Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1086 conjugacy classes of subgroups.
The subgroup lattice has 426 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#90457 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C22×C7×Q32 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11741332 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#89951 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11729815 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11729257 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11729256 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #11729166 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11729163 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#6551 | — | 2 | 1 | no | — |
| 11 | C22×C7×Q16 | C22 | 1 | 1 | yes | characteristic |
| 12 | C22×C7×Q16 | C22 | 1 | 1 | yes | characteristic |
| 13 | #90507 | — | 2 | 1 | no | — |
| 14 | C2×#6505 | — | 2 | 1 | no | — |
| 15 | #90457 | — | 2 | 4 | no | — |
| 16 | #90457 | — | 2 | 4 | no | — |
| 17 | C2×#6482 | C22 | 1 | 2 | yes | — |
| 18 | C2×#6481 | — | 2 | 2 | no | — |
| 19 | C2×D7×Q16 | C22 | 1 | 2 | yes | — |
| 20 | C2×#6467 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#6464 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×C7×Q32 | — | 2 | 4 | no | — |
| 23 | C2×C7×Q32 | C22 | 1 | 4 | yes | — |
| 24 | C22×C7×C16 | C22 | 1 | 1 | yes | characteristic |
| 25 | #89997 | — | 2 | 1 | no | — |
| 26 | #89961 | — | 2 | 2 | no | — |
| 27 | #89960 | C22 | 1 | 4 | yes | — |
| 28 | C2×#6403 | C22 | 1 | 2 | yes | — |
| 29 | #89951 | — | 2 | 4 | no | — |
| 30 | C2×#6402 | C22 | 1 | 2 | yes | — |
| 31 | #89878 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#6386 | C22 | 1 | 1 | yes | characteristic |
| 33 | #89359 | C22 | 1 | 4 | yes | — |
| 34 | #89304 | C22 | 1 | 2 | yes | — |
| 35 | (C2×D7)⋊C16 | C22 | 1 | 4 | yes | — |
| 36 | #89298 | C22 | 1 | 2 | yes | — |
| 37 | #33525 | — | 7 | 1 | no | maximal, Sylow |
| 38 | C22×C7×Q8 | — | 2 | 1 | no | — |
| 39 | C22×C7×Q8 | — | 2 | 1 | no | — |
| 40 | #6551 | — | 2 | 8 | no | — |
| 41 | #6551 | — | 4 | 4 | no | — |
| 42 | C2×#1161 | — | 2 | 2 | no | — |
| 43 | C2×#1161 | — | 4 | 1 | no | — |
| 44 | C2×Q8×D7 | — | 2 | 2 | no | — |
| 45 | C2×Q8×D7 | — | 4 | 1 | no | — |
| 46 | C2×#1157 | — | 2 | 1 | no | — |
| 47 | C2×#1157 | — | 4 | 2 | no | — |
| 48 | C2×#1157 | D4 | 1 | 1 | yes | characteristic |
| 49 | C2×C7×Q16 | — | 2 | 1 | no | — |
| 50 | C2×C7×Q16 | — | 2 | 2 | no | — |
| 51 | C2×C7×Q16 | — | 2 | 2 | no | — |
| 52 | C2×C7×Q16 | — | 2 | 2 | no | — |
| 53 | C2×C7×Q16 | — | 2 | 1 | no | — |
| 54 | C2×C7×Q16 | D4 | 1 | 4 | yes | — |
| 55 | C2×C7×Q16 | C23 | 1 | 2 | yes | — |
| 56 | C2×C7×Q16 | C23 | 1 | 2 | yes | — |
| 57 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 58 | #6510 | — | 4 | 1 | no | — |
| 59 | #6509 | — | 2 | 4 | no | — |
| 60 | #6507 | — | 4 | 1 | no | — |
| 61 | C2×#1144 | — | 2 | 2 | no | — |
| 62 | #6505 | — | 2 | 8 | no | — |
| 63 | C2×#1143 | — | 2 | 2 | no | — |
| 64 | #6492 | — | 4 | 2 | no | — |
| 65 | #6489 | — | 2 | 1 | no | — |
| 66 | C2×#1136 | D4 | 1 | 1 | yes | characteristic |
| 67 | #6482 | — | 2 | 4 | no | — |
| 68 | #6482 | — | 2 | 4 | no | — |
| 69 | #6481 | — | 2 | 16 | no | — |
| 70 | D7×Q16 | — | 2 | 4 | no | — |
| 71 | D7×Q16 | — | 2 | 4 | no | — |
| 72 | C2×Dic28 | C23 | 1 | 1 | yes | characteristic |
| 73 | #6467 | — | 2 | 2 | no | — |
| 74 | #6467 | D4 | 1 | 4 | yes | — |
| 75 | C2×D56 | C23 | 1 | 1 | yes | characteristic |
| 76 | C2×#1132 | — | 2 | 1 | no | — |
| 77 | #6464 | — | 2 | 2 | no | — |
| 78 | #6464 | — | 2 | 2 | no | — |
| 79 | C2×#1131 | D4 | 1 | 2 | yes | — |
| 80 | C2×C8×D7 | C23 | 1 | 2 | yes | — |
| 81 | C7×Q32 | — | 2 | 8 | no | — |
| 82 | C2×C7×C16 | — | 2 | 2 | no | — |
| 83 | C2×C7×C16 | C23 | 1 | 2 | yes | — |
| 84 | #6409 | — | 2 | 4 | no | — |
| 85 | #6403 | — | 2 | 4 | no | — |
| 86 | #6402 | — | 2 | 4 | no | — |
| 87 | #6392 | C23 | 1 | 2 | yes | — |
| 88 | #6391 | — | 2 | 1 | no | — |
| 89 | #6386 | — | 2 | 2 | no | — |
| 90 | C2×C7⋊C16 | C23 | 1 | 2 | yes | — |
| 91 | C2×#578 | — | 7 | 1 | no | — |
| 92 | C2×#510 | — | 7 | 1 | no | — |
| 93 | C22×Q32 | D7 | 1 | 1 | yes | characteristic, complemented |
| 94 | #3059 | — | 7 | 1 | no | — |
| 95 | #2189 | — | 7 | 4 | no | — |
| 96 | #2188 | — | 7 | 4 | no | — |
| 97 | #2141 | — | 7 | 1 | no | — |
| 98 | #2138 | — | 7 | 1 | no | — |
| 99 | #2113 | — | 7 | 1 | no | — |
| 100 | C2×C7×Q8 | — | 2 | 4 | no | — |
| 101 | C2×C7×Q8 | — | 2 | 2 | no | — |
| 102 | C2×C7×Q8 | — | 2 | 2 | no | — |
| 103 | C2×C7×Q8 | — | 4 | 1 | no | — |
| 104 | C2×C7×Q8 | — | 4 | 1 | no | — |
| 105 | C2×C7×Q8 | — | 4 | 2 | no | — |
| 106 | C2×C7×Q8 | — | 4 | 2 | no | — |
| 107 | C2×C7×Q8 | — | 4 | 2 | no | — |
| 108 | C22×C4×C7 | — | 4 | 1 | no | — |
| 109 | C22×C4×C7 | — | 4 | 1 | no | — |
| 110 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 112 | C2×C22⋊D7 | D8 | 1 | 2 | yes | — |
| 113 | #1161 | — | 2 | 8 | no | — |
| 114 | #1161 | — | 4 | 4 | no | — |
| 115 | #1161 | — | 4 | 8 | no | — |
| 116 | Q8×D7 | — | 2 | 8 | no | — |
| 117 | Q8×D7 | — | 4 | 8 | no | — |
| 118 | Q8×D7 | — | 4 | 4 | no | — |
| 119 | #1157 | — | 2 | 2 | no | — |
| 120 | #1157 | — | 2 | 2 | no | — |
| 121 | #1157 | — | 2 | 4 | no | — |
| 122 | #1157 | — | 4 | 16 | no | — |
| 123 | #1157 | — | 4 | 2 | no | — |
| 124 | C2×D28 | — | 2 | 1 | no | — |
| 125 | C2×D28 | — | 4 | 2 | no | — |
| 126 | C2×D28 | D8 | 1 | 1 | yes | characteristic |
| 127 | C2×C4×D7 | — | 4 | 2 | no | — |
| 128 | C2×C4×D7 | — | 4 | 1 | no | — |
| 129 | C2×C4×D7 | — | 4 | 2 | no | — |
| 130 | C2×C4×D7 | C2×D4 | 1 | 2 | yes | — |
| 131 | C2×Dic14 | — | 2 | 1 | no | — |
| 132 | C2×Dic14 | — | 4 | 2 | no | — |
| 133 | C2×Dic14 | D8 | 1 | 1 | yes | characteristic |
| 134 | C7×Q16 | — | 2 | 4 | no | — |
| 135 | C7×Q16 | — | 2 | 2 | no | — |
| 136 | C7×Q16 | — | 2 | 2 | no | — |
| 137 | C7×Q16 | — | 2 | 2 | no | — |
| 138 | C7×Q16 | — | 4 | 2 | no | — |
| 139 | C7×Q16 | C2×D4 | 1 | 4 | yes | — |
| 140 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C2×C7×C8 | C2×D4 | 1 | 2 | yes | — |
| 142 | C2×C7×C8 | C2×D4 | 1 | 2 | yes | — |
| 143 | C2×C7×C8 | C24 | 1 | 1 | yes | characteristic |
| 144 | C22⋊Dic7 | — | 4 | 1 | no | — |
| 145 | #1144 | — | 2 | 8 | no | — |
| 146 | #1143 | — | 2 | 8 | no | — |
| 147 | (C2×D7)⋊C4 | — | 4 | 4 | no | — |
| 148 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 149 | Dic7⋊C4 | — | 4 | 4 | no | — |
| 150 | C4×Dic7 | — | 4 | 1 | no | — |
| 151 | #1136 | — | 2 | 2 | no | — |
| 152 | C2×C7⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 153 | Dic28 | — | 2 | 1 | no | — |
| 154 | Dic28 | C2×D4 | 1 | 2 | yes | — |
| 155 | D56 | — | 2 | 1 | no | — |
| 156 | D56 | C2×D4 | 1 | 2 | yes | — |
| 157 | #1132 | — | 2 | 4 | no | — |
| 158 | #1131 | — | 2 | 4 | no | — |
| 159 | C8×D7 | — | 2 | 2 | no | — |
| 160 | C8×D7 | — | 2 | 2 | no | — |
| 161 | C7×C16 | — | 2 | 2 | no | — |
| 162 | C7⋊C16 | — | 2 | 2 | no | — |
| 163 | C2×2−1+4 | — | 14 | 1 | no | — |
| 164 | #578 | — | 14 | 4 | no | — |
| 165 | #578 | — | 14 | 4 | no | — |
| 166 | C2×#137 | — | 14 | 2 | no | — |
| 167 | C2×#137 | — | 14 | 1 | no | — |
| 168 | C2×#135 | — | 7 | 2 | no | — |
| 169 | C2×#135 | — | 7 | 1 | no | — |
| 170 | C22×Q16 | — | 7 | 2 | no | — |
| 171 | C22×Q16 | C2×D7 | 1 | 1 | yes | characteristic |
| 172 | C22×Q16 | C2×D7 | 1 | 1 | yes | characteristic |
| 173 | C2×#131 | — | 7 | 1 | no | — |
| 174 | #536 | — | 14 | 1 | no | — |
| 175 | #510 | — | 14 | 4 | no | — |
| 176 | C2×Q32 | — | 2 | 4 | no | — |
| 177 | C2×Q32 | — | 7 | 2 | no | — |
| 178 | C2×Q32 | C2×D7 | 1 | 4 | yes | — |
| 179 | C2×SD32 | — | 7 | 2 | no | — |
| 180 | C2×M32 | — | 7 | 1 | no | — |
| 181 | C22×C16 | C2×D7 | 1 | 1 | yes | characteristic |
| 182 | #470 | — | 14 | 2 | no | — |
| 183 | #467 | — | 7 | 4 | no | — |
| 184 | #427 | — | 7 | 1 | no | — |
| 185 | #419 | — | 14 | 1 | no | — |
| 186 | #358 | — | 7 | 4 | no | — |
| 187 | #358 | — | 7 | 2 | no | — |
| 188 | #357 | — | 7 | 2 | no | — |
| 189 | C22⋊C16 | — | 7 | 4 | no | — |
| 190 | C23×C7 | C2×D8 | 1 | 1 | yes | characteristic |
| 191 | C22×D7 | — | 4 | 1 | no | — |
| 192 | C22×D7 | C2×D8 | 1 | 2 | yes | — |
| 193 | C7×Q8 | — | 2 | 4 | no | — |
| 194 | C7×Q8 | — | 4 | 2 | no | — |
| 195 | C7×Q8 | — | 4 | 4 | no | — |
| 196 | C7×Q8 | — | 4 | 2 | no | — |
| 197 | C7×Q8 | — | 4 | 2 | no | — |
| 198 | C7×Q8 | — | 8 | 2 | no | — |
| 199 | C2×C4×C7 | — | 4 | 2 | no | — |
| 200 | C2×C4×C7 | — | 4 | 4 | no | — |
| 201 | C2×C4×C7 | — | 4 | 2 | no | — |
| 202 | C2×C4×C7 | — | 8 | 2 | no | — |
| 203 | C2×C4×C7 | #120 | 1 | 2 | yes | — |
| 204 | C2×C4×C7 | C2×D8 | 1 | 1 | yes | characteristic |
| 205 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 206 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 207 | C22⋊D7 | — | 2 | 4 | no | — |
| 208 | C22⋊D7 | — | 4 | 4 | no | — |
| 209 | C2×Dic7 | — | 4 | 1 | no | — |
| 210 | C2×Dic7 | — | 4 | 2 | no | — |
| 211 | C2×Dic7 | C2×D8 | 1 | 2 | yes | — |
| 212 | D28 | — | 2 | 2 | no | — |
| 213 | D28 | — | 2 | 2 | no | — |
| 214 | D28 | — | 4 | 8 | no | — |
| 215 | D28 | — | 4 | 1 | no | — |
| 216 | C4×D7 | — | 2 | 2 | no | — |
| 217 | C4×D7 | — | 2 | 2 | no | — |
| 218 | C4×D7 | — | 4 | 8 | no | — |
| 219 | C4×D7 | — | 4 | 8 | no | — |
| 220 | C4×D7 | — | 4 | 4 | no | — |
| 221 | Dic14 | — | 2 | 2 | no | — |
| 222 | Dic14 | — | 2 | 2 | no | — |
| 223 | Dic14 | — | 4 | 8 | no | — |
| 224 | Dic14 | — | 4 | 1 | no | — |
| 225 | C7×C8 | #120 | 1 | 2 | yes | — |
| 226 | C7×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 227 | C7×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 228 | C7⋊C8 | — | 2 | 2 | no | — |
| 229 | 2−1+4 | — | 14 | 8 | no | — |
| 230 | 2−1+4 | — | 28 | 4 | no | — |
| 231 | C2×#41 | — | 7 | 1 | no | — |
| 232 | C2×#41 | — | 14 | 2 | no | — |
| 233 | C2×#41 | — | 14 | 1 | no | — |
| 234 | C2×#41 | — | 28 | 2 | no | — |
| 235 | C2×#41 | — | 28 | 1 | no | — |
| 236 | C22×Q8 | — | 2 | 1 | no | — |
| 237 | C22×Q8 | — | 2 | 1 | no | — |
| 238 | C22×Q8 | — | 14 | 2 | no | — |
| 239 | C22×Q8 | — | 28 | 1 | no | — |
| 240 | #137 | — | 14 | 16 | no | — |
| 241 | #137 | — | 14 | 8 | no | — |
| 242 | #135 | — | 7 | 4 | no | — |
| 243 | #135 | — | 14 | 4 | no | — |
| 244 | #135 | — | 14 | 4 | no | — |
| 245 | #135 | — | 14 | 2 | no | — |
| 246 | C2×Q16 | — | 2 | 1 | no | — |
| 247 | C2×Q16 | — | 2 | 2 | no | — |
| 248 | C2×Q16 | — | 2 | 2 | no | — |
| 249 | C2×Q16 | — | 2 | 1 | no | — |
| 250 | C2×Q16 | — | 2 | 2 | no | — |
| 251 | C2×Q16 | — | 7 | 1 | no | — |
| 252 | C2×Q16 | — | 14 | 2 | no | — |
| 253 | C2×Q16 | — | 14 | 4 | no | — |
| 254 | C2×Q16 | — | 14 | 4 | no | — |
| 255 | C2×Q16 | C22⋊D7 | 1 | 4 | yes | — |
| 256 | C2×Q16 | C22×D7 | 1 | 2 | yes | — |
| 257 | C2×Q16 | C22×D7 | 1 | 2 | yes | — |
| 258 | C2×SD16 | — | 14 | 2 | no | — |
| 259 | C2×SD16 | — | 14 | 1 | no | — |
| 260 | C2×D8 | — | 7 | 1 | no | — |
| 261 | #131 | — | 14 | 2 | no | — |
| 262 | #131 | — | 14 | 2 | no | — |
| 263 | C2×M16 | — | 7 | 1 | no | — |
| 264 | C2×M16 | — | 7 | 2 | no | — |
| 265 | C22×C8 | — | 7 | 2 | no | — |
| 266 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 267 | C4⋊Q8 | — | 28 | 1 | no | — |
| 268 | #124 | — | 28 | 1 | no | — |
| 269 | #123 | — | 28 | 2 | no | — |
| 270 | C22⋊Q8 | — | 14 | 4 | no | — |
| 271 | #117 | — | 14 | 1 | no | — |
| 272 | Q32 | — | 2 | 8 | no | — |
| 273 | Q32 | — | 14 | 4 | no | — |
| 274 | SD32 | — | 14 | 4 | no | — |
| 275 | M32 | — | 14 | 2 | no | — |
| 276 | C2×C16 | — | 2 | 2 | no | — |
| 277 | C2×C16 | — | 7 | 2 | no | — |
| 278 | C2×C16 | C22×D7 | 1 | 2 | yes | — |
| 279 | #107 | — | 7 | 2 | no | — |
| 280 | #106 | — | 14 | 1 | no | — |
| 281 | #103 | — | 14 | 4 | no | — |
| 282 | C22×C7 | — | 2 | 2 | no | — |
| 283 | C22×C7 | #447 | 1 | 2 | yes | — |
| 284 | C22×C7 | C22×D8 | 1 | 1 | yes | characteristic |
| 285 | C2×D7 | — | 2 | 4 | no | — |
| 286 | C2×D7 | — | 2 | 2 | no | — |
| 287 | C2×D7 | — | 4 | 2 | no | — |
| 288 | C2×D7 | — | 8 | 2 | no | — |
| 289 | C4×C7 | — | 4 | 4 | no | — |
| 290 | C4×C7 | — | 8 | 2 | no | — |
| 291 | C4×C7 | #447 | 1 | 2 | yes | — |
| 292 | C4×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 293 | C4×C7 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 294 | Dic7 | — | 2 | 2 | no | — |
| 295 | Dic7 | — | 4 | 2 | no | — |
| 296 | Dic7 | — | 8 | 2 | no | — |
| 297 | #41 | — | 14 | 2 | no | — |
| 298 | #41 | — | 14 | 2 | no | — |
| 299 | #41 | — | 14 | 8 | no | — |
| 300 | #41 | — | 14 | 4 | no | — |
| 301 | #41 | — | 28 | 16 | no | — |
| 302 | #41 | — | 28 | 4 | no | — |
| 303 | #41 | — | 28 | 8 | no | — |
| 304 | #41 | — | 28 | 2 | no | — |
| 305 | C2×Q8 | — | 2 | 4 | no | — |
| 306 | C2×Q8 | — | 2 | 2 | no | — |
| 307 | C2×Q8 | — | 2 | 2 | no | — |
| 308 | C2×Q8 | — | 4 | 1 | no | — |
| 309 | C2×Q8 | — | 4 | 1 | no | — |
| 310 | C2×Q8 | — | 4 | 2 | no | — |
| 311 | C2×Q8 | — | 4 | 2 | no | — |
| 312 | C2×Q8 | — | 4 | 2 | no | — |
| 313 | C2×Q8 | — | 7 | 1 | no | — |
| 314 | C2×Q8 | — | 14 | 8 | no | — |
| 315 | C2×Q8 | — | 14 | 1 | no | — |
| 316 | C2×Q8 | — | 28 | 2 | no | — |
| 317 | C2×Q8 | — | 28 | 4 | no | — |
| 318 | C2×Q8 | — | 28 | 8 | no | — |
| 319 | C2×D4 | — | 7 | 2 | no | — |
| 320 | C2×D4 | — | 7 | 1 | no | — |
| 321 | C2×D4 | — | 14 | 1 | no | — |
| 322 | C2×D4 | — | 28 | 2 | no | — |
| 323 | C2×D4 | — | 28 | 1 | no | — |
| 324 | C22×C4 | — | 4 | 1 | no | — |
| 325 | C22×C4 | — | 4 | 1 | no | — |
| 326 | C22×C4 | — | 7 | 2 | no | — |
| 327 | C22×C4 | — | 28 | 2 | no | — |
| 328 | C22×C4 | — | 28 | 2 | no | — |
| 329 | C22×C4 | — | 28 | 1 | no | — |
| 330 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 331 | Q16 | — | 2 | 4 | no | — |
| 332 | Q16 | — | 2 | 2 | no | — |
| 333 | Q16 | — | 2 | 2 | no | — |
| 334 | Q16 | — | 2 | 2 | no | — |
| 335 | Q16 | — | 4 | 2 | no | — |
| 336 | Q16 | — | 7 | 2 | no | — |
| 337 | Q16 | — | 14 | 8 | no | — |
| 338 | Q16 | — | 14 | 1 | no | — |
| 339 | Q16 | C2×C22⋊D7 | 1 | 4 | yes | — |
| 340 | SD16 | — | 14 | 8 | no | — |
| 341 | SD16 | — | 14 | 4 | no | — |
| 342 | D8 | — | 7 | 2 | no | — |
| 343 | D8 | — | 14 | 1 | no | — |
| 344 | M16 | — | 14 | 2 | no | — |
| 345 | M16 | — | 14 | 4 | no | — |
| 346 | C2×C8 | — | 7 | 2 | no | — |
| 347 | C2×C8 | — | 14 | 2 | no | — |
| 348 | C2×C8 | — | 14 | 2 | no | — |
| 349 | C2×C8 | D4×D7 | 1 | 1 | yes | characteristic |
| 350 | C2×C8 | D4×D7 | 1 | 2 | yes | — |
| 351 | C2×C8 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 352 | C2×C8 | C23×D7 | 1 | 1 | yes | characteristic |
| 353 | C4⋊C4 | — | 14 | 2 | no | — |
| 354 | C4⋊C4 | — | 28 | 4 | no | — |
| 355 | C22⋊C4 | — | 28 | 4 | no | — |
| 356 | C22⋊C4 | — | 28 | 1 | no | — |
| 357 | C42 | — | 28 | 1 | no | — |
| 358 | C16 | — | 2 | 2 | no | — |
| 359 | C16 | — | 14 | 2 | no | — |
| 360 | C2×C7 | — | 2 | 2 | no | — |
| 361 | C2×C7 | C2×#447 | 1 | 1 | yes | characteristic |
| 362 | C2×C7 | #3417 | 1 | 2 | yes | — |
| 363 | D7 | — | 4 | 2 | no | — |
| 364 | D7 | — | 8 | 2 | no | — |
| 365 | C23 | — | 7 | 2 | no | — |
| 366 | C23 | — | 28 | 1 | no | — |
| 367 | C23 | D7×D8 | 1 | 1 | yes | characteristic |
| 368 | Q8 | — | 2 | 4 | no | — |
| 369 | Q8 | — | 4 | 4 | no | — |
| 370 | Q8 | — | 4 | 2 | no | — |
| 371 | Q8 | — | 4 | 2 | no | — |
| 372 | Q8 | — | 4 | 2 | no | — |
| 373 | Q8 | — | 8 | 2 | no | — |
| 374 | Q8 | — | 14 | 2 | no | — |
| 375 | Q8 | — | 14 | 2 | no | — |
| 376 | Q8 | — | 28 | 8 | no | — |
| 377 | Q8 | — | 28 | 1 | no | — |
| 378 | D4 | — | 14 | 4 | no | — |
| 379 | D4 | — | 14 | 2 | no | — |
| 380 | D4 | — | 14 | 2 | no | — |
| 381 | D4 | — | 28 | 8 | no | — |
| 382 | D4 | — | 28 | 4 | no | — |
| 383 | D4 | — | 28 | 1 | no | — |
| 384 | C2×C4 | — | 4 | 4 | no | — |
| 385 | C2×C4 | — | 4 | 2 | no | — |
| 386 | C2×C4 | — | 4 | 2 | no | — |
| 387 | C2×C4 | — | 7 | 2 | no | — |
| 388 | C2×C4 | — | 8 | 2 | no | — |
| 389 | C2×C4 | — | 14 | 2 | no | — |
| 390 | C2×C4 | — | 14 | 2 | no | — |
| 391 | C2×C4 | — | 28 | 8 | no | — |
| 392 | C2×C4 | — | 28 | 8 | no | — |
| 393 | C2×C4 | — | 28 | 1 | no | — |
| 394 | C2×C4 | — | 28 | 4 | no | — |
| 395 | C2×C4 | — | 28 | 2 | no | — |
| 396 | C2×C4 | D7×D8 | 1 | 1 | yes | characteristic |
| 397 | C2×C4 | #6474 | 1 | 2 | yes | — |
| 398 | C2×C4 | #6500 | 1 | 2 | yes | — |
| 399 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 400 | C8 | — | 14 | 2 | no | — |
| 401 | C8 | #6500 | 1 | 2 | yes | — |
| 402 | C8 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 403 | C8 | C22×C22⋊D7 | 1 | 1 | yes | characteristic |
| 404 | C7 | #33525 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 405 | C22 | — | 2 | 2 | no | — |
| 406 | C22 | — | 14 | 4 | no | — |
| 407 | C22 | — | 14 | 2 | no | — |
| 408 | C22 | — | 28 | 2 | no | — |
| 409 | C22 | — | 56 | 2 | no | — |
| 410 | C22 | #89928 | 1 | 2 | yes | — |
| 411 | C22 | C2×D7×D8 | 1 | 1 | yes | characteristic |
| 412 | C4 | — | 4 | 4 | no | — |
| 413 | C4 | — | 8 | 2 | no | — |
| 414 | C4 | — | 14 | 2 | no | — |
| 415 | C4 | — | 28 | 2 | no | — |
| 416 | C4 | — | 56 | 2 | no | — |
| 417 | C4 | #89928 | 1 | 2 | yes | — |
| 418 | C4 | C2×#6474 | 1 | 1 | yes | characteristic |
| 419 | C4 | C2×#6500 | 1 | 1 | yes | characteristic |
| 420 | C2 | — | 2 | 2 | no | — |
| 421 | C2 | — | 28 | 2 | no | — |
| 422 | C2 | — | 56 | 2 | no | — |
| 423 | C2 | #11739473 | 1 | 2 | yes | — |
| 424 | C2 | C2×#89928 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C7×Q32 | C2 | semidirect |
| 3. #11741332 | C2 | semidirect |
| 4. C2×#89951 | C2 | semidirect |
| 5. #11729815 | C2 | semidirect |
| 6. #11729257 | C2 | semidirect |
| 7. #11729256 | C2 | semidirect |
| 8. #11729166 | C2 | semidirect |
| 9. #11729163 | C2 | semidirect |
| 93. C22×Q32 | D7 | semidirect |
| 404. C7 | #33525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90457 | 2 |
| C22×C7×Q32 | 2 |
| #11741332 | 2 |
| C2×#89951 | 2 |
| #11729815 | 2 |
| #11729257 | 2 |
| #11729256 | 2 |
| #11729166 | 2 |
| #11729163 | 2 |
| #33525 | 7 |