Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1114 conjugacy classes of subgroups.
The subgroup lattice has 652 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #26034165 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #26030718 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #26029747 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #26026193 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #26021301 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #26021296 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #26021083 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #26020627 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #26020620 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #26020065 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C89×#1997 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#15668045 | C22 | 1 | 2 | yes | — |
| 13 | C2×#15668045 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#15668040 | C22 | 1 | 2 | yes | — |
| 15 | C2×#15668040 | C22 | 1 | 1 | yes | characteristic |
| 16 | #19152322 | — | 2 | 1 | no | — |
| 17 | #19152314 | — | 2 | 1 | no | — |
| 18 | #19152309 | — | 2 | 1 | no | — |
| 19 | #19152296 | — | 2 | 2 | no | — |
| 20 | #19152259 | — | 2 | 2 | no | — |
| 21 | #19152251 | — | 2 | 1 | no | — |
| 22 | #19152222 | — | 2 | 2 | no | — |
| 23 | #19152179 | C22 | 1 | 2 | yes | — |
| 24 | #19152153 | — | 2 | 1 | no | — |
| 25 | #19152149 | — | 2 | 1 | no | — |
| 26 | #19152148 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#15668000 | C22 | 1 | 1 | yes | characteristic |
| 28 | #19152079 | C22 | 1 | 2 | yes | — |
| 29 | C4×#13083574 | C22 | 1 | 1 | yes | characteristic |
| 30 | #19151992 | — | 2 | 1 | no | — |
| 31 | #19151987 | — | 2 | 1 | no | — |
| 32 | #19151982 | — | 2 | 2 | no | — |
| 33 | #19151821 | — | 2 | 1 | no | — |
| 34 | #19151821 | — | 2 | 1 | no | — |
| 35 | #19151814 | — | 2 | 1 | no | — |
| 36 | #19151814 | — | 2 | 1 | no | — |
| 37 | C2×#15667938 | C22 | 1 | 2 | yes | — |
| 38 | C2×#15667938 | C22 | 1 | 2 | yes | — |
| 39 | C2×#15667938 | C22 | 1 | 2 | yes | — |
| 40 | #19151608 | C22 | 1 | 1 | yes | characteristic |
| 41 | #19151604 | C22 | 1 | 1 | yes | characteristic |
| 42 | #19151524 | — | 2 | 2 | no | — |
| 43 | #19151509 | — | 2 | 2 | no | — |
| 44 | #19151503 | C22 | 1 | 2 | yes | — |
| 45 | #19151499 | C22 | 1 | 2 | yes | — |
| 46 | #19151444 | C22 | 1 | 1 | yes | characteristic |
| 47 | #19151359 | C22 | 1 | 2 | yes | — |
| 48 | C2×C4⋊Q8×C89 | C22 | 1 | 1 | yes | characteristic |
| 49 | #423×C89 | C22 | 1 | 1 | yes | characteristic |
| 50 | C4×M16×C89 | C22 | 1 | 1 | yes | characteristic |
| 51 | #343×C89 | C22 | 1 | 2 | yes | — |
| 52 | #343×C89 | C22 | 1 | 2 | yes | — |
| 53 | C2×#13083575 | — | 2 | 2 | no | — |
| 54 | C2×#13083574 | C23 | 1 | 2 | yes | — |
| 55 | C2×#13083574 | C23 | 1 | 1 | yes | characteristic |
| 56 | C22×Dic178 | C23 | 1 | 1 | yes | characteristic |
| 57 | C22×D356 | C23 | 1 | 1 | yes | characteristic |
| 58 | #15668045 | — | 2 | 4 | no | — |
| 59 | #15668045 | — | 4 | 2 | no | — |
| 60 | #15668045 | — | 4 | 2 | no | — |
| 61 | #15668040 | — | 2 | 4 | no | — |
| 62 | #15668040 | — | 4 | 2 | no | — |
| 63 | #15668040 | — | 4 | 2 | no | — |
| 64 | C2×Dic356 | — | 2 | 2 | no | — |
| 65 | C2×Dic356 | — | 2 | 1 | no | — |
| 66 | C2×#13083563 | — | 2 | 2 | no | — |
| 67 | C2×#13083563 | — | 2 | 1 | no | — |
| 68 | C2×#13083563 | — | 2 | 2 | no | — |
| 69 | C2×#13083563 | — | 2 | 1 | no | — |
| 70 | C2×D712 | — | 2 | 2 | no | — |
| 71 | C2×D712 | — | 2 | 1 | no | — |
| 72 | #15668012 | D4 | 1 | 1 | yes | characteristic |
| 73 | #15668009 | D4 | 1 | 1 | yes | characteristic |
| 74 | #15668007 | — | 2 | 4 | no | — |
| 75 | #15668003 | — | 2 | 2 | no | — |
| 76 | #15668001 | — | 2 | 2 | no | — |
| 77 | #15668001 | — | 2 | 4 | no | — |
| 78 | #15668000 | — | 2 | 1 | no | — |
| 79 | #15668000 | — | 2 | 1 | no | — |
| 80 | #15668000 | — | 2 | 1 | no | — |
| 81 | #15668000 | — | 2 | 1 | no | — |
| 82 | #15668000 | D4 | 1 | 2 | yes | — |
| 83 | #15667997 | — | 2 | 4 | no | — |
| 84 | #15667992 | — | 2 | 2 | no | — |
| 85 | #15667992 | — | 2 | 2 | no | — |
| 86 | #15667988 | — | 2 | 2 | no | — |
| 87 | #15667988 | — | 2 | 4 | no | — |
| 88 | #15667987 | — | 2 | 2 | no | — |
| 89 | #15667987 | — | 2 | 2 | no | — |
| 90 | #15667987 | — | 2 | 2 | no | — |
| 91 | #15667986 | — | 2 | 1 | no | — |
| 92 | #15667986 | — | 2 | 1 | no | — |
| 93 | #15667986 | — | 2 | 4 | no | — |
| 94 | Q8×Dic89 | — | 2 | 2 | no | — |
| 95 | C4×Dic178 | D4 | 1 | 1 | yes | characteristic |
| 96 | C4×Dic178 | D4 | 1 | 1 | yes | characteristic |
| 97 | #15667977 | — | 2 | 2 | no | — |
| 98 | C4×D356 | — | 2 | 1 | no | — |
| 99 | C4×D356 | — | 2 | 1 | no | — |
| 100 | C4×D356 | D4 | 1 | 1 | yes | characteristic |
| 101 | C4×D356 | D4 | 1 | 1 | yes | characteristic |
| 102 | #15667974 | — | 2 | 2 | no | — |
| 103 | #15667974 | — | 2 | 2 | no | — |
| 104 | C4×C22⋊D89 | — | 2 | 1 | no | — |
| 105 | C4×C22⋊D89 | — | 2 | 4 | no | — |
| 106 | C4×C22⋊D89 | — | 2 | 1 | no | — |
| 107 | #15667971 | C23 | 1 | 1 | yes | characteristic |
| 108 | #15667970 | — | 2 | 2 | no | — |
| 109 | #15667970 | — | 2 | 2 | no | — |
| 110 | #15667969 | — | 2 | 1 | no | — |
| 111 | C4⋊C4×D89 | — | 2 | 2 | no | — |
| 112 | C2×#13083551 | — | 2 | 1 | no | — |
| 113 | C2×#13083551 | — | 2 | 1 | no | — |
| 114 | C2×#13083551 | — | 2 | 4 | no | — |
| 115 | C2×C4×Dic89 | C23 | 1 | 2 | yes | — |
| 116 | C42×D89 | — | 2 | 1 | no | — |
| 117 | #15667938 | — | 2 | 4 | no | — |
| 118 | #15667938 | — | 4 | 2 | no | — |
| 119 | #15667938 | — | 4 | 2 | no | — |
| 120 | #15667937 | — | 2 | 1 | no | — |
| 121 | #15667937 | — | 2 | 1 | no | — |
| 122 | #15667934 | — | 2 | 1 | no | — |
| 123 | #15667934 | — | 2 | 1 | no | — |
| 124 | #15667919 | — | 2 | 1 | no | — |
| 125 | #15667919 | — | 2 | 1 | no | — |
| 126 | #15667919 | — | 2 | 4 | no | — |
| 127 | C22×Q8×C89 | D4 | 1 | 2 | yes | — |
| 128 | C2×M16×C89 | C23 | 1 | 1 | yes | characteristic |
| 129 | C2×M16×C89 | C23 | 1 | 1 | yes | characteristic |
| 130 | C2×M16×C89 | C23 | 1 | 2 | yes | — |
| 131 | C4⋊Q8×C89 | — | 2 | 1 | no | — |
| 132 | C4⋊Q8×C89 | — | 2 | 1 | no | — |
| 133 | C4⋊Q8×C89 | — | 2 | 1 | no | — |
| 134 | C4⋊Q8×C89 | — | 2 | 1 | no | — |
| 135 | C2×C4⋊C4×C89 | D4 | 1 | 2 | yes | — |
| 136 | C2×C4⋊C4×C89 | C23 | 1 | 2 | yes | — |
| 137 | C2×C42×C89 | C23 | 1 | 1 | yes | characteristic |
| 138 | C4⋊C8×C89 | — | 2 | 1 | no | — |
| 139 | C4⋊C8×C89 | — | 2 | 1 | no | — |
| 140 | #97×C89 | — | 2 | 1 | no | — |
| 141 | C4×C8×C89 | — | 2 | 1 | no | — |
| 142 | C23×D89 | — | 2 | 1 | no | — |
| 143 | #13083575 | — | 8 | 4 | no | — |
| 144 | #13083574 | — | 2 | 2 | no | — |
| 145 | #13083574 | — | 2 | 2 | no | — |
| 146 | #13083574 | — | 2 | 2 | no | — |
| 147 | #13083574 | — | 2 | 2 | no | — |
| 148 | #13083574 | — | 2 | 2 | no | — |
| 149 | #13083574 | — | 2 | 2 | no | — |
| 150 | C2×Dic178 | — | 2 | 1 | no | — |
| 151 | C2×Dic178 | — | 2 | 1 | no | — |
| 152 | C2×Dic178 | — | 2 | 2 | no | — |
| 153 | C2×Dic178 | — | 2 | 2 | no | — |
| 154 | C2×Dic178 | C2×D4 | 1 | 2 | yes | — |
| 155 | C2×Dic178 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C2×D356 | — | 2 | 1 | no | — |
| 157 | C2×D356 | — | 2 | 1 | no | — |
| 158 | C2×D356 | — | 2 | 1 | no | — |
| 159 | C2×D356 | — | 2 | 1 | no | — |
| 160 | C2×D356 | — | 2 | 2 | no | — |
| 161 | C2×D356 | — | 2 | 2 | no | — |
| 162 | C2×D356 | — | 2 | 4 | no | — |
| 163 | C2×D356 | C2×D4 | 1 | 2 | yes | — |
| 164 | C2×D356 | C2×D4 | 1 | 1 | yes | characteristic |
| 165 | C2×C22⋊D89 | — | 2 | 1 | no | — |
| 166 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 167 | C22×Dic89 | — | 2 | 1 | no | — |
| 168 | C22×Dic89 | — | 2 | 2 | no | — |
| 169 | C2×C4×D89 | — | 2 | 1 | no | — |
| 170 | C2×C4×D89 | — | 2 | 1 | no | — |
| 171 | C2×C4×D89 | — | 2 | 1 | no | — |
| 172 | C2×C4×D89 | — | 2 | 2 | no | — |
| 173 | C2×C4×D89 | — | 2 | 4 | no | — |
| 174 | Dic356 | — | 4 | 4 | no | — |
| 175 | Dic356 | — | 4 | 2 | no | — |
| 176 | #13083563 | — | 4 | 4 | no | — |
| 177 | #13083563 | — | 4 | 4 | no | — |
| 178 | #13083563 | — | 4 | 2 | no | — |
| 179 | #13083563 | — | 4 | 2 | no | — |
| 180 | D712 | — | 4 | 4 | no | — |
| 181 | D712 | — | 4 | 2 | no | — |
| 182 | C4⋊Dic89 | — | 2 | 4 | no | — |
| 183 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 184 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 185 | C4⋊Dic89 | C2×D4 | 1 | 1 | yes | characteristic |
| 186 | C4⋊Dic89 | C2×D4 | 1 | 1 | yes | characteristic |
| 187 | #13083553 | — | 2 | 4 | no | — |
| 188 | #13083553 | — | 2 | 1 | no | — |
| 189 | #13083553 | — | 2 | 1 | no | — |
| 190 | C22⋊Dic89 | — | 2 | 1 | no | — |
| 191 | #13083551 | — | 2 | 4 | no | — |
| 192 | #13083551 | — | 2 | 4 | no | — |
| 193 | #13083551 | — | 2 | 4 | no | — |
| 194 | #13083551 | — | 2 | 1 | no | — |
| 195 | #13083551 | — | 2 | 1 | no | — |
| 196 | #13083551 | — | 2 | 2 | no | — |
| 197 | #13083551 | — | 2 | 2 | no | — |
| 198 | #13083551 | — | 4 | 1 | no | — |
| 199 | #13083551 | — | 4 | 1 | no | — |
| 200 | #13083551 | — | 4 | 1 | no | — |
| 201 | #13083551 | — | 4 | 1 | no | — |
| 202 | #13083551 | — | 8 | 4 | no | — |
| 203 | C4×Dic89 | — | 2 | 4 | no | — |
| 204 | C4×Dic89 | — | 2 | 1 | no | — |
| 205 | C4×Dic89 | — | 2 | 1 | no | — |
| 206 | C4×Dic89 | — | 2 | 1 | no | — |
| 207 | C4×Dic89 | — | 2 | 2 | no | — |
| 208 | C4×Dic89 | — | 2 | 2 | no | — |
| 209 | C2×Q8×C89 | — | 2 | 2 | no | — |
| 210 | C2×Q8×C89 | — | 2 | 2 | no | — |
| 211 | C2×Q8×C89 | — | 8 | 2 | no | — |
| 212 | C22×C4×C89 | C2×D4 | 1 | 4 | yes | — |
| 213 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 214 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 215 | C22×C4×C89 | C24 | 1 | 1 | yes | characteristic |
| 216 | M16×C89 | — | 2 | 2 | no | — |
| 217 | M16×C89 | — | 2 | 2 | no | — |
| 218 | M16×C89 | — | 2 | 2 | no | — |
| 219 | M16×C89 | #41 | 1 | 4 | yes | complemented |
| 220 | C2×C8×C89 | — | 2 | 2 | no | — |
| 221 | C2×C8×C89 | — | 2 | 1 | no | — |
| 222 | C2×C8×C89 | — | 2 | 1 | no | — |
| 223 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 224 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 225 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 226 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 227 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 228 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 229 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 230 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 231 | C23×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 232 | C22×D89 | — | 2 | 1 | no | — |
| 233 | C22×D89 | — | 2 | 2 | no | — |
| 234 | C22×D89 | — | 4 | 2 | no | — |
| 235 | C22×D89 | — | 4 | 2 | no | — |
| 236 | C22×D89 | — | 4 | 1 | no | — |
| 237 | C22×D89 | — | 4 | 2 | no | — |
| 238 | Q8×C89 | — | 4 | 4 | no | — |
| 239 | Q8×C89 | — | 8 | 2 | no | — |
| 240 | C2×C4×C89 | — | 2 | 4 | no | — |
| 241 | C2×C4×C89 | — | 4 | 1 | no | — |
| 242 | C2×C4×C89 | — | 4 | 1 | no | — |
| 243 | C2×C4×C89 | — | 4 | 4 | no | — |
| 244 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 245 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 246 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 247 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 248 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 249 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 250 | C2×C4×C89 | C2×#41 | 1 | 2 | yes | — |
| 251 | C2×C4×C89 | H(5,𝔽2) | 1 | 2 | yes | — |
| 252 | C22⋊D89 | — | 4 | 2 | no | — |
| 253 | C22⋊D89 | — | 4 | 2 | no | — |
| 254 | C22⋊D89 | — | 4 | 2 | no | — |
| 255 | C2×Dic89 | — | 2 | 1 | no | — |
| 256 | C2×Dic89 | — | 2 | 2 | no | — |
| 257 | C2×Dic89 | — | 2 | 1 | no | — |
| 258 | C2×Dic89 | — | 2 | 1 | no | — |
| 259 | C2×Dic89 | — | 4 | 2 | no | — |
| 260 | C2×Dic89 | — | 4 | 2 | no | — |
| 261 | C2×Dic89 | — | 4 | 1 | no | — |
| 262 | C2×Dic89 | — | 4 | 2 | no | — |
| 263 | C2×Dic89 | — | 4 | 2 | no | — |
| 264 | D356 | — | 2 | 1 | no | — |
| 265 | D356 | — | 2 | 1 | no | — |
| 266 | D356 | — | 2 | 2 | no | — |
| 267 | D356 | — | 2 | 2 | no | — |
| 268 | D356 | — | 4 | 2 | no | — |
| 269 | D356 | — | 4 | 2 | no | — |
| 270 | D356 | — | 4 | 1 | no | — |
| 271 | D356 | — | 4 | 1 | no | — |
| 272 | D356 | — | 4 | 2 | no | — |
| 273 | D356 | — | 8 | 4 | no | — |
| 274 | C4×D89 | — | 4 | 2 | no | — |
| 275 | C4×D89 | — | 4 | 2 | no | — |
| 276 | C4×D89 | — | 4 | 2 | no | — |
| 277 | C4×D89 | — | 4 | 2 | no | — |
| 278 | C4×D89 | — | 4 | 2 | no | — |
| 279 | C4×D89 | — | 8 | 4 | no | — |
| 280 | Dic178 | — | 2 | 1 | no | — |
| 281 | Dic178 | — | 2 | 1 | no | — |
| 282 | Dic178 | — | 2 | 2 | no | — |
| 283 | Dic178 | — | 2 | 2 | no | — |
| 284 | Dic178 | — | 4 | 1 | no | — |
| 285 | Dic178 | — | 4 | 1 | no | — |
| 286 | Dic178 | — | 4 | 2 | no | — |
| 287 | C8×C89 | — | 2 | 4 | no | — |
| 288 | C8×C89 | — | 4 | 1 | no | — |
| 289 | C8×C89 | — | 4 | 1 | no | — |
| 290 | C22×C89 | — | 2 | 1 | no | — |
| 291 | C22×C89 | — | 2 | 1 | no | — |
| 292 | C22×C89 | C2×#120 | 1 | 1 | yes | characteristic |
| 293 | C22×C89 | #550 | 1 | 2 | yes | — |
| 294 | C2×D89 | — | 4 | 2 | no | — |
| 295 | C2×D89 | — | 4 | 1 | no | — |
| 296 | C2×D89 | — | 4 | 1 | no | — |
| 297 | C2×D89 | — | 4 | 2 | no | — |
| 298 | C2×D89 | — | 4 | 1 | no | — |
| 299 | C2×D89 | — | 4 | 2 | no | — |
| 300 | C2×D89 | — | 8 | 4 | no | — |
| 301 | C2×D89 | — | 8 | 1 | no | — |
| 302 | C2×D89 | — | 8 | 1 | no | — |
| 303 | C2×D89 | — | 8 | 1 | no | — |
| 304 | C4×C89 | — | 2 | 1 | no | — |
| 305 | C4×C89 | — | 2 | 1 | no | — |
| 306 | C4×C89 | — | 2 | 1 | no | — |
| 307 | C4×C89 | — | 2 | 1 | no | — |
| 308 | C4×C89 | — | 4 | 4 | no | — |
| 309 | C4×C89 | #532 | 1 | 1 | yes | characteristic |
| 310 | C4×C89 | #535 | 1 | 1 | yes | characteristic |
| 311 | C4×C89 | #546 | 1 | 2 | yes | — |
| 312 | Dic89 | — | 4 | 1 | no | — |
| 313 | Dic89 | — | 4 | 2 | no | — |
| 314 | Dic89 | — | 4 | 1 | no | — |
| 315 | Dic89 | — | 4 | 1 | no | — |
| 316 | Dic89 | — | 8 | 2 | no | — |
| 317 | Dic89 | — | 8 | 1 | no | — |
| 318 | #25618 | — | 89 | 1 | no | maximal, Sylow |
| 319 | C2×C89 | — | 2 | 2 | no | — |
| 320 | C2×C89 | #2431 | 1 | 1 | yes | characteristic |
| 321 | C2×C89 | #3019 | 1 | 1 | yes | characteristic |
| 322 | C2×C89 | #3020 | 1 | 1 | yes | characteristic |
| 323 | D89 | — | 8 | 1 | no | — |
| 324 | D89 | — | 8 | 2 | no | — |
| 325 | D89 | — | 16 | 1 | no | — |
| 326 | #3511 | — | 89 | 1 | no | — |
| 327 | #3153 | — | 89 | 1 | no | — |
| 328 | #3040 | — | 89 | 1 | no | — |
| 329 | #2640 | — | 89 | 1 | no | — |
| 330 | #2007 | — | 89 | 2 | no | — |
| 331 | #2006 | — | 89 | 2 | no | — |
| 332 | #1997 | D89 | 1 | 1 | yes | characteristic, complemented |
| 333 | #1963 | — | 89 | 1 | no | — |
| 334 | #1883 | — | 89 | 2 | no | — |
| 335 | #1882 | — | 89 | 2 | no | — |
| 336 | #1759 | — | 89 | 1 | no | — |
| 337 | C89 | #25618 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 338 | C2×#137 | — | 89 | 1 | no | — |
| 339 | C2×#137 | — | 89 | 2 | no | — |
| 340 | C2×AGL(1,ℤ/8) | — | 89 | 1 | no | — |
| 341 | C2×AGL(1,ℤ/8) | — | 89 | 2 | no | — |
| 342 | #556 | — | 178 | 1 | no | — |
| 343 | #555 | — | 178 | 1 | no | — |
| 344 | #554 | — | 178 | 1 | no | — |
| 345 | #553 | — | 178 | 2 | no | — |
| 346 | #548 | — | 178 | 2 | no | — |
| 347 | #547 | — | 178 | 1 | no | — |
| 348 | #542 | — | 178 | 2 | no | — |
| 349 | #537 | — | 89 | 2 | no | — |
| 350 | #533 | — | 178 | 1 | no | — |
| 351 | #532 | — | 89 | 1 | no | — |
| 352 | #532 | — | 178 | 1 | no | — |
| 353 | C2×C4⋊Q8 | C2×D89 | 1 | 1 | yes | characteristic |
| 354 | C2×#124 | — | 89 | 1 | no | — |
| 355 | #520 | — | 89 | 2 | no | — |
| 356 | C4×#41 | — | 89 | 1 | no | — |
| 357 | #497 | — | 178 | 1 | no | — |
| 358 | #496 | — | 178 | 1 | no | — |
| 359 | #495 | — | 178 | 2 | no | — |
| 360 | #464 | — | 178 | 1 | no | — |
| 361 | #464 | — | 178 | 1 | no | — |
| 362 | #463 | — | 178 | 1 | no | — |
| 363 | #463 | — | 178 | 1 | no | — |
| 364 | #423 | C2×D89 | 1 | 1 | yes | characteristic |
| 365 | C2×#104 | — | 89 | 2 | no | — |
| 366 | C2×#104 | — | 89 | 2 | no | — |
| 367 | C2×#104 | — | 89 | 2 | no | — |
| 368 | #419 | — | 89 | 1 | no | — |
| 369 | #418 | — | 89 | 1 | no | — |
| 370 | C4×M16 | C2×D89 | 1 | 1 | yes | characteristic |
| 371 | #397 | — | 178 | 2 | no | — |
| 372 | #393 | — | 178 | 2 | no | — |
| 373 | #391 | — | 89 | 2 | no | — |
| 374 | #390 | — | 89 | 2 | no | — |
| 375 | #376 | — | 89 | 1 | no | — |
| 376 | #343 | C2×D89 | 1 | 2 | yes | — |
| 377 | #343 | C2×D89 | 1 | 2 | yes | — |
| 378 | #339 | — | 89 | 2 | no | — |
| 379 | C2×#41 | — | 89 | 1 | no | — |
| 380 | C2×#41 | — | 89 | 2 | no | — |
| 381 | C2×#41 | — | 178 | 2 | no | — |
| 382 | C22×Q8 | — | 89 | 1 | no | — |
| 383 | C22×Q8 | D356 | 1 | 2 | yes | — |
| 384 | C22×D4 | — | 89 | 1 | no | — |
| 385 | #137 | — | 356 | 2 | no | — |
| 386 | #137 | — | 356 | 2 | no | — |
| 387 | #137 | — | 178 | 4 | no | — |
| 388 | AGL(1,ℤ/8) | — | 356 | 2 | no | — |
| 389 | AGL(1,ℤ/8) | — | 356 | 2 | no | — |
| 390 | AGL(1,ℤ/8) | — | 178 | 4 | no | — |
| 391 | C2×Q16 | — | 178 | 1 | no | — |
| 392 | C2×Q16 | — | 178 | 2 | no | — |
| 393 | C2×SD16 | — | 178 | 1 | no | — |
| 394 | C2×SD16 | — | 178 | 2 | no | — |
| 395 | C2×SD16 | — | 178 | 1 | no | — |
| 396 | C2×SD16 | — | 178 | 2 | no | — |
| 397 | C2×D8 | — | 178 | 1 | no | — |
| 398 | C2×D8 | — | 178 | 2 | no | — |
| 399 | C2×M16 | C22×D89 | 1 | 1 | yes | characteristic |
| 400 | C2×M16 | C22×D89 | 1 | 1 | yes | characteristic |
| 401 | C2×M16 | C22×D89 | 1 | 2 | yes | — |
| 402 | C4⋊Q8 | — | 2 | 1 | no | — |
| 403 | C4⋊Q8 | — | 2 | 1 | no | — |
| 404 | C4⋊Q8 | — | 2 | 1 | no | — |
| 405 | C4⋊Q8 | — | 2 | 1 | no | — |
| 406 | C4⋊Q8 | — | 89 | 1 | no | — |
| 407 | #127 | — | 89 | 1 | no | — |
| 408 | #126 | — | 178 | 4 | no | — |
| 409 | #125 | — | 178 | 2 | no | — |
| 410 | #124 | — | 89 | 2 | no | — |
| 411 | #124 | — | 178 | 2 | no | — |
| 412 | #124 | — | 178 | 4 | no | — |
| 413 | #124 | — | 178 | 1 | no | — |
| 414 | #124 | — | 178 | 1 | no | — |
| 415 | #124 | — | 178 | 1 | no | — |
| 416 | #124 | — | 178 | 1 | no | — |
| 417 | #123 | — | 178 | 4 | no | — |
| 418 | C22⋊Q8 | — | 178 | 2 | no | — |
| 419 | C22⋊Q8 | — | 178 | 2 | no | — |
| 420 | C22⋊Q8 | — | 178 | 2 | no | — |
| 421 | C22⋊Q8 | — | 178 | 4 | no | — |
| 422 | #121 | — | 178 | 2 | no | — |
| 423 | #121 | — | 178 | 2 | no | — |
| 424 | #121 | — | 178 | 2 | no | — |
| 425 | #121 | — | 178 | 1 | no | — |
| 426 | #121 | — | 178 | 1 | no | — |
| 427 | #121 | — | 178 | 4 | no | — |
| 428 | C4×Q8 | — | 89 | 1 | no | — |
| 429 | C4×Q8 | — | 89 | 1 | no | — |
| 430 | C4×Q8 | — | 178 | 2 | no | — |
| 431 | C4×Q8 | — | 178 | 2 | no | — |
| 432 | C4×D4 | — | 89 | 1 | no | — |
| 433 | C4×D4 | — | 89 | 1 | no | — |
| 434 | C4×D4 | — | 178 | 2 | no | — |
| 435 | C4×D4 | — | 178 | 2 | no | — |
| 436 | C4×D4 | — | 178 | 1 | no | — |
| 437 | C4×D4 | — | 178 | 1 | no | — |
| 438 | C4×D4 | — | 178 | 4 | no | — |
| 439 | C4×D4 | — | 178 | 1 | no | — |
| 440 | C4×D4 | — | 178 | 1 | no | — |
| 441 | #117 | — | 89 | 1 | no | — |
| 442 | #117 | — | 178 | 2 | no | — |
| 443 | #117 | — | 178 | 2 | no | — |
| 444 | #117 | — | 178 | 1 | no | — |
| 445 | C2×C4⋊C4 | — | 178 | 2 | no | — |
| 446 | C2×C4⋊C4 | D356 | 1 | 2 | yes | — |
| 447 | C2×C4⋊C4 | C22×D89 | 1 | 2 | yes | — |
| 448 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 449 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 450 | C2×C22⋊C4 | — | 178 | 4 | no | — |
| 451 | C2×C42 | — | 89 | 2 | no | — |
| 452 | C2×C42 | — | 178 | 1 | no | — |
| 453 | C2×C42 | C22×D89 | 1 | 1 | yes | characteristic |
| 454 | C4⋊C8 | — | 2 | 1 | no | — |
| 455 | C4⋊C8 | — | 2 | 1 | no | — |
| 456 | #104 | — | 356 | 2 | no | — |
| 457 | #104 | — | 356 | 2 | no | — |
| 458 | #104 | — | 178 | 4 | no | — |
| 459 | #103 | — | 178 | 1 | no | — |
| 460 | #103 | — | 178 | 1 | no | — |
| 461 | #102 | — | 178 | 1 | no | — |
| 462 | #102 | — | 178 | 1 | no | — |
| 463 | #97 | — | 2 | 1 | no | — |
| 464 | C4×C8 | — | 2 | 1 | no | — |
| 465 | #95 | — | 178 | 1 | no | — |
| 466 | #95 | — | 178 | 1 | no | — |
| 467 | #95 | — | 178 | 4 | no | — |
| 468 | C24 | — | 178 | 1 | no | — |
| 469 | #41 | — | 178 | 2 | no | — |
| 470 | #41 | — | 178 | 2 | no | — |
| 471 | #41 | — | 178 | 2 | no | — |
| 472 | #41 | — | 178 | 2 | no | — |
| 473 | #41 | — | 178 | 2 | no | — |
| 474 | #41 | — | 178 | 2 | no | — |
| 475 | #41 | — | 712 | 4 | no | — |
| 476 | C2×Q8 | — | 2 | 2 | no | — |
| 477 | C2×Q8 | — | 2 | 2 | no | — |
| 478 | C2×Q8 | — | 8 | 2 | no | — |
| 479 | C2×Q8 | — | 89 | 1 | no | — |
| 480 | C2×Q8 | — | 89 | 2 | no | — |
| 481 | C2×Q8 | — | 178 | 1 | no | — |
| 482 | C2×Q8 | — | 178 | 1 | no | — |
| 483 | C2×Q8 | — | 178 | 2 | no | — |
| 484 | C2×Q8 | — | 178 | 2 | no | — |
| 485 | C2×D4 | — | 89 | 1 | no | — |
| 486 | C2×D4 | — | 89 | 2 | no | — |
| 487 | C2×D4 | — | 178 | 4 | no | — |
| 488 | C2×D4 | — | 178 | 1 | no | — |
| 489 | C2×D4 | — | 178 | 2 | no | — |
| 490 | C2×D4 | — | 178 | 1 | no | — |
| 491 | C2×D4 | — | 178 | 1 | no | — |
| 492 | C2×D4 | — | 178 | 1 | no | — |
| 493 | C2×D4 | — | 178 | 1 | no | — |
| 494 | C2×D4 | — | 178 | 2 | no | — |
| 495 | C2×D4 | — | 178 | 2 | no | — |
| 496 | C22×C4 | — | 178 | 4 | no | — |
| 497 | C22×C4 | — | 178 | 2 | no | — |
| 498 | C22×C4 | — | 178 | 1 | no | — |
| 499 | C22×C4 | — | 178 | 1 | no | — |
| 500 | C22×C4 | — | 178 | 1 | no | — |
| 501 | C22×C4 | — | 178 | 1 | no | — |
| 502 | C22×C4 | — | 178 | 2 | no | — |
| 503 | C22×C4 | C2×D356 | 1 | 4 | yes | — |
| 504 | C22×C4 | C2×D356 | 1 | 1 | yes | characteristic |
| 505 | C22×C4 | C2×D356 | 1 | 1 | yes | characteristic |
| 506 | C22×C4 | C23×D89 | 1 | 1 | yes | characteristic |
| 507 | Q16 | — | 356 | 4 | no | — |
| 508 | Q16 | — | 356 | 2 | no | — |
| 509 | SD16 | — | 356 | 4 | no | — |
| 510 | SD16 | — | 356 | 4 | no | — |
| 511 | SD16 | — | 356 | 2 | no | — |
| 512 | SD16 | — | 356 | 2 | no | — |
| 513 | D8 | — | 356 | 4 | no | — |
| 514 | D8 | — | 356 | 2 | no | — |
| 515 | M16 | — | 2 | 2 | no | — |
| 516 | M16 | — | 2 | 2 | no | — |
| 517 | M16 | — | 2 | 2 | no | — |
| 518 | M16 | #13083575 | 1 | 4 | yes | complemented |
| 519 | C2×C8 | — | 2 | 2 | no | — |
| 520 | C2×C8 | — | 2 | 1 | no | — |
| 521 | C2×C8 | — | 2 | 1 | no | — |
| 522 | C4⋊C4 | — | 2 | 2 | no | — |
| 523 | C4⋊C4 | — | 2 | 2 | no | — |
| 524 | C4⋊C4 | — | 2 | 2 | no | — |
| 525 | C4⋊C4 | — | 2 | 2 | no | — |
| 526 | C4⋊C4 | — | 89 | 1 | no | — |
| 527 | C4⋊C4 | — | 89 | 1 | no | — |
| 528 | C4⋊C4 | — | 178 | 4 | no | — |
| 529 | C4⋊C4 | — | 178 | 4 | no | — |
| 530 | C4⋊C4 | — | 178 | 1 | no | — |
| 531 | C4⋊C4 | — | 178 | 1 | no | — |
| 532 | C4⋊C4 | — | 178 | 1 | no | — |
| 533 | C4⋊C4 | — | 178 | 1 | no | — |
| 534 | C22⋊C4 | — | 356 | 1 | no | — |
| 535 | C22⋊C4 | — | 356 | 1 | no | — |
| 536 | C22⋊C4 | — | 356 | 1 | no | — |
| 537 | C22⋊C4 | — | 356 | 1 | no | — |
| 538 | C22⋊C4 | — | 178 | 4 | no | — |
| 539 | C22⋊C4 | — | 178 | 4 | no | — |
| 540 | C22⋊C4 | — | 178 | 4 | no | — |
| 541 | C22⋊C4 | — | 178 | 1 | no | — |
| 542 | C22⋊C4 | — | 178 | 1 | no | — |
| 543 | C22⋊C4 | — | 178 | 1 | no | — |
| 544 | C22⋊C4 | — | 178 | 2 | no | — |
| 545 | C22⋊C4 | — | 178 | 2 | no | — |
| 546 | C22⋊C4 | — | 712 | 4 | no | — |
| 547 | C42 | — | 178 | 4 | no | — |
| 548 | C42 | — | 178 | 2 | no | — |
| 549 | C42 | — | 178 | 2 | no | — |
| 550 | C42 | — | 178 | 1 | no | — |
| 551 | C42 | — | 178 | 1 | no | — |
| 552 | C42 | — | 178 | 1 | no | — |
| 553 | C42 | D4×D89 | 1 | 1 | yes | characteristic |
| 554 | C42 | D4×D89 | 1 | 1 | yes | characteristic |
| 555 | C42 | D4×D89 | 1 | 1 | yes | characteristic |
| 556 | C42 | D4×D89 | 1 | 1 | yes | characteristic |
| 557 | C23 | — | 356 | 2 | no | — |
| 558 | C23 | — | 356 | 2 | no | — |
| 559 | C23 | — | 356 | 2 | no | — |
| 560 | C23 | — | 356 | 1 | no | — |
| 561 | C23 | — | 178 | 1 | no | — |
| 562 | C23 | — | 178 | 2 | no | — |
| 563 | C23 | C22×D356 | 1 | 1 | yes | characteristic |
| 564 | Q8 | — | 4 | 4 | no | — |
| 565 | Q8 | — | 8 | 2 | no | — |
| 566 | Q8 | — | 356 | 1 | no | — |
| 567 | Q8 | — | 356 | 1 | no | — |
| 568 | Q8 | — | 356 | 2 | no | — |
| 569 | Q8 | — | 178 | 1 | no | — |
| 570 | Q8 | — | 178 | 1 | no | — |
| 571 | Q8 | — | 178 | 2 | no | — |
| 572 | Q8 | — | 178 | 2 | no | — |
| 573 | D4 | — | 356 | 2 | no | — |
| 574 | D4 | — | 356 | 2 | no | — |
| 575 | D4 | — | 356 | 2 | no | — |
| 576 | D4 | — | 356 | 2 | no | — |
| 577 | D4 | — | 356 | 2 | no | — |
| 578 | D4 | — | 356 | 1 | no | — |
| 579 | D4 | — | 356 | 1 | no | — |
| 580 | D4 | — | 356 | 2 | no | — |
| 581 | D4 | — | 178 | 1 | no | — |
| 582 | D4 | — | 178 | 1 | no | — |
| 583 | D4 | — | 178 | 2 | no | — |
| 584 | D4 | — | 178 | 2 | no | — |
| 585 | D4 | — | 712 | 4 | no | — |
| 586 | C2×C4 | — | 2 | 4 | no | — |
| 587 | C2×C4 | — | 4 | 1 | no | — |
| 588 | C2×C4 | — | 4 | 1 | no | — |
| 589 | C2×C4 | — | 4 | 4 | no | — |
| 590 | C2×C4 | — | 356 | 2 | no | — |
| 591 | C2×C4 | — | 356 | 2 | no | — |
| 592 | C2×C4 | — | 356 | 2 | no | — |
| 593 | C2×C4 | — | 356 | 2 | no | — |
| 594 | C2×C4 | — | 356 | 2 | no | — |
| 595 | C2×C4 | — | 356 | 2 | no | — |
| 596 | C2×C4 | — | 356 | 2 | no | — |
| 597 | C2×C4 | — | 356 | 2 | no | — |
| 598 | C2×C4 | — | 356 | 2 | no | — |
| 599 | C2×C4 | — | 356 | 1 | no | — |
| 600 | C2×C4 | — | 178 | 1 | no | — |
| 601 | C2×C4 | — | 178 | 2 | no | — |
| 602 | C2×C4 | — | 178 | 1 | no | — |
| 603 | C2×C4 | — | 178 | 1 | no | — |
| 604 | C2×C4 | — | 712 | 4 | no | — |
| 605 | C2×C4 | #15667982 | 1 | 1 | yes | characteristic |
| 606 | C2×C4 | #15667982 | 1 | 1 | yes | characteristic |
| 607 | C2×C4 | #15667982 | 1 | 1 | yes | characteristic |
| 608 | C2×C4 | #15667982 | 1 | 1 | yes | characteristic |
| 609 | C2×C4 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 610 | C2×C4 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 611 | C2×C4 | C2×#13083575 | 1 | 2 | yes | — |
| 612 | C2×C4 | #15668058 | 1 | 2 | yes | — |
| 613 | C8 | — | 2 | 4 | no | — |
| 614 | C8 | — | 4 | 1 | no | — |
| 615 | C8 | — | 4 | 1 | no | — |
| 616 | C22 | — | 2 | 1 | no | — |
| 617 | C22 | — | 2 | 1 | no | — |
| 618 | C22 | — | 356 | 1 | no | — |
| 619 | C22 | — | 356 | 2 | no | — |
| 620 | C22 | — | 356 | 1 | no | — |
| 621 | C22 | — | 356 | 2 | no | — |
| 622 | C22 | — | 356 | 2 | no | — |
| 623 | C22 | — | 356 | 1 | no | — |
| 624 | C22 | — | 712 | 4 | no | — |
| 625 | C22 | — | 712 | 1 | no | — |
| 626 | C22 | — | 712 | 1 | no | — |
| 627 | C22 | — | 712 | 1 | no | — |
| 628 | C22 | C2×#15667982 | 1 | 1 | yes | characteristic |
| 629 | C22 | #19152270 | 1 | 2 | yes | — |
| 630 | C4 | — | 2 | 1 | no | — |
| 631 | C4 | — | 2 | 1 | no | — |
| 632 | C4 | — | 2 | 1 | no | — |
| 633 | C4 | — | 2 | 1 | no | — |
| 634 | C4 | — | 4 | 4 | no | — |
| 635 | C4 | — | 356 | 1 | no | — |
| 636 | C4 | — | 356 | 1 | no | — |
| 637 | C4 | — | 356 | 2 | no | — |
| 638 | C4 | — | 356 | 1 | no | — |
| 639 | C4 | — | 712 | 2 | no | — |
| 640 | C4 | — | 712 | 1 | no | — |
| 641 | C4 | #19152149 | 1 | 1 | yes | characteristic |
| 642 | C4 | #19152166 | 1 | 1 | yes | characteristic |
| 643 | C4 | #19152239 | 1 | 2 | yes | — |
| 644 | C2 | — | 2 | 2 | no | — |
| 645 | C2 | — | 1424 | 1 | no | — |
| 646 | C2 | — | 712 | 1 | no | — |
| 647 | C2 | — | 712 | 2 | no | — |
| 648 | C2 | #26023873 | 1 | 1 | yes | characteristic |
| 649 | C2 | #26029612 | 1 | 1 | yes | characteristic |
| 650 | C2 | #26029619 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26034165 | C2 | semidirect |
| 2. #26030718 | C2 | semidirect |
| 3. #26029747 | C2 | semidirect |
| 4. #26026193 | C2 | semidirect |
| 5. #26021301 | C2 | semidirect |
| 6. #26021296 | C2 | semidirect |
| 7. #26021083 | C2 | semidirect |
| 8. #26020627 | C2 | semidirect |
| 9. #26020620 | C2 | semidirect |
| 10. #26020065 | C2 | semidirect |
| 11. C89×#1997 | C2 | semidirect |
| 219. M16×C89 | #41 | semidirect |
| 332. #1997 | D89 | semidirect |
| 337. C89 | #25618 | semidirect |
| 518. M16 | #13083575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034165 | 2 |
| #26030718 | 2 |
| #26029747 | 2 |
| #26026193 | 2 |
| #26021301 | 2 |
| #26021296 | 2 |
| #26021083 | 2 |
| #26020627 | 2 |
| #26020620 | 2 |
| #26020065 | 2 |
| C89×#1997 | 2 |
| #25618 | 89 |