Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
996 conjugacy classes of subgroups.
The subgroup lattice has 590 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13131610 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #13131467 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13130973 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13130923 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13130873 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13130837 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #13130797 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #13130601 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #13124183 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #11719652 | C22 | 1 | 1 | yes | characteristic |
| 11 | #41×#261 | C22 | 1 | 2 | yes | — |
| 12 | #11719629 | C22 | 1 | 2 | yes | — |
| 13 | #11719621 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | #11719478 | C22 | 1 | 2 | yes | — |
| 15 | #11719373 | C22 | 1 | 1 | yes | characteristic |
| 16 | #11719166 | — | 2 | 2 | no | — |
| 17 | #11719166 | C22 | 1 | 2 | yes | — |
| 18 | D13⋊#104 | — | 2 | 2 | no | — |
| 19 | D13⋊#104 | C22 | 1 | 2 | yes | — |
| 20 | #11719155 | — | 2 | 2 | no | — |
| 21 | #11719155 | C22 | 1 | 2 | yes | — |
| 22 | C2×#88118 | — | 2 | 2 | no | — |
| 23 | C2×#88118 | C22 | 1 | 2 | yes | — |
| 24 | #11719142 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C2×#88116 | C22 | 1 | 2 | yes | complemented |
| 26 | #11719108 | — | 2 | 2 | no | — |
| 27 | #11719107 | — | 2 | 2 | no | — |
| 28 | #11719104 | — | 2 | 2 | no | — |
| 29 | #11719103 | — | 2 | 2 | no | — |
| 30 | #11719100 | C22 | 1 | 2 | yes | complemented |
| 31 | M16×#261 | C22 | 1 | 2 | yes | complemented |
| 32 | #11719057 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #11719052 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | C13×#454 | C4 | 1 | 1 | yes | characteristic, complemented |
| 35 | #11718907 | C4 | 1 | 1 | yes | characteristic, complemented |
| 36 | #11718859 | C4 | 1 | 2 | yes | complemented |
| 37 | #11718723 | C4 | 1 | 1 | yes | characteristic, complemented |
| 38 | #11718486 | C4 | 1 | 2 | yes | complemented |
| 39 | D13×#104 | C22 | 1 | 2 | yes | — |
| 40 | #11718413 | C4 | 1 | 1 | yes | characteristic, complemented |
| 41 | #11718412 | C22 | 1 | 1 | yes | characteristic |
| 42 | #11718274 | C22 | 1 | 2 | yes | complemented |
| 43 | #11718272 | C22 | 1 | 2 | yes | complemented |
| 44 | #11718234 | C22 | 1 | 2 | yes | complemented |
| 45 | C13×2−1+4 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | #88256 | — | 2 | 2 | no | — |
| 47 | #88256 | — | 4 | 1 | no | — |
| 48 | #88256 | C2×C4 | 1 | 2 | yes | — |
| 49 | #41×D13 | — | 2 | 2 | no | — |
| 50 | #41×D13 | — | 4 | 1 | no | — |
| 51 | #41×D13 | C23 | 1 | 2 | yes | — |
| 52 | #88254 | — | 2 | 2 | no | — |
| 53 | #88254 | C2×C4 | 1 | 1 | yes | characteristic |
| 54 | C2×#6131 | — | 2 | 2 | no | — |
| 55 | C2×#6131 | C23 | 1 | 1 | yes | characteristic |
| 56 | C2×#6129 | C23 | 1 | 1 | yes | characteristic |
| 57 | C2×#6122 | — | 4 | 1 | no | — |
| 58 | Q8×#261 | — | 2 | 2 | no | — |
| 59 | #88240 | — | 2 | 2 | no | — |
| 60 | D4×#261 | — | 2 | 2 | no | — |
| 61 | D4×#261 | — | 4 | 2 | no | — |
| 62 | #88238 | — | 2 | 2 | no | — |
| 63 | #88238 | — | 2 | 2 | no | — |
| 64 | #88238 | — | 2 | 2 | no | — |
| 65 | #88238 | — | 4 | 2 | no | — |
| 66 | #88237 | — | 2 | 2 | no | — |
| 67 | #88237 | C23 | 1 | 2 | yes | — |
| 68 | C2×C4×#261 | — | 2 | 2 | no | — |
| 69 | C2×C4×#261 | C23 | 1 | 2 | yes | — |
| 70 | D13⋊M16 | — | 2 | 2 | no | — |
| 71 | D13⋊M16 | C23 | 1 | 2 | yes | — |
| 72 | C2×#6118 | — | 2 | 2 | no | — |
| 73 | C2×#6118 | C23 | 1 | 2 | yes | — |
| 74 | C13×AGL(1,ℤ/8) | C2×C4 | 1 | 2 | yes | complemented |
| 75 | C13×#124 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 76 | #88205 | C2×C4 | 1 | 2 | yes | complemented |
| 77 | #88198 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 78 | #88194 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 79 | #88186 | C2×C4 | 1 | 2 | yes | complemented |
| 80 | #88170 | — | 2 | 2 | no | — |
| 81 | #88169 | — | 2 | 2 | no | — |
| 82 | #88166 | — | 2 | 2 | no | — |
| 83 | #88165 | — | 2 | 2 | no | — |
| 84 | #88163 | C2×C4 | 1 | 2 | yes | complemented |
| 85 | M16×D13 | C23 | 1 | 2 | yes | — |
| 86 | #88138 | — | 4 | 1 | no | — |
| 87 | #88135 | — | 4 | 1 | no | — |
| 88 | #88129 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 89 | C42×D13 | C23 | 1 | 1 | yes | characteristic |
| 90 | #88119 | — | 4 | 1 | no | — |
| 91 | #88118 | — | 2 | 2 | no | — |
| 92 | #88118 | — | 2 | 2 | no | — |
| 93 | #88118 | — | 2 | 2 | no | — |
| 94 | #88118 | — | 2 | 2 | no | — |
| 95 | #88118 | — | 2 | 2 | no | — |
| 96 | #88118 | D4 | 1 | 2 | yes | complemented |
| 97 | #88118 | D4 | 1 | 2 | yes | complemented |
| 98 | #88116 | — | 2 | 2 | no | — |
| 99 | #88116 | — | 2 | 2 | no | — |
| 100 | #88116 | — | 2 | 2 | no | — |
| 101 | #88116 | D4 | 1 | 2 | yes | complemented |
| 102 | #88116 | D4 | 1 | 2 | yes | complemented |
| 103 | (C2×#261)⋊C4 | — | 4 | 1 | no | — |
| 104 | C4⋊#1057 | — | 4 | 1 | no | — |
| 105 | #88104 | — | 2 | 2 | no | — |
| 106 | #88103 | — | 2 | 2 | no | — |
| 107 | #88100 | — | 2 | 2 | no | — |
| 108 | C8×#261 | — | 2 | 2 | no | — |
| 109 | C13×#104 | C2×C4 | 1 | 2 | yes | complemented |
| 110 | C13×#101 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 111 | #88077 | C2×C4 | 1 | 2 | yes | complemented |
| 112 | #88076 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 113 | #88065 | C2×C4 | 1 | 2 | yes | complemented |
| 114 | #88063 | C2×C4 | 1 | 2 | yes | complemented |
| 115 | #88045 | C2×C4 | 1 | 2 | yes | complemented |
| 116 | #22898 | — | 13 | 1 | no | maximal, Sylow |
| 117 | C22×#261 | — | 2 | 2 | no | — |
| 118 | C22×#261 | — | 4 | 2 | no | — |
| 119 | C13×#41 | — | 2 | 2 | no | — |
| 120 | C13×#41 | — | 4 | 1 | no | — |
| 121 | C13×#41 | C22×C4 | 1 | 2 | yes | — |
| 122 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 123 | C2×Q8×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 124 | C2×D4×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 125 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 126 | C2×C22⋊D13 | — | 4 | 1 | no | — |
| 127 | C22×Dic13 | — | 2 | 1 | no | — |
| 128 | #6131 | — | 2 | 2 | no | — |
| 129 | #6131 | — | 2 | 2 | no | — |
| 130 | #6131 | — | 2 | 2 | no | — |
| 131 | #6131 | — | 2 | 2 | no | — |
| 132 | #6131 | — | 4 | 1 | no | — |
| 133 | #6131 | — | 4 | 2 | no | — |
| 134 | #6131 | C2×D4 | 1 | 2 | yes | — |
| 135 | Q8×D13 | — | 2 | 2 | no | — |
| 136 | Q8×D13 | — | 4 | 1 | no | — |
| 137 | Q8×D13 | #41 | 1 | 2 | yes | — |
| 138 | #6129 | — | 2 | 2 | no | — |
| 139 | #6129 | — | 2 | 2 | no | — |
| 140 | #6129 | — | 2 | 2 | no | — |
| 141 | #6129 | — | 4 | 1 | no | — |
| 142 | #6129 | C2×D4 | 1 | 2 | yes | — |
| 143 | D4×D13 | — | 2 | 2 | no | — |
| 144 | D4×D13 | — | 2 | 2 | no | — |
| 145 | D4×D13 | — | 4 | 1 | no | — |
| 146 | D4×D13 | — | 4 | 2 | no | — |
| 147 | D4×D13 | — | 4 | 2 | no | — |
| 148 | D4×D13 | #41 | 1 | 2 | yes | — |
| 149 | #6127 | — | 2 | 2 | no | — |
| 150 | #6127 | — | 2 | 2 | no | — |
| 151 | #6127 | — | 4 | 2 | no | — |
| 152 | #6127 | — | 4 | 2 | no | — |
| 153 | #6127 | — | 4 | 1 | no | — |
| 154 | #6127 | C22×C4 | 1 | 2 | yes | — |
| 155 | C2×D52 | — | 2 | 2 | no | — |
| 156 | C2×D52 | — | 2 | 1 | no | — |
| 157 | C2×D52 | — | 4 | 2 | no | — |
| 158 | C2×D52 | C22×C4 | 1 | 1 | yes | characteristic |
| 159 | C2×C4×D13 | — | 2 | 2 | no | — |
| 160 | C2×C4×D13 | — | 2 | 1 | no | — |
| 161 | C2×C4×D13 | — | 2 | 1 | no | — |
| 162 | C2×C4×D13 | — | 4 | 2 | no | — |
| 163 | C2×C4×D13 | C24 | 1 | 1 | yes | characteristic |
| 164 | C2×Dic26 | C22×C4 | 1 | 1 | yes | characteristic |
| 165 | C22⋊#261 | — | 2 | 2 | no | — |
| 166 | C22⋊#261 | — | 4 | 2 | no | — |
| 167 | #6122 | — | 2 | 2 | no | — |
| 168 | #6122 | — | 4 | 2 | no | — |
| 169 | #6122 | — | 4 | 2 | no | — |
| 170 | C2×#1057 | — | 2 | 2 | no | — |
| 171 | C2×#1057 | — | 4 | 1 | no | — |
| 172 | C2×#1057 | — | 4 | 1 | no | — |
| 173 | C2×#1057 | — | 4 | 2 | no | — |
| 174 | C4⋊#261 | — | 2 | 2 | no | — |
| 175 | C4⋊#261 | — | 4 | 2 | no | — |
| 176 | C4×#261 | — | 2 | 2 | no | — |
| 177 | C4×#261 | — | 2 | 2 | no | — |
| 178 | C4×#261 | — | 4 | 2 | no | — |
| 179 | C4×#261 | C2×D4 | 1 | 2 | yes | — |
| 180 | C4×#261 | C2×D4 | 1 | 2 | yes | — |
| 181 | #6118 | — | 2 | 2 | no | — |
| 182 | #6118 | — | 2 | 2 | no | — |
| 183 | #6118 | — | 4 | 2 | no | — |
| 184 | #6118 | C2×D4 | 1 | 2 | yes | — |
| 185 | #6118 | C2×D4 | 1 | 2 | yes | — |
| 186 | D13⋊C8 | — | 2 | 2 | no | — |
| 187 | D13⋊C8 | — | 4 | 2 | no | — |
| 188 | C13×SD16 | — | 2 | 2 | no | — |
| 189 | C13×D8 | — | 2 | 2 | no | — |
| 190 | C13×M16 | C22×C4 | 1 | 2 | yes | — |
| 191 | C13×C22⋊C4 | — | 4 | 1 | no | — |
| 192 | C42×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 193 | #6107 | — | 2 | 2 | no | — |
| 194 | #6105 | — | 2 | 2 | no | — |
| 195 | #6105 | — | 2 | 2 | no | — |
| 196 | #6104 | — | 2 | 2 | no | — |
| 197 | #6103 | — | 4 | 1 | no | — |
| 198 | #6101 | — | 4 | 1 | no | — |
| 199 | C4×Dic13 | — | 2 | 1 | no | — |
| 200 | C4×Dic13 | C22×C4 | 1 | 1 | yes | characteristic |
| 201 | #6099 | C22×C4 | 1 | 2 | yes | — |
| 202 | Dic52 | — | 2 | 2 | no | — |
| 203 | #6095 | — | 2 | 2 | no | — |
| 204 | #6094 | — | 2 | 2 | no | — |
| 205 | C8×D13 | — | 2 | 2 | no | — |
| 206 | #3018 | — | 13 | 1 | no | — |
| 207 | #2956 | — | 13 | 2 | no | — |
| 208 | #2901 | — | 13 | 2 | no | — |
| 209 | #1963 | — | 13 | 1 | no | — |
| 210 | #1932 | — | 13 | 2 | no | — |
| 211 | #1906 | — | 13 | 2 | no | — |
| 212 | #1884 | — | 13 | 1 | no | — |
| 213 | #1861 | — | 13 | 2 | no | — |
| 214 | #1759 | — | 13 | 2 | no | — |
| 215 | C23×C13 | — | 2 | 1 | no | — |
| 216 | C22×D13 | — | 2 | 2 | no | — |
| 217 | C22×D13 | — | 2 | 1 | no | — |
| 218 | C22×D13 | — | 4 | 2 | no | — |
| 219 | C22×D13 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 220 | C2×#261 | — | 2 | 2 | no | — |
| 221 | C2×#261 | — | 2 | 2 | no | — |
| 222 | C2×#261 | — | 4 | 2 | no | — |
| 223 | C2×#261 | — | 8 | 2 | no | — |
| 224 | C2×#261 | — | 8 | 4 | no | — |
| 225 | Q8×C13 | — | 2 | 2 | no | — |
| 226 | Q8×C13 | — | 4 | 1 | no | — |
| 227 | Q8×C13 | C4×D4 | 1 | 2 | yes | — |
| 228 | D4×C13 | — | 2 | 2 | no | — |
| 229 | D4×C13 | — | 2 | 2 | no | — |
| 230 | D4×C13 | — | 4 | 1 | no | — |
| 231 | D4×C13 | C4×D4 | 1 | 2 | yes | — |
| 232 | C2×C4×C13 | — | 2 | 2 | no | — |
| 233 | C2×C4×C13 | — | 2 | 1 | no | — |
| 234 | C2×C4×C13 | — | 2 | 1 | no | — |
| 235 | C2×C4×C13 | — | 4 | 2 | no | — |
| 236 | C2×C4×C13 | C23×C4 | 1 | 1 | yes | characteristic |
| 237 | C22⋊D13 | — | 2 | 2 | no | — |
| 238 | C22⋊D13 | — | 2 | 2 | no | — |
| 239 | C22⋊D13 | — | 2 | 2 | no | — |
| 240 | C22⋊D13 | — | 4 | 2 | no | — |
| 241 | C22⋊D13 | — | 4 | 2 | no | — |
| 242 | C22⋊D13 | — | 8 | 2 | no | — |
| 243 | C2×Dic13 | — | 2 | 2 | no | — |
| 244 | C2×Dic13 | — | 2 | 1 | no | — |
| 245 | C2×Dic13 | — | 2 | 1 | no | — |
| 246 | C2×Dic13 | — | 4 | 1 | no | — |
| 247 | C2×Dic13 | — | 4 | 1 | no | — |
| 248 | C2×Dic13 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 249 | D52 | — | 2 | 2 | no | — |
| 250 | D52 | — | 2 | 2 | no | — |
| 251 | D52 | — | 4 | 2 | no | — |
| 252 | D52 | — | 4 | 1 | no | — |
| 253 | D52 | — | 4 | 2 | no | — |
| 254 | D52 | C4×D4 | 1 | 2 | yes | — |
| 255 | C4×D13 | — | 2 | 2 | no | — |
| 256 | C4×D13 | — | 2 | 2 | no | — |
| 257 | C4×D13 | — | 2 | 2 | no | — |
| 258 | C4×D13 | — | 4 | 2 | no | — |
| 259 | C4×D13 | — | 4 | 2 | no | — |
| 260 | C4×D13 | — | 4 | 1 | no | — |
| 261 | C4×D13 | — | 4 | 1 | no | — |
| 262 | C4×D13 | — | 8 | 1 | no | — |
| 263 | C4×D13 | C22×D4 | 1 | 2 | yes | — |
| 264 | C4×D13 | C2×#41 | 1 | 2 | yes | — |
| 265 | Dic26 | — | 2 | 2 | no | — |
| 266 | Dic26 | — | 2 | 2 | no | — |
| 267 | Dic26 | — | 4 | 1 | no | — |
| 268 | Dic26 | C4×D4 | 1 | 2 | yes | — |
| 269 | #1057 | — | 2 | 2 | no | — |
| 270 | #1057 | — | 2 | 2 | no | — |
| 271 | #1057 | — | 4 | 2 | no | — |
| 272 | C8×C13 | — | 2 | 2 | no | — |
| 273 | #1055 | — | 2 | 2 | no | — |
| 274 | #585 | — | 13 | 1 | no | — |
| 275 | #575 | — | 13 | 2 | no | — |
| 276 | #568 | — | 13 | 2 | no | — |
| 277 | #568 | — | 13 | 1 | no | — |
| 278 | #532 | — | 13 | 1 | no | — |
| 279 | C4×#41 | — | 13 | 2 | no | — |
| 280 | #456 | — | 13 | 1 | no | — |
| 281 | #456 | — | 13 | 1 | no | — |
| 282 | #455 | — | 13 | 2 | no | — |
| 283 | #454 | — | 13 | 1 | no | — |
| 284 | #454 | #261 | 1 | 1 | yes | characteristic, complemented |
| 285 | #453 | — | 13 | 2 | no | — |
| 286 | #444 | — | 26 | 2 | no | — |
| 287 | #444 | — | 26 | 2 | no | — |
| 288 | #443 | — | 26 | 2 | no | — |
| 289 | #443 | — | 26 | 2 | no | — |
| 290 | #430 | — | 13 | 2 | no | — |
| 291 | #423 | — | 13 | 1 | no | — |
| 292 | #421 | — | 13 | 2 | no | — |
| 293 | #421 | — | 13 | 2 | no | — |
| 294 | #421 | — | 26 | 2 | no | — |
| 295 | #421 | — | 26 | 2 | no | — |
| 296 | C2×#104 | — | 13 | 2 | no | — |
| 297 | C2×#104 | — | 13 | 2 | no | — |
| 298 | C2×#104 | — | 13 | 2 | no | — |
| 299 | C2×#104 | — | 13 | 2 | no | — |
| 300 | C2×#104 | — | 26 | 2 | no | — |
| 301 | C2×#104 | — | 26 | 2 | no | — |
| 302 | #413 | — | 13 | 1 | no | — |
| 303 | #410 | — | 13 | 1 | no | — |
| 304 | C4×M16 | — | 13 | 2 | no | — |
| 305 | #376 | — | 13 | 1 | no | — |
| 306 | #344 | — | 13 | 2 | no | — |
| 307 | #339 | — | 13 | 2 | no | — |
| 308 | #339 | — | 13 | 2 | no | — |
| 309 | C22×C13 | — | 2 | 2 | no | — |
| 310 | C22×C13 | — | 4 | 1 | no | — |
| 311 | C22×C13 | — | 8 | 1 | no | — |
| 312 | C22×C13 | #518 | 1 | 1 | yes | characteristic |
| 313 | C2×D13 | — | 2 | 2 | no | — |
| 314 | C2×D13 | — | 4 | 1 | no | — |
| 315 | C2×D13 | — | 4 | 1 | no | — |
| 316 | C2×D13 | — | 8 | 2 | no | — |
| 317 | C2×D13 | — | 8 | 1 | no | — |
| 318 | C2×D13 | — | 16 | 2 | no | — |
| 319 | C2×D13 | #546 | 1 | 2 | yes | — |
| 320 | #261 | — | 4 | 2 | no | — |
| 321 | #261 | — | 4 | 2 | no | — |
| 322 | #261 | — | 8 | 2 | no | — |
| 323 | C4×C13 | — | 2 | 2 | no | — |
| 324 | C4×C13 | — | 4 | 1 | no | — |
| 325 | C4×C13 | — | 4 | 1 | no | — |
| 326 | C4×C13 | C2×C4×D4 | 1 | 2 | yes | — |
| 327 | Dic13 | — | 2 | 2 | no | — |
| 328 | Dic13 | — | 4 | 1 | no | — |
| 329 | Dic13 | — | 4 | 1 | no | — |
| 330 | Dic13 | D42 | 1 | 1 | yes | characteristic |
| 331 | Dic13 | #551 | 1 | 1 | yes | characteristic |
| 332 | 2−1+4 | — | 13 | 1 | no | — |
| 333 | 2−1+4 | — | 26 | 2 | no | — |
| 334 | 2−1+4 | C2×#261 | 1 | 1 | yes | characteristic |
| 335 | H(5,𝔽2) | — | 13 | 2 | no | — |
| 336 | H(5,𝔽2) | — | 26 | 2 | no | — |
| 337 | H(5,𝔽2) | — | 52 | 1 | no | — |
| 338 | C2×#41 | — | 13 | 2 | no | — |
| 339 | C2×#41 | — | 13 | 1 | no | — |
| 340 | C2×#41 | — | 13 | 1 | no | — |
| 341 | C2×#41 | — | 26 | 2 | no | — |
| 342 | C2×#41 | — | 26 | 2 | no | — |
| 343 | C2×#41 | — | 52 | 1 | no | — |
| 344 | #137 | — | 13 | 2 | no | — |
| 345 | #137 | — | 13 | 2 | no | — |
| 346 | #137 | — | 26 | 2 | no | — |
| 347 | AGL(1,ℤ/8) | — | 13 | 2 | no | — |
| 348 | AGL(1,ℤ/8) | — | 26 | 2 | no | — |
| 349 | AGL(1,ℤ/8) | C2×#261 | 1 | 2 | yes | complemented |
| 350 | #135 | — | 26 | 2 | no | — |
| 351 | #135 | — | 26 | 2 | no | — |
| 352 | #131 | — | 26 | 2 | no | — |
| 353 | #131 | — | 26 | 2 | no | — |
| 354 | #131 | — | 26 | 2 | no | — |
| 355 | #131 | — | 26 | 2 | no | — |
| 356 | #131 | — | 52 | 2 | no | — |
| 357 | C2×M16 | — | 13 | 2 | no | — |
| 358 | C2×M16 | — | 13 | 2 | no | — |
| 359 | C2×M16 | — | 13 | 2 | no | — |
| 360 | C2×M16 | — | 26 | 2 | no | — |
| 361 | C2×M16 | — | 26 | 2 | no | — |
| 362 | C2×M16 | — | 52 | 1 | no | — |
| 363 | C4⋊Q8 | — | 13 | 1 | no | — |
| 364 | #127 | — | 13 | 1 | no | — |
| 365 | #124 | — | 13 | 1 | no | — |
| 366 | #124 | C2×#261 | 1 | 1 | yes | characteristic, complemented |
| 367 | #121 | — | 52 | 1 | no | — |
| 368 | C4×Q8 | — | 26 | 2 | no | — |
| 369 | C4×D4 | — | 26 | 2 | no | — |
| 370 | C4×D4 | — | 52 | 1 | no | — |
| 371 | C4×D4 | — | 52 | 2 | no | — |
| 372 | #117 | — | 13 | 2 | no | — |
| 373 | #117 | — | 26 | 2 | no | — |
| 374 | C2×C42 | — | 13 | 2 | no | — |
| 375 | C2×C42 | — | 13 | 1 | no | — |
| 376 | C2×C42 | — | 26 | 2 | no | — |
| 377 | #108 | — | 26 | 2 | no | — |
| 378 | #108 | — | 26 | 2 | no | — |
| 379 | C4⋊C8 | — | 52 | 1 | no | — |
| 380 | #104 | — | 13 | 2 | no | — |
| 381 | #104 | — | 13 | 2 | no | — |
| 382 | #104 | — | 13 | 2 | no | — |
| 383 | #104 | — | 13 | 2 | no | — |
| 384 | #104 | — | 13 | 2 | no | — |
| 385 | #104 | — | 13 | 2 | no | — |
| 386 | #104 | — | 13 | 2 | no | — |
| 387 | #104 | — | 26 | 2 | no | — |
| 388 | #104 | — | 26 | 2 | no | — |
| 389 | #104 | — | 26 | 2 | no | — |
| 390 | #104 | — | 26 | 2 | no | — |
| 391 | #104 | — | 26 | 2 | no | — |
| 392 | #104 | — | 26 | 2 | no | — |
| 393 | #104 | — | 26 | 2 | no | — |
| 394 | #104 | — | 26 | 2 | no | — |
| 395 | #104 | C2×#261 | 1 | 2 | yes | complemented |
| 396 | #101 | — | 13 | 1 | no | — |
| 397 | #101 | C2×#261 | 1 | 1 | yes | characteristic, complemented |
| 398 | #100 | — | 13 | 2 | no | — |
| 399 | #99 | — | 52 | 1 | no | — |
| 400 | #97 | — | 26 | 2 | no | — |
| 401 | C4×C8 | — | 26 | 2 | no | — |
| 402 | #95 | — | 52 | 1 | no | — |
| 403 | C2×C13 | — | 2 | 1 | no | — |
| 404 | C2×C13 | — | 4 | 2 | no | — |
| 405 | C2×C13 | — | 8 | 1 | no | — |
| 406 | C2×C13 | #2358 | 1 | 1 | yes | characteristic |
| 407 | D13 | — | 2 | 2 | no | — |
| 408 | D13 | — | 4 | 2 | no | — |
| 409 | D13 | — | 8 | 1 | no | — |
| 410 | #41 | — | 2 | 2 | no | — |
| 411 | #41 | — | 4 | 1 | no | — |
| 412 | #41 | — | 13 | 2 | no | — |
| 413 | #41 | — | 13 | 2 | no | — |
| 414 | #41 | — | 13 | 2 | no | — |
| 415 | #41 | — | 26 | 2 | no | — |
| 416 | #41 | — | 26 | 2 | no | — |
| 417 | #41 | — | 26 | 2 | no | — |
| 418 | #41 | — | 26 | 2 | no | — |
| 419 | #41 | — | 26 | 2 | no | — |
| 420 | #41 | — | 26 | 2 | no | — |
| 421 | #41 | — | 26 | 2 | no | — |
| 422 | #41 | — | 26 | 2 | no | — |
| 423 | #41 | — | 26 | 2 | no | — |
| 424 | #41 | — | 52 | 1 | no | — |
| 425 | #41 | — | 52 | 2 | no | — |
| 426 | #41 | — | 52 | 2 | no | — |
| 427 | #41 | — | 52 | 1 | no | — |
| 428 | #41 | — | 52 | 1 | no | — |
| 429 | #41 | — | 52 | 2 | no | — |
| 430 | #41 | C22×#261 | 1 | 2 | yes | — |
| 431 | C2×Q8 | — | 2 | 2 | no | — |
| 432 | C2×Q8 | — | 13 | 2 | no | — |
| 433 | C2×Q8 | — | 13 | 1 | no | — |
| 434 | C2×Q8 | — | 26 | 2 | no | — |
| 435 | C2×Q8 | — | 52 | 1 | no | — |
| 436 | C2×Q8 | C22×#261 | 1 | 1 | yes | characteristic |
| 437 | C2×D4 | — | 13 | 2 | no | — |
| 438 | C2×D4 | — | 13 | 1 | no | — |
| 439 | C2×D4 | — | 26 | 2 | no | — |
| 440 | C2×D4 | — | 26 | 1 | no | — |
| 441 | C2×D4 | — | 26 | 2 | no | — |
| 442 | C2×D4 | — | 26 | 2 | no | — |
| 443 | C2×D4 | — | 26 | 1 | no | — |
| 444 | C2×D4 | — | 52 | 2 | no | — |
| 445 | C2×D4 | — | 52 | 1 | no | — |
| 446 | C2×D4 | — | 52 | 2 | no | — |
| 447 | C2×D4 | — | 52 | 1 | no | — |
| 448 | C2×D4 | — | 52 | 2 | no | — |
| 449 | C2×D4 | C22×#261 | 1 | 1 | yes | characteristic |
| 450 | C22×C4 | — | 13 | 1 | no | — |
| 451 | C22×C4 | — | 26 | 2 | no | — |
| 452 | C22×C4 | — | 26 | 1 | no | — |
| 453 | C22×C4 | — | 26 | 1 | no | — |
| 454 | C22×C4 | — | 26 | 1 | no | — |
| 455 | C22×C4 | — | 26 | 2 | no | — |
| 456 | C22×C4 | — | 52 | 2 | no | — |
| 457 | C22×C4 | — | 52 | 2 | no | — |
| 458 | Q16 | — | 26 | 2 | no | — |
| 459 | Q16 | — | 26 | 2 | no | — |
| 460 | SD16 | — | 2 | 2 | no | — |
| 461 | SD16 | — | 26 | 2 | no | — |
| 462 | SD16 | — | 26 | 2 | no | — |
| 463 | SD16 | — | 26 | 2 | no | — |
| 464 | D8 | — | 2 | 2 | no | — |
| 465 | D8 | — | 26 | 2 | no | — |
| 466 | M16 | — | 13 | 2 | no | — |
| 467 | M16 | — | 13 | 2 | no | — |
| 468 | M16 | — | 13 | 2 | no | — |
| 469 | M16 | — | 26 | 2 | no | — |
| 470 | M16 | — | 26 | 2 | no | — |
| 471 | M16 | — | 26 | 2 | no | — |
| 472 | M16 | — | 26 | 2 | no | — |
| 473 | M16 | — | 52 | 2 | no | — |
| 474 | M16 | — | 52 | 2 | no | — |
| 475 | M16 | — | 52 | 2 | no | — |
| 476 | M16 | C22×#261 | 1 | 2 | yes | — |
| 477 | C2×C8 | — | 26 | 2 | no | — |
| 478 | C2×C8 | — | 26 | 2 | no | — |
| 479 | C2×C8 | — | 26 | 2 | no | — |
| 480 | C2×C8 | — | 52 | 1 | no | — |
| 481 | C2×C8 | — | 52 | 1 | no | — |
| 482 | C2×C8 | — | 52 | 2 | no | — |
| 483 | C2×C8 | — | 52 | 2 | no | — |
| 484 | C4⋊C4 | — | 26 | 2 | no | — |
| 485 | C4⋊C4 | — | 52 | 1 | no | — |
| 486 | C4⋊C4 | — | 52 | 2 | no | — |
| 487 | C22⋊C4 | — | 4 | 1 | no | — |
| 488 | C22⋊C4 | — | 26 | 2 | no | — |
| 489 | C22⋊C4 | — | 52 | 1 | no | — |
| 490 | C22⋊C4 | — | 52 | 2 | no | — |
| 491 | C42 | — | 13 | 2 | no | — |
| 492 | C42 | — | 13 | 2 | no | — |
| 493 | C42 | — | 13 | 1 | no | — |
| 494 | C42 | — | 26 | 1 | no | — |
| 495 | C42 | — | 26 | 2 | no | — |
| 496 | C42 | — | 26 | 2 | no | — |
| 497 | C42 | — | 52 | 2 | no | — |
| 498 | C42 | C22×#261 | 1 | 1 | yes | characteristic |
| 499 | C13 | #22898 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 500 | C23 | — | 2 | 1 | no | — |
| 501 | C23 | — | 13 | 1 | no | — |
| 502 | C23 | — | 26 | 2 | no | — |
| 503 | C23 | — | 26 | 1 | no | — |
| 504 | C23 | — | 52 | 2 | no | — |
| 505 | Q8 | — | 2 | 2 | no | — |
| 506 | Q8 | — | 4 | 1 | no | — |
| 507 | Q8 | — | 13 | 2 | no | — |
| 508 | Q8 | — | 26 | 2 | no | — |
| 509 | Q8 | — | 26 | 2 | no | — |
| 510 | Q8 | — | 52 | 1 | no | — |
| 511 | Q8 | D4×#261 | 1 | 2 | yes | — |
| 512 | D4 | — | 2 | 2 | no | — |
| 513 | D4 | — | 2 | 2 | no | — |
| 514 | D4 | — | 4 | 1 | no | — |
| 515 | D4 | — | 13 | 2 | no | — |
| 516 | D4 | — | 26 | 2 | no | — |
| 517 | D4 | — | 26 | 2 | no | — |
| 518 | D4 | — | 26 | 2 | no | — |
| 519 | D4 | — | 26 | 2 | no | — |
| 520 | D4 | — | 26 | 2 | no | — |
| 521 | D4 | — | 52 | 2 | no | — |
| 522 | D4 | — | 52 | 2 | no | — |
| 523 | D4 | — | 52 | 1 | no | — |
| 524 | D4 | — | 52 | 2 | no | — |
| 525 | D4 | — | 52 | 2 | no | — |
| 526 | D4 | — | 104 | 2 | no | — |
| 527 | D4 | D4×#261 | 1 | 2 | yes | — |
| 528 | C2×C4 | — | 2 | 2 | no | — |
| 529 | C2×C4 | — | 2 | 1 | no | — |
| 530 | C2×C4 | — | 2 | 1 | no | — |
| 531 | C2×C4 | — | 4 | 2 | no | — |
| 532 | C2×C4 | — | 13 | 1 | no | — |
| 533 | C2×C4 | — | 13 | 2 | no | — |
| 534 | C2×C4 | — | 13 | 2 | no | — |
| 535 | C2×C4 | — | 26 | 2 | no | — |
| 536 | C2×C4 | — | 26 | 2 | no | — |
| 537 | C2×C4 | — | 26 | 2 | no | — |
| 538 | C2×C4 | — | 26 | 2 | no | — |
| 539 | C2×C4 | — | 26 | 2 | no | — |
| 540 | C2×C4 | — | 26 | 2 | no | — |
| 541 | C2×C4 | — | 26 | 1 | no | — |
| 542 | C2×C4 | — | 26 | 1 | no | — |
| 543 | C2×C4 | — | 52 | 2 | no | — |
| 544 | C2×C4 | — | 52 | 1 | no | — |
| 545 | C2×C4 | — | 52 | 1 | no | — |
| 546 | C2×C4 | — | 52 | 2 | no | — |
| 547 | C2×C4 | — | 52 | 1 | no | — |
| 548 | C2×C4 | — | 52 | 1 | no | — |
| 549 | C2×C4 | — | 52 | 2 | no | — |
| 550 | C2×C4 | — | 104 | 1 | no | — |
| 551 | C2×C4 | — | 104 | 2 | no | — |
| 552 | C2×C4 | — | 104 | 4 | no | — |
| 553 | C2×C4 | C23×#261 | 1 | 1 | yes | characteristic |
| 554 | C8 | — | 2 | 2 | no | — |
| 555 | C8 | — | 26 | 2 | no | — |
| 556 | C8 | — | 26 | 2 | no | — |
| 557 | C8 | — | 26 | 2 | no | — |
| 558 | C8 | — | 52 | 2 | no | — |
| 559 | C22 | — | 2 | 2 | no | — |
| 560 | C22 | — | 4 | 1 | no | — |
| 561 | C22 | — | 8 | 1 | no | — |
| 562 | C22 | — | 13 | 2 | no | — |
| 563 | C22 | — | 26 | 2 | no | — |
| 564 | C22 | — | 52 | 1 | no | — |
| 565 | C22 | — | 52 | 1 | no | — |
| 566 | C22 | — | 104 | 1 | no | — |
| 567 | C22 | — | 104 | 2 | no | — |
| 568 | C22 | — | 208 | 2 | no | — |
| 569 | C22 | #11719623 | 1 | 1 | yes | characteristic |
| 570 | C4 | — | 2 | 2 | no | — |
| 571 | C4 | — | 4 | 1 | no | — |
| 572 | C4 | — | 4 | 1 | no | — |
| 573 | C4 | — | 13 | 1 | no | — |
| 574 | C4 | — | 13 | 1 | no | — |
| 575 | C4 | — | 26 | 2 | no | — |
| 576 | C4 | — | 52 | 1 | no | — |
| 577 | C4 | — | 52 | 2 | no | — |
| 578 | C4 | — | 52 | 2 | no | — |
| 579 | C4 | — | 52 | 1 | no | — |
| 580 | C4 | — | 104 | 2 | no | — |
| 581 | C4 | C2×D4×#261 | 1 | 2 | yes | — |
| 582 | C2 | — | 2 | 1 | no | — |
| 583 | C2 | — | 4 | 2 | no | — |
| 584 | C2 | — | 8 | 1 | no | — |
| 585 | C2 | — | 26 | 2 | no | — |
| 586 | C2 | — | 52 | 2 | no | — |
| 587 | C2 | — | 104 | 1 | no | — |
| 588 | C2 | #13131358 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13131610 | C2 | semidirect |
| 2. #13131467 | C2 | semidirect |
| 3. #13130973 | C2 | semidirect |
| 4. #13130923 | C2 | semidirect |
| 5. #13130873 | C2 | semidirect |
| 6. #13130837 | C2 | semidirect |
| 7. #13130797 | C2 | semidirect |
| 8. #13130601 | C2 | semidirect |
| 13. #11719621 | C22 | semidirect |
| 24. #11719142 | C22 | semidirect |
| 25. C2×#88116 | C22 | semidirect |
| 30. #11719100 | C22 | semidirect |
| 31. M16×#261 | C22 | semidirect |
| 32. #11719057 | C22 | semidirect |
| 33. #11719052 | C22 | semidirect |
| 34. C13×#454 | C4 | semidirect |
| 35. #11718907 | C4 | semidirect |
| 36. #11718859 | C4 | semidirect |
| 37. #11718723 | C4 | semidirect |
| 38. #11718486 | C4 | semidirect |
| 40. #11718413 | C4 | semidirect |
| 42. #11718274 | C22 | semidirect |
| 43. #11718272 | C22 | semidirect |
| 44. #11718234 | C22 | semidirect |
| 74. C13×AGL(1,ℤ/8) | C2×C4 | semidirect |
| 75. C13×#124 | C2×C4 | semidirect |
| 76. #88205 | C2×C4 | semidirect |
| 77. #88198 | C2×C4 | semidirect |
| 78. #88194 | C2×C4 | semidirect |
| 79. #88186 | C2×C4 | semidirect |
| 84. #88163 | C2×C4 | semidirect |
| 88. #88129 | C2×C4 | semidirect |
| 96. #88118 | D4 | semidirect |
| 97. #88118 | D4 | semidirect |
| 101. #88116 | D4 | semidirect |
| 102. #88116 | D4 | semidirect |
| 109. C13×#104 | C2×C4 | semidirect |
| 110. C13×#101 | C2×C4 | semidirect |
| 111. #88077 | C2×C4 | semidirect |
| 112. #88076 | C2×C4 | semidirect |
| 113. #88065 | C2×C4 | semidirect |
| 114. #88063 | C2×C4 | semidirect |
| 115. #88045 | C2×C4 | semidirect |
| 284. #454 | #261 | semidirect |
| 349. AGL(1,ℤ/8) | C2×#261 | semidirect |
| 366. #124 | C2×#261 | semidirect |
| 395. #104 | C2×#261 | semidirect |
| 397. #101 | C2×#261 | semidirect |
| 499. C13 | #22898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13131610 | 2 |
| #13131467 | 2 |
| #13130973 | 2 |
| #13130923 | 2 |
| #13130873 | 2 |
| #13130837 | 2 |
| #13130797 | 2 |
| #13130601 | 2 |
| #13124183 | 2 |
| #22898 | 13 |