Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1258 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 151 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 | #26034585 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #26029651 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×#19151765 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #26022262 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #26022250 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #26022238 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #26021896 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C2×#353×C89 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#15668057 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C2×#15668038 | — | 2 | 1 | no | — |
| 11 | #19152335 | — | 2 | 1 | no | — |
| 12 | #19152335 | C22 | 1 | 2 | yes | complemented |
| 13 | #19152334 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | #19152268 | — | 2 | 1 | no | — |
| 15 | #19152242 | — | 2 | 2 | no | — |
| 16 | #19152233 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | D4×C22⋊D89 | — | 2 | 2 | no | — |
| 18 | #19152202 | — | 2 | 2 | no | — |
| 19 | #19152161 | — | 2 | 2 | no | — |
| 20 | #19152160 | — | 2 | 2 | no | — |
| 21 | #19152157 | — | 2 | 1 | no | — |
| 22 | #19152157 | C22 | 1 | 2 | yes | — |
| 23 | #19152132 | — | 2 | 1 | no | — |
| 24 | #19151789 | — | 2 | 2 | no | — |
| 25 | #19151789 | C22 | 1 | 4 | yes | complemented |
| 26 | #19151786 | — | 2 | 2 | no | — |
| 27 | #19151786 | C22 | 1 | 4 | yes | complemented |
| 28 | #19151765 | — | 2 | 1 | no | — |
| 29 | #19151765 | — | 2 | 1 | no | — |
| 30 | #19151765 | C22 | 1 | 2 | yes | — |
| 31 | #19151765 | C22 | 1 | 2 | yes | complemented |
| 32 | C2×#15667940 | — | 2 | 1 | no | — |
| 33 | C2×#15667929 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | C2×#15667926 | — | 2 | 2 | no | — |
| 35 | #19151387 | C22 | 1 | 4 | yes | complemented |
| 36 | #19151384 | C22 | 1 | 4 | yes | complemented |
| 37 | C2×#127×C89 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×#99×C89 | C22 | 1 | 2 | yes | complemented |
| 39 | #353×C89 | C22 | 1 | 2 | yes | complemented |
| 40 | #353×C89 | C22 | 1 | 2 | yes | complemented |
| 41 | #15668057 | — | 2 | 2 | no | — |
| 42 | #15668057 | — | 2 | 1 | no | — |
| 43 | #15668057 | — | 4 | 2 | no | — |
| 44 | #15668057 | C23 | 1 | 2 | yes | — |
| 45 | C2×#13083574 | — | 2 | 1 | no | — |
| 46 | C2×#13083573 | — | 2 | 2 | no | — |
| 47 | C2×#13083573 | — | 4 | 1 | no | — |
| 48 | C22×C22⋊D89 | — | 2 | 1 | no | — |
| 49 | C22×C22⋊D89 | — | 2 | 2 | no | — |
| 50 | C22×C22⋊D89 | D4 | 1 | 2 | yes | complemented |
| 51 | C2×D4×D89 | — | 2 | 2 | no | — |
| 52 | C2×D4×D89 | — | 4 | 1 | no | — |
| 53 | #15668038 | — | 2 | 2 | no | — |
| 54 | #15668038 | — | 2 | 2 | no | — |
| 55 | #15668038 | — | 4 | 2 | no | — |
| 56 | C2×#13083562 | — | 4 | 1 | no | — |
| 57 | C2×#13083559 | — | 4 | 1 | no | — |
| 58 | C2×#13083558 | — | 2 | 1 | no | — |
| 59 | #15668008 | — | 2 | 2 | no | — |
| 60 | #15668006 | — | 2 | 2 | no | — |
| 61 | #15668004 | — | 2 | 1 | no | — |
| 62 | #15668000 | — | 2 | 1 | no | — |
| 63 | #15667999 | — | 2 | 2 | no | — |
| 64 | #15667996 | — | 2 | 4 | no | — |
| 65 | #15667996 | — | 4 | 2 | no | — |
| 66 | #15667995 | — | 2 | 2 | no | — |
| 67 | #15667993 | — | 2 | 1 | no | — |
| 68 | #15667993 | — | 2 | 2 | no | — |
| 69 | #15667993 | — | 2 | 2 | no | — |
| 70 | #15667993 | — | 2 | 1 | no | — |
| 71 | #15667993 | D4 | 1 | 2 | yes | complemented |
| 72 | #15667993 | C23 | 1 | 2 | yes | — |
| 73 | #15667991 | — | 2 | 1 | no | — |
| 74 | #15667986 | — | 2 | 1 | no | — |
| 75 | #15667986 | — | 4 | 4 | no | — |
| 76 | #15667984 | — | 2 | 2 | no | — |
| 77 | #15667984 | — | 2 | 2 | no | — |
| 78 | #15667984 | — | 2 | 2 | no | — |
| 79 | #15667984 | — | 2 | 2 | no | — |
| 80 | #15667984 | — | 2 | 2 | no | — |
| 81 | #15667984 | — | 2 | 2 | no | — |
| 82 | #15667984 | — | 2 | 2 | no | — |
| 83 | #15667984 | — | 2 | 2 | no | — |
| 84 | #15667983 | — | 2 | 2 | no | — |
| 85 | #15667983 | — | 2 | 2 | no | — |
| 86 | #15667982 | — | 2 | 4 | no | — |
| 87 | #15667982 | — | 4 | 2 | no | — |
| 88 | #15667981 | — | 2 | 2 | no | — |
| 89 | #15667981 | — | 2 | 2 | no | — |
| 90 | #15667980 | — | 2 | 1 | no | — |
| 91 | #15667980 | — | 2 | 2 | no | — |
| 92 | #15667980 | — | 2 | 2 | no | — |
| 93 | #15667980 | — | 2 | 1 | no | — |
| 94 | #15667980 | D4 | 1 | 2 | yes | complemented |
| 95 | #15667980 | C23 | 1 | 2 | yes | — |
| 96 | C4×Dic178 | — | 2 | 1 | no | — |
| 97 | C4×D356 | — | 2 | 1 | no | — |
| 98 | D4×Dic89 | — | 2 | 2 | no | — |
| 99 | D4×Dic89 | — | 2 | 2 | no | — |
| 100 | C4×C22⋊D89 | — | 2 | 2 | no | — |
| 101 | #15667969 | — | 2 | 2 | no | — |
| 102 | C2×C22⋊Dic89 | — | 2 | 1 | no | — |
| 103 | C2×C22⋊Dic89 | D4 | 1 | 2 | yes | complemented |
| 104 | #15667940 | — | 2 | 2 | no | — |
| 105 | #15667940 | — | 2 | 2 | no | — |
| 106 | #15667929 | — | 2 | 1 | no | — |
| 107 | #15667929 | C23 | 1 | 2 | yes | — |
| 108 | #15667926 | — | 2 | 4 | no | — |
| 109 | #15667926 | — | 2 | 4 | no | — |
| 110 | C22×D4×C89 | — | 2 | 2 | no | — |
| 111 | C22×D4×C89 | D4 | 1 | 1 | yes | characteristic, complemented |
| 112 | C22×D4×C89 | C23 | 1 | 1 | yes | characteristic |
| 113 | #127×C89 | — | 2 | 2 | no | — |
| 114 | #127×C89 | D4 | 1 | 1 | yes | characteristic, complemented |
| 115 | #127×C89 | D4 | 1 | 1 | yes | characteristic, complemented |
| 116 | #127×C89 | C23 | 1 | 1 | yes | characteristic |
| 117 | #127×C89 | C23 | 1 | 1 | yes | characteristic |
| 118 | C2×C22⋊C4×C89 | — | 2 | 2 | no | — |
| 119 | C2×C42×C89 | D4 | 1 | 1 | yes | characteristic, complemented |
| 120 | #99×C89 | — | 2 | 2 | no | — |
| 121 | #99×C89 | C23 | 1 | 4 | yes | — |
| 122 | C23×D89 | — | 2 | 2 | no | — |
| 123 | C23×D89 | — | 2 | 1 | no | — |
| 124 | C23×D89 | C2×D4 | 1 | 2 | yes | — |
| 125 | #13083574 | — | 2 | 2 | no | — |
| 126 | #13083574 | — | 2 | 2 | no | — |
| 127 | #13083574 | — | 4 | 1 | no | — |
| 128 | #13083574 | — | 4 | 1 | no | — |
| 129 | #13083573 | — | 4 | 2 | no | — |
| 130 | #13083573 | — | 4 | 2 | no | — |
| 131 | #13083573 | — | 4 | 4 | no | — |
| 132 | #13083573 | — | 8 | 4 | no | — |
| 133 | C2×Dic178 | — | 2 | 1 | no | — |
| 134 | C2×Dic178 | — | 2 | 1 | no | — |
| 135 | C2×D356 | — | 2 | 1 | no | — |
| 136 | C2×D356 | — | 2 | 1 | no | — |
| 137 | C2×D356 | — | 4 | 4 | no | — |
| 138 | C2×C22⋊D89 | — | 2 | 4 | no | — |
| 139 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 140 | C2×C22⋊D89 | — | 2 | 4 | no | — |
| 141 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 142 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 143 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 144 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 145 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 146 | C2×C22⋊D89 | — | 2 | 2 | no | — |
| 147 | C2×C22⋊D89 | — | 4 | 2 | no | — |
| 148 | C2×C22⋊D89 | — | 4 | 2 | no | — |
| 149 | C2×C22⋊D89 | — | 4 | 1 | no | — |
| 150 | C2×C22⋊D89 | — | 4 | 2 | no | — |
| 151 | C2×C22⋊D89 | — | 4 | 2 | no | — |
| 152 | C2×C22⋊D89 | — | 4 | 2 | no | — |
| 153 | C2×C22⋊D89 | — | 8 | 1 | no | — |
| 154 | C2×C22⋊D89 | — | 8 | 1 | no | — |
| 155 | D4×D89 | — | 4 | 2 | no | — |
| 156 | D4×D89 | — | 4 | 2 | no | — |
| 157 | D4×D89 | — | 4 | 4 | no | — |
| 158 | D4×D89 | — | 8 | 4 | no | — |
| 159 | C22×Dic89 | — | 2 | 2 | no | — |
| 160 | C22×Dic89 | — | 2 | 1 | no | — |
| 161 | C22×Dic89 | — | 2 | 2 | no | — |
| 162 | C22×Dic89 | — | 2 | 2 | no | — |
| 163 | C22×Dic89 | C2×D4 | 1 | 2 | yes | — |
| 164 | C2×C4×D89 | — | 2 | 2 | no | — |
| 165 | C2×C4×D89 | — | 4 | 1 | no | — |
| 166 | #13083562 | — | 4 | 2 | no | — |
| 167 | #13083562 | — | 4 | 2 | no | — |
| 168 | #13083559 | — | 4 | 2 | no | — |
| 169 | #13083559 | — | 4 | 2 | no | — |
| 170 | #13083558 | — | 2 | 2 | no | — |
| 171 | #13083558 | — | 4 | 1 | no | — |
| 172 | C2×#10623494 | — | 4 | 1 | no | — |
| 173 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 174 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 175 | C4⋊Dic89 | — | 4 | 4 | no | — |
| 176 | #13083553 | — | 2 | 2 | no | — |
| 177 | #13083553 | — | 2 | 2 | no | — |
| 178 | #13083553 | — | 2 | 2 | no | — |
| 179 | #13083553 | — | 2 | 2 | no | — |
| 180 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 181 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 182 | C22⋊Dic89 | — | 2 | 1 | no | — |
| 183 | C22⋊Dic89 | — | 2 | 1 | no | — |
| 184 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 185 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 186 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 187 | C22⋊Dic89 | C2×D4 | 1 | 2 | yes | — |
| 188 | C22⋊Dic89 | C2×D4 | 1 | 2 | yes | — |
| 189 | #13083551 | — | 2 | 2 | no | — |
| 190 | #13083551 | — | 2 | 2 | no | — |
| 191 | #13083551 | — | 2 | 2 | no | — |
| 192 | #13083551 | — | 2 | 2 | no | — |
| 193 | #13083551 | — | 4 | 4 | no | — |
| 194 | #13083551 | — | 4 | 4 | no | — |
| 195 | C4×Dic89 | — | 2 | 2 | no | — |
| 196 | C24×C89 | — | 2 | 1 | no | — |
| 197 | C24×C89 | C2×D4 | 1 | 2 | yes | — |
| 198 | C2×D4×C89 | — | 2 | 2 | no | — |
| 199 | C2×D4×C89 | — | 2 | 2 | no | — |
| 200 | C2×D4×C89 | — | 2 | 2 | no | — |
| 201 | C2×D4×C89 | — | 2 | 2 | no | — |
| 202 | C2×D4×C89 | — | 2 | 1 | no | — |
| 203 | C2×D4×C89 | — | 4 | 1 | no | — |
| 204 | C2×D4×C89 | — | 4 | 1 | no | — |
| 205 | C2×D4×C89 | — | 4 | 1 | no | — |
| 206 | C2×D4×C89 | — | 4 | 1 | no | — |
| 207 | C2×D4×C89 | — | 8 | 4 | no | — |
| 208 | C2×D4×C89 | C2×D4 | 1 | 2 | yes | — |
| 209 | C2×D4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 210 | C2×D4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 211 | C2×D4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 212 | C2×D4×C89 | C24 | 1 | 1 | yes | characteristic |
| 213 | C22×C4×C89 | — | 2 | 1 | no | — |
| 214 | C22×C4×C89 | — | 4 | 2 | no | — |
| 215 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 216 | C22⋊C4×C89 | — | 2 | 4 | no | — |
| 217 | C22⋊C4×C89 | — | 4 | 2 | no | — |
| 218 | C42×C89 | — | 2 | 1 | no | — |
| 219 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 220 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 221 | C23×C89 | — | 2 | 2 | no | — |
| 222 | C23×C89 | — | 2 | 2 | no | — |
| 223 | C23×C89 | — | 2 | 1 | no | — |
| 224 | C23×C89 | — | 2 | 1 | no | — |
| 225 | C23×C89 | — | 4 | 1 | no | — |
| 226 | C23×C89 | — | 4 | 1 | no | — |
| 227 | C23×C89 | — | 8 | 2 | no | — |
| 228 | C23×C89 | — | 8 | 2 | no | — |
| 229 | C23×C89 | #120 | 1 | 2 | yes | — |
| 230 | C23×C89 | #120 | 1 | 1 | yes | characteristic |
| 231 | C23×C89 | C22×D4 | 1 | 2 | yes | — |
| 232 | C22×D89 | — | 2 | 2 | no | — |
| 233 | C22×D89 | — | 2 | 4 | no | — |
| 234 | C22×D89 | — | 4 | 1 | no | — |
| 235 | C22×D89 | — | 4 | 2 | no | — |
| 236 | C22×D89 | — | 4 | 2 | no | — |
| 237 | C22×D89 | — | 8 | 2 | no | — |
| 238 | C22×D89 | — | 8 | 2 | no | — |
| 239 | C22×D89 | — | 8 | 1 | no | — |
| 240 | C22×D89 | — | 16 | 2 | no | — |
| 241 | D4×C89 | — | 4 | 2 | no | — |
| 242 | D4×C89 | — | 4 | 1 | no | — |
| 243 | D4×C89 | — | 4 | 1 | no | — |
| 244 | D4×C89 | — | 4 | 1 | no | — |
| 245 | D4×C89 | — | 4 | 1 | no | — |
| 246 | D4×C89 | — | 4 | 4 | no | — |
| 247 | D4×C89 | — | 4 | 4 | no | — |
| 248 | D4×C89 | — | 8 | 1 | no | — |
| 249 | D4×C89 | — | 8 | 2 | no | — |
| 250 | D4×C89 | — | 8 | 2 | no | — |
| 251 | C2×C4×C89 | — | 2 | 1 | no | — |
| 252 | C2×C4×C89 | — | 2 | 1 | no | — |
| 253 | C2×C4×C89 | — | 2 | 1 | no | — |
| 254 | C2×C4×C89 | — | 2 | 1 | no | — |
| 255 | C2×C4×C89 | — | 4 | 2 | no | — |
| 256 | C2×C4×C89 | — | 4 | 4 | no | — |
| 257 | C2×C4×C89 | — | 16 | 2 | no | — |
| 258 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 259 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 260 | C22⋊D89 | — | 4 | 4 | no | — |
| 261 | C22⋊D89 | — | 4 | 4 | no | — |
| 262 | C22⋊D89 | — | 4 | 2 | no | — |
| 263 | C22⋊D89 | — | 4 | 2 | no | — |
| 264 | C22⋊D89 | — | 4 | 2 | no | — |
| 265 | C22⋊D89 | — | 4 | 2 | no | — |
| 266 | C22⋊D89 | — | 8 | 2 | 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 | 4 | no | — |
| 273 | C2×Dic89 | — | 2 | 2 | no | — |
| 274 | C2×Dic89 | — | 2 | 2 | no | — |
| 275 | C2×Dic89 | — | 2 | 2 | no | — |
| 276 | C2×Dic89 | — | 4 | 2 | no | — |
| 277 | C2×Dic89 | — | 4 | 1 | no | — |
| 278 | C2×Dic89 | — | 4 | 2 | no | — |
| 279 | C2×Dic89 | — | 8 | 1 | no | — |
| 280 | C2×Dic89 | — | 8 | 2 | no | — |
| 281 | C2×Dic89 | — | 8 | 2 | no | — |
| 282 | D356 | — | 2 | 2 | no | — |
| 283 | D356 | — | 4 | 1 | no | — |
| 284 | D356 | — | 4 | 2 | no | — |
| 285 | D356 | — | 16 | 4 | no | — |
| 286 | C4×D89 | — | 4 | 4 | no | — |
| 287 | C4×D89 | — | 4 | 2 | no | — |
| 288 | C4×D89 | — | 4 | 2 | no | — |
| 289 | Dic178 | — | 2 | 2 | no | — |
| 290 | Dic178 | — | 4 | 1 | no | — |
| 291 | Dic178 | — | 4 | 2 | no | — |
| 292 | #10623494 | — | 4 | 2 | no | — |
| 293 | C22×C89 | — | 2 | 2 | no | — |
| 294 | C22×C89 | — | 2 | 2 | no | — |
| 295 | C22×C89 | — | 4 | 1 | no | — |
| 296 | C22×C89 | — | 4 | 2 | no | — |
| 297 | C22×C89 | — | 4 | 2 | no | — |
| 298 | C22×C89 | — | 4 | 2 | no | — |
| 299 | C22×C89 | — | 4 | 2 | no | — |
| 300 | C22×C89 | — | 4 | 1 | no | — |
| 301 | C22×C89 | — | 4 | 1 | no | — |
| 302 | C22×C89 | — | 8 | 2 | no | — |
| 303 | C22×C89 | — | 8 | 2 | no | — |
| 304 | C22×C89 | — | 16 | 1 | no | — |
| 305 | C22×C89 | — | 16 | 1 | no | — |
| 306 | C22×C89 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 307 | C22×C89 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 308 | C22×C89 | C2×#120 | 1 | 1 | yes | characteristic |
| 309 | C2×D89 | — | 4 | 2 | no | — |
| 310 | C2×D89 | — | 4 | 2 | no | — |
| 311 | C2×D89 | — | 4 | 2 | no | — |
| 312 | C2×D89 | — | 4 | 2 | no | — |
| 313 | C2×D89 | — | 8 | 2 | no | — |
| 314 | C2×D89 | — | 8 | 4 | no | — |
| 315 | C2×D89 | — | 8 | 4 | no | — |
| 316 | C2×D89 | — | 16 | 2 | no | — |
| 317 | C2×D89 | — | 16 | 2 | no | — |
| 318 | C4×C89 | — | 2 | 2 | no | — |
| 319 | C4×C89 | — | 2 | 1 | no | — |
| 320 | C4×C89 | — | 2 | 1 | no | — |
| 321 | C4×C89 | — | 4 | 1 | no | — |
| 322 | C4×C89 | — | 8 | 4 | no | — |
| 323 | Dic89 | — | 4 | 2 | no | — |
| 324 | Dic89 | — | 4 | 2 | no | — |
| 325 | Dic89 | — | 4 | 2 | no | — |
| 326 | Dic89 | — | 4 | 2 | no | — |
| 327 | #33557 | — | 89 | 1 | no | maximal, Sylow |
| 328 | C2×C89 | — | 2 | 1 | no | — |
| 329 | C2×C89 | — | 2 | 1 | no | — |
| 330 | C2×C89 | — | 2 | 1 | no | — |
| 331 | C2×C89 | — | 4 | 2 | no | — |
| 332 | C2×C89 | — | 4 | 2 | no | — |
| 333 | C2×C89 | — | 8 | 1 | no | — |
| 334 | C2×C89 | — | 8 | 1 | no | — |
| 335 | C2×C89 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 336 | D89 | — | 8 | 2 | no | — |
| 337 | D89 | — | 8 | 2 | no | — |
| 338 | #3543 | — | 89 | 1 | no | — |
| 339 | #3026 | — | 89 | 2 | no | — |
| 340 | C2×#453 | — | 89 | 1 | no | — |
| 341 | #2200 | — | 89 | 4 | no | — |
| 342 | #2198 | — | 89 | 2 | no | — |
| 343 | #2196 | — | 89 | 2 | no | — |
| 344 | C2×#353 | D89 | 1 | 1 | yes | characteristic, complemented |
| 345 | #2121 | — | 89 | 2 | no | — |
| 346 | C89 | #33557 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 347 | C2×H(5,𝔽2) | — | 89 | 1 | no | — |
| 348 | C2×AGL(1,ℤ/8) | — | 178 | 1 | no | — |
| 349 | #560 | — | 89 | 2 | no | — |
| 350 | #560 | — | 178 | 1 | no | — |
| 351 | #559 | — | 89 | 1 | no | — |
| 352 | #550 | — | 178 | 1 | no | — |
| 353 | #546 | — | 178 | 2 | no | — |
| 354 | D42 | — | 89 | 1 | no | — |
| 355 | D42 | — | 178 | 2 | no | — |
| 356 | #540 | — | 178 | 2 | no | — |
| 357 | #535 | — | 178 | 2 | no | — |
| 358 | #534 | — | 89 | 2 | no | — |
| 359 | #534 | — | 178 | 2 | no | — |
| 360 | #534 | — | 178 | 1 | no | — |
| 361 | C2×#127 | C2×D89 | 1 | 1 | yes | characteristic |
| 362 | #529 | — | 178 | 1 | no | — |
| 363 | #458 | — | 89 | 4 | no | — |
| 364 | #458 | — | 178 | 2 | no | — |
| 365 | B(4,𝔽2) | — | 89 | 4 | no | — |
| 366 | B(4,𝔽2) | — | 178 | 2 | no | — |
| 367 | #453 | — | 89 | 2 | no | — |
| 368 | #453 | — | 89 | 2 | no | — |
| 369 | #453 | — | 178 | 1 | no | — |
| 370 | #453 | — | 178 | 1 | no | — |
| 371 | C2×#104 | — | 178 | 1 | no | — |
| 372 | C2×#100 | — | 89 | 1 | no | — |
| 373 | C2×#99 | — | 178 | 2 | no | — |
| 374 | C2×#99 | C2×D89 | 1 | 2 | yes | complemented |
| 375 | #353 | C2×D89 | 1 | 2 | yes | complemented |
| 376 | #353 | C2×D89 | 1 | 2 | yes | complemented |
| 377 | #352 | — | 89 | 4 | no | — |
| 378 | AΣL(1,𝔽16) | — | 89 | 4 | no | — |
| 379 | H(5,𝔽2) | — | 89 | 2 | no | — |
| 380 | H(5,𝔽2) | — | 356 | 2 | no | — |
| 381 | H(5,𝔽2) | — | 178 | 1 | no | — |
| 382 | H(5,𝔽2) | — | 178 | 2 | no | — |
| 383 | C2×#41 | — | 356 | 1 | no | — |
| 384 | C2×#41 | — | 178 | 1 | no | — |
| 385 | C2×#41 | — | 178 | 2 | no | — |
| 386 | C22×D4 | — | 2 | 2 | no | — |
| 387 | C22×D4 | — | 89 | 2 | no | — |
| 388 | C22×D4 | — | 356 | 1 | no | — |
| 389 | C22×D4 | — | 178 | 2 | no | — |
| 390 | C22×D4 | — | 178 | 2 | no | — |
| 391 | C22×D4 | — | 178 | 1 | no | — |
| 392 | C22×D4 | D356 | 1 | 1 | yes | characteristic, complemented |
| 393 | C22×D4 | C22×D89 | 1 | 1 | yes | characteristic |
| 394 | AGL(1,ℤ/8) | — | 356 | 2 | no | — |
| 395 | AGL(1,ℤ/8) | — | 178 | 2 | no | — |
| 396 | AGL(1,ℤ/8) | — | 178 | 2 | no | — |
| 397 | C2×SD16 | — | 356 | 1 | no | — |
| 398 | C2×D8 | — | 356 | 1 | no | — |
| 399 | C2×M16 | — | 178 | 1 | no | — |
| 400 | #127 | — | 2 | 2 | no | — |
| 401 | #127 | — | 178 | 2 | no | — |
| 402 | #127 | D356 | 1 | 1 | yes | characteristic, complemented |
| 403 | #127 | D356 | 1 | 1 | yes | characteristic, complemented |
| 404 | #127 | C22×D89 | 1 | 1 | yes | characteristic |
| 405 | #127 | C22×D89 | 1 | 1 | yes | characteristic |
| 406 | #126 | — | 178 | 2 | no | — |
| 407 | #125 | — | 178 | 1 | no | — |
| 408 | #124 | — | 178 | 1 | no | — |
| 409 | #124 | — | 178 | 2 | no | — |
| 410 | #123 | — | 89 | 2 | no | — |
| 411 | #123 | — | 89 | 2 | no | — |
| 412 | #123 | — | 356 | 2 | no | — |
| 413 | #123 | — | 178 | 4 | no | — |
| 414 | #123 | — | 178 | 2 | no | — |
| 415 | #123 | — | 178 | 1 | no | — |
| 416 | #123 | — | 178 | 2 | no | — |
| 417 | #123 | — | 178 | 1 | no | — |
| 418 | #123 | — | 178 | 2 | no | — |
| 419 | C22⋊Q8 | — | 178 | 1 | no | — |
| 420 | #121 | — | 356 | 4 | no | — |
| 421 | #121 | — | 178 | 2 | no | — |
| 422 | #121 | — | 178 | 2 | no | — |
| 423 | #121 | — | 178 | 1 | no | — |
| 424 | #121 | — | 178 | 2 | no | — |
| 425 | #121 | — | 178 | 2 | no | — |
| 426 | #121 | — | 178 | 2 | no | — |
| 427 | #121 | — | 178 | 2 | no | — |
| 428 | #121 | — | 178 | 2 | no | — |
| 429 | #121 | — | 178 | 2 | no | — |
| 430 | #121 | — | 178 | 2 | no | — |
| 431 | #121 | — | 178 | 2 | no | — |
| 432 | #120 | — | 89 | 2 | no | — |
| 433 | #120 | — | 89 | 2 | no | — |
| 434 | #120 | — | 356 | 2 | no | — |
| 435 | #120 | — | 178 | 4 | no | — |
| 436 | #120 | — | 178 | 2 | no | — |
| 437 | #120 | — | 178 | 1 | no | — |
| 438 | #120 | — | 178 | 2 | no | — |
| 439 | #120 | — | 178 | 2 | no | — |
| 440 | #120 | — | 178 | 2 | no | — |
| 441 | #120 | — | 178 | 1 | no | — |
| 442 | C4×Q8 | — | 178 | 1 | no | — |
| 443 | C4×D4 | — | 178 | 2 | no | — |
| 444 | C4×D4 | — | 178 | 2 | no | — |
| 445 | C4×D4 | — | 178 | 2 | no | — |
| 446 | C4×D4 | — | 178 | 1 | no | — |
| 447 | #117 | — | 178 | 2 | no | — |
| 448 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 449 | C2×C22⋊C4 | — | 89 | 2 | no | — |
| 450 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 451 | C2×C42 | D356 | 1 | 1 | yes | characteristic, complemented |
| 452 | #104 | — | 178 | 2 | no | — |
| 453 | #104 | — | 178 | 2 | no | — |
| 454 | #100 | — | 89 | 2 | no | — |
| 455 | #100 | — | 178 | 1 | no | — |
| 456 | #99 | — | 2 | 2 | no | — |
| 457 | #99 | — | 178 | 4 | no | — |
| 458 | #99 | — | 178 | 4 | no | — |
| 459 | #99 | C22×D89 | 1 | 4 | yes | — |
| 460 | C24 | — | 2 | 1 | no | — |
| 461 | C24 | — | 89 | 2 | no | — |
| 462 | C24 | — | 178 | 2 | no | — |
| 463 | C24 | — | 178 | 1 | no | — |
| 464 | C24 | D4×D89 | 1 | 2 | yes | — |
| 465 | #41 | — | 356 | 1 | no | — |
| 466 | #41 | — | 356 | 2 | no | — |
| 467 | #41 | — | 356 | 4 | no | — |
| 468 | #41 | — | 356 | 1 | no | — |
| 469 | #41 | — | 356 | 2 | no | — |
| 470 | #41 | — | 178 | 2 | no | — |
| 471 | #41 | — | 178 | 2 | no | — |
| 472 | #41 | — | 712 | 4 | no | — |
| 473 | C2×Q8 | — | 178 | 1 | no | — |
| 474 | C2×Q8 | — | 178 | 1 | no | — |
| 475 | C2×D4 | — | 2 | 2 | no | — |
| 476 | C2×D4 | — | 2 | 2 | no | — |
| 477 | C2×D4 | — | 2 | 2 | no | — |
| 478 | C2×D4 | — | 2 | 2 | no | — |
| 479 | C2×D4 | — | 2 | 1 | no | — |
| 480 | C2×D4 | — | 4 | 1 | no | — |
| 481 | C2×D4 | — | 4 | 1 | no | — |
| 482 | C2×D4 | — | 4 | 1 | no | — |
| 483 | C2×D4 | — | 4 | 1 | no | — |
| 484 | C2×D4 | — | 8 | 4 | no | — |
| 485 | C2×D4 | — | 356 | 4 | no | — |
| 486 | C2×D4 | — | 356 | 4 | no | — |
| 487 | C2×D4 | — | 356 | 2 | no | — |
| 488 | C2×D4 | — | 356 | 2 | no | — |
| 489 | C2×D4 | — | 356 | 2 | no | — |
| 490 | C2×D4 | — | 356 | 2 | no | — |
| 491 | C2×D4 | — | 356 | 2 | no | — |
| 492 | C2×D4 | — | 356 | 1 | no | — |
| 493 | C2×D4 | — | 356 | 2 | no | — |
| 494 | C2×D4 | — | 356 | 2 | no | — |
| 495 | C2×D4 | — | 178 | 1 | no | — |
| 496 | C2×D4 | — | 178 | 1 | no | — |
| 497 | C2×D4 | — | 178 | 4 | no | — |
| 498 | C2×D4 | — | 178 | 2 | no | — |
| 499 | C2×D4 | — | 178 | 4 | no | — |
| 500 | C2×D4 | — | 178 | 2 | no | — |
| 501 | C2×D4 | — | 178 | 2 | no | — |
| 502 | C2×D4 | — | 178 | 2 | no | — |
| 503 | C2×D4 | — | 178 | 2 | no | — |
| 504 | C2×D4 | — | 178 | 2 | no | — |
| 505 | C2×D4 | — | 178 | 2 | no | — |
| 506 | C2×D4 | — | 712 | 4 | no | — |
| 507 | C2×D4 | — | 712 | 1 | no | — |
| 508 | C2×D4 | — | 712 | 1 | no | — |
| 509 | C2×D4 | D4×D89 | 1 | 2 | yes | — |
| 510 | C2×D4 | C2×D356 | 1 | 1 | yes | characteristic |
| 511 | C2×D4 | C2×D356 | 1 | 1 | yes | characteristic |
| 512 | C2×D4 | C2×D356 | 1 | 1 | yes | characteristic |
| 513 | C2×D4 | C23×D89 | 1 | 1 | yes | characteristic |
| 514 | C22×C4 | — | 2 | 1 | no | — |
| 515 | C22×C4 | — | 4 | 2 | no | — |
| 516 | C22×C4 | — | 89 | 2 | no | — |
| 517 | C22×C4 | — | 356 | 1 | no | — |
| 518 | C22×C4 | — | 178 | 2 | no | — |
| 519 | C22×C4 | — | 178 | 2 | no | — |
| 520 | C22×C4 | — | 178 | 2 | no | — |
| 521 | C22×C4 | — | 178 | 1 | no | — |
| 522 | C22×C4 | — | 178 | 2 | no | — |
| 523 | C22×C4 | C2×D356 | 1 | 1 | yes | characteristic |
| 524 | SD16 | — | 356 | 2 | no | — |
| 525 | SD16 | — | 356 | 2 | no | — |
| 526 | D8 | — | 356 | 2 | no | — |
| 527 | D8 | — | 356 | 2 | no | — |
| 528 | M16 | — | 356 | 1 | no | — |
| 529 | M16 | — | 178 | 2 | no | — |
| 530 | C2×C8 | — | 356 | 1 | no | — |
| 531 | C4⋊C4 | — | 356 | 4 | no | — |
| 532 | C4⋊C4 | — | 178 | 2 | no | — |
| 533 | C4⋊C4 | — | 178 | 1 | no | — |
| 534 | C4⋊C4 | — | 178 | 1 | no | — |
| 535 | C4⋊C4 | — | 178 | 2 | no | — |
| 536 | C4⋊C4 | — | 178 | 2 | no | — |
| 537 | C4⋊C4 | — | 178 | 2 | no | — |
| 538 | C22⋊C4 | — | 2 | 4 | no | — |
| 539 | C22⋊C4 | — | 4 | 2 | no | — |
| 540 | C22⋊C4 | — | 89 | 2 | no | — |
| 541 | C22⋊C4 | — | 89 | 2 | no | — |
| 542 | C22⋊C4 | — | 356 | 4 | no | — |
| 543 | C22⋊C4 | — | 356 | 4 | no | — |
| 544 | C22⋊C4 | — | 178 | 2 | no | — |
| 545 | C22⋊C4 | — | 178 | 2 | no | — |
| 546 | C22⋊C4 | — | 178 | 1 | no | — |
| 547 | C22⋊C4 | — | 178 | 1 | no | — |
| 548 | C22⋊C4 | — | 178 | 2 | no | — |
| 549 | C22⋊C4 | — | 178 | 2 | no | — |
| 550 | C22⋊C4 | — | 178 | 2 | no | — |
| 551 | C22⋊C4 | — | 178 | 2 | no | — |
| 552 | C22⋊C4 | — | 178 | 2 | no | — |
| 553 | C22⋊C4 | — | 178 | 2 | no | — |
| 554 | C22⋊C4 | — | 178 | 2 | no | — |
| 555 | C42 | — | 2 | 1 | no | — |
| 556 | C42 | — | 178 | 2 | no | — |
| 557 | C42 | C2×D356 | 1 | 1 | yes | characteristic |
| 558 | C42 | C2×D356 | 1 | 1 | yes | characteristic |
| 559 | C23 | — | 2 | 2 | no | — |
| 560 | C23 | — | 2 | 2 | no | — |
| 561 | C23 | — | 2 | 1 | no | — |
| 562 | C23 | — | 2 | 1 | no | — |
| 563 | C23 | — | 4 | 1 | no | — |
| 564 | C23 | — | 4 | 1 | no | — |
| 565 | C23 | — | 8 | 2 | no | — |
| 566 | C23 | — | 8 | 2 | no | — |
| 567 | C23 | — | 356 | 2 | no | — |
| 568 | C23 | — | 356 | 2 | no | — |
| 569 | C23 | — | 356 | 1 | no | — |
| 570 | C23 | — | 1424 | 2 | no | — |
| 571 | C23 | — | 178 | 4 | no | — |
| 572 | C23 | — | 178 | 2 | no | — |
| 573 | C23 | — | 712 | 2 | no | — |
| 574 | C23 | — | 712 | 1 | no | — |
| 575 | C23 | — | 712 | 2 | no | — |
| 576 | C23 | #15667982 | 1 | 2 | yes | — |
| 577 | C23 | #15667982 | 1 | 1 | yes | characteristic |
| 578 | C23 | C2×D4×D89 | 1 | 2 | yes | — |
| 579 | Q8 | — | 356 | 1 | no | — |
| 580 | Q8 | — | 356 | 2 | no | — |
| 581 | Q8 | — | 178 | 2 | no | — |
| 582 | D4 | — | 4 | 2 | no | — |
| 583 | D4 | — | 4 | 1 | no | — |
| 584 | D4 | — | 4 | 1 | no | — |
| 585 | D4 | — | 4 | 1 | no | — |
| 586 | D4 | — | 4 | 1 | no | — |
| 587 | D4 | — | 4 | 4 | no | — |
| 588 | D4 | — | 4 | 4 | no | — |
| 589 | D4 | — | 8 | 1 | no | — |
| 590 | D4 | — | 8 | 2 | no | — |
| 591 | D4 | — | 8 | 2 | no | — |
| 592 | D4 | — | 356 | 1 | no | — |
| 593 | D4 | — | 356 | 2 | no | — |
| 594 | D4 | — | 356 | 4 | no | — |
| 595 | D4 | — | 356 | 4 | no | — |
| 596 | D4 | — | 356 | 2 | no | — |
| 597 | D4 | — | 356 | 2 | no | — |
| 598 | D4 | — | 356 | 2 | no | — |
| 599 | D4 | — | 356 | 2 | no | — |
| 600 | D4 | — | 1424 | 4 | no | — |
| 601 | D4 | — | 178 | 2 | no | — |
| 602 | D4 | — | 712 | 2 | no | — |
| 603 | D4 | — | 712 | 2 | no | — |
| 604 | D4 | — | 712 | 2 | no | — |
| 605 | D4 | — | 712 | 2 | no | — |
| 606 | D4 | — | 712 | 2 | no | — |
| 607 | D4 | — | 712 | 2 | no | — |
| 608 | C2×C4 | — | 2 | 1 | no | — |
| 609 | C2×C4 | — | 2 | 1 | no | — |
| 610 | C2×C4 | — | 2 | 1 | no | — |
| 611 | C2×C4 | — | 2 | 1 | no | — |
| 612 | C2×C4 | — | 4 | 2 | no | — |
| 613 | C2×C4 | — | 4 | 4 | no | — |
| 614 | C2×C4 | — | 16 | 2 | no | — |
| 615 | C2×C4 | — | 356 | 2 | no | — |
| 616 | C2×C4 | — | 356 | 2 | no | — |
| 617 | C2×C4 | — | 356 | 4 | no | — |
| 618 | C2×C4 | — | 356 | 2 | no | — |
| 619 | C2×C4 | — | 356 | 1 | no | — |
| 620 | C2×C4 | — | 356 | 2 | no | — |
| 621 | C2×C4 | — | 178 | 4 | no | — |
| 622 | C2×C4 | — | 178 | 2 | no | — |
| 623 | C2×C4 | — | 178 | 2 | no | — |
| 624 | C2×C4 | — | 178 | 2 | no | — |
| 625 | C2×C4 | — | 712 | 1 | no | — |
| 626 | C2×C4 | — | 712 | 2 | no | — |
| 627 | C2×C4 | — | 712 | 2 | no | — |
| 628 | C2×C4 | #15667982 | 1 | 1 | yes | characteristic |
| 629 | C2×C4 | C22×D356 | 1 | 1 | yes | characteristic |
| 630 | C8 | — | 356 | 2 | no | — |
| 631 | C22 | — | 2 | 2 | no | — |
| 632 | C22 | — | 2 | 2 | no | — |
| 633 | C22 | — | 4 | 1 | no | — |
| 634 | C22 | — | 4 | 2 | no | — |
| 635 | C22 | — | 4 | 2 | no | — |
| 636 | C22 | — | 4 | 2 | no | — |
| 637 | C22 | — | 4 | 2 | no | — |
| 638 | C22 | — | 4 | 1 | no | — |
| 639 | C22 | — | 4 | 1 | no | — |
| 640 | C22 | — | 8 | 2 | no | — |
| 641 | C22 | — | 8 | 2 | no | — |
| 642 | C22 | — | 16 | 1 | no | — |
| 643 | C22 | — | 16 | 1 | no | — |
| 644 | C22 | — | 356 | 2 | no | — |
| 645 | C22 | — | 356 | 2 | no | — |
| 646 | C22 | — | 356 | 2 | no | — |
| 647 | C22 | — | 356 | 2 | no | — |
| 648 | C22 | — | 1424 | 2 | no | — |
| 649 | C22 | — | 1424 | 2 | no | — |
| 650 | C22 | — | 712 | 2 | no | — |
| 651 | C22 | — | 712 | 4 | no | — |
| 652 | C22 | — | 712 | 4 | no | — |
| 653 | C22 | #19151786 | 1 | 1 | yes | characteristic |
| 654 | C22 | #19151786 | 1 | 1 | yes | characteristic |
| 655 | C22 | C2×#15667982 | 1 | 1 | yes | characteristic |
| 656 | C4 | — | 2 | 2 | no | — |
| 657 | C4 | — | 2 | 1 | no | — |
| 658 | C4 | — | 2 | 1 | no | — |
| 659 | C4 | — | 4 | 1 | no | — |
| 660 | C4 | — | 8 | 4 | no | — |
| 661 | C4 | — | 356 | 2 | no | — |
| 662 | C4 | — | 356 | 2 | no | — |
| 663 | C4 | — | 356 | 2 | no | — |
| 664 | C4 | — | 356 | 2 | no | — |
| 665 | C2 | — | 2 | 1 | no | — |
| 666 | C2 | — | 2 | 1 | no | — |
| 667 | C2 | — | 2 | 1 | no | — |
| 668 | C2 | — | 4 | 2 | no | — |
| 669 | C2 | — | 4 | 2 | no | — |
| 670 | C2 | — | 8 | 1 | no | — |
| 671 | C2 | — | 8 | 1 | no | — |
| 672 | C2 | — | 712 | 2 | no | — |
| 673 | C2 | — | 712 | 2 | no | — |
| 674 | C2 | C2×#19151786 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26034585 | C2 | semidirect |
| 2. #26029651 | C2 | semidirect |
| 3. C2×#19151765 | C2 | semidirect |
| 4. #26022262 | C2 | semidirect |
| 5. #26022250 | C2 | semidirect |
| 6. #26022238 | C2 | semidirect |
| 7. #26021896 | C2 | semidirect |
| 8. C2×#353×C89 | C2 | semidirect |
| 9. C2×#15668057 | C22 | semidirect |
| 12. #19152335 | C22 | semidirect |
| 13. #19152334 | C22 | semidirect |
| 16. #19152233 | C22 | semidirect |
| 25. #19151789 | C22 | semidirect |
| 27. #19151786 | C22 | semidirect |
| 31. #19151765 | C22 | semidirect |
| 33. C2×#15667929 | C22 | semidirect |
| 35. #19151387 | C22 | semidirect |
| 36. #19151384 | C22 | semidirect |
| 38. C2×#99×C89 | C22 | semidirect |
| 39. #353×C89 | C22 | semidirect |
| 40. #353×C89 | C22 | semidirect |
| 50. C22×C22⋊D89 | D4 | semidirect |
| 71. #15667993 | D4 | semidirect |
| 94. #15667980 | D4 | semidirect |
| 103. C2×C22⋊Dic89 | D4 | semidirect |
| 111. C22×D4×C89 | D4 | semidirect |
| 114. #127×C89 | D4 | semidirect |
| 115. #127×C89 | D4 | semidirect |
| 119. C2×C42×C89 | D4 | semidirect |
| 344. C2×#353 | D89 | semidirect |
| 346. C89 | #33557 | semidirect |
| 374. C2×#99 | C2×D89 | semidirect |
| 375. #353 | C2×D89 | semidirect |
| 376. #353 | C2×D89 | semidirect |
| 392. C22×D4 | D356 | semidirect |
| 402. #127 | D356 | semidirect |
| 403. #127 | D356 | semidirect |
| 451. C2×C42 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034585 | 2 |
| #26029651 | 2 |
| C2×#19151765 | 2 |
| #26022262 | 2 |
| #26022250 | 2 |
| #26022238 | 2 |
| #26021896 | 2 |
| C2×#353×C89 | 2 |
| #33557 | 89 |