Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1078 conjugacy classes of subgroups.
The subgroup lattice has 564 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#11719471 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13127972 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#11718840 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13124557 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13116817 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #13116803 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #13116563 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13116465 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×C13×#362 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#88254 | — | 2 | 1 | no | — |
| 11 | C22×C13×Q16 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#88196 | — | 2 | 1 | no | — |
| 13 | #11719471 | — | 2 | 2 | no | — |
| 14 | #11719471 | — | 2 | 2 | no | — |
| 15 | #11719471 | — | 2 | 2 | no | — |
| 16 | #11719471 | C22 | 1 | 4 | yes | — |
| 17 | C2×#88173 | — | 2 | 1 | no | — |
| 18 | C2×#88172 | — | 2 | 2 | no | — |
| 19 | C2×Q16×D13 | — | 2 | 1 | no | — |
| 20 | #11719453 | — | 2 | 1 | no | — |
| 21 | C2×#88158 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#88158 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#88155 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×C13×M32 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×C13×#108 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#88069 | C22 | 1 | 2 | yes | complemented |
| 27 | #11718840 | — | 2 | 2 | no | — |
| 28 | #11718840 | — | 2 | 2 | no | — |
| 29 | C2×#88068 | C22 | 1 | 2 | yes | complemented |
| 30 | #11718793 | — | 2 | 1 | no | — |
| 31 | C2×#88052 | C22 | 1 | 1 | yes | characteristic |
| 32 | #11718570 | — | 2 | 1 | no | — |
| 33 | #11718570 | C22 | 1 | 2 | yes | complemented |
| 34 | #11718569 | — | 2 | 1 | no | — |
| 35 | #11718569 | C22 | 1 | 2 | yes | complemented |
| 36 | #11718565 | — | 2 | 2 | no | — |
| 37 | #11718559 | — | 2 | 2 | no | — |
| 38 | #11718558 | C22 | 1 | 2 | yes | complemented |
| 39 | #11718557 | C22 | 1 | 2 | yes | complemented |
| 40 | C13×#362 | C22 | 1 | 4 | yes | complemented |
| 41 | #11718107 | C22 | 1 | 4 | yes | complemented |
| 42 | #11718089 | C22 | 1 | 4 | yes | complemented |
| 43 | C22×Q8×C13 | — | 2 | 1 | no | — |
| 44 | #88254 | — | 2 | 4 | no | — |
| 45 | #88254 | — | 2 | 4 | no | — |
| 46 | #88254 | — | 4 | 2 | no | — |
| 47 | #88254 | — | 4 | 2 | no | — |
| 48 | C2×#6131 | — | 2 | 2 | no | — |
| 49 | C2×#6131 | — | 4 | 1 | no | — |
| 50 | C2×Q8×D13 | — | 2 | 2 | no | — |
| 51 | C2×Q8×D13 | — | 4 | 1 | no | — |
| 52 | C2×#6127 | — | 2 | 1 | no | — |
| 53 | C2×#6127 | — | 2 | 1 | no | — |
| 54 | C2×#6127 | — | 4 | 2 | no | — |
| 55 | C2×#6127 | D4 | 1 | 1 | yes | characteristic |
| 56 | C2×C13×Q16 | — | 2 | 1 | no | — |
| 57 | C2×C13×Q16 | — | 2 | 1 | no | — |
| 58 | C2×C13×Q16 | — | 2 | 1 | no | — |
| 59 | C2×C13×Q16 | D4 | 1 | 2 | yes | — |
| 60 | C2×C13×Q16 | D4 | 1 | 2 | yes | — |
| 61 | C2×C13×Q16 | C23 | 1 | 2 | yes | — |
| 62 | C2×C13×M16 | — | 2 | 1 | no | — |
| 63 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 64 | C2×#6107 | — | 2 | 2 | no | — |
| 65 | #88196 | — | 2 | 4 | no | — |
| 66 | #88196 | — | 2 | 4 | no | — |
| 67 | C2×#6106 | — | 2 | 2 | no | — |
| 68 | C2×#6099 | D4 | 1 | 1 | yes | characteristic |
| 69 | #88173 | — | 2 | 4 | no | — |
| 70 | #88173 | — | 2 | 4 | no | — |
| 71 | #88172 | — | 2 | 8 | no | — |
| 72 | #88172 | — | 2 | 8 | no | — |
| 73 | Q16×D13 | — | 2 | 4 | no | — |
| 74 | Q16×D13 | — | 2 | 4 | no | — |
| 75 | #88163 | — | 2 | 2 | no | — |
| 76 | #88163 | — | 4 | 1 | no | — |
| 77 | #88162 | — | 2 | 2 | no | — |
| 78 | #88162 | — | 4 | 1 | no | — |
| 79 | C2×Dic52 | D4 | 1 | 1 | yes | characteristic |
| 80 | C2×Dic52 | C23 | 1 | 1 | yes | characteristic |
| 81 | #88158 | — | 2 | 1 | no | — |
| 82 | #88158 | — | 2 | 1 | no | — |
| 83 | #88158 | — | 2 | 1 | no | — |
| 84 | #88158 | — | 2 | 1 | no | — |
| 85 | #88158 | — | 2 | 1 | no | — |
| 86 | #88158 | — | 2 | 1 | no | — |
| 87 | #88158 | — | 4 | 2 | no | — |
| 88 | #88158 | D4 | 1 | 2 | yes | — |
| 89 | #88158 | C23 | 1 | 2 | yes | — |
| 90 | C2×D104 | D4 | 1 | 1 | yes | characteristic |
| 91 | C2×D104 | C23 | 1 | 1 | yes | characteristic |
| 92 | C2×#6095 | — | 2 | 1 | no | — |
| 93 | C2×#6095 | — | 2 | 1 | no | — |
| 94 | #88155 | — | 2 | 1 | no | — |
| 95 | #88155 | — | 2 | 1 | no | — |
| 96 | #88155 | D4 | 1 | 2 | yes | — |
| 97 | #88155 | C23 | 1 | 2 | yes | — |
| 98 | C2×#6094 | — | 2 | 1 | no | — |
| 99 | C2×C8×D13 | — | 2 | 1 | no | — |
| 100 | C13×M32 | — | 2 | 1 | no | — |
| 101 | C13×M32 | C23 | 1 | 2 | yes | — |
| 102 | C2×C13×C16 | — | 2 | 1 | no | — |
| 103 | C13×#108 | — | 2 | 1 | no | — |
| 104 | C13×#108 | C23 | 1 | 2 | yes | — |
| 105 | #88069 | — | 2 | 4 | no | — |
| 106 | #88068 | — | 2 | 4 | no | — |
| 107 | #88064 | — | 2 | 2 | no | — |
| 108 | #88063 | — | 2 | 2 | no | — |
| 109 | #88052 | — | 2 | 1 | no | — |
| 110 | #88052 | — | 2 | 1 | no | — |
| 111 | C2×#6090 | C23 | 1 | 2 | yes | — |
| 112 | Dic104 | — | 2 | 2 | no | — |
| 113 | #88040 | — | 2 | 2 | no | — |
| 114 | #88040 | — | 2 | 2 | no | — |
| 115 | D208 | — | 2 | 2 | no | — |
| 116 | #33540 | — | 13 | 1 | no | maximal, Sylow |
| 117 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 118 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 119 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 120 | C2×Q8×C13 | — | 4 | 1 | no | — |
| 121 | C2×Q8×C13 | — | 4 | 1 | no | — |
| 122 | C2×Q8×C13 | — | 4 | 1 | no | — |
| 123 | C22×C4×C13 | — | 4 | 1 | no | — |
| 124 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 125 | C2×C22⋊D13 | — | 2 | 1 | no | — |
| 126 | C2×C22⋊D13 | — | 4 | 1 | no | — |
| 127 | C2×C22⋊D13 | — | 4 | 1 | no | — |
| 128 | #6131 | — | 2 | 8 | no | — |
| 129 | #6131 | — | 4 | 4 | no | — |
| 130 | #6131 | — | 4 | 4 | no | — |
| 131 | #6131 | — | 4 | 4 | no | — |
| 132 | Q8×D13 | — | 2 | 8 | no | — |
| 133 | Q8×D13 | — | 4 | 4 | no | — |
| 134 | Q8×D13 | — | 4 | 4 | no | — |
| 135 | Q8×D13 | — | 4 | 4 | no | — |
| 136 | #6127 | — | 2 | 1 | no | — |
| 137 | #6127 | — | 2 | 1 | no | — |
| 138 | #6127 | — | 2 | 2 | no | — |
| 139 | #6127 | — | 2 | 2 | no | — |
| 140 | #6127 | — | 4 | 8 | no | — |
| 141 | #6127 | — | 4 | 8 | no | — |
| 142 | #6127 | — | 4 | 1 | no | — |
| 143 | #6127 | — | 4 | 1 | no | — |
| 144 | #6127 | — | 4 | 1 | no | — |
| 145 | #6127 | — | 4 | 1 | no | — |
| 146 | #6127 | — | 4 | 1 | no | — |
| 147 | #6127 | — | 4 | 1 | no | — |
| 148 | #6127 | D8 | 1 | 2 | yes | — |
| 149 | #6127 | C2×D4 | 1 | 2 | yes | — |
| 150 | C2×D52 | — | 2 | 1 | no | — |
| 151 | C2×D52 | — | 2 | 1 | no | — |
| 152 | C2×D52 | — | 4 | 2 | no | — |
| 153 | C2×D52 | D8 | 1 | 1 | yes | characteristic |
| 154 | C2×C4×D13 | — | 2 | 1 | no | — |
| 155 | C2×C4×D13 | — | 4 | 2 | no | — |
| 156 | C2×C4×D13 | — | 4 | 2 | no | — |
| 157 | C2×C4×D13 | — | 4 | 1 | no | — |
| 158 | C2×C4×D13 | — | 4 | 1 | no | — |
| 159 | C2×Dic26 | — | 2 | 1 | no | — |
| 160 | C2×Dic26 | — | 2 | 1 | no | — |
| 161 | C2×Dic26 | — | 4 | 2 | no | — |
| 162 | C2×Dic26 | D8 | 1 | 1 | yes | characteristic |
| 163 | C13×Q16 | — | 2 | 2 | no | — |
| 164 | C13×Q16 | — | 2 | 2 | no | — |
| 165 | C13×Q16 | — | 2 | 2 | no | — |
| 166 | C13×Q16 | C2×D4 | 1 | 4 | yes | — |
| 167 | C13×M16 | — | 2 | 2 | no | — |
| 168 | C13×M16 | — | 4 | 1 | no | — |
| 169 | C2×C8×C13 | — | 4 | 1 | no | — |
| 170 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 171 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 176 | #6107 | — | 2 | 8 | no | — |
| 177 | #6106 | — | 2 | 8 | no | — |
| 178 | #6099 | — | 2 | 1 | no | — |
| 179 | #6099 | C2×D4 | 1 | 2 | yes | — |
| 180 | C2×#1055 | — | 2 | 1 | no | — |
| 181 | Dic52 | — | 2 | 1 | no | — |
| 182 | Dic52 | — | 2 | 1 | no | — |
| 183 | Dic52 | — | 2 | 1 | no | — |
| 184 | Dic52 | — | 4 | 2 | no | — |
| 185 | Dic52 | C2×D4 | 1 | 2 | yes | — |
| 186 | D104 | — | 2 | 1 | no | — |
| 187 | D104 | — | 2 | 1 | no | — |
| 188 | D104 | — | 2 | 1 | no | — |
| 189 | D104 | — | 4 | 2 | no | — |
| 190 | D104 | C2×D4 | 1 | 2 | yes | — |
| 191 | #6095 | — | 2 | 2 | no | — |
| 192 | #6095 | — | 2 | 2 | no | — |
| 193 | #6095 | — | 4 | 2 | no | — |
| 194 | #6095 | — | 4 | 2 | no | — |
| 195 | #6095 | — | 4 | 1 | no | — |
| 196 | #6095 | — | 4 | 1 | no | — |
| 197 | #6094 | — | 2 | 2 | no | — |
| 198 | #6094 | — | 2 | 2 | no | — |
| 199 | C8×D13 | — | 2 | 2 | no | — |
| 200 | C8×D13 | — | 2 | 2 | no | — |
| 201 | C13×C16 | — | 2 | 2 | no | — |
| 202 | #6090 | — | 2 | 2 | no | — |
| 203 | C2×#578 | — | 13 | 1 | no | — |
| 204 | #3414 | — | 13 | 1 | no | — |
| 205 | C2×#510 | — | 13 | 1 | no | — |
| 206 | #3067 | — | 13 | 1 | no | — |
| 207 | #2195 | — | 13 | 4 | no | — |
| 208 | #2193 | — | 13 | 4 | no | — |
| 209 | C2×#362 | D13 | 1 | 1 | yes | characteristic, complemented |
| 210 | #2143 | — | 13 | 1 | no | — |
| 211 | #2117 | — | 13 | 1 | no | — |
| 212 | C23×C13 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 213 | C22×D13 | — | 2 | 1 | no | — |
| 214 | C22×D13 | — | 4 | 1 | no | — |
| 215 | C22×D13 | — | 4 | 1 | no | — |
| 216 | Q8×C13 | — | 2 | 4 | no | — |
| 217 | Q8×C13 | — | 4 | 2 | no | — |
| 218 | Q8×C13 | — | 4 | 2 | no | — |
| 219 | Q8×C13 | — | 4 | 2 | no | — |
| 220 | C2×C4×C13 | — | 4 | 2 | no | — |
| 221 | C2×C4×C13 | — | 4 | 2 | no | — |
| 222 | C2×C4×C13 | — | 4 | 2 | no | — |
| 223 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 224 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 225 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 226 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 227 | C2×C4×C13 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 228 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 229 | C22⋊D13 | — | 2 | 2 | no | — |
| 230 | C22⋊D13 | — | 2 | 2 | no | — |
| 231 | C22⋊D13 | — | 4 | 2 | no | — |
| 232 | C22⋊D13 | — | 4 | 2 | no | — |
| 233 | C22⋊D13 | — | 8 | 1 | no | — |
| 234 | C22⋊D13 | — | 8 | 1 | no | — |
| 235 | C2×Dic13 | — | 2 | 1 | no | — |
| 236 | C2×Dic13 | — | 4 | 1 | no | — |
| 237 | C2×Dic13 | — | 4 | 1 | no | — |
| 238 | D52 | — | 2 | 2 | no | — |
| 239 | D52 | — | 2 | 1 | no | — |
| 240 | D52 | — | 4 | 8 | no | — |
| 241 | D52 | — | 4 | 1 | no | — |
| 242 | D52 | — | 4 | 1 | no | — |
| 243 | D52 | — | 4 | 1 | no | — |
| 244 | D52 | C2×D8 | 1 | 2 | yes | — |
| 245 | C4×D13 | — | 2 | 2 | no | — |
| 246 | C4×D13 | — | 2 | 2 | no | — |
| 247 | C4×D13 | — | 4 | 8 | no | — |
| 248 | C4×D13 | — | 4 | 8 | no | — |
| 249 | C4×D13 | — | 4 | 2 | no | — |
| 250 | C4×D13 | — | 4 | 2 | no | — |
| 251 | C4×D13 | — | 8 | 1 | no | — |
| 252 | C4×D13 | — | 8 | 1 | no | — |
| 253 | Dic26 | — | 2 | 1 | no | — |
| 254 | Dic26 | — | 2 | 2 | no | — |
| 255 | Dic26 | — | 4 | 8 | no | — |
| 256 | Dic26 | — | 4 | 1 | no | — |
| 257 | Dic26 | — | 4 | 1 | no | — |
| 258 | Dic26 | — | 4 | 1 | no | — |
| 259 | Dic26 | C2×D8 | 1 | 2 | yes | — |
| 260 | C8×C13 | — | 4 | 2 | no | — |
| 261 | C8×C13 | #120 | 1 | 1 | yes | characteristic |
| 262 | C8×C13 | #120 | 1 | 1 | yes | characteristic |
| 263 | C8×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 264 | C8×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 265 | #1055 | — | 2 | 2 | no | — |
| 266 | C2×2−1+4 | — | 26 | 1 | no | — |
| 267 | #578 | — | 13 | 4 | no | — |
| 268 | #578 | — | 26 | 2 | no | — |
| 269 | #578 | — | 26 | 2 | no | — |
| 270 | #578 | — | 26 | 2 | no | — |
| 271 | #575 | — | 26 | 1 | no | — |
| 272 | C2×#137 | — | 26 | 1 | no | — |
| 273 | C2×#137 | — | 26 | 2 | no | — |
| 274 | C2×#135 | — | 13 | 1 | no | — |
| 275 | C2×#135 | — | 13 | 1 | no | — |
| 276 | C2×#135 | — | 26 | 1 | no | — |
| 277 | C22×Q16 | — | 26 | 1 | no | — |
| 278 | C22×Q16 | C2×D13 | 1 | 1 | yes | characteristic |
| 279 | C2×#131 | — | 13 | 1 | no | — |
| 280 | #510 | — | 13 | 2 | no | — |
| 281 | #510 | — | 26 | 1 | no | — |
| 282 | #510 | — | 26 | 2 | no | — |
| 283 | #510 | — | 26 | 2 | no | — |
| 284 | #509 | — | 13 | 2 | no | — |
| 285 | #509 | — | 26 | 1 | no | — |
| 286 | #508 | — | 26 | 2 | no | — |
| 287 | C2×Q32 | — | 13 | 2 | no | — |
| 288 | C2×SD32 | — | 13 | 2 | no | — |
| 289 | C2×M32 | — | 13 | 1 | no | — |
| 290 | C2×M32 | C2×D13 | 1 | 1 | yes | characteristic |
| 291 | #473 | — | 13 | 2 | no | — |
| 292 | #472 | — | 13 | 2 | no | — |
| 293 | #471 | — | 26 | 2 | no | — |
| 294 | C2×#108 | C2×D13 | 1 | 1 | yes | characteristic |
| 295 | #413 | — | 26 | 1 | no | — |
| 296 | #362 | C2×D13 | 1 | 4 | yes | complemented |
| 297 | #359 | — | 13 | 4 | no | — |
| 298 | #350 | — | 13 | 4 | no | — |
| 299 | C22×C13 | — | 4 | 1 | no | — |
| 300 | C22×C13 | #447 | 1 | 1 | yes | characteristic |
| 301 | C22×C13 | #447 | 1 | 1 | yes | characteristic |
| 302 | C22×C13 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 303 | C2×D13 | — | 2 | 2 | no | — |
| 304 | C2×D13 | — | 4 | 2 | no | — |
| 305 | C2×D13 | — | 4 | 2 | no | — |
| 306 | C2×D13 | — | 8 | 2 | no | — |
| 307 | C2×D13 | — | 8 | 1 | no | — |
| 308 | C2×D13 | — | 16 | 1 | no | — |
| 309 | C4×C13 | — | 4 | 4 | no | — |
| 310 | C4×C13 | #447 | 1 | 1 | yes | characteristic |
| 311 | C4×C13 | #447 | 1 | 1 | yes | characteristic |
| 312 | C4×C13 | C2×#120 | 1 | 1 | yes | characteristic |
| 313 | C4×C13 | C22×D8 | 1 | 1 | yes | characteristic |
| 314 | Dic13 | — | 2 | 2 | no | — |
| 315 | Dic13 | — | 4 | 2 | no | — |
| 316 | Dic13 | — | 8 | 1 | no | — |
| 317 | 2−1+4 | — | 26 | 4 | no | — |
| 318 | 2−1+4 | — | 26 | 4 | no | — |
| 319 | 2−1+4 | — | 52 | 2 | no | — |
| 320 | 2−1+4 | — | 52 | 2 | no | — |
| 321 | C2×#41 | — | 13 | 1 | no | — |
| 322 | C2×#41 | — | 26 | 2 | no | — |
| 323 | C2×#41 | — | 26 | 1 | no | — |
| 324 | C2×#41 | — | 26 | 1 | no | — |
| 325 | C2×#41 | — | 52 | 2 | no | — |
| 326 | C2×#41 | — | 52 | 1 | no | — |
| 327 | C22×Q8 | — | 2 | 1 | no | — |
| 328 | C22×Q8 | — | 26 | 2 | no | — |
| 329 | C22×Q8 | — | 52 | 1 | no | — |
| 330 | #137 | — | 26 | 2 | no | — |
| 331 | #137 | — | 26 | 4 | no | — |
| 332 | #137 | — | 26 | 8 | no | — |
| 333 | #137 | — | 26 | 4 | no | — |
| 334 | #137 | — | 26 | 8 | no | — |
| 335 | #137 | — | 52 | 1 | no | — |
| 336 | AGL(1,ℤ/8) | — | 26 | 2 | no | — |
| 337 | AGL(1,ℤ/8) | — | 52 | 1 | no | — |
| 338 | #135 | — | 13 | 2 | no | — |
| 339 | #135 | — | 13 | 2 | no | — |
| 340 | #135 | — | 26 | 4 | no | — |
| 341 | #135 | — | 26 | 4 | no | — |
| 342 | #135 | — | 26 | 1 | no | — |
| 343 | #135 | — | 26 | 1 | no | — |
| 344 | #135 | — | 26 | 1 | no | — |
| 345 | #135 | — | 26 | 1 | no | — |
| 346 | #135 | — | 26 | 1 | no | — |
| 347 | #135 | — | 26 | 1 | no | — |
| 348 | #135 | — | 52 | 2 | no | — |
| 349 | C2×Q16 | — | 2 | 1 | no | — |
| 350 | C2×Q16 | — | 2 | 1 | no | — |
| 351 | C2×Q16 | — | 2 | 1 | no | — |
| 352 | C2×Q16 | — | 13 | 1 | no | — |
| 353 | C2×Q16 | — | 13 | 1 | no | — |
| 354 | C2×Q16 | — | 26 | 4 | no | — |
| 355 | C2×Q16 | — | 26 | 4 | no | — |
| 356 | C2×Q16 | — | 26 | 2 | no | — |
| 357 | C2×Q16 | D52 | 1 | 2 | yes | — |
| 358 | C2×Q16 | D52 | 1 | 2 | yes | — |
| 359 | C2×Q16 | C22×D13 | 1 | 2 | yes | — |
| 360 | C2×SD16 | — | 26 | 2 | no | — |
| 361 | C2×SD16 | — | 26 | 1 | no | — |
| 362 | C2×SD16 | — | 26 | 1 | no | — |
| 363 | C2×D8 | — | 13 | 1 | no | — |
| 364 | C2×D8 | — | 13 | 1 | no | — |
| 365 | #131 | — | 13 | 2 | no | — |
| 366 | #131 | — | 13 | 2 | no | — |
| 367 | #131 | — | 26 | 1 | no | — |
| 368 | #131 | — | 26 | 1 | no | — |
| 369 | C2×M16 | — | 2 | 1 | no | — |
| 370 | C2×M16 | — | 13 | 1 | no | — |
| 371 | C2×M16 | — | 26 | 1 | no | — |
| 372 | C22×C8 | — | 26 | 1 | no | — |
| 373 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 374 | Q32 | — | 26 | 2 | no | — |
| 375 | Q32 | — | 26 | 4 | no | — |
| 376 | SD32 | — | 26 | 2 | no | — |
| 377 | SD32 | — | 26 | 2 | no | — |
| 378 | SD32 | — | 26 | 4 | no | — |
| 379 | D16 | — | 26 | 2 | no | — |
| 380 | M32 | — | 2 | 1 | no | — |
| 381 | M32 | — | 26 | 1 | no | — |
| 382 | M32 | — | 26 | 1 | no | — |
| 383 | M32 | C22×D13 | 1 | 2 | yes | — |
| 384 | C2×C16 | — | 2 | 1 | no | — |
| 385 | C2×C16 | — | 13 | 2 | no | — |
| 386 | #108 | — | 2 | 1 | no | — |
| 387 | #108 | C22×D13 | 1 | 2 | yes | — |
| 388 | #101 | — | 26 | 2 | no | — |
| 389 | #100 | — | 26 | 2 | no | — |
| 390 | C2×C13 | — | 2 | 1 | no | — |
| 391 | C2×C13 | — | 2 | 1 | no | — |
| 392 | C2×C13 | — | 2 | 1 | no | — |
| 393 | C2×C13 | C2×#447 | 1 | 1 | yes | characteristic |
| 394 | D13 | — | 4 | 2 | no | — |
| 395 | D13 | — | 8 | 2 | no | — |
| 396 | D13 | — | 16 | 1 | no | — |
| 397 | #41 | — | 13 | 2 | no | — |
| 398 | #41 | — | 13 | 2 | no | — |
| 399 | #41 | — | 26 | 1 | no | — |
| 400 | #41 | — | 26 | 1 | no | — |
| 401 | #41 | — | 26 | 8 | no | — |
| 402 | #41 | — | 26 | 2 | no | — |
| 403 | #41 | — | 26 | 2 | no | — |
| 404 | #41 | — | 52 | 8 | no | — |
| 405 | #41 | — | 52 | 8 | no | — |
| 406 | #41 | — | 52 | 4 | no | — |
| 407 | #41 | — | 52 | 4 | no | — |
| 408 | #41 | — | 52 | 4 | no | — |
| 409 | #41 | — | 52 | 1 | no | — |
| 410 | #41 | — | 52 | 1 | no | — |
| 411 | #41 | — | 52 | 1 | no | — |
| 412 | #41 | — | 52 | 1 | no | — |
| 413 | #41 | — | 52 | 1 | no | — |
| 414 | #41 | — | 52 | 1 | no | — |
| 415 | C2×Q8 | — | 2 | 2 | no | — |
| 416 | C2×Q8 | — | 2 | 2 | no | — |
| 417 | C2×Q8 | — | 2 | 2 | no | — |
| 418 | C2×Q8 | — | 4 | 1 | no | — |
| 419 | C2×Q8 | — | 4 | 1 | no | — |
| 420 | C2×Q8 | — | 4 | 1 | no | — |
| 421 | C2×Q8 | — | 13 | 1 | no | — |
| 422 | C2×Q8 | — | 26 | 8 | no | — |
| 423 | C2×Q8 | — | 26 | 1 | no | — |
| 424 | C2×Q8 | — | 26 | 1 | no | — |
| 425 | C2×Q8 | — | 52 | 2 | no | — |
| 426 | C2×Q8 | — | 52 | 4 | no | — |
| 427 | C2×Q8 | — | 52 | 4 | no | — |
| 428 | C2×Q8 | — | 52 | 4 | no | — |
| 429 | C2×D4 | — | 13 | 1 | no | — |
| 430 | C2×D4 | — | 26 | 1 | no | — |
| 431 | C2×D4 | — | 26 | 1 | no | — |
| 432 | C2×D4 | — | 26 | 1 | no | — |
| 433 | C2×D4 | — | 52 | 2 | no | — |
| 434 | C2×D4 | — | 52 | 1 | no | — |
| 435 | C2×D4 | — | 52 | 1 | no | — |
| 436 | C22×C4 | — | 4 | 1 | no | — |
| 437 | C22×C4 | — | 26 | 1 | no | — |
| 438 | C22×C4 | — | 52 | 2 | no | — |
| 439 | C22×C4 | — | 52 | 2 | no | — |
| 440 | C22×C4 | — | 52 | 1 | no | — |
| 441 | C22×C4 | — | 52 | 1 | no | — |
| 442 | C22×C4 | D4×D13 | 1 | 1 | yes | characteristic |
| 443 | Q16 | — | 2 | 2 | no | — |
| 444 | Q16 | — | 2 | 2 | no | — |
| 445 | Q16 | — | 2 | 2 | no | — |
| 446 | Q16 | — | 13 | 2 | no | — |
| 447 | Q16 | — | 26 | 8 | no | — |
| 448 | Q16 | — | 26 | 1 | no | — |
| 449 | Q16 | — | 26 | 1 | no | — |
| 450 | Q16 | — | 26 | 1 | no | — |
| 451 | Q16 | — | 52 | 2 | no | — |
| 452 | Q16 | C2×D52 | 1 | 4 | yes | — |
| 453 | SD16 | — | 26 | 8 | no | — |
| 454 | SD16 | — | 26 | 2 | no | — |
| 455 | SD16 | — | 26 | 2 | no | — |
| 456 | SD16 | — | 52 | 2 | no | — |
| 457 | SD16 | — | 52 | 2 | no | — |
| 458 | SD16 | — | 52 | 1 | no | — |
| 459 | SD16 | — | 52 | 1 | no | — |
| 460 | D8 | — | 13 | 2 | no | — |
| 461 | D8 | — | 26 | 1 | no | — |
| 462 | D8 | — | 26 | 1 | no | — |
| 463 | D8 | — | 26 | 1 | no | — |
| 464 | D8 | — | 52 | 2 | no | — |
| 465 | M16 | — | 2 | 2 | no | — |
| 466 | M16 | — | 4 | 1 | no | — |
| 467 | M16 | — | 13 | 2 | no | — |
| 468 | M16 | — | 26 | 1 | no | — |
| 469 | M16 | — | 26 | 2 | no | — |
| 470 | M16 | — | 26 | 2 | no | — |
| 471 | C2×C8 | — | 4 | 1 | no | — |
| 472 | C2×C8 | — | 26 | 1 | no | — |
| 473 | C2×C8 | — | 26 | 2 | no | — |
| 474 | C2×C8 | — | 26 | 2 | no | — |
| 475 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 476 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 477 | C2×C8 | D4×D13 | 1 | 1 | yes | characteristic |
| 478 | C2×C8 | D4×D13 | 1 | 1 | yes | characteristic |
| 479 | C2×C8 | D4×D13 | 1 | 1 | yes | characteristic |
| 480 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 481 | C16 | — | 2 | 2 | no | — |
| 482 | C16 | — | 26 | 2 | no | — |
| 483 | C13 | #33540 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 484 | C23 | — | 26 | 1 | no | — |
| 485 | C23 | — | 52 | 1 | no | — |
| 486 | C23 | — | 52 | 1 | no | — |
| 487 | C23 | #88168 | 1 | 1 | yes | characteristic |
| 488 | Q8 | — | 2 | 4 | no | — |
| 489 | Q8 | — | 4 | 2 | no | — |
| 490 | Q8 | — | 4 | 2 | no | — |
| 491 | Q8 | — | 4 | 2 | no | — |
| 492 | Q8 | — | 13 | 2 | no | — |
| 493 | Q8 | — | 26 | 1 | no | — |
| 494 | Q8 | — | 26 | 2 | no | — |
| 495 | Q8 | — | 52 | 8 | no | — |
| 496 | Q8 | — | 52 | 1 | no | — |
| 497 | Q8 | — | 52 | 1 | no | — |
| 498 | Q8 | — | 52 | 1 | no | — |
| 499 | D4 | — | 13 | 2 | no | — |
| 500 | D4 | — | 26 | 2 | no | — |
| 501 | D4 | — | 26 | 2 | no | — |
| 502 | D4 | — | 26 | 2 | no | — |
| 503 | D4 | — | 26 | 1 | no | — |
| 504 | D4 | — | 52 | 8 | no | — |
| 505 | D4 | — | 52 | 2 | no | — |
| 506 | D4 | — | 52 | 2 | no | — |
| 507 | D4 | — | 52 | 1 | no | — |
| 508 | D4 | — | 52 | 1 | no | — |
| 509 | D4 | — | 52 | 1 | no | — |
| 510 | D4 | — | 104 | 1 | no | — |
| 511 | D4 | — | 104 | 1 | no | — |
| 512 | C2×C4 | — | 4 | 2 | no | — |
| 513 | C2×C4 | — | 4 | 2 | no | — |
| 514 | C2×C4 | — | 4 | 2 | no | — |
| 515 | C2×C4 | — | 26 | 1 | no | — |
| 516 | C2×C4 | — | 26 | 2 | no | — |
| 517 | C2×C4 | — | 26 | 2 | no | — |
| 518 | C2×C4 | — | 52 | 8 | no | — |
| 519 | C2×C4 | — | 52 | 8 | no | — |
| 520 | C2×C4 | — | 52 | 1 | no | — |
| 521 | C2×C4 | — | 52 | 2 | no | — |
| 522 | C2×C4 | — | 52 | 2 | no | — |
| 523 | C2×C4 | — | 52 | 1 | no | — |
| 524 | C2×C4 | — | 104 | 1 | no | — |
| 525 | C2×C4 | — | 104 | 1 | no | — |
| 526 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 527 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 528 | C2×C4 | D8×D13 | 1 | 1 | yes | characteristic |
| 529 | C2×C4 | D8×D13 | 1 | 1 | yes | characteristic |
| 530 | C2×C4 | #88168 | 1 | 1 | yes | characteristic |
| 531 | C2×C4 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 532 | C8 | — | 4 | 2 | no | — |
| 533 | C8 | — | 26 | 2 | no | — |
| 534 | C8 | #88136 | 1 | 1 | yes | characteristic |
| 535 | C8 | #88136 | 1 | 1 | yes | characteristic |
| 536 | C8 | C22×D52 | 1 | 1 | yes | characteristic |
| 537 | C8 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 538 | C22 | — | 4 | 1 | no | — |
| 539 | C22 | — | 26 | 2 | no | — |
| 540 | C22 | — | 52 | 2 | no | — |
| 541 | C22 | — | 52 | 2 | no | — |
| 542 | C22 | — | 104 | 2 | no | — |
| 543 | C22 | — | 104 | 1 | no | — |
| 544 | C22 | — | 208 | 1 | no | — |
| 545 | C22 | #11718434 | 1 | 1 | yes | characteristic |
| 546 | C22 | #11718434 | 1 | 1 | yes | characteristic |
| 547 | C22 | C2×#88168 | 1 | 1 | yes | characteristic |
| 548 | C4 | — | 4 | 4 | no | — |
| 549 | C4 | — | 26 | 2 | no | — |
| 550 | C4 | — | 52 | 2 | no | — |
| 551 | C4 | — | 104 | 1 | no | — |
| 552 | C4 | #11718434 | 1 | 1 | yes | characteristic |
| 553 | C4 | #11718434 | 1 | 1 | yes | characteristic |
| 554 | C4 | C2×#88136 | 1 | 1 | yes | characteristic |
| 555 | C4 | C2×D8×D13 | 1 | 1 | yes | characteristic |
| 556 | C2 | — | 2 | 1 | no | — |
| 557 | C2 | — | 2 | 1 | no | — |
| 558 | C2 | — | 2 | 1 | no | — |
| 559 | C2 | — | 52 | 2 | no | — |
| 560 | C2 | — | 104 | 2 | no | — |
| 561 | C2 | — | 208 | 1 | no | — |
| 562 | C2 | C2×#11718434 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11719471 | C2 | semidirect |
| 2. #13127972 | C2 | semidirect |
| 3. C2×#11718840 | C2 | semidirect |
| 4. #13124557 | C2 | semidirect |
| 5. #13116817 | C2 | semidirect |
| 6. #13116803 | C2 | semidirect |
| 7. #13116563 | C2 | semidirect |
| 8. #13116465 | C2 | semidirect |
| 9. C2×C13×#362 | C2 | semidirect |
| 26. C2×#88069 | C22 | semidirect |
| 29. C2×#88068 | C22 | semidirect |
| 33. #11718570 | C22 | semidirect |
| 35. #11718569 | C22 | semidirect |
| 38. #11718558 | C22 | semidirect |
| 39. #11718557 | C22 | semidirect |
| 40. C13×#362 | C22 | semidirect |
| 41. #11718107 | C22 | semidirect |
| 42. #11718089 | C22 | semidirect |
| 209. C2×#362 | D13 | semidirect |
| 296. #362 | C2×D13 | semidirect |
| 483. C13 | #33540 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11719471 | 2 |
| #13127972 | 2 |
| C2×#11718840 | 2 |
| #13124557 | 2 |
| #13116817 | 2 |
| #13116803 | 2 |
| #13116563 | 2 |
| #13116465 | 2 |
| C2×C13×#362 | 2 |
| #33540 | 13 |