Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
478 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 59 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 | #22597690 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22590022 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22586973 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22586489 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22586488 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22586487 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C71×#1403 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #17986834 | C4 | 1 | 1 | yes | characteristic |
| 9 | #17986798 | — | 2 | 1 | no | — |
| 10 | #17986548 | C22 | 1 | 1 | yes | characteristic |
| 11 | #17986180 | — | 2 | 1 | no | — |
| 12 | #17986176 | C22 | 1 | 1 | yes | characteristic |
| 13 | #17986173 | — | 2 | 1 | no | — |
| 14 | #17986169 | C4 | 1 | 1 | yes | characteristic |
| 15 | #17986167 | C4 | 1 | 1 | yes | characteristic |
| 16 | #17986054 | — | 2 | 1 | no | — |
| 17 | #104×D71 | — | 2 | 1 | no | — |
| 18 | #17985982 | — | 2 | 1 | no | — |
| 19 | #17985980 | C4 | 1 | 1 | yes | characteristic |
| 20 | #17985797 | — | 2 | 1 | no | — |
| 21 | #17985796 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #17985739 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #17985738 | — | 2 | 1 | no | — |
| 24 | #455×C71 | C22 | 1 | 1 | yes | characteristic |
| 25 | #355×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #329×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #14556175 | — | 2 | 1 | no | — |
| 28 | #14556175 | — | 4 | 1 | no | — |
| 29 | #14556173 | — | 4 | 1 | no | — |
| 30 | #14556173 | — | 4 | 1 | no | — |
| 31 | #14556173 | C2×C4 | 1 | 1 | yes | characteristic |
| 32 | C2×#11765866 | D4 | 1 | 1 | yes | characteristic |
| 33 | C2×#11765864 | — | 4 | 1 | no | — |
| 34 | C2×#11765864 | — | 4 | 1 | no | — |
| 35 | C2×#11765864 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | #41×D71 | — | 2 | 1 | no | — |
| 37 | #41×D71 | — | 4 | 1 | no | — |
| 38 | #14556160 | — | 4 | 1 | no | — |
| 39 | #14556159 | — | 2 | 1 | no | — |
| 40 | #14556156 | — | 2 | 1 | no | — |
| 41 | #14556155 | — | 4 | 1 | no | — |
| 42 | #14556153 | — | 2 | 1 | no | — |
| 43 | #14556151 | — | 4 | 1 | no | — |
| 44 | #14556149 | — | 4 | 1 | no | — |
| 45 | M16×D71 | — | 2 | 1 | no | — |
| 46 | M16×D71 | — | 4 | 1 | no | — |
| 47 | #14556126 | D4 | 1 | 1 | yes | characteristic |
| 48 | #14556124 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | #14556116 | D4 | 1 | 1 | yes | characteristic |
| 50 | #14556101 | — | 4 | 1 | no | — |
| 51 | (C22⋊D71)⋊C4 | — | 4 | 1 | no | — |
| 52 | C42×D71 | D4 | 1 | 1 | yes | characteristic |
| 53 | Dic71⋊C8 | — | 4 | 1 | no | — |
| 54 | #14556056 | — | 2 | 1 | no | — |
| 55 | #14556055 | — | 2 | 1 | no | — |
| 56 | #14556054 | — | 2 | 1 | no | — |
| 57 | #14556047 | — | 2 | 1 | no | — |
| 58 | #14556046 | — | 2 | 1 | no | — |
| 59 | #14556045 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | #14556044 | — | 4 | 1 | no | — |
| 61 | (C2×D71)⋊C8 | — | 4 | 1 | no | — |
| 62 | #14556039 | — | 2 | 1 | no | — |
| 63 | H(5,𝔽2)×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 64 | #137×C71 | — | 2 | 1 | no | — |
| 65 | #124×C71 | C23 | 1 | 1 | yes | characteristic |
| 66 | #104×C71 | — | 2 | 1 | no | — |
| 67 | #101×C71 | — | 2 | 1 | no | — |
| 68 | #100×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 69 | #97×C71 | — | 2 | 1 | no | — |
| 70 | #11765866 | — | 2 | 1 | no | — |
| 71 | #11765866 | — | 4 | 1 | no | — |
| 72 | #11765866 | — | 4 | 1 | no | — |
| 73 | #11765865 | — | 2 | 1 | no | — |
| 74 | #11765865 | — | 4 | 1 | no | — |
| 75 | #11765865 | — | 4 | 1 | no | — |
| 76 | #11765865 | — | 4 | 2 | no | — |
| 77 | #11765864 | — | 2 | 1 | no | — |
| 78 | #11765864 | — | 4 | 1 | no | — |
| 79 | #11765864 | — | 4 | 1 | no | — |
| 80 | #11765864 | — | 4 | 1 | no | — |
| 81 | #11765864 | — | 4 | 2 | no | — |
| 82 | #11765864 | — | 4 | 1 | no | — |
| 83 | #11765864 | — | 4 | 2 | no | — |
| 84 | #11765864 | — | 4 | 2 | no | — |
| 85 | #11765864 | — | 4 | 2 | no | — |
| 86 | #11765864 | — | 4 | 1 | no | — |
| 87 | C2×Dic142 | — | 4 | 1 | no | — |
| 88 | C2×Dic142 | — | 4 | 1 | no | — |
| 89 | C2×Dic142 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 90 | Q8×D71 | — | 2 | 1 | no | — |
| 91 | Q8×D71 | — | 4 | 1 | no | — |
| 92 | C2×D284 | — | 2 | 1 | no | — |
| 93 | C2×D284 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 94 | C2×C22⋊D71 | — | 2 | 1 | no | — |
| 95 | C2×C22⋊D71 | — | 4 | 1 | no | — |
| 96 | C2×C22⋊D71 | — | 4 | 2 | no | — |
| 97 | C2×C22⋊D71 | — | 4 | 1 | no | — |
| 98 | C2×C22⋊D71 | — | 4 | 1 | no | — |
| 99 | D4×D71 | — | 2 | 1 | no | — |
| 100 | D4×D71 | — | 4 | 1 | no | — |
| 101 | D4×D71 | — | 4 | 2 | no | — |
| 102 | D4×D71 | — | 4 | 1 | no | — |
| 103 | C22×Dic71 | — | 2 | 1 | no | — |
| 104 | C22×Dic71 | — | 4 | 1 | no | — |
| 105 | C2×C4×D71 | — | 2 | 1 | no | — |
| 106 | C2×C4×D71 | — | 2 | 1 | no | — |
| 107 | C2×C4×D71 | — | 4 | 1 | no | — |
| 108 | C2×C4×D71 | — | 4 | 1 | no | — |
| 109 | C2×C4×D71 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 110 | #11765855 | — | 4 | 1 | no | — |
| 111 | #11765854 | — | 4 | 1 | no | — |
| 112 | #11765852 | — | 4 | 1 | no | — |
| 113 | #11765852 | — | 4 | 1 | no | — |
| 114 | D568 | — | 4 | 1 | no | — |
| 115 | #11765850 | — | 4 | 1 | no | — |
| 116 | #11765849 | — | 2 | 1 | no | — |
| 117 | #11765849 | — | 4 | 1 | no | — |
| 118 | #11765848 | — | 4 | 1 | no | — |
| 119 | #11765848 | — | 8 | 1 | no | — |
| 120 | C2×C71⋊C8 | — | 4 | 1 | no | — |
| 121 | C8×D71 | — | 4 | 1 | no | — |
| 122 | C8×D71 | — | 8 | 1 | no | — |
| 123 | Dic71⋊C4 | — | 4 | 1 | no | — |
| 124 | (C2×D71)⋊C4 | — | 4 | 1 | no | — |
| 125 | C4×Dic71 | — | 2 | 1 | no | — |
| 126 | C4×Dic71 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 127 | #41×C71 | — | 2 | 1 | no | — |
| 128 | #41×C71 | — | 4 | 1 | no | — |
| 129 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C2×D4×C71 | — | 4 | 1 | no | — |
| 131 | C2×D4×C71 | — | 4 | 1 | no | — |
| 132 | C2×D4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 133 | Q16×C71 | — | 4 | 1 | no | — |
| 134 | SD16×C71 | — | 4 | 1 | no | — |
| 135 | M16×C71 | — | 2 | 1 | no | — |
| 136 | M16×C71 | — | 4 | 1 | no | — |
| 137 | C2×C8×C71 | — | 4 | 1 | no | — |
| 138 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 139 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 140 | C23×C71 | — | 2 | 1 | no | — |
| 141 | C23×C71 | — | 4 | 1 | no | — |
| 142 | C22×D71 | — | 2 | 1 | no | — |
| 143 | C22×D71 | — | 4 | 1 | no | — |
| 144 | C22×D71 | — | 4 | 1 | no | — |
| 145 | C22×D71 | #99 | 1 | 1 | yes | characteristic |
| 146 | Q8×C71 | — | 2 | 1 | no | — |
| 147 | Q8×C71 | — | 4 | 1 | no | — |
| 148 | D4×C71 | — | 2 | 1 | no | — |
| 149 | D4×C71 | — | 4 | 1 | no | — |
| 150 | D4×C71 | — | 4 | 2 | no | — |
| 151 | D4×C71 | — | 4 | 1 | no | — |
| 152 | C2×C4×C71 | — | 2 | 1 | no | — |
| 153 | C2×C4×C71 | — | 2 | 1 | no | — |
| 154 | C2×C4×C71 | — | 4 | 1 | no | — |
| 155 | C2×C4×C71 | — | 4 | 1 | no | — |
| 156 | C2×C4×C71 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 157 | C22⋊D71 | — | 4 | 2 | no | — |
| 158 | C22⋊D71 | — | 4 | 1 | no | — |
| 159 | C22⋊D71 | — | 4 | 2 | no | — |
| 160 | C22⋊D71 | — | 4 | 2 | no | — |
| 161 | C22⋊D71 | — | 4 | 1 | no | — |
| 162 | C22⋊D71 | — | 4 | 1 | no | — |
| 163 | C22⋊D71 | — | 8 | 2 | no | — |
| 164 | C2×Dic71 | — | 2 | 1 | no | — |
| 165 | C2×Dic71 | — | 2 | 1 | no | — |
| 166 | C2×Dic71 | — | 4 | 2 | no | — |
| 167 | C2×Dic71 | — | 4 | 1 | no | — |
| 168 | C2×Dic71 | — | 4 | 1 | no | — |
| 169 | C2×Dic71 | — | 4 | 1 | no | — |
| 170 | C2×Dic71 | — | 4 | 1 | no | — |
| 171 | C2×Dic71 | #99 | 1 | 1 | yes | characteristic |
| 172 | D284 | — | 2 | 1 | no | — |
| 173 | D284 | — | 4 | 1 | no | — |
| 174 | D284 | — | 4 | 1 | no | — |
| 175 | D284 | — | 8 | 1 | no | — |
| 176 | C4×D71 | — | 2 | 1 | no | — |
| 177 | C4×D71 | — | 2 | 1 | no | — |
| 178 | C4×D71 | — | 4 | 1 | no | — |
| 179 | C4×D71 | — | 4 | 1 | no | — |
| 180 | C4×D71 | — | 4 | 2 | no | — |
| 181 | C4×D71 | — | 4 | 1 | no | — |
| 182 | C4×D71 | — | 4 | 1 | no | — |
| 183 | C4×D71 | — | 4 | 1 | no | — |
| 184 | C4×D71 | — | 8 | 1 | no | — |
| 185 | Dic142 | — | 2 | 1 | no | — |
| 186 | Dic142 | — | 4 | 2 | no | — |
| 187 | Dic142 | — | 4 | 1 | no | — |
| 188 | Dic142 | — | 4 | 1 | no | — |
| 189 | C8×C71 | — | 4 | 1 | no | — |
| 190 | C8×C71 | — | 8 | 1 | no | — |
| 191 | C8×C71 | — | 8 | 1 | no | — |
| 192 | C71⋊C8 | — | 4 | 1 | no | — |
| 193 | C71⋊C8 | — | 8 | 1 | no | — |
| 194 | C71⋊C8 | — | 8 | 1 | no | — |
| 195 | C22×C71 | — | 4 | 1 | no | — |
| 196 | C22×C71 | — | 4 | 1 | no | — |
| 197 | C22×C71 | — | 8 | 1 | no | — |
| 198 | C22×C71 | — | 16 | 1 | no | — |
| 199 | C22×C71 | C2×#99 | 1 | 1 | yes | characteristic |
| 200 | C2×D71 | — | 2 | 1 | no | — |
| 201 | C2×D71 | — | 4 | 1 | no | — |
| 202 | C2×D71 | — | 4 | 1 | no | — |
| 203 | C2×D71 | — | 4 | 1 | no | — |
| 204 | C2×D71 | — | 8 | 1 | no | — |
| 205 | C2×D71 | — | 16 | 1 | no | — |
| 206 | C2×D71 | — | 16 | 1 | no | — |
| 207 | C4×C71 | — | 2 | 1 | no | — |
| 208 | C4×C71 | — | 4 | 1 | no | — |
| 209 | C4×C71 | — | 4 | 1 | no | — |
| 210 | C4×C71 | — | 4 | 1 | no | — |
| 211 | Dic71 | — | 4 | 1 | no | — |
| 212 | Dic71 | — | 4 | 1 | no | — |
| 213 | Dic71 | — | 4 | 1 | no | — |
| 214 | Dic71 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 215 | Dic71 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 216 | #13566 | — | 71 | 1 | no | maximal, Sylow |
| 217 | C2×C71 | — | 2 | 1 | no | — |
| 218 | C2×C71 | — | 8 | 1 | no | — |
| 219 | C2×C71 | — | 8 | 1 | no | — |
| 220 | C2×C71 | C2×AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 221 | D71 | — | 4 | 1 | no | — |
| 222 | D71 | — | 8 | 1 | no | — |
| 223 | D71 | — | 8 | 1 | no | — |
| 224 | #3018 | — | 71 | 1 | no | — |
| 225 | #2132 | — | 71 | 1 | no | — |
| 226 | #1536 | — | 71 | 1 | no | — |
| 227 | #1403 | — | 71 | 1 | no | — |
| 228 | #1403 | — | 71 | 1 | no | — |
| 229 | #1403 | — | 71 | 1 | no | — |
| 230 | #1403 | D71 | 1 | 1 | yes | characteristic, complemented |
| 231 | C71 | #13566 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 232 | #585 | — | 71 | 1 | no | — |
| 233 | #575 | — | 142 | 1 | no | — |
| 234 | #532 | — | 71 | 1 | no | — |
| 235 | #456 | — | 142 | 1 | no | — |
| 236 | #455 | — | 71 | 1 | no | — |
| 237 | #455 | C2×D71 | 1 | 1 | yes | characteristic |
| 238 | #454 | — | 142 | 1 | no | — |
| 239 | #453 | — | 71 | 1 | no | — |
| 240 | #453 | — | 71 | 1 | no | — |
| 241 | #432 | — | 142 | 1 | no | — |
| 242 | C2×#104 | — | 142 | 1 | no | — |
| 243 | #413 | — | 71 | 1 | no | — |
| 244 | #413 | — | 142 | 1 | no | — |
| 245 | #356 | — | 142 | 1 | no | — |
| 246 | #355 | — | 71 | 1 | no | — |
| 247 | #355 | C2×D71 | 1 | 1 | yes | characteristic, complemented |
| 248 | #329 | — | 71 | 1 | no | — |
| 249 | #329 | — | 142 | 1 | no | — |
| 250 | #329 | C2×D71 | 1 | 1 | yes | characteristic, complemented |
| 251 | 2−1+4 | — | 284 | 1 | no | — |
| 252 | 2−1+4 | — | 142 | 1 | no | — |
| 253 | H(5,𝔽2) | — | 284 | 1 | no | — |
| 254 | H(5,𝔽2) | — | 284 | 1 | no | — |
| 255 | H(5,𝔽2) | — | 71 | 1 | no | — |
| 256 | H(5,𝔽2) | C4×D71 | 1 | 1 | yes | characteristic |
| 257 | C2×#41 | — | 284 | 1 | no | — |
| 258 | C2×#41 | — | 284 | 1 | no | — |
| 259 | C2×#41 | — | 284 | 1 | no | — |
| 260 | C2×#41 | — | 71 | 1 | no | — |
| 261 | C2×#41 | — | 71 | 1 | no | — |
| 262 | C2×#41 | — | 142 | 1 | no | — |
| 263 | #137 | — | 2 | 1 | no | — |
| 264 | #137 | — | 284 | 1 | no | — |
| 265 | #137 | — | 142 | 1 | no | — |
| 266 | AGL(1,ℤ/8) | — | 284 | 1 | no | — |
| 267 | AGL(1,ℤ/8) | — | 142 | 1 | no | — |
| 268 | AGL(1,ℤ/8) | — | 142 | 1 | no | — |
| 269 | #135 | — | 284 | 1 | no | — |
| 270 | #135 | — | 284 | 1 | no | — |
| 271 | C2×M16 | — | 284 | 1 | no | — |
| 272 | C2×M16 | — | 142 | 1 | no | — |
| 273 | C4⋊Q8 | — | 71 | 1 | no | — |
| 274 | #127 | — | 71 | 1 | no | — |
| 275 | #124 | — | 71 | 1 | no | — |
| 276 | #124 | C22×D71 | 1 | 1 | yes | characteristic |
| 277 | #121 | — | 284 | 1 | no | — |
| 278 | C4×D4 | — | 284 | 1 | no | — |
| 279 | C2×C42 | — | 71 | 1 | no | — |
| 280 | C4⋊C8 | — | 284 | 1 | no | — |
| 281 | #104 | — | 2 | 1 | no | — |
| 282 | #104 | — | 142 | 1 | no | — |
| 283 | #104 | — | 142 | 1 | no | — |
| 284 | #104 | — | 142 | 1 | no | — |
| 285 | #101 | — | 2 | 1 | no | — |
| 286 | #101 | — | 142 | 1 | no | — |
| 287 | #101 | — | 142 | 1 | no | — |
| 288 | #100 | — | 284 | 1 | no | — |
| 289 | #100 | — | 71 | 1 | no | — |
| 290 | #100 | C4×D71 | 1 | 1 | yes | characteristic |
| 291 | C22⋊C8 | — | 284 | 1 | no | — |
| 292 | #97 | — | 2 | 1 | no | — |
| 293 | #97 | — | 142 | 1 | no | — |
| 294 | #41 | — | 2 | 1 | no | — |
| 295 | #41 | — | 4 | 1 | no | — |
| 296 | #41 | — | 284 | 2 | no | — |
| 297 | #41 | — | 284 | 1 | no | — |
| 298 | #41 | — | 284 | 1 | no | — |
| 299 | #41 | — | 284 | 1 | no | — |
| 300 | #41 | — | 284 | 2 | no | — |
| 301 | #41 | — | 284 | 2 | no | — |
| 302 | #41 | — | 284 | 2 | no | — |
| 303 | #41 | — | 284 | 1 | no | — |
| 304 | #41 | — | 284 | 2 | no | — |
| 305 | #41 | — | 284 | 1 | no | — |
| 306 | #41 | — | 284 | 1 | no | — |
| 307 | #41 | — | 284 | 1 | no | — |
| 308 | #41 | — | 284 | 1 | no | — |
| 309 | #41 | — | 284 | 1 | no | — |
| 310 | #41 | — | 142 | 1 | no | — |
| 311 | #41 | — | 142 | 1 | no | — |
| 312 | #41 | — | 142 | 1 | no | — |
| 313 | C2×Q8 | — | 284 | 1 | no | — |
| 314 | C2×Q8 | — | 284 | 1 | no | — |
| 315 | C2×Q8 | — | 284 | 1 | no | — |
| 316 | C2×Q8 | — | 71 | 1 | no | — |
| 317 | C2×Q8 | — | 142 | 1 | no | — |
| 318 | C2×Q8 | D4×D71 | 1 | 1 | yes | characteristic |
| 319 | C2×D4 | — | 4 | 1 | no | — |
| 320 | C2×D4 | — | 4 | 1 | no | — |
| 321 | C2×D4 | — | 284 | 2 | no | — |
| 322 | C2×D4 | — | 284 | 1 | no | — |
| 323 | C2×D4 | — | 284 | 1 | no | — |
| 324 | C2×D4 | — | 284 | 2 | no | — |
| 325 | C2×D4 | — | 284 | 1 | no | — |
| 326 | C2×D4 | — | 284 | 1 | no | — |
| 327 | C2×D4 | — | 284 | 1 | no | — |
| 328 | C2×D4 | — | 71 | 1 | no | — |
| 329 | C2×D4 | — | 142 | 1 | no | — |
| 330 | C2×D4 | — | 142 | 1 | no | — |
| 331 | C2×D4 | — | 142 | 1 | no | — |
| 332 | C2×D4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 333 | C22×C4 | — | 284 | 1 | no | — |
| 334 | C22×C4 | — | 284 | 1 | no | — |
| 335 | C22×C4 | — | 284 | 1 | no | — |
| 336 | C22×C4 | — | 71 | 1 | no | — |
| 337 | C22×C4 | — | 142 | 1 | no | — |
| 338 | C22×C4 | — | 142 | 1 | no | — |
| 339 | C22×C4 | — | 142 | 1 | no | — |
| 340 | Q16 | — | 4 | 1 | no | — |
| 341 | Q16 | — | 284 | 1 | no | — |
| 342 | SD16 | — | 4 | 1 | no | — |
| 343 | SD16 | — | 284 | 1 | no | — |
| 344 | SD16 | — | 284 | 1 | no | — |
| 345 | SD16 | — | 284 | 1 | no | — |
| 346 | D8 | — | 284 | 1 | no | — |
| 347 | D8 | — | 284 | 1 | no | — |
| 348 | M16 | — | 2 | 1 | no | — |
| 349 | M16 | — | 4 | 1 | no | — |
| 350 | M16 | — | 284 | 1 | no | — |
| 351 | M16 | — | 284 | 1 | no | — |
| 352 | M16 | — | 568 | 1 | no | — |
| 353 | M16 | — | 142 | 1 | no | — |
| 354 | C2×C8 | — | 4 | 1 | no | — |
| 355 | C2×C8 | — | 284 | 1 | no | — |
| 356 | C2×C8 | — | 284 | 1 | no | — |
| 357 | C2×C8 | — | 568 | 1 | no | — |
| 358 | C4⋊C4 | — | 284 | 1 | no | — |
| 359 | C22⋊C4 | — | 4 | 1 | no | — |
| 360 | C22⋊C4 | — | 284 | 1 | no | — |
| 361 | C42 | — | 71 | 1 | no | — |
| 362 | C42 | — | 142 | 1 | no | — |
| 363 | C42 | D4×D71 | 1 | 1 | yes | characteristic |
| 364 | C23 | — | 2 | 1 | no | — |
| 365 | C23 | — | 4 | 1 | no | — |
| 366 | C23 | — | 284 | 1 | no | — |
| 367 | C23 | — | 284 | 1 | no | — |
| 368 | C23 | — | 71 | 1 | no | — |
| 369 | C23 | — | 142 | 1 | no | — |
| 370 | Q8 | — | 2 | 1 | no | — |
| 371 | Q8 | — | 4 | 1 | no | — |
| 372 | Q8 | — | 284 | 1 | no | — |
| 373 | Q8 | — | 284 | 2 | no | — |
| 374 | Q8 | — | 284 | 1 | no | — |
| 375 | Q8 | — | 142 | 1 | no | — |
| 376 | D4 | — | 2 | 1 | no | — |
| 377 | D4 | — | 4 | 1 | no | — |
| 378 | D4 | — | 4 | 2 | no | — |
| 379 | D4 | — | 4 | 1 | no | — |
| 380 | D4 | — | 284 | 1 | no | — |
| 381 | D4 | — | 284 | 1 | no | — |
| 382 | D4 | — | 284 | 2 | no | — |
| 383 | D4 | — | 284 | 2 | no | — |
| 384 | D4 | — | 284 | 1 | no | — |
| 385 | D4 | — | 284 | 2 | no | — |
| 386 | D4 | — | 284 | 1 | no | — |
| 387 | D4 | — | 284 | 1 | no | — |
| 388 | D4 | — | 568 | 1 | no | — |
| 389 | D4 | — | 568 | 2 | no | — |
| 390 | D4 | — | 142 | 1 | no | — |
| 391 | C2×C4 | — | 2 | 1 | no | — |
| 392 | C2×C4 | — | 2 | 1 | no | — |
| 393 | C2×C4 | — | 4 | 1 | no | — |
| 394 | C2×C4 | — | 4 | 1 | no | — |
| 395 | C2×C4 | — | 284 | 1 | no | — |
| 396 | C2×C4 | — | 284 | 2 | no | — |
| 397 | C2×C4 | — | 284 | 1 | no | — |
| 398 | C2×C4 | — | 284 | 1 | no | — |
| 399 | C2×C4 | — | 284 | 1 | no | — |
| 400 | C2×C4 | — | 284 | 1 | no | — |
| 401 | C2×C4 | — | 284 | 2 | no | — |
| 402 | C2×C4 | — | 284 | 1 | no | — |
| 403 | C2×C4 | — | 284 | 1 | no | — |
| 404 | C2×C4 | — | 284 | 1 | no | — |
| 405 | C2×C4 | — | 284 | 1 | no | — |
| 406 | C2×C4 | — | 568 | 1 | no | — |
| 407 | C2×C4 | — | 71 | 1 | no | — |
| 408 | C2×C4 | — | 142 | 1 | no | — |
| 409 | C2×C4 | — | 142 | 1 | no | — |
| 410 | C2×C4 | — | 142 | 1 | no | — |
| 411 | C2×C4 | — | 142 | 1 | no | — |
| 412 | C2×C4 | C22⋊C4×D71 | 1 | 1 | yes | characteristic |
| 413 | C8 | — | 4 | 1 | no | — |
| 414 | C8 | — | 8 | 1 | no | — |
| 415 | C8 | — | 8 | 1 | no | — |
| 416 | C8 | — | 284 | 1 | no | — |
| 417 | C8 | — | 568 | 1 | no | — |
| 418 | C8 | — | 568 | 1 | no | — |
| 419 | C22 | — | 4 | 1 | no | — |
| 420 | C22 | — | 4 | 1 | no | — |
| 421 | C22 | — | 8 | 1 | no | — |
| 422 | C22 | — | 16 | 1 | no | — |
| 423 | C22 | — | 284 | 1 | no | — |
| 424 | C22 | — | 284 | 1 | no | — |
| 425 | C22 | — | 284 | 1 | no | — |
| 426 | C22 | — | 568 | 1 | no | — |
| 427 | C22 | — | 1136 | 1 | no | — |
| 428 | C22 | — | 1136 | 1 | no | — |
| 429 | C22 | — | 142 | 1 | no | — |
| 430 | C22 | #99×D71 | 1 | 1 | yes | characteristic |
| 431 | C4 | — | 2 | 1 | no | — |
| 432 | C4 | — | 4 | 1 | no | — |
| 433 | C4 | — | 4 | 1 | no | — |
| 434 | C4 | — | 4 | 1 | no | — |
| 435 | C4 | — | 284 | 1 | no | — |
| 436 | C4 | — | 284 | 1 | no | — |
| 437 | C4 | — | 284 | 1 | no | — |
| 438 | C4 | — | 71 | 1 | no | — |
| 439 | C4 | — | 71 | 1 | no | — |
| 440 | C2 | — | 2 | 1 | no | — |
| 441 | C2 | — | 8 | 1 | no | — |
| 442 | C2 | — | 8 | 1 | no | — |
| 443 | C2 | — | 284 | 1 | no | — |
| 444 | C2 | — | 568 | 1 | no | — |
| 445 | C2 | — | 568 | 1 | no | — |
| 446 | C2 | AΣL(1,𝔽16)×D71 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22590022 | C2 | semidirect |
| 3. #22586973 | C2 | semidirect |
| 4. #22586489 | C2 | semidirect |
| 5. #22586488 | C2 | semidirect |
| 6. #22586487 | C2 | semidirect |
| 7. C71×#1403 | C2 | semidirect |
| 21. #17985796 | C22 | semidirect |
| 22. #17985739 | C22 | semidirect |
| 25. #355×C71 | C22 | semidirect |
| 26. #329×C71 | C22 | semidirect |
| 230. #1403 | D71 | semidirect |
| 231. C71 | #13566 | semidirect |
| 247. #355 | C2×D71 | semidirect |
| 250. #329 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597690 | 2 |
| #22590022 | 2 |
| #22586973 | 2 |
| #22586489 | 2 |
| #22586488 | 2 |
| #22586487 | 2 |
| C71×#1403 | 2 |
| #13566 | 71 |