← C137×#28703 #46878089
Subgroups — C137×#28703 #46878089
Order 35072.
606 conjugacy classes of subgroups.
The subgroup lattice has 402 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #3166×C137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #3165×C137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×#501×C137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #2961×C137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #2090×C137 | C2 | 1 | 2 | yes | maximal |
| 6 | #2089×C137 | C2 | 1 | 2 | yes | maximal |
| 7 | #1998×C137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #1997×C137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #1952×C137 | C2 | 1 | 2 | yes | maximal |
| 10 | #1951×C137 | C2 | 1 | 2 | yes | maximal |
| 11 | #1778×C137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #533×C137 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C4⋊Q8×C137 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#125×C137 | C22 | 1 | 1 | yes | characteristic |
| 15 | #501×C137 | — | 2 | 1 | no | — |
| 16 | #501×C137 | — | 2 | 1 | no | — |
| 17 | #501×C137 | — | 2 | 2 | no | — |
| 18 | #501×C137 | — | 2 | 2 | no | — |
| 19 | #501×C137 | — | 2 | 2 | no | — |
| 20 | #500×C137 | — | 2 | 1 | no | — |
| 21 | #499×C137 | — | 2 | 2 | no | — |
| 22 | #498×C137 | — | 2 | 1 | no | — |
| 23 | #446×C137 | — | 2 | 2 | no | — |
| 24 | #446×C137 | — | 2 | 2 | no | — |
| 25 | C2×#108×C137 | C22 | 1 | 2 | yes | — |
| 26 | #428×C137 | C22 | 1 | 2 | yes | — |
| 27 | #428×C137 | C22 | 1 | 2 | yes | — |
| 28 | #428×C137 | C22 | 1 | 2 | yes | — |
| 29 | #428×C137 | C22 | 1 | 2 | yes | — |
| 30 | C2×#107×C137 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#107×C137 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#106×C137 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×#106×C137 | C22 | 1 | 1 | yes | characteristic |
| 34 | #424×C137 | C22 | 1 | 2 | yes | — |
| 35 | #423×C137 | C22 | 1 | 1 | yes | characteristic |
| 36 | #405×C137 | C22 | 1 | 2 | yes | — |
| 37 | C4×M16×C137 | C22 | 1 | 1 | yes | characteristic |
| 38 | C4×M16×C137 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#97×C137 | C22 | 1 | 1 | yes | characteristic |
| 40 | #343×C137 | C22 | 1 | 2 | yes | — |
| 41 | #343×C137 | C22 | 1 | 2 | yes | — |
| 42 | #343×C137 | C22 | 1 | 2 | yes | — |
| 43 | #343×C137 | C22 | 1 | 2 | yes | — |
| 44 | #341×C137 | C22 | 1 | 2 | yes | — |
| 45 | C22×Q8×C137 | — | 2 | 1 | no | — |
| 46 | C2×M16×C137 | C23 | 1 | 2 | yes | — |
| 47 | C2×M16×C137 | C23 | 1 | 2 | yes | — |
| 48 | C2×M16×C137 | C23 | 1 | 2 | yes | — |
| 49 | C22×C8×C137 | C23 | 1 | 1 | yes | characteristic |
| 50 | C22×C8×C137 | C23 | 1 | 1 | yes | characteristic |
| 51 | C4⋊Q8×C137 | — | 2 | 1 | no | — |
| 52 | C4⋊Q8×C137 | — | 2 | 1 | no | — |
| 53 | C4⋊Q8×C137 | — | 2 | 1 | no | — |
| 54 | C4⋊Q8×C137 | — | 2 | 1 | no | — |
| 55 | C4⋊Q8×C137 | D4 | 1 | 1 | yes | characteristic |
| 56 | C4⋊Q8×C137 | D4 | 1 | 1 | yes | characteristic |
| 57 | #125×C137 | — | 2 | 1 | no | — |
| 58 | #125×C137 | — | 2 | 1 | no | — |
| 59 | #125×C137 | — | 2 | 1 | no | — |
| 60 | #125×C137 | — | 2 | 1 | no | — |
| 61 | #125×C137 | D4 | 1 | 2 | yes | — |
| 62 | C22⋊Q8×C137 | — | 2 | 1 | no | — |
| 63 | C22⋊Q8×C137 | — | 2 | 1 | no | — |
| 64 | C4×Q8×C137 | — | 2 | 1 | no | — |
| 65 | C4×Q8×C137 | — | 2 | 1 | no | — |
| 66 | #117×C137 | C23 | 1 | 2 | yes | — |
| 67 | C2×C4⋊C4×C137 | — | 2 | 1 | no | — |
| 68 | C2×C4⋊C4×C137 | — | 2 | 1 | no | — |
| 69 | C2×C4⋊C4×C137 | — | 2 | 1 | no | — |
| 70 | C2×C4⋊C4×C137 | C23 | 1 | 1 | yes | characteristic |
| 71 | C2×C4⋊C4×C137 | C23 | 1 | 1 | yes | characteristic |
| 72 | C2×C4⋊C4×C137 | C23 | 1 | 1 | yes | characteristic |
| 73 | C2×C4⋊C4×C137 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×C42×C137 | C23 | 1 | 1 | yes | characteristic |
| 75 | #108×C137 | Q8 | 1 | 8 | yes | complemented |
| 76 | #107×C137 | — | 2 | 2 | no | — |
| 77 | #107×C137 | — | 2 | 2 | no | — |
| 78 | #107×C137 | — | 2 | 2 | no | — |
| 79 | #107×C137 | — | 2 | 2 | no | — |
| 80 | #107×C137 | — | 2 | 2 | no | — |
| 81 | #107×C137 | — | 2 | 2 | no | — |
| 82 | #106×C137 | — | 2 | 2 | no | — |
| 83 | #106×C137 | — | 2 | 2 | no | — |
| 84 | #106×C137 | — | 2 | 2 | no | — |
| 85 | #106×C137 | — | 2 | 2 | no | — |
| 86 | #106×C137 | — | 2 | 2 | no | — |
| 87 | #106×C137 | — | 2 | 2 | no | — |
| 88 | C4⋊C8×C137 | — | 2 | 4 | no | — |
| 89 | C4⋊C8×C137 | — | 2 | 1 | no | — |
| 90 | C4⋊C8×C137 | — | 2 | 1 | no | — |
| 91 | #97×C137 | — | 2 | 2 | no | — |
| 92 | #97×C137 | — | 2 | 1 | no | — |
| 93 | #97×C137 | — | 2 | 1 | no | — |
| 94 | #97×C137 | D4 | 1 | 2 | yes | — |
| 95 | #97×C137 | D4 | 1 | 2 | yes | — |
| 96 | C4×C8×C137 | — | 2 | 2 | no | — |
| 97 | C4×C8×C137 | — | 2 | 1 | no | — |
| 98 | C4×C8×C137 | — | 2 | 1 | no | — |
| 99 | C2×Q8×C137 | — | 2 | 1 | no | — |
| 100 | C2×Q8×C137 | — | 2 | 1 | no | — |
| 101 | C2×Q8×C137 | — | 4 | 1 | no | — |
| 102 | C2×Q8×C137 | — | 4 | 1 | no | — |
| 103 | C2×Q8×C137 | — | 8 | 2 | no | — |
| 104 | C22×C4×C137 | — | 2 | 1 | no | — |
| 105 | C22×C4×C137 | — | 2 | 1 | no | — |
| 106 | C22×C4×C137 | — | 2 | 1 | no | — |
| 107 | C22×C4×C137 | — | 2 | 1 | no | — |
| 108 | C22×C4×C137 | #41 | 1 | 1 | yes | characteristic |
| 109 | C22×C4×C137 | #41 | 1 | 1 | yes | characteristic |
| 110 | C22×C4×C137 | C24 | 1 | 1 | yes | characteristic |
| 111 | M16×C137 | — | 2 | 2 | no | — |
| 112 | M16×C137 | — | 2 | 2 | no | — |
| 113 | M16×C137 | — | 2 | 4 | no | — |
| 114 | M16×C137 | C2×Q8 | 1 | 4 | yes | — |
| 115 | M16×C137 | C2×Q8 | 1 | 4 | yes | — |
| 116 | C2×C8×C137 | — | 2 | 2 | no | — |
| 117 | C2×C8×C137 | — | 2 | 2 | no | — |
| 118 | C2×C8×C137 | — | 2 | 2 | no | — |
| 119 | C2×C8×C137 | — | 2 | 2 | no | — |
| 120 | C2×C8×C137 | C2×D4 | 1 | 2 | yes | — |
| 121 | C2×C8×C137 | C2×D4 | 1 | 2 | yes | — |
| 122 | C2×C8×C137 | C2×Q8 | 1 | 4 | yes | — |
| 123 | C4⋊C4×C137 | — | 2 | 2 | no | — |
| 124 | C4⋊C4×C137 | — | 2 | 2 | no | — |
| 125 | C4⋊C4×C137 | — | 2 | 1 | no | — |
| 126 | C4⋊C4×C137 | — | 2 | 1 | no | — |
| 127 | C4⋊C4×C137 | — | 2 | 1 | no | — |
| 128 | C4⋊C4×C137 | — | 2 | 1 | no | — |
| 129 | C4⋊C4×C137 | — | 2 | 1 | no | — |
| 130 | C4⋊C4×C137 | — | 2 | 1 | no | — |
| 131 | C4⋊C4×C137 | — | 2 | 1 | no | — |
| 132 | C4⋊C4×C137 | — | 2 | 1 | no | — |
| 133 | C4⋊C4×C137 | — | 2 | 1 | no | — |
| 134 | C4⋊C4×C137 | — | 2 | 1 | no | — |
| 135 | C4⋊C4×C137 | — | 4 | 1 | no | — |
| 136 | C4⋊C4×C137 | — | 4 | 1 | no | — |
| 137 | C4⋊C4×C137 | — | 4 | 1 | no | — |
| 138 | C4⋊C4×C137 | — | 4 | 1 | no | — |
| 139 | C4⋊C4×C137 | — | 4 | 1 | no | — |
| 140 | C4⋊C4×C137 | — | 4 | 1 | no | — |
| 141 | C4⋊C4×C137 | C2×D4 | 1 | 2 | yes | — |
| 142 | C4⋊C4×C137 | C2×D4 | 1 | 2 | yes | — |
| 143 | C22⋊C4×C137 | — | 2 | 2 | no | — |
| 144 | C42×C137 | — | 2 | 2 | no | — |
| 145 | C42×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 146 | C42×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 147 | C42×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C42×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 149 | C23×C137 | C2×#41 | 1 | 1 | yes | characteristic |
| 150 | Q8×C137 | — | 8 | 1 | no | — |
| 151 | Q8×C137 | — | 8 | 1 | no | — |
| 152 | Q8×C137 | — | 8 | 2 | no | — |
| 153 | Q8×C137 | — | 8 | 2 | no | — |
| 154 | C2×C4×C137 | — | 2 | 2 | no | — |
| 155 | C2×C4×C137 | — | 2 | 2 | no | — |
| 156 | C2×C4×C137 | — | 4 | 1 | no | — |
| 157 | C2×C4×C137 | — | 4 | 1 | no | — |
| 158 | C2×C4×C137 | — | 4 | 1 | no | — |
| 159 | C2×C4×C137 | — | 4 | 1 | no | — |
| 160 | C2×C4×C137 | — | 4 | 1 | no | — |
| 161 | C2×C4×C137 | — | 4 | 1 | no | — |
| 162 | C2×C4×C137 | — | 8 | 1 | no | — |
| 163 | C2×C4×C137 | — | 8 | 1 | no | — |
| 164 | C2×C4×C137 | — | 8 | 1 | no | — |
| 165 | C2×C4×C137 | — | 8 | 1 | no | — |
| 166 | C2×C4×C137 | #121 | 1 | 1 | yes | characteristic |
| 167 | C2×C4×C137 | #121 | 1 | 1 | yes | characteristic |
| 168 | C2×C4×C137 | #121 | 1 | 1 | yes | characteristic |
| 169 | C2×C4×C137 | #121 | 1 | 1 | yes | characteristic |
| 170 | C2×C4×C137 | C22×D4 | 1 | 1 | yes | characteristic |
| 171 | C2×C4×C137 | C22×D4 | 1 | 1 | yes | characteristic |
| 172 | C2×C4×C137 | C22×Q8 | 1 | 2 | yes | — |
| 173 | C2×C4×C137 | 2−1+4 | 1 | 2 | yes | — |
| 174 | C8×C137 | — | 2 | 2 | no | — |
| 175 | C8×C137 | — | 2 | 4 | no | — |
| 176 | C8×C137 | — | 2 | 4 | no | — |
| 177 | C8×C137 | — | 4 | 2 | no | — |
| 178 | C8×C137 | C4⋊Q8 | 1 | 4 | yes | — |
| 179 | C22×C137 | — | 2 | 1 | no | — |
| 180 | C22×C137 | — | 2 | 1 | no | — |
| 181 | C22×C137 | C2×#121 | 1 | 1 | yes | characteristic |
| 182 | C22×C137 | #557 | 1 | 2 | yes | — |
| 183 | C4×C137 | — | 2 | 1 | no | — |
| 184 | C4×C137 | — | 2 | 1 | no | — |
| 185 | C4×C137 | — | 2 | 1 | no | — |
| 186 | C4×C137 | — | 2 | 1 | no | — |
| 187 | C4×C137 | — | 4 | 2 | no | — |
| 188 | C4×C137 | — | 4 | 2 | no | — |
| 189 | C4×C137 | — | 8 | 1 | no | — |
| 190 | C4×C137 | — | 8 | 1 | no | — |
| 191 | C4×C137 | — | 8 | 1 | no | — |
| 192 | C4×C137 | — | 8 | 1 | no | — |
| 193 | C4×C137 | C2×C4⋊Q8 | 1 | 1 | yes | characteristic |
| 194 | C4×C137 | #536 | 1 | 1 | yes | characteristic |
| 195 | C4×C137 | D4×Q8 | 1 | 2 | yes | — |
| 196 | C2×C137 | — | 2 | 2 | no | — |
| 197 | C2×C137 | #2546 | 1 | 1 | yes | characteristic |
| 198 | C2×C137 | #3068 | 1 | 1 | yes | characteristic |
| 199 | C2×C137 | #3069 | 1 | 1 | yes | characteristic |
| 200 | #28703 | C137 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 201 | C137 | #28703 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 202 | #3166 | C2×C137 | 1 | 1 | yes | characteristic |
| 203 | #3165 | C2×C137 | 1 | 1 | yes | characteristic |
| 204 | C2×#501 | C2×C137 | 1 | 1 | yes | characteristic |
| 205 | #2961 | C2×C137 | 1 | 1 | yes | characteristic |
| 206 | #2090 | C2×C137 | 1 | 2 | yes | — |
| 207 | #2089 | C2×C137 | 1 | 2 | yes | — |
| 208 | #1998 | C2×C137 | 1 | 1 | yes | characteristic |
| 209 | #1997 | C2×C137 | 1 | 1 | yes | characteristic |
| 210 | #1952 | C2×C137 | 1 | 2 | yes | — |
| 211 | #1951 | C2×C137 | 1 | 2 | yes | — |
| 212 | #1778 | C2×C137 | 1 | 1 | yes | characteristic |
| 213 | #533 | C22×C137 | 1 | 1 | yes | characteristic |
| 214 | C2×C4⋊Q8 | C22×C137 | 1 | 1 | yes | characteristic |
| 215 | C2×#125 | C22×C137 | 1 | 1 | yes | characteristic |
| 216 | #501 | — | 2 | 1 | no | — |
| 217 | #501 | — | 2 | 1 | no | — |
| 218 | #501 | — | 2 | 2 | no | — |
| 219 | #501 | — | 2 | 2 | no | — |
| 220 | #501 | — | 2 | 2 | no | — |
| 221 | #500 | — | 2 | 1 | no | — |
| 222 | #499 | — | 2 | 2 | no | — |
| 223 | #498 | — | 2 | 1 | no | — |
| 224 | #446 | — | 2 | 2 | no | — |
| 225 | #446 | — | 2 | 2 | no | — |
| 226 | C2×#108 | C22×C137 | 1 | 2 | yes | — |
| 227 | #428 | C22×C137 | 1 | 2 | yes | — |
| 228 | #428 | C22×C137 | 1 | 2 | yes | — |
| 229 | #428 | C22×C137 | 1 | 2 | yes | — |
| 230 | #428 | C22×C137 | 1 | 2 | yes | — |
| 231 | C2×#107 | C22×C137 | 1 | 1 | yes | characteristic |
| 232 | C2×#107 | C22×C137 | 1 | 1 | yes | characteristic |
| 233 | C2×#106 | C22×C137 | 1 | 1 | yes | characteristic |
| 234 | C2×#106 | C22×C137 | 1 | 1 | yes | characteristic |
| 235 | #424 | C22×C137 | 1 | 2 | yes | — |
| 236 | #423 | C22×C137 | 1 | 1 | yes | characteristic |
| 237 | #405 | C22×C137 | 1 | 2 | yes | — |
| 238 | C4×M16 | C22×C137 | 1 | 1 | yes | characteristic |
| 239 | C4×M16 | C22×C137 | 1 | 1 | yes | characteristic |
| 240 | C2×#97 | C22×C137 | 1 | 1 | yes | characteristic |
| 241 | #343 | C22×C137 | 1 | 2 | yes | — |
| 242 | #343 | C22×C137 | 1 | 2 | yes | — |
| 243 | #343 | C22×C137 | 1 | 2 | yes | — |
| 244 | #343 | C22×C137 | 1 | 2 | yes | — |
| 245 | #341 | C22×C137 | 1 | 2 | yes | — |
| 246 | C22×Q8 | — | 2 | 1 | no | — |
| 247 | C2×M16 | C23×C137 | 1 | 2 | yes | — |
| 248 | C2×M16 | C23×C137 | 1 | 2 | yes | — |
| 249 | C2×M16 | C23×C137 | 1 | 2 | yes | — |
| 250 | C22×C8 | C23×C137 | 1 | 1 | yes | characteristic |
| 251 | C22×C8 | C23×C137 | 1 | 1 | yes | characteristic |
| 252 | C4⋊Q8 | — | 2 | 1 | no | — |
| 253 | C4⋊Q8 | — | 2 | 1 | no | — |
| 254 | C4⋊Q8 | — | 2 | 1 | no | — |
| 255 | C4⋊Q8 | — | 2 | 1 | no | — |
| 256 | C4⋊Q8 | D4×C137 | 1 | 1 | yes | characteristic |
| 257 | C4⋊Q8 | D4×C137 | 1 | 1 | yes | characteristic |
| 258 | #125 | — | 2 | 1 | no | — |
| 259 | #125 | — | 2 | 1 | no | — |
| 260 | #125 | — | 2 | 1 | no | — |
| 261 | #125 | — | 2 | 1 | no | — |
| 262 | #125 | D4×C137 | 1 | 2 | yes | — |
| 263 | C22⋊Q8 | — | 2 | 1 | no | — |
| 264 | C22⋊Q8 | — | 2 | 1 | no | — |
| 265 | C4×Q8 | — | 2 | 1 | no | — |
| 266 | C4×Q8 | — | 2 | 1 | no | — |
| 267 | #117 | C23×C137 | 1 | 2 | yes | — |
| 268 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 269 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 270 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 271 | C2×C4⋊C4 | C23×C137 | 1 | 1 | yes | characteristic |
| 272 | C2×C4⋊C4 | C23×C137 | 1 | 1 | yes | characteristic |
| 273 | C2×C4⋊C4 | C23×C137 | 1 | 1 | yes | characteristic |
| 274 | C2×C4⋊C4 | C23×C137 | 1 | 1 | yes | characteristic |
| 275 | C2×C42 | C23×C137 | 1 | 1 | yes | characteristic |
| 276 | #108 | Q8×C137 | 1 | 8 | yes | complemented |
| 277 | #107 | — | 2 | 2 | no | — |
| 278 | #107 | — | 2 | 2 | no | — |
| 279 | #107 | — | 2 | 2 | no | — |
| 280 | #107 | — | 2 | 2 | no | — |
| 281 | #107 | — | 2 | 2 | no | — |
| 282 | #107 | — | 2 | 2 | no | — |
| 283 | #106 | — | 2 | 2 | no | — |
| 284 | #106 | — | 2 | 2 | no | — |
| 285 | #106 | — | 2 | 2 | no | — |
| 286 | #106 | — | 2 | 2 | no | — |
| 287 | #106 | — | 2 | 2 | no | — |
| 288 | #106 | — | 2 | 2 | no | — |
| 289 | C4⋊C8 | — | 2 | 4 | no | — |
| 290 | C4⋊C8 | — | 2 | 1 | no | — |
| 291 | C4⋊C8 | — | 2 | 1 | no | — |
| 292 | #97 | — | 2 | 2 | no | — |
| 293 | #97 | — | 2 | 1 | no | — |
| 294 | #97 | — | 2 | 1 | no | — |
| 295 | #97 | D4×C137 | 1 | 2 | yes | — |
| 296 | #97 | D4×C137 | 1 | 2 | yes | — |
| 297 | C4×C8 | — | 2 | 2 | no | — |
| 298 | C4×C8 | — | 2 | 1 | no | — |
| 299 | C4×C8 | — | 2 | 1 | no | — |
| 300 | C2×Q8 | — | 2 | 1 | no | — |
| 301 | C2×Q8 | — | 2 | 1 | no | — |
| 302 | C2×Q8 | — | 4 | 1 | no | — |
| 303 | C2×Q8 | — | 4 | 1 | no | — |
| 304 | C2×Q8 | — | 8 | 2 | no | — |
| 305 | C22×C4 | — | 2 | 1 | no | — |
| 306 | C22×C4 | — | 2 | 1 | no | — |
| 307 | C22×C4 | — | 2 | 1 | no | — |
| 308 | C22×C4 | — | 2 | 1 | no | — |
| 309 | C22×C4 | #41×C137 | 1 | 1 | yes | characteristic |
| 310 | C22×C4 | #41×C137 | 1 | 1 | yes | characteristic |
| 311 | C22×C4 | C24×C137 | 1 | 1 | yes | characteristic |
| 312 | M16 | — | 2 | 2 | no | — |
| 313 | M16 | — | 2 | 2 | no | — |
| 314 | M16 | — | 2 | 4 | no | — |
| 315 | M16 | C2×Q8×C137 | 1 | 4 | yes | — |
| 316 | M16 | C2×Q8×C137 | 1 | 4 | yes | — |
| 317 | C2×C8 | — | 2 | 2 | no | — |
| 318 | C2×C8 | — | 2 | 2 | no | — |
| 319 | C2×C8 | — | 2 | 2 | no | — |
| 320 | C2×C8 | — | 2 | 2 | no | — |
| 321 | C2×C8 | C2×D4×C137 | 1 | 2 | yes | — |
| 322 | C2×C8 | C2×D4×C137 | 1 | 2 | yes | — |
| 323 | C2×C8 | C2×Q8×C137 | 1 | 4 | yes | — |
| 324 | C4⋊C4 | — | 2 | 2 | no | — |
| 325 | C4⋊C4 | — | 2 | 2 | no | — |
| 326 | C4⋊C4 | — | 2 | 1 | no | — |
| 327 | C4⋊C4 | — | 2 | 1 | no | — |
| 328 | C4⋊C4 | — | 2 | 1 | no | — |
| 329 | C4⋊C4 | — | 2 | 1 | no | — |
| 330 | C4⋊C4 | — | 2 | 1 | no | — |
| 331 | C4⋊C4 | — | 2 | 1 | no | — |
| 332 | C4⋊C4 | — | 2 | 1 | no | — |
| 333 | C4⋊C4 | — | 2 | 1 | no | — |
| 334 | C4⋊C4 | — | 2 | 1 | no | — |
| 335 | C4⋊C4 | — | 2 | 1 | no | — |
| 336 | C4⋊C4 | — | 4 | 1 | no | — |
| 337 | C4⋊C4 | — | 4 | 1 | no | — |
| 338 | C4⋊C4 | — | 4 | 1 | no | — |
| 339 | C4⋊C4 | — | 4 | 1 | no | — |
| 340 | C4⋊C4 | — | 4 | 1 | no | — |
| 341 | C4⋊C4 | — | 4 | 1 | no | — |
| 342 | C4⋊C4 | C2×D4×C137 | 1 | 2 | yes | — |
| 343 | C4⋊C4 | C2×D4×C137 | 1 | 2 | yes | — |
| 344 | C22⋊C4 | — | 2 | 2 | no | — |
| 345 | C42 | — | 2 | 2 | no | — |
| 346 | C42 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 347 | C42 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 348 | C42 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 349 | C42 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 350 | C23 | C2×#41×C137 | 1 | 1 | yes | characteristic |
| 351 | Q8 | — | 8 | 1 | no | — |
| 352 | Q8 | — | 8 | 1 | no | — |
| 353 | Q8 | — | 8 | 2 | no | — |
| 354 | Q8 | — | 8 | 2 | no | — |
| 355 | C2×C4 | — | 2 | 2 | no | — |
| 356 | C2×C4 | — | 2 | 2 | no | — |
| 357 | C2×C4 | — | 4 | 1 | no | — |
| 358 | C2×C4 | — | 4 | 1 | no | — |
| 359 | C2×C4 | — | 4 | 1 | no | — |
| 360 | C2×C4 | — | 4 | 1 | no | — |
| 361 | C2×C4 | — | 4 | 1 | no | — |
| 362 | C2×C4 | — | 4 | 1 | no | — |
| 363 | C2×C4 | — | 8 | 1 | no | — |
| 364 | C2×C4 | — | 8 | 1 | no | — |
| 365 | C2×C4 | — | 8 | 1 | no | — |
| 366 | C2×C4 | — | 8 | 1 | no | — |
| 367 | C2×C4 | #121×C137 | 1 | 1 | yes | characteristic |
| 368 | C2×C4 | #121×C137 | 1 | 1 | yes | characteristic |
| 369 | C2×C4 | #121×C137 | 1 | 1 | yes | characteristic |
| 370 | C2×C4 | #121×C137 | 1 | 1 | yes | characteristic |
| 371 | C2×C4 | C22×D4×C137 | 1 | 1 | yes | characteristic |
| 372 | C2×C4 | C22×D4×C137 | 1 | 1 | yes | characteristic |
| 373 | C2×C4 | C22×Q8×C137 | 1 | 2 | yes | — |
| 374 | C2×C4 | 2−1+4×C137 | 1 | 2 | yes | — |
| 375 | C8 | — | 2 | 2 | no | — |
| 376 | C8 | — | 2 | 4 | no | — |
| 377 | C8 | — | 2 | 4 | no | — |
| 378 | C8 | — | 4 | 2 | no | — |
| 379 | C8 | C4⋊Q8×C137 | 1 | 4 | yes | — |
| 380 | C22 | — | 2 | 1 | no | — |
| 381 | C22 | — | 2 | 1 | no | — |
| 382 | C22 | C2×#121×C137 | 1 | 1 | yes | characteristic |
| 383 | C22 | #557×C137 | 1 | 2 | yes | — |
| 384 | C4 | — | 2 | 1 | no | — |
| 385 | C4 | — | 2 | 1 | no | — |
| 386 | C4 | — | 2 | 1 | no | — |
| 387 | C4 | — | 2 | 1 | no | — |
| 388 | C4 | — | 4 | 2 | no | — |
| 389 | C4 | — | 4 | 2 | no | — |
| 390 | C4 | — | 8 | 1 | no | — |
| 391 | C4 | — | 8 | 1 | no | — |
| 392 | C4 | — | 8 | 1 | no | — |
| 393 | C4 | — | 8 | 1 | no | — |
| 394 | C4 | C2×C4⋊Q8×C137 | 1 | 1 | yes | characteristic |
| 395 | C4 | #536×C137 | 1 | 1 | yes | characteristic |
| 396 | C4 | D4×Q8×C137 | 1 | 2 | yes | — |
| 397 | C2 | — | 2 | 2 | no | — |
| 398 | C2 | #2546×C137 | 1 | 1 | yes | characteristic |
| 399 | C2 | #3068×C137 | 1 | 1 | yes | characteristic |
| 400 | C2 | #3069×C137 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta