Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1036 conjugacy classes of subgroups.
The subgroup lattice has 674 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #26034771 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #26031239 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #26030950 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #26030698 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #26019572 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #26019560 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #26019546 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #26019542 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #26018870 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #26018862 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C2×#329×C89 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#15668034 | — | 2 | 2 | no | — |
| 13 | #19152342 | C22 | 1 | 2 | yes | — |
| 14 | #19152340 | C22 | 1 | 2 | yes | — |
| 15 | #19152330 | — | 2 | 1 | no | — |
| 16 | #19152259 | — | 2 | 1 | no | — |
| 17 | #19152241 | — | 2 | 1 | no | — |
| 18 | #19152238 | — | 2 | 2 | no | — |
| 19 | D4×C22⋊D89 | — | 2 | 1 | no | — |
| 20 | #19152217 | — | 2 | 1 | no | — |
| 21 | #19152186 | — | 2 | 1 | no | — |
| 22 | #19152182 | — | 2 | 2 | no | — |
| 23 | #19152166 | — | 2 | 1 | no | — |
| 24 | #19152160 | — | 2 | 1 | no | — |
| 25 | #19152148 | C22 | 1 | 1 | yes | characteristic |
| 26 | #19152148 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #19152132 | C22 | 1 | 1 | yes | characteristic |
| 28 | #19152007 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #19151992 | — | 2 | 1 | no | — |
| 30 | #19151992 | C22 | 1 | 2 | yes | complemented |
| 31 | #19151988 | C22 | 1 | 2 | yes | complemented |
| 32 | #19151987 | — | 2 | 1 | no | — |
| 33 | #19151987 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #19151987 | C22 | 1 | 2 | yes | complemented |
| 35 | #19151963 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #19151958 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #19151957 | C22 | 1 | 2 | yes | complemented |
| 38 | #19151834 | — | 2 | 1 | no | — |
| 39 | #19151827 | — | 2 | 1 | no | — |
| 40 | #19151810 | — | 2 | 2 | no | — |
| 41 | #19151737 | — | 2 | 1 | no | — |
| 42 | #19151732 | — | 2 | 1 | no | — |
| 43 | #19151711 | — | 2 | 1 | no | — |
| 44 | #19151700 | — | 2 | 1 | no | — |
| 45 | #19151655 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #19151339 | C22 | 1 | 2 | yes | complemented |
| 47 | #19151337 | C22 | 1 | 2 | yes | complemented |
| 48 | #19151337 | C22 | 1 | 2 | yes | complemented |
| 49 | #19151337 | C22 | 1 | 2 | yes | complemented |
| 50 | C2×#124×C89 | C22 | 1 | 1 | yes | characteristic |
| 51 | C2×#97×C89 | C22 | 1 | 1 | yes | characteristic, complemented |
| 52 | C2×#97×C89 | C22 | 1 | 1 | yes | characteristic, complemented |
| 53 | #329×C89 | C22 | 1 | 2 | yes | complemented |
| 54 | #329×C89 | C22 | 1 | 2 | yes | complemented |
| 55 | C2×#13083575 | — | 2 | 1 | no | — |
| 56 | C2×#13083574 | — | 2 | 1 | no | — |
| 57 | C2×#13083574 | D4 | 1 | 2 | yes | — |
| 58 | C22×C22⋊D89 | — | 2 | 2 | no | — |
| 59 | C2×D4×D89 | — | 2 | 1 | no | — |
| 60 | #15668034 | — | 4 | 8 | no | — |
| 61 | C2×Dic356 | — | 2 | 2 | no | — |
| 62 | C2×#13083563 | — | 2 | 1 | no | — |
| 63 | C2×#13083563 | — | 2 | 2 | no | — |
| 64 | C2×#13083563 | — | 2 | 2 | no | — |
| 65 | C2×#13083561 | — | 2 | 2 | no | — |
| 66 | C2×D712 | — | 2 | 1 | no | — |
| 67 | C2×D712 | — | 2 | 2 | no | — |
| 68 | C2×#13083559 | — | 2 | 2 | no | — |
| 69 | #15668012 | D4 | 1 | 1 | yes | characteristic |
| 70 | #15668012 | C23 | 1 | 1 | yes | characteristic |
| 71 | #15668009 | D4 | 1 | 1 | yes | characteristic |
| 72 | #15668009 | C23 | 1 | 1 | yes | characteristic |
| 73 | #15668008 | — | 2 | 1 | no | — |
| 74 | #15668006 | — | 2 | 1 | no | — |
| 75 | #15668005 | — | 2 | 2 | no | — |
| 76 | #15668004 | C23 | 1 | 1 | yes | characteristic |
| 77 | #15668001 | — | 2 | 1 | no | — |
| 78 | #15668001 | — | 2 | 2 | no | — |
| 79 | #15668000 | — | 2 | 1 | no | — |
| 80 | #15668000 | C23 | 1 | 1 | yes | characteristic |
| 81 | #15668000 | C23 | 1 | 2 | yes | — |
| 82 | #15667998 | — | 2 | 2 | no | — |
| 83 | #15667998 | — | 2 | 2 | no | — |
| 84 | #15667996 | — | 2 | 2 | no | — |
| 85 | #15667996 | — | 2 | 2 | no | — |
| 86 | #15667995 | — | 2 | 1 | no | — |
| 87 | #15667994 | — | 2 | 2 | no | — |
| 88 | #15667994 | — | 2 | 2 | no | — |
| 89 | #15667991 | D4 | 1 | 1 | yes | characteristic |
| 90 | #15667989 | — | 2 | 2 | no | — |
| 91 | #15667988 | — | 2 | 1 | no | — |
| 92 | #15667988 | — | 2 | 2 | no | — |
| 93 | #15667986 | — | 2 | 2 | no | — |
| 94 | #15667986 | — | 2 | 1 | no | — |
| 95 | #15667986 | — | 2 | 1 | no | — |
| 96 | #15667986 | — | 2 | 1 | no | — |
| 97 | #15667986 | — | 2 | 1 | no | — |
| 98 | #15667986 | D4 | 1 | 1 | yes | characteristic |
| 99 | #15667985 | — | 2 | 2 | no | — |
| 100 | #15667985 | — | 2 | 2 | no | — |
| 101 | #15667985 | — | 2 | 2 | no | — |
| 102 | #15667984 | — | 2 | 2 | no | — |
| 103 | #15667983 | — | 2 | 1 | no | — |
| 104 | #15667982 | — | 2 | 2 | no | — |
| 105 | #15667982 | — | 2 | 2 | no | — |
| 106 | #15667982 | — | 2 | 2 | no | — |
| 107 | #15667981 | — | 2 | 2 | no | — |
| 108 | #15667980 | — | 2 | 2 | no | — |
| 109 | Q8×Dic89 | — | 2 | 1 | no | — |
| 110 | C4×Dic178 | D4 | 1 | 1 | yes | characteristic |
| 111 | C4×D356 | — | 2 | 1 | no | — |
| 112 | C4×D356 | — | 2 | 1 | no | — |
| 113 | C4×D356 | — | 2 | 1 | no | — |
| 114 | C4×D356 | — | 2 | 1 | no | — |
| 115 | C4×D356 | D4 | 1 | 1 | yes | characteristic |
| 116 | D4×Dic89 | — | 2 | 1 | no | — |
| 117 | C4×C22⋊D89 | — | 2 | 2 | no | — |
| 118 | C4×C22⋊D89 | — | 2 | 1 | no | — |
| 119 | #15667972 | — | 2 | 2 | no | — |
| 120 | #15667969 | — | 2 | 1 | no | — |
| 121 | C22⋊C4×D89 | — | 2 | 2 | no | — |
| 122 | #15667946 | — | 2 | 1 | no | — |
| 123 | #15667944 | — | 2 | 1 | no | — |
| 124 | C4⋊#10623494 | — | 2 | 1 | no | — |
| 125 | #15667937 | — | 2 | 1 | no | — |
| 126 | #15667936 | — | 2 | 2 | no | — |
| 127 | #15667934 | — | 2 | 1 | no | — |
| 128 | #15667934 | — | 2 | 1 | no | — |
| 129 | #15667934 | — | 2 | 1 | no | — |
| 130 | #15667933 | — | 2 | 2 | no | — |
| 131 | C22⋊#10623494 | — | 2 | 1 | no | — |
| 132 | #15667923 | C23 | 1 | 2 | yes | — |
| 133 | C22×Q8×C89 | D4 | 1 | 1 | yes | characteristic |
| 134 | C22×D4×C89 | D4 | 1 | 1 | yes | characteristic |
| 135 | C22×C8×C89 | — | 2 | 1 | no | — |
| 136 | C22×C8×C89 | — | 2 | 1 | no | — |
| 137 | #124×C89 | — | 2 | 1 | no | — |
| 138 | #124×C89 | — | 2 | 1 | no | — |
| 139 | #124×C89 | D4 | 1 | 2 | yes | — |
| 140 | #124×C89 | C23 | 1 | 2 | yes | — |
| 141 | C2×C22⋊C4×C89 | — | 2 | 1 | no | — |
| 142 | C2×C22⋊C4×C89 | — | 2 | 1 | no | — |
| 143 | C2×C42×C89 | C23 | 1 | 1 | yes | characteristic |
| 144 | #97×C89 | — | 2 | 1 | no | — |
| 145 | #97×C89 | — | 2 | 1 | no | — |
| 146 | #97×C89 | C23 | 1 | 1 | yes | characteristic |
| 147 | #97×C89 | C23 | 1 | 2 | yes | — |
| 148 | #97×C89 | C23 | 1 | 1 | yes | characteristic |
| 149 | C23×D89 | — | 2 | 2 | no | — |
| 150 | #13083575 | — | 8 | 2 | no | — |
| 151 | #13083574 | — | 4 | 4 | no | — |
| 152 | #13083574 | — | 4 | 4 | no | — |
| 153 | C2×Dic178 | — | 2 | 1 | no | — |
| 154 | C2×Dic178 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C2×Dic178 | C2×D4 | 1 | 2 | yes | — |
| 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 | 1 | no | — |
| 162 | C2×D356 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | C2×D356 | C2×D4 | 1 | 2 | yes | — |
| 164 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 165 | C2×C22⋊D89 | — | 2 | 1 | no | — |
| 166 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 167 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 168 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 169 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 170 | C2×C22⋊D89 | — | 4 | 1 | no | — |
| 171 | C2×C22⋊D89 | — | 8 | 4 | no | — |
| 172 | D4×D89 | — | 8 | 2 | no | — |
| 173 | C22×Dic89 | — | 2 | 2 | no | — |
| 174 | C2×C4×D89 | — | 2 | 1 | no | — |
| 175 | C2×C4×D89 | — | 2 | 2 | no | — |
| 176 | C2×C4×D89 | — | 2 | 2 | no | — |
| 177 | C2×C4×D89 | — | 4 | 1 | no | — |
| 178 | Dic356 | — | 4 | 4 | no | — |
| 179 | #13083563 | — | 4 | 2 | no | — |
| 180 | #13083563 | — | 4 | 4 | no | — |
| 181 | #13083563 | — | 4 | 4 | no | — |
| 182 | #13083561 | — | 8 | 2 | no | — |
| 183 | D712 | — | 4 | 2 | no | — |
| 184 | D712 | — | 4 | 4 | no | — |
| 185 | #13083559 | — | 8 | 2 | no | — |
| 186 | C2×#10623494 | — | 2 | 2 | no | — |
| 187 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 188 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 189 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 190 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 191 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 192 | C4⋊Dic89 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C4⋊Dic89 | C2×D4 | 1 | 1 | yes | characteristic |
| 194 | #13083553 | — | 2 | 2 | no | — |
| 195 | #13083553 | — | 2 | 1 | no | — |
| 196 | #13083553 | — | 2 | 1 | no | — |
| 197 | #13083553 | — | 2 | 1 | no | — |
| 198 | #13083553 | — | 2 | 1 | no | — |
| 199 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 200 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 201 | C22⋊Dic89 | — | 2 | 1 | no | — |
| 202 | #13083551 | — | 2 | 2 | no | — |
| 203 | #13083551 | — | 2 | 2 | no | — |
| 204 | #13083551 | — | 2 | 2 | no | — |
| 205 | #13083551 | — | 2 | 1 | no | — |
| 206 | #13083551 | — | 2 | 1 | no | — |
| 207 | #13083551 | — | 2 | 1 | no | — |
| 208 | #13083551 | — | 2 | 1 | no | — |
| 209 | #13083551 | — | 2 | 2 | no | — |
| 210 | #13083551 | — | 2 | 2 | no | — |
| 211 | #13083551 | — | 4 | 1 | no | — |
| 212 | #13083551 | — | 4 | 1 | no | — |
| 213 | C4×Dic89 | — | 2 | 2 | no | — |
| 214 | C4×Dic89 | — | 2 | 1 | no | — |
| 215 | C24×C89 | — | 2 | 1 | no | — |
| 216 | C2×Q8×C89 | — | 2 | 1 | no | — |
| 217 | C2×Q8×C89 | — | 8 | 1 | no | — |
| 218 | C2×Q8×C89 | C2×D4 | 1 | 2 | yes | — |
| 219 | C2×D4×C89 | — | 2 | 1 | no | — |
| 220 | C2×D4×C89 | — | 8 | 1 | no | — |
| 221 | C2×D4×C89 | C2×D4 | 1 | 2 | yes | — |
| 222 | C22×C4×C89 | — | 2 | 1 | no | — |
| 223 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 224 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 225 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 226 | C2×C8×C89 | — | 2 | 4 | no | — |
| 227 | C2×C8×C89 | — | 2 | 2 | no | — |
| 228 | C2×C8×C89 | — | 2 | 1 | no | — |
| 229 | C2×C8×C89 | — | 2 | 1 | no | — |
| 230 | C2×C8×C89 | — | 4 | 2 | no | — |
| 231 | C22⋊C4×C89 | — | 2 | 2 | no | — |
| 232 | C22⋊C4×C89 | — | 2 | 2 | no | — |
| 233 | C22⋊C4×C89 | — | 2 | 2 | no | — |
| 234 | C22⋊C4×C89 | — | 2 | 2 | no | — |
| 235 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 236 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | C42×C89 | C24 | 1 | 1 | yes | characteristic |
| 239 | C23×C89 | — | 2 | 2 | no | — |
| 240 | C23×C89 | — | 4 | 2 | no | — |
| 241 | C23×C89 | — | 8 | 1 | no | — |
| 242 | C23×C89 | — | 8 | 1 | no | — |
| 243 | C23×C89 | #120 | 1 | 1 | yes | characteristic |
| 244 | C22×D89 | — | 2 | 1 | no | — |
| 245 | C22×D89 | — | 2 | 2 | no | — |
| 246 | C22×D89 | — | 4 | 1 | no | — |
| 247 | C22×D89 | — | 8 | 2 | no | — |
| 248 | C22×D89 | — | 8 | 2 | no | — |
| 249 | C22×D89 | — | 8 | 2 | no | — |
| 250 | Q8×C89 | — | 4 | 2 | no | — |
| 251 | Q8×C89 | — | 4 | 2 | no | — |
| 252 | D4×C89 | — | 4 | 2 | no | — |
| 253 | D4×C89 | — | 4 | 2 | no | — |
| 254 | C2×C4×C89 | — | 2 | 2 | no | — |
| 255 | C2×C4×C89 | — | 2 | 2 | no | — |
| 256 | C2×C4×C89 | — | 4 | 1 | no | — |
| 257 | C2×C4×C89 | — | 4 | 1 | no | — |
| 258 | C2×C4×C89 | — | 8 | 1 | no | — |
| 259 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 260 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 261 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 262 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 263 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 264 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 265 | C22⋊D89 | — | 4 | 2 | no | — |
| 266 | C22⋊D89 | — | 4 | 4 | no | — |
| 267 | C22⋊D89 | — | 8 | 2 | no | — |
| 268 | C22⋊D89 | — | 8 | 2 | no | — |
| 269 | C22⋊D89 | — | 8 | 2 | no | — |
| 270 | C22⋊D89 | — | 8 | 2 | no | — |
| 271 | C22⋊D89 | — | 8 | 2 | no | — |
| 272 | C2×Dic89 | — | 2 | 1 | no | — |
| 273 | C2×Dic89 | — | 2 | 2 | no | — |
| 274 | C2×Dic89 | — | 2 | 1 | no | — |
| 275 | C2×Dic89 | — | 2 | 1 | no | — |
| 276 | C2×Dic89 | — | 4 | 1 | no | — |
| 277 | C2×Dic89 | — | 8 | 2 | no | — |
| 278 | D356 | — | 4 | 2 | no | — |
| 279 | D356 | — | 4 | 1 | no | — |
| 280 | D356 | — | 4 | 2 | no | — |
| 281 | D356 | — | 4 | 2 | no | — |
| 282 | D356 | — | 4 | 2 | no | — |
| 283 | D356 | — | 4 | 1 | no | — |
| 284 | D356 | — | 4 | 1 | no | — |
| 285 | D356 | — | 8 | 1 | no | — |
| 286 | D356 | — | 8 | 2 | no | — |
| 287 | C4×D89 | — | 4 | 2 | no | — |
| 288 | C4×D89 | — | 8 | 2 | no | — |
| 289 | C4×D89 | — | 8 | 2 | no | — |
| 290 | C4×D89 | — | 8 | 2 | no | — |
| 291 | Dic178 | — | 4 | 2 | no | — |
| 292 | Dic178 | — | 4 | 1 | no | — |
| 293 | Dic178 | — | 4 | 2 | no | — |
| 294 | C8×C89 | — | 2 | 4 | no | — |
| 295 | C8×C89 | — | 2 | 2 | no | — |
| 296 | C8×C89 | — | 4 | 1 | no | — |
| 297 | #10623494 | — | 4 | 2 | no | — |
| 298 | C22×C89 | — | 2 | 1 | no | — |
| 299 | C22×C89 | — | 2 | 1 | no | — |
| 300 | C22×C89 | — | 4 | 2 | no | — |
| 301 | C22×C89 | — | 4 | 2 | no | — |
| 302 | C22×C89 | — | 4 | 2 | no | — |
| 303 | C22×C89 | — | 16 | 2 | no | — |
| 304 | C22×C89 | #453 | 1 | 2 | yes | — |
| 305 | C22×C89 | C2×#120 | 1 | 1 | yes | characteristic |
| 306 | C2×D89 | — | 4 | 2 | no | — |
| 307 | C2×D89 | — | 4 | 1 | no | — |
| 308 | C2×D89 | — | 4 | 1 | no | — |
| 309 | C2×D89 | — | 4 | 2 | no | — |
| 310 | C2×D89 | — | 4 | 1 | no | — |
| 311 | C2×D89 | — | 4 | 2 | no | — |
| 312 | C2×D89 | — | 8 | 1 | no | — |
| 313 | C2×D89 | — | 8 | 1 | no | — |
| 314 | C2×D89 | — | 8 | 1 | no | — |
| 315 | C2×D89 | — | 16 | 4 | no | — |
| 316 | C4×C89 | — | 2 | 1 | no | — |
| 317 | C4×C89 | — | 2 | 1 | no | — |
| 318 | C4×C89 | — | 2 | 1 | no | — |
| 319 | C4×C89 | — | 2 | 1 | no | — |
| 320 | C4×C89 | — | 2 | 1 | no | — |
| 321 | C4×C89 | — | 2 | 1 | no | — |
| 322 | C4×C89 | — | 4 | 2 | no | — |
| 323 | Dic89 | — | 4 | 2 | no | — |
| 324 | Dic89 | — | 4 | 1 | no | — |
| 325 | Dic89 | — | 4 | 1 | no | — |
| 326 | Dic89 | — | 4 | 1 | no | — |
| 327 | Dic89 | — | 8 | 1 | no | — |
| 328 | #19042 | — | 89 | 1 | no | maximal, Sylow |
| 329 | C2×C89 | — | 2 | 2 | no | — |
| 330 | C2×C89 | — | 8 | 2 | no | — |
| 331 | C2×C89 | C2×#453 | 1 | 1 | yes | characteristic |
| 332 | C2×C89 | #3018 | 1 | 1 | yes | characteristic |
| 333 | C2×C89 | #3019 | 1 | 1 | yes | characteristic |
| 334 | D89 | — | 8 | 2 | no | — |
| 335 | D89 | — | 8 | 1 | no | — |
| 336 | D89 | — | 16 | 1 | no | — |
| 337 | #3558 | — | 89 | 1 | no | — |
| 338 | #3213 | — | 89 | 1 | no | — |
| 339 | #3180 | — | 89 | 1 | no | — |
| 340 | #3150 | — | 89 | 1 | no | — |
| 341 | #1661 | — | 89 | 2 | no | — |
| 342 | #1659 | — | 89 | 2 | no | — |
| 343 | #1656 | — | 89 | 2 | no | — |
| 344 | #1655 | — | 89 | 2 | no | — |
| 345 | #1532 | — | 89 | 1 | no | — |
| 346 | #1530 | — | 89 | 1 | no | — |
| 347 | C2×#329 | D89 | 1 | 1 | yes | characteristic, complemented |
| 348 | C89 | #19042 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 349 | C2×#135 | — | 178 | 2 | no | — |
| 350 | #562 | — | 89 | 2 | no | — |
| 351 | H(3,𝔽4) | — | 89 | 2 | no | — |
| 352 | #559 | — | 178 | 1 | no | — |
| 353 | #548 | — | 178 | 1 | no | — |
| 354 | #546 | — | 178 | 2 | no | — |
| 355 | #546 | — | 178 | 1 | no | — |
| 356 | D42 | — | 178 | 1 | no | — |
| 357 | #542 | — | 178 | 1 | no | — |
| 358 | #538 | — | 178 | 1 | no | — |
| 359 | #538 | — | 178 | 2 | no | — |
| 360 | #535 | — | 178 | 1 | no | — |
| 361 | #534 | — | 178 | 1 | no | — |
| 362 | #532 | — | 89 | 1 | no | — |
| 363 | #532 | — | 89 | 1 | no | — |
| 364 | #529 | — | 89 | 1 | no | — |
| 365 | C2×#124 | C2×D89 | 1 | 1 | yes | characteristic |
| 366 | #501 | — | 89 | 1 | no | — |
| 367 | #497 | — | 89 | 2 | no | — |
| 368 | #497 | — | 178 | 1 | no | — |
| 369 | #496 | — | 89 | 2 | no | — |
| 370 | #496 | — | 89 | 2 | no | — |
| 371 | #496 | — | 89 | 1 | no | — |
| 372 | #496 | — | 178 | 1 | no | — |
| 373 | #490 | — | 89 | 1 | no | — |
| 374 | #489 | — | 89 | 2 | no | — |
| 375 | #489 | — | 89 | 1 | no | — |
| 376 | #466 | — | 178 | 1 | no | — |
| 377 | #465 | — | 178 | 1 | no | — |
| 378 | #463 | — | 178 | 2 | no | — |
| 379 | #448 | — | 178 | 1 | no | — |
| 380 | #447 | — | 178 | 1 | no | — |
| 381 | #442 | — | 178 | 1 | no | — |
| 382 | #440 | — | 178 | 1 | no | — |
| 383 | #432 | — | 89 | 1 | no | — |
| 384 | C2×#97 | C2×D89 | 1 | 1 | yes | characteristic, complemented |
| 385 | C2×#97 | C2×D89 | 1 | 1 | yes | characteristic, complemented |
| 386 | #330 | — | 89 | 2 | no | — |
| 387 | #329 | — | 89 | 2 | no | — |
| 388 | #329 | — | 89 | 2 | no | — |
| 389 | #329 | — | 89 | 2 | no | — |
| 390 | #329 | C2×D89 | 1 | 2 | yes | complemented |
| 391 | #329 | C2×D89 | 1 | 2 | yes | complemented |
| 392 | C2×#41 | — | 89 | 2 | no | — |
| 393 | C2×#41 | — | 178 | 1 | no | — |
| 394 | C2×#41 | — | 178 | 1 | no | — |
| 395 | C22×Q8 | D356 | 1 | 1 | yes | characteristic |
| 396 | C22×D4 | — | 178 | 1 | no | — |
| 397 | C22×D4 | — | 178 | 2 | no | — |
| 398 | C22×D4 | D356 | 1 | 1 | yes | characteristic |
| 399 | #135 | — | 356 | 8 | no | — |
| 400 | C2×Q16 | — | 178 | 2 | no | — |
| 401 | C2×SD16 | — | 178 | 2 | no | — |
| 402 | C2×SD16 | — | 178 | 2 | no | — |
| 403 | C2×SD16 | — | 178 | 1 | no | — |
| 404 | C2×SD16 | — | 178 | 2 | no | — |
| 405 | C2×D8 | — | 178 | 2 | no | — |
| 406 | C2×D8 | — | 178 | 1 | no | — |
| 407 | C2×D8 | — | 178 | 2 | no | — |
| 408 | C22×C8 | — | 2 | 1 | no | — |
| 409 | C22×C8 | — | 2 | 1 | no | — |
| 410 | C4⋊Q8 | — | 89 | 1 | no | — |
| 411 | C4⋊Q8 | — | 89 | 1 | no | — |
| 412 | #127 | — | 89 | 1 | no | — |
| 413 | #127 | — | 89 | 1 | no | — |
| 414 | #127 | — | 178 | 1 | no | — |
| 415 | #126 | — | 178 | 2 | no | — |
| 416 | #126 | — | 178 | 1 | no | — |
| 417 | #125 | — | 89 | 1 | no | — |
| 418 | #124 | — | 2 | 1 | no | — |
| 419 | #124 | — | 2 | 1 | no | — |
| 420 | #124 | — | 89 | 1 | no | — |
| 421 | #124 | — | 89 | 2 | no | — |
| 422 | #124 | — | 178 | 2 | no | — |
| 423 | #124 | — | 178 | 2 | no | — |
| 424 | #124 | — | 178 | 1 | no | — |
| 425 | #124 | — | 178 | 2 | no | — |
| 426 | #124 | — | 178 | 1 | no | — |
| 427 | #124 | D356 | 1 | 2 | yes | — |
| 428 | #124 | C22×D89 | 1 | 2 | yes | — |
| 429 | #123 | — | 178 | 2 | no | — |
| 430 | #123 | — | 178 | 2 | no | — |
| 431 | #123 | — | 178 | 2 | no | — |
| 432 | #123 | — | 178 | 2 | no | — |
| 433 | #123 | — | 178 | 1 | no | — |
| 434 | C22⋊Q8 | — | 89 | 1 | no | — |
| 435 | C22⋊Q8 | — | 178 | 2 | no | — |
| 436 | C22⋊Q8 | — | 178 | 1 | no | — |
| 437 | C22⋊Q8 | — | 178 | 2 | no | — |
| 438 | #121 | — | 89 | 1 | no | — |
| 439 | #121 | — | 178 | 2 | no | — |
| 440 | #121 | — | 178 | 2 | no | — |
| 441 | #121 | — | 178 | 2 | no | — |
| 442 | #121 | — | 178 | 1 | no | — |
| 443 | #121 | — | 178 | 1 | no | — |
| 444 | #121 | — | 178 | 2 | no | — |
| 445 | #121 | — | 178 | 1 | no | — |
| 446 | #121 | — | 178 | 2 | no | — |
| 447 | #121 | — | 178 | 1 | no | — |
| 448 | #121 | — | 178 | 1 | no | — |
| 449 | #120 | — | 178 | 2 | no | — |
| 450 | #120 | — | 178 | 2 | no | — |
| 451 | #120 | — | 178 | 2 | no | — |
| 452 | #120 | — | 178 | 2 | no | — |
| 453 | #120 | — | 178 | 2 | no | — |
| 454 | C4×Q8 | — | 89 | 1 | no | — |
| 455 | C4×Q8 | — | 178 | 1 | no | — |
| 456 | C4×D4 | — | 89 | 1 | no | — |
| 457 | C4×D4 | — | 178 | 2 | no | — |
| 458 | C4×D4 | — | 178 | 2 | no | — |
| 459 | C4×D4 | — | 178 | 1 | no | — |
| 460 | C4×D4 | — | 178 | 1 | no | — |
| 461 | C4×D4 | — | 178 | 1 | no | — |
| 462 | C4×D4 | — | 178 | 1 | no | — |
| 463 | C4×D4 | — | 178 | 1 | no | — |
| 464 | C4×D4 | — | 178 | 1 | no | — |
| 465 | #117 | — | 178 | 1 | no | — |
| 466 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 467 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 468 | C2×C22⋊C4 | — | 178 | 2 | no | — |
| 469 | C2×C42 | C22×D89 | 1 | 1 | yes | characteristic |
| 470 | #107 | — | 178 | 1 | no | — |
| 471 | #106 | — | 178 | 1 | no | — |
| 472 | C4⋊C8 | — | 178 | 1 | no | — |
| 473 | #103 | — | 178 | 1 | no | — |
| 474 | #103 | — | 178 | 2 | no | — |
| 475 | #102 | — | 178 | 1 | no | — |
| 476 | #102 | — | 178 | 1 | no | — |
| 477 | #102 | — | 178 | 1 | no | — |
| 478 | #102 | — | 178 | 2 | no | — |
| 479 | C22⋊C8 | — | 178 | 1 | no | — |
| 480 | #97 | — | 2 | 1 | no | — |
| 481 | #97 | — | 2 | 1 | no | — |
| 482 | #97 | — | 89 | 2 | no | — |
| 483 | #97 | C22×D89 | 1 | 1 | yes | characteristic |
| 484 | #97 | C22×D89 | 1 | 1 | yes | characteristic |
| 485 | #97 | C22×D89 | 1 | 2 | yes | — |
| 486 | C24 | — | 2 | 1 | no | — |
| 487 | C24 | — | 178 | 2 | no | — |
| 488 | #41 | — | 356 | 4 | no | — |
| 489 | #41 | — | 356 | 4 | no | — |
| 490 | #41 | — | 712 | 2 | no | — |
| 491 | C2×Q8 | — | 2 | 1 | no | — |
| 492 | C2×Q8 | — | 8 | 1 | no | — |
| 493 | C2×Q8 | — | 89 | 1 | no | — |
| 494 | C2×Q8 | — | 89 | 2 | no | — |
| 495 | C2×Q8 | — | 178 | 1 | no | — |
| 496 | C2×Q8 | C2×D356 | 1 | 2 | yes | — |
| 497 | C2×D4 | — | 2 | 1 | no | — |
| 498 | C2×D4 | — | 8 | 1 | no | — |
| 499 | C2×D4 | — | 89 | 1 | no | — |
| 500 | C2×D4 | — | 89 | 2 | no | — |
| 501 | C2×D4 | — | 356 | 1 | no | — |
| 502 | C2×D4 | — | 178 | 2 | no | — |
| 503 | C2×D4 | — | 178 | 2 | no | — |
| 504 | C2×D4 | — | 178 | 1 | no | — |
| 505 | C2×D4 | — | 178 | 2 | no | — |
| 506 | C2×D4 | — | 178 | 2 | no | — |
| 507 | C2×D4 | — | 178 | 2 | no | — |
| 508 | C2×D4 | — | 178 | 2 | no | — |
| 509 | C2×D4 | — | 178 | 1 | no | — |
| 510 | C2×D4 | — | 178 | 1 | no | — |
| 511 | C2×D4 | — | 178 | 1 | no | — |
| 512 | C2×D4 | — | 178 | 1 | no | — |
| 513 | C2×D4 | — | 178 | 1 | no | — |
| 514 | C2×D4 | — | 712 | 2 | no | — |
| 515 | C2×D4 | — | 712 | 4 | no | — |
| 516 | C2×D4 | C2×D356 | 1 | 2 | yes | — |
| 517 | C22×C4 | — | 2 | 1 | no | — |
| 518 | C22×C4 | — | 356 | 1 | no | — |
| 519 | C22×C4 | — | 178 | 2 | no | — |
| 520 | C22×C4 | — | 178 | 1 | no | — |
| 521 | C22×C4 | — | 178 | 2 | no | — |
| 522 | C22×C4 | — | 178 | 2 | no | — |
| 523 | C22×C4 | D4×D89 | 1 | 1 | yes | characteristic |
| 524 | C22×C4 | D4×D89 | 1 | 1 | yes | characteristic |
| 525 | C22×C4 | C2×D356 | 1 | 1 | yes | characteristic |
| 526 | Q16 | — | 356 | 4 | no | — |
| 527 | SD16 | — | 356 | 4 | no | — |
| 528 | SD16 | — | 356 | 4 | no | — |
| 529 | SD16 | — | 356 | 2 | no | — |
| 530 | SD16 | — | 712 | 2 | no | — |
| 531 | D8 | — | 356 | 4 | no | — |
| 532 | D8 | — | 356 | 2 | no | — |
| 533 | D8 | — | 712 | 2 | no | — |
| 534 | C2×C8 | — | 2 | 4 | no | — |
| 535 | C2×C8 | — | 2 | 1 | no | — |
| 536 | C2×C8 | — | 2 | 2 | no | — |
| 537 | C2×C8 | — | 2 | 1 | no | — |
| 538 | C2×C8 | — | 4 | 2 | no | — |
| 539 | C2×C8 | — | 178 | 2 | no | — |
| 540 | C4⋊C4 | — | 89 | 1 | no | — |
| 541 | C4⋊C4 | — | 89 | 1 | no | — |
| 542 | C4⋊C4 | — | 178 | 2 | no | — |
| 543 | C4⋊C4 | — | 178 | 2 | no | — |
| 544 | C4⋊C4 | — | 178 | 1 | no | — |
| 545 | C4⋊C4 | — | 178 | 1 | no | — |
| 546 | C4⋊C4 | — | 178 | 1 | no | — |
| 547 | C4⋊C4 | — | 178 | 1 | no | — |
| 548 | C4⋊C4 | — | 178 | 1 | no | — |
| 549 | C4⋊C4 | — | 178 | 1 | no | — |
| 550 | C4⋊C4 | — | 178 | 1 | no | — |
| 551 | C4⋊C4 | — | 178 | 1 | no | — |
| 552 | C22⋊C4 | — | 2 | 2 | no | — |
| 553 | C22⋊C4 | — | 2 | 2 | no | — |
| 554 | C22⋊C4 | — | 2 | 2 | no | — |
| 555 | C22⋊C4 | — | 2 | 2 | no | — |
| 556 | C22⋊C4 | — | 356 | 1 | no | — |
| 557 | C22⋊C4 | — | 356 | 1 | no | — |
| 558 | C22⋊C4 | — | 178 | 2 | no | — |
| 559 | C22⋊C4 | — | 178 | 2 | no | — |
| 560 | C22⋊C4 | — | 178 | 2 | no | — |
| 561 | C22⋊C4 | — | 178 | 2 | no | — |
| 562 | C22⋊C4 | — | 178 | 2 | no | — |
| 563 | C22⋊C4 | — | 178 | 1 | no | — |
| 564 | C22⋊C4 | — | 178 | 1 | no | — |
| 565 | C22⋊C4 | — | 178 | 1 | no | — |
| 566 | C22⋊C4 | — | 178 | 1 | no | — |
| 567 | C22⋊C4 | — | 178 | 2 | no | — |
| 568 | C22⋊C4 | — | 178 | 1 | no | — |
| 569 | C22⋊C4 | — | 178 | 2 | no | — |
| 570 | C42 | — | 178 | 2 | no | — |
| 571 | C42 | — | 178 | 1 | no | — |
| 572 | C42 | D4×D89 | 1 | 1 | yes | characteristic |
| 573 | C42 | D4×D89 | 1 | 1 | yes | characteristic |
| 574 | C42 | C2×D356 | 1 | 1 | yes | characteristic |
| 575 | C42 | C23×D89 | 1 | 1 | yes | characteristic |
| 576 | C23 | — | 2 | 2 | no | — |
| 577 | C23 | — | 4 | 2 | no | — |
| 578 | C23 | — | 8 | 1 | no | — |
| 579 | C23 | — | 8 | 1 | no | — |
| 580 | C23 | — | 356 | 1 | no | — |
| 581 | C23 | — | 178 | 1 | no | — |
| 582 | C23 | — | 178 | 2 | no | — |
| 583 | C23 | — | 712 | 2 | no | — |
| 584 | C23 | — | 712 | 2 | no | — |
| 585 | C23 | — | 712 | 2 | no | — |
| 586 | C23 | #15667982 | 1 | 1 | yes | characteristic |
| 587 | Q8 | — | 4 | 2 | no | — |
| 588 | Q8 | — | 4 | 2 | no | — |
| 589 | Q8 | — | 356 | 2 | no | — |
| 590 | Q8 | — | 356 | 1 | no | — |
| 591 | Q8 | — | 356 | 2 | no | — |
| 592 | D4 | — | 4 | 2 | no | — |
| 593 | D4 | — | 4 | 2 | no | — |
| 594 | D4 | — | 356 | 2 | no | — |
| 595 | D4 | — | 356 | 1 | no | — |
| 596 | D4 | — | 356 | 2 | no | — |
| 597 | D4 | — | 356 | 2 | no | — |
| 598 | D4 | — | 356 | 1 | no | — |
| 599 | D4 | — | 356 | 2 | no | — |
| 600 | D4 | — | 356 | 1 | no | — |
| 601 | D4 | — | 356 | 2 | no | — |
| 602 | D4 | — | 356 | 4 | no | — |
| 603 | D4 | — | 712 | 1 | no | — |
| 604 | D4 | — | 712 | 2 | no | — |
| 605 | D4 | — | 712 | 2 | no | — |
| 606 | D4 | — | 712 | 2 | no | — |
| 607 | D4 | — | 712 | 2 | no | — |
| 608 | D4 | — | 712 | 2 | no | — |
| 609 | D4 | — | 712 | 2 | no | — |
| 610 | C2×C4 | — | 2 | 2 | no | — |
| 611 | C2×C4 | — | 2 | 2 | no | — |
| 612 | C2×C4 | — | 4 | 1 | no | — |
| 613 | C2×C4 | — | 4 | 1 | no | — |
| 614 | C2×C4 | — | 8 | 1 | no | — |
| 615 | C2×C4 | — | 356 | 2 | no | — |
| 616 | C2×C4 | — | 356 | 1 | no | — |
| 617 | C2×C4 | — | 178 | 1 | no | — |
| 618 | C2×C4 | — | 178 | 2 | no | — |
| 619 | C2×C4 | — | 178 | 1 | no | — |
| 620 | C2×C4 | — | 178 | 1 | no | — |
| 621 | C2×C4 | — | 712 | 2 | no | — |
| 622 | C2×C4 | — | 712 | 2 | no | — |
| 623 | C2×C4 | — | 712 | 2 | no | — |
| 624 | C2×C4 | — | 712 | 2 | no | — |
| 625 | C2×C4 | #15667982 | 1 | 1 | yes | characteristic |
| 626 | C2×C4 | #15667982 | 1 | 1 | yes | characteristic |
| 627 | C2×C4 | #15667982 | 1 | 1 | yes | characteristic |
| 628 | C2×C4 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 629 | C2×C4 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 630 | C2×C4 | C22×D356 | 1 | 1 | yes | characteristic |
| 631 | C8 | — | 2 | 4 | no | — |
| 632 | C8 | — | 2 | 2 | no | — |
| 633 | C8 | — | 4 | 1 | no | — |
| 634 | C8 | — | 356 | 2 | no | — |
| 635 | C22 | — | 2 | 1 | no | — |
| 636 | C22 | — | 2 | 1 | no | — |
| 637 | C22 | — | 4 | 2 | no | — |
| 638 | C22 | — | 4 | 2 | no | — |
| 639 | C22 | — | 4 | 2 | no | — |
| 640 | C22 | — | 16 | 2 | no | — |
| 641 | C22 | — | 356 | 2 | no | — |
| 642 | C22 | — | 356 | 1 | no | — |
| 643 | C22 | — | 356 | 1 | no | — |
| 644 | C22 | — | 356 | 2 | no | — |
| 645 | C22 | — | 356 | 1 | no | — |
| 646 | C22 | — | 356 | 2 | no | — |
| 647 | C22 | — | 1424 | 4 | no | — |
| 648 | C22 | — | 712 | 1 | no | — |
| 649 | C22 | — | 712 | 1 | no | — |
| 650 | C22 | — | 712 | 1 | no | — |
| 651 | C22 | #19151767 | 1 | 2 | yes | — |
| 652 | C22 | C2×#15667982 | 1 | 1 | yes | characteristic |
| 653 | C4 | — | 2 | 1 | no | — |
| 654 | C4 | — | 2 | 1 | no | — |
| 655 | C4 | — | 2 | 1 | no | — |
| 656 | C4 | — | 2 | 1 | no | — |
| 657 | C4 | — | 2 | 1 | no | — |
| 658 | C4 | — | 2 | 1 | no | — |
| 659 | C4 | — | 4 | 2 | no | — |
| 660 | C4 | — | 356 | 1 | no | — |
| 661 | C4 | — | 356 | 2 | no | — |
| 662 | C4 | — | 356 | 1 | no | — |
| 663 | C4 | — | 356 | 1 | no | — |
| 664 | C4 | — | 712 | 1 | no | — |
| 665 | C2 | — | 2 | 2 | no | — |
| 666 | C2 | — | 8 | 2 | no | — |
| 667 | C2 | — | 1424 | 1 | no | — |
| 668 | C2 | — | 712 | 2 | no | — |
| 669 | C2 | — | 712 | 1 | no | — |
| 670 | C2 | C2×#19151767 | 1 | 1 | yes | characteristic |
| 671 | C2 | #26029603 | 1 | 1 | yes | characteristic |
| 672 | C2 | #26029612 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26034771 | C2 | semidirect |
| 2. #26031239 | C2 | semidirect |
| 3. #26030950 | C2 | semidirect |
| 4. #26030698 | C2 | semidirect |
| 5. #26019572 | C2 | semidirect |
| 6. #26019560 | C2 | semidirect |
| 7. #26019546 | C2 | semidirect |
| 8. #26019542 | C2 | semidirect |
| 9. #26018870 | C2 | semidirect |
| 10. #26018862 | C2 | semidirect |
| 11. C2×#329×C89 | C2 | semidirect |
| 26. #19152148 | C22 | semidirect |
| 28. #19152007 | C22 | semidirect |
| 30. #19151992 | C22 | semidirect |
| 31. #19151988 | C22 | semidirect |
| 33. #19151987 | C22 | semidirect |
| 34. #19151987 | C22 | semidirect |
| 35. #19151963 | C22 | semidirect |
| 36. #19151958 | C22 | semidirect |
| 37. #19151957 | C22 | semidirect |
| 45. #19151655 | C22 | semidirect |
| 46. #19151339 | C22 | semidirect |
| 47. #19151337 | C22 | semidirect |
| 48. #19151337 | C22 | semidirect |
| 49. #19151337 | C22 | semidirect |
| 51. C2×#97×C89 | C22 | semidirect |
| 52. C2×#97×C89 | C22 | semidirect |
| 53. #329×C89 | C22 | semidirect |
| 54. #329×C89 | C22 | semidirect |
| 347. C2×#329 | D89 | semidirect |
| 348. C89 | #19042 | semidirect |
| 384. C2×#97 | C2×D89 | semidirect |
| 385. C2×#97 | C2×D89 | semidirect |
| 390. #329 | C2×D89 | semidirect |
| 391. #329 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034771 | 2 |
| #26031239 | 2 |
| #26030950 | 2 |
| #26030698 | 2 |
| #26019572 | 2 |
| #26019560 | 2 |
| #26019546 | 2 |
| #26019542 | 2 |
| #26018870 | 2 |
| #26018862 | 2 |
| C2×#329×C89 | 2 |
| #19042 | 89 |