Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2570 conjugacy classes of subgroups.
The subgroup lattice has 476 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#90318 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C7×#2817 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11740278 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11735846 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #11735574 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #11735171 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11734902 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #11734719 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #11734614 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #11731589 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11731495 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C22×#1161 | C22 | 1 | 2 | yes | — |
| 13 | C23×C4×D7 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C7×C22⋊Q8 | C22 | 1 | 2 | yes | — |
| 15 | C2×#6509 | C22 | 1 | 2 | yes | — |
| 16 | C2×#6493 | C22 | 1 | 2 | yes | — |
| 17 | #90318 | — | 2 | 16 | no | — |
| 18 | C2×#6458 | C22 | 1 | 2 | yes | — |
| 19 | C2×#6457 | C22 | 1 | 4 | yes | — |
| 20 | C2×#6456 | C22 | 1 | 4 | yes | — |
| 21 | C2×#6456 | C22 | 1 | 4 | yes | complemented |
| 22 | C2×#6455 | C22 | 1 | 2 | yes | — |
| 23 | C2×#6445 | C22 | 1 | 4 | yes | — |
| 24 | C2×(C22⋊D7)⋊C4 | C22 | 1 | 4 | yes | — |
| 25 | C2×#6440 | C22 | 1 | 2 | yes | — |
| 26 | C7×#400 | C22 | 1 | 4 | yes | complemented |
| 27 | C7×#397 | C22 | 1 | 4 | yes | — |
| 28 | C7×#395 | C22 | 1 | 4 | yes | complemented |
| 29 | C7×#381 | C22 | 1 | 1 | yes | characteristic |
| 30 | #90003 | C22 | 1 | 4 | yes | complemented |
| 31 | #89983 | C22 | 1 | 1 | yes | characteristic |
| 32 | #89764 | C22 | 1 | 4 | yes | complemented |
| 33 | #89763 | C22 | 1 | 8 | yes | — |
| 34 | #89763 | C22 | 1 | 4 | yes | complemented |
| 35 | #89755 | C22 | 1 | 4 | yes | complemented |
| 36 | #89752 | C22 | 1 | 4 | yes | complemented |
| 37 | #89732 | C22 | 1 | 4 | yes | — |
| 38 | #89731 | C22 | 1 | 8 | yes | — |
| 39 | #89727 | C22 | 1 | 2 | yes | — |
| 40 | #89448 | C22 | 1 | 8 | yes | complemented |
| 41 | #89447 | C22 | 1 | 8 | yes | — |
| 42 | #89446 | C22 | 1 | 4 | yes | complemented |
| 43 | #89444 | C22 | 1 | 8 | yes | — |
| 44 | #89444 | C22 | 1 | 4 | yes | complemented |
| 45 | #89443 | C22 | 1 | 8 | yes | — |
| 46 | #89443 | C22 | 1 | 4 | yes | complemented |
| 47 | #89439 | C22 | 1 | 4 | yes | — |
| 48 | #89438 | C22 | 1 | 4 | yes | — |
| 49 | #89438 | C22 | 1 | 8 | yes | complemented |
| 50 | #89421 | C22 | 1 | 4 | yes | complemented |
| 51 | #36652 | — | 7 | 1 | no | maximal, Sylow |
| 52 | C24×D7 | C23 | 1 | 1 | yes | characteristic |
| 53 | C22×C7×Q8 | C23 | 1 | 2 | yes | — |
| 54 | C23×C4×C7 | C23 | 1 | 1 | yes | characteristic |
| 55 | C22×C22⋊D7 | C23 | 1 | 4 | yes | — |
| 56 | C23×Dic7 | C23 | 1 | 1 | yes | characteristic |
| 57 | C2×#1161 | — | 2 | 8 | no | — |
| 58 | C2×#1161 | — | 4 | 8 | no | — |
| 59 | C22×D28 | C23 | 1 | 4 | yes | — |
| 60 | C22×D28 | C23 | 1 | 4 | yes | — |
| 61 | C22×D28 | C23 | 1 | 2 | yes | — |
| 62 | C22×D28 | C23 | 1 | 4 | yes | — |
| 63 | C22×C4×D7 | — | 4 | 4 | no | — |
| 64 | C22×C4×D7 | D4 | 1 | 8 | yes | complemented |
| 65 | C22×C4×D7 | C23 | 1 | 4 | yes | — |
| 66 | C22×C4×D7 | C23 | 1 | 2 | yes | — |
| 67 | C22×C4×D7 | C23 | 1 | 2 | yes | — |
| 68 | C7×C22⋊Q8 | — | 2 | 8 | no | — |
| 69 | C2×C7×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 70 | C2×C7×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 71 | C2×C7×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 72 | C2×C7×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 73 | C2×C7×C22⋊C4 | C23 | 1 | 2 | yes | — |
| 74 | C2×C22⋊Dic7 | C23 | 1 | 2 | yes | — |
| 75 | #6509 | — | 2 | 8 | no | — |
| 76 | #6493 | — | 2 | 8 | no | — |
| 77 | C2×(C2×D7)⋊C4 | C23 | 1 | 4 | yes | — |
| 78 | C2×(C2×D7)⋊C4 | C23 | 1 | 4 | yes | — |
| 79 | C2×(C2×D7)⋊C4 | C23 | 1 | 4 | yes | — |
| 80 | C2×(C2×D7)⋊C4 | C23 | 1 | 4 | yes | — |
| 81 | C2×(C2×D7)⋊C4 | C23 | 1 | 8 | yes | — |
| 82 | C2×(C2×D7)⋊C4 | C23 | 1 | 8 | yes | — |
| 83 | C2×(C2×D7)⋊C4 | C23 | 1 | 8 | yes | — |
| 84 | C2×(C2×D7)⋊C4 | C23 | 1 | 8 | yes | — |
| 85 | C2×C4⋊Dic7 | C23 | 1 | 2 | yes | — |
| 86 | C2×Dic7⋊C4 | C23 | 1 | 4 | yes | — |
| 87 | C2×Dic7⋊C4 | C23 | 1 | 4 | yes | — |
| 88 | C2×Dic7⋊C4 | C23 | 1 | 8 | yes | — |
| 89 | C2×C4×Dic7 | C23 | 1 | 4 | yes | — |
| 90 | C2×C4×Dic7 | C23 | 1 | 4 | yes | — |
| 91 | #6458 | — | 2 | 8 | no | — |
| 92 | #6457 | — | 2 | 16 | no | — |
| 93 | #6456 | — | 2 | 16 | no | — |
| 94 | #6456 | — | 4 | 8 | no | — |
| 95 | #6455 | — | 2 | 8 | no | — |
| 96 | #6445 | — | 2 | 16 | no | — |
| 97 | (C22⋊D7)⋊C4 | — | 2 | 16 | no | — |
| 98 | #6440 | — | 4 | 4 | no | — |
| 99 | C7×#95 | C23 | 1 | 4 | yes | — |
| 100 | C7×#95 | C23 | 1 | 4 | yes | — |
| 101 | C7×#95 | C23 | 1 | 8 | yes | — |
| 102 | C7⋊#95 | C23 | 1 | 4 | yes | — |
| 103 | C7⋊#95 | C23 | 1 | 4 | yes | — |
| 104 | C7⋊#95 | C23 | 1 | 8 | yes | — |
| 105 | C2×#525 | — | 7 | 2 | no | — |
| 106 | #2817 | D7 | 1 | 1 | yes | characteristic, complemented |
| 107 | #2816 | — | 7 | 2 | no | — |
| 108 | #2815 | — | 7 | 1 | no | — |
| 109 | #2814 | — | 7 | 4 | no | — |
| 110 | #2813 | — | 7 | 4 | no | — |
| 111 | #2812 | — | 7 | 4 | no | — |
| 112 | #2395 | — | 7 | 4 | no | — |
| 113 | #2392 | — | 7 | 4 | no | — |
| 114 | #2388 | — | 7 | 4 | no | — |
| 115 | #2280 | — | 7 | 1 | no | — |
| 116 | C24×C7 | C24 | 1 | 1 | yes | characteristic |
| 117 | C23×D7 | — | 4 | 2 | no | — |
| 118 | C23×D7 | — | 4 | 4 | no | — |
| 119 | C23×D7 | C2×D4 | 1 | 4 | yes | — |
| 120 | C23×D7 | C24 | 1 | 4 | yes | — |
| 121 | C23×D7 | C24 | 1 | 2 | yes | — |
| 122 | C2×C7×Q8 | — | 2 | 4 | no | — |
| 123 | C2×C7×Q8 | — | 4 | 4 | no | — |
| 124 | C22×C4×C7 | — | 4 | 2 | no | — |
| 125 | C22×C4×C7 | C2×D4 | 1 | 4 | yes | — |
| 126 | C22×C4×C7 | C24 | 1 | 4 | yes | — |
| 127 | C22×C4×C7 | C24 | 1 | 4 | yes | — |
| 128 | C22×C4×C7 | C24 | 1 | 4 | yes | — |
| 129 | C22×C4×C7 | C24 | 1 | 2 | yes | — |
| 130 | C2×C22⋊D7 | — | 2 | 8 | no | — |
| 131 | C2×C22⋊D7 | — | 4 | 8 | no | — |
| 132 | C22×Dic7 | — | 2 | 4 | no | — |
| 133 | C22×Dic7 | C2×D4 | 1 | 4 | yes | — |
| 134 | C22×Dic7 | C24 | 1 | 4 | yes | — |
| 135 | C22×Dic7 | C24 | 1 | 4 | yes | — |
| 136 | C22×Dic7 | C24 | 1 | 1 | yes | characteristic |
| 137 | C22×Dic7 | C24 | 1 | 1 | yes | characteristic |
| 138 | #1161 | — | 4 | 32 | no | — |
| 139 | C2×D28 | — | 2 | 8 | no | — |
| 140 | C2×D28 | — | 2 | 8 | no | — |
| 141 | C2×D28 | — | 2 | 4 | no | — |
| 142 | C2×D28 | — | 4 | 4 | no | — |
| 143 | C2×D28 | — | 4 | 4 | no | — |
| 144 | C2×D28 | — | 4 | 4 | no | — |
| 145 | C2×D28 | — | 4 | 8 | no | — |
| 146 | C2×D28 | — | 4 | 4 | no | — |
| 147 | C2×D28 | — | 4 | 8 | no | — |
| 148 | C2×C4×D7 | — | 2 | 8 | no | — |
| 149 | C2×C4×D7 | — | 2 | 8 | no | — |
| 150 | C2×C4×D7 | — | 2 | 16 | no | — |
| 151 | C2×C4×D7 | — | 4 | 16 | no | — |
| 152 | C2×C4×D7 | — | 4 | 4 | no | — |
| 153 | C2×C4×D7 | C2×D4 | 1 | 8 | yes | — |
| 154 | C2×C4×D7 | C2×D4 | 1 | 8 | yes | — |
| 155 | C7×C4⋊C4 | — | 2 | 4 | no | — |
| 156 | C7×C4⋊C4 | — | 2 | 8 | no | — |
| 157 | C7×C4⋊C4 | — | 4 | 4 | no | — |
| 158 | C7×C22⋊C4 | — | 2 | 8 | no | — |
| 159 | C7×C22⋊C4 | — | 4 | 2 | no | — |
| 160 | C22⋊Dic7 | — | 4 | 2 | no | — |
| 161 | (C2×D7)⋊C4 | — | 2 | 8 | no | — |
| 162 | (C2×D7)⋊C4 | — | 2 | 8 | no | — |
| 163 | (C2×D7)⋊C4 | — | 2 | 8 | no | — |
| 164 | (C2×D7)⋊C4 | — | 2 | 8 | no | — |
| 165 | (C2×D7)⋊C4 | — | 4 | 8 | no | — |
| 166 | (C2×D7)⋊C4 | — | 4 | 8 | no | — |
| 167 | (C2×D7)⋊C4 | — | 4 | 8 | no | — |
| 168 | (C2×D7)⋊C4 | — | 4 | 8 | no | — |
| 169 | C4⋊Dic7 | — | 2 | 4 | no | — |
| 170 | Dic7⋊C4 | — | 2 | 8 | no | — |
| 171 | Dic7⋊C4 | — | 4 | 4 | no | — |
| 172 | Dic7⋊C4 | — | 4 | 8 | no | — |
| 173 | C4×Dic7 | — | 2 | 8 | no | — |
| 174 | C4×Dic7 | — | 2 | 8 | no | — |
| 175 | C22×#41 | — | 7 | 2 | no | — |
| 176 | C24×C4 | — | 7 | 1 | no | — |
| 177 | #525 | — | 14 | 16 | no | — |
| 178 | C2×#123 | — | 7 | 4 | no | — |
| 179 | C2×C22⋊Q8 | — | 7 | 2 | no | — |
| 180 | C2×C22⋊Q8 | C2×D7 | 1 | 2 | yes | — |
| 181 | C2×#121 | — | 7 | 2 | no | — |
| 182 | C2×#121 | — | 7 | 2 | no | — |
| 183 | C2×#120 | — | 7 | 4 | no | — |
| 184 | C2×C4×D4 | — | 7 | 4 | no | — |
| 185 | C2×C4×D4 | — | 7 | 4 | no | — |
| 186 | C2×C4×D4 | — | 7 | 4 | no | — |
| 187 | C2×#117 | — | 7 | 2 | no | — |
| 188 | C2×#117 | — | 7 | 2 | no | — |
| 189 | #400 | C2×D7 | 1 | 4 | yes | complemented |
| 190 | #399 | — | 7 | 4 | no | — |
| 191 | #398 | — | 7 | 4 | no | — |
| 192 | #398 | — | 7 | 4 | no | — |
| 193 | #397 | — | 7 | 4 | no | — |
| 194 | #397 | — | 7 | 8 | no | — |
| 195 | #397 | C2×D7 | 1 | 4 | yes | — |
| 196 | #396 | — | 7 | 8 | no | — |
| 197 | #395 | C2×D7 | 1 | 4 | yes | complemented |
| 198 | #394 | — | 7 | 4 | no | — |
| 199 | #394 | — | 7 | 8 | no | — |
| 200 | #394 | — | 7 | 8 | no | — |
| 201 | #394 | — | 7 | 4 | no | — |
| 202 | #394 | — | 7 | 8 | no | — |
| 203 | #393 | — | 7 | 4 | no | — |
| 204 | #392 | — | 7 | 4 | no | — |
| 205 | #392 | — | 7 | 8 | no | — |
| 206 | #392 | — | 7 | 4 | no | — |
| 207 | #381 | — | 7 | 1 | no | — |
| 208 | #381 | C2×D7 | 1 | 1 | yes | characteristic |
| 209 | #380 | — | 7 | 4 | no | — |
| 210 | #379 | — | 7 | 2 | no | — |
| 211 | C4×C4⋊C4 | — | 7 | 4 | no | — |
| 212 | C4×C22⋊C4 | — | 7 | 8 | no | — |
| 213 | C4×C22⋊C4 | — | 7 | 4 | no | — |
| 214 | C23×C7 | — | 2 | 2 | no | — |
| 215 | C23×C7 | — | 2 | 4 | no | — |
| 216 | C23×C7 | C22×D4 | 1 | 2 | yes | — |
| 217 | C23×C7 | C25 | 1 | 1 | yes | characteristic |
| 218 | C22×D7 | — | 2 | 4 | no | — |
| 219 | C22×D7 | — | 2 | 4 | no | — |
| 220 | C22×D7 | — | 2 | 4 | no | — |
| 221 | C22×D7 | — | 2 | 4 | no | — |
| 222 | C22×D7 | — | 2 | 8 | no | — |
| 223 | C22×D7 | — | 2 | 4 | no | — |
| 224 | C22×D7 | — | 2 | 8 | no | — |
| 225 | C22×D7 | — | 2 | 4 | no | — |
| 226 | C22×D7 | — | 4 | 4 | no | — |
| 227 | C22×D7 | — | 4 | 8 | no | — |
| 228 | C22×D7 | — | 4 | 16 | no | — |
| 229 | C22×D7 | C22×D4 | 1 | 4 | yes | — |
| 230 | C7×Q8 | — | 4 | 8 | no | — |
| 231 | C2×C4×C7 | — | 2 | 4 | no | — |
| 232 | C2×C4×C7 | — | 2 | 4 | no | — |
| 233 | C2×C4×C7 | — | 2 | 4 | no | — |
| 234 | C2×C4×C7 | — | 2 | 4 | no | — |
| 235 | C2×C4×C7 | — | 2 | 8 | no | — |
| 236 | C2×C4×C7 | — | 2 | 4 | no | — |
| 237 | C2×C4×C7 | — | 2 | 4 | no | — |
| 238 | C2×C4×C7 | — | 2 | 8 | no | — |
| 239 | C2×C4×C7 | — | 4 | 4 | no | — |
| 240 | C2×C4×C7 | C22×D4 | 1 | 4 | yes | — |
| 241 | C22⋊D7 | — | 4 | 16 | no | — |
| 242 | C2×Dic7 | — | 2 | 2 | no | — |
| 243 | C2×Dic7 | — | 2 | 8 | no | — |
| 244 | C2×Dic7 | — | 2 | 4 | no | — |
| 245 | C2×Dic7 | — | 2 | 4 | no | — |
| 246 | C2×Dic7 | — | 2 | 8 | no | — |
| 247 | C2×Dic7 | — | 2 | 8 | no | — |
| 248 | C2×Dic7 | C22×D4 | 1 | 2 | yes | — |
| 249 | C2×Dic7 | C22×D4 | 1 | 2 | yes | — |
| 250 | C2×Dic7 | H(5,𝔽2) | 1 | 4 | yes | — |
| 251 | D28 | — | 4 | 8 | no | — |
| 252 | D28 | — | 4 | 16 | no | — |
| 253 | D28 | — | 4 | 16 | no | — |
| 254 | D28 | — | 4 | 16 | no | — |
| 255 | C4×D7 | — | 2 | 16 | no | — |
| 256 | C4×D7 | — | 4 | 8 | no | — |
| 257 | C4×D7 | — | 4 | 16 | no | — |
| 258 | C25 | — | 7 | 1 | no | — |
| 259 | C2×#41 | — | 14 | 8 | no | — |
| 260 | C2×#41 | — | 28 | 8 | no | — |
| 261 | C22×Q8 | C22×D7 | 1 | 2 | yes | — |
| 262 | C22×D4 | — | 7 | 4 | no | — |
| 263 | C22×D4 | — | 7 | 4 | no | — |
| 264 | C22×D4 | — | 7 | 4 | no | — |
| 265 | C22×D4 | — | 7 | 2 | no | — |
| 266 | C22×D4 | — | 7 | 4 | no | — |
| 267 | C23×C4 | — | 7 | 1 | no | — |
| 268 | C23×C4 | — | 7 | 2 | no | — |
| 269 | C23×C4 | — | 7 | 8 | no | — |
| 270 | C23×C4 | — | 7 | 2 | no | — |
| 271 | C23×C4 | — | 7 | 4 | no | — |
| 272 | C23×C4 | — | 28 | 4 | no | — |
| 273 | C23×C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 274 | #123 | — | 14 | 16 | no | — |
| 275 | C22⋊Q8 | — | 2 | 8 | no | — |
| 276 | C22⋊Q8 | — | 14 | 8 | no | — |
| 277 | #121 | — | 14 | 8 | no | — |
| 278 | #121 | — | 14 | 8 | no | — |
| 279 | #120 | — | 14 | 16 | no | — |
| 280 | C4×D4 | — | 14 | 16 | no | — |
| 281 | C4×D4 | — | 14 | 16 | no | — |
| 282 | C4×D4 | — | 28 | 8 | no | — |
| 283 | #117 | — | 14 | 8 | no | — |
| 284 | #117 | — | 28 | 4 | no | — |
| 285 | C2×C4⋊C4 | — | 7 | 2 | no | — |
| 286 | C2×C4⋊C4 | — | 7 | 4 | no | — |
| 287 | C2×C4⋊C4 | — | 7 | 4 | no | — |
| 288 | C2×C4⋊C4 | — | 7 | 8 | no | — |
| 289 | C2×C4⋊C4 | C22×D7 | 1 | 2 | yes | — |
| 290 | C2×C4⋊C4 | C22×D7 | 1 | 4 | yes | — |
| 291 | C2×C4⋊C4 | C22×D7 | 1 | 4 | yes | — |
| 292 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 293 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 294 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 295 | C2×C22⋊C4 | — | 7 | 4 | no | — |
| 296 | C2×C22⋊C4 | — | 7 | 2 | no | — |
| 297 | C2×C22⋊C4 | — | 7 | 8 | no | — |
| 298 | C2×C22⋊C4 | — | 7 | 8 | no | — |
| 299 | C2×C22⋊C4 | — | 7 | 8 | no | — |
| 300 | C2×C22⋊C4 | — | 7 | 8 | no | — |
| 301 | C2×C22⋊C4 | C22×D7 | 1 | 4 | yes | — |
| 302 | C2×C22⋊C4 | C22×D7 | 1 | 2 | yes | — |
| 303 | C2×C42 | — | 7 | 4 | no | — |
| 304 | C2×C42 | — | 7 | 4 | no | — |
| 305 | #95 | — | 7 | 4 | no | — |
| 306 | #95 | — | 7 | 8 | no | — |
| 307 | #95 | — | 7 | 4 | no | — |
| 308 | #95 | C22×D7 | 1 | 4 | yes | — |
| 309 | #95 | C22×D7 | 1 | 8 | yes | — |
| 310 | #95 | C22×D7 | 1 | 4 | yes | — |
| 311 | C22×C7 | — | 2 | 2 | no | — |
| 312 | C22×C7 | — | 2 | 4 | no | — |
| 313 | C22×C7 | — | 4 | 4 | no | — |
| 314 | C22×C7 | C23×D4 | 1 | 1 | yes | characteristic |
| 315 | C22×C7 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 316 | C22×C7 | #585 | 1 | 4 | yes | — |
| 317 | C2×D7 | — | 2 | 4 | no | — |
| 318 | C2×D7 | — | 2 | 4 | no | — |
| 319 | C2×D7 | — | 2 | 4 | no | — |
| 320 | C2×D7 | — | 4 | 16 | no | — |
| 321 | C2×D7 | — | 4 | 8 | no | — |
| 322 | C2×D7 | — | 4 | 4 | no | — |
| 323 | C2×D7 | — | 4 | 4 | no | — |
| 324 | C2×D7 | — | 4 | 4 | no | — |
| 325 | C2×D7 | — | 4 | 8 | no | — |
| 326 | C2×D7 | — | 4 | 8 | no | — |
| 327 | C4×C7 | — | 2 | 4 | no | — |
| 328 | C4×C7 | — | 4 | 4 | no | — |
| 329 | C4×C7 | — | 4 | 4 | no | — |
| 330 | C4×C7 | — | 4 | 4 | no | — |
| 331 | Dic7 | — | 2 | 2 | no | — |
| 332 | Dic7 | — | 4 | 4 | no | — |
| 333 | Dic7 | — | 4 | 4 | no | — |
| 334 | Dic7 | #534 | 1 | 4 | yes | — |
| 335 | C24 | — | 7 | 2 | no | — |
| 336 | C24 | — | 7 | 4 | no | — |
| 337 | C24 | — | 7 | 4 | no | — |
| 338 | C24 | — | 28 | 2 | no | — |
| 339 | C24 | — | 28 | 4 | no | — |
| 340 | C24 | C23×D7 | 1 | 1 | yes | characteristic |
| 341 | #41 | — | 28 | 32 | no | — |
| 342 | C2×Q8 | — | 2 | 4 | no | — |
| 343 | C2×Q8 | — | 4 | 4 | no | — |
| 344 | C2×D4 | — | 14 | 8 | no | — |
| 345 | C2×D4 | — | 14 | 8 | no | — |
| 346 | C2×D4 | — | 14 | 8 | no | — |
| 347 | C2×D4 | — | 14 | 4 | no | — |
| 348 | C2×D4 | — | 28 | 4 | no | — |
| 349 | C2×D4 | — | 28 | 4 | no | — |
| 350 | C2×D4 | — | 28 | 8 | no | — |
| 351 | C2×D4 | — | 28 | 4 | no | — |
| 352 | C2×D4 | — | 28 | 4 | no | — |
| 353 | C2×D4 | — | 28 | 8 | no | — |
| 354 | C2×D4 | — | 28 | 8 | no | — |
| 355 | C22×C4 | — | 4 | 2 | no | — |
| 356 | C22×C4 | — | 7 | 1 | no | — |
| 357 | C22×C4 | — | 7 | 4 | no | — |
| 358 | C22×C4 | — | 7 | 1 | no | — |
| 359 | C22×C4 | — | 7 | 8 | no | — |
| 360 | C22×C4 | — | 7 | 8 | no | — |
| 361 | C22×C4 | — | 7 | 4 | no | — |
| 362 | C22×C4 | — | 7 | 4 | no | — |
| 363 | C22×C4 | — | 14 | 8 | no | — |
| 364 | C22×C4 | — | 14 | 8 | no | — |
| 365 | C22×C4 | — | 14 | 16 | no | — |
| 366 | C22×C4 | — | 14 | 4 | no | — |
| 367 | C22×C4 | — | 28 | 4 | no | — |
| 368 | C22×C4 | — | 28 | 16 | no | — |
| 369 | C22×C4 | D4×D7 | 1 | 4 | yes | — |
| 370 | C22×C4 | C23×D7 | 1 | 4 | yes | — |
| 371 | C22×C4 | C23×D7 | 1 | 4 | yes | — |
| 372 | C22×C4 | C23×D7 | 1 | 4 | yes | — |
| 373 | C22×C4 | C23×D7 | 1 | 2 | yes | — |
| 374 | C4⋊C4 | — | 2 | 4 | no | — |
| 375 | C4⋊C4 | — | 2 | 8 | no | — |
| 376 | C4⋊C4 | — | 4 | 4 | no | — |
| 377 | C4⋊C4 | — | 14 | 8 | no | — |
| 378 | C4⋊C4 | — | 14 | 4 | no | — |
| 379 | C4⋊C4 | — | 28 | 8 | no | — |
| 380 | C4⋊C4 | — | 28 | 4 | no | — |
| 381 | C22⋊C4 | — | 2 | 8 | no | — |
| 382 | C22⋊C4 | — | 4 | 2 | no | — |
| 383 | C22⋊C4 | — | 14 | 8 | no | — |
| 384 | C22⋊C4 | — | 14 | 8 | no | — |
| 385 | C22⋊C4 | — | 14 | 8 | no | — |
| 386 | C22⋊C4 | — | 14 | 8 | no | — |
| 387 | C22⋊C4 | — | 28 | 8 | no | — |
| 388 | C22⋊C4 | — | 28 | 8 | no | — |
| 389 | C22⋊C4 | — | 28 | 8 | no | — |
| 390 | C22⋊C4 | — | 28 | 8 | no | — |
| 391 | C22⋊C4 | — | 28 | 2 | no | — |
| 392 | C42 | — | 14 | 8 | no | — |
| 393 | C42 | — | 14 | 8 | no | — |
| 394 | C2×C7 | — | 4 | 2 | no | — |
| 395 | C2×C7 | C2×#534 | 1 | 1 | yes | characteristic |
| 396 | C2×C7 | #3449 | 1 | 2 | yes | — |
| 397 | C2×C7 | #3529 | 1 | 4 | yes | — |
| 398 | D7 | — | 4 | 4 | no | — |
| 399 | D7 | — | 8 | 4 | no | — |
| 400 | C23 | — | 2 | 2 | no | — |
| 401 | C23 | — | 2 | 4 | no | — |
| 402 | C23 | — | 7 | 4 | no | — |
| 403 | C23 | — | 14 | 4 | no | — |
| 404 | C23 | — | 14 | 4 | no | — |
| 405 | C23 | — | 14 | 4 | no | — |
| 406 | C23 | — | 14 | 4 | no | — |
| 407 | C23 | — | 14 | 8 | no | — |
| 408 | C23 | — | 14 | 4 | no | — |
| 409 | C23 | — | 14 | 8 | no | — |
| 410 | C23 | — | 14 | 4 | no | — |
| 411 | C23 | — | 28 | 4 | no | — |
| 412 | C23 | — | 28 | 8 | no | — |
| 413 | C23 | — | 28 | 16 | no | — |
| 414 | C23 | C2×D4×D7 | 1 | 2 | yes | — |
| 415 | C23 | C24×D7 | 1 | 1 | yes | characteristic |
| 416 | Q8 | — | 4 | 8 | no | — |
| 417 | D4 | — | 28 | 8 | no | — |
| 418 | D4 | — | 28 | 16 | no | — |
| 419 | D4 | — | 28 | 16 | no | — |
| 420 | D4 | — | 28 | 16 | no | — |
| 421 | D4 | — | 28 | 16 | no | — |
| 422 | C2×C4 | — | 2 | 4 | no | — |
| 423 | C2×C4 | — | 2 | 4 | no | — |
| 424 | C2×C4 | — | 2 | 4 | no | — |
| 425 | C2×C4 | — | 2 | 4 | no | — |
| 426 | C2×C4 | — | 2 | 8 | no | — |
| 427 | C2×C4 | — | 2 | 4 | no | — |
| 428 | C2×C4 | — | 2 | 8 | no | — |
| 429 | C2×C4 | — | 2 | 4 | no | — |
| 430 | C2×C4 | — | 4 | 4 | no | — |
| 431 | C2×C4 | — | 7 | 2 | no | — |
| 432 | C2×C4 | — | 7 | 4 | no | — |
| 433 | C2×C4 | — | 7 | 2 | no | — |
| 434 | C2×C4 | — | 14 | 16 | no | — |
| 435 | C2×C4 | — | 14 | 8 | no | — |
| 436 | C2×C4 | — | 14 | 2 | no | — |
| 437 | C2×C4 | — | 14 | 4 | no | — |
| 438 | C2×C4 | — | 14 | 4 | no | — |
| 439 | C2×C4 | — | 14 | 8 | no | — |
| 440 | C2×C4 | — | 14 | 8 | no | — |
| 441 | C2×C4 | — | 28 | 8 | no | — |
| 442 | C2×C4 | — | 28 | 16 | no | — |
| 443 | C2×C4 | C2×D4×D7 | 1 | 4 | yes | — |
| 444 | C7 | #36652 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 445 | C22 | — | 2 | 2 | no | — |
| 446 | C22 | — | 2 | 4 | no | — |
| 447 | C22 | — | 4 | 4 | no | — |
| 448 | C22 | — | 14 | 4 | no | — |
| 449 | C22 | — | 14 | 4 | no | — |
| 450 | C22 | — | 14 | 4 | no | — |
| 451 | C22 | — | 28 | 16 | no | — |
| 452 | C22 | — | 28 | 8 | no | — |
| 453 | C22 | — | 28 | 4 | no | — |
| 454 | C22 | — | 28 | 4 | no | — |
| 455 | C22 | — | 28 | 4 | no | — |
| 456 | C22 | — | 28 | 8 | no | — |
| 457 | C22 | — | 28 | 8 | no | — |
| 458 | C22 | C22×D4×D7 | 1 | 1 | yes | characteristic |
| 459 | C22 | D7×H(5,𝔽2) | 1 | 2 | yes | — |
| 460 | C22 | #90620 | 1 | 4 | yes | — |
| 461 | C4 | — | 2 | 4 | no | — |
| 462 | C4 | — | 4 | 4 | no | — |
| 463 | C4 | — | 4 | 4 | no | — |
| 464 | C4 | — | 4 | 4 | no | — |
| 465 | C4 | — | 7 | 4 | no | — |
| 466 | C4 | — | 14 | 2 | no | — |
| 467 | C4 | — | 28 | 4 | no | — |
| 468 | C4 | — | 28 | 4 | no | — |
| 469 | C2 | — | 4 | 2 | no | — |
| 470 | C2 | — | 28 | 4 | no | — |
| 471 | C2 | — | 56 | 4 | no | — |
| 472 | C2 | D7×#534 | 1 | 1 | yes | characteristic |
| 473 | C2 | #11743406 | 1 | 2 | yes | — |
| 474 | C2 | #11744183 | 1 | 4 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D7 |
| commutator, socle, cosocle | C23×C7 | C25 |
| Fitting | C7×#2817 | C2 |
| hypercenter | #2817 | D7 |
| hypocenter | C7 | #36652 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #2817 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#90318 | C2 | semidirect |
| 2. C7×#2817 | C2 | semidirect |
| 3. #11740278 | C2 | semidirect |
| 4. #11735846 | C2 | semidirect |
| 5. #11735574 | C2 | semidirect |
| 6. #11735171 | C2 | semidirect |
| 7. #11734902 | C2 | semidirect |
| 8. #11734719 | C2 | semidirect |
| 9. #11734614 | C2 | semidirect |
| 10. #11731589 | C2 | semidirect |
| 11. #11731495 | C2 | semidirect |
| 21. C2×#6456 | C22 | semidirect |
| 26. C7×#400 | C22 | semidirect |
| 28. C7×#395 | C22 | semidirect |
| 30. #90003 | C22 | semidirect |
| 32. #89764 | C22 | semidirect |
| 34. #89763 | C22 | semidirect |
| 35. #89755 | C22 | semidirect |
| 36. #89752 | C22 | semidirect |
| 40. #89448 | C22 | semidirect |
| 42. #89446 | C22 | semidirect |
| 44. #89444 | C22 | semidirect |
| 46. #89443 | C22 | semidirect |
| 49. #89438 | C22 | semidirect |
| 50. #89421 | C22 | semidirect |
| 64. C22×C4×D7 | D4 | semidirect |
| 106. #2817 | D7 | semidirect |
| 189. #400 | C2×D7 | semidirect |
| 197. #395 | C2×D7 | semidirect |
| 444. C7 | #36652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90318 | 2 |
| C7×#2817 | 2 |
| #11740278 | 2 |
| #11735846 | 2 |
| #11735574 | 2 |
| #11735171 | 2 |
| #11734902 | 2 |
| #11734719 | 2 |
| #11734614 | 2 |
| #11731589 | 2 |
| #11731495 | 2 |
| #36652 | 7 |