Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
772 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 79 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 | C2×#17986174 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#17986171 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22595364 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#17985795 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22588301 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22586466 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×#355×C71 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#14556176 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#14556156 | — | 2 | 1 | no | — |
| 10 | C2×#14556154 | — | 2 | 1 | no | — |
| 11 | C2×#14556117 | C22 | 1 | 1 | yes | characteristic |
| 12 | #17986174 | — | 2 | 2 | no | — |
| 13 | #17986174 | — | 2 | 2 | no | — |
| 14 | #17986171 | — | 2 | 2 | no | — |
| 15 | #17986171 | — | 2 | 2 | no | — |
| 16 | C2×#14556056 | — | 2 | 1 | no | — |
| 17 | C2×#14556054 | — | 2 | 1 | no | — |
| 18 | C2×#14556054 | — | 2 | 1 | no | — |
| 19 | #17986001 | — | 2 | 1 | no | — |
| 20 | C2×#14556047 | C22 | 1 | 1 | yes | characteristic |
| 21 | #17985915 | — | 2 | 1 | no | — |
| 22 | #17985908 | — | 2 | 1 | no | — |
| 23 | #17985907 | — | 2 | 1 | no | — |
| 24 | #17985906 | C22 | 1 | 1 | yes | characteristic |
| 25 | #17985899 | — | 2 | 1 | no | — |
| 26 | #17985890 | — | 2 | 1 | no | — |
| 27 | #17985887 | — | 2 | 1 | no | — |
| 28 | #17985795 | — | 2 | 2 | no | — |
| 29 | C2×#124×C71 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×#101×C71 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#101×C71 | C22 | 1 | 1 | yes | characteristic |
| 32 | #355×C71 | — | 2 | 2 | no | — |
| 33 | #14556176 | — | 2 | 1 | no | — |
| 34 | #14556176 | — | 2 | 1 | no | — |
| 35 | #14556176 | — | 2 | 1 | no | — |
| 36 | #14556176 | — | 4 | 2 | no | — |
| 37 | #14556176 | D4 | 1 | 2 | yes | complemented |
| 38 | C2×#11765866 | — | 4 | 1 | no | — |
| 39 | C2×#11765865 | — | 2 | 1 | no | — |
| 40 | C2×#11765865 | — | 2 | 1 | no | — |
| 41 | C2×#11765865 | — | 2 | 1 | no | — |
| 42 | C2×Q8×D71 | — | 4 | 1 | no | — |
| 43 | C22×D284 | D4 | 1 | 1 | yes | characteristic |
| 44 | C22×C22⋊D71 | — | 2 | 1 | no | — |
| 45 | C22×C22⋊D71 | — | 2 | 1 | no | — |
| 46 | #14556156 | — | 2 | 4 | no | — |
| 47 | #14556156 | — | 4 | 2 | no | — |
| 48 | #14556154 | — | 2 | 4 | no | — |
| 49 | #14556154 | — | 4 | 2 | no | — |
| 50 | C2×#11765854 | — | 4 | 1 | no | — |
| 51 | C2×#11765853 | — | 4 | 1 | no | — |
| 52 | C2×D568 | — | 4 | 1 | no | — |
| 53 | C2×#11765850 | — | 4 | 1 | no | — |
| 54 | C2×#11765849 | — | 2 | 1 | no | — |
| 55 | #14556117 | — | 2 | 1 | no | — |
| 56 | #14556117 | — | 2 | 1 | no | — |
| 57 | #14556117 | — | 2 | 1 | no | — |
| 58 | #14556117 | — | 2 | 1 | no | — |
| 59 | C2×C4⋊Dic71 | D4 | 1 | 1 | yes | characteristic |
| 60 | C2×Dic71⋊C4 | — | 2 | 1 | no | — |
| 61 | C2×C22⋊Dic71 | — | 2 | 1 | no | — |
| 62 | C2×C22⋊Dic71 | — | 2 | 1 | no | — |
| 63 | C2×(C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 64 | C2×(C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 65 | C2×(C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 66 | C2×(C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 67 | C2×C4×Dic71 | D4 | 1 | 1 | yes | characteristic |
| 68 | C2×C4×Dic71 | D4 | 1 | 1 | yes | characteristic |
| 69 | #14556056 | — | 2 | 4 | no | — |
| 70 | #14556054 | — | 2 | 4 | no | — |
| 71 | #14556054 | — | 4 | 2 | no | — |
| 72 | #14556053 | — | 4 | 1 | no | — |
| 73 | #14556050 | — | 4 | 1 | no | — |
| 74 | #14556047 | — | 2 | 1 | no | — |
| 75 | #14556047 | D4 | 1 | 2 | yes | complemented |
| 76 | C71⋊#95 | — | 2 | 1 | no | — |
| 77 | C71⋊#95 | — | 2 | 1 | no | — |
| 78 | C71⋊#95 | — | 2 | 1 | no | — |
| 79 | C22×Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 80 | C22×D4×C71 | D4 | 1 | 1 | yes | characteristic |
| 81 | C2×M16×C71 | — | 2 | 1 | no | — |
| 82 | C2×M16×C71 | — | 2 | 1 | no | — |
| 83 | #124×C71 | — | 2 | 1 | no | — |
| 84 | #124×C71 | — | 2 | 1 | no | — |
| 85 | #124×C71 | — | 2 | 1 | no | — |
| 86 | #124×C71 | — | 2 | 1 | no | — |
| 87 | C2×C22⋊C4×C71 | — | 2 | 1 | no | — |
| 88 | C2×C22⋊C4×C71 | — | 2 | 1 | no | — |
| 89 | C2×C42×C71 | D4 | 1 | 1 | yes | characteristic |
| 90 | #101×C71 | — | 2 | 1 | no | — |
| 91 | #101×C71 | — | 2 | 1 | no | — |
| 92 | #101×C71 | — | 2 | 1 | no | — |
| 93 | #101×C71 | D4 | 1 | 2 | yes | complemented |
| 94 | C23×D71 | — | 2 | 1 | no | — |
| 95 | #11765866 | — | 4 | 2 | no | — |
| 96 | #11765866 | — | 4 | 2 | no | — |
| 97 | #11765866 | — | 4 | 2 | no | — |
| 98 | #11765866 | — | 4 | 2 | no | — |
| 99 | #11765865 | — | 2 | 2 | no | — |
| 100 | #11765865 | — | 2 | 2 | no | — |
| 101 | #11765865 | — | 2 | 2 | no | — |
| 102 | #11765865 | — | 2 | 2 | no | — |
| 103 | #11765865 | — | 2 | 2 | no | — |
| 104 | #11765865 | — | 2 | 2 | no | — |
| 105 | #11765865 | — | 4 | 1 | no | — |
| 106 | #11765865 | — | 4 | 1 | no | — |
| 107 | #11765865 | — | 4 | 1 | no | — |
| 108 | #11765865 | — | 4 | 1 | no | — |
| 109 | #11765865 | — | 4 | 1 | no | — |
| 110 | #11765865 | — | 4 | 1 | no | — |
| 111 | C2×Dic142 | — | 2 | 1 | no | — |
| 112 | C2×Dic142 | — | 2 | 1 | no | — |
| 113 | C2×Dic142 | — | 2 | 1 | no | — |
| 114 | Q8×D71 | — | 4 | 2 | no | — |
| 115 | Q8×D71 | — | 4 | 2 | no | — |
| 116 | Q8×D71 | — | 4 | 2 | no | — |
| 117 | Q8×D71 | — | 4 | 2 | no | — |
| 118 | C2×D284 | — | 2 | 1 | no | — |
| 119 | C2×D284 | — | 2 | 1 | no | — |
| 120 | C2×D284 | — | 2 | 1 | no | — |
| 121 | C2×D284 | — | 2 | 1 | no | — |
| 122 | C2×D284 | — | 2 | 1 | no | — |
| 123 | C2×D284 | — | 4 | 1 | no | — |
| 124 | C2×D284 | — | 4 | 1 | no | — |
| 125 | C2×C22⋊D71 | — | 4 | 2 | no | — |
| 126 | C2×C22⋊D71 | — | 4 | 1 | no | — |
| 127 | C2×C22⋊D71 | — | 8 | 1 | no | — |
| 128 | C2×C22⋊D71 | — | 8 | 1 | no | — |
| 129 | C2×C22⋊D71 | — | 8 | 1 | no | — |
| 130 | C2×C22⋊D71 | — | 8 | 1 | no | — |
| 131 | C2×C22⋊D71 | — | 8 | 1 | no | — |
| 132 | C22×Dic71 | — | 2 | 1 | no | — |
| 133 | C22×Dic71 | — | 2 | 1 | no | — |
| 134 | C22×Dic71 | — | 2 | 1 | no | — |
| 135 | C2×C4×D71 | — | 4 | 1 | no | — |
| 136 | C2×C4×D71 | — | 4 | 1 | no | — |
| 137 | C2×C4×D71 | — | 4 | 1 | no | — |
| 138 | #11765854 | — | 4 | 4 | no | — |
| 139 | #11765853 | — | 4 | 4 | no | — |
| 140 | D568 | — | 4 | 4 | no | — |
| 141 | #11765850 | — | 4 | 4 | no | — |
| 142 | #11765849 | — | 2 | 2 | no | — |
| 143 | #11765849 | — | 4 | 1 | no | — |
| 144 | C2×C71⋊C8 | — | 4 | 1 | no | — |
| 145 | C4⋊Dic71 | — | 4 | 1 | no | — |
| 146 | Dic71⋊C4 | — | 8 | 1 | no | — |
| 147 | C22⋊Dic71 | — | 4 | 2 | no | — |
| 148 | C22⋊Dic71 | — | 8 | 1 | no | — |
| 149 | (C2×D71)⋊C4 | — | 4 | 2 | no | — |
| 150 | (C2×D71)⋊C4 | — | 4 | 1 | no | — |
| 151 | (C2×D71)⋊C4 | — | 4 | 1 | no | — |
| 152 | (C2×D71)⋊C4 | — | 4 | 1 | no | — |
| 153 | (C2×D71)⋊C4 | — | 4 | 1 | no | — |
| 154 | (C2×D71)⋊C4 | — | 8 | 1 | no | — |
| 155 | C4×Dic71 | — | 2 | 1 | no | — |
| 156 | C4×Dic71 | — | 2 | 1 | no | — |
| 157 | C4×Dic71 | — | 4 | 1 | no | — |
| 158 | C24×C71 | — | 2 | 1 | no | — |
| 159 | C2×Q8×C71 | — | 4 | 1 | no | — |
| 160 | C2×Q8×C71 | — | 4 | 1 | no | — |
| 161 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 162 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C2×Q8×C71 | #41 | 1 | 1 | yes | characteristic |
| 165 | C2×D4×C71 | — | 2 | 1 | no | — |
| 166 | C2×D4×C71 | — | 2 | 1 | no | — |
| 167 | C2×D4×C71 | — | 4 | 1 | no | — |
| 168 | C2×D4×C71 | — | 4 | 1 | no | — |
| 169 | C22×C4×C71 | — | 2 | 1 | no | — |
| 170 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 171 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | M16×C71 | — | 2 | 2 | no | — |
| 174 | M16×C71 | — | 4 | 1 | no | — |
| 175 | M16×C71 | — | 4 | 1 | no | — |
| 176 | M16×C71 | — | 4 | 1 | no | — |
| 177 | C2×C8×C71 | — | 4 | 1 | no | — |
| 178 | C2×C8×C71 | — | 4 | 1 | no | — |
| 179 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 180 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 181 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 182 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 183 | C42×C71 | — | 2 | 1 | no | — |
| 184 | C42×C71 | — | 2 | 1 | no | — |
| 185 | C23×C71 | — | 4 | 1 | no | — |
| 186 | C23×C71 | — | 4 | 1 | no | — |
| 187 | C23×C71 | — | 4 | 1 | no | — |
| 188 | C23×C71 | — | 4 | 1 | no | — |
| 189 | C23×C71 | — | 4 | 1 | no | — |
| 190 | C23×C71 | — | 4 | 1 | no | — |
| 191 | C23×C71 | — | 4 | 1 | no | — |
| 192 | C23×C71 | #120 | 1 | 1 | yes | characteristic |
| 193 | C22×D71 | — | 4 | 1 | no | — |
| 194 | C22×D71 | — | 4 | 1 | no | — |
| 195 | C22×D71 | — | 4 | 1 | no | — |
| 196 | C22×D71 | — | 4 | 1 | no | — |
| 197 | C22×D71 | — | 4 | 1 | no | — |
| 198 | C22×D71 | — | 4 | 1 | no | — |
| 199 | C22×D71 | — | 4 | 1 | no | — |
| 200 | C22×D71 | — | 4 | 1 | no | — |
| 201 | Q8×C71 | — | 4 | 1 | no | — |
| 202 | Q8×C71 | — | 4 | 1 | no | — |
| 203 | Q8×C71 | — | 4 | 1 | no | — |
| 204 | Q8×C71 | — | 4 | 1 | no | — |
| 205 | D4×C71 | — | 4 | 2 | no | — |
| 206 | D4×C71 | — | 8 | 1 | no | — |
| 207 | C2×C4×C71 | — | 2 | 1 | no | — |
| 208 | C2×C4×C71 | — | 2 | 1 | no | — |
| 209 | C2×C4×C71 | — | 2 | 1 | no | — |
| 210 | C2×C4×C71 | — | 2 | 1 | no | — |
| 211 | C2×C4×C71 | — | 2 | 1 | no | — |
| 212 | C2×C4×C71 | — | 2 | 1 | no | — |
| 213 | C2×C4×C71 | — | 4 | 1 | no | — |
| 214 | C2×C4×C71 | — | 4 | 1 | no | — |
| 215 | C2×C4×C71 | — | 4 | 1 | no | — |
| 216 | C2×C4×C71 | #120 | 1 | 1 | yes | characteristic |
| 217 | C2×C4×C71 | #120 | 1 | 1 | yes | characteristic |
| 218 | C2×C4×C71 | #121 | 1 | 1 | yes | characteristic |
| 219 | C2×C4×C71 | #121 | 1 | 1 | yes | characteristic |
| 220 | C2×C4×C71 | #121 | 1 | 1 | yes | characteristic |
| 221 | C2×C4×C71 | #127 | 1 | 1 | yes | characteristic |
| 222 | C22⋊D71 | — | 4 | 2 | no | — |
| 223 | C22⋊D71 | — | 4 | 2 | no | — |
| 224 | C22⋊D71 | — | 8 | 4 | no | — |
| 225 | C22⋊D71 | — | 8 | 4 | no | — |
| 226 | C2×Dic71 | — | 2 | 2 | no | — |
| 227 | C2×Dic71 | — | 4 | 1 | no | — |
| 228 | C2×Dic71 | — | 4 | 1 | no | — |
| 229 | C2×Dic71 | — | 4 | 1 | no | — |
| 230 | C2×Dic71 | — | 4 | 1 | no | — |
| 231 | C2×Dic71 | — | 4 | 1 | no | — |
| 232 | C2×Dic71 | — | 4 | 1 | no | — |
| 233 | C2×Dic71 | — | 4 | 1 | no | — |
| 234 | C2×Dic71 | — | 4 | 1 | no | — |
| 235 | C2×Dic71 | — | 4 | 1 | no | — |
| 236 | D284 | — | 2 | 2 | no | — |
| 237 | D284 | — | 2 | 2 | no | — |
| 238 | D284 | — | 2 | 2 | no | — |
| 239 | D284 | — | 4 | 1 | no | — |
| 240 | D284 | — | 4 | 1 | no | — |
| 241 | D284 | — | 4 | 1 | no | — |
| 242 | D284 | — | 4 | 2 | no | — |
| 243 | D284 | — | 8 | 1 | no | — |
| 244 | C4×D71 | — | 4 | 2 | no | — |
| 245 | C4×D71 | — | 4 | 2 | no | — |
| 246 | C4×D71 | — | 4 | 2 | no | — |
| 247 | C4×D71 | — | 4 | 2 | no | — |
| 248 | C4×D71 | — | 4 | 2 | no | — |
| 249 | C4×D71 | — | 4 | 2 | no | — |
| 250 | Dic142 | — | 2 | 2 | no | — |
| 251 | Dic142 | — | 2 | 2 | no | — |
| 252 | Dic142 | — | 2 | 2 | no | — |
| 253 | Dic142 | — | 4 | 1 | no | — |
| 254 | Dic142 | — | 4 | 1 | no | — |
| 255 | Dic142 | — | 4 | 1 | no | — |
| 256 | C8×C71 | — | 4 | 2 | no | — |
| 257 | C8×C71 | — | 8 | 1 | no | — |
| 258 | C71⋊C8 | — | 4 | 2 | no | — |
| 259 | C22×C71 | — | 2 | 1 | no | — |
| 260 | C22×C71 | — | 2 | 1 | no | — |
| 261 | C22×C71 | — | 8 | 1 | no | — |
| 262 | C22×C71 | — | 8 | 1 | no | — |
| 263 | C22×C71 | — | 8 | 1 | no | — |
| 264 | C22×C71 | — | 8 | 1 | no | — |
| 265 | C22×C71 | — | 8 | 1 | no | — |
| 266 | C22×C71 | — | 8 | 1 | no | — |
| 267 | C22×C71 | — | 8 | 1 | no | — |
| 268 | C22×C71 | #392 | 1 | 1 | yes | characteristic |
| 269 | C22×C71 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 270 | C22×C71 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 271 | C2×D71 | — | 4 | 2 | no | — |
| 272 | C2×D71 | — | 8 | 1 | no | — |
| 273 | C2×D71 | — | 8 | 1 | no | — |
| 274 | C2×D71 | — | 8 | 1 | no | — |
| 275 | C2×D71 | — | 8 | 1 | no | — |
| 276 | C2×D71 | — | 8 | 1 | no | — |
| 277 | C2×D71 | — | 8 | 1 | no | — |
| 278 | C2×D71 | — | 8 | 1 | no | — |
| 279 | C2×D71 | — | 8 | 1 | no | — |
| 280 | C2×D71 | — | 8 | 1 | no | — |
| 281 | C4×C71 | — | 2 | 1 | no | — |
| 282 | C4×C71 | — | 2 | 1 | no | — |
| 283 | C4×C71 | — | 2 | 1 | no | — |
| 284 | C4×C71 | — | 2 | 1 | no | — |
| 285 | C4×C71 | — | 2 | 1 | no | — |
| 286 | C4×C71 | — | 2 | 1 | no | — |
| 287 | C4×C71 | — | 8 | 1 | no | — |
| 288 | Dic71 | — | 4 | 2 | no | — |
| 289 | Dic71 | — | 4 | 2 | no | — |
| 290 | Dic71 | — | 8 | 1 | no | — |
| 291 | Dic71 | — | 8 | 1 | no | — |
| 292 | #13357 | — | 71 | 1 | no | maximal, Sylow |
| 293 | C2×C71 | — | 2 | 1 | no | — |
| 294 | C2×C71 | — | 2 | 1 | no | — |
| 295 | C2×C71 | — | 16 | 1 | no | — |
| 296 | C2×C71 | #2021 | 1 | 1 | yes | characteristic |
| 297 | C2×C71 | #2202 | 1 | 1 | yes | characteristic |
| 298 | C2×C71 | #2204 | 1 | 1 | yes | characteristic |
| 299 | D71 | — | 8 | 2 | no | — |
| 300 | D71 | — | 16 | 1 | no | — |
| 301 | C2×#454 | — | 71 | 1 | no | — |
| 302 | C2×#454 | — | 71 | 1 | no | — |
| 303 | #2733 | — | 71 | 1 | no | — |
| 304 | C2×#355 | — | 71 | 1 | no | — |
| 305 | C2×#355 | D71 | 1 | 1 | yes | characteristic, complemented |
| 306 | #1793 | — | 71 | 1 | no | — |
| 307 | #1394 | — | 71 | 1 | no | — |
| 308 | C71 | #13357 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 309 | C2×2−1+4 | — | 71 | 1 | no | — |
| 310 | C2×AGL(1,ℤ/8) | — | 142 | 1 | no | — |
| 311 | C2×AGL(1,ℤ/8) | — | 142 | 1 | no | — |
| 312 | C2×#124 | — | 71 | 1 | no | — |
| 313 | C2×#124 | C2×D71 | 1 | 1 | yes | characteristic |
| 314 | #454 | — | 142 | 2 | no | — |
| 315 | #454 | — | 142 | 2 | no | — |
| 316 | #454 | — | 142 | 2 | no | — |
| 317 | #454 | — | 142 | 2 | no | — |
| 318 | C2×#104 | — | 142 | 1 | no | — |
| 319 | C2×#104 | — | 142 | 1 | no | — |
| 320 | C2×#104 | — | 142 | 1 | no | — |
| 321 | #417 | — | 142 | 1 | no | — |
| 322 | C2×#101 | — | 71 | 1 | no | — |
| 323 | C2×#101 | C2×D71 | 1 | 1 | yes | characteristic |
| 324 | C2×#101 | C2×D71 | 1 | 1 | yes | characteristic |
| 325 | #394 | — | 142 | 1 | no | — |
| 326 | #392 | — | 142 | 1 | no | — |
| 327 | #392 | — | 142 | 1 | no | — |
| 328 | #391 | — | 71 | 1 | no | — |
| 329 | #390 | — | 142 | 1 | no | — |
| 330 | #388 | — | 142 | 1 | no | — |
| 331 | #388 | — | 142 | 1 | no | — |
| 332 | #355 | — | 2 | 2 | no | — |
| 333 | #355 | — | 142 | 2 | no | — |
| 334 | 2−1+4 | — | 284 | 2 | no | — |
| 335 | 2−1+4 | — | 71 | 2 | no | — |
| 336 | 2−1+4 | — | 142 | 1 | no | — |
| 337 | 2−1+4 | — | 142 | 1 | no | — |
| 338 | 2−1+4 | — | 142 | 1 | no | — |
| 339 | C2×#41 | — | 284 | 1 | no | — |
| 340 | C2×#41 | — | 142 | 1 | no | — |
| 341 | C2×#41 | — | 142 | 1 | no | — |
| 342 | C2×#41 | — | 142 | 1 | no | — |
| 343 | C22×Q8 | — | 284 | 1 | no | — |
| 344 | C22×Q8 | C22×D71 | 1 | 1 | yes | characteristic |
| 345 | C22×D4 | — | 71 | 1 | no | — |
| 346 | C22×D4 | — | 142 | 1 | no | — |
| 347 | C22×D4 | — | 142 | 1 | no | — |
| 348 | C22×D4 | D284 | 1 | 1 | yes | characteristic |
| 349 | AGL(1,ℤ/8) | — | 284 | 2 | no | — |
| 350 | AGL(1,ℤ/8) | — | 284 | 2 | no | — |
| 351 | AGL(1,ℤ/8) | — | 142 | 4 | no | — |
| 352 | AGL(1,ℤ/8) | — | 142 | 4 | no | — |
| 353 | C2×SD16 | — | 284 | 1 | no | — |
| 354 | C2×SD16 | — | 284 | 1 | no | — |
| 355 | C2×D8 | — | 284 | 1 | no | — |
| 356 | C2×D8 | — | 284 | 1 | no | — |
| 357 | C2×M16 | — | 2 | 1 | no | — |
| 358 | C2×M16 | — | 2 | 1 | no | — |
| 359 | C2×M16 | — | 142 | 1 | no | — |
| 360 | #124 | — | 2 | 1 | no | — |
| 361 | #124 | — | 2 | 1 | no | — |
| 362 | #124 | — | 2 | 1 | no | — |
| 363 | #124 | — | 2 | 1 | no | — |
| 364 | #124 | — | 142 | 1 | no | — |
| 365 | #124 | — | 142 | 1 | no | — |
| 366 | #124 | — | 142 | 1 | no | — |
| 367 | #124 | — | 142 | 1 | no | — |
| 368 | C2×C4⋊C4 | — | 71 | 1 | no | — |
| 369 | C2×C4⋊C4 | — | 142 | 1 | no | — |
| 370 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 371 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 372 | C2×C22⋊C4 | — | 142 | 1 | no | — |
| 373 | C2×C22⋊C4 | — | 142 | 1 | no | — |
| 374 | C2×C22⋊C4 | — | 142 | 1 | no | — |
| 375 | C2×C22⋊C4 | — | 142 | 1 | no | — |
| 376 | C2×C22⋊C4 | — | 142 | 1 | no | — |
| 377 | C2×C22⋊C4 | — | 142 | 1 | no | — |
| 378 | C2×C42 | — | 71 | 1 | no | — |
| 379 | C2×C42 | — | 71 | 1 | no | — |
| 380 | C2×C42 | D284 | 1 | 1 | yes | characteristic |
| 381 | #104 | — | 284 | 2 | no | — |
| 382 | #104 | — | 142 | 4 | no | — |
| 383 | #104 | — | 142 | 4 | no | — |
| 384 | #103 | — | 284 | 1 | no | — |
| 385 | #102 | — | 284 | 1 | no | — |
| 386 | #101 | — | 2 | 1 | no | — |
| 387 | #101 | — | 2 | 1 | no | — |
| 388 | #101 | — | 2 | 1 | no | — |
| 389 | #101 | — | 71 | 2 | no | — |
| 390 | #101 | — | 142 | 1 | no | — |
| 391 | #101 | C22⋊D71 | 1 | 2 | yes | complemented |
| 392 | #95 | — | 142 | 1 | no | — |
| 393 | #95 | — | 142 | 1 | no | — |
| 394 | #95 | — | 142 | 1 | no | — |
| 395 | C24 | — | 2 | 1 | no | — |
| 396 | C24 | — | 142 | 1 | no | — |
| 397 | #41 | — | 284 | 1 | no | — |
| 398 | #41 | — | 284 | 1 | no | — |
| 399 | #41 | — | 284 | 1 | no | — |
| 400 | #41 | — | 284 | 2 | no | — |
| 401 | #41 | — | 284 | 2 | no | — |
| 402 | #41 | — | 284 | 2 | no | — |
| 403 | #41 | — | 284 | 2 | no | — |
| 404 | #41 | — | 284 | 1 | no | — |
| 405 | #41 | — | 284 | 1 | no | — |
| 406 | #41 | — | 284 | 1 | no | — |
| 407 | #41 | — | 142 | 2 | no | — |
| 408 | #41 | — | 142 | 2 | no | — |
| 409 | #41 | — | 142 | 2 | no | — |
| 410 | #41 | — | 142 | 2 | no | — |
| 411 | #41 | — | 142 | 2 | no | — |
| 412 | #41 | — | 142 | 2 | no | — |
| 413 | C2×Q8 | — | 4 | 1 | no | — |
| 414 | C2×Q8 | — | 4 | 1 | no | — |
| 415 | C2×Q8 | — | 284 | 2 | no | — |
| 416 | C2×Q8 | — | 284 | 2 | no | — |
| 417 | C2×Q8 | — | 284 | 2 | no | — |
| 418 | C2×Q8 | — | 284 | 2 | no | — |
| 419 | C2×Q8 | — | 142 | 1 | no | — |
| 420 | C2×Q8 | — | 142 | 1 | no | — |
| 421 | C2×Q8 | — | 142 | 1 | no | — |
| 422 | C2×Q8 | D4×D71 | 1 | 1 | yes | characteristic |
| 423 | C2×Q8 | D4×D71 | 1 | 1 | yes | characteristic |
| 424 | C2×Q8 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 425 | C2×Q8 | #11765865 | 1 | 1 | yes | characteristic |
| 426 | C2×D4 | — | 2 | 1 | no | — |
| 427 | C2×D4 | — | 2 | 1 | no | — |
| 428 | C2×D4 | — | 4 | 1 | no | — |
| 429 | C2×D4 | — | 4 | 1 | no | — |
| 430 | C2×D4 | — | 284 | 1 | no | — |
| 431 | C2×D4 | — | 284 | 1 | no | — |
| 432 | C2×D4 | — | 284 | 1 | no | — |
| 433 | C2×D4 | — | 284 | 2 | no | — |
| 434 | C2×D4 | — | 568 | 1 | no | — |
| 435 | C2×D4 | — | 568 | 1 | no | — |
| 436 | C2×D4 | — | 568 | 1 | no | — |
| 437 | C2×D4 | — | 568 | 1 | no | — |
| 438 | C2×D4 | — | 568 | 1 | no | — |
| 439 | C2×D4 | — | 142 | 1 | no | — |
| 440 | C2×D4 | — | 142 | 1 | no | — |
| 441 | C2×D4 | — | 142 | 1 | no | — |
| 442 | C2×D4 | — | 142 | 1 | no | — |
| 443 | C2×D4 | — | 142 | 1 | no | — |
| 444 | C22×C4 | — | 2 | 1 | no | — |
| 445 | C22×C4 | — | 284 | 1 | no | — |
| 446 | C22×C4 | — | 284 | 1 | no | — |
| 447 | C22×C4 | — | 284 | 1 | no | — |
| 448 | C22×C4 | — | 142 | 1 | no | — |
| 449 | C22×C4 | — | 142 | 1 | no | — |
| 450 | C22×C4 | — | 142 | 1 | no | — |
| 451 | C22×C4 | D4×D71 | 1 | 1 | yes | characteristic |
| 452 | C22×C4 | D4×D71 | 1 | 1 | yes | characteristic |
| 453 | C22×C4 | C2×D284 | 1 | 1 | yes | characteristic |
| 454 | SD16 | — | 284 | 4 | no | — |
| 455 | SD16 | — | 284 | 4 | no | — |
| 456 | D8 | — | 284 | 4 | no | — |
| 457 | D8 | — | 284 | 4 | no | — |
| 458 | M16 | — | 2 | 2 | no | — |
| 459 | M16 | — | 4 | 1 | no | — |
| 460 | M16 | — | 4 | 1 | no | — |
| 461 | M16 | — | 4 | 1 | no | — |
| 462 | M16 | — | 284 | 1 | no | — |
| 463 | M16 | — | 142 | 2 | no | — |
| 464 | C2×C8 | — | 4 | 1 | no | — |
| 465 | C2×C8 | — | 4 | 1 | no | — |
| 466 | C2×C8 | — | 284 | 1 | no | — |
| 467 | C4⋊C4 | — | 284 | 1 | no | — |
| 468 | C4⋊C4 | — | 568 | 1 | no | — |
| 469 | C22⋊C4 | — | 4 | 1 | no | — |
| 470 | C22⋊C4 | — | 4 | 1 | no | — |
| 471 | C22⋊C4 | — | 4 | 1 | no | — |
| 472 | C22⋊C4 | — | 4 | 1 | no | — |
| 473 | C22⋊C4 | — | 284 | 2 | no | — |
| 474 | C22⋊C4 | — | 284 | 2 | no | — |
| 475 | C22⋊C4 | — | 284 | 1 | no | — |
| 476 | C22⋊C4 | — | 284 | 1 | no | — |
| 477 | C22⋊C4 | — | 284 | 1 | no | — |
| 478 | C22⋊C4 | — | 284 | 1 | no | — |
| 479 | C22⋊C4 | — | 568 | 1 | no | — |
| 480 | C22⋊C4 | — | 568 | 1 | no | — |
| 481 | C42 | — | 2 | 1 | no | — |
| 482 | C42 | — | 2 | 1 | no | — |
| 483 | C42 | — | 284 | 1 | no | — |
| 484 | C42 | — | 142 | 1 | no | — |
| 485 | C42 | — | 142 | 1 | no | — |
| 486 | C23 | — | 4 | 1 | no | — |
| 487 | C23 | — | 4 | 1 | no | — |
| 488 | C23 | — | 4 | 1 | no | — |
| 489 | C23 | — | 4 | 1 | no | — |
| 490 | C23 | — | 4 | 1 | no | — |
| 491 | C23 | — | 4 | 1 | no | — |
| 492 | C23 | — | 4 | 1 | no | — |
| 493 | C23 | — | 284 | 1 | no | — |
| 494 | C23 | — | 284 | 1 | no | — |
| 495 | C23 | — | 284 | 1 | no | — |
| 496 | C23 | — | 284 | 1 | no | — |
| 497 | C23 | — | 284 | 1 | no | — |
| 498 | C23 | — | 284 | 1 | no | — |
| 499 | C23 | — | 284 | 1 | no | — |
| 500 | C23 | — | 284 | 1 | no | — |
| 501 | C23 | #14556098 | 1 | 1 | yes | characteristic |
| 502 | Q8 | — | 4 | 1 | no | — |
| 503 | Q8 | — | 4 | 1 | no | — |
| 504 | Q8 | — | 4 | 1 | no | — |
| 505 | Q8 | — | 4 | 1 | no | — |
| 506 | Q8 | — | 284 | 1 | no | — |
| 507 | Q8 | — | 284 | 1 | no | — |
| 508 | Q8 | — | 284 | 1 | no | — |
| 509 | Q8 | — | 142 | 2 | no | — |
| 510 | Q8 | — | 142 | 2 | no | — |
| 511 | Q8 | — | 142 | 2 | no | — |
| 512 | D4 | — | 4 | 2 | no | — |
| 513 | D4 | — | 8 | 1 | no | — |
| 514 | D4 | — | 284 | 1 | no | — |
| 515 | D4 | — | 284 | 1 | no | — |
| 516 | D4 | — | 284 | 1 | no | — |
| 517 | D4 | — | 284 | 2 | no | — |
| 518 | D4 | — | 284 | 2 | no | — |
| 519 | D4 | — | 284 | 2 | no | — |
| 520 | D4 | — | 568 | 1 | no | — |
| 521 | D4 | — | 568 | 4 | no | — |
| 522 | D4 | — | 568 | 4 | no | — |
| 523 | D4 | — | 142 | 2 | no | — |
| 524 | D4 | — | 142 | 2 | no | — |
| 525 | D4 | — | 142 | 2 | no | — |
| 526 | C2×C4 | — | 2 | 1 | no | — |
| 527 | C2×C4 | — | 2 | 1 | no | — |
| 528 | C2×C4 | — | 2 | 1 | no | — |
| 529 | C2×C4 | — | 2 | 1 | no | — |
| 530 | C2×C4 | — | 2 | 1 | no | — |
| 531 | C2×C4 | — | 2 | 1 | no | — |
| 532 | C2×C4 | — | 4 | 1 | no | — |
| 533 | C2×C4 | — | 4 | 1 | no | — |
| 534 | C2×C4 | — | 4 | 1 | no | — |
| 535 | C2×C4 | — | 284 | 2 | no | — |
| 536 | C2×C4 | — | 284 | 2 | no | — |
| 537 | C2×C4 | — | 284 | 2 | no | — |
| 538 | C2×C4 | — | 284 | 2 | no | — |
| 539 | C2×C4 | — | 284 | 2 | no | — |
| 540 | C2×C4 | — | 284 | 2 | no | — |
| 541 | C2×C4 | — | 284 | 1 | no | — |
| 542 | C2×C4 | — | 284 | 1 | no | — |
| 543 | C2×C4 | — | 284 | 1 | no | — |
| 544 | C2×C4 | — | 284 | 1 | no | — |
| 545 | C2×C4 | — | 284 | 1 | no | — |
| 546 | C2×C4 | — | 284 | 1 | no | — |
| 547 | C2×C4 | — | 284 | 1 | no | — |
| 548 | C2×C4 | — | 284 | 1 | no | — |
| 549 | C2×C4 | — | 284 | 1 | no | — |
| 550 | C2×C4 | — | 142 | 2 | no | — |
| 551 | C2×C4 | #14556096 | 1 | 1 | yes | characteristic |
| 552 | C2×C4 | #14556098 | 1 | 1 | yes | characteristic |
| 553 | C2×C4 | #14556101 | 1 | 1 | yes | characteristic |
| 554 | C2×C4 | #14556101 | 1 | 1 | yes | characteristic |
| 555 | C2×C4 | #14556102 | 1 | 1 | yes | characteristic |
| 556 | C2×C4 | #14556124 | 1 | 1 | yes | characteristic |
| 557 | C8 | — | 4 | 2 | no | — |
| 558 | C8 | — | 8 | 1 | no | — |
| 559 | C8 | — | 284 | 2 | no | — |
| 560 | C22 | — | 2 | 1 | no | — |
| 561 | C22 | — | 2 | 1 | no | — |
| 562 | C22 | — | 8 | 1 | no | — |
| 563 | C22 | — | 8 | 1 | no | — |
| 564 | C22 | — | 8 | 1 | no | — |
| 565 | C22 | — | 8 | 1 | no | — |
| 566 | C22 | — | 8 | 1 | no | — |
| 567 | C22 | — | 8 | 1 | no | — |
| 568 | C22 | — | 8 | 1 | no | — |
| 569 | C22 | — | 284 | 2 | no | — |
| 570 | C22 | — | 568 | 1 | no | — |
| 571 | C22 | — | 568 | 1 | no | — |
| 572 | C22 | — | 568 | 1 | no | — |
| 573 | C22 | — | 568 | 1 | no | — |
| 574 | C22 | — | 568 | 1 | no | — |
| 575 | C22 | — | 568 | 1 | no | — |
| 576 | C22 | — | 568 | 1 | no | — |
| 577 | C22 | — | 568 | 1 | no | — |
| 578 | C22 | — | 568 | 1 | no | — |
| 579 | C22 | #17985908 | 1 | 1 | yes | characteristic |
| 580 | C22 | #17986187 | 1 | 1 | yes | characteristic |
| 581 | C22 | #17986187 | 1 | 1 | yes | characteristic |
| 582 | C4 | — | 2 | 1 | no | — |
| 583 | C4 | — | 2 | 1 | no | — |
| 584 | C4 | — | 2 | 1 | no | — |
| 585 | C4 | — | 2 | 1 | no | — |
| 586 | C4 | — | 2 | 1 | no | — |
| 587 | C4 | — | 2 | 1 | no | — |
| 588 | C4 | — | 8 | 1 | no | — |
| 589 | C4 | — | 284 | 2 | no | — |
| 590 | C4 | — | 284 | 2 | no | — |
| 591 | C4 | — | 568 | 1 | no | — |
| 592 | C4 | — | 568 | 1 | no | — |
| 593 | C2 | — | 2 | 1 | no | — |
| 594 | C2 | — | 2 | 1 | no | — |
| 595 | C2 | — | 16 | 1 | no | — |
| 596 | C2 | — | 568 | 2 | no | — |
| 597 | C2 | — | 1136 | 1 | no | — |
| 598 | C2 | #22589465 | 1 | 1 | yes | characteristic |
| 599 | C2 | #22590358 | 1 | 1 | yes | characteristic |
| 600 | C2 | #22590367 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#17986174 | C2 | semidirect |
| 2. C2×#17986171 | C2 | semidirect |
| 3. #22595364 | C2 | semidirect |
| 4. C2×#17985795 | C2 | semidirect |
| 5. #22588301 | C2 | semidirect |
| 6. #22586466 | C2 | semidirect |
| 7. C2×#355×C71 | C2 | semidirect |
| 37. #14556176 | D4 | semidirect |
| 75. #14556047 | D4 | semidirect |
| 93. #101×C71 | D4 | semidirect |
| 305. C2×#355 | D71 | semidirect |
| 308. C71 | #13357 | semidirect |
| 391. #101 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986174 | 2 |
| C2×#17986171 | 2 |
| #22595364 | 2 |
| C2×#17985795 | 2 |
| #22588301 | 2 |
| #22586466 | 2 |
| C2×#355×C71 | 2 |
| #13357 | 71 |