Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1164 conjugacy classes of subgroups.
The subgroup lattice has 694 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #26033640 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #26029601 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #26028799 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #26021426 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #26021317 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #26020750 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #26020701 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #26020671 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #26020633 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #26020353 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C89×#3025 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #19152396 | C22 | 1 | 2 | yes | — |
| 13 | #19152365 | C22 | 1 | 1 | yes | characteristic |
| 14 | #19152221 | — | 2 | 1 | no | — |
| 15 | #19152215 | — | 2 | 1 | no | — |
| 16 | #19152208 | — | 2 | 1 | no | — |
| 17 | #19152201 | — | 2 | 1 | no | — |
| 18 | #19152192 | — | 2 | 2 | no | — |
| 19 | #19152183 | — | 2 | 2 | no | — |
| 20 | #19152151 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #19152144 | C22 | 1 | 1 | yes | characteristic |
| 22 | #19152130 | — | 2 | 2 | no | — |
| 23 | #19152128 | — | 2 | 2 | no | — |
| 24 | #19152109 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #41×Dic89 | C22 | 1 | 1 | yes | characteristic |
| 26 | #19152066 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×#15667971 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #19151781 | — | 2 | 1 | no | — |
| 29 | #19151776 | — | 2 | 1 | no | — |
| 30 | #19151771 | — | 2 | 1 | no | — |
| 31 | #19151766 | — | 2 | 1 | no | — |
| 32 | #19151616 | C22 | 1 | 2 | yes | complemented |
| 33 | #19151615 | — | 2 | 2 | no | — |
| 34 | #19151615 | C22 | 1 | 2 | yes | — |
| 35 | C2×#15667939 | — | 2 | 2 | no | — |
| 36 | C2×#15667939 | C22 | 1 | 2 | yes | — |
| 37 | C2×#15667939 | C22 | 1 | 2 | yes | — |
| 38 | #19151582 | C22 | 1 | 1 | yes | characteristic |
| 39 | #19151562 | C22 | 1 | 2 | yes | complemented |
| 40 | #19151368 | C22 | 1 | 2 | yes | complemented |
| 41 | #19151357 | C22 | 1 | 2 | yes | complemented |
| 42 | #19151357 | C22 | 1 | 2 | yes | complemented |
| 43 | #19151354 | C22 | 1 | 2 | yes | complemented |
| 44 | #585×C89 | C22 | 1 | 1 | yes | characteristic |
| 45 | #525×C89 | C22 | 1 | 1 | yes | characteristic |
| 46 | #525×C89 | C22 | 1 | 2 | yes | — |
| 47 | #458×C89 | — | 2 | 2 | no | — |
| 48 | B(4,𝔽2)×C89 | — | 2 | 2 | no | — |
| 49 | #410×C89 | C22 | 1 | 1 | yes | characteristic |
| 50 | #410×C89 | C22 | 1 | 2 | yes | — |
| 51 | C2×#13083574 | C23 | 1 | 1 | yes | characteristic |
| 52 | #15668043 | — | 2 | 2 | no | — |
| 53 | #15668042 | — | 2 | 2 | no | — |
| 54 | #15668038 | — | 2 | 2 | no | — |
| 55 | #15668037 | — | 2 | 2 | no | — |
| 56 | #15668032 | — | 4 | 2 | no | — |
| 57 | #15668019 | — | 4 | 2 | no | — |
| 58 | C2×#13083558 | — | 2 | 2 | no | — |
| 59 | C2×#13083558 | C23 | 1 | 2 | yes | — |
| 60 | C2×#13083558 | C23 | 1 | 2 | yes | — |
| 61 | #15668011 | — | 2 | 1 | no | — |
| 62 | #15668010 | D4 | 1 | 1 | yes | characteristic, complemented |
| 63 | #15668008 | D4 | 1 | 1 | yes | characteristic, complemented |
| 64 | #15668007 | — | 2 | 2 | no | — |
| 65 | #15668005 | — | 2 | 2 | no | — |
| 66 | #15668005 | — | 2 | 2 | no | — |
| 67 | #15668005 | — | 2 | 2 | no | — |
| 68 | #15668003 | — | 2 | 2 | no | — |
| 69 | #15668003 | — | 2 | 1 | no | — |
| 70 | #15668002 | — | 2 | 2 | no | — |
| 71 | #15668001 | D4 | 1 | 1 | yes | characteristic, complemented |
| 72 | #15667999 | — | 2 | 2 | no | — |
| 73 | #15667999 | D4 | 1 | 1 | yes | characteristic, complemented |
| 74 | #15667998 | — | 2 | 2 | no | — |
| 75 | #15667996 | — | 2 | 2 | no | — |
| 76 | #15667995 | — | 2 | 1 | no | — |
| 77 | #15667994 | — | 2 | 2 | no | — |
| 78 | #15667994 | — | 2 | 2 | no | — |
| 79 | #15667993 | — | 2 | 2 | no | — |
| 80 | #15667992 | — | 2 | 2 | no | — |
| 81 | #15667991 | — | 2 | 1 | no | — |
| 82 | #15667989 | — | 2 | 2 | no | — |
| 83 | #15667989 | — | 2 | 2 | no | — |
| 84 | #15667986 | — | 2 | 1 | no | — |
| 85 | #15667984 | — | 2 | 2 | no | — |
| 86 | #15667984 | — | 2 | 2 | no | — |
| 87 | #15667983 | — | 2 | 2 | no | — |
| 88 | #15667981 | — | 2 | 1 | no | — |
| 89 | Q8×Dic89 | — | 2 | 1 | no | — |
| 90 | C4×Dic178 | — | 2 | 2 | no | — |
| 91 | #15667977 | — | 2 | 1 | no | — |
| 92 | D4×Dic89 | — | 2 | 2 | no | — |
| 93 | D4×Dic89 | — | 2 | 1 | no | — |
| 94 | #15667974 | — | 2 | 1 | no | — |
| 95 | C4×C22⋊D89 | — | 2 | 2 | no | — |
| 96 | C4×C22⋊D89 | — | 2 | 2 | no | — |
| 97 | #15667972 | — | 2 | 2 | no | — |
| 98 | #15667971 | — | 2 | 1 | no | — |
| 99 | #15667971 | — | 2 | 1 | no | — |
| 100 | #15667971 | — | 2 | 1 | no | — |
| 101 | #15667971 | — | 2 | 1 | no | — |
| 102 | #15667971 | D4 | 1 | 2 | yes | complemented |
| 103 | #15667971 | C23 | 1 | 1 | yes | characteristic |
| 104 | #15667969 | — | 2 | 1 | no | — |
| 105 | C2×C4⋊Dic89 | — | 2 | 1 | no | — |
| 106 | C2×C22⋊Dic89 | — | 2 | 1 | no | — |
| 107 | C2×C4×Dic89 | D4 | 1 | 2 | yes | complemented |
| 108 | C2×C4×Dic89 | C23 | 1 | 1 | yes | characteristic |
| 109 | C2×C4×Dic89 | C23 | 1 | 1 | yes | characteristic |
| 110 | C42×D89 | — | 2 | 1 | no | — |
| 111 | #15667940 | — | 4 | 2 | no | — |
| 112 | #15667939 | — | 2 | 2 | no | — |
| 113 | #15667939 | — | 2 | 2 | no | — |
| 114 | #15667939 | — | 2 | 2 | no | — |
| 115 | #15667939 | — | 2 | 4 | no | — |
| 116 | #15667939 | — | 2 | 2 | no | — |
| 117 | #15667931 | — | 2 | 1 | no | — |
| 118 | #15667929 | — | 2 | 1 | no | — |
| 119 | C22⋊#10623494 | — | 4 | 2 | no | — |
| 120 | 2−1+4×C89 | — | 2 | 2 | no | — |
| 121 | 2−1+4×C89 | — | 2 | 1 | no | — |
| 122 | H(5,𝔽2)×C89 | — | 2 | 2 | no | — |
| 123 | H(5,𝔽2)×C89 | — | 2 | 2 | no | — |
| 124 | H(5,𝔽2)×C89 | — | 2 | 1 | no | — |
| 125 | C2×#41×C89 | — | 2 | 2 | no | — |
| 126 | C2×#41×C89 | — | 4 | 2 | no | — |
| 127 | C2×#41×C89 | C23 | 1 | 2 | yes | — |
| 128 | C2×#41×C89 | C23 | 1 | 1 | yes | characteristic |
| 129 | C23×C4×C89 | C23 | 1 | 1 | yes | characteristic |
| 130 | #123×C89 | — | 2 | 2 | no | — |
| 131 | #123×C89 | D4 | 1 | 2 | yes | — |
| 132 | C22⋊Q8×C89 | — | 2 | 1 | no | — |
| 133 | C22⋊Q8×C89 | — | 2 | 2 | no | — |
| 134 | #121×C89 | — | 2 | 1 | no | — |
| 135 | #121×C89 | — | 2 | 2 | no | — |
| 136 | #120×C89 | — | 2 | 2 | no | — |
| 137 | #120×C89 | D4 | 1 | 2 | yes | — |
| 138 | C4×D4×C89 | — | 2 | 2 | no | — |
| 139 | C4×D4×C89 | — | 4 | 2 | no | — |
| 140 | #117×C89 | C23 | 1 | 2 | yes | — |
| 141 | #117×C89 | C23 | 1 | 1 | yes | characteristic |
| 142 | #99×C89 | — | 2 | 2 | no | — |
| 143 | #99×C89 | — | 2 | 4 | no | — |
| 144 | #13083574 | — | 2 | 2 | no | — |
| 145 | #13083574 | — | 2 | 2 | no | — |
| 146 | C2×Dic178 | — | 2 | 2 | no | — |
| 147 | C2×Dic178 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C2×D356 | C2×D4 | 1 | 1 | yes | characteristic |
| 149 | C2×C22⋊D89 | — | 2 | 1 | no | — |
| 150 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 151 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 152 | C22×Dic89 | — | 2 | 2 | no | — |
| 153 | C22×Dic89 | — | 2 | 1 | no | — |
| 154 | C22×Dic89 | — | 2 | 1 | no | — |
| 155 | C2×C4×D89 | — | 2 | 1 | no | — |
| 156 | C2×C4×D89 | — | 2 | 2 | no | — |
| 157 | #13083564 | — | 4 | 2 | no | — |
| 158 | #13083562 | — | 4 | 2 | no | — |
| 159 | #13083561 | — | 4 | 2 | no | — |
| 160 | #13083559 | — | 4 | 2 | no | — |
| 161 | #13083558 | — | 2 | 2 | no | — |
| 162 | #13083558 | — | 2 | 2 | no | — |
| 163 | #13083558 | — | 2 | 2 | no | — |
| 164 | #13083558 | — | 2 | 2 | no | — |
| 165 | #13083558 | — | 4 | 2 | no | — |
| 166 | C2×#10623494 | — | 2 | 2 | no | — |
| 167 | C2×#10623494 | — | 2 | 2 | no | — |
| 168 | C2×#10623494 | — | 4 | 2 | no | — |
| 169 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 170 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 171 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 172 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 173 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 174 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 175 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 176 | #13083553 | — | 2 | 2 | no | — |
| 177 | #13083553 | — | 2 | 2 | no | — |
| 178 | #13083553 | — | 2 | 2 | no | — |
| 179 | #13083553 | — | 2 | 2 | no | — |
| 180 | #13083553 | — | 2 | 2 | no | — |
| 181 | C22⋊Dic89 | — | 2 | 1 | no | — |
| 182 | C22⋊Dic89 | — | 2 | 1 | no | — |
| 183 | C22⋊Dic89 | — | 2 | 1 | no | — |
| 184 | C22⋊Dic89 | — | 2 | 1 | no | — |
| 185 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 186 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 187 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 188 | C22⋊Dic89 | — | 2 | 1 | no | — |
| 189 | #13083551 | — | 2 | 2 | no | — |
| 190 | #13083551 | — | 2 | 2 | no | — |
| 191 | #13083551 | — | 2 | 2 | no | — |
| 192 | C4×Dic89 | — | 2 | 2 | no | — |
| 193 | C4×Dic89 | — | 2 | 2 | no | — |
| 194 | C4×Dic89 | — | 2 | 1 | no | — |
| 195 | C4×Dic89 | — | 2 | 1 | no | — |
| 196 | C4×Dic89 | C2×D4 | 1 | 1 | yes | characteristic |
| 197 | C4×Dic89 | C2×D4 | 1 | 1 | yes | characteristic |
| 198 | C4×Dic89 | C2×D4 | 1 | 1 | yes | characteristic |
| 199 | C4×Dic89 | C2×D4 | 1 | 1 | yes | characteristic |
| 200 | C4×Dic89 | C2×D4 | 1 | 2 | yes | — |
| 201 | C24×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 202 | #41×C89 | — | 2 | 2 | no | — |
| 203 | #41×C89 | — | 2 | 2 | no | — |
| 204 | #41×C89 | — | 2 | 4 | no | — |
| 205 | #41×C89 | — | 2 | 2 | no | — |
| 206 | #41×C89 | — | 2 | 2 | no | — |
| 207 | #41×C89 | — | 2 | 2 | no | — |
| 208 | #41×C89 | — | 2 | 2 | no | — |
| 209 | #41×C89 | — | 4 | 4 | no | — |
| 210 | #41×C89 | — | 4 | 2 | no | — |
| 211 | #41×C89 | — | 4 | 2 | no | — |
| 212 | #41×C89 | — | 4 | 2 | no | — |
| 213 | #41×C89 | — | 4 | 2 | no | — |
| 214 | C2×Q8×C89 | — | 2 | 2 | no | — |
| 215 | C2×Q8×C89 | — | 4 | 2 | no | — |
| 216 | C2×Q8×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 217 | C2×Q8×C89 | #41 | 1 | 2 | yes | — |
| 218 | C2×D4×C89 | — | 2 | 2 | no | — |
| 219 | C2×D4×C89 | — | 2 | 2 | no | — |
| 220 | C2×D4×C89 | — | 2 | 2 | no | — |
| 221 | C2×D4×C89 | — | 4 | 2 | no | — |
| 222 | C2×D4×C89 | — | 4 | 4 | no | — |
| 223 | C2×D4×C89 | — | 4 | 2 | no | — |
| 224 | C2×D4×C89 | — | 4 | 2 | no | — |
| 225 | C2×D4×C89 | C2×D4 | 1 | 2 | yes | — |
| 226 | C2×D4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 227 | C2×D4×C89 | #41 | 1 | 2 | yes | — |
| 228 | C22×C4×C89 | — | 2 | 1 | no | — |
| 229 | C22×C4×C89 | — | 2 | 1 | no | — |
| 230 | C22×C4×C89 | — | 2 | 2 | no | — |
| 231 | C22×C4×C89 | — | 2 | 2 | no | — |
| 232 | C22×C4×C89 | — | 2 | 2 | no | — |
| 233 | C22×C4×C89 | — | 4 | 2 | no | — |
| 234 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 235 | C22×C4×C89 | C2×D4 | 1 | 2 | yes | — |
| 236 | C22×C4×C89 | C24 | 1 | 1 | yes | characteristic |
| 237 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 238 | C4⋊C4×C89 | — | 2 | 1 | no | — |
| 239 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 240 | C4⋊C4×C89 | — | 4 | 2 | no | — |
| 241 | C22⋊C4×C89 | — | 2 | 2 | no | — |
| 242 | C22⋊C4×C89 | — | 2 | 2 | no | — |
| 243 | C22⋊C4×C89 | — | 2 | 2 | no | — |
| 244 | C22⋊C4×C89 | — | 4 | 2 | no | — |
| 245 | C22⋊C4×C89 | — | 4 | 2 | no | — |
| 246 | C22⋊C4×C89 | C2×D4 | 1 | 2 | yes | — |
| 247 | C42×C89 | — | 2 | 1 | no | — |
| 248 | C42×C89 | — | 2 | 2 | no | — |
| 249 | C23×C89 | — | 2 | 1 | no | — |
| 250 | C23×C89 | — | 2 | 2 | no | — |
| 251 | C23×C89 | — | 2 | 2 | no | — |
| 252 | C23×C89 | — | 4 | 2 | no | — |
| 253 | C23×C89 | — | 8 | 1 | no | — |
| 254 | C23×C89 | #120 | 1 | 2 | yes | — |
| 255 | C23×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 256 | C22×D89 | — | 2 | 1 | no | — |
| 257 | Q8×C89 | — | 2 | 2 | no | — |
| 258 | Q8×C89 | — | 2 | 2 | no | — |
| 259 | Q8×C89 | — | 2 | 2 | no | — |
| 260 | Q8×C89 | — | 4 | 2 | no | — |
| 261 | D4×C89 | — | 2 | 4 | no | — |
| 262 | D4×C89 | — | 2 | 2 | no | — |
| 263 | D4×C89 | — | 2 | 2 | no | — |
| 264 | D4×C89 | — | 2 | 2 | no | — |
| 265 | D4×C89 | — | 4 | 2 | no | — |
| 266 | D4×C89 | — | 4 | 4 | no | — |
| 267 | D4×C89 | — | 4 | 2 | no | — |
| 268 | D4×C89 | — | 4 | 2 | no | — |
| 269 | D4×C89 | — | 8 | 2 | no | — |
| 270 | D4×C89 | — | 8 | 4 | no | — |
| 271 | C2×C4×C89 | — | 2 | 2 | no | — |
| 272 | C2×C4×C89 | — | 2 | 2 | no | — |
| 273 | C2×C4×C89 | — | 2 | 2 | no | — |
| 274 | C2×C4×C89 | — | 2 | 1 | no | — |
| 275 | C2×C4×C89 | — | 2 | 2 | no | — |
| 276 | C2×C4×C89 | — | 2 | 2 | no | — |
| 277 | C2×C4×C89 | — | 4 | 4 | no | — |
| 278 | C2×C4×C89 | — | 4 | 2 | no | — |
| 279 | C2×C4×C89 | — | 4 | 1 | no | — |
| 280 | C2×C4×C89 | — | 4 | 1 | no | — |
| 281 | C2×C4×C89 | — | 4 | 2 | no | — |
| 282 | C2×C4×C89 | — | 4 | 2 | no | — |
| 283 | C2×C4×C89 | — | 4 | 2 | no | — |
| 284 | C2×C4×C89 | — | 4 | 2 | no | — |
| 285 | C2×C4×C89 | #120 | 1 | 2 | yes | — |
| 286 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 287 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 288 | C2×C4×C89 | C2×#41 | 1 | 2 | yes | — |
| 289 | C2×C4×C89 | H(5,𝔽2) | 1 | 2 | yes | — |
| 290 | C22⋊D89 | — | 4 | 2 | no | — |
| 291 | C22⋊D89 | — | 8 | 2 | no | — |
| 292 | C22⋊D89 | — | 8 | 2 | no | — |
| 293 | C2×Dic89 | — | 2 | 1 | no | — |
| 294 | C2×Dic89 | — | 2 | 1 | no | — |
| 295 | C2×Dic89 | — | 2 | 1 | no | — |
| 296 | C2×Dic89 | — | 2 | 1 | no | — |
| 297 | C2×Dic89 | — | 2 | 2 | no | — |
| 298 | C2×Dic89 | — | 2 | 1 | no | — |
| 299 | C2×Dic89 | — | 8 | 1 | no | — |
| 300 | C2×Dic89 | — | 8 | 2 | no | — |
| 301 | C2×Dic89 | — | 8 | 1 | no | — |
| 302 | D356 | — | 2 | 2 | no | — |
| 303 | C4×D89 | — | 4 | 1 | no | — |
| 304 | C4×D89 | — | 4 | 1 | no | — |
| 305 | C4×D89 | — | 8 | 2 | no | — |
| 306 | Dic178 | — | 2 | 2 | no | — |
| 307 | Dic178 | — | 8 | 2 | no | — |
| 308 | #10623494 | — | 4 | 2 | no | — |
| 309 | #10623494 | — | 4 | 2 | no | — |
| 310 | C22×C89 | — | 2 | 2 | no | — |
| 311 | C22×C89 | — | 4 | 1 | no | — |
| 312 | C22×C89 | — | 4 | 2 | no | — |
| 313 | C22×C89 | — | 4 | 1 | no | — |
| 314 | C22×C89 | — | 4 | 1 | no | — |
| 315 | C22×C89 | — | 4 | 2 | no | — |
| 316 | C22×C89 | — | 4 | 2 | no | — |
| 317 | C22×C89 | — | 4 | 2 | no | — |
| 318 | C22×C89 | — | 4 | 1 | no | — |
| 319 | C22×C89 | — | 8 | 2 | no | — |
| 320 | C22×C89 | — | 16 | 2 | no | — |
| 321 | C22×C89 | C2×#120 | 1 | 1 | yes | characteristic |
| 322 | C22×C89 | #546 | 1 | 2 | yes | — |
| 323 | C2×D89 | — | 4 | 2 | no | — |
| 324 | C2×D89 | — | 4 | 1 | no | — |
| 325 | C4×C89 | — | 2 | 2 | no | — |
| 326 | C4×C89 | — | 4 | 2 | no | — |
| 327 | C4×C89 | — | 4 | 1 | no | — |
| 328 | C4×C89 | — | 4 | 2 | no | — |
| 329 | C4×C89 | — | 8 | 2 | no | — |
| 330 | C4×C89 | #525 | 1 | 1 | yes | characteristic |
| 331 | C4×C89 | #535 | 1 | 1 | yes | characteristic |
| 332 | C4×C89 | #546 | 1 | 2 | yes | — |
| 333 | Dic89 | — | 4 | 1 | no | — |
| 334 | Dic89 | — | 4 | 2 | no | — |
| 335 | Dic89 | — | 4 | 1 | no | — |
| 336 | Dic89 | — | 4 | 1 | no | — |
| 337 | Dic89 | — | 4 | 1 | no | — |
| 338 | Dic89 | — | 4 | 1 | no | — |
| 339 | #23995 | — | 89 | 1 | no | maximal, Sylow |
| 340 | C2×C89 | — | 2 | 1 | no | — |
| 341 | C2×C89 | — | 2 | 2 | no | — |
| 342 | C2×C89 | — | 4 | 2 | no | — |
| 343 | C2×C89 | — | 8 | 1 | no | — |
| 344 | C2×C89 | — | 8 | 2 | no | — |
| 345 | C2×C89 | #2404 | 1 | 1 | yes | characteristic |
| 346 | D89 | — | 8 | 1 | no | — |
| 347 | #3455 | — | 89 | 1 | no | — |
| 348 | #3025 | D89 | 1 | 1 | yes | characteristic, complemented |
| 349 | #3018 | — | 89 | 1 | no | — |
| 350 | #2901 | — | 89 | 1 | no | — |
| 351 | #2031 | — | 89 | 2 | no | — |
| 352 | #2010 | — | 89 | 2 | no | — |
| 353 | #1906 | — | 89 | 2 | no | — |
| 354 | #1897 | — | 89 | 2 | no | — |
| 355 | #1891 | — | 89 | 1 | no | — |
| 356 | #1884 | — | 89 | 1 | no | — |
| 357 | #1827 | — | 89 | 1 | no | — |
| 358 | C89 | #23995 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 359 | #585 | C2×D89 | 1 | 1 | yes | characteristic |
| 360 | #575 | — | 89 | 2 | no | — |
| 361 | #568 | — | 89 | 1 | no | — |
| 362 | #542 | — | 178 | 1 | no | — |
| 363 | #542 | — | 178 | 1 | no | — |
| 364 | #541 | — | 178 | 1 | no | — |
| 365 | #540 | — | 178 | 1 | no | — |
| 366 | #539 | — | 178 | 2 | no | — |
| 367 | #538 | — | 178 | 2 | no | — |
| 368 | #533 | — | 89 | 1 | no | — |
| 369 | #532 | — | 89 | 1 | no | — |
| 370 | #529 | — | 178 | 2 | no | — |
| 371 | #529 | — | 178 | 2 | no | — |
| 372 | #525 | — | 89 | 1 | no | — |
| 373 | #525 | C2×D89 | 1 | 1 | yes | characteristic |
| 374 | #525 | C2×D89 | 1 | 2 | yes | — |
| 375 | C4×#41 | — | 89 | 1 | no | — |
| 376 | C4×#41 | — | 89 | 1 | no | — |
| 377 | C2×#117 | — | 89 | 1 | no | — |
| 378 | #458 | — | 2 | 2 | no | — |
| 379 | B(4,𝔽2) | — | 2 | 2 | no | — |
| 380 | #456 | — | 178 | 1 | no | — |
| 381 | #455 | — | 178 | 1 | no | — |
| 382 | #454 | — | 178 | 1 | no | — |
| 383 | #453 | — | 178 | 1 | no | — |
| 384 | #421 | — | 89 | 2 | no | — |
| 385 | #421 | — | 89 | 2 | no | — |
| 386 | #421 | — | 178 | 2 | no | — |
| 387 | C2×#104 | — | 89 | 2 | no | — |
| 388 | C2×#104 | — | 89 | 2 | no | — |
| 389 | C2×#104 | — | 178 | 2 | no | — |
| 390 | #413 | — | 89 | 1 | no | — |
| 391 | #410 | C2×D89 | 1 | 1 | yes | characteristic |
| 392 | #410 | C2×D89 | 1 | 2 | yes | — |
| 393 | #407 | — | 89 | 2 | no | — |
| 394 | #344 | — | 89 | 2 | no | — |
| 395 | #339 | — | 89 | 2 | no | — |
| 396 | #339 | — | 89 | 2 | no | — |
| 397 | H(3,ℤ/4) | — | 89 | 2 | no | — |
| 398 | 2−1+4 | — | 2 | 2 | no | — |
| 399 | 2−1+4 | — | 2 | 1 | no | — |
| 400 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 401 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 402 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 403 | C2×#41 | — | 2 | 2 | no | — |
| 404 | C2×#41 | — | 4 | 2 | no | — |
| 405 | C2×#41 | — | 89 | 1 | no | — |
| 406 | C2×#41 | C22×D89 | 1 | 2 | yes | — |
| 407 | C2×#41 | C22×D89 | 1 | 1 | yes | characteristic |
| 408 | C23×C4 | C22×D89 | 1 | 1 | yes | characteristic |
| 409 | #137 | — | 178 | 2 | no | — |
| 410 | #137 | — | 178 | 2 | no | — |
| 411 | AGL(1,ℤ/8) | — | 178 | 2 | no | — |
| 412 | AGL(1,ℤ/8) | — | 178 | 2 | no | — |
| 413 | #135 | — | 356 | 2 | no | — |
| 414 | #131 | — | 356 | 2 | no | — |
| 415 | C2×M16 | — | 89 | 2 | no | — |
| 416 | C2×M16 | — | 89 | 2 | no | — |
| 417 | C2×M16 | — | 178 | 2 | no | — |
| 418 | C4⋊Q8 | — | 89 | 1 | no | — |
| 419 | C4⋊Q8 | — | 178 | 1 | no | — |
| 420 | #127 | — | 89 | 1 | no | — |
| 421 | #126 | — | 178 | 2 | no | — |
| 422 | #126 | — | 178 | 2 | no | — |
| 423 | #126 | — | 178 | 2 | no | — |
| 424 | #126 | — | 178 | 2 | no | — |
| 425 | #125 | — | 178 | 1 | no | — |
| 426 | #125 | — | 178 | 2 | no | — |
| 427 | #125 | — | 178 | 2 | no | — |
| 428 | #124 | — | 89 | 1 | no | — |
| 429 | #124 | — | 89 | 1 | no | — |
| 430 | #124 | — | 178 | 2 | no | — |
| 431 | #124 | — | 178 | 2 | no | — |
| 432 | #123 | — | 2 | 2 | no | — |
| 433 | #123 | — | 178 | 2 | no | — |
| 434 | #123 | — | 178 | 2 | no | — |
| 435 | #123 | — | 178 | 2 | no | — |
| 436 | #123 | — | 178 | 2 | no | — |
| 437 | #123 | — | 178 | 1 | no | — |
| 438 | #123 | C22⋊D89 | 1 | 2 | yes | — |
| 439 | C22⋊Q8 | — | 2 | 1 | no | — |
| 440 | C22⋊Q8 | — | 2 | 2 | no | — |
| 441 | C22⋊Q8 | — | 178 | 2 | no | — |
| 442 | C22⋊Q8 | — | 178 | 2 | no | — |
| 443 | C22⋊Q8 | — | 178 | 1 | no | — |
| 444 | C22⋊Q8 | — | 178 | 2 | no | — |
| 445 | #121 | — | 2 | 1 | no | — |
| 446 | #121 | — | 2 | 2 | no | — |
| 447 | #121 | — | 178 | 1 | no | — |
| 448 | #121 | — | 178 | 2 | no | — |
| 449 | #121 | — | 178 | 2 | no | — |
| 450 | #121 | — | 178 | 2 | no | — |
| 451 | #120 | — | 2 | 2 | no | — |
| 452 | #120 | — | 178 | 1 | no | — |
| 453 | #120 | C22⋊D89 | 1 | 2 | yes | — |
| 454 | C4×Q8 | — | 178 | 2 | no | — |
| 455 | C4×Q8 | — | 178 | 1 | no | — |
| 456 | C4×Q8 | — | 178 | 1 | no | — |
| 457 | C4×D4 | — | 2 | 2 | no | — |
| 458 | C4×D4 | — | 4 | 2 | no | — |
| 459 | C4×D4 | — | 178 | 2 | no | — |
| 460 | C4×D4 | — | 178 | 1 | no | — |
| 461 | C4×D4 | — | 178 | 1 | no | — |
| 462 | C4×D4 | — | 178 | 2 | no | — |
| 463 | C4×D4 | — | 178 | 2 | no | — |
| 464 | C4×D4 | — | 178 | 2 | no | — |
| 465 | #117 | — | 89 | 2 | no | — |
| 466 | #117 | — | 89 | 1 | no | — |
| 467 | #117 | — | 178 | 1 | no | — |
| 468 | #117 | — | 178 | 1 | no | — |
| 469 | #117 | — | 178 | 1 | no | — |
| 470 | #117 | — | 178 | 1 | no | — |
| 471 | #117 | — | 178 | 1 | no | — |
| 472 | #117 | C22×D89 | 1 | 2 | yes | — |
| 473 | #117 | C22×D89 | 1 | 1 | yes | characteristic |
| 474 | C2×C4⋊C4 | — | 178 | 1 | no | — |
| 475 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 476 | C2×C42 | — | 89 | 2 | no | — |
| 477 | C2×C42 | — | 89 | 1 | no | — |
| 478 | C2×C42 | — | 89 | 1 | no | — |
| 479 | C2×C42 | — | 178 | 1 | no | — |
| 480 | #104 | — | 356 | 2 | no | — |
| 481 | #104 | — | 178 | 2 | no | — |
| 482 | #104 | — | 178 | 2 | no | — |
| 483 | #104 | — | 178 | 2 | no | — |
| 484 | #104 | — | 178 | 2 | no | — |
| 485 | #104 | — | 178 | 4 | no | — |
| 486 | #101 | — | 178 | 1 | no | — |
| 487 | #100 | — | 178 | 1 | no | — |
| 488 | #99 | — | 2 | 2 | no | — |
| 489 | #99 | — | 2 | 4 | no | — |
| 490 | C22⋊C8 | — | 356 | 2 | no | — |
| 491 | C24 | C2×C22⋊D89 | 1 | 1 | yes | characteristic |
| 492 | #41 | — | 2 | 2 | no | — |
| 493 | #41 | — | 2 | 2 | no | — |
| 494 | #41 | — | 2 | 4 | no | — |
| 495 | #41 | — | 2 | 2 | no | — |
| 496 | #41 | — | 2 | 2 | no | — |
| 497 | #41 | — | 2 | 2 | no | — |
| 498 | #41 | — | 2 | 2 | no | — |
| 499 | #41 | — | 4 | 4 | no | — |
| 500 | #41 | — | 4 | 2 | no | — |
| 501 | #41 | — | 4 | 2 | no | — |
| 502 | #41 | — | 4 | 2 | no | — |
| 503 | #41 | — | 4 | 2 | no | — |
| 504 | #41 | — | 178 | 2 | no | — |
| 505 | #41 | — | 178 | 2 | no | — |
| 506 | C2×Q8 | — | 2 | 2 | no | — |
| 507 | C2×Q8 | — | 4 | 2 | no | — |
| 508 | C2×Q8 | — | 89 | 1 | no | — |
| 509 | C2×Q8 | — | 178 | 2 | no | — |
| 510 | C2×Q8 | D4×D89 | 1 | 1 | yes | characteristic |
| 511 | C2×Q8 | #13083573 | 1 | 2 | yes | — |
| 512 | C2×D4 | — | 2 | 2 | no | — |
| 513 | C2×D4 | — | 2 | 2 | no | — |
| 514 | C2×D4 | — | 2 | 2 | no | — |
| 515 | C2×D4 | — | 4 | 2 | no | — |
| 516 | C2×D4 | — | 4 | 4 | no | — |
| 517 | C2×D4 | — | 4 | 2 | no | — |
| 518 | C2×D4 | — | 4 | 2 | no | — |
| 519 | C2×D4 | — | 89 | 1 | no | — |
| 520 | C2×D4 | — | 178 | 1 | no | — |
| 521 | C2×D4 | — | 178 | 2 | no | — |
| 522 | C2×D4 | — | 178 | 2 | no | — |
| 523 | C2×D4 | D4×D89 | 1 | 1 | yes | characteristic |
| 524 | C2×D4 | C2×C22⋊D89 | 1 | 2 | yes | — |
| 525 | C2×D4 | #13083573 | 1 | 2 | yes | — |
| 526 | C22×C4 | — | 2 | 1 | no | — |
| 527 | C22×C4 | — | 2 | 1 | no | — |
| 528 | C22×C4 | — | 2 | 2 | no | — |
| 529 | C22×C4 | — | 2 | 2 | no | — |
| 530 | C22×C4 | — | 2 | 2 | no | — |
| 531 | C22×C4 | — | 4 | 2 | no | — |
| 532 | C22×C4 | — | 178 | 2 | no | — |
| 533 | C22×C4 | — | 178 | 1 | no | — |
| 534 | C22×C4 | — | 178 | 2 | no | — |
| 535 | C22×C4 | — | 178 | 1 | no | — |
| 536 | C22×C4 | — | 178 | 1 | no | — |
| 537 | C22×C4 | D4×D89 | 1 | 2 | yes | — |
| 538 | C22×C4 | C2×C22⋊D89 | 1 | 1 | yes | characteristic |
| 539 | C22×C4 | C23×D89 | 1 | 1 | yes | characteristic |
| 540 | Q16 | — | 356 | 2 | no | — |
| 541 | SD16 | — | 356 | 2 | no | — |
| 542 | SD16 | — | 356 | 2 | no | — |
| 543 | D8 | — | 356 | 2 | no | — |
| 544 | M16 | — | 356 | 2 | no | — |
| 545 | M16 | — | 178 | 2 | no | — |
| 546 | M16 | — | 178 | 2 | no | — |
| 547 | M16 | — | 178 | 2 | no | — |
| 548 | M16 | — | 178 | 2 | no | — |
| 549 | C2×C8 | — | 356 | 2 | no | — |
| 550 | C2×C8 | — | 178 | 2 | no | — |
| 551 | C2×C8 | — | 178 | 2 | no | — |
| 552 | C4⋊C4 | — | 2 | 2 | no | — |
| 553 | C4⋊C4 | — | 2 | 1 | no | — |
| 554 | C4⋊C4 | — | 2 | 2 | no | — |
| 555 | C4⋊C4 | — | 4 | 2 | no | — |
| 556 | C4⋊C4 | — | 178 | 1 | no | — |
| 557 | C4⋊C4 | — | 178 | 1 | no | — |
| 558 | C4⋊C4 | — | 178 | 1 | no | — |
| 559 | C4⋊C4 | — | 178 | 1 | no | — |
| 560 | C4⋊C4 | — | 178 | 2 | no | — |
| 561 | C4⋊C4 | — | 178 | 2 | no | — |
| 562 | C4⋊C4 | — | 178 | 2 | no | — |
| 563 | C4⋊C4 | — | 178 | 2 | no | — |
| 564 | C4⋊C4 | — | 178 | 2 | no | — |
| 565 | C4⋊C4 | — | 178 | 2 | no | — |
| 566 | C4⋊C4 | — | 178 | 2 | no | — |
| 567 | C4⋊C4 | — | 178 | 1 | no | — |
| 568 | C22⋊C4 | — | 2 | 2 | no | — |
| 569 | C22⋊C4 | — | 2 | 2 | no | — |
| 570 | C22⋊C4 | — | 2 | 2 | no | — |
| 571 | C22⋊C4 | — | 4 | 2 | no | — |
| 572 | C22⋊C4 | — | 4 | 2 | no | — |
| 573 | C22⋊C4 | — | 178 | 2 | no | — |
| 574 | C22⋊C4 | — | 178 | 2 | no | — |
| 575 | C22⋊C4 | — | 178 | 1 | no | — |
| 576 | C22⋊C4 | — | 178 | 1 | no | — |
| 577 | C22⋊C4 | — | 178 | 1 | no | — |
| 578 | C22⋊C4 | — | 178 | 1 | no | — |
| 579 | C22⋊C4 | — | 178 | 2 | no | — |
| 580 | C22⋊C4 | — | 178 | 2 | no | — |
| 581 | C22⋊C4 | — | 178 | 2 | no | — |
| 582 | C22⋊C4 | — | 178 | 1 | no | — |
| 583 | C22⋊C4 | — | 178 | 2 | no | — |
| 584 | C22⋊C4 | C2×C22⋊D89 | 1 | 2 | yes | — |
| 585 | C42 | — | 2 | 1 | no | — |
| 586 | C42 | — | 2 | 2 | no | — |
| 587 | C42 | — | 89 | 1 | no | — |
| 588 | C42 | — | 89 | 1 | no | — |
| 589 | C42 | — | 89 | 2 | no | — |
| 590 | C42 | — | 89 | 1 | no | — |
| 591 | C42 | — | 89 | 1 | no | — |
| 592 | C42 | — | 178 | 2 | no | — |
| 593 | C42 | — | 178 | 2 | no | — |
| 594 | C42 | — | 178 | 1 | no | — |
| 595 | C42 | — | 178 | 1 | no | — |
| 596 | C23 | — | 2 | 2 | no | — |
| 597 | C23 | — | 2 | 1 | no | — |
| 598 | C23 | — | 2 | 2 | no | — |
| 599 | C23 | — | 4 | 2 | no | — |
| 600 | C23 | — | 8 | 1 | no | — |
| 601 | C23 | — | 178 | 1 | no | — |
| 602 | C23 | #15667980 | 1 | 2 | yes | — |
| 603 | C23 | C22×C22⋊D89 | 1 | 1 | yes | characteristic |
| 604 | Q8 | — | 2 | 2 | no | — |
| 605 | Q8 | — | 2 | 2 | no | — |
| 606 | Q8 | — | 2 | 2 | no | — |
| 607 | Q8 | — | 4 | 2 | no | — |
| 608 | Q8 | — | 178 | 2 | no | — |
| 609 | Q8 | — | 712 | 2 | no | — |
| 610 | D4 | — | 2 | 4 | no | — |
| 611 | D4 | — | 2 | 2 | no | — |
| 612 | D4 | — | 2 | 2 | no | — |
| 613 | D4 | — | 2 | 2 | no | — |
| 614 | D4 | — | 4 | 2 | no | — |
| 615 | D4 | — | 4 | 4 | no | — |
| 616 | D4 | — | 4 | 2 | no | — |
| 617 | D4 | — | 4 | 2 | no | — |
| 618 | D4 | — | 8 | 2 | no | — |
| 619 | D4 | — | 8 | 4 | no | — |
| 620 | D4 | — | 356 | 2 | no | — |
| 621 | D4 | — | 178 | 2 | no | — |
| 622 | D4 | — | 712 | 2 | no | — |
| 623 | D4 | — | 712 | 2 | no | — |
| 624 | C2×C4 | — | 2 | 2 | no | — |
| 625 | C2×C4 | — | 2 | 2 | no | — |
| 626 | C2×C4 | — | 2 | 2 | no | — |
| 627 | C2×C4 | — | 2 | 2 | no | — |
| 628 | C2×C4 | — | 2 | 2 | no | — |
| 629 | C2×C4 | — | 2 | 1 | no | — |
| 630 | C2×C4 | — | 4 | 4 | no | — |
| 631 | C2×C4 | — | 4 | 2 | no | — |
| 632 | C2×C4 | — | 4 | 1 | no | — |
| 633 | C2×C4 | — | 4 | 2 | no | — |
| 634 | C2×C4 | — | 4 | 2 | no | — |
| 635 | C2×C4 | — | 4 | 2 | no | — |
| 636 | C2×C4 | — | 4 | 1 | no | — |
| 637 | C2×C4 | — | 4 | 2 | no | — |
| 638 | C2×C4 | — | 356 | 1 | no | — |
| 639 | C2×C4 | — | 356 | 1 | no | — |
| 640 | C2×C4 | — | 178 | 1 | no | — |
| 641 | C2×C4 | — | 178 | 1 | no | — |
| 642 | C2×C4 | — | 178 | 1 | no | — |
| 643 | C2×C4 | — | 178 | 2 | no | — |
| 644 | C2×C4 | — | 178 | 1 | no | — |
| 645 | C2×C4 | — | 178 | 1 | no | — |
| 646 | C2×C4 | — | 712 | 2 | no | — |
| 647 | C2×C4 | — | 712 | 1 | no | — |
| 648 | C2×C4 | — | 712 | 2 | no | — |
| 649 | C2×C4 | — | 712 | 1 | no | — |
| 650 | C2×C4 | #15667980 | 1 | 2 | yes | — |
| 651 | C2×C4 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 652 | C2×C4 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 653 | C2×C4 | C2×#13083573 | 1 | 2 | yes | — |
| 654 | C2×C4 | #15668057 | 1 | 2 | yes | — |
| 655 | C8 | — | 356 | 2 | no | — |
| 656 | C8 | — | 356 | 2 | no | — |
| 657 | C22 | — | 2 | 2 | no | — |
| 658 | C22 | — | 4 | 1 | no | — |
| 659 | C22 | — | 4 | 2 | no | — |
| 660 | C22 | — | 4 | 1 | no | — |
| 661 | C22 | — | 4 | 2 | no | — |
| 662 | C22 | — | 4 | 1 | no | — |
| 663 | C22 | — | 4 | 2 | no | — |
| 664 | C22 | — | 4 | 2 | no | — |
| 665 | C22 | — | 4 | 1 | no | — |
| 666 | C22 | — | 8 | 2 | no | — |
| 667 | C22 | — | 16 | 2 | no | — |
| 668 | C22 | — | 356 | 2 | no | — |
| 669 | C22 | — | 356 | 1 | no | — |
| 670 | C22 | C2×#15667980 | 1 | 1 | yes | characteristic |
| 671 | C22 | #19152242 | 1 | 2 | yes | — |
| 672 | C4 | — | 2 | 2 | no | — |
| 673 | C4 | — | 4 | 2 | no | — |
| 674 | C4 | — | 4 | 1 | no | — |
| 675 | C4 | — | 4 | 2 | no | — |
| 676 | C4 | — | 8 | 2 | no | — |
| 677 | C4 | — | 356 | 1 | no | — |
| 678 | C4 | — | 356 | 1 | no | — |
| 679 | C4 | — | 356 | 1 | no | — |
| 680 | C4 | — | 356 | 2 | no | — |
| 681 | C4 | — | 356 | 1 | no | — |
| 682 | C4 | — | 356 | 1 | no | — |
| 683 | C4 | #19152104 | 1 | 1 | yes | characteristic |
| 684 | C4 | #19152163 | 1 | 1 | yes | characteristic |
| 685 | C4 | #19152235 | 1 | 2 | yes | — |
| 686 | C2 | — | 2 | 1 | no | — |
| 687 | C2 | — | 2 | 2 | no | — |
| 688 | C2 | — | 4 | 2 | no | — |
| 689 | C2 | — | 8 | 1 | no | — |
| 690 | C2 | — | 8 | 2 | no | — |
| 691 | C2 | — | 712 | 1 | no | — |
| 692 | C2 | #26023568 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26033640 | C2 | semidirect |
| 2. #26029601 | C2 | semidirect |
| 3. #26028799 | C2 | semidirect |
| 4. #26021426 | C2 | semidirect |
| 5. #26021317 | C2 | semidirect |
| 6. #26020750 | C2 | semidirect |
| 7. #26020701 | C2 | semidirect |
| 8. #26020671 | C2 | semidirect |
| 9. #26020633 | C2 | semidirect |
| 10. #26020353 | C2 | semidirect |
| 11. C89×#3025 | C2 | semidirect |
| 20. #19152151 | C22 | semidirect |
| 24. #19152109 | C22 | semidirect |
| 26. #19152066 | C22 | semidirect |
| 27. C2×#15667971 | C22 | semidirect |
| 32. #19151616 | C22 | semidirect |
| 39. #19151562 | C22 | semidirect |
| 40. #19151368 | C22 | semidirect |
| 41. #19151357 | C22 | semidirect |
| 42. #19151357 | C22 | semidirect |
| 43. #19151354 | C22 | semidirect |
| 62. #15668010 | D4 | semidirect |
| 63. #15668008 | D4 | semidirect |
| 71. #15668001 | D4 | semidirect |
| 73. #15667999 | D4 | semidirect |
| 102. #15667971 | D4 | semidirect |
| 107. C2×C4×Dic89 | D4 | semidirect |
| 348. #3025 | D89 | semidirect |
| 358. C89 | #23995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033640 | 2 |
| #26029601 | 2 |
| #26028799 | 2 |
| #26021426 | 2 |
| #26021317 | 2 |
| #26020750 | 2 |
| #26020701 | 2 |
| #26020671 | 2 |
| #26020633 | 2 |
| #26020353 | 2 |
| C89×#3025 | 2 |
| #23995 | 89 |