Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
640 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 89 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 | #11736160 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11736123 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #11727903 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11727900 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11727895 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C7×#1392 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11725498 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#6554 | C22 | 1 | 1 | yes | characteristic |
| 9 | #90521 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#6471 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | #90436 | — | 2 | 1 | no | — |
| 12 | C22×#1132 | C4 | 1 | 1 | yes | characteristic, complemented |
| 13 | C7×#413 | C22 | 1 | 1 | yes | characteristic |
| 14 | C7×#413 | C22 | 1 | 1 | yes | characteristic |
| 15 | C7×#408 | C22 | 1 | 1 | yes | characteristic |
| 16 | #90012 | C22 | 1 | 1 | yes | characteristic |
| 17 | #90009 | C22 | 1 | 1 | yes | characteristic |
| 18 | #89911 | — | 2 | 1 | no | — |
| 19 | C2×#6398 | — | 2 | 1 | no | — |
| 20 | #89892 | — | 2 | 1 | no | — |
| 21 | #89892 | C4 | 1 | 1 | yes | characteristic, complemented |
| 22 | #89885 | C4 | 1 | 1 | yes | characteristic, complemented |
| 23 | D7×#101 | — | 2 | 2 | no | — |
| 24 | #89517 | — | 2 | 2 | no | — |
| 25 | #89510 | — | 2 | 1 | no | — |
| 26 | #89510 | — | 2 | 1 | no | — |
| 27 | #89506 | — | 2 | 1 | no | — |
| 28 | #89506 | — | 2 | 1 | no | — |
| 29 | #89272 | — | 2 | 2 | no | — |
| 30 | #89270 | — | 2 | 2 | no | — |
| 31 | #13098 | — | 7 | 1 | no | maximal, Sylow |
| 32 | C2×C7×#41 | C23 | 1 | 1 | yes | characteristic |
| 33 | #6554 | — | 4 | 2 | no | — |
| 34 | #6554 | — | 4 | 2 | no | — |
| 35 | C2×Q8×D7 | — | 2 | 1 | no | — |
| 36 | C2×#1159 | — | 2 | 1 | no | — |
| 37 | C2×#1159 | — | 2 | 1 | no | — |
| 38 | C2×#1159 | — | 2 | 1 | no | — |
| 39 | C2×#1157 | C2×C4 | 1 | 1 | yes | characteristic |
| 40 | C2×#1157 | D4 | 1 | 1 | yes | characteristic |
| 41 | C2×#1157 | D4 | 1 | 1 | yes | characteristic |
| 42 | C22×D28 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | C22×Dic14 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | C22×Dic14 | D4 | 1 | 1 | yes | characteristic |
| 45 | C22×Dic14 | D4 | 1 | 1 | yes | characteristic |
| 46 | C2×C7×M16 | — | 2 | 1 | no | — |
| 47 | C2×C7×M16 | — | 2 | 1 | no | — |
| 48 | C2×C7×M16 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C22×C7×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | #6510 | — | 2 | 1 | no | — |
| 51 | #6503 | — | 2 | 1 | no | — |
| 52 | #6500 | — | 2 | 1 | no | — |
| 53 | #6500 | — | 2 | 1 | no | — |
| 54 | #6493 | — | 2 | 1 | no | — |
| 55 | #6493 | — | 2 | 1 | no | — |
| 56 | #6489 | — | 2 | 1 | no | — |
| 57 | #6489 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | C2×#1136 | — | 2 | 1 | no | — |
| 59 | #6471 | — | 4 | 2 | no | — |
| 60 | #6470 | — | 4 | 2 | no | — |
| 61 | D7×M16 | — | 2 | 4 | no | — |
| 62 | C2×D56 | — | 2 | 1 | no | — |
| 63 | C2×#1132 | — | 2 | 1 | no | — |
| 64 | C2×#1132 | — | 2 | 1 | no | — |
| 65 | C2×#1132 | — | 2 | 1 | no | — |
| 66 | C2×#1132 | — | 4 | 2 | no | — |
| 67 | #6464 | — | 4 | 2 | no | — |
| 68 | C7×#101 | — | 2 | 1 | no | — |
| 69 | C7×#101 | — | 2 | 1 | no | — |
| 70 | C7×#100 | — | 2 | 1 | no | — |
| 71 | C7×#100 | D4 | 1 | 2 | yes | — |
| 72 | C7×C22⋊C8 | — | 2 | 1 | no | — |
| 73 | C7×C22⋊C8 | — | 2 | 1 | no | — |
| 74 | #6410 | D4 | 1 | 2 | yes | — |
| 75 | #6408 | — | 2 | 1 | no | — |
| 76 | #6408 | — | 2 | 1 | no | — |
| 77 | #6407 | — | 2 | 1 | no | — |
| 78 | #6399 | — | 4 | 2 | no | — |
| 79 | #6398 | — | 2 | 4 | no | — |
| 80 | #6395 | — | 2 | 1 | no | — |
| 81 | #6390 | — | 2 | 1 | no | — |
| 82 | #6390 | — | 2 | 1 | no | — |
| 83 | #6390 | — | 2 | 1 | no | — |
| 84 | #6390 | — | 4 | 2 | no | — |
| 85 | #3010 | — | 7 | 1 | no | — |
| 86 | #2889 | — | 7 | 1 | no | — |
| 87 | #2134 | — | 7 | 1 | no | — |
| 88 | #2122 | — | 7 | 1 | no | — |
| 89 | #1796 | — | 7 | 1 | no | — |
| 90 | #1395 | — | 7 | 1 | no | — |
| 91 | #1392 | D7 | 1 | 1 | yes | characteristic, complemented |
| 92 | C23×D7 | — | 2 | 1 | no | — |
| 93 | C7×#41 | — | 4 | 1 | no | — |
| 94 | C7×#41 | — | 4 | 1 | no | — |
| 95 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C2×C7×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C2×C7×D4 | #41 | 1 | 1 | yes | characteristic |
| 98 | C2×C7×D4 | #41 | 1 | 1 | yes | characteristic |
| 99 | C22×C4×C7 | C22×C4 | 1 | 1 | yes | characteristic |
| 100 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 101 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 103 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 104 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 105 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 106 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 107 | C22×Dic7 | — | 2 | 1 | no | — |
| 108 | C22×Dic7 | — | 2 | 1 | no | — |
| 109 | C22×Dic7 | — | 2 | 1 | no | — |
| 110 | Q8×D7 | — | 4 | 4 | no | — |
| 111 | #1159 | — | 4 | 4 | no | — |
| 112 | #1159 | — | 4 | 4 | no | — |
| 113 | #1159 | — | 4 | 4 | no | — |
| 114 | #1157 | — | 2 | 2 | no | — |
| 115 | #1157 | — | 2 | 2 | no | — |
| 116 | #1157 | — | 2 | 2 | no | — |
| 117 | #1157 | — | 2 | 2 | no | — |
| 118 | #1157 | — | 4 | 1 | no | — |
| 119 | #1157 | — | 4 | 1 | no | — |
| 120 | C2×D28 | — | 2 | 1 | no | — |
| 121 | C2×D28 | — | 2 | 1 | no | — |
| 122 | C2×D28 | — | 4 | 1 | no | — |
| 123 | C2×D28 | — | 4 | 1 | no | — |
| 124 | C2×D28 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 125 | C2×C4×D7 | — | 2 | 1 | no | — |
| 126 | C2×C4×D7 | — | 2 | 1 | no | — |
| 127 | C2×C4×D7 | — | 2 | 1 | no | — |
| 128 | C2×Dic14 | — | 2 | 2 | no | — |
| 129 | C2×Dic14 | — | 2 | 2 | no | — |
| 130 | C2×Dic14 | — | 2 | 1 | no | — |
| 131 | C2×Dic14 | — | 2 | 1 | no | — |
| 132 | C2×Dic14 | — | 2 | 1 | no | — |
| 133 | C2×Dic14 | — | 4 | 1 | no | — |
| 134 | C2×Dic14 | — | 4 | 1 | no | — |
| 135 | C2×Dic14 | — | 4 | 1 | no | — |
| 136 | C2×Dic14 | — | 4 | 1 | no | — |
| 137 | C2×Dic14 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 138 | C2×Dic14 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 139 | C2×Dic14 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 140 | C7×M16 | — | 2 | 2 | no | — |
| 141 | C7×M16 | — | 4 | 1 | no | — |
| 142 | C7×M16 | — | 4 | 1 | no | — |
| 143 | C7×M16 | — | 4 | 1 | no | — |
| 144 | C7×M16 | — | 4 | 1 | no | — |
| 145 | C2×C7×C8 | — | 2 | 1 | no | — |
| 146 | C2×C7×C8 | — | 2 | 1 | no | — |
| 147 | C2×C7×C8 | — | 4 | 1 | no | — |
| 148 | C2×C7×C8 | — | 4 | 1 | no | — |
| 149 | C2×C7×C8 | — | 4 | 1 | no | — |
| 150 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 151 | C22⋊Dic7 | — | 4 | 1 | no | — |
| 152 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 153 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 154 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 155 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 156 | C4×Dic7 | — | 2 | 1 | no | — |
| 157 | C4×Dic7 | — | 4 | 1 | no | — |
| 158 | #1136 | — | 2 | 2 | no | — |
| 159 | #1136 | — | 4 | 1 | no | — |
| 160 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 161 | D56 | — | 4 | 2 | no | — |
| 162 | #1132 | — | 4 | 2 | no | — |
| 163 | #1132 | — | 4 | 2 | no | — |
| 164 | #1132 | — | 4 | 2 | no | — |
| 165 | #1131 | — | 4 | 4 | no | — |
| 166 | C8×D7 | — | 4 | 4 | no | — |
| 167 | C2×2−1+4 | — | 7 | 1 | no | — |
| 168 | C2×AGL(1,ℤ/8) | — | 7 | 1 | no | — |
| 169 | C22×SD16 | — | 7 | 1 | no | — |
| 170 | #568 | — | 14 | 1 | no | — |
| 171 | #535 | — | 7 | 1 | no | — |
| 172 | #449 | — | 14 | 1 | no | — |
| 173 | #449 | — | 14 | 1 | no | — |
| 174 | #448 | — | 14 | 1 | no | — |
| 175 | #448 | — | 14 | 1 | no | — |
| 176 | #421 | — | 14 | 1 | no | — |
| 177 | #419 | — | 7 | 1 | no | — |
| 178 | #419 | — | 14 | 1 | no | — |
| 179 | #416 | — | 7 | 1 | no | — |
| 180 | #413 | — | 7 | 1 | no | — |
| 181 | #413 | — | 14 | 2 | no | — |
| 182 | #413 | C2×D7 | 1 | 1 | yes | characteristic |
| 183 | #413 | C2×D7 | 1 | 1 | yes | characteristic |
| 184 | C2×#101 | — | 14 | 2 | no | — |
| 185 | C2×#101 | — | 14 | 1 | no | — |
| 186 | #410 | — | 7 | 1 | no | — |
| 187 | #408 | C2×D7 | 1 | 1 | yes | characteristic |
| 188 | #355 | — | 14 | 2 | no | — |
| 189 | AΣL(1,𝔽16) | — | 14 | 2 | no | — |
| 190 | C23×C7 | C4×D4 | 1 | 1 | yes | characteristic |
| 191 | C23×C7 | #121 | 1 | 1 | yes | characteristic |
| 192 | C23×C7 | #123 | 1 | 1 | yes | characteristic |
| 193 | C22×D7 | — | 2 | 1 | no | — |
| 194 | C22×D7 | — | 4 | 1 | no | — |
| 195 | C22×D7 | — | 8 | 1 | no | — |
| 196 | C22×D7 | — | 16 | 1 | no | — |
| 197 | C7×Q8 | — | 4 | 1 | no | — |
| 198 | C7×D4 | — | 4 | 1 | no | — |
| 199 | C7×D4 | — | 4 | 1 | no | — |
| 200 | C7×D4 | — | 4 | 1 | no | — |
| 201 | C2×C4×C7 | — | 2 | 1 | no | — |
| 202 | C2×C4×C7 | — | 2 | 1 | no | — |
| 203 | C2×C4×C7 | — | 2 | 1 | no | — |
| 204 | C2×C4×C7 | — | 2 | 1 | no | — |
| 205 | C2×C4×C7 | — | 2 | 1 | no | — |
| 206 | C2×C4×C7 | — | 2 | 1 | no | — |
| 207 | C2×C4×C7 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 208 | C2×C4×C7 | C4×D4 | 1 | 1 | yes | characteristic |
| 209 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 210 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 211 | C22⋊D7 | — | 2 | 4 | no | — |
| 212 | C22⋊D7 | — | 4 | 2 | no | — |
| 213 | C22⋊D7 | — | 4 | 2 | no | — |
| 214 | C22⋊D7 | — | 16 | 1 | no | — |
| 215 | C22⋊D7 | — | 16 | 1 | no | — |
| 216 | C2×Dic7 | — | 2 | 1 | no | — |
| 217 | C2×Dic7 | — | 2 | 1 | no | — |
| 218 | C2×Dic7 | — | 2 | 1 | no | — |
| 219 | C2×Dic7 | — | 4 | 2 | no | — |
| 220 | C2×Dic7 | — | 4 | 2 | no | — |
| 221 | C2×Dic7 | — | 4 | 2 | no | — |
| 222 | C2×Dic7 | — | 4 | 1 | no | — |
| 223 | C2×Dic7 | — | 8 | 1 | no | — |
| 224 | D28 | — | 2 | 1 | no | — |
| 225 | D28 | — | 4 | 1 | no | — |
| 226 | D28 | — | 4 | 1 | no | — |
| 227 | D28 | — | 8 | 1 | no | — |
| 228 | D28 | #99 | 1 | 2 | yes | — |
| 229 | C4×D7 | — | 2 | 4 | no | — |
| 230 | C4×D7 | — | 4 | 2 | no | — |
| 231 | C4×D7 | — | 4 | 2 | no | — |
| 232 | Dic14 | — | 2 | 1 | no | — |
| 233 | Dic14 | — | 2 | 1 | no | — |
| 234 | Dic14 | — | 2 | 1 | no | — |
| 235 | Dic14 | — | 2 | 1 | no | — |
| 236 | Dic14 | — | 2 | 1 | no | — |
| 237 | Dic14 | — | 4 | 2 | no | — |
| 238 | Dic14 | — | 4 | 2 | no | — |
| 239 | Dic14 | — | 4 | 2 | no | — |
| 240 | Dic14 | #99 | 1 | 2 | yes | — |
| 241 | C7×C8 | — | 4 | 2 | no | — |
| 242 | C7×C8 | — | 4 | 1 | no | — |
| 243 | C7×C8 | — | 4 | 1 | no | — |
| 244 | C7×C8 | — | 8 | 1 | no | — |
| 245 | C7⋊C8 | — | 4 | 2 | no | — |
| 246 | 2−1+4 | — | 28 | 2 | no | — |
| 247 | 2−1+4 | — | 28 | 2 | no | — |
| 248 | C2×#41 | — | 7 | 1 | no | — |
| 249 | C2×#41 | — | 7 | 1 | no | — |
| 250 | C2×#41 | — | 7 | 1 | no | — |
| 251 | C2×#41 | — | 14 | 1 | no | — |
| 252 | C2×#41 | — | 14 | 1 | no | — |
| 253 | C2×#41 | — | 14 | 1 | no | — |
| 254 | C2×#41 | C22×D7 | 1 | 1 | yes | characteristic |
| 255 | C22×Q8 | — | 7 | 1 | no | — |
| 256 | C22×Q8 | — | 7 | 1 | no | — |
| 257 | C22×Q8 | — | 7 | 1 | no | — |
| 258 | C22×Q8 | — | 14 | 1 | no | — |
| 259 | C22×D4 | — | 7 | 1 | no | — |
| 260 | AGL(1,ℤ/8) | — | 28 | 2 | no | — |
| 261 | C2×SD16 | — | 14 | 1 | no | — |
| 262 | C2×SD16 | — | 14 | 1 | no | — |
| 263 | C2×SD16 | — | 14 | 1 | no | — |
| 264 | C2×SD16 | — | 28 | 2 | no | — |
| 265 | C2×D8 | — | 14 | 1 | no | — |
| 266 | #131 | — | 28 | 2 | no | — |
| 267 | #131 | — | 28 | 2 | no | — |
| 268 | C2×M16 | — | 2 | 1 | no | — |
| 269 | C2×M16 | — | 2 | 1 | no | — |
| 270 | C2×M16 | — | 14 | 4 | no | — |
| 271 | C2×M16 | — | 14 | 1 | no | — |
| 272 | C2×M16 | C4×D7 | 1 | 1 | yes | characteristic |
| 273 | C22×C8 | C4×D7 | 1 | 1 | yes | characteristic |
| 274 | #127 | — | 14 | 1 | no | — |
| 275 | #124 | — | 14 | 1 | no | — |
| 276 | #121 | — | 14 | 1 | no | — |
| 277 | #121 | — | 14 | 1 | no | — |
| 278 | #120 | — | 14 | 1 | no | — |
| 279 | #120 | — | 14 | 1 | no | — |
| 280 | #117 | — | 7 | 1 | no | — |
| 281 | #117 | — | 14 | 1 | no | — |
| 282 | #104 | — | 28 | 2 | no | — |
| 283 | #103 | — | 14 | 1 | no | — |
| 284 | #103 | — | 14 | 1 | no | — |
| 285 | #103 | — | 14 | 1 | no | — |
| 286 | #103 | — | 28 | 2 | no | — |
| 287 | #102 | — | 14 | 1 | no | — |
| 288 | #101 | — | 2 | 1 | no | — |
| 289 | #101 | — | 2 | 1 | no | — |
| 290 | #101 | — | 7 | 2 | no | — |
| 291 | #101 | — | 14 | 4 | no | — |
| 292 | #100 | — | 2 | 1 | no | — |
| 293 | #100 | — | 14 | 1 | no | — |
| 294 | #100 | D28 | 1 | 2 | yes | — |
| 295 | #99 | — | 14 | 1 | no | — |
| 296 | #99 | — | 14 | 1 | no | — |
| 297 | C22⋊C8 | — | 2 | 1 | no | — |
| 298 | C22⋊C8 | — | 2 | 1 | no | — |
| 299 | C22×C7 | — | 2 | 1 | no | — |
| 300 | C22×C7 | — | 2 | 1 | no | — |
| 301 | C22×C7 | — | 2 | 1 | no | — |
| 302 | C22×C7 | — | 4 | 1 | no | — |
| 303 | C22×C7 | — | 4 | 1 | no | — |
| 304 | C22×C7 | — | 4 | 1 | no | — |
| 305 | C22×C7 | #386 | 1 | 1 | yes | characteristic |
| 306 | C2×D7 | — | 2 | 2 | no | — |
| 307 | C2×D7 | — | 8 | 1 | no | — |
| 308 | C2×D7 | — | 8 | 1 | no | — |
| 309 | C2×D7 | — | 8 | 1 | no | — |
| 310 | C2×D7 | — | 8 | 1 | no | — |
| 311 | C2×D7 | — | 16 | 2 | no | — |
| 312 | C4×C7 | — | 2 | 1 | no | — |
| 313 | C4×C7 | — | 2 | 1 | no | — |
| 314 | C4×C7 | — | 2 | 1 | no | — |
| 315 | C4×C7 | C2×#99 | 1 | 1 | yes | characteristic |
| 316 | C4×C7 | C2×#99 | 1 | 1 | yes | characteristic |
| 317 | Dic7 | — | 2 | 2 | no | — |
| 318 | Dic7 | — | 4 | 1 | no | — |
| 319 | Dic7 | — | 4 | 1 | no | — |
| 320 | Dic7 | — | 8 | 1 | no | — |
| 321 | Dic7 | — | 16 | 1 | no | — |
| 322 | C24 | — | 14 | 1 | no | — |
| 323 | #41 | — | 4 | 1 | no | — |
| 324 | #41 | — | 4 | 1 | no | — |
| 325 | #41 | — | 14 | 2 | no | — |
| 326 | #41 | — | 14 | 2 | no | — |
| 327 | #41 | — | 14 | 2 | no | — |
| 328 | #41 | — | 14 | 2 | no | — |
| 329 | #41 | — | 28 | 1 | no | — |
| 330 | #41 | — | 28 | 1 | no | — |
| 331 | #41 | — | 28 | 4 | no | — |
| 332 | #41 | — | 28 | 4 | no | — |
| 333 | #41 | — | 28 | 4 | no | — |
| 334 | C2×Q8 | — | 7 | 1 | no | — |
| 335 | C2×Q8 | — | 7 | 1 | no | — |
| 336 | C2×Q8 | — | 7 | 1 | no | — |
| 337 | C2×Q8 | — | 14 | 2 | no | — |
| 338 | C2×Q8 | — | 14 | 2 | no | — |
| 339 | C2×Q8 | — | 14 | 1 | no | — |
| 340 | C2×Q8 | — | 14 | 1 | no | — |
| 341 | C2×Q8 | — | 14 | 1 | no | — |
| 342 | C2×Q8 | — | 28 | 1 | no | — |
| 343 | C2×Q8 | — | 28 | 1 | no | — |
| 344 | C2×Q8 | — | 28 | 1 | no | — |
| 345 | C2×Q8 | — | 28 | 1 | no | — |
| 346 | C2×Q8 | — | 28 | 4 | no | — |
| 347 | C2×Q8 | D4×D7 | 1 | 1 | yes | characteristic |
| 348 | C2×D4 | — | 7 | 1 | no | — |
| 349 | C2×D4 | — | 14 | 1 | no | — |
| 350 | C2×D4 | — | 14 | 1 | no | — |
| 351 | C2×D4 | — | 14 | 1 | no | — |
| 352 | C2×D4 | — | 14 | 1 | no | — |
| 353 | C2×D4 | — | 14 | 1 | no | — |
| 354 | C2×D4 | — | 28 | 1 | no | — |
| 355 | C2×D4 | — | 28 | 1 | no | — |
| 356 | C2×D4 | — | 28 | 1 | no | — |
| 357 | C2×D4 | — | 28 | 1 | no | — |
| 358 | C2×D4 | C2×D28 | 1 | 1 | yes | characteristic |
| 359 | C2×D4 | #1157 | 1 | 1 | yes | characteristic |
| 360 | C2×D4 | #1161 | 1 | 1 | yes | characteristic |
| 361 | C22×C4 | — | 14 | 1 | no | — |
| 362 | C22×C4 | — | 14 | 1 | no | — |
| 363 | C22×C4 | — | 14 | 1 | no | — |
| 364 | C22×C4 | — | 14 | 1 | no | — |
| 365 | C22×C4 | — | 14 | 1 | no | — |
| 366 | C22×C4 | — | 14 | 1 | no | — |
| 367 | C22×C4 | C2×C4×D7 | 1 | 1 | yes | characteristic |
| 368 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 369 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 370 | SD16 | — | 28 | 2 | no | — |
| 371 | SD16 | — | 28 | 2 | no | — |
| 372 | SD16 | — | 28 | 2 | no | — |
| 373 | D8 | — | 28 | 2 | no | — |
| 374 | M16 | — | 2 | 2 | no | — |
| 375 | M16 | — | 4 | 1 | no | — |
| 376 | M16 | — | 4 | 1 | no | — |
| 377 | M16 | — | 4 | 1 | no | — |
| 378 | M16 | — | 4 | 1 | no | — |
| 379 | M16 | — | 14 | 2 | no | — |
| 380 | M16 | — | 28 | 4 | no | — |
| 381 | M16 | — | 28 | 1 | no | — |
| 382 | C2×C8 | — | 2 | 1 | no | — |
| 383 | C2×C8 | — | 2 | 1 | no | — |
| 384 | C2×C8 | — | 4 | 1 | no | — |
| 385 | C2×C8 | — | 4 | 1 | no | — |
| 386 | C2×C8 | — | 4 | 1 | no | — |
| 387 | C2×C8 | — | 28 | 4 | no | — |
| 388 | C2×C8 | — | 28 | 1 | no | — |
| 389 | C4⋊C4 | — | 14 | 1 | no | — |
| 390 | C4⋊C4 | — | 28 | 1 | no | — |
| 391 | C22⋊C4 | — | 14 | 1 | no | — |
| 392 | C22⋊C4 | — | 28 | 1 | no | — |
| 393 | C22⋊C4 | — | 28 | 1 | no | — |
| 394 | C22⋊C4 | — | 28 | 1 | no | — |
| 395 | C42 | — | 14 | 1 | no | — |
| 396 | C42 | — | 28 | 1 | no | — |
| 397 | C2×C7 | — | 2 | 1 | no | — |
| 398 | C2×C7 | — | 4 | 1 | no | — |
| 399 | C2×C7 | — | 4 | 1 | no | — |
| 400 | C2×C7 | — | 4 | 1 | no | — |
| 401 | C2×C7 | #1898 | 1 | 1 | yes | characteristic |
| 402 | D7 | — | 4 | 2 | no | — |
| 403 | D7 | — | 16 | 1 | no | — |
| 404 | C23 | — | 14 | 1 | no | — |
| 405 | C23 | — | 28 | 1 | no | — |
| 406 | C23 | — | 56 | 1 | no | — |
| 407 | C23 | — | 112 | 1 | no | — |
| 408 | C23 | C4×D28 | 1 | 1 | yes | characteristic |
| 409 | C23 | #6457 | 1 | 1 | yes | characteristic |
| 410 | C23 | #6458 | 1 | 1 | yes | characteristic |
| 411 | Q8 | — | 4 | 1 | no | — |
| 412 | Q8 | — | 7 | 2 | no | — |
| 413 | Q8 | — | 14 | 1 | no | — |
| 414 | Q8 | — | 14 | 1 | no | — |
| 415 | Q8 | — | 14 | 1 | no | — |
| 416 | Q8 | — | 14 | 1 | no | — |
| 417 | Q8 | — | 14 | 1 | no | — |
| 418 | Q8 | — | 28 | 2 | no | — |
| 419 | Q8 | — | 28 | 2 | no | — |
| 420 | Q8 | — | 28 | 2 | no | — |
| 421 | D4 | — | 4 | 1 | no | — |
| 422 | D4 | — | 4 | 1 | no | — |
| 423 | D4 | — | 4 | 1 | no | — |
| 424 | D4 | — | 7 | 2 | no | — |
| 425 | D4 | — | 14 | 4 | no | — |
| 426 | D4 | — | 14 | 1 | no | — |
| 427 | D4 | — | 28 | 2 | no | — |
| 428 | D4 | — | 28 | 2 | no | — |
| 429 | D4 | — | 28 | 1 | no | — |
| 430 | D4 | — | 28 | 1 | no | — |
| 431 | D4 | — | 56 | 1 | no | — |
| 432 | D4 | — | 112 | 1 | no | — |
| 433 | D4 | — | 112 | 1 | no | — |
| 434 | C2×C4 | — | 2 | 1 | no | — |
| 435 | C2×C4 | — | 2 | 1 | no | — |
| 436 | C2×C4 | — | 2 | 1 | no | — |
| 437 | C2×C4 | — | 2 | 1 | no | — |
| 438 | C2×C4 | — | 2 | 1 | no | — |
| 439 | C2×C4 | — | 2 | 1 | no | — |
| 440 | C2×C4 | — | 14 | 4 | no | — |
| 441 | C2×C4 | — | 14 | 1 | no | — |
| 442 | C2×C4 | — | 14 | 1 | no | — |
| 443 | C2×C4 | — | 14 | 1 | no | — |
| 444 | C2×C4 | — | 28 | 2 | no | — |
| 445 | C2×C4 | — | 28 | 2 | no | — |
| 446 | C2×C4 | — | 28 | 2 | no | — |
| 447 | C2×C4 | — | 28 | 2 | no | — |
| 448 | C2×C4 | — | 28 | 2 | no | — |
| 449 | C2×C4 | — | 28 | 1 | no | — |
| 450 | C2×C4 | — | 56 | 1 | no | — |
| 451 | C2×C4 | D7×C22⋊C4 | 1 | 1 | yes | characteristic |
| 452 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 453 | C2×C4 | #6447 | 1 | 1 | yes | characteristic |
| 454 | C2×C4 | #6456 | 1 | 1 | yes | characteristic |
| 455 | C8 | — | 4 | 2 | no | — |
| 456 | C8 | — | 4 | 1 | no | — |
| 457 | C8 | — | 4 | 1 | no | — |
| 458 | C8 | — | 8 | 1 | no | — |
| 459 | C8 | — | 28 | 2 | no | — |
| 460 | C7 | #13098 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 461 | C22 | — | 2 | 1 | no | — |
| 462 | C22 | — | 2 | 1 | no | — |
| 463 | C22 | — | 2 | 1 | no | — |
| 464 | C22 | — | 4 | 1 | no | — |
| 465 | C22 | — | 4 | 1 | no | — |
| 466 | C22 | — | 4 | 1 | no | — |
| 467 | C22 | — | 14 | 2 | no | — |
| 468 | C22 | — | 56 | 1 | no | — |
| 469 | C22 | — | 56 | 1 | no | — |
| 470 | C22 | — | 56 | 1 | no | — |
| 471 | C22 | — | 56 | 1 | no | — |
| 472 | C22 | — | 112 | 2 | no | — |
| 473 | C22 | #89437 | 1 | 1 | yes | characteristic |
| 474 | C4 | — | 2 | 1 | no | — |
| 475 | C4 | — | 2 | 1 | no | — |
| 476 | C4 | — | 2 | 1 | no | — |
| 477 | C4 | — | 14 | 2 | no | — |
| 478 | C4 | — | 28 | 1 | no | — |
| 479 | C4 | — | 28 | 1 | no | — |
| 480 | C4 | — | 56 | 1 | no | — |
| 481 | C4 | — | 112 | 1 | no | — |
| 482 | C4 | D7×#99 | 1 | 1 | yes | characteristic |
| 483 | C4 | D7×#99 | 1 | 1 | yes | characteristic |
| 484 | C2 | — | 2 | 1 | no | — |
| 485 | C2 | — | 4 | 1 | no | — |
| 486 | C2 | — | 4 | 1 | no | — |
| 487 | C2 | — | 4 | 1 | no | — |
| 488 | C2 | — | 28 | 2 | no | — |
| 489 | C2 | — | 112 | 1 | no | — |
| 490 | C2 | #11726724 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11736160 | C2 | semidirect |
| 3. #11727903 | C2 | semidirect |
| 4. #11727900 | C2 | semidirect |
| 5. #11727895 | C2 | semidirect |
| 6. C7×#1392 | C2 | semidirect |
| 7. #11725498 | C2 | semidirect |
| 10. C2×#6471 | C4 | semidirect |
| 12. C22×#1132 | C4 | semidirect |
| 21. #89892 | C4 | semidirect |
| 22. #89885 | C4 | semidirect |
| 91. #1392 | D7 | semidirect |
| 460. C7 | #13098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736160 | 2 |
| #11736123 | 2 |
| #11727903 | 2 |
| #11727900 | 2 |
| #11727895 | 2 |
| C7×#1392 | 2 |
| #11725498 | 2 |
| #13098 | 7 |