Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1288 conjugacy classes of subgroups.
The subgroup lattice has 550 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#90409 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C7×#3205 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11740759 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11740743 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11729513 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11729039 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11728961 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #11728521 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11728516 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C22×#1159 | — | 2 | 1 | no | — |
| 11 | C7×#532 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C7×#127 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#6514 | — | 2 | 1 | no | — |
| 14 | C2×#6503 | — | 2 | 1 | no | — |
| 15 | C2×#6502 | — | 2 | 2 | no | — |
| 16 | C2×#6501 | — | 2 | 1 | no | — |
| 17 | C2×D4×Dic7 | — | 2 | 1 | no | — |
| 18 | #90409 | — | 2 | 2 | no | — |
| 19 | #90409 | — | 2 | 2 | no | — |
| 20 | #90409 | — | 2 | 2 | no | — |
| 21 | #90409 | C22 | 1 | 4 | yes | — |
| 22 | C2×C4×D28 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×C4×Dic14 | C22 | 1 | 1 | yes | characteristic |
| 24 | C7×#493 | C22 | 1 | 2 | yes | complemented |
| 25 | C7×#486 | C22 | 1 | 2 | yes | complemented |
| 26 | C7×#459 | — | 2 | 2 | no | — |
| 27 | C7×#447 | — | 2 | 2 | no | — |
| 28 | C7×#431 | C22 | 1 | 1 | yes | characteristic |
| 29 | #90004 | — | 2 | 1 | no | — |
| 30 | #89862 | C22 | 1 | 2 | yes | complemented |
| 31 | #89859 | C22 | 1 | 2 | yes | complemented |
| 32 | #89847 | C22 | 1 | 2 | yes | complemented |
| 33 | #89844 | C22 | 1 | 2 | yes | complemented |
| 34 | #89826 | — | 2 | 2 | no | — |
| 35 | #89808 | — | 2 | 1 | no | — |
| 36 | #89805 | — | 2 | 1 | no | — |
| 37 | C4×#1141 | — | 2 | 2 | no | — |
| 38 | #89697 | C22 | 1 | 1 | yes | characteristic |
| 39 | #89696 | C22 | 1 | 1 | yes | characteristic |
| 40 | #89339 | C22 | 1 | 4 | yes | complemented |
| 41 | #89254 | C22 | 1 | 4 | yes | complemented |
| 42 | #89251 | C22 | 1 | 4 | yes | complemented |
| 43 | #18766 | — | 7 | 1 | no | maximal, Sylow |
| 44 | C2×C7×#41 | — | 2 | 1 | no | — |
| 45 | C22×C7×D4 | — | 2 | 1 | no | — |
| 46 | C22×C7×D4 | — | 2 | 1 | no | — |
| 47 | C22×C7×D4 | D4 | 1 | 2 | yes | — |
| 48 | C22×C22⋊D7 | — | 2 | 2 | no | — |
| 49 | C22×C22⋊D7 | — | 2 | 2 | no | — |
| 50 | C23×Dic7 | — | 2 | 2 | no | — |
| 51 | C2×#1159 | — | 2 | 4 | no | — |
| 52 | C2×#1159 | — | 2 | 4 | no | — |
| 53 | C2×#1159 | — | 4 | 4 | no | — |
| 54 | C2×#1159 | — | 4 | 4 | no | — |
| 55 | C22×D28 | D4 | 1 | 1 | yes | characteristic |
| 56 | C22×C4×D7 | — | 2 | 1 | no | — |
| 57 | C22×Dic14 | D4 | 1 | 1 | yes | characteristic |
| 58 | C2×C7×D8 | — | 2 | 4 | no | — |
| 59 | C7×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 60 | C7×#127 | — | 2 | 1 | no | — |
| 61 | C7×#127 | — | 2 | 1 | no | — |
| 62 | C7×#127 | D4 | 1 | 2 | yes | — |
| 63 | C7×#127 | C23 | 1 | 1 | yes | characteristic |
| 64 | C7×#127 | C23 | 1 | 2 | yes | — |
| 65 | C7×#124 | — | 2 | 1 | no | — |
| 66 | C7×#121 | — | 2 | 1 | no | — |
| 67 | C7×#121 | — | 2 | 1 | no | — |
| 68 | C4×C7×D4 | — | 2 | 1 | no | — |
| 69 | C4×C7×D4 | — | 2 | 1 | no | — |
| 70 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 71 | C2×C22⋊Dic7 | — | 2 | 2 | no | — |
| 72 | #6514 | — | 4 | 4 | no | — |
| 73 | C2×#1144 | — | 2 | 2 | no | — |
| 74 | #6503 | — | 2 | 4 | no | — |
| 75 | #6503 | — | 2 | 4 | no | — |
| 76 | #6502 | — | 2 | 8 | no | — |
| 77 | #6502 | — | 2 | 8 | no | — |
| 78 | #6501 | — | 2 | 4 | no | — |
| 79 | #6501 | — | 2 | 4 | no | — |
| 80 | D4×Dic7 | — | 2 | 4 | no | — |
| 81 | D4×Dic7 | — | 2 | 4 | no | — |
| 82 | C2×#1142 | — | 2 | 2 | no | — |
| 83 | C2×#1141 | — | 2 | 2 | no | — |
| 84 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 85 | C2×C4⋊Dic7 | D4 | 1 | 1 | yes | characteristic |
| 86 | C2×C4⋊Dic7 | D4 | 1 | 1 | yes | characteristic |
| 87 | C2×Dic7⋊C4 | — | 2 | 1 | no | — |
| 88 | C2×C4×Dic7 | — | 2 | 1 | no | — |
| 89 | C2×#1136 | — | 2 | 1 | no | — |
| 90 | C4×D28 | — | 2 | 1 | no | — |
| 91 | C4×D28 | — | 2 | 1 | no | — |
| 92 | C4×D28 | D4 | 1 | 2 | yes | — |
| 93 | C4×D28 | C23 | 1 | 2 | yes | — |
| 94 | C4×Dic14 | — | 2 | 1 | no | — |
| 95 | C4×Dic14 | — | 2 | 1 | no | — |
| 96 | C4×Dic14 | D4 | 1 | 2 | yes | — |
| 97 | C4×Dic14 | C23 | 1 | 2 | yes | — |
| 98 | C7×C4⋊C8 | — | 2 | 1 | no | — |
| 99 | C7×#102 | — | 2 | 4 | no | — |
| 100 | C7×C22⋊C8 | — | 2 | 1 | no | — |
| 101 | C4×C7×C8 | C23 | 1 | 2 | yes | — |
| 102 | #6409 | — | 2 | 2 | no | — |
| 103 | #6406 | — | 2 | 2 | no | — |
| 104 | #6406 | — | 2 | 2 | no | — |
| 105 | C22⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 106 | #6383 | — | 2 | 2 | no | — |
| 107 | #6381 | — | 2 | 2 | no | — |
| 108 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 109 | C4⋊(C7⋊C8) | C23 | 1 | 2 | yes | — |
| 110 | C4⋊(C7⋊C8) | C23 | 1 | 2 | yes | — |
| 111 | C4×C7⋊C8 | — | 2 | 1 | no | — |
| 112 | C2×#550 | — | 7 | 1 | no | — |
| 113 | #3205 | D7 | 1 | 1 | yes | characteristic, complemented |
| 114 | #3100 | — | 7 | 1 | no | — |
| 115 | #3037 | — | 7 | 1 | no | — |
| 116 | #1641 | — | 7 | 4 | no | — |
| 117 | #1621 | — | 7 | 4 | no | — |
| 118 | #1545 | — | 7 | 1 | no | — |
| 119 | #1486 | — | 7 | 1 | no | — |
| 120 | #1479 | — | 7 | 1 | no | — |
| 121 | C24×C7 | — | 2 | 2 | no | — |
| 122 | C23×D7 | — | 2 | 1 | no | — |
| 123 | C7×#41 | — | 4 | 2 | no | — |
| 124 | C7×#41 | — | 4 | 2 | no | — |
| 125 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 126 | C2×C7×D4 | — | 2 | 2 | no | — |
| 127 | C2×C7×D4 | — | 2 | 2 | no | — |
| 128 | C2×C7×D4 | — | 2 | 2 | no | — |
| 129 | C2×C7×D4 | — | 2 | 2 | no | — |
| 130 | C2×C7×D4 | — | 2 | 2 | no | — |
| 131 | C2×C7×D4 | — | 2 | 1 | no | — |
| 132 | C2×C7×D4 | — | 2 | 1 | no | — |
| 133 | C2×C7×D4 | — | 2 | 1 | no | — |
| 134 | C2×C7×D4 | — | 4 | 4 | no | — |
| 135 | C2×C7×D4 | — | 4 | 1 | no | — |
| 136 | C2×C7×D4 | — | 4 | 2 | no | — |
| 137 | C2×C7×D4 | — | 4 | 2 | no | — |
| 138 | C2×C7×D4 | — | 8 | 2 | no | — |
| 139 | C2×C7×D4 | C2×D4 | 1 | 4 | yes | — |
| 140 | C22×C4×C7 | — | 4 | 1 | no | — |
| 141 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 142 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | C2×C22⋊D7 | — | 2 | 8 | no | — |
| 145 | C2×C22⋊D7 | — | 2 | 8 | no | — |
| 146 | C2×C22⋊D7 | — | 4 | 8 | no | — |
| 147 | C2×C22⋊D7 | — | 8 | 4 | no | — |
| 148 | C22×Dic7 | — | 2 | 1 | no | — |
| 149 | C22×Dic7 | — | 2 | 8 | no | — |
| 150 | C22×Dic7 | — | 2 | 1 | no | — |
| 151 | C22×Dic7 | — | 2 | 1 | no | — |
| 152 | C22×Dic7 | — | 4 | 8 | no | — |
| 153 | #1159 | — | 4 | 8 | no | — |
| 154 | #1159 | — | 4 | 16 | no | — |
| 155 | #1159 | — | 4 | 8 | no | — |
| 156 | C2×D28 | — | 2 | 1 | no | — |
| 157 | C2×D28 | — | 4 | 2 | no | — |
| 158 | C2×D28 | C2×D4 | 1 | 2 | yes | — |
| 159 | C2×C4×D7 | — | 2 | 2 | no | — |
| 160 | C2×C4×D7 | — | 2 | 2 | no | — |
| 161 | C2×C4×D7 | — | 4 | 2 | no | — |
| 162 | C2×C4×D7 | — | 4 | 2 | no | — |
| 163 | C2×Dic14 | — | 2 | 1 | no | — |
| 164 | C2×Dic14 | — | 2 | 2 | no | — |
| 165 | C2×Dic14 | D8 | 1 | 4 | yes | complemented |
| 166 | C2×Dic14 | C2×D4 | 1 | 2 | yes | — |
| 167 | C7×D8 | — | 8 | 4 | no | — |
| 168 | C2×C7×C8 | — | 2 | 2 | no | — |
| 169 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 170 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 171 | C7×C22⋊C4 | — | 4 | 1 | no | — |
| 172 | C7×C22⋊C4 | — | 4 | 1 | no | — |
| 173 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 177 | C22⋊Dic7 | — | 2 | 8 | no | — |
| 178 | #1144 | — | 4 | 4 | no | — |
| 179 | #1142 | — | 4 | 4 | no | — |
| 180 | #1141 | — | 4 | 4 | no | — |
| 181 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 182 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 183 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 184 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 185 | C4⋊Dic7 | C2×D4 | 1 | 2 | yes | — |
| 186 | C4⋊Dic7 | C2×D4 | 1 | 2 | yes | — |
| 187 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 188 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 189 | C4×Dic7 | — | 2 | 2 | no | — |
| 190 | C4×Dic7 | — | 2 | 2 | no | — |
| 191 | #1136 | — | 4 | 2 | no | — |
| 192 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 193 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 194 | C22×#41 | — | 14 | 1 | no | — |
| 195 | C2×#137 | — | 14 | 1 | no | — |
| 196 | #550 | — | 7 | 4 | no | — |
| 197 | #550 | — | 14 | 2 | no | — |
| 198 | #550 | — | 14 | 2 | no | — |
| 199 | #550 | — | 14 | 2 | no | — |
| 200 | #532 | C2×D7 | 1 | 1 | yes | characteristic |
| 201 | C2×#127 | — | 14 | 1 | no | — |
| 202 | C2×#127 | C2×D7 | 1 | 1 | yes | characteristic |
| 203 | C2×#121 | — | 14 | 1 | no | — |
| 204 | C2×#121 | — | 14 | 2 | no | — |
| 205 | C2×C4×Q8 | — | 7 | 1 | no | — |
| 206 | C2×C4×D4 | — | 7 | 1 | no | — |
| 207 | C2×C4×D4 | — | 14 | 1 | no | — |
| 208 | #493 | C2×D7 | 1 | 2 | yes | complemented |
| 209 | #486 | C2×D7 | 1 | 2 | yes | complemented |
| 210 | #480 | — | 14 | 1 | no | — |
| 211 | #474 | — | 7 | 2 | no | — |
| 212 | #464 | — | 14 | 2 | no | — |
| 213 | #462 | — | 7 | 2 | no | — |
| 214 | #460 | — | 7 | 2 | no | — |
| 215 | #459 | — | 2 | 2 | no | — |
| 216 | #459 | — | 7 | 2 | no | — |
| 217 | #447 | — | 2 | 2 | no | — |
| 218 | #447 | — | 14 | 1 | no | — |
| 219 | C4×D8 | — | 14 | 2 | no | — |
| 220 | #431 | — | 7 | 1 | no | — |
| 221 | #431 | C2×D7 | 1 | 1 | yes | characteristic |
| 222 | #423 | — | 7 | 1 | no | — |
| 223 | #417 | — | 14 | 1 | no | — |
| 224 | #331 | — | 7 | 4 | no | — |
| 225 | Q8⋊C8 | — | 7 | 4 | no | — |
| 226 | D4⋊C8 | — | 7 | 4 | no | — |
| 227 | C23×C7 | — | 2 | 4 | no | — |
| 228 | C23×C7 | — | 4 | 4 | no | — |
| 229 | C23×C7 | — | 4 | 4 | no | — |
| 230 | C23×C7 | — | 4 | 4 | no | — |
| 231 | C23×C7 | — | 4 | 1 | no | — |
| 232 | C23×C7 | #120 | 1 | 1 | yes | characteristic |
| 233 | C22×D7 | — | 2 | 2 | no | — |
| 234 | C22×D7 | — | 4 | 2 | no | — |
| 235 | C22×D7 | — | 4 | 2 | no | — |
| 236 | C22×D7 | — | 4 | 2 | no | — |
| 237 | C7×Q8 | — | 4 | 1 | no | — |
| 238 | C7×Q8 | — | 4 | 1 | no | — |
| 239 | C7×D4 | — | 4 | 4 | no | — |
| 240 | C7×D4 | — | 4 | 4 | no | — |
| 241 | C7×D4 | — | 4 | 2 | no | — |
| 242 | C7×D4 | — | 4 | 2 | no | — |
| 243 | C7×D4 | — | 4 | 1 | no | — |
| 244 | C7×D4 | — | 4 | 2 | no | — |
| 245 | C7×D4 | — | 4 | 1 | no | — |
| 246 | C7×D4 | — | 4 | 4 | no | — |
| 247 | C7×D4 | — | 4 | 2 | no | — |
| 248 | C7×D4 | — | 4 | 4 | no | — |
| 249 | C7×D4 | — | 8 | 2 | no | — |
| 250 | C7×D4 | — | 8 | 2 | no | — |
| 251 | C2×C4×C7 | — | 2 | 2 | no | — |
| 252 | C2×C4×C7 | — | 4 | 1 | no | — |
| 253 | C2×C4×C7 | — | 4 | 1 | no | — |
| 254 | C2×C4×C7 | — | 8 | 2 | no | — |
| 255 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 256 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 257 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 258 | C2×C4×C7 | C2×D8 | 1 | 2 | yes | — |
| 259 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 260 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 261 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 262 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 263 | C22⋊D7 | — | 4 | 16 | no | — |
| 264 | C22⋊D7 | — | 8 | 8 | no | — |
| 265 | C2×Dic7 | — | 2 | 2 | no | — |
| 266 | C2×Dic7 | — | 2 | 4 | no | — |
| 267 | C2×Dic7 | — | 2 | 2 | no | — |
| 268 | C2×Dic7 | — | 2 | 2 | no | — |
| 269 | C2×Dic7 | — | 4 | 16 | no | — |
| 270 | C2×Dic7 | — | 4 | 2 | no | — |
| 271 | C2×Dic7 | — | 4 | 2 | no | — |
| 272 | D28 | — | 2 | 2 | no | — |
| 273 | D28 | — | 2 | 2 | no | — |
| 274 | D28 | — | 4 | 2 | no | — |
| 275 | C4×D7 | — | 4 | 2 | no | — |
| 276 | C4×D7 | — | 4 | 2 | no | — |
| 277 | C4×D7 | — | 4 | 4 | no | — |
| 278 | Dic14 | — | 2 | 2 | no | — |
| 279 | Dic14 | — | 2 | 4 | no | — |
| 280 | Dic14 | C2×D8 | 1 | 4 | yes | — |
| 281 | C7×C8 | — | 4 | 2 | no | — |
| 282 | C7⋊C8 | — | 4 | 2 | no | — |
| 283 | C7⋊C8 | — | 4 | 2 | no | — |
| 284 | C2×#41 | — | 2 | 1 | no | — |
| 285 | C2×#41 | — | 14 | 4 | no | — |
| 286 | C2×#41 | — | 14 | 4 | no | — |
| 287 | C2×#41 | — | 28 | 4 | no | — |
| 288 | C2×#41 | — | 28 | 4 | no | — |
| 289 | C22×Q8 | — | 7 | 1 | no | — |
| 290 | C22×D4 | — | 2 | 1 | no | — |
| 291 | C22×D4 | — | 2 | 1 | no | — |
| 292 | C22×D4 | — | 7 | 1 | no | — |
| 293 | C22×D4 | — | 14 | 2 | no | — |
| 294 | C22×D4 | — | 14 | 2 | no | — |
| 295 | C22×D4 | C22⋊D7 | 1 | 2 | yes | — |
| 296 | C23×C4 | — | 14 | 2 | no | — |
| 297 | C23×C4 | — | 14 | 1 | no | — |
| 298 | #137 | — | 28 | 4 | no | — |
| 299 | C2×Q16 | — | 14 | 2 | no | — |
| 300 | C2×SD16 | — | 14 | 2 | no | — |
| 301 | C2×D8 | — | 2 | 4 | no | — |
| 302 | C2×D8 | — | 14 | 2 | no | — |
| 303 | C2×M16 | — | 14 | 1 | no | — |
| 304 | C4⋊Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 305 | #127 | — | 2 | 1 | no | — |
| 306 | #127 | — | 2 | 1 | no | — |
| 307 | #127 | — | 14 | 4 | no | — |
| 308 | #127 | — | 14 | 4 | no | — |
| 309 | #127 | C22⋊D7 | 1 | 2 | yes | — |
| 310 | #127 | C22×D7 | 1 | 1 | yes | characteristic |
| 311 | #127 | C22×D7 | 1 | 2 | yes | — |
| 312 | #124 | — | 2 | 1 | no | — |
| 313 | #121 | — | 2 | 1 | no | — |
| 314 | #121 | — | 2 | 1 | no | — |
| 315 | #121 | — | 14 | 4 | no | — |
| 316 | #121 | — | 14 | 4 | no | — |
| 317 | #121 | — | 14 | 8 | no | — |
| 318 | #121 | — | 14 | 8 | no | — |
| 319 | C4×Q8 | — | 7 | 2 | no | — |
| 320 | C4×Q8 | — | 7 | 2 | no | — |
| 321 | C4×Q8 | — | 14 | 1 | no | — |
| 322 | C4×Q8 | — | 14 | 1 | no | — |
| 323 | C4×D4 | — | 2 | 1 | no | — |
| 324 | C4×D4 | — | 2 | 1 | no | — |
| 325 | C4×D4 | — | 7 | 2 | no | — |
| 326 | C4×D4 | — | 7 | 2 | no | — |
| 327 | C4×D4 | — | 14 | 4 | no | — |
| 328 | C4×D4 | — | 14 | 4 | no | — |
| 329 | C4×D4 | — | 14 | 1 | no | — |
| 330 | C4×D4 | — | 14 | 1 | no | — |
| 331 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 332 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 333 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 334 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 335 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 336 | C2×C42 | — | 14 | 1 | no | — |
| 337 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 338 | #107 | — | 14 | 2 | no | — |
| 339 | C4⋊C8 | — | 2 | 1 | no | — |
| 340 | C4⋊C8 | — | 7 | 2 | no | — |
| 341 | C4⋊C8 | — | 7 | 2 | no | — |
| 342 | C4⋊C8 | — | 14 | 1 | no | — |
| 343 | #103 | — | 14 | 2 | no | — |
| 344 | #102 | — | 2 | 4 | no | — |
| 345 | #102 | — | 14 | 2 | no | — |
| 346 | #102 | — | 14 | 2 | no | — |
| 347 | #102 | — | 14 | 2 | no | — |
| 348 | C22⋊C8 | — | 2 | 1 | no | — |
| 349 | C22⋊C8 | — | 14 | 1 | no | — |
| 350 | C4×C8 | — | 14 | 1 | no | — |
| 351 | C4×C8 | C22×D7 | 1 | 2 | yes | — |
| 352 | C22×C7 | — | 2 | 1 | no | — |
| 353 | C22×C7 | — | 2 | 1 | no | — |
| 354 | C22×C7 | — | 4 | 4 | no | — |
| 355 | C22×C7 | — | 4 | 4 | no | — |
| 356 | C22×C7 | — | 4 | 4 | no | — |
| 357 | C22×C7 | — | 8 | 8 | no | — |
| 358 | C22×C7 | — | 8 | 1 | no | — |
| 359 | C22×C7 | — | 8 | 1 | no | — |
| 360 | C22×C7 | — | 8 | 1 | no | — |
| 361 | C22×C7 | #447 | 1 | 2 | yes | — |
| 362 | C22×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 363 | C2×D7 | — | 4 | 2 | no | — |
| 364 | C2×D7 | — | 4 | 2 | no | — |
| 365 | C2×D7 | — | 4 | 2 | no | — |
| 366 | C2×D7 | — | 8 | 4 | no | — |
| 367 | C4×C7 | — | 2 | 1 | no | — |
| 368 | C4×C7 | — | 2 | 1 | no | — |
| 369 | C4×C7 | — | 2 | 1 | no | — |
| 370 | C4×C7 | — | 8 | 1 | no | — |
| 371 | C4×C7 | #447 | 1 | 2 | yes | — |
| 372 | C4×C7 | C22×D8 | 1 | 1 | yes | characteristic |
| 373 | C4×C7 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 374 | C4×C7 | #575 | 1 | 2 | yes | — |
| 375 | Dic7 | — | 2 | 4 | no | — |
| 376 | Dic7 | — | 4 | 2 | no | — |
| 377 | Dic7 | — | 4 | 2 | no | — |
| 378 | C24 | — | 2 | 2 | no | — |
| 379 | C24 | — | 14 | 1 | no | — |
| 380 | #41 | — | 4 | 2 | no | — |
| 381 | #41 | — | 4 | 2 | no | — |
| 382 | #41 | — | 28 | 8 | no | — |
| 383 | #41 | — | 28 | 16 | no | — |
| 384 | #41 | — | 28 | 8 | no | — |
| 385 | C2×Q8 | — | 2 | 1 | no | — |
| 386 | C2×Q8 | — | 7 | 4 | no | — |
| 387 | C2×Q8 | — | 7 | 2 | no | — |
| 388 | C2×Q8 | — | 14 | 2 | no | — |
| 389 | C2×Q8 | — | 14 | 1 | no | — |
| 390 | C2×D4 | — | 2 | 2 | no | — |
| 391 | C2×D4 | — | 2 | 2 | no | — |
| 392 | C2×D4 | — | 2 | 2 | no | — |
| 393 | C2×D4 | — | 2 | 2 | no | — |
| 394 | C2×D4 | — | 2 | 2 | no | — |
| 395 | C2×D4 | — | 2 | 1 | no | — |
| 396 | C2×D4 | — | 2 | 1 | no | — |
| 397 | C2×D4 | — | 2 | 1 | no | — |
| 398 | C2×D4 | — | 4 | 4 | no | — |
| 399 | C2×D4 | — | 4 | 1 | no | — |
| 400 | C2×D4 | — | 4 | 2 | no | — |
| 401 | C2×D4 | — | 4 | 2 | no | — |
| 402 | C2×D4 | — | 7 | 2 | no | — |
| 403 | C2×D4 | — | 8 | 2 | no | — |
| 404 | C2×D4 | — | 14 | 8 | no | — |
| 405 | C2×D4 | — | 14 | 8 | no | — |
| 406 | C2×D4 | — | 14 | 1 | no | — |
| 407 | C2×D4 | — | 28 | 2 | no | — |
| 408 | C2×D4 | — | 28 | 8 | no | — |
| 409 | C2×D4 | — | 56 | 4 | no | — |
| 410 | C2×D4 | C2×C22⋊D7 | 1 | 4 | yes | — |
| 411 | C22×C4 | — | 4 | 1 | no | — |
| 412 | C22×C4 | — | 14 | 1 | no | — |
| 413 | C22×C4 | — | 14 | 8 | no | — |
| 414 | C22×C4 | — | 14 | 1 | no | — |
| 415 | C22×C4 | — | 14 | 1 | no | — |
| 416 | C22×C4 | — | 14 | 2 | no | — |
| 417 | C22×C4 | — | 14 | 2 | no | — |
| 418 | C22×C4 | — | 28 | 8 | no | — |
| 419 | C22×C4 | — | 28 | 2 | no | — |
| 420 | C22×C4 | — | 28 | 2 | no | — |
| 421 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 422 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 423 | C22×C4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 424 | Q16 | — | 28 | 4 | no | — |
| 425 | SD16 | — | 28 | 4 | no | — |
| 426 | D8 | — | 8 | 4 | no | — |
| 427 | D8 | — | 28 | 4 | no | — |
| 428 | M16 | — | 28 | 2 | no | — |
| 429 | C2×C8 | — | 2 | 2 | no | — |
| 430 | C2×C8 | — | 14 | 2 | no | — |
| 431 | C2×C8 | — | 14 | 2 | no | — |
| 432 | C4⋊C4 | — | 2 | 1 | no | — |
| 433 | C4⋊C4 | — | 2 | 1 | no | — |
| 434 | C4⋊C4 | — | 7 | 2 | no | — |
| 435 | C4⋊C4 | — | 7 | 2 | no | — |
| 436 | C4⋊C4 | — | 14 | 2 | no | — |
| 437 | C4⋊C4 | — | 14 | 1 | no | — |
| 438 | C4⋊C4 | — | 14 | 1 | no | — |
| 439 | C4⋊C4 | — | 14 | 2 | no | — |
| 440 | C22⋊C4 | — | 4 | 1 | no | — |
| 441 | C22⋊C4 | — | 4 | 1 | no | — |
| 442 | C22⋊C4 | — | 14 | 8 | no | — |
| 443 | C22⋊C4 | — | 14 | 2 | no | — |
| 444 | C22⋊C4 | — | 14 | 2 | no | — |
| 445 | C42 | — | 14 | 2 | no | — |
| 446 | C42 | — | 14 | 2 | no | — |
| 447 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 448 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 449 | C42 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 450 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 451 | C2×C7 | — | 2 | 2 | no | — |
| 452 | C2×C7 | — | 8 | 4 | no | — |
| 453 | C2×C7 | — | 16 | 1 | no | — |
| 454 | C2×C7 | C2×#447 | 1 | 1 | yes | characteristic |
| 455 | C2×C7 | #3005 | 1 | 1 | yes | characteristic |
| 456 | C2×C7 | #3019 | 1 | 1 | yes | characteristic |
| 457 | D7 | — | 8 | 2 | no | — |
| 458 | C23 | — | 2 | 4 | no | — |
| 459 | C23 | — | 4 | 4 | no | — |
| 460 | C23 | — | 4 | 4 | no | — |
| 461 | C23 | — | 4 | 4 | no | — |
| 462 | C23 | — | 4 | 1 | no | — |
| 463 | C23 | — | 14 | 2 | no | — |
| 464 | C23 | — | 28 | 2 | no | — |
| 465 | C23 | — | 28 | 2 | no | — |
| 466 | C23 | — | 28 | 2 | no | — |
| 467 | C23 | #6500 | 1 | 1 | yes | characteristic |
| 468 | Q8 | — | 4 | 1 | no | — |
| 469 | Q8 | — | 4 | 1 | no | — |
| 470 | Q8 | — | 7 | 4 | no | — |
| 471 | Q8 | — | 14 | 4 | no | — |
| 472 | Q8 | — | 14 | 2 | no | — |
| 473 | D4 | — | 4 | 4 | no | — |
| 474 | D4 | — | 4 | 4 | no | — |
| 475 | D4 | — | 4 | 2 | no | — |
| 476 | D4 | — | 4 | 4 | no | — |
| 477 | D4 | — | 4 | 2 | no | — |
| 478 | D4 | — | 4 | 1 | no | — |
| 479 | D4 | — | 4 | 2 | no | — |
| 480 | D4 | — | 4 | 1 | no | — |
| 481 | D4 | — | 4 | 4 | no | — |
| 482 | D4 | — | 4 | 2 | no | — |
| 483 | D4 | — | 8 | 2 | no | — |
| 484 | D4 | — | 8 | 2 | no | — |
| 485 | D4 | — | 14 | 2 | no | — |
| 486 | D4 | — | 14 | 2 | no | — |
| 487 | D4 | — | 28 | 2 | no | — |
| 488 | D4 | — | 28 | 16 | no | — |
| 489 | D4 | — | 56 | 8 | no | — |
| 490 | C2×C4 | — | 2 | 2 | no | — |
| 491 | C2×C4 | — | 4 | 1 | no | — |
| 492 | C2×C4 | — | 4 | 1 | no | — |
| 493 | C2×C4 | — | 8 | 2 | no | — |
| 494 | C2×C4 | — | 14 | 4 | no | — |
| 495 | C2×C4 | — | 14 | 2 | no | — |
| 496 | C2×C4 | — | 14 | 2 | no | — |
| 497 | C2×C4 | — | 14 | 2 | no | — |
| 498 | C2×C4 | — | 28 | 16 | no | — |
| 499 | C2×C4 | — | 28 | 2 | no | — |
| 500 | C2×C4 | — | 28 | 2 | no | — |
| 501 | C2×C4 | — | 28 | 4 | no | — |
| 502 | C2×C4 | — | 28 | 2 | no | — |
| 503 | C2×C4 | — | 28 | 2 | no | — |
| 504 | C2×C4 | D7×D8 | 1 | 2 | yes | — |
| 505 | C2×C4 | #6474 | 1 | 2 | yes | — |
| 506 | C2×C4 | #6500 | 1 | 1 | yes | characteristic |
| 507 | C2×C4 | #6500 | 1 | 1 | yes | characteristic |
| 508 | C2×C4 | #6500 | 1 | 1 | yes | characteristic |
| 509 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 510 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 511 | C2×C4 | C22×C22⋊D7 | 1 | 1 | yes | characteristic |
| 512 | C8 | — | 4 | 2 | no | — |
| 513 | C8 | — | 28 | 2 | no | — |
| 514 | C8 | — | 28 | 2 | no | — |
| 515 | C7 | #18766 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 516 | C22 | — | 2 | 1 | no | — |
| 517 | C22 | — | 2 | 1 | no | — |
| 518 | C22 | — | 4 | 4 | no | — |
| 519 | C22 | — | 4 | 4 | no | — |
| 520 | C22 | — | 4 | 4 | no | — |
| 521 | C22 | — | 8 | 8 | no | — |
| 522 | C22 | — | 8 | 1 | no | — |
| 523 | C22 | — | 8 | 1 | no | — |
| 524 | C22 | — | 8 | 1 | no | — |
| 525 | C22 | — | 28 | 2 | no | — |
| 526 | C22 | — | 28 | 2 | no | — |
| 527 | C22 | — | 28 | 2 | no | — |
| 528 | C22 | — | 56 | 4 | no | — |
| 529 | C22 | #89928 | 1 | 2 | yes | — |
| 530 | C22 | C2×#6500 | 1 | 1 | yes | characteristic |
| 531 | C4 | — | 2 | 1 | no | — |
| 532 | C4 | — | 2 | 1 | no | — |
| 533 | C4 | — | 2 | 1 | no | — |
| 534 | C4 | — | 8 | 1 | no | — |
| 535 | C4 | — | 14 | 4 | no | — |
| 536 | C4 | — | 28 | 2 | no | — |
| 537 | C4 | — | 28 | 2 | no | — |
| 538 | C4 | #89928 | 1 | 2 | yes | — |
| 539 | C4 | C2×D7×D8 | 1 | 1 | yes | characteristic |
| 540 | C4 | C2×#6474 | 1 | 1 | yes | characteristic |
| 541 | C4 | #90464 | 1 | 2 | yes | — |
| 542 | C2 | — | 2 | 2 | no | — |
| 543 | C2 | — | 8 | 4 | no | — |
| 544 | C2 | — | 16 | 1 | no | — |
| 545 | C2 | — | 56 | 2 | no | — |
| 546 | C2 | #11740839 | 1 | 1 | yes | characteristic |
| 547 | C2 | C2×#89928 | 1 | 1 | yes | characteristic |
| 548 | C2 | #11741390 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#6500 |
| commutator, cosocle | C42×C7 | C24 |
| Frattini | C42 | C23×D7 |
| Fitting | C7×#3205 | C2 |
| socle | C22×C7 | C2×#120 |
| hypercenter | #3205 | D7 |
| hypocenter | C7 | #18766 |
| LCS | G ▷ C42×C7 ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #3205 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#90409 | C2 | semidirect |
| 2. C7×#3205 | C2 | semidirect |
| 3. #11740759 | C2 | semidirect |
| 4. #11740743 | C2 | semidirect |
| 5. #11729513 | C2 | semidirect |
| 6. #11729039 | C2 | semidirect |
| 7. #11728961 | C2 | semidirect |
| 8. #11728521 | C2 | semidirect |
| 9. #11728516 | C2 | semidirect |
| 24. C7×#493 | C22 | semidirect |
| 25. C7×#486 | C22 | semidirect |
| 30. #89862 | C22 | semidirect |
| 31. #89859 | C22 | semidirect |
| 32. #89847 | C22 | semidirect |
| 33. #89844 | C22 | semidirect |
| 40. #89339 | C22 | semidirect |
| 41. #89254 | C22 | semidirect |
| 42. #89251 | C22 | semidirect |
| 113. #3205 | D7 | semidirect |
| 165. C2×Dic14 | D8 | semidirect |
| 208. #493 | C2×D7 | semidirect |
| 209. #486 | C2×D7 | semidirect |
| 515. C7 | #18766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90409 | 2 |
| C7×#3205 | 2 |
| #11740759 | 2 |
| #11740743 | 2 |
| #11729513 | 2 |
| #11729039 | 2 |
| #11728961 | 2 |
| #11728521 | 2 |
| #11728516 | 2 |
| #18766 | 7 |