Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
2502 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 211 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 | #22601975 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C22×#14556124 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#17986169 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22597570 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22589357 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #22588781 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22588736 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C71×#1783 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#14556173 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C23×D284 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C23×C22⋊D71 | — | 2 | 2 | no | — |
| 12 | C2×#14556156 | C22 | 1 | 4 | yes | complemented |
| 13 | #17986643 | — | 2 | 4 | no | — |
| 14 | D4×C22⋊D71 | — | 2 | 4 | no | — |
| 15 | #17986566 | C22 | 1 | 2 | yes | complemented |
| 16 | #17986558 | — | 2 | 2 | no | — |
| 17 | C2×#14556124 | — | 2 | 8 | no | — |
| 18 | C2×#14556124 | — | 2 | 2 | no | — |
| 19 | C2×#14556124 | C22 | 1 | 2 | yes | — |
| 20 | C2×#14556124 | C22 | 1 | 2 | yes | complemented |
| 21 | #17986510 | C22 | 1 | 2 | yes | — |
| 22 | C2×#14556097 | — | 2 | 2 | no | — |
| 23 | #17986474 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C22×C4×Dic71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #17986169 | — | 2 | 8 | no | — |
| 26 | #17986152 | — | 2 | 4 | no | — |
| 27 | #17986135 | — | 2 | 4 | no | — |
| 28 | C2×#14556054 | C22 | 1 | 4 | yes | complemented |
| 29 | #17986005 | C22 | 1 | 4 | yes | complemented |
| 30 | #17985760 | C22 | 1 | 4 | yes | complemented |
| 31 | C23×D4×C71 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#100×C71 | C22 | 1 | 2 | yes | complemented |
| 33 | C2×#100×C71 | C22 | 1 | 2 | yes | complemented |
| 34 | #407×C71 | C22 | 1 | 2 | yes | complemented |
| 35 | C24×D71 | — | 2 | 1 | no | — |
| 36 | #14556173 | — | 2 | 4 | no | — |
| 37 | #14556173 | — | 4 | 2 | no | — |
| 38 | C2×#11765865 | C23 | 1 | 2 | yes | — |
| 39 | C2×#11765864 | — | 2 | 2 | no | — |
| 40 | C22×D284 | — | 2 | 4 | no | — |
| 41 | C22×D284 | — | 2 | 1 | no | — |
| 42 | C22×D284 | — | 2 | 4 | no | — |
| 43 | C22×D284 | — | 4 | 2 | no | — |
| 44 | C22×D284 | C23 | 1 | 2 | yes | — |
| 45 | C22×C22⋊D71 | — | 2 | 16 | no | — |
| 46 | C22×C22⋊D71 | — | 2 | 4 | no | — |
| 47 | C22×C22⋊D71 | — | 2 | 4 | no | — |
| 48 | C22×C22⋊D71 | — | 2 | 4 | no | — |
| 49 | C22×C22⋊D71 | — | 2 | 2 | no | — |
| 50 | C22×C22⋊D71 | — | 4 | 16 | no | — |
| 51 | C2×D4×D71 | — | 2 | 2 | no | — |
| 52 | C23×Dic71 | — | 2 | 1 | no | — |
| 53 | #14556156 | — | 2 | 8 | no | — |
| 54 | #14556156 | — | 4 | 4 | no | — |
| 55 | C2×#11765854 | — | 2 | 4 | no | — |
| 56 | C2×D568 | — | 2 | 4 | no | — |
| 57 | #14556124 | — | 2 | 16 | no | — |
| 58 | #14556124 | — | 2 | 2 | no | — |
| 59 | #14556124 | — | 2 | 4 | no | — |
| 60 | #14556124 | — | 2 | 4 | no | — |
| 61 | #14556124 | — | 2 | 4 | no | — |
| 62 | #14556124 | D4 | 1 | 8 | yes | complemented |
| 63 | #14556115 | — | 2 | 2 | no | — |
| 64 | #14556111 | — | 2 | 2 | no | — |
| 65 | #14556109 | — | 2 | 4 | no | — |
| 66 | #14556107 | D4 | 1 | 4 | yes | complemented |
| 67 | #14556102 | D4 | 1 | 4 | yes | complemented |
| 68 | #14556100 | — | 2 | 8 | no | — |
| 69 | #14556099 | — | 2 | 4 | no | — |
| 70 | #14556097 | — | 2 | 8 | no | — |
| 71 | #14556097 | — | 2 | 4 | no | — |
| 72 | #14556097 | — | 2 | 2 | no | — |
| 73 | #14556096 | — | 2 | 4 | no | — |
| 74 | D4×Dic71 | — | 2 | 4 | no | — |
| 75 | C4×C22⋊D71 | — | 2 | 4 | no | — |
| 76 | #14556087 | C23 | 1 | 2 | yes | — |
| 77 | C2×C22⋊Dic71 | — | 2 | 4 | no | — |
| 78 | C2×C22⋊Dic71 | — | 2 | 2 | no | — |
| 79 | C2×C4×Dic71 | — | 2 | 4 | no | — |
| 80 | C2×C4×Dic71 | — | 2 | 1 | no | — |
| 81 | C2×C4×Dic71 | C23 | 1 | 2 | yes | — |
| 82 | #14556054 | — | 2 | 8 | no | — |
| 83 | #14556050 | — | 2 | 8 | no | — |
| 84 | C25×C71 | D4 | 1 | 2 | yes | — |
| 85 | C22×D4×C71 | — | 2 | 4 | no | — |
| 86 | C22×D4×C71 | — | 2 | 4 | no | — |
| 87 | C22×D4×C71 | — | 4 | 2 | no | — |
| 88 | C22×D4×C71 | D4 | 1 | 2 | yes | — |
| 89 | C22×D4×C71 | C23 | 1 | 1 | yes | characteristic |
| 90 | C22×D4×C71 | C23 | 1 | 1 | yes | characteristic |
| 91 | C23×C4×C71 | C23 | 1 | 1 | yes | characteristic |
| 92 | C2×M16×C71 | C23 | 1 | 4 | yes | — |
| 93 | #100×C71 | — | 2 | 4 | no | — |
| 94 | #100×C71 | — | 4 | 2 | no | — |
| 95 | C22⋊C8×C71 | — | 2 | 4 | no | — |
| 96 | C23×D71 | — | 2 | 4 | no | — |
| 97 | C23×D71 | — | 2 | 2 | no | — |
| 98 | C23×D71 | — | 2 | 2 | no | — |
| 99 | C23×D71 | — | 4 | 8 | no | — |
| 100 | C23×D71 | — | 4 | 2 | no | — |
| 101 | C23×D71 | — | 4 | 2 | no | — |
| 102 | #11765865 | — | 2 | 4 | no | — |
| 103 | #11765865 | — | 2 | 4 | no | — |
| 104 | #11765864 | — | 4 | 8 | no | — |
| 105 | C2×Dic142 | C2×D4 | 1 | 2 | yes | complemented |
| 106 | C2×D284 | — | 2 | 4 | no | — |
| 107 | C2×D284 | — | 2 | 4 | no | — |
| 108 | C2×D284 | — | 2 | 4 | no | — |
| 109 | C2×D284 | — | 2 | 2 | no | — |
| 110 | C2×D284 | — | 4 | 16 | no | — |
| 111 | C2×D284 | — | 4 | 2 | no | — |
| 112 | C2×D284 | — | 4 | 2 | no | — |
| 113 | C2×D284 | C2×D4 | 1 | 2 | yes | complemented |
| 114 | C2×D284 | C2×D4 | 1 | 4 | yes | complemented |
| 115 | C2×C22⋊D71 | — | 2 | 4 | no | — |
| 116 | C2×C22⋊D71 | — | 2 | 16 | no | — |
| 117 | C2×C22⋊D71 | — | 2 | 16 | no | — |
| 118 | C2×C22⋊D71 | — | 2 | 4 | no | — |
| 119 | C2×C22⋊D71 | — | 2 | 2 | no | — |
| 120 | C2×C22⋊D71 | — | 2 | 8 | no | — |
| 121 | C2×C22⋊D71 | — | 4 | 16 | no | — |
| 122 | C2×C22⋊D71 | — | 4 | 16 | no | — |
| 123 | C2×C22⋊D71 | — | 4 | 64 | no | — |
| 124 | C2×C22⋊D71 | — | 4 | 4 | no | — |
| 125 | C2×C22⋊D71 | — | 4 | 4 | no | — |
| 126 | C2×C22⋊D71 | — | 8 | 8 | no | — |
| 127 | D4×D71 | — | 4 | 8 | no | — |
| 128 | C22×Dic71 | — | 2 | 4 | no | — |
| 129 | C22×Dic71 | — | 2 | 8 | no | — |
| 130 | C22×Dic71 | — | 2 | 2 | no | — |
| 131 | C22×Dic71 | — | 2 | 2 | no | — |
| 132 | C22×Dic71 | — | 2 | 4 | no | — |
| 133 | C2×C4×D71 | — | 2 | 2 | no | — |
| 134 | #11765854 | — | 4 | 8 | no | — |
| 135 | D568 | — | 4 | 8 | no | — |
| 136 | C4⋊Dic71 | C2×D4 | 1 | 4 | yes | complemented |
| 137 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 138 | C22⋊Dic71 | — | 2 | 4 | no | — |
| 139 | C22⋊Dic71 | — | 2 | 8 | no | — |
| 140 | C22⋊Dic71 | — | 2 | 4 | no | — |
| 141 | C22⋊Dic71 | — | 2 | 2 | no | — |
| 142 | (C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 143 | C4×Dic71 | — | 2 | 4 | no | — |
| 144 | C4×Dic71 | — | 2 | 2 | no | — |
| 145 | C4×Dic71 | — | 2 | 2 | no | — |
| 146 | C4×Dic71 | C2×D4 | 1 | 4 | yes | complemented |
| 147 | C24×C71 | — | 2 | 4 | no | — |
| 148 | C24×C71 | — | 2 | 4 | no | — |
| 149 | C24×C71 | — | 4 | 2 | no | — |
| 150 | C24×C71 | — | 4 | 8 | no | — |
| 151 | C24×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 152 | C24×C71 | C2×D4 | 1 | 2 | yes | — |
| 153 | C24×C71 | C2×D4 | 1 | 2 | yes | — |
| 154 | C2×D4×C71 | — | 2 | 4 | no | — |
| 155 | C2×D4×C71 | — | 2 | 4 | no | — |
| 156 | C2×D4×C71 | — | 2 | 2 | no | — |
| 157 | C2×D4×C71 | — | 2 | 2 | no | — |
| 158 | C2×D4×C71 | — | 2 | 2 | no | — |
| 159 | C2×D4×C71 | — | 2 | 2 | no | — |
| 160 | C2×D4×C71 | — | 2 | 2 | no | — |
| 161 | C2×D4×C71 | — | 4 | 16 | no | — |
| 162 | C2×D4×C71 | — | 4 | 2 | no | — |
| 163 | C2×D4×C71 | C2×D4 | 1 | 4 | yes | — |
| 164 | C22×C4×C71 | — | 2 | 2 | no | — |
| 165 | C22×C4×C71 | — | 2 | 2 | no | — |
| 166 | C22×C4×C71 | C2×D4 | 1 | 4 | yes | — |
| 167 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 169 | M16×C71 | — | 2 | 4 | no | — |
| 170 | M16×C71 | — | 2 | 4 | no | — |
| 171 | C2×C8×C71 | — | 2 | 4 | no | — |
| 172 | C23×C71 | — | 2 | 1 | no | — |
| 173 | C23×C71 | — | 2 | 1 | no | — |
| 174 | C23×C71 | — | 2 | 4 | no | — |
| 175 | C23×C71 | — | 2 | 2 | no | — |
| 176 | C23×C71 | — | 2 | 2 | no | — |
| 177 | C23×C71 | — | 2 | 2 | no | — |
| 178 | C23×C71 | — | 2 | 2 | no | — |
| 179 | C23×C71 | — | 2 | 2 | no | — |
| 180 | C23×C71 | — | 4 | 8 | no | — |
| 181 | C23×C71 | — | 4 | 4 | no | — |
| 182 | C23×C71 | — | 4 | 4 | no | — |
| 183 | C23×C71 | — | 4 | 16 | no | — |
| 184 | C23×C71 | — | 4 | 8 | no | — |
| 185 | C23×C71 | — | 8 | 4 | no | — |
| 186 | C23×C71 | — | 8 | 8 | no | — |
| 187 | C23×C71 | #120 | 1 | 2 | yes | — |
| 188 | C23×C71 | #120 | 1 | 4 | yes | — |
| 189 | C23×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 190 | C22×D71 | — | 2 | 2 | no | — |
| 191 | C22×D71 | — | 2 | 4 | no | — |
| 192 | C22×D71 | — | 4 | 16 | no | — |
| 193 | C22×D71 | — | 4 | 8 | no | — |
| 194 | C22×D71 | — | 4 | 8 | no | — |
| 195 | C22×D71 | — | 4 | 2 | no | — |
| 196 | C22×D71 | — | 4 | 2 | no | — |
| 197 | C22×D71 | — | 4 | 4 | no | — |
| 198 | C22×D71 | — | 8 | 4 | no | — |
| 199 | C22×D71 | — | 8 | 8 | no | — |
| 200 | C22×D71 | — | 8 | 4 | no | — |
| 201 | C22×D71 | — | 8 | 4 | no | — |
| 202 | D4×C71 | — | 2 | 8 | no | — |
| 203 | D4×C71 | — | 4 | 8 | no | — |
| 204 | D4×C71 | — | 4 | 4 | no | — |
| 205 | C2×C4×C71 | — | 2 | 1 | no | — |
| 206 | C2×C4×C71 | — | 2 | 1 | no | — |
| 207 | C2×C4×C71 | — | 2 | 8 | no | — |
| 208 | C2×C4×C71 | #120 | 1 | 2 | yes | — |
| 209 | C2×C4×C71 | C22×D4 | 1 | 2 | yes | — |
| 210 | C2×C4×C71 | C22×D4 | 1 | 2 | yes | — |
| 211 | C2×C4×C71 | H(5,𝔽2) | 1 | 2 | yes | — |
| 212 | C22⋊D71 | — | 4 | 32 | no | — |
| 213 | C22⋊D71 | — | 4 | 32 | no | — |
| 214 | C22⋊D71 | — | 4 | 8 | no | — |
| 215 | C22⋊D71 | — | 4 | 2 | no | — |
| 216 | C22⋊D71 | — | 4 | 2 | no | — |
| 217 | C22⋊D71 | — | 4 | 8 | no | — |
| 218 | C22⋊D71 | — | 8 | 8 | no | — |
| 219 | C2×Dic71 | — | 2 | 16 | no | — |
| 220 | C2×Dic71 | — | 2 | 8 | no | — |
| 221 | C2×Dic71 | — | 2 | 4 | no | — |
| 222 | C2×Dic71 | — | 2 | 4 | no | — |
| 223 | C2×Dic71 | — | 2 | 2 | no | — |
| 224 | C2×Dic71 | — | 4 | 4 | no | — |
| 225 | C2×Dic71 | — | 8 | 4 | no | — |
| 226 | D284 | — | 2 | 4 | no | — |
| 227 | D284 | — | 2 | 8 | no | — |
| 228 | D284 | — | 4 | 8 | no | — |
| 229 | D284 | — | 4 | 4 | no | — |
| 230 | C4×D71 | — | 4 | 4 | no | — |
| 231 | Dic142 | — | 2 | 4 | no | — |
| 232 | C8×C71 | — | 4 | 4 | no | — |
| 233 | C22×C71 | — | 2 | 4 | no | — |
| 234 | C22×C71 | — | 2 | 4 | no | — |
| 235 | C22×C71 | — | 2 | 2 | no | — |
| 236 | C22×C71 | — | 2 | 2 | no | — |
| 237 | C22×C71 | — | 2 | 2 | no | — |
| 238 | C22×C71 | — | 2 | 4 | no | — |
| 239 | C22×C71 | — | 4 | 4 | no | — |
| 240 | C22×C71 | — | 4 | 4 | no | — |
| 241 | C22×C71 | — | 4 | 4 | no | — |
| 242 | C22×C71 | — | 4 | 2 | no | — |
| 243 | C22×C71 | — | 4 | 4 | no | — |
| 244 | C22×C71 | — | 8 | 2 | no | — |
| 245 | C22×C71 | — | 8 | 16 | no | — |
| 246 | C22×C71 | — | 8 | 2 | no | — |
| 247 | C22×C71 | #453 | 1 | 4 | yes | complemented |
| 248 | C22×C71 | C2×#120 | 1 | 1 | yes | characteristic |
| 249 | C22×C71 | C2×#120 | 1 | 1 | yes | characteristic |
| 250 | C22×C71 | #534 | 1 | 1 | yes | characteristic |
| 251 | C2×D71 | — | 4 | 8 | no | — |
| 252 | C2×D71 | — | 4 | 2 | no | — |
| 253 | C2×D71 | — | 4 | 4 | no | — |
| 254 | C2×D71 | — | 4 | 4 | no | — |
| 255 | C2×D71 | — | 8 | 4 | no | — |
| 256 | C2×D71 | — | 8 | 16 | no | — |
| 257 | C2×D71 | — | 8 | 4 | no | — |
| 258 | C2×D71 | — | 16 | 4 | no | — |
| 259 | C4×C71 | — | 2 | 2 | no | — |
| 260 | C4×C71 | D42 | 1 | 4 | yes | — |
| 261 | Dic71 | — | 2 | 8 | no | — |
| 262 | Dic71 | — | 4 | 2 | no | — |
| 263 | Dic71 | — | 4 | 4 | no | — |
| 264 | #23906 | — | 71 | 1 | no | maximal, Sylow |
| 265 | C2×C71 | — | 2 | 1 | no | — |
| 266 | C2×C71 | — | 2 | 1 | no | — |
| 267 | C2×C71 | — | 2 | 4 | no | — |
| 268 | C2×C71 | — | 4 | 4 | no | — |
| 269 | C2×C71 | — | 8 | 2 | no | — |
| 270 | C2×C71 | #2403 | 1 | 1 | yes | characteristic |
| 271 | C2×C71 | C2×#453 | 1 | 2 | yes | — |
| 272 | D71 | — | 8 | 4 | no | — |
| 273 | D71 | — | 8 | 2 | no | — |
| 274 | #3484 | — | 71 | 1 | no | — |
| 275 | C22×#127 | — | 71 | 1 | no | — |
| 276 | C2×#453 | — | 71 | 2 | no | — |
| 277 | #3003 | — | 71 | 2 | no | — |
| 278 | #2002 | — | 71 | 4 | no | — |
| 279 | #1896 | — | 71 | 2 | no | — |
| 280 | #1887 | — | 71 | 2 | no | — |
| 281 | #1783 | D71 | 1 | 1 | yes | characteristic, complemented |
| 282 | C71 | #23906 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 283 | C2×H(5,𝔽2) | — | 71 | 1 | no | — |
| 284 | C23×D4 | — | 71 | 1 | no | — |
| 285 | C23×D4 | — | 142 | 2 | no | — |
| 286 | C23×D4 | C2×D71 | 1 | 1 | yes | characteristic |
| 287 | C2×AGL(1,ℤ/8) | — | 71 | 4 | no | — |
| 288 | #546 | — | 142 | 4 | no | — |
| 289 | D42 | — | 142 | 4 | no | — |
| 290 | #535 | — | 71 | 2 | no | — |
| 291 | #534 | — | 142 | 2 | no | — |
| 292 | C2×#127 | — | 71 | 2 | no | — |
| 293 | C2×#127 | — | 71 | 2 | no | — |
| 294 | C2×#127 | — | 142 | 8 | no | — |
| 295 | C2×#127 | — | 142 | 2 | no | — |
| 296 | #525 | — | 71 | 2 | no | — |
| 297 | C2×#120 | — | 142 | 2 | no | — |
| 298 | #518 | — | 71 | 1 | no | — |
| 299 | C22×C42 | — | 71 | 1 | no | — |
| 300 | #453 | — | 142 | 8 | no | — |
| 301 | #450 | — | 142 | 4 | no | — |
| 302 | #447 | — | 142 | 4 | no | — |
| 303 | C2×#104 | — | 71 | 4 | no | — |
| 304 | #418 | — | 71 | 4 | no | — |
| 305 | C2×#100 | C2×D71 | 1 | 2 | yes | complemented |
| 306 | C2×#100 | C2×D71 | 1 | 2 | yes | complemented |
| 307 | #407 | C2×D71 | 1 | 2 | yes | complemented |
| 308 | #339 | — | 71 | 4 | no | — |
| 309 | C25 | — | 142 | 1 | no | — |
| 310 | C25 | D284 | 1 | 2 | yes | — |
| 311 | H(5,𝔽2) | — | 284 | 2 | no | — |
| 312 | H(5,𝔽2) | — | 142 | 4 | no | — |
| 313 | C2×#41 | — | 71 | 2 | no | — |
| 314 | C2×#41 | — | 142 | 2 | no | — |
| 315 | C22×D4 | — | 2 | 4 | no | — |
| 316 | C22×D4 | — | 2 | 4 | no | — |
| 317 | C22×D4 | — | 4 | 2 | no | — |
| 318 | C22×D4 | — | 284 | 2 | no | — |
| 319 | C22×D4 | — | 284 | 16 | no | — |
| 320 | C22×D4 | — | 71 | 2 | no | — |
| 321 | C22×D4 | — | 142 | 4 | no | — |
| 322 | C22×D4 | — | 142 | 2 | no | — |
| 323 | C22×D4 | — | 142 | 16 | no | — |
| 324 | C22×D4 | — | 142 | 2 | no | — |
| 325 | C22×D4 | — | 142 | 4 | no | — |
| 326 | C22×D4 | — | 142 | 4 | no | — |
| 327 | C22×D4 | — | 142 | 4 | no | — |
| 328 | C22×D4 | — | 142 | 4 | no | — |
| 329 | C22×D4 | — | 142 | 1 | no | — |
| 330 | C22×D4 | D284 | 1 | 2 | yes | — |
| 331 | C22×D4 | C22×D71 | 1 | 1 | yes | characteristic |
| 332 | C22×D4 | C22×D71 | 1 | 1 | yes | characteristic |
| 333 | C23×C4 | — | 142 | 1 | no | — |
| 334 | C23×C4 | C22×D71 | 1 | 1 | yes | characteristic |
| 335 | AGL(1,ℤ/8) | — | 284 | 4 | no | — |
| 336 | AGL(1,ℤ/8) | — | 142 | 8 | no | — |
| 337 | C2×SD16 | — | 142 | 4 | no | — |
| 338 | C2×D8 | — | 142 | 4 | no | — |
| 339 | C2×M16 | C22×D71 | 1 | 4 | yes | — |
| 340 | #127 | — | 71 | 8 | no | — |
| 341 | #127 | — | 142 | 4 | no | — |
| 342 | #127 | — | 142 | 4 | no | — |
| 343 | #127 | — | 142 | 2 | no | — |
| 344 | #127 | — | 142 | 16 | no | — |
| 345 | #127 | — | 142 | 4 | no | — |
| 346 | #124 | — | 142 | 2 | no | — |
| 347 | #123 | — | 142 | 4 | no | — |
| 348 | #123 | — | 142 | 2 | no | — |
| 349 | C22⋊Q8 | — | 71 | 4 | no | — |
| 350 | #121 | — | 71 | 4 | no | — |
| 351 | #121 | — | 142 | 4 | no | — |
| 352 | #121 | — | 142 | 8 | no | — |
| 353 | #120 | — | 142 | 4 | no | — |
| 354 | #120 | — | 142 | 8 | no | — |
| 355 | #120 | — | 142 | 2 | no | — |
| 356 | #120 | — | 142 | 4 | no | — |
| 357 | C4×D4 | — | 142 | 4 | no | — |
| 358 | C4×D4 | — | 142 | 4 | no | — |
| 359 | #117 | — | 71 | 2 | no | — |
| 360 | C2×C22⋊C4 | — | 142 | 4 | no | — |
| 361 | C2×C22⋊C4 | — | 142 | 2 | no | — |
| 362 | C2×C42 | — | 71 | 2 | no | — |
| 363 | C2×C42 | — | 142 | 4 | no | — |
| 364 | C2×C42 | — | 142 | 1 | no | — |
| 365 | #104 | — | 142 | 8 | no | — |
| 366 | #102 | — | 142 | 8 | no | — |
| 367 | #100 | — | 2 | 4 | no | — |
| 368 | #100 | — | 4 | 2 | no | — |
| 369 | C22⋊C8 | — | 2 | 4 | no | — |
| 370 | C24 | — | 2 | 4 | no | — |
| 371 | C24 | — | 2 | 4 | no | — |
| 372 | C24 | — | 4 | 2 | no | — |
| 373 | C24 | — | 4 | 8 | no | — |
| 374 | C24 | — | 284 | 2 | no | — |
| 375 | C24 | — | 284 | 8 | no | — |
| 376 | C24 | — | 284 | 2 | no | — |
| 377 | C24 | — | 142 | 4 | no | — |
| 378 | C24 | — | 142 | 2 | no | — |
| 379 | C24 | — | 142 | 2 | no | — |
| 380 | C24 | C2×D284 | 1 | 1 | yes | characteristic |
| 381 | C24 | C2×D284 | 1 | 2 | yes | — |
| 382 | C24 | C2×D284 | 1 | 2 | yes | — |
| 383 | #41 | — | 284 | 8 | no | — |
| 384 | #41 | — | 142 | 4 | no | — |
| 385 | #41 | — | 142 | 4 | no | — |
| 386 | C2×Q8 | — | 71 | 2 | no | — |
| 387 | C2×D4 | — | 2 | 4 | no | — |
| 388 | C2×D4 | — | 2 | 2 | no | — |
| 389 | C2×D4 | — | 2 | 2 | no | — |
| 390 | C2×D4 | — | 2 | 2 | no | — |
| 391 | C2×D4 | — | 2 | 2 | no | — |
| 392 | C2×D4 | — | 2 | 2 | no | — |
| 393 | C2×D4 | — | 2 | 4 | no | — |
| 394 | C2×D4 | — | 4 | 16 | no | — |
| 395 | C2×D4 | — | 4 | 2 | no | — |
| 396 | C2×D4 | — | 284 | 2 | no | — |
| 397 | C2×D4 | — | 284 | 16 | no | — |
| 398 | C2×D4 | — | 284 | 8 | no | — |
| 399 | C2×D4 | — | 284 | 4 | no | — |
| 400 | C2×D4 | — | 284 | 4 | no | — |
| 401 | C2×D4 | — | 284 | 16 | no | — |
| 402 | C2×D4 | — | 284 | 16 | no | — |
| 403 | C2×D4 | — | 284 | 64 | no | — |
| 404 | C2×D4 | — | 284 | 2 | no | — |
| 405 | C2×D4 | — | 568 | 8 | no | — |
| 406 | C2×D4 | — | 71 | 2 | no | — |
| 407 | C2×D4 | — | 71 | 4 | no | — |
| 408 | C2×D4 | — | 142 | 4 | no | — |
| 409 | C2×D4 | — | 142 | 4 | no | — |
| 410 | C2×D4 | — | 142 | 16 | no | — |
| 411 | C2×D4 | — | 142 | 2 | no | — |
| 412 | C2×D4 | — | 142 | 4 | no | — |
| 413 | C2×D4 | — | 142 | 16 | no | — |
| 414 | C2×D4 | — | 142 | 8 | no | — |
| 415 | C2×D4 | — | 142 | 2 | no | — |
| 416 | C2×D4 | — | 142 | 4 | no | — |
| 417 | C2×D4 | — | 142 | 4 | no | — |
| 418 | C2×D4 | D4×D71 | 1 | 4 | yes | — |
| 419 | C22×C4 | — | 2 | 2 | no | — |
| 420 | C22×C4 | — | 2 | 2 | no | — |
| 421 | C22×C4 | — | 142 | 2 | no | — |
| 422 | C22×C4 | — | 142 | 2 | no | — |
| 423 | C22×C4 | — | 142 | 4 | no | — |
| 424 | C22×C4 | — | 142 | 4 | no | — |
| 425 | C22×C4 | — | 142 | 8 | no | — |
| 426 | C22×C4 | — | 142 | 2 | no | — |
| 427 | C22×C4 | D4×D71 | 1 | 4 | yes | — |
| 428 | C22×C4 | C2×D284 | 1 | 1 | yes | characteristic |
| 429 | C22×C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 430 | SD16 | — | 284 | 8 | no | — |
| 431 | D8 | — | 284 | 8 | no | — |
| 432 | M16 | — | 2 | 4 | no | — |
| 433 | M16 | — | 2 | 4 | no | — |
| 434 | C2×C8 | — | 2 | 4 | no | — |
| 435 | C4⋊C4 | — | 71 | 4 | no | — |
| 436 | C4⋊C4 | — | 142 | 4 | no | — |
| 437 | C22⋊C4 | — | 142 | 4 | no | — |
| 438 | C22⋊C4 | — | 142 | 8 | no | — |
| 439 | C22⋊C4 | — | 142 | 2 | no | — |
| 440 | C22⋊C4 | — | 142 | 4 | no | — |
| 441 | C22⋊C4 | — | 142 | 4 | no | — |
| 442 | C42 | — | 71 | 4 | no | — |
| 443 | C42 | — | 142 | 4 | no | — |
| 444 | C42 | — | 142 | 2 | no | — |
| 445 | C42 | — | 142 | 2 | no | — |
| 446 | C23 | — | 2 | 1 | no | — |
| 447 | C23 | — | 2 | 4 | no | — |
| 448 | C23 | — | 2 | 1 | no | — |
| 449 | C23 | — | 2 | 2 | no | — |
| 450 | C23 | — | 2 | 2 | no | — |
| 451 | C23 | — | 2 | 2 | no | — |
| 452 | C23 | — | 2 | 2 | no | — |
| 453 | C23 | — | 2 | 2 | no | — |
| 454 | C23 | — | 4 | 8 | no | — |
| 455 | C23 | — | 4 | 4 | no | — |
| 456 | C23 | — | 4 | 4 | no | — |
| 457 | C23 | — | 4 | 16 | no | — |
| 458 | C23 | — | 4 | 8 | no | — |
| 459 | C23 | — | 8 | 4 | no | — |
| 460 | C23 | — | 8 | 8 | no | — |
| 461 | C23 | — | 284 | 16 | no | — |
| 462 | C23 | — | 284 | 8 | no | — |
| 463 | C23 | — | 284 | 8 | no | — |
| 464 | C23 | — | 284 | 4 | no | — |
| 465 | C23 | — | 284 | 2 | no | — |
| 466 | C23 | — | 284 | 2 | no | — |
| 467 | C23 | — | 568 | 8 | no | — |
| 468 | C23 | — | 568 | 4 | no | — |
| 469 | C23 | — | 568 | 4 | no | — |
| 470 | C23 | — | 568 | 4 | no | — |
| 471 | C23 | — | 142 | 4 | no | — |
| 472 | C23 | — | 142 | 2 | no | — |
| 473 | C23 | #14556098 | 1 | 2 | yes | — |
| 474 | C23 | #14556098 | 1 | 4 | yes | — |
| 475 | C23 | C22×D284 | 1 | 1 | yes | characteristic |
| 476 | Q8 | — | 142 | 4 | no | — |
| 477 | D4 | — | 2 | 8 | no | — |
| 478 | D4 | — | 4 | 8 | no | — |
| 479 | D4 | — | 4 | 4 | no | — |
| 480 | D4 | — | 284 | 8 | no | — |
| 481 | D4 | — | 284 | 8 | no | — |
| 482 | D4 | — | 284 | 2 | no | — |
| 483 | D4 | — | 284 | 8 | no | — |
| 484 | D4 | — | 284 | 2 | no | — |
| 485 | D4 | — | 284 | 32 | no | — |
| 486 | D4 | — | 284 | 32 | no | — |
| 487 | D4 | — | 284 | 4 | no | — |
| 488 | D4 | — | 568 | 8 | no | — |
| 489 | D4 | — | 142 | 4 | no | — |
| 490 | D4 | — | 142 | 8 | no | — |
| 491 | C2×C4 | — | 2 | 1 | no | — |
| 492 | C2×C4 | — | 2 | 1 | no | — |
| 493 | C2×C4 | — | 2 | 8 | no | — |
| 494 | C2×C4 | — | 284 | 4 | no | — |
| 495 | C2×C4 | — | 284 | 4 | no | — |
| 496 | C2×C4 | — | 568 | 4 | no | — |
| 497 | C2×C4 | — | 142 | 4 | no | — |
| 498 | C2×C4 | — | 142 | 2 | no | — |
| 499 | C2×C4 | — | 142 | 16 | no | — |
| 500 | C2×C4 | — | 142 | 8 | no | — |
| 501 | C2×C4 | — | 142 | 4 | no | — |
| 502 | C2×C4 | #14556098 | 1 | 2 | yes | — |
| 503 | C2×C4 | C2×D4×D71 | 1 | 2 | yes | — |
| 504 | C2×C4 | C2×D4×D71 | 1 | 2 | yes | — |
| 505 | C2×C4 | #14556173 | 1 | 2 | yes | — |
| 506 | C8 | — | 4 | 4 | no | — |
| 507 | C22 | — | 2 | 4 | no | — |
| 508 | C22 | — | 2 | 4 | no | — |
| 509 | C22 | — | 2 | 2 | no | — |
| 510 | C22 | — | 2 | 2 | no | — |
| 511 | C22 | — | 2 | 2 | no | — |
| 512 | C22 | — | 2 | 4 | no | — |
| 513 | C22 | — | 4 | 4 | no | — |
| 514 | C22 | — | 4 | 4 | no | — |
| 515 | C22 | — | 4 | 4 | no | — |
| 516 | C22 | — | 4 | 4 | no | — |
| 517 | C22 | — | 4 | 2 | no | — |
| 518 | C22 | — | 8 | 2 | no | — |
| 519 | C22 | — | 8 | 16 | no | — |
| 520 | C22 | — | 8 | 2 | no | — |
| 521 | C22 | — | 284 | 8 | no | — |
| 522 | C22 | — | 284 | 4 | no | — |
| 523 | C22 | — | 284 | 2 | no | — |
| 524 | C22 | — | 284 | 4 | no | — |
| 525 | C22 | — | 568 | 4 | no | — |
| 526 | C22 | — | 568 | 16 | no | — |
| 527 | C22 | — | 568 | 4 | no | — |
| 528 | C22 | — | 1136 | 4 | no | — |
| 529 | C22 | #17986169 | 1 | 4 | yes | complemented |
| 530 | C22 | C2×#14556098 | 1 | 1 | yes | characteristic |
| 531 | C22 | C2×#14556098 | 1 | 1 | yes | characteristic |
| 532 | C22 | #17986561 | 1 | 1 | yes | characteristic |
| 533 | C4 | — | 2 | 2 | no | — |
| 534 | C4 | — | 284 | 4 | no | — |
| 535 | C4 | — | 284 | 2 | no | — |
| 536 | C4 | — | 142 | 8 | no | — |
| 537 | C4 | #17986631 | 1 | 4 | yes | — |
| 538 | C2 | — | 2 | 1 | no | — |
| 539 | C2 | — | 2 | 1 | no | — |
| 540 | C2 | — | 2 | 4 | no | — |
| 541 | C2 | — | 4 | 4 | no | — |
| 542 | C2 | — | 8 | 2 | no | — |
| 543 | C2 | — | 568 | 4 | no | — |
| 544 | C2 | — | 568 | 2 | no | — |
| 545 | C2 | #22591653 | 1 | 1 | yes | characteristic |
| 546 | C2 | C2×#17986169 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22601975 | C2 | semidirect |
| 2. C22×#14556124 | C2 | semidirect |
| 3. C2×#17986169 | C2 | semidirect |
| 4. #22597570 | C2 | semidirect |
| 5. #22589357 | C2 | semidirect |
| 6. #22588781 | C2 | semidirect |
| 7. #22588736 | C2 | semidirect |
| 8. C71×#1783 | C2 | semidirect |
| 9. C2×#14556173 | C22 | semidirect |
| 10. C23×D284 | C22 | semidirect |
| 12. C2×#14556156 | C22 | semidirect |
| 15. #17986566 | C22 | semidirect |
| 20. C2×#14556124 | C22 | semidirect |
| 23. #17986474 | C22 | semidirect |
| 24. C22×C4×Dic71 | C22 | semidirect |
| 28. C2×#14556054 | C22 | semidirect |
| 29. #17986005 | C22 | semidirect |
| 30. #17985760 | C22 | semidirect |
| 32. C2×#100×C71 | C22 | semidirect |
| 33. C2×#100×C71 | C22 | semidirect |
| 34. #407×C71 | C22 | semidirect |
| 62. #14556124 | D4 | semidirect |
| 66. #14556107 | D4 | semidirect |
| 67. #14556102 | D4 | semidirect |
| 105. C2×Dic142 | C2×D4 | semidirect |
| 113. C2×D284 | C2×D4 | semidirect |
| 114. C2×D284 | C2×D4 | semidirect |
| 136. C4⋊Dic71 | C2×D4 | semidirect |
| 146. C4×Dic71 | C2×D4 | semidirect |
| 247. C22×C71 | #453 | semidirect |
| 281. #1783 | D71 | semidirect |
| 282. C71 | #23906 | semidirect |
| 305. C2×#100 | C2×D71 | semidirect |
| 306. C2×#100 | C2×D71 | semidirect |
| 307. #407 | C2×D71 | semidirect |
| 529. C22 | #17986169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601975 | 2 |
| C22×#14556124 | 2 |
| C2×#17986169 | 2 |
| #22597570 | 2 |
| #22589357 | 2 |
| #22588781 | 2 |
| #22588736 | 2 |
| C71×#1783 | 2 |
| #23906 | 71 |