Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
608 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 72 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×#5945 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C3×#984 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5430 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3×#5428 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C3×#5423 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #85542 | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 7 | C3×#3022 | — | 3 | 1 | no | maximal |
| 8 | C3×2−1+4⋊C3 | — | 2 | 1 | no | — |
| 9 | C3×2−1+4⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 10 | C3×#994 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C3×#41⋊C3 | — | 2 | 1 | no | — |
| 12 | C2×C3×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 13 | C3×#984 | — | 2 | 1 | no | — |
| 14 | C3×#984 | C22 | 1 | 2 | yes | complemented |
| 15 | C2×C3×#226 | — | 2 | 1 | no | — |
| 16 | C3×#951 | — | 4 | 1 | no | maximal |
| 17 | C3×GU(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 18 | C3×#585 | D3 | 1 | 1 | yes | characteristic |
| 19 | #5945 | — | 2 | 1 | no | — |
| 20 | #5945 | C2×C3 | 1 | 1 | yes | characteristic |
| 21 | C2×#984 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 22 | C2×C3×#137 | — | 3 | 1 | no | — |
| 23 | C2×C3×#137 | — | 3 | 1 | no | — |
| 24 | C3×#536 | — | 3 | 1 | no | — |
| 25 | #5430 | C2×C3 | 1 | 2 | yes | complemented |
| 26 | #5428 | C2×C3 | 1 | 2 | yes | complemented |
| 27 | #5423 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 28 | C3×#456 | — | 3 | 2 | no | — |
| 29 | C3×#456 | — | 3 | 2 | no | — |
| 30 | C3×#455 | — | 3 | 2 | no | — |
| 31 | C3×#455 | — | 3 | 2 | no | — |
| 32 | C3×#421 | — | 3 | 1 | no | — |
| 33 | C3×#421 | — | 3 | 1 | no | — |
| 34 | C3×#413 | — | 3 | 1 | no | — |
| 35 | C32×#41 | — | 4 | 1 | no | — |
| 36 | C2×C3×Dic6 | — | 4 | 1 | no | — |
| 37 | C3×#41⋊C3 | — | 2 | 1 | no | — |
| 38 | C3×#41⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 39 | C3×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 40 | C2×C3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 41 | C2×C3×SL(2,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 42 | C3×#226 | — | 2 | 2 | no | — |
| 43 | C3×#216 | — | 4 | 2 | no | — |
| 44 | C3×#214 | — | 4 | 2 | no | — |
| 45 | C3×#208 | — | 4 | 1 | no | — |
| 46 | #3022 | — | 3 | 1 | no | Sylow |
| 47 | C3×2−1+4 | — | 2 | 1 | no | — |
| 48 | C3×2−1+4 | — | 3 | 1 | no | — |
| 49 | C3×2−1+4 | C2×D3 | 1 | 1 | yes | characteristic |
| 50 | C3×H(5,𝔽2) | — | 3 | 1 | no | — |
| 51 | C3×H(5,𝔽2) | — | 6 | 1 | no | — |
| 52 | C3×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 53 | C2×C3×#41 | — | 2 | 1 | no | — |
| 54 | C2×C3×#41 | — | 3 | 1 | no | — |
| 55 | C2×C3×#41 | — | 3 | 1 | no | — |
| 56 | C2×C3×#41 | — | 6 | 1 | no | — |
| 57 | C2×C3×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 58 | C22×C3×Q8 | — | 3 | 1 | no | — |
| 59 | 2−1+4⋊C3 | — | 2 | 2 | no | — |
| 60 | 2−1+4⋊C3 | — | 2 | 1 | no | — |
| 61 | 2−1+4⋊C3 | — | 2 | 1 | no | — |
| 62 | 2−1+4⋊C3 | C22×C3 | 1 | 1 | yes | characteristic |
| 63 | #994 | — | 2 | 1 | no | — |
| 64 | #994 | C22×C3 | 1 | 1 | yes | characteristic |
| 65 | C2×#41⋊C3 | — | 2 | 2 | no | — |
| 66 | C2×#41⋊C3 | — | 2 | 1 | no | — |
| 67 | C2×#41⋊C3 | — | 2 | 1 | no | — |
| 68 | C2×#41⋊C3 | C22×C3 | 1 | 1 | yes | characteristic |
| 69 | #984 | — | 2 | 1 | no | — |
| 70 | #984 | C22×C3 | 1 | 2 | yes | complemented |
| 71 | C2×#226 | — | 2 | 1 | no | — |
| 72 | C3×#137 | — | 3 | 2 | no | — |
| 73 | C3×#137 | — | 3 | 2 | no | — |
| 74 | C3×#137 | — | 3 | 2 | no | — |
| 75 | C3×#137 | — | 3 | 2 | no | — |
| 76 | C3×#137 | — | 6 | 1 | no | — |
| 77 | C3×#137 | — | 6 | 1 | no | — |
| 78 | C3×#137 | — | 6 | 1 | no | — |
| 79 | C3×#137 | — | 6 | 1 | no | — |
| 80 | C2×C3×Q16 | — | 6 | 1 | no | — |
| 81 | C2×C3×Q16 | — | 6 | 1 | no | — |
| 82 | C2×C3×SD16 | — | 6 | 1 | no | — |
| 83 | C2×C3×SD16 | — | 6 | 1 | no | — |
| 84 | C2×C3×M16 | — | 3 | 1 | no | — |
| 85 | C2×C3×M16 | — | 3 | 1 | no | — |
| 86 | C3×C4⋊Q8 | — | 3 | 2 | no | — |
| 87 | C3×#124 | — | 3 | 2 | no | — |
| 88 | C3×#123 | — | 6 | 2 | no | — |
| 89 | C3×C22⋊Q8 | — | 6 | 2 | no | — |
| 90 | C3×#117 | — | 3 | 1 | no | — |
| 91 | #951 | — | 4 | 1 | no | — |
| 92 | GU(2,𝔽3) | C22×C3 | 1 | 2 | yes | complemented |
| 93 | C3×#104 | — | 3 | 2 | no | — |
| 94 | C3×#104 | — | 3 | 2 | no | — |
| 95 | C3×#104 | — | 3 | 2 | no | — |
| 96 | C3×#104 | — | 3 | 2 | no | — |
| 97 | C3×#101 | — | 3 | 2 | no | — |
| 98 | C3×#100 | — | 3 | 2 | no | — |
| 99 | C32×Q8 | — | 4 | 1 | no | — |
| 100 | C32×D4 | — | 4 | 1 | no | — |
| 101 | C32×D4 | — | 8 | 1 | no | — |
| 102 | C2×C32×C4 | — | 4 | 1 | no | — |
| 103 | C2×C32×C4 | — | 8 | 1 | no | — |
| 104 | C2×C3×Dic3 | — | 8 | 1 | no | — |
| 105 | C3×Dic6 | — | 4 | 2 | no | — |
| 106 | C3×Dic6 | — | 8 | 1 | no | — |
| 107 | C3×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 108 | C3×C3⋊C8 | — | 4 | 2 | no | — |
| 109 | #585 | C3×D3 | 1 | 1 | yes | characteristic |
| 110 | C2×#137 | — | 3 | 1 | no | — |
| 111 | C2×#137 | — | 3 | 1 | no | — |
| 112 | #536 | — | 3 | 1 | no | — |
| 113 | #456 | — | 3 | 2 | no | — |
| 114 | #456 | — | 3 | 2 | no | — |
| 115 | #455 | — | 3 | 2 | no | — |
| 116 | #455 | — | 3 | 2 | no | — |
| 117 | #421 | — | 3 | 1 | no | — |
| 118 | #421 | — | 3 | 1 | no | — |
| 119 | #413 | — | 3 | 1 | no | — |
| 120 | C3×#41 | — | 2 | 1 | no | — |
| 121 | C3×#41 | — | 3 | 1 | no | — |
| 122 | C3×#41 | — | 3 | 1 | no | — |
| 123 | C3×#41 | — | 3 | 1 | no | — |
| 124 | C3×#41 | — | 3 | 1 | no | — |
| 125 | C3×#41 | — | 3 | 1 | no | — |
| 126 | C3×#41 | — | 4 | 1 | no | — |
| 127 | C3×#41 | — | 6 | 1 | no | — |
| 128 | C3×#41 | — | 6 | 1 | no | — |
| 129 | C3×#41 | — | 6 | 1 | no | — |
| 130 | C3×#41 | — | 6 | 1 | no | — |
| 131 | C3×#41 | — | 6 | 2 | no | — |
| 132 | C3×#41 | — | 6 | 1 | no | — |
| 133 | C3×#41 | — | 6 | 1 | no | — |
| 134 | C3×#41 | — | 6 | 1 | no | — |
| 135 | C3×#41 | — | 6 | 1 | no | — |
| 136 | C3×#41 | — | 8 | 1 | no | — |
| 137 | C3×#41 | #67 | 1 | 1 | yes | characteristic |
| 138 | C3×#41 | S4 | 1 | 1 | yes | characteristic |
| 139 | C3×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 140 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 141 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 142 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 143 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 144 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 145 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 146 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 147 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 148 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 149 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 150 | C2×C3×Q8 | #67 | 1 | 1 | yes | characteristic |
| 151 | C2×C3×D4 | — | 3 | 1 | no | — |
| 152 | C2×C3×D4 | — | 3 | 1 | no | — |
| 153 | C2×C3×D4 | — | 3 | 1 | no | — |
| 154 | C2×C3×D4 | — | 3 | 2 | no | — |
| 155 | C2×C3×D4 | — | 6 | 1 | no | — |
| 156 | C2×C3×D4 | — | 6 | 1 | no | — |
| 157 | C2×C3×D4 | — | 6 | 1 | no | — |
| 158 | C2×C3×D4 | — | 6 | 2 | no | — |
| 159 | C22×C3×C4 | — | 3 | 1 | no | — |
| 160 | C22×C3×C4 | — | 3 | 2 | no | — |
| 161 | C22×C3×C4 | — | 6 | 1 | no | — |
| 162 | C22×C3×C4 | — | 6 | 1 | no | — |
| 163 | C2×Dic6 | — | 4 | 1 | no | — |
| 164 | #41⋊C3 | — | 2 | 2 | no | — |
| 165 | #41⋊C3 | — | 2 | 1 | no | — |
| 166 | #41⋊C3 | — | 2 | 1 | no | — |
| 167 | #41⋊C3 | — | 2 | 1 | no | — |
| 168 | #41⋊C3 | C3×D4 | 1 | 1 | yes | characteristic |
| 169 | #41⋊C3 | C23×C3 | 1 | 1 | yes | characteristic |
| 170 | C2×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 171 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 172 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 173 | C2×SL(2,𝔽3) | C3×D4 | 1 | 1 | yes | characteristic |
| 174 | #226 | — | 2 | 2 | no | — |
| 175 | C3×Q16 | — | 6 | 2 | no | — |
| 176 | C3×Q16 | — | 6 | 2 | no | — |
| 177 | C3×Q16 | — | 6 | 2 | no | — |
| 178 | C3×Q16 | — | 6 | 2 | no | — |
| 179 | C3×SD16 | — | 6 | 2 | no | — |
| 180 | C3×SD16 | — | 6 | 2 | no | — |
| 181 | C3×SD16 | — | 6 | 2 | no | — |
| 182 | C3×SD16 | — | 6 | 2 | no | — |
| 183 | C3×M16 | — | 3 | 2 | no | — |
| 184 | C3×M16 | — | 3 | 2 | no | — |
| 185 | C3×M16 | — | 6 | 1 | no | — |
| 186 | C3×M16 | — | 6 | 1 | no | — |
| 187 | C2×C3×C8 | — | 6 | 1 | no | — |
| 188 | C2×C3×C8 | — | 6 | 1 | no | — |
| 189 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 190 | C3×C4⋊C4 | — | 6 | 4 | no | — |
| 191 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 192 | C3×C22⋊C4 | — | 6 | 4 | no | — |
| 193 | C3×C42 | — | 3 | 2 | no | — |
| 194 | #216 | — | 4 | 2 | no | — |
| 195 | #214 | — | 4 | 2 | no | — |
| 196 | #208 | — | 4 | 1 | no | — |
| 197 | C22×C32 | — | 4 | 1 | no | — |
| 198 | C22×C32 | — | 8 | 1 | no | — |
| 199 | C32×C4 | — | 4 | 1 | no | — |
| 200 | C32×C4 | — | 4 | 1 | no | — |
| 201 | C32×C4 | — | 8 | 1 | no | — |
| 202 | C3×Dic3 | — | 8 | 2 | no | — |
| 203 | 2−1+4 | — | 2 | 1 | no | — |
| 204 | 2−1+4 | — | 3 | 1 | no | — |
| 205 | 2−1+4 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 206 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 207 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 208 | H(5,𝔽2) | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 209 | C2×#41 | — | 2 | 1 | no | — |
| 210 | C2×#41 | — | 3 | 1 | no | — |
| 211 | C2×#41 | — | 3 | 1 | no | — |
| 212 | C2×#41 | — | 6 | 1 | no | — |
| 213 | C2×#41 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 214 | C22×Q8 | — | 3 | 1 | no | — |
| 215 | #137 | — | 3 | 2 | no | — |
| 216 | #137 | — | 3 | 2 | no | — |
| 217 | #137 | — | 3 | 2 | no | — |
| 218 | #137 | — | 3 | 2 | no | — |
| 219 | #137 | — | 6 | 1 | no | — |
| 220 | #137 | — | 6 | 1 | no | — |
| 221 | #137 | — | 6 | 1 | no | — |
| 222 | #137 | — | 6 | 1 | no | — |
| 223 | C2×Q16 | — | 6 | 1 | no | — |
| 224 | C2×Q16 | — | 6 | 1 | no | — |
| 225 | C2×SD16 | — | 6 | 1 | no | — |
| 226 | C2×SD16 | — | 6 | 1 | no | — |
| 227 | C2×M16 | — | 3 | 1 | no | — |
| 228 | C2×M16 | — | 3 | 1 | no | — |
| 229 | C4⋊Q8 | — | 3 | 2 | no | — |
| 230 | #124 | — | 3 | 2 | no | — |
| 231 | #123 | — | 6 | 2 | no | — |
| 232 | C22⋊Q8 | — | 6 | 2 | no | — |
| 233 | #117 | — | 3 | 1 | no | — |
| 234 | #104 | — | 3 | 2 | no | — |
| 235 | #104 | — | 3 | 2 | no | — |
| 236 | #104 | — | 3 | 2 | no | — |
| 237 | #104 | — | 3 | 2 | no | — |
| 238 | #101 | — | 3 | 2 | no | — |
| 239 | #100 | — | 3 | 2 | no | — |
| 240 | C23×C3 | — | 3 | 1 | no | — |
| 241 | C23×C3 | — | 3 | 2 | no | — |
| 242 | C23×C3 | — | 6 | 1 | no | — |
| 243 | C3×Q8 | — | 3 | 1 | no | — |
| 244 | C3×Q8 | — | 3 | 1 | no | — |
| 245 | C3×Q8 | — | 4 | 1 | no | — |
| 246 | C3×Q8 | — | 6 | 1 | no | — |
| 247 | C3×Q8 | — | 6 | 1 | no | — |
| 248 | C3×Q8 | — | 6 | 2 | no | — |
| 249 | C3×Q8 | — | 6 | 2 | no | — |
| 250 | C3×Q8 | — | 8 | 1 | no | — |
| 251 | C3×Q8 | — | 12 | 1 | no | — |
| 252 | C3×Q8 | — | 12 | 1 | no | — |
| 253 | C3×Q8 | C2×#67 | 1 | 1 | yes | characteristic |
| 254 | C3×Q8 | C2×S4 | 1 | 1 | yes | characteristic |
| 255 | C3×D4 | — | 2 | 1 | no | — |
| 256 | C3×D4 | — | 3 | 1 | no | — |
| 257 | C3×D4 | — | 3 | 1 | no | — |
| 258 | C3×D4 | — | 3 | 1 | no | — |
| 259 | C3×D4 | — | 4 | 1 | no | — |
| 260 | C3×D4 | — | 6 | 1 | no | — |
| 261 | C3×D4 | — | 6 | 1 | no | — |
| 262 | C3×D4 | — | 6 | 1 | no | — |
| 263 | C3×D4 | — | 6 | 1 | no | — |
| 264 | C3×D4 | — | 6 | 1 | no | — |
| 265 | C3×D4 | — | 6 | 2 | no | — |
| 266 | C3×D4 | — | 6 | 1 | no | — |
| 267 | C3×D4 | — | 8 | 1 | no | — |
| 268 | C3×D4 | — | 8 | 2 | no | — |
| 269 | C3×D4 | — | 8 | 1 | no | — |
| 270 | C3×D4 | C2×S4 | 1 | 1 | yes | characteristic |
| 271 | C2×C3×C4 | — | 2 | 1 | no | — |
| 272 | C2×C3×C4 | — | 3 | 1 | no | — |
| 273 | C2×C3×C4 | — | 3 | 1 | no | — |
| 274 | C2×C3×C4 | — | 3 | 1 | no | — |
| 275 | C2×C3×C4 | — | 3 | 1 | no | — |
| 276 | C2×C3×C4 | — | 3 | 1 | no | — |
| 277 | C2×C3×C4 | — | 3 | 2 | no | — |
| 278 | C2×C3×C4 | — | 4 | 1 | no | — |
| 279 | C2×C3×C4 | — | 6 | 1 | no | — |
| 280 | C2×C3×C4 | — | 6 | 1 | no | — |
| 281 | C2×C3×C4 | — | 6 | 1 | no | — |
| 282 | C2×C3×C4 | — | 6 | 2 | no | — |
| 283 | C2×C3×C4 | — | 6 | 1 | no | — |
| 284 | C2×C3×C4 | — | 6 | 2 | no | — |
| 285 | C2×C3×C4 | — | 6 | 2 | no | — |
| 286 | C2×C3×C4 | — | 8 | 1 | no | — |
| 287 | C2×C3×C4 | — | 8 | 2 | no | — |
| 288 | C2×C3×C4 | — | 8 | 1 | no | — |
| 289 | C2×C3×C4 | — | 12 | 1 | no | — |
| 290 | C2×C3×C4 | — | 12 | 1 | no | — |
| 291 | C2×C3×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 292 | C2×Dic3 | — | 8 | 1 | no | — |
| 293 | Dic6 | — | 4 | 2 | no | — |
| 294 | Dic6 | — | 8 | 1 | no | — |
| 295 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 296 | SL(2,𝔽3) | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 297 | C3×C8 | — | 6 | 2 | no | — |
| 298 | C3×C8 | — | 6 | 2 | no | — |
| 299 | C3⋊C8 | — | 4 | 2 | no | — |
| 300 | C2×C32 | — | 4 | 1 | no | — |
| 301 | C2×C32 | — | 8 | 1 | no | — |
| 302 | C2×C32 | — | 16 | 1 | no | — |
| 303 | #41 | — | 2 | 1 | no | — |
| 304 | #41 | — | 3 | 1 | no | — |
| 305 | #41 | — | 3 | 1 | no | — |
| 306 | #41 | — | 3 | 1 | no | — |
| 307 | #41 | — | 3 | 1 | no | — |
| 308 | #41 | — | 3 | 1 | no | — |
| 309 | #41 | — | 6 | 1 | no | — |
| 310 | #41 | — | 6 | 1 | no | — |
| 311 | #41 | — | 6 | 1 | no | — |
| 312 | #41 | — | 6 | 1 | no | — |
| 313 | #41 | — | 6 | 2 | no | — |
| 314 | #41 | — | 6 | 1 | no | — |
| 315 | #41 | — | 6 | 1 | no | — |
| 316 | #41 | — | 6 | 1 | no | — |
| 317 | #41 | — | 6 | 1 | no | — |
| 318 | #41 | C3×#67 | 1 | 1 | yes | characteristic |
| 319 | #41 | C3×S4 | 1 | 1 | yes | characteristic |
| 320 | #41 | C22×C3×D3 | 1 | 1 | yes | characteristic |
| 321 | C2×Q8 | — | 2 | 1 | no | — |
| 322 | C2×Q8 | — | 3 | 1 | no | — |
| 323 | C2×Q8 | — | 3 | 1 | no | — |
| 324 | C2×Q8 | — | 3 | 2 | no | — |
| 325 | C2×Q8 | — | 6 | 1 | no | — |
| 326 | C2×Q8 | — | 6 | 1 | no | — |
| 327 | C2×Q8 | — | 6 | 1 | no | — |
| 328 | C2×Q8 | — | 6 | 1 | no | — |
| 329 | C2×Q8 | — | 6 | 1 | no | — |
| 330 | C2×Q8 | — | 6 | 1 | no | — |
| 331 | C2×Q8 | C3×#67 | 1 | 1 | yes | characteristic |
| 332 | C2×D4 | — | 3 | 1 | no | — |
| 333 | C2×D4 | — | 3 | 1 | no | — |
| 334 | C2×D4 | — | 3 | 1 | no | — |
| 335 | C2×D4 | — | 3 | 2 | no | — |
| 336 | C2×D4 | — | 6 | 1 | no | — |
| 337 | C2×D4 | — | 6 | 1 | no | — |
| 338 | C2×D4 | — | 6 | 1 | no | — |
| 339 | C2×D4 | — | 6 | 2 | no | — |
| 340 | C22×C4 | — | 3 | 1 | no | — |
| 341 | C22×C4 | — | 3 | 2 | no | — |
| 342 | C22×C4 | — | 6 | 1 | no | — |
| 343 | C22×C4 | — | 6 | 1 | no | — |
| 344 | Q16 | — | 6 | 2 | no | — |
| 345 | Q16 | — | 6 | 2 | no | — |
| 346 | Q16 | — | 6 | 2 | no | — |
| 347 | Q16 | — | 6 | 2 | no | — |
| 348 | SD16 | — | 6 | 2 | no | — |
| 349 | SD16 | — | 6 | 2 | no | — |
| 350 | SD16 | — | 6 | 2 | no | — |
| 351 | SD16 | — | 6 | 2 | no | — |
| 352 | M16 | — | 3 | 2 | no | — |
| 353 | M16 | — | 3 | 2 | no | — |
| 354 | M16 | — | 6 | 1 | no | — |
| 355 | M16 | — | 6 | 1 | no | — |
| 356 | C2×C8 | — | 6 | 1 | no | — |
| 357 | C2×C8 | — | 6 | 1 | no | — |
| 358 | C4⋊C4 | — | 6 | 1 | no | — |
| 359 | C4⋊C4 | — | 6 | 4 | no | — |
| 360 | C22⋊C4 | — | 6 | 1 | no | — |
| 361 | C22⋊C4 | — | 6 | 4 | no | — |
| 362 | C42 | — | 3 | 2 | no | — |
| 363 | C22×C3 | — | 2 | 1 | no | — |
| 364 | C22×C3 | — | 3 | 1 | no | — |
| 365 | C22×C3 | — | 3 | 1 | no | — |
| 366 | C22×C3 | — | 4 | 1 | no | — |
| 367 | C22×C3 | — | 6 | 1 | no | — |
| 368 | C22×C3 | — | 8 | 1 | no | — |
| 369 | C22×C3 | — | 8 | 2 | no | — |
| 370 | C22×C3 | — | 8 | 1 | no | — |
| 371 | C22×C3 | — | 12 | 1 | no | — |
| 372 | C22×C3 | — | 12 | 2 | no | — |
| 373 | C22×C3 | — | 24 | 1 | no | — |
| 374 | C22×C3 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 375 | C3×C4 | — | 2 | 1 | no | — |
| 376 | C3×C4 | — | 3 | 1 | no | — |
| 377 | C3×C4 | — | 3 | 1 | no | — |
| 378 | C3×C4 | — | 4 | 1 | no | — |
| 379 | C3×C4 | — | 4 | 1 | no | — |
| 380 | C3×C4 | — | 6 | 1 | no | — |
| 381 | C3×C4 | — | 8 | 1 | no | — |
| 382 | C3×C4 | — | 8 | 2 | no | — |
| 383 | C3×C4 | — | 8 | 1 | no | — |
| 384 | C3×C4 | — | 8 | 1 | no | — |
| 385 | C3×C4 | — | 12 | 2 | no | — |
| 386 | C3×C4 | — | 12 | 2 | no | — |
| 387 | C3×C4 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 388 | C3×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 389 | Dic3 | — | 8 | 2 | no | — |
| 390 | C32 | — | 4 | 1 | no | Sylow |
| 391 | C23 | — | 3 | 1 | no | — |
| 392 | C23 | — | 3 | 2 | no | — |
| 393 | C23 | — | 6 | 1 | no | — |
| 394 | Q8 | — | 3 | 1 | no | — |
| 395 | Q8 | — | 3 | 1 | no | — |
| 396 | Q8 | — | 6 | 1 | no | — |
| 397 | Q8 | — | 6 | 1 | no | — |
| 398 | Q8 | — | 6 | 2 | no | — |
| 399 | Q8 | — | 6 | 2 | no | — |
| 400 | Q8 | — | 12 | 1 | no | — |
| 401 | Q8 | — | 12 | 1 | no | — |
| 402 | Q8 | C2×C3×#67 | 1 | 1 | yes | characteristic |
| 403 | Q8 | C2×C3×S4 | 1 | 1 | yes | characteristic |
| 404 | D4 | — | 2 | 1 | no | — |
| 405 | D4 | — | 3 | 1 | no | — |
| 406 | D4 | — | 3 | 1 | no | — |
| 407 | D4 | — | 3 | 1 | no | — |
| 408 | D4 | — | 6 | 1 | no | — |
| 409 | D4 | — | 6 | 1 | no | — |
| 410 | D4 | — | 6 | 1 | no | — |
| 411 | D4 | — | 6 | 1 | no | — |
| 412 | D4 | — | 6 | 1 | no | — |
| 413 | D4 | — | 6 | 2 | no | — |
| 414 | D4 | — | 6 | 1 | no | — |
| 415 | D4 | C2×C3×S4 | 1 | 1 | yes | characteristic |
| 416 | C2×C4 | — | 2 | 1 | no | — |
| 417 | C2×C4 | — | 3 | 1 | no | — |
| 418 | C2×C4 | — | 3 | 1 | no | — |
| 419 | C2×C4 | — | 3 | 1 | no | — |
| 420 | C2×C4 | — | 3 | 1 | no | — |
| 421 | C2×C4 | — | 3 | 1 | no | — |
| 422 | C2×C4 | — | 3 | 2 | no | — |
| 423 | C2×C4 | — | 6 | 1 | no | — |
| 424 | C2×C4 | — | 6 | 1 | no | — |
| 425 | C2×C4 | — | 6 | 1 | no | — |
| 426 | C2×C4 | — | 6 | 2 | no | — |
| 427 | C2×C4 | — | 6 | 1 | no | — |
| 428 | C2×C4 | — | 6 | 2 | no | — |
| 429 | C2×C4 | — | 6 | 2 | no | — |
| 430 | C2×C4 | — | 12 | 1 | no | — |
| 431 | C2×C4 | — | 12 | 1 | no | — |
| 432 | C2×C4 | C2×C3×S4 | 1 | 1 | yes | characteristic |
| 433 | C8 | — | 6 | 2 | no | — |
| 434 | C8 | — | 6 | 2 | no | — |
| 435 | C2×C3 | — | 2 | 1 | no | — |
| 436 | C2×C3 | — | 4 | 1 | no | — |
| 437 | C2×C3 | — | 4 | 1 | no | — |
| 438 | C2×C3 | — | 6 | 1 | no | — |
| 439 | C2×C3 | — | 6 | 1 | no | — |
| 440 | C2×C3 | — | 8 | 1 | no | — |
| 441 | C2×C3 | — | 8 | 1 | no | — |
| 442 | C2×C3 | — | 12 | 1 | no | — |
| 443 | C2×C3 | — | 16 | 1 | no | — |
| 444 | C2×C3 | — | 16 | 1 | no | — |
| 445 | C2×C3 | — | 16 | 2 | no | — |
| 446 | C2×C3 | C2×GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 447 | C22 | — | 2 | 1 | no | — |
| 448 | C22 | — | 3 | 1 | no | — |
| 449 | C22 | — | 3 | 1 | no | — |
| 450 | C22 | — | 6 | 1 | no | — |
| 451 | C22 | — | 12 | 1 | no | — |
| 452 | C22 | — | 12 | 2 | no | — |
| 453 | C22 | — | 24 | 1 | no | — |
| 454 | C22 | C3×GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 455 | C4 | — | 2 | 1 | no | — |
| 456 | C4 | — | 3 | 1 | no | — |
| 457 | C4 | — | 3 | 1 | no | — |
| 458 | C4 | — | 6 | 1 | no | — |
| 459 | C4 | — | 12 | 2 | no | — |
| 460 | C4 | — | 12 | 2 | no | — |
| 461 | C4 | C3×GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 462 | C4 | C22×C3×S4 | 1 | 1 | yes | characteristic |
| 463 | C3 | — | 4 | 1 | no | — |
| 464 | C3 | — | 8 | 1 | no | — |
| 465 | C3 | #85542 | 1 | 1 | yes | characteristic, direct product factor |
| 466 | C2 | — | 2 | 1 | no | — |
| 467 | C2 | — | 4 | 1 | no | — |
| 468 | C2 | — | 6 | 1 | no | — |
| 469 | C2 | — | 6 | 1 | no | — |
| 470 | C2 | — | 12 | 1 | no | — |
| 471 | C2 | C2×C3×GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×#984 | C2 | semidirect |
| 3. C3×#5430 | C2 | semidirect |
| 4. C3×#5428 | C2 | semidirect |
| 5. C3×#5423 | C2 | semidirect |
| 6. #85542 | C3 | direct (N × H) |
| 14. C3×#984 | C22 | semidirect |
| 17. C3×GU(2,𝔽3) | C22 | semidirect |
| 21. C2×#984 | C2×C3 | semidirect |
| 25. #5430 | C2×C3 | semidirect |
| 26. #5428 | C2×C3 | semidirect |
| 27. #5423 | C2×C3 | semidirect |
| 70. #984 | C22×C3 | semidirect |
| 92. GU(2,𝔽3) | C22×C3 | semidirect |
| 465. C3 | #85542 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5945 | 2 |
| C2×C3×#984 | 2 |
| C3×#5430 | 2 |
| C3×#5428 | 2 |
| C3×#5423 | 2 |
| #85542 | 3 |
| C3×#3022 | 3 |
| C3×#951 | 4 |