Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1450 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1450 conjugacy classes of subgroups — too many to draw. Only its 187 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #26033887 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #26030185 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #26022834 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #26021463 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #26020698 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #26020464 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #26020208 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C89×#1783 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#15668057 | C22 | 1 | 1 | yes | characteristic |
| 10 | #19152242 | — | 2 | 4 | no | — |
| 11 | D4×C22⋊D89 | — | 2 | 4 | no | — |
| 12 | #19152165 | C22 | 1 | 2 | yes | — |
| 13 | #19152157 | — | 2 | 2 | no | — |
| 14 | #19152109 | C22 | 1 | 2 | yes | — |
| 15 | C2×#15667981 | — | 2 | 2 | no | — |
| 16 | #19152073 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#15667971 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C2×#15667971 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #19151940 | — | 2 | 4 | no | — |
| 20 | #19151923 | — | 2 | 4 | no | — |
| 21 | #19151640 | C22 | 1 | 4 | yes | complemented |
| 22 | C2×#15667938 | C22 | 1 | 4 | yes | complemented |
| 23 | #19151600 | C22 | 1 | 4 | yes | complemented |
| 24 | #19151501 | — | 2 | 2 | no | — |
| 25 | #19151501 | C22 | 1 | 2 | yes | — |
| 26 | #19151501 | C22 | 1 | 2 | yes | complemented |
| 27 | #19151454 | — | 2 | 2 | no | — |
| 28 | #19151359 | C22 | 1 | 4 | yes | complemented |
| 29 | C23×D4×C89 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×#100×C89 | C22 | 1 | 2 | yes | — |
| 31 | C2×#100×C89 | C22 | 1 | 2 | yes | complemented |
| 32 | #407×C89 | C22 | 1 | 2 | yes | complemented |
| 33 | #15668057 | — | 2 | 4 | no | — |
| 34 | #15668057 | — | 4 | 2 | no | — |
| 35 | C2×#13083574 | C23 | 1 | 2 | yes | — |
| 36 | C2×#13083573 | — | 2 | 2 | no | — |
| 37 | C22×C22⋊D89 | — | 2 | 4 | no | — |
| 38 | C22×C22⋊D89 | — | 2 | 2 | no | — |
| 39 | C2×D4×D89 | — | 2 | 2 | no | — |
| 40 | #15668008 | — | 2 | 2 | no | — |
| 41 | #15667999 | — | 2 | 2 | no | — |
| 42 | #15667995 | — | 2 | 2 | no | — |
| 43 | #15667993 | — | 2 | 4 | no | — |
| 44 | #15667991 | D4 | 1 | 4 | yes | — |
| 45 | #15667986 | D4 | 1 | 4 | yes | — |
| 46 | #15667984 | — | 2 | 8 | no | — |
| 47 | #15667983 | — | 2 | 4 | no | — |
| 48 | #15667981 | — | 2 | 8 | no | — |
| 49 | #15667981 | — | 2 | 4 | no | — |
| 50 | #15667981 | — | 2 | 2 | no | — |
| 51 | #15667980 | — | 2 | 4 | no | — |
| 52 | D4×Dic89 | — | 2 | 4 | no | — |
| 53 | C4×C22⋊D89 | — | 2 | 4 | no | — |
| 54 | #15667971 | — | 2 | 4 | no | — |
| 55 | #15667971 | — | 4 | 2 | no | — |
| 56 | #15667971 | C23 | 1 | 2 | yes | — |
| 57 | C2×C4⋊Dic89 | — | 2 | 1 | no | — |
| 58 | C2×C4⋊Dic89 | C23 | 1 | 2 | yes | — |
| 59 | C2×C22⋊Dic89 | — | 2 | 4 | no | — |
| 60 | C2×C22⋊Dic89 | — | 2 | 2 | no | — |
| 61 | C2×C22⋊Dic89 | — | 2 | 1 | no | — |
| 62 | C2×C22⋊Dic89 | — | 2 | 1 | no | — |
| 63 | C2×C22⋊Dic89 | — | 2 | 4 | no | — |
| 64 | C2×C22⋊Dic89 | — | 2 | 4 | no | — |
| 65 | C2×C4×Dic89 | — | 2 | 1 | no | — |
| 66 | C2×C4×Dic89 | C23 | 1 | 2 | yes | — |
| 67 | #15667946 | — | 2 | 4 | no | — |
| 68 | #15667944 | — | 2 | 4 | no | — |
| 69 | #15667938 | — | 4 | 4 | no | — |
| 70 | #15667937 | — | 2 | 4 | no | — |
| 71 | #15667934 | — | 2 | 4 | no | — |
| 72 | C25×C89 | D4 | 1 | 2 | yes | — |
| 73 | C22×D4×C89 | — | 2 | 4 | no | — |
| 74 | C22×D4×C89 | — | 2 | 4 | no | — |
| 75 | C22×D4×C89 | — | 4 | 2 | no | — |
| 76 | C22×D4×C89 | D4 | 1 | 2 | yes | — |
| 77 | C22×D4×C89 | C23 | 1 | 1 | yes | characteristic |
| 78 | C22×D4×C89 | C23 | 1 | 1 | yes | characteristic |
| 79 | C23×C4×C89 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×M16×C89 | C23 | 1 | 4 | yes | — |
| 81 | #100×C89 | — | 2 | 4 | no | — |
| 82 | #100×C89 | — | 4 | 2 | no | — |
| 83 | C22⋊C8×C89 | — | 2 | 4 | no | — |
| 84 | C23×D89 | — | 2 | 2 | no | — |
| 85 | #13083574 | — | 2 | 4 | no | — |
| 86 | #13083574 | — | 2 | 4 | no | — |
| 87 | #13083573 | — | 4 | 8 | no | — |
| 88 | C2×Dic178 | C2×D4 | 1 | 2 | yes | — |
| 89 | C2×D356 | C2×D4 | 1 | 2 | yes | — |
| 90 | C2×C22⋊D89 | — | 2 | 4 | no | — |
| 91 | C2×C22⋊D89 | — | 2 | 4 | no | — |
| 92 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 93 | C2×C22⋊D89 | — | 2 | 8 | no | — |
| 94 | C2×C22⋊D89 | — | 4 | 4 | no | — |
| 95 | C2×C22⋊D89 | — | 4 | 4 | no | — |
| 96 | C2×C22⋊D89 | — | 8 | 8 | no | — |
| 97 | D4×D89 | — | 4 | 8 | no | — |
| 98 | C22×Dic89 | — | 2 | 2 | no | — |
| 99 | C22×Dic89 | — | 2 | 4 | no | — |
| 100 | C22×Dic89 | — | 2 | 2 | no | — |
| 101 | C22×Dic89 | — | 2 | 2 | no | — |
| 102 | C2×C4×D89 | — | 2 | 2 | no | — |
| 103 | C4⋊Dic89 | — | 2 | 4 | no | — |
| 104 | C4⋊Dic89 | — | 4 | 2 | no | — |
| 105 | C4⋊Dic89 | C2×D4 | 1 | 4 | yes | — |
| 106 | #13083553 | — | 2 | 4 | no | — |
| 107 | C22⋊Dic89 | — | 2 | 4 | no | — |
| 108 | C22⋊Dic89 | — | 2 | 8 | no | — |
| 109 | C22⋊Dic89 | — | 2 | 4 | no | — |
| 110 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 111 | C22⋊Dic89 | — | 4 | 2 | no | — |
| 112 | C22⋊Dic89 | — | 4 | 2 | no | — |
| 113 | C22⋊Dic89 | — | 8 | 4 | no | — |
| 114 | C22⋊Dic89 | — | 8 | 4 | no | — |
| 115 | #13083551 | — | 2 | 4 | no | — |
| 116 | C4×Dic89 | — | 2 | 2 | no | — |
| 117 | C4×Dic89 | — | 2 | 4 | no | — |
| 118 | C4×Dic89 | — | 4 | 2 | no | — |
| 119 | C24×C89 | — | 2 | 4 | no | — |
| 120 | C24×C89 | — | 2 | 4 | no | — |
| 121 | C24×C89 | — | 4 | 2 | no | — |
| 122 | C24×C89 | — | 8 | 4 | no | — |
| 123 | C24×C89 | C2×D4 | 1 | 2 | yes | — |
| 124 | C24×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 125 | C24×C89 | C2×D4 | 1 | 2 | yes | — |
| 126 | C2×D4×C89 | — | 2 | 4 | no | — |
| 127 | C2×D4×C89 | — | 2 | 4 | no | — |
| 128 | C2×D4×C89 | — | 2 | 2 | no | — |
| 129 | C2×D4×C89 | — | 2 | 2 | no | — |
| 130 | C2×D4×C89 | — | 2 | 2 | no | — |
| 131 | C2×D4×C89 | — | 2 | 2 | no | — |
| 132 | C2×D4×C89 | — | 2 | 2 | no | — |
| 133 | C2×D4×C89 | — | 4 | 16 | no | — |
| 134 | C2×D4×C89 | — | 4 | 2 | no | — |
| 135 | C2×D4×C89 | #41 | 1 | 4 | yes | — |
| 136 | C22×C4×C89 | — | 2 | 2 | no | — |
| 137 | C22×C4×C89 | — | 2 | 2 | no | — |
| 138 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C22×C4×C89 | C2×D4 | 1 | 4 | yes | — |
| 140 | C22×C4×C89 | C24 | 1 | 1 | yes | characteristic |
| 141 | M16×C89 | — | 2 | 4 | no | — |
| 142 | M16×C89 | — | 2 | 4 | no | — |
| 143 | C2×C8×C89 | — | 2 | 4 | no | — |
| 144 | C23×C89 | — | 2 | 2 | no | — |
| 145 | C23×C89 | — | 2 | 1 | no | — |
| 146 | C23×C89 | — | 2 | 1 | no | — |
| 147 | C23×C89 | — | 2 | 2 | no | — |
| 148 | C23×C89 | — | 2 | 2 | no | — |
| 149 | C23×C89 | — | 2 | 2 | no | — |
| 150 | C23×C89 | — | 2 | 2 | no | — |
| 151 | C23×C89 | — | 4 | 2 | no | — |
| 152 | C23×C89 | — | 4 | 8 | no | — |
| 153 | C23×C89 | — | 4 | 4 | no | — |
| 154 | C23×C89 | — | 4 | 4 | no | — |
| 155 | C23×C89 | — | 4 | 8 | no | — |
| 156 | C23×C89 | — | 8 | 4 | no | — |
| 157 | C23×C89 | — | 8 | 8 | no | — |
| 158 | C23×C89 | — | 8 | 8 | no | — |
| 159 | C23×C89 | #120 | 1 | 2 | yes | — |
| 160 | C23×C89 | #123 | 1 | 4 | yes | — |
| 161 | C23×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 162 | C22×D89 | — | 2 | 2 | no | — |
| 163 | C22×D89 | — | 4 | 4 | no | — |
| 164 | C22×D89 | — | 8 | 4 | no | — |
| 165 | D4×C89 | — | 2 | 8 | no | — |
| 166 | D4×C89 | — | 4 | 8 | no | — |
| 167 | D4×C89 | — | 4 | 4 | no | — |
| 168 | C2×C4×C89 | — | 2 | 1 | no | — |
| 169 | C2×C4×C89 | — | 2 | 1 | no | — |
| 170 | C2×C4×C89 | — | 2 | 8 | no | — |
| 171 | C2×C4×C89 | #120 | 1 | 2 | yes | — |
| 172 | C2×C4×C89 | C22×D4 | 1 | 2 | yes | — |
| 173 | C2×C4×C89 | C2×#41 | 1 | 2 | yes | — |
| 174 | C2×C4×C89 | H(5,𝔽2) | 1 | 2 | yes | — |
| 175 | C22⋊D89 | — | 4 | 8 | no | — |
| 176 | C22⋊D89 | — | 4 | 8 | no | — |
| 177 | C22⋊D89 | — | 4 | 2 | no | — |
| 178 | C22⋊D89 | — | 4 | 2 | no | — |
| 179 | C22⋊D89 | — | 8 | 8 | no | — |
| 180 | C2×Dic89 | — | 2 | 4 | no | — |
| 181 | C2×Dic89 | — | 2 | 2 | no | — |
| 182 | C2×Dic89 | — | 4 | 4 | no | — |
| 183 | C2×Dic89 | — | 4 | 2 | no | — |
| 184 | C2×Dic89 | — | 4 | 2 | no | — |
| 185 | C2×Dic89 | — | 4 | 4 | no | — |
| 186 | C2×Dic89 | — | 4 | 2 | no | — |
| 187 | C2×Dic89 | — | 4 | 2 | no | — |
| 188 | C2×Dic89 | — | 8 | 4 | no | — |
| 189 | D356 | — | 2 | 4 | no | — |
| 190 | C4×D89 | — | 4 | 4 | no | — |
| 191 | Dic178 | — | 2 | 4 | no | — |
| 192 | C8×C89 | — | 4 | 4 | no | — |
| 193 | C22×C89 | — | 2 | 2 | no | — |
| 194 | C22×C89 | — | 2 | 4 | no | — |
| 195 | C22×C89 | — | 2 | 2 | no | — |
| 196 | C22×C89 | — | 2 | 2 | no | — |
| 197 | C22×C89 | — | 2 | 2 | no | — |
| 198 | C22×C89 | — | 4 | 2 | no | — |
| 199 | C22×C89 | — | 4 | 2 | no | — |
| 200 | C22×C89 | — | 4 | 4 | no | — |
| 201 | C22×C89 | — | 4 | 4 | no | — |
| 202 | C22×C89 | — | 4 | 4 | no | — |
| 203 | C22×C89 | — | 4 | 2 | no | — |
| 204 | C22×C89 | — | 4 | 4 | no | — |
| 205 | C22×C89 | — | 8 | 2 | no | — |
| 206 | C22×C89 | — | 8 | 2 | no | — |
| 207 | C22×C89 | — | 8 | 16 | no | — |
| 208 | C22×C89 | C2×#120 | 1 | 1 | yes | characteristic |
| 209 | C22×C89 | C2×#123 | 1 | 1 | yes | characteristic |
| 210 | C22×C89 | #534 | 1 | 1 | yes | characteristic |
| 211 | C2×D89 | — | 4 | 2 | no | — |
| 212 | C2×D89 | — | 4 | 4 | no | — |
| 213 | C2×D89 | — | 16 | 4 | no | — |
| 214 | C4×C89 | — | 2 | 2 | no | — |
| 215 | C4×C89 | #546 | 1 | 4 | yes | — |
| 216 | Dic89 | — | 4 | 2 | no | — |
| 217 | Dic89 | — | 4 | 4 | no | — |
| 218 | Dic89 | — | 8 | 2 | no | — |
| 219 | Dic89 | — | 8 | 2 | no | — |
| 220 | #24022 | — | 89 | 1 | no | maximal, Sylow |
| 221 | C2×C89 | — | 2 | 1 | no | — |
| 222 | C2×C89 | — | 2 | 1 | no | — |
| 223 | C2×C89 | — | 4 | 4 | no | — |
| 224 | C2×C89 | — | 4 | 2 | no | — |
| 225 | C2×C89 | — | 8 | 2 | no | — |
| 226 | C2×C89 | #2405 | 1 | 1 | yes | characteristic |
| 227 | C2×C89 | #3019 | 1 | 2 | yes | — |
| 228 | D89 | — | 8 | 2 | no | — |
| 229 | #3484 | — | 89 | 1 | no | — |
| 230 | #3093 | — | 89 | 2 | no | — |
| 231 | #2309 | — | 89 | 1 | no | — |
| 232 | #2037 | — | 89 | 4 | no | — |
| 233 | #1897 | — | 89 | 2 | no | — |
| 234 | #1856 | — | 89 | 2 | no | — |
| 235 | #1792 | — | 89 | 2 | no | — |
| 236 | #1783 | D89 | 1 | 1 | yes | characteristic, complemented |
| 237 | C89 | #24022 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 238 | C2×H(5,𝔽2) | — | 89 | 1 | no | — |
| 239 | C23×D4 | C2×D89 | 1 | 1 | yes | characteristic |
| 240 | #546 | — | 178 | 4 | no | — |
| 241 | D42 | — | 178 | 4 | no | — |
| 242 | #535 | — | 89 | 2 | no | — |
| 243 | #534 | — | 178 | 2 | no | — |
| 244 | #525 | — | 89 | 2 | no | — |
| 245 | C2×#120 | — | 178 | 2 | no | — |
| 246 | #518 | — | 89 | 1 | no | — |
| 247 | C2×#117 | — | 89 | 1 | no | — |
| 248 | C2×#117 | — | 89 | 1 | no | — |
| 249 | #485 | — | 178 | 4 | no | — |
| 250 | #482 | — | 178 | 4 | no | — |
| 251 | #428 | — | 89 | 4 | no | — |
| 252 | C2×#104 | — | 89 | 4 | no | — |
| 253 | #417 | — | 89 | 4 | no | — |
| 254 | C2×#100 | C2×D89 | 1 | 2 | yes | — |
| 255 | C2×#100 | C2×D89 | 1 | 2 | yes | complemented |
| 256 | #407 | C2×D89 | 1 | 2 | yes | complemented |
| 257 | #390 | — | 89 | 2 | no | — |
| 258 | #390 | — | 89 | 2 | no | — |
| 259 | #390 | — | 178 | 2 | no | — |
| 260 | #379 | — | 178 | 2 | no | — |
| 261 | #339 | — | 89 | 4 | no | — |
| 262 | C25 | D356 | 1 | 2 | yes | — |
| 263 | H(5,𝔽2) | — | 356 | 2 | no | — |
| 264 | H(5,𝔽2) | — | 178 | 4 | no | — |
| 265 | C2×#41 | — | 89 | 2 | no | — |
| 266 | C2×#41 | — | 178 | 2 | no | — |
| 267 | C22×D4 | — | 2 | 4 | no | — |
| 268 | C22×D4 | — | 2 | 4 | no | — |
| 269 | C22×D4 | — | 4 | 2 | no | — |
| 270 | C22×D4 | — | 178 | 2 | no | — |
| 271 | C22×D4 | — | 178 | 2 | no | — |
| 272 | C22×D4 | — | 178 | 4 | no | — |
| 273 | C22×D4 | D356 | 1 | 2 | yes | — |
| 274 | C22×D4 | C22×D89 | 1 | 1 | yes | characteristic |
| 275 | C22×D4 | C22×D89 | 1 | 1 | yes | characteristic |
| 276 | C23×C4 | C22×D89 | 1 | 1 | yes | characteristic |
| 277 | C2×M16 | C22×D89 | 1 | 4 | yes | — |
| 278 | #127 | — | 178 | 2 | no | — |
| 279 | #124 | — | 178 | 2 | no | — |
| 280 | #123 | — | 178 | 4 | no | — |
| 281 | #123 | — | 178 | 2 | no | — |
| 282 | C22⋊Q8 | — | 89 | 4 | no | — |
| 283 | #121 | — | 89 | 4 | no | — |
| 284 | #121 | — | 178 | 4 | no | — |
| 285 | #121 | — | 178 | 8 | no | — |
| 286 | #120 | — | 178 | 4 | no | — |
| 287 | #120 | — | 178 | 8 | no | — |
| 288 | #120 | — | 178 | 2 | no | — |
| 289 | #120 | — | 178 | 4 | no | — |
| 290 | C4×D4 | — | 178 | 4 | no | — |
| 291 | C4×D4 | — | 178 | 4 | no | — |
| 292 | #117 | — | 89 | 2 | no | — |
| 293 | #117 | — | 356 | 2 | no | — |
| 294 | #117 | — | 178 | 4 | no | — |
| 295 | C2×C4⋊C4 | — | 89 | 2 | no | — |
| 296 | C2×C4⋊C4 | — | 178 | 1 | no | — |
| 297 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 298 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 299 | C2×C22⋊C4 | — | 178 | 4 | no | — |
| 300 | C2×C22⋊C4 | — | 178 | 2 | no | — |
| 301 | C2×C22⋊C4 | — | 178 | 4 | no | — |
| 302 | C2×C22⋊C4 | — | 178 | 4 | no | — |
| 303 | C2×C42 | — | 89 | 2 | no | — |
| 304 | C2×C42 | — | 178 | 1 | no | — |
| 305 | #107 | — | 178 | 4 | no | — |
| 306 | #106 | — | 178 | 4 | no | — |
| 307 | #104 | — | 356 | 4 | no | — |
| 308 | #103 | — | 178 | 4 | no | — |
| 309 | #102 | — | 178 | 4 | no | — |
| 310 | #100 | — | 2 | 4 | no | — |
| 311 | #100 | — | 4 | 2 | no | — |
| 312 | C22⋊C8 | — | 2 | 4 | no | — |
| 313 | C24 | — | 2 | 4 | no | — |
| 314 | C24 | — | 2 | 4 | no | — |
| 315 | C24 | — | 4 | 2 | no | — |
| 316 | C24 | — | 8 | 4 | no | — |
| 317 | C24 | — | 178 | 2 | no | — |
| 318 | C24 | C2×D356 | 1 | 2 | yes | — |
| 319 | C24 | C2×D356 | 1 | 1 | yes | characteristic |
| 320 | C24 | C2×D356 | 1 | 2 | yes | — |
| 321 | #41 | — | 356 | 8 | no | — |
| 322 | #41 | — | 178 | 4 | no | — |
| 323 | #41 | — | 178 | 4 | no | — |
| 324 | C2×Q8 | — | 89 | 2 | no | — |
| 325 | C2×D4 | — | 2 | 4 | no | — |
| 326 | C2×D4 | — | 2 | 4 | no | — |
| 327 | C2×D4 | — | 2 | 2 | no | — |
| 328 | C2×D4 | — | 2 | 2 | no | — |
| 329 | C2×D4 | — | 2 | 2 | no | — |
| 330 | C2×D4 | — | 2 | 2 | no | — |
| 331 | C2×D4 | — | 2 | 2 | no | — |
| 332 | C2×D4 | — | 4 | 16 | no | — |
| 333 | C2×D4 | — | 4 | 2 | no | — |
| 334 | C2×D4 | — | 89 | 2 | no | — |
| 335 | C2×D4 | — | 356 | 8 | no | — |
| 336 | C2×D4 | — | 356 | 4 | no | — |
| 337 | C2×D4 | — | 356 | 4 | no | — |
| 338 | C2×D4 | — | 178 | 4 | no | — |
| 339 | C2×D4 | — | 178 | 4 | no | — |
| 340 | C2×D4 | — | 178 | 2 | no | — |
| 341 | C2×D4 | — | 178 | 8 | no | — |
| 342 | C2×D4 | — | 712 | 8 | no | — |
| 343 | C2×D4 | #13083573 | 1 | 4 | yes | — |
| 344 | C22×C4 | — | 2 | 2 | no | — |
| 345 | C22×C4 | — | 2 | 2 | no | — |
| 346 | C22×C4 | — | 178 | 2 | no | — |
| 347 | C22×C4 | — | 178 | 2 | no | — |
| 348 | C22×C4 | — | 178 | 2 | no | — |
| 349 | C22×C4 | — | 178 | 2 | no | — |
| 350 | C22×C4 | — | 178 | 4 | no | — |
| 351 | C22×C4 | D4×D89 | 1 | 4 | yes | — |
| 352 | C22×C4 | C2×D356 | 1 | 1 | yes | characteristic |
| 353 | C22×C4 | C23×D89 | 1 | 1 | yes | characteristic |
| 354 | M16 | — | 2 | 4 | no | — |
| 355 | M16 | — | 2 | 4 | no | — |
| 356 | C2×C8 | — | 2 | 4 | no | — |
| 357 | C4⋊C4 | — | 89 | 4 | no | — |
| 358 | C4⋊C4 | — | 356 | 2 | no | — |
| 359 | C4⋊C4 | — | 178 | 4 | no | — |
| 360 | C4⋊C4 | — | 178 | 4 | no | — |
| 361 | C22⋊C4 | — | 356 | 2 | no | — |
| 362 | C22⋊C4 | — | 356 | 2 | no | — |
| 363 | C22⋊C4 | — | 178 | 4 | no | — |
| 364 | C22⋊C4 | — | 178 | 8 | no | — |
| 365 | C22⋊C4 | — | 178 | 4 | no | — |
| 366 | C22⋊C4 | — | 178 | 2 | no | — |
| 367 | C22⋊C4 | — | 178 | 4 | no | — |
| 368 | C22⋊C4 | — | 712 | 4 | no | — |
| 369 | C22⋊C4 | — | 712 | 4 | no | — |
| 370 | C42 | — | 356 | 2 | no | — |
| 371 | C42 | — | 178 | 4 | no | — |
| 372 | C42 | — | 178 | 2 | no | — |
| 373 | C23 | — | 2 | 1 | no | — |
| 374 | C23 | — | 2 | 2 | no | — |
| 375 | C23 | — | 2 | 1 | no | — |
| 376 | C23 | — | 2 | 2 | no | — |
| 377 | C23 | — | 2 | 2 | no | — |
| 378 | C23 | — | 2 | 2 | no | — |
| 379 | C23 | — | 2 | 2 | no | — |
| 380 | C23 | — | 4 | 2 | no | — |
| 381 | C23 | — | 4 | 8 | no | — |
| 382 | C23 | — | 4 | 4 | no | — |
| 383 | C23 | — | 4 | 4 | no | — |
| 384 | C23 | — | 4 | 8 | no | — |
| 385 | C23 | — | 8 | 4 | no | — |
| 386 | C23 | — | 8 | 8 | no | — |
| 387 | C23 | — | 8 | 8 | no | — |
| 388 | C23 | — | 356 | 4 | no | — |
| 389 | C23 | — | 178 | 2 | no | — |
| 390 | C23 | — | 712 | 4 | no | — |
| 391 | C23 | #15667982 | 1 | 2 | yes | — |
| 392 | C23 | #15667996 | 1 | 4 | yes | — |
| 393 | C23 | C22×D356 | 1 | 1 | yes | characteristic |
| 394 | Q8 | — | 178 | 4 | no | — |
| 395 | D4 | — | 2 | 8 | no | — |
| 396 | D4 | — | 4 | 8 | no | — |
| 397 | D4 | — | 4 | 4 | no | — |
| 398 | D4 | — | 356 | 8 | no | — |
| 399 | D4 | — | 356 | 8 | no | — |
| 400 | D4 | — | 356 | 2 | no | — |
| 401 | D4 | — | 356 | 2 | no | — |
| 402 | D4 | — | 178 | 4 | no | — |
| 403 | D4 | — | 712 | 8 | no | — |
| 404 | C2×C4 | — | 2 | 1 | no | — |
| 405 | C2×C4 | — | 2 | 1 | no | — |
| 406 | C2×C4 | — | 2 | 8 | no | — |
| 407 | C2×C4 | — | 356 | 4 | no | — |
| 408 | C2×C4 | — | 356 | 4 | no | — |
| 409 | C2×C4 | — | 356 | 2 | no | — |
| 410 | C2×C4 | — | 356 | 2 | no | — |
| 411 | C2×C4 | — | 356 | 4 | no | — |
| 412 | C2×C4 | — | 356 | 2 | no | — |
| 413 | C2×C4 | — | 356 | 2 | no | — |
| 414 | C2×C4 | — | 178 | 4 | no | — |
| 415 | C2×C4 | — | 178 | 2 | no | — |
| 416 | C2×C4 | — | 712 | 4 | no | — |
| 417 | C2×C4 | #15667982 | 1 | 2 | yes | — |
| 418 | C2×C4 | C2×D4×D89 | 1 | 2 | yes | — |
| 419 | C2×C4 | C2×#13083573 | 1 | 2 | yes | — |
| 420 | C2×C4 | #15668057 | 1 | 2 | yes | — |
| 421 | C8 | — | 4 | 4 | no | — |
| 422 | C22 | — | 2 | 2 | no | — |
| 423 | C22 | — | 2 | 2 | no | — |
| 424 | C22 | — | 2 | 2 | no | — |
| 425 | C22 | — | 2 | 2 | no | — |
| 426 | C22 | — | 2 | 4 | no | — |
| 427 | C22 | — | 4 | 4 | no | — |
| 428 | C22 | — | 4 | 2 | no | — |
| 429 | C22 | — | 4 | 2 | no | — |
| 430 | C22 | — | 4 | 4 | no | — |
| 431 | C22 | — | 4 | 4 | no | — |
| 432 | C22 | — | 4 | 4 | no | — |
| 433 | C22 | — | 4 | 2 | no | — |
| 434 | C22 | — | 8 | 2 | no | — |
| 435 | C22 | — | 8 | 2 | no | — |
| 436 | C22 | — | 8 | 16 | no | — |
| 437 | C22 | — | 356 | 4 | no | — |
| 438 | C22 | — | 356 | 2 | no | — |
| 439 | C22 | — | 1424 | 4 | no | — |
| 440 | C22 | C2×#15667982 | 1 | 1 | yes | characteristic |
| 441 | C22 | C2×#15667996 | 1 | 1 | yes | characteristic |
| 442 | C22 | #19152160 | 1 | 1 | yes | characteristic |
| 443 | C4 | — | 2 | 2 | no | — |
| 444 | C4 | — | 356 | 4 | no | — |
| 445 | C4 | — | 356 | 2 | no | — |
| 446 | C4 | — | 712 | 2 | no | — |
| 447 | C4 | — | 712 | 2 | no | — |
| 448 | C4 | #19152235 | 1 | 4 | yes | — |
| 449 | C2 | — | 2 | 1 | no | — |
| 450 | C2 | — | 2 | 1 | no | — |
| 451 | C2 | — | 4 | 2 | no | — |
| 452 | C2 | — | 4 | 4 | no | — |
| 453 | C2 | — | 8 | 2 | no | — |
| 454 | C2 | — | 712 | 2 | no | — |
| 455 | C2 | #26023580 | 1 | 1 | yes | characteristic |
| 456 | C2 | #26029612 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #26030185 | C2 | semidirect |
| 3. #26022834 | C2 | semidirect |
| 4. #26021463 | C2 | semidirect |
| 5. #26020698 | C2 | semidirect |
| 6. #26020464 | C2 | semidirect |
| 7. #26020208 | C2 | semidirect |
| 8. C89×#1783 | C2 | semidirect |
| 17. C2×#15667971 | C22 | semidirect |
| 18. C2×#15667971 | C22 | semidirect |
| 21. #19151640 | C22 | semidirect |
| 22. C2×#15667938 | C22 | semidirect |
| 23. #19151600 | C22 | semidirect |
| 26. #19151501 | C22 | semidirect |
| 28. #19151359 | C22 | semidirect |
| 31. C2×#100×C89 | C22 | semidirect |
| 32. #407×C89 | C22 | semidirect |
| 236. #1783 | D89 | semidirect |
| 237. C89 | #24022 | semidirect |
| 255. C2×#100 | C2×D89 | semidirect |
| 256. #407 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033887 | 2 |
| #26030185 | 2 |
| #26022834 | 2 |
| #26021463 | 2 |
| #26020698 | 2 |
| #26020464 | 2 |
| #26020208 | 2 |
| C89×#1783 | 2 |
| #24022 | 89 |