Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
728 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 90 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 | #13130973 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13130340 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13130210 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13130208 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13130194 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13130192 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #13128973 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C13×#562 | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | #11719404 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | #11719396 | C22 | 1 | 1 | yes | characteristic |
| 11 | #11719389 | C4 | 1 | 1 | yes | characteristic, complemented |
| 12 | #11719388 | C4 | 1 | 1 | yes | characteristic, complemented |
| 13 | #11719385 | C22 | 1 | 1 | yes | characteristic |
| 14 | #11719373 | C22 | 1 | 1 | yes | characteristic |
| 15 | #11719372 | — | 2 | 1 | no | — |
| 16 | #11719371 | — | 2 | 1 | no | — |
| 17 | #11719361 | — | 2 | 1 | no | — |
| 18 | #11719354 | — | 2 | 1 | no | — |
| 19 | #11719352 | — | 2 | 1 | no | — |
| 20 | #11719351 | — | 2 | 1 | no | — |
| 21 | #11719332 | — | 2 | 1 | no | — |
| 22 | #11719329 | — | 2 | 1 | no | — |
| 23 | #11719325 | — | 2 | 1 | no | — |
| 24 | #11719325 | — | 2 | 1 | no | — |
| 25 | #11719311 | — | 2 | 1 | no | — |
| 26 | #11719301 | — | 2 | 1 | no | — |
| 27 | C2×#88118 | — | 2 | 1 | no | — |
| 28 | C2×#88116 | — | 2 | 1 | no | — |
| 29 | #11719057 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #11719052 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #11719049 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #11719049 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #11718303 | — | 2 | 1 | no | — |
| 34 | Q8⋊#1057 | — | 2 | 1 | no | — |
| 35 | #11718298 | — | 2 | 1 | no | — |
| 36 | #11718297 | — | 2 | 1 | no | — |
| 37 | D4⋊#1057 | — | 2 | 1 | no | — |
| 38 | #11718292 | — | 2 | 1 | no | — |
| 39 | #11718244 | — | 2 | 1 | no | — |
| 40 | #11718243 | — | 2 | 1 | no | — |
| 41 | #11718241 | — | 2 | 1 | no | — |
| 42 | #11718240 | — | 2 | 1 | no | — |
| 43 | C2×#6131 | D4 | 1 | 1 | yes | characteristic |
| 44 | C2×#6129 | — | 2 | 1 | no | — |
| 45 | C2×#6129 | D4 | 1 | 1 | yes | characteristic |
| 46 | C22×C4×D13 | — | 2 | 1 | no | — |
| 47 | C2×C4×#261 | — | 2 | 1 | no | — |
| 48 | C2×#6118 | — | 2 | 1 | no | — |
| 49 | C13×#125 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | C13×#124 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C13×#124 | C2×C4 | 1 | 1 | yes | characteristic |
| 52 | C13×#123 | — | 2 | 1 | no | — |
| 53 | C13×#123 | — | 2 | 1 | no | — |
| 54 | C13×C22⋊Q8 | — | 2 | 1 | no | — |
| 55 | C13×C22⋊Q8 | — | 2 | 1 | no | — |
| 56 | C13×#121 | — | 2 | 1 | no | — |
| 57 | C13×#121 | — | 2 | 1 | no | — |
| 58 | #88201 | — | 2 | 1 | no | — |
| 59 | #88200 | — | 2 | 1 | no | — |
| 60 | #88200 | D4 | 1 | 1 | yes | characteristic |
| 61 | Q8×Dic13 | D4 | 1 | 1 | yes | characteristic |
| 62 | #88198 | D4 | 1 | 1 | yes | characteristic |
| 63 | #88194 | — | 2 | 1 | no | — |
| 64 | #88194 | D4 | 1 | 1 | yes | characteristic |
| 65 | #88193 | — | 2 | 1 | no | — |
| 66 | #88193 | — | 2 | 1 | no | — |
| 67 | #88193 | — | 2 | 1 | no | — |
| 68 | #88192 | — | 2 | 1 | no | — |
| 69 | #88192 | D4 | 1 | 1 | yes | characteristic |
| 70 | #88191 | — | 2 | 1 | no | — |
| 71 | #88191 | — | 2 | 1 | no | — |
| 72 | #88191 | — | 2 | 1 | no | — |
| 73 | D4×Dic13 | — | 2 | 1 | no | — |
| 74 | D4×Dic13 | D4 | 1 | 1 | yes | characteristic |
| 75 | #88184 | — | 2 | 1 | no | — |
| 76 | #88184 | — | 2 | 1 | no | — |
| 77 | #88184 | — | 2 | 1 | no | — |
| 78 | #88183 | — | 2 | 1 | no | — |
| 79 | #88183 | — | 2 | 1 | no | — |
| 80 | #88178 | — | 2 | 1 | no | — |
| 81 | C2×C4×Dic13 | — | 2 | 1 | no | — |
| 82 | #88152 | — | 2 | 1 | no | — |
| 83 | #88152 | — | 2 | 1 | no | — |
| 84 | #88152 | — | 2 | 1 | no | — |
| 85 | #88152 | — | 2 | 1 | no | — |
| 86 | #88151 | — | 2 | 1 | no | — |
| 87 | #88151 | D4 | 1 | 1 | yes | characteristic |
| 88 | #88150 | — | 2 | 1 | no | — |
| 89 | #88150 | — | 2 | 1 | no | — |
| 90 | #88149 | — | 2 | 1 | no | — |
| 91 | #88149 | D4 | 1 | 1 | yes | characteristic |
| 92 | #88148 | — | 2 | 1 | no | — |
| 93 | #88148 | — | 2 | 1 | no | — |
| 94 | #88148 | — | 2 | 1 | no | — |
| 95 | #88147 | — | 2 | 1 | no | — |
| 96 | #88147 | — | 2 | 1 | no | — |
| 97 | #88147 | D4 | 1 | 1 | yes | characteristic |
| 98 | #88146 | — | 2 | 1 | no | — |
| 99 | #88146 | — | 2 | 1 | no | — |
| 100 | #88144 | — | 2 | 1 | no | — |
| 101 | #88143 | — | 2 | 1 | no | — |
| 102 | #88142 | — | 2 | 1 | no | — |
| 103 | #88141 | D4 | 1 | 1 | yes | characteristic |
| 104 | #88140 | — | 2 | 1 | no | — |
| 105 | #88140 | — | 2 | 1 | no | — |
| 106 | #88139 | — | 2 | 1 | no | — |
| 107 | #88139 | — | 2 | 1 | no | — |
| 108 | #88139 | — | 2 | 1 | no | — |
| 109 | #88138 | — | 2 | 1 | no | — |
| 110 | #88138 | — | 2 | 1 | no | — |
| 111 | #88138 | — | 2 | 1 | no | — |
| 112 | #88138 | — | 2 | 1 | no | — |
| 113 | #88137 | — | 2 | 1 | no | — |
| 114 | #88137 | — | 2 | 1 | no | — |
| 115 | #88137 | — | 2 | 1 | no | — |
| 116 | #88136 | — | 2 | 1 | no | — |
| 117 | #88136 | — | 2 | 1 | no | — |
| 118 | #88136 | — | 2 | 1 | no | — |
| 119 | #88135 | — | 2 | 1 | no | — |
| 120 | #88135 | — | 2 | 1 | no | — |
| 121 | #88135 | — | 2 | 1 | no | — |
| 122 | #88135 | — | 2 | 1 | no | — |
| 123 | #88135 | — | 2 | 1 | no | — |
| 124 | #88133 | — | 2 | 1 | no | — |
| 125 | #88133 | — | 2 | 1 | no | — |
| 126 | #88132 | — | 2 | 1 | no | — |
| 127 | #88131 | — | 2 | 1 | no | — |
| 128 | #88129 | C2×C4 | 1 | 1 | yes | characteristic |
| 129 | #88129 | C2×C4 | 1 | 1 | yes | characteristic |
| 130 | C42×D13 | C23 | 1 | 1 | yes | characteristic |
| 131 | #88124 | C2×C4 | 1 | 1 | yes | characteristic |
| 132 | #88118 | — | 4 | 2 | no | — |
| 133 | #88116 | — | 4 | 2 | no | — |
| 134 | (C2×#261)⋊C4 | — | 2 | 1 | no | — |
| 135 | (C2×#261)⋊C4 | — | 2 | 1 | no | — |
| 136 | #88112 | — | 2 | 1 | no | — |
| 137 | #88112 | — | 2 | 1 | no | — |
| 138 | #88111 | — | 2 | 1 | no | — |
| 139 | #88111 | — | 2 | 1 | no | — |
| 140 | C4⋊#1057 | — | 2 | 1 | no | — |
| 141 | C4⋊#1057 | — | 2 | 1 | no | — |
| 142 | C4×#1057 | — | 2 | 1 | no | — |
| 143 | C4×#1057 | — | 2 | 1 | no | — |
| 144 | #8504 | — | 13 | 1 | no | maximal, Sylow |
| 145 | C23×D13 | — | 2 | 1 | no | — |
| 146 | C22×#261 | — | 4 | 1 | no | — |
| 147 | C2×Q8×C13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 148 | C2×Q8×C13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 149 | C2×D4×C13 | — | 2 | 1 | no | — |
| 150 | C2×D4×C13 | — | 2 | 1 | no | — |
| 151 | C2×D4×C13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 152 | C2×D4×C13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 153 | C22×C4×C13 | — | 2 | 1 | no | — |
| 154 | C22×C4×C13 | — | 2 | 1 | no | — |
| 155 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 156 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 157 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 158 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 159 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 160 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 161 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 162 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 163 | C22×Dic13 | — | 2 | 1 | no | — |
| 164 | C22×Dic13 | — | 2 | 1 | no | — |
| 165 | C22×Dic13 | — | 2 | 1 | no | — |
| 166 | #6131 | — | 4 | 1 | no | — |
| 167 | #6131 | — | 4 | 1 | no | — |
| 168 | #6129 | — | 4 | 1 | no | — |
| 169 | #6129 | — | 4 | 1 | no | — |
| 170 | #6129 | — | 8 | 1 | no | — |
| 171 | #6129 | — | 8 | 1 | no | — |
| 172 | C2×D52 | — | 2 | 1 | no | — |
| 173 | C2×D52 | — | 2 | 1 | no | — |
| 174 | C2×D52 | — | 2 | 1 | no | — |
| 175 | C2×D52 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 176 | C2×D52 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 177 | C2×C4×D13 | — | 2 | 1 | no | — |
| 178 | C2×C4×D13 | — | 2 | 1 | no | — |
| 179 | C2×C4×D13 | — | 2 | 1 | no | — |
| 180 | C2×C4×D13 | — | 2 | 1 | no | — |
| 181 | C2×C4×D13 | — | 8 | 1 | no | — |
| 182 | C2×C4×D13 | — | 8 | 1 | no | — |
| 183 | C2×C4×D13 | C2×D4 | 1 | 1 | yes | characteristic |
| 184 | C2×C4×D13 | C2×D4 | 1 | 1 | yes | characteristic |
| 185 | C2×C4×D13 | C2×D4 | 1 | 1 | yes | characteristic |
| 186 | C2×Dic26 | — | 2 | 1 | no | — |
| 187 | C2×Dic26 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 188 | C2×Dic26 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 189 | C2×#1057 | — | 4 | 1 | no | — |
| 190 | C2×#1057 | — | 4 | 1 | no | — |
| 191 | C2×#1057 | — | 4 | 1 | no | — |
| 192 | C4×#261 | — | 2 | 2 | no | — |
| 193 | C4×#261 | — | 4 | 1 | no | — |
| 194 | #6118 | — | 4 | 1 | no | — |
| 195 | #6118 | — | 4 | 1 | no | — |
| 196 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 197 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 198 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 199 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 200 | C13×C4⋊C4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 201 | C13×C4⋊C4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 202 | C13×C22⋊C4 | — | 2 | 1 | no | — |
| 203 | C13×C22⋊C4 | — | 2 | 1 | no | — |
| 204 | C13×C22⋊C4 | — | 2 | 1 | no | — |
| 205 | C13×C22⋊C4 | — | 2 | 1 | no | — |
| 206 | C13×C22⋊C4 | — | 2 | 1 | no | — |
| 207 | C13×C22⋊C4 | — | 2 | 1 | no | — |
| 208 | C42×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 209 | C22⋊Dic13 | — | 2 | 1 | no | — |
| 210 | C22⋊Dic13 | — | 2 | 1 | no | — |
| 211 | C22⋊Dic13 | — | 2 | 1 | no | — |
| 212 | C22⋊Dic13 | — | 2 | 1 | no | — |
| 213 | #6103 | — | 2 | 1 | no | — |
| 214 | #6103 | — | 2 | 1 | no | — |
| 215 | #6103 | — | 2 | 1 | no | — |
| 216 | #6103 | — | 2 | 1 | no | — |
| 217 | #6103 | — | 2 | 1 | no | — |
| 218 | #6103 | — | 2 | 1 | no | — |
| 219 | #6103 | — | 2 | 1 | no | — |
| 220 | #6103 | — | 2 | 1 | no | — |
| 221 | #6103 | — | 2 | 1 | no | — |
| 222 | #6103 | — | 2 | 1 | no | — |
| 223 | #6103 | — | 2 | 1 | no | — |
| 224 | #6103 | — | 2 | 1 | no | — |
| 225 | #6103 | — | 2 | 1 | no | — |
| 226 | #6103 | — | 2 | 1 | no | — |
| 227 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 228 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 229 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 230 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 231 | C4⋊Dic13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 232 | C4⋊Dic13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 233 | #6101 | — | 2 | 1 | no | — |
| 234 | #6101 | — | 2 | 1 | no | — |
| 235 | #6101 | — | 2 | 1 | no | — |
| 236 | #6101 | — | 2 | 1 | no | — |
| 237 | #6101 | — | 2 | 1 | no | — |
| 238 | #6101 | — | 2 | 1 | no | — |
| 239 | #6101 | — | 2 | 1 | no | — |
| 240 | #6101 | — | 2 | 1 | no | — |
| 241 | C4×Dic13 | — | 2 | 1 | no | — |
| 242 | C4×Dic13 | — | 2 | 1 | no | — |
| 243 | C4×Dic13 | — | 2 | 1 | no | — |
| 244 | C4×Dic13 | — | 2 | 1 | no | — |
| 245 | C4×Dic13 | C2×D4 | 1 | 1 | yes | characteristic |
| 246 | C4×Dic13 | C2×D4 | 1 | 1 | yes | characteristic |
| 247 | C4×Dic13 | C2×D4 | 1 | 1 | yes | characteristic |
| 248 | #3529 | — | 13 | 1 | no | — |
| 249 | #1963 | — | 13 | 1 | no | — |
| 250 | #1543 | — | 13 | 1 | no | — |
| 251 | #1500 | — | 13 | 1 | no | — |
| 252 | #1500 | — | 13 | 1 | no | — |
| 253 | #1495 | — | 13 | 1 | no | — |
| 254 | #1495 | — | 13 | 1 | no | — |
| 255 | C23×C13 | — | 2 | 1 | no | — |
| 256 | C23×C13 | — | 2 | 1 | no | — |
| 257 | C22×D13 | — | 2 | 1 | no | — |
| 258 | C22×D13 | — | 2 | 1 | no | — |
| 259 | C22×D13 | — | 8 | 1 | no | — |
| 260 | C22×D13 | — | 8 | 1 | no | — |
| 261 | C22×D13 | — | 8 | 1 | no | — |
| 262 | C22×D13 | #120 | 1 | 1 | yes | characteristic |
| 263 | C2×#261 | — | 4 | 2 | no | — |
| 264 | C2×#261 | — | 8 | 1 | no | — |
| 265 | C2×#261 | — | 8 | 1 | no | — |
| 266 | Q8×C13 | — | 4 | 1 | no | — |
| 267 | Q8×C13 | — | 4 | 1 | no | — |
| 268 | D4×C13 | — | 4 | 1 | no | — |
| 269 | D4×C13 | — | 4 | 1 | no | — |
| 270 | D4×C13 | — | 8 | 1 | no | — |
| 271 | D4×C13 | — | 8 | 1 | no | — |
| 272 | C2×C4×C13 | — | 2 | 1 | no | — |
| 273 | C2×C4×C13 | — | 2 | 1 | no | — |
| 274 | C2×C4×C13 | — | 2 | 1 | no | — |
| 275 | C2×C4×C13 | — | 2 | 1 | no | — |
| 276 | C2×C4×C13 | — | 8 | 1 | no | — |
| 277 | C2×C4×C13 | — | 8 | 1 | no | — |
| 278 | C2×C4×C13 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 279 | C2×C4×C13 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 280 | C2×C4×C13 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 281 | C22⋊D13 | — | 8 | 1 | no | — |
| 282 | C22⋊D13 | — | 8 | 1 | no | — |
| 283 | C22⋊D13 | — | 8 | 1 | no | — |
| 284 | C22⋊D13 | — | 8 | 1 | no | — |
| 285 | C22⋊D13 | — | 8 | 1 | no | — |
| 286 | C22⋊D13 | — | 8 | 1 | no | — |
| 287 | C22⋊D13 | — | 8 | 1 | no | — |
| 288 | C22⋊D13 | — | 8 | 1 | no | — |
| 289 | C2×Dic13 | — | 2 | 1 | no | — |
| 290 | C2×Dic13 | — | 2 | 1 | no | — |
| 291 | C2×Dic13 | — | 2 | 1 | no | — |
| 292 | C2×Dic13 | — | 2 | 1 | no | — |
| 293 | C2×Dic13 | — | 4 | 1 | no | — |
| 294 | C2×Dic13 | — | 4 | 1 | no | — |
| 295 | C2×Dic13 | — | 4 | 1 | no | — |
| 296 | C2×Dic13 | — | 4 | 1 | no | — |
| 297 | C2×Dic13 | — | 8 | 1 | no | — |
| 298 | C2×Dic13 | #120 | 1 | 1 | yes | characteristic |
| 299 | C2×Dic13 | #120 | 1 | 1 | yes | characteristic |
| 300 | C2×Dic13 | #120 | 1 | 1 | yes | characteristic |
| 301 | D52 | — | 4 | 1 | no | — |
| 302 | D52 | — | 4 | 1 | no | — |
| 303 | D52 | — | 8 | 1 | no | — |
| 304 | D52 | — | 8 | 1 | no | — |
| 305 | D52 | — | 8 | 1 | no | — |
| 306 | C4×D13 | — | 2 | 1 | no | — |
| 307 | C4×D13 | — | 2 | 1 | no | — |
| 308 | C4×D13 | — | 4 | 1 | no | — |
| 309 | C4×D13 | — | 4 | 1 | no | — |
| 310 | C4×D13 | — | 4 | 1 | no | — |
| 311 | C4×D13 | — | 4 | 1 | no | — |
| 312 | C4×D13 | — | 4 | 1 | no | — |
| 313 | C4×D13 | — | 4 | 1 | no | — |
| 314 | C4×D13 | — | 8 | 1 | no | — |
| 315 | C4×D13 | — | 8 | 1 | no | — |
| 316 | Dic26 | — | 4 | 1 | no | — |
| 317 | Dic26 | — | 4 | 1 | no | — |
| 318 | Dic26 | — | 8 | 1 | no | — |
| 319 | #1057 | — | 8 | 1 | no | — |
| 320 | #1057 | — | 8 | 1 | no | — |
| 321 | #1057 | — | 8 | 1 | no | — |
| 322 | #563 | — | 13 | 1 | no | — |
| 323 | #563 | — | 26 | 1 | no | — |
| 324 | #562 | — | 13 | 1 | no | — |
| 325 | #562 | — | 26 | 1 | no | — |
| 326 | #562 | — | 26 | 1 | no | — |
| 327 | #562 | #261 | 1 | 1 | yes | characteristic, complemented |
| 328 | H(3,𝔽4) | — | 13 | 1 | no | — |
| 329 | #560 | — | 26 | 1 | no | — |
| 330 | #560 | — | 26 | 1 | no | — |
| 331 | #560 | — | 26 | 1 | no | — |
| 332 | #532 | — | 13 | 1 | no | — |
| 333 | #532 | — | 26 | 1 | no | — |
| 334 | #529 | — | 13 | 1 | no | — |
| 335 | #529 | — | 13 | 1 | no | — |
| 336 | #529 | — | 26 | 1 | no | — |
| 337 | #529 | — | 26 | 1 | no | — |
| 338 | #525 | — | 26 | 1 | no | — |
| 339 | #525 | — | 26 | 1 | no | — |
| 340 | #525 | — | 26 | 1 | no | — |
| 341 | #431 | — | 13 | 1 | no | — |
| 342 | #431 | — | 13 | 1 | no | — |
| 343 | #423 | — | 13 | 1 | no | — |
| 344 | C2×#104 | — | 26 | 1 | no | — |
| 345 | C2×#104 | — | 26 | 1 | no | — |
| 346 | #376 | — | 13 | 1 | no | — |
| 347 | #333 | — | 26 | 1 | no | — |
| 348 | #331 | — | 26 | 1 | no | — |
| 349 | #328 | — | 26 | 1 | no | — |
| 350 | #328 | — | 26 | 1 | no | — |
| 351 | #327 | — | 26 | 1 | no | — |
| 352 | #327 | — | 26 | 1 | no | — |
| 353 | Q8⋊C8 | — | 26 | 1 | no | — |
| 354 | Q8⋊C8 | — | 26 | 1 | no | — |
| 355 | D4⋊C8 | — | 26 | 1 | no | — |
| 356 | D4⋊C8 | — | 26 | 1 | no | — |
| 357 | C22×C13 | — | 4 | 1 | no | — |
| 358 | C22×C13 | — | 4 | 1 | no | — |
| 359 | C22×C13 | — | 4 | 1 | no | — |
| 360 | C22×C13 | — | 4 | 1 | no | — |
| 361 | C22×C13 | — | 4 | 1 | no | — |
| 362 | C22×C13 | — | 4 | 1 | no | — |
| 363 | C22×C13 | #379 | 1 | 1 | yes | characteristic |
| 364 | C2×D13 | — | 2 | 1 | no | — |
| 365 | C2×D13 | — | 2 | 1 | no | — |
| 366 | C2×D13 | — | 2 | 1 | no | — |
| 367 | C2×D13 | — | 4 | 1 | no | — |
| 368 | C2×D13 | — | 4 | 1 | no | — |
| 369 | C2×D13 | — | 4 | 1 | no | — |
| 370 | C2×D13 | — | 4 | 1 | no | — |
| 371 | C2×D13 | — | 4 | 1 | no | — |
| 372 | C2×D13 | — | 4 | 1 | no | — |
| 373 | C2×D13 | — | 8 | 4 | no | — |
| 374 | #261 | — | 8 | 2 | no | — |
| 375 | C4×C13 | — | 2 | 1 | no | — |
| 376 | C4×C13 | — | 2 | 1 | no | — |
| 377 | C4×C13 | — | 2 | 1 | no | — |
| 378 | C4×C13 | — | 4 | 1 | no | — |
| 379 | C4×C13 | — | 4 | 1 | no | — |
| 380 | C4×C13 | — | 4 | 1 | no | — |
| 381 | C4×C13 | — | 4 | 1 | no | — |
| 382 | Dic13 | — | 2 | 1 | no | — |
| 383 | Dic13 | — | 2 | 1 | no | — |
| 384 | Dic13 | — | 4 | 1 | no | — |
| 385 | Dic13 | — | 4 | 1 | no | — |
| 386 | Dic13 | — | 4 | 1 | no | — |
| 387 | Dic13 | — | 4 | 1 | no | — |
| 388 | Dic13 | #453 | 1 | 1 | yes | characteristic |
| 389 | Dic13 | #455 | 1 | 1 | yes | characteristic |
| 390 | C2×#41 | — | 13 | 1 | no | — |
| 391 | C2×#41 | — | 13 | 1 | no | — |
| 392 | C2×#41 | — | 26 | 1 | no | — |
| 393 | C23×C4 | — | 26 | 1 | no | — |
| 394 | C2×M16 | — | 26 | 1 | no | — |
| 395 | C4⋊Q8 | — | 13 | 1 | no | — |
| 396 | C4⋊Q8 | — | 26 | 1 | no | — |
| 397 | #127 | — | 13 | 1 | no | — |
| 398 | #127 | — | 26 | 1 | no | — |
| 399 | #126 | — | 26 | 1 | no | — |
| 400 | #126 | — | 26 | 1 | no | — |
| 401 | #126 | — | 26 | 1 | no | — |
| 402 | #126 | — | 26 | 1 | no | — |
| 403 | #126 | — | 26 | 1 | no | — |
| 404 | #126 | — | 26 | 1 | no | — |
| 405 | #125 | — | 13 | 1 | no | — |
| 406 | #125 | — | 26 | 1 | no | — |
| 407 | #125 | — | 26 | 1 | no | — |
| 408 | #125 | C2×#261 | 1 | 1 | yes | characteristic |
| 409 | #124 | — | 13 | 1 | no | — |
| 410 | #124 | — | 13 | 1 | no | — |
| 411 | #124 | — | 26 | 1 | no | — |
| 412 | #124 | — | 26 | 1 | no | — |
| 413 | #124 | — | 26 | 1 | no | — |
| 414 | #124 | — | 26 | 1 | no | — |
| 415 | #124 | C2×#261 | 1 | 1 | yes | characteristic |
| 416 | #124 | C2×#261 | 1 | 1 | yes | characteristic |
| 417 | #123 | — | 2 | 1 | no | — |
| 418 | #123 | — | 2 | 1 | no | — |
| 419 | #123 | — | 26 | 1 | no | — |
| 420 | #123 | — | 26 | 1 | no | — |
| 421 | #123 | — | 26 | 1 | no | — |
| 422 | #123 | — | 26 | 1 | no | — |
| 423 | #123 | — | 26 | 1 | no | — |
| 424 | #123 | — | 26 | 1 | no | — |
| 425 | #123 | — | 26 | 1 | no | — |
| 426 | #123 | — | 26 | 1 | no | — |
| 427 | #123 | — | 26 | 1 | no | — |
| 428 | #123 | — | 26 | 1 | no | — |
| 429 | C22⋊Q8 | — | 2 | 1 | no | — |
| 430 | C22⋊Q8 | — | 2 | 1 | no | — |
| 431 | C22⋊Q8 | — | 13 | 1 | no | — |
| 432 | C22⋊Q8 | — | 13 | 1 | no | — |
| 433 | C22⋊Q8 | — | 26 | 1 | no | — |
| 434 | C22⋊Q8 | — | 26 | 1 | no | — |
| 435 | C22⋊Q8 | — | 26 | 1 | no | — |
| 436 | C22⋊Q8 | — | 26 | 1 | no | — |
| 437 | C22⋊Q8 | — | 26 | 1 | no | — |
| 438 | C22⋊Q8 | — | 26 | 1 | no | — |
| 439 | #121 | — | 2 | 1 | no | — |
| 440 | #121 | — | 2 | 1 | no | — |
| 441 | #121 | — | 13 | 1 | no | — |
| 442 | #121 | — | 13 | 1 | no | — |
| 443 | #121 | — | 26 | 1 | no | — |
| 444 | #121 | — | 26 | 1 | no | — |
| 445 | #121 | — | 26 | 1 | no | — |
| 446 | #121 | — | 26 | 1 | no | — |
| 447 | #121 | — | 26 | 1 | no | — |
| 448 | #121 | — | 26 | 1 | no | — |
| 449 | #121 | — | 26 | 1 | no | — |
| 450 | #121 | — | 26 | 1 | no | — |
| 451 | #121 | — | 26 | 1 | no | — |
| 452 | #121 | — | 26 | 1 | no | — |
| 453 | #121 | — | 26 | 1 | no | — |
| 454 | #121 | — | 26 | 1 | no | — |
| 455 | #120 | — | 26 | 1 | no | — |
| 456 | #120 | — | 26 | 1 | no | — |
| 457 | #120 | — | 26 | 1 | no | — |
| 458 | #120 | — | 26 | 1 | no | — |
| 459 | #120 | — | 26 | 1 | no | — |
| 460 | #120 | — | 26 | 1 | no | — |
| 461 | C4×Q8 | — | 13 | 1 | no | — |
| 462 | C4×Q8 | — | 13 | 1 | no | — |
| 463 | C4×D4 | — | 13 | 1 | no | — |
| 464 | C4×D4 | — | 13 | 1 | no | — |
| 465 | C4×D4 | — | 26 | 1 | no | — |
| 466 | C4×D4 | — | 26 | 1 | no | — |
| 467 | C4×D4 | — | 26 | 1 | no | — |
| 468 | C4×D4 | — | 26 | 1 | no | — |
| 469 | C4×D4 | — | 26 | 1 | no | — |
| 470 | C4×D4 | — | 26 | 1 | no | — |
| 471 | C4×D4 | — | 26 | 1 | no | — |
| 472 | C4×D4 | — | 26 | 1 | no | — |
| 473 | #117 | — | 26 | 1 | no | — |
| 474 | #117 | — | 26 | 1 | no | — |
| 475 | #117 | — | 26 | 1 | no | — |
| 476 | C2×C42 | — | 13 | 1 | no | — |
| 477 | C2×C42 | — | 26 | 1 | no | — |
| 478 | C2×C42 | — | 26 | 1 | no | — |
| 479 | C4⋊C8 | — | 26 | 1 | no | — |
| 480 | C4⋊C8 | — | 26 | 1 | no | — |
| 481 | C4⋊C8 | — | 26 | 1 | no | — |
| 482 | C4⋊C8 | — | 26 | 1 | no | — |
| 483 | #104 | — | 52 | 2 | no | — |
| 484 | #104 | — | 52 | 2 | no | — |
| 485 | C22⋊C8 | — | 26 | 1 | no | — |
| 486 | C22⋊C8 | — | 26 | 1 | no | — |
| 487 | C4×C8 | — | 26 | 1 | no | — |
| 488 | C4×C8 | — | 26 | 1 | no | — |
| 489 | #95 | — | 26 | 1 | no | — |
| 490 | #95 | — | 26 | 1 | no | — |
| 491 | C2×C13 | — | 8 | 1 | no | — |
| 492 | C2×C13 | — | 8 | 1 | no | — |
| 493 | C2×C13 | #1792 | 1 | 1 | yes | characteristic |
| 494 | C2×C13 | #1794 | 1 | 1 | yes | characteristic |
| 495 | C2×C13 | #1794 | 1 | 1 | yes | characteristic |
| 496 | D13 | — | 4 | 1 | no | — |
| 497 | D13 | — | 8 | 1 | no | — |
| 498 | D13 | — | 8 | 1 | no | — |
| 499 | C24 | — | 26 | 1 | no | — |
| 500 | #41 | — | 52 | 1 | no | — |
| 501 | #41 | — | 52 | 1 | no | — |
| 502 | #41 | — | 52 | 1 | no | — |
| 503 | #41 | — | 52 | 1 | no | — |
| 504 | #41 | — | 104 | 1 | no | — |
| 505 | #41 | — | 104 | 1 | no | — |
| 506 | C2×Q8 | — | 13 | 1 | no | — |
| 507 | C2×Q8 | — | 13 | 1 | no | — |
| 508 | C2×Q8 | — | 26 | 1 | no | — |
| 509 | C2×Q8 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 510 | C2×Q8 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 511 | C2×D4 | — | 2 | 1 | no | — |
| 512 | C2×D4 | — | 2 | 1 | no | — |
| 513 | C2×D4 | — | 13 | 1 | no | — |
| 514 | C2×D4 | — | 13 | 1 | no | — |
| 515 | C2×D4 | — | 26 | 1 | no | — |
| 516 | C2×D4 | — | 26 | 1 | no | — |
| 517 | C2×D4 | — | 26 | 1 | no | — |
| 518 | C2×D4 | — | 26 | 1 | no | — |
| 519 | C2×D4 | — | 26 | 1 | no | — |
| 520 | C2×D4 | — | 26 | 1 | no | — |
| 521 | C2×D4 | — | 26 | 1 | no | — |
| 522 | C2×D4 | — | 26 | 1 | no | — |
| 523 | C2×D4 | — | 26 | 1 | no | — |
| 524 | C2×D4 | — | 26 | 1 | no | — |
| 525 | C2×D4 | — | 26 | 1 | no | — |
| 526 | C2×D4 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 527 | C2×D4 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 528 | C22×C4 | — | 2 | 1 | no | — |
| 529 | C22×C4 | — | 2 | 1 | no | — |
| 530 | C22×C4 | — | 13 | 1 | no | — |
| 531 | C22×C4 | — | 13 | 1 | no | — |
| 532 | C22×C4 | — | 13 | 1 | no | — |
| 533 | C22×C4 | — | 26 | 1 | no | — |
| 534 | C22×C4 | — | 26 | 1 | no | — |
| 535 | C22×C4 | — | 26 | 1 | no | — |
| 536 | C22×C4 | — | 26 | 1 | no | — |
| 537 | C22×C4 | — | 26 | 1 | no | — |
| 538 | C22×C4 | — | 26 | 1 | no | — |
| 539 | C22×C4 | — | 26 | 1 | no | — |
| 540 | C22×C4 | — | 52 | 1 | no | — |
| 541 | C22×C4 | — | 104 | 1 | no | — |
| 542 | C22×C4 | — | 104 | 1 | no | — |
| 543 | M16 | — | 52 | 1 | no | — |
| 544 | M16 | — | 52 | 1 | no | — |
| 545 | C2×C8 | — | 52 | 1 | no | — |
| 546 | C2×C8 | — | 52 | 1 | no | — |
| 547 | C2×C8 | — | 52 | 1 | no | — |
| 548 | C4⋊C4 | — | 2 | 1 | no | — |
| 549 | C4⋊C4 | — | 2 | 1 | no | — |
| 550 | C4⋊C4 | — | 2 | 1 | no | — |
| 551 | C4⋊C4 | — | 2 | 1 | no | — |
| 552 | C4⋊C4 | — | 13 | 1 | no | — |
| 553 | C4⋊C4 | — | 13 | 1 | no | — |
| 554 | C4⋊C4 | — | 26 | 1 | no | — |
| 555 | C4⋊C4 | — | 26 | 1 | no | — |
| 556 | C4⋊C4 | — | 26 | 1 | no | — |
| 557 | C4⋊C4 | — | 26 | 1 | no | — |
| 558 | C4⋊C4 | — | 26 | 1 | no | — |
| 559 | C4⋊C4 | — | 26 | 1 | no | — |
| 560 | C4⋊C4 | — | 26 | 1 | no | — |
| 561 | C4⋊C4 | — | 26 | 1 | no | — |
| 562 | C4⋊C4 | — | 26 | 1 | no | — |
| 563 | C4⋊C4 | — | 26 | 1 | no | — |
| 564 | C4⋊C4 | — | 26 | 1 | no | — |
| 565 | C4⋊C4 | — | 26 | 1 | no | — |
| 566 | C4⋊C4 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 567 | C4⋊C4 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 568 | C22⋊C4 | — | 2 | 1 | no | — |
| 569 | C22⋊C4 | — | 2 | 1 | no | — |
| 570 | C22⋊C4 | — | 2 | 1 | no | — |
| 571 | C22⋊C4 | — | 2 | 1 | no | — |
| 572 | C22⋊C4 | — | 2 | 1 | no | — |
| 573 | C22⋊C4 | — | 2 | 1 | no | — |
| 574 | C22⋊C4 | — | 26 | 1 | no | — |
| 575 | C22⋊C4 | — | 26 | 1 | no | — |
| 576 | C22⋊C4 | — | 26 | 1 | no | — |
| 577 | C22⋊C4 | — | 26 | 1 | no | — |
| 578 | C22⋊C4 | — | 26 | 1 | no | — |
| 579 | C22⋊C4 | — | 26 | 1 | no | — |
| 580 | C22⋊C4 | — | 26 | 1 | no | — |
| 581 | C22⋊C4 | — | 26 | 1 | no | — |
| 582 | C22⋊C4 | — | 26 | 1 | no | — |
| 583 | C22⋊C4 | — | 26 | 1 | no | — |
| 584 | C22⋊C4 | — | 26 | 1 | no | — |
| 585 | C22⋊C4 | — | 26 | 1 | no | — |
| 586 | C22⋊C4 | — | 26 | 1 | no | — |
| 587 | C22⋊C4 | — | 26 | 1 | no | — |
| 588 | C22⋊C4 | — | 26 | 1 | no | — |
| 589 | C22⋊C4 | — | 26 | 1 | no | — |
| 590 | C22⋊C4 | — | 26 | 1 | no | — |
| 591 | C22⋊C4 | — | 26 | 1 | no | — |
| 592 | C42 | — | 13 | 1 | no | — |
| 593 | C42 | — | 13 | 1 | no | — |
| 594 | C42 | — | 13 | 1 | no | — |
| 595 | C42 | — | 26 | 1 | no | — |
| 596 | C42 | — | 26 | 1 | no | — |
| 597 | C42 | — | 26 | 1 | no | — |
| 598 | C42 | — | 26 | 1 | no | — |
| 599 | C42 | — | 26 | 2 | no | — |
| 600 | C42 | — | 52 | 1 | no | — |
| 601 | C42 | C22×#261 | 1 | 1 | yes | characteristic |
| 602 | C13 | #8504 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 603 | C23 | — | 2 | 1 | no | — |
| 604 | C23 | — | 2 | 1 | no | — |
| 605 | C23 | — | 13 | 1 | no | — |
| 606 | C23 | — | 26 | 1 | no | — |
| 607 | C23 | — | 26 | 1 | no | — |
| 608 | C23 | — | 104 | 1 | no | — |
| 609 | C23 | — | 104 | 1 | no | — |
| 610 | C23 | — | 104 | 1 | no | — |
| 611 | Q8 | — | 4 | 1 | no | — |
| 612 | Q8 | — | 4 | 1 | no | — |
| 613 | Q8 | — | 52 | 1 | no | — |
| 614 | Q8 | — | 52 | 1 | no | — |
| 615 | Q8 | — | 104 | 1 | no | — |
| 616 | D4 | — | 4 | 1 | no | — |
| 617 | D4 | — | 4 | 1 | no | — |
| 618 | D4 | — | 8 | 1 | no | — |
| 619 | D4 | — | 8 | 1 | no | — |
| 620 | D4 | — | 52 | 1 | no | — |
| 621 | D4 | — | 52 | 1 | no | — |
| 622 | D4 | — | 104 | 1 | no | — |
| 623 | D4 | — | 104 | 1 | no | — |
| 624 | D4 | — | 104 | 1 | no | — |
| 625 | D4 | — | 104 | 1 | no | — |
| 626 | D4 | — | 104 | 1 | no | — |
| 627 | D4 | — | 104 | 1 | no | — |
| 628 | D4 | — | 104 | 1 | no | — |
| 629 | D4 | — | 104 | 1 | no | — |
| 630 | D4 | — | 104 | 1 | no | — |
| 631 | D4 | — | 104 | 1 | no | — |
| 632 | D4 | — | 104 | 1 | no | — |
| 633 | C2×C4 | — | 2 | 1 | no | — |
| 634 | C2×C4 | — | 2 | 1 | no | — |
| 635 | C2×C4 | — | 2 | 1 | no | — |
| 636 | C2×C4 | — | 2 | 1 | no | — |
| 637 | C2×C4 | — | 8 | 1 | no | — |
| 638 | C2×C4 | — | 8 | 1 | no | — |
| 639 | C2×C4 | — | 13 | 1 | no | — |
| 640 | C2×C4 | — | 13 | 1 | no | — |
| 641 | C2×C4 | — | 13 | 1 | no | — |
| 642 | C2×C4 | — | 26 | 1 | no | — |
| 643 | C2×C4 | — | 26 | 1 | no | — |
| 644 | C2×C4 | — | 26 | 1 | no | — |
| 645 | C2×C4 | — | 26 | 1 | no | — |
| 646 | C2×C4 | — | 26 | 1 | no | — |
| 647 | C2×C4 | — | 26 | 1 | no | — |
| 648 | C2×C4 | — | 52 | 1 | no | — |
| 649 | C2×C4 | — | 52 | 1 | no | — |
| 650 | C2×C4 | — | 52 | 1 | no | — |
| 651 | C2×C4 | — | 52 | 1 | no | — |
| 652 | C2×C4 | — | 52 | 1 | no | — |
| 653 | C2×C4 | — | 52 | 1 | no | — |
| 654 | C2×C4 | — | 52 | 1 | no | — |
| 655 | C2×C4 | — | 52 | 1 | no | — |
| 656 | C2×C4 | — | 52 | 1 | no | — |
| 657 | C2×C4 | — | 52 | 1 | no | — |
| 658 | C2×C4 | — | 52 | 2 | no | — |
| 659 | C2×C4 | — | 104 | 1 | no | — |
| 660 | C2×C4 | — | 104 | 1 | no | — |
| 661 | C2×C4 | — | 104 | 1 | no | — |
| 662 | C2×C4 | — | 104 | 1 | no | — |
| 663 | C2×C4 | — | 104 | 1 | no | — |
| 664 | C2×C4 | C2×C22⋊#261 | 1 | 1 | yes | characteristic |
| 665 | C2×C4 | C2×C22⋊#261 | 1 | 1 | yes | characteristic |
| 666 | C2×C4 | C2×C22⋊#261 | 1 | 1 | yes | characteristic |
| 667 | C8 | — | 104 | 1 | no | — |
| 668 | C8 | — | 104 | 1 | no | — |
| 669 | C8 | — | 104 | 1 | no | — |
| 670 | C22 | — | 4 | 1 | no | — |
| 671 | C22 | — | 4 | 1 | no | — |
| 672 | C22 | — | 4 | 1 | no | — |
| 673 | C22 | — | 4 | 1 | no | — |
| 674 | C22 | — | 4 | 1 | no | — |
| 675 | C22 | — | 4 | 1 | no | — |
| 676 | C22 | — | 26 | 1 | no | — |
| 677 | C22 | — | 26 | 1 | no | — |
| 678 | C22 | — | 26 | 1 | no | — |
| 679 | C22 | — | 52 | 1 | no | — |
| 680 | C22 | — | 52 | 1 | no | — |
| 681 | C22 | — | 52 | 1 | no | — |
| 682 | C22 | — | 52 | 1 | no | — |
| 683 | C22 | — | 52 | 1 | no | — |
| 684 | C22 | — | 52 | 1 | no | — |
| 685 | C22 | — | 104 | 4 | no | — |
| 686 | C22 | #11719171 | 1 | 1 | yes | characteristic |
| 687 | C4 | — | 2 | 1 | no | — |
| 688 | C4 | — | 2 | 1 | no | — |
| 689 | C4 | — | 2 | 1 | no | — |
| 690 | C4 | — | 4 | 1 | no | — |
| 691 | C4 | — | 4 | 1 | no | — |
| 692 | C4 | — | 4 | 1 | no | — |
| 693 | C4 | — | 4 | 1 | no | — |
| 694 | C4 | — | 13 | 1 | no | — |
| 695 | C4 | — | 13 | 1 | no | — |
| 696 | C4 | — | 26 | 1 | no | — |
| 697 | C4 | — | 26 | 1 | no | — |
| 698 | C4 | — | 52 | 1 | no | — |
| 699 | C4 | — | 52 | 1 | no | — |
| 700 | C4 | — | 52 | 1 | no | — |
| 701 | C4 | — | 52 | 1 | no | — |
| 702 | C4 | — | 104 | 2 | no | — |
| 703 | C2 | — | 8 | 1 | no | — |
| 704 | C2 | — | 8 | 1 | no | — |
| 705 | C2 | — | 52 | 1 | no | — |
| 706 | C2 | — | 104 | 1 | no | — |
| 707 | C2 | — | 104 | 1 | no | — |
| 708 | C2 | #13130682 | 1 | 1 | yes | characteristic |
| 709 | C2 | #13130684 | 1 | 1 | yes | characteristic |
| 710 | C2 | #13130685 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13130973 | C2 | semidirect |
| 2. #13130340 | C2 | semidirect |
| 3. #13130210 | C2 | semidirect |
| 4. #13130208 | C2 | semidirect |
| 5. #13130194 | C2 | semidirect |
| 6. #13130192 | C2 | semidirect |
| 8. C13×#562 | C4 | semidirect |
| 9. #11719404 | C4 | semidirect |
| 11. #11719389 | C4 | semidirect |
| 12. #11719388 | C4 | semidirect |
| 29. #11719057 | C22 | semidirect |
| 30. #11719052 | C22 | semidirect |
| 31. #11719049 | C22 | semidirect |
| 32. #11719049 | C22 | semidirect |
| 327. #562 | #261 | semidirect |
| 602. C13 | #8504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13130973 | 2 |
| #13130340 | 2 |
| #13130210 | 2 |
| #13130208 | 2 |
| #13130194 | 2 |
| #13130192 | 2 |
| #13128973 | 2 |
| #8504 | 13 |