Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
847 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 847 conjugacy classes of subgroups — too many to draw. Only its 134 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 | #11874322 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11870763 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×C8×PSU(3,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11781002 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11780937 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11780871 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11776820 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11776151 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C2×C4×PSU(3,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 10 | #10596511 | C22 | 1 | 2 | yes | — |
| 11 | #10596500 | — | 2 | 1 | no | — |
| 12 | #10596484 | C22 | 1 | 2 | yes | — |
| 13 | #10596418 | — | 2 | 2 | no | — |
| 14 | #10596412 | — | 2 | 2 | no | — |
| 15 | #10596410 | C22 | 1 | 4 | yes | — |
| 16 | C4×AΓL(1,𝔽9) | — | 2 | 4 | no | — |
| 17 | PSU(3,𝔽2)⋊Q8 | C22 | 1 | 4 | yes | — |
| 18 | #10594684 | — | 2 | 1 | no | — |
| 19 | C2×C8×#157 | — | 2 | 1 | no | — |
| 20 | C2×C8×#157 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#63744 | — | 2 | 1 | no | — |
| 22 | C2×#63744 | C22 | 1 | 1 | yes | characteristic |
| 23 | C8×PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 24 | C8×PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 25 | C8×PSU(3,𝔽2) | C22 | 1 | 2 | yes | — |
| 26 | C8×PSU(3,𝔽2) | C22 | 1 | 2 | yes | — |
| 27 | #10593296 | — | 2 | 1 | no | — |
| 28 | #10593295 | C22 | 1 | 1 | yes | characteristic |
| 29 | #10593293 | C22 | 1 | 1 | yes | characteristic |
| 30 | #10593292 | C22 | 1 | 2 | yes | — |
| 31 | #10593290 | — | 2 | 1 | no | — |
| 32 | #10593253 | C22 | 1 | 2 | yes | — |
| 33 | #10593252 | C22 | 1 | 2 | yes | — |
| 34 | #10593156 | C22 | 1 | 4 | yes | — |
| 35 | #10593155 | C22 | 1 | 4 | yes | — |
| 36 | C22×PSU(3,𝔽2) | D4 | 1 | 1 | yes | characteristic |
| 37 | C2×AΓL(1,𝔽9) | — | 2 | 4 | no | — |
| 38 | #64306 | — | 2 | 2 | no | — |
| 39 | C2×C4×#157 | — | 2 | 1 | no | — |
| 40 | C2×C4×#157 | C23 | 1 | 1 | yes | characteristic |
| 41 | C2×#3787 | — | 2 | 1 | no | — |
| 42 | C2×#3787 | D4 | 1 | 1 | yes | characteristic |
| 43 | C2×#3777 | — | 2 | 1 | no | — |
| 44 | C2×#3777 | D4 | 1 | 1 | yes | characteristic |
| 45 | C4×PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 46 | C4×PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 47 | C4×PSU(3,𝔽2) | D4 | 1 | 2 | yes | — |
| 48 | C4×PSU(3,𝔽2) | C23 | 1 | 2 | yes | — |
| 49 | #64242 | — | 2 | 2 | no | — |
| 50 | #64242 | — | 2 | 2 | no | — |
| 51 | #64237 | — | 4 | 2 | no | — |
| 52 | #64231 | C23 | 1 | 2 | yes | — |
| 53 | C4×GO+(4,𝔽2) | — | 2 | 2 | no | — |
| 54 | C4×GO+(4,𝔽2) | — | 2 | 2 | no | — |
| 55 | #64228 | — | 2 | 1 | no | — |
| 56 | #64227 | — | 2 | 2 | no | — |
| 57 | #64225 | — | 2 | 1 | no | — |
| 58 | #64223 | — | 4 | 2 | no | — |
| 59 | #64222 | C23 | 1 | 2 | yes | — |
| 60 | #64221 | — | 2 | 2 | no | — |
| 61 | C22⋊AGL(1,𝔽9) | — | 2 | 2 | no | — |
| 62 | C4⋊AGL(1,𝔽9) | C23 | 1 | 4 | yes | — |
| 63 | C4×AGL(1,𝔽9) | — | 2 | 2 | no | — |
| 64 | AGL(1,𝔽9)⋊C4 | — | 2 | 4 | no | — |
| 65 | PSU(3,𝔽2)⋊C4 | — | 2 | 4 | no | — |
| 66 | GO+(4,𝔽2)⋊C4 | — | 2 | 4 | no | — |
| 67 | C2×C8×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 68 | C3×#904 | — | 4 | 1 | no | — |
| 69 | #63822 | — | 4 | 1 | no | — |
| 70 | #63810 | — | 4 | 1 | no | — |
| 71 | #63809 | — | 4 | 1 | no | — |
| 72 | #63802 | — | 2 | 1 | no | — |
| 73 | #63797 | — | 2 | 1 | no | — |
| 74 | #63796 | — | 2 | 2 | no | — |
| 75 | C8×#157 | — | 2 | 2 | no | — |
| 76 | C8×#157 | — | 2 | 2 | no | — |
| 77 | C8×#157 | D4 | 1 | 1 | yes | characteristic |
| 78 | C8×#157 | D4 | 1 | 1 | yes | characteristic |
| 79 | C8×#157 | C23 | 1 | 1 | yes | characteristic |
| 80 | C8×#157 | C23 | 1 | 1 | yes | characteristic |
| 81 | #63744 | — | 2 | 1 | no | — |
| 82 | #63744 | — | 2 | 2 | no | — |
| 83 | #63744 | — | 2 | 2 | no | — |
| 84 | #63744 | C23 | 1 | 2 | yes | — |
| 85 | #19114 | — | 9 | 1 | no | maximal, Sylow |
| 86 | D3×#135 | — | 12 | 1 | no | — |
| 87 | C22×#157 | — | 2 | 1 | no | — |
| 88 | C22×#157 | — | 2 | 1 | no | — |
| 89 | C22×#157 | C2×D4 | 1 | 1 | yes | characteristic |
| 90 | C22×#157 | #41 | 1 | 1 | yes | characteristic |
| 91 | C2×PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 92 | C2×PSU(3,𝔽2) | — | 2 | 4 | no | — |
| 93 | C2×PSU(3,𝔽2) | C2×D4 | 1 | 2 | yes | — |
| 94 | C2×GO+(4,𝔽2) | — | 2 | 2 | no | — |
| 95 | C2×GO+(4,𝔽2) | — | 2 | 2 | no | — |
| 96 | C2×AGL(1,𝔽9) | — | 2 | 4 | no | — |
| 97 | AΓL(1,𝔽9) | — | 4 | 8 | no | — |
| 98 | C2×C4×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | C3×#235 | — | 4 | 2 | no | — |
| 100 | #3811 | — | 4 | 2 | no | — |
| 101 | #3805 | — | 4 | 2 | no | — |
| 102 | #3802 | — | 2 | 2 | no | — |
| 103 | C4×D32 | — | 4 | 2 | no | — |
| 104 | #3798 | — | 4 | 2 | no | — |
| 105 | #3797 | — | 2 | 2 | no | — |
| 106 | #3796 | — | 4 | 2 | no | — |
| 107 | C2×#622 | — | 2 | 1 | no | — |
| 108 | C2×#622 | — | 4 | 1 | no | — |
| 109 | C4×#157 | — | 2 | 2 | no | — |
| 110 | C4×#157 | — | 2 | 2 | no | — |
| 111 | C4×#157 | C2×D4 | 1 | 1 | yes | characteristic |
| 112 | C4×#157 | C2×D4 | 1 | 1 | yes | characteristic |
| 113 | C4×#157 | #41 | 1 | 1 | yes | characteristic |
| 114 | C4×#157 | C24 | 1 | 1 | yes | characteristic |
| 115 | #3787 | — | 2 | 1 | no | — |
| 116 | #3787 | — | 2 | 2 | no | — |
| 117 | #3787 | — | 4 | 1 | no | — |
| 118 | #3787 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | #3787 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | #3777 | — | 2 | 1 | no | — |
| 121 | #3777 | — | 2 | 2 | no | — |
| 122 | #3777 | — | 2 | 2 | no | — |
| 123 | #3777 | C2×D4 | 1 | 2 | yes | — |
| 124 | #3776 | — | 4 | 2 | no | — |
| 125 | #3775 | — | 4 | 4 | no | — |
| 126 | #3774 | — | 4 | 2 | no | — |
| 127 | #3773 | — | 2 | 2 | no | — |
| 128 | #3773 | — | 2 | 2 | no | — |
| 129 | D32⋊C4 | — | 4 | 2 | no | — |
| 130 | D32⋊C4 | — | 4 | 2 | no | — |
| 131 | C2×C32×C8 | SD16 | 1 | 1 | yes | characteristic, complemented |
| 132 | C2×C3⋊(C3⋊C8) | SD16 | 1 | 1 | yes | characteristic, complemented |
| 133 | C8×C3⋊D3 | SD16 | 1 | 1 | yes | characteristic, complemented |
| 134 | C8×C3⋊D3 | SD16 | 1 | 1 | yes | characteristic, complemented |
| 135 | C8×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | C8×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C3×Dic12 | — | 4 | 1 | no | — |
| 138 | C3×D24 | — | 4 | 1 | no | — |
| 139 | C3×#204 | — | 4 | 2 | no | — |
| 140 | #3718 | — | 4 | 1 | no | — |
| 141 | #3715 | — | 4 | 2 | no | — |
| 142 | #3713 | — | 4 | 1 | no | — |
| 143 | #3147 | — | 9 | 1 | no | — |
| 144 | #3103 | — | 9 | 2 | no | — |
| 145 | C2×C8×Q8 | — | 9 | 1 | no | — |
| 146 | #1670 | — | 9 | 2 | no | — |
| 147 | #1668 | — | 9 | 2 | no | — |
| 148 | #1666 | — | 9 | 4 | no | — |
| 149 | #1564 | — | 9 | 1 | no | — |
| 150 | #1540 | — | 9 | 2 | no | — |
| 151 | D3×#41 | — | 12 | 2 | no | — |
| 152 | C3×#135 | — | 12 | 1 | no | — |
| 153 | #950 | — | 12 | 1 | no | — |
| 154 | #950 | — | 12 | 1 | no | — |
| 155 | #919 | — | 12 | 1 | no | — |
| 156 | D3×Q16 | — | 12 | 1 | no | — |
| 157 | #916 | — | 12 | 1 | no | — |
| 158 | #916 | — | 12 | 1 | no | — |
| 159 | D3×SD16 | — | 12 | 2 | no | — |
| 160 | #912 | — | 12 | 1 | no | — |
| 161 | D3×D8 | — | 12 | 1 | no | — |
| 162 | #904 | — | 4 | 1 | no | — |
| 163 | C2×D3×C8 | — | 12 | 1 | no | — |
| 164 | C22×C3⋊D3 | #121 | 1 | 1 | yes | characteristic |
| 165 | C2×D32 | — | 4 | 2 | no | — |
| 166 | C2×#157 | — | 2 | 4 | no | — |
| 167 | C2×#157 | — | 2 | 2 | no | — |
| 168 | C2×#157 | — | 2 | 2 | no | — |
| 169 | C2×#157 | — | 2 | 2 | no | — |
| 170 | C2×#157 | — | 4 | 1 | no | — |
| 171 | C2×#157 | — | 4 | 2 | no | — |
| 172 | C2×#157 | #121 | 1 | 1 | yes | characteristic |
| 173 | C2×#157 | #121 | 1 | 1 | yes | characteristic |
| 174 | C2×#157 | C22×D4 | 1 | 1 | yes | characteristic |
| 175 | C2×#157 | C2×#41 | 1 | 1 | yes | characteristic |
| 176 | PSU(3,𝔽2) | — | 2 | 4 | no | — |
| 177 | PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 178 | PSU(3,𝔽2) | #135 | 1 | 4 | yes | complemented |
| 179 | GO+(4,𝔽2) | — | 4 | 4 | no | — |
| 180 | GO+(4,𝔽2) | — | 8 | 2 | no | — |
| 181 | AGL(1,𝔽9) | — | 4 | 4 | no | — |
| 182 | C2×C32×C4 | C2×SD16 | 1 | 1 | yes | characteristic |
| 183 | C2×C3⋊Dic3 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 184 | C4×C3⋊D3 | #121 | 1 | 1 | yes | characteristic |
| 185 | C4×C3⋊D3 | C2×SD16 | 1 | 1 | yes | characteristic |
| 186 | C4×C3⋊D3 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 187 | C4×C3⋊D3 | C22×D4 | 1 | 1 | yes | characteristic |
| 188 | C3×#67 | — | 8 | 2 | no | — |
| 189 | C3×D12 | — | 4 | 2 | no | — |
| 190 | C3×C4×D3 | — | 8 | 2 | no | — |
| 191 | C3×Dic6 | — | 4 | 2 | no | — |
| 192 | #627 | — | 4 | 2 | no | — |
| 193 | #626 | — | 8 | 2 | no | — |
| 194 | #625 | — | 4 | 2 | no | — |
| 195 | #624 | — | 4 | 2 | no | — |
| 196 | D3×Dic3 | — | 8 | 2 | no | — |
| 197 | #622 | — | 2 | 1 | no | — |
| 198 | #622 | — | 2 | 1 | no | — |
| 199 | #622 | — | 4 | 2 | no | — |
| 200 | C32×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 201 | C32×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 202 | C3⋊(C3⋊C8) | C2×SD16 | 1 | 1 | yes | characteristic |
| 203 | C3⋊(C3⋊C8) | C2×SD16 | 1 | 1 | yes | characteristic |
| 204 | C2×#135 | — | 18 | 1 | no | — |
| 205 | C2×#135 | — | 18 | 1 | no | — |
| 206 | #532 | — | 9 | 2 | no | — |
| 207 | C2×C4×Q8 | — | 9 | 1 | no | — |
| 208 | #495 | — | 18 | 1 | no | — |
| 209 | #495 | — | 18 | 1 | no | — |
| 210 | #494 | — | 9 | 1 | no | — |
| 211 | #493 | — | 9 | 1 | no | — |
| 212 | #492 | — | 9 | 2 | no | — |
| 213 | #481 | — | 18 | 2 | no | — |
| 214 | #475 | — | 9 | 4 | no | — |
| 215 | #460 | — | 9 | 4 | no | — |
| 216 | #448 | — | 18 | 2 | no | — |
| 217 | C8×Q8 | — | 9 | 2 | no | — |
| 218 | C8×Q8 | — | 9 | 2 | no | — |
| 219 | C8×Q8 | — | 18 | 1 | no | — |
| 220 | C8×Q8 | — | 18 | 1 | no | — |
| 221 | C4×SD16 | — | 18 | 4 | no | — |
| 222 | #431 | — | 9 | 2 | no | — |
| 223 | C2×C4⋊C8 | — | 9 | 1 | no | — |
| 224 | C2×C4⋊C8 | — | 18 | 1 | no | — |
| 225 | C2×C4×C8 | — | 9 | 1 | no | — |
| 226 | C2×C4×C8 | — | 18 | 1 | no | — |
| 227 | #335 | — | 9 | 2 | no | — |
| 228 | #334 | — | 9 | 2 | no | — |
| 229 | #332 | — | 9 | 4 | no | — |
| 230 | #331 | — | 9 | 4 | no | — |
| 231 | C3×#41 | — | 12 | 2 | no | — |
| 232 | #239 | — | 12 | 2 | no | — |
| 233 | D3×Q8 | — | 12 | 2 | no | — |
| 234 | #237 | — | 12 | 2 | no | — |
| 235 | #237 | — | 24 | 2 | no | — |
| 236 | D3×D4 | — | 12 | 2 | no | — |
| 237 | D3×D4 | — | 24 | 2 | no | — |
| 238 | #235 | — | 4 | 2 | no | — |
| 239 | #235 | — | 24 | 2 | no | — |
| 240 | C2×C4×D3 | — | 12 | 1 | no | — |
| 241 | C2×C4×D3 | — | 24 | 2 | no | — |
| 242 | C3×Q16 | — | 12 | 1 | no | — |
| 243 | C3×SD16 | — | 12 | 2 | no | — |
| 244 | C3×D8 | — | 12 | 1 | no | — |
| 245 | C2×C3×C8 | — | 4 | 1 | no | — |
| 246 | #216 | — | 12 | 1 | no | — |
| 247 | #216 | — | 12 | 1 | no | — |
| 248 | #215 | — | 12 | 2 | no | — |
| 249 | #214 | — | 12 | 2 | no | — |
| 250 | #213 | — | 12 | 1 | no | — |
| 251 | #213 | — | 12 | 1 | no | — |
| 252 | C2×C3⋊C8 | — | 12 | 1 | no | — |
| 253 | Dic12 | — | 4 | 1 | no | — |
| 254 | D24 | — | 4 | 1 | no | — |
| 255 | #204 | — | 4 | 2 | no | — |
| 256 | D3×C8 | — | 12 | 1 | no | — |
| 257 | D3×C8 | — | 12 | 1 | no | — |
| 258 | D3×C8 | — | 12 | 1 | no | — |
| 259 | D3×C8 | — | 12 | 1 | no | — |
| 260 | C22×C32 | #460 | 1 | 1 | yes | characteristic |
| 261 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 262 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 263 | C2×C3⋊D3 | #460 | 1 | 1 | yes | characteristic |
| 264 | C2×C3⋊D3 | C2×#121 | 1 | 1 | yes | characteristic |
| 265 | C2×C3×D3 | — | 8 | 2 | no | — |
| 266 | D32 | — | 8 | 2 | no | — |
| 267 | D32 | — | 8 | 2 | no | — |
| 268 | #157 | — | 2 | 1 | no | — |
| 269 | #157 | — | 2 | 4 | no | — |
| 270 | #157 | — | 2 | 1 | no | — |
| 271 | #157 | — | 2 | 1 | no | — |
| 272 | #157 | — | 4 | 2 | no | — |
| 273 | #157 | C2×#135 | 1 | 2 | yes | — |
| 274 | C32×C4 | #460 | 1 | 1 | yes | characteristic |
| 275 | C32×C4 | C22×SD16 | 1 | 1 | yes | characteristic |
| 276 | C3⋊Dic3 | #460 | 1 | 1 | yes | characteristic |
| 277 | C3⋊Dic3 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 278 | C3×Dic3 | — | 8 | 2 | no | — |
| 279 | C2×#41 | — | 18 | 2 | no | — |
| 280 | C22×Q8 | — | 9 | 1 | no | — |
| 281 | #135 | — | 12 | 1 | no | — |
| 282 | #135 | — | 36 | 1 | no | — |
| 283 | #135 | — | 36 | 1 | no | — |
| 284 | #135 | — | 36 | 1 | no | — |
| 285 | #135 | — | 36 | 2 | no | — |
| 286 | #135 | — | 36 | 2 | no | — |
| 287 | C2×Q16 | — | 18 | 1 | no | — |
| 288 | C2×Q16 | — | 18 | 1 | no | — |
| 289 | C2×SD16 | — | 18 | 2 | no | — |
| 290 | C2×SD16 | — | 18 | 2 | no | — |
| 291 | C2×SD16 | — | 18 | 4 | no | — |
| 292 | C2×D8 | — | 18 | 1 | no | — |
| 293 | C2×D8 | — | 18 | 1 | no | — |
| 294 | C22×C8 | — | 9 | 1 | no | — |
| 295 | C22×C8 | — | 9 | 1 | no | — |
| 296 | C22×C8 | — | 18 | 1 | no | — |
| 297 | C4⋊Q8 | — | 9 | 2 | no | — |
| 298 | #127 | — | 9 | 2 | no | — |
| 299 | #124 | — | 18 | 2 | no | — |
| 300 | #121 | — | 18 | 2 | no | — |
| 301 | #121 | — | 18 | 2 | no | — |
| 302 | C4×Q8 | — | 9 | 2 | no | — |
| 303 | C4×Q8 | — | 9 | 2 | no | — |
| 304 | C4×Q8 | — | 18 | 1 | no | — |
| 305 | C4×Q8 | — | 18 | 1 | no | — |
| 306 | C4×D4 | — | 18 | 2 | no | — |
| 307 | C4×D4 | — | 18 | 2 | no | — |
| 308 | C2×C4⋊C4 | — | 9 | 1 | no | — |
| 309 | C2×C4⋊C4 | — | 18 | 1 | no | — |
| 310 | C2×C42 | — | 9 | 1 | no | — |
| 311 | C2×C42 | — | 18 | 1 | no | — |
| 312 | #106 | — | 18 | 4 | no | — |
| 313 | C4⋊C8 | — | 9 | 2 | no | — |
| 314 | C4⋊C8 | — | 9 | 4 | no | — |
| 315 | C4⋊C8 | — | 18 | 1 | no | — |
| 316 | C4⋊C8 | — | 18 | 2 | no | — |
| 317 | C4⋊C8 | — | 18 | 2 | no | — |
| 318 | #103 | — | 18 | 4 | no | — |
| 319 | #102 | — | 18 | 4 | no | — |
| 320 | C22⋊C8 | — | 18 | 2 | no | — |
| 321 | C4×C8 | — | 9 | 1 | no | — |
| 322 | C4×C8 | — | 9 | 1 | no | — |
| 323 | C4×C8 | — | 9 | 1 | no | — |
| 324 | C4×C8 | — | 9 | 1 | no | — |
| 325 | C4×C8 | — | 18 | 2 | no | — |
| 326 | C4×C8 | — | 18 | 2 | no | — |
| 327 | C4×C8 | — | 18 | 2 | no | — |
| 328 | C22×D3 | — | 12 | 1 | no | — |
| 329 | C22×D3 | — | 24 | 2 | no | — |
| 330 | C3×Q8 | — | 12 | 2 | no | — |
| 331 | C3×D4 | — | 12 | 2 | no | — |
| 332 | C3×D4 | — | 24 | 2 | no | — |
| 333 | C2×C3×C4 | — | 4 | 1 | no | — |
| 334 | C2×C3×C4 | — | 24 | 2 | no | — |
| 335 | #67 | — | 8 | 2 | no | — |
| 336 | #67 | — | 24 | 2 | no | — |
| 337 | #67 | — | 24 | 2 | no | — |
| 338 | C2×Dic3 | — | 12 | 1 | no | — |
| 339 | C2×Dic3 | — | 24 | 2 | no | — |
| 340 | D12 | — | 4 | 2 | no | — |
| 341 | D12 | — | 24 | 2 | no | — |
| 342 | C4×D3 | — | 8 | 2 | no | — |
| 343 | C4×D3 | — | 12 | 1 | no | — |
| 344 | C4×D3 | — | 12 | 1 | no | — |
| 345 | C4×D3 | — | 12 | 1 | no | — |
| 346 | C4×D3 | — | 12 | 1 | no | — |
| 347 | C4×D3 | — | 24 | 2 | no | — |
| 348 | C4×D3 | — | 24 | 2 | no | — |
| 349 | Dic6 | — | 4 | 2 | no | — |
| 350 | Dic6 | — | 24 | 2 | no | — |
| 351 | C3×C8 | — | 4 | 1 | no | — |
| 352 | C3×C8 | — | 4 | 1 | no | — |
| 353 | C3⋊C8 | — | 12 | 1 | no | — |
| 354 | C3⋊C8 | — | 12 | 1 | no | — |
| 355 | C2×C32 | — | 2 | 1 | no | — |
| 356 | C2×C32 | C2×#460 | 1 | 1 | yes | characteristic |
| 357 | C3⋊D3 | — | 2 | 1 | no | — |
| 358 | C3⋊D3 | #3050 | 1 | 1 | yes | characteristic |
| 359 | C3⋊D3 | #3067 | 1 | 1 | yes | characteristic |
| 360 | C3×D3 | — | 16 | 2 | no | — |
| 361 | #41 | — | 12 | 2 | no | — |
| 362 | #41 | — | 36 | 2 | no | — |
| 363 | #41 | — | 36 | 2 | no | — |
| 364 | #41 | — | 36 | 2 | no | — |
| 365 | C2×Q8 | — | 9 | 2 | no | — |
| 366 | C2×Q8 | — | 18 | 1 | no | — |
| 367 | C2×Q8 | — | 18 | 2 | no | — |
| 368 | C2×Q8 | — | 18 | 4 | no | — |
| 369 | C2×D4 | — | 18 | 2 | no | — |
| 370 | C2×D4 | — | 18 | 2 | no | — |
| 371 | C2×D4 | — | 18 | 2 | no | — |
| 372 | C2×D4 | — | 36 | 2 | no | — |
| 373 | C22×C4 | — | 9 | 1 | no | — |
| 374 | C22×C4 | — | 9 | 1 | no | — |
| 375 | C22×C4 | — | 9 | 1 | no | — |
| 376 | C22×C4 | — | 18 | 1 | no | — |
| 377 | C22×C4 | — | 18 | 1 | no | — |
| 378 | C22×C4 | — | 36 | 2 | no | — |
| 379 | Q16 | — | 12 | 1 | no | — |
| 380 | Q16 | — | 36 | 1 | no | — |
| 381 | Q16 | — | 36 | 2 | no | — |
| 382 | SD16 | — | 12 | 2 | no | — |
| 383 | SD16 | — | 36 | 2 | no | — |
| 384 | SD16 | — | 36 | 4 | no | — |
| 385 | SD16 | — | 36 | 8 | no | — |
| 386 | D8 | — | 12 | 1 | no | — |
| 387 | D8 | — | 36 | 1 | no | — |
| 388 | D8 | — | 36 | 2 | no | — |
| 389 | C2×C8 | — | 9 | 1 | no | — |
| 390 | C2×C8 | — | 9 | 1 | no | — |
| 391 | C2×C8 | — | 9 | 1 | no | — |
| 392 | C2×C8 | — | 9 | 1 | no | — |
| 393 | C2×C8 | — | 9 | 1 | no | — |
| 394 | C2×C8 | — | 9 | 1 | no | — |
| 395 | C2×C8 | — | 9 | 1 | no | — |
| 396 | C2×C8 | — | 18 | 1 | no | — |
| 397 | C2×C8 | — | 18 | 1 | no | — |
| 398 | C2×C8 | — | 18 | 4 | no | — |
| 399 | C2×C8 | — | 18 | 2 | no | — |
| 400 | C2×C8 | — | 36 | 1 | no | — |
| 401 | C2×C8 | — | 36 | 1 | no | — |
| 402 | C2×C8 | AΓL(1,𝔽9) | 1 | 1 | yes | characteristic, complemented |
| 403 | C4⋊C4 | — | 9 | 2 | no | — |
| 404 | C4⋊C4 | — | 18 | 1 | no | — |
| 405 | C4⋊C4 | — | 18 | 2 | no | — |
| 406 | C4⋊C4 | — | 18 | 2 | no | — |
| 407 | C4⋊C4 | — | 18 | 2 | no | — |
| 408 | C4⋊C4 | — | 18 | 2 | no | — |
| 409 | C22⋊C4 | — | 36 | 2 | no | — |
| 410 | C22⋊C4 | — | 36 | 2 | no | — |
| 411 | C42 | — | 9 | 1 | no | — |
| 412 | C42 | — | 9 | 1 | no | — |
| 413 | C42 | — | 9 | 1 | no | — |
| 414 | C42 | — | 9 | 1 | no | — |
| 415 | C42 | — | 18 | 2 | no | — |
| 416 | C42 | — | 18 | 2 | no | — |
| 417 | C22×C3 | — | 4 | 1 | no | — |
| 418 | C22×C3 | — | 24 | 2 | no | — |
| 419 | C2×D3 | — | 8 | 2 | no | — |
| 420 | C2×D3 | — | 12 | 1 | no | — |
| 421 | C2×D3 | — | 12 | 1 | no | — |
| 422 | C2×D3 | — | 24 | 1 | no | — |
| 423 | C2×D3 | — | 24 | 1 | no | — |
| 424 | C2×D3 | — | 48 | 2 | no | — |
| 425 | C2×D3 | — | 48 | 2 | no | — |
| 426 | C3×C4 | — | 4 | 1 | no | — |
| 427 | C3×C4 | — | 4 | 1 | no | — |
| 428 | C3×C4 | — | 24 | 2 | no | — |
| 429 | Dic3 | — | 8 | 2 | no | — |
| 430 | Dic3 | — | 12 | 1 | no | — |
| 431 | Dic3 | — | 12 | 1 | no | — |
| 432 | C32 | #19114 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 433 | C23 | — | 9 | 1 | no | — |
| 434 | C23 | — | 36 | 2 | no | — |
| 435 | Q8 | — | 9 | 4 | no | — |
| 436 | Q8 | — | 12 | 2 | no | — |
| 437 | Q8 | — | 18 | 2 | no | — |
| 438 | Q8 | — | 18 | 4 | no | — |
| 439 | Q8 | — | 36 | 2 | no | — |
| 440 | D4 | — | 12 | 2 | no | — |
| 441 | D4 | — | 24 | 2 | no | — |
| 442 | D4 | — | 36 | 2 | no | — |
| 443 | D4 | — | 36 | 4 | no | — |
| 444 | D4 | — | 72 | 2 | no | — |
| 445 | D4 | — | 72 | 2 | no | — |
| 446 | C2×C4 | — | 9 | 1 | no | — |
| 447 | C2×C4 | — | 9 | 1 | no | — |
| 448 | C2×C4 | — | 9 | 1 | no | — |
| 449 | C2×C4 | — | 9 | 1 | no | — |
| 450 | C2×C4 | — | 9 | 1 | no | — |
| 451 | C2×C4 | — | 9 | 1 | no | — |
| 452 | C2×C4 | — | 9 | 1 | no | — |
| 453 | C2×C4 | — | 9 | 1 | no | — |
| 454 | C2×C4 | — | 9 | 1 | no | — |
| 455 | C2×C4 | — | 18 | 2 | no | — |
| 456 | C2×C4 | — | 18 | 2 | no | — |
| 457 | C2×C4 | — | 18 | 4 | no | — |
| 458 | C2×C4 | — | 18 | 2 | no | — |
| 459 | C2×C4 | — | 24 | 2 | no | — |
| 460 | C2×C4 | — | 36 | 1 | no | — |
| 461 | C2×C4 | — | 36 | 2 | no | — |
| 462 | C2×C4 | — | 36 | 2 | no | — |
| 463 | C2×C4 | — | 72 | 2 | no | — |
| 464 | C2×C4 | C2×AΓL(1,𝔽9) | 1 | 1 | yes | characteristic |
| 465 | C8 | — | 9 | 1 | no | — |
| 466 | C8 | — | 9 | 1 | no | — |
| 467 | C8 | — | 18 | 1 | no | — |
| 468 | C8 | — | 18 | 1 | no | — |
| 469 | C8 | — | 36 | 2 | no | — |
| 470 | C8 | — | 36 | 4 | no | — |
| 471 | C8 | C2×AΓL(1,𝔽9) | 1 | 1 | yes | characteristic |
| 472 | C8 | C2×AΓL(1,𝔽9) | 1 | 1 | yes | characteristic |
| 473 | C2×C3 | — | 4 | 1 | no | — |
| 474 | C2×C3 | — | 8 | 1 | no | — |
| 475 | C2×C3 | — | 48 | 2 | no | — |
| 476 | D3 | — | 12 | 1 | no | — |
| 477 | D3 | — | 12 | 1 | no | — |
| 478 | D3 | — | 16 | 2 | no | — |
| 479 | D3 | — | 24 | 1 | no | — |
| 480 | C22 | — | 9 | 1 | no | — |
| 481 | C22 | — | 9 | 1 | no | — |
| 482 | C22 | — | 18 | 1 | no | — |
| 483 | C22 | — | 18 | 1 | no | — |
| 484 | C22 | — | 24 | 2 | no | — |
| 485 | C22 | — | 72 | 2 | no | — |
| 486 | C22 | — | 72 | 2 | no | — |
| 487 | C22 | #10596410 | 1 | 1 | yes | characteristic |
| 488 | C4 | — | 9 | 2 | no | — |
| 489 | C4 | — | 9 | 1 | no | — |
| 490 | C4 | — | 9 | 1 | no | — |
| 491 | C4 | — | 18 | 1 | no | — |
| 492 | C4 | — | 18 | 1 | no | — |
| 493 | C4 | — | 18 | 1 | no | — |
| 494 | C4 | — | 18 | 4 | no | — |
| 495 | C4 | — | 24 | 2 | no | — |
| 496 | C4 | — | 36 | 2 | no | — |
| 497 | C4 | #10596410 | 1 | 1 | yes | characteristic |
| 498 | C4 | C22×AΓL(1,𝔽9) | 1 | 1 | yes | characteristic |
| 499 | C3 | — | 4 | 1 | no | — |
| 500 | C2 | — | 2 | 1 | no | — |
| 501 | C2 | — | 9 | 1 | no | — |
| 502 | C2 | — | 9 | 1 | no | — |
| 503 | C2 | — | 18 | 1 | no | — |
| 504 | C2 | — | 48 | 2 | no | — |
| 505 | C2 | C2×#10596410 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11870763 | C2 | semidirect |
| 3. C2×C8×PSU(3,𝔽2) | C2 | semidirect |
| 4. #11781002 | C2 | semidirect |
| 5. #11780937 | C2 | semidirect |
| 6. #11780871 | C2 | semidirect |
| 7. #11776820 | C2 | semidirect |
| 8. #11776151 | C2 | semidirect |
| 131. C2×C32×C8 | SD16 | semidirect |
| 132. C2×C3⋊(C3⋊C8) | SD16 | semidirect |
| 133. C8×C3⋊D3 | SD16 | semidirect |
| 134. C8×C3⋊D3 | SD16 | semidirect |
| 178. PSU(3,𝔽2) | #135 | semidirect |
| 402. C2×C8 | AΓL(1,𝔽9) | semidirect |
| 432. C32 | #19114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11874322 | 2 |
| #11870763 | 2 |
| C2×C8×PSU(3,𝔽2) | 2 |
| #11781002 | 2 |
| #11780937 | 2 |
| #11780871 | 2 |
| #11776820 | 2 |
| #11776151 | 2 |
| #19114 | 9 |