Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
889 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 889 conjugacy classes of subgroups — too many to draw. Only its 118 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, complemented |
| 2 | C3×#71295 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C3×#67787 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#67443 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C32×#1721 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10708598 | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 7 | C3×#12314 | — | 3 | 1 | no | maximal |
| 8 | C3×#5762 | — | 2 | 2 | no | — |
| 9 | C32×#493 | — | 2 | 1 | no | — |
| 10 | C32×#493 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C32×#492 | C22 | 1 | 1 | yes | characteristic |
| 12 | C32×#486 | — | 2 | 1 | no | — |
| 13 | C3×#5177 | — | 2 | 2 | no | — |
| 14 | C3×#5147 | — | 2 | 2 | no | — |
| 15 | C3×#5095 | — | 2 | 1 | no | — |
| 16 | C3×#5077 | — | 2 | 1 | no | — |
| 17 | C3×#4700 | C22 | 1 | 2 | yes | — |
| 18 | C32×#322 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C3×#4563 | — | 2 | 2 | no | — |
| 20 | C3×#4463 | C22 | 1 | 2 | yes | complemented |
| 21 | C3×#3291 | — | 3 | 1 | no | — |
| 22 | #81774 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 23 | C3×#2213 | — | 3 | 2 | no | — |
| 24 | C3×#1721 | — | 2 | 1 | no | — |
| 25 | C3×#1721 | D3 | 1 | 1 | yes | characteristic, complemented |
| 26 | C3×#1721 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 27 | #71295 | C2×C3 | 1 | 2 | yes | complemented |
| 28 | C3×#1359 | — | 3 | 1 | no | — |
| 29 | C3×#1336 | — | 3 | 2 | no | — |
| 30 | #67787 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 31 | #67443 | C2×C3 | 1 | 2 | yes | complemented |
| 32 | C3×#1007 | — | 2 | 1 | no | — |
| 33 | C3×#1004 | — | 2 | 1 | no | — |
| 34 | C2×C32×SD16 | — | 2 | 2 | no | — |
| 35 | C2×C32×D8 | — | 2 | 2 | no | — |
| 36 | C2×C32×D8 | — | 4 | 2 | no | — |
| 37 | C32×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 38 | C32×#127 | — | 2 | 1 | no | — |
| 39 | C32×#127 | D4 | 1 | 1 | yes | characteristic |
| 40 | C3×#942 | — | 2 | 2 | no | — |
| 41 | C3×#932 | — | 2 | 2 | no | — |
| 42 | C3×#916 | — | 4 | 2 | no | — |
| 43 | C3×#915 | — | 4 | 2 | no | — |
| 44 | C3×#914 | — | 4 | 2 | no | — |
| 45 | C3×D3×SD16 | — | 4 | 2 | no | — |
| 46 | C3×#904 | D4 | 1 | 2 | yes | — |
| 47 | C3×#901 | — | 2 | 2 | no | — |
| 48 | C32×#102 | — | 4 | 2 | no | — |
| 49 | C32×C4×C8 | — | 2 | 1 | no | — |
| 50 | C32×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 51 | C3×#836 | — | 2 | 1 | no | — |
| 52 | C3×#833 | — | 2 | 1 | no | — |
| 53 | C3×#827 | — | 4 | 2 | no | — |
| 54 | C3×#826 | — | 4 | 2 | no | — |
| 55 | C3×#819 | D4 | 1 | 2 | yes | — |
| 56 | C3×#812 | — | 2 | 2 | no | — |
| 57 | C3×#805 | — | 2 | 2 | no | — |
| 58 | #12314 | — | 3 | 1 | no | Sylow |
| 59 | C3×#577 | — | 6 | 2 | no | — |
| 60 | #5762 | — | 2 | 2 | no | — |
| 61 | C3×#509 | — | 6 | 2 | no | — |
| 62 | C3×#493 | — | 2 | 2 | no | — |
| 63 | C3×#493 | — | 2 | 1 | no | — |
| 64 | C3×#493 | — | 2 | 1 | no | — |
| 65 | C3×#493 | — | 2 | 1 | no | — |
| 66 | C3×#493 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 67 | C3×#493 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 68 | C3×#492 | — | 2 | 1 | no | — |
| 69 | C3×#492 | C2×D3 | 1 | 1 | yes | characteristic |
| 70 | C3×#492 | C22×C3 | 1 | 1 | yes | characteristic |
| 71 | C3×#486 | — | 2 | 2 | no | — |
| 72 | C3×#486 | — | 2 | 1 | no | — |
| 73 | C3×#486 | — | 2 | 1 | no | — |
| 74 | C3×#471 | — | 6 | 2 | no | — |
| 75 | C3×#456 | — | 6 | 1 | no | — |
| 76 | C3×#453 | — | 6 | 1 | no | — |
| 77 | C3×#443 | — | 3 | 2 | no | — |
| 78 | #5177 | — | 2 | 2 | no | — |
| 79 | #5147 | — | 2 | 2 | no | — |
| 80 | #5095 | — | 2 | 1 | no | — |
| 81 | #5077 | — | 2 | 1 | no | — |
| 82 | #4700 | C22×C3 | 1 | 2 | yes | — |
| 83 | C3×#364 | — | 3 | 2 | no | — |
| 84 | C3×#361 | — | 6 | 2 | no | — |
| 85 | C3×#322 | — | 2 | 1 | no | — |
| 86 | C3×#322 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 87 | C3×#322 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 88 | #4563 | — | 2 | 2 | no | — |
| 89 | #4463 | C22×C3 | 1 | 2 | yes | complemented |
| 90 | C2×C32×Q8 | — | 2 | 1 | no | — |
| 91 | C2×C32×D4 | — | 2 | 1 | no | — |
| 92 | C2×C32×D4 | — | 4 | 1 | no | — |
| 93 | C2×C32×D4 | — | 4 | 1 | no | — |
| 94 | C2×C32×D4 | — | 4 | 1 | no | — |
| 95 | C2×C32×D4 | — | 4 | 1 | no | — |
| 96 | C2×C3×#67 | — | 8 | 1 | no | — |
| 97 | C3×#239 | — | 4 | 2 | no | — |
| 98 | C3×D3×Q8 | — | 4 | 2 | no | — |
| 99 | C3×#237 | — | 4 | 2 | no | — |
| 100 | C3×D3×D4 | — | 4 | 2 | no | — |
| 101 | C3×#235 | — | 2 | 2 | no | — |
| 102 | C3×#235 | — | 8 | 1 | no | — |
| 103 | C32×SD16 | — | 4 | 2 | no | — |
| 104 | C32×SD16 | — | 4 | 2 | no | — |
| 105 | C32×D8 | — | 4 | 2 | no | — |
| 106 | C32×D8 | — | 4 | 2 | no | — |
| 107 | C32×D8 | — | 8 | 4 | no | — |
| 108 | C2×C32×C8 | — | 2 | 2 | no | — |
| 109 | C2×C32×C8 | C2×D4 | 1 | 2 | yes | — |
| 110 | C32×C4⋊C4 | — | 4 | 1 | no | — |
| 111 | C32×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 112 | C3×#216 | — | 4 | 2 | no | — |
| 113 | C3×#215 | — | 4 | 2 | no | — |
| 114 | C3×#214 | — | 4 | 2 | no | — |
| 115 | C3×#213 | — | 4 | 2 | no | — |
| 116 | C3×#208 | — | 2 | 2 | no | — |
| 117 | C3×Dic12 | D8 | 1 | 2 | yes | complemented |
| 118 | C3×D24 | D8 | 1 | 2 | yes | complemented |
| 119 | C3×#204 | — | 2 | 2 | no | — |
| 120 | C3×ΓL(1,𝔽25) | — | 4 | 2 | no | — |
| 121 | C3×D3×C8 | — | 4 | 2 | no | — |
| 122 | C3×C3⋊C16 | — | 4 | 2 | no | — |
| 123 | #3291 | — | 3 | 1 | no | — |
| 124 | #2213 | — | 3 | 2 | no | — |
| 125 | #1721 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 126 | #1359 | — | 3 | 1 | no | — |
| 127 | #1336 | — | 3 | 2 | no | — |
| 128 | C3×2−1+4 | — | 6 | 1 | no | — |
| 129 | C3×H(5,𝔽2) | — | 6 | 1 | no | — |
| 130 | #1007 | — | 2 | 1 | no | — |
| 131 | #1004 | — | 2 | 1 | no | — |
| 132 | C3×#137 | — | 6 | 2 | no | — |
| 133 | C3×#137 | — | 12 | 2 | no | — |
| 134 | C3×AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 135 | C3×AGL(1,ℤ/8) | — | 12 | 2 | no | — |
| 136 | C3×#135 | — | 3 | 2 | no | — |
| 137 | C3×#135 | — | 12 | 2 | no | — |
| 138 | C2×C3×SD16 | — | 2 | 2 | no | — |
| 139 | C2×C3×SD16 | — | 2 | 2 | no | — |
| 140 | C2×C3×SD16 | — | 4 | 2 | no | — |
| 141 | C2×C3×SD16 | — | 12 | 2 | no | — |
| 142 | C2×C3×D8 | — | 2 | 2 | no | — |
| 143 | C2×C3×D8 | — | 2 | 2 | no | — |
| 144 | C2×C3×D8 | — | 4 | 2 | no | — |
| 145 | C2×C3×D8 | — | 4 | 2 | no | — |
| 146 | C2×C3×D8 | — | 4 | 2 | no | — |
| 147 | C2×C3×D8 | — | 4 | 4 | no | — |
| 148 | C3×#131 | — | 6 | 2 | no | — |
| 149 | C3×C4⋊Q8 | — | 2 | 1 | no | — |
| 150 | C3×C4⋊Q8 | #67 | 1 | 1 | yes | characteristic |
| 151 | C3×C4⋊Q8 | C3×D4 | 1 | 1 | yes | characteristic |
| 152 | C3×#127 | — | 2 | 2 | no | — |
| 153 | C3×#127 | — | 2 | 1 | no | — |
| 154 | C3×#127 | — | 2 | 1 | no | — |
| 155 | C3×#127 | — | 2 | 1 | no | — |
| 156 | C3×#127 | #67 | 1 | 1 | yes | characteristic |
| 157 | C3×#127 | C3×D4 | 1 | 1 | yes | characteristic |
| 158 | #942 | — | 2 | 2 | no | — |
| 159 | #932 | — | 2 | 2 | no | — |
| 160 | #916 | — | 4 | 2 | no | — |
| 161 | #915 | — | 4 | 2 | no | — |
| 162 | #914 | — | 4 | 2 | no | — |
| 163 | D3×SD16 | — | 4 | 2 | no | — |
| 164 | #904 | C3×D4 | 1 | 2 | yes | — |
| 165 | #901 | — | 2 | 2 | no | — |
| 166 | C3×SD32 | — | 12 | 2 | no | — |
| 167 | C3×D16 | — | 12 | 2 | no | — |
| 168 | C3×M32 | — | 6 | 2 | no | — |
| 169 | C3×#108 | — | 3 | 2 | no | — |
| 170 | C3×#104 | — | 6 | 2 | no | — |
| 171 | C3×#102 | — | 4 | 2 | no | — |
| 172 | C3×#102 | — | 4 | 2 | no | — |
| 173 | C3×#102 | — | 4 | 4 | no | — |
| 174 | C3×#101 | — | 6 | 1 | no | — |
| 175 | C3×#100 | — | 6 | 1 | no | — |
| 176 | C3×C4×C8 | — | 2 | 2 | no | — |
| 177 | C3×C4×C8 | — | 2 | 1 | no | — |
| 178 | C3×C4×C8 | — | 2 | 1 | no | — |
| 179 | C3×C4×C8 | — | 2 | 1 | no | — |
| 180 | C3×C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 181 | C3×C4×C8 | C23×C3 | 1 | 1 | yes | characteristic |
| 182 | #836 | — | 2 | 1 | no | — |
| 183 | #833 | — | 2 | 1 | no | — |
| 184 | #827 | — | 4 | 2 | no | — |
| 185 | #826 | — | 4 | 2 | no | — |
| 186 | #819 | C3×D4 | 1 | 2 | yes | — |
| 187 | #812 | — | 2 | 2 | no | — |
| 188 | #805 | — | 2 | 2 | no | — |
| 189 | C23×C32 | — | 4 | 1 | no | — |
| 190 | C23×C32 | — | 8 | 1 | no | — |
| 191 | C22×C3×D3 | — | 8 | 1 | no | — |
| 192 | C32×Q8 | — | 4 | 2 | no | — |
| 193 | C32×D4 | — | 4 | 2 | no | — |
| 194 | C32×D4 | — | 8 | 2 | no | — |
| 195 | C32×D4 | — | 8 | 2 | no | — |
| 196 | C32×D4 | — | 8 | 2 | no | — |
| 197 | C32×D4 | — | 8 | 2 | no | — |
| 198 | C2×C32×C4 | — | 2 | 1 | no | — |
| 199 | C2×C32×C4 | — | 4 | 1 | no | — |
| 200 | C2×C32×C4 | #120 | 1 | 1 | yes | characteristic |
| 201 | C3×#67 | — | 4 | 2 | no | — |
| 202 | C3×#67 | — | 8 | 2 | no | — |
| 203 | C2×C3×Dic3 | — | 8 | 1 | no | — |
| 204 | C3×D12 | — | 2 | 2 | no | — |
| 205 | C3×D12 | — | 8 | 1 | no | — |
| 206 | C3×C4×D3 | — | 4 | 2 | no | — |
| 207 | C3×C4×D3 | — | 8 | 2 | no | — |
| 208 | C3×Dic6 | — | 2 | 2 | no | — |
| 209 | C3×Dic6 | — | 8 | 1 | no | — |
| 210 | C32×C8 | — | 4 | 2 | no | — |
| 211 | C32×C8 | C2×D8 | 1 | 2 | yes | — |
| 212 | C32×C8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 213 | C3×C3⋊C8 | — | 4 | 2 | no | — |
| 214 | #577 | — | 6 | 2 | no | — |
| 215 | #509 | — | 6 | 2 | no | — |
| 216 | #493 | — | 2 | 1 | no | — |
| 217 | #493 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 218 | #492 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 219 | #486 | — | 2 | 1 | no | — |
| 220 | #471 | — | 6 | 2 | no | — |
| 221 | #456 | — | 6 | 1 | no | — |
| 222 | #453 | — | 6 | 1 | no | — |
| 223 | #443 | — | 3 | 2 | no | — |
| 224 | #364 | — | 3 | 2 | no | — |
| 225 | #361 | — | 6 | 2 | no | — |
| 226 | #322 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 227 | C3×#41 | — | 6 | 2 | no | — |
| 228 | C3×#41 | — | 12 | 2 | no | — |
| 229 | C3×#41 | — | 12 | 2 | no | — |
| 230 | C3×#41 | — | 24 | 1 | no | — |
| 231 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 232 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 233 | C2×C3×Q8 | — | 4 | 1 | no | — |
| 234 | C2×C3×Q8 | — | 12 | 2 | no | — |
| 235 | C2×C3×D4 | — | 2 | 1 | no | — |
| 236 | C2×C3×D4 | — | 2 | 1 | no | — |
| 237 | C2×C3×D4 | — | 4 | 1 | no | — |
| 238 | C2×C3×D4 | — | 4 | 1 | no | — |
| 239 | C2×C3×D4 | — | 4 | 1 | no | — |
| 240 | C2×C3×D4 | — | 4 | 2 | no | — |
| 241 | C2×C3×D4 | — | 4 | 1 | no | — |
| 242 | C2×C3×D4 | — | 4 | 1 | no | — |
| 243 | C2×C3×D4 | — | 4 | 2 | no | — |
| 244 | C2×C3×D4 | — | 4 | 2 | no | — |
| 245 | C2×C3×D4 | — | 4 | 1 | no | — |
| 246 | C2×C3×D4 | — | 4 | 1 | no | — |
| 247 | C2×C3×D4 | — | 4 | 2 | no | — |
| 248 | C2×C3×D4 | — | 4 | 1 | no | — |
| 249 | C2×C3×D4 | — | 4 | 1 | no | — |
| 250 | C2×C3×D4 | — | 12 | 2 | no | — |
| 251 | C2×C3×D4 | — | 24 | 1 | no | — |
| 252 | C2×#67 | — | 8 | 1 | no | — |
| 253 | #239 | — | 4 | 2 | no | — |
| 254 | D3×Q8 | — | 4 | 2 | no | — |
| 255 | #237 | — | 4 | 2 | no | — |
| 256 | D3×D4 | — | 4 | 2 | no | — |
| 257 | #235 | — | 2 | 2 | no | — |
| 258 | #235 | — | 8 | 1 | no | — |
| 259 | C3×Q16 | — | 3 | 2 | no | — |
| 260 | C3×Q16 | — | 12 | 2 | no | — |
| 261 | C3×SD16 | — | 4 | 2 | no | — |
| 262 | C3×SD16 | — | 4 | 2 | no | — |
| 263 | C3×SD16 | — | 4 | 2 | no | — |
| 264 | C3×SD16 | — | 4 | 2 | no | — |
| 265 | C3×SD16 | — | 6 | 2 | no | — |
| 266 | C3×SD16 | — | 8 | 2 | no | — |
| 267 | C3×SD16 | — | 8 | 2 | no | — |
| 268 | C3×SD16 | — | 12 | 2 | no | — |
| 269 | C3×SD16 | — | 12 | 2 | no | — |
| 270 | C3×D8 | — | 3 | 2 | no | — |
| 271 | C3×D8 | — | 4 | 2 | no | — |
| 272 | C3×D8 | — | 4 | 2 | no | — |
| 273 | C3×D8 | — | 4 | 2 | no | — |
| 274 | C3×D8 | — | 4 | 2 | no | — |
| 275 | C3×D8 | — | 8 | 2 | no | — |
| 276 | C3×D8 | — | 8 | 2 | no | — |
| 277 | C3×D8 | — | 8 | 4 | no | — |
| 278 | C3×D8 | — | 8 | 4 | no | — |
| 279 | C3×D8 | — | 8 | 8 | no | — |
| 280 | C3×D8 | — | 12 | 2 | no | — |
| 281 | C3×M16 | — | 6 | 2 | no | — |
| 282 | C3×M16 | — | 12 | 2 | no | — |
| 283 | C2×C3×C8 | — | 2 | 4 | no | — |
| 284 | C2×C3×C8 | — | 2 | 2 | no | — |
| 285 | C2×C3×C8 | — | 2 | 2 | no | — |
| 286 | C2×C3×C8 | — | 2 | 2 | no | — |
| 287 | C2×C3×C8 | — | 12 | 2 | no | — |
| 288 | C2×C3×C8 | D3×D4 | 1 | 2 | yes | — |
| 289 | C2×C3×C8 | C2×C3×D4 | 1 | 2 | yes | — |
| 290 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 291 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 292 | C3×C4⋊C4 | — | 4 | 2 | no | — |
| 293 | C3×C42 | — | 2 | 1 | no | — |
| 294 | C3×C42 | C2×#67 | 1 | 1 | yes | characteristic |
| 295 | C3×C42 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 296 | #216 | — | 4 | 2 | no | — |
| 297 | #215 | — | 4 | 2 | no | — |
| 298 | #214 | — | 4 | 2 | no | — |
| 299 | #213 | — | 4 | 2 | no | — |
| 300 | #208 | — | 2 | 2 | no | — |
| 301 | Dic12 | C3×D8 | 1 | 2 | yes | complemented |
| 302 | D24 | C3×D8 | 1 | 2 | yes | complemented |
| 303 | #204 | — | 2 | 2 | no | — |
| 304 | ΓL(1,𝔽25) | — | 4 | 2 | no | — |
| 305 | D3×C8 | — | 4 | 2 | no | — |
| 306 | C3×C16 | — | 12 | 2 | no | — |
| 307 | C3⋊C16 | — | 4 | 2 | no | — |
| 308 | C22×C32 | — | 8 | 1 | no | — |
| 309 | C22×C32 | — | 16 | 1 | no | — |
| 310 | C22×C32 | — | 16 | 1 | no | — |
| 311 | C22×C32 | — | 16 | 1 | no | — |
| 312 | C22×C32 | — | 16 | 1 | no | — |
| 313 | C22×C32 | #453 | 1 | 1 | yes | characteristic |
| 314 | C2×C3×D3 | — | 4 | 2 | no | — |
| 315 | C2×C3×D3 | — | 32 | 1 | no | — |
| 316 | C32×C4 | — | 2 | 2 | no | — |
| 317 | C32×C4 | — | 8 | 1 | no | — |
| 318 | C32×C4 | #447 | 1 | 2 | yes | — |
| 319 | C3×Dic3 | — | 4 | 2 | no | — |
| 320 | 2−1+4 | — | 6 | 1 | no | — |
| 321 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 322 | #137 | — | 6 | 2 | no | — |
| 323 | #137 | — | 12 | 2 | no | — |
| 324 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 325 | AGL(1,ℤ/8) | — | 12 | 2 | no | — |
| 326 | #135 | — | 3 | 2 | no | — |
| 327 | #135 | — | 12 | 2 | no | — |
| 328 | C2×SD16 | — | 2 | 2 | no | — |
| 329 | C2×SD16 | — | 12 | 2 | no | — |
| 330 | C2×D8 | — | 2 | 2 | no | — |
| 331 | C2×D8 | — | 4 | 2 | no | — |
| 332 | #131 | — | 6 | 2 | no | — |
| 333 | C4⋊Q8 | C3×#67 | 1 | 1 | yes | characteristic |
| 334 | #127 | — | 2 | 1 | no | — |
| 335 | #127 | C3×#67 | 1 | 1 | yes | characteristic |
| 336 | SD32 | — | 12 | 2 | no | — |
| 337 | D16 | — | 12 | 2 | no | — |
| 338 | M32 | — | 6 | 2 | no | — |
| 339 | #108 | — | 3 | 2 | no | — |
| 340 | #104 | — | 6 | 2 | no | — |
| 341 | #102 | — | 4 | 2 | no | — |
| 342 | #101 | — | 6 | 1 | no | — |
| 343 | #100 | — | 6 | 1 | no | — |
| 344 | C4×C8 | — | 2 | 1 | no | — |
| 345 | C4×C8 | C22×C3×D3 | 1 | 1 | yes | characteristic |
| 346 | C23×C3 | — | 4 | 1 | no | — |
| 347 | C23×C3 | — | 4 | 1 | no | — |
| 348 | C23×C3 | — | 8 | 1 | no | — |
| 349 | C23×C3 | — | 8 | 2 | no | — |
| 350 | C23×C3 | — | 8 | 1 | no | — |
| 351 | C23×C3 | — | 8 | 1 | no | — |
| 352 | C23×C3 | — | 24 | 1 | no | — |
| 353 | C22×D3 | — | 8 | 1 | no | — |
| 354 | C3×Q8 | — | 4 | 2 | no | — |
| 355 | C3×Q8 | — | 4 | 2 | no | — |
| 356 | C3×Q8 | — | 6 | 2 | no | — |
| 357 | C3×Q8 | — | 8 | 2 | no | — |
| 358 | C3×Q8 | — | 24 | 1 | no | — |
| 359 | C3×D4 | — | 4 | 2 | no | — |
| 360 | C3×D4 | — | 4 | 2 | no | — |
| 361 | C3×D4 | — | 6 | 2 | no | — |
| 362 | C3×D4 | — | 8 | 2 | no | — |
| 363 | C3×D4 | — | 8 | 2 | no | — |
| 364 | C3×D4 | — | 8 | 2 | no | — |
| 365 | C3×D4 | — | 8 | 4 | no | — |
| 366 | C3×D4 | — | 8 | 4 | no | — |
| 367 | C3×D4 | — | 8 | 2 | no | — |
| 368 | C3×D4 | — | 8 | 2 | no | — |
| 369 | C3×D4 | — | 8 | 4 | no | — |
| 370 | C3×D4 | — | 8 | 4 | no | — |
| 371 | C3×D4 | — | 8 | 2 | no | — |
| 372 | C3×D4 | — | 8 | 2 | no | — |
| 373 | C3×D4 | — | 8 | 2 | no | — |
| 374 | C3×D4 | — | 8 | 2 | no | — |
| 375 | C3×D4 | — | 12 | 2 | no | — |
| 376 | C3×D4 | — | 24 | 1 | no | — |
| 377 | C3×D4 | — | 24 | 2 | no | — |
| 378 | C2×C3×C4 | — | 2 | 2 | no | — |
| 379 | C2×C3×C4 | — | 2 | 1 | no | — |
| 380 | C2×C3×C4 | — | 2 | 1 | no | — |
| 381 | C2×C3×C4 | — | 2 | 1 | no | — |
| 382 | C2×C3×C4 | — | 4 | 1 | no | — |
| 383 | C2×C3×C4 | — | 4 | 1 | no | — |
| 384 | C2×C3×C4 | — | 8 | 1 | no | — |
| 385 | C2×C3×C4 | — | 12 | 2 | no | — |
| 386 | C2×C3×C4 | — | 24 | 2 | no | — |
| 387 | C2×C3×C4 | — | 24 | 1 | no | — |
| 388 | C2×C3×C4 | #937 | 1 | 1 | yes | characteristic |
| 389 | C2×C3×C4 | C3×#120 | 1 | 1 | yes | characteristic |
| 390 | #67 | — | 4 | 2 | no | — |
| 391 | #67 | — | 8 | 2 | no | — |
| 392 | C2×Dic3 | — | 8 | 1 | no | — |
| 393 | D12 | — | 2 | 2 | no | — |
| 394 | D12 | — | 8 | 1 | no | — |
| 395 | C4×D3 | — | 4 | 2 | no | — |
| 396 | C4×D3 | — | 8 | 2 | no | — |
| 397 | Dic6 | — | 2 | 2 | no | — |
| 398 | Dic6 | — | 8 | 1 | no | — |
| 399 | C3×C8 | — | 2 | 2 | no | — |
| 400 | C3×C8 | — | 2 | 2 | no | — |
| 401 | C3×C8 | — | 4 | 4 | no | — |
| 402 | C3×C8 | — | 4 | 2 | no | — |
| 403 | C3×C8 | — | 4 | 2 | no | — |
| 404 | C3×C8 | — | 12 | 2 | no | — |
| 405 | C3×C8 | D3×D8 | 1 | 2 | yes | — |
| 406 | C3×C8 | #911 | 1 | 2 | yes | — |
| 407 | C3×C8 | C2×C3×D8 | 1 | 2 | yes | — |
| 408 | C3×C8 | C3×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 409 | C3⋊C8 | — | 4 | 2 | no | — |
| 410 | C2×C32 | — | 2 | 1 | no | — |
| 411 | C2×C32 | — | 16 | 1 | no | — |
| 412 | C2×C32 | — | 32 | 1 | no | — |
| 413 | C2×C32 | #1619 | 1 | 1 | yes | characteristic |
| 414 | C3×D3 | — | 8 | 2 | no | — |
| 415 | #41 | — | 6 | 2 | no | — |
| 416 | #41 | — | 12 | 2 | no | — |
| 417 | #41 | — | 12 | 2 | no | — |
| 418 | #41 | — | 24 | 1 | no | — |
| 419 | C2×Q8 | — | 2 | 1 | no | — |
| 420 | C2×Q8 | — | 12 | 2 | no | — |
| 421 | C2×D4 | — | 2 | 1 | no | — |
| 422 | C2×D4 | — | 4 | 1 | no | — |
| 423 | C2×D4 | — | 4 | 1 | no | — |
| 424 | C2×D4 | — | 4 | 1 | no | — |
| 425 | C2×D4 | — | 4 | 1 | no | — |
| 426 | C2×D4 | — | 12 | 2 | no | — |
| 427 | C2×D4 | — | 24 | 1 | no | — |
| 428 | Q16 | — | 3 | 2 | no | — |
| 429 | Q16 | — | 12 | 2 | no | — |
| 430 | SD16 | — | 4 | 2 | no | — |
| 431 | SD16 | — | 4 | 2 | no | — |
| 432 | SD16 | — | 6 | 2 | no | — |
| 433 | SD16 | — | 12 | 2 | no | — |
| 434 | SD16 | — | 12 | 2 | no | — |
| 435 | D8 | — | 3 | 2 | no | — |
| 436 | D8 | — | 4 | 2 | no | — |
| 437 | D8 | — | 4 | 2 | no | — |
| 438 | D8 | — | 8 | 4 | no | — |
| 439 | D8 | — | 12 | 2 | no | — |
| 440 | M16 | — | 6 | 2 | no | — |
| 441 | M16 | — | 12 | 2 | no | — |
| 442 | C2×C8 | — | 2 | 2 | no | — |
| 443 | C2×C8 | — | 12 | 2 | no | — |
| 444 | C2×C8 | C3×D3×D4 | 1 | 2 | yes | — |
| 445 | C4⋊C4 | — | 4 | 1 | no | — |
| 446 | C42 | C2×C3×#67 | 1 | 1 | yes | characteristic |
| 447 | C16 | — | 12 | 2 | no | — |
| 448 | C22×C3 | — | 2 | 1 | no | — |
| 449 | C22×C3 | — | 8 | 1 | no | — |
| 450 | C22×C3 | — | 8 | 1 | no | — |
| 451 | C22×C3 | — | 12 | 2 | no | — |
| 452 | C22×C3 | — | 16 | 1 | no | — |
| 453 | C22×C3 | — | 16 | 1 | no | — |
| 454 | C22×C3 | — | 16 | 1 | no | — |
| 455 | C22×C3 | — | 16 | 2 | no | — |
| 456 | C22×C3 | — | 16 | 2 | no | — |
| 457 | C22×C3 | — | 16 | 2 | no | — |
| 458 | C22×C3 | — | 16 | 1 | no | — |
| 459 | C22×C3 | — | 16 | 1 | no | — |
| 460 | C22×C3 | — | 16 | 1 | no | — |
| 461 | C22×C3 | — | 16 | 1 | no | — |
| 462 | C22×C3 | — | 16 | 2 | no | — |
| 463 | C22×C3 | — | 16 | 1 | no | — |
| 464 | C22×C3 | — | 16 | 1 | no | — |
| 465 | C22×C3 | — | 96 | 1 | no | — |
| 466 | C22×C3 | #5077 | 1 | 1 | yes | characteristic |
| 467 | C22×C3 | C3×#453 | 1 | 1 | yes | characteristic |
| 468 | C2×D3 | — | 4 | 2 | no | — |
| 469 | C2×D3 | — | 32 | 1 | no | — |
| 470 | C3×C4 | — | 2 | 4 | no | — |
| 471 | C3×C4 | — | 2 | 2 | no | — |
| 472 | C3×C4 | — | 2 | 2 | no | — |
| 473 | C3×C4 | — | 2 | 2 | no | — |
| 474 | C3×C4 | — | 8 | 1 | no | — |
| 475 | C3×C4 | — | 8 | 1 | no | — |
| 476 | C3×C4 | — | 12 | 2 | no | — |
| 477 | C3×C4 | — | 16 | 1 | no | — |
| 478 | C3×C4 | #5156 | 1 | 2 | yes | — |
| 479 | C3×C4 | C3×#447 | 1 | 2 | yes | — |
| 480 | Dic3 | — | 4 | 2 | no | — |
| 481 | C32 | #12314 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 482 | C23 | — | 4 | 1 | no | — |
| 483 | C23 | — | 8 | 1 | no | — |
| 484 | C23 | — | 24 | 1 | no | — |
| 485 | Q8 | — | 4 | 2 | no | — |
| 486 | Q8 | — | 6 | 2 | no | — |
| 487 | Q8 | — | 24 | 1 | no | — |
| 488 | D4 | — | 4 | 2 | no | — |
| 489 | D4 | — | 6 | 2 | no | — |
| 490 | D4 | — | 8 | 2 | no | — |
| 491 | D4 | — | 8 | 2 | no | — |
| 492 | D4 | — | 8 | 2 | no | — |
| 493 | D4 | — | 8 | 2 | no | — |
| 494 | D4 | — | 12 | 2 | no | — |
| 495 | D4 | — | 24 | 1 | no | — |
| 496 | D4 | — | 24 | 2 | no | — |
| 497 | C2×C4 | — | 2 | 1 | no | — |
| 498 | C2×C4 | — | 4 | 1 | no | — |
| 499 | C2×C4 | — | 12 | 2 | no | — |
| 500 | C2×C4 | — | 24 | 2 | no | — |
| 501 | C2×C4 | — | 24 | 1 | no | — |
| 502 | C2×C4 | C3×#937 | 1 | 1 | yes | characteristic |
| 503 | C8 | — | 4 | 2 | no | — |
| 504 | C8 | — | 12 | 2 | no | — |
| 505 | C8 | C3×D3×D8 | 1 | 2 | yes | — |
| 506 | C8 | C3×#911 | 1 | 2 | yes | — |
| 507 | C2×C3 | — | 2 | 2 | no | — |
| 508 | C2×C3 | — | 2 | 1 | no | — |
| 509 | C2×C3 | — | 2 | 1 | no | — |
| 510 | C2×C3 | — | 2 | 1 | no | — |
| 511 | C2×C3 | — | 16 | 1 | no | — |
| 512 | C2×C3 | — | 16 | 1 | no | — |
| 513 | C2×C3 | — | 24 | 2 | no | — |
| 514 | C2×C3 | — | 32 | 1 | no | — |
| 515 | C2×C3 | — | 32 | 2 | no | — |
| 516 | C2×C3 | — | 32 | 1 | no | — |
| 517 | C2×C3 | — | 32 | 1 | no | — |
| 518 | C2×C3 | #71281 | 1 | 1 | yes | characteristic |
| 519 | C2×C3 | C3×#1619 | 1 | 1 | yes | characteristic |
| 520 | D3 | — | 8 | 2 | no | — |
| 521 | C22 | — | 8 | 1 | no | — |
| 522 | C22 | — | 12 | 2 | no | — |
| 523 | C22 | — | 16 | 1 | no | — |
| 524 | C22 | — | 16 | 1 | no | — |
| 525 | C22 | — | 16 | 1 | no | — |
| 526 | C22 | — | 16 | 1 | no | — |
| 527 | C22 | — | 96 | 1 | no | — |
| 528 | C22 | C3×#5077 | 1 | 1 | yes | characteristic |
| 529 | C4 | — | 2 | 2 | no | — |
| 530 | C4 | — | 8 | 1 | no | — |
| 531 | C4 | — | 12 | 2 | no | — |
| 532 | C4 | C3×#5156 | 1 | 2 | yes | — |
| 533 | C3 | — | 2 | 1 | no | — |
| 534 | C3 | C3×#12314 | 1 | 1 | yes | characteristic, complemented |
| 535 | C3 | #10708598 | 1 | 1 | yes | characteristic, direct product factor |
| 536 | C2 | — | 2 | 1 | no | — |
| 537 | C2 | — | 16 | 1 | no | — |
| 538 | C2 | — | 24 | 2 | no | — |
| 539 | C2 | — | 32 | 1 | no | — |
| 540 | C2 | C3×#71281 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#81774 | C2 | semidirect |
| 2. C3×#71295 | C2 | semidirect |
| 3. C3×#67787 | C2 | semidirect |
| 4. C3×#67443 | C2 | semidirect |
| 5. C32×#1721 | C2 | semidirect |
| 6. #10708598 | C3 | direct (N × H) |
| 10. C32×#493 | C22 | semidirect |
| 18. C32×#322 | C22 | semidirect |
| 20. C3×#4463 | C22 | semidirect |
| 22. #81774 | C2×C3 | semidirect |
| 25. C3×#1721 | D3 | semidirect |
| 26. C3×#1721 | C2×C3 | semidirect |
| 27. #71295 | C2×C3 | semidirect |
| 30. #67787 | C2×C3 | semidirect |
| 31. #67443 | C2×C3 | semidirect |
| 66. C3×#493 | C2×D3 | semidirect |
| 67. C3×#493 | C22×C3 | semidirect |
| 86. C3×#322 | C2×D3 | semidirect |
| 87. C3×#322 | C22×C3 | semidirect |
| 89. #4463 | C22×C3 | semidirect |
| 117. C3×Dic12 | D8 | semidirect |
| 118. C3×D24 | D8 | semidirect |
| 125. #1721 | C3×D3 | semidirect |
| 217. #493 | C2×C3×D3 | semidirect |
| 226. #322 | C2×C3×D3 | semidirect |
| 301. Dic12 | C3×D8 | semidirect |
| 302. D24 | C3×D8 | semidirect |
| 481. C32 | #12314 | semidirect |
| 534. C3 | C3×#12314 | semidirect |
| 535. C3 | #10708598 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#81774 | 2 |
| C3×#71295 | 2 |
| C3×#67787 | 2 |
| C3×#67443 | 2 |
| C32×#1721 | 2 |
| #10708598 | 3 |
| C3×#12314 | 3 |