Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
2598 conjugacy classes of subgroups.
The subgroup lattice has 592 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #578×D47 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #20255193 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #20255192 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20255191 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #20255190 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #20255189 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #494×D47 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #473×D47 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #456×D47 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #443×D47 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C47×#3293 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | 2−1+4×D47 | C22 | 1 | 4 | yes | — |
| 13 | #15689940 | C22 | 1 | 4 | yes | complemented |
| 14 | #15689939 | — | 2 | 8 | no | — |
| 15 | #15689939 | C22 | 1 | 8 | yes | complemented |
| 16 | #15689938 | C22 | 1 | 8 | yes | complemented |
| 17 | #15689937 | — | 2 | 4 | no | — |
| 18 | #15689937 | C22 | 1 | 4 | yes | complemented |
| 19 | #15689936 | — | 2 | 4 | no | — |
| 20 | #15689936 | C22 | 1 | 4 | yes | complemented |
| 21 | #137×D47 | — | 2 | 8 | no | — |
| 22 | #137×D47 | C22 | 1 | 8 | yes | — |
| 23 | #135×D47 | — | 2 | 4 | no | — |
| 24 | #135×D47 | C22 | 1 | 2 | yes | — |
| 25 | C2×Q16×D47 | — | 2 | 4 | no | — |
| 26 | C2×Q16×D47 | C22 | 1 | 4 | yes | — |
| 27 | #131×D47 | C22 | 1 | 4 | yes | — |
| 28 | C4⋊Q8×D47 | C22 | 1 | 2 | yes | — |
| 29 | #15689503 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #15689502 | C22 | 1 | 2 | yes | complemented |
| 31 | #15689501 | C22 | 1 | 4 | yes | complemented |
| 32 | #15689399 | C22 | 1 | 4 | yes | complemented |
| 33 | #15689398 | C22 | 1 | 4 | yes | complemented |
| 34 | #15689397 | C22 | 1 | 8 | yes | complemented |
| 35 | #15689396 | C22 | 1 | 8 | yes | complemented |
| 36 | #15689395 | C22 | 1 | 4 | yes | complemented |
| 37 | #15689308 | C22 | 1 | 4 | yes | complemented |
| 38 | #15689307 | C22 | 1 | 8 | yes | complemented |
| 39 | #15689306 | C22 | 1 | 4 | yes | complemented |
| 40 | #15689305 | C22 | 1 | 4 | yes | complemented |
| 41 | #15689304 | C22 | 1 | 8 | yes | complemented |
| 42 | #15689241 | C22 | 1 | 2 | yes | complemented |
| 43 | #15689240 | C22 | 1 | 2 | yes | complemented |
| 44 | #15689239 | C22 | 1 | 2 | yes | complemented |
| 45 | #15689238 | C22 | 1 | 4 | yes | complemented |
| 46 | #15689237 | C22 | 1 | 4 | yes | complemented |
| 47 | #108×D47 | C22 | 1 | 2 | yes | — |
| 48 | #104×D47 | C22 | 1 | 4 | yes | — |
| 49 | #101×D47 | C22 | 1 | 4 | yes | — |
| 50 | C4×C8×D47 | C22 | 1 | 1 | yes | characteristic |
| 51 | C47×#578 | C22 | 1 | 4 | yes | complemented |
| 52 | C47×#494 | C22 | 1 | 1 | yes | characteristic, complemented |
| 53 | C47×#473 | C22 | 1 | 4 | yes | complemented |
| 54 | C47×#456 | C22 | 1 | 4 | yes | complemented |
| 55 | C47×#443 | C22 | 1 | 2 | yes | complemented |
| 56 | #13094072 | — | 2 | 8 | no | — |
| 57 | #13094072 | C23 | 1 | 4 | yes | — |
| 58 | #13094071 | — | 2 | 8 | no | — |
| 59 | #13094071 | — | 4 | 4 | no | — |
| 60 | #13094071 | C23 | 1 | 8 | yes | — |
| 61 | #41×D47 | — | 2 | 8 | no | — |
| 62 | #41×D47 | — | 4 | 4 | no | — |
| 63 | #41×D47 | C23 | 1 | 4 | yes | — |
| 64 | C2×Q8×D47 | — | 2 | 8 | no | — |
| 65 | C2×Q8×D47 | C23 | 1 | 4 | yes | — |
| 66 | #13094057 | — | 2 | 8 | no | — |
| 67 | #13094057 | C23 | 1 | 8 | yes | — |
| 68 | #13094056 | — | 2 | 8 | no | — |
| 69 | #13094056 | — | 2 | 8 | no | — |
| 70 | #13094056 | — | 2 | 8 | no | — |
| 71 | #13094055 | — | 2 | 8 | no | — |
| 72 | #13094055 | C23 | 1 | 8 | yes | — |
| 73 | #13094054 | — | 2 | 8 | no | — |
| 74 | #13094054 | C23 | 1 | 8 | yes | — |
| 75 | #13094053 | — | 2 | 8 | no | — |
| 76 | #13094053 | — | 2 | 8 | no | — |
| 77 | #13094053 | — | 2 | 8 | no | — |
| 78 | #13094047 | — | 2 | 4 | no | — |
| 79 | #13094047 | D4 | 1 | 2 | yes | — |
| 80 | #13094046 | — | 2 | 4 | no | — |
| 81 | #13094046 | C23 | 1 | 2 | yes | — |
| 82 | #13094045 | — | 2 | 8 | no | — |
| 83 | #13094045 | D4 | 1 | 4 | yes | — |
| 84 | #13094044 | — | 2 | 8 | no | — |
| 85 | #13094044 | C23 | 1 | 4 | yes | — |
| 86 | #13094043 | — | 2 | 4 | no | — |
| 87 | #13094043 | D4 | 1 | 2 | yes | — |
| 88 | C2×Dic188 | — | 2 | 4 | no | — |
| 89 | C2×Dic188 | C23 | 1 | 4 | yes | — |
| 90 | C2×#10625337 | — | 2 | 8 | no | — |
| 91 | C2×#10625337 | C23 | 1 | 8 | yes | — |
| 92 | Q16×D47 | — | 2 | 8 | no | — |
| 93 | Q16×D47 | — | 2 | 4 | no | — |
| 94 | Q16×D47 | — | 2 | 8 | no | — |
| 95 | Q16×D47 | — | 2 | 4 | no | — |
| 96 | Q16×D47 | — | 2 | 4 | no | — |
| 97 | Q16×D47 | — | 2 | 4 | no | — |
| 98 | Q16×D47 | — | 2 | 4 | no | — |
| 99 | Q16×D47 | — | 2 | 4 | no | — |
| 100 | Q16×D47 | D4 | 1 | 2 | yes | — |
| 101 | SD16×D47 | — | 2 | 8 | no | — |
| 102 | SD16×D47 | D4 | 1 | 4 | yes | — |
| 103 | D8×D47 | D4 | 1 | 2 | yes | — |
| 104 | #13094032 | — | 2 | 4 | no | — |
| 105 | #13094032 | C23 | 1 | 4 | yes | — |
| 106 | #13094031 | C23 | 1 | 4 | yes | — |
| 107 | #13094030 | — | 2 | 4 | no | — |
| 108 | #13094030 | C23 | 1 | 4 | yes | — |
| 109 | M16×D47 | — | 2 | 4 | no | — |
| 110 | M16×D47 | C23 | 1 | 4 | yes | — |
| 111 | C2×C8×D47 | — | 2 | 4 | no | — |
| 112 | C2×C8×D47 | C23 | 1 | 2 | yes | — |
| 113 | #13094024 | C23 | 1 | 2 | yes | — |
| 114 | #13094023 | — | 4 | 2 | no | — |
| 115 | #13094022 | C23 | 1 | 4 | yes | — |
| 116 | C4⋊C4×D47 | — | 4 | 2 | no | — |
| 117 | C42×D47 | C23 | 1 | 1 | yes | characteristic |
| 118 | #13093960 | C23 | 1 | 2 | yes | — |
| 119 | #13093959 | C23 | 1 | 4 | yes | — |
| 120 | #13093952 | C23 | 1 | 4 | yes | — |
| 121 | #13093951 | C23 | 1 | 4 | yes | — |
| 122 | #13093950 | C23 | 1 | 4 | yes | — |
| 123 | #13093943 | C23 | 1 | 4 | yes | — |
| 124 | #13093942 | C23 | 1 | 8 | yes | — |
| 125 | C4×C47⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 126 | C8×Dic47 | C23 | 1 | 2 | yes | — |
| 127 | 2−1+4×C47 | C23 | 1 | 4 | yes | — |
| 128 | #137×C47 | — | 2 | 8 | no | — |
| 129 | #137×C47 | C23 | 1 | 8 | yes | — |
| 130 | #135×C47 | — | 2 | 4 | no | — |
| 131 | #135×C47 | C23 | 1 | 2 | yes | — |
| 132 | C2×Q16×C47 | — | 2 | 4 | no | — |
| 133 | C2×Q16×C47 | C23 | 1 | 4 | yes | — |
| 134 | #131×C47 | C23 | 1 | 4 | yes | — |
| 135 | C4⋊Q8×C47 | C23 | 1 | 2 | yes | — |
| 136 | #108×C47 | C23 | 1 | 2 | yes | — |
| 137 | #104×C47 | C23 | 1 | 4 | yes | — |
| 138 | #101×C47 | C23 | 1 | 4 | yes | — |
| 139 | C4×C8×C47 | C23 | 1 | 1 | yes | characteristic |
| 140 | #41×C47 | — | 2 | 8 | no | — |
| 141 | #41×C47 | — | 4 | 4 | no | — |
| 142 | #41×C47 | C24 | 1 | 4 | yes | — |
| 143 | C2×Q8×C47 | — | 2 | 8 | no | — |
| 144 | C2×Q8×C47 | C24 | 1 | 4 | yes | — |
| 145 | #10625354 | — | 2 | 8 | no | — |
| 146 | #10625354 | — | 4 | 4 | no | — |
| 147 | #10625354 | C2×D4 | 1 | 4 | yes | — |
| 148 | Q8×D47 | — | 2 | 8 | no | — |
| 149 | Q8×D47 | — | 2 | 8 | no | — |
| 150 | Q8×D47 | — | 2 | 8 | no | — |
| 151 | Q8×D47 | — | 2 | 8 | no | — |
| 152 | Q8×D47 | — | 4 | 8 | no | — |
| 153 | Q8×D47 | — | 4 | 4 | no | — |
| 154 | Q8×D47 | C2×D4 | 1 | 4 | yes | — |
| 155 | #10625352 | — | 2 | 4 | no | — |
| 156 | #10625352 | — | 2 | 8 | no | — |
| 157 | #10625352 | — | 4 | 8 | no | — |
| 158 | #10625352 | — | 4 | 8 | no | — |
| 159 | #10625352 | — | 4 | 4 | no | — |
| 160 | #10625352 | C2×D4 | 1 | 4 | yes | — |
| 161 | D4×D47 | — | 2 | 4 | no | — |
| 162 | D4×D47 | — | 4 | 4 | no | — |
| 163 | D4×D47 | C2×D4 | 1 | 4 | yes | — |
| 164 | #10625350 | — | 2 | 4 | no | — |
| 165 | #10625350 | — | 2 | 8 | no | — |
| 166 | #10625350 | — | 4 | 8 | no | — |
| 167 | #10625350 | — | 4 | 8 | no | — |
| 168 | #10625350 | — | 4 | 4 | no | — |
| 169 | #10625350 | C24 | 1 | 4 | yes | — |
| 170 | C2×C4×D47 | — | 2 | 1 | no | — |
| 171 | C2×C4×D47 | — | 2 | 4 | no | — |
| 172 | C2×C4×D47 | — | 2 | 4 | no | — |
| 173 | C2×C4×D47 | — | 4 | 8 | no | — |
| 174 | C2×C4×D47 | C24 | 1 | 1 | yes | characteristic |
| 175 | C2×Dic94 | — | 2 | 8 | no | — |
| 176 | C2×Dic94 | — | 2 | 4 | no | — |
| 177 | C2×Dic94 | — | 4 | 8 | no | — |
| 178 | C2×Dic94 | C24 | 1 | 4 | yes | — |
| 179 | Q16×C47 | — | 2 | 8 | no | — |
| 180 | Q16×C47 | — | 2 | 4 | no | — |
| 181 | Q16×C47 | — | 2 | 4 | no | — |
| 182 | Q16×C47 | C2×D4 | 1 | 2 | yes | — |
| 183 | SD16×C47 | — | 2 | 8 | no | — |
| 184 | SD16×C47 | C2×D4 | 1 | 4 | yes | — |
| 185 | D8×C47 | C2×D4 | 1 | 2 | yes | — |
| 186 | M16×C47 | — | 2 | 4 | no | — |
| 187 | M16×C47 | C24 | 1 | 4 | yes | — |
| 188 | C2×C8×C47 | — | 2 | 4 | no | — |
| 189 | C2×C8×C47 | C24 | 1 | 2 | yes | — |
| 190 | C4⋊C4×C47 | — | 4 | 2 | no | — |
| 191 | C42×C47 | C24 | 1 | 1 | yes | characteristic |
| 192 | #10625337 | — | 2 | 8 | no | — |
| 193 | #10625337 | — | 2 | 8 | no | — |
| 194 | #10625337 | — | 2 | 8 | no | — |
| 195 | #10625337 | — | 2 | 8 | no | — |
| 196 | #10625337 | C2×D4 | 1 | 4 | yes | — |
| 197 | #10625336 | — | 2 | 8 | no | — |
| 198 | #10625336 | C2×D4 | 1 | 4 | yes | — |
| 199 | #10625335 | — | 2 | 8 | no | — |
| 200 | #10625335 | C2×D4 | 1 | 4 | yes | — |
| 201 | #10625334 | C2×D4 | 1 | 4 | yes | — |
| 202 | C4⋊Dic47 | — | 4 | 2 | no | — |
| 203 | Dic47⋊C4 | — | 4 | 4 | no | — |
| 204 | C4×Dic47 | — | 2 | 1 | no | — |
| 205 | C4×Dic47 | C24 | 1 | 1 | yes | characteristic |
| 206 | #10625329 | — | 2 | 4 | no | — |
| 207 | #10625329 | C24 | 1 | 4 | yes | — |
| 208 | C2×C47⋊C8 | — | 2 | 4 | no | — |
| 209 | C2×C47⋊C8 | C24 | 1 | 2 | yes | — |
| 210 | Dic188 | — | 2 | 8 | no | — |
| 211 | Dic188 | — | 2 | 4 | no | — |
| 212 | Dic188 | — | 2 | 4 | no | — |
| 213 | Dic188 | C2×D4 | 1 | 2 | yes | — |
| 214 | D376 | C2×D4 | 1 | 2 | yes | — |
| 215 | #10625325 | — | 2 | 8 | no | — |
| 216 | #10625325 | C2×D4 | 1 | 4 | yes | — |
| 217 | #10625324 | — | 2 | 4 | no | — |
| 218 | #10625324 | — | 2 | 4 | no | — |
| 219 | #10625324 | — | 2 | 4 | no | — |
| 220 | C8×D47 | — | 2 | 4 | no | — |
| 221 | C8×D47 | — | 2 | 4 | no | — |
| 222 | C8×D47 | — | 2 | 4 | no | — |
| 223 | C8×D47 | C2×D4 | 1 | 2 | yes | — |
| 224 | C8×D47 | C2×D4 | 1 | 2 | yes | — |
| 225 | C8×D47 | C2×D4 | 1 | 2 | yes | — |
| 226 | C8×D47 | C2×D4 | 1 | 2 | yes | — |
| 227 | C22×D47 | — | 2 | 4 | no | — |
| 228 | C22×D47 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 229 | Q8×C47 | — | 2 | 8 | no | — |
| 230 | Q8×C47 | — | 4 | 4 | no | — |
| 231 | Q8×C47 | C22×D4 | 1 | 4 | yes | — |
| 232 | D4×C47 | — | 2 | 4 | no | — |
| 233 | D4×C47 | — | 4 | 4 | no | — |
| 234 | D4×C47 | C22×D4 | 1 | 4 | yes | — |
| 235 | C2×C4×C47 | — | 2 | 1 | no | — |
| 236 | C2×C4×C47 | — | 2 | 4 | no | — |
| 237 | C2×C4×C47 | — | 2 | 4 | no | — |
| 238 | C2×C4×C47 | — | 4 | 8 | no | — |
| 239 | C2×C4×C47 | C25 | 1 | 1 | yes | characteristic |
| 240 | C22⋊D47 | — | 2 | 4 | no | — |
| 241 | C22⋊D47 | — | 2 | 4 | no | — |
| 242 | C22⋊D47 | — | 2 | 4 | no | — |
| 243 | C22⋊D47 | — | 4 | 8 | no | — |
| 244 | C2×Dic47 | — | 2 | 1 | no | — |
| 245 | C2×Dic47 | — | 2 | 4 | no | — |
| 246 | C2×Dic47 | — | 2 | 4 | no | — |
| 247 | C2×Dic47 | — | 4 | 8 | no | — |
| 248 | C2×Dic47 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 249 | D188 | — | 2 | 4 | no | — |
| 250 | D188 | — | 4 | 4 | no | — |
| 251 | D188 | C22×D4 | 1 | 4 | yes | — |
| 252 | C4×D47 | — | 2 | 4 | no | — |
| 253 | C4×D47 | — | 2 | 4 | no | — |
| 254 | C4×D47 | — | 2 | 4 | no | — |
| 255 | C4×D47 | — | 2 | 4 | no | — |
| 256 | C4×D47 | — | 4 | 8 | no | — |
| 257 | C4×D47 | — | 4 | 8 | no | — |
| 258 | C4×D47 | — | 4 | 4 | no | — |
| 259 | C4×D47 | — | 4 | 4 | no | — |
| 260 | C4×D47 | C22×D4 | 1 | 2 | yes | — |
| 261 | C4×D47 | C22×D4 | 1 | 2 | yes | — |
| 262 | Dic94 | — | 2 | 4 | no | — |
| 263 | Dic94 | — | 2 | 8 | no | — |
| 264 | Dic94 | — | 4 | 4 | no | — |
| 265 | Dic94 | — | 4 | 8 | no | — |
| 266 | Dic94 | — | 4 | 8 | no | — |
| 267 | Dic94 | C22×D4 | 1 | 4 | yes | — |
| 268 | C8×C47 | — | 2 | 4 | no | — |
| 269 | C8×C47 | C22×D4 | 1 | 2 | yes | — |
| 270 | C8×C47 | C22×D4 | 1 | 2 | yes | — |
| 271 | C47⋊C8 | — | 2 | 4 | no | — |
| 272 | C47⋊C8 | C22×D4 | 1 | 2 | yes | — |
| 273 | C47⋊C8 | C22×D4 | 1 | 2 | yes | — |
| 274 | C2×#3293 | — | 47 | 1 | no | maximal, Sylow |
| 275 | C22×C47 | — | 2 | 4 | no | — |
| 276 | C22×C47 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 277 | C2×D47 | — | 2 | 2 | no | — |
| 278 | C2×D47 | — | 2 | 4 | no | — |
| 279 | C2×D47 | — | 4 | 8 | no | — |
| 280 | C2×D47 | D42 | 1 | 1 | yes | characteristic |
| 281 | C2×D47 | D42 | 1 | 1 | yes | characteristic |
| 282 | C4×C47 | — | 2 | 2 | no | — |
| 283 | C4×C47 | — | 2 | 4 | no | — |
| 284 | C4×C47 | — | 4 | 4 | no | — |
| 285 | C4×C47 | C23×D4 | 1 | 2 | yes | — |
| 286 | Dic47 | — | 2 | 2 | no | — |
| 287 | Dic47 | — | 2 | 4 | no | — |
| 288 | Dic47 | — | 4 | 4 | no | — |
| 289 | Dic47 | D42 | 1 | 2 | yes | — |
| 290 | C2×#578 | — | 47 | 4 | no | — |
| 291 | #3293 | — | 47 | 1 | no | — |
| 292 | #3293 | — | 47 | 4 | no | — |
| 293 | #3293 | — | 47 | 4 | no | — |
| 294 | #3293 | — | 47 | 2 | no | — |
| 295 | #3293 | — | 47 | 4 | no | — |
| 296 | #3293 | D47 | 1 | 1 | yes | characteristic, direct product factor |
| 297 | C2×#494 | — | 47 | 1 | no | — |
| 298 | C2×#473 | — | 47 | 4 | no | — |
| 299 | C2×#456 | — | 47 | 4 | no | — |
| 300 | C2×#443 | — | 47 | 2 | no | — |
| 301 | C2×C47 | — | 2 | 1 | no | — |
| 302 | C2×C47 | — | 4 | 4 | no | — |
| 303 | C2×C47 | C2×D42 | 1 | 1 | yes | characteristic |
| 304 | D47 | — | 2 | 1 | no | — |
| 305 | D47 | — | 4 | 4 | no | — |
| 306 | D47 | #3293 | 1 | 2 | yes | direct product factor |
| 307 | C2×2−1+4 | — | 47 | 4 | no | — |
| 308 | #578 | — | 47 | 8 | no | — |
| 309 | #578 | — | 47 | 8 | no | — |
| 310 | #578 | — | 47 | 4 | no | — |
| 311 | #578 | — | 47 | 4 | no | — |
| 312 | #578 | — | 47 | 4 | no | — |
| 313 | #578 | — | 94 | 4 | no | — |
| 314 | #578 | — | 94 | 4 | no | — |
| 315 | #578 | — | 94 | 8 | no | — |
| 316 | #578 | C2×D47 | 1 | 4 | yes | complemented |
| 317 | C2×#137 | — | 47 | 8 | no | — |
| 318 | C2×#137 | — | 94 | 8 | no | — |
| 319 | C2×#135 | — | 47 | 2 | no | — |
| 320 | C2×#135 | — | 94 | 4 | no | — |
| 321 | C22×Q16 | — | 47 | 4 | no | — |
| 322 | C22×Q16 | — | 94 | 4 | no | — |
| 323 | C2×#131 | — | 47 | 4 | no | — |
| 324 | C2×C4⋊Q8 | — | 47 | 2 | no | — |
| 325 | #494 | — | 47 | 4 | no | — |
| 326 | #494 | — | 47 | 2 | no | — |
| 327 | #494 | — | 47 | 1 | no | — |
| 328 | #494 | C2×D47 | 1 | 1 | yes | characteristic, complemented |
| 329 | #473 | — | 47 | 8 | no | — |
| 330 | #473 | — | 47 | 4 | no | — |
| 331 | #473 | — | 47 | 4 | no | — |
| 332 | #473 | — | 47 | 4 | no | — |
| 333 | #473 | — | 47 | 8 | no | — |
| 334 | #473 | C2×D47 | 1 | 4 | yes | complemented |
| 335 | #456 | — | 47 | 4 | no | — |
| 336 | #456 | — | 47 | 8 | no | — |
| 337 | #456 | — | 47 | 4 | no | — |
| 338 | #456 | — | 47 | 8 | no | — |
| 339 | #456 | — | 47 | 4 | no | — |
| 340 | #456 | C2×D47 | 1 | 4 | yes | complemented |
| 341 | #443 | — | 47 | 2 | no | — |
| 342 | #443 | — | 47 | 4 | no | — |
| 343 | #443 | — | 47 | 2 | no | — |
| 344 | #443 | — | 47 | 4 | no | — |
| 345 | #443 | — | 47 | 2 | no | — |
| 346 | #443 | C2×D47 | 1 | 2 | yes | complemented |
| 347 | C2×#108 | — | 47 | 2 | no | — |
| 348 | C2×#104 | — | 47 | 4 | no | — |
| 349 | C2×#101 | — | 47 | 4 | no | — |
| 350 | C2×C4×C8 | — | 47 | 1 | no | — |
| 351 | C47 | C2×#3293 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 352 | 2−1+4 | — | 47 | 8 | no | — |
| 353 | 2−1+4 | — | 47 | 4 | no | — |
| 354 | 2−1+4 | — | 94 | 8 | no | — |
| 355 | 2−1+4 | — | 94 | 8 | no | — |
| 356 | 2−1+4 | — | 188 | 4 | no | — |
| 357 | 2−1+4 | C22×D47 | 1 | 4 | yes | — |
| 358 | C2×#41 | — | 47 | 4 | no | — |
| 359 | C2×#41 | — | 94 | 8 | no | — |
| 360 | C2×#41 | — | 188 | 4 | no | — |
| 361 | C22×Q8 | — | 47 | 4 | no | — |
| 362 | C22×Q8 | — | 94 | 8 | no | — |
| 363 | #137 | — | 2 | 8 | no | — |
| 364 | #137 | — | 47 | 8 | no | — |
| 365 | #137 | — | 47 | 8 | no | — |
| 366 | #137 | — | 47 | 8 | no | — |
| 367 | #137 | — | 94 | 8 | no | — |
| 368 | #137 | — | 94 | 8 | no | — |
| 369 | #137 | — | 94 | 8 | no | — |
| 370 | #137 | — | 94 | 8 | no | — |
| 371 | #137 | — | 94 | 8 | no | — |
| 372 | #137 | — | 94 | 8 | no | — |
| 373 | #137 | — | 94 | 8 | no | — |
| 374 | #137 | — | 94 | 8 | no | — |
| 375 | #137 | — | 94 | 8 | no | — |
| 376 | #137 | C22×D47 | 1 | 8 | yes | — |
| 377 | #135 | — | 2 | 4 | no | — |
| 378 | #135 | — | 47 | 4 | no | — |
| 379 | #135 | — | 47 | 2 | no | — |
| 380 | #135 | — | 47 | 4 | no | — |
| 381 | #135 | — | 47 | 2 | no | — |
| 382 | #135 | — | 47 | 2 | no | — |
| 383 | #135 | — | 94 | 4 | no | — |
| 384 | #135 | — | 94 | 8 | no | — |
| 385 | #135 | — | 94 | 4 | no | — |
| 386 | #135 | — | 94 | 8 | no | — |
| 387 | #135 | — | 94 | 4 | no | — |
| 388 | #135 | C22×D47 | 1 | 2 | yes | — |
| 389 | C2×Q16 | — | 2 | 4 | no | — |
| 390 | C2×Q16 | — | 47 | 2 | no | — |
| 391 | C2×Q16 | — | 47 | 8 | no | — |
| 392 | C2×Q16 | — | 47 | 4 | no | — |
| 393 | C2×Q16 | — | 94 | 4 | no | — |
| 394 | C2×Q16 | — | 94 | 4 | no | — |
| 395 | C2×Q16 | — | 94 | 4 | no | — |
| 396 | C2×Q16 | — | 94 | 4 | no | — |
| 397 | C2×Q16 | — | 94 | 4 | no | — |
| 398 | C2×Q16 | — | 94 | 8 | no | — |
| 399 | C2×Q16 | — | 94 | 4 | no | — |
| 400 | C2×Q16 | — | 94 | 8 | no | — |
| 401 | C2×Q16 | — | 94 | 8 | no | — |
| 402 | C2×Q16 | — | 94 | 4 | no | — |
| 403 | C2×Q16 | C22×D47 | 1 | 4 | yes | — |
| 404 | C2×SD16 | — | 47 | 4 | no | — |
| 405 | C2×SD16 | — | 94 | 8 | no | — |
| 406 | C2×D8 | — | 47 | 2 | no | — |
| 407 | #131 | — | 47 | 4 | no | — |
| 408 | #131 | — | 47 | 4 | no | — |
| 409 | #131 | — | 47 | 4 | no | — |
| 410 | #131 | — | 94 | 4 | no | — |
| 411 | #131 | — | 94 | 4 | no | — |
| 412 | #131 | C22×D47 | 1 | 4 | yes | — |
| 413 | C2×M16 | — | 47 | 4 | no | — |
| 414 | C2×M16 | — | 94 | 4 | no | — |
| 415 | C22×C8 | — | 47 | 2 | no | — |
| 416 | C22×C8 | — | 94 | 4 | no | — |
| 417 | C4⋊Q8 | — | 47 | 4 | no | — |
| 418 | C4⋊Q8 | — | 47 | 2 | no | — |
| 419 | C4⋊Q8 | — | 188 | 2 | no | — |
| 420 | C4⋊Q8 | C22×D47 | 1 | 2 | yes | — |
| 421 | C2×C4⋊C4 | — | 188 | 2 | no | — |
| 422 | C2×C42 | — | 47 | 1 | no | — |
| 423 | #108 | — | 47 | 4 | no | — |
| 424 | #108 | — | 47 | 2 | no | — |
| 425 | #108 | C22×D47 | 1 | 2 | yes | — |
| 426 | #104 | — | 47 | 4 | no | — |
| 427 | #104 | — | 47 | 4 | no | — |
| 428 | #104 | — | 47 | 4 | no | — |
| 429 | #104 | C22×D47 | 1 | 4 | yes | — |
| 430 | #101 | — | 47 | 4 | no | — |
| 431 | #101 | — | 47 | 8 | no | — |
| 432 | #101 | C22×D47 | 1 | 4 | yes | — |
| 433 | C4×C8 | — | 47 | 2 | no | — |
| 434 | C4×C8 | — | 47 | 1 | no | — |
| 435 | C4×C8 | C22×D47 | 1 | 1 | yes | characteristic |
| 436 | #41 | — | 2 | 8 | no | — |
| 437 | #41 | — | 4 | 4 | no | — |
| 438 | #41 | — | 47 | 4 | no | — |
| 439 | #41 | — | 47 | 4 | no | — |
| 440 | #41 | — | 47 | 4 | no | — |
| 441 | #41 | — | 94 | 4 | no | — |
| 442 | #41 | — | 94 | 8 | no | — |
| 443 | #41 | — | 94 | 4 | no | — |
| 444 | #41 | — | 94 | 8 | no | — |
| 445 | #41 | — | 94 | 8 | no | — |
| 446 | #41 | — | 188 | 4 | no | — |
| 447 | #41 | — | 188 | 8 | no | — |
| 448 | #41 | — | 188 | 8 | no | — |
| 449 | #41 | — | 188 | 8 | no | — |
| 450 | #41 | — | 188 | 8 | no | — |
| 451 | #41 | — | 188 | 4 | no | — |
| 452 | #41 | — | 188 | 4 | no | — |
| 453 | #41 | C23×D47 | 1 | 4 | yes | — |
| 454 | C2×Q8 | — | 2 | 8 | no | — |
| 455 | C2×Q8 | — | 47 | 4 | no | — |
| 456 | C2×Q8 | — | 47 | 4 | no | — |
| 457 | C2×Q8 | — | 94 | 4 | no | — |
| 458 | C2×Q8 | — | 94 | 8 | no | — |
| 459 | C2×Q8 | — | 94 | 8 | no | — |
| 460 | C2×Q8 | — | 94 | 8 | no | — |
| 461 | C2×Q8 | — | 94 | 8 | no | — |
| 462 | C2×Q8 | — | 94 | 8 | no | — |
| 463 | C2×Q8 | — | 188 | 8 | no | — |
| 464 | C2×Q8 | — | 188 | 4 | no | — |
| 465 | C2×Q8 | — | 188 | 8 | no | — |
| 466 | C2×Q8 | C23×D47 | 1 | 4 | yes | — |
| 467 | C2×D4 | — | 47 | 4 | no | — |
| 468 | C2×D4 | — | 94 | 4 | no | — |
| 469 | C2×D4 | — | 188 | 4 | no | — |
| 470 | C22×C4 | — | 47 | 1 | no | — |
| 471 | C22×C4 | — | 94 | 4 | no | — |
| 472 | C22×C4 | — | 94 | 1 | no | — |
| 473 | C22×C4 | — | 94 | 4 | no | — |
| 474 | C22×C4 | — | 188 | 8 | no | — |
| 475 | Q16 | — | 2 | 8 | no | — |
| 476 | Q16 | — | 2 | 4 | no | — |
| 477 | Q16 | — | 2 | 4 | no | — |
| 478 | Q16 | — | 47 | 4 | no | — |
| 479 | Q16 | — | 47 | 2 | no | — |
| 480 | Q16 | — | 94 | 8 | no | — |
| 481 | Q16 | — | 94 | 8 | no | — |
| 482 | Q16 | — | 94 | 8 | no | — |
| 483 | Q16 | — | 94 | 8 | no | — |
| 484 | Q16 | — | 94 | 8 | no | — |
| 485 | Q16 | — | 94 | 4 | no | — |
| 486 | Q16 | — | 94 | 4 | no | — |
| 487 | Q16 | D4×D47 | 1 | 2 | yes | — |
| 488 | SD16 | — | 2 | 8 | no | — |
| 489 | SD16 | — | 47 | 4 | no | — |
| 490 | SD16 | — | 47 | 4 | no | — |
| 491 | SD16 | — | 47 | 4 | no | — |
| 492 | SD16 | — | 94 | 8 | no | — |
| 493 | SD16 | — | 94 | 8 | no | — |
| 494 | SD16 | — | 94 | 8 | no | — |
| 495 | SD16 | D4×D47 | 1 | 4 | yes | — |
| 496 | D8 | — | 47 | 4 | no | — |
| 497 | D8 | — | 47 | 2 | no | — |
| 498 | D8 | D4×D47 | 1 | 2 | yes | — |
| 499 | M16 | — | 2 | 4 | no | — |
| 500 | M16 | — | 47 | 4 | no | — |
| 501 | M16 | — | 94 | 4 | no | — |
| 502 | M16 | — | 94 | 4 | no | — |
| 503 | M16 | — | 94 | 4 | no | — |
| 504 | M16 | — | 94 | 4 | no | — |
| 505 | M16 | C23×D47 | 1 | 4 | yes | — |
| 506 | C2×C8 | — | 2 | 4 | no | — |
| 507 | C2×C8 | — | 47 | 2 | no | — |
| 508 | C2×C8 | — | 47 | 2 | no | — |
| 509 | C2×C8 | — | 47 | 2 | no | — |
| 510 | C2×C8 | — | 47 | 2 | no | — |
| 511 | C2×C8 | — | 47 | 2 | no | — |
| 512 | C2×C8 | — | 94 | 4 | no | — |
| 513 | C2×C8 | — | 94 | 4 | no | — |
| 514 | C2×C8 | — | 94 | 4 | no | — |
| 515 | C2×C8 | — | 94 | 4 | no | — |
| 516 | C2×C8 | C23×D47 | 1 | 2 | yes | — |
| 517 | C4⋊C4 | — | 4 | 2 | no | — |
| 518 | C4⋊C4 | — | 188 | 4 | no | — |
| 519 | C4⋊C4 | — | 188 | 2 | no | — |
| 520 | C42 | — | 47 | 1 | no | — |
| 521 | C42 | — | 94 | 1 | no | — |
| 522 | C42 | C23×D47 | 1 | 1 | yes | characteristic |
| 523 | C23 | — | 47 | 1 | no | — |
| 524 | C23 | — | 94 | 4 | no | — |
| 525 | Q8 | — | 2 | 8 | no | — |
| 526 | Q8 | — | 4 | 4 | no | — |
| 527 | Q8 | — | 47 | 4 | no | — |
| 528 | Q8 | — | 94 | 4 | no | — |
| 529 | Q8 | — | 94 | 8 | no | — |
| 530 | Q8 | — | 188 | 8 | no | — |
| 531 | Q8 | — | 188 | 8 | no | — |
| 532 | Q8 | — | 188 | 4 | no | — |
| 533 | Q8 | C2×D4×D47 | 1 | 4 | yes | — |
| 534 | D4 | — | 2 | 4 | no | — |
| 535 | D4 | — | 4 | 4 | no | — |
| 536 | D4 | — | 47 | 4 | no | — |
| 537 | D4 | — | 94 | 4 | no | — |
| 538 | D4 | — | 94 | 4 | no | — |
| 539 | D4 | — | 94 | 4 | no | — |
| 540 | D4 | — | 94 | 4 | no | — |
| 541 | D4 | — | 188 | 4 | no | — |
| 542 | D4 | — | 188 | 8 | no | — |
| 543 | D4 | C2×D4×D47 | 1 | 4 | yes | — |
| 544 | C2×C4 | — | 2 | 1 | no | — |
| 545 | C2×C4 | — | 2 | 4 | no | — |
| 546 | C2×C4 | — | 2 | 4 | no | — |
| 547 | C2×C4 | — | 4 | 8 | no | — |
| 548 | C2×C4 | — | 47 | 1 | no | — |
| 549 | C2×C4 | — | 47 | 2 | no | — |
| 550 | C2×C4 | — | 47 | 2 | no | — |
| 551 | C2×C4 | — | 94 | 4 | no | — |
| 552 | C2×C4 | — | 94 | 4 | no | — |
| 553 | C2×C4 | — | 94 | 4 | no | — |
| 554 | C2×C4 | — | 94 | 4 | no | — |
| 555 | C2×C4 | — | 94 | 1 | no | — |
| 556 | C2×C4 | — | 94 | 4 | no | — |
| 557 | C2×C4 | — | 94 | 4 | no | — |
| 558 | C2×C4 | — | 188 | 8 | no | — |
| 559 | C2×C4 | — | 188 | 8 | no | — |
| 560 | C2×C4 | — | 188 | 4 | no | — |
| 561 | C2×C4 | — | 188 | 4 | no | — |
| 562 | C2×C4 | — | 188 | 8 | no | — |
| 563 | C2×C4 | C24×D47 | 1 | 1 | yes | characteristic |
| 564 | C8 | — | 2 | 4 | no | — |
| 565 | C8 | — | 47 | 2 | no | — |
| 566 | C8 | — | 47 | 2 | no | — |
| 567 | C8 | — | 94 | 4 | no | — |
| 568 | C8 | C2×D4×D47 | 1 | 2 | yes | — |
| 569 | C8 | C2×D4×D47 | 1 | 2 | yes | — |
| 570 | C22 | — | 2 | 4 | no | — |
| 571 | C22 | — | 47 | 1 | no | — |
| 572 | C22 | — | 47 | 1 | no | — |
| 573 | C22 | — | 94 | 2 | no | — |
| 574 | C22 | — | 94 | 4 | no | — |
| 575 | C22 | — | 188 | 8 | no | — |
| 576 | C22 | H(5,𝔽2)×D47 | 1 | 1 | yes | characteristic |
| 577 | C4 | — | 2 | 2 | no | — |
| 578 | C4 | — | 2 | 4 | no | — |
| 579 | C4 | — | 4 | 4 | no | — |
| 580 | C4 | — | 47 | 2 | no | — |
| 581 | C4 | — | 94 | 2 | no | — |
| 582 | C4 | — | 94 | 4 | no | — |
| 583 | C4 | — | 188 | 4 | no | — |
| 584 | C4 | C22×D4×D47 | 1 | 2 | yes | — |
| 585 | C2 | — | 2 | 1 | no | — |
| 586 | C2 | — | 4 | 4 | no | — |
| 587 | C2 | — | 47 | 2 | no | — |
| 588 | C2 | — | 94 | 1 | no | — |
| 589 | C2 | — | 188 | 4 | no | — |
| 590 | C2 | D42×D47 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #578×D47 | C2 | semidirect |
| 2. #20255193 | C2 | semidirect |
| 3. #20255192 | C2 | semidirect |
| 4. #20255191 | C2 | semidirect |
| 5. #20255190 | C2 | semidirect |
| 6. #20255189 | C2 | semidirect |
| 7. #494×D47 | C2 | semidirect |
| 8. #473×D47 | C2 | semidirect |
| 9. #456×D47 | C2 | semidirect |
| 10. #443×D47 | C2 | semidirect |
| 11. C47×#3293 | C2 | semidirect |
| 13. #15689940 | C22 | semidirect |
| 15. #15689939 | C22 | semidirect |
| 16. #15689938 | C22 | semidirect |
| 18. #15689937 | C22 | semidirect |
| 20. #15689936 | C22 | semidirect |
| 29. #15689503 | C22 | semidirect |
| 30. #15689502 | C22 | semidirect |
| 31. #15689501 | C22 | semidirect |
| 32. #15689399 | C22 | semidirect |
| 33. #15689398 | C22 | semidirect |
| 34. #15689397 | C22 | semidirect |
| 35. #15689396 | C22 | semidirect |
| 36. #15689395 | C22 | semidirect |
| 37. #15689308 | C22 | semidirect |
| 38. #15689307 | C22 | semidirect |
| 39. #15689306 | C22 | semidirect |
| 40. #15689305 | C22 | semidirect |
| 41. #15689304 | C22 | semidirect |
| 42. #15689241 | C22 | semidirect |
| 43. #15689240 | C22 | semidirect |
| 44. #15689239 | C22 | semidirect |
| 45. #15689238 | C22 | semidirect |
| 46. #15689237 | C22 | semidirect |
| 51. C47×#578 | C22 | semidirect |
| 52. C47×#494 | C22 | semidirect |
| 53. C47×#473 | C22 | semidirect |
| 54. C47×#456 | C22 | semidirect |
| 55. C47×#443 | C22 | semidirect |
| 296. #3293 | D47 | direct (N × H) |
| 306. D47 | #3293 | direct (N × H) |
| 316. #578 | C2×D47 | semidirect |
| 328. #494 | C2×D47 | semidirect |
| 334. #473 | C2×D47 | semidirect |
| 340. #456 | C2×D47 | semidirect |
| 346. #443 | C2×D47 | semidirect |
| 351. C47 | C2×#3293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #578×D47 | 2 |
| #20255193 | 2 |
| #20255192 | 2 |
| #20255191 | 2 |
| #20255190 | 2 |
| #20255189 | 2 |
| #494×D47 | 2 |
| #473×D47 | 2 |
| #456×D47 | 2 |
| #443×D47 | 2 |
| C47×#3293 | 2 |
| C2×#3293 | 47 |