Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
689 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 689 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #11870763 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C42×PSU(3,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11790795 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11775070 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #11774597 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11771213 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11770742 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×C4×PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 9 | C2×C4×PSU(3,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 10 | #10596511 | C22 | 1 | 1 | yes | characteristic |
| 11 | #10596484 | C22 | 1 | 1 | yes | characteristic |
| 12 | #10596484 | C22 | 1 | 1 | yes | characteristic |
| 13 | #10596418 | — | 2 | 1 | no | — |
| 14 | #10596412 | — | 2 | 1 | no | — |
| 15 | #10596410 | C4 | 1 | 2 | yes | complemented |
| 16 | C4×AΓL(1,𝔽9) | — | 2 | 2 | no | — |
| 17 | PSU(3,𝔽2)⋊Q8 | C4 | 1 | 2 | yes | complemented |
| 18 | C42×#157 | — | 2 | 1 | no | — |
| 19 | C42×#157 | C22 | 1 | 1 | yes | characteristic |
| 20 | C4×#3777 | — | 2 | 1 | no | — |
| 21 | C4×#3777 | — | 2 | 1 | no | — |
| 22 | C4×#3777 | — | 2 | 2 | no | — |
| 23 | C4×#3777 | C22 | 1 | 1 | yes | characteristic |
| 24 | #10593328 | C22 | 1 | 1 | yes | characteristic |
| 25 | #10593325 | — | 2 | 1 | no | — |
| 26 | #10593164 | — | 2 | 2 | no | — |
| 27 | PSU(3,𝔽2)⋊C8 | — | 2 | 2 | no | — |
| 28 | #10590393 | — | 2 | 1 | no | — |
| 29 | C22×PSU(3,𝔽2) | D4 | 1 | 1 | yes | characteristic |
| 30 | C2×AΓL(1,𝔽9) | — | 2 | 2 | no | — |
| 31 | #64306 | — | 2 | 1 | no | — |
| 32 | C2×C4×#157 | — | 2 | 2 | no | — |
| 33 | C2×C4×#157 | — | 2 | 1 | no | — |
| 34 | C2×C4×#157 | — | 2 | 2 | no | — |
| 35 | C2×C4×#157 | — | 2 | 1 | no | — |
| 36 | C2×C4×#157 | — | 2 | 1 | no | — |
| 37 | C2×C4×#157 | — | 2 | 1 | no | — |
| 38 | C2×C4×#157 | D4 | 1 | 1 | yes | characteristic |
| 39 | C2×C4×#157 | C23 | 1 | 1 | yes | characteristic |
| 40 | C2×#3777 | — | 2 | 2 | no | — |
| 41 | C2×#3777 | — | 2 | 1 | no | — |
| 42 | C2×#3777 | — | 2 | 1 | no | — |
| 43 | C2×#3777 | D4 | 1 | 1 | yes | characteristic |
| 44 | C4×PSU(3,𝔽2) | — | 2 | 8 | no | — |
| 45 | C4×PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 46 | C4×PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 47 | C4×PSU(3,𝔽2) | C2×C4 | 1 | 2 | yes | — |
| 48 | C4×PSU(3,𝔽2) | D4 | 1 | 2 | yes | — |
| 49 | #64242 | — | 2 | 1 | no | — |
| 50 | #64242 | — | 2 | 1 | no | — |
| 51 | #64231 | C2×C4 | 1 | 1 | yes | characteristic |
| 52 | C4×GO+(4,𝔽2) | — | 2 | 1 | no | — |
| 53 | C4×GO+(4,𝔽2) | — | 2 | 1 | no | — |
| 54 | #64222 | C2×C4 | 1 | 1 | yes | characteristic |
| 55 | #64221 | — | 2 | 1 | no | — |
| 56 | C22⋊AGL(1,𝔽9) | — | 2 | 1 | no | — |
| 57 | C22⋊AGL(1,𝔽9) | — | 2 | 1 | no | — |
| 58 | C4⋊AGL(1,𝔽9) | — | 2 | 1 | no | — |
| 59 | C4⋊AGL(1,𝔽9) | C2×C4 | 1 | 2 | yes | — |
| 60 | C4×AGL(1,𝔽9) | — | 2 | 1 | no | — |
| 61 | C4×AGL(1,𝔽9) | — | 2 | 1 | no | — |
| 62 | AGL(1,𝔽9)⋊C4 | — | 2 | 2 | no | — |
| 63 | PSU(3,𝔽2)⋊C4 | — | 2 | 2 | no | — |
| 64 | GO+(4,𝔽2)⋊C4 | — | 2 | 2 | no | — |
| 65 | C42×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 66 | #63818 | — | 2 | 1 | no | — |
| 67 | #63747 | — | 2 | 2 | no | — |
| 68 | #63747 | D4 | 1 | 2 | yes | — |
| 69 | #63732 | — | 2 | 1 | no | — |
| 70 | #63732 | — | 2 | 1 | no | — |
| 71 | #63731 | — | 4 | 2 | no | — |
| 72 | C3×#805 | — | 4 | 1 | no | — |
| 73 | #63568 | — | 4 | 1 | no | — |
| 74 | #9234 | — | 9 | 1 | no | maximal, Sylow |
| 75 | D3×#104 | — | 12 | 1 | no | — |
| 76 | C22×#157 | — | 2 | 1 | no | — |
| 77 | C22×#157 | — | 2 | 1 | no | — |
| 78 | C22×#157 | — | 2 | 1 | no | — |
| 79 | C22×#157 | — | 2 | 2 | no | — |
| 80 | C22×#157 | C2×D4 | 1 | 1 | yes | characteristic |
| 81 | C22×#157 | C2×D4 | 1 | 1 | yes | characteristic |
| 82 | C2×PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 83 | C2×PSU(3,𝔽2) | — | 2 | 4 | no | — |
| 84 | C2×PSU(3,𝔽2) | C22⋊C4 | 1 | 2 | yes | — |
| 85 | C2×GO+(4,𝔽2) | — | 2 | 1 | no | — |
| 86 | C2×GO+(4,𝔽2) | — | 2 | 1 | no | — |
| 87 | C2×AGL(1,𝔽9) | — | 2 | 2 | no | — |
| 88 | C2×AGL(1,𝔽9) | — | 4 | 1 | no | — |
| 89 | AΓL(1,𝔽9) | — | 4 | 4 | no | — |
| 90 | C2×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 91 | C2×C4×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 92 | C3×#235 | — | 4 | 1 | no | — |
| 93 | #3811 | — | 4 | 1 | no | — |
| 94 | #3805 | — | 4 | 1 | no | — |
| 95 | #3802 | — | 2 | 1 | no | — |
| 96 | C4×D32 | — | 4 | 1 | no | — |
| 97 | #3798 | — | 4 | 1 | no | — |
| 98 | #3797 | — | 2 | 1 | no | — |
| 99 | #3796 | — | 4 | 1 | no | — |
| 100 | C4×#157 | — | 2 | 8 | no | — |
| 101 | C4×#157 | — | 2 | 4 | no | — |
| 102 | C4×#157 | — | 2 | 2 | no | — |
| 103 | C4×#157 | — | 2 | 2 | no | — |
| 104 | C4×#157 | — | 2 | 1 | no | — |
| 105 | C4×#157 | — | 2 | 1 | no | — |
| 106 | C4×#157 | — | 4 | 2 | no | — |
| 107 | C4×#157 | — | 4 | 4 | no | — |
| 108 | C4×#157 | — | 4 | 1 | no | — |
| 109 | C4×#157 | — | 4 | 1 | no | — |
| 110 | C4×#157 | C22×C4 | 1 | 1 | yes | characteristic |
| 111 | C4×#157 | C2×D4 | 1 | 1 | yes | characteristic |
| 112 | C4×#157 | #41 | 1 | 1 | yes | characteristic |
| 113 | C4×#157 | #41 | 1 | 1 | yes | characteristic |
| 114 | #3777 | — | 2 | 8 | no | — |
| 115 | #3777 | — | 2 | 4 | no | — |
| 116 | #3777 | — | 2 | 2 | no | — |
| 117 | #3777 | — | 2 | 2 | no | — |
| 118 | #3777 | — | 2 | 1 | no | — |
| 119 | #3777 | C22⋊C4 | 1 | 2 | yes | — |
| 120 | #3773 | — | 2 | 1 | no | — |
| 121 | #3773 | — | 2 | 1 | no | — |
| 122 | D32⋊C4 | — | 4 | 1 | no | — |
| 123 | D32⋊C4 | — | 4 | 1 | no | — |
| 124 | C32×C42 | SD16 | 1 | 1 | yes | characteristic, complemented |
| 125 | C4×C3⋊Dic3 | — | 2 | 1 | no | — |
| 126 | C4×C3⋊Dic3 | SD16 | 1 | 1 | yes | characteristic, complemented |
| 127 | C3×#208 | — | 4 | 1 | no | — |
| 128 | #3712 | — | 4 | 1 | no | — |
| 129 | #3710 | — | 4 | 1 | no | — |
| 130 | #3103 | — | 9 | 1 | no | — |
| 131 | C42×Q8 | — | 9 | 1 | no | — |
| 132 | #1962 | — | 9 | 1 | no | — |
| 133 | #1502 | — | 9 | 1 | no | — |
| 134 | #1487 | — | 9 | 1 | no | — |
| 135 | #1303 | — | 9 | 1 | no | — |
| 136 | #1276 | — | 9 | 1 | no | — |
| 137 | D3×#41 | — | 12 | 1 | no | — |
| 138 | D3×M16 | — | 12 | 1 | no | — |
| 139 | C42×D3 | — | 12 | 1 | no | — |
| 140 | C3×#104 | — | 12 | 1 | no | — |
| 141 | #837 | — | 12 | 1 | no | — |
| 142 | #825 | — | 12 | 1 | no | — |
| 143 | #805 | — | 4 | 1 | no | — |
| 144 | C22×C3⋊D3 | #120 | 1 | 1 | yes | characteristic |
| 145 | C2×D32 | — | 4 | 1 | no | — |
| 146 | C2×#157 | — | 2 | 4 | no | — |
| 147 | C2×#157 | — | 2 | 2 | no | — |
| 148 | C2×#157 | — | 2 | 2 | no | — |
| 149 | C2×#157 | — | 2 | 2 | no | — |
| 150 | C2×#157 | — | 2 | 4 | no | — |
| 151 | C2×#157 | — | 2 | 2 | no | — |
| 152 | C2×#157 | — | 4 | 1 | no | — |
| 153 | C2×#157 | — | 4 | 1 | no | — |
| 154 | C2×#157 | — | 4 | 2 | no | — |
| 155 | C2×#157 | — | 4 | 2 | no | — |
| 156 | C2×#157 | — | 4 | 1 | no | — |
| 157 | C2×#157 | — | 4 | 2 | no | — |
| 158 | C2×#157 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 159 | C2×#157 | C4×D4 | 1 | 1 | yes | characteristic |
| 160 | C2×#157 | #121 | 1 | 1 | yes | characteristic |
| 161 | C2×#157 | #123 | 1 | 1 | yes | characteristic |
| 162 | PSU(3,𝔽2) | — | 2 | 4 | no | — |
| 163 | PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 164 | PSU(3,𝔽2) | #104 | 1 | 4 | yes | complemented |
| 165 | GO+(4,𝔽2) | — | 4 | 2 | no | — |
| 166 | GO+(4,𝔽2) | — | 8 | 1 | no | — |
| 167 | AGL(1,𝔽9) | — | 4 | 2 | no | — |
| 168 | AGL(1,𝔽9) | — | 8 | 1 | no | — |
| 169 | C2×C32×C4 | — | 2 | 1 | no | — |
| 170 | C2×C32×C4 | C2×SD16 | 1 | 1 | yes | characteristic |
| 171 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 172 | C2×C3⋊Dic3 | #137 | 1 | 1 | yes | characteristic |
| 173 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 174 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 175 | C4×C3⋊D3 | C4×D4 | 1 | 1 | yes | characteristic |
| 176 | C4×C3⋊D3 | #121 | 1 | 1 | yes | characteristic |
| 177 | C4×C3⋊D3 | #135 | 1 | 1 | yes | characteristic |
| 178 | C4×C3⋊D3 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 179 | C3×#67 | — | 8 | 1 | no | — |
| 180 | C3×D12 | — | 4 | 1 | no | — |
| 181 | C3×C4×D3 | — | 8 | 1 | no | — |
| 182 | C3×Dic6 | — | 4 | 1 | no | — |
| 183 | #627 | — | 4 | 1 | no | — |
| 184 | #626 | — | 8 | 1 | no | — |
| 185 | #625 | — | 4 | 1 | no | — |
| 186 | #624 | — | 4 | 1 | no | — |
| 187 | D3×Dic3 | — | 8 | 1 | no | — |
| 188 | C3×C3⋊C8 | — | 8 | 1 | no | — |
| 189 | #532 | — | 9 | 1 | no | — |
| 190 | C2×C4×Q8 | — | 9 | 1 | no | — |
| 191 | C2×C4×Q8 | — | 18 | 1 | no | — |
| 192 | #481 | — | 18 | 1 | no | — |
| 193 | #475 | — | 9 | 2 | no | — |
| 194 | #460 | — | 9 | 2 | no | — |
| 195 | #448 | — | 18 | 1 | no | — |
| 196 | C4×SD16 | — | 18 | 2 | no | — |
| 197 | #431 | — | 9 | 1 | no | — |
| 198 | #431 | — | 9 | 1 | no | — |
| 199 | #423 | — | 9 | 1 | no | — |
| 200 | C2×#104 | — | 18 | 1 | no | — |
| 201 | C2×#104 | — | 18 | 1 | no | — |
| 202 | C4×C4⋊C4 | — | 9 | 1 | no | — |
| 203 | C4×C4⋊C4 | — | 18 | 2 | no | — |
| 204 | C4×C4⋊C4 | — | 18 | 1 | no | — |
| 205 | C4×C4⋊C4 | — | 18 | 1 | no | — |
| 206 | C43 | — | 9 | 1 | no | — |
| 207 | C43 | — | 18 | 1 | no | — |
| 208 | #327 | — | 18 | 2 | no | — |
| 209 | Q8⋊C8 | — | 18 | 2 | no | — |
| 210 | C3×#41 | — | 12 | 1 | no | — |
| 211 | #239 | — | 12 | 1 | no | — |
| 212 | D3×Q8 | — | 12 | 1 | no | — |
| 213 | #237 | — | 12 | 1 | no | — |
| 214 | #237 | — | 24 | 1 | no | — |
| 215 | D3×D4 | — | 12 | 1 | no | — |
| 216 | D3×D4 | — | 24 | 1 | no | — |
| 217 | #235 | — | 4 | 1 | no | — |
| 218 | #235 | — | 24 | 1 | no | — |
| 219 | C2×C4×D3 | — | 12 | 1 | no | — |
| 220 | C2×C4×D3 | — | 24 | 1 | no | — |
| 221 | C2×C4×D3 | — | 24 | 1 | no | — |
| 222 | C3×M16 | — | 12 | 1 | no | — |
| 223 | C3×C42 | — | 4 | 1 | no | — |
| 224 | C4×Dic3 | — | 12 | 1 | no | — |
| 225 | C4×Dic3 | — | 24 | 1 | no | — |
| 226 | #208 | — | 4 | 1 | no | — |
| 227 | ΓL(1,𝔽25) | — | 24 | 1 | no | — |
| 228 | D3×C8 | — | 24 | 1 | no | — |
| 229 | C22×C32 | #448 | 1 | 1 | yes | characteristic |
| 230 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 231 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 232 | C2×C3⋊D3 | #386 | 1 | 1 | yes | characteristic |
| 233 | C2×C3⋊D3 | #449 | 1 | 1 | yes | characteristic |
| 234 | C2×C3×D3 | — | 8 | 1 | no | — |
| 235 | D32 | — | 8 | 1 | no | — |
| 236 | D32 | — | 8 | 1 | no | — |
| 237 | #157 | — | 2 | 1 | no | — |
| 238 | #157 | — | 2 | 4 | no | — |
| 239 | #157 | — | 2 | 1 | no | — |
| 240 | #157 | — | 2 | 1 | no | — |
| 241 | #157 | — | 4 | 2 | no | — |
| 242 | #157 | — | 4 | 4 | no | — |
| 243 | #157 | — | 4 | 2 | no | — |
| 244 | #157 | C2×#104 | 1 | 2 | yes | — |
| 245 | C32×C4 | — | 2 | 2 | no | — |
| 246 | C32×C4 | C4×SD16 | 1 | 1 | yes | characteristic |
| 247 | C32×C4 | #460 | 1 | 1 | yes | characteristic |
| 248 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 249 | C3⋊Dic3 | #440 | 1 | 1 | yes | characteristic |
| 250 | C3⋊Dic3 | #464 | 1 | 1 | yes | characteristic |
| 251 | C3×Dic3 | — | 8 | 1 | no | — |
| 252 | C2×#41 | — | 18 | 1 | no | — |
| 253 | C22×Q8 | — | 9 | 1 | no | — |
| 254 | C2×SD16 | — | 18 | 2 | no | — |
| 255 | C2×M16 | — | 18 | 1 | no | — |
| 256 | C4⋊Q8 | — | 9 | 1 | no | — |
| 257 | #127 | — | 9 | 1 | no | — |
| 258 | #124 | — | 18 | 1 | no | — |
| 259 | #121 | — | 18 | 1 | no | — |
| 260 | #121 | — | 18 | 1 | no | — |
| 261 | C4×Q8 | — | 9 | 2 | no | — |
| 262 | C4×Q8 | — | 9 | 2 | no | — |
| 263 | C4×Q8 | — | 18 | 1 | no | — |
| 264 | C4×Q8 | — | 18 | 1 | no | — |
| 265 | C4×Q8 | — | 18 | 8 | no | — |
| 266 | C4×D4 | — | 18 | 1 | no | — |
| 267 | C4×D4 | — | 18 | 1 | no | — |
| 268 | C2×C4⋊C4 | — | 9 | 1 | no | — |
| 269 | C2×C4⋊C4 | — | 18 | 1 | no | — |
| 270 | C2×C4⋊C4 | — | 18 | 1 | no | — |
| 271 | C2×C4⋊C4 | — | 18 | 2 | no | — |
| 272 | C2×C42 | — | 9 | 1 | no | — |
| 273 | C2×C42 | — | 9 | 1 | no | — |
| 274 | C2×C42 | — | 9 | 1 | no | — |
| 275 | C2×C42 | — | 18 | 1 | no | — |
| 276 | C2×C42 | — | 18 | 1 | no | — |
| 277 | C2×C42 | — | 18 | 2 | no | — |
| 278 | C2×C42 | — | 18 | 1 | no | — |
| 279 | C2×C42 | — | 18 | 1 | no | — |
| 280 | C2×C42 | — | 18 | 2 | no | — |
| 281 | #106 | — | 18 | 2 | no | — |
| 282 | C4⋊C8 | — | 9 | 2 | no | — |
| 283 | C4⋊C8 | — | 18 | 1 | no | — |
| 284 | C4⋊C8 | — | 18 | 1 | no | — |
| 285 | C4⋊C8 | — | 18 | 1 | no | — |
| 286 | #104 | — | 12 | 1 | no | — |
| 287 | #104 | — | 36 | 1 | no | — |
| 288 | #104 | — | 36 | 2 | no | — |
| 289 | #103 | — | 18 | 2 | no | — |
| 290 | #102 | — | 18 | 2 | no | — |
| 291 | C22⋊C8 | — | 18 | 1 | no | — |
| 292 | C22⋊C8 | — | 18 | 1 | no | — |
| 293 | C4×C8 | — | 18 | 1 | no | — |
| 294 | C4×C8 | — | 18 | 1 | no | — |
| 295 | #95 | — | 9 | 2 | no | — |
| 296 | #95 | — | 18 | 2 | no | — |
| 297 | C22×D3 | — | 12 | 1 | no | — |
| 298 | C22×D3 | — | 24 | 1 | no | — |
| 299 | C3×Q8 | — | 12 | 1 | no | — |
| 300 | C3×D4 | — | 12 | 1 | no | — |
| 301 | C3×D4 | — | 24 | 1 | no | — |
| 302 | C2×C3×C4 | — | 4 | 1 | no | — |
| 303 | C2×C3×C4 | — | 8 | 1 | no | — |
| 304 | C2×C3×C4 | — | 24 | 1 | no | — |
| 305 | #67 | — | 8 | 1 | no | — |
| 306 | #67 | — | 24 | 1 | no | — |
| 307 | #67 | — | 24 | 1 | no | — |
| 308 | C2×Dic3 | — | 12 | 1 | no | — |
| 309 | C2×Dic3 | — | 24 | 1 | no | — |
| 310 | C2×Dic3 | — | 24 | 1 | no | — |
| 311 | D12 | — | 4 | 1 | no | — |
| 312 | D12 | — | 24 | 1 | no | — |
| 313 | C4×D3 | — | 8 | 1 | no | — |
| 314 | C4×D3 | — | 12 | 1 | no | — |
| 315 | C4×D3 | — | 12 | 1 | no | — |
| 316 | C4×D3 | — | 12 | 1 | no | — |
| 317 | C4×D3 | — | 12 | 1 | no | — |
| 318 | C4×D3 | — | 24 | 2 | no | — |
| 319 | C4×D3 | — | 24 | 2 | no | — |
| 320 | C4×D3 | — | 24 | 1 | no | — |
| 321 | C4×D3 | — | 24 | 1 | no | — |
| 322 | Dic6 | — | 4 | 1 | no | — |
| 323 | Dic6 | — | 24 | 1 | no | — |
| 324 | C3×C8 | — | 24 | 1 | no | — |
| 325 | C3⋊C8 | — | 8 | 1 | no | — |
| 326 | C2×C32 | — | 2 | 1 | no | — |
| 327 | C2×C32 | #1880 | 1 | 1 | yes | characteristic |
| 328 | C3⋊D3 | — | 2 | 1 | no | — |
| 329 | C3⋊D3 | #1896 | 1 | 1 | yes | characteristic |
| 330 | C3⋊D3 | #1906 | 1 | 1 | yes | characteristic |
| 331 | C3×D3 | — | 16 | 1 | no | — |
| 332 | #41 | — | 12 | 1 | no | — |
| 333 | #41 | — | 36 | 1 | no | — |
| 334 | #41 | — | 36 | 1 | no | — |
| 335 | #41 | — | 36 | 1 | no | — |
| 336 | C2×Q8 | — | 9 | 2 | no | — |
| 337 | C2×Q8 | — | 18 | 1 | no | — |
| 338 | C2×Q8 | — | 18 | 1 | no | — |
| 339 | C2×Q8 | — | 18 | 4 | no | — |
| 340 | C2×D4 | — | 18 | 1 | no | — |
| 341 | C2×D4 | — | 18 | 1 | no | — |
| 342 | C2×D4 | — | 18 | 1 | no | — |
| 343 | C2×D4 | — | 36 | 1 | no | — |
| 344 | C22×C4 | — | 9 | 1 | no | — |
| 345 | C22×C4 | — | 9 | 1 | no | — |
| 346 | C22×C4 | — | 9 | 1 | no | — |
| 347 | C22×C4 | — | 18 | 1 | no | — |
| 348 | C22×C4 | — | 18 | 1 | no | — |
| 349 | C22×C4 | — | 18 | 2 | no | — |
| 350 | C22×C4 | — | 18 | 1 | no | — |
| 351 | C22×C4 | — | 18 | 1 | no | — |
| 352 | C22×C4 | — | 36 | 1 | no | — |
| 353 | SD16 | — | 36 | 4 | no | — |
| 354 | M16 | — | 12 | 1 | no | — |
| 355 | M16 | — | 36 | 1 | no | — |
| 356 | C2×C8 | — | 18 | 2 | no | — |
| 357 | C2×C8 | — | 36 | 1 | no | — |
| 358 | C2×C8 | — | 36 | 1 | no | — |
| 359 | C4⋊C4 | — | 9 | 2 | no | — |
| 360 | C4⋊C4 | — | 18 | 1 | no | — |
| 361 | C4⋊C4 | — | 18 | 2 | no | — |
| 362 | C4⋊C4 | — | 18 | 2 | no | — |
| 363 | C4⋊C4 | — | 18 | 1 | no | — |
| 364 | C4⋊C4 | — | 18 | 1 | no | — |
| 365 | C4⋊C4 | — | 18 | 4 | no | — |
| 366 | C4⋊C4 | — | 18 | 8 | no | — |
| 367 | C22⋊C4 | — | 36 | 1 | no | — |
| 368 | C22⋊C4 | — | 36 | 1 | no | — |
| 369 | C42 | — | 9 | 1 | no | — |
| 370 | C42 | — | 9 | 1 | no | — |
| 371 | C42 | — | 9 | 1 | no | — |
| 372 | C42 | — | 9 | 1 | no | — |
| 373 | C42 | — | 9 | 1 | no | — |
| 374 | C42 | — | 18 | 1 | no | — |
| 375 | C42 | — | 18 | 2 | no | — |
| 376 | C42 | — | 18 | 2 | no | — |
| 377 | C42 | — | 18 | 1 | no | — |
| 378 | C42 | — | 18 | 1 | no | — |
| 379 | C42 | — | 18 | 4 | no | — |
| 380 | C42 | — | 18 | 8 | no | — |
| 381 | C42 | — | 36 | 1 | no | — |
| 382 | C42 | — | 36 | 1 | no | — |
| 383 | C42 | — | 36 | 2 | no | — |
| 384 | C42 | — | 36 | 4 | no | — |
| 385 | C42 | AΓL(1,𝔽9) | 1 | 1 | yes | characteristic, complemented |
| 386 | C22×C3 | — | 4 | 1 | no | — |
| 387 | C22×C3 | — | 24 | 1 | no | — |
| 388 | C2×D3 | — | 8 | 1 | no | — |
| 389 | C2×D3 | — | 12 | 1 | no | — |
| 390 | C2×D3 | — | 12 | 1 | no | — |
| 391 | C2×D3 | — | 24 | 1 | no | — |
| 392 | C2×D3 | — | 24 | 1 | no | — |
| 393 | C2×D3 | — | 48 | 1 | no | — |
| 394 | C2×D3 | — | 48 | 1 | no | — |
| 395 | C3×C4 | — | 4 | 1 | no | — |
| 396 | C3×C4 | — | 4 | 1 | no | — |
| 397 | C3×C4 | — | 8 | 2 | no | — |
| 398 | C3×C4 | — | 24 | 1 | no | — |
| 399 | Dic3 | — | 8 | 1 | no | — |
| 400 | Dic3 | — | 12 | 1 | no | — |
| 401 | Dic3 | — | 12 | 1 | no | — |
| 402 | Dic3 | — | 24 | 2 | no | — |
| 403 | C32 | #9234 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 404 | C23 | — | 9 | 1 | no | — |
| 405 | C23 | — | 36 | 1 | no | — |
| 406 | Q8 | — | 9 | 4 | no | — |
| 407 | Q8 | — | 12 | 1 | no | — |
| 408 | Q8 | — | 18 | 2 | no | — |
| 409 | Q8 | — | 18 | 4 | no | — |
| 410 | Q8 | — | 36 | 1 | no | — |
| 411 | D4 | — | 12 | 1 | no | — |
| 412 | D4 | — | 24 | 1 | no | — |
| 413 | D4 | — | 36 | 1 | no | — |
| 414 | D4 | — | 36 | 2 | no | — |
| 415 | D4 | — | 72 | 1 | no | — |
| 416 | D4 | — | 72 | 1 | no | — |
| 417 | C2×C4 | — | 2 | 1 | no | — |
| 418 | C2×C4 | — | 9 | 1 | no | — |
| 419 | C2×C4 | — | 9 | 1 | no | — |
| 420 | C2×C4 | — | 9 | 1 | no | — |
| 421 | C2×C4 | — | 9 | 1 | no | — |
| 422 | C2×C4 | — | 9 | 1 | no | — |
| 423 | C2×C4 | — | 9 | 1 | no | — |
| 424 | C2×C4 | — | 9 | 1 | no | — |
| 425 | C2×C4 | — | 9 | 1 | no | — |
| 426 | C2×C4 | — | 9 | 1 | no | — |
| 427 | C2×C4 | — | 18 | 2 | no | — |
| 428 | C2×C4 | — | 18 | 2 | no | — |
| 429 | C2×C4 | — | 18 | 2 | no | — |
| 430 | C2×C4 | — | 18 | 2 | no | — |
| 431 | C2×C4 | — | 18 | 4 | no | — |
| 432 | C2×C4 | — | 18 | 1 | no | — |
| 433 | C2×C4 | — | 18 | 2 | no | — |
| 434 | C2×C4 | — | 18 | 4 | no | — |
| 435 | C2×C4 | — | 18 | 2 | no | — |
| 436 | C2×C4 | — | 24 | 1 | no | — |
| 437 | C2×C4 | — | 36 | 1 | no | — |
| 438 | C2×C4 | — | 36 | 1 | no | — |
| 439 | C2×C4 | — | 36 | 1 | no | — |
| 440 | C2×C4 | — | 36 | 2 | no | — |
| 441 | C2×C4 | — | 36 | 2 | no | — |
| 442 | C2×C4 | — | 36 | 2 | no | — |
| 443 | C2×C4 | — | 36 | 1 | no | — |
| 444 | C2×C4 | — | 72 | 1 | no | — |
| 445 | C2×C4 | C2×AΓL(1,𝔽9) | 1 | 1 | yes | characteristic |
| 446 | C8 | — | 24 | 1 | no | — |
| 447 | C8 | — | 36 | 2 | no | — |
| 448 | C8 | — | 72 | 1 | no | — |
| 449 | C2×C3 | — | 4 | 1 | no | — |
| 450 | C2×C3 | — | 8 | 1 | no | — |
| 451 | C2×C3 | — | 48 | 1 | no | — |
| 452 | D3 | — | 12 | 1 | no | — |
| 453 | D3 | — | 12 | 1 | no | — |
| 454 | D3 | — | 16 | 1 | no | — |
| 455 | D3 | — | 24 | 1 | no | — |
| 456 | C22 | — | 9 | 1 | no | — |
| 457 | C22 | — | 9 | 1 | no | — |
| 458 | C22 | — | 18 | 1 | no | — |
| 459 | C22 | — | 18 | 1 | no | — |
| 460 | C22 | — | 24 | 1 | no | — |
| 461 | C22 | — | 72 | 1 | no | — |
| 462 | C22 | — | 72 | 1 | no | — |
| 463 | C22 | #10596418 | 1 | 1 | yes | characteristic |
| 464 | C4 | — | 2 | 2 | no | — |
| 465 | C4 | — | 9 | 2 | no | — |
| 466 | C4 | — | 9 | 1 | no | — |
| 467 | C4 | — | 9 | 1 | no | — |
| 468 | C4 | — | 18 | 2 | no | — |
| 469 | C4 | — | 18 | 1 | no | — |
| 470 | C4 | — | 18 | 1 | no | — |
| 471 | C4 | — | 18 | 1 | no | — |
| 472 | C4 | — | 18 | 4 | no | — |
| 473 | C4 | — | 24 | 1 | no | — |
| 474 | C4 | — | 36 | 2 | no | — |
| 475 | C4 | — | 36 | 2 | no | — |
| 476 | C4 | — | 36 | 4 | no | — |
| 477 | C4 | C4×AΓL(1,𝔽9) | 1 | 1 | yes | characteristic |
| 478 | C4 | #10596410 | 1 | 1 | yes | characteristic |
| 479 | C3 | — | 4 | 1 | no | — |
| 480 | C2 | — | 2 | 1 | no | — |
| 481 | C2 | — | 9 | 1 | no | — |
| 482 | C2 | — | 9 | 1 | no | — |
| 483 | C2 | — | 18 | 1 | no | — |
| 484 | C2 | — | 48 | 1 | no | — |
| 485 | C2 | #11787609 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C42×PSU(3,𝔽2) | C2 | semidirect |
| 5. #11774597 | C2 | semidirect |
| 6. #11771213 | C2 | semidirect |
| 7. #11770742 | C2 | semidirect |
| 15. #10596410 | C4 | semidirect |
| 17. PSU(3,𝔽2)⋊Q8 | C4 | semidirect |
| 124. C32×C42 | SD16 | semidirect |
| 126. C4×C3⋊Dic3 | SD16 | semidirect |
| 164. PSU(3,𝔽2) | #104 | semidirect |
| 385. C42 | AΓL(1,𝔽9) | semidirect |
| 403. C32 | #9234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11870763 | 2 |
| C42×PSU(3,𝔽2) | 2 |
| #11790795 | 2 |
| #11775070 | 2 |
| #11774597 | 2 |
| #11771213 | 2 |
| #11770742 | 2 |
| #9234 | 9 |