Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1330 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 1330 conjugacy classes of subgroups — too many to draw. Only its 117 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 | #87497 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#5927 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #3586⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #85542 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #85533 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #85475 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #85474 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #85472 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #85471 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #85455 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #85452 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #61108 | — | 3 | 1 | no | maximal, Sylow |
| 13 | #5945 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×2−1+4⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #5927 | — | 2 | 1 | no | — |
| 16 | #5927 | — | 2 | 1 | no | — |
| 17 | #5927 | — | 2 | 1 | no | — |
| 18 | #5927 | C22 | 1 | 2 | yes | complemented |
| 19 | #5927 | C22 | 1 | 2 | yes | complemented |
| 20 | #5927 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #5926 | — | 2 | 1 | no | — |
| 22 | #5926 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #5925 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #5924 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #5923 | — | 2 | 1 | no | — |
| 26 | #5923 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#985 | — | 2 | 1 | no | — |
| 28 | C2×#985 | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×#984 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | C2×#983 | — | 2 | 1 | no | — |
| 31 | C22×#226 | — | 2 | 1 | no | — |
| 32 | #5773 | — | 4 | 1 | no | maximal |
| 33 | #578⋊C3 | C22 | 1 | 2 | yes | complemented |
| 34 | #577⋊C3 | C22 | 1 | 2 | yes | complemented |
| 35 | #568⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #5431 | C22 | 1 | 2 | yes | complemented |
| 37 | #5430 | C22 | 1 | 2 | yes | complemented |
| 38 | #5430 | C22 | 1 | 2 | yes | complemented |
| 39 | #5428 | C22 | 1 | 2 | yes | complemented |
| 40 | #5423 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #5406 | C22 | 1 | 2 | yes | complemented |
| 42 | #5405 | C22 | 1 | 2 | yes | complemented |
| 43 | #5404 | C22 | 1 | 2 | yes | complemented |
| 44 | #5403 | C22 | 1 | 2 | yes | complemented |
| 45 | #3586 | — | 3 | 1 | no | — |
| 46 | #3586 | D3 | 1 | 1 | yes | characteristic, complemented |
| 47 | #3584 | — | 3 | 1 | no | — |
| 48 | C2×#578 | — | 3 | 1 | no | — |
| 49 | #3293 | — | 3 | 2 | no | — |
| 50 | #3293 | — | 3 | 2 | no | — |
| 51 | #3290 | — | 3 | 2 | no | — |
| 52 | #3290 | — | 3 | 2 | no | — |
| 53 | #3289 | — | 3 | 2 | no | — |
| 54 | #3289 | — | 3 | 2 | no | — |
| 55 | #3289 | — | 3 | 2 | no | — |
| 56 | #3289 | — | 3 | 2 | no | — |
| 57 | #3156 | — | 3 | 1 | no | — |
| 58 | #3069 | — | 3 | 1 | no | — |
| 59 | #3069 | — | 3 | 1 | no | — |
| 60 | #3067 | — | 3 | 1 | no | — |
| 61 | C2×#473 | — | 3 | 1 | no | — |
| 62 | #3022 | — | 3 | 1 | no | — |
| 63 | #3022 | — | 3 | 1 | no | — |
| 64 | #3020 | — | 3 | 1 | no | — |
| 65 | #3020 | — | 3 | 1 | no | — |
| 66 | #2957 | — | 3 | 1 | no | — |
| 67 | #2955 | — | 3 | 1 | no | — |
| 68 | D3×#41 | — | 4 | 1 | no | — |
| 69 | C2×#237 | — | 4 | 1 | no | — |
| 70 | 2−1+4⋊C3 | — | 2 | 1 | no | — |
| 71 | 2−1+4⋊C3 | — | 2 | 1 | no | — |
| 72 | 2−1+4⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 73 | 2−1+4⋊C3 | C23 | 1 | 2 | yes | — |
| 74 | #994 | C23 | 1 | 1 | yes | characteristic |
| 75 | C2×#41⋊C3 | — | 2 | 1 | no | — |
| 76 | C2×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 77 | C22×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 78 | #986 | — | 2 | 1 | no | — |
| 79 | #986 | C23 | 1 | 1 | yes | characteristic |
| 80 | #985 | — | 2 | 1 | no | — |
| 81 | #985 | — | 2 | 1 | no | — |
| 82 | #985 | — | 2 | 1 | no | — |
| 83 | #985 | D4 | 1 | 1 | yes | characteristic |
| 84 | #985 | D4 | 1 | 1 | yes | characteristic |
| 85 | #985 | C23 | 1 | 1 | yes | characteristic |
| 86 | #985 | C23 | 1 | 1 | yes | characteristic |
| 87 | #984 | — | 2 | 1 | no | — |
| 88 | #984 | — | 2 | 1 | no | — |
| 89 | #984 | C23 | 1 | 1 | yes | characteristic |
| 90 | #984 | C23 | 1 | 2 | yes | — |
| 91 | #983 | — | 2 | 1 | no | — |
| 92 | #983 | — | 2 | 2 | no | — |
| 93 | #983 | — | 2 | 2 | no | — |
| 94 | #983 | — | 2 | 1 | no | — |
| 95 | #983 | — | 2 | 1 | no | — |
| 96 | C2×GL(2,𝔽3) | — | 2 | 1 | no | — |
| 97 | C2×GL(2,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 98 | C2×#226 | — | 2 | 1 | no | — |
| 99 | C2×#226 | — | 2 | 2 | no | — |
| 100 | C2×#226 | — | 2 | 2 | no | — |
| 101 | C2×#226 | — | 2 | 1 | no | — |
| 102 | C2×#226 | D4 | 1 | 1 | yes | characteristic |
| 103 | C3×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 104 | #951 | — | 4 | 1 | no | — |
| 105 | #932 | — | 4 | 1 | no | — |
| 106 | #916 | — | 4 | 2 | no | — |
| 107 | #915 | — | 4 | 2 | no | — |
| 108 | #912 | — | 4 | 2 | no | — |
| 109 | #911 | — | 4 | 2 | no | — |
| 110 | #909 | — | 4 | 1 | no | — |
| 111 | D3×M16 | — | 4 | 1 | no | — |
| 112 | #131⋊C3 | C23 | 1 | 2 | yes | — |
| 113 | GU(2,𝔽3) | C23 | 1 | 2 | yes | — |
| 114 | #585 | — | 3 | 1 | no | — |
| 115 | #585 | C2×D3 | 1 | 1 | yes | characteristic |
| 116 | C2×2−1+4 | — | 3 | 1 | no | — |
| 117 | C2×2−1+4 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 118 | #578 | — | 3 | 2 | no | — |
| 119 | #578 | — | 3 | 1 | no | — |
| 120 | #578 | — | 3 | 2 | no | — |
| 121 | #578 | — | 3 | 2 | no | — |
| 122 | #578 | — | 3 | 2 | no | — |
| 123 | #578 | — | 3 | 2 | no | — |
| 124 | #578 | — | 3 | 1 | no | — |
| 125 | #578 | — | 3 | 2 | no | — |
| 126 | #578 | — | 3 | 2 | no | — |
| 127 | #578 | — | 6 | 1 | no | — |
| 128 | #578 | — | 6 | 1 | no | — |
| 129 | #578 | — | 6 | 1 | no | — |
| 130 | #578 | — | 6 | 1 | no | — |
| 131 | #578 | — | 6 | 1 | no | — |
| 132 | #578 | — | 6 | 2 | no | — |
| 133 | #578 | C2×D3 | 1 | 2 | yes | complemented |
| 134 | #577 | — | 3 | 2 | no | — |
| 135 | #577 | — | 3 | 1 | no | — |
| 136 | #577 | — | 3 | 1 | no | — |
| 137 | #577 | — | 3 | 2 | no | — |
| 138 | #577 | — | 3 | 2 | no | — |
| 139 | #577 | — | 3 | 1 | no | — |
| 140 | #577 | — | 3 | 1 | no | — |
| 141 | #577 | — | 6 | 1 | no | — |
| 142 | #577 | — | 6 | 1 | no | — |
| 143 | #577 | — | 6 | 2 | no | — |
| 144 | #577 | C2×D3 | 1 | 2 | yes | complemented |
| 145 | #576 | — | 3 | 1 | no | — |
| 146 | #576 | — | 3 | 1 | no | — |
| 147 | #576 | — | 6 | 1 | no | — |
| 148 | #575 | — | 3 | 1 | no | — |
| 149 | #575 | — | 3 | 1 | no | — |
| 150 | #575 | — | 3 | 1 | no | — |
| 151 | #575 | — | 3 | 1 | no | — |
| 152 | #575 | — | 3 | 1 | no | — |
| 153 | #575 | — | 6 | 1 | no | — |
| 154 | #575 | — | 6 | 1 | no | — |
| 155 | #575 | — | 6 | 1 | no | — |
| 156 | #575 | — | 6 | 1 | no | — |
| 157 | C2×#137 | — | 3 | 1 | no | — |
| 158 | C2×#137 | — | 3 | 1 | no | — |
| 159 | C2×#137 | — | 3 | 1 | no | — |
| 160 | C2×#137 | — | 3 | 1 | no | — |
| 161 | C2×#137 | — | 3 | 1 | no | — |
| 162 | C2×#137 | — | 3 | 1 | no | — |
| 163 | C2×#137 | — | 6 | 1 | no | — |
| 164 | C2×#137 | — | 6 | 1 | no | — |
| 165 | C2×#137 | — | 6 | 1 | no | — |
| 166 | C2×#137 | — | 6 | 1 | no | — |
| 167 | C2×#135 | — | 3 | 1 | no | — |
| 168 | C2×#135 | — | 3 | 1 | no | — |
| 169 | C2×#135 | — | 6 | 1 | no | — |
| 170 | C2×#135 | — | 6 | 1 | no | — |
| 171 | C2×#135 | — | 6 | 1 | no | — |
| 172 | C22×Q16 | — | 3 | 1 | no | — |
| 173 | C22×Q16 | — | 6 | 1 | no | — |
| 174 | #568 | — | 3 | 1 | no | — |
| 175 | #568 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 176 | C2×#131 | — | 3 | 1 | no | — |
| 177 | C2×#131 | — | 3 | 1 | no | — |
| 178 | #536 | — | 3 | 1 | no | — |
| 179 | #536 | — | 3 | 1 | no | — |
| 180 | #497 | — | 3 | 2 | no | — |
| 181 | #497 | — | 3 | 2 | no | — |
| 182 | #495 | — | 3 | 2 | no | — |
| 183 | #494 | — | 3 | 2 | no | — |
| 184 | #473 | — | 3 | 2 | no | — |
| 185 | #473 | — | 3 | 2 | no | — |
| 186 | #473 | — | 3 | 2 | no | — |
| 187 | #473 | — | 3 | 2 | no | — |
| 188 | #473 | — | 3 | 2 | no | — |
| 189 | #473 | — | 3 | 2 | no | — |
| 190 | #473 | — | 3 | 2 | no | — |
| 191 | #473 | — | 3 | 2 | no | — |
| 192 | #473 | — | 3 | 2 | no | — |
| 193 | #472 | — | 3 | 2 | no | — |
| 194 | #471 | — | 3 | 2 | no | — |
| 195 | #471 | — | 3 | 2 | no | — |
| 196 | #471 | — | 3 | 2 | no | — |
| 197 | #471 | — | 3 | 2 | no | — |
| 198 | #471 | — | 3 | 2 | no | — |
| 199 | #471 | — | 3 | 2 | no | — |
| 200 | #456 | — | 3 | 2 | no | — |
| 201 | #456 | — | 3 | 2 | no | — |
| 202 | #456 | — | 3 | 2 | no | — |
| 203 | #456 | — | 3 | 2 | no | — |
| 204 | #456 | — | 3 | 2 | no | — |
| 205 | #456 | — | 3 | 2 | no | — |
| 206 | #456 | — | 3 | 2 | no | — |
| 207 | #456 | — | 3 | 2 | no | — |
| 208 | #455 | — | 3 | 2 | no | — |
| 209 | #455 | — | 3 | 2 | no | — |
| 210 | #455 | — | 3 | 2 | no | — |
| 211 | #455 | — | 3 | 2 | no | — |
| 212 | #454 | — | 3 | 2 | no | — |
| 213 | #454 | — | 3 | 2 | no | — |
| 214 | #454 | — | 3 | 2 | no | — |
| 215 | #454 | — | 3 | 2 | no | — |
| 216 | #444 | — | 3 | 2 | no | — |
| 217 | #444 | — | 3 | 2 | no | — |
| 218 | #444 | — | 3 | 2 | no | — |
| 219 | #444 | — | 3 | 2 | no | — |
| 220 | #443 | — | 3 | 2 | no | — |
| 221 | #443 | — | 3 | 2 | no | — |
| 222 | #443 | — | 3 | 2 | no | — |
| 223 | #443 | — | 3 | 2 | no | — |
| 224 | #430 | — | 3 | 1 | no | — |
| 225 | C2×#108 | — | 3 | 1 | no | — |
| 226 | #421 | — | 3 | 1 | no | — |
| 227 | #421 | — | 3 | 1 | no | — |
| 228 | #421 | — | 3 | 1 | no | — |
| 229 | #421 | — | 3 | 1 | no | — |
| 230 | #413 | — | 3 | 1 | no | — |
| 231 | #413 | — | 3 | 1 | no | — |
| 232 | C2×#101 | — | 3 | 1 | no | — |
| 233 | C2×#101 | — | 3 | 1 | no | — |
| 234 | #405 | — | 3 | 1 | no | — |
| 235 | C3×#41 | — | 4 | 1 | no | — |
| 236 | C2×C3×D4 | — | 4 | 1 | no | — |
| 237 | C2×#67 | — | 8 | 1 | no | — |
| 238 | C22×Dic3 | — | 8 | 1 | no | — |
| 239 | #239 | — | 4 | 1 | no | — |
| 240 | D3×Q8 | — | 4 | 1 | no | — |
| 241 | #237 | — | 4 | 2 | no | — |
| 242 | #237 | — | 4 | 1 | no | — |
| 243 | #237 | — | 4 | 2 | no | — |
| 244 | #237 | — | 8 | 1 | no | — |
| 245 | #237 | — | 8 | 1 | no | — |
| 246 | #237 | — | 8 | 1 | no | — |
| 247 | D3×D4 | — | 4 | 1 | no | — |
| 248 | D3×D4 | — | 8 | 1 | no | — |
| 249 | #235 | — | 4 | 1 | no | — |
| 250 | #235 | — | 8 | 1 | no | — |
| 251 | C2×C4×D3 | — | 4 | 1 | no | — |
| 252 | C2×C4×D3 | — | 8 | 1 | no | — |
| 253 | C2×Dic6 | — | 4 | 1 | no | — |
| 254 | #41⋊C3 | — | 2 | 1 | no | — |
| 255 | #41⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 256 | #41⋊C3 | C24 | 1 | 1 | yes | characteristic |
| 257 | C2×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 258 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 259 | C2×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 260 | GL(2,𝔽3) | — | 2 | 1 | no | — |
| 261 | GL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 262 | GL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 263 | #226 | — | 2 | 2 | no | — |
| 264 | #226 | — | 2 | 1 | no | — |
| 265 | #226 | C2×D4 | 1 | 1 | yes | characteristic |
| 266 | #226 | C2×D4 | 1 | 1 | yes | characteristic |
| 267 | C3×SD16 | — | 4 | 2 | no | — |
| 268 | C3×D8 | — | 4 | 2 | no | — |
| 269 | C3×M16 | — | 4 | 1 | no | — |
| 270 | #216 | — | 4 | 2 | no | — |
| 271 | #214 | — | 4 | 2 | no | — |
| 272 | #214 | — | 4 | 2 | no | — |
| 273 | #213 | — | 4 | 2 | no | — |
| 274 | #208 | — | 4 | 1 | no | — |
| 275 | Dic12 | — | 4 | 2 | no | — |
| 276 | #204 | — | 4 | 2 | no | — |
| 277 | ΓL(1,𝔽25) | — | 4 | 2 | no | — |
| 278 | D3×C8 | — | 4 | 2 | no | — |
| 279 | 2−1+4 | — | 2 | 1 | no | — |
| 280 | 2−1+4 | — | 2 | 1 | no | — |
| 281 | 2−1+4 | — | 3 | 1 | no | — |
| 282 | 2−1+4 | — | 3 | 2 | no | — |
| 283 | 2−1+4 | — | 3 | 2 | no | — |
| 284 | 2−1+4 | — | 3 | 2 | no | — |
| 285 | 2−1+4 | — | 3 | 1 | no | — |
| 286 | 2−1+4 | — | 3 | 1 | no | — |
| 287 | 2−1+4 | — | 6 | 1 | no | — |
| 288 | 2−1+4 | — | 6 | 1 | no | — |
| 289 | 2−1+4 | — | 6 | 1 | no | — |
| 290 | 2−1+4 | — | 6 | 2 | no | — |
| 291 | 2−1+4 | — | 6 | 1 | no | — |
| 292 | 2−1+4 | — | 6 | 1 | no | — |
| 293 | 2−1+4 | — | 12 | 1 | no | — |
| 294 | 2−1+4 | C22×D3 | 1 | 1 | yes | characteristic |
| 295 | 2−1+4 | C22×D3 | 1 | 2 | yes | — |
| 296 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 297 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 298 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 299 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 300 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 301 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 302 | H(5,𝔽2) | — | 12 | 1 | no | — |
| 303 | H(5,𝔽2) | C22×D3 | 1 | 1 | yes | characteristic |
| 304 | C2×#41 | — | 2 | 1 | no | — |
| 305 | C2×#41 | — | 3 | 1 | no | — |
| 306 | C2×#41 | — | 3 | 1 | no | — |
| 307 | C2×#41 | — | 3 | 1 | no | — |
| 308 | C2×#41 | — | 3 | 1 | no | — |
| 309 | C2×#41 | — | 3 | 1 | no | — |
| 310 | C2×#41 | — | 6 | 1 | no | — |
| 311 | C2×#41 | — | 6 | 1 | no | — |
| 312 | C2×#41 | — | 6 | 1 | no | — |
| 313 | C2×#41 | — | 6 | 1 | no | — |
| 314 | C2×#41 | — | 6 | 1 | no | — |
| 315 | C2×#41 | — | 6 | 1 | no | — |
| 316 | C2×#41 | — | 6 | 1 | no | — |
| 317 | C2×#41 | — | 6 | 1 | no | — |
| 318 | C2×#41 | — | 12 | 1 | no | — |
| 319 | C2×#41 | — | 12 | 1 | no | — |
| 320 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 321 | C22×Q8 | — | 2 | 1 | no | — |
| 322 | C22×Q8 | — | 3 | 1 | no | — |
| 323 | C22×Q8 | — | 3 | 1 | no | — |
| 324 | C22×Q8 | — | 6 | 1 | no | — |
| 325 | C22×Q8 | — | 6 | 1 | no | — |
| 326 | #137 | — | 3 | 1 | no | — |
| 327 | #137 | — | 3 | 2 | no | — |
| 328 | #137 | — | 3 | 2 | no | — |
| 329 | #137 | — | 3 | 2 | no | — |
| 330 | #137 | — | 3 | 2 | no | — |
| 331 | #137 | — | 3 | 2 | no | — |
| 332 | #137 | — | 3 | 2 | no | — |
| 333 | #137 | — | 3 | 2 | no | — |
| 334 | #137 | — | 3 | 2 | no | — |
| 335 | #137 | — | 3 | 2 | no | — |
| 336 | #137 | — | 3 | 1 | no | — |
| 337 | #137 | — | 3 | 1 | no | — |
| 338 | #137 | — | 3 | 1 | no | — |
| 339 | #137 | — | 3 | 2 | no | — |
| 340 | #137 | — | 3 | 2 | no | — |
| 341 | #137 | — | 3 | 1 | no | — |
| 342 | #137 | — | 3 | 1 | no | — |
| 343 | #137 | — | 6 | 2 | no | — |
| 344 | #137 | — | 6 | 1 | no | — |
| 345 | #137 | — | 6 | 1 | no | — |
| 346 | #137 | — | 6 | 2 | no | — |
| 347 | #137 | — | 6 | 2 | no | — |
| 348 | #137 | — | 6 | 2 | no | — |
| 349 | #137 | — | 6 | 1 | no | — |
| 350 | #137 | — | 6 | 2 | no | — |
| 351 | #137 | — | 6 | 2 | no | — |
| 352 | #137 | — | 6 | 2 | no | — |
| 353 | #137 | — | 6 | 2 | no | — |
| 354 | #137 | — | 6 | 2 | no | — |
| 355 | #137 | — | 6 | 2 | no | — |
| 356 | #137 | — | 6 | 2 | no | — |
| 357 | #137 | — | 6 | 2 | no | — |
| 358 | #137 | — | 6 | 1 | no | — |
| 359 | #137 | — | 6 | 1 | no | — |
| 360 | #137 | — | 6 | 1 | no | — |
| 361 | #137 | — | 6 | 2 | no | — |
| 362 | #137 | — | 6 | 1 | no | — |
| 363 | #137 | — | 6 | 1 | no | — |
| 364 | #137 | — | 6 | 2 | no | — |
| 365 | #137 | — | 6 | 2 | no | — |
| 366 | #137 | — | 6 | 1 | no | — |
| 367 | #137 | — | 6 | 1 | no | — |
| 368 | #137 | — | 6 | 1 | no | — |
| 369 | #137 | — | 6 | 1 | no | — |
| 370 | #137 | — | 6 | 1 | no | — |
| 371 | #137 | — | 6 | 1 | no | — |
| 372 | #137 | — | 6 | 1 | no | — |
| 373 | #137 | — | 6 | 1 | no | — |
| 374 | #137 | — | 6 | 1 | no | — |
| 375 | #137 | — | 6 | 1 | no | — |
| 376 | #137 | — | 6 | 1 | no | — |
| 377 | #137 | — | 6 | 2 | no | — |
| 378 | #137 | — | 6 | 1 | no | — |
| 379 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 380 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 381 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 382 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 383 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 384 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 385 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 386 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 387 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 388 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 389 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 390 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 391 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 392 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 393 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 394 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 395 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 396 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 397 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 398 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 399 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 400 | AGL(1,ℤ/8) | S4 | 1 | 1 | yes | characteristic |
| 401 | #135 | — | 3 | 1 | no | — |
| 402 | #135 | — | 3 | 1 | no | — |
| 403 | #135 | — | 3 | 1 | no | — |
| 404 | #135 | — | 3 | 1 | no | — |
| 405 | #135 | — | 3 | 1 | no | — |
| 406 | #135 | — | 3 | 1 | no | — |
| 407 | #135 | — | 3 | 1 | no | — |
| 408 | #135 | — | 3 | 1 | no | — |
| 409 | #135 | — | 3 | 2 | no | — |
| 410 | #135 | — | 3 | 2 | no | — |
| 411 | #135 | — | 6 | 1 | no | — |
| 412 | #135 | — | 6 | 1 | no | — |
| 413 | #135 | — | 6 | 1 | no | — |
| 414 | #135 | — | 6 | 1 | no | — |
| 415 | #135 | — | 6 | 2 | no | — |
| 416 | #135 | — | 6 | 1 | no | — |
| 417 | #135 | — | 6 | 1 | no | — |
| 418 | #135 | — | 6 | 2 | no | — |
| 419 | #135 | — | 6 | 2 | no | — |
| 420 | #135 | — | 6 | 2 | no | — |
| 421 | #135 | — | 6 | 2 | no | — |
| 422 | #135 | — | 6 | 2 | no | — |
| 423 | #135 | — | 6 | 1 | no | — |
| 424 | #135 | — | 6 | 1 | no | — |
| 425 | #135 | — | 6 | 1 | no | — |
| 426 | #135 | — | 6 | 1 | no | — |
| 427 | #135 | — | 6 | 2 | no | — |
| 428 | #135 | — | 6 | 1 | no | — |
| 429 | #135 | — | 6 | 1 | no | — |
| 430 | #135 | — | 6 | 1 | no | — |
| 431 | #135 | — | 6 | 1 | no | — |
| 432 | #135 | — | 6 | 1 | no | — |
| 433 | #135 | — | 6 | 2 | no | — |
| 434 | #135 | — | 6 | 1 | no | — |
| 435 | #135 | — | 6 | 2 | no | — |
| 436 | #135 | — | 6 | 2 | no | — |
| 437 | C2×Q16 | — | 3 | 1 | no | — |
| 438 | C2×Q16 | — | 3 | 2 | no | — |
| 439 | C2×Q16 | — | 3 | 2 | no | — |
| 440 | C2×Q16 | — | 3 | 2 | no | — |
| 441 | C2×Q16 | — | 3 | 1 | no | — |
| 442 | C2×Q16 | — | 3 | 2 | no | — |
| 443 | C2×Q16 | — | 6 | 1 | no | — |
| 444 | C2×Q16 | — | 6 | 1 | no | — |
| 445 | C2×Q16 | — | 6 | 1 | no | — |
| 446 | C2×Q16 | — | 6 | 1 | no | — |
| 447 | C2×Q16 | — | 6 | 1 | no | — |
| 448 | C2×Q16 | — | 6 | 2 | no | — |
| 449 | C2×Q16 | — | 6 | 2 | no | — |
| 450 | C2×Q16 | — | 6 | 1 | no | — |
| 451 | C2×Q16 | — | 6 | 2 | no | — |
| 452 | C2×Q16 | — | 6 | 2 | no | — |
| 453 | C2×Q16 | — | 6 | 1 | no | — |
| 454 | C2×Q16 | — | 6 | 2 | no | — |
| 455 | C2×Q16 | — | 6 | 2 | no | — |
| 456 | C2×Q16 | — | 6 | 1 | no | — |
| 457 | C2×Q16 | — | 6 | 1 | no | — |
| 458 | C2×Q16 | — | 6 | 1 | no | — |
| 459 | C2×SD16 | — | 3 | 1 | no | — |
| 460 | C2×SD16 | — | 3 | 1 | no | — |
| 461 | C2×SD16 | — | 3 | 2 | no | — |
| 462 | C2×SD16 | — | 3 | 1 | no | — |
| 463 | C2×SD16 | — | 3 | 1 | no | — |
| 464 | C2×SD16 | — | 3 | 2 | no | — |
| 465 | C2×SD16 | — | 6 | 1 | no | — |
| 466 | C2×SD16 | — | 6 | 1 | no | — |
| 467 | C2×SD16 | — | 6 | 1 | no | — |
| 468 | C2×SD16 | — | 6 | 1 | no | — |
| 469 | C2×SD16 | — | 6 | 1 | no | — |
| 470 | C2×SD16 | — | 6 | 2 | no | — |
| 471 | C2×SD16 | — | 6 | 2 | no | — |
| 472 | C2×SD16 | — | 6 | 1 | no | — |
| 473 | C2×SD16 | — | 6 | 1 | no | — |
| 474 | C2×SD16 | — | 6 | 1 | no | — |
| 475 | C2×D8 | — | 3 | 1 | no | — |
| 476 | C2×D8 | — | 3 | 1 | no | — |
| 477 | C2×D8 | — | 6 | 1 | no | — |
| 478 | C2×D8 | — | 6 | 1 | no | — |
| 479 | #131 | — | 3 | 2 | no | — |
| 480 | #131 | — | 3 | 1 | no | — |
| 481 | #131 | — | 3 | 1 | no | — |
| 482 | #131 | — | 3 | 1 | no | — |
| 483 | #131 | — | 3 | 1 | no | — |
| 484 | #131 | — | 3 | 2 | no | — |
| 485 | #131 | — | 3 | 2 | no | — |
| 486 | #131 | — | 3 | 2 | no | — |
| 487 | #131 | — | 3 | 2 | no | — |
| 488 | #131 | — | 6 | 1 | no | — |
| 489 | #131 | — | 6 | 1 | no | — |
| 490 | #131 | — | 6 | 1 | no | — |
| 491 | #131 | — | 6 | 1 | no | — |
| 492 | #131 | — | 6 | 2 | no | — |
| 493 | #131 | C22×D3 | 1 | 2 | yes | — |
| 494 | C2×M16 | — | 3 | 1 | no | — |
| 495 | C2×M16 | — | 3 | 1 | no | — |
| 496 | C2×M16 | — | 3 | 1 | no | — |
| 497 | C2×M16 | — | 3 | 1 | no | — |
| 498 | C2×M16 | — | 3 | 1 | no | — |
| 499 | C2×M16 | — | 6 | 1 | no | — |
| 500 | C2×M16 | — | 6 | 1 | no | — |
| 501 | C2×M16 | — | 6 | 1 | no | — |
| 502 | C2×M16 | — | 6 | 1 | no | — |
| 503 | C22×C8 | — | 3 | 1 | no | — |
| 504 | C22×C8 | — | 6 | 1 | no | — |
| 505 | C22×C8 | — | 6 | 1 | no | — |
| 506 | C4⋊Q8 | — | 3 | 2 | no | — |
| 507 | C4⋊Q8 | — | 3 | 2 | no | — |
| 508 | #124 | — | 3 | 2 | no | — |
| 509 | #124 | — | 3 | 2 | no | — |
| 510 | #123 | — | 12 | 1 | no | — |
| 511 | #123 | — | 12 | 1 | no | — |
| 512 | C22⋊Q8 | — | 12 | 1 | no | — |
| 513 | C22⋊Q8 | — | 12 | 1 | no | — |
| 514 | #117 | — | 3 | 1 | no | — |
| 515 | #108 | — | 3 | 2 | no | — |
| 516 | #108 | — | 3 | 2 | no | — |
| 517 | #108 | — | 3 | 2 | no | — |
| 518 | #108 | — | 3 | 2 | no | — |
| 519 | #104 | — | 3 | 2 | no | — |
| 520 | #104 | — | 3 | 2 | no | — |
| 521 | #104 | — | 3 | 2 | no | — |
| 522 | #104 | — | 3 | 2 | no | — |
| 523 | #104 | — | 3 | 2 | no | — |
| 524 | #104 | — | 3 | 2 | no | — |
| 525 | #104 | — | 3 | 2 | no | — |
| 526 | #104 | — | 3 | 2 | no | — |
| 527 | #101 | — | 3 | 2 | no | — |
| 528 | #101 | — | 3 | 2 | no | — |
| 529 | #101 | — | 3 | 2 | no | — |
| 530 | #101 | — | 3 | 2 | no | — |
| 531 | #101 | — | 3 | 2 | no | — |
| 532 | #101 | — | 3 | 2 | no | — |
| 533 | #100 | — | 3 | 2 | no | — |
| 534 | #100 | — | 3 | 2 | no | — |
| 535 | #97 | — | 3 | 2 | no | — |
| 536 | C4×C8 | — | 3 | 2 | no | — |
| 537 | C23×C3 | — | 8 | 1 | no | — |
| 538 | C22×D3 | — | 4 | 1 | no | — |
| 539 | C22×D3 | — | 8 | 1 | no | — |
| 540 | C3×Q8 | — | 4 | 1 | no | — |
| 541 | C3×D4 | — | 4 | 2 | no | — |
| 542 | C3×D4 | — | 4 | 1 | no | — |
| 543 | C3×D4 | — | 8 | 1 | no | — |
| 544 | C3×D4 | — | 8 | 1 | no | — |
| 545 | C2×C3×C4 | — | 4 | 1 | no | — |
| 546 | C2×C3×C4 | — | 8 | 1 | no | — |
| 547 | #67 | — | 8 | 1 | no | — |
| 548 | #67 | — | 8 | 1 | no | — |
| 549 | #67 | — | 8 | 2 | no | — |
| 550 | #67 | — | 8 | 2 | no | — |
| 551 | #67 | — | 8 | 1 | no | — |
| 552 | C2×Dic3 | — | 4 | 1 | no | — |
| 553 | C2×Dic3 | — | 8 | 1 | no | — |
| 554 | C2×Dic3 | — | 8 | 2 | no | — |
| 555 | C2×Dic3 | — | 8 | 2 | no | — |
| 556 | C2×Dic3 | — | 8 | 1 | no | — |
| 557 | D12 | — | 4 | 1 | no | — |
| 558 | D12 | — | 8 | 1 | no | — |
| 559 | C4×D3 | — | 4 | 1 | no | — |
| 560 | C4×D3 | — | 4 | 1 | no | — |
| 561 | C4×D3 | — | 4 | 1 | no | — |
| 562 | C4×D3 | — | 4 | 1 | no | — |
| 563 | C4×D3 | — | 8 | 1 | no | — |
| 564 | C4×D3 | — | 8 | 1 | no | — |
| 565 | C4×D3 | — | 8 | 1 | no | — |
| 566 | Dic6 | — | 4 | 2 | no | — |
| 567 | Dic6 | — | 4 | 1 | no | — |
| 568 | Dic6 | — | 8 | 1 | no | — |
| 569 | Dic6 | — | 8 | 1 | no | — |
| 570 | SL(2,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 571 | C3×C8 | — | 4 | 2 | no | — |
| 572 | C3⋊C8 | — | 4 | 2 | no | — |
| 573 | #41 | — | 2 | 1 | no | — |
| 574 | #41 | — | 3 | 1 | no | — |
| 575 | #41 | — | 3 | 1 | no | — |
| 576 | #41 | — | 3 | 1 | no | — |
| 577 | #41 | — | 3 | 1 | no | — |
| 578 | #41 | — | 3 | 1 | no | — |
| 579 | #41 | — | 3 | 1 | no | — |
| 580 | #41 | — | 3 | 1 | no | — |
| 581 | #41 | — | 3 | 2 | no | — |
| 582 | #41 | — | 3 | 1 | no | — |
| 583 | #41 | — | 3 | 2 | no | — |
| 584 | #41 | — | 3 | 1 | no | — |
| 585 | #41 | — | 6 | 1 | no | — |
| 586 | #41 | — | 6 | 1 | no | — |
| 587 | #41 | — | 6 | 1 | no | — |
| 588 | #41 | — | 6 | 1 | no | — |
| 589 | #41 | — | 6 | 1 | no | — |
| 590 | #41 | — | 6 | 1 | no | — |
| 591 | #41 | — | 6 | 1 | no | — |
| 592 | #41 | — | 6 | 1 | no | — |
| 593 | #41 | — | 6 | 1 | no | — |
| 594 | #41 | — | 6 | 1 | no | — |
| 595 | #41 | — | 6 | 1 | no | — |
| 596 | #41 | — | 6 | 1 | no | — |
| 597 | #41 | — | 6 | 1 | no | — |
| 598 | #41 | — | 6 | 2 | no | — |
| 599 | #41 | — | 6 | 1 | no | — |
| 600 | #41 | — | 6 | 2 | no | — |
| 601 | #41 | — | 6 | 1 | no | — |
| 602 | #41 | — | 6 | 1 | no | — |
| 603 | #41 | — | 6 | 1 | no | — |
| 604 | #41 | — | 6 | 2 | no | — |
| 605 | #41 | — | 6 | 2 | no | — |
| 606 | #41 | — | 6 | 1 | no | — |
| 607 | #41 | — | 6 | 1 | no | — |
| 608 | #41 | — | 6 | 1 | no | — |
| 609 | #41 | — | 6 | 1 | no | — |
| 610 | #41 | — | 6 | 1 | no | — |
| 611 | #41 | — | 6 | 2 | no | — |
| 612 | #41 | — | 6 | 2 | no | — |
| 613 | #41 | — | 6 | 1 | no | — |
| 614 | #41 | — | 6 | 1 | no | — |
| 615 | #41 | — | 12 | 1 | no | — |
| 616 | #41 | — | 12 | 2 | no | — |
| 617 | #41 | — | 12 | 1 | no | — |
| 618 | #41 | — | 12 | 1 | no | — |
| 619 | #41 | — | 12 | 1 | no | — |
| 620 | #41 | — | 12 | 1 | no | — |
| 621 | #41 | — | 12 | 1 | no | — |
| 622 | #41 | — | 12 | 1 | no | — |
| 623 | #41 | — | 12 | 1 | no | — |
| 624 | #41 | — | 12 | 2 | no | — |
| 625 | #41 | — | 12 | 2 | no | — |
| 626 | #41 | — | 12 | 1 | no | — |
| 627 | #41 | — | 12 | 1 | no | — |
| 628 | #41 | — | 12 | 1 | no | — |
| 629 | #41 | — | 12 | 2 | no | — |
| 630 | #41 | — | 12 | 2 | no | — |
| 631 | #41 | — | 12 | 2 | no | — |
| 632 | #41 | — | 12 | 1 | no | — |
| 633 | #41 | — | 12 | 1 | no | — |
| 634 | #41 | D3×D4 | 1 | 1 | yes | characteristic |
| 635 | #41 | C2×S4 | 1 | 1 | yes | characteristic |
| 636 | #41 | C23×D3 | 1 | 1 | yes | characteristic |
| 637 | C2×Q8 | — | 2 | 1 | no | — |
| 638 | C2×Q8 | — | 2 | 2 | no | — |
| 639 | C2×Q8 | — | 3 | 1 | no | — |
| 640 | C2×Q8 | — | 3 | 2 | no | — |
| 641 | C2×Q8 | — | 3 | 1 | no | — |
| 642 | C2×Q8 | — | 3 | 1 | no | — |
| 643 | C2×Q8 | — | 3 | 2 | no | — |
| 644 | C2×Q8 | — | 3 | 1 | no | — |
| 645 | C2×Q8 | — | 3 | 1 | no | — |
| 646 | C2×Q8 | — | 6 | 1 | no | — |
| 647 | C2×Q8 | — | 6 | 1 | no | — |
| 648 | C2×Q8 | — | 6 | 1 | no | — |
| 649 | C2×Q8 | — | 6 | 1 | no | — |
| 650 | C2×Q8 | — | 6 | 1 | no | — |
| 651 | C2×Q8 | — | 6 | 1 | no | — |
| 652 | C2×Q8 | — | 6 | 1 | no | — |
| 653 | C2×Q8 | — | 6 | 1 | no | — |
| 654 | C2×Q8 | — | 6 | 2 | no | — |
| 655 | C2×Q8 | — | 6 | 1 | no | — |
| 656 | C2×Q8 | — | 6 | 2 | no | — |
| 657 | C2×Q8 | — | 6 | 2 | no | — |
| 658 | C2×Q8 | — | 6 | 1 | no | — |
| 659 | C2×Q8 | — | 6 | 1 | no | — |
| 660 | C2×Q8 | — | 6 | 2 | no | — |
| 661 | C2×Q8 | — | 6 | 2 | no | — |
| 662 | C2×Q8 | — | 6 | 1 | no | — |
| 663 | C2×Q8 | — | 6 | 1 | no | — |
| 664 | C2×Q8 | — | 6 | 1 | no | — |
| 665 | C2×Q8 | — | 12 | 1 | no | — |
| 666 | C2×Q8 | — | 12 | 2 | no | — |
| 667 | C2×Q8 | — | 12 | 1 | no | — |
| 668 | C2×Q8 | — | 12 | 1 | no | — |
| 669 | C2×Q8 | — | 12 | 1 | no | — |
| 670 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 671 | C2×D4 | — | 3 | 1 | no | — |
| 672 | C2×D4 | — | 3 | 1 | no | — |
| 673 | C2×D4 | — | 3 | 1 | no | — |
| 674 | C2×D4 | — | 3 | 1 | no | — |
| 675 | C2×D4 | — | 3 | 1 | no | — |
| 676 | C2×D4 | — | 6 | 1 | no | — |
| 677 | C2×D4 | — | 6 | 1 | no | — |
| 678 | C2×D4 | — | 6 | 1 | no | — |
| 679 | C2×D4 | — | 6 | 1 | no | — |
| 680 | C2×D4 | — | 6 | 1 | no | — |
| 681 | C2×D4 | — | 6 | 1 | no | — |
| 682 | C2×D4 | — | 6 | 1 | no | — |
| 683 | C2×D4 | — | 6 | 1 | no | — |
| 684 | C2×D4 | — | 6 | 1 | no | — |
| 685 | C2×D4 | — | 6 | 1 | no | — |
| 686 | C2×D4 | — | 6 | 1 | no | — |
| 687 | C2×D4 | — | 12 | 1 | no | — |
| 688 | C2×D4 | — | 12 | 1 | no | — |
| 689 | C2×D4 | — | 12 | 1 | no | — |
| 690 | C2×D4 | — | 12 | 1 | no | — |
| 691 | C2×D4 | — | 12 | 1 | no | — |
| 692 | C2×D4 | — | 12 | 1 | no | — |
| 693 | C2×D4 | — | 12 | 1 | no | — |
| 694 | C2×D4 | — | 12 | 1 | no | — |
| 695 | C2×D4 | — | 12 | 1 | no | — |
| 696 | C2×D4 | C2×S4 | 1 | 1 | yes | characteristic |
| 697 | C22×C4 | — | 3 | 1 | no | — |
| 698 | C22×C4 | — | 6 | 1 | no | — |
| 699 | C22×C4 | — | 6 | 1 | no | — |
| 700 | C22×C4 | — | 6 | 1 | no | — |
| 701 | C22×C4 | — | 6 | 1 | no | — |
| 702 | C22×C4 | — | 6 | 1 | no | — |
| 703 | C22×C4 | — | 6 | 1 | no | — |
| 704 | C22×C4 | — | 6 | 1 | no | — |
| 705 | C22×C4 | — | 12 | 1 | no | — |
| 706 | C22×C4 | — | 12 | 1 | no | — |
| 707 | C22×C4 | — | 12 | 1 | no | — |
| 708 | C22×C4 | — | 12 | 1 | no | — |
| 709 | Q16 | — | 3 | 1 | no | — |
| 710 | Q16 | — | 3 | 1 | no | — |
| 711 | Q16 | — | 3 | 1 | no | — |
| 712 | Q16 | — | 3 | 1 | no | — |
| 713 | Q16 | — | 3 | 2 | no | — |
| 714 | Q16 | — | 3 | 2 | no | — |
| 715 | Q16 | — | 6 | 2 | no | — |
| 716 | Q16 | — | 6 | 2 | no | — |
| 717 | Q16 | — | 6 | 2 | no | — |
| 718 | Q16 | — | 6 | 1 | no | — |
| 719 | Q16 | — | 6 | 2 | no | — |
| 720 | Q16 | — | 6 | 2 | no | — |
| 721 | Q16 | — | 6 | 2 | no | — |
| 722 | Q16 | — | 6 | 1 | no | — |
| 723 | Q16 | — | 6 | 2 | no | — |
| 724 | Q16 | — | 6 | 2 | no | — |
| 725 | Q16 | — | 6 | 2 | no | — |
| 726 | Q16 | — | 6 | 2 | no | — |
| 727 | Q16 | — | 6 | 2 | no | — |
| 728 | Q16 | — | 6 | 1 | no | — |
| 729 | Q16 | — | 6 | 1 | no | — |
| 730 | Q16 | — | 6 | 1 | no | — |
| 731 | Q16 | — | 6 | 2 | no | — |
| 732 | Q16 | — | 6 | 1 | no | — |
| 733 | Q16 | — | 6 | 2 | no | — |
| 734 | Q16 | — | 6 | 2 | no | — |
| 735 | SD16 | — | 3 | 1 | no | — |
| 736 | SD16 | — | 3 | 1 | no | — |
| 737 | SD16 | — | 3 | 1 | no | — |
| 738 | SD16 | — | 3 | 1 | no | — |
| 739 | SD16 | — | 3 | 1 | no | — |
| 740 | SD16 | — | 3 | 1 | no | — |
| 741 | SD16 | — | 3 | 1 | no | — |
| 742 | SD16 | — | 3 | 1 | no | — |
| 743 | SD16 | — | 3 | 2 | no | — |
| 744 | SD16 | — | 3 | 2 | no | — |
| 745 | SD16 | — | 3 | 2 | no | — |
| 746 | SD16 | — | 6 | 2 | no | — |
| 747 | SD16 | — | 6 | 1 | no | — |
| 748 | SD16 | — | 6 | 1 | no | — |
| 749 | SD16 | — | 6 | 2 | no | — |
| 750 | SD16 | — | 6 | 1 | no | — |
| 751 | SD16 | — | 6 | 1 | no | — |
| 752 | SD16 | — | 6 | 2 | no | — |
| 753 | SD16 | — | 6 | 1 | no | — |
| 754 | SD16 | — | 6 | 1 | no | — |
| 755 | SD16 | — | 6 | 1 | no | — |
| 756 | SD16 | — | 6 | 1 | no | — |
| 757 | SD16 | — | 6 | 2 | no | — |
| 758 | SD16 | — | 6 | 2 | no | — |
| 759 | SD16 | — | 6 | 2 | no | — |
| 760 | SD16 | — | 6 | 2 | no | — |
| 761 | SD16 | — | 6 | 2 | no | — |
| 762 | SD16 | — | 6 | 1 | no | — |
| 763 | SD16 | — | 6 | 1 | no | — |
| 764 | SD16 | — | 6 | 1 | no | — |
| 765 | SD16 | — | 6 | 1 | no | — |
| 766 | SD16 | — | 6 | 2 | no | — |
| 767 | SD16 | — | 6 | 2 | no | — |
| 768 | SD16 | — | 6 | 2 | no | — |
| 769 | SD16 | C2×S4 | 1 | 2 | yes | — |
| 770 | D8 | — | 3 | 1 | no | — |
| 771 | D8 | — | 3 | 1 | no | — |
| 772 | D8 | — | 3 | 1 | no | — |
| 773 | D8 | — | 3 | 1 | no | — |
| 774 | D8 | — | 3 | 2 | no | — |
| 775 | D8 | — | 6 | 1 | no | — |
| 776 | D8 | — | 6 | 1 | no | — |
| 777 | D8 | — | 6 | 1 | no | — |
| 778 | D8 | — | 6 | 1 | no | — |
| 779 | D8 | — | 6 | 1 | no | — |
| 780 | D8 | — | 6 | 1 | no | — |
| 781 | D8 | — | 6 | 2 | no | — |
| 782 | D8 | C2×S4 | 1 | 2 | yes | — |
| 783 | M16 | — | 3 | 1 | no | — |
| 784 | M16 | — | 3 | 2 | no | — |
| 785 | M16 | — | 3 | 2 | no | — |
| 786 | M16 | — | 3 | 2 | no | — |
| 787 | M16 | — | 3 | 2 | no | — |
| 788 | M16 | — | 3 | 1 | no | — |
| 789 | M16 | — | 3 | 1 | no | — |
| 790 | M16 | — | 6 | 1 | no | — |
| 791 | M16 | — | 6 | 1 | no | — |
| 792 | M16 | — | 6 | 1 | no | — |
| 793 | M16 | — | 6 | 1 | no | — |
| 794 | M16 | — | 6 | 2 | no | — |
| 795 | M16 | — | 6 | 2 | no | — |
| 796 | M16 | — | 6 | 2 | no | — |
| 797 | M16 | — | 6 | 1 | no | — |
| 798 | M16 | — | 6 | 1 | no | — |
| 799 | M16 | — | 6 | 1 | no | — |
| 800 | M16 | — | 6 | 2 | no | — |
| 801 | M16 | C2×S4 | 1 | 1 | yes | characteristic |
| 802 | C2×C8 | — | 3 | 1 | no | — |
| 803 | C2×C8 | — | 3 | 1 | no | — |
| 804 | C2×C8 | — | 3 | 1 | no | — |
| 805 | C2×C8 | — | 3 | 1 | no | — |
| 806 | C2×C8 | — | 3 | 1 | no | — |
| 807 | C2×C8 | — | 3 | 1 | no | — |
| 808 | C2×C8 | — | 3 | 2 | no | — |
| 809 | C2×C8 | — | 6 | 1 | no | — |
| 810 | C2×C8 | — | 6 | 1 | no | — |
| 811 | C2×C8 | — | 6 | 1 | no | — |
| 812 | C2×C8 | — | 6 | 1 | no | — |
| 813 | C2×C8 | — | 6 | 1 | no | — |
| 814 | C2×C8 | — | 6 | 2 | no | — |
| 815 | C2×C8 | — | 6 | 2 | no | — |
| 816 | C2×C8 | — | 6 | 2 | no | — |
| 817 | C2×C8 | — | 6 | 1 | no | — |
| 818 | C2×C8 | — | 6 | 1 | no | — |
| 819 | C2×C8 | — | 6 | 1 | no | — |
| 820 | C2×C8 | — | 6 | 2 | no | — |
| 821 | C4⋊C4 | — | 6 | 1 | no | — |
| 822 | C4⋊C4 | — | 12 | 2 | no | — |
| 823 | C4⋊C4 | — | 12 | 2 | no | — |
| 824 | C22⋊C4 | — | 6 | 1 | no | — |
| 825 | C22⋊C4 | — | 12 | 2 | no | — |
| 826 | C22⋊C4 | — | 12 | 2 | no | — |
| 827 | C42 | — | 3 | 2 | no | — |
| 828 | C22×C3 | — | 4 | 1 | no | — |
| 829 | C22×C3 | — | 8 | 2 | no | — |
| 830 | C22×C3 | — | 8 | 1 | no | — |
| 831 | C22×C3 | — | 16 | 2 | no | — |
| 832 | C2×D3 | — | 4 | 1 | no | — |
| 833 | C2×D3 | — | 4 | 1 | no | — |
| 834 | C2×D3 | — | 8 | 1 | no | — |
| 835 | C2×D3 | — | 16 | 1 | no | — |
| 836 | C2×D3 | — | 16 | 2 | no | — |
| 837 | C3×C4 | — | 4 | 1 | no | — |
| 838 | C3×C4 | — | 4 | 1 | no | — |
| 839 | C3×C4 | — | 8 | 1 | no | — |
| 840 | Dic3 | — | 4 | 1 | no | — |
| 841 | Dic3 | — | 4 | 1 | no | — |
| 842 | Dic3 | — | 8 | 1 | no | — |
| 843 | Dic3 | — | 8 | 2 | no | — |
| 844 | C23 | — | 2 | 1 | no | — |
| 845 | C23 | — | 3 | 1 | no | — |
| 846 | C23 | — | 6 | 1 | no | — |
| 847 | C23 | — | 6 | 1 | no | — |
| 848 | C23 | — | 6 | 1 | no | — |
| 849 | C23 | — | 6 | 1 | no | — |
| 850 | C23 | — | 12 | 1 | no | — |
| 851 | C23 | — | 12 | 1 | no | — |
| 852 | Q8 | — | 3 | 1 | no | — |
| 853 | Q8 | — | 3 | 1 | no | — |
| 854 | Q8 | — | 3 | 1 | no | — |
| 855 | Q8 | — | 3 | 2 | no | — |
| 856 | Q8 | — | 3 | 1 | no | — |
| 857 | Q8 | — | 6 | 1 | no | — |
| 858 | Q8 | — | 6 | 1 | no | — |
| 859 | Q8 | — | 6 | 2 | no | — |
| 860 | Q8 | — | 6 | 1 | no | — |
| 861 | Q8 | — | 6 | 1 | no | — |
| 862 | Q8 | — | 6 | 2 | no | — |
| 863 | Q8 | — | 6 | 1 | no | — |
| 864 | Q8 | — | 6 | 2 | no | — |
| 865 | Q8 | — | 6 | 1 | no | — |
| 866 | Q8 | — | 12 | 1 | no | — |
| 867 | Q8 | — | 12 | 1 | no | — |
| 868 | Q8 | — | 12 | 1 | no | — |
| 869 | Q8 | — | 12 | 2 | no | — |
| 870 | Q8 | — | 12 | 2 | no | — |
| 871 | Q8 | — | 12 | 1 | no | — |
| 872 | Q8 | — | 12 | 1 | no | — |
| 873 | Q8 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 874 | Q8 | C22×S4 | 1 | 1 | yes | characteristic |
| 875 | D4 | — | 2 | 1 | no | — |
| 876 | D4 | — | 2 | 1 | no | — |
| 877 | D4 | — | 3 | 1 | no | — |
| 878 | D4 | — | 3 | 1 | no | — |
| 879 | D4 | — | 3 | 1 | no | — |
| 880 | D4 | — | 3 | 1 | no | — |
| 881 | D4 | — | 3 | 1 | no | — |
| 882 | D4 | — | 6 | 1 | no | — |
| 883 | D4 | — | 6 | 1 | no | — |
| 884 | D4 | — | 6 | 1 | no | — |
| 885 | D4 | — | 6 | 1 | no | — |
| 886 | D4 | — | 6 | 1 | no | — |
| 887 | D4 | — | 6 | 1 | no | — |
| 888 | D4 | — | 6 | 1 | no | — |
| 889 | D4 | — | 6 | 2 | no | — |
| 890 | D4 | — | 6 | 2 | no | — |
| 891 | D4 | — | 6 | 1 | no | — |
| 892 | D4 | — | 6 | 1 | no | — |
| 893 | D4 | — | 6 | 1 | no | — |
| 894 | D4 | — | 6 | 1 | no | — |
| 895 | D4 | — | 6 | 1 | no | — |
| 896 | D4 | — | 6 | 1 | no | — |
| 897 | D4 | — | 12 | 1 | no | — |
| 898 | D4 | — | 12 | 1 | no | — |
| 899 | D4 | — | 12 | 1 | no | — |
| 900 | D4 | — | 12 | 1 | no | — |
| 901 | D4 | — | 12 | 1 | no | — |
| 902 | D4 | — | 12 | 1 | no | — |
| 903 | D4 | — | 12 | 2 | no | — |
| 904 | D4 | — | 12 | 2 | no | — |
| 905 | D4 | — | 12 | 1 | no | — |
| 906 | D4 | — | 12 | 1 | no | — |
| 907 | D4 | — | 12 | 1 | no | — |
| 908 | D4 | C22×S4 | 1 | 2 | yes | — |
| 909 | D4 | C22×S4 | 1 | 1 | yes | characteristic |
| 910 | C2×C4 | — | 2 | 1 | no | — |
| 911 | C2×C4 | — | 3 | 1 | no | — |
| 912 | C2×C4 | — | 3 | 1 | no | — |
| 913 | C2×C4 | — | 3 | 1 | no | — |
| 914 | C2×C4 | — | 3 | 1 | no | — |
| 915 | C2×C4 | — | 3 | 1 | no | — |
| 916 | C2×C4 | — | 6 | 1 | no | — |
| 917 | C2×C4 | — | 6 | 1 | no | — |
| 918 | C2×C4 | — | 6 | 1 | no | — |
| 919 | C2×C4 | — | 6 | 2 | no | — |
| 920 | C2×C4 | — | 6 | 2 | no | — |
| 921 | C2×C4 | — | 6 | 1 | no | — |
| 922 | C2×C4 | — | 6 | 1 | no | — |
| 923 | C2×C4 | — | 6 | 1 | no | — |
| 924 | C2×C4 | — | 6 | 1 | no | — |
| 925 | C2×C4 | — | 6 | 1 | no | — |
| 926 | C2×C4 | — | 6 | 1 | no | — |
| 927 | C2×C4 | — | 6 | 1 | no | — |
| 928 | C2×C4 | — | 6 | 2 | no | — |
| 929 | C2×C4 | — | 6 | 1 | no | — |
| 930 | C2×C4 | — | 6 | 2 | no | — |
| 931 | C2×C4 | — | 6 | 2 | no | — |
| 932 | C2×C4 | — | 6 | 1 | no | — |
| 933 | C2×C4 | — | 12 | 1 | no | — |
| 934 | C2×C4 | — | 12 | 1 | no | — |
| 935 | C2×C4 | — | 12 | 1 | no | — |
| 936 | C2×C4 | — | 12 | 1 | no | — |
| 937 | C2×C4 | — | 12 | 1 | no | — |
| 938 | C2×C4 | — | 12 | 1 | no | — |
| 939 | C2×C4 | — | 12 | 1 | no | — |
| 940 | C2×C4 | — | 12 | 2 | no | — |
| 941 | C2×C4 | — | 12 | 2 | no | — |
| 942 | C2×C4 | — | 12 | 1 | no | — |
| 943 | C2×C4 | — | 12 | 1 | no | — |
| 944 | C2×C4 | — | 12 | 2 | no | — |
| 945 | C2×C4 | — | 12 | 2 | no | — |
| 946 | C2×C4 | — | 12 | 1 | no | — |
| 947 | C2×C4 | — | 12 | 1 | no | — |
| 948 | C2×C4 | — | 12 | 1 | no | — |
| 949 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 950 | C8 | — | 3 | 1 | no | — |
| 951 | C8 | — | 3 | 1 | no | — |
| 952 | C8 | — | 3 | 1 | no | — |
| 953 | C8 | — | 3 | 1 | no | — |
| 954 | C8 | — | 3 | 2 | no | — |
| 955 | C8 | — | 6 | 1 | no | — |
| 956 | C8 | — | 6 | 1 | no | — |
| 957 | C8 | — | 6 | 2 | no | — |
| 958 | C8 | — | 6 | 2 | no | — |
| 959 | C8 | C22×S4 | 1 | 2 | yes | — |
| 960 | C2×C3 | — | 4 | 1 | no | — |
| 961 | C2×C3 | — | 8 | 1 | no | — |
| 962 | C2×C3 | — | 16 | 1 | no | — |
| 963 | C2×C3 | — | 16 | 2 | no | — |
| 964 | D3 | — | 8 | 1 | no | — |
| 965 | D3 | — | 8 | 1 | no | — |
| 966 | D3 | — | 16 | 1 | no | — |
| 967 | C22 | — | 2 | 1 | no | — |
| 968 | C22 | — | 2 | 2 | no | — |
| 969 | C22 | — | 3 | 1 | no | — |
| 970 | C22 | — | 3 | 1 | no | — |
| 971 | C22 | — | 4 | 2 | no | — |
| 972 | C22 | — | 6 | 1 | no | — |
| 973 | C22 | — | 6 | 1 | no | — |
| 974 | C22 | — | 6 | 1 | no | — |
| 975 | C22 | — | 12 | 1 | no | — |
| 976 | C22 | — | 12 | 1 | no | — |
| 977 | C22 | — | 24 | 1 | no | — |
| 978 | C22 | — | 24 | 1 | no | — |
| 979 | C22 | — | 24 | 1 | no | — |
| 980 | C22 | — | 24 | 1 | no | — |
| 981 | C22 | — | 48 | 1 | no | — |
| 982 | C22 | — | 48 | 1 | no | — |
| 983 | C22 | D4×S4 | 1 | 1 | yes | characteristic |
| 984 | C4 | — | 2 | 1 | no | — |
| 985 | C4 | — | 3 | 1 | no | — |
| 986 | C4 | — | 3 | 1 | no | — |
| 987 | C4 | — | 6 | 1 | no | — |
| 988 | C4 | — | 6 | 2 | no | — |
| 989 | C4 | — | 6 | 1 | no | — |
| 990 | C4 | — | 6 | 1 | no | — |
| 991 | C4 | — | 12 | 2 | no | — |
| 992 | C4 | — | 12 | 1 | no | — |
| 993 | C4 | — | 12 | 2 | no | — |
| 994 | C4 | D4×S4 | 1 | 1 | yes | characteristic |
| 995 | C4 | C23×S4 | 1 | 1 | yes | characteristic |
| 996 | C3 | — | 4 | 1 | no | Sylow |
| 997 | C2 | — | 2 | 1 | no | — |
| 998 | C2 | — | 4 | 2 | no | — |
| 999 | C2 | — | 4 | 1 | no | — |
| 1000 | C2 | — | 6 | 1 | no | — |
| 1001 | C2 | — | 6 | 1 | no | — |
| 1002 | C2 | — | 12 | 1 | no | — |
| 1003 | C2 | — | 12 | 1 | no | — |
| 1004 | C2 | — | 12 | 1 | no | — |
| 1005 | C2 | — | 24 | 1 | no | — |
| 1006 | C2 | C2×D4×S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C2×D4×S4 |
| commutator, cosocle | #41⋊C3 | C24 |
| Frattini | C4 | C23×S4 |
| Fitting | #3586 | D3 |
| hypercenter | AGL(1,ℤ/8) | S4 |
| hypocenter | SL(2,𝔽3) | C22×D4 |
| LCS | G ▷ #41⋊C3 ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #87497 | C2 | semidirect |
| 2. C2×#5927 | C2 | semidirect |
| 3. #3586⋊C3 | C2 | semidirect |
| 4. #85542 | C2 | semidirect |
| 5. #85533 | C2 | semidirect |
| 6. #85475 | C2 | semidirect |
| 7. #85474 | C2 | semidirect |
| 8. #85472 | C2 | semidirect |
| 9. #85471 | C2 | semidirect |
| 10. #85455 | C2 | semidirect |
| 11. #85452 | C2 | semidirect |
| 14. C2×2−1+4⋊C3 | C22 | semidirect |
| 18. #5927 | C22 | semidirect |
| 19. #5927 | C22 | semidirect |
| 20. #5927 | C22 | semidirect |
| 22. #5926 | C22 | semidirect |
| 23. #5925 | C22 | semidirect |
| 24. #5924 | C22 | semidirect |
| 29. C2×#984 | C22 | semidirect |
| 33. #578⋊C3 | C22 | semidirect |
| 34. #577⋊C3 | C22 | semidirect |
| 35. #568⋊C3 | C22 | semidirect |
| 36. #5431 | C22 | semidirect |
| 37. #5430 | C22 | semidirect |
| 38. #5430 | C22 | semidirect |
| 39. #5428 | C22 | semidirect |
| 40. #5423 | C22 | semidirect |
| 41. #5406 | C22 | semidirect |
| 42. #5405 | C22 | semidirect |
| 43. #5404 | C22 | semidirect |
| 44. #5403 | C22 | semidirect |
| 46. #3586 | D3 | semidirect |
| 117. C2×2−1+4 | C2×D3 | semidirect |
| 133. #578 | C2×D3 | semidirect |
| 144. #577 | C2×D3 | semidirect |
| 175. #568 | C2×D3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #87497 | 2 |
| C2×#5927 | 2 |
| #3586⋊C3 | 2 |
| #85542 | 2 |
| #85533 | 2 |
| #85475 | 2 |
| #85474 | 2 |
| #85472 | 2 |
| #85471 | 2 |
| #85455 | 2 |
| #85452 | 2 |
| #61108 | 3 |
| #5773 | 4 |