Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
823 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 823 conjugacy classes of subgroups — too many to draw. Only its 104 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 | C3×#81774 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11799714 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #11782415 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#67787 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11771648 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10708947 | — | 3 | 1 | no | maximal |
| 7 | #10708946 | — | 3 | 1 | no | maximal |
| 8 | C3×#5762 | — | 2 | 2 | no | — |
| 9 | C32×#492 | C22 | 1 | 1 | yes | characteristic |
| 10 | #10592779 | — | 2 | 1 | no | — |
| 11 | #10592775 | — | 2 | 1 | no | — |
| 12 | #10592379 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C3×#5177 | — | 2 | 2 | no | — |
| 14 | C3×#5095 | — | 2 | 1 | no | — |
| 15 | C3×#5077 | — | 2 | 1 | no | — |
| 16 | C3×#4700 | C22 | 1 | 2 | yes | — |
| 17 | C8×C3⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C3×#4463 | C22 | 1 | 2 | yes | complemented |
| 19 | #10589137 | — | 2 | 2 | no | — |
| 20 | #10589124 | — | 2 | 2 | no | — |
| 21 | C3×#3291 | — | 3 | 1 | no | — |
| 22 | #81774 | D3 | 1 | 1 | yes | characteristic |
| 23 | #71254 | — | 3 | 1 | no | — |
| 24 | #71254 | — | 3 | 1 | no | — |
| 25 | #71254 | — | 6 | 1 | no | — |
| 26 | #70919 | — | 3 | 2 | no | — |
| 27 | #69307 | — | 3 | 2 | no | — |
| 28 | C3×#1359 | — | 3 | 1 | no | — |
| 29 | #67787 | D3 | 1 | 1 | yes | characteristic, complemented |
| 30 | #67766 | — | 3 | 2 | no | — |
| 31 | #67568 | — | 3 | 2 | no | — |
| 32 | C3×#1007 | — | 2 | 1 | no | — |
| 33 | C3×#1004 | — | 2 | 1 | no | — |
| 34 | C2×C32×SD16 | — | 2 | 2 | no | — |
| 35 | C32×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 36 | C32×#127 | D4 | 1 | 1 | yes | characteristic |
| 37 | C2×#3754 | — | 4 | 2 | no | — |
| 38 | #64078 | — | 2 | 1 | no | — |
| 39 | C3×#942 | — | 2 | 2 | no | — |
| 40 | C3×#932 | — | 2 | 2 | no | — |
| 41 | C3×#916 | — | 4 | 2 | no | — |
| 42 | C3×#915 | — | 4 | 2 | no | — |
| 43 | C3×#914 | — | 4 | 2 | no | — |
| 44 | C3×D3×SD16 | — | 4 | 2 | no | — |
| 45 | C3×#904 | D4 | 1 | 2 | yes | — |
| 46 | C3×#901 | — | 2 | 2 | no | — |
| 47 | C32×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 48 | #63644 | — | 2 | 2 | no | — |
| 49 | #63635 | — | 4 | 2 | no | — |
| 50 | C4×C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 51 | C3×#836 | — | 2 | 1 | no | — |
| 52 | C3×#833 | — | 2 | 1 | no | — |
| 53 | C3×#819 | D4 | 1 | 2 | yes | — |
| 54 | C3×#812 | — | 2 | 2 | no | — |
| 55 | C3×#805 | — | 2 | 2 | no | — |
| 56 | #12364 | — | 9 | 1 | no | Sylow |
| 57 | C3×#577 | — | 6 | 2 | no | — |
| 58 | #5762 | — | 2 | 2 | no | — |
| 59 | C3×#492 | — | 2 | 1 | no | — |
| 60 | C3×#492 | C2×D3 | 1 | 1 | yes | characteristic |
| 61 | C3×#492 | C2×D3 | 1 | 1 | yes | characteristic |
| 62 | C3×#471 | — | 6 | 2 | no | — |
| 63 | C3×#456 | — | 6 | 1 | no | — |
| 64 | C3×#453 | — | 6 | 1 | no | — |
| 65 | C3×#443 | — | 3 | 2 | no | — |
| 66 | #5177 | — | 2 | 2 | no | — |
| 67 | #5095 | — | 2 | 1 | no | — |
| 68 | #5080 | — | 6 | 2 | no | — |
| 69 | #5080 | — | 6 | 1 | no | — |
| 70 | #5080 | — | 6 | 1 | no | — |
| 71 | #5077 | — | 2 | 1 | no | — |
| 72 | #5076 | — | 6 | 2 | no | — |
| 73 | #5076 | — | 6 | 1 | no | — |
| 74 | #5076 | — | 6 | 1 | no | — |
| 75 | #4700 | C2×D3 | 1 | 2 | yes | — |
| 76 | #4680 | — | 3 | 1 | no | — |
| 77 | #4680 | — | 3 | 1 | no | — |
| 78 | #4680 | — | 6 | 1 | no | — |
| 79 | C3×#364 | — | 3 | 2 | no | — |
| 80 | #4566 | — | 6 | 2 | no | — |
| 81 | #4518 | — | 6 | 2 | no | — |
| 82 | #4513 | — | 6 | 2 | no | — |
| 83 | #4494 | — | 6 | 2 | no | — |
| 84 | #4463 | C2×D3 | 1 | 2 | yes | complemented |
| 85 | C8×C3⋊C8 | — | 3 | 1 | no | — |
| 86 | C8×C3⋊C8 | — | 3 | 1 | no | — |
| 87 | C8×C3⋊C8 | — | 6 | 1 | no | — |
| 88 | C2×C32×Q8 | — | 2 | 1 | no | — |
| 89 | C2×C32×D4 | — | 2 | 1 | no | — |
| 90 | C2×C32×D4 | — | 4 | 1 | no | — |
| 91 | C2×#634 | — | 4 | 1 | no | — |
| 92 | C2×C3×#67 | — | 8 | 1 | no | — |
| 93 | C3×#239 | — | 4 | 2 | no | — |
| 94 | C3×D3×Q8 | — | 4 | 2 | no | — |
| 95 | C3×#237 | — | 4 | 2 | no | — |
| 96 | C3×D3×D4 | — | 4 | 2 | no | — |
| 97 | C3×#235 | — | 2 | 2 | no | — |
| 98 | C3×#235 | — | 8 | 1 | no | — |
| 99 | C32×SD16 | — | 4 | 2 | no | — |
| 100 | C32×SD16 | — | 4 | 2 | no | — |
| 101 | C2×C32×C8 | C2×D4 | 1 | 2 | yes | — |
| 102 | C32×C4⋊C4 | — | 4 | 1 | no | — |
| 103 | C32×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 104 | #3754 | — | 8 | 4 | no | — |
| 105 | C4⋊(C3⋊Dic3) | — | 4 | 1 | no | — |
| 106 | C4⋊(C3⋊Dic3) | — | 4 | 1 | no | — |
| 107 | C2×C3⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 108 | C3×#216 | — | 4 | 2 | no | — |
| 109 | C3×#215 | — | 4 | 2 | no | — |
| 110 | C3×#214 | — | 4 | 2 | no | — |
| 111 | C3×#213 | — | 4 | 2 | no | — |
| 112 | C3×#208 | — | 2 | 2 | no | — |
| 113 | C3×Dic12 | SD16 | 1 | 2 | yes | complemented |
| 114 | C3×D24 | SD16 | 1 | 2 | yes | complemented |
| 115 | C3×#204 | — | 2 | 2 | no | — |
| 116 | C3×ΓL(1,𝔽25) | — | 4 | 2 | no | — |
| 117 | C3×D3×C8 | — | 4 | 2 | no | — |
| 118 | C3×C3⋊C16 | — | 4 | 2 | no | — |
| 119 | #3291 | — | 3 | 1 | no | — |
| 120 | #2230 | — | 9 | 2 | no | — |
| 121 | #1705 | — | 9 | 1 | no | — |
| 122 | #1359 | — | 3 | 1 | no | — |
| 123 | #1335 | — | 9 | 2 | no | — |
| 124 | C3×2−1+4 | — | 6 | 1 | no | — |
| 125 | C3×H(5,𝔽2) | — | 6 | 1 | no | — |
| 126 | #1007 | — | 2 | 1 | no | — |
| 127 | #1004 | — | 2 | 1 | no | — |
| 128 | C3×#137 | — | 6 | 2 | no | — |
| 129 | C3×#137 | — | 12 | 2 | no | — |
| 130 | C3×AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 131 | C3×AGL(1,ℤ/8) | — | 12 | 2 | no | — |
| 132 | C3×#135 | — | 3 | 2 | no | — |
| 133 | C3×#135 | — | 12 | 2 | no | — |
| 134 | C2×C3×SD16 | — | 2 | 2 | no | — |
| 135 | C2×C3×SD16 | — | 2 | 2 | no | — |
| 136 | C2×C3×SD16 | — | 4 | 2 | no | — |
| 137 | C2×C3×SD16 | — | 12 | 2 | no | — |
| 138 | C3×#131 | — | 6 | 2 | no | — |
| 139 | C3×C4⋊Q8 | — | 2 | 1 | no | — |
| 140 | C3×C4⋊Q8 | D12 | 1 | 1 | yes | characteristic |
| 141 | C3×C4⋊Q8 | #67 | 1 | 1 | yes | characteristic |
| 142 | C3×#127 | — | 2 | 1 | no | — |
| 143 | C3×#127 | D12 | 1 | 1 | yes | characteristic |
| 144 | C3×#127 | #67 | 1 | 1 | yes | characteristic |
| 145 | #942 | — | 2 | 2 | no | — |
| 146 | C2×#214 | — | 12 | 2 | no | — |
| 147 | C2×#214 | — | 12 | 2 | no | — |
| 148 | C2×#214 | — | 12 | 4 | no | — |
| 149 | #932 | — | 2 | 2 | no | — |
| 150 | #916 | — | 4 | 2 | no | — |
| 151 | #915 | — | 4 | 2 | no | — |
| 152 | #914 | — | 4 | 2 | no | — |
| 153 | D3×SD16 | — | 4 | 2 | no | — |
| 154 | #904 | #67 | 1 | 2 | yes | — |
| 155 | #901 | — | 2 | 2 | no | — |
| 156 | #869 | — | 6 | 2 | no | — |
| 157 | #869 | — | 6 | 1 | no | — |
| 158 | #869 | — | 6 | 1 | no | — |
| 159 | C3×M32 | — | 6 | 2 | no | — |
| 160 | C3×#108 | — | 3 | 2 | no | — |
| 161 | C3×#104 | — | 6 | 2 | no | — |
| 162 | C3×#101 | — | 6 | 1 | no | — |
| 163 | C3×#100 | — | 6 | 1 | no | — |
| 164 | C3×C4×C8 | — | 2 | 1 | no | — |
| 165 | C3×C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 166 | C3×C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 167 | #836 | — | 2 | 1 | no | — |
| 168 | #833 | — | 2 | 1 | no | — |
| 169 | #819 | #67 | 1 | 2 | yes | — |
| 170 | #817 | — | 6 | 2 | no | — |
| 171 | #817 | — | 6 | 2 | no | — |
| 172 | #817 | — | 12 | 2 | no | — |
| 173 | #812 | — | 2 | 2 | no | — |
| 174 | #808 | — | 12 | 2 | no | — |
| 175 | #808 | — | 12 | 2 | no | — |
| 176 | #808 | — | 12 | 4 | no | — |
| 177 | #805 | — | 2 | 2 | no | — |
| 178 | C4×C3⋊C8 | — | 6 | 2 | no | — |
| 179 | C4×C3⋊C8 | — | 6 | 1 | no | — |
| 180 | C4×C3⋊C8 | — | 6 | 1 | no | — |
| 181 | C23×C32 | — | 4 | 1 | no | — |
| 182 | C22×C3×D3 | — | 8 | 1 | no | — |
| 183 | C32×Q8 | — | 4 | 2 | no | — |
| 184 | C32×D4 | — | 4 | 2 | no | — |
| 185 | C32×D4 | — | 8 | 2 | no | — |
| 186 | C2×C32×C4 | — | 2 | 1 | no | — |
| 187 | C2×C32×C4 | — | 4 | 1 | no | — |
| 188 | C2×C32×C4 | #120 | 1 | 1 | yes | characteristic |
| 189 | C2×C3⋊Dic3 | — | 8 | 1 | no | — |
| 190 | #634 | — | 8 | 2 | no | — |
| 191 | C3×#67 | — | 4 | 2 | no | — |
| 192 | C3×#67 | — | 8 | 2 | no | — |
| 193 | C2×C3×Dic3 | — | 8 | 1 | no | — |
| 194 | C3×D12 | — | 2 | 2 | no | — |
| 195 | C3×D12 | — | 8 | 1 | no | — |
| 196 | C3×C4×D3 | — | 4 | 2 | no | — |
| 197 | C3×C4×D3 | — | 8 | 2 | no | — |
| 198 | C3×Dic6 | — | 2 | 2 | no | — |
| 199 | C3×Dic6 | — | 8 | 1 | no | — |
| 200 | C32×C8 | C2×SD16 | 1 | 2 | yes | — |
| 201 | C32×C8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 202 | C3⋊(C3⋊C8) | — | 2 | 4 | no | — |
| 203 | C3×C3⋊C8 | — | 4 | 2 | no | — |
| 204 | #577 | — | 6 | 2 | no | — |
| 205 | #498 | — | 9 | 1 | no | — |
| 206 | #498 | — | 18 | 1 | no | — |
| 207 | #492 | — | 18 | 1 | no | — |
| 208 | #492 | D32 | 1 | 1 | yes | characteristic |
| 209 | #471 | — | 6 | 2 | no | — |
| 210 | #456 | — | 6 | 1 | no | — |
| 211 | #453 | — | 6 | 1 | no | — |
| 212 | #443 | — | 3 | 2 | no | — |
| 213 | #365 | — | 18 | 2 | no | — |
| 214 | #364 | — | 3 | 2 | no | — |
| 215 | #360 | — | 18 | 2 | no | — |
| 216 | C82 | — | 9 | 1 | no | — |
| 217 | C3×#41 | — | 6 | 2 | no | — |
| 218 | C3×#41 | — | 12 | 2 | no | — |
| 219 | C3×#41 | — | 12 | 2 | no | — |
| 220 | C3×#41 | — | 24 | 1 | no | — |
| 221 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 222 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 223 | C2×C3×Q8 | — | 4 | 1 | no | — |
| 224 | C2×C3×Q8 | — | 12 | 2 | no | — |
| 225 | C2×C3×D4 | — | 2 | 1 | no | — |
| 226 | C2×C3×D4 | — | 2 | 1 | no | — |
| 227 | C2×C3×D4 | — | 4 | 1 | no | — |
| 228 | C2×C3×D4 | — | 4 | 1 | no | — |
| 229 | C2×C3×D4 | — | 4 | 1 | no | — |
| 230 | C2×C3×D4 | — | 4 | 2 | no | — |
| 231 | C2×C3×D4 | — | 12 | 2 | no | — |
| 232 | C2×C3×D4 | — | 24 | 1 | no | — |
| 233 | C2×#67 | — | 8 | 1 | no | — |
| 234 | #239 | — | 4 | 2 | no | — |
| 235 | D3×Q8 | — | 4 | 2 | no | — |
| 236 | #237 | — | 4 | 2 | no | — |
| 237 | D3×D4 | — | 4 | 2 | no | — |
| 238 | #235 | — | 2 | 2 | no | — |
| 239 | #235 | — | 8 | 1 | no | — |
| 240 | C2×Dic6 | — | 12 | 2 | no | — |
| 241 | C2×Dic6 | — | 12 | 1 | no | — |
| 242 | C2×Dic6 | — | 12 | 1 | no | — |
| 243 | C3×Q16 | — | 3 | 2 | no | — |
| 244 | C3×Q16 | — | 12 | 2 | no | — |
| 245 | C3×SD16 | — | 4 | 2 | no | — |
| 246 | C3×SD16 | — | 4 | 2 | no | — |
| 247 | C3×SD16 | — | 4 | 2 | no | — |
| 248 | C3×SD16 | — | 4 | 2 | no | — |
| 249 | C3×SD16 | — | 6 | 2 | no | — |
| 250 | C3×SD16 | — | 8 | 2 | no | — |
| 251 | C3×SD16 | — | 8 | 2 | no | — |
| 252 | C3×SD16 | — | 12 | 2 | no | — |
| 253 | C3×SD16 | — | 12 | 2 | no | — |
| 254 | C3×D8 | — | 3 | 2 | no | — |
| 255 | C3×D8 | — | 12 | 2 | no | — |
| 256 | C3×M16 | — | 6 | 2 | no | — |
| 257 | C3×M16 | — | 12 | 2 | no | — |
| 258 | C2×C3×C8 | — | 2 | 2 | no | — |
| 259 | C2×C3×C8 | — | 12 | 2 | no | — |
| 260 | C2×C3×C8 | D3×D4 | 1 | 2 | yes | — |
| 261 | C2×C3×C8 | C2×#67 | 1 | 2 | yes | — |
| 262 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 263 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 264 | C3×C4⋊C4 | — | 4 | 2 | no | — |
| 265 | C3×C42 | — | 2 | 1 | no | — |
| 266 | C3×C42 | C2×D12 | 1 | 1 | yes | characteristic |
| 267 | C3×C42 | C2×#67 | 1 | 1 | yes | characteristic |
| 268 | #216 | — | 4 | 2 | no | — |
| 269 | #215 | — | 4 | 2 | no | — |
| 270 | #214 | — | 4 | 2 | no | — |
| 271 | #214 | — | 24 | 4 | no | — |
| 272 | #214 | — | 24 | 4 | no | — |
| 273 | #214 | — | 24 | 8 | no | — |
| 274 | #213 | — | 4 | 2 | no | — |
| 275 | C4⋊Dic3 | — | 12 | 2 | no | — |
| 276 | C4⋊Dic3 | — | 12 | 1 | no | — |
| 277 | C4⋊Dic3 | — | 12 | 1 | no | — |
| 278 | C4⋊Dic3 | — | 12 | 2 | no | — |
| 279 | C4⋊Dic3 | — | 12 | 1 | no | — |
| 280 | C4⋊Dic3 | — | 12 | 1 | no | — |
| 281 | #208 | — | 2 | 2 | no | — |
| 282 | C2×C3⋊C8 | — | 6 | 4 | no | — |
| 283 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 284 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 285 | Dic12 | #214 | 1 | 2 | yes | complemented |
| 286 | D24 | #214 | 1 | 2 | yes | complemented |
| 287 | #204 | — | 2 | 2 | no | — |
| 288 | ΓL(1,𝔽25) | — | 4 | 2 | no | — |
| 289 | D3×C8 | — | 4 | 2 | no | — |
| 290 | C3×C16 | — | 12 | 2 | no | — |
| 291 | C3⋊C16 | — | 4 | 2 | no | — |
| 292 | C22×C32 | — | 8 | 1 | no | — |
| 293 | C22×C32 | — | 16 | 1 | no | — |
| 294 | C22×C32 | #453 | 1 | 1 | yes | characteristic |
| 295 | C2×C3×D3 | — | 4 | 2 | no | — |
| 296 | C2×C3×D3 | — | 32 | 1 | no | — |
| 297 | C32×C4 | — | 2 | 2 | no | — |
| 298 | C32×C4 | — | 8 | 1 | no | — |
| 299 | C32×C4 | #450 | 1 | 2 | yes | — |
| 300 | C3⋊Dic3 | — | 16 | 1 | no | — |
| 301 | C3×Dic3 | — | 4 | 2 | no | — |
| 302 | 2−1+4 | — | 6 | 1 | no | — |
| 303 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 304 | #137 | — | 6 | 2 | no | — |
| 305 | #137 | — | 12 | 2 | no | — |
| 306 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 307 | AGL(1,ℤ/8) | — | 12 | 2 | no | — |
| 308 | #135 | — | 3 | 2 | no | — |
| 309 | #135 | — | 12 | 2 | no | — |
| 310 | C2×SD16 | — | 2 | 2 | no | — |
| 311 | C2×SD16 | — | 12 | 2 | no | — |
| 312 | C2×SD16 | — | 36 | 2 | no | — |
| 313 | #131 | — | 6 | 2 | no | — |
| 314 | C4⋊Q8 | — | 18 | 1 | no | — |
| 315 | C4⋊Q8 | #626 | 1 | 1 | yes | characteristic |
| 316 | #127 | #626 | 1 | 1 | yes | characteristic |
| 317 | M32 | — | 6 | 2 | no | — |
| 318 | #108 | — | 3 | 2 | no | — |
| 319 | #106 | — | 18 | 2 | no | — |
| 320 | #106 | — | 36 | 2 | no | — |
| 321 | #104 | — | 6 | 2 | no | — |
| 322 | #101 | — | 6 | 1 | no | — |
| 323 | #100 | — | 6 | 1 | no | — |
| 324 | C4×C8 | — | 18 | 1 | no | — |
| 325 | C4×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 326 | C23×C3 | — | 4 | 1 | no | — |
| 327 | C23×C3 | — | 4 | 1 | no | — |
| 328 | C23×C3 | — | 8 | 1 | no | — |
| 329 | C23×C3 | — | 24 | 1 | no | — |
| 330 | C22×D3 | — | 8 | 1 | no | — |
| 331 | C3×Q8 | — | 4 | 2 | no | — |
| 332 | C3×Q8 | — | 4 | 2 | no | — |
| 333 | C3×Q8 | — | 6 | 2 | no | — |
| 334 | C3×Q8 | — | 8 | 2 | no | — |
| 335 | C3×Q8 | — | 24 | 1 | no | — |
| 336 | C3×D4 | — | 4 | 2 | no | — |
| 337 | C3×D4 | — | 4 | 2 | no | — |
| 338 | C3×D4 | — | 6 | 2 | no | — |
| 339 | C3×D4 | — | 8 | 2 | no | — |
| 340 | C3×D4 | — | 8 | 2 | no | — |
| 341 | C3×D4 | — | 8 | 2 | no | — |
| 342 | C3×D4 | — | 8 | 4 | no | — |
| 343 | C3×D4 | — | 12 | 2 | no | — |
| 344 | C3×D4 | — | 24 | 1 | no | — |
| 345 | C3×D4 | — | 24 | 2 | no | — |
| 346 | C2×C3×C4 | — | 2 | 2 | no | — |
| 347 | C2×C3×C4 | — | 2 | 1 | no | — |
| 348 | C2×C3×C4 | — | 2 | 1 | no | — |
| 349 | C2×C3×C4 | — | 2 | 1 | no | — |
| 350 | C2×C3×C4 | — | 4 | 1 | no | — |
| 351 | C2×C3×C4 | — | 4 | 1 | no | — |
| 352 | C2×C3×C4 | — | 8 | 1 | no | — |
| 353 | C2×C3×C4 | — | 12 | 2 | no | — |
| 354 | C2×C3×C4 | — | 24 | 2 | no | — |
| 355 | C2×C3×C4 | — | 24 | 1 | no | — |
| 356 | C2×C3×C4 | #882 | 1 | 1 | yes | characteristic |
| 357 | C2×C3×C4 | #953 | 1 | 1 | yes | characteristic |
| 358 | #67 | — | 4 | 2 | no | — |
| 359 | #67 | — | 8 | 2 | no | — |
| 360 | C2×Dic3 | — | 8 | 1 | no | — |
| 361 | C2×Dic3 | — | 24 | 2 | no | — |
| 362 | C2×Dic3 | — | 24 | 1 | no | — |
| 363 | C2×Dic3 | — | 24 | 1 | no | — |
| 364 | D12 | — | 2 | 2 | no | — |
| 365 | D12 | — | 8 | 1 | no | — |
| 366 | C4×D3 | — | 4 | 2 | no | — |
| 367 | C4×D3 | — | 8 | 2 | no | — |
| 368 | Dic6 | — | 2 | 2 | no | — |
| 369 | Dic6 | — | 8 | 1 | no | — |
| 370 | Dic6 | — | 24 | 4 | no | — |
| 371 | Dic6 | — | 24 | 2 | no | — |
| 372 | Dic6 | — | 24 | 2 | no | — |
| 373 | C3×C8 | — | 2 | 2 | no | — |
| 374 | C3×C8 | — | 2 | 2 | no | — |
| 375 | C3×C8 | — | 12 | 2 | no | — |
| 376 | C3×C8 | #911 | 1 | 2 | yes | — |
| 377 | C3×C8 | D3×SD16 | 1 | 2 | yes | — |
| 378 | C3×C8 | #932 | 1 | 2 | yes | — |
| 379 | C3×C8 | C2×#214 | 1 | 2 | yes | — |
| 380 | C3⋊C8 | — | 4 | 2 | no | — |
| 381 | C3⋊C8 | — | 6 | 8 | no | — |
| 382 | C3⋊C8 | — | 6 | 4 | no | — |
| 383 | C3⋊C8 | — | 6 | 4 | no | — |
| 384 | C2×C32 | — | 2 | 1 | no | — |
| 385 | C2×C32 | — | 16 | 1 | no | — |
| 386 | C2×C32 | #1629 | 1 | 1 | yes | characteristic |
| 387 | C3×D3 | — | 8 | 2 | no | — |
| 388 | #41 | — | 6 | 2 | no | — |
| 389 | #41 | — | 12 | 2 | no | — |
| 390 | #41 | — | 12 | 2 | no | — |
| 391 | #41 | — | 24 | 1 | no | — |
| 392 | C2×Q8 | — | 2 | 1 | no | — |
| 393 | C2×Q8 | — | 12 | 2 | no | — |
| 394 | C2×Q8 | — | 36 | 1 | no | — |
| 395 | C2×D4 | — | 2 | 1 | no | — |
| 396 | C2×D4 | — | 4 | 1 | no | — |
| 397 | C2×D4 | — | 12 | 2 | no | — |
| 398 | C2×D4 | — | 24 | 1 | no | — |
| 399 | Q16 | — | 3 | 2 | no | — |
| 400 | Q16 | — | 12 | 2 | no | — |
| 401 | SD16 | — | 4 | 2 | no | — |
| 402 | SD16 | — | 4 | 2 | no | — |
| 403 | SD16 | — | 6 | 2 | no | — |
| 404 | SD16 | — | 12 | 2 | no | — |
| 405 | SD16 | — | 12 | 2 | no | — |
| 406 | SD16 | — | 72 | 4 | no | — |
| 407 | D8 | — | 3 | 2 | no | — |
| 408 | D8 | — | 12 | 2 | no | — |
| 409 | M16 | — | 6 | 2 | no | — |
| 410 | M16 | — | 12 | 2 | no | — |
| 411 | C2×C8 | — | 12 | 2 | no | — |
| 412 | C2×C8 | — | 18 | 2 | no | — |
| 413 | C2×C8 | D3×#67 | 1 | 2 | yes | — |
| 414 | C4⋊C4 | — | 4 | 1 | no | — |
| 415 | C4⋊C4 | — | 36 | 1 | no | — |
| 416 | C4⋊C4 | — | 36 | 1 | no | — |
| 417 | C42 | C2×#626 | 1 | 1 | yes | characteristic |
| 418 | C16 | — | 12 | 2 | no | — |
| 419 | C22×C3 | — | 2 | 1 | no | — |
| 420 | C22×C3 | — | 8 | 1 | no | — |
| 421 | C22×C3 | — | 8 | 1 | no | — |
| 422 | C22×C3 | — | 12 | 2 | no | — |
| 423 | C22×C3 | — | 16 | 1 | no | — |
| 424 | C22×C3 | — | 16 | 1 | no | — |
| 425 | C22×C3 | — | 16 | 1 | no | — |
| 426 | C22×C3 | — | 16 | 2 | no | — |
| 427 | C22×C3 | — | 96 | 1 | no | — |
| 428 | C22×C3 | #4747 | 1 | 1 | yes | characteristic |
| 429 | C22×C3 | #5241 | 1 | 1 | yes | characteristic |
| 430 | C2×D3 | — | 4 | 2 | no | — |
| 431 | C2×D3 | — | 32 | 1 | no | — |
| 432 | C3×C4 | — | 2 | 4 | no | — |
| 433 | C3×C4 | — | 2 | 2 | no | — |
| 434 | C3×C4 | — | 2 | 2 | no | — |
| 435 | C3×C4 | — | 2 | 2 | no | — |
| 436 | C3×C4 | — | 8 | 1 | no | — |
| 437 | C3×C4 | — | 8 | 1 | no | — |
| 438 | C3×C4 | — | 12 | 2 | no | — |
| 439 | C3×C4 | — | 16 | 1 | no | — |
| 440 | C3×C4 | #4776 | 1 | 2 | yes | — |
| 441 | C3×C4 | #5218 | 1 | 2 | yes | — |
| 442 | Dic3 | — | 4 | 2 | no | — |
| 443 | Dic3 | — | 48 | 2 | no | — |
| 444 | Dic3 | — | 48 | 1 | no | — |
| 445 | Dic3 | — | 48 | 1 | no | — |
| 446 | C32 | #12364 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 447 | C23 | — | 4 | 1 | no | — |
| 448 | C23 | — | 24 | 1 | no | — |
| 449 | Q8 | — | 4 | 2 | no | — |
| 450 | Q8 | — | 6 | 2 | no | — |
| 451 | Q8 | — | 24 | 1 | no | — |
| 452 | Q8 | — | 72 | 2 | no | — |
| 453 | D4 | — | 4 | 2 | no | — |
| 454 | D4 | — | 6 | 2 | no | — |
| 455 | D4 | — | 8 | 2 | no | — |
| 456 | D4 | — | 12 | 2 | no | — |
| 457 | D4 | — | 24 | 1 | no | — |
| 458 | D4 | — | 24 | 2 | no | — |
| 459 | C2×C4 | — | 2 | 1 | no | — |
| 460 | C2×C4 | — | 4 | 1 | no | — |
| 461 | C2×C4 | — | 12 | 2 | no | — |
| 462 | C2×C4 | — | 24 | 2 | no | — |
| 463 | C2×C4 | — | 24 | 1 | no | — |
| 464 | C2×C4 | — | 72 | 1 | no | — |
| 465 | C2×C4 | #63977 | 1 | 1 | yes | characteristic |
| 466 | C8 | — | 12 | 2 | no | — |
| 467 | C8 | — | 18 | 4 | no | — |
| 468 | C8 | D3×#214 | 1 | 2 | yes | — |
| 469 | C8 | #63932 | 1 | 2 | yes | — |
| 470 | C2×C3 | — | 2 | 2 | no | — |
| 471 | C2×C3 | — | 2 | 1 | no | — |
| 472 | C2×C3 | — | 2 | 1 | no | — |
| 473 | C2×C3 | — | 2 | 1 | no | — |
| 474 | C2×C3 | — | 16 | 1 | no | — |
| 475 | C2×C3 | — | 16 | 1 | no | — |
| 476 | C2×C3 | — | 24 | 2 | no | — |
| 477 | C2×C3 | — | 32 | 1 | no | — |
| 478 | C2×C3 | #68391 | 1 | 1 | yes | characteristic |
| 479 | C2×C3 | #71907 | 1 | 1 | yes | characteristic |
| 480 | D3 | — | 8 | 2 | no | — |
| 481 | C22 | — | 8 | 1 | no | — |
| 482 | C22 | — | 12 | 2 | no | — |
| 483 | C22 | — | 16 | 1 | no | — |
| 484 | C22 | — | 96 | 1 | no | — |
| 485 | C22 | #10591510 | 1 | 1 | yes | characteristic |
| 486 | C4 | — | 2 | 2 | no | — |
| 487 | C4 | — | 8 | 1 | no | — |
| 488 | C4 | — | 12 | 2 | no | — |
| 489 | C4 | — | 144 | 1 | no | — |
| 490 | C4 | #10591459 | 1 | 2 | yes | — |
| 491 | C3 | — | 2 | 1 | no | — |
| 492 | C3 | #10708946 | 1 | 1 | yes | characteristic, complemented |
| 493 | C3 | #10708947 | 1 | 1 | yes | characteristic, complemented |
| 494 | C2 | — | 2 | 1 | no | — |
| 495 | C2 | — | 16 | 1 | no | — |
| 496 | C2 | — | 24 | 2 | no | — |
| 497 | C2 | #11779307 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11799714 | C2 | semidirect |
| 3. #11782415 | C2 | semidirect |
| 4. C3×#67787 | C2 | semidirect |
| 5. #11771648 | C2 | semidirect |
| 12. #10592379 | C22 | semidirect |
| 17. C8×C3⋊(C3⋊C8) | C22 | semidirect |
| 18. C3×#4463 | C22 | semidirect |
| 29. #67787 | D3 | semidirect |
| 84. #4463 | C2×D3 | semidirect |
| 113. C3×Dic12 | SD16 | semidirect |
| 114. C3×D24 | SD16 | semidirect |
| 285. Dic12 | #214 | semidirect |
| 286. D24 | #214 | semidirect |
| 446. C32 | #12364 | semidirect |
| 492. C3 | #10708946 | semidirect |
| 493. C3 | #10708947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#81774 | 2 |
| #11799714 | 2 |
| #11782415 | 2 |
| C3×#67787 | 2 |
| #11771648 | 2 |
| #10708947 | 3 |
| #10708946 | 3 |