Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
522 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 57 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 | #26026626 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #26021296 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #26019223 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #26019220 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #26018281 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #26018183 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C89×#1354 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#15668040 | — | 2 | 1 | no | — |
| 9 | #19152179 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#15667990 | — | 2 | 1 | no | — |
| 11 | C2×#15667988 | — | 2 | 1 | no | — |
| 12 | #19151739 | — | 2 | 1 | no | — |
| 13 | #19151737 | — | 2 | 1 | no | — |
| 14 | C2×#15667938 | — | 2 | 1 | no | — |
| 15 | #19151522 | — | 2 | 1 | no | — |
| 16 | #19151520 | — | 2 | 1 | no | — |
| 17 | #19151518 | C22 | 1 | 1 | yes | characteristic |
| 18 | #19151499 | C22 | 1 | 1 | yes | characteristic |
| 19 | #19151495 | — | 2 | 1 | no | — |
| 20 | #19151476 | — | 2 | 1 | no | — |
| 21 | #19151333 | — | 2 | 1 | no | — |
| 22 | #19151331 | — | 2 | 1 | no | — |
| 23 | #19151324 | C22 | 1 | 1 | yes | characteristic |
| 24 | #395×C89 | C22 | 1 | 1 | yes | characteristic |
| 25 | #343×C89 | C22 | 1 | 1 | yes | characteristic |
| 26 | #324×C89 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#13083574 | — | 2 | 1 | no | — |
| 28 | C22×Dic178 | D4 | 1 | 1 | yes | characteristic |
| 29 | C22×D356 | D4 | 1 | 1 | yes | characteristic |
| 30 | C22×C4×D89 | — | 2 | 1 | no | — |
| 31 | #15668040 | — | 4 | 2 | no | — |
| 32 | #15668040 | — | 4 | 2 | no | — |
| 33 | C2×#13083563 | — | 4 | 1 | no | — |
| 34 | C2×#13083563 | — | 4 | 1 | no | — |
| 35 | C2×#13083561 | — | 4 | 1 | no | — |
| 36 | C2×D712 | — | 4 | 1 | no | — |
| 37 | #15667992 | — | 4 | 1 | no | — |
| 38 | #15667990 | — | 4 | 4 | no | — |
| 39 | #15667988 | — | 4 | 4 | no | — |
| 40 | #15667987 | — | 4 | 1 | no | — |
| 41 | #15667986 | — | 2 | 1 | no | — |
| 42 | #15667986 | — | 2 | 1 | no | — |
| 43 | C2×C4⋊Dic89 | — | 2 | 1 | no | — |
| 44 | C2×#13083553 | — | 2 | 1 | no | — |
| 45 | C2×#13083553 | — | 2 | 1 | no | — |
| 46 | C2×#13083553 | — | 2 | 1 | no | — |
| 47 | C2×#13083553 | — | 2 | 1 | no | — |
| 48 | C2×#13083551 | — | 2 | 1 | no | — |
| 49 | C2×#13083551 | — | 2 | 1 | no | — |
| 50 | C2×#13083551 | — | 2 | 1 | no | — |
| 51 | C2×#13083551 | — | 2 | 1 | no | — |
| 52 | C2×#13083551 | — | 2 | 1 | no | — |
| 53 | C2×C4×Dic89 | D4 | 1 | 1 | yes | characteristic |
| 54 | #15667938 | — | 4 | 2 | no | — |
| 55 | #15667937 | — | 4 | 1 | no | — |
| 56 | #15667936 | — | 4 | 1 | no | — |
| 57 | C22⋊#10623494 | — | 2 | 1 | no | — |
| 58 | #15667919 | — | 2 | 1 | no | — |
| 59 | #15667919 | D4 | 1 | 1 | yes | characteristic |
| 60 | C22×Q8×C89 | D4 | 1 | 1 | yes | characteristic |
| 61 | C2×M16×C89 | — | 2 | 1 | no | — |
| 62 | C2×C4⋊C4×C89 | — | 2 | 1 | no | — |
| 63 | C2×C4⋊C4×C89 | C23 | 1 | 1 | yes | characteristic |
| 64 | C22⋊C8×C89 | — | 2 | 1 | no | — |
| 65 | #95×C89 | — | 2 | 1 | no | — |
| 66 | #95×C89 | D4 | 1 | 1 | yes | characteristic |
| 67 | C23×D89 | — | 2 | 1 | no | — |
| 68 | #13083574 | — | 4 | 1 | no | — |
| 69 | #13083574 | — | 4 | 1 | no | — |
| 70 | #13083574 | — | 4 | 1 | no | — |
| 71 | #13083574 | — | 4 | 1 | no | — |
| 72 | C2×Dic178 | — | 2 | 1 | no | — |
| 73 | C2×Dic178 | — | 4 | 1 | no | — |
| 74 | C2×Dic178 | — | 4 | 2 | no | — |
| 75 | C2×D356 | — | 2 | 1 | no | — |
| 76 | C2×D356 | — | 2 | 1 | no | — |
| 77 | C2×D356 | — | 2 | 1 | no | — |
| 78 | C2×D356 | — | 2 | 1 | no | — |
| 79 | C2×D356 | — | 4 | 1 | no | — |
| 80 | C2×D356 | — | 4 | 1 | no | — |
| 81 | C2×D356 | SD16 | 1 | 2 | yes | complemented |
| 82 | C2×C22⋊D89 | — | 4 | 1 | no | — |
| 83 | C22×Dic89 | — | 2 | 1 | no | — |
| 84 | C22×Dic89 | — | 2 | 1 | no | — |
| 85 | C22×Dic89 | — | 2 | 1 | no | — |
| 86 | C2×C4×D89 | — | 4 | 2 | no | — |
| 87 | C2×C4×D89 | — | 4 | 1 | no | — |
| 88 | C2×C4×D89 | — | 4 | 2 | no | — |
| 89 | C2×C4×D89 | — | 8 | 1 | no | — |
| 90 | #13083563 | — | 4 | 4 | no | — |
| 91 | #13083563 | — | 8 | 2 | no | — |
| 92 | #13083561 | — | 8 | 2 | no | — |
| 93 | D712 | — | 4 | 4 | no | — |
| 94 | C2×#10623494 | — | 4 | 1 | no | — |
| 95 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 96 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 97 | C4⋊Dic89 | — | 4 | 2 | no | — |
| 98 | #13083553 | — | 2 | 4 | no | — |
| 99 | #13083553 | — | 4 | 2 | no | — |
| 100 | #13083553 | — | 4 | 2 | no | — |
| 101 | #13083553 | — | 8 | 1 | no | — |
| 102 | #13083551 | — | 4 | 2 | no | — |
| 103 | #13083551 | — | 4 | 2 | no | — |
| 104 | #13083551 | — | 4 | 2 | no | — |
| 105 | #13083551 | — | 4 | 1 | no | — |
| 106 | #13083551 | — | 4 | 1 | no | — |
| 107 | #13083551 | — | 4 | 2 | no | — |
| 108 | #13083551 | — | 8 | 1 | no | — |
| 109 | C4×Dic89 | — | 4 | 1 | no | — |
| 110 | C2×Q8×C89 | — | 4 | 2 | no | — |
| 111 | C2×Q8×C89 | — | 4 | 1 | no | — |
| 112 | C22×C4×C89 | — | 2 | 1 | no | — |
| 113 | C22×C4×C89 | — | 2 | 1 | no | — |
| 114 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 117 | M16×C89 | — | 2 | 2 | no | — |
| 118 | M16×C89 | — | 4 | 1 | no | — |
| 119 | C2×C8×C89 | — | 4 | 1 | no | — |
| 120 | C2×C8×C89 | — | 4 | 1 | no | — |
| 121 | C4⋊C4×C89 | — | 4 | 1 | no | — |
| 122 | C4⋊C4×C89 | — | 4 | 2 | no | — |
| 123 | C23×C89 | #120 | 1 | 1 | yes | characteristic |
| 124 | C22×D89 | — | 2 | 2 | no | — |
| 125 | C22×D89 | — | 4 | 1 | no | — |
| 126 | C22×D89 | — | 4 | 1 | no | — |
| 127 | C22×D89 | — | 4 | 1 | no | — |
| 128 | C22×D89 | — | 4 | 1 | no | — |
| 129 | C22×D89 | — | 4 | 1 | no | — |
| 130 | C22×D89 | — | 4 | 1 | no | — |
| 131 | C22×D89 | — | 4 | 1 | no | — |
| 132 | Q8×C89 | — | 4 | 2 | no | — |
| 133 | Q8×C89 | — | 8 | 1 | no | — |
| 134 | C2×C4×C89 | — | 2 | 1 | no | — |
| 135 | C2×C4×C89 | — | 2 | 1 | no | — |
| 136 | C2×C4×C89 | — | 2 | 2 | no | — |
| 137 | C2×C4×C89 | — | 2 | 1 | no | — |
| 138 | C2×C4×C89 | — | 2 | 1 | no | — |
| 139 | C2×C4×C89 | — | 4 | 1 | no | — |
| 140 | C2×C4×C89 | — | 4 | 1 | no | — |
| 141 | C2×C4×C89 | — | 4 | 1 | no | — |
| 142 | C2×C4×C89 | — | 4 | 1 | no | — |
| 143 | C2×C4×C89 | — | 4 | 1 | no | — |
| 144 | C2×C4×C89 | — | 4 | 1 | no | — |
| 145 | C2×C4×C89 | — | 4 | 1 | no | — |
| 146 | C2×C4×C89 | C2×SD16 | 1 | 1 | yes | characteristic |
| 147 | C2×C4×C89 | #137 | 1 | 1 | yes | characteristic |
| 148 | C22⋊D89 | — | 8 | 1 | no | — |
| 149 | C22⋊D89 | — | 8 | 1 | no | — |
| 150 | C2×Dic89 | — | 2 | 2 | no | — |
| 151 | C2×Dic89 | — | 2 | 2 | no | — |
| 152 | C2×Dic89 | — | 4 | 1 | no | — |
| 153 | C2×Dic89 | — | 4 | 1 | no | — |
| 154 | C2×Dic89 | — | 4 | 1 | no | — |
| 155 | C2×Dic89 | — | 4 | 1 | no | — |
| 156 | C2×Dic89 | — | 4 | 1 | no | — |
| 157 | C2×Dic89 | — | 4 | 1 | no | — |
| 158 | C2×Dic89 | — | 4 | 1 | no | — |
| 159 | C2×Dic89 | — | 4 | 1 | no | — |
| 160 | D356 | — | 4 | 2 | no | — |
| 161 | D356 | — | 4 | 1 | no | — |
| 162 | D356 | — | 4 | 1 | no | — |
| 163 | D356 | — | 8 | 1 | no | — |
| 164 | D356 | — | 8 | 1 | no | — |
| 165 | D356 | — | 8 | 1 | no | — |
| 166 | C4×D89 | — | 8 | 4 | no | — |
| 167 | C4×D89 | — | 8 | 1 | no | — |
| 168 | C4×D89 | — | 8 | 1 | no | — |
| 169 | Dic178 | — | 4 | 2 | no | — |
| 170 | Dic178 | — | 4 | 1 | no | — |
| 171 | Dic178 | — | 4 | 1 | no | — |
| 172 | Dic178 | — | 8 | 1 | no | — |
| 173 | C8×C89 | — | 4 | 2 | no | — |
| 174 | C8×C89 | — | 8 | 1 | no | — |
| 175 | #10623494 | — | 8 | 1 | no | — |
| 176 | C22×C89 | — | 2 | 1 | no | — |
| 177 | C22×C89 | — | 2 | 1 | no | — |
| 178 | C22×C89 | #448 | 1 | 1 | yes | characteristic |
| 179 | C22×C89 | #453 | 1 | 1 | yes | characteristic |
| 180 | C22×C89 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 181 | C2×D89 | — | 4 | 2 | no | — |
| 182 | C2×D89 | — | 4 | 2 | no | — |
| 183 | C2×D89 | — | 4 | 2 | no | — |
| 184 | C2×D89 | — | 8 | 1 | no | — |
| 185 | C2×D89 | — | 8 | 1 | no | — |
| 186 | C2×D89 | — | 8 | 1 | no | — |
| 187 | C2×D89 | — | 8 | 1 | no | — |
| 188 | C2×D89 | — | 8 | 1 | no | — |
| 189 | C2×D89 | — | 8 | 1 | no | — |
| 190 | C2×D89 | — | 8 | 1 | no | — |
| 191 | C4×C89 | — | 2 | 1 | no | — |
| 192 | C4×C89 | — | 2 | 1 | no | — |
| 193 | C4×C89 | — | 4 | 1 | no | — |
| 194 | C4×C89 | — | 4 | 1 | no | — |
| 195 | C4×C89 | — | 4 | 2 | no | — |
| 196 | C4×C89 | — | 8 | 1 | no | — |
| 197 | Dic89 | — | 4 | 2 | no | — |
| 198 | Dic89 | — | 4 | 2 | no | — |
| 199 | Dic89 | — | 8 | 1 | no | — |
| 200 | Dic89 | — | 8 | 1 | no | — |
| 201 | #12126 | — | 89 | 1 | no | maximal, Sylow |
| 202 | C2×C89 | — | 2 | 1 | no | — |
| 203 | C2×C89 | — | 2 | 1 | no | — |
| 204 | C2×C89 | #1596 | 1 | 1 | yes | characteristic |
| 205 | C2×C89 | #2196 | 1 | 1 | yes | characteristic |
| 206 | C2×C89 | #2203 | 1 | 1 | yes | characteristic |
| 207 | D89 | — | 8 | 2 | no | — |
| 208 | D89 | — | 16 | 1 | no | — |
| 209 | #2683 | — | 89 | 1 | no | — |
| 210 | #2006 | — | 89 | 1 | no | — |
| 211 | #1604 | — | 89 | 1 | no | — |
| 212 | #1604 | — | 89 | 1 | no | — |
| 213 | #1354 | — | 89 | 1 | no | — |
| 214 | #1354 | D89 | 1 | 1 | yes | characteristic, complemented |
| 215 | #1318 | — | 89 | 1 | no | — |
| 216 | C89 | #12126 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 217 | C2×AGL(1,ℤ/8) | — | 178 | 1 | no | — |
| 218 | #537 | — | 89 | 1 | no | — |
| 219 | C2×C22⋊Q8 | — | 178 | 1 | no | — |
| 220 | C2×C22⋊Q8 | — | 178 | 1 | no | — |
| 221 | #448 | — | 178 | 1 | no | — |
| 222 | #448 | — | 178 | 1 | no | — |
| 223 | C2×#104 | — | 178 | 1 | no | — |
| 224 | #396 | — | 178 | 1 | no | — |
| 225 | #396 | — | 178 | 1 | no | — |
| 226 | #395 | — | 89 | 1 | no | — |
| 227 | #395 | C2×D89 | 1 | 1 | yes | characteristic |
| 228 | #390 | — | 89 | 1 | no | — |
| 229 | #389 | — | 178 | 1 | no | — |
| 230 | #386 | — | 178 | 1 | no | — |
| 231 | #343 | C2×D89 | 1 | 1 | yes | characteristic |
| 232 | #327 | — | 178 | 1 | no | — |
| 233 | #327 | — | 178 | 1 | no | — |
| 234 | #324 | — | 89 | 1 | no | — |
| 235 | #324 | C2×D89 | 1 | 1 | yes | characteristic |
| 236 | C2×#41 | — | 178 | 1 | no | — |
| 237 | C22×Q8 | — | 89 | 1 | no | — |
| 238 | C22×Q8 | D356 | 1 | 1 | yes | characteristic |
| 239 | C22×D4 | — | 89 | 1 | no | — |
| 240 | C23×C4 | — | 178 | 1 | no | — |
| 241 | AGL(1,ℤ/8) | — | 356 | 2 | no | — |
| 242 | AGL(1,ℤ/8) | — | 356 | 2 | no | — |
| 243 | C2×SD16 | — | 356 | 1 | no | — |
| 244 | C2×SD16 | — | 356 | 1 | no | — |
| 245 | C2×SD16 | — | 356 | 1 | no | — |
| 246 | C2×D8 | — | 356 | 1 | no | — |
| 247 | C2×M16 | — | 2 | 1 | no | — |
| 248 | C22⋊Q8 | — | 356 | 4 | no | — |
| 249 | C22⋊Q8 | — | 356 | 1 | no | — |
| 250 | C22⋊Q8 | — | 356 | 4 | no | — |
| 251 | #121 | — | 356 | 1 | no | — |
| 252 | #121 | — | 178 | 1 | no | — |
| 253 | #121 | — | 178 | 1 | no | — |
| 254 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 255 | C2×C4⋊C4 | — | 178 | 1 | no | — |
| 256 | C2×C4⋊C4 | — | 178 | 1 | no | — |
| 257 | C2×C4⋊C4 | — | 178 | 1 | no | — |
| 258 | C2×C4⋊C4 | — | 178 | 1 | no | — |
| 259 | C2×C4⋊C4 | — | 178 | 1 | no | — |
| 260 | C2×C4⋊C4 | C22×D89 | 1 | 1 | yes | characteristic |
| 261 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 262 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 263 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 264 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 265 | C2×C22⋊C4 | — | 178 | 1 | no | — |
| 266 | C2×C42 | — | 89 | 1 | no | — |
| 267 | #104 | — | 356 | 2 | no | — |
| 268 | #103 | — | 356 | 1 | no | — |
| 269 | #103 | — | 356 | 1 | no | — |
| 270 | C22⋊C8 | — | 2 | 1 | no | — |
| 271 | C22⋊C8 | — | 178 | 1 | no | — |
| 272 | #95 | — | 2 | 1 | no | — |
| 273 | #95 | — | 89 | 1 | no | — |
| 274 | #95 | — | 178 | 1 | no | — |
| 275 | #95 | D356 | 1 | 1 | yes | characteristic |
| 276 | C24 | — | 178 | 1 | no | — |
| 277 | #41 | — | 356 | 1 | no | — |
| 278 | #41 | — | 356 | 1 | no | — |
| 279 | #41 | — | 356 | 1 | no | — |
| 280 | #41 | — | 356 | 1 | no | — |
| 281 | C2×Q8 | — | 4 | 2 | no | — |
| 282 | C2×Q8 | — | 4 | 1 | no | — |
| 283 | C2×Q8 | — | 356 | 1 | no | — |
| 284 | C2×Q8 | — | 356 | 2 | no | — |
| 285 | C2×Q8 | — | 178 | 1 | no | — |
| 286 | C2×D4 | — | 89 | 2 | no | — |
| 287 | C2×D4 | — | 356 | 1 | no | — |
| 288 | C2×D4 | — | 356 | 1 | no | — |
| 289 | C2×D4 | — | 356 | 1 | no | — |
| 290 | C2×D4 | — | 178 | 1 | no | — |
| 291 | C2×D4 | — | 178 | 1 | no | — |
| 292 | C2×D4 | — | 178 | 1 | no | — |
| 293 | C2×D4 | — | 178 | 1 | no | — |
| 294 | C22×C4 | — | 2 | 1 | no | — |
| 295 | C22×C4 | — | 2 | 1 | no | — |
| 296 | C22×C4 | — | 356 | 1 | no | — |
| 297 | C22×C4 | — | 356 | 2 | no | — |
| 298 | C22×C4 | — | 356 | 2 | no | — |
| 299 | C22×C4 | — | 178 | 1 | no | — |
| 300 | C22×C4 | — | 178 | 1 | no | — |
| 301 | C22×C4 | — | 178 | 1 | no | — |
| 302 | C22×C4 | — | 712 | 1 | no | — |
| 303 | C22×C4 | D4×D89 | 1 | 1 | yes | characteristic |
| 304 | C22×C4 | D4×D89 | 1 | 1 | yes | characteristic |
| 305 | C22×C4 | C2×D356 | 1 | 1 | yes | characteristic |
| 306 | SD16 | — | 356 | 4 | no | — |
| 307 | SD16 | — | 712 | 2 | no | — |
| 308 | SD16 | — | 712 | 2 | no | — |
| 309 | D8 | — | 356 | 4 | no | — |
| 310 | M16 | — | 2 | 2 | no | — |
| 311 | M16 | — | 4 | 1 | no | — |
| 312 | C2×C8 | — | 4 | 1 | no | — |
| 313 | C2×C8 | — | 4 | 1 | no | — |
| 314 | C2×C8 | — | 356 | 1 | no | — |
| 315 | C4⋊C4 | — | 4 | 1 | no | — |
| 316 | C4⋊C4 | — | 4 | 2 | no | — |
| 317 | C4⋊C4 | — | 356 | 2 | no | — |
| 318 | C4⋊C4 | — | 356 | 2 | no | — |
| 319 | C4⋊C4 | — | 356 | 2 | no | — |
| 320 | C4⋊C4 | — | 178 | 1 | no | — |
| 321 | C4⋊C4 | — | 178 | 1 | no | — |
| 322 | C4⋊C4 | — | 178 | 4 | no | — |
| 323 | C4⋊C4 | — | 712 | 1 | no | — |
| 324 | C22⋊C4 | — | 356 | 2 | no | — |
| 325 | C22⋊C4 | — | 356 | 1 | no | — |
| 326 | C22⋊C4 | — | 356 | 1 | no | — |
| 327 | C22⋊C4 | — | 356 | 2 | no | — |
| 328 | C22⋊C4 | — | 356 | 2 | no | — |
| 329 | C22⋊C4 | — | 356 | 2 | no | — |
| 330 | C22⋊C4 | — | 712 | 1 | no | — |
| 331 | C42 | — | 356 | 1 | no | — |
| 332 | C23 | — | 356 | 1 | no | — |
| 333 | C23 | — | 356 | 1 | no | — |
| 334 | C23 | — | 356 | 1 | no | — |
| 335 | C23 | — | 356 | 1 | no | — |
| 336 | C23 | — | 356 | 1 | no | — |
| 337 | C23 | — | 356 | 1 | no | — |
| 338 | C23 | — | 356 | 1 | no | — |
| 339 | C23 | — | 178 | 2 | no | — |
| 340 | C23 | #15667982 | 1 | 1 | yes | characteristic |
| 341 | Q8 | — | 4 | 2 | no | — |
| 342 | Q8 | — | 8 | 1 | no | — |
| 343 | Q8 | — | 356 | 1 | no | — |
| 344 | Q8 | — | 356 | 1 | no | — |
| 345 | Q8 | — | 356 | 2 | no | — |
| 346 | Q8 | — | 712 | 1 | no | — |
| 347 | D4 | — | 356 | 2 | no | — |
| 348 | D4 | — | 356 | 1 | no | — |
| 349 | D4 | — | 356 | 1 | no | — |
| 350 | D4 | — | 712 | 1 | no | — |
| 351 | D4 | — | 712 | 1 | no | — |
| 352 | D4 | — | 712 | 1 | no | — |
| 353 | D4 | — | 712 | 1 | no | — |
| 354 | D4 | — | 712 | 1 | no | — |
| 355 | C2×C4 | — | 2 | 1 | no | — |
| 356 | C2×C4 | — | 2 | 1 | no | — |
| 357 | C2×C4 | — | 2 | 2 | no | — |
| 358 | C2×C4 | — | 2 | 1 | no | — |
| 359 | C2×C4 | — | 2 | 1 | no | — |
| 360 | C2×C4 | — | 4 | 1 | no | — |
| 361 | C2×C4 | — | 4 | 1 | no | — |
| 362 | C2×C4 | — | 4 | 1 | no | — |
| 363 | C2×C4 | — | 4 | 1 | no | — |
| 364 | C2×C4 | — | 4 | 1 | no | — |
| 365 | C2×C4 | — | 4 | 1 | no | — |
| 366 | C2×C4 | — | 4 | 1 | no | — |
| 367 | C2×C4 | — | 356 | 1 | no | — |
| 368 | C2×C4 | — | 356 | 1 | no | — |
| 369 | C2×C4 | — | 356 | 1 | no | — |
| 370 | C2×C4 | — | 356 | 1 | no | — |
| 371 | C2×C4 | — | 356 | 1 | no | — |
| 372 | C2×C4 | — | 356 | 1 | no | — |
| 373 | C2×C4 | — | 356 | 1 | no | — |
| 374 | C2×C4 | — | 356 | 1 | no | — |
| 375 | C2×C4 | — | 178 | 2 | no | — |
| 376 | C2×C4 | — | 178 | 2 | no | — |
| 377 | C2×C4 | — | 712 | 1 | no | — |
| 378 | C2×C4 | — | 712 | 1 | no | — |
| 379 | C2×C4 | — | 712 | 4 | no | — |
| 380 | C2×C4 | SD16×D89 | 1 | 1 | yes | characteristic |
| 381 | C2×C4 | #15668044 | 1 | 1 | yes | characteristic |
| 382 | C8 | — | 4 | 2 | no | — |
| 383 | C8 | — | 8 | 1 | no | — |
| 384 | C8 | — | 712 | 1 | no | — |
| 385 | C22 | — | 2 | 1 | no | — |
| 386 | C22 | — | 2 | 1 | no | — |
| 387 | C22 | — | 356 | 2 | no | — |
| 388 | C22 | — | 356 | 2 | no | — |
| 389 | C22 | — | 356 | 2 | no | — |
| 390 | C22 | — | 712 | 1 | no | — |
| 391 | C22 | — | 712 | 1 | no | — |
| 392 | C22 | — | 712 | 1 | no | — |
| 393 | C22 | — | 712 | 1 | no | — |
| 394 | C22 | — | 712 | 1 | no | — |
| 395 | C22 | — | 712 | 1 | no | — |
| 396 | C22 | — | 712 | 1 | no | — |
| 397 | C22 | #19151738 | 1 | 1 | yes | characteristic |
| 398 | C22 | #19151767 | 1 | 1 | yes | characteristic |
| 399 | C22 | #19151786 | 1 | 1 | yes | characteristic |
| 400 | C4 | — | 2 | 1 | no | — |
| 401 | C4 | — | 2 | 1 | no | — |
| 402 | C4 | — | 4 | 1 | no | — |
| 403 | C4 | — | 4 | 1 | no | — |
| 404 | C4 | — | 4 | 2 | no | — |
| 405 | C4 | — | 8 | 1 | no | — |
| 406 | C4 | — | 356 | 2 | no | — |
| 407 | C4 | — | 356 | 2 | no | — |
| 408 | C4 | — | 712 | 1 | no | — |
| 409 | C4 | — | 712 | 1 | no | — |
| 410 | C2 | — | 2 | 1 | no | — |
| 411 | C2 | — | 2 | 1 | no | — |
| 412 | C2 | — | 1424 | 1 | no | — |
| 413 | C2 | — | 712 | 2 | no | — |
| 414 | C2 | #26019176 | 1 | 1 | yes | characteristic |
| 415 | C2 | #26022237 | 1 | 1 | yes | characteristic |
| 416 | C2 | #26022274 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26026626 | C2 | semidirect |
| 3. #26019223 | C2 | semidirect |
| 4. #26019220 | C2 | semidirect |
| 5. #26018281 | C2 | semidirect |
| 6. #26018183 | C2 | semidirect |
| 7. C89×#1354 | C2 | semidirect |
| 81. C2×D356 | SD16 | semidirect |
| 214. #1354 | D89 | semidirect |
| 216. C89 | #12126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026626 | 2 |
| #26021296 | 2 |
| #26019223 | 2 |
| #26019220 | 2 |
| #26018281 | 2 |
| #26018183 | 2 |
| C89×#1354 | 2 |
| #12126 | 89 |