Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
1567 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 1567 conjugacy classes of subgroups — too many to draw. Only its 125 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 | H(5,𝔽2)×#157 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11787155 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #11773799 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | C23×AGL(1,𝔽9) | C22 | 1 | 1 | yes | characteristic, complemented |
| 5 | C3⋊D3×H(5,𝔽2) | C4 | 1 | 1 | yes | characteristic |
| 6 | #10596650 | — | 2 | 3 | no | — |
| 7 | #41×#157 | — | 2 | 3 | no | — |
| 8 | #10596642 | — | 2 | 3 | no | — |
| 9 | #10596642 | C4 | 1 | 3 | yes | — |
| 10 | C2×D4×#157 | — | 2 | 3 | no | — |
| 11 | C2×D4×#157 | C22 | 1 | 3 | yes | — |
| 12 | C2×C22⋊AGL(1,𝔽9) | — | 2 | 3 | no | — |
| 13 | C2×C22⋊AGL(1,𝔽9) | C22 | 1 | 3 | yes | complemented |
| 14 | #10593272 | — | 2 | 3 | no | — |
| 15 | #10593267 | — | 2 | 3 | no | — |
| 16 | #10593260 | — | 2 | 3 | no | — |
| 17 | C23×#157 | — | 2 | 1 | no | — |
| 18 | C23×#157 | D4 | 1 | 3 | yes | — |
| 19 | C23×#157 | C23 | 1 | 1 | yes | characteristic |
| 20 | C22×AGL(1,𝔽9) | — | 2 | 3 | no | — |
| 21 | C22×AGL(1,𝔽9) | — | 2 | 3 | no | — |
| 22 | C22×AGL(1,𝔽9) | — | 4 | 2 | no | — |
| 23 | C32×H(5,𝔽2) | C8 | 1 | 1 | yes | characteristic, complemented |
| 24 | #64366 | — | 2 | 3 | no | — |
| 25 | #41×C3⋊D3 | — | 2 | 3 | no | — |
| 26 | #64361 | — | 2 | 3 | no | — |
| 27 | #64361 | C8 | 1 | 3 | yes | complemented |
| 28 | C2×D4×C3⋊D3 | — | 2 | 3 | no | — |
| 29 | C2×D4×C3⋊D3 | C2×C4 | 1 | 3 | yes | — |
| 30 | C2×C22⋊#157 | — | 2 | 3 | no | — |
| 31 | C2×C22⋊#157 | — | 2 | 3 | no | — |
| 32 | C2×C22⋊#157 | C2×C4 | 1 | 3 | yes | — |
| 33 | C2×C22⋊#157 | D4 | 1 | 3 | yes | — |
| 34 | Q8×#157 | — | 2 | 1 | no | — |
| 35 | Q8×#157 | — | 2 | 3 | no | — |
| 36 | D4×#157 | — | 2 | 3 | no | — |
| 37 | D4×#157 | — | 2 | 6 | no | — |
| 38 | D4×#157 | — | 2 | 3 | no | — |
| 39 | D4×#157 | — | 2 | 6 | no | — |
| 40 | D4×#157 | — | 2 | 6 | no | — |
| 41 | D4×#157 | — | 2 | 6 | no | — |
| 42 | D4×#157 | — | 2 | 6 | no | — |
| 43 | #64286 | — | 2 | 6 | no | — |
| 44 | #64286 | — | 2 | 3 | no | — |
| 45 | C2×C4⋊#157 | — | 2 | 3 | no | — |
| 46 | C2×C4⋊#157 | D4 | 1 | 3 | yes | — |
| 47 | C2×C4×#157 | — | 2 | 3 | no | — |
| 48 | C2×C4×#157 | D4 | 1 | 3 | yes | — |
| 49 | C22⋊AGL(1,𝔽9) | — | 2 | 6 | no | — |
| 50 | C22⋊AGL(1,𝔽9) | — | 4 | 6 | no | — |
| 51 | #8316 | — | 9 | 1 | no | maximal, Sylow |
| 52 | D3×H(5,𝔽2) | — | 12 | 1 | no | — |
| 53 | C23×C3⋊D3 | — | 2 | 1 | no | — |
| 54 | C23×C3⋊D3 | C22⋊C4 | 1 | 3 | yes | — |
| 55 | C23×C3⋊D3 | C22×C4 | 1 | 1 | yes | characteristic |
| 56 | C22×#157 | — | 2 | 3 | no | — |
| 57 | C22×#157 | — | 2 | 3 | no | — |
| 58 | C22×#157 | — | 2 | 3 | no | — |
| 59 | C22×#157 | — | 2 | 3 | no | — |
| 60 | C22×#157 | — | 4 | 1 | no | — |
| 61 | C22×#157 | — | 4 | 1 | no | — |
| 62 | C22×#157 | — | 4 | 3 | no | — |
| 63 | C22×#157 | — | 4 | 3 | no | — |
| 64 | C22×#157 | — | 8 | 1 | no | — |
| 65 | C22×#157 | — | 8 | 1 | no | — |
| 66 | C22×#157 | C22⋊C4 | 1 | 3 | yes | — |
| 67 | C22×#157 | C22⋊C4 | 1 | 3 | yes | — |
| 68 | C22×#157 | C2×D4 | 1 | 3 | yes | — |
| 69 | C22×#157 | C2×D4 | 1 | 3 | yes | — |
| 70 | C2×AGL(1,𝔽9) | — | 2 | 6 | no | — |
| 71 | C2×AGL(1,𝔽9) | — | 4 | 3 | no | — |
| 72 | C2×AGL(1,𝔽9) | — | 4 | 1 | no | — |
| 73 | C2×AGL(1,𝔽9) | — | 4 | 3 | no | — |
| 74 | C2×AGL(1,𝔽9) | — | 4 | 3 | no | — |
| 75 | C2×AGL(1,𝔽9) | — | 4 | 3 | no | — |
| 76 | C32×#41 | — | 2 | 3 | no | — |
| 77 | C2×C32×D4 | — | 2 | 3 | no | — |
| 78 | C2×C32×D4 | C2×C8 | 1 | 3 | yes | — |
| 79 | C2×#638 | — | 2 | 3 | no | — |
| 80 | C2×#638 | — | 2 | 3 | no | — |
| 81 | C2×#638 | C2×C8 | 1 | 3 | yes | — |
| 82 | C2×#638 | M16 | 1 | 3 | yes | — |
| 83 | #3832 | — | 2 | 3 | no | — |
| 84 | Q8×C3⋊D3 | — | 2 | 1 | no | — |
| 85 | #3830 | — | 2 | 3 | no | — |
| 86 | #3830 | — | 2 | 6 | no | — |
| 87 | D4×C3⋊D3 | — | 2 | 3 | no | — |
| 88 | D4×C3⋊D3 | — | 2 | 6 | no | — |
| 89 | D4×C3⋊D3 | — | 2 | 6 | no | — |
| 90 | D4×C3⋊D3 | — | 2 | 6 | no | — |
| 91 | D4×C3⋊D3 | — | 2 | 6 | no | — |
| 92 | #3828 | — | 2 | 6 | no | — |
| 93 | #3828 | — | 2 | 3 | no | — |
| 94 | C2×C4⋊(C3⋊D3) | — | 2 | 3 | no | — |
| 95 | C2×C4⋊(C3⋊D3) | M16 | 1 | 3 | yes | — |
| 96 | C2×C4×C3⋊D3 | — | 2 | 3 | no | — |
| 97 | C2×C4×C3⋊D3 | C22⋊C4 | 1 | 3 | yes | — |
| 98 | C22⋊#157 | — | 2 | 6 | no | — |
| 99 | C22⋊#157 | — | 2 | 6 | no | — |
| 100 | C22⋊#157 | — | 2 | 6 | no | — |
| 101 | C4⋊#157 | — | 2 | 3 | no | — |
| 102 | C4⋊#157 | — | 2 | 3 | no | — |
| 103 | C4⋊#157 | — | 2 | 6 | no | — |
| 104 | C4×#157 | — | 2 | 6 | no | — |
| 105 | C4×#157 | — | 2 | 3 | no | — |
| 106 | C4×#157 | — | 2 | 3 | no | — |
| 107 | C4×H(5,𝔽2) | — | 9 | 1 | no | — |
| 108 | #1869 | — | 9 | 3 | no | — |
| 109 | #1459 | — | 9 | 3 | no | — |
| 110 | C3×H(5,𝔽2) | — | 4 | 1 | no | — |
| 111 | #1009 | — | 12 | 3 | no | — |
| 112 | #1009 | — | 12 | 3 | no | — |
| 113 | D3×#41 | — | 12 | 3 | no | — |
| 114 | D3×#41 | — | 12 | 3 | no | — |
| 115 | #1004 | — | 12 | 3 | no | — |
| 116 | #1004 | — | 12 | 3 | no | — |
| 117 | #1004 | — | 12 | 3 | no | — |
| 118 | C2×D3×D4 | — | 12 | 3 | no | — |
| 119 | C2×D3×D4 | — | 12 | 3 | no | — |
| 120 | C2×D3×D4 | — | 12 | 3 | no | — |
| 121 | C23×C32 | — | 2 | 1 | no | — |
| 122 | C23×C32 | C22⋊C8 | 1 | 3 | yes | complemented |
| 123 | C23×C32 | C22×C8 | 1 | 1 | yes | characteristic |
| 124 | C22×C3⋊D3 | — | 2 | 3 | no | — |
| 125 | C22×C3⋊D3 | — | 2 | 3 | no | — |
| 126 | C22×C3⋊D3 | — | 2 | 3 | no | — |
| 127 | C22×C3⋊D3 | — | 4 | 1 | no | — |
| 128 | C22×C3⋊D3 | — | 4 | 1 | no | — |
| 129 | C22×C3⋊D3 | — | 4 | 3 | no | — |
| 130 | C22×C3⋊D3 | — | 4 | 3 | no | — |
| 131 | C22×C3⋊D3 | — | 8 | 1 | no | — |
| 132 | C22×C3⋊D3 | — | 8 | 1 | no | — |
| 133 | C22×C3⋊D3 | C22⋊C8 | 1 | 3 | yes | complemented |
| 134 | C22×C3⋊D3 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 135 | C22×C3⋊D3 | C2×M16 | 1 | 3 | yes | — |
| 136 | C2×#157 | — | 2 | 3 | no | — |
| 137 | C2×#157 | — | 2 | 3 | no | — |
| 138 | C2×#157 | — | 2 | 3 | no | — |
| 139 | C2×#157 | — | 2 | 3 | no | — |
| 140 | C2×#157 | — | 4 | 3 | no | — |
| 141 | C2×#157 | — | 4 | 3 | no | — |
| 142 | C2×#157 | — | 4 | 3 | no | — |
| 143 | C2×#157 | — | 4 | 3 | no | — |
| 144 | C2×#157 | — | 4 | 3 | no | — |
| 145 | C2×#157 | — | 8 | 3 | no | — |
| 146 | C2×#157 | — | 8 | 3 | no | — |
| 147 | C2×#157 | — | 8 | 3 | no | — |
| 148 | C2×#157 | #120 | 1 | 3 | yes | — |
| 149 | C2×#157 | #120 | 1 | 1 | yes | characteristic |
| 150 | AGL(1,𝔽9) | — | 4 | 2 | no | — |
| 151 | AGL(1,𝔽9) | — | 8 | 3 | no | — |
| 152 | C32×Q8 | — | 2 | 1 | no | — |
| 153 | C32×D4 | — | 2 | 3 | no | — |
| 154 | C32×D4 | — | 2 | 6 | no | — |
| 155 | C2×C32×C4 | — | 2 | 3 | no | — |
| 156 | C2×C32×C4 | C22⋊C8 | 1 | 3 | yes | complemented |
| 157 | #638 | — | 2 | 6 | no | — |
| 158 | #638 | — | 2 | 6 | no | — |
| 159 | #638 | — | 2 | 6 | no | — |
| 160 | C2×C3⋊Dic3 | — | 2 | 3 | no | — |
| 161 | C2×C3⋊Dic3 | C22⋊C8 | 1 | 3 | yes | complemented |
| 162 | C4⋊(C3⋊D3) | — | 2 | 3 | no | — |
| 163 | C4⋊(C3⋊D3) | — | 2 | 6 | no | — |
| 164 | C4×C3⋊D3 | — | 2 | 6 | no | — |
| 165 | C4×C3⋊D3 | — | 2 | 3 | no | — |
| 166 | C4×C3⋊D3 | — | 2 | 3 | no | — |
| 167 | #634 | — | 2 | 3 | no | — |
| 168 | C2×H(5,𝔽2) | — | 9 | 1 | no | — |
| 169 | C23×C8 | — | 9 | 1 | no | — |
| 170 | #520 | — | 18 | 3 | no | — |
| 171 | #518 | — | 9 | 3 | no | — |
| 172 | #518 | — | 18 | 3 | no | — |
| 173 | C4×#41 | — | 18 | 3 | no | — |
| 174 | C2×C4×D4 | — | 9 | 3 | no | — |
| 175 | C2×C4×D4 | — | 18 | 3 | no | — |
| 176 | C2×C22⋊C8 | — | 9 | 3 | no | — |
| 177 | C2×C22⋊C8 | — | 18 | 3 | no | — |
| 178 | #336 | — | 18 | 3 | no | — |
| 179 | #324 | — | 18 | 3 | no | — |
| 180 | #323 | — | 18 | 3 | no | — |
| 181 | C23×D3 | — | 12 | 1 | no | — |
| 182 | C23×D3 | — | 12 | 3 | no | — |
| 183 | C23×D3 | — | 12 | 1 | no | — |
| 184 | C23×D3 | — | 12 | 1 | no | — |
| 185 | C3×#41 | — | 4 | 3 | no | — |
| 186 | C3×#41 | — | 4 | 3 | no | — |
| 187 | C2×C3×D4 | — | 4 | 3 | no | — |
| 188 | C2×C3×D4 | — | 4 | 3 | no | — |
| 189 | C2×C3×D4 | — | 4 | 3 | no | — |
| 190 | C2×#67 | — | 12 | 3 | no | — |
| 191 | C2×#67 | — | 12 | 3 | no | — |
| 192 | C2×#67 | — | 12 | 3 | no | — |
| 193 | C2×#67 | — | 12 | 3 | no | — |
| 194 | C2×#67 | — | 12 | 3 | no | — |
| 195 | C2×#67 | — | 12 | 3 | no | — |
| 196 | #239 | — | 12 | 3 | no | — |
| 197 | #239 | — | 12 | 3 | no | — |
| 198 | D3×Q8 | — | 12 | 1 | no | — |
| 199 | D3×Q8 | — | 12 | 1 | no | — |
| 200 | #237 | — | 12 | 6 | no | — |
| 201 | #237 | — | 12 | 3 | no | — |
| 202 | #237 | — | 12 | 3 | no | — |
| 203 | #237 | — | 12 | 6 | no | — |
| 204 | D3×D4 | — | 12 | 6 | no | — |
| 205 | D3×D4 | — | 12 | 3 | no | — |
| 206 | D3×D4 | — | 12 | 3 | no | — |
| 207 | D3×D4 | — | 12 | 6 | no | — |
| 208 | D3×D4 | — | 12 | 6 | no | — |
| 209 | D3×D4 | — | 12 | 6 | no | — |
| 210 | D3×D4 | — | 12 | 6 | no | — |
| 211 | D3×D4 | — | 12 | 6 | no | — |
| 212 | D3×D4 | — | 12 | 6 | no | — |
| 213 | D3×D4 | — | 12 | 6 | no | — |
| 214 | #235 | — | 12 | 6 | no | — |
| 215 | #235 | — | 12 | 6 | no | — |
| 216 | #235 | — | 12 | 3 | no | — |
| 217 | #235 | — | 12 | 3 | no | — |
| 218 | C2×D12 | — | 12 | 3 | no | — |
| 219 | C2×D12 | — | 12 | 3 | no | — |
| 220 | C2×D12 | — | 12 | 3 | no | — |
| 221 | C2×C4×D3 | — | 12 | 3 | no | — |
| 222 | C2×C4×D3 | — | 12 | 3 | no | — |
| 223 | C2×C4×D3 | — | 12 | 3 | no | — |
| 224 | C22×C32 | — | 2 | 3 | no | — |
| 225 | C22×C32 | — | 4 | 1 | no | — |
| 226 | C22×C32 | — | 4 | 3 | no | — |
| 227 | C22×C32 | — | 8 | 1 | no | — |
| 228 | C22×C32 | C2×C22⋊C8 | 1 | 3 | yes | — |
| 229 | C2×C3⋊D3 | — | 2 | 3 | no | — |
| 230 | C2×C3⋊D3 | — | 2 | 3 | no | — |
| 231 | C2×C3⋊D3 | — | 2 | 3 | no | — |
| 232 | C2×C3⋊D3 | — | 4 | 3 | no | — |
| 233 | C2×C3⋊D3 | — | 4 | 3 | no | — |
| 234 | C2×C3⋊D3 | — | 4 | 3 | no | — |
| 235 | C2×C3⋊D3 | — | 4 | 3 | no | — |
| 236 | C2×C3⋊D3 | — | 8 | 3 | no | — |
| 237 | C2×C3⋊D3 | — | 8 | 3 | no | — |
| 238 | C2×C3⋊D3 | #379 | 1 | 1 | yes | characteristic |
| 239 | C2×C3⋊D3 | #407 | 1 | 3 | yes | — |
| 240 | #157 | — | 2 | 3 | no | — |
| 241 | #157 | — | 4 | 3 | no | — |
| 242 | #157 | — | 4 | 3 | no | — |
| 243 | #157 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 244 | #157 | #458 | 1 | 1 | yes | characteristic |
| 245 | C32×C4 | — | 2 | 3 | no | — |
| 246 | C3⋊Dic3 | — | 2 | 3 | no | — |
| 247 | H(5,𝔽2) | — | 9 | 3 | no | — |
| 248 | H(5,𝔽2) | — | 18 | 3 | no | — |
| 249 | H(5,𝔽2) | — | 18 | 3 | no | — |
| 250 | H(5,𝔽2) | AGL(1,𝔽9) | 1 | 1 | yes | characteristic, complemented |
| 251 | C2×#41 | — | 18 | 3 | no | — |
| 252 | C22×D4 | — | 9 | 3 | no | — |
| 253 | C22×D4 | — | 18 | 3 | no | — |
| 254 | C23×C4 | — | 9 | 1 | no | — |
| 255 | C23×C4 | — | 9 | 3 | no | — |
| 256 | C23×C4 | — | 18 | 1 | no | — |
| 257 | C22×C8 | — | 18 | 3 | no | — |
| 258 | C22×C8 | — | 18 | 3 | no | — |
| 259 | C22×C8 | — | 36 | 2 | no | — |
| 260 | C4×Q8 | — | 18 | 1 | no | — |
| 261 | C4×Q8 | — | 18 | 3 | no | — |
| 262 | C4×D4 | — | 18 | 6 | no | — |
| 263 | C4×D4 | — | 18 | 6 | no | — |
| 264 | C4×D4 | — | 18 | 6 | no | — |
| 265 | C4×D4 | — | 18 | 6 | no | — |
| 266 | C4×D4 | — | 18 | 3 | no | — |
| 267 | C4×D4 | — | 18 | 6 | no | — |
| 268 | C4×D4 | — | 18 | 3 | no | — |
| 269 | #117 | — | 18 | 3 | no | — |
| 270 | #117 | — | 18 | 6 | no | — |
| 271 | C2×C4⋊C4 | — | 9 | 3 | no | — |
| 272 | C2×C4⋊C4 | — | 18 | 3 | no | — |
| 273 | C2×C22⋊C4 | — | 9 | 3 | no | — |
| 274 | C2×C22⋊C4 | — | 9 | 3 | no | — |
| 275 | C2×C22⋊C4 | — | 18 | 3 | no | — |
| 276 | C2×C22⋊C4 | — | 18 | 3 | no | — |
| 277 | C2×C42 | — | 9 | 3 | no | — |
| 278 | C2×C42 | — | 18 | 3 | no | — |
| 279 | C22⋊C8 | — | 18 | 6 | no | — |
| 280 | C22⋊C8 | — | 36 | 6 | no | — |
| 281 | C23×C3 | — | 4 | 1 | no | — |
| 282 | C23×C3 | — | 4 | 1 | no | — |
| 283 | C23×C3 | — | 4 | 1 | no | — |
| 284 | C23×C3 | — | 4 | 3 | no | — |
| 285 | C22×D3 | — | 12 | 3 | no | — |
| 286 | C22×D3 | — | 12 | 3 | no | — |
| 287 | C22×D3 | — | 12 | 3 | no | — |
| 288 | C22×D3 | — | 12 | 3 | no | — |
| 289 | C22×D3 | — | 12 | 3 | no | — |
| 290 | C22×D3 | — | 12 | 3 | no | — |
| 291 | C22×D3 | — | 12 | 3 | no | — |
| 292 | C22×D3 | — | 12 | 3 | no | — |
| 293 | C22×D3 | — | 12 | 3 | no | — |
| 294 | C22×D3 | — | 48 | 1 | no | — |
| 295 | C22×D3 | — | 48 | 1 | no | — |
| 296 | C22×D3 | — | 48 | 3 | no | — |
| 297 | C22×D3 | — | 48 | 3 | no | — |
| 298 | C22×D3 | — | 48 | 1 | no | — |
| 299 | C22×D3 | — | 48 | 1 | no | — |
| 300 | C22×D3 | — | 48 | 1 | no | — |
| 301 | C22×D3 | — | 48 | 1 | no | — |
| 302 | C3×Q8 | — | 4 | 1 | no | — |
| 303 | C3×Q8 | — | 4 | 1 | no | — |
| 304 | C3×D4 | — | 4 | 3 | no | — |
| 305 | C3×D4 | — | 4 | 3 | no | — |
| 306 | C3×D4 | — | 4 | 6 | no | — |
| 307 | C3×D4 | — | 4 | 6 | no | — |
| 308 | C2×C3×C4 | — | 4 | 3 | no | — |
| 309 | C2×C3×C4 | — | 4 | 3 | no | — |
| 310 | C2×C3×C4 | — | 4 | 3 | no | — |
| 311 | #67 | — | 12 | 6 | no | — |
| 312 | #67 | — | 12 | 6 | no | — |
| 313 | #67 | — | 12 | 6 | no | — |
| 314 | #67 | — | 12 | 6 | no | — |
| 315 | #67 | — | 12 | 6 | no | — |
| 316 | #67 | — | 12 | 6 | no | — |
| 317 | C2×Dic3 | — | 12 | 3 | no | — |
| 318 | C2×Dic3 | — | 12 | 3 | no | — |
| 319 | C2×Dic3 | — | 12 | 3 | no | — |
| 320 | D12 | — | 12 | 6 | no | — |
| 321 | D12 | — | 12 | 3 | no | — |
| 322 | D12 | — | 12 | 3 | no | — |
| 323 | D12 | — | 12 | 6 | no | — |
| 324 | C4×D3 | — | 12 | 3 | no | — |
| 325 | C4×D3 | — | 12 | 3 | no | — |
| 326 | C4×D3 | — | 12 | 3 | no | — |
| 327 | C4×D3 | — | 12 | 6 | no | — |
| 328 | C4×D3 | — | 12 | 6 | no | — |
| 329 | C4×D3 | — | 12 | 3 | no | — |
| 330 | Dic6 | — | 12 | 3 | no | — |
| 331 | Dic6 | — | 12 | 3 | no | — |
| 332 | C2×C32 | — | 2 | 3 | no | — |
| 333 | C2×C32 | — | 4 | 3 | no | — |
| 334 | C2×C32 | #1779 | 1 | 1 | yes | characteristic |
| 335 | C3⋊D3 | — | 2 | 3 | no | — |
| 336 | C3⋊D3 | — | 4 | 3 | no | — |
| 337 | C3⋊D3 | #1790 | 1 | 1 | yes | characteristic |
| 338 | C3⋊D3 | #1791 | 1 | 1 | yes | characteristic |
| 339 | C24 | — | 9 | 1 | no | — |
| 340 | C24 | — | 9 | 3 | no | — |
| 341 | C24 | — | 18 | 1 | no | — |
| 342 | #41 | — | 2 | 3 | no | — |
| 343 | #41 | — | 18 | 6 | no | — |
| 344 | #41 | — | 18 | 6 | no | — |
| 345 | #41 | — | 18 | 3 | no | — |
| 346 | #41 | — | 18 | 3 | no | — |
| 347 | #41 | — | 18 | 3 | no | — |
| 348 | C2×Q8 | — | 18 | 1 | no | — |
| 349 | C2×D4 | — | 2 | 3 | no | — |
| 350 | C2×D4 | — | 9 | 3 | no | — |
| 351 | C2×D4 | — | 9 | 3 | no | — |
| 352 | C2×D4 | — | 9 | 3 | no | — |
| 353 | C2×D4 | — | 18 | 3 | no | — |
| 354 | C2×D4 | — | 18 | 6 | no | — |
| 355 | C2×D4 | — | 18 | 6 | no | — |
| 356 | C2×D4 | — | 18 | 6 | no | — |
| 357 | C2×D4 | — | 18 | 3 | no | — |
| 358 | C2×D4 | — | 18 | 6 | no | — |
| 359 | C2×D4 | — | 18 | 3 | no | — |
| 360 | C2×D4 | — | 18 | 3 | no | — |
| 361 | C2×D4 | C2×AGL(1,𝔽9) | 1 | 3 | yes | — |
| 362 | C22×C4 | — | 9 | 3 | no | — |
| 363 | C22×C4 | — | 9 | 3 | no | — |
| 364 | C22×C4 | — | 9 | 3 | no | — |
| 365 | C22×C4 | — | 9 | 3 | no | — |
| 366 | C22×C4 | — | 9 | 3 | no | — |
| 367 | C22×C4 | — | 18 | 3 | no | — |
| 368 | C22×C4 | — | 18 | 3 | no | — |
| 369 | C22×C4 | — | 18 | 3 | no | — |
| 370 | C22×C4 | — | 18 | 3 | no | — |
| 371 | C22×C4 | — | 18 | 3 | no | — |
| 372 | C22×C4 | — | 36 | 1 | no | — |
| 373 | C22×C4 | — | 36 | 1 | no | — |
| 374 | C22×C4 | — | 36 | 3 | no | — |
| 375 | C22×C4 | — | 36 | 3 | no | — |
| 376 | C22×C4 | — | 72 | 1 | no | — |
| 377 | C22×C4 | — | 72 | 1 | no | — |
| 378 | C2×C8 | — | 18 | 6 | no | — |
| 379 | C2×C8 | — | 36 | 1 | no | — |
| 380 | C2×C8 | — | 36 | 3 | no | — |
| 381 | C2×C8 | — | 36 | 3 | no | — |
| 382 | C2×C8 | — | 36 | 3 | no | — |
| 383 | C2×C8 | — | 36 | 3 | no | — |
| 384 | C4⋊C4 | — | 18 | 6 | no | — |
| 385 | C4⋊C4 | — | 18 | 3 | no | — |
| 386 | C4⋊C4 | — | 18 | 3 | no | — |
| 387 | C22⋊C4 | — | 18 | 6 | no | — |
| 388 | C22⋊C4 | — | 18 | 6 | no | — |
| 389 | C22⋊C4 | — | 18 | 6 | no | — |
| 390 | C42 | — | 18 | 3 | no | — |
| 391 | C42 | — | 18 | 3 | no | — |
| 392 | C42 | — | 18 | 6 | no | — |
| 393 | C22×C3 | — | 4 | 3 | no | — |
| 394 | C22×C3 | — | 4 | 3 | no | — |
| 395 | C22×C3 | — | 4 | 3 | no | — |
| 396 | C22×C3 | — | 16 | 3 | no | — |
| 397 | C22×C3 | — | 16 | 1 | no | — |
| 398 | C22×C3 | — | 16 | 1 | no | — |
| 399 | C22×C3 | — | 16 | 1 | no | — |
| 400 | C2×D3 | — | 12 | 1 | no | — |
| 401 | C2×D3 | — | 12 | 3 | no | — |
| 402 | C2×D3 | — | 12 | 3 | no | — |
| 403 | C2×D3 | — | 12 | 3 | no | — |
| 404 | C2×D3 | — | 24 | 3 | no | — |
| 405 | C2×D3 | — | 24 | 3 | no | — |
| 406 | C2×D3 | — | 24 | 3 | no | — |
| 407 | C2×D3 | — | 24 | 3 | no | — |
| 408 | C2×D3 | — | 24 | 3 | no | — |
| 409 | C2×D3 | — | 24 | 3 | no | — |
| 410 | C2×D3 | — | 48 | 3 | no | — |
| 411 | C2×D3 | — | 48 | 3 | no | — |
| 412 | C2×D3 | — | 48 | 3 | no | — |
| 413 | C2×D3 | — | 48 | 3 | no | — |
| 414 | C2×D3 | — | 48 | 3 | no | — |
| 415 | C2×D3 | — | 48 | 3 | no | — |
| 416 | C3×C4 | — | 4 | 3 | no | — |
| 417 | C3×C4 | — | 4 | 3 | no | — |
| 418 | Dic3 | — | 12 | 3 | no | — |
| 419 | Dic3 | — | 12 | 3 | no | — |
| 420 | C32 | #8316 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 421 | C23 | — | 2 | 1 | no | — |
| 422 | C23 | — | 9 | 3 | no | — |
| 423 | C23 | — | 9 | 3 | no | — |
| 424 | C23 | — | 9 | 3 | no | — |
| 425 | C23 | — | 18 | 3 | no | — |
| 426 | C23 | — | 18 | 3 | no | — |
| 427 | C23 | — | 18 | 3 | no | — |
| 428 | C23 | — | 36 | 1 | no | — |
| 429 | C23 | — | 36 | 1 | no | — |
| 430 | C23 | — | 36 | 3 | no | — |
| 431 | C23 | — | 36 | 3 | no | — |
| 432 | C23 | — | 72 | 1 | no | — |
| 433 | C23 | — | 72 | 1 | no | — |
| 434 | C23 | C22⋊AGL(1,𝔽9) | 1 | 3 | yes | complemented |
| 435 | C23 | C22×AGL(1,𝔽9) | 1 | 1 | yes | characteristic |
| 436 | Q8 | — | 2 | 1 | no | — |
| 437 | Q8 | — | 18 | 3 | no | — |
| 438 | D4 | — | 2 | 3 | no | — |
| 439 | D4 | — | 2 | 6 | no | — |
| 440 | D4 | — | 18 | 6 | no | — |
| 441 | D4 | — | 18 | 3 | no | — |
| 442 | D4 | — | 18 | 6 | no | — |
| 443 | D4 | — | 18 | 6 | no | — |
| 444 | D4 | — | 18 | 6 | no | — |
| 445 | C2×C4 | — | 2 | 3 | no | — |
| 446 | C2×C4 | — | 9 | 1 | no | — |
| 447 | C2×C4 | — | 9 | 3 | no | — |
| 448 | C2×C4 | — | 9 | 3 | no | — |
| 449 | C2×C4 | — | 18 | 3 | no | — |
| 450 | C2×C4 | — | 18 | 3 | no | — |
| 451 | C2×C4 | — | 18 | 6 | no | — |
| 452 | C2×C4 | — | 18 | 3 | no | — |
| 453 | C2×C4 | — | 18 | 3 | no | — |
| 454 | C2×C4 | — | 18 | 3 | no | — |
| 455 | C2×C4 | — | 18 | 3 | no | — |
| 456 | C2×C4 | — | 18 | 3 | no | — |
| 457 | C2×C4 | — | 36 | 3 | no | — |
| 458 | C2×C4 | — | 36 | 3 | no | — |
| 459 | C2×C4 | — | 36 | 3 | no | — |
| 460 | C2×C4 | — | 36 | 3 | no | — |
| 461 | C2×C4 | — | 36 | 3 | no | — |
| 462 | C2×C4 | — | 72 | 3 | no | — |
| 463 | C2×C4 | — | 72 | 3 | no | — |
| 464 | C2×C4 | — | 72 | 3 | no | — |
| 465 | C2×C4 | C22⋊AGL(1,𝔽9) | 1 | 3 | yes | complemented |
| 466 | C8 | — | 36 | 2 | no | — |
| 467 | C8 | — | 72 | 3 | no | — |
| 468 | C2×C3 | — | 4 | 1 | no | — |
| 469 | C2×C3 | — | 8 | 3 | no | — |
| 470 | C2×C3 | — | 8 | 3 | no | — |
| 471 | C2×C3 | — | 8 | 3 | no | — |
| 472 | D3 | — | 12 | 1 | no | — |
| 473 | D3 | — | 12 | 1 | no | — |
| 474 | D3 | — | 24 | 3 | no | — |
| 475 | D3 | — | 24 | 3 | no | — |
| 476 | D3 | — | 24 | 3 | no | — |
| 477 | C22 | — | 2 | 3 | no | — |
| 478 | C22 | — | 4 | 1 | no | — |
| 479 | C22 | — | 4 | 3 | no | — |
| 480 | C22 | — | 8 | 1 | no | — |
| 481 | C22 | — | 9 | 1 | no | — |
| 482 | C22 | — | 9 | 3 | no | — |
| 483 | C22 | — | 18 | 3 | no | — |
| 484 | C22 | — | 18 | 3 | no | — |
| 485 | C22 | — | 18 | 3 | no | — |
| 486 | C22 | — | 36 | 3 | no | — |
| 487 | C22 | — | 36 | 3 | no | — |
| 488 | C22 | — | 36 | 3 | no | — |
| 489 | C22 | — | 36 | 3 | no | — |
| 490 | C22 | — | 72 | 3 | no | — |
| 491 | C22 | — | 72 | 3 | no | — |
| 492 | C22 | C2×C22⋊AGL(1,𝔽9) | 1 | 3 | yes | — |
| 493 | C4 | — | 2 | 3 | no | — |
| 494 | C4 | — | 9 | 1 | no | — |
| 495 | C4 | — | 9 | 1 | no | — |
| 496 | C4 | — | 18 | 3 | no | — |
| 497 | C4 | — | 18 | 3 | no | — |
| 498 | C4 | — | 36 | 3 | no | — |
| 499 | C4 | — | 36 | 3 | no | — |
| 500 | C3 | — | 4 | 1 | no | — |
| 501 | C2 | — | 2 | 3 | no | — |
| 502 | C2 | — | 4 | 3 | no | — |
| 503 | C2 | — | 9 | 1 | no | — |
| 504 | C2 | — | 9 | 1 | no | — |
| 505 | C2 | — | 18 | 3 | no | — |
| 506 | C2 | — | 36 | 3 | no | — |
| 507 | C2 | #11784576 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11787155 | C2 | semidirect |
| 3. #11773799 | C2 | semidirect |
| 4. C23×AGL(1,𝔽9) | C22 | semidirect |
| 13. C2×C22⋊AGL(1,𝔽9) | C22 | semidirect |
| 23. C32×H(5,𝔽2) | C8 | semidirect |
| 27. #64361 | C8 | semidirect |
| 122. C23×C32 | C22⋊C8 | semidirect |
| 133. C22×C3⋊D3 | C22⋊C8 | semidirect |
| 156. C2×C32×C4 | C22⋊C8 | semidirect |
| 161. C2×C3⋊Dic3 | C22⋊C8 | semidirect |
| 250. H(5,𝔽2) | AGL(1,𝔽9) | semidirect |
| 420. C32 | #8316 | semidirect |
| 434. C23 | C22⋊AGL(1,𝔽9) | semidirect |
| 465. C2×C4 | C22⋊AGL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(5,𝔽2)×#157 | 2 |
| #11787155 | 2 |
| #11773799 | 2 |
| #8316 | 9 |