Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1716 conjugacy classes of subgroups.
The subgroup lattice has 454 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #14537004 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #14536989 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #14536922 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #14536908 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #14532065 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #14532047 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #14532024 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #14532024 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #14531279 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #14531245 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C17×#2402 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×C4×D68 | C22 | 1 | 2 | yes | — |
| 13 | C2×C4×D68 | C22 | 1 | 4 | yes | — |
| 14 | C2×C4×D68 | C22 | 1 | 4 | yes | — |
| 15 | C2×#10587558 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#10587558 | C22 | 1 | 4 | yes | — |
| 17 | #11762751 | C22 | 1 | 4 | yes | — |
| 18 | #11762746 | C22 | 1 | 4 | yes | — |
| 19 | #11762744 | C22 | 1 | 4 | yes | — |
| 20 | #11762742 | C22 | 1 | 4 | yes | — |
| 21 | #11762741 | C22 | 1 | 4 | yes | — |
| 22 | #11762741 | C22 | 1 | 2 | yes | — |
| 23 | #11762738 | C22 | 1 | 4 | yes | — |
| 24 | #11762738 | C22 | 1 | 4 | yes | — |
| 25 | #11762736 | C22 | 1 | 4 | yes | — |
| 26 | #11762736 | C22 | 1 | 2 | yes | — |
| 27 | #11762735 | C22 | 1 | 4 | yes | — |
| 28 | #11762731 | C22 | 1 | 4 | yes | — |
| 29 | #11762731 | C22 | 1 | 4 | yes | — |
| 30 | #11762731 | C22 | 1 | 4 | yes | — |
| 31 | #11762727 | C22 | 1 | 4 | yes | — |
| 32 | #11762727 | C22 | 1 | 2 | yes | — |
| 33 | #11762727 | C22 | 1 | 4 | yes | — |
| 34 | #11762726 | C22 | 1 | 4 | yes | — |
| 35 | #11762726 | C22 | 1 | 4 | yes | — |
| 36 | #11762726 | C22 | 1 | 4 | yes | — |
| 37 | #11762726 | C22 | 1 | 4 | yes | — |
| 38 | #11762719 | C22 | 1 | 2 | yes | — |
| 39 | #11762719 | C22 | 1 | 4 | yes | — |
| 40 | #11762719 | C22 | 1 | 4 | yes | — |
| 41 | #11762710 | C22 | 1 | 4 | yes | — |
| 42 | #11762705 | C22 | 1 | 4 | yes | — |
| 43 | #11762698 | C22 | 1 | 4 | yes | — |
| 44 | #11762698 | C22 | 1 | 4 | yes | — |
| 45 | #11762698 | C22 | 1 | 4 | yes | — |
| 46 | #11762691 | C22 | 1 | 4 | yes | — |
| 47 | C4×#63225 | C22 | 1 | 2 | yes | — |
| 48 | C4×#63227 | C22 | 1 | 4 | yes | — |
| 49 | C4×#63227 | C22 | 1 | 2 | yes | — |
| 50 | C4×#63227 | C22 | 1 | 4 | yes | — |
| 51 | C42×Dic17 | C22 | 1 | 1 | yes | characteristic |
| 52 | C17×#400 | C22 | 1 | 4 | yes | — |
| 53 | C17×#398 | C22 | 1 | 4 | yes | — |
| 54 | C4×C4⋊C4×C17 | C22 | 1 | 2 | yes | — |
| 55 | C4×C4⋊C4×C17 | C22 | 1 | 4 | yes | — |
| 56 | C17×#376 | C22 | 1 | 1 | yes | characteristic |
| 57 | C22×D68 | C23 | 1 | 2 | yes | — |
| 58 | C22×D68 | C23 | 1 | 4 | yes | — |
| 59 | C22×D68 | C23 | 1 | 4 | yes | — |
| 60 | C22×C4×D17 | C23 | 1 | 1 | yes | characteristic |
| 61 | C22×C4×D17 | C23 | 1 | 4 | yes | — |
| 62 | C2×C4⋊C4×C17 | C23 | 1 | 4 | yes | — |
| 63 | C2×C4⋊C4×C17 | C23 | 1 | 4 | yes | — |
| 64 | C2×C4⋊C4×C17 | C23 | 1 | 4 | yes | — |
| 65 | C2×C42×C17 | C23 | 1 | 4 | yes | — |
| 66 | C2×C42×C17 | C23 | 1 | 2 | yes | — |
| 67 | C2×C42×C17 | C23 | 1 | 1 | yes | characteristic |
| 68 | C2×#63227 | C23 | 1 | 2 | yes | — |
| 69 | C2×#63227 | C23 | 1 | 4 | yes | — |
| 70 | C2×#63227 | C23 | 1 | 4 | yes | — |
| 71 | C2×#63227 | C23 | 1 | 4 | yes | — |
| 72 | C2×#63227 | C23 | 1 | 4 | yes | — |
| 73 | C2×#63227 | C23 | 1 | 4 | yes | — |
| 74 | C2×#63227 | C23 | 1 | 4 | yes | — |
| 75 | C2×#63227 | C23 | 1 | 4 | yes | — |
| 76 | C2×#63227 | C23 | 1 | 4 | yes | — |
| 77 | C2×#63227 | C23 | 1 | 4 | yes | — |
| 78 | C2×#63227 | C23 | 1 | 4 | yes | — |
| 79 | C2×#63227 | C23 | 1 | 4 | yes | — |
| 80 | C2×#63227 | C23 | 1 | 4 | yes | — |
| 81 | C2×C4⋊Dic17 | C23 | 1 | 2 | yes | — |
| 82 | C2×C4⋊Dic17 | C23 | 1 | 4 | yes | — |
| 83 | C2×C4⋊Dic17 | C23 | 1 | 4 | yes | — |
| 84 | C2×#63225 | C23 | 1 | 2 | yes | — |
| 85 | C2×#63225 | C23 | 1 | 4 | yes | — |
| 86 | C2×#63225 | C23 | 1 | 4 | yes | — |
| 87 | C2×#63225 | C23 | 1 | 4 | yes | — |
| 88 | C2×C4×Dic17 | C23 | 1 | 2 | yes | — |
| 89 | C2×C4×Dic17 | C23 | 1 | 1 | yes | characteristic |
| 90 | C2×C4×Dic17 | C23 | 1 | 4 | yes | — |
| 91 | C4×D68 | — | 2 | 8 | no | — |
| 92 | C4×D68 | — | 4 | 8 | no | — |
| 93 | C4×D68 | — | 4 | 8 | no | — |
| 94 | #10587558 | — | 2 | 4 | no | — |
| 95 | #10587558 | — | 4 | 8 | no | — |
| 96 | C17×#95 | C23 | 1 | 4 | yes | — |
| 97 | C17×#95 | C23 | 1 | 2 | yes | — |
| 98 | C17×#95 | C23 | 1 | 2 | yes | — |
| 99 | C17×#95 | C23 | 1 | 4 | yes | — |
| 100 | C17×#95 | C23 | 1 | 4 | yes | — |
| 101 | #10587502 | C23 | 1 | 4 | yes | — |
| 102 | #10587502 | C23 | 1 | 4 | yes | — |
| 103 | #10587502 | C23 | 1 | 4 | yes | — |
| 104 | #10587502 | C23 | 1 | 4 | yes | — |
| 105 | #10587502 | C23 | 1 | 4 | yes | — |
| 106 | #10587502 | C23 | 1 | 4 | yes | — |
| 107 | C23×D17 | C24 | 1 | 4 | yes | — |
| 108 | C23×D17 | C24 | 1 | 1 | yes | characteristic |
| 109 | C22×C4×C17 | C24 | 1 | 4 | yes | — |
| 110 | C22×C4×C17 | C24 | 1 | 4 | yes | — |
| 111 | C22×C4×C17 | C24 | 1 | 4 | yes | — |
| 112 | C22×C4×C17 | C24 | 1 | 2 | yes | — |
| 113 | C22×C4×C17 | C24 | 1 | 1 | yes | characteristic |
| 114 | C22×Dic17 | C24 | 1 | 1 | yes | characteristic |
| 115 | C22×Dic17 | C24 | 1 | 4 | yes | — |
| 116 | C22×Dic17 | C24 | 1 | 2 | yes | — |
| 117 | C22×Dic17 | C24 | 1 | 4 | yes | — |
| 118 | C2×D68 | — | 2 | 4 | no | — |
| 119 | C2×D68 | — | 4 | 4 | no | — |
| 120 | C2×D68 | — | 4 | 4 | no | — |
| 121 | C2×D68 | — | 4 | 4 | no | — |
| 122 | C2×D68 | — | 4 | 4 | no | — |
| 123 | C2×D68 | — | 4 | 4 | no | — |
| 124 | C2×D68 | — | 4 | 4 | no | — |
| 125 | C2×D68 | — | 4 | 4 | no | — |
| 126 | C2×C4×D17 | — | 2 | 2 | no | — |
| 127 | C2×C4×D17 | — | 2 | 8 | no | — |
| 128 | C2×C4×D17 | — | 2 | 8 | no | — |
| 129 | C2×C4×D17 | — | 2 | 4 | no | — |
| 130 | C2×C4×D17 | — | 2 | 8 | no | — |
| 131 | C4⋊C4×C17 | — | 4 | 4 | no | — |
| 132 | C4⋊C4×C17 | — | 4 | 4 | no | — |
| 133 | C4⋊C4×C17 | — | 4 | 4 | no | — |
| 134 | C42×C17 | — | 2 | 8 | no | — |
| 135 | C42×C17 | — | 2 | 4 | no | — |
| 136 | C42×C17 | #41 | 1 | 4 | yes | — |
| 137 | #63227 | — | 2 | 4 | no | — |
| 138 | #63227 | — | 2 | 8 | no | — |
| 139 | #63227 | — | 4 | 4 | no | — |
| 140 | #63227 | — | 4 | 4 | no | — |
| 141 | #63227 | — | 4 | 4 | no | — |
| 142 | #63227 | — | 4 | 4 | no | — |
| 143 | #63227 | — | 4 | 4 | no | — |
| 144 | #63227 | — | 4 | 4 | no | — |
| 145 | #63227 | — | 4 | 4 | no | — |
| 146 | #63227 | — | 4 | 4 | no | — |
| 147 | #63227 | — | 4 | 4 | no | — |
| 148 | #63227 | — | 4 | 4 | no | — |
| 149 | #63227 | — | 4 | 4 | no | — |
| 150 | C4⋊Dic17 | — | 2 | 4 | no | — |
| 151 | C4⋊Dic17 | — | 4 | 4 | no | — |
| 152 | C4⋊Dic17 | — | 4 | 4 | no | — |
| 153 | #63225 | — | 2 | 4 | no | — |
| 154 | #63225 | — | 4 | 4 | no | — |
| 155 | #63225 | — | 4 | 4 | no | — |
| 156 | #63225 | — | 4 | 4 | no | — |
| 157 | C4×Dic17 | — | 2 | 2 | no | — |
| 158 | C4×Dic17 | — | 2 | 4 | no | — |
| 159 | C4×Dic17 | — | 4 | 4 | no | — |
| 160 | #36692 | — | 17 | 1 | no | maximal, Sylow |
| 161 | C23×C17 | C25 | 1 | 1 | yes | characteristic |
| 162 | C22×D17 | — | 2 | 4 | no | — |
| 163 | C22×D17 | — | 2 | 1 | no | — |
| 164 | C22×D17 | — | 2 | 4 | no | — |
| 165 | C22×D17 | — | 2 | 2 | no | — |
| 166 | C22×D17 | — | 2 | 4 | no | — |
| 167 | C22×D17 | — | 2 | 4 | no | — |
| 168 | C22×D17 | — | 2 | 4 | no | — |
| 169 | C22×D17 | — | 2 | 4 | no | — |
| 170 | C22×D17 | — | 2 | 4 | no | — |
| 171 | C22×D17 | — | 2 | 4 | no | — |
| 172 | C2×C4×C17 | — | 2 | 4 | no | — |
| 173 | C2×C4×C17 | — | 2 | 4 | no | — |
| 174 | C2×C4×C17 | — | 2 | 4 | no | — |
| 175 | C2×C4×C17 | — | 2 | 4 | no | — |
| 176 | C2×C4×C17 | — | 2 | 4 | no | — |
| 177 | C2×C4×C17 | — | 2 | 4 | no | — |
| 178 | C2×C4×C17 | — | 2 | 4 | no | — |
| 179 | C2×C4×C17 | — | 2 | 4 | no | — |
| 180 | C2×C4×C17 | — | 2 | 4 | no | — |
| 181 | C2×C4×C17 | — | 2 | 4 | no | — |
| 182 | C2×C4×C17 | C2×#41 | 1 | 4 | yes | — |
| 183 | C2×C4×C17 | C2×#41 | 1 | 2 | yes | — |
| 184 | C2×C4×C17 | H(5,𝔽2) | 1 | 4 | yes | — |
| 185 | C2×Dic17 | — | 2 | 1 | no | — |
| 186 | C2×Dic17 | — | 2 | 4 | no | — |
| 187 | C2×Dic17 | — | 2 | 2 | no | — |
| 188 | C2×Dic17 | — | 2 | 4 | no | — |
| 189 | C2×Dic17 | — | 2 | 2 | no | — |
| 190 | C2×Dic17 | — | 2 | 4 | no | — |
| 191 | C2×Dic17 | — | 2 | 4 | no | — |
| 192 | C2×Dic17 | — | 2 | 4 | no | — |
| 193 | C2×Dic17 | — | 2 | 4 | no | — |
| 194 | C2×Dic17 | — | 2 | 4 | no | — |
| 195 | D68 | — | 4 | 8 | no | — |
| 196 | D68 | — | 4 | 16 | no | — |
| 197 | D68 | — | 4 | 16 | no | — |
| 198 | C4×D17 | — | 4 | 4 | no | — |
| 199 | C4×D17 | — | 4 | 16 | no | — |
| 200 | #2837 | — | 17 | 4 | no | — |
| 201 | #2836 | — | 17 | 4 | no | — |
| 202 | #2829 | — | 17 | 4 | no | — |
| 203 | #2828 | — | 17 | 4 | no | — |
| 204 | #2402 | D17 | 1 | 1 | yes | characteristic, complemented |
| 205 | #2397 | — | 17 | 1 | no | — |
| 206 | #2395 | — | 17 | 4 | no | — |
| 207 | #2392 | — | 17 | 2 | no | — |
| 208 | #2392 | — | 17 | 4 | no | — |
| 209 | #2298 | — | 17 | 1 | no | — |
| 210 | #2293 | — | 17 | 2 | no | — |
| 211 | C22×C17 | C22×#41 | 1 | 1 | yes | characteristic |
| 212 | C22×C17 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 213 | C22×C17 | #585 | 1 | 4 | yes | — |
| 214 | C2×D17 | — | 4 | 4 | no | — |
| 215 | C2×D17 | — | 4 | 1 | no | — |
| 216 | C2×D17 | — | 4 | 4 | no | — |
| 217 | C2×D17 | — | 4 | 4 | no | — |
| 218 | C2×D17 | — | 4 | 2 | no | — |
| 219 | C2×D17 | — | 4 | 4 | no | — |
| 220 | C2×D17 | — | 4 | 4 | no | — |
| 221 | C2×D17 | — | 4 | 4 | no | — |
| 222 | C2×D17 | — | 4 | 4 | no | — |
| 223 | C2×D17 | — | 4 | 4 | no | — |
| 224 | C4×C17 | — | 2 | 4 | no | — |
| 225 | C4×C17 | — | 4 | 4 | no | — |
| 226 | C4×C17 | — | 4 | 4 | no | — |
| 227 | C4×C17 | — | 4 | 4 | no | — |
| 228 | C4×C17 | #540 | 1 | 4 | yes | — |
| 229 | Dic17 | — | 4 | 1 | no | — |
| 230 | Dic17 | — | 4 | 4 | no | — |
| 231 | Dic17 | — | 4 | 2 | no | — |
| 232 | Dic17 | — | 4 | 4 | no | — |
| 233 | C2×C4×D4 | — | 17 | 2 | no | — |
| 234 | C2×C4×D4 | — | 17 | 4 | no | — |
| 235 | C2×C4×D4 | — | 17 | 4 | no | — |
| 236 | C2×#117 | — | 17 | 1 | no | — |
| 237 | C2×#117 | — | 17 | 4 | no | — |
| 238 | #400 | — | 17 | 4 | no | — |
| 239 | #400 | C2×D17 | 1 | 4 | yes | — |
| 240 | #399 | — | 17 | 4 | no | — |
| 241 | #399 | — | 17 | 4 | no | — |
| 242 | #398 | — | 17 | 4 | no | — |
| 243 | #398 | — | 17 | 4 | no | — |
| 244 | #398 | — | 17 | 2 | no | — |
| 245 | #398 | C2×D17 | 1 | 4 | yes | — |
| 246 | #397 | — | 17 | 4 | no | — |
| 247 | #397 | — | 17 | 4 | no | — |
| 248 | #397 | — | 17 | 4 | no | — |
| 249 | #397 | — | 17 | 4 | no | — |
| 250 | #397 | — | 17 | 2 | no | — |
| 251 | #396 | — | 17 | 4 | no | — |
| 252 | #396 | — | 17 | 4 | no | — |
| 253 | #396 | — | 17 | 4 | no | — |
| 254 | #394 | — | 17 | 4 | no | — |
| 255 | #394 | — | 17 | 4 | no | — |
| 256 | #394 | — | 17 | 4 | no | — |
| 257 | #394 | — | 17 | 4 | no | — |
| 258 | #394 | — | 17 | 4 | no | — |
| 259 | #394 | — | 17 | 4 | no | — |
| 260 | #394 | — | 17 | 2 | no | — |
| 261 | #392 | — | 17 | 2 | no | — |
| 262 | #392 | — | 17 | 4 | no | — |
| 263 | #392 | — | 17 | 4 | no | — |
| 264 | #390 | — | 17 | 4 | no | — |
| 265 | #389 | — | 17 | 4 | no | — |
| 266 | #388 | — | 17 | 4 | no | — |
| 267 | #388 | — | 17 | 4 | no | — |
| 268 | #388 | — | 17 | 4 | no | — |
| 269 | #387 | — | 17 | 4 | no | — |
| 270 | C4×C4⋊C4 | — | 17 | 2 | no | — |
| 271 | C4×C4⋊C4 | C2×D17 | 1 | 4 | yes | — |
| 272 | C4×C4⋊C4 | C2×D17 | 1 | 2 | yes | — |
| 273 | C4×C22⋊C4 | — | 17 | 2 | no | — |
| 274 | C4×C22⋊C4 | — | 17 | 4 | no | — |
| 275 | C4×C22⋊C4 | — | 17 | 4 | no | — |
| 276 | #376 | C2×D17 | 1 | 1 | yes | characteristic |
| 277 | C43 | — | 17 | 1 | no | — |
| 278 | C2×C17 | C2×#540 | 1 | 1 | yes | characteristic |
| 279 | C2×C17 | #3455 | 1 | 2 | yes | — |
| 280 | C2×C17 | #3529 | 1 | 4 | yes | — |
| 281 | D17 | — | 8 | 4 | no | — |
| 282 | D17 | — | 8 | 1 | no | — |
| 283 | C22×D4 | — | 17 | 2 | no | — |
| 284 | C22×D4 | — | 17 | 4 | no | — |
| 285 | C22×D4 | — | 17 | 4 | no | — |
| 286 | C23×C4 | — | 17 | 1 | no | — |
| 287 | C23×C4 | — | 17 | 4 | no | — |
| 288 | C4×D4 | — | 34 | 8 | no | — |
| 289 | C4×D4 | — | 68 | 8 | no | — |
| 290 | C4×D4 | — | 68 | 8 | no | — |
| 291 | #117 | — | 34 | 4 | no | — |
| 292 | #117 | — | 68 | 8 | no | — |
| 293 | C2×C4⋊C4 | — | 17 | 2 | no | — |
| 294 | C2×C4⋊C4 | — | 17 | 2 | no | — |
| 295 | C2×C4⋊C4 | — | 17 | 4 | no | — |
| 296 | C2×C4⋊C4 | — | 17 | 4 | no | — |
| 297 | C2×C4⋊C4 | — | 17 | 4 | no | — |
| 298 | C2×C4⋊C4 | — | 17 | 4 | no | — |
| 299 | C2×C4⋊C4 | — | 17 | 4 | no | — |
| 300 | C2×C4⋊C4 | C22×D17 | 1 | 4 | yes | — |
| 301 | C2×C4⋊C4 | C22×D17 | 1 | 4 | yes | — |
| 302 | C2×C4⋊C4 | C22×D17 | 1 | 4 | yes | — |
| 303 | C2×C22⋊C4 | — | 17 | 2 | no | — |
| 304 | C2×C22⋊C4 | — | 17 | 4 | no | — |
| 305 | C2×C22⋊C4 | — | 17 | 4 | no | — |
| 306 | C2×C22⋊C4 | — | 17 | 4 | no | — |
| 307 | C2×C22⋊C4 | — | 17 | 4 | no | — |
| 308 | C2×C22⋊C4 | — | 17 | 4 | no | — |
| 309 | C2×C22⋊C4 | — | 17 | 4 | no | — |
| 310 | C2×C22⋊C4 | — | 17 | 4 | no | — |
| 311 | C2×C22⋊C4 | — | 17 | 4 | no | — |
| 312 | C2×C22⋊C4 | — | 17 | 4 | no | — |
| 313 | C2×C22⋊C4 | — | 17 | 4 | no | — |
| 314 | C2×C22⋊C4 | — | 17 | 4 | no | — |
| 315 | C2×C22⋊C4 | — | 17 | 4 | no | — |
| 316 | C2×C42 | — | 17 | 2 | no | — |
| 317 | C2×C42 | — | 17 | 1 | no | — |
| 318 | C2×C42 | — | 17 | 4 | no | — |
| 319 | C2×C42 | C22×D17 | 1 | 4 | yes | — |
| 320 | C2×C42 | C22×D17 | 1 | 2 | yes | — |
| 321 | C2×C42 | C22×D17 | 1 | 1 | yes | characteristic |
| 322 | #95 | — | 17 | 4 | no | — |
| 323 | #95 | — | 17 | 4 | no | — |
| 324 | #95 | — | 17 | 4 | no | — |
| 325 | #95 | — | 17 | 4 | no | — |
| 326 | #95 | — | 17 | 4 | no | — |
| 327 | #95 | — | 17 | 4 | no | — |
| 328 | #95 | C22×D17 | 1 | 4 | yes | — |
| 329 | #95 | C22×D17 | 1 | 2 | yes | — |
| 330 | #95 | C22×D17 | 1 | 2 | yes | — |
| 331 | #95 | C22×D17 | 1 | 4 | yes | — |
| 332 | #95 | C22×D17 | 1 | 4 | yes | — |
| 333 | C17 | #36692 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 334 | C24 | — | 17 | 1 | no | — |
| 335 | C24 | — | 17 | 4 | no | — |
| 336 | C2×D4 | — | 34 | 4 | no | — |
| 337 | C2×D4 | — | 68 | 4 | no | — |
| 338 | C2×D4 | — | 68 | 4 | no | — |
| 339 | C2×D4 | — | 68 | 4 | no | — |
| 340 | C2×D4 | — | 68 | 4 | no | — |
| 341 | C2×D4 | — | 68 | 4 | no | — |
| 342 | C2×D4 | — | 68 | 4 | no | — |
| 343 | C2×D4 | — | 68 | 4 | no | — |
| 344 | C22×C4 | — | 17 | 2 | no | — |
| 345 | C22×C4 | — | 17 | 4 | no | — |
| 346 | C22×C4 | — | 17 | 4 | no | — |
| 347 | C22×C4 | — | 17 | 1 | no | — |
| 348 | C22×C4 | — | 34 | 2 | no | — |
| 349 | C22×C4 | — | 34 | 8 | no | — |
| 350 | C22×C4 | — | 34 | 8 | no | — |
| 351 | C22×C4 | — | 34 | 4 | no | — |
| 352 | C22×C4 | — | 34 | 8 | no | — |
| 353 | C22×C4 | C23×D17 | 1 | 4 | yes | — |
| 354 | C22×C4 | C23×D17 | 1 | 4 | yes | — |
| 355 | C22×C4 | C23×D17 | 1 | 4 | yes | — |
| 356 | C22×C4 | C23×D17 | 1 | 2 | yes | — |
| 357 | C22×C4 | C23×D17 | 1 | 1 | yes | characteristic |
| 358 | C4⋊C4 | — | 4 | 4 | no | — |
| 359 | C4⋊C4 | — | 4 | 4 | no | — |
| 360 | C4⋊C4 | — | 4 | 4 | no | — |
| 361 | C4⋊C4 | — | 34 | 4 | no | — |
| 362 | C4⋊C4 | — | 34 | 4 | no | — |
| 363 | C4⋊C4 | — | 68 | 4 | no | — |
| 364 | C4⋊C4 | — | 68 | 4 | no | — |
| 365 | C4⋊C4 | — | 68 | 4 | no | — |
| 366 | C4⋊C4 | — | 68 | 4 | no | — |
| 367 | C4⋊C4 | — | 68 | 4 | no | — |
| 368 | C22⋊C4 | — | 34 | 4 | no | — |
| 369 | C22⋊C4 | — | 34 | 8 | no | — |
| 370 | C22⋊C4 | — | 68 | 4 | no | — |
| 371 | C22⋊C4 | — | 68 | 4 | no | — |
| 372 | C22⋊C4 | — | 68 | 4 | no | — |
| 373 | C22⋊C4 | — | 68 | 4 | no | — |
| 374 | C22⋊C4 | — | 68 | 4 | no | — |
| 375 | C22⋊C4 | — | 68 | 4 | no | — |
| 376 | C22⋊C4 | — | 68 | 4 | no | — |
| 377 | C22⋊C4 | — | 68 | 4 | no | — |
| 378 | C22⋊C4 | — | 68 | 4 | no | — |
| 379 | C22⋊C4 | — | 68 | 4 | no | — |
| 380 | C22⋊C4 | — | 68 | 4 | no | — |
| 381 | C42 | — | 2 | 8 | no | — |
| 382 | C42 | — | 2 | 4 | no | — |
| 383 | C42 | — | 34 | 2 | no | — |
| 384 | C42 | — | 34 | 4 | no | — |
| 385 | C42 | — | 68 | 4 | no | — |
| 386 | C42 | #63256 | 1 | 4 | yes | — |
| 387 | C23 | — | 34 | 1 | no | — |
| 388 | C23 | — | 34 | 4 | no | — |
| 389 | C23 | — | 34 | 4 | no | — |
| 390 | C23 | — | 34 | 2 | no | — |
| 391 | C23 | — | 34 | 4 | no | — |
| 392 | C23 | — | 34 | 4 | no | — |
| 393 | C23 | — | 34 | 4 | no | — |
| 394 | C23 | — | 34 | 4 | no | — |
| 395 | C23 | — | 34 | 4 | no | — |
| 396 | C23 | — | 34 | 4 | no | — |
| 397 | C23 | C24×D17 | 1 | 1 | yes | characteristic |
| 398 | D4 | — | 68 | 8 | no | — |
| 399 | D4 | — | 68 | 16 | no | — |
| 400 | D4 | — | 68 | 16 | no | — |
| 401 | C2×C4 | — | 2 | 4 | no | — |
| 402 | C2×C4 | — | 2 | 4 | no | — |
| 403 | C2×C4 | — | 2 | 4 | no | — |
| 404 | C2×C4 | — | 2 | 4 | no | — |
| 405 | C2×C4 | — | 2 | 4 | no | — |
| 406 | C2×C4 | — | 2 | 4 | no | — |
| 407 | C2×C4 | — | 2 | 4 | no | — |
| 408 | C2×C4 | — | 2 | 4 | no | — |
| 409 | C2×C4 | — | 2 | 4 | no | — |
| 410 | C2×C4 | — | 2 | 4 | no | — |
| 411 | C2×C4 | — | 34 | 2 | no | — |
| 412 | C2×C4 | — | 34 | 4 | no | — |
| 413 | C2×C4 | — | 34 | 1 | no | — |
| 414 | C2×C4 | — | 34 | 4 | no | — |
| 415 | C2×C4 | — | 34 | 4 | no | — |
| 416 | C2×C4 | — | 34 | 2 | no | — |
| 417 | C2×C4 | — | 34 | 4 | no | — |
| 418 | C2×C4 | — | 34 | 4 | no | — |
| 419 | C2×C4 | — | 34 | 4 | no | — |
| 420 | C2×C4 | — | 34 | 4 | no | — |
| 421 | C2×C4 | — | 68 | 4 | no | — |
| 422 | C2×C4 | — | 68 | 16 | no | — |
| 423 | C2×C4 | C2×#63256 | 1 | 4 | yes | — |
| 424 | C2×C4 | C2×#63256 | 1 | 2 | yes | — |
| 425 | C2×C4 | #10587696 | 1 | 4 | yes | — |
| 426 | C22 | — | 68 | 1 | no | — |
| 427 | C22 | — | 68 | 4 | no | — |
| 428 | C22 | — | 68 | 4 | no | — |
| 429 | C22 | — | 68 | 4 | no | — |
| 430 | C22 | — | 68 | 4 | no | — |
| 431 | C22 | — | 68 | 4 | no | — |
| 432 | C22 | — | 68 | 4 | no | — |
| 433 | C22 | — | 68 | 4 | no | — |
| 434 | C22 | — | 68 | 2 | no | — |
| 435 | C22 | — | 68 | 4 | no | — |
| 436 | C22 | C22×#63256 | 1 | 1 | yes | characteristic |
| 437 | C22 | C2×#10587696 | 1 | 2 | yes | — |
| 438 | C22 | #11763645 | 1 | 4 | yes | — |
| 439 | C4 | — | 2 | 4 | no | — |
| 440 | C4 | — | 4 | 4 | no | — |
| 441 | C4 | — | 4 | 4 | no | — |
| 442 | C4 | — | 4 | 4 | no | — |
| 443 | C4 | — | 68 | 4 | no | — |
| 444 | C4 | — | 68 | 1 | no | — |
| 445 | C4 | — | 68 | 4 | no | — |
| 446 | C4 | — | 68 | 2 | no | — |
| 447 | C4 | #11763415 | 1 | 4 | yes | — |
| 448 | C2 | — | 136 | 1 | no | — |
| 449 | C2 | — | 136 | 4 | no | — |
| 450 | C2 | C2×#11763415 | 1 | 1 | yes | characteristic |
| 451 | C2 | #14542176 | 1 | 2 | yes | — |
| 452 | C2 | #14542923 | 1 | 4 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D17 |
| commutator, socle, cosocle | C23×C17 | C25 |
| Frattini | C23 | C24×D17 |
| Fitting | C17×#2402 | C2 |
| hypercenter | #2402 | D17 |
| hypocenter | C17 | #36692 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C22×C4 ◁ #2402 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14537004 | C2 | semidirect |
| 2. #14536989 | C2 | semidirect |
| 3. #14536922 | C2 | semidirect |
| 4. #14536908 | C2 | semidirect |
| 5. #14532065 | C2 | semidirect |
| 6. #14532047 | C2 | semidirect |
| 7. #14532024 | C2 | semidirect |
| 8. #14532024 | C2 | semidirect |
| 9. #14531279 | C2 | semidirect |
| 10. #14531245 | C2 | semidirect |
| 11. C17×#2402 | C2 | semidirect |
| 204. #2402 | D17 | semidirect |
| 333. C17 | #36692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537004 | 2 |
| #14536989 | 2 |
| #14536922 | 2 |
| #14536908 | 2 |
| #14532065 | 2 |
| #14532047 | 2 |
| #14532024 | 2 |
| #14531279 | 2 |
| #14531245 | 2 |
| C17×#2402 | 2 |
| #36692 | 17 |