Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
720 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 77 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 | #22569610 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22569580 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22561901 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22561859 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22560159 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22558338 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C67×#3199 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #16864232 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#14524069 | — | 2 | 1 | no | — |
| 10 | #16863963 | — | 2 | 1 | no | — |
| 11 | #16863582 | — | 2 | 2 | no | — |
| 12 | #16863582 | — | 2 | 2 | no | — |
| 13 | #16863568 | — | 2 | 2 | no | — |
| 14 | #16863563 | — | 2 | 2 | no | — |
| 15 | #16863414 | — | 2 | 1 | no | — |
| 16 | #16863380 | C22 | 1 | 1 | yes | characteristic |
| 17 | #16863380 | C22 | 1 | 1 | yes | characteristic |
| 18 | #16863378 | — | 2 | 1 | no | — |
| 19 | #16863370 | C22 | 1 | 1 | yes | characteristic |
| 20 | #16863369 | — | 2 | 1 | no | — |
| 21 | #16863362 | — | 2 | 1 | no | — |
| 22 | #16863193 | — | 2 | 2 | no | — |
| 23 | #16863183 | — | 2 | 2 | no | — |
| 24 | #535×C67 | C22 | 1 | 1 | yes | characteristic |
| 25 | #535×C67 | C22 | 1 | 1 | yes | characteristic |
| 26 | #482×C67 | — | 2 | 1 | no | — |
| 27 | #482×C67 | — | 2 | 1 | no | — |
| 28 | #469×C67 | — | 2 | 1 | no | — |
| 29 | #466×C67 | — | 2 | 1 | no | — |
| 30 | #447×C67 | — | 2 | 1 | no | — |
| 31 | #447×C67 | — | 2 | 1 | no | — |
| 32 | #408×C67 | C22 | 1 | 1 | yes | characteristic |
| 33 | #14524091 | — | 2 | 1 | no | — |
| 34 | #14524090 | — | 4 | 1 | no | — |
| 35 | #14524089 | — | 4 | 1 | no | — |
| 36 | #14524088 | — | 2 | 1 | no | — |
| 37 | #14524088 | — | 2 | 1 | no | — |
| 38 | #14524088 | D4 | 1 | 2 | yes | — |
| 39 | C2×#11761628 | — | 2 | 1 | no | — |
| 40 | C2×#11761628 | — | 2 | 1 | no | — |
| 41 | C2×#11761628 | — | 2 | 1 | no | — |
| 42 | #41×D67 | — | 4 | 2 | no | — |
| 43 | #14524069 | — | 2 | 4 | no | — |
| 44 | #14524069 | — | 4 | 2 | no | — |
| 45 | C2×#11761616 | — | 4 | 1 | no | — |
| 46 | C2×#11761613 | — | 4 | 1 | no | — |
| 47 | C2×#11761612 | — | 2 | 1 | no | — |
| 48 | C2×#11761612 | — | 2 | 1 | no | — |
| 49 | #14524039 | — | 4 | 1 | no | — |
| 50 | #14524030 | — | 4 | 1 | no | — |
| 51 | #14524014 | — | 4 | 2 | no | — |
| 52 | #14524012 | — | 2 | 4 | no | — |
| 53 | #14524002 | — | 2 | 1 | no | — |
| 54 | #14523971 | — | 2 | 4 | no | — |
| 55 | #14523962 | — | 2 | 1 | no | — |
| 56 | #14523962 | D4 | 1 | 2 | yes | complemented |
| 57 | #14523961 | — | 4 | 1 | no | — |
| 58 | #14523960 | — | 2 | 1 | no | — |
| 59 | #14523960 | — | 2 | 1 | no | — |
| 60 | #14523959 | — | 4 | 1 | no | — |
| 61 | #14523958 | — | 2 | 1 | no | — |
| 62 | #14523958 | D4 | 1 | 2 | yes | — |
| 63 | #14523957 | — | 2 | 4 | no | — |
| 64 | (C2×D67)⋊C8 | — | 4 | 2 | no | — |
| 65 | C2×#41×C67 | C23 | 1 | 1 | yes | characteristic |
| 66 | C22×D4×C67 | D4 | 1 | 1 | yes | characteristic |
| 67 | C22×D4×C67 | D4 | 1 | 1 | yes | characteristic, complemented |
| 68 | C2×D8×C67 | — | 2 | 1 | no | — |
| 69 | C2×D8×C67 | — | 2 | 1 | no | — |
| 70 | C2×M16×C67 | D4 | 1 | 1 | yes | characteristic, complemented |
| 71 | C22×C8×C67 | D4 | 1 | 1 | yes | characteristic, complemented |
| 72 | #127×C67 | — | 2 | 1 | no | — |
| 73 | #127×C67 | — | 2 | 1 | no | — |
| 74 | #124×C67 | — | 2 | 1 | no | — |
| 75 | #124×C67 | — | 2 | 1 | no | — |
| 76 | #121×C67 | — | 2 | 1 | no | — |
| 77 | #121×C67 | — | 2 | 1 | no | — |
| 78 | #121×C67 | — | 2 | 1 | no | — |
| 79 | #121×C67 | — | 2 | 1 | no | — |
| 80 | #120×C67 | — | 2 | 1 | no | — |
| 81 | #120×C67 | — | 2 | 1 | no | — |
| 82 | #120×C67 | — | 2 | 1 | no | — |
| 83 | #120×C67 | — | 2 | 1 | no | — |
| 84 | #117×C67 | D4 | 1 | 1 | yes | characteristic |
| 85 | #117×C67 | D4 | 1 | 1 | yes | characteristic, complemented |
| 86 | #107×C67 | — | 2 | 1 | no | — |
| 87 | #106×C67 | — | 2 | 1 | no | — |
| 88 | #102×C67 | — | 2 | 1 | no | — |
| 89 | #102×C67 | — | 2 | 1 | no | — |
| 90 | #102×C67 | — | 2 | 1 | no | — |
| 91 | #102×C67 | — | 2 | 1 | no | — |
| 92 | C22⋊C8×C67 | — | 2 | 1 | no | — |
| 93 | C22⋊C8×C67 | — | 2 | 1 | no | — |
| 94 | #11761629 | — | 4 | 2 | no | — |
| 95 | #11761628 | — | 2 | 2 | no | — |
| 96 | #11761628 | — | 2 | 2 | no | — |
| 97 | #11761628 | — | 4 | 1 | no | — |
| 98 | #11761628 | — | 4 | 1 | no | — |
| 99 | #11761628 | — | 4 | 1 | no | — |
| 100 | #11761628 | — | 4 | 1 | no | — |
| 101 | #11761628 | — | 4 | 1 | no | — |
| 102 | #11761628 | — | 4 | 1 | no | — |
| 103 | #11761628 | — | 4 | 1 | no | — |
| 104 | #11761628 | — | 4 | 1 | no | — |
| 105 | #11761627 | — | 4 | 2 | no | — |
| 106 | #11761627 | — | 4 | 2 | no | — |
| 107 | #11761627 | — | 4 | 2 | no | — |
| 108 | C2×Dic134 | — | 2 | 1 | no | — |
| 109 | C2×Dic134 | — | 2 | 1 | no | — |
| 110 | C2×Dic134 | — | 2 | 1 | no | — |
| 111 | Q8×D67 | — | 4 | 2 | no | — |
| 112 | C2×D268 | — | 2 | 1 | no | — |
| 113 | C2×D268 | — | 2 | 1 | no | — |
| 114 | C2×D268 | — | 2 | 1 | no | — |
| 115 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 116 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 117 | C2×C22⋊D67 | — | 4 | 1 | no | — |
| 118 | C2×C22⋊D67 | — | 4 | 4 | no | — |
| 119 | D4×D67 | — | 4 | 2 | no | — |
| 120 | D4×D67 | — | 4 | 2 | no | — |
| 121 | D4×D67 | — | 4 | 2 | no | — |
| 122 | C2×C4×D67 | — | 2 | 2 | no | — |
| 123 | C2×C4×D67 | — | 2 | 2 | no | — |
| 124 | C2×C4×D67 | — | 4 | 1 | no | — |
| 125 | #11761616 | — | 4 | 4 | no | — |
| 126 | #11761613 | — | 4 | 4 | no | — |
| 127 | #11761612 | — | 2 | 2 | no | — |
| 128 | #11761612 | — | 4 | 1 | no | — |
| 129 | #11761612 | — | 4 | 1 | no | — |
| 130 | #11761612 | — | 4 | 1 | no | — |
| 131 | C2×C67⋊C8 | — | 4 | 1 | no | — |
| 132 | C2×C67⋊C8 | — | 4 | 1 | no | — |
| 133 | C4⋊Dic67 | — | 4 | 1 | no | — |
| 134 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 135 | C22⋊Dic67 | — | 4 | 4 | no | — |
| 136 | C4×Dic67 | — | 4 | 1 | no | — |
| 137 | C24×C67 | — | 2 | 1 | no | — |
| 138 | C24×C67 | — | 2 | 1 | no | — |
| 139 | #41×C67 | — | 4 | 1 | no | — |
| 140 | #41×C67 | — | 4 | 1 | no | — |
| 141 | C2×Q8×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 142 | C2×D4×C67 | — | 2 | 1 | no | — |
| 143 | C2×D4×C67 | — | 2 | 1 | no | — |
| 144 | C2×D4×C67 | — | 2 | 1 | no | — |
| 145 | C2×D4×C67 | — | 2 | 1 | no | — |
| 146 | C2×D4×C67 | — | 4 | 1 | no | — |
| 147 | C2×D4×C67 | — | 4 | 1 | no | — |
| 148 | C2×D4×C67 | — | 4 | 1 | no | — |
| 149 | C2×D4×C67 | — | 4 | 1 | no | — |
| 150 | C2×D4×C67 | — | 4 | 1 | no | — |
| 151 | C2×D4×C67 | — | 4 | 1 | no | — |
| 152 | C2×D4×C67 | — | 4 | 1 | no | — |
| 153 | C2×D4×C67 | — | 4 | 1 | no | — |
| 154 | C2×D4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C2×D4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C2×D4×C67 | #41 | 1 | 1 | yes | characteristic |
| 157 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 158 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 160 | D8×C67 | — | 8 | 1 | no | — |
| 161 | D8×C67 | — | 8 | 1 | no | — |
| 162 | M16×C67 | — | 4 | 1 | no | — |
| 163 | C2×C8×C67 | — | 2 | 1 | no | — |
| 164 | C2×C8×C67 | — | 2 | 1 | no | — |
| 165 | C2×C8×C67 | — | 4 | 1 | no | — |
| 166 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 167 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 168 | C22⋊C4×C67 | — | 2 | 1 | no | — |
| 169 | C22⋊C4×C67 | — | 2 | 1 | no | — |
| 170 | C22⋊C4×C67 | — | 4 | 1 | no | — |
| 171 | C22⋊C4×C67 | — | 4 | 1 | no | — |
| 172 | C22⋊C4×C67 | — | 4 | 1 | no | — |
| 173 | C22⋊C4×C67 | — | 4 | 1 | no | — |
| 174 | C42×C67 | — | 2 | 1 | no | — |
| 175 | C42×C67 | — | 2 | 1 | no | — |
| 176 | C23×C67 | — | 4 | 2 | no | — |
| 177 | C23×C67 | — | 4 | 1 | no | — |
| 178 | C23×C67 | — | 4 | 1 | no | — |
| 179 | C23×C67 | — | 8 | 1 | no | — |
| 180 | C23×C67 | — | 16 | 1 | no | — |
| 181 | C23×C67 | — | 16 | 1 | no | — |
| 182 | C23×C67 | #120 | 1 | 1 | yes | characteristic |
| 183 | C23×C67 | #121 | 1 | 1 | yes | characteristic |
| 184 | C23×C67 | #121 | 1 | 1 | yes | characteristic |
| 185 | C22×D67 | — | 2 | 2 | no | — |
| 186 | C22×D67 | — | 2 | 2 | no | — |
| 187 | C22×D67 | — | 4 | 1 | no | — |
| 188 | Q8×C67 | — | 4 | 1 | no | — |
| 189 | D4×C67 | — | 4 | 1 | no | — |
| 190 | D4×C67 | — | 4 | 1 | no | — |
| 191 | D4×C67 | — | 4 | 1 | no | — |
| 192 | D4×C67 | — | 4 | 2 | no | — |
| 193 | D4×C67 | — | 4 | 1 | no | — |
| 194 | D4×C67 | — | 4 | 1 | no | — |
| 195 | D4×C67 | — | 4 | 1 | no | — |
| 196 | D4×C67 | — | 4 | 1 | no | — |
| 197 | D4×C67 | — | 8 | 1 | no | — |
| 198 | D4×C67 | — | 16 | 1 | no | — |
| 199 | D4×C67 | — | 16 | 1 | no | — |
| 200 | D4×C67 | — | 16 | 1 | no | — |
| 201 | D4×C67 | — | 16 | 1 | no | — |
| 202 | C2×C4×C67 | — | 2 | 1 | no | — |
| 203 | C2×C4×C67 | — | 2 | 1 | no | — |
| 204 | C2×C4×C67 | — | 2 | 1 | no | — |
| 205 | C2×C4×C67 | — | 2 | 1 | no | — |
| 206 | C2×C4×C67 | — | 2 | 1 | no | — |
| 207 | C2×C4×C67 | — | 2 | 1 | no | — |
| 208 | C2×C4×C67 | — | 4 | 1 | no | — |
| 209 | C2×C4×C67 | — | 4 | 1 | no | — |
| 210 | C2×C4×C67 | #120 | 1 | 1 | yes | characteristic |
| 211 | C2×C4×C67 | #120 | 1 | 1 | yes | characteristic |
| 212 | C2×C4×C67 | #121 | 1 | 1 | yes | characteristic |
| 213 | C2×C4×C67 | #127 | 1 | 1 | yes | characteristic |
| 214 | C22⋊D67 | — | 4 | 2 | no | — |
| 215 | C22⋊D67 | — | 4 | 2 | no | — |
| 216 | C22⋊D67 | — | 4 | 2 | no | — |
| 217 | C22⋊D67 | — | 4 | 2 | no | — |
| 218 | C22⋊D67 | — | 16 | 4 | no | — |
| 219 | C2×Dic67 | — | 2 | 2 | no | — |
| 220 | C2×Dic67 | — | 2 | 2 | no | — |
| 221 | C2×Dic67 | — | 4 | 1 | no | — |
| 222 | C2×Dic67 | — | 4 | 2 | no | — |
| 223 | D268 | — | 2 | 2 | no | — |
| 224 | D268 | — | 4 | 1 | no | — |
| 225 | D268 | — | 4 | 1 | no | — |
| 226 | D268 | — | 4 | 1 | no | — |
| 227 | C4×D67 | — | 4 | 2 | no | — |
| 228 | C4×D67 | — | 4 | 2 | no | — |
| 229 | C4×D67 | — | 4 | 2 | no | — |
| 230 | C4×D67 | — | 4 | 2 | no | — |
| 231 | Dic134 | — | 2 | 2 | no | — |
| 232 | Dic134 | — | 4 | 1 | no | — |
| 233 | Dic134 | — | 4 | 1 | no | — |
| 234 | Dic134 | — | 4 | 1 | no | — |
| 235 | C8×C67 | — | 4 | 1 | no | — |
| 236 | C8×C67 | — | 4 | 1 | no | — |
| 237 | C67⋊C8 | — | 4 | 2 | no | — |
| 238 | C67⋊C8 | — | 8 | 1 | no | — |
| 239 | C22×C67 | — | 2 | 1 | no | — |
| 240 | C22×C67 | — | 2 | 1 | no | — |
| 241 | C22×C67 | — | 2 | 1 | no | — |
| 242 | C22×C67 | — | 4 | 1 | no | — |
| 243 | C22×C67 | — | 4 | 1 | no | — |
| 244 | C22×C67 | — | 4 | 1 | no | — |
| 245 | C22×C67 | — | 8 | 1 | no | — |
| 246 | C22×C67 | — | 8 | 1 | no | — |
| 247 | C22×C67 | — | 8 | 1 | no | — |
| 248 | C22×C67 | — | 8 | 1 | no | — |
| 249 | C22×C67 | — | 8 | 4 | no | — |
| 250 | C22×C67 | — | 8 | 1 | no | — |
| 251 | C22×C67 | — | 8 | 1 | no | — |
| 252 | C22×C67 | — | 16 | 2 | no | — |
| 253 | C22×C67 | #392 | 1 | 1 | yes | characteristic |
| 254 | C2×D67 | — | 4 | 2 | no | — |
| 255 | C2×D67 | — | 8 | 2 | no | — |
| 256 | C2×D67 | — | 8 | 2 | no | — |
| 257 | C2×D67 | — | 16 | 1 | no | — |
| 258 | C4×C67 | — | 2 | 1 | no | — |
| 259 | C4×C67 | — | 2 | 1 | no | — |
| 260 | C4×C67 | — | 2 | 1 | no | — |
| 261 | C4×C67 | — | 8 | 1 | no | — |
| 262 | C4×C67 | — | 8 | 1 | no | — |
| 263 | C4×C67 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 264 | C4×C67 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 265 | Dic67 | — | 4 | 2 | no | — |
| 266 | Dic67 | — | 8 | 2 | no | — |
| 267 | #13353 | — | 67 | 1 | no | maximal, Sylow |
| 268 | C2×C67 | — | 2 | 1 | no | — |
| 269 | C2×C67 | — | 4 | 1 | no | — |
| 270 | C2×C67 | — | 4 | 1 | no | — |
| 271 | C2×C67 | — | 4 | 1 | no | — |
| 272 | C2×C67 | — | 16 | 1 | no | — |
| 273 | C2×C67 | — | 16 | 1 | no | — |
| 274 | C2×C67 | #2021 | 1 | 1 | yes | characteristic |
| 275 | D67 | — | 8 | 2 | no | — |
| 276 | #3199 | D67 | 1 | 1 | yes | characteristic, complemented |
| 277 | #3027 | — | 67 | 1 | no | — |
| 278 | #3021 | — | 67 | 1 | no | — |
| 279 | #2134 | — | 67 | 1 | no | — |
| 280 | #2122 | — | 67 | 1 | no | — |
| 281 | #1791 | — | 67 | 1 | no | — |
| 282 | #1395 | — | 67 | 1 | no | — |
| 283 | C67 | #13353 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 284 | #585 | — | 67 | 1 | no | — |
| 285 | C2×AGL(1,ℤ/8) | — | 134 | 1 | no | — |
| 286 | #535 | — | 134 | 1 | no | — |
| 287 | #535 | C2×D67 | 1 | 1 | yes | characteristic |
| 288 | #535 | C2×D67 | 1 | 1 | yes | characteristic |
| 289 | #482 | — | 2 | 1 | no | — |
| 290 | #482 | — | 2 | 1 | no | — |
| 291 | #469 | — | 2 | 1 | no | — |
| 292 | #466 | — | 2 | 1 | no | — |
| 293 | B(4,𝔽2) | — | 134 | 2 | no | — |
| 294 | B(4,𝔽2) | — | 134 | 2 | no | — |
| 295 | #454 | — | 134 | 2 | no | — |
| 296 | #453 | — | 134 | 2 | no | — |
| 297 | #447 | — | 2 | 1 | no | — |
| 298 | #447 | — | 2 | 1 | no | — |
| 299 | #421 | — | 134 | 1 | no | — |
| 300 | #413 | — | 67 | 1 | no | — |
| 301 | #413 | — | 67 | 1 | no | — |
| 302 | #413 | — | 134 | 1 | no | — |
| 303 | #410 | — | 67 | 1 | no | — |
| 304 | #410 | — | 134 | 1 | no | — |
| 305 | #408 | — | 134 | 1 | no | — |
| 306 | #408 | C2×D67 | 1 | 1 | yes | characteristic |
| 307 | #355 | — | 134 | 2 | no | — |
| 308 | AΣL(1,𝔽16) | — | 134 | 2 | no | — |
| 309 | 2−1+4 | — | 268 | 1 | no | — |
| 310 | 2−1+4 | — | 134 | 1 | no | — |
| 311 | H(5,𝔽2) | — | 268 | 1 | no | — |
| 312 | H(5,𝔽2) | — | 67 | 2 | no | — |
| 313 | H(5,𝔽2) | — | 134 | 1 | no | — |
| 314 | H(5,𝔽2) | — | 134 | 1 | no | — |
| 315 | C2×#41 | — | 268 | 2 | no | — |
| 316 | C2×#41 | — | 134 | 1 | no | — |
| 317 | C2×#41 | — | 134 | 1 | no | — |
| 318 | C2×#41 | — | 134 | 1 | no | — |
| 319 | C2×#41 | C22×D67 | 1 | 1 | yes | characteristic |
| 320 | C22×D4 | C22⋊D67 | 1 | 1 | yes | characteristic |
| 321 | C22×D4 | C22⋊D67 | 1 | 1 | yes | characteristic, complemented |
| 322 | AGL(1,ℤ/8) | — | 268 | 2 | no | — |
| 323 | AGL(1,ℤ/8) | — | 134 | 4 | no | — |
| 324 | C2×SD16 | — | 268 | 1 | no | — |
| 325 | C2×D8 | — | 2 | 1 | no | — |
| 326 | C2×D8 | — | 2 | 1 | no | — |
| 327 | C2×D8 | — | 268 | 1 | no | — |
| 328 | C2×M16 | — | 134 | 1 | no | — |
| 329 | C2×M16 | — | 134 | 1 | no | — |
| 330 | C2×M16 | C22⋊D67 | 1 | 1 | yes | characteristic, complemented |
| 331 | C22×C8 | C22⋊D67 | 1 | 1 | yes | characteristic, complemented |
| 332 | #127 | — | 2 | 1 | no | — |
| 333 | #127 | — | 2 | 1 | no | — |
| 334 | #127 | — | 268 | 1 | no | — |
| 335 | #124 | — | 2 | 1 | no | — |
| 336 | #124 | — | 2 | 1 | no | — |
| 337 | #124 | — | 268 | 1 | no | — |
| 338 | #121 | — | 2 | 1 | no | — |
| 339 | #121 | — | 2 | 1 | no | — |
| 340 | #121 | — | 2 | 1 | no | — |
| 341 | #121 | — | 2 | 1 | no | — |
| 342 | #121 | — | 268 | 2 | no | — |
| 343 | #120 | — | 2 | 1 | no | — |
| 344 | #120 | — | 2 | 1 | no | — |
| 345 | #120 | — | 2 | 1 | no | — |
| 346 | #120 | — | 2 | 1 | no | — |
| 347 | #120 | — | 134 | 4 | no | — |
| 348 | #117 | — | 134 | 1 | no | — |
| 349 | #117 | C22⋊D67 | 1 | 1 | yes | characteristic |
| 350 | #117 | C22⋊D67 | 1 | 1 | yes | characteristic, complemented |
| 351 | #107 | — | 2 | 1 | no | — |
| 352 | #106 | — | 2 | 1 | no | — |
| 353 | #104 | — | 134 | 4 | no | — |
| 354 | #102 | — | 2 | 1 | no | — |
| 355 | #102 | — | 2 | 1 | no | — |
| 356 | #102 | — | 2 | 1 | no | — |
| 357 | #102 | — | 2 | 1 | no | — |
| 358 | #101 | — | 268 | 1 | no | — |
| 359 | #101 | — | 67 | 2 | no | — |
| 360 | #101 | — | 134 | 1 | no | — |
| 361 | #100 | — | 268 | 1 | no | — |
| 362 | #100 | — | 134 | 1 | no | — |
| 363 | #100 | — | 134 | 1 | no | — |
| 364 | #99 | — | 67 | 2 | no | — |
| 365 | #99 | — | 134 | 4 | no | — |
| 366 | #99 | — | 134 | 1 | no | — |
| 367 | C22⋊C8 | — | 2 | 1 | no | — |
| 368 | C22⋊C8 | — | 2 | 1 | no | — |
| 369 | C22⋊C8 | — | 268 | 2 | no | — |
| 370 | C24 | — | 2 | 1 | no | — |
| 371 | C24 | — | 2 | 1 | no | — |
| 372 | #41 | — | 4 | 1 | no | — |
| 373 | #41 | — | 4 | 1 | no | — |
| 374 | #41 | — | 268 | 1 | no | — |
| 375 | #41 | — | 268 | 1 | no | — |
| 376 | #41 | — | 268 | 1 | no | — |
| 377 | #41 | — | 268 | 1 | no | — |
| 378 | #41 | — | 268 | 1 | no | — |
| 379 | #41 | — | 268 | 2 | no | — |
| 380 | #41 | — | 268 | 2 | no | — |
| 381 | #41 | — | 268 | 2 | no | — |
| 382 | #41 | — | 268 | 1 | no | — |
| 383 | #41 | — | 268 | 1 | no | — |
| 384 | #41 | — | 268 | 1 | no | — |
| 385 | #41 | — | 268 | 2 | no | — |
| 386 | #41 | — | 134 | 2 | no | — |
| 387 | #41 | — | 134 | 2 | no | — |
| 388 | C2×Q8 | — | 268 | 2 | no | — |
| 389 | C2×Q8 | — | 134 | 1 | no | — |
| 390 | C2×Q8 | — | 134 | 1 | no | — |
| 391 | C2×Q8 | — | 134 | 1 | no | — |
| 392 | C2×Q8 | D4×D67 | 1 | 1 | yes | characteristic |
| 393 | C2×D4 | — | 2 | 1 | no | — |
| 394 | C2×D4 | — | 2 | 1 | no | — |
| 395 | C2×D4 | — | 2 | 1 | no | — |
| 396 | C2×D4 | — | 2 | 1 | no | — |
| 397 | C2×D4 | — | 4 | 1 | no | — |
| 398 | C2×D4 | — | 4 | 1 | no | — |
| 399 | C2×D4 | — | 4 | 1 | no | — |
| 400 | C2×D4 | — | 4 | 1 | no | — |
| 401 | C2×D4 | — | 4 | 1 | no | — |
| 402 | C2×D4 | — | 4 | 1 | no | — |
| 403 | C2×D4 | — | 4 | 1 | no | — |
| 404 | C2×D4 | — | 4 | 1 | no | — |
| 405 | C2×D4 | — | 268 | 2 | no | — |
| 406 | C2×D4 | — | 268 | 2 | no | — |
| 407 | C2×D4 | — | 268 | 2 | no | — |
| 408 | C2×D4 | — | 268 | 1 | no | — |
| 409 | C2×D4 | — | 268 | 4 | no | — |
| 410 | C2×D4 | — | 134 | 1 | no | — |
| 411 | C2×D4 | — | 134 | 1 | no | — |
| 412 | C2×D4 | — | 134 | 1 | no | — |
| 413 | C2×D4 | — | 134 | 2 | no | — |
| 414 | C2×D4 | — | 134 | 2 | no | — |
| 415 | C2×D4 | D4×D67 | 1 | 1 | yes | characteristic |
| 416 | C2×D4 | D4×D67 | 1 | 1 | yes | characteristic |
| 417 | C2×D4 | #11761627 | 1 | 1 | yes | characteristic |
| 418 | C22×C4 | — | 268 | 1 | no | — |
| 419 | C22×C4 | — | 134 | 2 | no | — |
| 420 | C22×C4 | — | 134 | 2 | no | — |
| 421 | C22×C4 | C2×C22⋊D67 | 1 | 1 | yes | characteristic |
| 422 | C22×C4 | C2×C22⋊D67 | 1 | 1 | yes | characteristic |
| 423 | C22×C4 | C2×C22⋊D67 | 1 | 1 | yes | characteristic |
| 424 | SD16 | — | 268 | 4 | no | — |
| 425 | D8 | — | 8 | 1 | no | — |
| 426 | D8 | — | 8 | 1 | no | — |
| 427 | D8 | — | 268 | 4 | no | — |
| 428 | M16 | — | 4 | 1 | no | — |
| 429 | M16 | — | 268 | 1 | no | — |
| 430 | M16 | — | 268 | 1 | no | — |
| 431 | M16 | — | 268 | 1 | no | — |
| 432 | M16 | — | 134 | 2 | no | — |
| 433 | C2×C8 | — | 2 | 1 | no | — |
| 434 | C2×C8 | — | 2 | 1 | no | — |
| 435 | C2×C8 | — | 4 | 1 | no | — |
| 436 | C2×C8 | — | 268 | 1 | no | — |
| 437 | C2×C8 | — | 268 | 1 | no | — |
| 438 | C4⋊C4 | — | 2 | 1 | no | — |
| 439 | C4⋊C4 | — | 2 | 1 | no | — |
| 440 | C4⋊C4 | — | 268 | 1 | no | — |
| 441 | C22⋊C4 | — | 2 | 1 | no | — |
| 442 | C22⋊C4 | — | 2 | 1 | no | — |
| 443 | C22⋊C4 | — | 4 | 1 | no | — |
| 444 | C22⋊C4 | — | 4 | 1 | no | — |
| 445 | C22⋊C4 | — | 4 | 1 | no | — |
| 446 | C22⋊C4 | — | 4 | 1 | no | — |
| 447 | C22⋊C4 | — | 268 | 4 | no | — |
| 448 | C22⋊C4 | — | 134 | 2 | no | — |
| 449 | C42 | — | 2 | 1 | no | — |
| 450 | C42 | — | 2 | 1 | no | — |
| 451 | C42 | — | 268 | 1 | no | — |
| 452 | C23 | — | 4 | 2 | no | — |
| 453 | C23 | — | 4 | 1 | no | — |
| 454 | C23 | — | 4 | 1 | no | — |
| 455 | C23 | — | 8 | 1 | no | — |
| 456 | C23 | — | 268 | 1 | no | — |
| 457 | C23 | — | 16 | 1 | no | — |
| 458 | C23 | — | 16 | 1 | no | — |
| 459 | C23 | — | 134 | 2 | no | — |
| 460 | C23 | — | 134 | 2 | no | — |
| 461 | C23 | #14524011 | 1 | 1 | yes | characteristic |
| 462 | C23 | #14524014 | 1 | 1 | yes | characteristic |
| 463 | C23 | #14524015 | 1 | 1 | yes | characteristic |
| 464 | Q8 | — | 4 | 1 | no | — |
| 465 | Q8 | — | 268 | 1 | no | — |
| 466 | Q8 | — | 268 | 1 | no | — |
| 467 | Q8 | — | 268 | 1 | no | — |
| 468 | Q8 | — | 134 | 2 | no | — |
| 469 | D4 | — | 4 | 1 | no | — |
| 470 | D4 | — | 4 | 1 | no | — |
| 471 | D4 | — | 4 | 1 | no | — |
| 472 | D4 | — | 4 | 2 | no | — |
| 473 | D4 | — | 4 | 1 | no | — |
| 474 | D4 | — | 4 | 1 | no | — |
| 475 | D4 | — | 4 | 1 | no | — |
| 476 | D4 | — | 4 | 1 | no | — |
| 477 | D4 | — | 8 | 1 | no | — |
| 478 | D4 | — | 268 | 1 | no | — |
| 479 | D4 | — | 268 | 1 | no | — |
| 480 | D4 | — | 268 | 2 | no | — |
| 481 | D4 | — | 268 | 2 | no | — |
| 482 | D4 | — | 268 | 2 | no | — |
| 483 | D4 | — | 268 | 2 | no | — |
| 484 | D4 | — | 268 | 1 | no | — |
| 485 | D4 | — | 16 | 1 | no | — |
| 486 | D4 | — | 16 | 1 | no | — |
| 487 | D4 | — | 16 | 1 | no | — |
| 488 | D4 | — | 16 | 1 | no | — |
| 489 | D4 | — | 1072 | 4 | no | — |
| 490 | D4 | — | 134 | 2 | no | — |
| 491 | C2×C4 | — | 2 | 1 | no | — |
| 492 | C2×C4 | — | 2 | 1 | no | — |
| 493 | C2×C4 | — | 2 | 1 | no | — |
| 494 | C2×C4 | — | 2 | 1 | no | — |
| 495 | C2×C4 | — | 2 | 1 | no | — |
| 496 | C2×C4 | — | 2 | 1 | no | — |
| 497 | C2×C4 | — | 4 | 1 | no | — |
| 498 | C2×C4 | — | 4 | 1 | no | — |
| 499 | C2×C4 | — | 268 | 2 | no | — |
| 500 | C2×C4 | — | 268 | 2 | no | — |
| 501 | C2×C4 | — | 268 | 2 | no | — |
| 502 | C2×C4 | — | 268 | 1 | no | — |
| 503 | C2×C4 | — | 268 | 2 | no | — |
| 504 | C2×C4 | — | 268 | 2 | no | — |
| 505 | C2×C4 | — | 134 | 2 | no | — |
| 506 | C2×C4 | — | 134 | 2 | no | — |
| 507 | C2×C4 | #14524011 | 1 | 1 | yes | characteristic |
| 508 | C2×C4 | #14524012 | 1 | 1 | yes | characteristic |
| 509 | C2×C4 | #14524015 | 1 | 1 | yes | characteristic |
| 510 | C2×C4 | #14524039 | 1 | 1 | yes | characteristic |
| 511 | C8 | — | 4 | 1 | no | — |
| 512 | C8 | — | 4 | 1 | no | — |
| 513 | C8 | — | 268 | 2 | no | — |
| 514 | C8 | — | 536 | 1 | no | — |
| 515 | C22 | — | 2 | 1 | no | — |
| 516 | C22 | — | 2 | 1 | no | — |
| 517 | C22 | — | 2 | 1 | no | — |
| 518 | C22 | — | 4 | 1 | no | — |
| 519 | C22 | — | 4 | 1 | no | — |
| 520 | C22 | — | 4 | 1 | no | — |
| 521 | C22 | — | 8 | 1 | no | — |
| 522 | C22 | — | 8 | 1 | no | — |
| 523 | C22 | — | 8 | 1 | no | — |
| 524 | C22 | — | 8 | 1 | no | — |
| 525 | C22 | — | 8 | 4 | no | — |
| 526 | C22 | — | 8 | 1 | no | — |
| 527 | C22 | — | 8 | 1 | no | — |
| 528 | C22 | — | 268 | 2 | no | — |
| 529 | C22 | — | 16 | 2 | no | — |
| 530 | C22 | — | 536 | 2 | no | — |
| 531 | C22 | — | 536 | 2 | no | — |
| 532 | C22 | — | 1072 | 1 | no | — |
| 533 | C22 | #16863304 | 1 | 1 | yes | characteristic |
| 534 | C4 | — | 2 | 1 | no | — |
| 535 | C4 | — | 2 | 1 | no | — |
| 536 | C4 | — | 2 | 1 | no | — |
| 537 | C4 | — | 8 | 1 | no | — |
| 538 | C4 | — | 8 | 1 | no | — |
| 539 | C4 | — | 268 | 2 | no | — |
| 540 | C4 | — | 536 | 2 | no | — |
| 541 | C4 | #16863583 | 1 | 1 | yes | characteristic |
| 542 | C4 | #16863583 | 1 | 1 | yes | characteristic |
| 543 | C2 | — | 2 | 1 | no | — |
| 544 | C2 | — | 4 | 1 | no | — |
| 545 | C2 | — | 4 | 1 | no | — |
| 546 | C2 | — | 4 | 1 | no | — |
| 547 | C2 | — | 16 | 1 | no | — |
| 548 | C2 | — | 16 | 1 | no | — |
| 549 | C2 | — | 536 | 2 | no | — |
| 550 | C2 | #22561333 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22569610 | C2 | semidirect |
| 2. #22569580 | C2 | semidirect |
| 3. #22561901 | C2 | semidirect |
| 4. #22561859 | C2 | semidirect |
| 5. #22560159 | C2 | semidirect |
| 6. #22558338 | C2 | semidirect |
| 7. C67×#3199 | C2 | semidirect |
| 56. #14523962 | D4 | semidirect |
| 67. C22×D4×C67 | D4 | semidirect |
| 70. C2×M16×C67 | D4 | semidirect |
| 71. C22×C8×C67 | D4 | semidirect |
| 85. #117×C67 | D4 | semidirect |
| 276. #3199 | D67 | semidirect |
| 283. C67 | #13353 | semidirect |
| 321. C22×D4 | C22⋊D67 | semidirect |
| 330. C2×M16 | C22⋊D67 | semidirect |
| 331. C22×C8 | C22⋊D67 | semidirect |
| 350. #117 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569610 | 2 |
| #22569580 | 2 |
| #22561901 | 2 |
| #22561859 | 2 |
| #22560159 | 2 |
| #22558338 | 2 |
| C67×#3199 | 2 |
| #13353 | 67 |