Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 1350 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 | #87498 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #87496 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #3586⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #85544 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#5431 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #85474 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #85473 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #85472 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #85470 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #85454 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #85453 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #61109 | — | 3 | 1 | no | maximal, Sylow |
| 13 | #5945 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C2×2−1+4⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #5927 | — | 2 | 1 | no | — |
| 16 | #5927 | C22 | 1 | 2 | yes | complemented |
| 17 | #5926 | — | 2 | 1 | no | — |
| 18 | #5926 | — | 2 | 2 | no | — |
| 19 | #5926 | C22 | 1 | 2 | yes | complemented |
| 20 | #5926 | C22 | 1 | 2 | yes | complemented |
| 21 | #5925 | C22 | 1 | 2 | yes | complemented |
| 22 | #5923 | — | 2 | 1 | no | — |
| 23 | #5923 | C22 | 1 | 1 | yes | characteristic |
| 24 | #5923 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C2×#986 | — | 2 | 1 | no | — |
| 26 | C2×#986 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×#983 | — | 2 | 2 | no | — |
| 28 | #5774 | — | 4 | 1 | no | maximal |
| 29 | #578⋊C3 | C22 | 1 | 2 | yes | complemented |
| 30 | #577⋊C3 | C22 | 1 | 2 | yes | complemented |
| 31 | #568⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #5431 | C22 | 1 | 2 | yes | complemented |
| 33 | #5431 | C22 | 1 | 2 | yes | complemented |
| 34 | #5431 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #5430 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #5429 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #5428 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | C2×GU(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #5407 | C22 | 1 | 2 | yes | complemented |
| 40 | #5406 | C22 | 1 | 2 | yes | complemented |
| 41 | #5405 | C22 | 1 | 2 | yes | complemented |
| 42 | #5404 | C22 | 1 | 2 | yes | complemented |
| 43 | #3586 | — | 3 | 1 | no | — |
| 44 | #3586 | D3 | 1 | 1 | yes | characteristic, complemented |
| 45 | #3585 | — | 3 | 1 | no | — |
| 46 | #3585 | — | 3 | 1 | no | — |
| 47 | #3290 | — | 3 | 2 | no | — |
| 48 | #3290 | — | 3 | 2 | no | — |
| 49 | #3290 | — | 3 | 2 | no | — |
| 50 | #3290 | — | 3 | 2 | no | — |
| 51 | #3289 | — | 3 | 2 | no | — |
| 52 | #3289 | — | 3 | 2 | no | — |
| 53 | #3288 | — | 3 | 2 | no | — |
| 54 | #3288 | — | 3 | 2 | no | — |
| 55 | #3153 | — | 3 | 1 | no | — |
| 56 | #3069 | — | 3 | 1 | no | — |
| 57 | #3069 | — | 3 | 1 | no | — |
| 58 | #3068 | — | 3 | 1 | no | — |
| 59 | #3068 | — | 3 | 1 | no | — |
| 60 | #3018 | — | 3 | 1 | no | — |
| 61 | #3018 | — | 3 | 1 | no | — |
| 62 | C2×#454 | — | 3 | 1 | no | — |
| 63 | C2×#455 | — | 3 | 1 | no | — |
| 64 | #2956 | — | 3 | 1 | no | — |
| 65 | #2956 | — | 3 | 1 | no | — |
| 66 | #1009 | — | 4 | 1 | no | — |
| 67 | #1004 | — | 4 | 1 | no | — |
| 68 | 2−1+4⋊C3 | — | 2 | 1 | no | — |
| 69 | 2−1+4⋊C3 | — | 2 | 1 | no | — |
| 70 | 2−1+4⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 71 | 2−1+4⋊C3 | C23 | 1 | 2 | yes | complemented |
| 72 | #994 | C23 | 1 | 1 | yes | characteristic |
| 73 | C2×#41⋊C3 | — | 2 | 1 | no | — |
| 74 | C2×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 75 | C22×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 76 | #986 | — | 2 | 1 | no | — |
| 77 | #986 | — | 2 | 2 | no | — |
| 78 | #986 | D4 | 1 | 1 | yes | characteristic, complemented |
| 79 | #986 | C23 | 1 | 2 | yes | — |
| 80 | #986 | C23 | 1 | 1 | yes | characteristic, complemented |
| 81 | #985 | — | 2 | 1 | no | — |
| 82 | #985 | — | 2 | 2 | no | — |
| 83 | #985 | C23 | 1 | 2 | yes | — |
| 84 | #984 | D4 | 1 | 1 | yes | characteristic, complemented |
| 85 | #984 | C23 | 1 | 1 | yes | characteristic, complemented |
| 86 | #983 | — | 2 | 1 | no | — |
| 87 | #983 | — | 2 | 2 | no | — |
| 88 | #983 | — | 2 | 2 | no | — |
| 89 | #983 | — | 2 | 2 | no | — |
| 90 | #983 | D4 | 1 | 2 | yes | complemented |
| 91 | C2×GL(2,𝔽3) | — | 2 | 1 | no | — |
| 92 | C2×GL(2,𝔽3) | — | 2 | 2 | no | — |
| 93 | C2×GL(2,𝔽3) | — | 2 | 2 | no | — |
| 94 | C2×#226 | — | 2 | 2 | no | — |
| 95 | C3×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 96 | #950 | — | 4 | 1 | no | — |
| 97 | C2×#213 | — | 4 | 1 | no | — |
| 98 | #916 | — | 4 | 2 | no | — |
| 99 | #914 | — | 4 | 2 | no | — |
| 100 | #911 | — | 4 | 2 | no | — |
| 101 | D3×D8 | — | 4 | 2 | no | — |
| 102 | #908 | — | 4 | 1 | no | — |
| 103 | #907 | — | 4 | 1 | no | — |
| 104 | #131⋊C3 | C23 | 1 | 2 | yes | complemented |
| 105 | GU(2,𝔽3) | C23 | 1 | 1 | yes | characteristic, complemented |
| 106 | GU(2,𝔽3) | C23 | 1 | 1 | yes | characteristic, complemented |
| 107 | #585 | — | 3 | 1 | no | — |
| 108 | #585 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 109 | C2×2−1+4 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 110 | C2×H(5,𝔽2) | — | 3 | 1 | no | — |
| 111 | #578 | — | 3 | 2 | no | — |
| 112 | #578 | — | 3 | 2 | no | — |
| 113 | #578 | — | 3 | 2 | no | — |
| 114 | #578 | — | 6 | 1 | no | — |
| 115 | #578 | — | 6 | 1 | no | — |
| 116 | #578 | C2×D3 | 1 | 2 | yes | complemented |
| 117 | #577 | — | 3 | 2 | no | — |
| 118 | #577 | — | 3 | 2 | no | — |
| 119 | #577 | — | 3 | 2 | no | — |
| 120 | #577 | — | 3 | 2 | no | — |
| 121 | #577 | — | 3 | 2 | no | — |
| 122 | #577 | — | 3 | 2 | no | — |
| 123 | #577 | — | 3 | 2 | no | — |
| 124 | #577 | — | 6 | 1 | no | — |
| 125 | #577 | — | 6 | 1 | no | — |
| 126 | #577 | — | 6 | 2 | no | — |
| 127 | #577 | — | 6 | 1 | no | — |
| 128 | #577 | — | 6 | 1 | no | — |
| 129 | #577 | C2×D3 | 1 | 2 | yes | complemented |
| 130 | #576 | — | 3 | 2 | no | — |
| 131 | #576 | — | 3 | 2 | no | — |
| 132 | #576 | — | 3 | 2 | no | — |
| 133 | #576 | — | 3 | 2 | no | — |
| 134 | #576 | — | 6 | 2 | no | — |
| 135 | #576 | — | 6 | 1 | no | — |
| 136 | #576 | — | 6 | 1 | no | — |
| 137 | #575 | — | 3 | 1 | no | — |
| 138 | #575 | — | 3 | 1 | no | — |
| 139 | #575 | — | 3 | 1 | no | — |
| 140 | #575 | — | 3 | 1 | no | — |
| 141 | #575 | — | 3 | 1 | no | — |
| 142 | #575 | — | 3 | 1 | no | — |
| 143 | #575 | — | 6 | 2 | no | — |
| 144 | #575 | — | 6 | 1 | no | — |
| 145 | #575 | — | 6 | 1 | no | — |
| 146 | #575 | — | 6 | 2 | no | — |
| 147 | C2×#137 | — | 3 | 1 | no | — |
| 148 | C2×#137 | — | 3 | 1 | no | — |
| 149 | C2×#137 | — | 3 | 1 | no | — |
| 150 | C2×#137 | — | 3 | 1 | no | — |
| 151 | C2×#137 | — | 6 | 2 | no | — |
| 152 | C2×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 153 | C2×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 154 | C2×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 155 | C2×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 156 | C2×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 157 | C2×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 158 | C2×AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 159 | #568 | — | 3 | 1 | no | — |
| 160 | #568 | — | 3 | 1 | no | — |
| 161 | #568 | — | 3 | 1 | no | — |
| 162 | #568 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 163 | #532 | — | 3 | 1 | no | — |
| 164 | C2×#124 | — | 3 | 1 | no | — |
| 165 | #497 | — | 3 | 2 | no | — |
| 166 | #496 | — | 3 | 2 | no | — |
| 167 | #495 | — | 3 | 2 | no | — |
| 168 | #495 | — | 3 | 2 | no | — |
| 169 | #473 | — | 3 | 2 | no | — |
| 170 | #473 | — | 3 | 2 | no | — |
| 171 | #473 | — | 3 | 2 | no | — |
| 172 | #473 | — | 3 | 2 | no | — |
| 173 | #472 | — | 3 | 2 | no | — |
| 174 | #472 | — | 3 | 2 | no | — |
| 175 | #472 | — | 3 | 2 | no | — |
| 176 | #472 | — | 3 | 2 | no | — |
| 177 | #471 | — | 3 | 2 | no | — |
| 178 | #471 | — | 3 | 2 | no | — |
| 179 | #471 | — | 3 | 2 | no | — |
| 180 | #471 | — | 3 | 2 | no | — |
| 181 | #471 | — | 3 | 2 | no | — |
| 182 | #471 | — | 3 | 2 | no | — |
| 183 | #471 | — | 3 | 2 | no | — |
| 184 | #471 | — | 3 | 2 | no | — |
| 185 | #456 | — | 3 | 2 | no | — |
| 186 | #456 | — | 3 | 1 | no | — |
| 187 | #456 | — | 3 | 1 | no | — |
| 188 | #455 | — | 3 | 2 | no | — |
| 189 | #455 | — | 3 | 2 | no | — |
| 190 | #455 | — | 3 | 2 | no | — |
| 191 | #455 | — | 3 | 2 | no | — |
| 192 | #455 | — | 3 | 2 | no | — |
| 193 | #455 | — | 3 | 1 | no | — |
| 194 | #455 | — | 3 | 1 | no | — |
| 195 | #454 | — | 3 | 2 | no | — |
| 196 | #454 | — | 3 | 2 | no | — |
| 197 | #454 | — | 3 | 2 | no | — |
| 198 | #454 | — | 3 | 1 | no | — |
| 199 | #454 | — | 3 | 2 | no | — |
| 200 | #454 | — | 3 | 2 | no | — |
| 201 | #454 | — | 3 | 1 | no | — |
| 202 | #453 | — | 3 | 2 | no | — |
| 203 | #453 | — | 3 | 1 | no | — |
| 204 | #453 | — | 3 | 1 | no | — |
| 205 | #444 | — | 3 | 2 | no | — |
| 206 | #444 | — | 3 | 2 | no | — |
| 207 | #444 | — | 3 | 2 | no | — |
| 208 | #444 | — | 3 | 2 | no | — |
| 209 | #443 | — | 3 | 2 | no | — |
| 210 | #443 | — | 3 | 2 | no | — |
| 211 | #443 | — | 3 | 2 | no | — |
| 212 | #443 | — | 3 | 2 | no | — |
| 213 | #430 | — | 3 | 1 | no | — |
| 214 | #430 | — | 3 | 1 | no | — |
| 215 | C2×#104 | — | 3 | 1 | no | — |
| 216 | C2×#104 | — | 3 | 1 | no | — |
| 217 | C2×#104 | — | 3 | 1 | no | — |
| 218 | C2×#104 | — | 3 | 1 | no | — |
| 219 | #413 | — | 3 | 1 | no | — |
| 220 | #413 | — | 3 | 1 | no | — |
| 221 | C2×#101 | — | 3 | 1 | no | — |
| 222 | C2×#100 | — | 3 | 1 | no | — |
| 223 | C4×M16 | — | 3 | 1 | no | — |
| 224 | C3×#41 | — | 4 | 1 | no | — |
| 225 | C2×C3×D4 | — | 4 | 1 | no | — |
| 226 | C2×#67 | — | 8 | 2 | no | — |
| 227 | #239 | — | 4 | 2 | no | — |
| 228 | #237 | — | 4 | 2 | no | — |
| 229 | #237 | — | 8 | 1 | no | — |
| 230 | D3×D4 | — | 4 | 2 | no | — |
| 231 | D3×D4 | — | 4 | 2 | no | — |
| 232 | D3×D4 | — | 8 | 1 | no | — |
| 233 | D3×D4 | — | 8 | 2 | no | — |
| 234 | #235 | — | 4 | 1 | no | — |
| 235 | #235 | — | 4 | 1 | no | — |
| 236 | #235 | — | 8 | 1 | no | — |
| 237 | C2×D12 | — | 4 | 1 | no | — |
| 238 | C2×D12 | — | 8 | 1 | no | — |
| 239 | #41⋊C3 | — | 2 | 1 | no | — |
| 240 | #41⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 241 | #41⋊C3 | C24 | 1 | 1 | yes | characteristic |
| 242 | C2×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 243 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 244 | C2×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 245 | GL(2,𝔽3) | — | 2 | 1 | no | — |
| 246 | GL(2,𝔽3) | — | 2 | 2 | no | — |
| 247 | GL(2,𝔽3) | C2×D4 | 1 | 2 | yes | — |
| 248 | #226 | — | 2 | 1 | no | — |
| 249 | #226 | C2×D4 | 1 | 2 | yes | — |
| 250 | C3×SD16 | — | 4 | 2 | no | — |
| 251 | C3×D8 | — | 4 | 2 | no | — |
| 252 | C3×M16 | — | 4 | 1 | no | — |
| 253 | #216 | — | 4 | 1 | no | — |
| 254 | #215 | — | 4 | 1 | no | — |
| 255 | #214 | — | 4 | 1 | no | — |
| 256 | #213 | — | 4 | 1 | no | — |
| 257 | #213 | — | 4 | 2 | no | — |
| 258 | #213 | — | 4 | 2 | no | — |
| 259 | C2×C3⋊C8 | — | 4 | 1 | no | — |
| 260 | D24 | — | 4 | 2 | no | — |
| 261 | #204 | — | 4 | 2 | no | — |
| 262 | ΓL(1,𝔽25) | — | 4 | 2 | no | — |
| 263 | D3×C8 | — | 4 | 2 | no | — |
| 264 | 2−1+4 | — | 2 | 1 | no | — |
| 265 | 2−1+4 | — | 2 | 1 | no | — |
| 266 | 2−1+4 | — | 3 | 1 | no | — |
| 267 | 2−1+4 | — | 3 | 2 | no | — |
| 268 | 2−1+4 | — | 3 | 2 | no | — |
| 269 | 2−1+4 | — | 6 | 1 | no | — |
| 270 | 2−1+4 | — | 6 | 1 | no | — |
| 271 | 2−1+4 | — | 6 | 1 | no | — |
| 272 | 2−1+4 | C22×D3 | 1 | 1 | yes | characteristic |
| 273 | 2−1+4 | C22×D3 | 1 | 2 | yes | — |
| 274 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 275 | H(5,𝔽2) | — | 3 | 2 | no | — |
| 276 | H(5,𝔽2) | — | 3 | 2 | no | — |
| 277 | H(5,𝔽2) | — | 3 | 2 | no | — |
| 278 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 279 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 280 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 281 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 282 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 283 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 284 | H(5,𝔽2) | — | 12 | 1 | no | — |
| 285 | H(5,𝔽2) | — | 12 | 1 | no | — |
| 286 | H(5,𝔽2) | C22×D3 | 1 | 1 | yes | characteristic |
| 287 | C2×#41 | — | 2 | 1 | no | — |
| 288 | C2×#41 | — | 3 | 1 | no | — |
| 289 | C2×#41 | — | 3 | 1 | no | — |
| 290 | C2×#41 | — | 3 | 1 | no | — |
| 291 | C2×#41 | — | 3 | 1 | no | — |
| 292 | C2×#41 | — | 3 | 1 | no | — |
| 293 | C2×#41 | — | 6 | 1 | no | — |
| 294 | C2×#41 | — | 6 | 1 | no | — |
| 295 | C2×#41 | — | 6 | 1 | no | — |
| 296 | C2×#41 | — | 6 | 1 | no | — |
| 297 | C2×#41 | — | 6 | 2 | no | — |
| 298 | C2×#41 | — | 6 | 2 | no | — |
| 299 | C2×#41 | — | 12 | 1 | no | — |
| 300 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 301 | C22×Q8 | — | 2 | 1 | no | — |
| 302 | C22×Q8 | — | 3 | 1 | no | — |
| 303 | C22×D4 | — | 3 | 1 | no | — |
| 304 | C22×D4 | — | 6 | 1 | no | — |
| 305 | C22×D4 | — | 6 | 1 | no | — |
| 306 | C22×D4 | — | 12 | 1 | no | — |
| 307 | #137 | — | 3 | 1 | no | — |
| 308 | #137 | — | 3 | 1 | no | — |
| 309 | #137 | — | 3 | 1 | no | — |
| 310 | #137 | — | 3 | 2 | no | — |
| 311 | #137 | — | 3 | 2 | no | — |
| 312 | #137 | — | 3 | 2 | no | — |
| 313 | #137 | — | 3 | 2 | no | — |
| 314 | #137 | — | 3 | 2 | no | — |
| 315 | #137 | — | 3 | 2 | no | — |
| 316 | #137 | — | 3 | 2 | no | — |
| 317 | #137 | — | 3 | 2 | no | — |
| 318 | #137 | — | 3 | 1 | no | — |
| 319 | #137 | — | 3 | 1 | no | — |
| 320 | #137 | — | 3 | 1 | no | — |
| 321 | #137 | — | 3 | 1 | no | — |
| 322 | #137 | — | 3 | 1 | no | — |
| 323 | #137 | — | 6 | 2 | no | — |
| 324 | #137 | — | 6 | 1 | no | — |
| 325 | #137 | — | 6 | 2 | no | — |
| 326 | #137 | — | 6 | 1 | no | — |
| 327 | #137 | — | 6 | 1 | no | — |
| 328 | #137 | — | 6 | 2 | no | — |
| 329 | #137 | — | 6 | 2 | no | — |
| 330 | #137 | — | 6 | 2 | no | — |
| 331 | #137 | — | 6 | 2 | no | — |
| 332 | #137 | — | 6 | 2 | no | — |
| 333 | #137 | — | 6 | 2 | no | — |
| 334 | #137 | — | 6 | 2 | no | — |
| 335 | #137 | — | 6 | 2 | no | — |
| 336 | #137 | — | 6 | 2 | no | — |
| 337 | #137 | — | 6 | 2 | no | — |
| 338 | #137 | — | 6 | 1 | no | — |
| 339 | #137 | — | 6 | 1 | no | — |
| 340 | #137 | — | 6 | 2 | no | — |
| 341 | #137 | — | 6 | 1 | no | — |
| 342 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 343 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 344 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 345 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 346 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 347 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 348 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 349 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 350 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 351 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 352 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 353 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 354 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 355 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 356 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 357 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 358 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 359 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 360 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 361 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 362 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 363 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 364 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 365 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 366 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 367 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 368 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 369 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 370 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 371 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 372 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 373 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 374 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 375 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 376 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 377 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 378 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 379 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 380 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 381 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 382 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 383 | AGL(1,ℤ/8) | S4 | 1 | 1 | yes | characteristic |
| 384 | #135 | — | 3 | 2 | no | — |
| 385 | #135 | — | 3 | 2 | no | — |
| 386 | #135 | — | 3 | 2 | no | — |
| 387 | #135 | — | 3 | 2 | no | — |
| 388 | #135 | — | 6 | 2 | no | — |
| 389 | #135 | — | 6 | 2 | no | — |
| 390 | #135 | — | 6 | 2 | no | — |
| 391 | #135 | — | 6 | 2 | no | — |
| 392 | #135 | — | 6 | 2 | no | — |
| 393 | #135 | — | 6 | 2 | no | — |
| 394 | #135 | — | 6 | 2 | no | — |
| 395 | #135 | — | 6 | 2 | no | — |
| 396 | #135 | — | 6 | 2 | no | — |
| 397 | #135 | — | 6 | 2 | no | — |
| 398 | #135 | — | 6 | 2 | no | — |
| 399 | #135 | — | 6 | 2 | no | — |
| 400 | #135 | — | 6 | 2 | no | — |
| 401 | #135 | — | 6 | 1 | no | — |
| 402 | #135 | — | 6 | 1 | no | — |
| 403 | #135 | — | 6 | 1 | no | — |
| 404 | #135 | — | 6 | 1 | no | — |
| 405 | #135 | — | 6 | 2 | no | — |
| 406 | C2×Q16 | — | 3 | 2 | no | — |
| 407 | C2×Q16 | — | 3 | 2 | no | — |
| 408 | C2×Q16 | — | 6 | 1 | no | — |
| 409 | C2×Q16 | — | 6 | 2 | no | — |
| 410 | C2×Q16 | — | 6 | 2 | no | — |
| 411 | C2×Q16 | — | 6 | 1 | no | — |
| 412 | C2×SD16 | — | 3 | 2 | no | — |
| 413 | C2×SD16 | — | 3 | 2 | no | — |
| 414 | C2×SD16 | — | 3 | 2 | no | — |
| 415 | C2×SD16 | — | 3 | 2 | no | — |
| 416 | C2×SD16 | — | 6 | 1 | no | — |
| 417 | C2×SD16 | — | 6 | 2 | no | — |
| 418 | C2×SD16 | — | 6 | 2 | no | — |
| 419 | C2×SD16 | — | 6 | 2 | no | — |
| 420 | C2×SD16 | — | 6 | 2 | no | — |
| 421 | C2×SD16 | — | 6 | 2 | no | — |
| 422 | C2×SD16 | — | 6 | 2 | no | — |
| 423 | C2×SD16 | — | 6 | 1 | no | — |
| 424 | C2×SD16 | — | 6 | 1 | no | — |
| 425 | C2×SD16 | — | 6 | 1 | no | — |
| 426 | C2×D8 | — | 3 | 2 | no | — |
| 427 | C2×D8 | — | 3 | 2 | no | — |
| 428 | C2×D8 | — | 6 | 2 | no | — |
| 429 | C2×D8 | — | 6 | 2 | no | — |
| 430 | C2×D8 | — | 6 | 2 | no | — |
| 431 | C2×D8 | — | 6 | 1 | no | — |
| 432 | C2×D8 | — | 6 | 1 | no | — |
| 433 | C2×D8 | — | 6 | 2 | no | — |
| 434 | #131 | — | 3 | 2 | no | — |
| 435 | #131 | — | 3 | 2 | no | — |
| 436 | #131 | — | 3 | 2 | no | — |
| 437 | #131 | — | 3 | 2 | no | — |
| 438 | #131 | — | 3 | 2 | no | — |
| 439 | #131 | — | 3 | 2 | no | — |
| 440 | #131 | — | 3 | 2 | no | — |
| 441 | #131 | — | 6 | 2 | no | — |
| 442 | #131 | — | 6 | 1 | no | — |
| 443 | #131 | — | 6 | 1 | no | — |
| 444 | #131 | — | 6 | 1 | no | — |
| 445 | #131 | — | 6 | 1 | no | — |
| 446 | #131 | C22×D3 | 1 | 2 | yes | — |
| 447 | C2×M16 | — | 3 | 1 | no | — |
| 448 | C2×M16 | — | 3 | 1 | no | — |
| 449 | C2×M16 | — | 3 | 1 | no | — |
| 450 | C2×M16 | — | 3 | 1 | no | — |
| 451 | C2×M16 | — | 3 | 1 | no | — |
| 452 | C2×M16 | — | 3 | 1 | no | — |
| 453 | C2×M16 | — | 6 | 1 | no | — |
| 454 | C2×M16 | — | 6 | 1 | no | — |
| 455 | C2×M16 | — | 6 | 2 | no | — |
| 456 | C2×M16 | — | 6 | 2 | no | — |
| 457 | C4⋊Q8 | — | 3 | 1 | no | — |
| 458 | #127 | — | 3 | 1 | no | — |
| 459 | #124 | — | 3 | 2 | no | — |
| 460 | #124 | — | 3 | 2 | no | — |
| 461 | #124 | — | 3 | 1 | no | — |
| 462 | #124 | — | 3 | 1 | no | — |
| 463 | #124 | — | 12 | 1 | no | — |
| 464 | #121 | — | 12 | 1 | no | — |
| 465 | C4×D4 | — | 12 | 1 | no | — |
| 466 | C2×C22⋊C4 | — | 12 | 1 | no | — |
| 467 | C2×C42 | — | 3 | 1 | no | — |
| 468 | #108 | — | 3 | 2 | no | — |
| 469 | #108 | — | 3 | 2 | no | — |
| 470 | #108 | — | 3 | 2 | no | — |
| 471 | #108 | — | 3 | 2 | no | — |
| 472 | #104 | — | 3 | 1 | no | — |
| 473 | #104 | — | 3 | 2 | no | — |
| 474 | #104 | — | 3 | 2 | no | — |
| 475 | #104 | — | 3 | 1 | no | — |
| 476 | #104 | — | 3 | 1 | no | — |
| 477 | #104 | — | 3 | 1 | no | — |
| 478 | #104 | — | 3 | 2 | no | — |
| 479 | #104 | — | 3 | 2 | no | — |
| 480 | #104 | — | 3 | 1 | no | — |
| 481 | #104 | — | 3 | 1 | no | — |
| 482 | #104 | — | 3 | 1 | no | — |
| 483 | #104 | — | 3 | 1 | no | — |
| 484 | #101 | — | 3 | 2 | no | — |
| 485 | #101 | — | 3 | 2 | no | — |
| 486 | #101 | — | 3 | 2 | no | — |
| 487 | #101 | — | 3 | 1 | no | — |
| 488 | #101 | — | 3 | 1 | no | — |
| 489 | #100 | — | 3 | 2 | no | — |
| 490 | #100 | — | 3 | 2 | no | — |
| 491 | #100 | — | 3 | 2 | no | — |
| 492 | #100 | — | 3 | 1 | no | — |
| 493 | #100 | — | 3 | 1 | no | — |
| 494 | #97 | — | 3 | 2 | no | — |
| 495 | C4×C8 | — | 3 | 2 | no | — |
| 496 | C23×C3 | — | 8 | 1 | no | — |
| 497 | C22×D3 | — | 8 | 2 | no | — |
| 498 | C22×D3 | — | 8 | 2 | no | — |
| 499 | C22×D3 | — | 8 | 1 | no | — |
| 500 | C3×Q8 | — | 4 | 1 | no | — |
| 501 | C3×D4 | — | 4 | 2 | no | — |
| 502 | C3×D4 | — | 4 | 1 | no | — |
| 503 | C3×D4 | — | 8 | 1 | no | — |
| 504 | C3×D4 | — | 8 | 1 | no | — |
| 505 | C2×C3×C4 | — | 4 | 1 | no | — |
| 506 | C2×C3×C4 | — | 8 | 1 | no | — |
| 507 | #67 | — | 4 | 2 | no | — |
| 508 | #67 | — | 8 | 2 | no | — |
| 509 | #67 | — | 8 | 2 | no | — |
| 510 | #67 | — | 8 | 2 | no | — |
| 511 | #67 | — | 8 | 1 | no | — |
| 512 | C2×Dic3 | — | 8 | 2 | no | — |
| 513 | D12 | — | 4 | 1 | no | — |
| 514 | D12 | — | 4 | 2 | no | — |
| 515 | D12 | — | 4 | 1 | no | — |
| 516 | D12 | — | 8 | 1 | no | — |
| 517 | D12 | — | 8 | 2 | no | — |
| 518 | C4×D3 | — | 4 | 2 | no | — |
| 519 | C4×D3 | — | 8 | 2 | no | — |
| 520 | C4×D3 | — | 8 | 1 | no | — |
| 521 | Dic6 | — | 4 | 1 | no | — |
| 522 | Dic6 | — | 4 | 1 | no | — |
| 523 | SL(2,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 524 | C3×C8 | — | 4 | 2 | no | — |
| 525 | C3⋊C8 | — | 4 | 1 | no | — |
| 526 | C3⋊C8 | — | 4 | 1 | no | — |
| 527 | C24 | — | 6 | 1 | no | — |
| 528 | C24 | — | 12 | 1 | no | — |
| 529 | #41 | — | 2 | 1 | no | — |
| 530 | #41 | — | 3 | 1 | no | — |
| 531 | #41 | — | 3 | 1 | no | — |
| 532 | #41 | — | 3 | 2 | no | — |
| 533 | #41 | — | 3 | 2 | no | — |
| 534 | #41 | — | 3 | 1 | no | — |
| 535 | #41 | — | 3 | 2 | no | — |
| 536 | #41 | — | 3 | 1 | no | — |
| 537 | #41 | — | 3 | 2 | no | — |
| 538 | #41 | — | 3 | 1 | no | — |
| 539 | #41 | — | 6 | 1 | no | — |
| 540 | #41 | — | 6 | 1 | no | — |
| 541 | #41 | — | 6 | 1 | no | — |
| 542 | #41 | — | 6 | 1 | no | — |
| 543 | #41 | — | 6 | 1 | no | — |
| 544 | #41 | — | 6 | 1 | no | — |
| 545 | #41 | — | 6 | 1 | no | — |
| 546 | #41 | — | 6 | 1 | no | — |
| 547 | #41 | — | 6 | 1 | no | — |
| 548 | #41 | — | 6 | 1 | no | — |
| 549 | #41 | — | 6 | 1 | no | — |
| 550 | #41 | — | 6 | 1 | no | — |
| 551 | #41 | — | 6 | 1 | no | — |
| 552 | #41 | — | 6 | 2 | no | — |
| 553 | #41 | — | 6 | 1 | no | — |
| 554 | #41 | — | 6 | 2 | no | — |
| 555 | #41 | — | 6 | 2 | no | — |
| 556 | #41 | — | 6 | 1 | no | — |
| 557 | #41 | — | 6 | 2 | no | — |
| 558 | #41 | — | 6 | 2 | no | — |
| 559 | #41 | — | 6 | 2 | no | — |
| 560 | #41 | — | 6 | 2 | no | — |
| 561 | #41 | — | 6 | 2 | no | — |
| 562 | #41 | — | 6 | 2 | no | — |
| 563 | #41 | — | 6 | 2 | no | — |
| 564 | #41 | — | 6 | 1 | no | — |
| 565 | #41 | — | 12 | 1 | no | — |
| 566 | #41 | — | 12 | 2 | no | — |
| 567 | #41 | — | 12 | 1 | no | — |
| 568 | #41 | — | 12 | 2 | no | — |
| 569 | #41 | — | 12 | 2 | no | — |
| 570 | #41 | — | 12 | 2 | no | — |
| 571 | #41 | — | 12 | 2 | no | — |
| 572 | #41 | — | 12 | 2 | no | — |
| 573 | #41 | — | 12 | 1 | no | — |
| 574 | #41 | — | 12 | 1 | no | — |
| 575 | #41 | — | 12 | 1 | no | — |
| 576 | #41 | D3×D4 | 1 | 1 | yes | characteristic |
| 577 | #41 | C2×S4 | 1 | 1 | yes | characteristic |
| 578 | #41 | C23×D3 | 1 | 1 | yes | characteristic |
| 579 | C2×Q8 | — | 2 | 1 | no | — |
| 580 | C2×Q8 | — | 2 | 2 | no | — |
| 581 | C2×Q8 | — | 3 | 1 | no | — |
| 582 | C2×Q8 | — | 3 | 2 | no | — |
| 583 | C2×Q8 | — | 3 | 1 | no | — |
| 584 | C2×Q8 | — | 3 | 1 | no | — |
| 585 | C2×Q8 | — | 3 | 1 | no | — |
| 586 | C2×Q8 | — | 3 | 1 | no | — |
| 587 | C2×Q8 | — | 6 | 1 | no | — |
| 588 | C2×Q8 | — | 6 | 1 | no | — |
| 589 | C2×Q8 | — | 6 | 1 | no | — |
| 590 | C2×Q8 | — | 6 | 1 | no | — |
| 591 | C2×Q8 | — | 6 | 2 | no | — |
| 592 | C2×Q8 | — | 6 | 1 | no | — |
| 593 | C2×Q8 | — | 6 | 2 | no | — |
| 594 | C2×Q8 | — | 6 | 2 | no | — |
| 595 | C2×Q8 | — | 12 | 1 | no | — |
| 596 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 597 | C2×D4 | — | 3 | 1 | no | — |
| 598 | C2×D4 | — | 3 | 1 | no | — |
| 599 | C2×D4 | — | 3 | 1 | no | — |
| 600 | C2×D4 | — | 3 | 1 | no | — |
| 601 | C2×D4 | — | 3 | 2 | no | — |
| 602 | C2×D4 | — | 3 | 1 | no | — |
| 603 | C2×D4 | — | 6 | 1 | no | — |
| 604 | C2×D4 | — | 6 | 1 | no | — |
| 605 | C2×D4 | — | 6 | 1 | no | — |
| 606 | C2×D4 | — | 6 | 1 | no | — |
| 607 | C2×D4 | — | 6 | 1 | no | — |
| 608 | C2×D4 | — | 6 | 1 | no | — |
| 609 | C2×D4 | — | 6 | 1 | no | — |
| 610 | C2×D4 | — | 6 | 2 | no | — |
| 611 | C2×D4 | — | 6 | 2 | no | — |
| 612 | C2×D4 | — | 6 | 2 | no | — |
| 613 | C2×D4 | — | 6 | 2 | no | — |
| 614 | C2×D4 | — | 6 | 1 | no | — |
| 615 | C2×D4 | — | 6 | 1 | no | — |
| 616 | C2×D4 | — | 6 | 2 | no | — |
| 617 | C2×D4 | — | 6 | 2 | no | — |
| 618 | C2×D4 | — | 6 | 1 | no | — |
| 619 | C2×D4 | — | 6 | 1 | no | — |
| 620 | C2×D4 | — | 6 | 1 | no | — |
| 621 | C2×D4 | — | 12 | 1 | no | — |
| 622 | C2×D4 | — | 12 | 2 | no | — |
| 623 | C2×D4 | — | 12 | 1 | no | — |
| 624 | C2×D4 | — | 12 | 1 | no | — |
| 625 | C2×D4 | — | 12 | 1 | no | — |
| 626 | C2×D4 | — | 12 | 1 | no | — |
| 627 | C2×D4 | — | 12 | 2 | no | — |
| 628 | C2×D4 | — | 12 | 1 | no | — |
| 629 | C2×D4 | — | 12 | 1 | no | — |
| 630 | C2×D4 | — | 12 | 2 | no | — |
| 631 | C2×D4 | — | 12 | 2 | no | — |
| 632 | C2×D4 | — | 12 | 2 | no | — |
| 633 | C2×D4 | — | 12 | 2 | no | — |
| 634 | C2×D4 | — | 12 | 2 | no | — |
| 635 | C2×D4 | — | 12 | 2 | no | — |
| 636 | C2×D4 | C2×S4 | 1 | 1 | yes | characteristic |
| 637 | C22×C4 | — | 3 | 1 | no | — |
| 638 | C22×C4 | — | 6 | 1 | no | — |
| 639 | C22×C4 | — | 6 | 1 | no | — |
| 640 | C22×C4 | — | 6 | 1 | no | — |
| 641 | C22×C4 | — | 6 | 1 | no | — |
| 642 | C22×C4 | — | 6 | 1 | no | — |
| 643 | C22×C4 | — | 6 | 1 | no | — |
| 644 | C22×C4 | — | 6 | 1 | no | — |
| 645 | C22×C4 | — | 12 | 1 | no | — |
| 646 | C22×C4 | — | 12 | 2 | no | — |
| 647 | Q16 | — | 3 | 2 | no | — |
| 648 | Q16 | — | 3 | 2 | no | — |
| 649 | Q16 | — | 3 | 2 | no | — |
| 650 | Q16 | — | 3 | 2 | no | — |
| 651 | Q16 | — | 6 | 2 | no | — |
| 652 | Q16 | — | 6 | 2 | no | — |
| 653 | Q16 | — | 6 | 2 | no | — |
| 654 | Q16 | — | 6 | 1 | no | — |
| 655 | Q16 | — | 6 | 2 | no | — |
| 656 | Q16 | — | 6 | 2 | no | — |
| 657 | Q16 | — | 6 | 2 | no | — |
| 658 | Q16 | — | 6 | 1 | no | — |
| 659 | Q16 | — | 6 | 1 | no | — |
| 660 | Q16 | — | 6 | 1 | no | — |
| 661 | SD16 | — | 3 | 2 | no | — |
| 662 | SD16 | — | 3 | 2 | no | — |
| 663 | SD16 | — | 3 | 2 | no | — |
| 664 | SD16 | — | 3 | 2 | no | — |
| 665 | SD16 | — | 3 | 2 | no | — |
| 666 | SD16 | — | 3 | 2 | no | — |
| 667 | SD16 | — | 3 | 2 | no | — |
| 668 | SD16 | — | 6 | 2 | no | — |
| 669 | SD16 | — | 6 | 2 | no | — |
| 670 | SD16 | — | 6 | 2 | no | — |
| 671 | SD16 | — | 6 | 2 | no | — |
| 672 | SD16 | — | 6 | 2 | no | — |
| 673 | SD16 | — | 6 | 2 | no | — |
| 674 | SD16 | — | 6 | 2 | no | — |
| 675 | SD16 | — | 6 | 1 | no | — |
| 676 | SD16 | — | 6 | 2 | no | — |
| 677 | SD16 | — | 6 | 2 | no | — |
| 678 | SD16 | — | 6 | 1 | no | — |
| 679 | SD16 | — | 6 | 1 | no | — |
| 680 | SD16 | — | 6 | 2 | no | — |
| 681 | SD16 | — | 6 | 2 | no | — |
| 682 | SD16 | — | 6 | 2 | no | — |
| 683 | SD16 | — | 6 | 1 | no | — |
| 684 | SD16 | — | 6 | 2 | no | — |
| 685 | SD16 | — | 6 | 1 | no | — |
| 686 | SD16 | — | 6 | 2 | no | — |
| 687 | SD16 | — | 6 | 1 | no | — |
| 688 | SD16 | — | 6 | 1 | no | — |
| 689 | SD16 | — | 6 | 1 | no | — |
| 690 | SD16 | — | 6 | 2 | no | — |
| 691 | SD16 | C2×S4 | 1 | 2 | yes | — |
| 692 | D8 | — | 3 | 2 | no | — |
| 693 | D8 | — | 3 | 2 | no | — |
| 694 | D8 | — | 3 | 2 | no | — |
| 695 | D8 | — | 6 | 2 | no | — |
| 696 | D8 | — | 6 | 2 | no | — |
| 697 | D8 | — | 6 | 2 | no | — |
| 698 | D8 | — | 6 | 2 | no | — |
| 699 | D8 | — | 6 | 2 | no | — |
| 700 | D8 | — | 6 | 2 | no | — |
| 701 | D8 | — | 6 | 1 | no | — |
| 702 | D8 | — | 6 | 1 | no | — |
| 703 | D8 | — | 6 | 1 | no | — |
| 704 | D8 | — | 6 | 1 | no | — |
| 705 | D8 | — | 6 | 2 | no | — |
| 706 | D8 | — | 6 | 2 | no | — |
| 707 | D8 | — | 6 | 2 | no | — |
| 708 | D8 | C2×S4 | 1 | 2 | yes | — |
| 709 | M16 | — | 3 | 2 | no | — |
| 710 | M16 | — | 3 | 1 | no | — |
| 711 | M16 | — | 3 | 1 | no | — |
| 712 | M16 | — | 3 | 1 | no | — |
| 713 | M16 | — | 3 | 2 | no | — |
| 714 | M16 | — | 3 | 2 | no | — |
| 715 | M16 | — | 3 | 1 | no | — |
| 716 | M16 | — | 3 | 1 | no | — |
| 717 | M16 | — | 3 | 2 | no | — |
| 718 | M16 | — | 3 | 1 | no | — |
| 719 | M16 | — | 3 | 1 | no | — |
| 720 | M16 | — | 6 | 2 | no | — |
| 721 | M16 | — | 6 | 2 | no | — |
| 722 | M16 | — | 6 | 2 | no | — |
| 723 | M16 | — | 6 | 2 | no | — |
| 724 | M16 | — | 6 | 2 | no | — |
| 725 | M16 | — | 6 | 1 | no | — |
| 726 | M16 | — | 6 | 1 | no | — |
| 727 | M16 | — | 6 | 1 | no | — |
| 728 | M16 | — | 6 | 2 | no | — |
| 729 | M16 | C2×S4 | 1 | 1 | yes | characteristic |
| 730 | C2×C8 | — | 3 | 2 | no | — |
| 731 | C2×C8 | — | 3 | 2 | no | — |
| 732 | C2×C8 | — | 6 | 1 | no | — |
| 733 | C2×C8 | — | 6 | 2 | no | — |
| 734 | C2×C8 | — | 6 | 2 | no | — |
| 735 | C2×C8 | — | 6 | 2 | no | — |
| 736 | C2×C8 | — | 6 | 2 | no | — |
| 737 | C2×C8 | — | 6 | 2 | no | — |
| 738 | C2×C8 | — | 6 | 1 | no | — |
| 739 | C2×C8 | — | 6 | 1 | no | — |
| 740 | C2×C8 | — | 6 | 1 | no | — |
| 741 | C2×C8 | — | 6 | 2 | no | — |
| 742 | C4⋊C4 | — | 12 | 1 | no | — |
| 743 | C22⋊C4 | — | 12 | 2 | no | — |
| 744 | C22⋊C4 | — | 12 | 2 | no | — |
| 745 | C22⋊C4 | — | 12 | 1 | no | — |
| 746 | C22⋊C4 | — | 12 | 1 | no | — |
| 747 | C42 | — | 3 | 1 | no | — |
| 748 | C42 | — | 3 | 1 | no | — |
| 749 | C42 | — | 6 | 1 | no | — |
| 750 | C22×C3 | — | 4 | 1 | no | — |
| 751 | C22×C3 | — | 8 | 2 | no | — |
| 752 | C22×C3 | — | 8 | 1 | no | — |
| 753 | C22×C3 | — | 32 | 1 | no | — |
| 754 | C2×D3 | — | 4 | 2 | no | — |
| 755 | C2×D3 | — | 8 | 2 | no | — |
| 756 | C2×D3 | — | 8 | 1 | no | — |
| 757 | C2×D3 | — | 32 | 2 | no | — |
| 758 | C2×D3 | — | 32 | 2 | no | — |
| 759 | C2×D3 | — | 32 | 1 | no | — |
| 760 | C3×C4 | — | 4 | 1 | no | — |
| 761 | C3×C4 | — | 4 | 1 | no | — |
| 762 | C3×C4 | — | 8 | 1 | no | — |
| 763 | Dic3 | — | 4 | 2 | no | — |
| 764 | Dic3 | — | 8 | 1 | no | — |
| 765 | C23 | — | 2 | 1 | no | — |
| 766 | C23 | — | 3 | 1 | no | — |
| 767 | C23 | — | 6 | 1 | no | — |
| 768 | C23 | — | 6 | 1 | no | — |
| 769 | C23 | — | 6 | 1 | no | — |
| 770 | C23 | — | 6 | 2 | no | — |
| 771 | C23 | — | 6 | 1 | no | — |
| 772 | C23 | — | 12 | 2 | no | — |
| 773 | C23 | — | 12 | 2 | no | — |
| 774 | C23 | — | 12 | 1 | no | — |
| 775 | C23 | — | 12 | 2 | no | — |
| 776 | C23 | — | 12 | 1 | no | — |
| 777 | C23 | — | 24 | 2 | no | — |
| 778 | C23 | — | 48 | 2 | no | — |
| 779 | Q8 | — | 3 | 1 | no | — |
| 780 | Q8 | — | 3 | 2 | no | — |
| 781 | Q8 | — | 3 | 2 | no | — |
| 782 | Q8 | — | 3 | 1 | no | — |
| 783 | Q8 | — | 6 | 1 | no | — |
| 784 | Q8 | — | 6 | 1 | no | — |
| 785 | Q8 | — | 6 | 2 | no | — |
| 786 | Q8 | — | 6 | 1 | no | — |
| 787 | Q8 | — | 6 | 1 | no | — |
| 788 | Q8 | — | 6 | 1 | no | — |
| 789 | Q8 | — | 6 | 1 | no | — |
| 790 | Q8 | — | 12 | 1 | no | — |
| 791 | Q8 | — | 12 | 2 | no | — |
| 792 | Q8 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 793 | Q8 | C22×S4 | 1 | 1 | yes | characteristic |
| 794 | D4 | — | 2 | 1 | no | — |
| 795 | D4 | — | 2 | 1 | no | — |
| 796 | D4 | — | 3 | 1 | no | — |
| 797 | D4 | — | 3 | 1 | no | — |
| 798 | D4 | — | 3 | 2 | no | — |
| 799 | D4 | — | 3 | 1 | no | — |
| 800 | D4 | — | 6 | 1 | no | — |
| 801 | D4 | — | 6 | 1 | no | — |
| 802 | D4 | — | 6 | 1 | no | — |
| 803 | D4 | — | 6 | 1 | no | — |
| 804 | D4 | — | 6 | 2 | no | — |
| 805 | D4 | — | 6 | 1 | no | — |
| 806 | D4 | — | 6 | 1 | no | — |
| 807 | D4 | — | 6 | 2 | no | — |
| 808 | D4 | — | 6 | 2 | no | — |
| 809 | D4 | — | 6 | 2 | no | — |
| 810 | D4 | — | 6 | 1 | no | — |
| 811 | D4 | — | 6 | 2 | no | — |
| 812 | D4 | — | 6 | 1 | no | — |
| 813 | D4 | — | 6 | 1 | no | — |
| 814 | D4 | — | 6 | 2 | no | — |
| 815 | D4 | — | 12 | 2 | no | — |
| 816 | D4 | — | 12 | 1 | no | — |
| 817 | D4 | — | 12 | 2 | no | — |
| 818 | D4 | — | 12 | 2 | no | — |
| 819 | D4 | — | 12 | 1 | no | — |
| 820 | D4 | — | 12 | 2 | no | — |
| 821 | D4 | — | 12 | 2 | no | — |
| 822 | D4 | — | 12 | 2 | no | — |
| 823 | D4 | — | 12 | 2 | no | — |
| 824 | D4 | — | 12 | 1 | no | — |
| 825 | D4 | — | 12 | 1 | no | — |
| 826 | D4 | — | 12 | 1 | no | — |
| 827 | D4 | — | 24 | 2 | no | — |
| 828 | D4 | C22×S4 | 1 | 2 | yes | — |
| 829 | D4 | C22×S4 | 1 | 1 | yes | characteristic |
| 830 | C2×C4 | — | 2 | 1 | no | — |
| 831 | C2×C4 | — | 3 | 1 | no | — |
| 832 | C2×C4 | — | 3 | 1 | no | — |
| 833 | C2×C4 | — | 3 | 1 | no | — |
| 834 | C2×C4 | — | 3 | 1 | no | — |
| 835 | C2×C4 | — | 3 | 1 | no | — |
| 836 | C2×C4 | — | 6 | 1 | no | — |
| 837 | C2×C4 | — | 6 | 1 | no | — |
| 838 | C2×C4 | — | 6 | 1 | no | — |
| 839 | C2×C4 | — | 6 | 2 | no | — |
| 840 | C2×C4 | — | 6 | 2 | no | — |
| 841 | C2×C4 | — | 6 | 2 | no | — |
| 842 | C2×C4 | — | 6 | 1 | no | — |
| 843 | C2×C4 | — | 6 | 1 | no | — |
| 844 | C2×C4 | — | 6 | 1 | no | — |
| 845 | C2×C4 | — | 6 | 2 | no | — |
| 846 | C2×C4 | — | 6 | 2 | no | — |
| 847 | C2×C4 | — | 6 | 1 | no | — |
| 848 | C2×C4 | — | 6 | 1 | no | — |
| 849 | C2×C4 | — | 6 | 1 | no | — |
| 850 | C2×C4 | — | 6 | 1 | no | — |
| 851 | C2×C4 | — | 12 | 2 | no | — |
| 852 | C2×C4 | — | 12 | 1 | no | — |
| 853 | C2×C4 | — | 12 | 1 | no | — |
| 854 | C2×C4 | — | 12 | 1 | no | — |
| 855 | C2×C4 | — | 12 | 2 | no | — |
| 856 | C2×C4 | — | 12 | 2 | no | — |
| 857 | C2×C4 | — | 12 | 2 | no | — |
| 858 | C2×C4 | — | 12 | 2 | no | — |
| 859 | C2×C4 | — | 12 | 1 | no | — |
| 860 | C2×C4 | — | 24 | 1 | no | — |
| 861 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 862 | C8 | — | 3 | 2 | no | — |
| 863 | C8 | — | 3 | 2 | no | — |
| 864 | C8 | — | 3 | 2 | no | — |
| 865 | C8 | — | 6 | 2 | no | — |
| 866 | C8 | — | 6 | 1 | no | — |
| 867 | C8 | — | 6 | 1 | no | — |
| 868 | C8 | — | 6 | 1 | no | — |
| 869 | C8 | — | 6 | 1 | no | — |
| 870 | C8 | C22×S4 | 1 | 2 | yes | — |
| 871 | C2×C3 | — | 4 | 1 | no | — |
| 872 | C2×C3 | — | 8 | 1 | no | — |
| 873 | C2×C3 | — | 16 | 1 | no | — |
| 874 | C2×C3 | — | 16 | 2 | no | — |
| 875 | D3 | — | 8 | 2 | no | — |
| 876 | D3 | — | 16 | 2 | no | — |
| 877 | D3 | — | 16 | 1 | no | — |
| 878 | C22 | — | 2 | 1 | no | — |
| 879 | C22 | — | 2 | 2 | no | — |
| 880 | C22 | — | 3 | 1 | no | — |
| 881 | C22 | — | 3 | 1 | no | — |
| 882 | C22 | — | 6 | 1 | no | — |
| 883 | C22 | — | 6 | 2 | no | — |
| 884 | C22 | — | 8 | 1 | no | — |
| 885 | C22 | — | 12 | 1 | no | — |
| 886 | C22 | — | 12 | 1 | no | — |
| 887 | C22 | — | 12 | 2 | no | — |
| 888 | C22 | — | 24 | 1 | no | — |
| 889 | C22 | — | 24 | 1 | no | — |
| 890 | C22 | — | 24 | 1 | no | — |
| 891 | C22 | — | 24 | 1 | no | — |
| 892 | C22 | — | 24 | 2 | no | — |
| 893 | C22 | — | 24 | 2 | no | — |
| 894 | C22 | — | 48 | 1 | no | — |
| 895 | C22 | — | 48 | 2 | no | — |
| 896 | C22 | — | 48 | 2 | no | — |
| 897 | C22 | — | 48 | 2 | no | — |
| 898 | C22 | D4×S4 | 1 | 1 | yes | characteristic |
| 899 | C4 | — | 2 | 1 | no | — |
| 900 | C4 | — | 3 | 1 | no | — |
| 901 | C4 | — | 3 | 1 | no | — |
| 902 | C4 | — | 6 | 1 | no | — |
| 903 | C4 | — | 6 | 2 | no | — |
| 904 | C4 | — | 6 | 2 | no | — |
| 905 | C4 | — | 12 | 1 | no | — |
| 906 | C4 | — | 12 | 1 | no | — |
| 907 | C4 | — | 12 | 1 | no | — |
| 908 | C4 | D4×S4 | 1 | 1 | yes | characteristic |
| 909 | C4 | C23×S4 | 1 | 1 | yes | characteristic |
| 910 | C3 | — | 4 | 1 | no | Sylow |
| 911 | C2 | — | 2 | 1 | no | — |
| 912 | C2 | — | 4 | 2 | no | — |
| 913 | C2 | — | 4 | 1 | no | — |
| 914 | C2 | — | 6 | 1 | no | — |
| 915 | C2 | — | 6 | 1 | no | — |
| 916 | C2 | — | 12 | 1 | no | — |
| 917 | C2 | — | 12 | 2 | no | — |
| 918 | C2 | — | 24 | 2 | no | — |
| 919 | C2 | — | 24 | 1 | no | — |
| 920 | 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. #87498 | C2 | semidirect |
| 2. #87496 | C2 | semidirect |
| 3. #3586⋊C3 | C2 | semidirect |
| 4. #85544 | C2 | semidirect |
| 5. C2×#5431 | C2 | semidirect |
| 6. #85474 | C2 | semidirect |
| 7. #85473 | C2 | semidirect |
| 8. #85472 | C2 | semidirect |
| 9. #85470 | C2 | semidirect |
| 10. #85454 | C2 | semidirect |
| 11. #85453 | C2 | semidirect |
| 13. #5945 | C22 | semidirect |
| 14. C2×2−1+4⋊C3 | C22 | semidirect |
| 16. #5927 | C22 | semidirect |
| 19. #5926 | C22 | semidirect |
| 20. #5926 | C22 | semidirect |
| 21. #5925 | C22 | semidirect |
| 24. #5923 | C22 | semidirect |
| 26. C2×#986 | C22 | semidirect |
| 29. #578⋊C3 | C22 | semidirect |
| 30. #577⋊C3 | C22 | semidirect |
| 31. #568⋊C3 | C22 | semidirect |
| 32. #5431 | C22 | semidirect |
| 33. #5431 | C22 | semidirect |
| 34. #5431 | C22 | semidirect |
| 35. #5430 | C22 | semidirect |
| 36. #5429 | C22 | semidirect |
| 37. #5428 | C22 | semidirect |
| 38. C2×GU(2,𝔽3) | C22 | semidirect |
| 39. #5407 | C22 | semidirect |
| 40. #5406 | C22 | semidirect |
| 41. #5405 | C22 | semidirect |
| 42. #5404 | C22 | semidirect |
| 44. #3586 | D3 | semidirect |
| 71. 2−1+4⋊C3 | C23 | semidirect |
| 78. #986 | D4 | semidirect |
| 80. #986 | C23 | semidirect |
| 84. #984 | D4 | semidirect |
| 85. #984 | C23 | semidirect |
| 90. #983 | D4 | semidirect |
| 104. #131⋊C3 | C23 | semidirect |
| 105. GU(2,𝔽3) | C23 | semidirect |
| 106. GU(2,𝔽3) | C23 | semidirect |
| 108. #585 | C2×D3 | semidirect |
| 109. C2×2−1+4 | C2×D3 | semidirect |
| 116. #578 | C2×D3 | semidirect |
| 129. #577 | C2×D3 | semidirect |
| 162. #568 | C2×D3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #87498 | 2 |
| #87496 | 2 |
| #3586⋊C3 | 2 |
| #85544 | 2 |
| C2×#5431 | 2 |
| #85474 | 2 |
| #85473 | 2 |
| #85472 | 2 |
| #85470 | 2 |
| #85454 | 2 |
| #85453 | 2 |
| #61109 | 3 |
| #5774 | 4 |