Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1082 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 179 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C7×#3549 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11740758 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #11740730 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11729682 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11729681 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11729661 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11729660 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11729564 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11729556 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C7×H(3,𝔽4) | — | 2 | 2 | no | — |
| 11 | C7×#555 | — | 2 | 2 | no | — |
| 12 | C7×#555 | C22 | 1 | 2 | yes | — |
| 13 | C7×D42 | — | 2 | 2 | no | — |
| 14 | C7×D42 | C22 | 1 | 2 | yes | — |
| 15 | C7×#535 | — | 2 | 2 | no | — |
| 16 | C7×#535 | — | 2 | 4 | no | — |
| 17 | C7×#532 | C22 | 1 | 1 | yes | characteristic |
| 18 | C7×#532 | C22 | 1 | 2 | yes | — |
| 19 | C2×#6513 | — | 2 | 2 | no | — |
| 20 | #90168 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #89864 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #89857 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #89856 | — | 2 | 2 | no | — |
| 24 | #89848 | C22 | 1 | 1 | yes | characteristic |
| 25 | #89845 | C22 | 1 | 1 | yes | characteristic |
| 26 | #89844 | — | 2 | 2 | no | — |
| 27 | #89831 | — | 2 | 2 | no | — |
| 28 | #89811 | — | 2 | 4 | no | — |
| 29 | #89787 | C22 | 1 | 4 | yes | complemented |
| 30 | #89780 | C22 | 1 | 4 | yes | complemented |
| 31 | #89696 | C22 | 1 | 2 | yes | complemented |
| 32 | C2×C4×C7⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #89341 | C22 | 1 | 2 | yes | complemented |
| 34 | #89339 | C22 | 1 | 2 | yes | — |
| 35 | D4⋊(C7⋊C8) | C22 | 1 | 4 | yes | complemented |
| 36 | D4⋊(C7⋊C8) | C22 | 1 | 4 | yes | complemented |
| 37 | #18686 | — | 7 | 1 | no | maximal, Sylow |
| 38 | C2×C7×#41 | — | 2 | 2 | no | — |
| 39 | C2×C7×#41 | D4 | 1 | 2 | yes | — |
| 40 | C22×C7×D4 | — | 2 | 2 | no | — |
| 41 | C22×C7×D4 | — | 2 | 4 | no | — |
| 42 | C2×#1157 | — | 2 | 1 | no | — |
| 43 | C7×C4⋊Q8 | D4 | 1 | 2 | yes | — |
| 44 | C7×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 45 | C7×#127 | — | 2 | 4 | no | — |
| 46 | C7×#127 | D4 | 1 | 2 | yes | — |
| 47 | C7×#127 | C23 | 1 | 1 | yes | characteristic |
| 48 | C7×#124 | — | 2 | 8 | no | — |
| 49 | C7×#124 | — | 2 | 4 | no | — |
| 50 | C7×#124 | — | 2 | 2 | no | — |
| 51 | C7×#124 | D4 | 1 | 2 | yes | — |
| 52 | C7×#121 | — | 2 | 4 | no | — |
| 53 | C7×#121 | — | 2 | 4 | no | — |
| 54 | C7×#121 | — | 2 | 2 | no | — |
| 55 | C7×#121 | — | 2 | 2 | no | — |
| 56 | C7×#121 | — | 2 | 4 | no | — |
| 57 | C7×#121 | D4 | 1 | 4 | yes | — |
| 58 | C7×#120 | — | 2 | 4 | no | — |
| 59 | C7×#120 | — | 2 | 8 | no | — |
| 60 | C7×#120 | — | 2 | 4 | no | — |
| 61 | C4×C7×D4 | — | 2 | 2 | no | — |
| 62 | C4×C7×D4 | — | 2 | 2 | no | — |
| 63 | C4×C7×D4 | C23 | 1 | 4 | yes | — |
| 64 | C7×#117 | — | 2 | 2 | no | — |
| 65 | C7×#117 | — | 2 | 4 | no | — |
| 66 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 67 | #6513 | — | 4 | 8 | no | — |
| 68 | C2×#1144 | — | 2 | 2 | no | — |
| 69 | C2×#1143 | — | 2 | 2 | no | — |
| 70 | C2×#1142 | — | 2 | 2 | no | — |
| 71 | C2×#1141 | — | 2 | 2 | no | — |
| 72 | C2×#1141 | — | 2 | 4 | no | — |
| 73 | #6493 | — | 2 | 2 | no | — |
| 74 | C2×#1136 | — | 2 | 2 | no | — |
| 75 | C22×C7⋊C8 | — | 2 | 1 | no | — |
| 76 | #6438 | — | 2 | 1 | no | — |
| 77 | #6437 | C23 | 1 | 1 | yes | characteristic |
| 78 | C4×D28 | — | 2 | 2 | no | — |
| 79 | #6432 | C23 | 1 | 1 | yes | characteristic |
| 80 | #6406 | — | 2 | 4 | no | — |
| 81 | #6383 | — | 2 | 4 | no | — |
| 82 | #6382 | — | 2 | 4 | no | — |
| 83 | C4⋊(C7⋊C8) | — | 2 | 2 | no | — |
| 84 | C4⋊(C7⋊C8) | C23 | 1 | 4 | yes | — |
| 85 | C4×C7⋊C8 | — | 2 | 1 | no | — |
| 86 | C4×C7⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 87 | C4×C7⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 88 | #3549 | D7 | 1 | 1 | yes | characteristic, complemented |
| 89 | #3253 | — | 7 | 2 | no | — |
| 90 | #3147 | — | 7 | 1 | no | — |
| 91 | #1634 | — | 7 | 2 | no | — |
| 92 | #1629 | — | 7 | 2 | no | — |
| 93 | #1624 | — | 7 | 2 | no | — |
| 94 | #1619 | — | 7 | 2 | no | — |
| 95 | #1560 | — | 7 | 1 | no | — |
| 96 | #1492 | — | 7 | 2 | no | — |
| 97 | C24×C7 | — | 2 | 4 | no | — |
| 98 | C7×#41 | — | 4 | 4 | no | — |
| 99 | C7×#41 | — | 8 | 2 | no | — |
| 100 | C7×#41 | — | 8 | 2 | no | — |
| 101 | C2×C7×Q8 | — | 2 | 2 | no | — |
| 102 | C2×C7×Q8 | C2×D4 | 1 | 2 | yes | — |
| 103 | C2×C7×D4 | — | 2 | 4 | no | — |
| 104 | C2×C7×D4 | — | 2 | 8 | no | — |
| 105 | C2×C7×D4 | — | 2 | 2 | no | — |
| 106 | C2×C7×D4 | — | 2 | 4 | no | — |
| 107 | C2×C7×D4 | — | 2 | 2 | no | — |
| 108 | C2×C7×D4 | — | 2 | 2 | no | — |
| 109 | C2×C7×D4 | — | 2 | 2 | no | — |
| 110 | C2×C7×D4 | — | 8 | 4 | no | — |
| 111 | C2×C7×D4 | — | 8 | 4 | no | — |
| 112 | C2×C7×D4 | — | 8 | 4 | no | — |
| 113 | C2×C7×D4 | C2×D4 | 1 | 4 | yes | — |
| 114 | C2×C7×D4 | C2×D4 | 1 | 2 | yes | — |
| 115 | C22×C4×C7 | — | 2 | 2 | no | — |
| 116 | C22×C4×C7 | — | 2 | 4 | no | — |
| 117 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | C22×C4×C7 | C2×D4 | 1 | 2 | yes | — |
| 119 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 120 | #1157 | — | 4 | 4 | no | — |
| 121 | C2×D28 | — | 2 | 2 | no | — |
| 122 | C2×D28 | — | 2 | 1 | no | — |
| 123 | C2×C4×D7 | — | 4 | 1 | no | — |
| 124 | C2×Dic14 | — | 2 | 1 | no | — |
| 125 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 126 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 127 | C7×C4⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 128 | C7×C22⋊C4 | — | 2 | 8 | no | — |
| 129 | C7×C22⋊C4 | — | 2 | 4 | no | — |
| 130 | C7×C22⋊C4 | — | 2 | 4 | no | — |
| 131 | C7×C22⋊C4 | — | 2 | 4 | no | — |
| 132 | C7×C22⋊C4 | — | 2 | 4 | no | — |
| 133 | C42×C7 | — | 2 | 4 | no | — |
| 134 | C42×C7 | C2×D4 | 1 | 2 | yes | — |
| 135 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 137 | #1144 | — | 4 | 4 | no | — |
| 138 | #1143 | — | 4 | 4 | no | — |
| 139 | #1142 | — | 4 | 4 | no | — |
| 140 | #1141 | — | 4 | 4 | no | — |
| 141 | #1141 | — | 8 | 4 | no | — |
| 142 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 143 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 144 | #1136 | — | 8 | 2 | no | — |
| 145 | C2×C7⋊C8 | — | 2 | 4 | no | — |
| 146 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 147 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 148 | C2×C7⋊C8 | — | 2 | 4 | no | — |
| 149 | C2×#135 | — | 14 | 2 | no | — |
| 150 | H(3,𝔽4) | — | 2 | 2 | no | — |
| 151 | #555 | — | 2 | 2 | no | — |
| 152 | #555 | C2×D7 | 1 | 2 | yes | — |
| 153 | D42 | — | 2 | 2 | no | — |
| 154 | D42 | C2×D7 | 1 | 2 | yes | — |
| 155 | #535 | — | 2 | 2 | no | — |
| 156 | #535 | — | 2 | 4 | no | — |
| 157 | #532 | — | 7 | 1 | no | — |
| 158 | #532 | C2×D7 | 1 | 1 | yes | characteristic |
| 159 | #532 | C2×D7 | 1 | 2 | yes | — |
| 160 | #495 | — | 14 | 2 | no | — |
| 161 | #494 | — | 7 | 1 | no | — |
| 162 | #493 | — | 7 | 1 | no | — |
| 163 | #492 | — | 7 | 1 | no | — |
| 164 | #492 | — | 7 | 1 | no | — |
| 165 | #476 | — | 7 | 4 | no | — |
| 166 | #476 | — | 14 | 2 | no | — |
| 167 | #469 | — | 14 | 4 | no | — |
| 168 | #459 | — | 7 | 4 | no | — |
| 169 | #459 | — | 14 | 2 | no | — |
| 170 | #423 | — | 7 | 2 | no | — |
| 171 | C2×C4×C8 | — | 7 | 1 | no | — |
| 172 | #333 | — | 7 | 2 | no | — |
| 173 | #331 | — | 7 | 2 | no | — |
| 174 | D4⋊C8 | — | 7 | 4 | no | — |
| 175 | D4⋊C8 | — | 7 | 4 | no | — |
| 176 | C23×C7 | — | 2 | 4 | no | — |
| 177 | C23×C7 | — | 2 | 2 | no | — |
| 178 | C23×C7 | — | 8 | 8 | no | — |
| 179 | C23×C7 | — | 8 | 4 | no | — |
| 180 | C23×C7 | #120 | 1 | 1 | yes | characteristic |
| 181 | C22×D7 | — | 4 | 1 | no | — |
| 182 | C7×Q8 | — | 4 | 2 | no | — |
| 183 | C7×Q8 | — | 8 | 2 | no | — |
| 184 | C7×D4 | — | 2 | 4 | no | — |
| 185 | C7×D4 | — | 2 | 4 | no | — |
| 186 | C7×D4 | — | 4 | 2 | no | — |
| 187 | C7×D4 | — | 4 | 2 | no | — |
| 188 | C7×D4 | — | 4 | 2 | no | — |
| 189 | C7×D4 | — | 4 | 4 | no | — |
| 190 | C7×D4 | — | 8 | 2 | no | — |
| 191 | C7×D4 | — | 8 | 2 | no | — |
| 192 | C7×D4 | — | 8 | 4 | no | — |
| 193 | C7×D4 | — | 8 | 8 | no | — |
| 194 | C7×D4 | — | 8 | 4 | no | — |
| 195 | C2×C4×C7 | — | 2 | 2 | no | — |
| 196 | C2×C4×C7 | — | 2 | 2 | no | — |
| 197 | C2×C4×C7 | — | 2 | 2 | no | — |
| 198 | C2×C4×C7 | — | 2 | 2 | no | — |
| 199 | C2×C4×C7 | — | 2 | 4 | no | — |
| 200 | C2×C4×C7 | — | 4 | 4 | no | — |
| 201 | C2×C4×C7 | — | 4 | 4 | no | — |
| 202 | C2×C4×C7 | — | 4 | 4 | no | — |
| 203 | C2×C4×C7 | #120 | 1 | 2 | yes | — |
| 204 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 205 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 206 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 207 | C22⋊D7 | — | 8 | 2 | no | — |
| 208 | C2×Dic7 | — | 4 | 1 | no | — |
| 209 | D28 | — | 4 | 2 | no | — |
| 210 | D28 | — | 4 | 2 | no | — |
| 211 | D28 | — | 4 | 2 | no | — |
| 212 | C4×D7 | — | 8 | 2 | no | — |
| 213 | Dic14 | — | 4 | 2 | no | — |
| 214 | C7⋊C8 | — | 2 | 2 | no | — |
| 215 | C7⋊C8 | — | 2 | 2 | no | — |
| 216 | C7⋊C8 | — | 4 | 4 | no | — |
| 217 | C2×#41 | — | 2 | 2 | no | — |
| 218 | C2×#41 | — | 14 | 1 | no | — |
| 219 | C2×#41 | C22⋊D7 | 1 | 2 | yes | — |
| 220 | C22×D4 | — | 2 | 2 | no | — |
| 221 | C22×D4 | — | 2 | 4 | no | — |
| 222 | #135 | — | 28 | 8 | no | — |
| 223 | C2×Q16 | — | 14 | 2 | no | — |
| 224 | C2×SD16 | — | 14 | 2 | no | — |
| 225 | C2×SD16 | — | 14 | 2 | no | — |
| 226 | C2×D8 | — | 14 | 2 | no | — |
| 227 | C2×D8 | — | 14 | 4 | no | — |
| 228 | C2×M16 | — | 14 | 2 | no | — |
| 229 | C22×C8 | — | 14 | 1 | no | — |
| 230 | C4⋊Q8 | — | 7 | 1 | no | — |
| 231 | C4⋊Q8 | C22⋊D7 | 1 | 2 | yes | — |
| 232 | C4⋊Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 233 | #127 | — | 2 | 4 | no | — |
| 234 | #127 | — | 7 | 1 | no | — |
| 235 | #127 | C22⋊D7 | 1 | 2 | yes | — |
| 236 | #127 | C22×D7 | 1 | 1 | yes | characteristic |
| 237 | #124 | — | 2 | 8 | no | — |
| 238 | #124 | — | 2 | 4 | no | — |
| 239 | #124 | — | 2 | 2 | no | — |
| 240 | #124 | — | 14 | 1 | no | — |
| 241 | #124 | C22⋊D7 | 1 | 2 | yes | — |
| 242 | #121 | — | 2 | 4 | no | — |
| 243 | #121 | — | 2 | 4 | no | — |
| 244 | #121 | — | 2 | 2 | no | — |
| 245 | #121 | — | 2 | 2 | no | — |
| 246 | #121 | — | 2 | 4 | no | — |
| 247 | #121 | — | 14 | 2 | no | — |
| 248 | #121 | C22⋊D7 | 1 | 4 | yes | — |
| 249 | #120 | — | 2 | 4 | no | — |
| 250 | #120 | — | 2 | 8 | no | — |
| 251 | #120 | — | 2 | 4 | no | — |
| 252 | C4×D4 | — | 2 | 2 | no | — |
| 253 | C4×D4 | — | 2 | 2 | no | — |
| 254 | C4×D4 | — | 14 | 2 | no | — |
| 255 | C4×D4 | C22×D7 | 1 | 4 | yes | — |
| 256 | #117 | — | 2 | 2 | no | — |
| 257 | #117 | — | 2 | 4 | no | — |
| 258 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 259 | #106 | — | 14 | 4 | no | — |
| 260 | C4⋊C8 | — | 7 | 4 | no | — |
| 261 | C4⋊C8 | — | 14 | 2 | no | — |
| 262 | #102 | — | 14 | 4 | no | — |
| 263 | #102 | — | 14 | 4 | no | — |
| 264 | C4×C8 | — | 7 | 1 | no | — |
| 265 | C4×C8 | — | 7 | 1 | no | — |
| 266 | C4×C8 | — | 14 | 1 | no | — |
| 267 | C22×C7 | — | 2 | 2 | no | — |
| 268 | C22×C7 | — | 2 | 1 | no | — |
| 269 | C22×C7 | — | 4 | 4 | no | — |
| 270 | C22×C7 | — | 4 | 4 | no | — |
| 271 | C22×C7 | — | 4 | 4 | no | — |
| 272 | C22×C7 | — | 4 | 2 | no | — |
| 273 | C22×C7 | — | 4 | 4 | no | — |
| 274 | C22×C7 | — | 16 | 8 | no | — |
| 275 | C22×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 276 | C2×D7 | — | 8 | 2 | no | — |
| 277 | C2×D7 | — | 8 | 1 | no | — |
| 278 | C4×C7 | — | 2 | 2 | no | — |
| 279 | C4×C7 | — | 2 | 1 | no | — |
| 280 | C4×C7 | — | 4 | 4 | no | — |
| 281 | C4×C7 | — | 4 | 2 | no | — |
| 282 | C4×C7 | #453 | 1 | 2 | yes | — |
| 283 | C4×C7 | #576 | 1 | 2 | yes | — |
| 284 | C4×C7 | #577 | 1 | 2 | yes | — |
| 285 | Dic7 | — | 8 | 1 | no | — |
| 286 | C24 | — | 2 | 4 | no | — |
| 287 | #41 | — | 4 | 4 | no | — |
| 288 | #41 | — | 8 | 2 | no | — |
| 289 | #41 | — | 8 | 2 | no | — |
| 290 | #41 | — | 28 | 4 | no | — |
| 291 | C2×Q8 | — | 2 | 2 | no | — |
| 292 | C2×Q8 | — | 14 | 1 | no | — |
| 293 | C2×Q8 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 294 | C2×D4 | — | 2 | 4 | no | — |
| 295 | C2×D4 | — | 2 | 8 | no | — |
| 296 | C2×D4 | — | 2 | 2 | no | — |
| 297 | C2×D4 | — | 2 | 4 | no | — |
| 298 | C2×D4 | — | 2 | 2 | no | — |
| 299 | C2×D4 | — | 2 | 2 | no | — |
| 300 | C2×D4 | — | 2 | 2 | no | — |
| 301 | C2×D4 | — | 8 | 4 | no | — |
| 302 | C2×D4 | — | 8 | 4 | no | — |
| 303 | C2×D4 | — | 8 | 4 | no | — |
| 304 | C2×D4 | — | 14 | 2 | no | — |
| 305 | C2×D4 | — | 14 | 1 | no | — |
| 306 | C2×D4 | — | 28 | 1 | no | — |
| 307 | C2×D4 | C2×C22⋊D7 | 1 | 4 | yes | — |
| 308 | C2×D4 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 309 | C22×C4 | — | 2 | 2 | no | — |
| 310 | C22×C4 | — | 2 | 4 | no | — |
| 311 | C22×C4 | — | 28 | 1 | no | — |
| 312 | C22×C4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 313 | C22×C4 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 314 | Q16 | — | 28 | 4 | no | — |
| 315 | SD16 | — | 28 | 4 | no | — |
| 316 | SD16 | — | 28 | 4 | no | — |
| 317 | D8 | — | 28 | 4 | no | — |
| 318 | D8 | — | 56 | 4 | no | — |
| 319 | M16 | — | 56 | 2 | no | — |
| 320 | C2×C8 | — | 14 | 4 | no | — |
| 321 | C2×C8 | — | 14 | 1 | no | — |
| 322 | C2×C8 | — | 14 | 1 | no | — |
| 323 | C2×C8 | — | 14 | 4 | no | — |
| 324 | C4⋊C4 | — | 2 | 2 | no | — |
| 325 | C4⋊C4 | — | 2 | 2 | no | — |
| 326 | C4⋊C4 | — | 14 | 2 | no | — |
| 327 | C4⋊C4 | C2×C22⋊D7 | 1 | 4 | yes | — |
| 328 | C22⋊C4 | — | 2 | 8 | no | — |
| 329 | C22⋊C4 | — | 2 | 4 | no | — |
| 330 | C22⋊C4 | — | 2 | 4 | no | — |
| 331 | C22⋊C4 | — | 2 | 4 | no | — |
| 332 | C22⋊C4 | — | 2 | 4 | no | — |
| 333 | C22⋊C4 | — | 28 | 2 | no | — |
| 334 | C42 | — | 2 | 4 | no | — |
| 335 | C42 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 336 | C42 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 337 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 338 | C2×C7 | — | 4 | 1 | no | — |
| 339 | C2×C7 | — | 8 | 4 | no | — |
| 340 | C2×C7 | — | 8 | 2 | no | — |
| 341 | C2×C7 | #3012 | 1 | 2 | yes | — |
| 342 | C2×C7 | C2×#453 | 1 | 1 | yes | characteristic |
| 343 | D7 | — | 16 | 1 | no | — |
| 344 | C23 | — | 2 | 4 | no | — |
| 345 | C23 | — | 2 | 2 | no | — |
| 346 | C23 | — | 8 | 8 | no | — |
| 347 | C23 | — | 8 | 4 | no | — |
| 348 | C23 | — | 28 | 1 | no | — |
| 349 | C23 | #6516 | 1 | 1 | yes | characteristic |
| 350 | Q8 | — | 4 | 2 | no | — |
| 351 | Q8 | — | 8 | 2 | no | — |
| 352 | Q8 | — | 28 | 2 | no | — |
| 353 | D4 | — | 2 | 4 | no | — |
| 354 | D4 | — | 2 | 4 | no | — |
| 355 | D4 | — | 4 | 2 | no | — |
| 356 | D4 | — | 4 | 4 | no | — |
| 357 | D4 | — | 4 | 2 | no | — |
| 358 | D4 | — | 4 | 2 | no | — |
| 359 | D4 | — | 8 | 2 | no | — |
| 360 | D4 | — | 8 | 2 | no | — |
| 361 | D4 | — | 8 | 4 | no | — |
| 362 | D4 | — | 8 | 8 | no | — |
| 363 | D4 | — | 8 | 4 | no | — |
| 364 | D4 | — | 28 | 2 | no | — |
| 365 | D4 | — | 28 | 2 | no | — |
| 366 | D4 | — | 28 | 2 | no | — |
| 367 | D4 | — | 56 | 2 | no | — |
| 368 | C2×C4 | — | 2 | 2 | no | — |
| 369 | C2×C4 | — | 2 | 2 | no | — |
| 370 | C2×C4 | — | 2 | 2 | no | — |
| 371 | C2×C4 | — | 2 | 2 | no | — |
| 372 | C2×C4 | — | 2 | 4 | no | — |
| 373 | C2×C4 | — | 4 | 4 | no | — |
| 374 | C2×C4 | — | 4 | 4 | no | — |
| 375 | C2×C4 | — | 4 | 4 | no | — |
| 376 | C2×C4 | — | 28 | 1 | no | — |
| 377 | C2×C4 | — | 56 | 2 | no | — |
| 378 | C2×C4 | #6516 | 1 | 2 | yes | — |
| 379 | C2×C4 | #6516 | 1 | 1 | yes | characteristic |
| 380 | C2×C4 | C22×C22⋊D7 | 1 | 1 | yes | characteristic |
| 381 | C2×C4 | C22×C22⋊D7 | 1 | 2 | yes | — |
| 382 | C8 | — | 14 | 2 | no | — |
| 383 | C8 | — | 14 | 2 | no | — |
| 384 | C8 | — | 28 | 4 | no | — |
| 385 | C7 | #18686 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 386 | C22 | — | 2 | 2 | no | — |
| 387 | C22 | — | 2 | 1 | no | — |
| 388 | C22 | — | 4 | 4 | no | — |
| 389 | C22 | — | 4 | 4 | no | — |
| 390 | C22 | — | 4 | 4 | no | — |
| 391 | C22 | — | 4 | 2 | no | — |
| 392 | C22 | — | 4 | 4 | no | — |
| 393 | C22 | — | 16 | 8 | no | — |
| 394 | C22 | — | 56 | 2 | no | — |
| 395 | C22 | — | 56 | 1 | no | — |
| 396 | C22 | C2×#6516 | 1 | 1 | yes | characteristic |
| 397 | C4 | — | 2 | 2 | no | — |
| 398 | C4 | — | 2 | 1 | no | — |
| 399 | C4 | — | 4 | 4 | no | — |
| 400 | C4 | — | 4 | 2 | no | — |
| 401 | C4 | — | 56 | 1 | no | — |
| 402 | C4 | #90013 | 1 | 2 | yes | — |
| 403 | C4 | #90526 | 1 | 2 | yes | — |
| 404 | C4 | #90527 | 1 | 2 | yes | — |
| 405 | C2 | — | 4 | 1 | no | — |
| 406 | C2 | — | 8 | 4 | no | — |
| 407 | C2 | — | 8 | 2 | no | — |
| 408 | C2 | — | 112 | 1 | no | — |
| 409 | C2 | #11741547 | 1 | 2 | yes | — |
| 410 | C2 | C2×#90013 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#6516 |
| commutator, cosocle | C42×C7 | C24 |
| Frattini | C42 | C23×D7 |
| Fitting | C7×#3549 | C2 |
| socle | C22×C7 | C2×#120 |
| hypercenter | #3549 | D7 |
| hypocenter | C7 | #18686 |
| LCS | G ▷ C42×C7 ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #3549 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#3549 | C2 | semidirect |
| 2. #11740758 | C2 | semidirect |
| 3. #11740730 | C2 | semidirect |
| 4. #11729682 | C2 | semidirect |
| 5. #11729681 | C2 | semidirect |
| 6. #11729661 | C2 | semidirect |
| 7. #11729660 | C2 | semidirect |
| 8. #11729564 | C2 | semidirect |
| 9. #11729556 | C2 | semidirect |
| 20. #90168 | C22 | semidirect |
| 21. #89864 | C22 | semidirect |
| 22. #89857 | C22 | semidirect |
| 29. #89787 | C22 | semidirect |
| 30. #89780 | C22 | semidirect |
| 31. #89696 | C22 | semidirect |
| 32. C2×C4×C7⋊C8 | C22 | semidirect |
| 33. #89341 | C22 | semidirect |
| 35. D4⋊(C7⋊C8) | C22 | semidirect |
| 36. D4⋊(C7⋊C8) | C22 | semidirect |
| 88. #3549 | D7 | semidirect |
| 385. C7 | #18686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3549 | 2 |
| #11740758 | 2 |
| #11740730 | 2 |
| #11729682 | 2 |
| #11729681 | 2 |
| #11729661 | 2 |
| #11729660 | 2 |
| #11729564 | 2 |
| #11729556 | 2 |
| #18686 | 7 |