Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
860 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 860 conjugacy classes of subgroups — too many to draw. Only its 103 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 | #22574614 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22561880 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22561874 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22560736 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C67×#1884 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #16864138 | — | 2 | 1 | no | — |
| 7 | #16864138 | C4 | 1 | 2 | yes | complemented |
| 8 | #16864112 | C4 | 1 | 2 | yes | complemented |
| 9 | #16864111 | — | 2 | 2 | no | — |
| 10 | D4×D268 | — | 2 | 2 | no | — |
| 11 | #16864031 | — | 2 | 1 | no | — |
| 12 | #16863962 | — | 2 | 4 | no | — |
| 13 | #16863960 | — | 2 | 1 | no | — |
| 14 | #16863960 | C22 | 1 | 2 | yes | — |
| 15 | #16863946 | — | 2 | 1 | no | — |
| 16 | #16863402 | — | 2 | 2 | no | — |
| 17 | #16863370 | C22 | 1 | 2 | yes | complemented |
| 18 | #16863191 | — | 2 | 1 | no | — |
| 19 | #16863189 | — | 2 | 1 | no | — |
| 20 | #16863188 | — | 2 | 4 | no | — |
| 21 | #16863153 | — | 2 | 2 | no | — |
| 22 | #568×C67 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #532×C67 | C22 | 1 | 1 | yes | characteristic |
| 24 | #421×C67 | — | 2 | 1 | no | — |
| 25 | #410×C67 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #339×C67 | — | 2 | 1 | no | — |
| 27 | C2×#11761628 | — | 2 | 2 | no | — |
| 28 | C22×D268 | — | 2 | 1 | no | — |
| 29 | C22×D268 | D4 | 1 | 2 | yes | — |
| 30 | C2×D4×D67 | — | 2 | 4 | no | — |
| 31 | #14524043 | — | 2 | 1 | no | — |
| 32 | #14524040 | — | 2 | 1 | no | — |
| 33 | #14524039 | — | 2 | 2 | no | — |
| 34 | #14524039 | D4 | 1 | 4 | yes | — |
| 35 | #14524032 | — | 2 | 2 | no | — |
| 36 | #14524032 | C2×C4 | 1 | 4 | yes | — |
| 37 | #14524031 | — | 2 | 2 | no | — |
| 38 | #14524029 | — | 2 | 4 | no | — |
| 39 | #14524029 | — | 2 | 4 | no | — |
| 40 | #14524018 | — | 2 | 4 | no | — |
| 41 | #14524017 | — | 2 | 2 | no | — |
| 42 | #14524017 | — | 2 | 2 | no | — |
| 43 | #14524017 | — | 2 | 2 | no | — |
| 44 | #14524017 | — | 2 | 2 | no | — |
| 45 | #14524014 | — | 2 | 4 | no | — |
| 46 | #14524013 | — | 2 | 4 | no | — |
| 47 | #14524013 | — | 2 | 4 | no | — |
| 48 | #14524011 | — | 2 | 2 | no | — |
| 49 | #14524011 | — | 2 | 2 | no | — |
| 50 | #14524011 | — | 2 | 2 | no | — |
| 51 | #14524011 | — | 2 | 2 | no | — |
| 52 | C4×D268 | — | 2 | 2 | no | — |
| 53 | C4×D268 | — | 2 | 2 | no | — |
| 54 | #14524002 | — | 2 | 1 | no | — |
| 55 | #14524002 | — | 2 | 2 | no | — |
| 56 | #14524002 | D4 | 1 | 2 | yes | — |
| 57 | #14524001 | — | 2 | 4 | no | — |
| 58 | #14523965 | — | 4 | 4 | no | — |
| 59 | #14523958 | — | 2 | 2 | no | — |
| 60 | #14523958 | — | 2 | 2 | no | — |
| 61 | C2×#41×C67 | D4 | 1 | 1 | yes | characteristic |
| 62 | C2×#41×C67 | C23 | 1 | 1 | yes | characteristic |
| 63 | #131×C67 | — | 4 | 2 | no | — |
| 64 | C2×M16×C67 | — | 2 | 2 | no | — |
| 65 | C2×M16×C67 | — | 2 | 1 | no | — |
| 66 | C4⋊Q8×C67 | C2×C4 | 1 | 1 | yes | characteristic |
| 67 | #127×C67 | D4 | 1 | 1 | yes | characteristic |
| 68 | #124×C67 | C2×C4 | 1 | 1 | yes | characteristic |
| 69 | #124×C67 | D4 | 1 | 1 | yes | characteristic |
| 70 | #121×C67 | — | 2 | 2 | no | — |
| 71 | C4×D4×C67 | — | 2 | 2 | no | — |
| 72 | #117×C67 | — | 2 | 1 | no | — |
| 73 | C2×C42×C67 | D4 | 1 | 1 | yes | characteristic |
| 74 | #104×C67 | — | 4 | 2 | no | — |
| 75 | #99×C67 | — | 2 | 2 | no | — |
| 76 | C23×D67 | — | 2 | 2 | no | — |
| 77 | C23×D67 | — | 2 | 2 | no | — |
| 78 | #11761628 | — | 8 | 4 | no | — |
| 79 | C2×Dic134 | — | 2 | 2 | no | — |
| 80 | C2×D268 | — | 2 | 2 | no | — |
| 81 | C2×D268 | — | 2 | 2 | no | — |
| 82 | C2×D268 | — | 2 | 2 | no | — |
| 83 | C2×D268 | — | 2 | 2 | no | — |
| 84 | C2×D268 | — | 4 | 2 | no | — |
| 85 | C2×D268 | — | 4 | 2 | no | — |
| 86 | C2×D268 | — | 8 | 1 | no | — |
| 87 | C2×D268 | — | 8 | 1 | no | — |
| 88 | C2×D268 | C22⋊C4 | 1 | 4 | yes | — |
| 89 | C2×C22⋊D67 | — | 2 | 4 | no | — |
| 90 | C2×C22⋊D67 | — | 2 | 4 | no | — |
| 91 | C2×C22⋊D67 | — | 2 | 4 | no | — |
| 92 | D4×D67 | — | 8 | 8 | no | — |
| 93 | C2×C4×D67 | — | 2 | 4 | no | — |
| 94 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 95 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 96 | C4⋊Dic67 | — | 4 | 2 | no | — |
| 97 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 98 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 99 | C22⋊Dic67 | — | 4 | 2 | no | — |
| 100 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 101 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 102 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 103 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 104 | C4×Dic67 | — | 2 | 2 | no | — |
| 105 | C4×Dic67 | — | 4 | 2 | no | — |
| 106 | C4×Dic67 | C22⋊C4 | 1 | 4 | yes | — |
| 107 | #41×C67 | — | 4 | 1 | no | — |
| 108 | #41×C67 | — | 4 | 1 | no | — |
| 109 | #41×C67 | — | 4 | 1 | no | — |
| 110 | #41×C67 | — | 4 | 1 | no | — |
| 111 | C2×Q8×C67 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 112 | C2×Q8×C67 | C22×C4 | 1 | 1 | yes | characteristic |
| 113 | C2×D4×C67 | — | 2 | 2 | no | — |
| 114 | C2×D4×C67 | — | 2 | 1 | no | — |
| 115 | C2×D4×C67 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 116 | C2×D4×C67 | C2×D4 | 1 | 2 | yes | — |
| 117 | C2×D4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | C22×C4×C67 | — | 2 | 1 | no | — |
| 119 | C22×C4×C67 | — | 2 | 1 | no | — |
| 120 | C22×C4×C67 | C2×D4 | 1 | 2 | yes | — |
| 121 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | M16×C67 | — | 2 | 2 | no | — |
| 123 | M16×C67 | — | 4 | 2 | no | — |
| 124 | M16×C67 | — | 4 | 1 | no | — |
| 125 | C2×C8×C67 | — | 2 | 4 | no | — |
| 126 | C2×C8×C67 | — | 4 | 1 | no | — |
| 127 | C4⋊C4×C67 | — | 2 | 2 | no | — |
| 128 | C4⋊C4×C67 | — | 4 | 1 | no | — |
| 129 | C22⋊C4×C67 | — | 2 | 2 | no | — |
| 130 | C22⋊C4×C67 | — | 2 | 2 | no | — |
| 131 | C22⋊C4×C67 | — | 4 | 1 | no | — |
| 132 | C42×C67 | — | 2 | 1 | no | — |
| 133 | C42×C67 | — | 4 | 1 | no | — |
| 134 | C42×C67 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 135 | C42×C67 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 136 | C23×C67 | — | 2 | 1 | no | — |
| 137 | C23×C67 | #120 | 1 | 1 | yes | characteristic |
| 138 | C23×C67 | #120 | 1 | 2 | yes | — |
| 139 | C22×D67 | — | 2 | 4 | no | — |
| 140 | C22×D67 | — | 8 | 2 | no | — |
| 141 | C22×D67 | — | 8 | 4 | no | — |
| 142 | C22×D67 | — | 8 | 4 | no | — |
| 143 | C22×D67 | — | 8 | 2 | no | — |
| 144 | Q8×C67 | — | 4 | 1 | no | — |
| 145 | Q8×C67 | — | 4 | 1 | no | — |
| 146 | D4×C67 | — | 4 | 2 | no | — |
| 147 | D4×C67 | — | 4 | 1 | no | — |
| 148 | D4×C67 | — | 4 | 1 | no | — |
| 149 | D4×C67 | — | 4 | 4 | no | — |
| 150 | D4×C67 | — | 8 | 1 | no | — |
| 151 | C2×C4×C67 | — | 2 | 1 | no | — |
| 152 | C2×C4×C67 | — | 2 | 1 | no | — |
| 153 | C2×C4×C67 | — | 2 | 2 | no | — |
| 154 | C2×C4×C67 | — | 2 | 1 | no | — |
| 155 | C2×C4×C67 | — | 2 | 2 | no | — |
| 156 | C2×C4×C67 | — | 2 | 1 | no | — |
| 157 | C2×C4×C67 | — | 2 | 1 | no | — |
| 158 | C2×C4×C67 | — | 4 | 2 | no | — |
| 159 | C2×C4×C67 | — | 4 | 1 | no | — |
| 160 | C2×C4×C67 | — | 4 | 1 | no | — |
| 161 | C2×C4×C67 | — | 8 | 1 | no | — |
| 162 | C2×C4×C67 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 163 | C2×C4×C67 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 164 | C2×C4×C67 | #120 | 1 | 1 | yes | characteristic |
| 165 | C22⋊D67 | — | 8 | 4 | no | — |
| 166 | C22⋊D67 | — | 8 | 4 | no | — |
| 167 | C22⋊D67 | — | 8 | 4 | no | — |
| 168 | C2×Dic67 | — | 2 | 4 | no | — |
| 169 | C2×Dic67 | — | 8 | 2 | no | — |
| 170 | D268 | — | 4 | 4 | no | — |
| 171 | D268 | — | 4 | 4 | no | — |
| 172 | D268 | — | 4 | 2 | no | — |
| 173 | D268 | — | 4 | 2 | no | — |
| 174 | D268 | — | 8 | 2 | no | — |
| 175 | D268 | — | 8 | 2 | no | — |
| 176 | C4×D67 | — | 4 | 8 | no | — |
| 177 | Dic134 | — | 8 | 2 | no | — |
| 178 | C8×C67 | — | 4 | 2 | no | — |
| 179 | C22×C67 | — | 2 | 2 | no | — |
| 180 | C22×C67 | — | 2 | 1 | no | — |
| 181 | C22×C67 | — | 4 | 1 | no | — |
| 182 | C22×C67 | — | 4 | 2 | no | — |
| 183 | C22×C67 | — | 4 | 2 | no | — |
| 184 | C22×C67 | — | 4 | 1 | no | — |
| 185 | C22×C67 | #379 | 1 | 1 | yes | characteristic |
| 186 | C2×D67 | — | 4 | 4 | no | — |
| 187 | C2×D67 | — | 4 | 4 | no | — |
| 188 | C2×D67 | — | 4 | 4 | no | — |
| 189 | C2×D67 | — | 16 | 4 | no | — |
| 190 | C2×D67 | — | 16 | 4 | no | — |
| 191 | C4×C67 | — | 2 | 2 | no | — |
| 192 | C4×C67 | — | 2 | 2 | no | — |
| 193 | C4×C67 | — | 2 | 1 | no | — |
| 194 | C4×C67 | — | 4 | 1 | no | — |
| 195 | C4×C67 | — | 4 | 1 | no | — |
| 196 | C4×C67 | — | 16 | 1 | no | — |
| 197 | C4×C67 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 198 | C4×C67 | #458 | 1 | 1 | yes | characteristic |
| 199 | Dic67 | — | 4 | 4 | no | — |
| 200 | Dic67 | — | 16 | 2 | no | — |
| 201 | #12778 | — | 67 | 1 | no | maximal, Sylow |
| 202 | C2×C67 | — | 2 | 1 | no | — |
| 203 | C2×C67 | — | 4 | 2 | no | — |
| 204 | C2×C67 | — | 4 | 1 | no | — |
| 205 | C2×C67 | — | 8 | 1 | no | — |
| 206 | C2×C67 | #1790 | 1 | 1 | yes | characteristic |
| 207 | D67 | — | 8 | 4 | no | — |
| 208 | #3549 | — | 67 | 1 | no | — |
| 209 | #2128 | — | 67 | 2 | no | — |
| 210 | #2126 | — | 67 | 1 | no | — |
| 211 | #1910 | — | 67 | 2 | no | — |
| 212 | #1884 | D67 | 1 | 1 | yes | characteristic, complemented |
| 213 | C67 | #12778 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 214 | #568 | C2×D67 | 1 | 1 | yes | characteristic, complemented |
| 215 | H(3,𝔽4) | — | 67 | 2 | no | — |
| 216 | H(3,𝔽4) | — | 134 | 1 | no | — |
| 217 | #555 | — | 67 | 2 | no | — |
| 218 | #555 | — | 134 | 2 | no | — |
| 219 | D42 | — | 134 | 2 | no | — |
| 220 | D42 | — | 134 | 1 | no | — |
| 221 | #535 | — | 67 | 2 | no | — |
| 222 | #535 | — | 134 | 4 | no | — |
| 223 | #535 | — | 134 | 1 | no | — |
| 224 | #532 | — | 134 | 1 | no | — |
| 225 | #532 | C2×D67 | 1 | 1 | yes | characteristic |
| 226 | #421 | — | 2 | 1 | no | — |
| 227 | #418 | — | 134 | 2 | no | — |
| 228 | #410 | — | 67 | 2 | no | — |
| 229 | #410 | C2×D67 | 1 | 1 | yes | characteristic, complemented |
| 230 | #354 | — | 134 | 1 | no | — |
| 231 | #353 | — | 134 | 4 | no | — |
| 232 | #353 | — | 134 | 1 | no | — |
| 233 | #339 | — | 2 | 1 | no | — |
| 234 | H(3,ℤ/4) | — | 134 | 2 | no | — |
| 235 | C2×#41 | — | 134 | 2 | no | — |
| 236 | C2×#41 | C22⋊D67 | 1 | 1 | yes | characteristic |
| 237 | C2×#41 | C22×D67 | 1 | 1 | yes | characteristic |
| 238 | C22×D4 | — | 67 | 2 | no | — |
| 239 | C22×D4 | — | 134 | 1 | no | — |
| 240 | C22×D4 | — | 134 | 4 | no | — |
| 241 | #131 | — | 4 | 2 | no | — |
| 242 | C2×M16 | — | 2 | 2 | no | — |
| 243 | C2×M16 | — | 2 | 1 | no | — |
| 244 | C4⋊Q8 | — | 134 | 1 | no | — |
| 245 | C4⋊Q8 | C4×D67 | 1 | 1 | yes | characteristic |
| 246 | #127 | — | 67 | 4 | no | — |
| 247 | #127 | — | 134 | 1 | no | — |
| 248 | #127 | — | 134 | 2 | no | — |
| 249 | #127 | D268 | 1 | 1 | yes | characteristic |
| 250 | #124 | — | 67 | 4 | no | — |
| 251 | #124 | — | 134 | 4 | no | — |
| 252 | #124 | — | 134 | 4 | no | — |
| 253 | #124 | — | 134 | 2 | no | — |
| 254 | #124 | — | 134 | 2 | no | — |
| 255 | #124 | C4×D67 | 1 | 1 | yes | characteristic |
| 256 | #124 | D268 | 1 | 1 | yes | characteristic |
| 257 | #121 | — | 2 | 2 | no | — |
| 258 | #121 | — | 134 | 4 | no | — |
| 259 | #121 | — | 134 | 2 | no | — |
| 260 | #121 | — | 134 | 2 | no | — |
| 261 | #121 | — | 134 | 4 | no | — |
| 262 | #121 | — | 134 | 2 | no | — |
| 263 | #121 | — | 134 | 2 | no | — |
| 264 | #120 | — | 134 | 4 | no | — |
| 265 | #120 | — | 134 | 4 | no | — |
| 266 | #120 | — | 134 | 2 | no | — |
| 267 | #120 | — | 134 | 2 | no | — |
| 268 | #120 | — | 134 | 2 | no | — |
| 269 | #120 | — | 134 | 2 | no | — |
| 270 | C4×D4 | — | 2 | 2 | no | — |
| 271 | C4×D4 | — | 134 | 2 | no | — |
| 272 | C4×D4 | — | 134 | 2 | no | — |
| 273 | #117 | — | 2 | 1 | no | — |
| 274 | #117 | — | 67 | 2 | no | — |
| 275 | #117 | — | 134 | 2 | no | — |
| 276 | #117 | — | 134 | 4 | no | — |
| 277 | #117 | — | 134 | 1 | no | — |
| 278 | C2×C42 | C22⋊D67 | 1 | 1 | yes | characteristic |
| 279 | #104 | — | 4 | 2 | no | — |
| 280 | #102 | — | 268 | 4 | no | — |
| 281 | #99 | — | 2 | 2 | no | — |
| 282 | #99 | — | 134 | 2 | no | — |
| 283 | #99 | — | 134 | 2 | no | — |
| 284 | C24 | — | 134 | 2 | no | — |
| 285 | C24 | — | 134 | 2 | no | — |
| 286 | #41 | — | 4 | 1 | no | — |
| 287 | #41 | — | 4 | 1 | no | — |
| 288 | #41 | — | 4 | 1 | no | — |
| 289 | #41 | — | 4 | 1 | no | — |
| 290 | #41 | — | 536 | 4 | no | — |
| 291 | C2×Q8 | — | 134 | 2 | no | — |
| 292 | C2×Q8 | (C2×D67)⋊C4 | 1 | 1 | yes | characteristic |
| 293 | C2×Q8 | C2×C4×D67 | 1 | 1 | yes | characteristic |
| 294 | C2×D4 | — | 2 | 2 | no | — |
| 295 | C2×D4 | — | 2 | 1 | no | — |
| 296 | C2×D4 | — | 268 | 2 | no | — |
| 297 | C2×D4 | — | 268 | 2 | no | — |
| 298 | C2×D4 | — | 536 | 1 | no | — |
| 299 | C2×D4 | — | 536 | 1 | no | — |
| 300 | C2×D4 | — | 536 | 8 | no | — |
| 301 | C2×D4 | — | 67 | 4 | no | — |
| 302 | C2×D4 | — | 134 | 2 | no | — |
| 303 | C2×D4 | — | 134 | 2 | no | — |
| 304 | C2×D4 | — | 134 | 2 | no | — |
| 305 | C2×D4 | — | 134 | 4 | no | — |
| 306 | C2×D4 | — | 134 | 4 | no | — |
| 307 | C2×D4 | — | 134 | 4 | no | — |
| 308 | C2×D4 | — | 134 | 2 | no | — |
| 309 | C2×D4 | (C2×D67)⋊C4 | 1 | 1 | yes | characteristic |
| 310 | C2×D4 | D4×D67 | 1 | 2 | yes | — |
| 311 | C2×D4 | C2×D268 | 1 | 1 | yes | characteristic |
| 312 | C22×C4 | — | 2 | 1 | no | — |
| 313 | C22×C4 | — | 2 | 1 | no | — |
| 314 | C22×C4 | — | 134 | 4 | no | — |
| 315 | C22×C4 | D4×D67 | 1 | 2 | yes | — |
| 316 | C22×C4 | C2×C22⋊D67 | 1 | 1 | yes | characteristic |
| 317 | M16 | — | 2 | 2 | no | — |
| 318 | M16 | — | 4 | 2 | no | — |
| 319 | M16 | — | 4 | 1 | no | — |
| 320 | C2×C8 | — | 2 | 4 | no | — |
| 321 | C2×C8 | — | 4 | 1 | no | — |
| 322 | C4⋊C4 | — | 2 | 2 | no | — |
| 323 | C4⋊C4 | — | 4 | 1 | no | — |
| 324 | C4⋊C4 | — | 268 | 2 | no | — |
| 325 | C4⋊C4 | — | 134 | 2 | no | — |
| 326 | C4⋊C4 | — | 134 | 2 | no | — |
| 327 | C22⋊C4 | — | 2 | 2 | no | — |
| 328 | C22⋊C4 | — | 2 | 2 | no | — |
| 329 | C22⋊C4 | — | 4 | 1 | no | — |
| 330 | C22⋊C4 | — | 268 | 2 | no | — |
| 331 | C22⋊C4 | — | 134 | 4 | no | — |
| 332 | C22⋊C4 | — | 134 | 4 | no | — |
| 333 | C22⋊C4 | — | 134 | 2 | no | — |
| 334 | C22⋊C4 | — | 134 | 2 | no | — |
| 335 | C22⋊C4 | — | 134 | 4 | no | — |
| 336 | C22⋊C4 | — | 134 | 4 | no | — |
| 337 | C42 | — | 2 | 1 | no | — |
| 338 | C42 | — | 4 | 1 | no | — |
| 339 | C42 | — | 268 | 2 | no | — |
| 340 | C42 | — | 67 | 4 | no | — |
| 341 | C42 | — | 134 | 2 | no | — |
| 342 | C42 | (C2×D67)⋊C4 | 1 | 1 | yes | characteristic |
| 343 | C42 | (C2×D67)⋊C4 | 1 | 1 | yes | characteristic |
| 344 | C23 | — | 2 | 1 | no | — |
| 345 | C23 | — | 536 | 2 | no | — |
| 346 | C23 | — | 536 | 4 | no | — |
| 347 | C23 | — | 536 | 4 | no | — |
| 348 | C23 | — | 536 | 2 | no | — |
| 349 | C23 | — | 134 | 4 | no | — |
| 350 | C23 | #14524011 | 1 | 1 | yes | characteristic |
| 351 | C23 | #14524013 | 1 | 2 | yes | — |
| 352 | Q8 | — | 4 | 1 | no | — |
| 353 | Q8 | — | 4 | 1 | no | — |
| 354 | Q8 | — | 536 | 2 | no | — |
| 355 | D4 | — | 4 | 2 | no | — |
| 356 | D4 | — | 4 | 1 | no | — |
| 357 | D4 | — | 4 | 1 | no | — |
| 358 | D4 | — | 4 | 4 | no | — |
| 359 | D4 | — | 8 | 1 | no | — |
| 360 | D4 | — | 268 | 4 | no | — |
| 361 | D4 | — | 268 | 4 | no | — |
| 362 | D4 | — | 268 | 2 | no | — |
| 363 | D4 | — | 268 | 2 | no | — |
| 364 | D4 | — | 536 | 2 | no | — |
| 365 | D4 | — | 536 | 2 | no | — |
| 366 | D4 | — | 536 | 4 | no | — |
| 367 | D4 | — | 536 | 4 | no | — |
| 368 | D4 | — | 536 | 4 | no | — |
| 369 | C2×C4 | — | 2 | 1 | no | — |
| 370 | C2×C4 | — | 2 | 1 | no | — |
| 371 | C2×C4 | — | 2 | 2 | no | — |
| 372 | C2×C4 | — | 2 | 2 | no | — |
| 373 | C2×C4 | — | 2 | 1 | no | — |
| 374 | C2×C4 | — | 2 | 1 | no | — |
| 375 | C2×C4 | — | 2 | 1 | no | — |
| 376 | C2×C4 | — | 4 | 2 | no | — |
| 377 | C2×C4 | — | 4 | 1 | no | — |
| 378 | C2×C4 | — | 4 | 1 | no | — |
| 379 | C2×C4 | — | 8 | 1 | no | — |
| 380 | C2×C4 | — | 268 | 8 | no | — |
| 381 | C2×C4 | — | 536 | 2 | no | — |
| 382 | C2×C4 | — | 134 | 4 | no | — |
| 383 | C2×C4 | C22⋊C4×D67 | 1 | 2 | yes | — |
| 384 | C2×C4 | C2×(C2×D67)⋊C4 | 1 | 1 | yes | characteristic |
| 385 | C2×C4 | #14524011 | 1 | 1 | yes | characteristic |
| 386 | C8 | — | 4 | 2 | no | — |
| 387 | C22 | — | 2 | 1 | no | — |
| 388 | C22 | — | 2 | 2 | no | — |
| 389 | C22 | — | 4 | 1 | no | — |
| 390 | C22 | — | 4 | 2 | no | — |
| 391 | C22 | — | 4 | 2 | no | — |
| 392 | C22 | — | 4 | 1 | no | — |
| 393 | C22 | — | 268 | 4 | no | — |
| 394 | C22 | — | 268 | 4 | no | — |
| 395 | C22 | — | 268 | 4 | no | — |
| 396 | C22 | — | 1072 | 4 | no | — |
| 397 | C22 | — | 1072 | 4 | no | — |
| 398 | C22 | #16863251 | 1 | 1 | yes | characteristic |
| 399 | C4 | — | 2 | 2 | no | — |
| 400 | C4 | — | 2 | 2 | no | — |
| 401 | C4 | — | 2 | 1 | no | — |
| 402 | C4 | — | 4 | 1 | no | — |
| 403 | C4 | — | 4 | 1 | no | — |
| 404 | C4 | — | 268 | 4 | no | — |
| 405 | C4 | — | 16 | 1 | no | — |
| 406 | C4 | — | 1072 | 2 | no | — |
| 407 | C4 | #16863582 | 1 | 1 | yes | characteristic |
| 408 | C4 | #16863585 | 1 | 1 | yes | characteristic |
| 409 | C2 | — | 2 | 1 | no | — |
| 410 | C2 | — | 4 | 1 | no | — |
| 411 | C2 | — | 4 | 2 | no | — |
| 412 | C2 | — | 8 | 1 | no | — |
| 413 | C2 | — | 536 | 4 | no | — |
| 414 | C2 | #22560156 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22561880 | C2 | semidirect |
| 3. #22561874 | C2 | semidirect |
| 4. #22560736 | C2 | semidirect |
| 5. C67×#1884 | C2 | semidirect |
| 7. #16864138 | C4 | semidirect |
| 8. #16864112 | C4 | semidirect |
| 17. #16863370 | C22 | semidirect |
| 22. #568×C67 | C22 | semidirect |
| 25. #410×C67 | C22 | semidirect |
| 212. #1884 | D67 | semidirect |
| 213. C67 | #12778 | semidirect |
| 214. #568 | C2×D67 | semidirect |
| 229. #410 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574614 | 2 |
| #22561880 | 2 |
| #22561874 | 2 |
| #22560736 | 2 |
| C67×#1884 | 2 |
| #12778 | 67 |