Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1250 conjugacy classes of subgroups.
The subgroup lattice has 578 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #26034014 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #26030375 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #26030370 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #26023538 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #26019239 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #26019205 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #26018759 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #26018592 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C89×#1505 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#15668058 | — | 2 | 1 | no | — |
| 11 | #19152253 | — | 2 | 1 | no | — |
| 12 | #19152251 | — | 2 | 1 | no | — |
| 13 | #19152244 | — | 2 | 2 | no | — |
| 14 | #19152241 | — | 2 | 2 | no | — |
| 15 | D4×D356 | — | 2 | 1 | no | — |
| 16 | #19152233 | — | 2 | 1 | no | — |
| 17 | #19152176 | — | 2 | 1 | no | — |
| 18 | #19152156 | C22 | 1 | 4 | yes | — |
| 19 | #19152148 | C22 | 1 | 1 | yes | characteristic |
| 20 | #121×D89 | — | 2 | 2 | no | — |
| 21 | C2×C4×Dic178 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C2×C4×D356 | C22 | 1 | 1 | yes | characteristic |
| 23 | #19151912 | C22 | 1 | 2 | yes | complemented |
| 24 | #19151909 | C22 | 1 | 2 | yes | complemented |
| 25 | #19151894 | — | 2 | 1 | no | — |
| 26 | #19151890 | — | 2 | 1 | no | — |
| 27 | #19151799 | — | 2 | 1 | no | — |
| 28 | #19151795 | — | 2 | 1 | no | — |
| 29 | #19151739 | C22 | 1 | 2 | yes | complemented |
| 30 | #19151736 | C22 | 1 | 2 | yes | complemented |
| 31 | #19151700 | — | 2 | 2 | no | — |
| 32 | #19151698 | — | 2 | 2 | no | — |
| 33 | #19151655 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #19151538 | — | 2 | 1 | no | — |
| 35 | #19151525 | C22 | 1 | 2 | yes | complemented |
| 36 | #19151516 | — | 2 | 1 | no | — |
| 37 | #19151511 | C22 | 1 | 2 | yes | complemented |
| 38 | C4×#13083551 | — | 2 | 2 | no | — |
| 39 | #19151331 | C22 | 1 | 4 | yes | complemented |
| 40 | #19151321 | C22 | 1 | 4 | yes | complemented |
| 41 | #532×C89 | C22 | 1 | 1 | yes | characteristic |
| 42 | #432×C89 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | #376×C89 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | #327×C89 | C22 | 1 | 4 | yes | complemented |
| 45 | #15668058 | — | 4 | 8 | no | — |
| 46 | C2×#13083575 | — | 2 | 2 | no | — |
| 47 | C2×#13083574 | — | 2 | 2 | no | — |
| 48 | C2×#13083574 | — | 2 | 1 | no | — |
| 49 | C22×Dic178 | C23 | 1 | 1 | yes | characteristic |
| 50 | C22×D356 | — | 2 | 2 | no | — |
| 51 | C22×D356 | D4 | 1 | 1 | yes | characteristic |
| 52 | C2×D4×D89 | — | 2 | 2 | no | — |
| 53 | C2×D4×D89 | — | 2 | 4 | no | — |
| 54 | C2×D4×D89 | — | 2 | 2 | no | — |
| 55 | C22×C4×D89 | D4 | 1 | 2 | yes | — |
| 56 | C2×#13083563 | — | 2 | 2 | no | — |
| 57 | C2×#13083562 | — | 2 | 2 | no | — |
| 58 | #15668012 | D4 | 1 | 1 | yes | characteristic |
| 59 | #15668009 | D4 | 1 | 1 | yes | characteristic |
| 60 | #15668000 | — | 2 | 1 | no | — |
| 61 | #15667997 | — | 2 | 4 | no | — |
| 62 | #15667994 | — | 2 | 4 | no | — |
| 63 | #15667991 | — | 2 | 2 | no | — |
| 64 | #15667988 | — | 2 | 2 | no | — |
| 65 | #15667987 | — | 2 | 2 | no | — |
| 66 | #15667986 | — | 2 | 2 | no | — |
| 67 | #15667986 | — | 2 | 1 | no | — |
| 68 | #15667986 | C23 | 1 | 2 | yes | — |
| 69 | #15667985 | — | 2 | 4 | no | — |
| 70 | #15667984 | — | 2 | 4 | no | — |
| 71 | #15667983 | — | 2 | 2 | no | — |
| 72 | #15667983 | — | 2 | 2 | no | — |
| 73 | #15667982 | — | 2 | 4 | no | — |
| 74 | #15667980 | — | 2 | 4 | no | — |
| 75 | C4×Dic178 | — | 2 | 1 | no | — |
| 76 | C4×Dic178 | — | 2 | 1 | no | — |
| 77 | C4×Dic178 | — | 2 | 1 | no | — |
| 78 | C4×Dic178 | — | 2 | 1 | no | — |
| 79 | C4×D356 | — | 2 | 1 | no | — |
| 80 | C4×D356 | — | 2 | 1 | no | — |
| 81 | C4×D356 | — | 2 | 1 | no | — |
| 82 | C4×D356 | — | 2 | 1 | no | — |
| 83 | C4×D356 | — | 2 | 1 | no | — |
| 84 | C4×D356 | D4 | 1 | 2 | yes | — |
| 85 | C2×C4⋊Dic89 | D4 | 1 | 1 | yes | characteristic |
| 86 | C2×C4⋊Dic89 | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×#13083553 | — | 2 | 1 | no | — |
| 88 | C4⋊C4×D89 | — | 2 | 2 | no | — |
| 89 | C2×#13083551 | — | 2 | 2 | no | — |
| 90 | C2×#13083551 | — | 2 | 2 | no | — |
| 91 | C2×#13083551 | C23 | 1 | 2 | yes | — |
| 92 | C22⋊C4×D89 | — | 2 | 4 | no | — |
| 93 | C2×C4×Dic89 | — | 2 | 1 | no | — |
| 94 | #15667946 | — | 2 | 2 | no | — |
| 95 | #15667945 | — | 2 | 2 | no | — |
| 96 | C4⋊#10623494 | — | 2 | 1 | no | — |
| 97 | #15667937 | — | 2 | 2 | no | — |
| 98 | #15667935 | — | 2 | 2 | no | — |
| 99 | #15667934 | — | 2 | 2 | no | — |
| 100 | #15667933 | — | 2 | 2 | no | — |
| 101 | C22⋊#10623494 | C23 | 1 | 2 | yes | — |
| 102 | #15667923 | — | 2 | 1 | no | — |
| 103 | #15667919 | — | 2 | 2 | no | — |
| 104 | #15667919 | — | 2 | 2 | no | — |
| 105 | C2×#41×C89 | — | 2 | 1 | no | — |
| 106 | C4⋊Q8×C89 | D4 | 1 | 1 | yes | characteristic |
| 107 | #127×C89 | D4 | 1 | 1 | yes | characteristic |
| 108 | #124×C89 | — | 2 | 1 | no | — |
| 109 | #121×C89 | — | 2 | 1 | no | — |
| 110 | #121×C89 | C23 | 1 | 2 | yes | — |
| 111 | C4×D4×C89 | — | 2 | 1 | no | — |
| 112 | C4×D4×C89 | D4 | 1 | 2 | yes | — |
| 113 | C2×C42×C89 | — | 2 | 1 | no | — |
| 114 | C2×C42×C89 | C23 | 1 | 1 | yes | characteristic |
| 115 | C4⋊C8×C89 | — | 2 | 1 | no | — |
| 116 | C22⋊C8×C89 | C23 | 1 | 2 | yes | — |
| 117 | #97×C89 | — | 2 | 1 | no | — |
| 118 | #95×C89 | — | 2 | 1 | no | — |
| 119 | #95×C89 | C23 | 1 | 2 | yes | — |
| 120 | C23×D89 | — | 2 | 4 | no | — |
| 121 | C23×D89 | C2×D4 | 1 | 2 | yes | — |
| 122 | #13083575 | — | 4 | 8 | no | — |
| 123 | #13083574 | — | 4 | 8 | no | — |
| 124 | #13083574 | — | 4 | 4 | no | — |
| 125 | C2×Dic178 | — | 2 | 1 | no | — |
| 126 | C2×Dic178 | — | 2 | 1 | no | — |
| 127 | C2×Dic178 | — | 2 | 1 | no | — |
| 128 | C2×Dic178 | — | 4 | 2 | no | — |
| 129 | C2×D356 | — | 2 | 4 | no | — |
| 130 | C2×D356 | — | 2 | 1 | no | — |
| 131 | C2×D356 | — | 2 | 1 | no | — |
| 132 | C2×D356 | — | 2 | 4 | no | — |
| 133 | C2×D356 | — | 2 | 1 | no | — |
| 134 | C2×D356 | — | 2 | 1 | no | — |
| 135 | C2×D356 | — | 4 | 8 | no | — |
| 136 | C2×D356 | C2×D4 | 1 | 2 | yes | — |
| 137 | C2×C22⋊D89 | — | 2 | 4 | no | — |
| 138 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 139 | C2×C22⋊D89 | — | 2 | 4 | no | — |
| 140 | D4×D89 | — | 4 | 8 | no | — |
| 141 | D4×D89 | — | 4 | 8 | no | — |
| 142 | D4×D89 | — | 4 | 8 | no | — |
| 143 | D4×D89 | — | 8 | 4 | no | — |
| 144 | C22×Dic89 | — | 2 | 1 | no | — |
| 145 | C22×Dic89 | — | 2 | 1 | no | — |
| 146 | C22×Dic89 | C2×D4 | 1 | 2 | yes | — |
| 147 | C2×C4×D89 | — | 2 | 4 | no | — |
| 148 | C2×C4×D89 | — | 2 | 2 | no | — |
| 149 | C2×C4×D89 | — | 2 | 2 | no | — |
| 150 | C2×C4×D89 | — | 2 | 2 | no | — |
| 151 | C2×C4×D89 | — | 4 | 4 | no | — |
| 152 | #13083563 | — | 4 | 4 | no | — |
| 153 | #13083562 | — | 4 | 4 | no | — |
| 154 | C2×#10623494 | — | 2 | 2 | no | — |
| 155 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 156 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 157 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 158 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 159 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 160 | C4⋊Dic89 | C2×D4 | 1 | 2 | yes | — |
| 161 | #13083553 | — | 2 | 4 | no | — |
| 162 | #13083553 | — | 4 | 1 | no | — |
| 163 | #13083553 | — | 4 | 1 | no | — |
| 164 | C22⋊Dic89 | — | 2 | 4 | no | — |
| 165 | #13083551 | — | 2 | 4 | no | — |
| 166 | #13083551 | — | 2 | 2 | no | — |
| 167 | #13083551 | — | 2 | 2 | no | — |
| 168 | #13083551 | — | 2 | 2 | no | — |
| 169 | #13083551 | — | 2 | 2 | no | — |
| 170 | #13083551 | — | 4 | 4 | no | — |
| 171 | #13083551 | — | 4 | 4 | no | — |
| 172 | C4×Dic89 | — | 4 | 1 | no | — |
| 173 | C4×Dic89 | — | 4 | 1 | no | — |
| 174 | #41×C89 | — | 4 | 4 | no | — |
| 175 | C2×Q8×C89 | — | 2 | 1 | no | — |
| 176 | C2×D4×C89 | — | 2 | 2 | no | — |
| 177 | C2×D4×C89 | — | 2 | 1 | no | — |
| 178 | C2×D4×C89 | — | 2 | 1 | no | — |
| 179 | C2×D4×C89 | C2×D4 | 1 | 2 | yes | — |
| 180 | C22×C4×C89 | — | 2 | 2 | no | — |
| 181 | C22×C4×C89 | — | 2 | 2 | no | — |
| 182 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 183 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 184 | C22×C4×C89 | C24 | 1 | 1 | yes | characteristic |
| 185 | C2×C8×C89 | — | 2 | 2 | no | — |
| 186 | C4⋊C4×C89 | — | 2 | 1 | no | — |
| 187 | C4⋊C4×C89 | C2×D4 | 1 | 2 | yes | — |
| 188 | C22⋊C4×C89 | — | 2 | 2 | no | — |
| 189 | C22⋊C4×C89 | — | 2 | 2 | no | — |
| 190 | C42×C89 | — | 4 | 2 | no | — |
| 191 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 194 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 195 | C23×C89 | — | 2 | 2 | no | — |
| 196 | C23×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 197 | C22×D89 | — | 2 | 2 | no | — |
| 198 | C22×D89 | — | 2 | 2 | no | — |
| 199 | C22×D89 | — | 2 | 2 | no | — |
| 200 | C22×D89 | — | 4 | 8 | no | — |
| 201 | C22×D89 | — | 4 | 2 | no | — |
| 202 | C22×D89 | — | 4 | 2 | no | — |
| 203 | C22×D89 | — | 8 | 4 | no | — |
| 204 | C22×D89 | — | 8 | 4 | no | — |
| 205 | C22×D89 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 206 | Q8×C89 | — | 4 | 2 | no | — |
| 207 | D4×C89 | — | 4 | 2 | no | — |
| 208 | D4×C89 | — | 4 | 2 | no | — |
| 209 | D4×C89 | — | 4 | 4 | no | — |
| 210 | D4×C89 | — | 4 | 2 | no | — |
| 211 | C2×C4×C89 | — | 2 | 2 | no | — |
| 212 | C2×C4×C89 | — | 2 | 2 | no | — |
| 213 | C2×C4×C89 | — | 2 | 2 | no | — |
| 214 | C2×C4×C89 | — | 4 | 1 | no | — |
| 215 | C2×C4×C89 | — | 4 | 4 | no | — |
| 216 | C2×C4×C89 | — | 4 | 2 | no | — |
| 217 | C2×C4×C89 | — | 4 | 2 | no | — |
| 218 | C2×C4×C89 | — | 4 | 2 | no | — |
| 219 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 220 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 221 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 222 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 223 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 224 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 225 | C22⋊D89 | — | 4 | 8 | no | — |
| 226 | C22⋊D89 | — | 4 | 4 | no | — |
| 227 | C22⋊D89 | — | 8 | 4 | no | — |
| 228 | C2×Dic89 | — | 2 | 2 | no | — |
| 229 | C2×Dic89 | — | 2 | 2 | no | — |
| 230 | C2×Dic89 | — | 2 | 2 | no | — |
| 231 | C2×Dic89 | — | 4 | 1 | no | — |
| 232 | C2×Dic89 | — | 4 | 1 | no | — |
| 233 | C2×Dic89 | — | 4 | 2 | no | — |
| 234 | C2×Dic89 | — | 4 | 1 | no | — |
| 235 | C2×Dic89 | — | 4 | 2 | no | — |
| 236 | D356 | — | 2 | 4 | no | — |
| 237 | D356 | — | 2 | 4 | no | — |
| 238 | D356 | — | 4 | 2 | no | — |
| 239 | D356 | — | 4 | 2 | no | — |
| 240 | D356 | — | 4 | 8 | no | — |
| 241 | D356 | — | 4 | 2 | no | — |
| 242 | C4×D89 | — | 4 | 4 | no | — |
| 243 | C4×D89 | — | 4 | 8 | no | — |
| 244 | C4×D89 | — | 4 | 4 | no | — |
| 245 | C4×D89 | — | 8 | 2 | no | — |
| 246 | Dic178 | — | 2 | 2 | no | — |
| 247 | Dic178 | — | 2 | 2 | no | — |
| 248 | Dic178 | — | 4 | 1 | no | — |
| 249 | Dic178 | — | 4 | 1 | no | — |
| 250 | Dic178 | — | 4 | 2 | no | — |
| 251 | C8×C89 | — | 4 | 2 | no | — |
| 252 | #10623494 | — | 4 | 2 | no | — |
| 253 | C22×C89 | — | 2 | 1 | no | — |
| 254 | C22×C89 | — | 2 | 1 | no | — |
| 255 | C22×C89 | — | 4 | 2 | no | — |
| 256 | C22×C89 | — | 4 | 2 | no | — |
| 257 | C22×C89 | — | 4 | 2 | no | — |
| 258 | C22×C89 | C2×#120 | 1 | 1 | yes | characteristic |
| 259 | C22×C89 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 260 | C2×D89 | — | 2 | 4 | no | — |
| 261 | C2×D89 | — | 4 | 2 | no | — |
| 262 | C2×D89 | — | 4 | 2 | no | — |
| 263 | C2×D89 | — | 4 | 4 | no | — |
| 264 | C2×D89 | — | 4 | 2 | no | — |
| 265 | C2×D89 | — | 4 | 2 | no | — |
| 266 | C2×D89 | — | 4 | 2 | no | — |
| 267 | C2×D89 | — | 8 | 2 | no | — |
| 268 | C2×D89 | — | 16 | 8 | no | — |
| 269 | C4×C89 | — | 2 | 1 | no | — |
| 270 | C4×C89 | — | 2 | 1 | no | — |
| 271 | C4×C89 | — | 2 | 1 | no | — |
| 272 | C4×C89 | — | 2 | 1 | no | — |
| 273 | C4×C89 | — | 2 | 1 | no | — |
| 274 | C4×C89 | — | 4 | 2 | no | — |
| 275 | C4×C89 | — | 8 | 2 | no | — |
| 276 | C4×C89 | #455 | 1 | 2 | yes | — |
| 277 | Dic89 | — | 4 | 2 | no | — |
| 278 | Dic89 | — | 4 | 2 | no | — |
| 279 | Dic89 | — | 4 | 2 | no | — |
| 280 | Dic89 | — | 8 | 1 | no | — |
| 281 | #18179 | — | 89 | 1 | no | maximal, Sylow |
| 282 | C2×C89 | — | 2 | 2 | no | — |
| 283 | C2×C89 | — | 8 | 2 | no | — |
| 284 | C2×C89 | #3003 | 1 | 1 | yes | characteristic |
| 285 | C2×C89 | C2×#455 | 1 | 1 | yes | characteristic |
| 286 | C2×C89 | #3025 | 1 | 1 | yes | characteristic |
| 287 | D89 | — | 4 | 4 | no | — |
| 288 | D89 | — | 8 | 2 | no | — |
| 289 | #3496 | — | 89 | 1 | no | — |
| 290 | #3112 | — | 89 | 1 | no | — |
| 291 | #3112 | — | 89 | 1 | no | — |
| 292 | #2398 | — | 89 | 1 | no | — |
| 293 | #1607 | — | 89 | 4 | no | — |
| 294 | #1601 | — | 89 | 4 | no | — |
| 295 | #1505 | — | 89 | 1 | no | — |
| 296 | #1505 | D89 | 1 | 1 | yes | characteristic, complemented |
| 297 | #1466 | — | 89 | 1 | no | — |
| 298 | C89 | #18179 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 299 | C2×H(5,𝔽2) | — | 178 | 1 | no | — |
| 300 | #547 | — | 178 | 1 | no | — |
| 301 | #547 | — | 178 | 1 | no | — |
| 302 | #546 | — | 178 | 2 | no | — |
| 303 | #546 | — | 178 | 2 | no | — |
| 304 | D42 | — | 178 | 1 | no | — |
| 305 | D42 | — | 178 | 1 | no | — |
| 306 | #537 | — | 178 | 1 | no | — |
| 307 | #534 | — | 89 | 4 | no | — |
| 308 | #532 | — | 89 | 1 | no | — |
| 309 | #532 | C2×D89 | 1 | 1 | yes | characteristic |
| 310 | C2×#121 | — | 178 | 2 | no | — |
| 311 | C2×C4×Q8 | — | 89 | 1 | no | — |
| 312 | C2×C4×D4 | — | 89 | 1 | no | — |
| 313 | #480 | — | 89 | 2 | no | — |
| 314 | #480 | — | 89 | 2 | no | — |
| 315 | #477 | — | 178 | 1 | no | — |
| 316 | #477 | — | 178 | 1 | no | — |
| 317 | #460 | — | 178 | 1 | no | — |
| 318 | #460 | — | 178 | 1 | no | — |
| 319 | #448 | — | 89 | 2 | no | — |
| 320 | #448 | — | 89 | 2 | no | — |
| 321 | #440 | — | 178 | 2 | no | — |
| 322 | #440 | — | 178 | 2 | no | — |
| 323 | #432 | — | 89 | 1 | no | — |
| 324 | #432 | C2×D89 | 1 | 1 | yes | characteristic, complemented |
| 325 | #400 | — | 178 | 1 | no | — |
| 326 | #397 | — | 89 | 2 | no | — |
| 327 | #394 | — | 178 | 1 | no | — |
| 328 | #393 | — | 89 | 2 | no | — |
| 329 | C4×C22⋊C4 | — | 178 | 2 | no | — |
| 330 | #376 | C2×D89 | 1 | 1 | yes | characteristic, complemented |
| 331 | #327 | — | 89 | 4 | no | — |
| 332 | #327 | C2×D89 | 1 | 4 | yes | complemented |
| 333 | #323 | — | 89 | 4 | no | — |
| 334 | H(5,𝔽2) | — | 356 | 8 | no | — |
| 335 | C2×#41 | — | 2 | 1 | no | — |
| 336 | C2×#41 | — | 178 | 2 | no | — |
| 337 | C2×#41 | — | 178 | 2 | no | — |
| 338 | C2×#41 | — | 178 | 1 | no | — |
| 339 | C22×Q8 | — | 89 | 1 | no | — |
| 340 | C22×D4 | — | 89 | 1 | no | — |
| 341 | C22×D4 | — | 178 | 2 | no | — |
| 342 | C22×D4 | — | 178 | 4 | no | — |
| 343 | C22×D4 | — | 178 | 2 | no | — |
| 344 | C22×D4 | — | 178 | 2 | no | — |
| 345 | C23×C4 | — | 89 | 2 | no | — |
| 346 | C2×SD16 | — | 178 | 2 | no | — |
| 347 | C2×SD16 | — | 178 | 2 | no | — |
| 348 | C4⋊Q8 | — | 89 | 1 | no | — |
| 349 | C4⋊Q8 | D356 | 1 | 1 | yes | characteristic |
| 350 | #127 | — | 89 | 1 | no | — |
| 351 | #127 | D356 | 1 | 1 | yes | characteristic |
| 352 | #124 | — | 2 | 1 | no | — |
| 353 | #124 | — | 178 | 1 | no | — |
| 354 | #123 | — | 178 | 4 | no | — |
| 355 | #123 | — | 178 | 4 | no | — |
| 356 | C22⋊Q8 | — | 178 | 2 | no | — |
| 357 | C22⋊Q8 | — | 178 | 2 | no | — |
| 358 | #121 | — | 2 | 1 | no | — |
| 359 | #121 | — | 89 | 2 | no | — |
| 360 | #121 | — | 178 | 4 | no | — |
| 361 | #121 | — | 178 | 2 | no | — |
| 362 | #121 | — | 178 | 2 | no | — |
| 363 | #121 | — | 178 | 4 | no | — |
| 364 | #121 | — | 178 | 2 | no | — |
| 365 | #121 | — | 178 | 2 | no | — |
| 366 | #121 | — | 178 | 1 | no | — |
| 367 | #121 | C22×D89 | 1 | 2 | yes | — |
| 368 | #120 | — | 178 | 4 | no | — |
| 369 | #120 | — | 178 | 4 | no | — |
| 370 | C4×Q8 | — | 178 | 1 | no | — |
| 371 | C4×Q8 | — | 178 | 1 | no | — |
| 372 | C4×Q8 | — | 178 | 1 | no | — |
| 373 | C4×Q8 | — | 178 | 1 | no | — |
| 374 | C4×D4 | — | 2 | 1 | no | — |
| 375 | C4×D4 | — | 89 | 2 | no | — |
| 376 | C4×D4 | — | 178 | 1 | no | — |
| 377 | C4×D4 | — | 178 | 1 | no | — |
| 378 | C4×D4 | — | 178 | 1 | no | — |
| 379 | C4×D4 | — | 178 | 1 | no | — |
| 380 | C4×D4 | — | 178 | 1 | no | — |
| 381 | C4×D4 | D356 | 1 | 2 | yes | — |
| 382 | C2×C4⋊C4 | — | 89 | 1 | no | — |
| 383 | C2×C4⋊C4 | — | 89 | 1 | no | — |
| 384 | C2×C4⋊C4 | — | 178 | 2 | no | — |
| 385 | C2×C4⋊C4 | — | 178 | 1 | no | — |
| 386 | C2×C22⋊C4 | — | 89 | 2 | no | — |
| 387 | C2×C22⋊C4 | — | 178 | 4 | no | — |
| 388 | C2×C22⋊C4 | — | 178 | 2 | no | — |
| 389 | C2×C22⋊C4 | — | 178 | 2 | no | — |
| 390 | C2×C42 | — | 2 | 1 | no | — |
| 391 | C2×C42 | — | 178 | 1 | no | — |
| 392 | C2×C42 | C22×D89 | 1 | 1 | yes | characteristic |
| 393 | #107 | — | 178 | 2 | no | — |
| 394 | #107 | — | 178 | 2 | no | — |
| 395 | C4⋊C8 | — | 2 | 1 | no | — |
| 396 | C4⋊C8 | — | 178 | 1 | no | — |
| 397 | #103 | — | 178 | 2 | no | — |
| 398 | #103 | — | 178 | 2 | no | — |
| 399 | #102 | — | 178 | 2 | no | — |
| 400 | #102 | — | 178 | 2 | no | — |
| 401 | C22⋊C8 | — | 89 | 2 | no | — |
| 402 | C22⋊C8 | C22×D89 | 1 | 2 | yes | — |
| 403 | #97 | — | 2 | 1 | no | — |
| 404 | #97 | — | 178 | 1 | no | — |
| 405 | #95 | — | 2 | 1 | no | — |
| 406 | #95 | — | 178 | 2 | no | — |
| 407 | #95 | — | 178 | 2 | no | — |
| 408 | #95 | C22×D89 | 1 | 2 | yes | — |
| 409 | C24 | — | 89 | 2 | no | — |
| 410 | C24 | — | 178 | 4 | no | — |
| 411 | #41 | — | 4 | 4 | no | — |
| 412 | #41 | — | 356 | 4 | no | — |
| 413 | #41 | — | 356 | 8 | no | — |
| 414 | #41 | — | 356 | 8 | no | — |
| 415 | C2×Q8 | — | 2 | 1 | no | — |
| 416 | C2×Q8 | — | 356 | 2 | no | — |
| 417 | C2×Q8 | — | 178 | 1 | no | — |
| 418 | C2×Q8 | — | 178 | 1 | no | — |
| 419 | C2×Q8 | — | 178 | 1 | no | — |
| 420 | C2×D4 | — | 2 | 2 | no | — |
| 421 | C2×D4 | — | 2 | 1 | no | — |
| 422 | C2×D4 | — | 2 | 1 | no | — |
| 423 | C2×D4 | — | 89 | 2 | no | — |
| 424 | C2×D4 | — | 356 | 8 | no | — |
| 425 | C2×D4 | — | 356 | 8 | no | — |
| 426 | C2×D4 | — | 356 | 8 | no | — |
| 427 | C2×D4 | — | 356 | 8 | no | — |
| 428 | C2×D4 | — | 178 | 4 | no | — |
| 429 | C2×D4 | — | 178 | 4 | no | — |
| 430 | C2×D4 | — | 178 | 4 | no | — |
| 431 | C2×D4 | — | 178 | 2 | no | — |
| 432 | C2×D4 | — | 178 | 4 | no | — |
| 433 | C2×D4 | — | 178 | 1 | no | — |
| 434 | C2×D4 | — | 178 | 1 | no | — |
| 435 | C2×D4 | — | 178 | 1 | no | — |
| 436 | C2×D4 | — | 178 | 1 | no | — |
| 437 | C2×D4 | — | 712 | 4 | no | — |
| 438 | C2×D4 | C2×D356 | 1 | 2 | yes | — |
| 439 | C22×C4 | — | 2 | 2 | no | — |
| 440 | C22×C4 | — | 2 | 2 | no | — |
| 441 | C22×C4 | — | 89 | 2 | no | — |
| 442 | C22×C4 | — | 356 | 4 | no | — |
| 443 | C22×C4 | — | 178 | 4 | no | — |
| 444 | C22×C4 | — | 178 | 1 | no | — |
| 445 | C22×C4 | — | 178 | 1 | no | — |
| 446 | C22×C4 | — | 178 | 2 | no | — |
| 447 | C22×C4 | — | 178 | 2 | no | — |
| 448 | C22×C4 | — | 178 | 2 | no | — |
| 449 | C22×C4 | D4×D89 | 1 | 1 | yes | characteristic |
| 450 | C22×C4 | D4×D89 | 1 | 1 | yes | characteristic |
| 451 | C22×C4 | C23×D89 | 1 | 1 | yes | characteristic |
| 452 | SD16 | — | 356 | 4 | no | — |
| 453 | SD16 | — | 356 | 4 | no | — |
| 454 | C2×C8 | — | 2 | 2 | no | — |
| 455 | C2×C8 | — | 178 | 2 | no | — |
| 456 | C4⋊C4 | — | 2 | 1 | no | — |
| 457 | C4⋊C4 | — | 89 | 2 | no | — |
| 458 | C4⋊C4 | — | 356 | 1 | no | — |
| 459 | C4⋊C4 | — | 356 | 1 | no | — |
| 460 | C4⋊C4 | — | 178 | 4 | no | — |
| 461 | C4⋊C4 | — | 178 | 1 | no | — |
| 462 | C4⋊C4 | — | 178 | 1 | no | — |
| 463 | C4⋊C4 | — | 178 | 1 | no | — |
| 464 | C4⋊C4 | — | 178 | 1 | no | — |
| 465 | C4⋊C4 | — | 178 | 1 | no | — |
| 466 | C4⋊C4 | C2×D356 | 1 | 2 | yes | — |
| 467 | C22⋊C4 | — | 2 | 2 | no | — |
| 468 | C22⋊C4 | — | 2 | 2 | no | — |
| 469 | C22⋊C4 | — | 356 | 4 | no | — |
| 470 | C22⋊C4 | — | 356 | 4 | no | — |
| 471 | C22⋊C4 | — | 178 | 4 | no | — |
| 472 | C22⋊C4 | — | 178 | 4 | no | — |
| 473 | C22⋊C4 | — | 178 | 2 | no | — |
| 474 | C22⋊C4 | — | 178 | 2 | no | — |
| 475 | C22⋊C4 | — | 178 | 2 | no | — |
| 476 | C22⋊C4 | — | 178 | 2 | no | — |
| 477 | C42 | — | 4 | 2 | no | — |
| 478 | C42 | — | 356 | 1 | no | — |
| 479 | C42 | — | 356 | 1 | no | — |
| 480 | C42 | D4×D89 | 1 | 1 | yes | characteristic |
| 481 | C42 | D4×D89 | 1 | 1 | yes | characteristic |
| 482 | C42 | C2×D356 | 1 | 1 | yes | characteristic |
| 483 | C42 | C2×D356 | 1 | 1 | yes | characteristic |
| 484 | C23 | — | 2 | 2 | no | — |
| 485 | C23 | — | 89 | 4 | no | — |
| 486 | C23 | — | 356 | 2 | no | — |
| 487 | C23 | — | 356 | 2 | no | — |
| 488 | C23 | — | 356 | 8 | no | — |
| 489 | C23 | — | 178 | 2 | no | — |
| 490 | C23 | — | 178 | 2 | no | — |
| 491 | C23 | — | 178 | 2 | no | — |
| 492 | C23 | — | 712 | 4 | no | — |
| 493 | C23 | — | 712 | 4 | no | — |
| 494 | C23 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 495 | Q8 | — | 4 | 2 | no | — |
| 496 | Q8 | — | 356 | 1 | no | — |
| 497 | Q8 | — | 356 | 1 | no | — |
| 498 | Q8 | — | 356 | 2 | no | — |
| 499 | Q8 | — | 178 | 2 | no | — |
| 500 | Q8 | — | 178 | 2 | no | — |
| 501 | D4 | — | 4 | 2 | no | — |
| 502 | D4 | — | 4 | 2 | no | — |
| 503 | D4 | — | 4 | 4 | no | — |
| 504 | D4 | — | 4 | 2 | no | — |
| 505 | D4 | — | 356 | 2 | no | — |
| 506 | D4 | — | 356 | 2 | no | — |
| 507 | D4 | — | 356 | 8 | no | — |
| 508 | D4 | — | 356 | 8 | no | — |
| 509 | D4 | — | 356 | 4 | no | — |
| 510 | D4 | — | 356 | 2 | no | — |
| 511 | D4 | — | 178 | 4 | no | — |
| 512 | D4 | — | 178 | 4 | no | — |
| 513 | D4 | — | 712 | 4 | no | — |
| 514 | C2×C4 | — | 2 | 2 | no | — |
| 515 | C2×C4 | — | 2 | 2 | no | — |
| 516 | C2×C4 | — | 2 | 2 | no | — |
| 517 | C2×C4 | — | 4 | 1 | no | — |
| 518 | C2×C4 | — | 4 | 4 | no | — |
| 519 | C2×C4 | — | 4 | 2 | no | — |
| 520 | C2×C4 | — | 4 | 2 | no | — |
| 521 | C2×C4 | — | 4 | 2 | no | — |
| 522 | C2×C4 | — | 356 | 4 | no | — |
| 523 | C2×C4 | — | 356 | 8 | no | — |
| 524 | C2×C4 | — | 356 | 1 | no | — |
| 525 | C2×C4 | — | 356 | 1 | no | — |
| 526 | C2×C4 | — | 356 | 4 | no | — |
| 527 | C2×C4 | — | 356 | 2 | no | — |
| 528 | C2×C4 | — | 356 | 1 | no | — |
| 529 | C2×C4 | — | 356 | 2 | no | — |
| 530 | C2×C4 | — | 178 | 2 | no | — |
| 531 | C2×C4 | — | 178 | 2 | no | — |
| 532 | C2×C4 | — | 178 | 2 | no | — |
| 533 | C2×C4 | — | 712 | 2 | no | — |
| 534 | C2×C4 | #15667982 | 1 | 1 | yes | characteristic |
| 535 | C2×C4 | #15667982 | 1 | 1 | yes | characteristic |
| 536 | C2×C4 | #15667982 | 1 | 1 | yes | characteristic |
| 537 | C2×C4 | #15667982 | 1 | 1 | yes | characteristic |
| 538 | C2×C4 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 539 | C2×C4 | C22×D356 | 1 | 1 | yes | characteristic |
| 540 | C8 | — | 4 | 2 | no | — |
| 541 | C8 | — | 356 | 2 | no | — |
| 542 | C22 | — | 2 | 1 | no | — |
| 543 | C22 | — | 2 | 1 | no | — |
| 544 | C22 | — | 4 | 2 | no | — |
| 545 | C22 | — | 4 | 2 | no | — |
| 546 | C22 | — | 4 | 2 | no | — |
| 547 | C22 | — | 356 | 4 | no | — |
| 548 | C22 | — | 356 | 2 | no | — |
| 549 | C22 | — | 356 | 2 | no | — |
| 550 | C22 | — | 356 | 2 | no | — |
| 551 | C22 | — | 356 | 2 | no | — |
| 552 | C22 | — | 356 | 2 | no | — |
| 553 | C22 | — | 1424 | 8 | no | — |
| 554 | C22 | — | 178 | 4 | no | — |
| 555 | C22 | — | 712 | 2 | no | — |
| 556 | C22 | C2×#15667982 | 1 | 1 | yes | characteristic |
| 557 | C22 | AGL(1,ℤ/8)×D89 | 1 | 2 | yes | — |
| 558 | C4 | — | 2 | 1 | no | — |
| 559 | C4 | — | 2 | 1 | no | — |
| 560 | C4 | — | 2 | 1 | no | — |
| 561 | C4 | — | 2 | 1 | no | — |
| 562 | C4 | — | 2 | 1 | no | — |
| 563 | C4 | — | 4 | 2 | no | — |
| 564 | C4 | — | 8 | 2 | no | — |
| 565 | C4 | — | 356 | 2 | no | — |
| 566 | C4 | — | 356 | 2 | no | — |
| 567 | C4 | — | 356 | 2 | no | — |
| 568 | C4 | — | 712 | 1 | no | — |
| 569 | C4 | #19151777 | 1 | 2 | yes | — |
| 570 | C2 | — | 2 | 2 | no | — |
| 571 | C2 | — | 8 | 2 | no | — |
| 572 | C2 | — | 356 | 4 | no | — |
| 573 | C2 | — | 712 | 2 | no | — |
| 574 | C2 | #26029481 | 1 | 1 | yes | characteristic |
| 575 | C2 | C2×#19151777 | 1 | 1 | yes | characteristic |
| 576 | C2 | #26029646 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #26030375 | C2 | semidirect |
| 3. #26030370 | C2 | semidirect |
| 4. #26023538 | C2 | semidirect |
| 5. #26019239 | C2 | semidirect |
| 6. #26019205 | C2 | semidirect |
| 7. #26018759 | C2 | semidirect |
| 8. #26018592 | C2 | semidirect |
| 9. C89×#1505 | C2 | semidirect |
| 21. C2×C4×Dic178 | C22 | semidirect |
| 23. #19151912 | C22 | semidirect |
| 24. #19151909 | C22 | semidirect |
| 29. #19151739 | C22 | semidirect |
| 30. #19151736 | C22 | semidirect |
| 33. #19151655 | C22 | semidirect |
| 35. #19151525 | C22 | semidirect |
| 37. #19151511 | C22 | semidirect |
| 39. #19151331 | C22 | semidirect |
| 40. #19151321 | C22 | semidirect |
| 42. #432×C89 | C22 | semidirect |
| 43. #376×C89 | C22 | semidirect |
| 44. #327×C89 | C22 | semidirect |
| 296. #1505 | D89 | semidirect |
| 298. C89 | #18179 | semidirect |
| 324. #432 | C2×D89 | semidirect |
| 330. #376 | C2×D89 | semidirect |
| 332. #327 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034014 | 2 |
| #26030375 | 2 |
| #26030370 | 2 |
| #26023538 | 2 |
| #26019239 | 2 |
| #26019205 | 2 |
| #26018759 | 2 |
| #26018592 | 2 |
| C89×#1505 | 2 |
| #18179 | 89 |