Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
1059 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 1059 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×D4×PSU(3,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11785131 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #11776370 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11774597 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11773820 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C23×PSU(3,𝔽2) | C4 | 1 | 2 | yes | — |
| 7 | C2×D4×#157 | — | 2 | 1 | no | — |
| 8 | C2×D4×#157 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×C22⋊PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 10 | C2×C22⋊PSU(3,𝔽2) | C4 | 1 | 2 | yes | — |
| 11 | D4×PSU(3,𝔽2) | — | 2 | 4 | no | — |
| 12 | D4×PSU(3,𝔽2) | — | 2 | 4 | no | — |
| 13 | C2×C4⋊PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 14 | C2×C4⋊PSU(3,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C4×PSU(3,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 16 | #10596484 | C22 | 1 | 2 | yes | — |
| 17 | #10593328 | C22 | 1 | 2 | yes | — |
| 18 | #10593272 | — | 2 | 2 | no | — |
| 19 | #10593158 | — | 2 | 4 | no | — |
| 20 | PSU(3,𝔽2)⋊C8 | — | 2 | 4 | no | — |
| 21 | #10591503 | — | 2 | 1 | no | — |
| 22 | #10590053 | — | 2 | 1 | no | — |
| 23 | C23×#157 | — | 2 | 2 | no | — |
| 24 | C23×#157 | C2×C4 | 1 | 2 | yes | — |
| 25 | C22×PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 26 | C22×PSU(3,𝔽2) | — | 2 | 4 | no | — |
| 27 | C22×PSU(3,𝔽2) | — | 2 | 4 | no | — |
| 28 | C22×PSU(3,𝔽2) | — | 4 | 8 | no | — |
| 29 | C22×PSU(3,𝔽2) | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | C22×PSU(3,𝔽2) | C2×C4 | 1 | 2 | yes | — |
| 31 | C2×D4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 32 | C2×C22⋊#157 | — | 2 | 2 | no | — |
| 33 | C2×C22⋊#157 | D4 | 1 | 2 | yes | — |
| 34 | D4×#157 | — | 2 | 8 | no | — |
| 35 | D4×#157 | — | 2 | 2 | no | — |
| 36 | D4×#157 | — | 2 | 2 | no | — |
| 37 | C2×C4⋊#157 | — | 2 | 1 | no | — |
| 38 | C2×C4⋊#157 | D4 | 1 | 1 | yes | characteristic |
| 39 | C2×C4×#157 | — | 2 | 1 | no | — |
| 40 | C2×C4×#157 | C23 | 1 | 1 | yes | characteristic |
| 41 | C22⋊PSU(3,𝔽2) | — | 2 | 16 | no | — |
| 42 | C22⋊PSU(3,𝔽2) | — | 2 | 4 | no | — |
| 43 | C22⋊PSU(3,𝔽2) | — | 2 | 4 | no | — |
| 44 | C2×#3777 | — | 2 | 2 | no | — |
| 45 | C2×#3777 | — | 2 | 1 | no | — |
| 46 | C2×#3777 | — | 2 | 1 | no | — |
| 47 | C2×#3777 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | C4⋊PSU(3,𝔽2) | — | 2 | 8 | no | — |
| 49 | C4⋊PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 50 | C4⋊PSU(3,𝔽2) | D4 | 1 | 4 | yes | — |
| 51 | C4×PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 52 | C4×PSU(3,𝔽2) | D4 | 1 | 4 | yes | — |
| 53 | C22⋊AGL(1,𝔽9) | — | 2 | 2 | no | — |
| 54 | C4⋊AGL(1,𝔽9) | — | 2 | 2 | no | — |
| 55 | C4×AGL(1,𝔽9) | — | 2 | 2 | no | — |
| 56 | #63818 | — | 2 | 2 | no | — |
| 57 | #63732 | — | 2 | 2 | no | — |
| 58 | #63732 | — | 2 | 2 | no | — |
| 59 | C3×#833 | — | 4 | 1 | no | — |
| 60 | #63559 | — | 4 | 1 | no | — |
| 61 | #8391 | — | 9 | 1 | no | maximal, Sylow |
| 62 | D3×#100 | — | 12 | 1 | no | — |
| 63 | C23×C3⋊D3 | C22⋊C4 | 1 | 2 | yes | — |
| 64 | C22×#157 | — | 2 | 1 | no | — |
| 65 | C22×#157 | — | 2 | 8 | no | — |
| 66 | C22×#157 | — | 2 | 1 | no | — |
| 67 | C22×#157 | — | 2 | 2 | no | — |
| 68 | C22×#157 | — | 2 | 2 | no | — |
| 69 | C22×#157 | — | 2 | 2 | no | — |
| 70 | C22×#157 | — | 4 | 8 | no | — |
| 71 | C22×#157 | — | 4 | 4 | no | — |
| 72 | C22×#157 | C22⋊C4 | 1 | 2 | yes | — |
| 73 | C22×#157 | C22×C4 | 1 | 1 | yes | characteristic |
| 74 | C22×#157 | C2×D4 | 1 | 1 | yes | characteristic |
| 75 | C2×PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 76 | C2×PSU(3,𝔽2) | — | 2 | 4 | no | — |
| 77 | C2×PSU(3,𝔽2) | — | 2 | 8 | no | — |
| 78 | C2×PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 79 | C2×PSU(3,𝔽2) | — | 4 | 16 | no | — |
| 80 | C2×PSU(3,𝔽2) | — | 4 | 8 | no | — |
| 81 | C2×PSU(3,𝔽2) | — | 4 | 8 | no | — |
| 82 | C2×PSU(3,𝔽2) | — | 4 | 8 | no | — |
| 83 | C2×PSU(3,𝔽2) | — | 4 | 4 | no | — |
| 84 | C2×PSU(3,𝔽2) | C22⋊C4 | 1 | 2 | yes | — |
| 85 | C2×PSU(3,𝔽2) | C22⋊C4 | 1 | 4 | yes | — |
| 86 | C2×AGL(1,𝔽9) | — | 4 | 2 | no | — |
| 87 | C2×C32×D4 | SD16 | 1 | 1 | yes | characteristic |
| 88 | C2×#638 | Q16 | 1 | 2 | yes | — |
| 89 | D4×C3⋊D3 | — | 2 | 2 | no | — |
| 90 | D4×C3⋊D3 | — | 2 | 2 | no | — |
| 91 | C2×C4⋊(C3⋊D3) | SD16 | 1 | 1 | yes | characteristic |
| 92 | C2×C4×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 93 | C22⋊#157 | — | 2 | 8 | no | — |
| 94 | C22⋊#157 | — | 2 | 4 | no | — |
| 95 | C4⋊#157 | — | 2 | 4 | no | — |
| 96 | C4⋊#157 | — | 2 | 2 | no | — |
| 97 | C4×#157 | — | 2 | 4 | no | — |
| 98 | C4×#157 | C2×D4 | 1 | 2 | yes | — |
| 99 | C4×#157 | C2×D4 | 1 | 2 | yes | — |
| 100 | #3777 | — | 2 | 8 | no | — |
| 101 | #3777 | — | 2 | 1 | no | — |
| 102 | #3777 | — | 2 | 4 | no | — |
| 103 | #3777 | — | 2 | 4 | no | — |
| 104 | #3777 | C22⋊C4 | 1 | 2 | yes | — |
| 105 | C3×#208 | — | 4 | 2 | no | — |
| 106 | #3712 | — | 4 | 2 | no | — |
| 107 | #3710 | — | 4 | 2 | no | — |
| 108 | C2×D4×Q8 | — | 9 | 1 | no | — |
| 109 | #1800 | — | 9 | 1 | no | — |
| 110 | #1548 | — | 9 | 2 | no | — |
| 111 | #1487 | — | 9 | 2 | no | — |
| 112 | #1460 | — | 9 | 1 | no | — |
| 113 | C2×D3×D4 | — | 12 | 1 | no | — |
| 114 | D3×M16 | — | 12 | 2 | no | — |
| 115 | C3×#100 | — | 12 | 1 | no | — |
| 116 | #833 | — | 4 | 1 | no | — |
| 117 | #823 | — | 12 | 2 | no | — |
| 118 | C23×C32 | #103 | 1 | 2 | yes | — |
| 119 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 120 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 121 | C22×C3⋊D3 | — | 4 | 2 | no | — |
| 122 | C22×C3⋊D3 | — | 4 | 2 | no | — |
| 123 | C22×C3⋊D3 | #103 | 1 | 2 | yes | — |
| 124 | C22×C3⋊D3 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 125 | C2×#157 | — | 2 | 4 | no | — |
| 126 | C2×#157 | — | 2 | 2 | no | — |
| 127 | C2×#157 | — | 2 | 2 | no | — |
| 128 | C2×#157 | — | 2 | 2 | no | — |
| 129 | C2×#157 | — | 2 | 4 | no | — |
| 130 | C2×#157 | — | 2 | 2 | no | — |
| 131 | C2×#157 | — | 4 | 1 | no | — |
| 132 | C2×#157 | — | 4 | 4 | no | — |
| 133 | C2×#157 | — | 4 | 16 | no | — |
| 134 | C2×#157 | — | 4 | 4 | no | — |
| 135 | C2×#157 | — | 4 | 2 | no | — |
| 136 | C2×#157 | — | 4 | 4 | no | — |
| 137 | C2×#157 | — | 4 | 2 | no | — |
| 138 | C2×#157 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 139 | C2×#157 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 140 | C2×#157 | #120 | 1 | 2 | yes | — |
| 141 | PSU(3,𝔽2) | — | 2 | 4 | no | — |
| 142 | PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 143 | PSU(3,𝔽2) | — | 4 | 4 | no | — |
| 144 | PSU(3,𝔽2) | — | 4 | 16 | no | — |
| 145 | PSU(3,𝔽2) | — | 4 | 4 | no | — |
| 146 | PSU(3,𝔽2) | #100 | 1 | 4 | yes | complemented |
| 147 | AGL(1,𝔽9) | — | 8 | 2 | no | — |
| 148 | C32×D4 | — | 2 | 2 | no | — |
| 149 | C2×C32×C4 | C2×SD16 | 1 | 1 | yes | characteristic |
| 150 | #638 | — | 2 | 4 | no | — |
| 151 | C2×C3⋊Dic3 | C2×Q16 | 1 | 1 | yes | characteristic |
| 152 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 153 | C4×C3⋊D3 | #120 | 1 | 2 | yes | — |
| 154 | C4×C3⋊D3 | #137 | 1 | 2 | yes | — |
| 155 | C3×C3⋊C8 | — | 8 | 2 | no | — |
| 156 | C23×Q8 | — | 9 | 2 | no | — |
| 157 | D4×Q8 | — | 18 | 4 | no | — |
| 158 | D4×Q8 | — | 18 | 4 | no | — |
| 159 | C2×C4⋊Q8 | — | 9 | 1 | no | — |
| 160 | C2×C4⋊Q8 | — | 18 | 1 | no | — |
| 161 | C2×C22⋊Q8 | — | 9 | 2 | no | — |
| 162 | C2×C22⋊Q8 | — | 18 | 2 | no | — |
| 163 | C2×C4×Q8 | — | 9 | 1 | no | — |
| 164 | C2×C4×D4 | — | 9 | 1 | no | — |
| 165 | C2×C4×D4 | — | 18 | 1 | no | — |
| 166 | #431 | — | 9 | 2 | no | — |
| 167 | #423 | — | 9 | 2 | no | — |
| 168 | C2×#100 | — | 18 | 1 | no | — |
| 169 | #343 | — | 18 | 1 | no | — |
| 170 | #333 | — | 18 | 4 | no | — |
| 171 | Q8⋊C8 | — | 18 | 4 | no | — |
| 172 | #323 | — | 18 | 2 | no | — |
| 173 | C23×D3 | — | 12 | 2 | no | — |
| 174 | C2×C3×D4 | — | 4 | 1 | no | — |
| 175 | C2×#67 | — | 12 | 2 | no | — |
| 176 | D3×D4 | — | 24 | 2 | no | — |
| 177 | D3×D4 | — | 24 | 2 | no | — |
| 178 | C2×D12 | — | 12 | 1 | no | — |
| 179 | C2×C4×D3 | — | 12 | 1 | no | — |
| 180 | C3×M16 | — | 12 | 2 | no | — |
| 181 | #208 | — | 4 | 2 | no | — |
| 182 | ΓL(1,𝔽25) | — | 24 | 2 | no | — |
| 183 | D3×C8 | — | 24 | 2 | no | — |
| 184 | C22×C32 | — | 2 | 2 | no | — |
| 185 | C22×C32 | — | 4 | 2 | no | — |
| 186 | C22×C32 | C2×#103 | 1 | 1 | yes | characteristic |
| 187 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 188 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 189 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 190 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 191 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 192 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 193 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 194 | C2×C3⋊D3 | #379 | 1 | 1 | yes | characteristic |
| 195 | C2×C3⋊D3 | #419 | 1 | 1 | yes | characteristic |
| 196 | #157 | — | 2 | 2 | no | — |
| 197 | #157 | — | 2 | 1 | no | — |
| 198 | #157 | — | 2 | 4 | no | — |
| 199 | #157 | — | 4 | 2 | no | — |
| 200 | #157 | — | 4 | 2 | no | — |
| 201 | #157 | — | 4 | 4 | no | — |
| 202 | #157 | C2×#100 | 1 | 2 | yes | — |
| 203 | C32×C4 | #448 | 1 | 2 | yes | — |
| 204 | C3⋊Dic3 | #451 | 1 | 2 | yes | — |
| 205 | C22×Q8 | — | 9 | 1 | no | — |
| 206 | C22×Q8 | — | 9 | 2 | no | — |
| 207 | C22×Q8 | — | 18 | 2 | no | — |
| 208 | C22×Q8 | — | 18 | 4 | no | — |
| 209 | C22×Q8 | — | 18 | 4 | no | — |
| 210 | C22×Q8 | — | 36 | 8 | no | — |
| 211 | C22×D4 | — | 9 | 1 | no | — |
| 212 | C23×C4 | — | 9 | 2 | no | — |
| 213 | C23×C4 | — | 18 | 2 | no | — |
| 214 | C2×M16 | — | 18 | 2 | no | — |
| 215 | C4⋊Q8 | — | 9 | 4 | no | — |
| 216 | C4⋊Q8 | — | 18 | 2 | no | — |
| 217 | C4⋊Q8 | — | 18 | 8 | no | — |
| 218 | C22⋊Q8 | — | 18 | 4 | no | — |
| 219 | C22⋊Q8 | — | 18 | 4 | no | — |
| 220 | C22⋊Q8 | — | 18 | 16 | no | — |
| 221 | C4×Q8 | — | 9 | 4 | no | — |
| 222 | C4×Q8 | — | 18 | 2 | no | — |
| 223 | C4×D4 | — | 18 | 2 | no | — |
| 224 | C4×D4 | — | 18 | 2 | no | — |
| 225 | C4×D4 | — | 18 | 8 | no | — |
| 226 | C2×C4⋊C4 | — | 9 | 1 | no | — |
| 227 | C2×C4⋊C4 | — | 9 | 1 | no | — |
| 228 | C2×C4⋊C4 | — | 18 | 1 | no | — |
| 229 | C2×C4⋊C4 | — | 18 | 1 | no | — |
| 230 | C2×C4⋊C4 | — | 18 | 2 | no | — |
| 231 | C2×C4⋊C4 | — | 18 | 1 | no | — |
| 232 | C2×C22⋊C4 | — | 9 | 2 | no | — |
| 233 | C2×C22⋊C4 | — | 18 | 2 | no | — |
| 234 | C2×C42 | — | 9 | 1 | no | — |
| 235 | C2×C42 | — | 18 | 1 | no | — |
| 236 | C4⋊C8 | — | 18 | 2 | no | — |
| 237 | C4⋊C8 | — | 18 | 2 | no | — |
| 238 | C4⋊C8 | — | 18 | 2 | no | — |
| 239 | #100 | — | 12 | 1 | no | — |
| 240 | #100 | — | 36 | 1 | no | — |
| 241 | C22⋊C8 | — | 18 | 2 | no | — |
| 242 | C4×C8 | — | 18 | 2 | no | — |
| 243 | C23×C3 | — | 4 | 2 | no | — |
| 244 | C22×D3 | — | 12 | 1 | no | — |
| 245 | C22×D3 | — | 12 | 2 | no | — |
| 246 | C22×D3 | — | 24 | 2 | no | — |
| 247 | C22×D3 | — | 24 | 2 | no | — |
| 248 | C22×D3 | — | 48 | 2 | no | — |
| 249 | C22×D3 | — | 48 | 2 | no | — |
| 250 | C3×D4 | — | 8 | 2 | no | — |
| 251 | C2×C3×C4 | — | 4 | 1 | no | — |
| 252 | #67 | — | 24 | 4 | no | — |
| 253 | C2×Dic3 | — | 12 | 1 | no | — |
| 254 | D12 | — | 24 | 2 | no | — |
| 255 | C4×D3 | — | 12 | 2 | no | — |
| 256 | C4×D3 | — | 12 | 2 | no | — |
| 257 | C3×C8 | — | 24 | 2 | no | — |
| 258 | C3⋊C8 | — | 8 | 2 | no | — |
| 259 | C2×C32 | — | 2 | 1 | no | — |
| 260 | C2×C32 | — | 4 | 2 | no | — |
| 261 | C2×C32 | #1787 | 1 | 1 | yes | characteristic |
| 262 | C3⋊D3 | — | 2 | 1 | no | — |
| 263 | C3⋊D3 | — | 4 | 2 | no | — |
| 264 | C3⋊D3 | #1783 | 1 | 1 | yes | characteristic |
| 265 | C3⋊D3 | #1796 | 1 | 1 | yes | characteristic |
| 266 | C24 | — | 9 | 2 | no | — |
| 267 | C2×Q8 | — | 9 | 2 | no | — |
| 268 | C2×Q8 | — | 9 | 4 | no | — |
| 269 | C2×Q8 | — | 18 | 1 | no | — |
| 270 | C2×Q8 | — | 18 | 2 | no | — |
| 271 | C2×Q8 | — | 18 | 4 | no | — |
| 272 | C2×Q8 | — | 18 | 8 | no | — |
| 273 | C2×Q8 | — | 36 | 4 | no | — |
| 274 | C2×Q8 | — | 36 | 8 | no | — |
| 275 | C2×Q8 | — | 36 | 8 | no | — |
| 276 | C2×Q8 | — | 36 | 8 | no | — |
| 277 | C2×Q8 | — | 36 | 16 | no | — |
| 278 | C2×D4 | — | 9 | 2 | no | — |
| 279 | C2×D4 | — | 9 | 1 | no | — |
| 280 | C2×D4 | — | 18 | 2 | no | — |
| 281 | C2×D4 | — | 18 | 2 | no | — |
| 282 | C2×D4 | AΓL(1,𝔽9) | 1 | 1 | yes | characteristic |
| 283 | C22×C4 | — | 9 | 1 | no | — |
| 284 | C22×C4 | — | 9 | 1 | no | — |
| 285 | C22×C4 | — | 9 | 1 | no | — |
| 286 | C22×C4 | — | 9 | 2 | no | — |
| 287 | C22×C4 | — | 18 | 2 | no | — |
| 288 | C22×C4 | — | 18 | 2 | no | — |
| 289 | C22×C4 | — | 18 | 1 | no | — |
| 290 | C22×C4 | — | 18 | 1 | no | — |
| 291 | C22×C4 | — | 18 | 2 | no | — |
| 292 | C22×C4 | — | 18 | 8 | no | — |
| 293 | C22×C4 | — | 36 | 8 | no | — |
| 294 | C22×C4 | — | 36 | 4 | no | — |
| 295 | M16 | — | 12 | 2 | no | — |
| 296 | M16 | — | 36 | 2 | no | — |
| 297 | C2×C8 | — | 36 | 2 | no | — |
| 298 | C2×C8 | — | 36 | 2 | no | — |
| 299 | C4⋊C4 | — | 9 | 2 | no | — |
| 300 | C4⋊C4 | — | 18 | 2 | no | — |
| 301 | C4⋊C4 | — | 18 | 1 | no | — |
| 302 | C4⋊C4 | — | 18 | 4 | no | — |
| 303 | C4⋊C4 | — | 18 | 4 | no | — |
| 304 | C4⋊C4 | — | 18 | 4 | no | — |
| 305 | C4⋊C4 | — | 18 | 8 | no | — |
| 306 | C22⋊C4 | — | 18 | 4 | no | — |
| 307 | C22⋊C4 | — | 18 | 8 | no | — |
| 308 | C42 | — | 9 | 2 | no | — |
| 309 | C42 | — | 9 | 2 | no | — |
| 310 | C42 | — | 18 | 4 | no | — |
| 311 | C22×C3 | — | 4 | 1 | no | — |
| 312 | C22×C3 | — | 8 | 2 | no | — |
| 313 | C22×C3 | — | 16 | 2 | no | — |
| 314 | C2×D3 | — | 12 | 1 | no | — |
| 315 | C2×D3 | — | 12 | 1 | no | — |
| 316 | C2×D3 | — | 24 | 1 | no | — |
| 317 | C2×D3 | — | 24 | 1 | no | — |
| 318 | C2×D3 | — | 24 | 2 | no | — |
| 319 | C2×D3 | — | 48 | 2 | no | — |
| 320 | C2×D3 | — | 48 | 2 | no | — |
| 321 | C2×D3 | — | 48 | 4 | no | — |
| 322 | C2×D3 | — | 48 | 2 | no | — |
| 323 | C3×C4 | — | 4 | 2 | no | — |
| 324 | Dic3 | — | 12 | 2 | no | — |
| 325 | C32 | #8391 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 326 | C23 | — | 9 | 1 | no | — |
| 327 | C23 | — | 9 | 2 | no | — |
| 328 | C23 | — | 18 | 2 | no | — |
| 329 | C23 | — | 18 | 2 | no | — |
| 330 | C23 | — | 36 | 2 | no | — |
| 331 | C23 | — | 36 | 2 | no | — |
| 332 | C23 | PSU(3,𝔽2)⋊C4 | 1 | 2 | yes | — |
| 333 | Q8 | — | 9 | 4 | no | — |
| 334 | Q8 | — | 18 | 2 | no | — |
| 335 | Q8 | — | 18 | 4 | no | — |
| 336 | Q8 | — | 36 | 4 | no | — |
| 337 | Q8 | — | 36 | 4 | no | — |
| 338 | Q8 | — | 36 | 16 | no | — |
| 339 | D4 | — | 2 | 2 | no | — |
| 340 | D4 | — | 18 | 4 | no | — |
| 341 | D4 | — | 18 | 2 | no | — |
| 342 | C2×C4 | — | 9 | 1 | no | — |
| 343 | C2×C4 | — | 9 | 1 | no | — |
| 344 | C2×C4 | — | 9 | 2 | no | — |
| 345 | C2×C4 | — | 9 | 2 | no | — |
| 346 | C2×C4 | — | 9 | 2 | no | — |
| 347 | C2×C4 | — | 9 | 1 | no | — |
| 348 | C2×C4 | — | 18 | 2 | no | — |
| 349 | C2×C4 | — | 18 | 2 | no | — |
| 350 | C2×C4 | — | 18 | 4 | no | — |
| 351 | C2×C4 | — | 18 | 2 | no | — |
| 352 | C2×C4 | — | 18 | 2 | no | — |
| 353 | C2×C4 | — | 18 | 4 | no | — |
| 354 | C2×C4 | — | 36 | 4 | no | — |
| 355 | C2×C4 | — | 36 | 1 | no | — |
| 356 | C2×C4 | — | 36 | 4 | no | — |
| 357 | C2×C4 | — | 36 | 16 | no | — |
| 358 | C2×C4 | — | 36 | 4 | no | — |
| 359 | C2×C4 | — | 36 | 2 | no | — |
| 360 | C2×C4 | — | 36 | 2 | no | — |
| 361 | C2×C4 | C2×AΓL(1,𝔽9) | 1 | 1 | yes | characteristic |
| 362 | C8 | — | 24 | 2 | no | — |
| 363 | C8 | — | 72 | 2 | no | — |
| 364 | C2×C3 | — | 4 | 1 | no | — |
| 365 | C2×C3 | — | 8 | 1 | no | — |
| 366 | C2×C3 | — | 16 | 2 | no | — |
| 367 | D3 | — | 12 | 1 | no | — |
| 368 | D3 | — | 12 | 1 | no | — |
| 369 | D3 | — | 24 | 1 | no | — |
| 370 | D3 | — | 48 | 2 | no | — |
| 371 | C22 | — | 2 | 2 | no | — |
| 372 | C22 | — | 4 | 2 | no | — |
| 373 | C22 | — | 9 | 1 | no | — |
| 374 | C22 | — | 9 | 1 | no | — |
| 375 | C22 | — | 18 | 1 | no | — |
| 376 | C22 | — | 18 | 1 | no | — |
| 377 | C22 | — | 18 | 2 | no | — |
| 378 | C22 | — | 36 | 2 | no | — |
| 379 | C22 | — | 36 | 2 | no | — |
| 380 | C22 | — | 36 | 2 | no | — |
| 381 | C22 | — | 36 | 4 | no | — |
| 382 | C22 | C2×PSU(3,𝔽2)⋊C4 | 1 | 1 | yes | characteristic |
| 383 | C4 | — | 9 | 2 | no | — |
| 384 | C4 | — | 9 | 2 | no | — |
| 385 | C4 | — | 18 | 2 | no | — |
| 386 | C4 | — | 18 | 1 | no | — |
| 387 | C4 | — | 18 | 4 | no | — |
| 388 | C4 | — | 36 | 4 | no | — |
| 389 | C4 | — | 36 | 2 | no | — |
| 390 | C4 | — | 36 | 2 | no | — |
| 391 | C4 | #10596418 | 1 | 2 | yes | — |
| 392 | C3 | — | 4 | 1 | no | — |
| 393 | C2 | — | 2 | 1 | no | — |
| 394 | C2 | — | 4 | 2 | no | — |
| 395 | C2 | — | 9 | 1 | no | — |
| 396 | C2 | — | 9 | 1 | no | — |
| 397 | C2 | — | 18 | 1 | no | — |
| 398 | C2 | — | 36 | 2 | no | — |
| 399 | C2 | #11784747 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11776370 | C2 | semidirect |
| 4. #11774597 | C2 | semidirect |
| 146. PSU(3,𝔽2) | #100 | semidirect |
| 325. C32 | #8391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×PSU(3,𝔽2) | 2 |
| #11785131 | 2 |
| #11776370 | 2 |
| #11774597 | 2 |
| #11773820 | 2 |
| #8391 | 9 |