← #36573326
Subgroups — #36573326
Order 22784.
638 conjugacy classes of subgroups.
The subgroup lattice has 398 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | M16×Dic178 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #26029203 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×#19151725 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #26021028 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #26021026 | C2 | 1 | 2 | yes | maximal |
| 6 | #26021024 | C2 | 1 | 2 | yes | maximal |
| 7 | #26020425 | C2 | 1 | 2 | yes | maximal |
| 8 | #26020423 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #26020157 | C2 | 1 | 2 | yes | maximal |
| 10 | C4×#15667947 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | C89×#1950 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C2×C4×Dic178 | C22 | 1 | 1 | yes | characteristic |
| 13 | #19151728 | — | 2 | 1 | no | — |
| 14 | #19151727 | — | 2 | 2 | no | — |
| 15 | #19151726 | — | 2 | 2 | no | — |
| 16 | #19151725 | — | 2 | 1 | no | — |
| 17 | #19151725 | C4 | 1 | 2 | yes | — |
| 18 | #19151725 | C4 | 1 | 2 | yes | — |
| 19 | #19151725 | C4 | 1 | 4 | yes | — |
| 20 | C8×Dic178 | — | 2 | 1 | no | — |
| 21 | #19151722 | — | 2 | 1 | no | — |
| 22 | C2×#15667948 | C22 | 1 | 2 | yes | — |
| 23 | C2×#15667947 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#15667947 | C22 | 1 | 2 | yes | — |
| 25 | C2×#15667947 | C22 | 1 | 2 | yes | — |
| 26 | C2×#15667947 | C22 | 1 | 1 | yes | characteristic |
| 27 | #19151622 | C22 | 1 | 1 | yes | characteristic |
| 28 | #19151621 | C22 | 1 | 2 | yes | — |
| 29 | #19151621 | C22 | 1 | 2 | yes | — |
| 30 | C2×#15667941 | C22 | 1 | 2 | yes | — |
| 31 | C4×#13083558 | C22 | 1 | 1 | yes | characteristic |
| 32 | M16×Dic89 | C22 | 1 | 2 | yes | — |
| 33 | M16×Dic89 | C22 | 1 | 2 | yes | — |
| 34 | C2×#15667922 | C22 | 1 | 2 | yes | — |
| 35 | C2×C4×#10623494 | C22 | 1 | 1 | yes | characteristic |
| 36 | #19151363 | C22 | 1 | 2 | yes | — |
| 37 | #19151362 | C22 | 1 | 1 | yes | characteristic |
| 38 | #19151362 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#108×C89 | C22 | 1 | 2 | yes | — |
| 40 | #423×C89 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×C4⋊C8×C89 | C22 | 1 | 1 | yes | characteristic |
| 42 | C4×M16×C89 | C22 | 1 | 1 | yes | characteristic |
| 43 | #341×C89 | C22 | 1 | 2 | yes | — |
| 44 | C22×Dic178 | Q8 | 1 | 1 | yes | characteristic |
| 45 | C2×#13083558 | C23 | 1 | 1 | yes | characteristic |
| 46 | C2×#13083558 | C23 | 1 | 2 | yes | — |
| 47 | C2×#13083558 | C23 | 1 | 1 | yes | characteristic |
| 48 | C22×#10623494 | C23 | 1 | 1 | yes | characteristic |
| 49 | C22×#10623494 | C23 | 1 | 1 | yes | characteristic |
| 50 | C4×Dic178 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C4×Dic178 | C2×C4 | 1 | 1 | yes | characteristic |
| 52 | C4×Dic178 | C2×C4 | 1 | 2 | yes | — |
| 53 | C4×Dic178 | D4 | 1 | 1 | yes | characteristic |
| 54 | C4×Dic178 | D4 | 1 | 1 | yes | characteristic |
| 55 | C4×Dic178 | D4 | 1 | 2 | yes | — |
| 56 | C2×C4⋊Dic89 | Q8 | 1 | 1 | yes | characteristic |
| 57 | C2×#13083553 | Q8 | 1 | 2 | yes | — |
| 58 | C2×C4×Dic89 | C23 | 1 | 2 | yes | — |
| 59 | #15667948 | — | 4 | 2 | no | — |
| 60 | #15667947 | — | 2 | 2 | no | — |
| 61 | #15667947 | — | 2 | 4 | no | — |
| 62 | #15667947 | — | 4 | 2 | no | — |
| 63 | #15667947 | Q8 | 1 | 4 | yes | complemented |
| 64 | C4⋊#10623494 | — | 2 | 1 | no | — |
| 65 | C4⋊#10623494 | — | 2 | 1 | no | — |
| 66 | #15667941 | — | 2 | 2 | no | — |
| 67 | #15667941 | — | 2 | 2 | no | — |
| 68 | #15667941 | — | 2 | 2 | no | — |
| 69 | #15667941 | — | 2 | 2 | no | — |
| 70 | #15667941 | C2×C4 | 1 | 4 | yes | — |
| 71 | #15667941 | C2×C4 | 1 | 4 | yes | — |
| 72 | #15667923 | — | 2 | 1 | no | — |
| 73 | #15667922 | — | 2 | 2 | no | — |
| 74 | #15667922 | — | 2 | 2 | no | — |
| 75 | #15667922 | C2×C4 | 1 | 4 | yes | — |
| 76 | #15667922 | C2×C4 | 1 | 4 | yes | — |
| 77 | C4×#10623494 | — | 2 | 1 | no | — |
| 78 | C4×#10623494 | C2×C4 | 1 | 2 | yes | — |
| 79 | C4×#10623494 | C2×C4 | 1 | 2 | yes | — |
| 80 | C8×Dic89 | — | 2 | 2 | no | — |
| 81 | C8×Dic89 | — | 2 | 2 | no | — |
| 82 | C2×M16×C89 | C23 | 1 | 1 | yes | characteristic |
| 83 | C2×M16×C89 | C23 | 1 | 2 | yes | — |
| 84 | C2×M16×C89 | C23 | 1 | 1 | yes | characteristic |
| 85 | C22×C8×C89 | C23 | 1 | 2 | yes | — |
| 86 | C2×C42×C89 | C23 | 1 | 1 | yes | characteristic |
| 87 | #108×C89 | — | 4 | 2 | no | — |
| 88 | C4⋊C8×C89 | — | 2 | 1 | no | — |
| 89 | C4⋊C8×C89 | — | 2 | 1 | no | — |
| 90 | C4⋊C8×C89 | C2×C4 | 1 | 2 | yes | — |
| 91 | C4⋊C8×C89 | C2×C4 | 1 | 2 | yes | — |
| 92 | #97×C89 | — | 2 | 1 | no | — |
| 93 | C4×C8×C89 | — | 2 | 1 | no | — |
| 94 | C2×Dic178 | — | 4 | 2 | no | — |
| 95 | C2×Dic178 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 96 | C2×Dic178 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 97 | C2×Dic178 | C4⋊C4 | 1 | 2 | yes | — |
| 98 | C22×Dic89 | C2×Q8 | 1 | 2 | yes | — |
| 99 | C22×Dic89 | C2×Q8 | 1 | 2 | yes | — |
| 100 | #13083558 | — | 2 | 1 | no | — |
| 101 | #13083558 | — | 2 | 1 | no | — |
| 102 | #13083558 | — | 2 | 2 | no | — |
| 103 | #13083558 | — | 2 | 2 | no | — |
| 104 | #13083558 | — | 2 | 1 | no | — |
| 105 | #13083558 | C2×Q8 | 1 | 2 | yes | — |
| 106 | C2×#10623494 | — | 2 | 1 | no | — |
| 107 | C2×#10623494 | — | 2 | 1 | no | — |
| 108 | C2×#10623494 | — | 2 | 1 | no | — |
| 109 | C2×#10623494 | — | 2 | 2 | no | — |
| 110 | C2×#10623494 | — | 2 | 1 | no | — |
| 111 | C2×#10623494 | C22×C4 | 1 | 2 | yes | — |
| 112 | C2×#10623494 | C22×C4 | 1 | 2 | yes | — |
| 113 | C2×#10623494 | C2×Q8 | 1 | 2 | yes | — |
| 114 | C2×#10623494 | #41 | 1 | 2 | yes | — |
| 115 | C4⋊Dic89 | C4⋊C4 | 1 | 2 | yes | — |
| 116 | C4⋊Dic89 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 117 | C4⋊Dic89 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 118 | #13083553 | C4⋊C4 | 1 | 2 | yes | — |
| 119 | #13083553 | C4⋊C4 | 1 | 2 | yes | — |
| 120 | #13083553 | C4⋊C4 | 1 | 2 | yes | — |
| 121 | #13083553 | C4⋊C4 | 1 | 2 | yes | — |
| 122 | C4×Dic89 | C22×C4 | 1 | 2 | yes | — |
| 123 | C4×Dic89 | C22×C4 | 1 | 2 | yes | — |
| 124 | C4×Dic89 | C2×D4 | 1 | 2 | yes | — |
| 125 | C4×Dic89 | C2×D4 | 1 | 2 | yes | — |
| 126 | C22×C4×C89 | C2×Q8 | 1 | 1 | yes | characteristic |
| 127 | C22×C4×C89 | C2×Q8 | 1 | 1 | yes | characteristic |
| 128 | C22×C4×C89 | C24 | 1 | 1 | yes | characteristic |
| 129 | M16×C89 | — | 2 | 1 | no | — |
| 130 | M16×C89 | — | 2 | 1 | no | — |
| 131 | M16×C89 | — | 2 | 2 | no | — |
| 132 | M16×C89 | — | 2 | 1 | no | — |
| 133 | M16×C89 | — | 2 | 2 | no | — |
| 134 | M16×C89 | C2×Q8 | 1 | 2 | yes | — |
| 135 | C2×C8×C89 | — | 2 | 1 | no | — |
| 136 | C2×C8×C89 | — | 2 | 2 | no | — |
| 137 | C2×C8×C89 | — | 2 | 2 | no | — |
| 138 | C2×C8×C89 | — | 2 | 1 | no | — |
| 139 | C2×C8×C89 | — | 2 | 2 | no | — |
| 140 | C2×C8×C89 | C22×C4 | 1 | 4 | yes | — |
| 141 | C42×C89 | C22×C4 | 1 | 1 | yes | characteristic |
| 142 | C42×C89 | C22×C4 | 1 | 1 | yes | characteristic |
| 143 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | C23×C89 | C22×Q8 | 1 | 1 | yes | characteristic |
| 146 | C2×C4×C89 | — | 2 | 2 | no | — |
| 147 | C2×C4×C89 | — | 4 | 1 | no | — |
| 148 | C2×C4×C89 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 149 | C2×C4×C89 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 150 | C2×C4×C89 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 151 | C2×C4×C89 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 152 | C2×C4×C89 | C23×C4 | 1 | 1 | yes | characteristic |
| 153 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 154 | C2×C4×C89 | C22×Q8 | 1 | 1 | yes | characteristic |
| 155 | C2×C4×C89 | C2×#41 | 1 | 1 | yes | characteristic |
| 156 | C2×C4×C89 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 157 | C2×C4×C89 | 2−1+4 | 1 | 1 | yes | characteristic |
| 158 | C2×Dic89 | — | 4 | 2 | no | — |
| 159 | C2×Dic89 | — | 4 | 2 | no | — |
| 160 | C2×Dic89 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 161 | C2×Dic89 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 162 | C2×Dic89 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 163 | C2×Dic89 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 164 | Dic178 | — | 2 | 2 | no | — |
| 165 | Dic178 | — | 2 | 2 | no | — |
| 166 | Dic178 | — | 4 | 2 | no | — |
| 167 | C8×C89 | — | 2 | 4 | no | — |
| 168 | C8×C89 | — | 2 | 2 | no | — |
| 169 | C8×C89 | — | 4 | 1 | no | — |
| 170 | C8×C89 | — | 4 | 2 | no | — |
| 171 | #10623494 | — | 2 | 2 | no | — |
| 172 | #10623494 | — | 2 | 2 | no | — |
| 173 | #10623494 | — | 4 | 2 | no | — |
| 174 | #10623494 | — | 4 | 1 | no | — |
| 175 | #10623494 | C4×Q8 | 1 | 4 | yes | — |
| 176 | C22×C89 | — | 2 | 1 | no | — |
| 177 | C22×C89 | — | 2 | 1 | no | — |
| 178 | C22×C89 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 179 | C22×C89 | #557 | 1 | 1 | yes | characteristic |
| 180 | C22×C89 | Q82 | 1 | 1 | yes | characteristic |
| 181 | C4×C89 | — | 2 | 1 | no | — |
| 182 | C4×C89 | — | 2 | 1 | no | — |
| 183 | C4×C89 | — | 2 | 1 | no | — |
| 184 | C4×C89 | #430 | 1 | 2 | yes | — |
| 185 | C4×C89 | C2×C4×Q8 | 1 | 1 | yes | characteristic |
| 186 | C4×C89 | #520 | 1 | 1 | yes | characteristic |
| 187 | C4×C89 | D4×Q8 | 1 | 1 | yes | characteristic |
| 188 | C4×C89 | #550 | 1 | 1 | yes | characteristic |
| 189 | Dic89 | — | 2 | 2 | no | — |
| 190 | Dic89 | — | 2 | 2 | no | — |
| 191 | Dic89 | — | 2 | 2 | no | — |
| 192 | Dic89 | — | 2 | 2 | no | — |
| 193 | #22733 | — | 89 | 1 | no | maximal, Sylow |
| 194 | C2×C89 | — | 2 | 1 | no | — |
| 195 | C2×C89 | — | 2 | 1 | no | — |
| 196 | C2×C89 | Q8×C4⋊C4 | 1 | 1 | yes | characteristic |
| 197 | C2×C89 | C2×#430 | 1 | 1 | yes | characteristic |
| 198 | C2×C89 | #2916 | 1 | 1 | yes | characteristic |
| 199 | Q8×M16 | — | 89 | 1 | no | — |
| 200 | Q8×M16 | — | 89 | 1 | no | — |
| 201 | C2×#446 | — | 89 | 1 | no | — |
| 202 | #1950 | — | 89 | 2 | no | — |
| 203 | #1950 | — | 89 | 1 | no | — |
| 204 | #1950 | — | 89 | 2 | no | — |
| 205 | #1950 | D89 | 1 | 1 | yes | characteristic |
| 206 | #1849 | — | 89 | 2 | no | — |
| 207 | #1848 | — | 89 | 1 | no | — |
| 208 | #1778 | — | 89 | 2 | no | — |
| 209 | C4×#108 | — | 89 | 1 | no | — |
| 210 | C89 | #22733 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 211 | C2×C4×Q8 | — | 89 | 1 | no | — |
| 212 | #446 | — | 89 | 4 | no | — |
| 213 | #446 | — | 89 | 2 | no | — |
| 214 | #446 | — | 89 | 2 | no | — |
| 215 | #446 | — | 178 | 1 | no | — |
| 216 | #446 | — | 178 | 2 | no | — |
| 217 | #446 | — | 178 | 1 | no | — |
| 218 | #446 | — | 178 | 2 | no | — |
| 219 | C8×Q8 | — | 178 | 1 | no | — |
| 220 | C8×Q8 | — | 178 | 1 | no | — |
| 221 | C2×#108 | — | 89 | 1 | no | — |
| 222 | C2×#108 | — | 89 | 2 | no | — |
| 223 | C2×#108 | — | 89 | 2 | no | — |
| 224 | C2×#108 | — | 89 | 2 | no | — |
| 225 | C2×#108 | — | 89 | 1 | no | — |
| 226 | C2×#108 | C2×D89 | 1 | 2 | yes | — |
| 227 | #423 | — | 89 | 2 | no | — |
| 228 | #423 | — | 89 | 2 | no | — |
| 229 | #423 | — | 89 | 1 | no | — |
| 230 | #423 | C2×D89 | 1 | 1 | yes | characteristic |
| 231 | C2×C4⋊C8 | — | 89 | 2 | no | — |
| 232 | C2×C4⋊C8 | C2×D89 | 1 | 1 | yes | characteristic |
| 233 | C4×M16 | — | 89 | 2 | no | — |
| 234 | C4×M16 | — | 89 | 2 | no | — |
| 235 | C4×M16 | — | 89 | 1 | no | — |
| 236 | C4×M16 | C2×D89 | 1 | 1 | yes | characteristic |
| 237 | C2×#97 | — | 89 | 2 | no | — |
| 238 | C2×C4×C8 | — | 89 | 1 | no | — |
| 239 | #341 | — | 89 | 1 | no | — |
| 240 | #341 | — | 89 | 1 | no | — |
| 241 | #341 | — | 89 | 2 | no | — |
| 242 | #341 | C2×D89 | 1 | 2 | yes | — |
| 243 | C22×Q8 | — | 89 | 1 | no | — |
| 244 | C2×M16 | — | 89 | 1 | no | — |
| 245 | C2×M16 | — | 89 | 1 | no | — |
| 246 | C2×M16 | — | 89 | 2 | no | — |
| 247 | C2×M16 | C22×D89 | 1 | 1 | yes | characteristic |
| 248 | C2×M16 | C22×D89 | 1 | 2 | yes | — |
| 249 | C2×M16 | C22×D89 | 1 | 1 | yes | characteristic |
| 250 | C22×C8 | — | 89 | 1 | no | — |
| 251 | C22×C8 | — | 89 | 1 | no | — |
| 252 | C22×C8 | C22×D89 | 1 | 2 | yes | — |
| 253 | C4×Q8 | — | 89 | 2 | no | — |
| 254 | C4×Q8 | — | 89 | 1 | no | — |
| 255 | C4×Q8 | — | 89 | 1 | no | — |
| 256 | C4×Q8 | — | 89 | 1 | no | — |
| 257 | C4×Q8 | — | 89 | 1 | no | — |
| 258 | C4×Q8 | — | 89 | 2 | no | — |
| 259 | C2×C4⋊C4 | — | 89 | 2 | no | — |
| 260 | C2×C4⋊C4 | — | 89 | 1 | no | — |
| 261 | C2×C42 | — | 89 | 2 | no | — |
| 262 | C2×C42 | C22×D89 | 1 | 1 | yes | characteristic |
| 263 | #108 | — | 4 | 2 | no | — |
| 264 | #108 | — | 89 | 4 | no | — |
| 265 | #108 | — | 356 | 2 | no | — |
| 266 | #108 | — | 356 | 2 | no | — |
| 267 | #108 | — | 178 | 4 | no | — |
| 268 | #108 | — | 178 | 2 | no | — |
| 269 | C4⋊C8 | — | 2 | 1 | no | — |
| 270 | C4⋊C8 | — | 2 | 1 | no | — |
| 271 | C4⋊C8 | — | 89 | 4 | no | — |
| 272 | C4⋊C8 | — | 89 | 4 | no | — |
| 273 | C4⋊C8 | — | 178 | 2 | no | — |
| 274 | C4⋊C8 | — | 178 | 2 | no | — |
| 275 | C4⋊C8 | — | 178 | 2 | no | — |
| 276 | C4⋊C8 | — | 178 | 2 | no | — |
| 277 | C4⋊C8 | — | 178 | 1 | no | — |
| 278 | C4⋊C8 | — | 178 | 1 | no | — |
| 279 | C4⋊C8 | C4×D89 | 1 | 2 | yes | — |
| 280 | C4⋊C8 | C4×D89 | 1 | 2 | yes | — |
| 281 | #97 | — | 2 | 1 | no | — |
| 282 | #97 | — | 89 | 4 | no | — |
| 283 | #97 | — | 89 | 4 | no | — |
| 284 | #97 | — | 178 | 2 | no | — |
| 285 | #97 | — | 178 | 2 | no | — |
| 286 | #97 | — | 178 | 1 | no | — |
| 287 | C4×C8 | — | 2 | 1 | no | — |
| 288 | C4×C8 | — | 89 | 2 | no | — |
| 289 | C4×C8 | — | 89 | 2 | no | — |
| 290 | C4×C8 | — | 178 | 2 | no | — |
| 291 | C4×C8 | — | 178 | 2 | no | — |
| 292 | C4×C8 | — | 178 | 1 | no | — |
| 293 | C2×Q8 | — | 89 | 2 | no | — |
| 294 | C2×Q8 | — | 89 | 1 | no | — |
| 295 | C2×Q8 | — | 89 | 1 | no | — |
| 296 | C2×Q8 | — | 356 | 2 | no | — |
| 297 | C22×C4 | — | 89 | 2 | no | — |
| 298 | C22×C4 | — | 89 | 2 | no | — |
| 299 | C22×C4 | Q8×D89 | 1 | 1 | yes | characteristic |
| 300 | C22×C4 | Q8×D89 | 1 | 1 | yes | characteristic |
| 301 | C22×C4 | C23×D89 | 1 | 1 | yes | characteristic |
| 302 | M16 | — | 2 | 1 | no | — |
| 303 | M16 | — | 2 | 1 | no | — |
| 304 | M16 | — | 2 | 2 | no | — |
| 305 | M16 | — | 2 | 1 | no | — |
| 306 | M16 | — | 2 | 2 | no | — |
| 307 | M16 | — | 89 | 2 | no | — |
| 308 | M16 | — | 178 | 2 | no | — |
| 309 | M16 | — | 178 | 1 | no | — |
| 310 | M16 | — | 178 | 1 | no | — |
| 311 | M16 | — | 178 | 2 | no | — |
| 312 | M16 | — | 178 | 1 | no | — |
| 313 | M16 | Q8×D89 | 1 | 2 | yes | — |
| 314 | C2×C8 | — | 2 | 1 | no | — |
| 315 | C2×C8 | — | 2 | 2 | no | — |
| 316 | C2×C8 | — | 2 | 2 | no | — |
| 317 | C2×C8 | — | 2 | 1 | no | — |
| 318 | C2×C8 | — | 2 | 2 | no | — |
| 319 | C2×C8 | — | 89 | 2 | no | — |
| 320 | C2×C8 | — | 89 | 2 | no | — |
| 321 | C2×C8 | — | 89 | 2 | no | — |
| 322 | C2×C8 | — | 89 | 2 | no | — |
| 323 | C2×C8 | — | 178 | 2 | no | — |
| 324 | C2×C8 | — | 178 | 1 | no | — |
| 325 | C2×C8 | — | 178 | 1 | no | — |
| 326 | C2×C8 | — | 178 | 1 | no | — |
| 327 | C2×C8 | — | 178 | 1 | no | — |
| 328 | C2×C8 | C2×C4×D89 | 1 | 4 | yes | — |
| 329 | C4⋊C4 | — | 89 | 2 | no | — |
| 330 | C4⋊C4 | — | 89 | 2 | no | — |
| 331 | C4⋊C4 | — | 89 | 2 | no | — |
| 332 | C4⋊C4 | — | 89 | 2 | no | — |
| 333 | C4⋊C4 | — | 89 | 2 | no | — |
| 334 | C4⋊C4 | — | 89 | 1 | no | — |
| 335 | C4⋊C4 | — | 89 | 1 | no | — |
| 336 | C42 | — | 89 | 2 | no | — |
| 337 | C42 | — | 89 | 2 | no | — |
| 338 | C42 | — | 89 | 2 | no | — |
| 339 | C42 | — | 89 | 2 | no | — |
| 340 | C42 | C2×C4×D89 | 1 | 1 | yes | characteristic |
| 341 | C42 | C2×C4×D89 | 1 | 1 | yes | characteristic |
| 342 | C42 | D4×D89 | 1 | 1 | yes | characteristic |
| 343 | C42 | D4×D89 | 1 | 1 | yes | characteristic |
| 344 | C23 | C2×Q8×D89 | 1 | 1 | yes | characteristic |
| 345 | Q8 | — | 356 | 2 | no | — |
| 346 | Q8 | — | 178 | 2 | no | — |
| 347 | Q8 | — | 178 | 2 | no | — |
| 348 | C2×C4 | — | 2 | 2 | no | — |
| 349 | C2×C4 | — | 4 | 1 | no | — |
| 350 | C2×C4 | — | 89 | 2 | no | — |
| 351 | C2×C4 | — | 89 | 2 | no | — |
| 352 | C2×C4 | — | 89 | 2 | no | — |
| 353 | C2×C4 | — | 89 | 2 | no | — |
| 354 | C2×C4 | — | 356 | 2 | no | — |
| 355 | C2×C4 | — | 356 | 2 | no | — |
| 356 | C2×C4 | C4⋊C4×D89 | 1 | 1 | yes | characteristic |
| 357 | C2×C4 | C4⋊C4×D89 | 1 | 1 | yes | characteristic |
| 358 | C2×C4 | C4⋊C4×D89 | 1 | 1 | yes | characteristic |
| 359 | C2×C4 | C4⋊C4×D89 | 1 | 1 | yes | characteristic |
| 360 | C2×C4 | C22×C4×D89 | 1 | 1 | yes | characteristic |
| 361 | C2×C4 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 362 | C2×C4 | C2×Q8×D89 | 1 | 1 | yes | characteristic |
| 363 | C2×C4 | #41×D89 | 1 | 1 | yes | characteristic |
| 364 | C2×C4 | #15668057 | 1 | 1 | yes | characteristic |
| 365 | C2×C4 | #15668059 | 1 | 1 | yes | characteristic |
| 366 | C8 | — | 2 | 2 | no | — |
| 367 | C8 | — | 2 | 4 | no | — |
| 368 | C8 | — | 4 | 1 | no | — |
| 369 | C8 | — | 4 | 2 | no | — |
| 370 | C8 | — | 89 | 4 | no | — |
| 371 | C8 | — | 356 | 2 | no | — |
| 372 | C8 | — | 356 | 1 | no | — |
| 373 | C8 | — | 178 | 2 | no | — |
| 374 | C8 | — | 178 | 2 | no | — |
| 375 | C22 | — | 2 | 1 | no | — |
| 376 | C22 | — | 2 | 1 | no | — |
| 377 | C22 | C2×C4⋊C4×D89 | 1 | 1 | yes | characteristic |
| 378 | C22 | #19152325 | 1 | 1 | yes | characteristic |
| 379 | C22 | #19152328 | 1 | 1 | yes | characteristic |
| 380 | C4 | — | 2 | 1 | no | — |
| 381 | C4 | — | 2 | 1 | no | — |
| 382 | C4 | — | 2 | 1 | no | — |
| 383 | C4 | — | 178 | 2 | no | — |
| 384 | C4 | — | 178 | 2 | no | — |
| 385 | C4 | — | 178 | 2 | no | — |
| 386 | C4 | — | 178 | 2 | no | — |
| 387 | C4 | #19151645 | 1 | 2 | yes | — |
| 388 | C4 | C4×Q8×D89 | 1 | 1 | yes | characteristic |
| 389 | C4 | #19152077 | 1 | 1 | yes | characteristic |
| 390 | C4 | #19152261 | 1 | 1 | yes | characteristic |
| 391 | C4 | #19152266 | 1 | 1 | yes | characteristic |
| 392 | C2 | — | 2 | 1 | no | — |
| 393 | C2 | — | 2 | 1 | no | — |
| 394 | C2 | #26023166 | 1 | 1 | yes | characteristic |
| 395 | C2 | C2×#19151645 | 1 | 1 | yes | characteristic |
| 396 | C2 | #26028862 | 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