Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1240 conjugacy classes of subgroups.
The subgroup lattice has 582 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22574122 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22570661 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22569690 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22568567 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22561253 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #22561036 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #22560584 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | C4×#14523969 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C67×#1997 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#14524071 | C22 | 1 | 4 | yes | — |
| 11 | C2×#14524071 | C22 | 1 | 2 | yes | — |
| 12 | #16864120 | — | 2 | 1 | no | — |
| 13 | #16864112 | — | 2 | 1 | no | — |
| 14 | #16864107 | — | 2 | 1 | no | — |
| 15 | #16864094 | — | 2 | 2 | no | — |
| 16 | #16864057 | — | 2 | 2 | no | — |
| 17 | #16864049 | — | 2 | 1 | no | — |
| 18 | #16864020 | — | 2 | 2 | no | — |
| 19 | #16863977 | C22 | 1 | 2 | yes | — |
| 20 | #16863951 | — | 2 | 1 | no | — |
| 21 | #16863947 | — | 2 | 1 | no | — |
| 22 | #16863946 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#14524040 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#14524032 | — | 2 | 2 | no | — |
| 25 | #16863877 | C22 | 1 | 2 | yes | — |
| 26 | C4×#11761628 | C22 | 1 | 1 | yes | characteristic |
| 27 | #16863785 | — | 2 | 2 | no | — |
| 28 | #16863773 | — | 2 | 1 | no | — |
| 29 | #16863769 | — | 2 | 1 | no | — |
| 30 | #16863597 | — | 2 | 1 | no | — |
| 31 | #16863597 | — | 2 | 1 | no | — |
| 32 | #16863592 | — | 2 | 1 | no | — |
| 33 | #16863592 | — | 2 | 1 | no | — |
| 34 | C2×#14523969 | C22 | 1 | 2 | yes | — |
| 35 | C2×#14523969 | C22 | 1 | 4 | yes | — |
| 36 | #16863402 | C22 | 1 | 2 | yes | — |
| 37 | #16863297 | — | 2 | 2 | no | — |
| 38 | #16863297 | C22 | 1 | 4 | yes | — |
| 39 | C42×Dic67 | C22 | 1 | 1 | yes | characteristic |
| 40 | #16863157 | C22 | 1 | 2 | yes | — |
| 41 | C2×C4⋊Q8×C67 | C22 | 1 | 1 | yes | characteristic |
| 42 | #423×C67 | C22 | 1 | 1 | yes | characteristic |
| 43 | C4×M16×C67 | C22 | 1 | 1 | yes | characteristic |
| 44 | #343×C67 | C22 | 1 | 4 | yes | — |
| 45 | C2×#11761629 | — | 2 | 2 | no | — |
| 46 | C2×#11761628 | C23 | 1 | 1 | yes | characteristic |
| 47 | C2×#11761628 | C23 | 1 | 2 | yes | — |
| 48 | C22×D268 | — | 2 | 1 | no | — |
| 49 | C22×D268 | — | 2 | 1 | no | — |
| 50 | C22×D268 | C23 | 1 | 2 | yes | — |
| 51 | #14524071 | — | 2 | 8 | no | — |
| 52 | #14524071 | — | 4 | 4 | no | — |
| 53 | #14524071 | — | 4 | 4 | no | — |
| 54 | C2×#11761617 | — | 2 | 4 | no | — |
| 55 | C2×#11761617 | — | 2 | 2 | no | — |
| 56 | C2×D536 | — | 2 | 4 | no | — |
| 57 | C2×D536 | — | 2 | 2 | no | — |
| 58 | #14524043 | D4 | 1 | 1 | yes | characteristic |
| 59 | #14524040 | — | 2 | 1 | no | — |
| 60 | #14524040 | — | 2 | 1 | no | — |
| 61 | #14524040 | — | 2 | 1 | no | — |
| 62 | #14524040 | — | 2 | 1 | no | — |
| 63 | #14524040 | D4 | 1 | 1 | yes | characteristic |
| 64 | #14524038 | — | 2 | 4 | no | — |
| 65 | #14524034 | — | 2 | 2 | no | — |
| 66 | #14524032 | — | 2 | 4 | no | — |
| 67 | #14524032 | — | 2 | 2 | no | — |
| 68 | #14524032 | — | 4 | 8 | no | — |
| 69 | #14524031 | D4 | 1 | 2 | yes | — |
| 70 | #14524028 | — | 2 | 4 | no | — |
| 71 | #14524023 | — | 2 | 2 | no | — |
| 72 | #14524023 | — | 2 | 2 | no | — |
| 73 | #14524019 | — | 2 | 4 | no | — |
| 74 | #14524019 | — | 2 | 2 | no | — |
| 75 | #14524018 | — | 2 | 2 | no | — |
| 76 | #14524018 | — | 2 | 2 | no | — |
| 77 | #14524018 | — | 2 | 2 | no | — |
| 78 | #14524017 | — | 2 | 1 | no | — |
| 79 | #14524017 | — | 2 | 4 | no | — |
| 80 | #14524017 | — | 2 | 1 | no | — |
| 81 | Q8×Dic67 | — | 2 | 2 | no | — |
| 82 | C4×Dic134 | D4 | 1 | 1 | yes | characteristic |
| 83 | C4×Dic134 | D4 | 1 | 1 | yes | characteristic |
| 84 | #14524008 | — | 2 | 2 | no | — |
| 85 | C4×D268 | — | 2 | 1 | no | — |
| 86 | C4×D268 | — | 2 | 1 | no | — |
| 87 | C4×D268 | D4 | 1 | 1 | yes | characteristic |
| 88 | C4×D268 | D4 | 1 | 1 | yes | characteristic |
| 89 | #14524005 | — | 2 | 2 | no | — |
| 90 | #14524005 | — | 2 | 2 | no | — |
| 91 | C4×C22⋊D67 | — | 2 | 1 | no | — |
| 92 | C4×C22⋊D67 | — | 2 | 4 | no | — |
| 93 | C4×C22⋊D67 | — | 2 | 1 | no | — |
| 94 | #14524002 | C23 | 1 | 1 | yes | characteristic |
| 95 | #14524001 | — | 2 | 2 | no | — |
| 96 | #14524001 | — | 2 | 2 | no | — |
| 97 | #14524000 | — | 2 | 1 | no | — |
| 98 | C4⋊C4×D67 | — | 2 | 2 | no | — |
| 99 | C2×(C2×D67)⋊C4 | — | 2 | 8 | no | — |
| 100 | C2×C4×Dic67 | — | 2 | 1 | no | — |
| 101 | C2×C4×Dic67 | — | 2 | 1 | no | — |
| 102 | C2×C4×Dic67 | C23 | 1 | 2 | yes | — |
| 103 | C42×D67 | — | 2 | 1 | no | — |
| 104 | #14523969 | — | 2 | 4 | no | — |
| 105 | #14523969 | — | 4 | 4 | no | — |
| 106 | #14523965 | — | 2 | 2 | no | — |
| 107 | #14523965 | — | 2 | 2 | no | — |
| 108 | C22×Q8×C67 | D4 | 1 | 2 | yes | — |
| 109 | C2×M16×C67 | C23 | 1 | 2 | yes | — |
| 110 | C2×M16×C67 | C23 | 1 | 2 | yes | — |
| 111 | C4⋊Q8×C67 | — | 2 | 1 | no | — |
| 112 | C4⋊Q8×C67 | — | 2 | 1 | no | — |
| 113 | C4⋊Q8×C67 | — | 2 | 1 | no | — |
| 114 | C4⋊Q8×C67 | — | 2 | 1 | no | — |
| 115 | C2×C4⋊C4×C67 | D4 | 1 | 2 | yes | — |
| 116 | C2×C4⋊C4×C67 | C23 | 1 | 2 | yes | — |
| 117 | C2×C42×C67 | C23 | 1 | 1 | yes | characteristic |
| 118 | C4⋊C8×C67 | — | 2 | 1 | no | — |
| 119 | C4⋊C8×C67 | — | 2 | 1 | no | — |
| 120 | #97×C67 | — | 2 | 1 | no | — |
| 121 | C4×C8×C67 | — | 2 | 1 | no | — |
| 122 | C23×D67 | — | 2 | 2 | no | — |
| 123 | #11761629 | — | 8 | 4 | no | — |
| 124 | #11761628 | — | 2 | 2 | no | — |
| 125 | #11761628 | — | 2 | 4 | no | — |
| 126 | #11761628 | — | 2 | 4 | no | — |
| 127 | #11761628 | — | 2 | 2 | no | — |
| 128 | C2×Dic134 | C2×D4 | 1 | 2 | yes | — |
| 129 | C2×Dic134 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C2×D268 | — | 2 | 1 | no | — |
| 131 | C2×D268 | — | 2 | 1 | no | — |
| 132 | C2×D268 | — | 2 | 2 | no | — |
| 133 | C2×D268 | — | 2 | 2 | no | — |
| 134 | C2×D268 | — | 2 | 4 | no | — |
| 135 | C2×D268 | — | 2 | 4 | no | — |
| 136 | C2×D268 | — | 2 | 4 | no | — |
| 137 | C2×D268 | — | 4 | 4 | no | — |
| 138 | C2×D268 | — | 4 | 4 | no | — |
| 139 | C2×D268 | — | 4 | 1 | no | — |
| 140 | C2×D268 | — | 4 | 1 | no | — |
| 141 | C2×D268 | — | 4 | 1 | no | — |
| 142 | C2×D268 | — | 4 | 1 | no | — |
| 143 | C2×D268 | C2×D4 | 1 | 2 | yes | — |
| 144 | C2×D268 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | C2×C22⋊D67 | — | 2 | 1 | no | — |
| 146 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 147 | C22×Dic67 | — | 2 | 2 | no | — |
| 148 | C2×C4×D67 | — | 2 | 1 | no | — |
| 149 | C2×C4×D67 | — | 2 | 1 | no | — |
| 150 | C2×C4×D67 | — | 2 | 1 | no | — |
| 151 | C2×C4×D67 | — | 2 | 2 | no | — |
| 152 | C2×C4×D67 | — | 2 | 4 | no | — |
| 153 | #11761617 | — | 4 | 8 | no | — |
| 154 | #11761617 | — | 4 | 4 | no | — |
| 155 | D536 | — | 4 | 8 | no | — |
| 156 | D536 | — | 4 | 4 | no | — |
| 157 | C4⋊Dic67 | — | 2 | 4 | no | — |
| 158 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 159 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 160 | C4⋊Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | C4⋊Dic67 | C2×D4 | 1 | 1 | yes | characteristic |
| 162 | Dic67⋊C4 | — | 2 | 4 | no | — |
| 163 | Dic67⋊C4 | — | 2 | 1 | no | — |
| 164 | Dic67⋊C4 | — | 2 | 1 | no | — |
| 165 | C22⋊Dic67 | — | 2 | 1 | no | — |
| 166 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 167 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 168 | (C2×D67)⋊C4 | — | 2 | 4 | no | — |
| 169 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 170 | (C2×D67)⋊C4 | — | 2 | 1 | no | — |
| 171 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 172 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 173 | (C2×D67)⋊C4 | — | 4 | 16 | no | — |
| 174 | C4×Dic67 | — | 2 | 4 | no | — |
| 175 | C4×Dic67 | — | 2 | 4 | no | — |
| 176 | C4×Dic67 | — | 2 | 1 | no | — |
| 177 | C4×Dic67 | — | 2 | 1 | no | — |
| 178 | C4×Dic67 | — | 2 | 1 | no | — |
| 179 | C4×Dic67 | — | 2 | 2 | no | — |
| 180 | C4×Dic67 | — | 2 | 2 | no | — |
| 181 | C4×Dic67 | — | 4 | 2 | no | — |
| 182 | C2×Q8×C67 | — | 2 | 2 | no | — |
| 183 | C2×Q8×C67 | — | 2 | 2 | no | — |
| 184 | C2×Q8×C67 | — | 4 | 4 | no | — |
| 185 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 186 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 187 | C22×C4×C67 | C2×D4 | 1 | 4 | yes | — |
| 188 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 189 | M16×C67 | — | 2 | 2 | no | — |
| 190 | M16×C67 | — | 2 | 4 | no | — |
| 191 | M16×C67 | #41 | 1 | 4 | yes | complemented |
| 192 | C2×C8×C67 | — | 2 | 2 | no | — |
| 193 | C2×C8×C67 | — | 2 | 2 | no | — |
| 194 | C4⋊C4×C67 | — | 2 | 2 | no | — |
| 195 | C4⋊C4×C67 | — | 2 | 2 | no | — |
| 196 | C4⋊C4×C67 | — | 2 | 2 | no | — |
| 197 | C4⋊C4×C67 | — | 2 | 2 | no | — |
| 198 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 199 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 200 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 201 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 202 | C23×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 203 | C22×D67 | — | 2 | 1 | no | — |
| 204 | C22×D67 | — | 2 | 2 | no | — |
| 205 | C22×D67 | — | 4 | 4 | no | — |
| 206 | C22×D67 | — | 4 | 4 | no | — |
| 207 | C22×D67 | — | 4 | 2 | no | — |
| 208 | C22×D67 | — | 4 | 4 | no | — |
| 209 | Q8×C67 | — | 4 | 4 | no | — |
| 210 | Q8×C67 | — | 8 | 2 | no | — |
| 211 | C2×C4×C67 | — | 2 | 2 | no | — |
| 212 | C2×C4×C67 | — | 2 | 2 | no | — |
| 213 | C2×C4×C67 | — | 2 | 4 | no | — |
| 214 | C2×C4×C67 | — | 4 | 4 | no | — |
| 215 | C2×C4×C67 | #120 | 1 | 1 | yes | characteristic |
| 216 | C2×C4×C67 | #120 | 1 | 1 | yes | characteristic |
| 217 | C2×C4×C67 | #120 | 1 | 1 | yes | characteristic |
| 218 | C2×C4×C67 | #120 | 1 | 1 | yes | characteristic |
| 219 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 220 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 221 | C2×C4×C67 | C2×#41 | 1 | 2 | yes | — |
| 222 | C2×C4×C67 | H(5,𝔽2) | 1 | 2 | yes | — |
| 223 | C22⋊D67 | — | 4 | 2 | no | — |
| 224 | C22⋊D67 | — | 4 | 4 | no | — |
| 225 | C2×Dic67 | — | 2 | 4 | no | — |
| 226 | C2×Dic67 | — | 2 | 1 | no | — |
| 227 | C2×Dic67 | — | 2 | 2 | no | — |
| 228 | C2×Dic67 | — | 2 | 1 | no | — |
| 229 | C2×Dic67 | — | 2 | 1 | no | — |
| 230 | C2×Dic67 | — | 4 | 2 | no | — |
| 231 | C2×Dic67 | — | 4 | 2 | no | — |
| 232 | D268 | — | 2 | 1 | no | — |
| 233 | D268 | — | 2 | 1 | no | — |
| 234 | D268 | — | 2 | 4 | no | — |
| 235 | D268 | — | 4 | 2 | no | — |
| 236 | D268 | — | 4 | 2 | no | — |
| 237 | D268 | — | 4 | 4 | no | — |
| 238 | D268 | — | 4 | 2 | no | — |
| 239 | D268 | — | 4 | 2 | no | — |
| 240 | D268 | — | 8 | 2 | no | — |
| 241 | D268 | — | 8 | 2 | no | — |
| 242 | D268 | — | 8 | 4 | no | — |
| 243 | D268 | — | 8 | 2 | no | — |
| 244 | D268 | — | 8 | 2 | no | — |
| 245 | C4×D67 | — | 4 | 2 | no | — |
| 246 | C4×D67 | — | 4 | 2 | no | — |
| 247 | C4×D67 | — | 4 | 2 | no | — |
| 248 | C4×D67 | — | 4 | 2 | no | — |
| 249 | C4×D67 | — | 4 | 2 | no | — |
| 250 | C4×D67 | — | 8 | 4 | no | — |
| 251 | Dic134 | — | 2 | 1 | no | — |
| 252 | Dic134 | — | 2 | 1 | no | — |
| 253 | Dic134 | — | 2 | 4 | no | — |
| 254 | C8×C67 | — | 2 | 4 | no | — |
| 255 | C8×C67 | — | 4 | 2 | no | — |
| 256 | C22×C67 | — | 2 | 1 | no | — |
| 257 | C22×C67 | — | 2 | 1 | no | — |
| 258 | C22×C67 | C2×#120 | 1 | 1 | yes | characteristic |
| 259 | C22×C67 | #550 | 1 | 2 | yes | — |
| 260 | C2×D67 | — | 4 | 2 | no | — |
| 261 | C2×D67 | — | 4 | 1 | no | — |
| 262 | C2×D67 | — | 4 | 1 | no | — |
| 263 | C2×D67 | — | 4 | 2 | no | — |
| 264 | C2×D67 | — | 4 | 1 | no | — |
| 265 | C2×D67 | — | 4 | 2 | no | — |
| 266 | C2×D67 | — | 8 | 8 | no | — |
| 267 | C2×D67 | — | 8 | 2 | no | — |
| 268 | C2×D67 | — | 8 | 2 | no | — |
| 269 | C2×D67 | — | 8 | 2 | no | — |
| 270 | C4×C67 | — | 2 | 1 | no | — |
| 271 | C4×C67 | — | 2 | 1 | no | — |
| 272 | C4×C67 | — | 4 | 4 | no | — |
| 273 | C4×C67 | #453 | 1 | 2 | yes | — |
| 274 | C4×C67 | #454 | 1 | 2 | yes | — |
| 275 | C4×C67 | #532 | 1 | 1 | yes | characteristic |
| 276 | C4×C67 | #535 | 1 | 1 | yes | characteristic |
| 277 | C4×C67 | #546 | 1 | 2 | yes | — |
| 278 | Dic67 | — | 4 | 4 | no | — |
| 279 | Dic67 | — | 4 | 1 | no | — |
| 280 | Dic67 | — | 4 | 2 | no | — |
| 281 | Dic67 | — | 4 | 1 | no | — |
| 282 | Dic67 | — | 4 | 1 | no | — |
| 283 | #25616 | — | 67 | 1 | no | maximal, Sylow |
| 284 | C2×C67 | — | 2 | 2 | no | — |
| 285 | C2×C67 | #2431 | 1 | 1 | yes | characteristic |
| 286 | C2×C67 | C2×#453 | 1 | 1 | yes | characteristic |
| 287 | C2×C67 | C2×#454 | 1 | 1 | yes | characteristic |
| 288 | D67 | — | 8 | 1 | no | — |
| 289 | D67 | — | 8 | 2 | no | — |
| 290 | D67 | — | 16 | 2 | no | — |
| 291 | #3511 | — | 67 | 1 | no | — |
| 292 | #3151 | — | 67 | 1 | no | — |
| 293 | #3038 | — | 67 | 1 | no | — |
| 294 | #2858 | — | 67 | 1 | no | — |
| 295 | #2006 | — | 67 | 4 | no | — |
| 296 | #1997 | D67 | 1 | 1 | yes | characteristic, complemented |
| 297 | #1962 | — | 67 | 1 | no | — |
| 298 | #1883 | — | 67 | 4 | no | — |
| 299 | C4×#104 | — | 67 | 1 | no | — |
| 300 | C67 | #25616 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 301 | C2×AGL(1,ℤ/8) | — | 67 | 2 | no | — |
| 302 | C2×AGL(1,ℤ/8) | — | 67 | 4 | no | — |
| 303 | #556 | — | 134 | 1 | no | — |
| 304 | #555 | — | 134 | 1 | no | — |
| 305 | #554 | — | 134 | 1 | no | — |
| 306 | #553 | — | 134 | 2 | no | — |
| 307 | #548 | — | 134 | 2 | no | — |
| 308 | #547 | — | 134 | 1 | no | — |
| 309 | #542 | — | 134 | 2 | no | — |
| 310 | #537 | — | 67 | 2 | no | — |
| 311 | #533 | — | 134 | 1 | no | — |
| 312 | #532 | — | 67 | 1 | no | — |
| 313 | #532 | — | 134 | 1 | no | — |
| 314 | C2×C4⋊Q8 | C2×D67 | 1 | 1 | yes | characteristic |
| 315 | C2×#127 | — | 67 | 1 | no | — |
| 316 | C2×#124 | — | 134 | 2 | no | — |
| 317 | #520 | — | 67 | 2 | no | — |
| 318 | C4×#41 | — | 67 | 1 | no | — |
| 319 | #496 | — | 134 | 2 | no | — |
| 320 | #493 | — | 134 | 1 | no | — |
| 321 | #492 | — | 134 | 1 | no | — |
| 322 | #460 | — | 134 | 1 | no | — |
| 323 | #460 | — | 134 | 1 | no | — |
| 324 | #459 | — | 134 | 1 | no | — |
| 325 | #459 | — | 134 | 1 | no | — |
| 326 | #423 | C2×D67 | 1 | 1 | yes | characteristic |
| 327 | C2×#104 | — | 67 | 4 | no | — |
| 328 | C2×#104 | — | 67 | 2 | no | — |
| 329 | #418 | — | 67 | 2 | no | — |
| 330 | C4×M16 | C2×D67 | 1 | 1 | yes | characteristic |
| 331 | #390 | — | 67 | 4 | no | — |
| 332 | #390 | — | 134 | 2 | no | — |
| 333 | C43 | — | 67 | 1 | no | — |
| 334 | #343 | C2×D67 | 1 | 4 | yes | — |
| 335 | #339 | — | 67 | 2 | no | — |
| 336 | C2×#41 | — | 67 | 1 | no | — |
| 337 | C2×#41 | — | 67 | 2 | no | — |
| 338 | C2×#41 | — | 134 | 2 | no | — |
| 339 | C22×Q8 | D268 | 1 | 2 | yes | — |
| 340 | C22×D4 | — | 67 | 2 | no | — |
| 341 | C22×D4 | — | 134 | 1 | no | — |
| 342 | C22×D4 | — | 134 | 1 | no | — |
| 343 | AGL(1,ℤ/8) | — | 268 | 4 | no | — |
| 344 | AGL(1,ℤ/8) | — | 268 | 4 | no | — |
| 345 | AGL(1,ℤ/8) | — | 134 | 8 | no | — |
| 346 | C2×SD16 | — | 134 | 2 | no | — |
| 347 | C2×SD16 | — | 134 | 4 | no | — |
| 348 | C2×D8 | — | 134 | 2 | no | — |
| 349 | C2×D8 | — | 134 | 4 | no | — |
| 350 | C2×M16 | C22×D67 | 1 | 2 | yes | — |
| 351 | C2×M16 | C22×D67 | 1 | 2 | yes | — |
| 352 | C4⋊Q8 | — | 2 | 1 | no | — |
| 353 | C4⋊Q8 | — | 2 | 1 | no | — |
| 354 | C4⋊Q8 | — | 2 | 1 | no | — |
| 355 | C4⋊Q8 | — | 2 | 1 | no | — |
| 356 | C4⋊Q8 | — | 67 | 1 | no | — |
| 357 | #127 | — | 67 | 1 | no | — |
| 358 | #127 | — | 134 | 1 | no | — |
| 359 | #127 | — | 134 | 1 | no | — |
| 360 | #127 | — | 134 | 1 | no | — |
| 361 | #127 | — | 134 | 1 | no | — |
| 362 | #126 | — | 134 | 4 | no | — |
| 363 | #125 | — | 134 | 2 | no | — |
| 364 | #124 | — | 268 | 8 | no | — |
| 365 | #124 | — | 67 | 2 | no | — |
| 366 | #124 | — | 134 | 2 | no | — |
| 367 | #124 | — | 134 | 4 | no | — |
| 368 | #123 | — | 134 | 4 | no | — |
| 369 | C22⋊Q8 | — | 134 | 2 | no | — |
| 370 | C22⋊Q8 | — | 134 | 2 | no | — |
| 371 | C22⋊Q8 | — | 134 | 2 | no | — |
| 372 | C22⋊Q8 | — | 134 | 4 | no | — |
| 373 | #121 | — | 134 | 2 | no | — |
| 374 | #121 | — | 134 | 2 | no | — |
| 375 | #121 | — | 134 | 2 | no | — |
| 376 | #121 | — | 134 | 1 | no | — |
| 377 | #121 | — | 134 | 1 | no | — |
| 378 | #121 | — | 134 | 4 | no | — |
| 379 | C4×Q8 | — | 67 | 1 | no | — |
| 380 | C4×Q8 | — | 67 | 1 | no | — |
| 381 | C4×Q8 | — | 134 | 2 | no | — |
| 382 | C4×Q8 | — | 134 | 2 | no | — |
| 383 | C4×D4 | — | 67 | 1 | no | — |
| 384 | C4×D4 | — | 67 | 1 | no | — |
| 385 | C4×D4 | — | 134 | 2 | no | — |
| 386 | C4×D4 | — | 134 | 2 | no | — |
| 387 | C4×D4 | — | 134 | 1 | no | — |
| 388 | C4×D4 | — | 134 | 1 | no | — |
| 389 | C4×D4 | — | 134 | 4 | no | — |
| 390 | C4×D4 | — | 134 | 1 | no | — |
| 391 | C4×D4 | — | 134 | 1 | no | — |
| 392 | #117 | — | 67 | 1 | no | — |
| 393 | #117 | — | 134 | 2 | no | — |
| 394 | #117 | — | 134 | 2 | no | — |
| 395 | #117 | — | 134 | 1 | no | — |
| 396 | C2×C4⋊C4 | — | 134 | 2 | no | — |
| 397 | C2×C4⋊C4 | D268 | 1 | 2 | yes | — |
| 398 | C2×C4⋊C4 | C22×D67 | 1 | 2 | yes | — |
| 399 | C2×C22⋊C4 | — | 134 | 8 | no | — |
| 400 | C2×C42 | — | 67 | 2 | no | — |
| 401 | C2×C42 | — | 134 | 1 | no | — |
| 402 | C2×C42 | — | 134 | 1 | no | — |
| 403 | C2×C42 | — | 134 | 1 | no | — |
| 404 | C2×C42 | C22×D67 | 1 | 1 | yes | characteristic |
| 405 | C4⋊C8 | — | 2 | 1 | no | — |
| 406 | C4⋊C8 | — | 2 | 1 | no | — |
| 407 | #104 | — | 268 | 4 | no | — |
| 408 | #104 | — | 134 | 4 | no | — |
| 409 | #102 | — | 134 | 2 | no | — |
| 410 | #102 | — | 134 | 2 | no | — |
| 411 | #97 | — | 2 | 1 | no | — |
| 412 | C4×C8 | — | 2 | 1 | no | — |
| 413 | C24 | — | 134 | 2 | no | — |
| 414 | #41 | — | 536 | 4 | no | — |
| 415 | #41 | — | 134 | 2 | no | — |
| 416 | #41 | — | 134 | 4 | no | — |
| 417 | #41 | — | 134 | 4 | no | — |
| 418 | #41 | — | 134 | 2 | no | — |
| 419 | C2×Q8 | — | 2 | 2 | no | — |
| 420 | C2×Q8 | — | 2 | 2 | no | — |
| 421 | C2×Q8 | — | 4 | 4 | no | — |
| 422 | C2×Q8 | — | 67 | 1 | no | — |
| 423 | C2×Q8 | — | 67 | 2 | no | — |
| 424 | C2×D4 | — | 268 | 4 | no | — |
| 425 | C2×D4 | — | 268 | 4 | no | — |
| 426 | C2×D4 | — | 268 | 1 | no | — |
| 427 | C2×D4 | — | 268 | 1 | no | — |
| 428 | C2×D4 | — | 268 | 1 | no | — |
| 429 | C2×D4 | — | 268 | 1 | no | — |
| 430 | C2×D4 | — | 67 | 1 | no | — |
| 431 | C2×D4 | — | 67 | 2 | no | — |
| 432 | C2×D4 | — | 134 | 4 | no | — |
| 433 | C2×D4 | — | 134 | 1 | no | — |
| 434 | C2×D4 | — | 134 | 2 | no | — |
| 435 | C2×D4 | — | 134 | 1 | no | — |
| 436 | C2×D4 | — | 134 | 1 | no | — |
| 437 | C2×D4 | — | 134 | 2 | no | — |
| 438 | C2×D4 | — | 134 | 2 | no | — |
| 439 | C2×D4 | — | 134 | 4 | no | — |
| 440 | C2×D4 | — | 134 | 4 | no | — |
| 441 | C22×C4 | — | 134 | 4 | no | — |
| 442 | C22×C4 | — | 134 | 2 | no | — |
| 443 | C22×C4 | — | 134 | 1 | no | — |
| 444 | C22×C4 | — | 134 | 1 | no | — |
| 445 | C22×C4 | — | 134 | 1 | no | — |
| 446 | C22×C4 | — | 134 | 2 | no | — |
| 447 | C22×C4 | C2×D268 | 1 | 1 | yes | characteristic |
| 448 | C22×C4 | C2×D268 | 1 | 1 | yes | characteristic |
| 449 | C22×C4 | C2×D268 | 1 | 4 | yes | — |
| 450 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 451 | SD16 | — | 268 | 8 | no | — |
| 452 | SD16 | — | 268 | 4 | no | — |
| 453 | D8 | — | 268 | 8 | no | — |
| 454 | D8 | — | 268 | 4 | no | — |
| 455 | M16 | — | 2 | 2 | no | — |
| 456 | M16 | — | 2 | 4 | no | — |
| 457 | M16 | #11761629 | 1 | 4 | yes | complemented |
| 458 | C2×C8 | — | 2 | 2 | no | — |
| 459 | C2×C8 | — | 2 | 2 | no | — |
| 460 | C4⋊C4 | — | 2 | 2 | no | — |
| 461 | C4⋊C4 | — | 2 | 2 | no | — |
| 462 | C4⋊C4 | — | 2 | 2 | no | — |
| 463 | C4⋊C4 | — | 2 | 2 | no | — |
| 464 | C4⋊C4 | — | 67 | 1 | no | — |
| 465 | C4⋊C4 | — | 67 | 1 | no | — |
| 466 | C4⋊C4 | — | 134 | 4 | no | — |
| 467 | C4⋊C4 | — | 134 | 4 | no | — |
| 468 | C4⋊C4 | — | 134 | 1 | no | — |
| 469 | C4⋊C4 | — | 134 | 1 | no | — |
| 470 | C4⋊C4 | — | 134 | 1 | no | — |
| 471 | C4⋊C4 | — | 134 | 1 | no | — |
| 472 | C22⋊C4 | — | 268 | 16 | no | — |
| 473 | C22⋊C4 | — | 134 | 4 | no | — |
| 474 | C22⋊C4 | — | 134 | 4 | no | — |
| 475 | C22⋊C4 | — | 134 | 4 | no | — |
| 476 | C22⋊C4 | — | 134 | 1 | no | — |
| 477 | C22⋊C4 | — | 134 | 1 | no | — |
| 478 | C22⋊C4 | — | 134 | 1 | no | — |
| 479 | C22⋊C4 | — | 134 | 2 | no | — |
| 480 | C22⋊C4 | — | 134 | 2 | no | — |
| 481 | C42 | — | 268 | 2 | no | — |
| 482 | C42 | — | 134 | 4 | no | — |
| 483 | C42 | — | 134 | 4 | no | — |
| 484 | C42 | — | 134 | 2 | no | — |
| 485 | C42 | — | 134 | 2 | no | — |
| 486 | C42 | — | 134 | 1 | no | — |
| 487 | C42 | — | 134 | 1 | no | — |
| 488 | C42 | — | 134 | 1 | no | — |
| 489 | C42 | D4×D67 | 1 | 1 | yes | characteristic |
| 490 | C42 | D4×D67 | 1 | 1 | yes | characteristic |
| 491 | C42 | D4×D67 | 1 | 1 | yes | characteristic |
| 492 | C42 | D4×D67 | 1 | 1 | yes | characteristic |
| 493 | C23 | — | 268 | 4 | no | — |
| 494 | C23 | — | 268 | 4 | no | — |
| 495 | C23 | — | 268 | 4 | no | — |
| 496 | C23 | — | 268 | 2 | no | — |
| 497 | C23 | — | 134 | 1 | no | — |
| 498 | C23 | — | 134 | 2 | no | — |
| 499 | C23 | C22×D268 | 1 | 1 | yes | characteristic |
| 500 | Q8 | — | 4 | 4 | no | — |
| 501 | Q8 | — | 8 | 2 | no | — |
| 502 | Q8 | — | 134 | 4 | no | — |
| 503 | Q8 | — | 134 | 1 | no | — |
| 504 | Q8 | — | 134 | 1 | no | — |
| 505 | D4 | — | 268 | 2 | no | — |
| 506 | D4 | — | 268 | 4 | no | — |
| 507 | D4 | — | 268 | 4 | no | — |
| 508 | D4 | — | 268 | 2 | no | — |
| 509 | D4 | — | 268 | 2 | no | — |
| 510 | D4 | — | 268 | 2 | no | — |
| 511 | D4 | — | 268 | 2 | no | — |
| 512 | D4 | — | 536 | 2 | no | — |
| 513 | D4 | — | 536 | 2 | no | — |
| 514 | D4 | — | 536 | 4 | no | — |
| 515 | D4 | — | 536 | 2 | no | — |
| 516 | D4 | — | 536 | 2 | no | — |
| 517 | D4 | — | 134 | 4 | no | — |
| 518 | D4 | — | 134 | 1 | no | — |
| 519 | D4 | — | 134 | 1 | no | — |
| 520 | C2×C4 | — | 2 | 2 | no | — |
| 521 | C2×C4 | — | 2 | 2 | no | — |
| 522 | C2×C4 | — | 2 | 4 | no | — |
| 523 | C2×C4 | — | 4 | 4 | no | — |
| 524 | C2×C4 | — | 268 | 2 | no | — |
| 525 | C2×C4 | — | 268 | 2 | no | — |
| 526 | C2×C4 | — | 268 | 2 | no | — |
| 527 | C2×C4 | — | 268 | 2 | no | — |
| 528 | C2×C4 | — | 268 | 2 | no | — |
| 529 | C2×C4 | — | 268 | 2 | no | — |
| 530 | C2×C4 | — | 268 | 2 | no | — |
| 531 | C2×C4 | — | 536 | 4 | no | — |
| 532 | C2×C4 | — | 134 | 4 | no | — |
| 533 | C2×C4 | — | 134 | 1 | no | — |
| 534 | C2×C4 | — | 134 | 2 | no | — |
| 535 | C2×C4 | — | 134 | 1 | no | — |
| 536 | C2×C4 | — | 134 | 1 | no | — |
| 537 | C2×C4 | #14524013 | 1 | 1 | yes | characteristic |
| 538 | C2×C4 | #14524013 | 1 | 1 | yes | characteristic |
| 539 | C2×C4 | #14524013 | 1 | 1 | yes | characteristic |
| 540 | C2×C4 | #14524013 | 1 | 1 | yes | characteristic |
| 541 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 542 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 543 | C2×C4 | C2×#11761629 | 1 | 2 | yes | — |
| 544 | C2×C4 | #14524089 | 1 | 2 | yes | — |
| 545 | C8 | — | 2 | 4 | no | — |
| 546 | C8 | — | 4 | 2 | no | — |
| 547 | C22 | — | 2 | 1 | no | — |
| 548 | C22 | — | 2 | 1 | no | — |
| 549 | C22 | — | 268 | 1 | no | — |
| 550 | C22 | — | 268 | 2 | no | — |
| 551 | C22 | — | 268 | 1 | no | — |
| 552 | C22 | — | 268 | 2 | no | — |
| 553 | C22 | — | 268 | 1 | no | — |
| 554 | C22 | — | 268 | 2 | no | — |
| 555 | C22 | — | 536 | 8 | no | — |
| 556 | C22 | — | 536 | 2 | no | — |
| 557 | C22 | — | 536 | 2 | no | — |
| 558 | C22 | — | 536 | 2 | no | — |
| 559 | C22 | C2×#14524013 | 1 | 1 | yes | characteristic |
| 560 | C22 | #16864068 | 1 | 2 | yes | — |
| 561 | C4 | — | 2 | 1 | no | — |
| 562 | C4 | — | 2 | 1 | no | — |
| 563 | C4 | — | 4 | 4 | no | — |
| 564 | C4 | — | 268 | 4 | no | — |
| 565 | C4 | — | 268 | 1 | no | — |
| 566 | C4 | — | 268 | 1 | no | — |
| 567 | C4 | — | 268 | 1 | no | — |
| 568 | C4 | — | 268 | 2 | no | — |
| 569 | C4 | #16863566 | 1 | 2 | yes | — |
| 570 | C4 | #16863571 | 1 | 2 | yes | — |
| 571 | C4 | #16863947 | 1 | 1 | yes | characteristic |
| 572 | C4 | #16863964 | 1 | 1 | yes | characteristic |
| 573 | C4 | #16864037 | 1 | 2 | yes | — |
| 574 | C2 | — | 2 | 2 | no | — |
| 575 | C2 | — | 536 | 1 | no | — |
| 576 | C2 | — | 536 | 2 | no | — |
| 577 | C2 | — | 1072 | 2 | no | — |
| 578 | C2 | #22563830 | 1 | 1 | yes | characteristic |
| 579 | C2 | C2×#16863566 | 1 | 1 | yes | characteristic |
| 580 | C2 | C2×#16863571 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22574122 | C2 | semidirect |
| 2. #22570661 | C2 | semidirect |
| 3. #22569690 | C2 | semidirect |
| 4. #22568567 | C2 | semidirect |
| 5. #22561253 | C2 | semidirect |
| 6. #22561036 | C2 | semidirect |
| 7. #22560584 | C2 | semidirect |
| 8. C4×#14523969 | C2 | semidirect |
| 9. C67×#1997 | C2 | semidirect |
| 191. M16×C67 | #41 | semidirect |
| 296. #1997 | D67 | semidirect |
| 300. C67 | #25616 | semidirect |
| 457. M16 | #11761629 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574122 | 2 |
| #22570661 | 2 |
| #22569690 | 2 |
| #22568567 | 2 |
| #22561253 | 2 |
| #22561036 | 2 |
| #22560584 | 2 |
| C4×#14523969 | 2 |
| C67×#1997 | 2 |
| #25616 | 67 |