Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
742 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 742 conjugacy classes of subgroups — too many to draw. Only its 89 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 | #14538038 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #14531549 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #14528729 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #14528701 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #14527312 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #14526693 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C17×#1284 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×#63252 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#10587594 | — | 2 | 1 | no | — |
| 10 | C2×#10587616 | C22 | 1 | 1 | yes | characteristic |
| 11 | #11762956 | — | 2 | 2 | no | — |
| 12 | #11762950 | C4 | 1 | 2 | yes | complemented |
| 13 | #11762945 | C4 | 1 | 2 | yes | complemented |
| 14 | C2×#10587476 | — | 2 | 1 | no | — |
| 15 | C2×#10587476 | — | 2 | 1 | no | — |
| 16 | #11762811 | — | 2 | 1 | no | — |
| 17 | C2×#10587477 | — | 2 | 1 | no | — |
| 18 | C2×#10587477 | — | 2 | 1 | no | — |
| 19 | #11762773 | C22 | 1 | 1 | yes | characteristic |
| 20 | #11762709 | — | 2 | 1 | no | — |
| 21 | #11762700 | — | 2 | 1 | no | — |
| 22 | #11762692 | — | 2 | 1 | no | — |
| 23 | #11762687 | — | 2 | 1 | no | — |
| 24 | #11762685 | — | 2 | 1 | no | — |
| 25 | #11762672 | C22 | 1 | 1 | yes | characteristic |
| 26 | C4×#63227 | — | 2 | 1 | no | — |
| 27 | #11762542 | — | 2 | 2 | no | — |
| 28 | C17×#407 | C22 | 1 | 1 | yes | characteristic |
| 29 | C17×#381 | C22 | 1 | 1 | yes | characteristic |
| 30 | C4×C22⋊C4×C17 | C22 | 1 | 1 | yes | characteristic |
| 31 | C23×C4×C17 | C23 | 1 | 1 | yes | characteristic |
| 32 | C22×C22⋊D17 | — | 2 | 1 | no | — |
| 33 | C22×C22⋊D17 | — | 2 | 1 | no | — |
| 34 | C2×#63252 | — | 2 | 1 | no | — |
| 35 | C2×#63252 | — | 2 | 1 | no | — |
| 36 | C2×#63252 | — | 2 | 1 | no | — |
| 37 | C2×#63252 | — | 2 | 1 | no | — |
| 38 | C2×#63252 | — | 4 | 2 | no | — |
| 39 | C2×#63252 | — | 4 | 2 | no | — |
| 40 | C22×D68 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 41 | C22×D68 | D4 | 1 | 1 | yes | characteristic |
| 42 | C22×C4×D17 | — | 2 | 1 | no | — |
| 43 | C22×C4×D17 | — | 2 | 1 | no | — |
| 44 | C22×Dic34 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 45 | C2×M16×C17 | — | 2 | 1 | no | — |
| 46 | C2×C22⋊C4×C17 | — | 2 | 1 | no | — |
| 47 | C2×C22⋊C4×C17 | — | 2 | 1 | no | — |
| 48 | C2×C42×C17 | D4 | 1 | 1 | yes | characteristic |
| 49 | C2×C42×C17 | D4 | 1 | 1 | yes | characteristic |
| 50 | C2×C22⋊Dic17 | D4 | 1 | 1 | yes | characteristic |
| 51 | C2×C22⋊Dic17 | D4 | 1 | 1 | yes | characteristic |
| 52 | #10587616 | — | 2 | 1 | no | — |
| 53 | #10587616 | — | 2 | 1 | no | — |
| 54 | #10587616 | C2×C4 | 1 | 2 | yes | — |
| 55 | #10587616 | D4 | 1 | 2 | yes | — |
| 56 | C2×#63227 | — | 2 | 1 | no | — |
| 57 | C2×#63227 | — | 2 | 1 | no | — |
| 58 | C2×#63227 | — | 2 | 1 | no | — |
| 59 | C2×#63227 | — | 2 | 1 | no | — |
| 60 | C2×C4⋊Dic17 | D4 | 1 | 1 | yes | characteristic |
| 61 | C2×#63225 | — | 2 | 1 | no | — |
| 62 | C2×C4×Dic17 | — | 2 | 1 | no | — |
| 63 | C2×#63223 | — | 2 | 1 | no | — |
| 64 | #10587594 | — | 4 | 2 | no | — |
| 65 | #10587594 | — | 4 | 2 | no | — |
| 66 | C2×D136 | — | 2 | 2 | no | — |
| 67 | C2×#63219 | — | 2 | 2 | no | — |
| 68 | C17×C22⋊C8 | — | 2 | 1 | no | — |
| 69 | C17×C22⋊C8 | C2×C4 | 1 | 2 | yes | complemented |
| 70 | C17×#95 | — | 2 | 1 | no | — |
| 71 | C17×#95 | — | 2 | 1 | no | — |
| 72 | C17×#95 | — | 2 | 1 | no | — |
| 73 | #10587502 | — | 2 | 1 | no | — |
| 74 | #10587502 | — | 2 | 1 | no | — |
| 75 | #10587502 | — | 2 | 1 | no | — |
| 76 | #10587502 | — | 2 | 1 | no | — |
| 77 | C22⋊#3622 | — | 2 | 1 | no | — |
| 78 | C22⋊#3622 | — | 2 | 1 | no | — |
| 79 | #10587492 | — | 2 | 2 | no | — |
| 80 | #10587487 | — | 2 | 2 | no | — |
| 81 | #10587477 | — | 4 | 2 | no | — |
| 82 | #10587477 | — | 4 | 2 | no | — |
| 83 | #10587476 | — | 4 | 2 | no | — |
| 84 | #10587476 | — | 4 | 2 | no | — |
| 85 | C24×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 86 | C23×D17 | — | 2 | 1 | no | — |
| 87 | C23×D17 | — | 2 | 1 | no | — |
| 88 | C22×C4×C17 | — | 2 | 1 | no | — |
| 89 | C22×C4×C17 | — | 2 | 1 | no | — |
| 90 | C22×C4×C17 | — | 4 | 1 | no | — |
| 91 | C22×C4×C17 | — | 4 | 1 | no | — |
| 92 | C22×C4×C17 | — | 4 | 1 | no | — |
| 93 | C22×C4×C17 | C22×C4 | 1 | 1 | yes | characteristic |
| 94 | C22×C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 95 | C22×C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C22×C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C22×C4×C17 | #41 | 1 | 1 | yes | characteristic |
| 98 | C22×C4×C17 | #41 | 1 | 1 | yes | characteristic |
| 99 | C2×C22⋊D17 | — | 2 | 2 | no | — |
| 100 | C2×C22⋊D17 | — | 2 | 2 | no | — |
| 101 | C2×C22⋊D17 | — | 2 | 2 | no | — |
| 102 | C2×C22⋊D17 | — | 2 | 2 | no | — |
| 103 | C2×C22⋊D17 | — | 4 | 1 | no | — |
| 104 | C2×C22⋊D17 | — | 4 | 1 | no | — |
| 105 | C2×C22⋊D17 | — | 4 | 1 | no | — |
| 106 | C2×C22⋊D17 | — | 4 | 1 | no | — |
| 107 | C2×C22⋊D17 | — | 8 | 1 | no | — |
| 108 | C2×C22⋊D17 | — | 8 | 1 | no | — |
| 109 | C22×Dic17 | — | 2 | 1 | no | — |
| 110 | C22×Dic17 | — | 2 | 1 | no | — |
| 111 | C22×Dic17 | — | 2 | 1 | no | — |
| 112 | C22×Dic17 | — | 2 | 1 | no | — |
| 113 | #63252 | — | 2 | 2 | no | — |
| 114 | #63252 | — | 2 | 2 | no | — |
| 115 | #63252 | — | 2 | 2 | no | — |
| 116 | #63252 | — | 2 | 2 | no | — |
| 117 | #63252 | — | 4 | 2 | no | — |
| 118 | #63252 | — | 4 | 2 | no | — |
| 119 | #63252 | — | 4 | 2 | no | — |
| 120 | #63252 | — | 4 | 2 | no | — |
| 121 | #63252 | — | 4 | 1 | no | — |
| 122 | #63252 | — | 4 | 1 | no | — |
| 123 | #63252 | — | 4 | 1 | no | — |
| 124 | #63252 | — | 4 | 1 | no | — |
| 125 | C2×D68 | — | 2 | 1 | no | — |
| 126 | C2×D68 | — | 2 | 1 | no | — |
| 127 | C2×D68 | — | 2 | 1 | no | — |
| 128 | C2×D68 | — | 4 | 2 | no | — |
| 129 | C2×D68 | — | 4 | 1 | no | — |
| 130 | C2×D68 | — | 4 | 1 | no | — |
| 131 | C2×D68 | C22⋊C4 | 1 | 2 | yes | — |
| 132 | C2×C4×D17 | — | 4 | 2 | no | — |
| 133 | C2×C4×D17 | — | 4 | 2 | no | — |
| 134 | C2×C4×D17 | — | 4 | 1 | no | — |
| 135 | C2×C4×D17 | — | 4 | 1 | no | — |
| 136 | C2×C4×D17 | — | 4 | 2 | no | — |
| 137 | C2×C4×D17 | — | 8 | 1 | no | — |
| 138 | C2×C4×D17 | — | 8 | 1 | no | — |
| 139 | C2×Dic34 | — | 2 | 1 | no | — |
| 140 | C2×Dic34 | — | 2 | 1 | no | — |
| 141 | C2×Dic34 | — | 4 | 2 | no | — |
| 142 | M16×C17 | — | 4 | 1 | no | — |
| 143 | M16×C17 | — | 4 | 1 | no | — |
| 144 | C2×C8×C17 | — | 2 | 2 | no | — |
| 145 | C22⋊C4×C17 | — | 4 | 2 | no | — |
| 146 | C22⋊C4×C17 | — | 4 | 1 | no | — |
| 147 | C22⋊C4×C17 | — | 4 | 1 | no | — |
| 148 | C42×C17 | — | 4 | 1 | no | — |
| 149 | C42×C17 | — | 4 | 1 | no | — |
| 150 | C22⋊Dic17 | — | 4 | 1 | no | — |
| 151 | C22⋊Dic17 | — | 4 | 1 | no | — |
| 152 | #63227 | — | 2 | 2 | no | — |
| 153 | #63227 | — | 2 | 2 | no | — |
| 154 | #63227 | — | 4 | 2 | no | — |
| 155 | #63227 | — | 8 | 1 | no | — |
| 156 | #63227 | — | 8 | 1 | no | — |
| 157 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 158 | C4⋊Dic17 | C22⋊C4 | 1 | 2 | yes | — |
| 159 | #63225 | — | 8 | 1 | no | — |
| 160 | C4×Dic17 | — | 8 | 1 | no | — |
| 161 | #63223 | — | 4 | 1 | no | — |
| 162 | #63223 | — | 4 | 1 | no | — |
| 163 | C2×#3622 | — | 4 | 1 | no | — |
| 164 | D136 | — | 4 | 4 | no | — |
| 165 | #63219 | — | 4 | 4 | no | — |
| 166 | #9523 | — | 17 | 1 | no | maximal, Sylow |
| 167 | C23×C17 | — | 2 | 1 | no | — |
| 168 | C23×C17 | — | 2 | 1 | no | — |
| 169 | C23×C17 | — | 4 | 1 | no | — |
| 170 | C23×C17 | — | 4 | 1 | no | — |
| 171 | C23×C17 | C4×D4 | 1 | 1 | yes | characteristic |
| 172 | C23×C17 | #120 | 1 | 1 | yes | characteristic |
| 173 | C23×C17 | #121 | 1 | 1 | yes | characteristic |
| 174 | C22×D17 | — | 2 | 2 | no | — |
| 175 | C22×D17 | — | 2 | 2 | no | — |
| 176 | C22×D17 | — | 4 | 1 | no | — |
| 177 | C22×D17 | — | 4 | 1 | no | — |
| 178 | C22×D17 | — | 4 | 1 | no | — |
| 179 | C22×D17 | — | 4 | 1 | no | — |
| 180 | C22×D17 | — | 4 | 1 | no | — |
| 181 | C22×D17 | — | 4 | 1 | no | — |
| 182 | C22×D17 | — | 4 | 1 | no | — |
| 183 | C22×D17 | — | 4 | 1 | no | — |
| 184 | C22×D17 | — | 8 | 1 | no | — |
| 185 | C22×D17 | — | 8 | 1 | no | — |
| 186 | C2×C4×C17 | — | 2 | 1 | no | — |
| 187 | C2×C4×C17 | — | 2 | 1 | no | — |
| 188 | C2×C4×C17 | — | 2 | 1 | no | — |
| 189 | C2×C4×C17 | — | 2 | 1 | no | — |
| 190 | C2×C4×C17 | — | 2 | 2 | no | — |
| 191 | C2×C4×C17 | — | 4 | 1 | no | — |
| 192 | C2×C4×C17 | — | 4 | 1 | no | — |
| 193 | C2×C4×C17 | — | 4 | 1 | no | — |
| 194 | C2×C4×C17 | — | 4 | 1 | no | — |
| 195 | C2×C4×C17 | — | 4 | 1 | no | — |
| 196 | C2×C4×C17 | — | 4 | 1 | no | — |
| 197 | C2×C4×C17 | — | 4 | 1 | no | — |
| 198 | C2×C4×C17 | — | 4 | 1 | no | — |
| 199 | C2×C4×C17 | — | 4 | 1 | no | — |
| 200 | C2×C4×C17 | — | 8 | 1 | no | — |
| 201 | C2×C4×C17 | — | 8 | 1 | no | — |
| 202 | C2×C4×C17 | — | 8 | 1 | no | — |
| 203 | C2×C4×C17 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 204 | C2×C4×C17 | C4×D4 | 1 | 1 | yes | characteristic |
| 205 | C2×C4×C17 | #121 | 1 | 1 | yes | characteristic |
| 206 | C2×C4×C17 | #123 | 1 | 1 | yes | characteristic |
| 207 | C22⋊D17 | — | 4 | 2 | no | — |
| 208 | C22⋊D17 | — | 4 | 2 | no | — |
| 209 | C22⋊D17 | — | 4 | 2 | no | — |
| 210 | C22⋊D17 | — | 4 | 2 | no | — |
| 211 | C22⋊D17 | — | 8 | 2 | no | — |
| 212 | C22⋊D17 | — | 8 | 2 | no | — |
| 213 | C2×Dic17 | — | 2 | 2 | no | — |
| 214 | C2×Dic17 | — | 2 | 2 | no | — |
| 215 | C2×Dic17 | — | 4 | 1 | no | — |
| 216 | C2×Dic17 | — | 4 | 1 | no | — |
| 217 | C2×Dic17 | — | 4 | 1 | no | — |
| 218 | C2×Dic17 | — | 4 | 1 | no | — |
| 219 | C2×Dic17 | — | 4 | 1 | no | — |
| 220 | C2×Dic17 | — | 4 | 1 | no | — |
| 221 | C2×Dic17 | — | 4 | 1 | no | — |
| 222 | C2×Dic17 | — | 4 | 1 | no | — |
| 223 | C2×Dic17 | — | 4 | 1 | no | — |
| 224 | C2×Dic17 | — | 4 | 1 | no | — |
| 225 | D68 | — | 2 | 2 | no | — |
| 226 | D68 | — | 2 | 2 | no | — |
| 227 | D68 | — | 4 | 2 | no | — |
| 228 | D68 | — | 4 | 1 | no | — |
| 229 | D68 | — | 4 | 1 | no | — |
| 230 | D68 | — | 8 | 1 | no | — |
| 231 | C4×D17 | — | 4 | 2 | no | — |
| 232 | C4×D17 | — | 4 | 2 | no | — |
| 233 | C4×D17 | — | 4 | 2 | no | — |
| 234 | C4×D17 | — | 4 | 2 | no | — |
| 235 | C4×D17 | — | 8 | 4 | no | — |
| 236 | Dic34 | — | 2 | 2 | no | — |
| 237 | Dic34 | — | 2 | 2 | no | — |
| 238 | Dic34 | — | 4 | 1 | no | — |
| 239 | Dic34 | — | 4 | 1 | no | — |
| 240 | C8×C17 | — | 4 | 2 | no | — |
| 241 | #3622 | — | 8 | 1 | no | — |
| 242 | #3006 | — | 17 | 1 | no | — |
| 243 | #2333 | — | 17 | 1 | no | — |
| 244 | #1789 | — | 17 | 1 | no | — |
| 245 | #1782 | — | 17 | 1 | no | — |
| 246 | #1510 | — | 17 | 1 | no | — |
| 247 | #1306 | — | 17 | 1 | no | — |
| 248 | #1284 | D17 | 1 | 1 | yes | characteristic, complemented |
| 249 | C22×C17 | — | 2 | 1 | no | — |
| 250 | C22×C17 | — | 2 | 1 | no | — |
| 251 | C22×C17 | — | 2 | 1 | no | — |
| 252 | C22×C17 | — | 2 | 1 | no | — |
| 253 | C22×C17 | — | 2 | 1 | no | — |
| 254 | C22×C17 | — | 2 | 1 | no | — |
| 255 | C22×C17 | — | 2 | 1 | no | — |
| 256 | C22×C17 | — | 2 | 1 | no | — |
| 257 | C22×C17 | — | 8 | 1 | no | — |
| 258 | C22×C17 | — | 8 | 1 | no | — |
| 259 | C22×C17 | #386 | 1 | 1 | yes | characteristic |
| 260 | C22×C17 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 261 | C22×C17 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 262 | C2×D17 | — | 4 | 2 | no | — |
| 263 | C2×D17 | — | 4 | 2 | no | — |
| 264 | C2×D17 | — | 4 | 2 | no | — |
| 265 | C2×D17 | — | 4 | 2 | no | — |
| 266 | C2×D17 | — | 8 | 1 | no | — |
| 267 | C2×D17 | — | 8 | 1 | no | — |
| 268 | C2×D17 | — | 8 | 1 | no | — |
| 269 | C2×D17 | — | 8 | 1 | no | — |
| 270 | C2×D17 | — | 8 | 2 | no | — |
| 271 | C2×D17 | — | 8 | 1 | no | — |
| 272 | C2×D17 | — | 8 | 1 | no | — |
| 273 | C2×D17 | — | 8 | 2 | no | — |
| 274 | C4×C17 | — | 2 | 1 | no | — |
| 275 | C4×C17 | — | 2 | 1 | no | — |
| 276 | C4×C17 | — | 2 | 1 | no | — |
| 277 | C4×C17 | — | 2 | 1 | no | — |
| 278 | C4×C17 | — | 4 | 2 | no | — |
| 279 | C4×C17 | — | 8 | 1 | no | — |
| 280 | C4×C17 | — | 16 | 1 | no | — |
| 281 | Dic17 | — | 4 | 2 | no | — |
| 282 | Dic17 | — | 4 | 2 | no | — |
| 283 | Dic17 | — | 8 | 1 | no | — |
| 284 | Dic17 | — | 8 | 1 | no | — |
| 285 | C22×#41 | — | 17 | 1 | no | — |
| 286 | C2×AGL(1,ℤ/8) | — | 34 | 1 | no | — |
| 287 | C2×#121 | — | 17 | 1 | no | — |
| 288 | #449 | — | 34 | 2 | no | — |
| 289 | #448 | — | 17 | 2 | no | — |
| 290 | #447 | — | 17 | 2 | no | — |
| 291 | C2×#104 | — | 34 | 1 | no | — |
| 292 | C2×#104 | — | 34 | 1 | no | — |
| 293 | #417 | — | 34 | 1 | no | — |
| 294 | C2×#99 | — | 34 | 1 | no | — |
| 295 | C2×#99 | — | 34 | 1 | no | — |
| 296 | #407 | — | 17 | 1 | no | — |
| 297 | #407 | C2×D17 | 1 | 1 | yes | characteristic |
| 298 | #390 | — | 34 | 1 | no | — |
| 299 | #388 | — | 34 | 1 | no | — |
| 300 | #387 | — | 34 | 1 | no | — |
| 301 | #386 | — | 34 | 1 | no | — |
| 302 | #386 | — | 34 | 1 | no | — |
| 303 | #381 | — | 17 | 1 | no | — |
| 304 | #381 | C2×D17 | 1 | 1 | yes | characteristic |
| 305 | C4×C22⋊C4 | — | 34 | 1 | no | — |
| 306 | C4×C22⋊C4 | C2×D17 | 1 | 1 | yes | characteristic |
| 307 | #327 | — | 34 | 2 | no | — |
| 308 | C2×C17 | — | 2 | 1 | no | — |
| 309 | C2×C17 | — | 2 | 1 | no | — |
| 310 | C2×C17 | — | 4 | 1 | no | — |
| 311 | C2×C17 | — | 4 | 1 | no | — |
| 312 | C2×C17 | #1889 | 1 | 1 | yes | characteristic |
| 313 | C2×C17 | #1904 | 1 | 1 | yes | characteristic |
| 314 | C2×C17 | #1906 | 1 | 1 | yes | characteristic |
| 315 | D17 | — | 8 | 2 | no | — |
| 316 | D17 | — | 8 | 2 | no | — |
| 317 | C2×#41 | — | 34 | 1 | no | — |
| 318 | C2×#41 | — | 34 | 1 | no | — |
| 319 | C2×#41 | — | 34 | 1 | no | — |
| 320 | C2×#41 | — | 34 | 1 | no | — |
| 321 | C2×#41 | — | 68 | 2 | no | — |
| 322 | C2×#41 | — | 68 | 2 | no | — |
| 323 | C22×Q8 | — | 17 | 1 | no | — |
| 324 | C22×D4 | — | 17 | 1 | no | — |
| 325 | C22×D4 | — | 17 | 1 | no | — |
| 326 | C22×D4 | — | 34 | 1 | no | — |
| 327 | C22×D4 | — | 34 | 1 | no | — |
| 328 | C23×C4 | — | 34 | 1 | no | — |
| 329 | C23×C4 | — | 34 | 1 | no | — |
| 330 | C23×C4 | C22×D17 | 1 | 1 | yes | characteristic |
| 331 | AGL(1,ℤ/8) | — | 68 | 2 | no | — |
| 332 | AGL(1,ℤ/8) | — | 68 | 2 | no | — |
| 333 | C2×SD16 | — | 34 | 2 | no | — |
| 334 | C2×D8 | — | 34 | 2 | no | — |
| 335 | C2×M16 | — | 2 | 1 | no | — |
| 336 | C2×M16 | — | 34 | 1 | no | — |
| 337 | #121 | — | 17 | 2 | no | — |
| 338 | #121 | — | 17 | 2 | no | — |
| 339 | #121 | — | 34 | 1 | no | — |
| 340 | #121 | — | 34 | 1 | no | — |
| 341 | C2×C4⋊C4 | — | 17 | 1 | no | — |
| 342 | C2×C4⋊C4 | — | 34 | 1 | no | — |
| 343 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 344 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 345 | C2×C22⋊C4 | — | 17 | 1 | no | — |
| 346 | C2×C22⋊C4 | — | 17 | 1 | no | — |
| 347 | C2×C22⋊C4 | — | 34 | 1 | no | — |
| 348 | C2×C22⋊C4 | — | 34 | 1 | no | — |
| 349 | C2×C22⋊C4 | — | 34 | 1 | no | — |
| 350 | C2×C22⋊C4 | — | 34 | 1 | no | — |
| 351 | C2×C42 | — | 34 | 1 | no | — |
| 352 | C2×C42 | D68 | 1 | 1 | yes | characteristic |
| 353 | C2×C42 | D68 | 1 | 1 | yes | characteristic |
| 354 | #104 | — | 68 | 2 | no | — |
| 355 | #104 | — | 68 | 2 | no | — |
| 356 | #103 | — | 34 | 2 | no | — |
| 357 | #102 | — | 34 | 2 | no | — |
| 358 | #99 | — | 68 | 2 | no | — |
| 359 | #99 | — | 68 | 2 | no | — |
| 360 | C22⋊C8 | — | 2 | 1 | no | — |
| 361 | C22⋊C8 | — | 34 | 1 | no | — |
| 362 | C22⋊C8 | — | 34 | 1 | no | — |
| 363 | C22⋊C8 | C4×D17 | 1 | 2 | yes | complemented |
| 364 | #95 | — | 2 | 1 | no | — |
| 365 | #95 | — | 2 | 1 | no | — |
| 366 | #95 | — | 2 | 1 | no | — |
| 367 | #95 | — | 34 | 1 | no | — |
| 368 | #95 | — | 34 | 1 | no | — |
| 369 | #95 | — | 34 | 1 | no | — |
| 370 | #95 | — | 34 | 1 | no | — |
| 371 | C17 | #9523 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 372 | C24 | — | 34 | 1 | no | — |
| 373 | C24 | — | 34 | 1 | no | — |
| 374 | C24 | D4×D17 | 1 | 1 | yes | characteristic |
| 375 | #41 | — | 34 | 2 | no | — |
| 376 | #41 | — | 34 | 2 | no | — |
| 377 | #41 | — | 34 | 2 | no | — |
| 378 | #41 | — | 34 | 2 | no | — |
| 379 | #41 | — | 68 | 1 | no | — |
| 380 | #41 | — | 68 | 1 | no | — |
| 381 | #41 | — | 68 | 1 | no | — |
| 382 | #41 | — | 68 | 1 | no | — |
| 383 | #41 | — | 68 | 2 | no | — |
| 384 | #41 | — | 68 | 2 | no | — |
| 385 | #41 | — | 68 | 2 | no | — |
| 386 | #41 | — | 68 | 2 | no | — |
| 387 | C2×Q8 | — | 34 | 1 | no | — |
| 388 | C2×Q8 | — | 34 | 1 | no | — |
| 389 | C2×Q8 | — | 68 | 2 | no | — |
| 390 | C2×D4 | — | 17 | 2 | no | — |
| 391 | C2×D4 | — | 34 | 2 | no | — |
| 392 | C2×D4 | — | 34 | 2 | no | — |
| 393 | C2×D4 | — | 34 | 2 | no | — |
| 394 | C2×D4 | — | 34 | 2 | no | — |
| 395 | C2×D4 | — | 34 | 1 | no | — |
| 396 | C2×D4 | — | 34 | 1 | no | — |
| 397 | C2×D4 | — | 34 | 1 | no | — |
| 398 | C2×D4 | — | 68 | 1 | no | — |
| 399 | C2×D4 | — | 68 | 1 | no | — |
| 400 | C2×D4 | — | 68 | 2 | no | — |
| 401 | C2×D4 | — | 68 | 1 | no | — |
| 402 | C2×D4 | — | 68 | 1 | no | — |
| 403 | C2×D4 | — | 68 | 1 | no | — |
| 404 | C2×D4 | — | 68 | 1 | no | — |
| 405 | C2×D4 | — | 136 | 1 | no | — |
| 406 | C2×D4 | — | 136 | 1 | no | — |
| 407 | C22×C4 | — | 2 | 1 | no | — |
| 408 | C22×C4 | — | 2 | 1 | no | — |
| 409 | C22×C4 | — | 4 | 1 | no | — |
| 410 | C22×C4 | — | 4 | 1 | no | — |
| 411 | C22×C4 | — | 4 | 1 | no | — |
| 412 | C22×C4 | — | 34 | 1 | no | — |
| 413 | C22×C4 | — | 34 | 1 | no | — |
| 414 | C22×C4 | — | 34 | 1 | no | — |
| 415 | C22×C4 | — | 34 | 1 | no | — |
| 416 | C22×C4 | — | 68 | 2 | no | — |
| 417 | C22×C4 | — | 68 | 2 | no | — |
| 418 | C22×C4 | — | 68 | 2 | no | — |
| 419 | C22×C4 | — | 68 | 1 | no | — |
| 420 | C22×C4 | — | 68 | 1 | no | — |
| 421 | C22×C4 | — | 136 | 1 | no | — |
| 422 | C22×C4 | — | 136 | 1 | no | — |
| 423 | C22×C4 | C2×C4×D17 | 1 | 1 | yes | characteristic |
| 424 | C22×C4 | C2×D68 | 1 | 1 | yes | characteristic |
| 425 | C22×C4 | #63252 | 1 | 1 | yes | characteristic |
| 426 | C22×C4 | D4×D17 | 1 | 1 | yes | characteristic |
| 427 | C22×C4 | D4×D17 | 1 | 1 | yes | characteristic |
| 428 | C22×C4 | #63256 | 1 | 1 | yes | characteristic |
| 429 | SD16 | — | 68 | 4 | no | — |
| 430 | D8 | — | 68 | 4 | no | — |
| 431 | M16 | — | 4 | 1 | no | — |
| 432 | M16 | — | 4 | 1 | no | — |
| 433 | M16 | — | 68 | 1 | no | — |
| 434 | M16 | — | 68 | 1 | no | — |
| 435 | C2×C8 | — | 2 | 2 | no | — |
| 436 | C2×C8 | — | 68 | 1 | no | — |
| 437 | C4⋊C4 | — | 17 | 2 | no | — |
| 438 | C4⋊C4 | — | 34 | 1 | no | — |
| 439 | C4⋊C4 | — | 136 | 1 | no | — |
| 440 | C22⋊C4 | — | 4 | 2 | no | — |
| 441 | C22⋊C4 | — | 4 | 1 | no | — |
| 442 | C22⋊C4 | — | 4 | 1 | no | — |
| 443 | C22⋊C4 | — | 34 | 2 | no | — |
| 444 | C22⋊C4 | — | 34 | 2 | no | — |
| 445 | C22⋊C4 | — | 68 | 2 | no | — |
| 446 | C22⋊C4 | — | 68 | 1 | no | — |
| 447 | C22⋊C4 | — | 68 | 1 | no | — |
| 448 | C22⋊C4 | — | 136 | 1 | no | — |
| 449 | C22⋊C4 | — | 136 | 1 | no | — |
| 450 | C42 | — | 4 | 1 | no | — |
| 451 | C42 | — | 4 | 1 | no | — |
| 452 | C42 | — | 136 | 1 | no | — |
| 453 | C23 | — | 2 | 1 | no | — |
| 454 | C23 | — | 2 | 1 | no | — |
| 455 | C23 | — | 4 | 1 | no | — |
| 456 | C23 | — | 4 | 1 | no | — |
| 457 | C23 | — | 34 | 2 | no | — |
| 458 | C23 | — | 34 | 2 | no | — |
| 459 | C23 | — | 68 | 1 | no | — |
| 460 | C23 | — | 68 | 1 | no | — |
| 461 | C23 | — | 68 | 1 | no | — |
| 462 | C23 | — | 68 | 1 | no | — |
| 463 | C23 | — | 68 | 1 | no | — |
| 464 | C23 | — | 68 | 1 | no | — |
| 465 | C23 | — | 68 | 1 | no | — |
| 466 | C23 | — | 68 | 1 | no | — |
| 467 | C23 | — | 136 | 1 | no | — |
| 468 | C23 | — | 136 | 1 | no | — |
| 469 | C23 | #10587568 | 1 | 1 | yes | characteristic |
| 470 | C23 | #10587570 | 1 | 1 | yes | characteristic |
| 471 | C23 | #10587579 | 1 | 1 | yes | characteristic |
| 472 | Q8 | — | 34 | 2 | no | — |
| 473 | Q8 | — | 34 | 2 | no | — |
| 474 | Q8 | — | 68 | 1 | no | — |
| 475 | Q8 | — | 68 | 1 | no | — |
| 476 | D4 | — | 34 | 2 | no | — |
| 477 | D4 | — | 34 | 2 | no | — |
| 478 | D4 | — | 68 | 2 | no | — |
| 479 | D4 | — | 68 | 1 | no | — |
| 480 | D4 | — | 68 | 1 | no | — |
| 481 | D4 | — | 68 | 2 | no | — |
| 482 | D4 | — | 68 | 2 | no | — |
| 483 | D4 | — | 68 | 2 | no | — |
| 484 | D4 | — | 68 | 2 | no | — |
| 485 | D4 | — | 136 | 1 | no | — |
| 486 | D4 | — | 136 | 2 | no | — |
| 487 | D4 | — | 136 | 2 | no | — |
| 488 | C2×C4 | — | 2 | 1 | no | — |
| 489 | C2×C4 | — | 2 | 1 | no | — |
| 490 | C2×C4 | — | 2 | 1 | no | — |
| 491 | C2×C4 | — | 2 | 1 | no | — |
| 492 | C2×C4 | — | 2 | 2 | no | — |
| 493 | C2×C4 | — | 4 | 1 | no | — |
| 494 | C2×C4 | — | 4 | 1 | no | — |
| 495 | C2×C4 | — | 4 | 1 | no | — |
| 496 | C2×C4 | — | 4 | 1 | no | — |
| 497 | C2×C4 | — | 4 | 1 | no | — |
| 498 | C2×C4 | — | 4 | 1 | no | — |
| 499 | C2×C4 | — | 4 | 1 | no | — |
| 500 | C2×C4 | — | 4 | 1 | no | — |
| 501 | C2×C4 | — | 4 | 1 | no | — |
| 502 | C2×C4 | — | 8 | 1 | no | — |
| 503 | C2×C4 | — | 8 | 1 | no | — |
| 504 | C2×C4 | — | 8 | 1 | no | — |
| 505 | C2×C4 | — | 34 | 2 | no | — |
| 506 | C2×C4 | — | 34 | 2 | no | — |
| 507 | C2×C4 | — | 68 | 2 | no | — |
| 508 | C2×C4 | — | 68 | 2 | no | — |
| 509 | C2×C4 | — | 68 | 2 | no | — |
| 510 | C2×C4 | — | 68 | 2 | no | — |
| 511 | C2×C4 | — | 68 | 1 | no | — |
| 512 | C2×C4 | — | 68 | 1 | no | — |
| 513 | C2×C4 | — | 68 | 1 | no | — |
| 514 | C2×C4 | — | 68 | 1 | no | — |
| 515 | C2×C4 | — | 68 | 1 | no | — |
| 516 | C2×C4 | — | 68 | 1 | no | — |
| 517 | C2×C4 | — | 68 | 1 | no | — |
| 518 | C2×C4 | — | 68 | 1 | no | — |
| 519 | C2×C4 | — | 68 | 1 | no | — |
| 520 | C2×C4 | — | 68 | 1 | no | — |
| 521 | C2×C4 | — | 136 | 4 | no | — |
| 522 | C2×C4 | C4×D68 | 1 | 1 | yes | characteristic |
| 523 | C2×C4 | C22⋊C4×D17 | 1 | 1 | yes | characteristic |
| 524 | C2×C4 | #10587580 | 1 | 1 | yes | characteristic |
| 525 | C2×C4 | #10587581 | 1 | 1 | yes | characteristic |
| 526 | C8 | — | 4 | 2 | no | — |
| 527 | C8 | — | 136 | 1 | no | — |
| 528 | C22 | — | 2 | 1 | no | — |
| 529 | C22 | — | 2 | 1 | no | — |
| 530 | C22 | — | 2 | 1 | no | — |
| 531 | C22 | — | 2 | 1 | no | — |
| 532 | C22 | — | 2 | 1 | no | — |
| 533 | C22 | — | 2 | 1 | no | — |
| 534 | C22 | — | 2 | 1 | no | — |
| 535 | C22 | — | 2 | 1 | no | — |
| 536 | C22 | — | 8 | 1 | no | — |
| 537 | C22 | — | 8 | 1 | no | — |
| 538 | C22 | — | 68 | 2 | no | — |
| 539 | C22 | — | 68 | 2 | no | — |
| 540 | C22 | — | 68 | 2 | no | — |
| 541 | C22 | — | 68 | 2 | no | — |
| 542 | C22 | — | 136 | 1 | no | — |
| 543 | C22 | — | 136 | 1 | no | — |
| 544 | C22 | — | 136 | 1 | no | — |
| 545 | C22 | — | 136 | 1 | no | — |
| 546 | C22 | — | 136 | 2 | no | — |
| 547 | C22 | — | 136 | 2 | no | — |
| 548 | C22 | — | 136 | 1 | no | — |
| 549 | C22 | — | 136 | 1 | no | — |
| 550 | C22 | #11762687 | 1 | 1 | yes | characteristic |
| 551 | C22 | #11762997 | 1 | 1 | yes | characteristic |
| 552 | C22 | #11762997 | 1 | 1 | yes | characteristic |
| 553 | C4 | — | 2 | 1 | no | — |
| 554 | C4 | — | 2 | 1 | no | — |
| 555 | C4 | — | 2 | 1 | no | — |
| 556 | C4 | — | 2 | 1 | no | — |
| 557 | C4 | — | 4 | 2 | no | — |
| 558 | C4 | — | 8 | 1 | no | — |
| 559 | C4 | — | 16 | 1 | no | — |
| 560 | C4 | — | 68 | 2 | no | — |
| 561 | C4 | — | 68 | 2 | no | — |
| 562 | C4 | — | 136 | 1 | no | — |
| 563 | C4 | — | 136 | 1 | no | — |
| 564 | C2 | — | 2 | 1 | no | — |
| 565 | C2 | — | 2 | 1 | no | — |
| 566 | C2 | — | 4 | 1 | no | — |
| 567 | C2 | — | 4 | 1 | no | — |
| 568 | C2 | — | 136 | 2 | no | — |
| 569 | C2 | — | 136 | 2 | no | — |
| 570 | C2 | #14529191 | 1 | 1 | yes | characteristic |
| 571 | C2 | #14529272 | 1 | 1 | yes | characteristic |
| 572 | C2 | #14529284 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14531549 | C2 | semidirect |
| 3. #14528729 | C2 | semidirect |
| 4. #14528701 | C2 | semidirect |
| 5. #14527312 | C2 | semidirect |
| 6. #14526693 | C2 | semidirect |
| 7. C17×#1284 | C2 | semidirect |
| 12. #11762950 | C4 | semidirect |
| 13. #11762945 | C4 | semidirect |
| 40. C22×D68 | C2×C4 | semidirect |
| 44. C22×Dic34 | C2×C4 | semidirect |
| 69. C17×C22⋊C8 | C2×C4 | semidirect |
| 248. #1284 | D17 | semidirect |
| 363. C22⋊C8 | C4×D17 | semidirect |
| 371. C17 | #9523 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538038 | 2 |
| #14531549 | 2 |
| #14528729 | 2 |
| #14528701 | 2 |
| #14527312 | 2 |
| #14526693 | 2 |
| C17×#1284 | 2 |
| #9523 | 17 |