Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
526 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 57 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 | #22566791 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22561253 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22559214 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22559143 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22558214 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22558140 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C67×#1345 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#14524071 | — | 2 | 1 | no | — |
| 9 | #16863977 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#14524016 | — | 2 | 1 | no | — |
| 11 | #16863710 | — | 2 | 1 | no | — |
| 12 | #16863530 | — | 2 | 1 | no | — |
| 13 | C2×#14523969 | — | 2 | 1 | no | — |
| 14 | #16863326 | C22 | 1 | 1 | yes | characteristic |
| 15 | #16863312 | — | 2 | 1 | no | — |
| 16 | #16863304 | — | 2 | 1 | no | — |
| 17 | #16863297 | C22 | 1 | 1 | yes | characteristic |
| 18 | #16863290 | — | 2 | 1 | no | — |
| 19 | #16863272 | — | 2 | 1 | no | — |
| 20 | #16863258 | — | 2 | 1 | no | — |
| 21 | #16863131 | — | 2 | 1 | no | — |
| 22 | #16863129 | — | 2 | 1 | no | — |
| 23 | #16863122 | C22 | 1 | 1 | yes | characteristic |
| 24 | #394×C67 | C22 | 1 | 1 | yes | characteristic |
| 25 | #343×C67 | C22 | 1 | 1 | yes | characteristic |
| 26 | #324×C67 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#11761628 | — | 2 | 1 | no | — |
| 28 | C22×D268 | D4 | 1 | 1 | yes | characteristic |
| 29 | C22×C22⋊D67 | — | 2 | 1 | no | — |
| 30 | C22×C22⋊D67 | — | 2 | 1 | no | — |
| 31 | C22×C4×D67 | — | 2 | 1 | no | — |
| 32 | #14524071 | — | 4 | 2 | no | — |
| 33 | #14524071 | — | 4 | 2 | no | — |
| 34 | C2×#11761617 | — | 4 | 1 | no | — |
| 35 | C2×D536 | — | 4 | 1 | no | — |
| 36 | C2×#11761613 | — | 4 | 1 | no | — |
| 37 | #14524023 | — | 4 | 1 | no | — |
| 38 | #14524018 | — | 4 | 1 | no | — |
| 39 | #14524017 | — | 2 | 1 | no | — |
| 40 | #14524017 | — | 2 | 1 | no | — |
| 41 | #14524016 | — | 4 | 2 | no | — |
| 42 | #14524016 | — | 4 | 2 | no | — |
| 43 | C2×C4⋊Dic67 | D4 | 1 | 1 | yes | characteristic |
| 44 | C2×Dic67⋊C4 | — | 2 | 1 | no | — |
| 45 | C2×C22⋊Dic67 | — | 2 | 1 | no | — |
| 46 | C2×C22⋊Dic67 | — | 2 | 1 | no | — |
| 47 | C2×(C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 48 | C2×(C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 49 | C2×(C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 50 | C2×C4×Dic67 | D4 | 1 | 1 | yes | characteristic |
| 51 | #14523977 | — | 4 | 1 | no | — |
| 52 | #14523969 | — | 4 | 2 | no | — |
| 53 | #14523965 | — | 4 | 1 | no | — |
| 54 | #14523964 | — | 4 | 1 | no | — |
| 55 | C22⋊(C67⋊C8) | — | 2 | 1 | no | — |
| 56 | C67⋊#95 | — | 2 | 1 | no | — |
| 57 | C67⋊#95 | — | 2 | 1 | no | — |
| 58 | C67⋊#95 | — | 2 | 1 | no | — |
| 59 | C67⋊#95 | D4 | 1 | 1 | yes | characteristic |
| 60 | C22×D4×C67 | D4 | 1 | 1 | yes | characteristic |
| 61 | C2×M16×C67 | — | 2 | 1 | no | — |
| 62 | C2×C4⋊C4×C67 | C23 | 1 | 1 | yes | characteristic |
| 63 | C2×C22⋊C4×C67 | — | 2 | 1 | no | — |
| 64 | C2×C22⋊C4×C67 | — | 2 | 1 | no | — |
| 65 | C22⋊C8×C67 | — | 2 | 1 | no | — |
| 66 | #95×C67 | D4 | 1 | 1 | yes | characteristic |
| 67 | C23×D67 | — | 2 | 1 | no | — |
| 68 | #11761628 | — | 4 | 1 | no | — |
| 69 | #11761628 | — | 4 | 1 | no | — |
| 70 | #11761628 | — | 4 | 1 | no | — |
| 71 | #11761628 | — | 4 | 1 | no | — |
| 72 | C2×Dic134 | — | 2 | 1 | no | — |
| 73 | C2×D268 | — | 2 | 1 | no | — |
| 74 | C2×D268 | — | 2 | 1 | no | — |
| 75 | C2×D268 | — | 2 | 1 | no | — |
| 76 | C2×D268 | — | 2 | 1 | no | — |
| 77 | C2×D268 | — | 4 | 1 | no | — |
| 78 | C2×D268 | — | 4 | 1 | no | — |
| 79 | C2×D268 | D8 | 1 | 2 | yes | complemented |
| 80 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 81 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 82 | C2×C22⋊D67 | — | 4 | 2 | no | — |
| 83 | C2×C22⋊D67 | — | 4 | 1 | no | — |
| 84 | C2×C22⋊D67 | — | 8 | 1 | no | — |
| 85 | C2×C22⋊D67 | — | 8 | 1 | no | — |
| 86 | C2×C22⋊D67 | — | 8 | 1 | no | — |
| 87 | C22×Dic67 | — | 2 | 1 | no | — |
| 88 | C22×Dic67 | — | 2 | 1 | no | — |
| 89 | C22×Dic67 | — | 2 | 1 | no | — |
| 90 | C2×C4×D67 | — | 4 | 2 | no | — |
| 91 | C2×C4×D67 | — | 4 | 1 | no | — |
| 92 | C2×C4×D67 | — | 4 | 2 | no | — |
| 93 | C2×C4×D67 | — | 8 | 1 | no | — |
| 94 | #11761617 | — | 4 | 4 | no | — |
| 95 | D536 | — | 4 | 4 | no | — |
| 96 | #11761613 | — | 8 | 2 | no | — |
| 97 | C2×C67⋊C8 | — | 4 | 1 | no | — |
| 98 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 99 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 100 | C4⋊Dic67 | — | 4 | 1 | no | — |
| 101 | Dic67⋊C4 | — | 4 | 1 | no | — |
| 102 | Dic67⋊C4 | — | 4 | 1 | no | — |
| 103 | C22⋊Dic67 | — | 4 | 2 | no | — |
| 104 | C22⋊Dic67 | — | 8 | 1 | no | — |
| 105 | (C2×D67)⋊C4 | — | 4 | 1 | no | — |
| 106 | (C2×D67)⋊C4 | — | 4 | 1 | no | — |
| 107 | (C2×D67)⋊C4 | — | 4 | 2 | no | — |
| 108 | (C2×D67)⋊C4 | — | 8 | 1 | no | — |
| 109 | (C2×D67)⋊C4 | — | 8 | 1 | no | — |
| 110 | C4×Dic67 | — | 4 | 1 | no | — |
| 111 | C24×C67 | — | 2 | 1 | no | — |
| 112 | C2×D4×C67 | — | 4 | 1 | no | — |
| 113 | C2×D4×C67 | — | 8 | 1 | no | — |
| 114 | C22×C4×C67 | — | 2 | 1 | no | — |
| 115 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 117 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | M16×C67 | — | 2 | 2 | no | — |
| 119 | M16×C67 | — | 4 | 1 | no | — |
| 120 | C2×C8×C67 | — | 4 | 1 | no | — |
| 121 | C2×C8×C67 | — | 4 | 1 | no | — |
| 122 | C4⋊C4×C67 | — | 4 | 1 | no | — |
| 123 | C22⋊C4×C67 | — | 4 | 1 | no | — |
| 124 | C22⋊C4×C67 | — | 4 | 1 | no | — |
| 125 | C22⋊C4×C67 | — | 8 | 1 | no | — |
| 126 | C23×C67 | — | 4 | 1 | no | — |
| 127 | C23×C67 | — | 4 | 1 | no | — |
| 128 | C23×C67 | — | 4 | 1 | no | — |
| 129 | C23×C67 | — | 4 | 1 | no | — |
| 130 | C23×C67 | — | 4 | 1 | no | — |
| 131 | C23×C67 | — | 4 | 1 | no | — |
| 132 | C23×C67 | — | 4 | 1 | no | — |
| 133 | C23×C67 | #120 | 1 | 1 | yes | characteristic |
| 134 | C22×D67 | — | 2 | 2 | no | — |
| 135 | C22×D67 | — | 4 | 1 | no | — |
| 136 | C22×D67 | — | 4 | 1 | no | — |
| 137 | C22×D67 | — | 4 | 1 | no | — |
| 138 | C22×D67 | — | 4 | 1 | no | — |
| 139 | C22×D67 | — | 4 | 1 | no | — |
| 140 | C22×D67 | — | 4 | 1 | no | — |
| 141 | C22×D67 | — | 4 | 1 | no | — |
| 142 | D4×C67 | — | 4 | 2 | no | — |
| 143 | D4×C67 | — | 8 | 1 | no | — |
| 144 | C2×C4×C67 | — | 2 | 1 | no | — |
| 145 | C2×C4×C67 | — | 2 | 1 | no | — |
| 146 | C2×C4×C67 | — | 2 | 1 | no | — |
| 147 | C2×C4×C67 | — | 2 | 1 | no | — |
| 148 | C2×C4×C67 | — | 4 | 1 | no | — |
| 149 | C2×C4×C67 | — | 4 | 1 | no | — |
| 150 | C2×C4×C67 | — | 4 | 1 | no | — |
| 151 | C2×C4×C67 | — | 4 | 1 | no | — |
| 152 | C2×C4×C67 | — | 4 | 1 | no | — |
| 153 | C2×C4×C67 | C2×D8 | 1 | 1 | yes | characteristic |
| 154 | C2×C4×C67 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 155 | C22⋊D67 | — | 8 | 4 | no | — |
| 156 | C22⋊D67 | — | 8 | 4 | no | — |
| 157 | C22⋊D67 | — | 8 | 1 | no | — |
| 158 | C22⋊D67 | — | 8 | 1 | no | — |
| 159 | C2×Dic67 | — | 2 | 2 | no | — |
| 160 | C2×Dic67 | — | 4 | 1 | no | — |
| 161 | C2×Dic67 | — | 4 | 1 | no | — |
| 162 | C2×Dic67 | — | 4 | 1 | no | — |
| 163 | C2×Dic67 | — | 4 | 1 | no | — |
| 164 | C2×Dic67 | — | 4 | 1 | no | — |
| 165 | C2×Dic67 | — | 4 | 1 | no | — |
| 166 | C2×Dic67 | — | 4 | 1 | no | — |
| 167 | C2×Dic67 | — | 4 | 1 | no | — |
| 168 | C2×Dic67 | — | 4 | 1 | no | — |
| 169 | D268 | — | 4 | 2 | no | — |
| 170 | D268 | — | 4 | 1 | no | — |
| 171 | D268 | — | 4 | 1 | no | — |
| 172 | D268 | — | 8 | 1 | no | — |
| 173 | D268 | — | 8 | 1 | no | — |
| 174 | D268 | — | 8 | 1 | no | — |
| 175 | C4×D67 | — | 8 | 4 | no | — |
| 176 | C4×D67 | — | 8 | 1 | no | — |
| 177 | C4×D67 | — | 8 | 1 | no | — |
| 178 | Dic134 | — | 4 | 1 | no | — |
| 179 | Dic134 | — | 4 | 1 | no | — |
| 180 | C8×C67 | — | 4 | 2 | no | — |
| 181 | C8×C67 | — | 8 | 1 | no | — |
| 182 | C67⋊C8 | — | 8 | 1 | no | — |
| 183 | C22×C67 | — | 2 | 1 | no | — |
| 184 | C22×C67 | — | 2 | 1 | no | — |
| 185 | C22×C67 | — | 8 | 1 | no | — |
| 186 | C22×C67 | — | 8 | 1 | no | — |
| 187 | C22×C67 | — | 8 | 1 | no | — |
| 188 | C22×C67 | — | 8 | 1 | no | — |
| 189 | C22×C67 | — | 8 | 1 | no | — |
| 190 | C22×C67 | — | 8 | 1 | no | — |
| 191 | C22×C67 | — | 8 | 1 | no | — |
| 192 | C22×C67 | #447 | 1 | 1 | yes | characteristic |
| 193 | C22×C67 | #453 | 1 | 1 | yes | characteristic |
| 194 | C22×C67 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 195 | C2×D67 | — | 4 | 2 | no | — |
| 196 | C2×D67 | — | 4 | 2 | no | — |
| 197 | C2×D67 | — | 4 | 2 | no | — |
| 198 | C2×D67 | — | 8 | 1 | no | — |
| 199 | C2×D67 | — | 8 | 1 | no | — |
| 200 | C2×D67 | — | 8 | 1 | no | — |
| 201 | C2×D67 | — | 8 | 1 | no | — |
| 202 | C2×D67 | — | 8 | 1 | no | — |
| 203 | C2×D67 | — | 8 | 1 | no | — |
| 204 | C2×D67 | — | 8 | 1 | no | — |
| 205 | C4×C67 | — | 2 | 1 | no | — |
| 206 | C4×C67 | — | 2 | 1 | no | — |
| 207 | C4×C67 | — | 4 | 1 | no | — |
| 208 | C4×C67 | — | 4 | 1 | no | — |
| 209 | C4×C67 | — | 8 | 1 | no | — |
| 210 | Dic67 | — | 4 | 2 | no | — |
| 211 | Dic67 | — | 8 | 1 | no | — |
| 212 | Dic67 | — | 8 | 1 | no | — |
| 213 | Dic67 | — | 8 | 1 | no | — |
| 214 | #12099 | — | 67 | 1 | no | maximal, Sylow |
| 215 | C2×C67 | — | 2 | 1 | no | — |
| 216 | C2×C67 | — | 2 | 1 | no | — |
| 217 | C2×C67 | — | 16 | 1 | no | — |
| 218 | C2×C67 | #1595 | 1 | 1 | yes | characteristic |
| 219 | C2×C67 | #2200 | 1 | 1 | yes | characteristic |
| 220 | C2×C67 | #2204 | 1 | 1 | yes | characteristic |
| 221 | D67 | — | 8 | 2 | no | — |
| 222 | D67 | — | 16 | 1 | no | — |
| 223 | #2699 | — | 67 | 1 | no | — |
| 224 | #2006 | — | 67 | 1 | no | — |
| 225 | #1610 | — | 67 | 1 | no | — |
| 226 | #1598 | — | 67 | 1 | no | — |
| 227 | #1346 | — | 67 | 1 | no | — |
| 228 | #1345 | D67 | 1 | 1 | yes | characteristic, complemented |
| 229 | #1318 | — | 67 | 1 | no | — |
| 230 | C67 | #12099 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 231 | C2×AGL(1,ℤ/8) | — | 134 | 1 | no | — |
| 232 | #537 | — | 67 | 1 | no | — |
| 233 | C2×#121 | — | 134 | 1 | no | — |
| 234 | #480 | — | 134 | 1 | no | — |
| 235 | #447 | — | 134 | 1 | no | — |
| 236 | C2×#104 | — | 134 | 1 | no | — |
| 237 | #398 | — | 67 | 1 | no | — |
| 238 | #394 | — | 134 | 1 | no | — |
| 239 | #394 | C2×D67 | 1 | 1 | yes | characteristic |
| 240 | #392 | — | 134 | 1 | no | — |
| 241 | #390 | — | 67 | 1 | no | — |
| 242 | #388 | — | 134 | 1 | no | — |
| 243 | #386 | — | 134 | 1 | no | — |
| 244 | #381 | — | 134 | 1 | no | — |
| 245 | #343 | C2×D67 | 1 | 1 | yes | characteristic |
| 246 | #327 | — | 134 | 1 | no | — |
| 247 | #327 | — | 134 | 1 | no | — |
| 248 | #324 | — | 67 | 1 | no | — |
| 249 | #324 | C2×D67 | 1 | 1 | yes | characteristic |
| 250 | C2×#41 | — | 134 | 1 | no | — |
| 251 | C22×D4 | — | 67 | 1 | no | — |
| 252 | C22×D4 | — | 134 | 1 | no | — |
| 253 | C22×D4 | — | 134 | 1 | no | — |
| 254 | C22×D4 | D268 | 1 | 1 | yes | characteristic |
| 255 | C23×C4 | — | 134 | 1 | no | — |
| 256 | AGL(1,ℤ/8) | — | 268 | 2 | no | — |
| 257 | AGL(1,ℤ/8) | — | 268 | 2 | no | — |
| 258 | C2×SD16 | — | 268 | 1 | no | — |
| 259 | C2×D8 | — | 268 | 1 | no | — |
| 260 | C2×D8 | — | 268 | 1 | no | — |
| 261 | C2×M16 | — | 2 | 1 | no | — |
| 262 | C22⋊Q8 | — | 268 | 1 | no | — |
| 263 | #121 | — | 268 | 2 | no | — |
| 264 | #121 | — | 268 | 2 | no | — |
| 265 | #121 | — | 268 | 1 | no | — |
| 266 | #121 | — | 134 | 1 | no | — |
| 267 | #121 | — | 134 | 1 | no | — |
| 268 | C2×C4⋊C4 | — | 67 | 1 | no | — |
| 269 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 270 | C2×C4⋊C4 | C22×D67 | 1 | 1 | yes | characteristic |
| 271 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 272 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 273 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 274 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 275 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 276 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 277 | C2×C22⋊C4 | — | 134 | 1 | no | — |
| 278 | C2×C42 | — | 67 | 1 | no | — |
| 279 | #107 | — | 268 | 1 | no | — |
| 280 | #104 | — | 268 | 2 | no | — |
| 281 | #102 | — | 268 | 1 | no | — |
| 282 | #102 | — | 268 | 1 | no | — |
| 283 | C22⋊C8 | — | 2 | 1 | no | — |
| 284 | C22⋊C8 | — | 134 | 1 | no | — |
| 285 | #95 | — | 67 | 1 | no | — |
| 286 | #95 | — | 134 | 1 | no | — |
| 287 | #95 | — | 134 | 1 | no | — |
| 288 | #95 | — | 134 | 1 | no | — |
| 289 | #95 | D268 | 1 | 1 | yes | characteristic |
| 290 | C24 | — | 2 | 1 | no | — |
| 291 | C24 | — | 134 | 1 | no | — |
| 292 | #41 | — | 268 | 1 | no | — |
| 293 | #41 | — | 268 | 1 | no | — |
| 294 | #41 | — | 268 | 1 | no | — |
| 295 | #41 | — | 268 | 1 | no | — |
| 296 | C2×Q8 | — | 134 | 1 | no | — |
| 297 | C2×D4 | — | 4 | 1 | no | — |
| 298 | C2×D4 | — | 8 | 1 | no | — |
| 299 | C2×D4 | — | 268 | 1 | no | — |
| 300 | C2×D4 | — | 268 | 1 | no | — |
| 301 | C2×D4 | — | 268 | 2 | no | — |
| 302 | C2×D4 | — | 268 | 2 | no | — |
| 303 | C2×D4 | — | 268 | 1 | no | — |
| 304 | C2×D4 | — | 268 | 2 | no | — |
| 305 | C2×D4 | — | 536 | 1 | no | — |
| 306 | C2×D4 | — | 536 | 1 | no | — |
| 307 | C2×D4 | — | 536 | 1 | no | — |
| 308 | C2×D4 | — | 67 | 2 | no | — |
| 309 | C2×D4 | — | 134 | 1 | no | — |
| 310 | C2×D4 | — | 134 | 1 | no | — |
| 311 | C2×D4 | — | 134 | 1 | no | — |
| 312 | C2×D4 | — | 134 | 1 | no | — |
| 313 | C22×C4 | — | 2 | 1 | no | — |
| 314 | C22×C4 | — | 268 | 1 | no | — |
| 315 | C22×C4 | — | 268 | 2 | no | — |
| 316 | C22×C4 | — | 268 | 2 | no | — |
| 317 | C22×C4 | — | 536 | 1 | no | — |
| 318 | C22×C4 | — | 134 | 1 | no | — |
| 319 | C22×C4 | — | 134 | 1 | no | — |
| 320 | C22×C4 | — | 134 | 1 | no | — |
| 321 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 322 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 323 | C22×C4 | C2×D268 | 1 | 1 | yes | characteristic |
| 324 | SD16 | — | 268 | 4 | no | — |
| 325 | D8 | — | 268 | 4 | no | — |
| 326 | D8 | — | 536 | 2 | no | — |
| 327 | M16 | — | 2 | 2 | no | — |
| 328 | M16 | — | 4 | 1 | no | — |
| 329 | C2×C8 | — | 4 | 1 | no | — |
| 330 | C2×C8 | — | 4 | 1 | no | — |
| 331 | C2×C8 | — | 268 | 1 | no | — |
| 332 | C4⋊C4 | — | 4 | 1 | no | — |
| 333 | C4⋊C4 | — | 268 | 1 | no | — |
| 334 | C4⋊C4 | — | 268 | 1 | no | — |
| 335 | C4⋊C4 | — | 268 | 1 | no | — |
| 336 | C4⋊C4 | — | 134 | 1 | no | — |
| 337 | C4⋊C4 | — | 134 | 1 | no | — |
| 338 | C22⋊C4 | — | 4 | 1 | no | — |
| 339 | C22⋊C4 | — | 4 | 1 | no | — |
| 340 | C22⋊C4 | — | 8 | 1 | no | — |
| 341 | C22⋊C4 | — | 268 | 1 | no | — |
| 342 | C22⋊C4 | — | 268 | 1 | no | — |
| 343 | C22⋊C4 | — | 268 | 2 | no | — |
| 344 | C22⋊C4 | — | 268 | 2 | no | — |
| 345 | C22⋊C4 | — | 536 | 1 | no | — |
| 346 | C22⋊C4 | — | 536 | 1 | no | — |
| 347 | C22⋊C4 | — | 536 | 1 | no | — |
| 348 | C42 | — | 268 | 1 | no | — |
| 349 | C23 | — | 4 | 1 | no | — |
| 350 | C23 | — | 4 | 1 | no | — |
| 351 | C23 | — | 4 | 1 | no | — |
| 352 | C23 | — | 4 | 1 | no | — |
| 353 | C23 | — | 4 | 1 | no | — |
| 354 | C23 | — | 4 | 1 | no | — |
| 355 | C23 | — | 4 | 1 | no | — |
| 356 | C23 | — | 268 | 1 | no | — |
| 357 | C23 | — | 268 | 1 | no | — |
| 358 | C23 | — | 268 | 1 | no | — |
| 359 | C23 | — | 268 | 1 | no | — |
| 360 | C23 | — | 268 | 1 | no | — |
| 361 | C23 | — | 268 | 1 | no | — |
| 362 | C23 | — | 268 | 1 | no | — |
| 363 | C23 | — | 134 | 2 | no | — |
| 364 | C23 | #14524013 | 1 | 1 | yes | characteristic |
| 365 | Q8 | — | 268 | 1 | no | — |
| 366 | Q8 | — | 268 | 1 | no | — |
| 367 | D4 | — | 4 | 2 | no | — |
| 368 | D4 | — | 8 | 1 | no | — |
| 369 | D4 | — | 268 | 2 | no | — |
| 370 | D4 | — | 268 | 1 | no | — |
| 371 | D4 | — | 268 | 1 | no | — |
| 372 | D4 | — | 536 | 1 | no | — |
| 373 | D4 | — | 536 | 1 | no | — |
| 374 | D4 | — | 536 | 1 | no | — |
| 375 | D4 | — | 536 | 4 | no | — |
| 376 | D4 | — | 536 | 4 | no | — |
| 377 | D4 | — | 536 | 1 | no | — |
| 378 | D4 | — | 536 | 1 | no | — |
| 379 | C2×C4 | — | 2 | 1 | no | — |
| 380 | C2×C4 | — | 2 | 1 | no | — |
| 381 | C2×C4 | — | 2 | 1 | no | — |
| 382 | C2×C4 | — | 2 | 1 | no | — |
| 383 | C2×C4 | — | 4 | 1 | no | — |
| 384 | C2×C4 | — | 4 | 1 | no | — |
| 385 | C2×C4 | — | 4 | 1 | no | — |
| 386 | C2×C4 | — | 4 | 1 | no | — |
| 387 | C2×C4 | — | 4 | 1 | no | — |
| 388 | C2×C4 | — | 268 | 1 | no | — |
| 389 | C2×C4 | — | 268 | 1 | no | — |
| 390 | C2×C4 | — | 268 | 1 | no | — |
| 391 | C2×C4 | — | 268 | 1 | no | — |
| 392 | C2×C4 | — | 268 | 1 | no | — |
| 393 | C2×C4 | — | 268 | 1 | no | — |
| 394 | C2×C4 | — | 268 | 1 | no | — |
| 395 | C2×C4 | — | 268 | 1 | no | — |
| 396 | C2×C4 | — | 268 | 1 | no | — |
| 397 | C2×C4 | — | 536 | 1 | no | — |
| 398 | C2×C4 | — | 536 | 1 | no | — |
| 399 | C2×C4 | — | 536 | 4 | no | — |
| 400 | C2×C4 | — | 134 | 2 | no | — |
| 401 | C2×C4 | D8×D67 | 1 | 1 | yes | characteristic |
| 402 | C2×C4 | #14524070 | 1 | 1 | yes | characteristic |
| 403 | C8 | — | 4 | 2 | no | — |
| 404 | C8 | — | 8 | 1 | no | — |
| 405 | C8 | — | 536 | 1 | no | — |
| 406 | C22 | — | 2 | 1 | no | — |
| 407 | C22 | — | 2 | 1 | no | — |
| 408 | C22 | — | 8 | 1 | no | — |
| 409 | C22 | — | 8 | 1 | no | — |
| 410 | C22 | — | 8 | 1 | no | — |
| 411 | C22 | — | 8 | 1 | no | — |
| 412 | C22 | — | 8 | 1 | no | — |
| 413 | C22 | — | 8 | 1 | no | — |
| 414 | C22 | — | 8 | 1 | no | — |
| 415 | C22 | — | 268 | 2 | no | — |
| 416 | C22 | — | 268 | 2 | no | — |
| 417 | C22 | — | 268 | 2 | no | — |
| 418 | C22 | — | 536 | 1 | no | — |
| 419 | C22 | — | 536 | 1 | no | — |
| 420 | C22 | — | 536 | 1 | no | — |
| 421 | C22 | — | 536 | 1 | no | — |
| 422 | C22 | — | 536 | 1 | no | — |
| 423 | C22 | — | 536 | 1 | no | — |
| 424 | C22 | — | 536 | 1 | no | — |
| 425 | C22 | #16863531 | 1 | 1 | yes | characteristic |
| 426 | C22 | #16863565 | 1 | 1 | yes | characteristic |
| 427 | C22 | #16863584 | 1 | 1 | yes | characteristic |
| 428 | C4 | — | 2 | 1 | no | — |
| 429 | C4 | — | 2 | 1 | no | — |
| 430 | C4 | — | 4 | 1 | no | — |
| 431 | C4 | — | 4 | 1 | no | — |
| 432 | C4 | — | 8 | 1 | no | — |
| 433 | C4 | — | 268 | 2 | no | — |
| 434 | C4 | — | 536 | 1 | no | — |
| 435 | C4 | — | 536 | 1 | no | — |
| 436 | C4 | — | 536 | 1 | no | — |
| 437 | C2 | — | 2 | 1 | no | — |
| 438 | C2 | — | 2 | 1 | no | — |
| 439 | C2 | — | 16 | 1 | no | — |
| 440 | C2 | — | 536 | 2 | no | — |
| 441 | C2 | — | 1072 | 1 | no | — |
| 442 | C2 | #22559128 | 1 | 1 | yes | characteristic |
| 443 | C2 | #22562218 | 1 | 1 | yes | characteristic |
| 444 | C2 | #22562236 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22566791 | C2 | semidirect |
| 2. #22561253 | C2 | semidirect |
| 3. #22559214 | C2 | semidirect |
| 4. #22559143 | C2 | semidirect |
| 5. #22558214 | C2 | semidirect |
| 6. #22558140 | C2 | semidirect |
| 7. C67×#1345 | C2 | semidirect |
| 79. C2×D268 | D8 | semidirect |
| 228. #1345 | D67 | semidirect |
| 230. C67 | #12099 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22566791 | 2 |
| #22561253 | 2 |
| #22559214 | 2 |
| #22559143 | 2 |
| #22558214 | 2 |
| #22558140 | 2 |
| C67×#1345 | 2 |
| #12099 | 67 |