Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
578 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 81 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×#3153 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11740753 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11740392 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11729557 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11729474 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11727607 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11725476 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×C7×#137 | — | 2 | 1 | no | — |
| 9 | C2×C7×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 10 | C7×#532 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C7×#124 | C22 | 1 | 1 | yes | characteristic |
| 12 | #90168 | C22 | 1 | 1 | yes | characteristic |
| 13 | C7×#497 | — | 2 | 1 | no | — |
| 14 | C7×#496 | — | 2 | 1 | no | — |
| 15 | C7×#495 | — | 2 | 2 | no | — |
| 16 | C4×C7×M16 | C22 | 1 | 1 | yes | characteristic |
| 17 | #89999 | — | 2 | 1 | no | — |
| 18 | #89989 | — | 2 | 1 | no | — |
| 19 | #89861 | — | 2 | 1 | no | — |
| 20 | #89846 | — | 2 | 1 | no | — |
| 21 | #89830 | — | 2 | 1 | no | — |
| 22 | #89829 | — | 2 | 2 | no | — |
| 23 | #89827 | — | 2 | 1 | no | — |
| 24 | #89809 | — | 2 | 2 | no | — |
| 25 | #89791 | — | 2 | 1 | no | — |
| 26 | #89787 | — | 2 | 1 | no | — |
| 27 | #89698 | C22 | 1 | 1 | yes | characteristic |
| 28 | #89698 | C22 | 1 | 1 | yes | characteristic |
| 29 | #89697 | C22 | 1 | 1 | yes | characteristic |
| 30 | D4⋊(C7⋊C8) | — | 2 | 2 | no | — |
| 31 | #89320 | — | 2 | 2 | no | — |
| 32 | #89254 | — | 2 | 2 | no | — |
| 33 | #10120 | — | 7 | 1 | no | maximal, Sylow |
| 34 | C2×C7×#41 | — | 2 | 1 | no | — |
| 35 | C22×C7×Q8 | D4 | 1 | 1 | yes | characteristic |
| 36 | C22×C7×D4 | D4 | 1 | 1 | yes | characteristic |
| 37 | C2×#1157 | — | 2 | 1 | no | — |
| 38 | C7×#137 | — | 4 | 4 | no | — |
| 39 | C7×AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 40 | C2×C7×Q16 | — | 2 | 2 | no | — |
| 41 | C2×C7×SD16 | — | 2 | 2 | no | — |
| 42 | C2×C7×SD16 | — | 2 | 2 | no | — |
| 43 | C2×C7×D8 | — | 2 | 2 | no | — |
| 44 | C2×C7×M16 | — | 2 | 1 | no | — |
| 45 | C7×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 46 | C7×#127 | D4 | 1 | 1 | yes | characteristic |
| 47 | C7×#124 | — | 2 | 1 | no | — |
| 48 | C7×#124 | — | 2 | 1 | no | — |
| 49 | C7×#124 | — | 2 | 1 | no | — |
| 50 | C7×#124 | — | 2 | 1 | no | — |
| 51 | C7×#124 | — | 2 | 1 | no | — |
| 52 | C7×#121 | — | 2 | 1 | no | — |
| 53 | C7×#121 | — | 2 | 1 | no | — |
| 54 | C4×C7×D4 | — | 2 | 1 | no | — |
| 55 | C4×C7×D4 | — | 2 | 1 | no | — |
| 56 | C2×C7×C22⋊C4 | — | 2 | 1 | no | — |
| 57 | C2×C7×C22⋊C4 | — | 2 | 1 | no | — |
| 58 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 59 | C2×#1143 | — | 2 | 2 | no | — |
| 60 | C2×#1142 | — | 2 | 2 | no | — |
| 61 | C2×#1141 | — | 2 | 2 | no | — |
| 62 | C2×#1141 | — | 2 | 2 | no | — |
| 63 | #6493 | — | 2 | 1 | no | — |
| 64 | #6493 | — | 2 | 1 | no | — |
| 65 | #6438 | — | 2 | 1 | no | — |
| 66 | #6437 | D4 | 1 | 1 | yes | characteristic |
| 67 | C4×D28 | — | 2 | 1 | no | — |
| 68 | C4×D28 | — | 2 | 1 | no | — |
| 69 | #6432 | D4 | 1 | 1 | yes | characteristic |
| 70 | C7×#97 | — | 2 | 1 | no | — |
| 71 | C4×C7×C8 | D4 | 1 | 2 | yes | — |
| 72 | #6409 | — | 2 | 2 | no | — |
| 73 | #6406 | — | 2 | 2 | no | — |
| 74 | C22⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 75 | C22⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 76 | C22⋊(C7⋊C8) | D4 | 1 | 2 | yes | — |
| 77 | #6384 | — | 2 | 2 | no | — |
| 78 | #6383 | — | 2 | 2 | no | — |
| 79 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 80 | C4⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 81 | C4⋊(C7⋊C8) | D4 | 1 | 2 | yes | — |
| 82 | #6377 | — | 2 | 1 | no | — |
| 83 | #6377 | — | 2 | 1 | no | — |
| 84 | C4×C7⋊C8 | — | 2 | 1 | no | — |
| 85 | #3214 | — | 7 | 1 | no | — |
| 86 | #3213 | — | 7 | 1 | no | — |
| 87 | #3153 | D7 | 1 | 1 | yes | characteristic, complemented |
| 88 | #1496 | — | 7 | 1 | no | — |
| 89 | #1484 | — | 7 | 1 | no | — |
| 90 | #1469 | — | 7 | 1 | no | — |
| 91 | #1291 | — | 7 | 1 | no | — |
| 92 | C24×C7 | — | 2 | 1 | no | — |
| 93 | C7×#41 | — | 4 | 2 | no | — |
| 94 | C7×#41 | — | 4 | 2 | no | — |
| 95 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 96 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 97 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 98 | C2×C7×Q8 | — | 4 | 2 | no | — |
| 99 | C2×C7×D4 | — | 2 | 1 | no | — |
| 100 | C2×C7×D4 | — | 2 | 1 | no | — |
| 101 | C2×C7×D4 | — | 2 | 1 | no | — |
| 102 | C2×C7×D4 | — | 2 | 1 | no | — |
| 103 | C2×C7×D4 | — | 2 | 1 | no | — |
| 104 | C2×C7×D4 | — | 4 | 2 | no | — |
| 105 | C2×C7×D4 | — | 4 | 1 | no | — |
| 106 | C22×C4×C7 | — | 2 | 1 | no | — |
| 107 | C22×C4×C7 | — | 4 | 1 | no | — |
| 108 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | C22×C4×C7 | #41 | 1 | 1 | yes | characteristic |
| 111 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 112 | #1157 | — | 8 | 2 | no | — |
| 113 | C2×D28 | — | 2 | 1 | no | — |
| 114 | C2×D28 | — | 2 | 1 | no | — |
| 115 | C2×D28 | — | 2 | 1 | no | — |
| 116 | C2×C4×D7 | — | 4 | 1 | no | — |
| 117 | C2×Dic14 | — | 2 | 1 | no | — |
| 118 | C7×Q16 | — | 4 | 4 | no | — |
| 119 | C7×SD16 | — | 4 | 4 | no | — |
| 120 | C7×SD16 | — | 4 | 4 | no | — |
| 121 | C7×D8 | — | 4 | 4 | no | — |
| 122 | C7×M16 | — | 2 | 4 | no | — |
| 123 | C2×C7×C8 | — | 2 | 2 | no | — |
| 124 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 125 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 126 | C7×C22⋊C4 | — | 4 | 1 | no | — |
| 127 | C7×C22⋊C4 | — | 4 | 1 | no | — |
| 128 | C7×C22⋊C4 | — | 4 | 1 | no | — |
| 129 | C7×C22⋊C4 | — | 4 | 1 | no | — |
| 130 | C7×C22⋊C4 | — | 4 | 1 | no | — |
| 131 | C7×C22⋊C4 | — | 4 | 1 | no | — |
| 132 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 134 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 135 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | #1143 | — | 8 | 2 | no | — |
| 137 | #1142 | — | 8 | 2 | no | — |
| 138 | #1141 | — | 8 | 2 | no | — |
| 139 | #1141 | — | 8 | 2 | no | — |
| 140 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 141 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 142 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 143 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 144 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 145 | C2×C7⋊C8 | — | 2 | 2 | no | — |
| 146 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 147 | C2×#137 | — | 2 | 1 | no | — |
| 148 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 149 | #532 | — | 7 | 1 | no | — |
| 150 | #532 | C2×D7 | 1 | 1 | yes | characteristic |
| 151 | C2×#124 | C2×D7 | 1 | 1 | yes | characteristic |
| 152 | #497 | — | 2 | 1 | no | — |
| 153 | #496 | — | 2 | 1 | no | — |
| 154 | #496 | — | 14 | 1 | no | — |
| 155 | #496 | — | 14 | 1 | no | — |
| 156 | #495 | — | 2 | 2 | no | — |
| 157 | #489 | — | 14 | 1 | no | — |
| 158 | #489 | — | 14 | 1 | no | — |
| 159 | #463 | — | 14 | 2 | no | — |
| 160 | #461 | — | 14 | 1 | no | — |
| 161 | #459 | — | 14 | 1 | no | — |
| 162 | #449 | — | 14 | 2 | no | — |
| 163 | #448 | — | 14 | 1 | no | — |
| 164 | #447 | — | 14 | 1 | no | — |
| 165 | #432 | — | 7 | 1 | no | — |
| 166 | #432 | — | 7 | 1 | no | — |
| 167 | #431 | — | 7 | 1 | no | — |
| 168 | C4×M16 | C2×D7 | 1 | 1 | yes | characteristic |
| 169 | D4⋊C8 | — | 14 | 2 | no | — |
| 170 | D4⋊C8 | — | 14 | 2 | no | — |
| 171 | #323 | — | 14 | 2 | no | — |
| 172 | C23×C7 | — | 4 | 2 | no | — |
| 173 | C23×C7 | — | 4 | 1 | no | — |
| 174 | C23×C7 | — | 4 | 1 | no | — |
| 175 | C23×C7 | — | 8 | 1 | no | — |
| 176 | C23×C7 | — | 8 | 1 | no | — |
| 177 | C23×C7 | #121 | 1 | 1 | yes | characteristic |
| 178 | C22×D7 | — | 4 | 1 | no | — |
| 179 | C7×Q8 | — | 4 | 1 | no | — |
| 180 | C7×Q8 | — | 4 | 2 | no | — |
| 181 | C7×Q8 | — | 4 | 1 | no | — |
| 182 | C7×Q8 | — | 4 | 2 | no | — |
| 183 | C7×D4 | — | 4 | 1 | no | — |
| 184 | C7×D4 | — | 4 | 1 | no | — |
| 185 | C7×D4 | — | 4 | 1 | no | — |
| 186 | C7×D4 | — | 4 | 2 | no | — |
| 187 | C7×D4 | — | 4 | 1 | no | — |
| 188 | C7×D4 | — | 4 | 2 | no | — |
| 189 | C7×D4 | — | 4 | 2 | no | — |
| 190 | C7×D4 | — | 8 | 2 | no | — |
| 191 | C2×C4×C7 | — | 2 | 2 | no | — |
| 192 | C2×C4×C7 | — | 4 | 1 | no | — |
| 193 | C2×C4×C7 | — | 4 | 1 | no | — |
| 194 | C2×C4×C7 | — | 4 | 1 | no | — |
| 195 | C2×C4×C7 | — | 4 | 1 | no | — |
| 196 | C2×C4×C7 | — | 8 | 2 | no | — |
| 197 | C2×C4×C7 | — | 8 | 1 | no | — |
| 198 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 199 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 200 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 201 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 202 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 203 | C2×C4×C7 | #127 | 1 | 1 | yes | characteristic |
| 204 | C22⋊D7 | — | 8 | 2 | no | — |
| 205 | C2×Dic7 | — | 4 | 1 | no | — |
| 206 | D28 | — | 4 | 2 | no | — |
| 207 | D28 | — | 4 | 2 | no | — |
| 208 | D28 | — | 4 | 2 | no | — |
| 209 | C4×D7 | — | 8 | 2 | no | — |
| 210 | Dic14 | — | 4 | 2 | no | — |
| 211 | C7×C8 | — | 2 | 4 | no | — |
| 212 | C7⋊C8 | — | 4 | 2 | no | — |
| 213 | C7⋊C8 | — | 4 | 2 | no | — |
| 214 | C7⋊C8 | — | 8 | 1 | no | — |
| 215 | C2×#41 | — | 2 | 1 | no | — |
| 216 | C2×#41 | — | 14 | 1 | no | — |
| 217 | C22×Q8 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 218 | C22×D4 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 219 | #137 | — | 4 | 4 | no | — |
| 220 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 221 | C2×Q16 | — | 2 | 2 | no | — |
| 222 | C2×SD16 | — | 2 | 2 | no | — |
| 223 | C2×SD16 | — | 2 | 2 | no | — |
| 224 | C2×SD16 | — | 14 | 2 | no | — |
| 225 | C2×SD16 | — | 14 | 2 | no | — |
| 226 | C2×D8 | — | 2 | 2 | no | — |
| 227 | C2×D8 | — | 14 | 2 | no | — |
| 228 | C2×D8 | — | 14 | 2 | no | — |
| 229 | C2×M16 | — | 2 | 1 | no | — |
| 230 | C4⋊Q8 | — | 7 | 1 | no | — |
| 231 | C4⋊Q8 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 232 | #127 | — | 7 | 1 | no | — |
| 233 | #127 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 234 | #124 | — | 2 | 1 | no | — |
| 235 | #124 | — | 2 | 1 | no | — |
| 236 | #124 | — | 2 | 1 | no | — |
| 237 | #124 | — | 2 | 1 | no | — |
| 238 | #124 | — | 2 | 1 | no | — |
| 239 | #124 | — | 14 | 1 | no | — |
| 240 | #121 | — | 2 | 1 | no | — |
| 241 | #121 | — | 2 | 1 | no | — |
| 242 | #121 | — | 14 | 1 | no | — |
| 243 | #121 | — | 14 | 1 | no | — |
| 244 | C4×D4 | — | 2 | 1 | no | — |
| 245 | C4×D4 | — | 2 | 1 | no | — |
| 246 | C4×D4 | — | 14 | 1 | no | — |
| 247 | C4×D4 | — | 14 | 1 | no | — |
| 248 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 249 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 250 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 251 | C4⋊C8 | — | 7 | 2 | no | — |
| 252 | C4⋊C8 | — | 14 | 1 | no | — |
| 253 | C4⋊C8 | — | 14 | 1 | no | — |
| 254 | #103 | — | 14 | 2 | no | — |
| 255 | #103 | — | 14 | 2 | no | — |
| 256 | #102 | — | 14 | 2 | no | — |
| 257 | #102 | — | 14 | 2 | no | — |
| 258 | C22⋊C8 | — | 7 | 2 | no | — |
| 259 | C22⋊C8 | — | 14 | 1 | no | — |
| 260 | C22⋊C8 | — | 14 | 1 | no | — |
| 261 | #97 | — | 2 | 1 | no | — |
| 262 | #97 | — | 14 | 1 | no | — |
| 263 | #97 | — | 14 | 1 | no | — |
| 264 | C4×C8 | — | 14 | 1 | no | — |
| 265 | C4×C8 | C22⋊D7 | 1 | 2 | yes | — |
| 266 | C22×C7 | — | 2 | 1 | no | — |
| 267 | C22×C7 | — | 2 | 1 | no | — |
| 268 | C22×C7 | — | 2 | 1 | no | — |
| 269 | C22×C7 | — | 8 | 1 | no | — |
| 270 | C22×C7 | — | 8 | 1 | no | — |
| 271 | C22×C7 | — | 8 | 1 | no | — |
| 272 | C22×C7 | — | 8 | 1 | no | — |
| 273 | C22×C7 | — | 8 | 1 | no | — |
| 274 | C22×C7 | — | 8 | 1 | no | — |
| 275 | C22×C7 | — | 16 | 2 | no | — |
| 276 | C22×C7 | #392 | 1 | 1 | yes | characteristic |
| 277 | C2×D7 | — | 8 | 1 | no | — |
| 278 | C2×D7 | — | 8 | 1 | no | — |
| 279 | C2×D7 | — | 8 | 1 | no | — |
| 280 | C4×C7 | — | 2 | 1 | no | — |
| 281 | C4×C7 | — | 2 | 1 | no | — |
| 282 | C4×C7 | — | 2 | 1 | no | — |
| 283 | C4×C7 | — | 2 | 1 | no | — |
| 284 | C4×C7 | — | 2 | 1 | no | — |
| 285 | C4×C7 | — | 8 | 1 | no | — |
| 286 | C4×C7 | — | 8 | 1 | no | — |
| 287 | C4×C7 | #453 | 1 | 2 | yes | — |
| 288 | Dic7 | — | 8 | 1 | no | — |
| 289 | C24 | — | 2 | 1 | no | — |
| 290 | #41 | — | 4 | 2 | no | — |
| 291 | #41 | — | 4 | 2 | no | — |
| 292 | #41 | — | 56 | 2 | no | — |
| 293 | C2×Q8 | — | 2 | 1 | no | — |
| 294 | C2×Q8 | — | 2 | 1 | no | — |
| 295 | C2×Q8 | — | 2 | 1 | no | — |
| 296 | C2×Q8 | — | 4 | 2 | no | — |
| 297 | C2×Q8 | — | 14 | 1 | no | — |
| 298 | C2×D4 | — | 2 | 1 | no | — |
| 299 | C2×D4 | — | 2 | 1 | no | — |
| 300 | C2×D4 | — | 2 | 1 | no | — |
| 301 | C2×D4 | — | 2 | 1 | no | — |
| 302 | C2×D4 | — | 2 | 1 | no | — |
| 303 | C2×D4 | — | 4 | 2 | no | — |
| 304 | C2×D4 | — | 4 | 1 | no | — |
| 305 | C2×D4 | — | 14 | 1 | no | — |
| 306 | C2×D4 | — | 14 | 1 | no | — |
| 307 | C2×D4 | — | 14 | 1 | no | — |
| 308 | C2×D4 | — | 28 | 1 | no | — |
| 309 | C22×C4 | — | 2 | 1 | no | — |
| 310 | C22×C4 | — | 4 | 1 | no | — |
| 311 | C22×C4 | — | 28 | 1 | no | — |
| 312 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 313 | C22×C4 | #1159 | 1 | 1 | yes | characteristic |
| 314 | C22×C4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 315 | Q16 | — | 4 | 4 | no | — |
| 316 | SD16 | — | 4 | 4 | no | — |
| 317 | SD16 | — | 4 | 4 | no | — |
| 318 | SD16 | — | 56 | 2 | no | — |
| 319 | SD16 | — | 56 | 2 | no | — |
| 320 | D8 | — | 4 | 4 | no | — |
| 321 | D8 | — | 56 | 2 | no | — |
| 322 | D8 | — | 56 | 2 | no | — |
| 323 | M16 | — | 2 | 4 | no | — |
| 324 | C2×C8 | — | 2 | 2 | no | — |
| 325 | C2×C8 | — | 14 | 2 | no | — |
| 326 | C2×C8 | — | 14 | 2 | no | — |
| 327 | C2×C8 | — | 28 | 1 | no | — |
| 328 | C4⋊C4 | — | 2 | 1 | no | — |
| 329 | C4⋊C4 | — | 2 | 1 | no | — |
| 330 | C4⋊C4 | — | 14 | 1 | no | — |
| 331 | C4⋊C4 | — | 14 | 1 | no | — |
| 332 | C22⋊C4 | — | 4 | 1 | no | — |
| 333 | C22⋊C4 | — | 4 | 1 | no | — |
| 334 | C22⋊C4 | — | 4 | 1 | no | — |
| 335 | C22⋊C4 | — | 4 | 1 | no | — |
| 336 | C22⋊C4 | — | 4 | 1 | no | — |
| 337 | C22⋊C4 | — | 4 | 1 | no | — |
| 338 | C22⋊C4 | — | 28 | 1 | no | — |
| 339 | C22⋊C4 | — | 28 | 1 | no | — |
| 340 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 341 | C42 | D4×D7 | 1 | 1 | yes | characteristic |
| 342 | C42 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 343 | C42 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 344 | C2×C7 | — | 4 | 1 | no | — |
| 345 | C2×C7 | — | 16 | 1 | no | — |
| 346 | C2×C7 | — | 16 | 1 | no | — |
| 347 | C2×C7 | #2002 | 1 | 1 | yes | characteristic |
| 348 | C2×C7 | #2008 | 1 | 1 | yes | characteristic |
| 349 | C2×C7 | #2017 | 1 | 1 | yes | characteristic |
| 350 | D7 | — | 16 | 1 | no | — |
| 351 | C23 | — | 4 | 2 | no | — |
| 352 | C23 | — | 4 | 1 | no | — |
| 353 | C23 | — | 4 | 1 | no | — |
| 354 | C23 | — | 8 | 1 | no | — |
| 355 | C23 | — | 8 | 1 | no | — |
| 356 | C23 | — | 28 | 1 | no | — |
| 357 | C23 | #6502 | 1 | 1 | yes | characteristic |
| 358 | Q8 | — | 4 | 1 | no | — |
| 359 | Q8 | — | 4 | 2 | no | — |
| 360 | Q8 | — | 4 | 1 | no | — |
| 361 | Q8 | — | 4 | 2 | no | — |
| 362 | Q8 | — | 28 | 2 | no | — |
| 363 | D4 | — | 4 | 1 | no | — |
| 364 | D4 | — | 4 | 2 | no | — |
| 365 | D4 | — | 4 | 1 | no | — |
| 366 | D4 | — | 4 | 1 | no | — |
| 367 | D4 | — | 4 | 1 | no | — |
| 368 | D4 | — | 4 | 2 | no | — |
| 369 | D4 | — | 4 | 2 | no | — |
| 370 | D4 | — | 8 | 2 | no | — |
| 371 | D4 | — | 28 | 2 | no | — |
| 372 | D4 | — | 28 | 2 | no | — |
| 373 | D4 | — | 28 | 2 | no | — |
| 374 | D4 | — | 56 | 2 | no | — |
| 375 | C2×C4 | — | 2 | 2 | no | — |
| 376 | C2×C4 | — | 4 | 1 | no | — |
| 377 | C2×C4 | — | 4 | 1 | no | — |
| 378 | C2×C4 | — | 4 | 1 | no | — |
| 379 | C2×C4 | — | 4 | 1 | no | — |
| 380 | C2×C4 | — | 8 | 2 | no | — |
| 381 | C2×C4 | — | 8 | 1 | no | — |
| 382 | C2×C4 | — | 28 | 1 | no | — |
| 383 | C2×C4 | — | 56 | 2 | no | — |
| 384 | C2×C4 | #6500 | 1 | 1 | yes | characteristic |
| 385 | C2×C4 | #6500 | 1 | 1 | yes | characteristic |
| 386 | C2×C4 | #6501 | 1 | 1 | yes | characteristic |
| 387 | C2×C4 | #6502 | 1 | 1 | yes | characteristic |
| 388 | C2×C4 | #6503 | 1 | 1 | yes | characteristic |
| 389 | C2×C4 | #6516 | 1 | 1 | yes | characteristic |
| 390 | C8 | — | 2 | 4 | no | — |
| 391 | C8 | — | 28 | 2 | no | — |
| 392 | C8 | — | 28 | 2 | no | — |
| 393 | C8 | — | 56 | 1 | no | — |
| 394 | C7 | #10120 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 395 | C22 | — | 2 | 1 | no | — |
| 396 | C22 | — | 2 | 1 | no | — |
| 397 | C22 | — | 2 | 1 | no | — |
| 398 | C22 | — | 8 | 1 | no | — |
| 399 | C22 | — | 8 | 1 | no | — |
| 400 | C22 | — | 8 | 1 | no | — |
| 401 | C22 | — | 8 | 1 | no | — |
| 402 | C22 | — | 8 | 1 | no | — |
| 403 | C22 | — | 8 | 1 | no | — |
| 404 | C22 | — | 16 | 2 | no | — |
| 405 | C22 | — | 56 | 1 | no | — |
| 406 | C22 | — | 56 | 1 | no | — |
| 407 | C22 | — | 56 | 1 | no | — |
| 408 | C22 | #89995 | 1 | 1 | yes | characteristic |
| 409 | C4 | — | 2 | 1 | no | — |
| 410 | C4 | — | 2 | 1 | no | — |
| 411 | C4 | — | 2 | 1 | no | — |
| 412 | C4 | — | 2 | 1 | no | — |
| 413 | C4 | — | 2 | 1 | no | — |
| 414 | C4 | — | 8 | 1 | no | — |
| 415 | C4 | — | 8 | 1 | no | — |
| 416 | C4 | — | 56 | 1 | no | — |
| 417 | C4 | #89849 | 1 | 2 | yes | — |
| 418 | C2 | — | 4 | 1 | no | — |
| 419 | C2 | — | 16 | 1 | no | — |
| 420 | C2 | — | 16 | 1 | no | — |
| 421 | C2 | — | 112 | 1 | no | — |
| 422 | C2 | #11729523 | 1 | 1 | yes | characteristic |
| 423 | C2 | #11729873 | 1 | 1 | yes | characteristic |
| 424 | C2 | #11729875 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#3153 | C2 | semidirect |
| 2. #11740753 | C2 | semidirect |
| 3. #11740392 | C2 | semidirect |
| 4. #11729557 | C2 | semidirect |
| 5. #11729474 | C2 | semidirect |
| 6. #11727607 | C2 | semidirect |
| 7. #11725476 | C2 | semidirect |
| 87. #3153 | D7 | semidirect |
| 394. C7 | #10120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3153 | 2 |
| #11740753 | 2 |
| #11740392 | 2 |
| #11729557 | 2 |
| #11729474 | 2 |
| #11727607 | 2 |
| #11725476 | 2 |
| #10120 | 7 |