Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
888 conjugacy classes of subgroups.
The subgroup lattice has 518 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11744255 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C7×#2148 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#89361 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#89313 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11729191 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11728474 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11728444 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #90616 | — | 2 | 1 | no | — |
| 9 | C2×C7×#135 | C22 | 1 | 1 | yes | characteristic |
| 10 | #90513 | — | 2 | 1 | no | — |
| 11 | #90462 | C4 | 1 | 2 | yes | complemented |
| 12 | #90461 | — | 2 | 2 | no | — |
| 13 | #90460 | C4 | 1 | 2 | yes | complemented |
| 14 | #90459 | — | 2 | 2 | no | — |
| 15 | D7×#135 | — | 2 | 2 | no | — |
| 16 | #90457 | — | 2 | 1 | no | — |
| 17 | #90453 | — | 2 | 2 | no | — |
| 18 | #90448 | — | 2 | 1 | no | — |
| 19 | C2×#6467 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#6464 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×C7×M32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C2×C7×#108 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #89905 | — | 2 | 1 | no | — |
| 24 | C2×#6391 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C2×#6386 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C7×#362 | — | 2 | 1 | no | — |
| 27 | C7×#361 | — | 2 | 1 | no | — |
| 28 | #89361 | — | 2 | 2 | no | — |
| 29 | #89349 | — | 2 | 1 | no | — |
| 30 | #89313 | — | 2 | 2 | no | — |
| 31 | #89303 | — | 2 | 2 | no | — |
| 32 | #89292 | — | 2 | 2 | no | — |
| 33 | #12752 | — | 7 | 1 | no | maximal, Sylow |
| 34 | C2×C7×#41 | — | 2 | 1 | no | — |
| 35 | #6554 | — | 2 | 2 | no | — |
| 36 | #6554 | — | 4 | 1 | no | — |
| 37 | #6553 | — | 2 | 2 | no | — |
| 38 | #6553 | — | 4 | 1 | no | — |
| 39 | D7×#41 | — | 2 | 4 | no | — |
| 40 | D7×#41 | — | 4 | 2 | no | — |
| 41 | #6551 | — | 2 | 2 | no | — |
| 42 | #6548 | — | 2 | 2 | no | — |
| 43 | #6548 | — | 4 | 2 | no | — |
| 44 | C2×#1157 | — | 2 | 1 | no | — |
| 45 | C2×#1157 | — | 4 | 2 | no | — |
| 46 | C2×#1157 | D4 | 1 | 1 | yes | characteristic |
| 47 | C7×#135 | — | 2 | 1 | no | — |
| 48 | C7×#135 | — | 2 | 1 | no | — |
| 49 | C7×#135 | C2×C4 | 1 | 2 | yes | — |
| 50 | C7×#135 | D4 | 1 | 2 | yes | — |
| 51 | C2×C7×Q16 | D4 | 1 | 1 | yes | characteristic |
| 52 | C2×C7×SD16 | — | 2 | 1 | no | — |
| 53 | C2×C7×D8 | D4 | 1 | 1 | yes | characteristic |
| 54 | C2×C7×M16 | — | 2 | 1 | no | — |
| 55 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 56 | #6514 | — | 2 | 2 | no | — |
| 57 | #6513 | — | 2 | 4 | no | — |
| 58 | #6512 | — | 2 | 2 | no | — |
| 59 | #6505 | — | 2 | 2 | no | — |
| 60 | #6495 | — | 2 | 2 | no | — |
| 61 | C2×C4⋊Dic7 | — | 2 | 1 | no | — |
| 62 | C2×#1136 | D4 | 1 | 1 | yes | characteristic |
| 63 | #6482 | — | 2 | 2 | no | — |
| 64 | #6481 | — | 2 | 4 | no | — |
| 65 | D7×Q16 | — | 2 | 2 | no | — |
| 66 | #6479 | — | 2 | 4 | no | — |
| 67 | #6478 | — | 2 | 4 | no | — |
| 68 | #6477 | — | 2 | 4 | no | — |
| 69 | D7×SD16 | — | 2 | 4 | no | — |
| 70 | #6475 | — | 2 | 2 | no | — |
| 71 | #6474 | — | 2 | 4 | no | — |
| 72 | D7×D8 | — | 2 | 2 | no | — |
| 73 | C2×Dic28 | C2×C4 | 1 | 1 | yes | characteristic |
| 74 | #6467 | — | 2 | 1 | no | — |
| 75 | #6467 | — | 2 | 1 | no | — |
| 76 | #6467 | D4 | 1 | 2 | yes | — |
| 77 | #6467 | D4 | 1 | 2 | yes | — |
| 78 | C2×D56 | C2×C4 | 1 | 1 | yes | characteristic |
| 79 | C2×#1132 | — | 2 | 1 | no | — |
| 80 | #6464 | — | 2 | 1 | no | — |
| 81 | #6464 | — | 2 | 1 | no | — |
| 82 | #6464 | C2×C4 | 1 | 2 | yes | — |
| 83 | #6464 | D4 | 1 | 2 | yes | — |
| 84 | C2×#1131 | — | 2 | 1 | no | — |
| 85 | C2×C8×D7 | — | 2 | 1 | no | — |
| 86 | C7×M32 | — | 2 | 1 | no | — |
| 87 | C7×M32 | — | 2 | 1 | no | — |
| 88 | C2×C7×C16 | — | 2 | 1 | no | — |
| 89 | C7×#108 | — | 2 | 1 | no | — |
| 90 | C7×#108 | — | 2 | 1 | no | — |
| 91 | #6395 | — | 4 | 1 | no | — |
| 92 | #6391 | — | 2 | 1 | no | — |
| 93 | #6391 | — | 2 | 1 | no | — |
| 94 | #6390 | — | 4 | 1 | no | — |
| 95 | #6386 | — | 2 | 1 | no | — |
| 96 | #6386 | — | 2 | 1 | no | — |
| 97 | C2×C7⋊C16 | — | 2 | 1 | no | — |
| 98 | #3584 | — | 7 | 1 | no | — |
| 99 | #2148 | D7 | 1 | 1 | yes | characteristic, complemented |
| 100 | C2×#360 | — | 7 | 1 | no | — |
| 101 | C2×#360 | — | 7 | 1 | no | — |
| 102 | #2143 | — | 7 | 1 | no | — |
| 103 | #2117 | — | 7 | 1 | no | — |
| 104 | #1815 | — | 7 | 1 | no | — |
| 105 | C7×#41 | — | 2 | 2 | no | — |
| 106 | C7×#41 | — | 2 | 2 | no | — |
| 107 | C7×#41 | — | 4 | 1 | no | — |
| 108 | C7×#41 | — | 4 | 1 | no | — |
| 109 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 110 | C2×C7×D4 | — | 2 | 1 | no | — |
| 111 | C2×C7×D4 | — | 4 | 1 | no | — |
| 112 | C22×C4×C7 | — | 4 | 1 | no | — |
| 113 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 115 | C2×C22⋊D7 | — | 4 | 4 | no | — |
| 116 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 117 | C22×Dic7 | — | 4 | 1 | no | — |
| 118 | #1161 | — | 2 | 4 | no | — |
| 119 | #1161 | — | 4 | 2 | no | — |
| 120 | Q8×D7 | — | 2 | 4 | no | — |
| 121 | Q8×D7 | — | 4 | 2 | no | — |
| 122 | #1159 | — | 2 | 4 | no | — |
| 123 | #1159 | — | 4 | 2 | no | — |
| 124 | #1159 | — | 4 | 4 | no | — |
| 125 | #1159 | — | 4 | 4 | no | — |
| 126 | D4×D7 | — | 2 | 4 | no | — |
| 127 | D4×D7 | — | 4 | 2 | no | — |
| 128 | D4×D7 | — | 4 | 4 | no | — |
| 129 | D4×D7 | — | 4 | 4 | no | — |
| 130 | #1157 | — | 2 | 1 | no | — |
| 131 | #1157 | — | 2 | 1 | no | — |
| 132 | #1157 | — | 2 | 2 | no | — |
| 133 | #1157 | — | 2 | 2 | no | — |
| 134 | #1157 | — | 4 | 4 | no | — |
| 135 | #1157 | — | 4 | 4 | no | — |
| 136 | #1157 | — | 4 | 1 | no | — |
| 137 | #1157 | — | 4 | 1 | no | — |
| 138 | #1157 | — | 4 | 2 | no | — |
| 139 | #1157 | — | 4 | 2 | no | — |
| 140 | #1157 | C22⋊C4 | 1 | 2 | yes | — |
| 141 | #1157 | SD16 | 1 | 2 | yes | — |
| 142 | C2×D28 | — | 2 | 1 | no | — |
| 143 | C2×D28 | — | 4 | 2 | no | — |
| 144 | C2×D28 | D8 | 1 | 1 | yes | characteristic |
| 145 | C2×C4×D7 | — | 2 | 1 | no | — |
| 146 | C2×C4×D7 | — | 4 | 4 | no | — |
| 147 | C2×C4×D7 | — | 4 | 1 | no | — |
| 148 | C2×Dic14 | — | 2 | 1 | no | — |
| 149 | C2×Dic14 | — | 4 | 2 | no | — |
| 150 | C2×Dic14 | D8 | 1 | 1 | yes | characteristic |
| 151 | C7×Q16 | — | 2 | 1 | no | — |
| 152 | C7×Q16 | C22⋊C4 | 1 | 2 | yes | — |
| 153 | C7×SD16 | — | 2 | 2 | no | — |
| 154 | C7×SD16 | — | 2 | 2 | no | — |
| 155 | C7×D8 | — | 2 | 1 | no | — |
| 156 | C7×D8 | C22⋊C4 | 1 | 2 | yes | — |
| 157 | C7×M16 | — | 4 | 1 | no | — |
| 158 | C7×M16 | — | 4 | 1 | no | — |
| 159 | C2×C7×C8 | — | 4 | 1 | no | — |
| 160 | C2×C7×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 161 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 162 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 165 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 166 | #1144 | — | 2 | 4 | no | — |
| 167 | #1143 | — | 2 | 4 | no | — |
| 168 | #1142 | — | 2 | 4 | no | — |
| 169 | #1141 | — | 2 | 4 | no | — |
| 170 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 171 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 172 | #1136 | — | 2 | 1 | no | — |
| 173 | #1136 | C22⋊C4 | 1 | 2 | yes | — |
| 174 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 175 | Dic28 | — | 2 | 1 | no | — |
| 176 | Dic28 | C22⋊C4 | 1 | 2 | yes | — |
| 177 | D56 | — | 2 | 1 | no | — |
| 178 | D56 | C22⋊C4 | 1 | 2 | yes | — |
| 179 | #1132 | — | 2 | 2 | no | — |
| 180 | #1132 | — | 2 | 2 | no | — |
| 181 | #1131 | — | 2 | 2 | no | — |
| 182 | #1131 | — | 2 | 2 | no | — |
| 183 | C8×D7 | — | 2 | 2 | no | — |
| 184 | C8×D7 | — | 2 | 2 | no | — |
| 185 | C7×C16 | — | 4 | 1 | no | — |
| 186 | C7⋊C16 | — | 4 | 1 | no | — |
| 187 | #585 | — | 14 | 1 | no | — |
| 188 | #578 | — | 7 | 2 | no | — |
| 189 | #578 | — | 14 | 1 | no | — |
| 190 | #577 | — | 14 | 2 | no | — |
| 191 | #577 | — | 14 | 2 | no | — |
| 192 | #576 | — | 7 | 2 | no | — |
| 193 | #576 | — | 14 | 1 | no | — |
| 194 | #575 | — | 14 | 1 | no | — |
| 195 | #575 | — | 14 | 2 | no | — |
| 196 | C2×#135 | — | 7 | 1 | no | — |
| 197 | C2×#135 | — | 14 | 2 | no | — |
| 198 | C2×#135 | C2×D7 | 1 | 1 | yes | characteristic |
| 199 | C2×#131 | — | 7 | 1 | no | — |
| 200 | C2×M32 | — | 7 | 1 | no | — |
| 201 | C2×M32 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 202 | C2×#108 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 203 | C2×#106 | — | 7 | 1 | no | — |
| 204 | #417 | — | 14 | 1 | no | — |
| 205 | #362 | — | 2 | 1 | no | — |
| 206 | #361 | — | 2 | 1 | no | — |
| 207 | #360 | — | 14 | 2 | no | — |
| 208 | #360 | — | 14 | 2 | no | — |
| 209 | #359 | — | 14 | 2 | no | — |
| 210 | #350 | — | 14 | 2 | no | — |
| 211 | #343 | — | 14 | 1 | no | — |
| 212 | C23×C7 | — | 4 | 1 | no | — |
| 213 | C23×C7 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 214 | C22×D7 | — | 2 | 1 | no | — |
| 215 | C22×D7 | — | 4 | 4 | no | — |
| 216 | C22×D7 | — | 4 | 1 | no | — |
| 217 | C7×Q8 | — | 2 | 2 | no | — |
| 218 | C7×Q8 | — | 4 | 1 | no | — |
| 219 | C7×D4 | — | 2 | 2 | no | — |
| 220 | C7×D4 | — | 4 | 2 | no | — |
| 221 | C7×D4 | — | 4 | 2 | no | — |
| 222 | C7×D4 | — | 4 | 1 | no | — |
| 223 | C2×C4×C7 | — | 4 | 1 | no | — |
| 224 | C2×C4×C7 | — | 4 | 2 | no | — |
| 225 | C2×C4×C7 | — | 4 | 2 | no | — |
| 226 | C2×C4×C7 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 227 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 228 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 229 | C2×C4×C7 | C2×D8 | 1 | 1 | yes | characteristic |
| 230 | C2×C4×C7 | C2×SD16 | 1 | 1 | yes | characteristic |
| 231 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 232 | C22⋊D7 | — | 2 | 2 | no | — |
| 233 | C22⋊D7 | — | 2 | 2 | no | — |
| 234 | C22⋊D7 | — | 4 | 4 | no | — |
| 235 | C22⋊D7 | — | 4 | 4 | no | — |
| 236 | C22⋊D7 | — | 4 | 2 | no | — |
| 237 | C22⋊D7 | — | 4 | 2 | no | — |
| 238 | C2×Dic7 | — | 2 | 1 | no | — |
| 239 | C2×Dic7 | — | 4 | 4 | no | — |
| 240 | C2×Dic7 | — | 4 | 1 | no | — |
| 241 | C2×Dic7 | — | 8 | 1 | no | — |
| 242 | C2×Dic7 | — | 16 | 1 | no | — |
| 243 | D28 | — | 2 | 2 | no | — |
| 244 | D28 | — | 2 | 1 | no | — |
| 245 | D28 | — | 4 | 4 | no | — |
| 246 | D28 | — | 4 | 1 | no | — |
| 247 | D28 | #102 | 1 | 2 | yes | — |
| 248 | C4×D7 | — | 2 | 2 | no | — |
| 249 | C4×D7 | — | 2 | 2 | no | — |
| 250 | C4×D7 | — | 4 | 4 | no | — |
| 251 | C4×D7 | — | 4 | 4 | no | — |
| 252 | C4×D7 | — | 4 | 2 | no | — |
| 253 | C4×D7 | — | 4 | 2 | no | — |
| 254 | Dic14 | — | 2 | 1 | no | — |
| 255 | Dic14 | — | 2 | 2 | no | — |
| 256 | Dic14 | — | 4 | 4 | no | — |
| 257 | Dic14 | — | 4 | 1 | no | — |
| 258 | Dic14 | #102 | 1 | 2 | yes | — |
| 259 | C7×C8 | — | 8 | 1 | no | — |
| 260 | C7×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 261 | C7×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 262 | C7×C8 | #120 | 1 | 1 | yes | characteristic |
| 263 | C7×C8 | #120 | 1 | 1 | yes | characteristic |
| 264 | C7⋊C8 | — | 2 | 2 | no | — |
| 265 | 2−1+4 | — | 14 | 2 | no | — |
| 266 | 2−1+4 | — | 14 | 2 | no | — |
| 267 | 2−1+4 | — | 28 | 1 | no | — |
| 268 | H(5,𝔽2) | — | 14 | 2 | no | — |
| 269 | H(5,𝔽2) | — | 14 | 2 | no | — |
| 270 | H(5,𝔽2) | — | 28 | 2 | no | — |
| 271 | H(5,𝔽2) | — | 28 | 1 | no | — |
| 272 | C2×#41 | — | 2 | 1 | no | — |
| 273 | C2×#41 | — | 7 | 1 | no | — |
| 274 | C2×#41 | — | 14 | 4 | no | — |
| 275 | C2×#41 | — | 14 | 1 | no | — |
| 276 | C2×#41 | — | 28 | 2 | no | — |
| 277 | C2×#41 | — | 28 | 2 | no | — |
| 278 | #137 | — | 14 | 2 | no | — |
| 279 | #137 | — | 14 | 4 | no | — |
| 280 | #137 | — | 14 | 4 | no | — |
| 281 | #137 | — | 14 | 2 | no | — |
| 282 | AGL(1,ℤ/8) | — | 14 | 2 | no | — |
| 283 | AGL(1,ℤ/8) | — | 14 | 4 | no | — |
| 284 | AGL(1,ℤ/8) | — | 14 | 4 | no | — |
| 285 | AGL(1,ℤ/8) | — | 14 | 2 | no | — |
| 286 | #135 | — | 2 | 1 | no | — |
| 287 | #135 | — | 2 | 1 | no | — |
| 288 | #135 | — | 7 | 2 | no | — |
| 289 | #135 | — | 7 | 2 | no | — |
| 290 | #135 | — | 14 | 4 | no | — |
| 291 | #135 | — | 14 | 4 | no | — |
| 292 | #135 | — | 14 | 2 | no | — |
| 293 | #135 | — | 14 | 2 | no | — |
| 294 | #135 | — | 14 | 1 | no | — |
| 295 | #135 | — | 14 | 1 | no | — |
| 296 | #135 | C4×D7 | 1 | 2 | yes | — |
| 297 | #135 | D28 | 1 | 2 | yes | — |
| 298 | C2×Q16 | — | 7 | 1 | no | — |
| 299 | C2×Q16 | — | 14 | 2 | no | — |
| 300 | C2×Q16 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 301 | C2×SD16 | — | 2 | 1 | no | — |
| 302 | C2×SD16 | — | 14 | 4 | no | — |
| 303 | C2×SD16 | — | 14 | 1 | no | — |
| 304 | C2×D8 | — | 7 | 1 | no | — |
| 305 | C2×D8 | — | 14 | 2 | no | — |
| 306 | C2×D8 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 307 | #131 | — | 7 | 2 | no | — |
| 308 | #131 | — | 7 | 2 | no | — |
| 309 | #131 | — | 14 | 1 | no | — |
| 310 | #131 | — | 14 | 1 | no | — |
| 311 | C2×M16 | — | 2 | 1 | no | — |
| 312 | C2×M16 | — | 7 | 1 | no | — |
| 313 | C2×M16 | — | 14 | 1 | no | — |
| 314 | C22×C8 | — | 14 | 1 | no | — |
| 315 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 316 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 317 | M32 | — | 2 | 1 | no | — |
| 318 | M32 | — | 2 | 1 | no | — |
| 319 | M32 | — | 14 | 1 | no | — |
| 320 | M32 | — | 14 | 1 | no | — |
| 321 | C2×C16 | — | 2 | 1 | no | — |
| 322 | C2×C16 | — | 14 | 1 | no | — |
| 323 | #108 | — | 2 | 1 | no | — |
| 324 | #108 | — | 2 | 1 | no | — |
| 325 | #106 | — | 14 | 1 | no | — |
| 326 | #106 | — | 14 | 1 | no | — |
| 327 | #103 | — | 28 | 1 | no | — |
| 328 | #102 | — | 28 | 1 | no | — |
| 329 | C22×C7 | — | 4 | 1 | no | — |
| 330 | C22×C7 | — | 4 | 2 | no | — |
| 331 | C22×C7 | — | 16 | 1 | no | — |
| 332 | C22×C7 | #418 | 1 | 1 | yes | characteristic |
| 333 | C22×C7 | #447 | 1 | 1 | yes | characteristic |
| 334 | C22×C7 | #450 | 1 | 1 | yes | characteristic |
| 335 | C2×D7 | — | 2 | 2 | no | — |
| 336 | C2×D7 | — | 4 | 2 | no | — |
| 337 | C2×D7 | — | 8 | 1 | no | — |
| 338 | C2×D7 | — | 16 | 4 | no | — |
| 339 | C2×D7 | — | 16 | 1 | no | — |
| 340 | C4×C7 | — | 4 | 2 | no | — |
| 341 | C4×C7 | #379 | 1 | 1 | yes | characteristic |
| 342 | C4×C7 | C2×#102 | 1 | 1 | yes | characteristic |
| 343 | C4×C7 | #447 | 1 | 1 | yes | characteristic |
| 344 | C4×C7 | #450 | 1 | 1 | yes | characteristic |
| 345 | Dic7 | — | 2 | 2 | no | — |
| 346 | Dic7 | — | 4 | 2 | no | — |
| 347 | Dic7 | — | 16 | 1 | no | — |
| 348 | #41 | — | 2 | 2 | no | — |
| 349 | #41 | — | 2 | 2 | no | — |
| 350 | #41 | — | 4 | 1 | no | — |
| 351 | #41 | — | 4 | 1 | no | — |
| 352 | #41 | — | 7 | 2 | no | — |
| 353 | #41 | — | 7 | 2 | no | — |
| 354 | #41 | — | 14 | 1 | no | — |
| 355 | #41 | — | 14 | 1 | no | — |
| 356 | #41 | — | 14 | 4 | no | — |
| 357 | #41 | — | 14 | 4 | no | — |
| 358 | #41 | — | 14 | 2 | no | — |
| 359 | #41 | — | 14 | 2 | no | — |
| 360 | #41 | — | 28 | 4 | no | — |
| 361 | #41 | — | 28 | 2 | no | — |
| 362 | #41 | — | 28 | 4 | no | — |
| 363 | #41 | — | 28 | 2 | no | — |
| 364 | #41 | — | 28 | 4 | no | — |
| 365 | #41 | — | 28 | 4 | no | — |
| 366 | #41 | — | 28 | 2 | no | — |
| 367 | #41 | — | 28 | 2 | no | — |
| 368 | #41 | — | 28 | 1 | no | — |
| 369 | #41 | — | 28 | 1 | no | — |
| 370 | C2×Q8 | — | 2 | 1 | no | — |
| 371 | C2×Q8 | — | 7 | 1 | no | — |
| 372 | C2×Q8 | — | 14 | 4 | no | — |
| 373 | C2×Q8 | — | 14 | 1 | no | — |
| 374 | C2×Q8 | — | 28 | 2 | no | — |
| 375 | C2×Q8 | — | 28 | 2 | no | — |
| 376 | C2×D4 | — | 2 | 1 | no | — |
| 377 | C2×D4 | — | 4 | 1 | no | — |
| 378 | C2×D4 | — | 7 | 1 | no | — |
| 379 | C2×D4 | — | 14 | 4 | no | — |
| 380 | C2×D4 | — | 14 | 1 | no | — |
| 381 | C2×D4 | — | 14 | 1 | no | — |
| 382 | C2×D4 | — | 28 | 2 | no | — |
| 383 | C2×D4 | — | 28 | 4 | no | — |
| 384 | C2×D4 | — | 28 | 2 | no | — |
| 385 | C2×D4 | — | 28 | 4 | no | — |
| 386 | C2×D4 | — | 28 | 4 | no | — |
| 387 | C2×D4 | — | 28 | 1 | no | — |
| 388 | C22×C4 | — | 4 | 1 | no | — |
| 389 | C22×C4 | — | 14 | 1 | no | — |
| 390 | C22×C4 | — | 28 | 4 | no | — |
| 391 | C22×C4 | — | 28 | 1 | no | — |
| 392 | C22×C4 | — | 28 | 1 | no | — |
| 393 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 394 | Q16 | — | 2 | 1 | no | — |
| 395 | Q16 | — | 7 | 2 | no | — |
| 396 | Q16 | — | 14 | 4 | no | — |
| 397 | Q16 | — | 14 | 1 | no | — |
| 398 | Q16 | (C2×D7)⋊C4 | 1 | 2 | yes | — |
| 399 | SD16 | — | 2 | 2 | no | — |
| 400 | SD16 | — | 2 | 2 | no | — |
| 401 | SD16 | — | 14 | 4 | no | — |
| 402 | SD16 | — | 14 | 4 | no | — |
| 403 | SD16 | — | 14 | 2 | no | — |
| 404 | SD16 | — | 14 | 2 | no | — |
| 405 | D8 | — | 2 | 1 | no | — |
| 406 | D8 | — | 7 | 2 | no | — |
| 407 | D8 | — | 14 | 4 | no | — |
| 408 | D8 | — | 14 | 1 | no | — |
| 409 | D8 | (C2×D7)⋊C4 | 1 | 2 | yes | — |
| 410 | M16 | — | 4 | 1 | no | — |
| 411 | M16 | — | 4 | 1 | no | — |
| 412 | M16 | — | 7 | 2 | no | — |
| 413 | M16 | — | 14 | 1 | no | — |
| 414 | M16 | — | 14 | 2 | no | — |
| 415 | M16 | — | 14 | 2 | no | — |
| 416 | C2×C8 | — | 4 | 1 | no | — |
| 417 | C2×C8 | — | 14 | 1 | no | — |
| 418 | C2×C8 | — | 14 | 2 | no | — |
| 419 | C2×C8 | — | 14 | 2 | no | — |
| 420 | C2×C8 | C2×C4×D7 | 1 | 1 | yes | characteristic |
| 421 | C2×C8 | C2×D28 | 1 | 1 | yes | characteristic |
| 422 | C2×C8 | D4×D7 | 1 | 1 | yes | characteristic |
| 423 | C2×C8 | D4×D7 | 1 | 1 | yes | characteristic |
| 424 | C2×C8 | D4×D7 | 1 | 1 | yes | characteristic |
| 425 | C2×C8 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 426 | C4⋊C4 | — | 28 | 1 | no | — |
| 427 | C4⋊C4 | — | 28 | 1 | no | — |
| 428 | C16 | — | 4 | 1 | no | — |
| 429 | C16 | — | 28 | 1 | no | — |
| 430 | C2×C7 | — | 2 | 1 | no | — |
| 431 | C2×C7 | — | 2 | 1 | no | — |
| 432 | C2×C7 | — | 2 | 1 | no | — |
| 433 | C2×C7 | — | 8 | 2 | no | — |
| 434 | C2×C7 | #1786 | 1 | 1 | yes | characteristic |
| 435 | D7 | — | 4 | 2 | no | — |
| 436 | D7 | — | 8 | 2 | no | — |
| 437 | C23 | — | 4 | 1 | no | — |
| 438 | C23 | — | 14 | 1 | no | — |
| 439 | C23 | — | 28 | 4 | no | — |
| 440 | C23 | — | 28 | 1 | no | — |
| 441 | C23 | #6477 | 1 | 1 | yes | characteristic |
| 442 | Q8 | — | 2 | 2 | no | — |
| 443 | Q8 | — | 4 | 1 | no | — |
| 444 | Q8 | — | 7 | 2 | no | — |
| 445 | Q8 | — | 14 | 1 | no | — |
| 446 | Q8 | — | 14 | 2 | no | — |
| 447 | Q8 | — | 28 | 4 | no | — |
| 448 | Q8 | — | 28 | 1 | no | — |
| 449 | D4 | — | 2 | 2 | no | — |
| 450 | D4 | — | 4 | 2 | no | — |
| 451 | D4 | — | 4 | 2 | no | — |
| 452 | D4 | — | 4 | 1 | no | — |
| 453 | D4 | — | 7 | 2 | no | — |
| 454 | D4 | — | 14 | 2 | no | — |
| 455 | D4 | — | 14 | 2 | no | — |
| 456 | D4 | — | 14 | 1 | no | — |
| 457 | D4 | — | 14 | 2 | no | — |
| 458 | D4 | — | 28 | 4 | no | — |
| 459 | D4 | — | 28 | 4 | no | — |
| 460 | D4 | — | 28 | 4 | no | — |
| 461 | D4 | — | 28 | 2 | no | — |
| 462 | D4 | — | 28 | 2 | no | — |
| 463 | D4 | — | 28 | 1 | no | — |
| 464 | C2×C4 | — | 4 | 1 | no | — |
| 465 | C2×C4 | — | 4 | 2 | no | — |
| 466 | C2×C4 | — | 4 | 2 | no | — |
| 467 | C2×C4 | — | 14 | 1 | no | — |
| 468 | C2×C4 | — | 14 | 2 | no | — |
| 469 | C2×C4 | — | 14 | 2 | no | — |
| 470 | C2×C4 | — | 28 | 4 | no | — |
| 471 | C2×C4 | — | 28 | 4 | no | — |
| 472 | C2×C4 | — | 28 | 4 | no | — |
| 473 | C2×C4 | — | 28 | 1 | no | — |
| 474 | C2×C4 | — | 28 | 2 | no | — |
| 475 | C2×C4 | — | 28 | 2 | no | — |
| 476 | C2×C4 | — | 56 | 1 | no | — |
| 477 | C2×C4 | — | 112 | 1 | no | — |
| 478 | C2×C4 | D7×C22⋊C4 | 1 | 1 | yes | characteristic |
| 479 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 480 | C2×C4 | D7×D8 | 1 | 1 | yes | characteristic |
| 481 | C2×C4 | #6474 | 1 | 1 | yes | characteristic |
| 482 | C2×C4 | D7×SD16 | 1 | 1 | yes | characteristic |
| 483 | C2×C4 | #6500 | 1 | 1 | yes | characteristic |
| 484 | C8 | — | 8 | 1 | no | — |
| 485 | C8 | — | 14 | 2 | no | — |
| 486 | C8 | D7×C22⋊C4 | 1 | 1 | yes | characteristic |
| 487 | C8 | #6445 | 1 | 1 | yes | characteristic |
| 488 | C8 | C2×(C2×D7)⋊C4 | 1 | 1 | yes | characteristic |
| 489 | C8 | #6500 | 1 | 1 | yes | characteristic |
| 490 | C7 | #12752 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 491 | C22 | — | 4 | 1 | no | — |
| 492 | C22 | — | 4 | 2 | no | — |
| 493 | C22 | — | 14 | 2 | no | — |
| 494 | C22 | — | 16 | 1 | no | — |
| 495 | C22 | — | 28 | 2 | no | — |
| 496 | C22 | — | 56 | 1 | no | — |
| 497 | C22 | — | 112 | 1 | no | — |
| 498 | C22 | — | 112 | 4 | no | — |
| 499 | C22 | #89542 | 1 | 1 | yes | characteristic |
| 500 | C22 | #89545 | 1 | 1 | yes | characteristic |
| 501 | C22 | #89941 | 1 | 1 | yes | characteristic |
| 502 | C4 | — | 4 | 2 | no | — |
| 503 | C4 | — | 14 | 2 | no | — |
| 504 | C4 | — | 28 | 2 | no | — |
| 505 | C4 | — | 112 | 1 | no | — |
| 506 | C4 | D7×#102 | 1 | 1 | yes | characteristic |
| 507 | C4 | #89548 | 1 | 1 | yes | characteristic |
| 508 | C4 | #89727 | 1 | 1 | yes | characteristic |
| 509 | C4 | #89928 | 1 | 1 | yes | characteristic |
| 510 | C2 | — | 2 | 1 | no | — |
| 511 | C2 | — | 2 | 1 | no | — |
| 512 | C2 | — | 2 | 1 | no | — |
| 513 | C2 | — | 8 | 2 | no | — |
| 514 | C2 | — | 28 | 2 | no | — |
| 515 | C2 | — | 56 | 2 | no | — |
| 516 | C2 | #11727952 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#2148 | C2 | semidirect |
| 3. C2×#89361 | C2 | semidirect |
| 4. C2×#89313 | C2 | semidirect |
| 5. #11729191 | C2 | semidirect |
| 6. #11728474 | C2 | semidirect |
| 7. #11728444 | C2 | semidirect |
| 11. #90462 | C4 | semidirect |
| 13. #90460 | C4 | semidirect |
| 21. C2×C7×M32 | C22 | semidirect |
| 22. C2×C7×#108 | C22 | semidirect |
| 24. C2×#6391 | C22 | semidirect |
| 25. C2×#6386 | C22 | semidirect |
| 99. #2148 | D7 | semidirect |
| 201. C2×M32 | C2×D7 | semidirect |
| 202. C2×#108 | C2×D7 | semidirect |
| 490. C7 | #12752 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11744255 | 2 |
| C7×#2148 | 2 |
| C2×#89361 | 2 |
| C2×#89313 | 2 |
| #11729191 | 2 |
| #11728474 | 2 |
| #11728444 | 2 |
| #12752 | 7 |