Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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 | C2×#89680 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11736701 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11736628 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11729192 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#89290 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11728410 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C7×#1389 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #90439 | — | 2 | 1 | no | — |
| 9 | C2×#6467 | C22 | 1 | 1 | yes | characteristic |
| 10 | C22×D56 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#6464 | C22 | 1 | 1 | yes | characteristic |
| 12 | #90216 | — | 2 | 1 | no | — |
| 13 | C2×C7×M32 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C7×#108 | C22 | 1 | 1 | yes | characteristic |
| 15 | C7×#427 | C22 | 1 | 1 | yes | characteristic |
| 16 | #89904 | — | 2 | 1 | no | — |
| 17 | C2×#6386 | C22 | 1 | 1 | yes | characteristic |
| 18 | #89773 | — | 2 | 1 | no | — |
| 19 | #89680 | — | 2 | 2 | no | — |
| 20 | #89680 | — | 2 | 2 | no | — |
| 21 | C2×#6374 | — | 2 | 1 | no | — |
| 22 | C2×D112 | — | 2 | 1 | no | — |
| 23 | #89670 | — | 2 | 2 | no | — |
| 24 | #89669 | — | 2 | 1 | no | — |
| 25 | #89668 | — | 2 | 1 | no | — |
| 26 | #89655 | — | 2 | 2 | no | — |
| 27 | #89637 | — | 2 | 2 | no | — |
| 28 | #89310 | — | 2 | 2 | no | — |
| 29 | #89290 | — | 2 | 2 | no | — |
| 30 | #89283 | — | 2 | 2 | no | — |
| 31 | #13310 | — | 7 | 1 | no | maximal, Sylow |
| 32 | C2×#1157 | — | 2 | 1 | no | — |
| 33 | C2×#1157 | D4 | 1 | 1 | yes | characteristic |
| 34 | C22×D28 | — | 2 | 1 | no | — |
| 35 | C2×C7×M16 | — | 2 | 1 | no | — |
| 36 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 37 | C7×#117 | — | 2 | 1 | no | — |
| 38 | C2×#1136 | D4 | 1 | 1 | yes | characteristic |
| 39 | #6472 | — | 2 | 2 | no | — |
| 40 | #6472 | — | 4 | 1 | no | — |
| 41 | #6471 | — | 2 | 2 | no | — |
| 42 | #6471 | — | 4 | 1 | no | — |
| 43 | C2×Dic28 | D4 | 1 | 1 | yes | characteristic, complemented |
| 44 | #6467 | — | 2 | 1 | no | — |
| 45 | #6467 | — | 2 | 1 | no | — |
| 46 | #6467 | — | 2 | 1 | no | — |
| 47 | #6467 | — | 2 | 1 | no | — |
| 48 | #6467 | — | 4 | 2 | no | — |
| 49 | C2×D56 | — | 2 | 1 | no | — |
| 50 | C2×D56 | — | 2 | 1 | no | — |
| 51 | C2×D56 | — | 2 | 1 | no | — |
| 52 | C2×D56 | — | 2 | 1 | no | — |
| 53 | C2×D56 | — | 2 | 1 | no | — |
| 54 | C2×D56 | D4 | 1 | 2 | yes | — |
| 55 | C2×D56 | D4 | 1 | 1 | yes | characteristic, complemented |
| 56 | C2×#1132 | — | 2 | 1 | no | — |
| 57 | #6464 | — | 2 | 1 | no | — |
| 58 | #6464 | — | 2 | 1 | no | — |
| 59 | #6464 | — | 2 | 1 | no | — |
| 60 | #6464 | — | 2 | 1 | no | — |
| 61 | C2×#1131 | — | 2 | 1 | no | — |
| 62 | C2×C8×D7 | — | 2 | 1 | no | — |
| 63 | #6458 | — | 2 | 4 | no | — |
| 64 | #6445 | — | 4 | 2 | no | — |
| 65 | #6438 | — | 4 | 1 | no | — |
| 66 | #6437 | — | 4 | 1 | no | — |
| 67 | C7×M32 | — | 2 | 1 | no | — |
| 68 | C7×M32 | D4 | 1 | 2 | yes | complemented |
| 69 | C2×C7×C16 | — | 2 | 1 | no | — |
| 70 | C7×#108 | — | 2 | 1 | no | — |
| 71 | C7×#108 | D4 | 1 | 2 | yes | complemented |
| 72 | C7×#107 | — | 2 | 1 | no | — |
| 73 | C7×#106 | D4 | 1 | 2 | yes | — |
| 74 | #6398 | — | 2 | 2 | no | — |
| 75 | #6397 | — | 2 | 2 | no | — |
| 76 | #6386 | — | 2 | 1 | no | — |
| 77 | #6386 | — | 2 | 1 | no | — |
| 78 | C2×C7⋊C16 | — | 2 | 1 | no | — |
| 79 | #6383 | — | 2 | 4 | no | — |
| 80 | #6374 | — | 2 | 4 | no | — |
| 81 | D112 | — | 2 | 4 | no | — |
| 82 | C2×#509 | — | 7 | 1 | no | — |
| 83 | #3067 | — | 7 | 1 | no | — |
| 84 | #3058 | — | 7 | 1 | no | — |
| 85 | C2×#361 | — | 7 | 1 | no | — |
| 86 | #2145 | — | 7 | 1 | no | — |
| 87 | #2117 | — | 7 | 1 | no | — |
| 88 | #1389 | D7 | 1 | 1 | yes | characteristic, complemented |
| 89 | C23×D7 | — | 4 | 1 | no | — |
| 90 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 92 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 93 | #1157 | — | 2 | 1 | no | — |
| 94 | #1157 | — | 2 | 1 | no | — |
| 95 | #1157 | — | 2 | 1 | no | — |
| 96 | #1157 | — | 2 | 1 | no | — |
| 97 | #1157 | — | 4 | 1 | no | — |
| 98 | #1157 | — | 4 | 1 | no | — |
| 99 | #1157 | — | 4 | 1 | no | — |
| 100 | #1157 | — | 4 | 1 | no | — |
| 101 | C2×D28 | — | 2 | 2 | no | — |
| 102 | C2×D28 | — | 2 | 1 | no | — |
| 103 | C2×D28 | — | 4 | 1 | no | — |
| 104 | C2×D28 | — | 4 | 1 | no | — |
| 105 | C2×D28 | — | 4 | 1 | no | — |
| 106 | C2×D28 | — | 4 | 1 | no | — |
| 107 | C2×D28 | — | 4 | 1 | no | — |
| 108 | C2×D28 | — | 4 | 4 | no | — |
| 109 | C2×D28 | D8 | 1 | 1 | yes | characteristic |
| 110 | C2×C4×D7 | — | 2 | 1 | no | — |
| 111 | C2×C4×D7 | — | 4 | 1 | no | — |
| 112 | C2×Dic14 | — | 2 | 1 | no | — |
| 113 | C2×Dic14 | D8 | 1 | 1 | yes | characteristic |
| 114 | C7×M16 | — | 2 | 2 | no | — |
| 115 | C7×M16 | — | 4 | 1 | no | — |
| 116 | C2×C7×C8 | — | 4 | 1 | no | — |
| 117 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 121 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | C2×C7×C8 | #41 | 1 | 1 | yes | characteristic |
| 123 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 124 | C7×C22⋊C4 | — | 4 | 1 | no | — |
| 125 | C42×C7 | — | 4 | 1 | no | — |
| 126 | (C2×D7)⋊C4 | — | 4 | 4 | no | — |
| 127 | #1136 | — | 2 | 1 | no | — |
| 128 | #1136 | — | 2 | 1 | no | — |
| 129 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 130 | Dic28 | — | 2 | 1 | no | — |
| 131 | Dic28 | — | 2 | 1 | no | — |
| 132 | Dic28 | — | 4 | 2 | no | — |
| 133 | D56 | — | 2 | 2 | no | — |
| 134 | D56 | — | 2 | 1 | no | — |
| 135 | D56 | — | 2 | 2 | no | — |
| 136 | D56 | — | 2 | 1 | no | — |
| 137 | D56 | — | 4 | 2 | no | — |
| 138 | D56 | — | 4 | 1 | no | — |
| 139 | D56 | — | 4 | 1 | no | — |
| 140 | #1132 | — | 4 | 2 | no | — |
| 141 | #1132 | — | 4 | 2 | no | — |
| 142 | #1132 | — | 4 | 1 | no | — |
| 143 | #1132 | — | 4 | 1 | no | — |
| 144 | #1131 | — | 4 | 1 | no | — |
| 145 | #1131 | — | 4 | 1 | no | — |
| 146 | C8×D7 | — | 4 | 1 | no | — |
| 147 | C8×D7 | — | 4 | 1 | no | — |
| 148 | C7×C16 | — | 2 | 2 | no | — |
| 149 | C7⋊C16 | — | 4 | 1 | no | — |
| 150 | #575 | — | 14 | 1 | no | — |
| 151 | C2×#135 | — | 7 | 1 | no | — |
| 152 | C22×D8 | — | 7 | 1 | no | — |
| 153 | C2×#131 | — | 7 | 1 | no | — |
| 154 | #535 | — | 14 | 1 | no | — |
| 155 | #509 | — | 14 | 2 | no | — |
| 156 | #509 | — | 14 | 2 | no | — |
| 157 | C2×SD32 | — | 14 | 1 | no | — |
| 158 | C2×D16 | — | 14 | 1 | no | — |
| 159 | C2×M32 | — | 7 | 1 | no | — |
| 160 | C2×M32 | C2×D7 | 1 | 1 | yes | characteristic |
| 161 | #473 | — | 14 | 1 | no | — |
| 162 | #472 | — | 14 | 1 | no | — |
| 163 | #471 | — | 14 | 2 | no | — |
| 164 | #469 | — | 14 | 2 | no | — |
| 165 | #466 | — | 14 | 2 | no | — |
| 166 | C2×#108 | C2×D7 | 1 | 1 | yes | characteristic |
| 167 | #427 | C2×D7 | 1 | 1 | yes | characteristic |
| 168 | #418 | — | 14 | 1 | no | — |
| 169 | #413 | — | 14 | 1 | no | — |
| 170 | #361 | — | 14 | 2 | no | — |
| 171 | #360 | — | 14 | 2 | no | — |
| 172 | #350 | — | 14 | 2 | no | — |
| 173 | C23×C7 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 174 | C22×D7 | — | 2 | 1 | no | — |
| 175 | C22×D7 | — | 4 | 2 | no | — |
| 176 | C22×D7 | — | 4 | 1 | no | — |
| 177 | C22×D7 | — | 8 | 1 | no | — |
| 178 | C22×D7 | — | 8 | 1 | no | — |
| 179 | C22×D7 | — | 16 | 2 | no | — |
| 180 | C2×C4×C7 | — | 4 | 2 | no | — |
| 181 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 182 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 183 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 184 | C2×C4×C7 | C2×D8 | 1 | 1 | yes | characteristic |
| 185 | C2×C4×C7 | #135 | 1 | 1 | yes | characteristic |
| 186 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 187 | C22⋊D7 | — | 4 | 1 | no | — |
| 188 | C22⋊D7 | — | 4 | 1 | no | — |
| 189 | C22⋊D7 | — | 8 | 1 | no | — |
| 190 | C22⋊D7 | — | 8 | 1 | no | — |
| 191 | C2×Dic7 | — | 2 | 1 | no | — |
| 192 | C2×Dic7 | — | 4 | 1 | no | — |
| 193 | D28 | — | 2 | 1 | no | — |
| 194 | D28 | — | 2 | 1 | no | — |
| 195 | D28 | — | 4 | 1 | no | — |
| 196 | D28 | — | 4 | 2 | no | — |
| 197 | D28 | — | 4 | 1 | no | — |
| 198 | D28 | — | 4 | 2 | no | — |
| 199 | D28 | — | 8 | 1 | no | — |
| 200 | D28 | — | 8 | 1 | no | — |
| 201 | D28 | — | 16 | 4 | no | — |
| 202 | C4×D7 | — | 4 | 1 | no | — |
| 203 | C4×D7 | — | 4 | 1 | no | — |
| 204 | C4×D7 | — | 8 | 1 | no | — |
| 205 | C4×D7 | — | 8 | 1 | no | — |
| 206 | Dic14 | — | 2 | 1 | no | — |
| 207 | Dic14 | — | 2 | 1 | no | — |
| 208 | Dic14 | — | 4 | 1 | no | — |
| 209 | Dic14 | — | 4 | 1 | no | — |
| 210 | C7×C8 | — | 4 | 2 | no | — |
| 211 | C7×C8 | #120 | 1 | 1 | yes | characteristic |
| 212 | C7×C8 | #121 | 1 | 1 | yes | characteristic |
| 213 | C7×C8 | #121 | 1 | 1 | yes | characteristic |
| 214 | C7×C8 | #127 | 1 | 1 | yes | characteristic |
| 215 | C7⋊C8 | — | 4 | 1 | no | — |
| 216 | C2×#41 | — | 7 | 1 | no | — |
| 217 | C2×#41 | — | 14 | 1 | no | — |
| 218 | C22×D4 | — | 14 | 1 | no | — |
| 219 | #137 | — | 14 | 2 | no | — |
| 220 | #137 | — | 28 | 1 | no | — |
| 221 | AGL(1,ℤ/8) | — | 14 | 2 | no | — |
| 222 | AGL(1,ℤ/8) | — | 28 | 1 | no | — |
| 223 | #135 | — | 14 | 1 | no | — |
| 224 | #135 | — | 14 | 1 | no | — |
| 225 | #135 | — | 14 | 1 | no | — |
| 226 | #135 | — | 14 | 1 | no | — |
| 227 | #135 | — | 28 | 2 | no | — |
| 228 | C2×Q16 | — | 7 | 1 | no | — |
| 229 | C2×SD16 | — | 14 | 1 | no | — |
| 230 | C2×D8 | — | 7 | 2 | no | — |
| 231 | C2×D8 | — | 7 | 1 | no | — |
| 232 | C2×D8 | — | 14 | 1 | no | — |
| 233 | C2×D8 | — | 14 | 1 | no | — |
| 234 | C2×D8 | — | 14 | 1 | no | — |
| 235 | C2×D8 | — | 14 | 1 | no | — |
| 236 | C2×D8 | — | 14 | 1 | no | — |
| 237 | #131 | — | 14 | 1 | no | — |
| 238 | #131 | — | 14 | 1 | no | — |
| 239 | #131 | — | 14 | 1 | no | — |
| 240 | #131 | — | 14 | 1 | no | — |
| 241 | C2×M16 | — | 2 | 1 | no | — |
| 242 | C2×M16 | — | 7 | 1 | no | — |
| 243 | C2×M16 | — | 14 | 1 | no | — |
| 244 | C22×C8 | — | 14 | 1 | no | — |
| 245 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 246 | #127 | — | 28 | 1 | no | — |
| 247 | #124 | — | 28 | 1 | no | — |
| 248 | #121 | — | 14 | 4 | no | — |
| 249 | #120 | — | 28 | 2 | no | — |
| 250 | #117 | — | 2 | 1 | no | — |
| 251 | SD32 | — | 14 | 4 | no | — |
| 252 | D16 | — | 14 | 4 | no | — |
| 253 | M32 | — | 2 | 1 | no | — |
| 254 | M32 | — | 14 | 1 | no | — |
| 255 | M32 | — | 14 | 1 | no | — |
| 256 | M32 | D28 | 1 | 2 | yes | complemented |
| 257 | C2×C16 | — | 2 | 1 | no | — |
| 258 | C2×C16 | — | 14 | 1 | no | — |
| 259 | #108 | — | 2 | 1 | no | — |
| 260 | #108 | D28 | 1 | 2 | yes | complemented |
| 261 | #107 | — | 2 | 1 | no | — |
| 262 | #106 | D28 | 1 | 2 | yes | — |
| 263 | #102 | — | 14 | 4 | no | — |
| 264 | #101 | — | 14 | 2 | no | — |
| 265 | #100 | — | 14 | 2 | no | — |
| 266 | C22×C7 | — | 4 | 1 | no | — |
| 267 | C22×C7 | #447 | 1 | 1 | yes | characteristic |
| 268 | C22×C7 | #449 | 1 | 1 | yes | characteristic |
| 269 | C22×C7 | #469 | 1 | 1 | yes | characteristic |
| 270 | C2×D7 | — | 4 | 2 | no | — |
| 271 | C2×D7 | — | 4 | 1 | no | — |
| 272 | C2×D7 | — | 8 | 4 | no | — |
| 273 | C2×D7 | — | 8 | 1 | no | — |
| 274 | C2×D7 | — | 8 | 2 | no | — |
| 275 | C2×D7 | — | 16 | 2 | no | — |
| 276 | C2×D7 | — | 16 | 2 | no | — |
| 277 | C2×D7 | — | 16 | 1 | no | — |
| 278 | C4×C7 | — | 8 | 2 | no | — |
| 279 | C4×C7 | #392 | 1 | 1 | yes | characteristic |
| 280 | C4×C7 | #447 | 1 | 1 | yes | characteristic |
| 281 | C4×C7 | #449 | 1 | 1 | yes | characteristic |
| 282 | C4×C7 | #466 | 1 | 1 | yes | characteristic |
| 283 | Dic7 | — | 4 | 1 | no | — |
| 284 | Dic7 | — | 8 | 1 | no | — |
| 285 | C24 | — | 28 | 1 | no | — |
| 286 | #41 | — | 14 | 1 | no | — |
| 287 | #41 | — | 14 | 1 | no | — |
| 288 | #41 | — | 14 | 1 | no | — |
| 289 | #41 | — | 14 | 1 | no | — |
| 290 | #41 | — | 28 | 1 | no | — |
| 291 | #41 | — | 28 | 1 | no | — |
| 292 | #41 | — | 28 | 1 | no | — |
| 293 | #41 | — | 28 | 1 | no | — |
| 294 | C2×Q8 | — | 7 | 1 | no | — |
| 295 | C2×Q8 | — | 14 | 1 | no | — |
| 296 | C2×D4 | — | 7 | 1 | no | — |
| 297 | C2×D4 | — | 14 | 1 | no | — |
| 298 | C2×D4 | — | 14 | 1 | no | — |
| 299 | C2×D4 | — | 14 | 2 | no | — |
| 300 | C2×D4 | — | 28 | 4 | no | — |
| 301 | C2×D4 | — | 28 | 1 | no | — |
| 302 | C2×D4 | — | 28 | 1 | no | — |
| 303 | C2×D4 | — | 28 | 1 | no | — |
| 304 | C2×D4 | — | 28 | 1 | no | — |
| 305 | C2×D4 | — | 28 | 1 | no | — |
| 306 | C2×D4 | — | 28 | 1 | no | — |
| 307 | C22×C4 | — | 14 | 1 | no | — |
| 308 | C22×C4 | — | 28 | 1 | no | — |
| 309 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 310 | Q16 | — | 14 | 1 | no | — |
| 311 | Q16 | — | 14 | 1 | no | — |
| 312 | Q16 | — | 28 | 2 | no | — |
| 313 | SD16 | — | 28 | 2 | no | — |
| 314 | SD16 | — | 28 | 2 | no | — |
| 315 | SD16 | — | 28 | 1 | no | — |
| 316 | SD16 | — | 28 | 1 | no | — |
| 317 | D8 | — | 14 | 1 | no | — |
| 318 | D8 | — | 14 | 2 | no | — |
| 319 | D8 | — | 14 | 2 | no | — |
| 320 | D8 | — | 14 | 1 | no | — |
| 321 | D8 | — | 28 | 2 | no | — |
| 322 | D8 | — | 28 | 1 | no | — |
| 323 | D8 | — | 28 | 1 | no | — |
| 324 | M16 | — | 2 | 2 | no | — |
| 325 | M16 | — | 4 | 1 | no | — |
| 326 | M16 | — | 14 | 1 | no | — |
| 327 | M16 | — | 14 | 1 | no | — |
| 328 | M16 | — | 28 | 1 | no | — |
| 329 | M16 | — | 28 | 1 | no | — |
| 330 | C2×C8 | — | 4 | 1 | no | — |
| 331 | C2×C8 | — | 14 | 1 | no | — |
| 332 | C2×C8 | — | 28 | 1 | no | — |
| 333 | C2×C8 | — | 28 | 1 | no | — |
| 334 | C2×C8 | C2×D28 | 1 | 1 | yes | characteristic |
| 335 | C2×C8 | C2×D28 | 1 | 1 | yes | characteristic |
| 336 | C2×C8 | C2×D28 | 1 | 1 | yes | characteristic |
| 337 | C2×C8 | D4×D7 | 1 | 1 | yes | characteristic |
| 338 | C2×C8 | D4×D7 | 1 | 1 | yes | characteristic |
| 339 | C2×C8 | #1161 | 1 | 1 | yes | characteristic |
| 340 | C4⋊C4 | — | 2 | 2 | no | — |
| 341 | C22⋊C4 | — | 4 | 1 | no | — |
| 342 | C22⋊C4 | — | 28 | 4 | no | — |
| 343 | C42 | — | 4 | 1 | no | — |
| 344 | C16 | — | 2 | 2 | no | — |
| 345 | C16 | — | 28 | 1 | no | — |
| 346 | C2×C7 | — | 2 | 1 | no | — |
| 347 | C2×C7 | — | 2 | 1 | no | — |
| 348 | C2×C7 | — | 2 | 1 | no | — |
| 349 | C2×C7 | #1999 | 1 | 1 | yes | characteristic |
| 350 | D7 | — | 8 | 1 | no | — |
| 351 | D7 | — | 16 | 2 | no | — |
| 352 | D7 | — | 16 | 1 | no | — |
| 353 | C23 | — | 14 | 1 | no | — |
| 354 | C23 | — | 28 | 2 | no | — |
| 355 | C23 | — | 28 | 1 | no | — |
| 356 | C23 | — | 56 | 1 | no | — |
| 357 | C23 | — | 56 | 1 | no | — |
| 358 | C23 | — | 112 | 2 | no | — |
| 359 | C23 | #6477 | 1 | 1 | yes | characteristic |
| 360 | Q8 | — | 14 | 1 | no | — |
| 361 | Q8 | — | 14 | 1 | no | — |
| 362 | Q8 | — | 28 | 1 | no | — |
| 363 | Q8 | — | 28 | 1 | no | — |
| 364 | D4 | — | 14 | 1 | no | — |
| 365 | D4 | — | 14 | 1 | no | — |
| 366 | D4 | — | 28 | 1 | no | — |
| 367 | D4 | — | 28 | 1 | no | — |
| 368 | D4 | — | 28 | 2 | no | — |
| 369 | D4 | — | 28 | 1 | no | — |
| 370 | D4 | — | 28 | 1 | no | — |
| 371 | D4 | — | 28 | 2 | no | — |
| 372 | D4 | — | 56 | 1 | no | — |
| 373 | D4 | — | 56 | 1 | no | — |
| 374 | D4 | — | 56 | 1 | no | — |
| 375 | D4 | — | 56 | 1 | no | — |
| 376 | D4 | — | 112 | 4 | no | — |
| 377 | C2×C4 | — | 4 | 2 | no | — |
| 378 | C2×C4 | — | 14 | 1 | no | — |
| 379 | C2×C4 | — | 28 | 1 | no | — |
| 380 | C2×C4 | — | 28 | 1 | no | — |
| 381 | C2×C4 | — | 28 | 1 | no | — |
| 382 | C2×C4 | — | 56 | 1 | no | — |
| 383 | C2×C4 | — | 56 | 1 | no | — |
| 384 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 385 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 386 | C2×C4 | #6458 | 1 | 1 | yes | characteristic |
| 387 | C2×C4 | D7×D8 | 1 | 1 | yes | characteristic |
| 388 | C2×C4 | #6477 | 1 | 1 | yes | characteristic |
| 389 | C2×C4 | #6482 | 1 | 1 | yes | characteristic |
| 390 | C8 | — | 4 | 2 | no | — |
| 391 | C8 | — | 28 | 1 | no | — |
| 392 | C8 | #6437 | 1 | 1 | yes | characteristic |
| 393 | C8 | #6445 | 1 | 1 | yes | characteristic |
| 394 | C8 | #6458 | 1 | 1 | yes | characteristic |
| 395 | C8 | #6458 | 1 | 1 | yes | characteristic |
| 396 | C7 | #13310 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 397 | C22 | — | 4 | 1 | no | — |
| 398 | C22 | — | 28 | 2 | no | — |
| 399 | C22 | — | 28 | 1 | no | — |
| 400 | C22 | — | 56 | 4 | no | — |
| 401 | C22 | — | 56 | 1 | no | — |
| 402 | C22 | — | 56 | 2 | no | — |
| 403 | C22 | — | 112 | 1 | no | — |
| 404 | C22 | — | 112 | 2 | no | — |
| 405 | C22 | — | 112 | 2 | no | — |
| 406 | C22 | #89545 | 1 | 1 | yes | characteristic |
| 407 | C22 | #89583 | 1 | 1 | yes | characteristic |
| 408 | C22 | #89637 | 1 | 1 | yes | characteristic |
| 409 | C4 | — | 8 | 2 | no | — |
| 410 | C4 | — | 28 | 1 | no | — |
| 411 | C4 | — | 56 | 1 | no | — |
| 412 | C4 | #89443 | 1 | 1 | yes | characteristic |
| 413 | C4 | #89545 | 1 | 1 | yes | characteristic |
| 414 | C4 | #89583 | 1 | 1 | yes | characteristic |
| 415 | C4 | #89655 | 1 | 1 | yes | characteristic |
| 416 | C2 | — | 2 | 1 | no | — |
| 417 | C2 | — | 2 | 1 | no | — |
| 418 | C2 | — | 2 | 1 | no | — |
| 419 | C2 | — | 56 | 1 | no | — |
| 420 | C2 | — | 112 | 2 | no | — |
| 421 | C2 | — | 112 | 1 | no | — |
| 422 | C2 | #11726640 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#89680 | C2 | semidirect |
| 2. #11736701 | C2 | semidirect |
| 3. #11736628 | C2 | semidirect |
| 4. #11729192 | C2 | semidirect |
| 5. C2×#89290 | C2 | semidirect |
| 6. #11728410 | C2 | semidirect |
| 7. C7×#1389 | C2 | semidirect |
| 43. C2×Dic28 | D4 | semidirect |
| 55. C2×D56 | D4 | semidirect |
| 68. C7×M32 | D4 | semidirect |
| 71. C7×#108 | D4 | semidirect |
| 88. #1389 | D7 | semidirect |
| 256. M32 | D28 | semidirect |
| 260. #108 | D28 | semidirect |
| 396. C7 | #13310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89680 | 2 |
| #11736701 | 2 |
| #11736628 | 2 |
| #11729192 | 2 |
| C2×#89290 | 2 |
| #11728410 | 2 |
| C7×#1389 | 2 |
| #13310 | 7 |