Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
676 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 77 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 | #14539675 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #14538190 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #14530478 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #14530438 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #14528735 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #14526914 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C17×#3022 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #11763380 | — | 2 | 1 | no | — |
| 9 | #11763380 | C22 | 1 | 1 | yes | characteristic |
| 10 | #11763150 | — | 2 | 1 | no | — |
| 11 | #11763147 | — | 2 | 1 | no | — |
| 12 | #11763065 | — | 2 | 1 | no | — |
| 13 | #11763048 | — | 2 | 1 | no | — |
| 14 | #11762999 | — | 2 | 2 | no | — |
| 15 | #11762999 | — | 2 | 2 | no | — |
| 16 | #11762965 | — | 2 | 1 | no | — |
| 17 | #11762964 | — | 2 | 1 | no | — |
| 18 | #11762793 | — | 2 | 1 | no | — |
| 19 | #11762793 | C22 | 1 | 1 | yes | characteristic |
| 20 | #11762783 | — | 2 | 1 | no | — |
| 21 | #11762783 | C22 | 1 | 1 | yes | characteristic |
| 22 | #11762776 | — | 2 | 1 | no | — |
| 23 | #11762776 | C22 | 1 | 1 | yes | characteristic |
| 24 | #11762607 | — | 2 | 2 | no | — |
| 25 | #11762599 | — | 2 | 2 | no | — |
| 26 | C17×#585 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×C17×#137 | — | 2 | 1 | no | — |
| 28 | C17×#536 | C22 | 1 | 1 | yes | characteristic |
| 29 | C17×#456 | — | 2 | 2 | no | — |
| 30 | C17×#455 | — | 2 | 2 | no | — |
| 31 | C17×#421 | — | 2 | 1 | no | — |
| 32 | C17×#413 | C22 | 1 | 1 | yes | characteristic |
| 33 | C17×2−1+4 | — | 2 | 1 | no | — |
| 34 | C17×2−1+4 | — | 4 | 1 | no | — |
| 35 | C17×H(5,𝔽2) | — | 2 | 1 | no | — |
| 36 | C17×H(5,𝔽2) | — | 2 | 1 | no | — |
| 37 | C17×H(5,𝔽2) | — | 4 | 1 | no | — |
| 38 | C17×H(5,𝔽2) | D4 | 1 | 2 | yes | — |
| 39 | C2×#41×C17 | — | 2 | 1 | no | — |
| 40 | C2×#41×C17 | — | 2 | 1 | no | — |
| 41 | C2×#41×C17 | — | 2 | 1 | no | — |
| 42 | C2×#41×C17 | — | 4 | 2 | no | — |
| 43 | C2×#41×C17 | C23 | 1 | 1 | yes | characteristic |
| 44 | C22×Q8×C17 | D4 | 1 | 1 | yes | characteristic |
| 45 | C22×Dic34 | D4 | 1 | 1 | yes | characteristic |
| 46 | C17×#137 | — | 2 | 4 | no | — |
| 47 | C17×#137 | — | 4 | 2 | no | — |
| 48 | C2×Q16×C17 | — | 4 | 1 | no | — |
| 49 | C2×SD16×C17 | — | 4 | 1 | no | — |
| 50 | C2×M16×C17 | — | 2 | 1 | no | — |
| 51 | C17×C4⋊Q8 | — | 2 | 1 | no | — |
| 52 | C17×#124 | — | 2 | 1 | no | — |
| 53 | C17×#123 | — | 2 | 1 | no | — |
| 54 | C17×#123 | — | 2 | 1 | no | — |
| 55 | C17×C22⋊Q8 | — | 2 | 1 | no | — |
| 56 | C17×C22⋊Q8 | — | 2 | 1 | no | — |
| 57 | C17×#117 | D4 | 1 | 1 | yes | characteristic |
| 58 | #10587630 | — | 2 | 1 | no | — |
| 59 | #10587630 | — | 4 | 1 | no | — |
| 60 | C2×#63231 | — | 2 | 1 | no | — |
| 61 | C2×#63231 | — | 2 | 1 | no | — |
| 62 | #10587622 | — | 2 | 1 | no | — |
| 63 | #10587622 | — | 4 | 1 | no | — |
| 64 | #10587621 | — | 2 | 4 | no | — |
| 65 | #10587621 | — | 2 | 1 | no | — |
| 66 | #10587621 | — | 2 | 1 | no | — |
| 67 | #10587612 | — | 2 | 1 | no | — |
| 68 | #10587612 | D4 | 1 | 1 | yes | characteristic |
| 69 | #10587610 | — | 2 | 1 | no | — |
| 70 | #10587610 | — | 2 | 1 | no | — |
| 71 | #10587610 | — | 4 | 2 | no | — |
| 72 | C2×#63223 | — | 2 | 1 | no | — |
| 73 | C2×#63223 | D4 | 1 | 1 | yes | characteristic |
| 74 | C22×#3622 | D4 | 1 | 1 | yes | characteristic |
| 75 | C17×#104 | — | 2 | 4 | no | — |
| 76 | C17×#101 | D4 | 1 | 2 | yes | — |
| 77 | C17×#100 | — | 2 | 1 | no | — |
| 78 | #10587507 | — | 2 | 1 | no | — |
| 79 | #10587507 | — | 4 | 1 | no | — |
| 80 | #10587506 | — | 2 | 1 | no | — |
| 81 | #10587506 | — | 2 | 1 | no | — |
| 82 | #10587505 | — | 2 | 4 | no | — |
| 83 | #10587505 | — | 2 | 1 | no | — |
| 84 | #10587505 | D4 | 1 | 2 | yes | — |
| 85 | #10587504 | — | 2 | 1 | no | — |
| 86 | #10587504 | — | 4 | 1 | no | — |
| 87 | C22⋊#3622 | — | 2 | 1 | no | — |
| 88 | C22⋊#3622 | — | 2 | 1 | no | — |
| 89 | C22⋊#3622 | — | 4 | 2 | no | — |
| 90 | #10587481 | — | 2 | 1 | no | — |
| 91 | #10587481 | — | 2 | 1 | no | — |
| 92 | #10587479 | — | 2 | 1 | no | — |
| 93 | #10587478 | — | 2 | 1 | no | — |
| 94 | #41×C17 | — | 2 | 2 | no | — |
| 95 | #41×C17 | — | 2 | 2 | no | — |
| 96 | #41×C17 | — | 4 | 1 | no | — |
| 97 | #41×C17 | — | 4 | 1 | no | — |
| 98 | #41×C17 | — | 4 | 2 | no | — |
| 99 | #41×C17 | — | 4 | 1 | no | — |
| 100 | #41×C17 | — | 4 | 1 | no | — |
| 101 | #41×C17 | — | 4 | 1 | no | — |
| 102 | #41×C17 | — | 4 | 1 | no | — |
| 103 | #41×C17 | — | 4 | 1 | no | — |
| 104 | #41×C17 | — | 4 | 2 | no | — |
| 105 | #41×C17 | — | 4 | 2 | no | — |
| 106 | #41×C17 | — | 4 | 2 | no | — |
| 107 | #41×C17 | — | 4 | 1 | no | — |
| 108 | #41×C17 | — | 4 | 1 | no | — |
| 109 | #41×C17 | — | 4 | 1 | no | — |
| 110 | C2×Q8×C17 | — | 2 | 1 | no | — |
| 111 | C2×Q8×C17 | — | 2 | 1 | no | — |
| 112 | C2×Q8×C17 | — | 2 | 1 | no | — |
| 113 | C2×Q8×C17 | — | 2 | 1 | no | — |
| 114 | C2×Q8×C17 | — | 2 | 1 | no | — |
| 115 | C2×Q8×C17 | — | 4 | 1 | no | — |
| 116 | C2×Q8×C17 | — | 4 | 1 | no | — |
| 117 | C2×Q8×C17 | — | 4 | 2 | no | — |
| 118 | C2×Q8×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C2×D4×C17 | — | 2 | 1 | no | — |
| 120 | C2×D4×C17 | — | 2 | 1 | no | — |
| 121 | C2×D4×C17 | — | 2 | 1 | no | — |
| 122 | C2×D4×C17 | — | 2 | 2 | no | — |
| 123 | C2×D4×C17 | — | 2 | 2 | no | — |
| 124 | C2×D4×C17 | — | 4 | 2 | no | — |
| 125 | C2×D4×C17 | — | 4 | 2 | no | — |
| 126 | C2×D4×C17 | — | 4 | 2 | no | — |
| 127 | C2×D4×C17 | — | 4 | 1 | no | — |
| 128 | C2×D4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C2×D4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C2×D4×C17 | #41 | 1 | 1 | yes | characteristic |
| 131 | C22×C4×C17 | — | 2 | 2 | no | — |
| 132 | C22×C4×C17 | — | 2 | 2 | no | — |
| 133 | C22×C4×C17 | — | 2 | 1 | no | — |
| 134 | C22×C4×C17 | — | 4 | 1 | no | — |
| 135 | C22×C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | C22×C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C22×C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | C22×Dic17 | — | 2 | 1 | no | — |
| 139 | C2×Dic34 | — | 2 | 1 | no | — |
| 140 | C2×Dic34 | — | 2 | 1 | no | — |
| 141 | C2×Dic34 | — | 4 | 1 | no | — |
| 142 | C2×Dic34 | — | 4 | 1 | no | — |
| 143 | Q16×C17 | — | 4 | 4 | no | — |
| 144 | SD16×C17 | — | 4 | 4 | no | — |
| 145 | M16×C17 | — | 2 | 2 | no | — |
| 146 | M16×C17 | — | 4 | 1 | no | — |
| 147 | C2×C8×C17 | — | 4 | 1 | no | — |
| 148 | C4⋊C4×C17 | — | 2 | 1 | no | — |
| 149 | C4⋊C4×C17 | — | 4 | 1 | no | — |
| 150 | C4⋊C4×C17 | — | 4 | 1 | no | — |
| 151 | C22⋊C4×C17 | — | 2 | 1 | no | — |
| 152 | C22⋊C4×C17 | — | 4 | 1 | no | — |
| 153 | C22⋊C4×C17 | — | 4 | 1 | no | — |
| 154 | C42×C17 | — | 2 | 1 | no | — |
| 155 | C22⋊Dic17 | — | 2 | 1 | no | — |
| 156 | C22⋊Dic17 | — | 2 | 2 | no | — |
| 157 | C22⋊Dic17 | — | 4 | 4 | no | — |
| 158 | C22⋊Dic17 | — | 4 | 1 | no | — |
| 159 | C22⋊Dic17 | — | 4 | 1 | no | — |
| 160 | #63231 | — | 8 | 1 | no | — |
| 161 | #63231 | — | 8 | 1 | no | — |
| 162 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 163 | C4⋊Dic17 | — | 4 | 1 | no | — |
| 164 | #63225 | — | 4 | 4 | no | — |
| 165 | #63225 | — | 4 | 1 | no | — |
| 166 | #63225 | — | 4 | 1 | no | — |
| 167 | C4×Dic17 | — | 2 | 1 | no | — |
| 168 | C4×Dic17 | — | 4 | 1 | no | — |
| 169 | #63223 | — | 4 | 1 | no | — |
| 170 | #63223 | — | 4 | 1 | no | — |
| 171 | #63223 | — | 4 | 1 | no | — |
| 172 | C2×#3622 | — | 2 | 1 | no | — |
| 173 | C2×#3622 | — | 2 | 1 | no | — |
| 174 | C2×#3622 | — | 4 | 1 | no | — |
| 175 | C2×#3622 | — | 4 | 1 | no | — |
| 176 | #13356 | — | 17 | 1 | no | maximal, Sylow |
| 177 | C23×C17 | — | 2 | 2 | no | — |
| 178 | C23×C17 | — | 2 | 2 | no | — |
| 179 | C23×C17 | — | 4 | 1 | no | — |
| 180 | C23×C17 | #120 | 1 | 1 | yes | characteristic |
| 181 | C23×C17 | #121 | 1 | 1 | yes | characteristic |
| 182 | C23×C17 | #121 | 1 | 1 | yes | characteristic |
| 183 | Q8×C17 | — | 2 | 2 | no | — |
| 184 | Q8×C17 | — | 4 | 1 | no | — |
| 185 | Q8×C17 | — | 4 | 1 | no | — |
| 186 | Q8×C17 | — | 4 | 1 | no | — |
| 187 | Q8×C17 | — | 4 | 2 | no | — |
| 188 | Q8×C17 | — | 4 | 1 | no | — |
| 189 | Q8×C17 | — | 4 | 1 | no | — |
| 190 | Q8×C17 | — | 4 | 1 | no | — |
| 191 | D4×C17 | — | 2 | 2 | no | — |
| 192 | D4×C17 | — | 4 | 1 | no | — |
| 193 | D4×C17 | — | 4 | 1 | no | — |
| 194 | D4×C17 | — | 4 | 1 | no | — |
| 195 | D4×C17 | — | 4 | 1 | no | — |
| 196 | D4×C17 | — | 4 | 1 | no | — |
| 197 | D4×C17 | — | 4 | 2 | no | — |
| 198 | D4×C17 | — | 4 | 2 | no | — |
| 199 | D4×C17 | — | 4 | 2 | no | — |
| 200 | D4×C17 | — | 4 | 2 | no | — |
| 201 | D4×C17 | — | 4 | 1 | no | — |
| 202 | C2×C4×C17 | — | 2 | 1 | no | — |
| 203 | C2×C4×C17 | — | 2 | 1 | no | — |
| 204 | C2×C4×C17 | — | 2 | 1 | no | — |
| 205 | C2×C4×C17 | — | 2 | 1 | no | — |
| 206 | C2×C4×C17 | — | 2 | 1 | no | — |
| 207 | C2×C4×C17 | — | 2 | 1 | no | — |
| 208 | C2×C4×C17 | — | 2 | 2 | no | — |
| 209 | C2×C4×C17 | — | 2 | 2 | no | — |
| 210 | C2×C4×C17 | — | 4 | 2 | no | — |
| 211 | C2×C4×C17 | — | 4 | 2 | no | — |
| 212 | C2×C4×C17 | — | 4 | 2 | no | — |
| 213 | C2×C4×C17 | — | 4 | 1 | no | — |
| 214 | C2×C4×C17 | — | 4 | 2 | no | — |
| 215 | C2×C4×C17 | — | 4 | 1 | no | — |
| 216 | C2×C4×C17 | — | 4 | 1 | no | — |
| 217 | C2×C4×C17 | — | 8 | 1 | no | — |
| 218 | C2×C4×C17 | #120 | 1 | 1 | yes | characteristic |
| 219 | C2×C4×C17 | #120 | 1 | 1 | yes | characteristic |
| 220 | C2×C4×C17 | #121 | 1 | 1 | yes | characteristic |
| 221 | C2×C4×C17 | #127 | 1 | 1 | yes | characteristic |
| 222 | C2×Dic17 | — | 4 | 2 | no | — |
| 223 | C2×Dic17 | — | 4 | 2 | no | — |
| 224 | C2×Dic17 | — | 4 | 1 | no | — |
| 225 | C2×Dic17 | — | 4 | 1 | no | — |
| 226 | Dic34 | — | 4 | 1 | no | — |
| 227 | Dic34 | — | 4 | 1 | no | — |
| 228 | Dic34 | — | 8 | 1 | no | — |
| 229 | C8×C17 | — | 4 | 2 | no | — |
| 230 | #3622 | — | 4 | 1 | no | — |
| 231 | #3622 | — | 4 | 1 | no | — |
| 232 | #3622 | — | 8 | 1 | no | — |
| 233 | #3202 | — | 17 | 1 | no | — |
| 234 | #3028 | — | 17 | 1 | no | — |
| 235 | #3022 | D17 | 1 | 1 | yes | characteristic |
| 236 | #2135 | — | 17 | 1 | no | — |
| 237 | #2123 | — | 17 | 1 | no | — |
| 238 | #1791 | — | 17 | 1 | no | — |
| 239 | #1395 | — | 17 | 1 | no | — |
| 240 | C22×C17 | — | 2 | 1 | no | — |
| 241 | C22×C17 | — | 2 | 1 | no | — |
| 242 | C22×C17 | — | 2 | 1 | no | — |
| 243 | C22×C17 | — | 4 | 1 | no | — |
| 244 | C22×C17 | — | 4 | 1 | no | — |
| 245 | C22×C17 | — | 4 | 1 | no | — |
| 246 | C22×C17 | — | 4 | 2 | no | — |
| 247 | C22×C17 | — | 8 | 2 | no | — |
| 248 | C22×C17 | — | 8 | 2 | no | — |
| 249 | C22×C17 | — | 16 | 1 | no | — |
| 250 | C22×C17 | #392 | 1 | 1 | yes | characteristic |
| 251 | C4×C17 | — | 2 | 1 | no | — |
| 252 | C4×C17 | — | 2 | 1 | no | — |
| 253 | C4×C17 | — | 2 | 1 | no | — |
| 254 | C4×C17 | — | 4 | 2 | no | — |
| 255 | C4×C17 | — | 8 | 1 | no | — |
| 256 | C4×C17 | — | 8 | 1 | no | — |
| 257 | C4×C17 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 258 | C4×C17 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 259 | Dic17 | — | 8 | 1 | no | — |
| 260 | Dic17 | — | 8 | 2 | no | — |
| 261 | Dic17 | — | 8 | 1 | no | — |
| 262 | #585 | C2×D17 | 1 | 1 | yes | characteristic |
| 263 | C2×#137 | — | 2 | 1 | no | — |
| 264 | #536 | — | 17 | 1 | no | — |
| 265 | #536 | — | 34 | 1 | no | — |
| 266 | #536 | C2×D17 | 1 | 1 | yes | characteristic |
| 267 | #485 | — | 34 | 1 | no | — |
| 268 | #485 | — | 34 | 1 | no | — |
| 269 | #470 | — | 34 | 1 | no | — |
| 270 | #467 | — | 34 | 1 | no | — |
| 271 | #458 | — | 34 | 2 | no | — |
| 272 | #458 | — | 34 | 2 | no | — |
| 273 | #456 | — | 2 | 2 | no | — |
| 274 | #455 | — | 2 | 2 | no | — |
| 275 | #451 | — | 34 | 1 | no | — |
| 276 | #451 | — | 34 | 1 | no | — |
| 277 | #421 | — | 2 | 1 | no | — |
| 278 | #413 | — | 17 | 1 | no | — |
| 279 | #413 | — | 34 | 1 | no | — |
| 280 | #413 | C2×D17 | 1 | 1 | yes | characteristic |
| 281 | #410 | — | 17 | 1 | no | — |
| 282 | #410 | — | 34 | 1 | no | — |
| 283 | #408 | — | 17 | 1 | no | — |
| 284 | #408 | — | 34 | 1 | no | — |
| 285 | #356 | — | 34 | 2 | no | — |
| 286 | #352 | — | 34 | 2 | no | — |
| 287 | C2×C17 | — | 2 | 1 | no | — |
| 288 | C2×C17 | — | 4 | 1 | no | — |
| 289 | C2×C17 | — | 4 | 1 | no | — |
| 290 | C2×C17 | — | 4 | 1 | no | — |
| 291 | C2×C17 | — | 8 | 2 | no | — |
| 292 | C2×C17 | #2021 | 1 | 1 | yes | characteristic |
| 293 | 2−1+4 | — | 2 | 1 | no | — |
| 294 | 2−1+4 | — | 4 | 1 | no | — |
| 295 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 296 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 297 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 298 | H(5,𝔽2) | C22⋊D17 | 1 | 2 | yes | — |
| 299 | C2×#41 | — | 2 | 1 | no | — |
| 300 | C2×#41 | — | 2 | 1 | no | — |
| 301 | C2×#41 | — | 2 | 1 | no | — |
| 302 | C2×#41 | — | 4 | 2 | no | — |
| 303 | C2×#41 | C22×D17 | 1 | 1 | yes | characteristic |
| 304 | C22×Q8 | — | 17 | 1 | no | — |
| 305 | C22×Q8 | C22⋊D17 | 1 | 1 | yes | characteristic |
| 306 | #137 | — | 2 | 4 | no | — |
| 307 | #137 | — | 4 | 2 | no | — |
| 308 | C2×Q16 | — | 4 | 1 | no | — |
| 309 | C2×Q16 | — | 34 | 1 | no | — |
| 310 | C2×Q16 | — | 34 | 1 | no | — |
| 311 | C2×SD16 | — | 4 | 1 | no | — |
| 312 | C2×M16 | — | 2 | 1 | no | — |
| 313 | C2×M16 | — | 17 | 1 | no | — |
| 314 | C2×M16 | — | 34 | 1 | no | — |
| 315 | C22×C8 | — | 17 | 1 | no | — |
| 316 | C4⋊Q8 | — | 2 | 1 | no | — |
| 317 | C4⋊Q8 | — | 34 | 1 | no | — |
| 318 | C4⋊Q8 | — | 68 | 1 | no | — |
| 319 | #124 | — | 2 | 1 | no | — |
| 320 | #124 | — | 34 | 1 | no | — |
| 321 | #124 | — | 68 | 1 | no | — |
| 322 | #123 | — | 2 | 1 | no | — |
| 323 | #123 | — | 2 | 1 | no | — |
| 324 | #123 | — | 34 | 4 | no | — |
| 325 | #123 | — | 34 | 1 | no | — |
| 326 | #123 | — | 34 | 1 | no | — |
| 327 | C22⋊Q8 | — | 2 | 1 | no | — |
| 328 | C22⋊Q8 | — | 2 | 1 | no | — |
| 329 | C22⋊Q8 | — | 34 | 1 | no | — |
| 330 | C22⋊Q8 | — | 34 | 1 | no | — |
| 331 | C22⋊Q8 | — | 68 | 2 | no | — |
| 332 | #117 | — | 17 | 1 | no | — |
| 333 | #117 | — | 34 | 1 | no | — |
| 334 | #117 | C22⋊D17 | 1 | 1 | yes | characteristic |
| 335 | #107 | — | 34 | 1 | no | — |
| 336 | #106 | — | 34 | 1 | no | — |
| 337 | #104 | — | 2 | 4 | no | — |
| 338 | #103 | — | 34 | 1 | no | — |
| 339 | #103 | — | 34 | 1 | no | — |
| 340 | #103 | — | 34 | 1 | no | — |
| 341 | #103 | — | 34 | 1 | no | — |
| 342 | #101 | — | 34 | 1 | no | — |
| 343 | #101 | — | 68 | 1 | no | — |
| 344 | #101 | C22⋊D17 | 1 | 2 | yes | — |
| 345 | #100 | — | 2 | 1 | no | — |
| 346 | #100 | — | 34 | 1 | no | — |
| 347 | #100 | — | 68 | 1 | no | — |
| 348 | #99 | — | 17 | 2 | no | — |
| 349 | #99 | — | 34 | 4 | no | — |
| 350 | #99 | — | 34 | 1 | no | — |
| 351 | C22⋊C8 | — | 34 | 1 | no | — |
| 352 | C22⋊C8 | — | 34 | 1 | no | — |
| 353 | C22⋊C8 | — | 68 | 2 | no | — |
| 354 | C17 | #13356 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 355 | #41 | — | 2 | 2 | no | — |
| 356 | #41 | — | 2 | 2 | no | — |
| 357 | #41 | — | 4 | 1 | no | — |
| 358 | #41 | — | 4 | 1 | no | — |
| 359 | #41 | — | 4 | 2 | no | — |
| 360 | #41 | — | 4 | 1 | no | — |
| 361 | #41 | — | 4 | 1 | no | — |
| 362 | #41 | — | 4 | 1 | no | — |
| 363 | #41 | — | 4 | 1 | no | — |
| 364 | #41 | — | 4 | 1 | no | — |
| 365 | #41 | — | 4 | 2 | no | — |
| 366 | #41 | — | 4 | 2 | no | — |
| 367 | #41 | — | 4 | 2 | no | — |
| 368 | #41 | — | 4 | 1 | no | — |
| 369 | #41 | — | 4 | 1 | no | — |
| 370 | #41 | — | 4 | 1 | no | — |
| 371 | C2×Q8 | — | 2 | 1 | no | — |
| 372 | C2×Q8 | — | 2 | 1 | no | — |
| 373 | C2×Q8 | — | 2 | 1 | no | — |
| 374 | C2×Q8 | — | 2 | 1 | no | — |
| 375 | C2×Q8 | — | 2 | 1 | no | — |
| 376 | C2×Q8 | — | 4 | 1 | no | — |
| 377 | C2×Q8 | — | 4 | 1 | no | — |
| 378 | C2×Q8 | — | 4 | 2 | no | — |
| 379 | C2×Q8 | — | 34 | 1 | no | — |
| 380 | C2×Q8 | — | 34 | 1 | no | — |
| 381 | C2×Q8 | — | 68 | 1 | no | — |
| 382 | C2×Q8 | — | 68 | 1 | no | — |
| 383 | C2×Q8 | C2×C22⋊D17 | 1 | 1 | yes | characteristic |
| 384 | C2×D4 | — | 2 | 1 | no | — |
| 385 | C2×D4 | — | 2 | 1 | no | — |
| 386 | C2×D4 | — | 2 | 1 | no | — |
| 387 | C2×D4 | — | 2 | 2 | no | — |
| 388 | C2×D4 | — | 2 | 2 | no | — |
| 389 | C2×D4 | — | 4 | 2 | no | — |
| 390 | C2×D4 | — | 4 | 2 | no | — |
| 391 | C2×D4 | — | 4 | 2 | no | — |
| 392 | C2×D4 | — | 4 | 1 | no | — |
| 393 | C2×D4 | D4×D17 | 1 | 1 | yes | characteristic |
| 394 | C2×D4 | #63254 | 1 | 1 | yes | characteristic |
| 395 | C2×D4 | C2×C22⋊D17 | 1 | 1 | yes | characteristic |
| 396 | C22×C4 | — | 2 | 2 | no | — |
| 397 | C22×C4 | — | 2 | 2 | no | — |
| 398 | C22×C4 | — | 2 | 1 | no | — |
| 399 | C22×C4 | — | 4 | 1 | no | — |
| 400 | C22×C4 | — | 34 | 1 | no | — |
| 401 | C22×C4 | D4×D17 | 1 | 1 | yes | characteristic |
| 402 | C22×C4 | D4×D17 | 1 | 1 | yes | characteristic |
| 403 | C22×C4 | C2×C22⋊D17 | 1 | 1 | yes | characteristic |
| 404 | Q16 | — | 4 | 4 | no | — |
| 405 | Q16 | — | 136 | 1 | no | — |
| 406 | Q16 | — | 136 | 1 | no | — |
| 407 | SD16 | — | 4 | 4 | no | — |
| 408 | M16 | — | 2 | 2 | no | — |
| 409 | M16 | — | 4 | 1 | no | — |
| 410 | M16 | — | 68 | 1 | no | — |
| 411 | M16 | — | 68 | 1 | no | — |
| 412 | M16 | — | 68 | 1 | no | — |
| 413 | C2×C8 | — | 4 | 1 | no | — |
| 414 | C2×C8 | — | 34 | 1 | no | — |
| 415 | C2×C8 | — | 34 | 1 | no | — |
| 416 | C2×C8 | — | 68 | 1 | no | — |
| 417 | C2×C8 | — | 68 | 1 | no | — |
| 418 | C4⋊C4 | — | 2 | 1 | no | — |
| 419 | C4⋊C4 | — | 4 | 1 | no | — |
| 420 | C4⋊C4 | — | 4 | 1 | no | — |
| 421 | C4⋊C4 | — | 34 | 1 | no | — |
| 422 | C4⋊C4 | — | 68 | 1 | no | — |
| 423 | C4⋊C4 | — | 68 | 4 | no | — |
| 424 | C4⋊C4 | — | 68 | 1 | no | — |
| 425 | C4⋊C4 | — | 68 | 1 | no | — |
| 426 | C22⋊C4 | — | 2 | 1 | no | — |
| 427 | C22⋊C4 | — | 4 | 1 | no | — |
| 428 | C22⋊C4 | — | 4 | 1 | no | — |
| 429 | C22⋊C4 | — | 34 | 2 | no | — |
| 430 | C22⋊C4 | — | 34 | 1 | no | — |
| 431 | C22⋊C4 | — | 68 | 4 | no | — |
| 432 | C22⋊C4 | — | 68 | 1 | no | — |
| 433 | C22⋊C4 | — | 68 | 1 | no | — |
| 434 | C42 | — | 2 | 1 | no | — |
| 435 | C42 | — | 34 | 1 | no | — |
| 436 | C42 | — | 68 | 1 | no | — |
| 437 | C23 | — | 2 | 2 | no | — |
| 438 | C23 | — | 2 | 2 | no | — |
| 439 | C23 | — | 4 | 1 | no | — |
| 440 | C23 | #10587623 | 1 | 1 | yes | characteristic |
| 441 | C23 | #10587625 | 1 | 1 | yes | characteristic |
| 442 | C23 | #10587625 | 1 | 1 | yes | characteristic |
| 443 | Q8 | — | 2 | 2 | no | — |
| 444 | Q8 | — | 4 | 1 | no | — |
| 445 | Q8 | — | 4 | 1 | no | — |
| 446 | Q8 | — | 4 | 1 | no | — |
| 447 | Q8 | — | 4 | 2 | no | — |
| 448 | Q8 | — | 4 | 1 | no | — |
| 449 | Q8 | — | 4 | 1 | no | — |
| 450 | Q8 | — | 4 | 1 | no | — |
| 451 | Q8 | — | 68 | 1 | no | — |
| 452 | Q8 | — | 68 | 1 | no | — |
| 453 | Q8 | — | 136 | 1 | no | — |
| 454 | D4 | — | 2 | 2 | no | — |
| 455 | D4 | — | 4 | 1 | no | — |
| 456 | D4 | — | 4 | 1 | no | — |
| 457 | D4 | — | 4 | 1 | no | — |
| 458 | D4 | — | 4 | 1 | no | — |
| 459 | D4 | — | 4 | 1 | no | — |
| 460 | D4 | — | 4 | 2 | no | — |
| 461 | D4 | — | 4 | 2 | no | — |
| 462 | D4 | — | 4 | 2 | no | — |
| 463 | D4 | — | 4 | 2 | no | — |
| 464 | D4 | — | 4 | 1 | no | — |
| 465 | C2×C4 | — | 2 | 1 | no | — |
| 466 | C2×C4 | — | 2 | 1 | no | — |
| 467 | C2×C4 | — | 2 | 1 | no | — |
| 468 | C2×C4 | — | 2 | 1 | no | — |
| 469 | C2×C4 | — | 2 | 1 | no | — |
| 470 | C2×C4 | — | 2 | 1 | no | — |
| 471 | C2×C4 | — | 2 | 2 | no | — |
| 472 | C2×C4 | — | 2 | 2 | no | — |
| 473 | C2×C4 | — | 4 | 2 | no | — |
| 474 | C2×C4 | — | 4 | 2 | no | — |
| 475 | C2×C4 | — | 4 | 2 | no | — |
| 476 | C2×C4 | — | 4 | 1 | no | — |
| 477 | C2×C4 | — | 4 | 2 | no | — |
| 478 | C2×C4 | — | 4 | 1 | no | — |
| 479 | C2×C4 | — | 4 | 1 | no | — |
| 480 | C2×C4 | — | 8 | 1 | no | — |
| 481 | C2×C4 | — | 68 | 2 | no | — |
| 482 | C2×C4 | — | 68 | 2 | no | — |
| 483 | C2×C4 | — | 68 | 1 | no | — |
| 484 | C2×C4 | — | 68 | 1 | no | — |
| 485 | C2×C4 | #10587623 | 1 | 1 | yes | characteristic |
| 486 | C2×C4 | #10587624 | 1 | 1 | yes | characteristic |
| 487 | C2×C4 | #10587626 | 1 | 1 | yes | characteristic |
| 488 | C2×C4 | #10587639 | 1 | 1 | yes | characteristic |
| 489 | C8 | — | 4 | 2 | no | — |
| 490 | C8 | — | 68 | 1 | no | — |
| 491 | C8 | — | 68 | 1 | no | — |
| 492 | C8 | — | 136 | 1 | no | — |
| 493 | C22 | — | 2 | 1 | no | — |
| 494 | C22 | — | 2 | 1 | no | — |
| 495 | C22 | — | 2 | 1 | no | — |
| 496 | C22 | — | 4 | 1 | no | — |
| 497 | C22 | — | 4 | 1 | no | — |
| 498 | C22 | — | 4 | 1 | no | — |
| 499 | C22 | — | 4 | 2 | no | — |
| 500 | C22 | — | 8 | 2 | no | — |
| 501 | C22 | — | 8 | 2 | no | — |
| 502 | C22 | — | 16 | 1 | no | — |
| 503 | C22 | #11762717 | 1 | 1 | yes | characteristic |
| 504 | C4 | — | 2 | 1 | no | — |
| 505 | C4 | — | 2 | 1 | no | — |
| 506 | C4 | — | 2 | 1 | no | — |
| 507 | C4 | — | 4 | 2 | no | — |
| 508 | C4 | — | 8 | 1 | no | — |
| 509 | C4 | — | 8 | 1 | no | — |
| 510 | C4 | — | 136 | 1 | no | — |
| 511 | C4 | — | 136 | 2 | no | — |
| 512 | C4 | — | 136 | 1 | no | — |
| 513 | C4 | #11762995 | 1 | 1 | yes | characteristic |
| 514 | C4 | #11762995 | 1 | 1 | yes | characteristic |
| 515 | C2 | — | 2 | 1 | no | — |
| 516 | C2 | — | 4 | 1 | no | — |
| 517 | C2 | — | 4 | 1 | no | — |
| 518 | C2 | — | 4 | 1 | no | — |
| 519 | C2 | — | 8 | 2 | no | — |
| 520 | C2 | #14529907 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14539675 | C2 | semidirect |
| 3. #14530478 | C2 | semidirect |
| 4. #14530438 | C2 | semidirect |
| 6. #14526914 | C2 | semidirect |
| 354. C17 | #13356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539675 | 2 |
| #14538190 | 2 |
| #14530478 | 2 |
| #14530438 | 2 |
| #14528735 | 2 |
| #14526914 | 2 |
| C17×#3022 | 2 |
| #13356 | 17 |