1 | 2 | yes | — |
| 430 | C4 | #11718408 | 1 | 1 | yes | characteristic |
| 431 | C4 | #11718414 | 1 | 1 | yes | characteristic |
| 432 | C4 | #11718504 | 1 | 2 | yes | — |
| 433 | C2 | — | 2 | 1 | no | — |
| 434 | C2 | — | 2 | 1 | no | — |
| 435 | C2 | — | 208 | 2 | no | — |
| 436 | C2 | — | 208 | 1 | no | — |
| 437 | C2 | — | 208 | 1 | no | — |
| 438 | C2 | #13115880 | 1 | 1 | yes | characteristic |
| 439 | C2 | #13115892 | 1 | 1 | yes | characteristic |
| 440 | C2 | #13115909 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13126146 | C2 | semidirect |
| 2. #13125756 | C2 | semidirect |
| 3. #13125288 | C2 | semidirect |
| 4. #13115762 | C2 | semidirect |
| 5. #13115755 | C2 | semidirect |
| 6. #13113332 | C2 | semidirect |
| 7. C13×#1283 | C2 | semidirect |
| 113. C13×M16 | D8 | semidirect |
| 143. #1283 | D13 | semidirect |
| 336. M16 | D104 | semidirect |
| 356. C13 | #10192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13126146 | 2 |
| #13125756 | 2 |
| #13125288 | 2 |
| #13115762 | 2 |
| #13115755 | 2 |
| #13113332 | 2 |
| C13×#1283 | 2 |
| #10192 | 13 |