Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
550 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 56 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 | D17⋊#353 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #14544312 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #14543904 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #14543903 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | D17×#453 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #11763832 | — | 2 | 1 | no | — |
| 7 | D17⋊#99 | — | 2 | 1 | no | — |
| 8 | #11763714 | — | 2 | 1 | no | — |
| 9 | #11763713 | C22 | 1 | 2 | yes | complemented |
| 10 | #11763667 | — | 2 | 1 | no | — |
| 11 | #11763667 | C22 | 1 | 2 | yes | complemented |
| 12 | H(5,𝔽2)×D17 | C4 | 1 | 1 | yes | characteristic, complemented |
| 13 | AGL(1,ℤ/8)×D17 | — | 2 | 1 | no | — |
| 14 | #127×D17 | C22 | 1 | 1 | yes | characteristic |
| 15 | #11762979 | C22 | 1 | 1 | yes | characteristic |
| 16 | #11762978 | — | 2 | 1 | no | — |
| 17 | #11762977 | C22 | 1 | 1 | yes | characteristic |
| 18 | #11762976 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | #11762975 | — | 2 | 1 | no | — |
| 20 | #104×D17 | — | 2 | 1 | no | — |
| 21 | #100×D17 | C4 | 1 | 1 | yes | characteristic, complemented |
| 22 | C17×#453 | C4 | 1 | 1 | yes | characteristic, complemented |
| 23 | C17×H(5,𝔽2) | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | #10587696 | — | 2 | 1 | no | — |
| 25 | #10587696 | — | 4 | 1 | no | — |
| 26 | #41×D17 | — | 2 | 1 | no | — |
| 27 | #41×D17 | — | 4 | 1 | no | — |
| 28 | #10587691 | — | 4 | 1 | no | — |
| 29 | #10587691 | — | 4 | 1 | no | — |
| 30 | #10587691 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 31 | C2×D4×D17 | — | 4 | 1 | no | — |
| 32 | C2×D4×D17 | — | 4 | 1 | no | — |
| 33 | C2×D4×D17 | — | 4 | 1 | no | — |
| 34 | C2×D4×D17 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | C2×D4×D17 | D4 | 1 | 1 | yes | characteristic |
| 36 | C2×C22⋊#595 | — | 4 | 1 | no | — |
| 37 | C17×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 38 | C17×#127 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | #10587635 | — | 2 | 1 | no | — |
| 40 | #10587626 | — | 4 | 1 | no | — |
| 41 | #10587626 | D4 | 1 | 1 | yes | characteristic |
| 42 | #10587626 | C23 | 1 | 1 | yes | characteristic |
| 43 | #10587618 | — | 2 | 1 | no | — |
| 44 | #10587600 | — | 4 | 1 | no | — |
| 45 | SD16×D17 | — | 4 | 1 | no | — |
| 46 | #10587597 | — | 4 | 1 | no | — |
| 47 | D8×D17 | — | 4 | 1 | no | — |
| 48 | #10587594 | — | 2 | 1 | no | — |
| 49 | M16×D17 | — | 2 | 1 | no | — |
| 50 | #10587560 | D4 | 1 | 1 | yes | characteristic |
| 51 | C42×D17 | D4 | 1 | 1 | yes | characteristic |
| 52 | #10587551 | — | 4 | 1 | no | — |
| 53 | #10587544 | — | 2 | 2 | no | — |
| 54 | #10587543 | — | 4 | 1 | no | — |
| 55 | #10587542 | — | 4 | 1 | no | — |
| 56 | #10587539 | — | 2 | 2 | no | — |
| 57 | C17×#104 | — | 2 | 1 | no | — |
| 58 | C17×#100 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 59 | #10587508 | — | 2 | 1 | no | — |
| 60 | #10587504 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 61 | #10587496 | — | 2 | 1 | no | — |
| 62 | #10587494 | — | 2 | 1 | no | — |
| 63 | #10587476 | — | 2 | 1 | no | — |
| 64 | C23×D17 | — | 2 | 1 | no | — |
| 65 | C23×D17 | — | 2 | 1 | no | — |
| 66 | C23×D17 | — | 4 | 1 | no | — |
| 67 | C22×#595 | — | 8 | 1 | no | — |
| 68 | #41×C17 | — | 2 | 1 | no | — |
| 69 | #41×C17 | — | 4 | 1 | no | — |
| 70 | C2×D4×C17 | — | 4 | 1 | no | — |
| 71 | C2×D4×C17 | — | 4 | 1 | no | — |
| 72 | C2×D4×C17 | — | 4 | 1 | no | — |
| 73 | C2×D4×C17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 74 | C2×D4×C17 | C22×C4 | 1 | 1 | yes | characteristic |
| 75 | C2×C22⋊D17 | — | 2 | 1 | no | — |
| 76 | C2×C22⋊D17 | — | 2 | 1 | no | — |
| 77 | C2×C22⋊D17 | — | 4 | 1 | no | — |
| 78 | C2×C22⋊D17 | — | 4 | 1 | no | — |
| 79 | C2×C22⋊D17 | — | 4 | 2 | no | — |
| 80 | C2×C22⋊D17 | — | 4 | 1 | no | — |
| 81 | C2×C22⋊D17 | — | 4 | 1 | no | — |
| 82 | #63256 | — | 2 | 1 | no | — |
| 83 | #63256 | — | 4 | 1 | no | — |
| 84 | Q8×D17 | — | 2 | 1 | no | — |
| 85 | #63254 | — | 2 | 1 | no | — |
| 86 | #63254 | — | 4 | 1 | no | — |
| 87 | #63254 | — | 4 | 2 | no | — |
| 88 | #63254 | — | 4 | 1 | no | — |
| 89 | D4×D17 | — | 2 | 1 | no | — |
| 90 | D4×D17 | — | 4 | 1 | no | — |
| 91 | D4×D17 | — | 4 | 1 | no | — |
| 92 | D4×D17 | — | 4 | 1 | no | — |
| 93 | D4×D17 | — | 4 | 1 | no | — |
| 94 | D4×D17 | — | 4 | 1 | no | — |
| 95 | D4×D17 | — | 4 | 1 | no | — |
| 96 | D4×D17 | — | 4 | 2 | no | — |
| 97 | D4×D17 | — | 4 | 2 | no | — |
| 98 | D4×D17 | — | 4 | 2 | no | — |
| 99 | D4×D17 | — | 4 | 2 | no | — |
| 100 | D4×D17 | — | 4 | 1 | no | — |
| 101 | D4×D17 | — | 8 | 4 | no | — |
| 102 | #63252 | — | 2 | 1 | no | — |
| 103 | #63252 | — | 4 | 1 | no | — |
| 104 | #63252 | — | 4 | 1 | no | — |
| 105 | #63252 | — | 4 | 2 | no | — |
| 106 | C2×D68 | — | 4 | 1 | no | — |
| 107 | C2×D68 | — | 4 | 1 | no | — |
| 108 | C2×D68 | — | 4 | 1 | no | — |
| 109 | C2×D68 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 110 | C2×D68 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | C2×C4×D17 | — | 2 | 1 | no | — |
| 112 | C2×C4×D17 | — | 4 | 1 | no | — |
| 113 | C2×C4×D17 | — | 4 | 1 | no | — |
| 114 | C2×C4×D17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 115 | C22⋊#595 | — | 4 | 2 | no | — |
| 116 | C22⋊#595 | — | 8 | 1 | no | — |
| 117 | C2×#3624 | — | 4 | 2 | no | — |
| 118 | SD16×C17 | — | 4 | 1 | no | — |
| 119 | D8×C17 | — | 4 | 1 | no | — |
| 120 | M16×C17 | — | 2 | 1 | no | — |
| 121 | C42×C17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 122 | #63230 | — | 4 | 1 | no | — |
| 123 | #63229 | — | 4 | 1 | no | — |
| 124 | #63228 | — | 4 | 1 | no | — |
| 125 | #63228 | — | 4 | 1 | no | — |
| 126 | C4×Dic17 | — | 2 | 1 | no | — |
| 127 | C4×Dic17 | C2×D4 | 1 | 1 | yes | characteristic |
| 128 | #63223 | — | 2 | 1 | no | — |
| 129 | D136 | — | 4 | 1 | no | — |
| 130 | #63219 | — | 4 | 1 | no | — |
| 131 | #63218 | — | 4 | 1 | no | — |
| 132 | C8×D17 | — | 4 | 1 | no | — |
| 133 | #13561 | — | 17 | 1 | no | maximal, Sylow |
| 134 | C23×C17 | — | 2 | 1 | no | — |
| 135 | C23×C17 | — | 2 | 1 | no | — |
| 136 | C23×C17 | — | 4 | 1 | no | — |
| 137 | C22×D17 | — | 2 | 1 | no | — |
| 138 | C22×D17 | — | 2 | 1 | no | — |
| 139 | C22×D17 | — | 4 | 2 | no | — |
| 140 | C22×D17 | — | 4 | 1 | no | — |
| 141 | C22×D17 | — | 4 | 1 | no | — |
| 142 | C22×D17 | — | 4 | 1 | no | — |
| 143 | C22×D17 | — | 4 | 1 | no | — |
| 144 | C22×D17 | — | 4 | 1 | no | — |
| 145 | C22×D17 | — | 4 | 1 | no | — |
| 146 | C22×D17 | — | 8 | 2 | no | — |
| 147 | C22×D17 | — | 8 | 2 | no | — |
| 148 | C22×D17 | — | 16 | 2 | no | — |
| 149 | C22×D17 | #99 | 1 | 1 | yes | characteristic |
| 150 | C2×#595 | — | 8 | 2 | no | — |
| 151 | C2×#595 | — | 16 | 2 | no | — |
| 152 | Q8×C17 | — | 2 | 1 | no | — |
| 153 | D4×C17 | — | 2 | 1 | no | — |
| 154 | D4×C17 | — | 4 | 1 | no | — |
| 155 | D4×C17 | — | 4 | 1 | no | — |
| 156 | D4×C17 | — | 4 | 2 | no | — |
| 157 | D4×C17 | — | 4 | 1 | no | — |
| 158 | D4×C17 | — | 8 | 2 | no | — |
| 159 | C2×C4×C17 | — | 2 | 1 | no | — |
| 160 | C2×C4×C17 | — | 4 | 1 | no | — |
| 161 | C2×C4×C17 | — | 4 | 1 | no | — |
| 162 | C2×C4×C17 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 163 | C22⋊D17 | — | 4 | 1 | no | — |
| 164 | C22⋊D17 | — | 4 | 2 | no | — |
| 165 | C22⋊D17 | — | 4 | 2 | no | — |
| 166 | C22⋊D17 | — | 4 | 2 | no | — |
| 167 | C22⋊D17 | — | 4 | 1 | no | — |
| 168 | C22⋊D17 | — | 4 | 1 | no | — |
| 169 | C22⋊D17 | — | 8 | 1 | no | — |
| 170 | C22⋊D17 | — | 8 | 2 | no | — |
| 171 | C22⋊D17 | — | 8 | 2 | no | — |
| 172 | C2×Dic17 | — | 2 | 1 | no | — |
| 173 | C2×Dic17 | — | 4 | 1 | no | — |
| 174 | C2×Dic17 | — | 4 | 1 | no | — |
| 175 | C2×Dic17 | #99 | 1 | 1 | yes | characteristic |
| 176 | D68 | — | 2 | 1 | no | — |
| 177 | D68 | — | 4 | 1 | no | — |
| 178 | D68 | — | 4 | 1 | no | — |
| 179 | D68 | — | 4 | 2 | no | — |
| 180 | D68 | — | 4 | 1 | no | — |
| 181 | D68 | — | 8 | 2 | no | — |
| 182 | C4×D17 | — | 2 | 1 | no | — |
| 183 | C4×D17 | — | 2 | 1 | no | — |
| 184 | C4×D17 | — | 4 | 2 | no | — |
| 185 | C4×D17 | — | 4 | 1 | no | — |
| 186 | C4×D17 | — | 4 | 1 | no | — |
| 187 | C4×D17 | — | 4 | 2 | no | — |
| 188 | C4×D17 | — | 4 | 1 | no | — |
| 189 | Dic34 | — | 2 | 1 | no | — |
| 190 | Dic34 | — | 4 | 1 | no | — |
| 191 | #3624 | — | 8 | 2 | no | — |
| 192 | C8×C17 | — | 4 | 1 | no | — |
| 193 | #3622 | — | 4 | 1 | no | — |
| 194 | C2×#453 | — | 17 | 1 | no | — |
| 195 | C2×#353 | — | 17 | 1 | no | — |
| 196 | #1555 | — | 17 | 1 | no | — |
| 197 | #1402 | — | 17 | 2 | no | — |
| 198 | #1402 | — | 17 | 2 | no | — |
| 199 | C22×C17 | — | 4 | 1 | no | — |
| 200 | C22×C17 | — | 4 | 1 | no | — |
| 201 | C22×C17 | — | 4 | 1 | no | — |
| 202 | C22×C17 | — | 8 | 1 | no | — |
| 203 | C22×C17 | — | 8 | 1 | no | — |
| 204 | C22×C17 | — | 16 | 1 | no | — |
| 205 | C22×C17 | C2×#99 | 1 | 1 | yes | characteristic |
| 206 | C2×D17 | — | 4 | 1 | no | — |
| 207 | C2×D17 | — | 4 | 1 | no | — |
| 208 | C2×D17 | — | 4 | 1 | no | — |
| 209 | C2×D17 | — | 4 | 1 | no | — |
| 210 | C2×D17 | — | 8 | 2 | no | — |
| 211 | C2×D17 | — | 8 | 2 | no | — |
| 212 | C2×D17 | — | 8 | 2 | no | — |
| 213 | C2×D17 | — | 8 | 1 | no | — |
| 214 | C2×D17 | — | 8 | 1 | no | — |
| 215 | C2×D17 | — | 16 | 1 | no | — |
| 216 | C2×D17 | — | 16 | 1 | no | — |
| 217 | C2×D17 | — | 16 | 2 | no | — |
| 218 | C2×D17 | — | 16 | 1 | no | — |
| 219 | C2×D17 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 220 | C2×D17 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 221 | #595 | — | 16 | 2 | no | — |
| 222 | C4×C17 | — | 2 | 1 | no | — |
| 223 | C4×C17 | — | 4 | 1 | no | — |
| 224 | C4×C17 | — | 4 | 1 | no | — |
| 225 | Dic17 | — | 2 | 2 | no | — |
| 226 | Dic17 | — | 2 | 1 | no | — |
| 227 | Dic17 | — | 4 | 1 | no | — |
| 228 | C2×H(5,𝔽2) | — | 17 | 1 | no | — |
| 229 | C2×AGL(1,ℤ/8) | — | 34 | 1 | no | — |
| 230 | C2×#127 | — | 17 | 1 | no | — |
| 231 | #453 | — | 17 | 1 | no | — |
| 232 | #453 | — | 17 | 1 | no | — |
| 233 | #453 | — | 17 | 1 | no | — |
| 234 | #453 | — | 34 | 1 | no | — |
| 235 | #453 | — | 34 | 1 | no | — |
| 236 | #453 | #595 | 1 | 1 | yes | characteristic, complemented |
| 237 | #432 | — | 34 | 1 | no | — |
| 238 | C2×#104 | — | 34 | 1 | no | — |
| 239 | C2×#100 | — | 17 | 1 | no | — |
| 240 | C2×#99 | — | 34 | 1 | no | — |
| 241 | #353 | — | 17 | 2 | no | — |
| 242 | #353 | — | 34 | 1 | no | — |
| 243 | #331 | — | 17 | 2 | no | — |
| 244 | #331 | — | 34 | 1 | no | — |
| 245 | C2×C17 | — | 2 | 1 | no | — |
| 246 | C2×C17 | — | 8 | 1 | no | — |
| 247 | C2×C17 | — | 8 | 1 | no | — |
| 248 | C2×C17 | — | 8 | 1 | no | — |
| 249 | C2×C17 | C2×AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 250 | D17 | — | 2 | 1 | no | — |
| 251 | D17 | — | 2 | 1 | no | — |
| 252 | D17 | — | 8 | 1 | no | — |
| 253 | D17 | — | 8 | 1 | no | — |
| 254 | D17 | — | 8 | 1 | no | — |
| 255 | H(5,𝔽2) | — | 17 | 1 | no | — |
| 256 | H(5,𝔽2) | — | 34 | 1 | no | — |
| 257 | H(5,𝔽2) | — | 68 | 1 | no | — |
| 258 | H(5,𝔽2) | — | 68 | 1 | no | — |
| 259 | H(5,𝔽2) | — | 68 | 1 | no | — |
| 260 | H(5,𝔽2) | C2×#595 | 1 | 1 | yes | characteristic, complemented |
| 261 | C2×#41 | — | 34 | 1 | no | — |
| 262 | C2×#41 | — | 68 | 1 | no | — |
| 263 | C22×D4 | — | 17 | 1 | no | — |
| 264 | C22×D4 | — | 17 | 1 | no | — |
| 265 | C22×D4 | — | 68 | 1 | no | — |
| 266 | C22×D4 | — | 68 | 1 | no | — |
| 267 | C22×D4 | — | 68 | 1 | no | — |
| 268 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 269 | AGL(1,ℤ/8) | — | 34 | 1 | no | — |
| 270 | AGL(1,ℤ/8) | — | 34 | 1 | no | — |
| 271 | AGL(1,ℤ/8) | — | 34 | 1 | no | — |
| 272 | AGL(1,ℤ/8) | — | 68 | 1 | no | — |
| 273 | AGL(1,ℤ/8) | — | 68 | 1 | no | — |
| 274 | C2×SD16 | — | 68 | 1 | no | — |
| 275 | C2×D8 | — | 68 | 1 | no | — |
| 276 | C2×M16 | — | 34 | 1 | no | — |
| 277 | #127 | — | 17 | 1 | no | — |
| 278 | #127 | — | 17 | 1 | no | — |
| 279 | #127 | — | 17 | 1 | no | — |
| 280 | #127 | — | 68 | 1 | no | — |
| 281 | #127 | C2×#595 | 1 | 1 | yes | characteristic |
| 282 | C2×C22⋊C4 | — | 68 | 1 | no | — |
| 283 | C2×C42 | — | 17 | 1 | no | — |
| 284 | C4⋊C8 | — | 34 | 2 | no | — |
| 285 | #104 | — | 2 | 1 | no | — |
| 286 | #104 | — | 34 | 1 | no | — |
| 287 | #104 | — | 34 | 1 | no | — |
| 288 | #104 | — | 34 | 1 | no | — |
| 289 | #100 | — | 17 | 1 | no | — |
| 290 | #100 | — | 34 | 1 | no | — |
| 291 | #100 | C2×#595 | 1 | 1 | yes | characteristic, complemented |
| 292 | #99 | — | 34 | 2 | no | — |
| 293 | #99 | — | 68 | 1 | no | — |
| 294 | C22⋊C8 | — | 68 | 1 | no | — |
| 295 | #97 | — | 68 | 1 | no | — |
| 296 | C17 | #13561 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 297 | C24 | — | 34 | 1 | no | — |
| 298 | C24 | — | 34 | 1 | no | — |
| 299 | C24 | — | 68 | 1 | no | — |
| 300 | #41 | — | 2 | 1 | no | — |
| 301 | #41 | — | 4 | 1 | no | — |
| 302 | #41 | — | 34 | 1 | no | — |
| 303 | #41 | — | 34 | 1 | no | — |
| 304 | #41 | — | 34 | 1 | no | — |
| 305 | #41 | — | 68 | 1 | no | — |
| 306 | #41 | — | 68 | 1 | no | — |
| 307 | #41 | — | 68 | 2 | no | — |
| 308 | #41 | — | 68 | 1 | no | — |
| 309 | #41 | — | 68 | 2 | no | — |
| 310 | #41 | — | 68 | 1 | no | — |
| 311 | #41 | — | 68 | 1 | no | — |
| 312 | C2×Q8 | — | 34 | 1 | no | — |
| 313 | C2×D4 | — | 4 | 1 | no | — |
| 314 | C2×D4 | — | 4 | 1 | no | — |
| 315 | C2×D4 | — | 4 | 1 | no | — |
| 316 | C2×D4 | — | 17 | 1 | no | — |
| 317 | C2×D4 | — | 17 | 1 | no | — |
| 318 | C2×D4 | — | 34 | 1 | no | — |
| 319 | C2×D4 | — | 34 | 1 | no | — |
| 320 | C2×D4 | — | 34 | 1 | no | — |
| 321 | C2×D4 | — | 68 | 1 | no | — |
| 322 | C2×D4 | — | 68 | 1 | no | — |
| 323 | C2×D4 | — | 68 | 1 | no | — |
| 324 | C2×D4 | — | 68 | 1 | no | — |
| 325 | C2×D4 | — | 68 | 1 | no | — |
| 326 | C2×D4 | — | 68 | 1 | no | — |
| 327 | C2×D4 | — | 68 | 1 | no | — |
| 328 | C2×D4 | — | 68 | 1 | no | — |
| 329 | C2×D4 | — | 68 | 1 | no | — |
| 330 | C2×D4 | — | 68 | 1 | no | — |
| 331 | C2×D4 | — | 68 | 1 | no | — |
| 332 | C2×D4 | — | 68 | 1 | no | — |
| 333 | C2×D4 | — | 68 | 2 | no | — |
| 334 | C2×D4 | — | 68 | 2 | no | — |
| 335 | C2×D4 | — | 68 | 2 | no | — |
| 336 | C2×D4 | — | 68 | 2 | no | — |
| 337 | C2×D4 | — | 68 | 2 | no | — |
| 338 | C2×D4 | — | 68 | 1 | no | — |
| 339 | C2×D4 | — | 68 | 1 | no | — |
| 340 | C2×D4 | — | 136 | 4 | no | — |
| 341 | C2×D4 | C22⋊#595 | 1 | 1 | yes | characteristic |
| 342 | C2×D4 | C22×#595 | 1 | 1 | yes | characteristic |
| 343 | C22×C4 | — | 17 | 1 | no | — |
| 344 | C22×C4 | — | 34 | 1 | no | — |
| 345 | C22×C4 | — | 68 | 1 | no | — |
| 346 | C22×C4 | — | 68 | 1 | no | — |
| 347 | C22×C4 | — | 136 | 1 | no | — |
| 348 | SD16 | — | 4 | 1 | no | — |
| 349 | SD16 | — | 68 | 1 | no | — |
| 350 | SD16 | — | 68 | 1 | no | — |
| 351 | SD16 | — | 68 | 1 | no | — |
| 352 | D8 | — | 4 | 1 | no | — |
| 353 | D8 | — | 68 | 1 | no | — |
| 354 | D8 | — | 68 | 1 | no | — |
| 355 | D8 | — | 68 | 1 | no | — |
| 356 | M16 | — | 2 | 1 | no | — |
| 357 | M16 | — | 34 | 1 | no | — |
| 358 | M16 | — | 68 | 1 | no | — |
| 359 | C2×C8 | — | 68 | 1 | no | — |
| 360 | C2×C8 | — | 68 | 2 | no | — |
| 361 | C22⋊C4 | — | 68 | 2 | no | — |
| 362 | C22⋊C4 | — | 136 | 1 | no | — |
| 363 | C42 | — | 17 | 1 | no | — |
| 364 | C42 | — | 34 | 1 | no | — |
| 365 | C42 | C22⋊#595 | 1 | 1 | yes | characteristic |
| 366 | C23 | — | 2 | 1 | no | — |
| 367 | C23 | — | 2 | 1 | no | — |
| 368 | C23 | — | 4 | 1 | no | — |
| 369 | C23 | — | 272 | 2 | no | — |
| 370 | C23 | — | 17 | 1 | no | — |
| 371 | C23 | — | 34 | 1 | no | — |
| 372 | C23 | — | 34 | 1 | no | — |
| 373 | C23 | — | 68 | 1 | no | — |
| 374 | C23 | — | 68 | 1 | no | — |
| 375 | C23 | — | 68 | 1 | no | — |
| 376 | C23 | — | 68 | 2 | no | — |
| 377 | C23 | — | 68 | 1 | no | — |
| 378 | C23 | — | 68 | 1 | no | — |
| 379 | C23 | — | 68 | 1 | no | — |
| 380 | C23 | — | 136 | 2 | no | — |
| 381 | C23 | — | 136 | 2 | no | — |
| 382 | Q8 | — | 2 | 1 | no | — |
| 383 | Q8 | — | 34 | 1 | no | — |
| 384 | Q8 | — | 68 | 1 | no | — |
| 385 | D4 | — | 2 | 1 | no | — |
| 386 | D4 | — | 4 | 1 | no | — |
| 387 | D4 | — | 4 | 1 | no | — |
| 388 | D4 | — | 4 | 2 | no | — |
| 389 | D4 | — | 4 | 1 | no | — |
| 390 | D4 | — | 8 | 2 | no | — |
| 391 | D4 | — | 34 | 1 | no | — |
| 392 | D4 | — | 68 | 1 | no | — |
| 393 | D4 | — | 68 | 1 | no | — |
| 394 | D4 | — | 68 | 1 | no | — |
| 395 | D4 | — | 68 | 2 | no | — |
| 396 | D4 | — | 68 | 1 | no | — |
| 397 | D4 | — | 68 | 2 | no | — |
| 398 | D4 | — | 68 | 1 | no | — |
| 399 | D4 | — | 68 | 2 | no | — |
| 400 | D4 | — | 68 | 2 | no | — |
| 401 | D4 | — | 68 | 1 | no | — |
| 402 | D4 | — | 136 | 2 | no | — |
| 403 | D4 | — | 136 | 1 | no | — |
| 404 | D4 | — | 136 | 2 | no | — |
| 405 | D4 | — | 136 | 2 | no | — |
| 406 | C2×C4 | — | 2 | 1 | no | — |
| 407 | C2×C4 | — | 4 | 1 | no | — |
| 408 | C2×C4 | — | 4 | 1 | no | — |
| 409 | C2×C4 | — | 272 | 2 | no | — |
| 410 | C2×C4 | — | 17 | 1 | no | — |
| 411 | C2×C4 | — | 34 | 1 | no | — |
| 412 | C2×C4 | — | 34 | 1 | no | — |
| 413 | C2×C4 | — | 34 | 1 | no | — |
| 414 | C2×C4 | — | 68 | 1 | no | — |
| 415 | C2×C4 | — | 68 | 2 | no | — |
| 416 | C2×C4 | — | 68 | 1 | no | — |
| 417 | C2×C4 | — | 68 | 1 | no | — |
| 418 | C2×C4 | — | 68 | 2 | no | — |
| 419 | C2×C4 | — | 68 | 1 | no | — |
| 420 | C2×C4 | — | 68 | 1 | no | — |
| 421 | C2×C4 | — | 136 | 2 | no | — |
| 422 | C2×C4 | C2×C22⋊#595 | 1 | 1 | yes | characteristic |
| 423 | C8 | — | 4 | 1 | no | — |
| 424 | C8 | — | 68 | 1 | no | — |
| 425 | C8 | — | 136 | 2 | no | — |
| 426 | C22 | — | 4 | 1 | no | — |
| 427 | C22 | — | 4 | 1 | no | — |
| 428 | C22 | — | 4 | 1 | no | — |
| 429 | C22 | — | 8 | 1 | no | — |
| 430 | C22 | — | 8 | 1 | no | — |
| 431 | C22 | — | 16 | 1 | no | — |
| 432 | C22 | — | 272 | 1 | no | — |
| 433 | C22 | — | 272 | 1 | no | — |
| 434 | C22 | — | 272 | 1 | no | — |
| 435 | C22 | — | 272 | 2 | no | — |
| 436 | C22 | — | 17 | 1 | no | — |
| 437 | C22 | — | 17 | 1 | no | — |
| 438 | C22 | — | 68 | 1 | no | — |
| 439 | C22 | — | 68 | 1 | no | — |
| 440 | C22 | — | 68 | 1 | no | — |
| 441 | C22 | — | 68 | 1 | no | — |
| 442 | C22 | — | 136 | 1 | no | — |
| 443 | C22 | — | 136 | 1 | no | — |
| 444 | C22 | — | 136 | 2 | no | — |
| 445 | C22 | — | 136 | 2 | no | — |
| 446 | C22 | — | 136 | 2 | no | — |
| 447 | C22 | D17⋊#99 | 1 | 1 | yes | characteristic |
| 448 | C4 | — | 2 | 1 | no | — |
| 449 | C4 | — | 4 | 1 | no | — |
| 450 | C4 | — | 4 | 1 | no | — |
| 451 | C4 | — | 272 | 2 | no | — |
| 452 | C4 | — | 34 | 2 | no | — |
| 453 | C4 | — | 34 | 1 | no | — |
| 454 | C4 | — | 68 | 1 | no | — |
| 455 | C2 | — | 2 | 1 | no | — |
| 456 | C2 | — | 8 | 1 | no | — |
| 457 | C2 | — | 8 | 1 | no | — |
| 458 | C2 | — | 8 | 1 | no | — |
| 459 | C2 | — | 34 | 1 | no | — |
| 460 | C2 | — | 34 | 1 | no | — |
| 461 | C2 | — | 136 | 1 | no | — |
| 462 | C2 | — | 136 | 1 | no | — |
| 463 | C2 | — | 136 | 1 | no | — |
| 464 | C2 | D17⋊AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D17⋊#353 | C2 | semidirect |
| 2. #14544312 | C2 | semidirect |
| 3. #14543904 | C2 | semidirect |
| 4. #14543903 | C2 | semidirect |
| 9. #11763713 | C22 | semidirect |
| 11. #11763667 | C22 | semidirect |
| 12. H(5,𝔽2)×D17 | C4 | semidirect |
| 18. #11762976 | C4 | semidirect |
| 21. #100×D17 | C4 | semidirect |
| 22. C17×#453 | C4 | semidirect |
| 23. C17×H(5,𝔽2) | C2×C4 | semidirect |
| 30. #10587691 | C2×C4 | semidirect |
| 58. C17×#100 | C2×C4 | semidirect |
| 60. #10587504 | C2×C4 | semidirect |
| 236. #453 | #595 | semidirect |
| 260. H(5,𝔽2) | C2×#595 | semidirect |
| 291. #100 | C2×#595 | semidirect |
| 296. C17 | #13561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17⋊#353 | 2 |
| #14544312 | 2 |
| #14543904 | 2 |
| #14543903 | 2 |
| D17×#453 | 2 |
| #13561 | 17 |