Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
456 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 59 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 | #14536485 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #14529825 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #14527823 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #14527755 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #14526815 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #14526812 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C17×#1318 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#10587618 | — | 2 | 1 | no | — |
| 9 | #11763390 | C22 | 1 | 1 | yes | characteristic |
| 10 | #11763128 | — | 2 | 1 | no | — |
| 11 | #11762950 | — | 2 | 1 | no | — |
| 12 | C2×#10587476 | — | 2 | 1 | no | — |
| 13 | #11762748 | C22 | 1 | 1 | yes | characteristic |
| 14 | #11762732 | — | 2 | 1 | no | — |
| 15 | #11762729 | C22 | 1 | 1 | yes | characteristic |
| 16 | #11762721 | — | 2 | 1 | no | — |
| 17 | #11762693 | — | 2 | 1 | no | — |
| 18 | #11762689 | — | 2 | 1 | no | — |
| 19 | #11762681 | — | 2 | 1 | no | — |
| 20 | #11762667 | — | 2 | 1 | no | — |
| 21 | #11762578 | C22 | 1 | 1 | yes | characteristic |
| 22 | #11762544 | — | 2 | 1 | no | — |
| 23 | #11762544 | — | 2 | 1 | no | — |
| 24 | C17×#390 | C22 | 1 | 1 | yes | characteristic |
| 25 | C17×#324 | C22 | 1 | 1 | yes | characteristic |
| 26 | C17×#324 | C22 | 1 | 1 | yes | characteristic |
| 27 | C22×D4×C17 | D4 | 1 | 1 | yes | characteristic |
| 28 | C23×Dic17 | — | 2 | 1 | no | — |
| 29 | C2×#63252 | — | 2 | 1 | no | — |
| 30 | C22×Dic34 | D4 | 1 | 1 | yes | characteristic |
| 31 | C2×C4⋊C4×C17 | C23 | 1 | 1 | yes | characteristic |
| 32 | C2×C22⋊C4×C17 | — | 2 | 1 | no | — |
| 33 | C2×C22⋊C4×C17 | — | 2 | 1 | no | — |
| 34 | C2×C42×C17 | D4 | 1 | 1 | yes | characteristic |
| 35 | C2×C22⋊Dic17 | — | 2 | 1 | no | — |
| 36 | C2×C22⋊Dic17 | — | 2 | 1 | no | — |
| 37 | C2×C22⋊Dic17 | — | 2 | 1 | no | — |
| 38 | C2×#63229 | — | 4 | 1 | no | — |
| 39 | #10587618 | — | 4 | 2 | no | — |
| 40 | #10587618 | — | 4 | 2 | no | — |
| 41 | C2×#63228 | — | 4 | 1 | no | — |
| 42 | #10587616 | — | 2 | 1 | no | — |
| 43 | #10587616 | — | 2 | 1 | no | — |
| 44 | C2×C4⋊Dic17 | D4 | 1 | 1 | yes | characteristic |
| 45 | C2×#63225 | — | 2 | 1 | no | — |
| 46 | C2×#63225 | — | 2 | 1 | no | — |
| 47 | C2×#63225 | — | 2 | 1 | no | — |
| 48 | C2×#63223 | — | 2 | 1 | no | — |
| 49 | C2×#63219 | — | 4 | 1 | no | — |
| 50 | #10587583 | — | 4 | 1 | no | — |
| 51 | #10587581 | — | 4 | 1 | no | — |
| 52 | C17×C22⋊C8 | — | 2 | 1 | no | — |
| 53 | C17×C22⋊C8 | — | 2 | 1 | no | — |
| 54 | #10587502 | — | 2 | 1 | no | — |
| 55 | #10587502 | — | 2 | 1 | no | — |
| 56 | #10587502 | — | 2 | 1 | no | — |
| 57 | #10587502 | — | 2 | 1 | no | — |
| 58 | #10587502 | — | 2 | 1 | no | — |
| 59 | #10587502 | D4 | 1 | 1 | yes | characteristic |
| 60 | #10587502 | D4 | 1 | 1 | yes | characteristic |
| 61 | #10587492 | — | 4 | 1 | no | — |
| 62 | #10587488 | — | 4 | 1 | no | — |
| 63 | #10587487 | — | 4 | 1 | no | — |
| 64 | #10587476 | — | 4 | 2 | no | — |
| 65 | C24×C17 | — | 2 | 1 | no | — |
| 66 | C2×D4×C17 | — | 2 | 1 | no | — |
| 67 | C2×D4×C17 | — | 4 | 1 | no | — |
| 68 | C2×D4×C17 | — | 4 | 1 | no | — |
| 69 | C2×D4×C17 | SD16 | 1 | 2 | yes | complemented |
| 70 | C22×C4×C17 | — | 2 | 1 | no | — |
| 71 | C22×C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 72 | C22×C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 73 | C22×C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 74 | C2×C22⋊D17 | — | 4 | 1 | no | — |
| 75 | C22×Dic17 | — | 2 | 1 | no | — |
| 76 | C22×Dic17 | — | 2 | 1 | no | — |
| 77 | C22×Dic17 | — | 2 | 1 | no | — |
| 78 | C22×Dic17 | — | 2 | 1 | no | — |
| 79 | C22×Dic17 | — | 4 | 2 | no | — |
| 80 | C22×Dic17 | — | 8 | 1 | no | — |
| 81 | C22×Dic17 | — | 8 | 1 | no | — |
| 82 | #63252 | — | 4 | 1 | no | — |
| 83 | #63252 | — | 4 | 1 | no | — |
| 84 | #63252 | — | 4 | 1 | no | — |
| 85 | #63252 | — | 4 | 1 | no | — |
| 86 | C2×D68 | — | 2 | 1 | no | — |
| 87 | C2×D68 | — | 2 | 1 | no | — |
| 88 | C2×D68 | — | 2 | 1 | no | — |
| 89 | C2×C4×D17 | — | 4 | 1 | no | — |
| 90 | C2×Dic34 | — | 2 | 1 | no | — |
| 91 | C2×Dic34 | — | 4 | 1 | no | — |
| 92 | C2×Dic34 | — | 8 | 1 | no | — |
| 93 | C2×C8×C17 | — | 4 | 1 | no | — |
| 94 | C2×C8×C17 | — | 4 | 1 | no | — |
| 95 | C4⋊C4×C17 | — | 4 | 1 | no | — |
| 96 | C22⋊C4×C17 | — | 8 | 1 | no | — |
| 97 | C22⋊C4×C17 | — | 8 | 1 | no | — |
| 98 | C42×C17 | — | 4 | 1 | no | — |
| 99 | C22⋊Dic17 | — | 4 | 2 | no | — |
| 100 | C22⋊Dic17 | — | 8 | 1 | no | — |
| 101 | C22⋊Dic17 | — | 8 | 1 | no | — |
| 102 | #63229 | — | 4 | 4 | no | — |
| 103 | #63228 | — | 4 | 4 | no | — |
| 104 | #63227 | — | 4 | 1 | no | — |
| 105 | #63227 | — | 4 | 1 | no | — |
| 106 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 107 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 108 | C4⋊Dic17 | — | 4 | 1 | no | — |
| 109 | #63225 | — | 4 | 2 | no | — |
| 110 | #63225 | — | 8 | 1 | no | — |
| 111 | #63225 | — | 8 | 1 | no | — |
| 112 | #63223 | — | 2 | 2 | no | — |
| 113 | #63223 | — | 4 | 1 | no | — |
| 114 | C2×#3622 | — | 4 | 1 | no | — |
| 115 | #63219 | — | 8 | 2 | no | — |
| 116 | #12129 | — | 17 | 1 | no | maximal, Sylow |
| 117 | C23×C17 | — | 2 | 2 | no | — |
| 118 | C23×C17 | — | 4 | 1 | no | — |
| 119 | C23×C17 | — | 4 | 1 | no | — |
| 120 | C23×C17 | — | 4 | 1 | no | — |
| 121 | C23×C17 | — | 4 | 1 | no | — |
| 122 | C23×C17 | — | 4 | 1 | no | — |
| 123 | C23×C17 | — | 4 | 1 | no | — |
| 124 | C23×C17 | #120 | 1 | 1 | yes | characteristic |
| 125 | C22×D17 | — | 4 | 1 | no | — |
| 126 | D4×C17 | — | 4 | 2 | no | — |
| 127 | D4×C17 | — | 8 | 1 | no | — |
| 128 | C2×C4×C17 | — | 2 | 1 | no | — |
| 129 | C2×C4×C17 | — | 2 | 1 | no | — |
| 130 | C2×C4×C17 | — | 2 | 1 | no | — |
| 131 | C2×C4×C17 | — | 2 | 1 | no | — |
| 132 | C2×C4×C17 | — | 4 | 1 | no | — |
| 133 | C2×C4×C17 | — | 4 | 1 | no | — |
| 134 | C2×C4×C17 | — | 4 | 1 | no | — |
| 135 | C2×C4×C17 | — | 4 | 1 | no | — |
| 136 | C2×C4×C17 | — | 4 | 1 | no | — |
| 137 | C2×C4×C17 | C2×SD16 | 1 | 1 | yes | characteristic |
| 138 | C2×C4×C17 | #137 | 1 | 1 | yes | characteristic |
| 139 | C22⋊D17 | — | 8 | 1 | no | — |
| 140 | C22⋊D17 | — | 8 | 1 | no | — |
| 141 | C2×Dic17 | — | 2 | 2 | no | — |
| 142 | C2×Dic17 | — | 4 | 1 | no | — |
| 143 | C2×Dic17 | — | 4 | 1 | no | — |
| 144 | C2×Dic17 | — | 4 | 1 | no | — |
| 145 | C2×Dic17 | — | 4 | 1 | no | — |
| 146 | C2×Dic17 | — | 4 | 1 | no | — |
| 147 | C2×Dic17 | — | 4 | 1 | no | — |
| 148 | C2×Dic17 | — | 4 | 1 | no | — |
| 149 | C2×Dic17 | — | 4 | 1 | no | — |
| 150 | C2×Dic17 | — | 4 | 1 | no | — |
| 151 | C2×Dic17 | — | 4 | 1 | no | — |
| 152 | C2×Dic17 | — | 4 | 1 | no | — |
| 153 | C2×Dic17 | — | 4 | 1 | no | — |
| 154 | C2×Dic17 | — | 8 | 4 | no | — |
| 155 | D68 | — | 4 | 1 | no | — |
| 156 | D68 | — | 4 | 1 | no | — |
| 157 | D68 | — | 8 | 1 | no | — |
| 158 | D68 | — | 8 | 1 | no | — |
| 159 | C4×D17 | — | 8 | 1 | no | — |
| 160 | C4×D17 | — | 8 | 1 | no | — |
| 161 | Dic34 | — | 4 | 1 | no | — |
| 162 | Dic34 | — | 4 | 1 | no | — |
| 163 | Dic34 | — | 4 | 2 | no | — |
| 164 | Dic34 | — | 8 | 1 | no | — |
| 165 | C8×C17 | — | 8 | 1 | no | — |
| 166 | C8×C17 | — | 8 | 1 | no | — |
| 167 | #3622 | — | 4 | 2 | no | — |
| 168 | #2784 | — | 17 | 1 | no | — |
| 169 | #2006 | — | 17 | 1 | no | — |
| 170 | #1616 | — | 17 | 1 | no | — |
| 171 | #1604 | — | 17 | 1 | no | — |
| 172 | #1354 | — | 17 | 1 | no | — |
| 173 | #1353 | — | 17 | 1 | no | — |
| 174 | #1318 | D17 | 1 | 1 | yes | characteristic, complemented |
| 175 | C22×C17 | — | 2 | 1 | no | — |
| 176 | C22×C17 | — | 2 | 1 | no | — |
| 177 | C22×C17 | — | 4 | 2 | no | — |
| 178 | C22×C17 | — | 4 | 2 | no | — |
| 179 | C22×C17 | — | 4 | 2 | no | — |
| 180 | C22×C17 | — | 8 | 1 | no | — |
| 181 | C22×C17 | — | 8 | 1 | no | — |
| 182 | C22×C17 | — | 8 | 1 | no | — |
| 183 | C22×C17 | — | 8 | 1 | no | — |
| 184 | C22×C17 | #448 | 1 | 1 | yes | characteristic |
| 185 | C22×C17 | #453 | 1 | 1 | yes | characteristic |
| 186 | C22×C17 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 187 | C2×D17 | — | 8 | 1 | no | — |
| 188 | C2×D17 | — | 8 | 1 | no | — |
| 189 | C2×D17 | — | 8 | 1 | no | — |
| 190 | C4×C17 | — | 2 | 1 | no | — |
| 191 | C4×C17 | — | 2 | 1 | no | — |
| 192 | C4×C17 | — | 4 | 1 | no | — |
| 193 | C4×C17 | — | 4 | 1 | no | — |
| 194 | C4×C17 | — | 8 | 1 | no | — |
| 195 | Dic17 | — | 4 | 2 | no | — |
| 196 | Dic17 | — | 8 | 1 | no | — |
| 197 | Dic17 | — | 8 | 1 | no | — |
| 198 | Dic17 | — | 8 | 1 | no | — |
| 199 | Dic17 | — | 8 | 1 | no | — |
| 200 | C2×AGL(1,ℤ/8) | — | 34 | 1 | no | — |
| 201 | #537 | — | 17 | 1 | no | — |
| 202 | #481 | — | 34 | 1 | no | — |
| 203 | #448 | — | 34 | 1 | no | — |
| 204 | C2×#104 | — | 34 | 1 | no | — |
| 205 | #400 | — | 17 | 1 | no | — |
| 206 | #396 | — | 34 | 1 | no | — |
| 207 | #395 | — | 17 | 1 | no | — |
| 208 | #393 | — | 34 | 1 | no | — |
| 209 | #390 | C2×D17 | 1 | 1 | yes | characteristic |
| 210 | #387 | — | 34 | 1 | no | — |
| 211 | #386 | — | 34 | 1 | no | — |
| 212 | #385 | — | 34 | 1 | no | — |
| 213 | #380 | — | 34 | 1 | no | — |
| 214 | #343 | — | 17 | 1 | no | — |
| 215 | #327 | — | 34 | 1 | no | — |
| 216 | #327 | — | 34 | 1 | no | — |
| 217 | #324 | C2×D17 | 1 | 1 | yes | characteristic |
| 218 | #324 | C2×D17 | 1 | 1 | yes | characteristic |
| 219 | C2×C17 | — | 2 | 1 | no | — |
| 220 | C2×C17 | — | 2 | 1 | no | — |
| 221 | C2×C17 | — | 8 | 2 | no | — |
| 222 | C2×C17 | #1596 | 1 | 1 | yes | characteristic |
| 223 | C2×C17 | #2200 | 1 | 1 | yes | characteristic |
| 224 | C2×C17 | #2204 | 1 | 1 | yes | characteristic |
| 225 | D17 | — | 16 | 1 | no | — |
| 226 | C2×#41 | — | 34 | 1 | no | — |
| 227 | C22×Q8 | — | 17 | 1 | no | — |
| 228 | C22×D4 | D68 | 1 | 1 | yes | characteristic |
| 229 | C23×C4 | — | 34 | 1 | no | — |
| 230 | AGL(1,ℤ/8) | — | 68 | 2 | no | — |
| 231 | AGL(1,ℤ/8) | — | 68 | 2 | no | — |
| 232 | C2×SD16 | — | 68 | 1 | no | — |
| 233 | C2×SD16 | — | 68 | 1 | no | — |
| 234 | C2×D8 | — | 68 | 1 | no | — |
| 235 | C2×M16 | — | 34 | 1 | no | — |
| 236 | C22⋊Q8 | — | 68 | 1 | no | — |
| 237 | #121 | — | 34 | 1 | no | — |
| 238 | #121 | — | 34 | 1 | no | — |
| 239 | #121 | — | 68 | 1 | no | — |
| 240 | C2×C4⋊C4 | — | 17 | 1 | no | — |
| 241 | C2×C4⋊C4 | — | 34 | 1 | no | — |
| 242 | C2×C4⋊C4 | — | 34 | 1 | no | — |
| 243 | C2×C4⋊C4 | — | 34 | 1 | no | — |
| 244 | C2×C4⋊C4 | C22×D17 | 1 | 1 | yes | characteristic |
| 245 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 246 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 247 | C2×C22⋊C4 | — | 34 | 1 | no | — |
| 248 | C2×C22⋊C4 | — | 34 | 1 | no | — |
| 249 | C2×C22⋊C4 | — | 34 | 1 | no | — |
| 250 | C2×C42 | D68 | 1 | 1 | yes | characteristic |
| 251 | #106 | — | 68 | 1 | no | — |
| 252 | #104 | — | 68 | 2 | no | — |
| 253 | #103 | — | 68 | 1 | no | — |
| 254 | #102 | — | 68 | 1 | no | — |
| 255 | C22⋊C8 | — | 2 | 1 | no | — |
| 256 | C22⋊C8 | — | 2 | 1 | no | — |
| 257 | #95 | — | 17 | 1 | no | — |
| 258 | #95 | — | 17 | 1 | no | — |
| 259 | #95 | — | 34 | 1 | no | — |
| 260 | #95 | — | 34 | 1 | no | — |
| 261 | #95 | — | 34 | 1 | no | — |
| 262 | #95 | — | 34 | 1 | no | — |
| 263 | #95 | — | 34 | 1 | no | — |
| 264 | C17 | #12129 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 265 | C24 | — | 2 | 1 | no | — |
| 266 | #41 | — | 68 | 1 | no | — |
| 267 | #41 | — | 68 | 1 | no | — |
| 268 | #41 | — | 68 | 1 | no | — |
| 269 | #41 | — | 68 | 1 | no | — |
| 270 | C2×Q8 | — | 34 | 1 | no | — |
| 271 | C2×Q8 | — | 68 | 1 | no | — |
| 272 | C2×Q8 | — | 136 | 1 | no | — |
| 273 | C2×D4 | — | 2 | 1 | no | — |
| 274 | C2×D4 | — | 4 | 1 | no | — |
| 275 | C2×D4 | — | 4 | 1 | no | — |
| 276 | C2×D4 | — | 34 | 1 | no | — |
| 277 | C2×D4 | — | 34 | 1 | no | — |
| 278 | C2×D4 | — | 34 | 1 | no | — |
| 279 | C2×D4 | — | 68 | 1 | no | — |
| 280 | C2×D4 | #63219 | 1 | 2 | yes | complemented |
| 281 | C22×C4 | — | 2 | 1 | no | — |
| 282 | C22×C4 | — | 34 | 1 | no | — |
| 283 | C22×C4 | — | 34 | 1 | no | — |
| 284 | C22×C4 | — | 34 | 1 | no | — |
| 285 | C22×C4 | — | 34 | 1 | no | — |
| 286 | C22×C4 | — | 68 | 1 | no | — |
| 287 | C22×C4 | — | 68 | 2 | no | — |
| 288 | C22×C4 | — | 136 | 1 | no | — |
| 289 | C22×C4 | — | 136 | 1 | no | — |
| 290 | C22×C4 | C2×D68 | 1 | 1 | yes | characteristic |
| 291 | C22×C4 | D4×D17 | 1 | 1 | yes | characteristic |
| 292 | C22×C4 | D4×D17 | 1 | 1 | yes | characteristic |
| 293 | SD16 | — | 68 | 4 | no | — |
| 294 | SD16 | — | 136 | 2 | no | — |
| 295 | D8 | — | 68 | 4 | no | — |
| 296 | M16 | — | 34 | 2 | no | — |
| 297 | M16 | — | 68 | 1 | no | — |
| 298 | C2×C8 | — | 4 | 1 | no | — |
| 299 | C2×C8 | — | 4 | 1 | no | — |
| 300 | C2×C8 | — | 68 | 1 | no | — |
| 301 | C4⋊C4 | — | 4 | 1 | no | — |
| 302 | C4⋊C4 | — | 34 | 1 | no | — |
| 303 | C4⋊C4 | — | 34 | 1 | no | — |
| 304 | C4⋊C4 | — | 68 | 1 | no | — |
| 305 | C4⋊C4 | — | 68 | 2 | no | — |
| 306 | C4⋊C4 | — | 136 | 1 | no | — |
| 307 | C4⋊C4 | — | 136 | 1 | no | — |
| 308 | C22⋊C4 | — | 8 | 1 | no | — |
| 309 | C22⋊C4 | — | 8 | 1 | no | — |
| 310 | C22⋊C4 | — | 68 | 1 | no | — |
| 311 | C22⋊C4 | — | 68 | 1 | no | — |
| 312 | C22⋊C4 | — | 68 | 2 | no | — |
| 313 | C22⋊C4 | — | 136 | 1 | no | — |
| 314 | C22⋊C4 | — | 136 | 1 | no | — |
| 315 | C42 | — | 4 | 1 | no | — |
| 316 | C23 | — | 2 | 2 | no | — |
| 317 | C23 | — | 4 | 1 | no | — |
| 318 | C23 | — | 4 | 1 | no | — |
| 319 | C23 | — | 4 | 1 | no | — |
| 320 | C23 | — | 4 | 1 | no | — |
| 321 | C23 | — | 4 | 1 | no | — |
| 322 | C23 | — | 4 | 1 | no | — |
| 323 | C23 | — | 68 | 1 | no | — |
| 324 | C23 | #10587568 | 1 | 1 | yes | characteristic |
| 325 | Q8 | — | 68 | 1 | no | — |
| 326 | Q8 | — | 68 | 1 | no | — |
| 327 | Q8 | — | 68 | 2 | no | — |
| 328 | Q8 | — | 136 | 1 | no | — |
| 329 | D4 | — | 4 | 2 | no | — |
| 330 | D4 | — | 8 | 1 | no | — |
| 331 | D4 | — | 68 | 1 | no | — |
| 332 | D4 | — | 68 | 1 | no | — |
| 333 | D4 | — | 136 | 1 | no | — |
| 334 | D4 | — | 136 | 1 | no | — |
| 335 | D4 | — | 136 | 1 | no | — |
| 336 | D4 | — | 136 | 1 | no | — |
| 337 | C2×C4 | — | 2 | 1 | no | — |
| 338 | C2×C4 | — | 2 | 1 | no | — |
| 339 | C2×C4 | — | 2 | 1 | no | — |
| 340 | C2×C4 | — | 2 | 1 | no | — |
| 341 | C2×C4 | — | 4 | 1 | no | — |
| 342 | C2×C4 | — | 4 | 1 | no | — |
| 343 | C2×C4 | — | 4 | 1 | no | — |
| 344 | C2×C4 | — | 4 | 1 | no | — |
| 345 | C2×C4 | — | 4 | 1 | no | — |
| 346 | C2×C4 | — | 34 | 2 | no | — |
| 347 | C2×C4 | — | 68 | 1 | no | — |
| 348 | C2×C4 | — | 68 | 1 | no | — |
| 349 | C2×C4 | — | 68 | 1 | no | — |
| 350 | C2×C4 | — | 68 | 1 | no | — |
| 351 | C2×C4 | — | 68 | 1 | no | — |
| 352 | C2×C4 | — | 68 | 1 | no | — |
| 353 | C2×C4 | — | 68 | 1 | no | — |
| 354 | C2×C4 | — | 68 | 1 | no | — |
| 355 | C2×C4 | — | 68 | 1 | no | — |
| 356 | C2×C4 | — | 68 | 1 | no | — |
| 357 | C2×C4 | — | 68 | 1 | no | — |
| 358 | C2×C4 | — | 68 | 1 | no | — |
| 359 | C2×C4 | — | 136 | 1 | no | — |
| 360 | C2×C4 | — | 136 | 1 | no | — |
| 361 | C2×C4 | — | 136 | 4 | no | — |
| 362 | C2×C4 | C2×#63219 | 1 | 1 | yes | characteristic |
| 363 | C2×C4 | #10587595 | 1 | 1 | yes | characteristic |
| 364 | C8 | — | 8 | 1 | no | — |
| 365 | C8 | — | 8 | 1 | no | — |
| 366 | C8 | — | 68 | 2 | no | — |
| 367 | C22 | — | 2 | 1 | no | — |
| 368 | C22 | — | 2 | 1 | no | — |
| 369 | C22 | — | 4 | 2 | no | — |
| 370 | C22 | — | 4 | 2 | no | — |
| 371 | C22 | — | 4 | 2 | no | — |
| 372 | C22 | — | 8 | 1 | no | — |
| 373 | C22 | — | 8 | 1 | no | — |
| 374 | C22 | — | 8 | 1 | no | — |
| 375 | C22 | — | 8 | 1 | no | — |
| 376 | C22 | — | 136 | 1 | no | — |
| 377 | C22 | — | 136 | 1 | no | — |
| 378 | C22 | — | 136 | 1 | no | — |
| 379 | C22 | #11762950 | 1 | 1 | yes | characteristic |
| 380 | C22 | #11762979 | 1 | 1 | yes | characteristic |
| 381 | C22 | #11762997 | 1 | 1 | yes | characteristic |
| 382 | C4 | — | 2 | 1 | no | — |
| 383 | C4 | — | 2 | 1 | no | — |
| 384 | C4 | — | 4 | 1 | no | — |
| 385 | C4 | — | 4 | 1 | no | — |
| 386 | C4 | — | 8 | 1 | no | — |
| 387 | C4 | — | 68 | 2 | no | — |
| 388 | C4 | — | 136 | 1 | no | — |
| 389 | C4 | — | 136 | 1 | no | — |
| 390 | C4 | — | 136 | 1 | no | — |
| 391 | C4 | — | 136 | 1 | no | — |
| 392 | C2 | — | 2 | 1 | no | — |
| 393 | C2 | — | 2 | 1 | no | — |
| 394 | C2 | — | 8 | 2 | no | — |
| 395 | C2 | — | 272 | 1 | no | — |
| 396 | C2 | #14527709 | 1 | 1 | yes | characteristic |
| 397 | C2 | #14530794 | 1 | 1 | yes | characteristic |
| 398 | C2 | #14530811 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14536485 | C2 | semidirect |
| 3. #14527823 | C2 | semidirect |
| 4. #14527755 | C2 | semidirect |
| 5. #14526815 | C2 | semidirect |
| 6. #14526812 | C2 | semidirect |
| 7. C17×#1318 | C2 | semidirect |
| 69. C2×D4×C17 | SD16 | semidirect |
| 174. #1318 | D17 | semidirect |
| 264. C17 | #12129 | semidirect |
| 280. C2×D4 | #63219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14536485 | 2 |
| #14529825 | 2 |
| #14527823 | 2 |
| #14527755 | 2 |
| #14526815 | 2 |
| #14526812 | 2 |
| C17×#1318 | 2 |
| #12129 | 17 |