Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1654 conjugacy classes of subgroups.
The subgroup lattice has 980 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11743018 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11740155 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#89513 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11731476 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11731014 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C7×#1964 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11727791 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11727787 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11727786 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11727284 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11727210 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#6548 | C22 | 1 | 2 | yes | — |
| 13 | C2×C7×#121 | C22 | 1 | 1 | yes | characteristic |
| 14 | #90495 | C22 | 1 | 2 | yes | — |
| 15 | D4×C22⋊D7 | — | 2 | 1 | no | — |
| 16 | C2×#6500 | C22 | 1 | 2 | yes | complemented |
| 17 | C2×#6493 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C4×C22⋊D7 | C22 | 1 | 1 | yes | characteristic |
| 19 | C22×(C2×D7)⋊C4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #90302 | — | 2 | 1 | no | — |
| 21 | #90301 | — | 2 | 2 | no | — |
| 22 | #90300 | — | 2 | 1 | no | — |
| 23 | #90296 | — | 2 | 1 | no | — |
| 24 | D7×#121 | — | 2 | 1 | no | — |
| 25 | #90288 | — | 2 | 1 | no | — |
| 26 | #90287 | — | 2 | 1 | no | — |
| 27 | #90198 | — | 2 | 1 | no | — |
| 28 | #90181 | — | 2 | 2 | no | — |
| 29 | C2×#6445 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×#6445 | C22 | 1 | 2 | yes | complemented |
| 31 | C2×C7×#99 | C22 | 1 | 2 | yes | complemented |
| 32 | C2×C7×#99 | C22 | 1 | 2 | yes | complemented |
| 33 | C7×#380 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | C4×C7×C22⋊C4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #89995 | — | 2 | 1 | no | — |
| 36 | #89992 | C22 | 1 | 2 | yes | complemented |
| 37 | #89984 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | #89765 | — | 2 | 1 | no | — |
| 39 | #89763 | — | 2 | 2 | no | — |
| 40 | #89733 | — | 2 | 2 | no | — |
| 41 | #89730 | C22 | 1 | 1 | yes | characteristic |
| 42 | #89730 | C22 | 1 | 2 | yes | complemented |
| 43 | #89727 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | C2×#6380 | C22 | 1 | 2 | yes | — |
| 45 | C2×#6380 | C22 | 1 | 2 | yes | complemented |
| 46 | C2×#6380 | C22 | 1 | 2 | yes | complemented |
| 47 | #89722 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #89712 | — | 2 | 1 | no | — |
| 49 | #89711 | — | 2 | 1 | no | — |
| 50 | #89513 | — | 2 | 8 | no | — |
| 51 | #89446 | — | 2 | 1 | no | — |
| 52 | #89443 | — | 2 | 1 | no | — |
| 53 | #89442 | — | 2 | 1 | no | — |
| 54 | #89437 | — | 2 | 1 | no | — |
| 55 | #89322 | C22 | 1 | 2 | yes | complemented |
| 56 | #24262 | — | 7 | 1 | no | maximal, Sylow |
| 57 | C24×D7 | C23 | 1 | 1 | yes | characteristic |
| 58 | C22×C7×D4 | D4 | 1 | 1 | yes | characteristic, complemented |
| 59 | C22×C7×D4 | C23 | 1 | 2 | yes | — |
| 60 | C23×C4×C7 | C23 | 1 | 1 | yes | characteristic |
| 61 | C22×C22⋊D7 | — | 2 | 2 | no | — |
| 62 | C22×C22⋊D7 | — | 2 | 2 | no | — |
| 63 | C22×C22⋊D7 | C23 | 1 | 2 | yes | — |
| 64 | C22×C22⋊D7 | C23 | 1 | 1 | yes | characteristic |
| 65 | C23×Dic7 | C23 | 1 | 1 | yes | characteristic |
| 66 | #6548 | — | 2 | 4 | no | — |
| 67 | #6548 | — | 2 | 4 | no | — |
| 68 | #6548 | — | 4 | 2 | no | — |
| 69 | #6548 | — | 4 | 2 | no | — |
| 70 | C2×#1159 | — | 2 | 2 | no | — |
| 71 | C2×#1159 | — | 2 | 2 | no | — |
| 72 | C2×D4×D7 | — | 2 | 2 | no | — |
| 73 | C2×D4×D7 | — | 2 | 2 | no | — |
| 74 | C2×D4×D7 | — | 2 | 1 | no | — |
| 75 | C2×#1157 | — | 2 | 2 | no | — |
| 76 | C22×D28 | — | 2 | 1 | no | — |
| 77 | C22×D28 | — | 2 | 2 | no | — |
| 78 | C22×D28 | D4 | 1 | 1 | yes | characteristic, complemented |
| 79 | C22×C4×D7 | D4 | 1 | 1 | yes | characteristic, complemented |
| 80 | C7×#121 | — | 2 | 1 | no | — |
| 81 | C7×#121 | — | 2 | 1 | no | — |
| 82 | C7×#121 | — | 2 | 1 | no | — |
| 83 | C7×#121 | — | 2 | 1 | no | — |
| 84 | C2×C7×C4⋊C4 | — | 2 | 1 | no | — |
| 85 | C2×C7×C4⋊C4 | D4 | 1 | 1 | yes | characteristic, complemented |
| 86 | C2×C7×C22⋊C4 | D4 | 1 | 2 | yes | complemented |
| 87 | C2×C7×C22⋊C4 | C23 | 1 | 2 | yes | — |
| 88 | C2×C7×C22⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 89 | C2×C7×C22⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 90 | C2×C42×C7 | — | 2 | 1 | no | — |
| 91 | #6516 | — | 2 | 2 | no | — |
| 92 | C2×C22⋊Dic7 | — | 2 | 2 | no | — |
| 93 | C2×C22⋊Dic7 | C23 | 1 | 2 | yes | — |
| 94 | C2×C22⋊Dic7 | C23 | 1 | 1 | yes | characteristic |
| 95 | #6503 | — | 2 | 1 | no | — |
| 96 | #6502 | — | 2 | 2 | no | — |
| 97 | #6502 | — | 2 | 2 | no | — |
| 98 | #6502 | — | 2 | 2 | no | — |
| 99 | #6501 | — | 2 | 1 | no | — |
| 100 | #6500 | — | 2 | 2 | no | — |
| 101 | #6500 | — | 2 | 2 | no | — |
| 102 | #6500 | — | 2 | 4 | no | — |
| 103 | #6500 | — | 4 | 2 | no | — |
| 104 | #6498 | — | 2 | 2 | no | — |
| 105 | D4×Dic7 | — | 2 | 1 | no | — |
| 106 | #6493 | — | 2 | 1 | no | — |
| 107 | #6493 | — | 2 | 1 | no | — |
| 108 | #6493 | — | 2 | 1 | no | — |
| 109 | #6493 | — | 2 | 1 | no | — |
| 110 | #6492 | — | 2 | 2 | no | — |
| 111 | C4×C22⋊D7 | — | 2 | 1 | no | — |
| 112 | C4×C22⋊D7 | — | 2 | 1 | no | — |
| 113 | C4×C22⋊D7 | — | 2 | 1 | no | — |
| 114 | C4×C22⋊D7 | — | 2 | 1 | no | — |
| 115 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 116 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 117 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 118 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 119 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 120 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 121 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 122 | C2×(C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 123 | C2×(C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 124 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 125 | C2×(C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 126 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 127 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 128 | C2×(C2×D7)⋊C4 | D4 | 1 | 1 | yes | characteristic, complemented |
| 129 | C2×(C2×D7)⋊C4 | D4 | 1 | 2 | yes | complemented |
| 130 | C2×C4⋊Dic7 | — | 2 | 1 | no | — |
| 131 | C2×C4⋊Dic7 | — | 2 | 1 | no | — |
| 132 | C2×C4⋊Dic7 | D4 | 1 | 1 | yes | characteristic, complemented |
| 133 | C2×Dic7⋊C4 | D4 | 1 | 1 | yes | characteristic, complemented |
| 134 | C2×C4×Dic7 | D4 | 1 | 1 | yes | characteristic, complemented |
| 135 | #6459 | — | 2 | 2 | no | — |
| 136 | #6458 | — | 2 | 1 | no | — |
| 137 | #6457 | — | 2 | 2 | no | — |
| 138 | #6456 | — | 2 | 1 | no | — |
| 139 | D7×C4⋊C4 | — | 2 | 1 | no | — |
| 140 | #6451 | — | 2 | 1 | no | — |
| 141 | #6448 | — | 2 | 2 | no | — |
| 142 | #6447 | — | 2 | 2 | no | — |
| 143 | #6447 | — | 2 | 2 | no | — |
| 144 | #6446 | — | 2 | 2 | no | — |
| 145 | #6445 | — | 2 | 2 | no | — |
| 146 | #6445 | — | 2 | 2 | no | — |
| 147 | #6445 | — | 2 | 4 | no | — |
| 148 | #6445 | — | 4 | 2 | no | — |
| 149 | #6445 | D4 | 1 | 4 | yes | complemented |
| 150 | (C22⋊D7)⋊C4 | — | 2 | 2 | no | — |
| 151 | D7×C22⋊C4 | — | 2 | 2 | no | — |
| 152 | #6441 | — | 2 | 2 | no | — |
| 153 | C7×#99 | — | 2 | 4 | no | — |
| 154 | C7×#99 | — | 4 | 2 | no | — |
| 155 | C7×#95 | — | 2 | 1 | no | — |
| 156 | C7×#95 | — | 2 | 1 | no | — |
| 157 | C7⋊#95 | — | 2 | 1 | no | — |
| 158 | C7⋊#95 | — | 2 | 2 | no | — |
| 159 | C7⋊#95 | — | 2 | 1 | no | — |
| 160 | C7⋊#95 | — | 2 | 1 | no | — |
| 161 | C7⋊#95 | — | 2 | 2 | no | — |
| 162 | #6380 | — | 2 | 4 | no | — |
| 163 | #6380 | — | 2 | 4 | no | — |
| 164 | #6380 | — | 4 | 2 | no | — |
| 165 | #3496 | — | 7 | 1 | no | — |
| 166 | C2×B(4,𝔽2) | — | 7 | 2 | no | — |
| 167 | #2617 | — | 7 | 1 | no | — |
| 168 | #2617 | — | 7 | 1 | no | — |
| 169 | #2321 | — | 7 | 1 | no | — |
| 170 | #2044 | — | 7 | 2 | no | — |
| 171 | #2021 | — | 7 | 2 | no | — |
| 172 | #1964 | — | 7 | 1 | no | — |
| 173 | #1964 | D7 | 1 | 1 | yes | characteristic, complemented |
| 174 | #1799 | — | 7 | 1 | no | — |
| 175 | #1790 | — | 7 | 2 | no | — |
| 176 | C24×C7 | C2×D4 | 1 | 2 | yes | — |
| 177 | C24×C7 | C24 | 1 | 1 | yes | characteristic |
| 178 | C23×D7 | — | 2 | 1 | no | — |
| 179 | C23×D7 | — | 2 | 1 | no | — |
| 180 | C23×D7 | — | 2 | 1 | no | — |
| 181 | C23×D7 | — | 2 | 2 | no | — |
| 182 | C23×D7 | — | 2 | 1 | no | — |
| 183 | C23×D7 | — | 2 | 1 | no | — |
| 184 | C23×D7 | — | 2 | 1 | no | — |
| 185 | C23×D7 | — | 8 | 1 | no | — |
| 186 | C23×D7 | — | 8 | 1 | no | — |
| 187 | C23×D7 | C2×D4 | 1 | 2 | yes | — |
| 188 | C23×D7 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C23×D7 | C2×D4 | 1 | 2 | yes | complemented |
| 190 | C2×C7×D4 | — | 2 | 2 | no | — |
| 191 | C2×C7×D4 | — | 2 | 2 | no | — |
| 192 | C2×C7×D4 | — | 2 | 2 | no | — |
| 193 | C2×C7×D4 | — | 2 | 2 | no | — |
| 194 | C2×C7×D4 | — | 2 | 2 | no | — |
| 195 | C2×C7×D4 | — | 2 | 2 | no | — |
| 196 | C2×C7×D4 | — | 2 | 1 | no | — |
| 197 | C2×C7×D4 | — | 2 | 1 | no | — |
| 198 | C2×C7×D4 | — | 8 | 1 | no | — |
| 199 | C22×C4×C7 | — | 2 | 1 | no | — |
| 200 | C22×C4×C7 | — | 2 | 1 | no | — |
| 201 | C22×C4×C7 | — | 2 | 2 | no | — |
| 202 | C22×C4×C7 | — | 8 | 1 | no | — |
| 203 | C22×C4×C7 | C2×D4 | 1 | 2 | yes | — |
| 204 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 205 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 206 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 208 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 209 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 210 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 211 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 212 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 213 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 214 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 215 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 216 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 217 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 218 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 219 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 220 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 221 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 222 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 223 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 224 | C2×C22⋊D7 | — | 4 | 4 | no | — |
| 225 | C2×C22⋊D7 | — | 4 | 4 | no | — |
| 226 | C2×C22⋊D7 | — | 4 | 4 | no | — |
| 227 | C2×C22⋊D7 | — | 8 | 2 | no | — |
| 228 | C2×C22⋊D7 | — | 8 | 2 | no | — |
| 229 | C2×C22⋊D7 | C2×D4 | 1 | 2 | yes | — |
| 230 | C2×C22⋊D7 | #41 | 1 | 2 | yes | — |
| 231 | C22×Dic7 | — | 2 | 2 | no | — |
| 232 | C22×Dic7 | — | 2 | 1 | no | — |
| 233 | C22×Dic7 | — | 2 | 2 | no | — |
| 234 | C22×Dic7 | — | 2 | 1 | no | — |
| 235 | C22×Dic7 | — | 2 | 1 | no | — |
| 236 | C22×Dic7 | — | 8 | 1 | no | — |
| 237 | C22×Dic7 | C2×D4 | 1 | 2 | yes | — |
| 238 | C22×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 239 | C22×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 240 | C22×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 241 | #1159 | — | 4 | 4 | no | — |
| 242 | #1159 | — | 4 | 4 | no | — |
| 243 | #1159 | — | 4 | 4 | no | — |
| 244 | #1159 | — | 4 | 4 | no | — |
| 245 | D4×D7 | — | 4 | 4 | no | — |
| 246 | D4×D7 | — | 4 | 4 | no | — |
| 247 | D4×D7 | — | 4 | 4 | no | — |
| 248 | D4×D7 | — | 4 | 4 | no | — |
| 249 | D4×D7 | — | 8 | 2 | no | — |
| 250 | #1157 | — | 4 | 4 | no | — |
| 251 | #1157 | — | 4 | 4 | no | — |
| 252 | C2×D28 | — | 2 | 2 | no | — |
| 253 | C2×D28 | — | 2 | 1 | no | — |
| 254 | C2×D28 | — | 2 | 4 | no | — |
| 255 | C2×D28 | — | 2 | 1 | no | — |
| 256 | C2×D28 | — | 4 | 4 | no | — |
| 257 | C2×D28 | — | 8 | 1 | no | — |
| 258 | C2×D28 | — | 8 | 1 | no | — |
| 259 | C2×D28 | — | 8 | 1 | no | — |
| 260 | C2×D28 | — | 8 | 2 | no | — |
| 261 | C2×D28 | — | 8 | 2 | no | — |
| 262 | C2×C4×D7 | — | 2 | 2 | no | — |
| 263 | C2×C4×D7 | — | 2 | 2 | no | — |
| 264 | C2×C4×D7 | — | 2 | 1 | no | — |
| 265 | C2×C4×D7 | — | 2 | 1 | no | — |
| 266 | C2×C4×D7 | — | 8 | 1 | no | — |
| 267 | C2×Dic14 | — | 2 | 2 | no | — |
| 268 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 269 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 270 | C7×C4⋊C4 | — | 8 | 1 | no | — |
| 271 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 272 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 273 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 274 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 275 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 276 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 277 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 278 | C7×C22⋊C4 | C2×D4 | 1 | 2 | yes | complemented |
| 279 | C42×C7 | — | 8 | 1 | no | — |
| 280 | C22⋊Dic7 | — | 2 | 2 | no | — |
| 281 | C22⋊Dic7 | — | 2 | 2 | no | — |
| 282 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 283 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 284 | C22⋊Dic7 | — | 2 | 2 | no | — |
| 285 | C22⋊Dic7 | — | 2 | 2 | no | — |
| 286 | C22⋊Dic7 | — | 8 | 2 | no | — |
| 287 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 288 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 289 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 290 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 291 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 292 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 293 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 294 | (C2×D7)⋊C4 | — | 4 | 4 | no | — |
| 295 | (C2×D7)⋊C4 | — | 4 | 4 | no | — |
| 296 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 297 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 298 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 299 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 300 | (C2×D7)⋊C4 | — | 8 | 1 | no | — |
| 301 | (C2×D7)⋊C4 | — | 8 | 1 | no | — |
| 302 | (C2×D7)⋊C4 | — | 8 | 1 | no | — |
| 303 | (C2×D7)⋊C4 | — | 8 | 2 | no | — |
| 304 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 305 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 306 | C4⋊Dic7 | — | 8 | 1 | no | — |
| 307 | C4⋊Dic7 | — | 8 | 1 | no | — |
| 308 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 309 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 310 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 311 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 312 | C4×Dic7 | — | 2 | 1 | no | — |
| 313 | C4×Dic7 | — | 2 | 1 | no | — |
| 314 | C2×H(5,𝔽2) | — | 7 | 2 | no | — |
| 315 | #547 | — | 14 | 1 | no | — |
| 316 | #547 | — | 14 | 1 | no | — |
| 317 | #546 | — | 14 | 2 | no | — |
| 318 | #546 | — | 14 | 2 | no | — |
| 319 | D42 | — | 14 | 1 | no | — |
| 320 | D42 | — | 14 | 1 | no | — |
| 321 | #537 | — | 14 | 1 | no | — |
| 322 | #534 | — | 7 | 2 | no | — |
| 323 | #534 | — | 14 | 1 | no | — |
| 324 | #532 | — | 14 | 1 | no | — |
| 325 | C2×#121 | — | 7 | 1 | no | — |
| 326 | C2×#121 | — | 14 | 1 | no | — |
| 327 | C2×#121 | C2×D7 | 1 | 1 | yes | characteristic |
| 328 | C2×#120 | — | 7 | 2 | no | — |
| 329 | C2×#120 | — | 7 | 1 | no | — |
| 330 | C2×#120 | — | 7 | 2 | no | — |
| 331 | C2×C4×D4 | — | 7 | 1 | no | — |
| 332 | C22×C22⋊C4 | — | 7 | 1 | no | — |
| 333 | B(4,𝔽2) | — | 14 | 8 | no | — |
| 334 | C2×#99 | — | 7 | 2 | no | — |
| 335 | C2×#99 | — | 7 | 2 | no | — |
| 336 | C2×#99 | — | 7 | 2 | no | — |
| 337 | C2×#99 | C2×D7 | 1 | 2 | yes | complemented |
| 338 | C2×#99 | C2×D7 | 1 | 2 | yes | complemented |
| 339 | #397 | — | 14 | 1 | no | — |
| 340 | #397 | — | 14 | 1 | no | — |
| 341 | #394 | — | 14 | 2 | no | — |
| 342 | #394 | — | 14 | 2 | no | — |
| 343 | #392 | — | 14 | 1 | no | — |
| 344 | #392 | — | 14 | 1 | no | — |
| 345 | #390 | — | 14 | 1 | no | — |
| 346 | #388 | — | 14 | 1 | no | — |
| 347 | #388 | — | 14 | 1 | no | — |
| 348 | #386 | — | 7 | 2 | no | — |
| 349 | #386 | — | 7 | 1 | no | — |
| 350 | #386 | — | 7 | 2 | no | — |
| 351 | #386 | — | 14 | 1 | no | — |
| 352 | #385 | — | 7 | 1 | no | — |
| 353 | #380 | — | 7 | 1 | no | — |
| 354 | #380 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 355 | #379 | — | 7 | 1 | no | — |
| 356 | C4×C22⋊C4 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 357 | #342 | — | 7 | 2 | no | — |
| 358 | C23×C7 | — | 2 | 2 | no | — |
| 359 | C23×C7 | — | 2 | 2 | no | — |
| 360 | C23×C7 | — | 2 | 2 | no | — |
| 361 | C23×C7 | — | 4 | 1 | no | — |
| 362 | C23×C7 | — | 4 | 1 | no | — |
| 363 | C23×C7 | — | 4 | 2 | no | — |
| 364 | C23×C7 | — | 4 | 2 | no | — |
| 365 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 366 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 367 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 368 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 369 | C23×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 370 | C23×C7 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 371 | C23×C7 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 372 | C22×D7 | — | 2 | 1 | no | — |
| 373 | C22×D7 | — | 2 | 1 | no | — |
| 374 | C22×D7 | — | 2 | 2 | no | — |
| 375 | C22×D7 | — | 2 | 2 | no | — |
| 376 | C22×D7 | — | 2 | 2 | no | — |
| 377 | C22×D7 | — | 2 | 2 | no | — |
| 378 | C22×D7 | — | 2 | 2 | no | — |
| 379 | C22×D7 | — | 2 | 2 | no | — |
| 380 | C22×D7 | — | 4 | 4 | no | — |
| 381 | C22×D7 | — | 4 | 1 | no | — |
| 382 | C22×D7 | — | 4 | 1 | no | — |
| 383 | C22×D7 | — | 4 | 1 | no | — |
| 384 | C22×D7 | — | 4 | 1 | no | — |
| 385 | C22×D7 | — | 4 | 1 | no | — |
| 386 | C22×D7 | — | 4 | 2 | no | — |
| 387 | C22×D7 | — | 4 | 1 | no | — |
| 388 | C22×D7 | — | 4 | 2 | no | — |
| 389 | C22×D7 | — | 4 | 2 | no | — |
| 390 | C22×D7 | — | 4 | 2 | no | — |
| 391 | C22×D7 | — | 4 | 1 | no | — |
| 392 | C22×D7 | — | 4 | 1 | no | — |
| 393 | C22×D7 | — | 4 | 1 | no | — |
| 394 | C22×D7 | — | 4 | 1 | no | — |
| 395 | C22×D7 | — | 4 | 2 | no | — |
| 396 | C22×D7 | — | 4 | 2 | no | — |
| 397 | C22×D7 | — | 8 | 2 | no | — |
| 398 | C22×D7 | — | 8 | 2 | no | — |
| 399 | C22×D7 | — | 8 | 2 | no | — |
| 400 | C22×D7 | — | 8 | 2 | no | — |
| 401 | C22×D7 | — | 8 | 2 | no | — |
| 402 | C22×D7 | — | 8 | 2 | no | — |
| 403 | C22×D7 | #121 | 1 | 2 | yes | — |
| 404 | C7×D4 | — | 4 | 2 | no | — |
| 405 | C7×D4 | — | 4 | 2 | no | — |
| 406 | C7×D4 | — | 4 | 2 | no | — |
| 407 | C7×D4 | — | 4 | 2 | no | — |
| 408 | C7×D4 | — | 4 | 2 | no | — |
| 409 | C7×D4 | — | 8 | 1 | no | — |
| 410 | C2×C4×C7 | — | 2 | 2 | no | — |
| 411 | C2×C4×C7 | — | 2 | 2 | no | — |
| 412 | C2×C4×C7 | — | 2 | 2 | no | — |
| 413 | C2×C4×C7 | — | 2 | 2 | no | — |
| 414 | C2×C4×C7 | — | 4 | 1 | no | — |
| 415 | C2×C4×C7 | — | 4 | 1 | no | — |
| 416 | C2×C4×C7 | — | 4 | 1 | no | — |
| 417 | C2×C4×C7 | — | 4 | 1 | no | — |
| 418 | C2×C4×C7 | — | 4 | 1 | no | — |
| 419 | C2×C4×C7 | — | 4 | 1 | no | — |
| 420 | C2×C4×C7 | — | 4 | 1 | no | — |
| 421 | C2×C4×C7 | — | 4 | 1 | no | — |
| 422 | C2×C4×C7 | — | 4 | 1 | no | — |
| 423 | C2×C4×C7 | — | 4 | 1 | no | — |
| 424 | C2×C4×C7 | — | 4 | 2 | no | — |
| 425 | C2×C4×C7 | — | 4 | 2 | no | — |
| 426 | C2×C4×C7 | — | 4 | 1 | no | — |
| 427 | C2×C4×C7 | — | 4 | 2 | no | — |
| 428 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 429 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 430 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 431 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 432 | C22⋊D7 | — | 2 | 2 | no | — |
| 433 | C22⋊D7 | — | 2 | 2 | no | — |
| 434 | C22⋊D7 | — | 2 | 2 | no | — |
| 435 | C22⋊D7 | — | 2 | 2 | no | — |
| 436 | C22⋊D7 | — | 4 | 4 | no | — |
| 437 | C22⋊D7 | — | 4 | 4 | no | — |
| 438 | C22⋊D7 | — | 4 | 2 | no | — |
| 439 | C22⋊D7 | — | 4 | 2 | no | — |
| 440 | C22⋊D7 | — | 4 | 2 | no | — |
| 441 | C22⋊D7 | — | 4 | 2 | no | — |
| 442 | C22⋊D7 | — | 8 | 2 | no | — |
| 443 | C22⋊D7 | — | 8 | 2 | no | — |
| 444 | C22⋊D7 | — | 8 | 8 | no | — |
| 445 | C2×Dic7 | — | 2 | 1 | no | — |
| 446 | C2×Dic7 | — | 2 | 1 | no | — |
| 447 | C2×Dic7 | — | 2 | 1 | no | — |
| 448 | C2×Dic7 | — | 2 | 1 | no | — |
| 449 | C2×Dic7 | — | 2 | 2 | no | — |
| 450 | C2×Dic7 | — | 2 | 2 | no | — |
| 451 | C2×Dic7 | — | 2 | 2 | no | — |
| 452 | C2×Dic7 | — | 4 | 4 | no | — |
| 453 | C2×Dic7 | — | 4 | 1 | no | — |
| 454 | C2×Dic7 | — | 4 | 1 | no | — |
| 455 | C2×Dic7 | — | 4 | 1 | no | — |
| 456 | C2×Dic7 | — | 4 | 2 | no | — |
| 457 | C2×Dic7 | — | 4 | 1 | no | — |
| 458 | C2×Dic7 | — | 4 | 2 | no | — |
| 459 | C2×Dic7 | — | 4 | 2 | no | — |
| 460 | C2×Dic7 | — | 4 | 2 | no | — |
| 461 | C2×Dic7 | — | 4 | 1 | no | — |
| 462 | C2×Dic7 | — | 4 | 2 | no | — |
| 463 | C2×Dic7 | #121 | 1 | 2 | yes | — |
| 464 | D28 | — | 4 | 2 | no | — |
| 465 | D28 | — | 4 | 4 | no | — |
| 466 | D28 | — | 8 | 1 | no | — |
| 467 | D28 | — | 8 | 4 | no | — |
| 468 | D28 | — | 8 | 8 | no | — |
| 469 | C4×D7 | — | 4 | 4 | no | — |
| 470 | C4×D7 | — | 4 | 2 | no | — |
| 471 | C4×D7 | — | 4 | 4 | no | — |
| 472 | C4×D7 | — | 8 | 1 | no | — |
| 473 | Dic14 | — | 4 | 4 | no | — |
| 474 | C25 | — | 7 | 1 | no | — |
| 475 | H(5,𝔽2) | — | 14 | 4 | no | — |
| 476 | H(5,𝔽2) | — | 14 | 4 | no | — |
| 477 | H(5,𝔽2) | — | 28 | 2 | no | — |
| 478 | H(5,𝔽2) | — | 28 | 2 | no | — |
| 479 | C2×#41 | — | 14 | 2 | no | — |
| 480 | C2×#41 | — | 14 | 2 | no | — |
| 481 | C2×#41 | — | 14 | 2 | no | — |
| 482 | C22×D4 | — | 7 | 1 | no | — |
| 483 | C22×D4 | — | 7 | 2 | no | — |
| 484 | C22×D4 | — | 7 | 1 | no | — |
| 485 | C22×D4 | — | 14 | 1 | no | — |
| 486 | C22×D4 | — | 14 | 2 | no | — |
| 487 | C22×D4 | — | 14 | 2 | no | — |
| 488 | C22×D4 | — | 14 | 2 | no | — |
| 489 | C22×D4 | — | 14 | 1 | no | — |
| 490 | C22×D4 | — | 14 | 2 | no | — |
| 491 | C22×D4 | — | 14 | 2 | no | — |
| 492 | C22×D4 | D28 | 1 | 1 | yes | characteristic, complemented |
| 493 | C22×D4 | C22×D7 | 1 | 2 | yes | — |
| 494 | C23×C4 | — | 7 | 1 | no | — |
| 495 | C23×C4 | — | 7 | 1 | no | — |
| 496 | C23×C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 497 | C4⋊Q8 | — | 14 | 1 | no | — |
| 498 | #127 | — | 14 | 1 | no | — |
| 499 | #124 | — | 14 | 2 | no | — |
| 500 | #123 | — | 14 | 2 | no | — |
| 501 | #123 | — | 14 | 2 | no | — |
| 502 | #123 | — | 14 | 2 | no | — |
| 503 | #123 | — | 14 | 2 | no | — |
| 504 | C22⋊Q8 | — | 14 | 2 | no | — |
| 505 | C22⋊Q8 | — | 14 | 2 | no | — |
| 506 | #121 | — | 2 | 1 | no | — |
| 507 | #121 | — | 2 | 1 | no | — |
| 508 | #121 | — | 2 | 1 | no | — |
| 509 | #121 | — | 2 | 1 | no | — |
| 510 | #121 | — | 14 | 2 | no | — |
| 511 | #121 | — | 14 | 2 | no | — |
| 512 | #121 | — | 14 | 1 | no | — |
| 513 | #121 | — | 14 | 2 | no | — |
| 514 | #121 | — | 14 | 2 | no | — |
| 515 | #121 | — | 14 | 1 | no | — |
| 516 | #121 | — | 14 | 2 | no | — |
| 517 | #121 | — | 14 | 1 | no | — |
| 518 | #121 | — | 14 | 1 | no | — |
| 519 | #121 | — | 14 | 1 | no | — |
| 520 | #121 | — | 14 | 1 | no | — |
| 521 | #120 | — | 7 | 4 | no | — |
| 522 | #120 | — | 14 | 2 | no | — |
| 523 | #120 | — | 14 | 2 | no | — |
| 524 | #120 | — | 14 | 4 | no | — |
| 525 | #120 | — | 14 | 2 | no | — |
| 526 | #120 | — | 14 | 2 | no | — |
| 527 | #120 | — | 14 | 2 | no | — |
| 528 | #120 | — | 14 | 4 | no | — |
| 529 | #120 | — | 28 | 2 | no | — |
| 530 | #120 | — | 28 | 2 | no | — |
| 531 | C4×D4 | — | 14 | 2 | no | — |
| 532 | C4×D4 | — | 14 | 1 | no | — |
| 533 | C4×D4 | — | 14 | 1 | no | — |
| 534 | C4×D4 | — | 14 | 1 | no | — |
| 535 | C4×D4 | — | 14 | 1 | no | — |
| 536 | C4×D4 | — | 14 | 1 | no | — |
| 537 | C4×D4 | — | 14 | 1 | no | — |
| 538 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 539 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 540 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 541 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 542 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 543 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 544 | C2×C4⋊C4 | D28 | 1 | 1 | yes | characteristic, complemented |
| 545 | C2×C22⋊C4 | — | 7 | 1 | no | — |
| 546 | C2×C22⋊C4 | — | 7 | 1 | no | — |
| 547 | C2×C22⋊C4 | — | 7 | 2 | no | — |
| 548 | C2×C22⋊C4 | — | 7 | 2 | no | — |
| 549 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 550 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 551 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 552 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 553 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 554 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 555 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 556 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 557 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 558 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 559 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 560 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 561 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 562 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 563 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 564 | C2×C22⋊C4 | D28 | 1 | 2 | yes | complemented |
| 565 | C2×C22⋊C4 | C22×D7 | 1 | 2 | yes | — |
| 566 | C2×C22⋊C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 567 | C2×C22⋊C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 568 | C2×C42 | — | 2 | 1 | no | — |
| 569 | C2×C42 | — | 7 | 1 | no | — |
| 570 | #99 | — | 2 | 4 | no | — |
| 571 | #99 | — | 4 | 2 | no | — |
| 572 | #99 | — | 14 | 4 | no | — |
| 573 | #99 | — | 14 | 4 | no | — |
| 574 | #99 | — | 28 | 2 | no | — |
| 575 | #95 | — | 2 | 1 | no | — |
| 576 | #95 | — | 2 | 1 | no | — |
| 577 | #95 | — | 14 | 1 | no | — |
| 578 | #95 | — | 14 | 1 | no | — |
| 579 | #95 | — | 14 | 2 | no | — |
| 580 | #95 | — | 14 | 1 | no | — |
| 581 | #95 | — | 14 | 2 | no | — |
| 582 | C22×C7 | — | 2 | 1 | no | — |
| 583 | C22×C7 | — | 2 | 1 | no | — |
| 584 | C22×C7 | — | 2 | 1 | no | — |
| 585 | C22×C7 | — | 2 | 1 | no | — |
| 586 | C22×C7 | — | 2 | 1 | no | — |
| 587 | C22×C7 | — | 2 | 1 | no | — |
| 588 | C22×C7 | — | 4 | 1 | no | — |
| 589 | C22×C7 | — | 4 | 1 | no | — |
| 590 | C22×C7 | — | 4 | 1 | no | — |
| 591 | C22×C7 | — | 4 | 1 | no | — |
| 592 | C22×C7 | — | 4 | 2 | no | — |
| 593 | C22×C7 | — | 4 | 2 | no | — |
| 594 | C22×C7 | — | 4 | 2 | no | — |
| 595 | C22×C7 | — | 8 | 2 | no | — |
| 596 | C22×C7 | — | 8 | 2 | no | — |
| 597 | C22×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 598 | C22×C7 | C2×#121 | 1 | 1 | yes | characteristic |
| 599 | C22×C7 | #535 | 1 | 1 | yes | characteristic |
| 600 | C22×C7 | D42 | 1 | 1 | yes | characteristic |
| 601 | C22×C7 | D42 | 1 | 1 | yes | characteristic |
| 602 | C22×C7 | #546 | 1 | 1 | yes | characteristic |
| 603 | C22×C7 | #546 | 1 | 1 | yes | characteristic |
| 604 | C2×D7 | — | 2 | 2 | no | — |
| 605 | C2×D7 | — | 4 | 1 | no | — |
| 606 | C2×D7 | — | 4 | 1 | no | — |
| 607 | C2×D7 | — | 4 | 2 | no | — |
| 608 | C2×D7 | — | 4 | 2 | no | — |
| 609 | C2×D7 | — | 4 | 4 | no | — |
| 610 | C2×D7 | — | 4 | 4 | no | — |
| 611 | C2×D7 | — | 4 | 2 | no | — |
| 612 | C2×D7 | — | 4 | 2 | no | — |
| 613 | C2×D7 | — | 4 | 2 | no | — |
| 614 | C2×D7 | — | 4 | 2 | no | — |
| 615 | C2×D7 | — | 4 | 2 | no | — |
| 616 | C2×D7 | — | 8 | 1 | no | — |
| 617 | C2×D7 | — | 8 | 1 | no | — |
| 618 | C2×D7 | — | 8 | 1 | no | — |
| 619 | C2×D7 | — | 8 | 2 | no | — |
| 620 | C2×D7 | — | 8 | 2 | no | — |
| 621 | C2×D7 | — | 8 | 1 | no | — |
| 622 | C2×D7 | — | 8 | 1 | no | — |
| 623 | C2×D7 | — | 8 | 2 | no | — |
| 624 | C2×D7 | — | 8 | 2 | no | — |
| 625 | C2×D7 | — | 16 | 4 | no | — |
| 626 | C4×C7 | — | 2 | 1 | no | — |
| 627 | C4×C7 | — | 2 | 1 | no | — |
| 628 | C4×C7 | — | 2 | 1 | no | — |
| 629 | C4×C7 | — | 2 | 1 | no | — |
| 630 | C4×C7 | — | 4 | 2 | no | — |
| 631 | C4×C7 | — | 4 | 2 | no | — |
| 632 | C4×C7 | — | 8 | 2 | no | — |
| 633 | C4×C7 | — | 8 | 1 | no | — |
| 634 | Dic7 | — | 2 | 2 | no | — |
| 635 | Dic7 | — | 4 | 2 | no | — |
| 636 | Dic7 | — | 4 | 1 | no | — |
| 637 | Dic7 | — | 4 | 1 | no | — |
| 638 | Dic7 | — | 8 | 2 | no | — |
| 639 | Dic7 | — | 8 | 1 | no | — |
| 640 | C24 | — | 7 | 1 | no | — |
| 641 | C24 | — | 7 | 2 | no | — |
| 642 | C24 | — | 7 | 2 | no | — |
| 643 | C24 | — | 14 | 2 | no | — |
| 644 | C24 | — | 14 | 1 | no | — |
| 645 | C24 | — | 14 | 1 | no | — |
| 646 | C24 | — | 14 | 1 | no | — |
| 647 | C24 | — | 14 | 1 | no | — |
| 648 | C24 | — | 14 | 1 | no | — |
| 649 | C24 | — | 14 | 1 | no | — |
| 650 | C24 | — | 56 | 1 | no | — |
| 651 | C24 | — | 56 | 1 | no | — |
| 652 | C24 | C2×D28 | 1 | 2 | yes | — |
| 653 | C24 | C23×D7 | 1 | 1 | yes | characteristic |
| 654 | #41 | — | 28 | 4 | no | — |
| 655 | #41 | — | 28 | 4 | no | — |
| 656 | #41 | — | 28 | 4 | no | — |
| 657 | #41 | — | 28 | 4 | no | — |
| 658 | #41 | — | 28 | 4 | no | — |
| 659 | #41 | — | 28 | 4 | no | — |
| 660 | C2×Q8 | — | 14 | 2 | no | — |
| 661 | C2×D4 | — | 2 | 2 | no | — |
| 662 | C2×D4 | — | 2 | 2 | no | — |
| 663 | C2×D4 | — | 2 | 2 | no | — |
| 664 | C2×D4 | — | 2 | 2 | no | — |
| 665 | C2×D4 | — | 2 | 2 | no | — |
| 666 | C2×D4 | — | 2 | 2 | no | — |
| 667 | C2×D4 | — | 2 | 1 | no | — |
| 668 | C2×D4 | — | 2 | 1 | no | — |
| 669 | C2×D4 | — | 7 | 2 | no | — |
| 670 | C2×D4 | — | 7 | 2 | no | — |
| 671 | C2×D4 | — | 8 | 1 | no | — |
| 672 | C2×D4 | — | 14 | 2 | no | — |
| 673 | C2×D4 | — | 14 | 4 | no | — |
| 674 | C2×D4 | — | 14 | 1 | no | — |
| 675 | C2×D4 | — | 14 | 1 | no | — |
| 676 | C2×D4 | — | 14 | 1 | no | — |
| 677 | C2×D4 | — | 14 | 1 | no | — |
| 678 | C2×D4 | — | 14 | 2 | no | — |
| 679 | C2×D4 | — | 14 | 2 | no | — |
| 680 | C2×D4 | — | 14 | 2 | no | — |
| 681 | C2×D4 | — | 14 | 2 | no | — |
| 682 | C2×D4 | — | 14 | 2 | no | — |
| 683 | C2×D4 | — | 14 | 2 | no | — |
| 684 | C2×D4 | — | 14 | 2 | no | — |
| 685 | C2×D4 | — | 14 | 2 | no | — |
| 686 | C2×D4 | — | 14 | 2 | no | — |
| 687 | C2×D4 | — | 14 | 2 | no | — |
| 688 | C2×D4 | — | 14 | 1 | no | — |
| 689 | C2×D4 | — | 14 | 1 | no | — |
| 690 | C2×D4 | — | 28 | 4 | no | — |
| 691 | C2×D4 | — | 28 | 4 | no | — |
| 692 | C2×D4 | — | 28 | 4 | no | — |
| 693 | C2×D4 | — | 28 | 4 | no | — |
| 694 | C2×D4 | — | 28 | 4 | no | — |
| 695 | C2×D4 | — | 28 | 4 | no | — |
| 696 | C2×D4 | — | 28 | 4 | no | — |
| 697 | C2×D4 | — | 28 | 4 | no | — |
| 698 | C2×D4 | — | 56 | 1 | no | — |
| 699 | C2×D4 | — | 56 | 1 | no | — |
| 700 | C2×D4 | — | 56 | 1 | no | — |
| 701 | C2×D4 | — | 56 | 2 | no | — |
| 702 | C2×D4 | — | 56 | 2 | no | — |
| 703 | C2×D4 | — | 56 | 2 | no | — |
| 704 | C2×D4 | — | 56 | 2 | no | — |
| 705 | C2×D4 | — | 56 | 2 | no | — |
| 706 | C22×C4 | — | 2 | 1 | no | — |
| 707 | C22×C4 | — | 2 | 1 | no | — |
| 708 | C22×C4 | — | 2 | 2 | no | — |
| 709 | C22×C4 | — | 7 | 1 | no | — |
| 710 | C22×C4 | — | 7 | 2 | no | — |
| 711 | C22×C4 | — | 7 | 1 | no | — |
| 712 | C22×C4 | — | 7 | 1 | no | — |
| 713 | C22×C4 | — | 8 | 1 | no | — |
| 714 | C22×C4 | — | 14 | 2 | no | — |
| 715 | C22×C4 | — | 14 | 2 | no | — |
| 716 | C22×C4 | — | 14 | 2 | no | — |
| 717 | C22×C4 | — | 14 | 1 | no | — |
| 718 | C22×C4 | — | 14 | 1 | no | — |
| 719 | C22×C4 | — | 14 | 2 | no | — |
| 720 | C22×C4 | — | 14 | 1 | no | — |
| 721 | C22×C4 | — | 14 | 1 | no | — |
| 722 | C22×C4 | — | 14 | 1 | no | — |
| 723 | C22×C4 | — | 56 | 1 | no | — |
| 724 | C22×C4 | — | 56 | 1 | no | — |
| 725 | C22×C4 | C2×D28 | 1 | 2 | yes | — |
| 726 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 727 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 728 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 729 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 730 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 731 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 732 | C4⋊C4 | — | 2 | 1 | no | — |
| 733 | C4⋊C4 | — | 2 | 1 | no | — |
| 734 | C4⋊C4 | — | 8 | 1 | no | — |
| 735 | C4⋊C4 | — | 14 | 2 | no | — |
| 736 | C4⋊C4 | — | 14 | 2 | no | — |
| 737 | C4⋊C4 | — | 14 | 1 | no | — |
| 738 | C4⋊C4 | — | 14 | 1 | no | — |
| 739 | C4⋊C4 | — | 14 | 1 | no | — |
| 740 | C4⋊C4 | — | 14 | 1 | no | — |
| 741 | C4⋊C4 | — | 56 | 1 | no | — |
| 742 | C4⋊C4 | — | 56 | 1 | no | — |
| 743 | C22⋊C4 | — | 2 | 1 | no | — |
| 744 | C22⋊C4 | — | 2 | 2 | no | — |
| 745 | C22⋊C4 | — | 2 | 2 | no | — |
| 746 | C22⋊C4 | — | 2 | 2 | no | — |
| 747 | C22⋊C4 | — | 2 | 1 | no | — |
| 748 | C22⋊C4 | — | 2 | 2 | no | — |
| 749 | C22⋊C4 | — | 2 | 1 | no | — |
| 750 | C22⋊C4 | — | 14 | 4 | no | — |
| 751 | C22⋊C4 | — | 14 | 2 | no | — |
| 752 | C22⋊C4 | — | 14 | 2 | no | — |
| 753 | C22⋊C4 | — | 14 | 2 | no | — |
| 754 | C22⋊C4 | — | 14 | 2 | no | — |
| 755 | C22⋊C4 | — | 14 | 1 | no | — |
| 756 | C22⋊C4 | — | 14 | 1 | no | — |
| 757 | C22⋊C4 | — | 14 | 2 | no | — |
| 758 | C22⋊C4 | — | 14 | 1 | no | — |
| 759 | C22⋊C4 | — | 14 | 1 | no | — |
| 760 | C22⋊C4 | — | 14 | 2 | no | — |
| 761 | C22⋊C4 | — | 14 | 2 | no | — |
| 762 | C22⋊C4 | — | 14 | 2 | no | — |
| 763 | C22⋊C4 | — | 28 | 4 | no | — |
| 764 | C22⋊C4 | — | 28 | 4 | no | — |
| 765 | C22⋊C4 | — | 28 | 1 | no | — |
| 766 | C22⋊C4 | — | 28 | 1 | no | — |
| 767 | C22⋊C4 | — | 28 | 1 | no | — |
| 768 | C22⋊C4 | — | 28 | 1 | no | — |
| 769 | C22⋊C4 | — | 56 | 1 | no | — |
| 770 | C22⋊C4 | — | 56 | 1 | no | — |
| 771 | C22⋊C4 | — | 56 | 1 | no | — |
| 772 | C22⋊C4 | — | 56 | 2 | no | — |
| 773 | C22⋊C4 | — | 56 | 2 | no | — |
| 774 | C22⋊C4 | D4×D7 | 1 | 2 | yes | complemented |
| 775 | C42 | — | 8 | 1 | no | — |
| 776 | C42 | — | 14 | 1 | no | — |
| 777 | C42 | — | 14 | 1 | no | — |
| 778 | C2×C7 | — | 2 | 1 | no | — |
| 779 | C2×C7 | — | 2 | 1 | no | — |
| 780 | C2×C7 | — | 2 | 1 | no | — |
| 781 | C2×C7 | — | 2 | 1 | no | — |
| 782 | C2×C7 | — | 2 | 1 | no | — |
| 783 | C2×C7 | — | 2 | 1 | no | — |
| 784 | C2×C7 | — | 8 | 2 | no | — |
| 785 | C2×C7 | #2408 | 1 | 1 | yes | characteristic |
| 786 | C2×C7 | #3026 | 1 | 1 | yes | characteristic |
| 787 | C2×C7 | #3027 | 1 | 1 | yes | characteristic |
| 788 | D7 | — | 4 | 2 | no | — |
| 789 | D7 | — | 8 | 2 | no | — |
| 790 | D7 | — | 8 | 2 | no | — |
| 791 | C23 | — | 2 | 2 | no | — |
| 792 | C23 | — | 2 | 2 | no | — |
| 793 | C23 | — | 2 | 2 | no | — |
| 794 | C23 | — | 4 | 1 | no | — |
| 795 | C23 | — | 4 | 1 | no | — |
| 796 | C23 | — | 4 | 2 | no | — |
| 797 | C23 | — | 4 | 2 | no | — |
| 798 | C23 | — | 7 | 2 | no | — |
| 799 | C23 | — | 14 | 1 | no | — |
| 800 | C23 | — | 14 | 1 | no | — |
| 801 | C23 | — | 14 | 2 | no | — |
| 802 | C23 | — | 14 | 2 | no | — |
| 803 | C23 | — | 14 | 2 | no | — |
| 804 | C23 | — | 14 | 2 | no | — |
| 805 | C23 | — | 14 | 2 | no | — |
| 806 | C23 | — | 14 | 2 | no | — |
| 807 | C23 | — | 28 | 1 | no | — |
| 808 | C23 | — | 28 | 1 | no | — |
| 809 | C23 | — | 28 | 1 | no | — |
| 810 | C23 | — | 28 | 1 | no | — |
| 811 | C23 | — | 28 | 1 | no | — |
| 812 | C23 | — | 28 | 2 | no | — |
| 813 | C23 | — | 28 | 2 | no | — |
| 814 | C23 | — | 28 | 1 | no | — |
| 815 | C23 | — | 28 | 2 | no | — |
| 816 | C23 | — | 28 | 2 | no | — |
| 817 | C23 | — | 28 | 2 | no | — |
| 818 | C23 | — | 28 | 2 | no | — |
| 819 | C23 | — | 28 | 4 | no | — |
| 820 | C23 | — | 28 | 1 | no | — |
| 821 | C23 | — | 28 | 1 | no | — |
| 822 | C23 | — | 28 | 1 | no | — |
| 823 | C23 | — | 28 | 1 | no | — |
| 824 | C23 | — | 56 | 2 | no | — |
| 825 | C23 | — | 56 | 2 | no | — |
| 826 | C23 | — | 56 | 2 | no | — |
| 827 | C23 | — | 56 | 2 | no | — |
| 828 | C23 | — | 56 | 2 | no | — |
| 829 | C23 | — | 56 | 2 | no | — |
| 830 | C23 | C22×D28 | 1 | 1 | yes | characteristic |
| 831 | C23 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 832 | C23 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 833 | C23 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 834 | C23 | #6548 | 1 | 1 | yes | characteristic |
| 835 | C23 | D7×#41 | 1 | 1 | yes | characteristic |
| 836 | C23 | #6553 | 1 | 1 | yes | characteristic |
| 837 | Q8 | — | 28 | 4 | no | — |
| 838 | D4 | — | 4 | 2 | no | — |
| 839 | D4 | — | 4 | 2 | no | — |
| 840 | D4 | — | 4 | 2 | no | — |
| 841 | D4 | — | 4 | 2 | no | — |
| 842 | D4 | — | 4 | 2 | no | — |
| 843 | D4 | — | 8 | 1 | no | — |
| 844 | D4 | — | 14 | 2 | no | — |
| 845 | D4 | — | 14 | 2 | no | — |
| 846 | D4 | — | 14 | 2 | no | — |
| 847 | D4 | — | 14 | 2 | no | — |
| 848 | D4 | — | 28 | 2 | no | — |
| 849 | D4 | — | 28 | 4 | no | — |
| 850 | D4 | — | 28 | 4 | no | — |
| 851 | D4 | — | 28 | 4 | no | — |
| 852 | D4 | — | 28 | 2 | no | — |
| 853 | D4 | — | 28 | 2 | no | — |
| 854 | D4 | — | 28 | 2 | no | — |
| 855 | D4 | — | 28 | 2 | no | — |
| 856 | D4 | — | 56 | 1 | no | — |
| 857 | D4 | — | 56 | 4 | no | — |
| 858 | D4 | — | 56 | 8 | no | — |
| 859 | D4 | — | 56 | 2 | no | — |
| 860 | D4 | — | 56 | 2 | no | — |
| 861 | D4 | — | 56 | 8 | no | — |
| 862 | C2×C4 | — | 2 | 2 | no | — |
| 863 | C2×C4 | — | 2 | 2 | no | — |
| 864 | C2×C4 | — | 2 | 2 | no | — |
| 865 | C2×C4 | — | 2 | 2 | no | — |
| 866 | C2×C4 | — | 4 | 1 | no | — |
| 867 | C2×C4 | — | 4 | 1 | no | — |
| 868 | C2×C4 | — | 4 | 1 | no | — |
| 869 | C2×C4 | — | 4 | 1 | no | — |
| 870 | C2×C4 | — | 4 | 1 | no | — |
| 871 | C2×C4 | — | 4 | 1 | no | — |
| 872 | C2×C4 | — | 4 | 1 | no | — |
| 873 | C2×C4 | — | 4 | 1 | no | — |
| 874 | C2×C4 | — | 4 | 1 | no | — |
| 875 | C2×C4 | — | 4 | 1 | no | — |
| 876 | C2×C4 | — | 4 | 2 | no | — |
| 877 | C2×C4 | — | 4 | 2 | no | — |
| 878 | C2×C4 | — | 4 | 2 | no | — |
| 879 | C2×C4 | — | 4 | 1 | no | — |
| 880 | C2×C4 | — | 7 | 2 | no | — |
| 881 | C2×C4 | — | 14 | 1 | no | — |
| 882 | C2×C4 | — | 14 | 1 | no | — |
| 883 | C2×C4 | — | 14 | 2 | no | — |
| 884 | C2×C4 | — | 14 | 1 | no | — |
| 885 | C2×C4 | — | 14 | 1 | no | — |
| 886 | C2×C4 | — | 14 | 2 | no | — |
| 887 | C2×C4 | — | 14 | 2 | no | — |
| 888 | C2×C4 | — | 28 | 2 | no | — |
| 889 | C2×C4 | — | 28 | 4 | no | — |
| 890 | C2×C4 | — | 28 | 4 | no | — |
| 891 | C2×C4 | — | 28 | 4 | no | — |
| 892 | C2×C4 | — | 28 | 1 | no | — |
| 893 | C2×C4 | — | 28 | 1 | no | — |
| 894 | C2×C4 | — | 28 | 1 | no | — |
| 895 | C2×C4 | — | 28 | 2 | no | — |
| 896 | C2×C4 | — | 28 | 2 | no | — |
| 897 | C2×C4 | — | 28 | 2 | no | — |
| 898 | C2×C4 | — | 28 | 1 | no | — |
| 899 | C2×C4 | — | 28 | 2 | no | — |
| 900 | C2×C4 | — | 28 | 1 | no | — |
| 901 | C2×C4 | — | 28 | 2 | no | — |
| 902 | C2×C4 | — | 56 | 1 | no | — |
| 903 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 904 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 905 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 906 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 907 | C7 | #24262 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 908 | C22 | — | 2 | 1 | no | — |
| 909 | C22 | — | 2 | 1 | no | — |
| 910 | C22 | — | 2 | 1 | no | — |
| 911 | C22 | — | 2 | 1 | no | — |
| 912 | C22 | — | 2 | 1 | no | — |
| 913 | C22 | — | 2 | 1 | no | — |
| 914 | C22 | — | 4 | 1 | no | — |
| 915 | C22 | — | 4 | 1 | no | — |
| 916 | C22 | — | 4 | 1 | no | — |
| 917 | C22 | — | 4 | 1 | no | — |
| 918 | C22 | — | 4 | 2 | no | — |
| 919 | C22 | — | 4 | 2 | no | — |
| 920 | C22 | — | 4 | 2 | no | — |
| 921 | C22 | — | 8 | 2 | no | — |
| 922 | C22 | — | 8 | 2 | no | — |
| 923 | C22 | — | 14 | 2 | no | — |
| 924 | C22 | — | 28 | 2 | no | — |
| 925 | C22 | — | 28 | 2 | no | — |
| 926 | C22 | — | 28 | 4 | no | — |
| 927 | C22 | — | 28 | 4 | no | — |
| 928 | C22 | — | 28 | 2 | no | — |
| 929 | C22 | — | 28 | 1 | no | — |
| 930 | C22 | — | 28 | 1 | no | — |
| 931 | C22 | — | 28 | 2 | no | — |
| 932 | C22 | — | 28 | 2 | no | — |
| 933 | C22 | — | 28 | 2 | no | — |
| 934 | C22 | — | 28 | 2 | no | — |
| 935 | C22 | — | 56 | 1 | no | — |
| 936 | C22 | — | 56 | 2 | no | — |
| 937 | C22 | — | 56 | 2 | no | — |
| 938 | C22 | — | 56 | 1 | no | — |
| 939 | C22 | — | 56 | 1 | no | — |
| 940 | C22 | — | 56 | 2 | no | — |
| 941 | C22 | — | 56 | 2 | no | — |
| 942 | C22 | — | 56 | 1 | no | — |
| 943 | C22 | — | 56 | 1 | no | — |
| 944 | C22 | — | 112 | 4 | no | — |
| 945 | C22 | C2×#6445 | 1 | 1 | yes | characteristic |
| 946 | C22 | D4×D28 | 1 | 1 | yes | characteristic |
| 947 | C22 | #90245 | 1 | 1 | yes | characteristic |
| 948 | C22 | D7×#121 | 1 | 1 | yes | characteristic |
| 949 | C22 | #90298 | 1 | 1 | yes | characteristic |
| 950 | C22 | #90367 | 1 | 1 | yes | characteristic |
| 951 | C22 | #90408 | 1 | 1 | yes | characteristic |
| 952 | C4 | — | 2 | 1 | no | — |
| 953 | C4 | — | 2 | 1 | no | — |
| 954 | C4 | — | 2 | 1 | no | — |
| 955 | C4 | — | 2 | 1 | no | — |
| 956 | C4 | — | 4 | 2 | no | — |
| 957 | C4 | — | 4 | 2 | no | — |
| 958 | C4 | — | 8 | 2 | no | — |
| 959 | C4 | — | 8 | 1 | no | — |
| 960 | C4 | — | 14 | 2 | no | — |
| 961 | C4 | — | 28 | 1 | no | — |
| 962 | C4 | — | 28 | 1 | no | — |
| 963 | C4 | — | 28 | 2 | no | — |
| 964 | C4 | — | 56 | 2 | no | — |
| 965 | C4 | — | 56 | 1 | no | — |
| 966 | C2 | — | 2 | 1 | no | — |
| 967 | C2 | — | 2 | 1 | no | — |
| 968 | C2 | — | 2 | 1 | no | — |
| 969 | C2 | — | 2 | 1 | no | — |
| 970 | C2 | — | 2 | 1 | no | — |
| 971 | C2 | — | 2 | 1 | no | — |
| 972 | C2 | — | 8 | 2 | no | — |
| 973 | C2 | — | 28 | 2 | no | — |
| 974 | C2 | — | 56 | 2 | no | — |
| 975 | C2 | — | 56 | 2 | no | — |
| 976 | C2 | #11733881 | 1 | 1 | yes | characteristic |
| 977 | C2 | #11736131 | 1 | 1 | yes | characteristic |
| 978 | C2 | #11736136 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#6445 |
| commutator, cosocle | C24×C7 | C24 |
| Frattini | C24 | C23×D7 |
| Fitting | C7×#1964 | C2 |
| socle | C22×C7 | C2×#120 |
| hypercenter | #1964 | D7 |
| hypocenter | C7 | #24262 |
| LCS | G ▷ C24×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ #1964 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11743018 | C2 | semidirect |
| 2. #11740155 | C2 | semidirect |
| 3. C2×#89513 | C2 | semidirect |
| 4. #11731476 | C2 | semidirect |
| 5. #11731014 | C2 | semidirect |
| 6. C7×#1964 | C2 | semidirect |
| 7. #11727791 | C2 | semidirect |
| 8. #11727787 | C2 | semidirect |
| 9. #11727786 | C2 | semidirect |
| 10. #11727284 | C2 | semidirect |
| 11. #11727210 | C2 | semidirect |
| 16. C2×#6500 | C22 | semidirect |
| 19. C22×(C2×D7)⋊C4 | C22 | semidirect |
| 30. C2×#6445 | C22 | semidirect |
| 31. C2×C7×#99 | C22 | semidirect |
| 32. C2×C7×#99 | C22 | semidirect |
| 33. C7×#380 | C22 | semidirect |
| 34. C4×C7×C22⋊C4 | C22 | semidirect |
| 36. #89992 | C22 | semidirect |
| 37. #89984 | C22 | semidirect |
| 42. #89730 | C22 | semidirect |
| 43. #89727 | C22 | semidirect |
| 45. C2×#6380 | C22 | semidirect |
| 46. C2×#6380 | C22 | semidirect |
| 47. #89722 | C22 | semidirect |
| 55. #89322 | C22 | semidirect |
| 58. C22×C7×D4 | D4 | semidirect |
| 78. C22×D28 | D4 | semidirect |
| 79. C22×C4×D7 | D4 | semidirect |
| 85. C2×C7×C4⋊C4 | D4 | semidirect |
| 86. C2×C7×C22⋊C4 | D4 | semidirect |
| 128. C2×(C2×D7)⋊C4 | D4 | semidirect |
| 129. C2×(C2×D7)⋊C4 | D4 | semidirect |
| 132. C2×C4⋊Dic7 | D4 | semidirect |
| 133. C2×Dic7⋊C4 | D4 | semidirect |
| 134. C2×C4×Dic7 | D4 | semidirect |
| 149. #6445 | D4 | semidirect |
| 173. #1964 | D7 | semidirect |
| 189. C23×D7 | C2×D4 | semidirect |
| 278. C7×C22⋊C4 | C2×D4 | semidirect |
| 337. C2×#99 | C2×D7 | semidirect |
| 338. C2×#99 | C2×D7 | semidirect |
| 354. #380 | C2×D7 | semidirect |
| 356. C4×C22⋊C4 | C2×D7 | semidirect |
| 492. C22×D4 | D28 | semidirect |
| 544. C2×C4⋊C4 | D28 | semidirect |
| 564. C2×C22⋊C4 | D28 | semidirect |
| 774. C22⋊C4 | D4×D7 | semidirect |
| 907. C7 | #24262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11743018 | 2 |
| #11740155 | 2 |
| C2×#89513 | 2 |
| #11731476 | 2 |
| #11731014 | 2 |
| C7×#1964 | 2 |
| #11727791 | 2 |
| #11727787 | 2 |
| #11727786 | 2 |
| #11727284 | 2 |
| #11727210 | 2 |
| #24262 | 7 |