Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
746 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 746 conjugacy classes of subgroups — too many to draw. Only its 111 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 | C2×#64287 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#64227 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#63931 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#63927 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #10593467 | C2 | 1 | 8 | yes | maximal, direct product factor |
| 6 | C2×#63733 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×#63728 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#63727 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#3830 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#3802 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#3797 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#3792 | — | 2 | 1 | no | — |
| 13 | C22×#622 | — | 2 | 1 | no | — |
| 14 | #64287 | — | 2 | 2 | no | — |
| 15 | #64287 | C22 | 1 | 4 | yes | complemented |
| 16 | C2×#3788 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#3787 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#3775 | — | 2 | 1 | no | — |
| 19 | C2×#3775 | — | 2 | 1 | no | — |
| 20 | #64227 | — | 2 | 2 | no | — |
| 21 | #64227 | C22 | 1 | 4 | yes | complemented |
| 22 | C2×C3×#214 | — | 2 | 1 | no | — |
| 23 | C2×C3×#213 | — | 2 | 1 | no | — |
| 24 | #63931 | — | 2 | 2 | no | — |
| 25 | #63931 | C22 | 1 | 4 | yes | complemented |
| 26 | #63927 | — | 2 | 2 | no | — |
| 27 | #63927 | C22 | 1 | 4 | yes | — |
| 28 | C2×#3719 | — | 2 | 1 | no | — |
| 29 | C2×#3716 | — | 2 | 1 | no | — |
| 30 | C2×#3712 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#3712 | C22 | 1 | 1 | yes | characteristic |
| 32 | #63733 | C22 | 1 | 4 | yes | complemented |
| 33 | #63728 | C22 | 1 | 4 | yes | complemented |
| 34 | #63727 | C22 | 1 | 4 | yes | complemented |
| 35 | C2×#915 | — | 6 | 1 | no | — |
| 36 | C2×#911 | — | 6 | 1 | no | — |
| 37 | C22×D32 | — | 2 | 1 | no | — |
| 38 | C2×C32×D4 | D4 | 1 | 1 | yes | characteristic |
| 39 | C2×#638 | — | 2 | 1 | no | — |
| 40 | C22×C3⋊Dic3 | — | 2 | 1 | no | — |
| 41 | #3830 | — | 2 | 1 | no | — |
| 42 | #3830 | — | 2 | 1 | no | — |
| 43 | #3830 | D4 | 1 | 2 | yes | — |
| 44 | #3830 | C23 | 1 | 2 | yes | — |
| 45 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 46 | C2×#634 | D4 | 1 | 1 | yes | characteristic |
| 47 | C2×C3×D12 | — | 2 | 1 | no | — |
| 48 | C2×C3×Dic6 | — | 2 | 1 | no | — |
| 49 | C2×#627 | — | 2 | 1 | no | — |
| 50 | C2×#625 | — | 2 | 1 | no | — |
| 51 | C2×#624 | — | 2 | 1 | no | — |
| 52 | #3802 | — | 2 | 1 | no | — |
| 53 | #3802 | — | 2 | 1 | no | — |
| 54 | #3802 | — | 2 | 1 | no | — |
| 55 | #3802 | C23 | 1 | 2 | yes | — |
| 56 | #3797 | — | 2 | 1 | no | — |
| 57 | #3797 | — | 2 | 1 | no | — |
| 58 | #3797 | — | 2 | 1 | no | — |
| 59 | #3797 | C23 | 1 | 2 | yes | — |
| 60 | #3792 | — | 2 | 4 | no | — |
| 61 | C2×#622 | — | 2 | 1 | no | — |
| 62 | C2×#622 | — | 2 | 4 | no | — |
| 63 | C2×#622 | D4 | 1 | 1 | yes | characteristic |
| 64 | C2×#622 | D4 | 1 | 1 | yes | characteristic |
| 65 | #3788 | — | 2 | 1 | no | — |
| 66 | #3788 | C23 | 1 | 2 | yes | — |
| 67 | #3787 | D4 | 1 | 2 | yes | — |
| 68 | #3787 | C23 | 1 | 2 | yes | — |
| 69 | #3775 | — | 2 | 4 | no | — |
| 70 | #3775 | — | 2 | 4 | no | — |
| 71 | C3×#214 | — | 2 | 4 | no | — |
| 72 | C3×#213 | — | 2 | 4 | no | — |
| 73 | C2×C3×C3⋊C8 | — | 2 | 1 | no | — |
| 74 | C2×C3×C3⋊C8 | — | 2 | 1 | no | — |
| 75 | #3719 | — | 2 | 4 | no | — |
| 76 | #3716 | — | 2 | 4 | no | — |
| 77 | #3712 | — | 2 | 1 | no | — |
| 78 | #3712 | — | 2 | 1 | no | — |
| 79 | #3712 | C23 | 1 | 2 | yes | — |
| 80 | #3712 | C23 | 1 | 2 | yes | — |
| 81 | C2×#471 | — | 9 | 1 | no | maximal, Sylow |
| 82 | C2×D3×Q8 | — | 6 | 1 | no | — |
| 83 | C2×#237 | — | 6 | 1 | no | — |
| 84 | C2×#237 | — | 6 | 1 | no | — |
| 85 | C2×D3×D4 | — | 6 | 1 | no | — |
| 86 | C2×C3×SD16 | — | 6 | 1 | no | — |
| 87 | C2×C3×D8 | — | 6 | 1 | no | — |
| 88 | C2×#216 | — | 6 | 1 | no | — |
| 89 | C2×#214 | — | 2 | 1 | no | — |
| 90 | C2×#214 | — | 6 | 1 | no | — |
| 91 | C2×#213 | — | 2 | 1 | no | — |
| 92 | #915 | — | 6 | 4 | no | — |
| 93 | #915 | — | 6 | 4 | no | — |
| 94 | #911 | — | 6 | 4 | no | — |
| 95 | #911 | — | 6 | 4 | no | — |
| 96 | C2×Dic12 | — | 6 | 1 | no | — |
| 97 | C2×#204 | — | 6 | 1 | no | — |
| 98 | C2×ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 99 | C2×ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 100 | C23×C32 | — | 2 | 1 | no | — |
| 101 | C22×C3⋊D3 | #41 | 1 | 1 | yes | characteristic |
| 102 | C22×C3×D3 | — | 4 | 1 | no | — |
| 103 | C2×D32 | — | 2 | 2 | no | — |
| 104 | C2×D32 | — | 4 | 1 | no | — |
| 105 | C2×D32 | — | 8 | 2 | no | — |
| 106 | C32×D4 | — | 2 | 1 | no | — |
| 107 | C32×D4 | C2×D4 | 1 | 2 | yes | — |
| 108 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | #638 | — | 2 | 2 | no | — |
| 110 | #638 | — | 2 | 2 | no | — |
| 111 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 112 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 113 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 114 | C2×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C4×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C4×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 117 | C4×C3⋊D3 | #41 | 1 | 1 | yes | characteristic |
| 118 | C4×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 119 | #634 | — | 2 | 1 | no | — |
| 120 | #634 | C2×D4 | 1 | 2 | yes | — |
| 121 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 122 | C3×D12 | — | 2 | 2 | no | — |
| 123 | C3×D12 | — | 4 | 1 | no | — |
| 124 | C3×Dic6 | — | 2 | 2 | no | — |
| 125 | C3×Dic6 | — | 4 | 1 | no | — |
| 126 | #627 | — | 2 | 2 | no | — |
| 127 | #627 | — | 4 | 1 | no | — |
| 128 | #625 | — | 2 | 2 | no | — |
| 129 | #625 | — | 4 | 1 | no | — |
| 130 | #624 | — | 2 | 2 | no | — |
| 131 | #624 | — | 4 | 1 | no | — |
| 132 | #622 | — | 2 | 2 | no | — |
| 133 | #622 | C2×D4 | 1 | 2 | yes | — |
| 134 | #622 | C2×D4 | 1 | 2 | yes | — |
| 135 | C3×C3⋊C8 | — | 2 | 2 | no | — |
| 136 | C3×C3⋊C8 | — | 2 | 2 | no | — |
| 137 | C2×#137 | — | 9 | 1 | no | — |
| 138 | C2×AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 139 | C22×SD16 | — | 9 | 1 | no | — |
| 140 | C2×#131 | — | 9 | 1 | no | — |
| 141 | #471 | — | 9 | 8 | no | — |
| 142 | C2×#108 | — | 9 | 1 | no | — |
| 143 | C2×#101 | — | 9 | 1 | no | — |
| 144 | C2×#100 | — | 9 | 1 | no | — |
| 145 | C23×D3 | — | 12 | 1 | no | — |
| 146 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 147 | C2×C3×D4 | — | 2 | 1 | no | — |
| 148 | C2×C3×D4 | — | 2 | 1 | no | — |
| 149 | C2×C3×D4 | — | 6 | 1 | no | — |
| 150 | C2×#67 | — | 12 | 1 | no | — |
| 151 | C2×#67 | — | 12 | 1 | no | — |
| 152 | C2×#67 | — | 12 | 1 | no | — |
| 153 | C22×Dic3 | — | 12 | 1 | no | — |
| 154 | C22×Dic3 | — | 12 | 1 | no | — |
| 155 | D3×Q8 | — | 6 | 2 | no | — |
| 156 | D3×Q8 | — | 6 | 2 | no | — |
| 157 | D3×Q8 | — | 12 | 1 | no | — |
| 158 | D3×Q8 | — | 12 | 1 | no | — |
| 159 | #237 | — | 6 | 2 | no | — |
| 160 | #237 | — | 6 | 2 | no | — |
| 161 | #237 | — | 6 | 2 | no | — |
| 162 | #237 | — | 6 | 2 | no | — |
| 163 | #237 | — | 12 | 1 | no | — |
| 164 | #237 | — | 12 | 1 | no | — |
| 165 | #237 | — | 12 | 1 | no | — |
| 166 | #237 | — | 12 | 1 | no | — |
| 167 | D3×D4 | — | 6 | 2 | no | — |
| 168 | D3×D4 | — | 6 | 2 | no | — |
| 169 | D3×D4 | — | 12 | 1 | no | — |
| 170 | D3×D4 | — | 12 | 1 | no | — |
| 171 | C2×D12 | — | 2 | 1 | no | — |
| 172 | C2×C4×D3 | — | 6 | 1 | no | — |
| 173 | C2×C4×D3 | — | 6 | 1 | no | — |
| 174 | C2×C4×D3 | — | 12 | 1 | no | — |
| 175 | C2×Dic6 | — | 2 | 1 | no | — |
| 176 | C2×Dic6 | — | 6 | 1 | no | — |
| 177 | C2×Dic6 | — | 6 | 1 | no | — |
| 178 | C2×Dic6 | — | 12 | 1 | no | — |
| 179 | C3×SD16 | — | 6 | 4 | no | — |
| 180 | C3×D8 | — | 6 | 4 | no | — |
| 181 | C2×C3×C8 | — | 6 | 1 | no | — |
| 182 | C2×C3×C8 | — | 6 | 1 | no | — |
| 183 | #216 | — | 6 | 4 | no | — |
| 184 | #214 | — | 2 | 4 | no | — |
| 185 | #214 | — | 6 | 4 | no | — |
| 186 | #213 | — | 2 | 4 | no | — |
| 187 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 188 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 189 | Dic12 | — | 6 | 4 | no | — |
| 190 | #204 | — | 6 | 4 | no | — |
| 191 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 192 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 193 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 194 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 195 | C22×C32 | — | 2 | 2 | no | — |
| 196 | C22×C32 | — | 4 | 2 | no | — |
| 197 | C22×C32 | #121 | 1 | 1 | yes | characteristic |
| 198 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 199 | C2×C3⋊D3 | #121 | 1 | 1 | yes | characteristic |
| 200 | C2×C3⋊D3 | C2×#41 | 1 | 1 | yes | characteristic |
| 201 | C2×C3×D3 | — | 4 | 2 | no | — |
| 202 | C2×C3×D3 | — | 8 | 2 | no | — |
| 203 | D32 | — | 8 | 2 | no | — |
| 204 | D32 | — | 8 | 2 | no | — |
| 205 | C32×C4 | #121 | 1 | 1 | yes | characteristic |
| 206 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 207 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 208 | C3⋊Dic3 | #121 | 1 | 1 | yes | characteristic |
| 209 | C3⋊Dic3 | C22×D4 | 1 | 1 | yes | characteristic |
| 210 | C3×Dic3 | — | 4 | 2 | no | — |
| 211 | C2×#41 | — | 9 | 1 | no | — |
| 212 | C22×Q8 | — | 9 | 1 | no | — |
| 213 | C22×D4 | — | 9 | 1 | no | — |
| 214 | #137 | — | 9 | 4 | no | — |
| 215 | #137 | — | 18 | 2 | no | — |
| 216 | AGL(1,ℤ/8) | — | 9 | 4 | no | — |
| 217 | AGL(1,ℤ/8) | — | 18 | 2 | no | — |
| 218 | C2×Q16 | — | 18 | 1 | no | — |
| 219 | C2×SD16 | — | 6 | 1 | no | — |
| 220 | C2×SD16 | — | 9 | 4 | no | — |
| 221 | C2×SD16 | — | 18 | 1 | no | — |
| 222 | C2×SD16 | — | 18 | 2 | no | — |
| 223 | C2×SD16 | — | 18 | 1 | no | — |
| 224 | C2×SD16 | — | 18 | 1 | no | — |
| 225 | C2×D8 | — | 6 | 1 | no | — |
| 226 | #131 | — | 9 | 4 | no | — |
| 227 | #131 | — | 18 | 2 | no | — |
| 228 | C2×M16 | — | 9 | 1 | no | — |
| 229 | C2×M16 | — | 9 | 1 | no | — |
| 230 | C2×M16 | — | 9 | 1 | no | — |
| 231 | C2×M16 | — | 18 | 1 | no | — |
| 232 | C22×C8 | — | 9 | 1 | no | — |
| 233 | C22×C8 | — | 18 | 1 | no | — |
| 234 | #108 | — | 9 | 4 | no | — |
| 235 | #101 | — | 9 | 4 | no | — |
| 236 | #100 | — | 9 | 4 | no | — |
| 237 | C23×C3 | — | 4 | 1 | no | — |
| 238 | C23×C3 | — | 4 | 1 | no | — |
| 239 | C23×C3 | — | 12 | 1 | no | — |
| 240 | C22×D3 | — | 4 | 1 | no | — |
| 241 | C22×D3 | — | 6 | 1 | no | — |
| 242 | C22×D3 | — | 6 | 1 | no | — |
| 243 | C22×D3 | — | 12 | 2 | no | — |
| 244 | C22×D3 | — | 12 | 2 | no | — |
| 245 | C22×D3 | — | 24 | 4 | no | — |
| 246 | C3×Q8 | — | 6 | 2 | no | — |
| 247 | C3×Q8 | — | 12 | 1 | no | — |
| 248 | C3×D4 | — | 2 | 2 | no | — |
| 249 | C3×D4 | — | 2 | 2 | no | — |
| 250 | C3×D4 | — | 4 | 1 | no | — |
| 251 | C3×D4 | — | 4 | 1 | no | — |
| 252 | C3×D4 | — | 6 | 2 | no | — |
| 253 | C3×D4 | — | 12 | 1 | no | — |
| 254 | C2×C3×C4 | — | 2 | 1 | no | — |
| 255 | C2×C3×C4 | — | 2 | 1 | no | — |
| 256 | C2×C3×C4 | — | 12 | 1 | no | — |
| 257 | #67 | — | 12 | 2 | no | — |
| 258 | #67 | — | 12 | 2 | no | — |
| 259 | #67 | — | 12 | 2 | no | — |
| 260 | #67 | — | 12 | 2 | no | — |
| 261 | #67 | — | 12 | 2 | no | — |
| 262 | #67 | — | 12 | 2 | no | — |
| 263 | C2×Dic3 | — | 4 | 1 | no | — |
| 264 | C2×Dic3 | — | 6 | 1 | no | — |
| 265 | C2×Dic3 | — | 6 | 1 | no | — |
| 266 | C2×Dic3 | — | 12 | 2 | no | — |
| 267 | C2×Dic3 | — | 12 | 2 | no | — |
| 268 | C2×Dic3 | — | 12 | 2 | no | — |
| 269 | C2×Dic3 | — | 12 | 2 | no | — |
| 270 | C2×Dic3 | — | 12 | 1 | no | — |
| 271 | C2×Dic3 | — | 12 | 1 | no | — |
| 272 | D12 | — | 2 | 2 | no | — |
| 273 | D12 | — | 4 | 1 | no | — |
| 274 | C4×D3 | — | 6 | 1 | no | — |
| 275 | C4×D3 | — | 6 | 1 | no | — |
| 276 | C4×D3 | — | 6 | 1 | no | — |
| 277 | C4×D3 | — | 6 | 1 | no | — |
| 278 | C4×D3 | — | 6 | 1 | no | — |
| 279 | C4×D3 | — | 6 | 1 | no | — |
| 280 | C4×D3 | — | 6 | 1 | no | — |
| 281 | C4×D3 | — | 6 | 1 | no | — |
| 282 | C4×D3 | — | 12 | 2 | no | — |
| 283 | C4×D3 | — | 12 | 2 | no | — |
| 284 | Dic6 | — | 2 | 2 | no | — |
| 285 | Dic6 | — | 4 | 1 | no | — |
| 286 | Dic6 | — | 6 | 2 | no | — |
| 287 | Dic6 | — | 6 | 2 | no | — |
| 288 | Dic6 | — | 12 | 2 | no | — |
| 289 | Dic6 | — | 12 | 1 | no | — |
| 290 | Dic6 | — | 12 | 1 | no | — |
| 291 | Dic6 | — | 12 | 2 | no | — |
| 292 | C3×C8 | — | 6 | 2 | no | — |
| 293 | C3×C8 | — | 6 | 2 | no | — |
| 294 | C3⋊C8 | — | 2 | 2 | no | — |
| 295 | C3⋊C8 | — | 2 | 2 | no | — |
| 296 | C2×C32 | — | 4 | 2 | no | — |
| 297 | C2×C32 | #471 | 1 | 2 | yes | complemented |
| 298 | C2×C32 | C2×#121 | 1 | 1 | yes | characteristic |
| 299 | C3⋊D3 | — | 2 | 1 | no | — |
| 300 | C3⋊D3 | — | 2 | 1 | no | — |
| 301 | C3×D3 | — | 8 | 2 | no | — |
| 302 | C24 | — | 18 | 1 | no | — |
| 303 | #41 | — | 9 | 2 | no | — |
| 304 | #41 | — | 9 | 2 | no | — |
| 305 | #41 | — | 18 | 1 | no | — |
| 306 | #41 | — | 18 | 1 | no | — |
| 307 | C2×Q8 | — | 6 | 1 | no | — |
| 308 | C2×Q8 | — | 9 | 2 | no | — |
| 309 | C2×Q8 | — | 9 | 1 | no | — |
| 310 | C2×Q8 | — | 18 | 1 | no | — |
| 311 | C2×Q8 | — | 18 | 1 | no | — |
| 312 | C2×Q8 | — | 18 | 1 | no | — |
| 313 | C2×Q8 | — | 18 | 1 | no | — |
| 314 | C2×D4 | — | 6 | 1 | no | — |
| 315 | C2×D4 | — | 9 | 2 | no | — |
| 316 | C2×D4 | — | 18 | 1 | no | — |
| 317 | C2×D4 | — | 18 | 1 | no | — |
| 318 | C2×D4 | — | 18 | 1 | no | — |
| 319 | C2×D4 | — | 18 | 1 | no | — |
| 320 | C2×D4 | — | 18 | 1 | no | — |
| 321 | C2×D4 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 322 | C22×C4 | — | 9 | 1 | no | — |
| 323 | C22×C4 | — | 18 | 1 | no | — |
| 324 | C22×C4 | — | 18 | 1 | no | — |
| 325 | Q16 | — | 18 | 4 | no | — |
| 326 | SD16 | — | 6 | 4 | no | — |
| 327 | SD16 | — | 18 | 4 | no | — |
| 328 | SD16 | — | 18 | 4 | no | — |
| 329 | SD16 | — | 18 | 4 | no | — |
| 330 | D8 | — | 6 | 4 | no | — |
| 331 | M16 | — | 9 | 2 | no | — |
| 332 | M16 | — | 9 | 2 | no | — |
| 333 | M16 | — | 9 | 2 | no | — |
| 334 | M16 | — | 18 | 1 | no | — |
| 335 | M16 | — | 18 | 1 | no | — |
| 336 | M16 | — | 18 | 4 | no | — |
| 337 | M16 | — | 18 | 1 | no | — |
| 338 | C2×C8 | — | 6 | 1 | no | — |
| 339 | C2×C8 | — | 6 | 1 | no | — |
| 340 | C2×C8 | — | 9 | 2 | no | — |
| 341 | C2×C8 | — | 9 | 1 | no | — |
| 342 | C2×C8 | — | 9 | 1 | no | — |
| 343 | C2×C8 | — | 9 | 2 | no | — |
| 344 | C2×C8 | — | 18 | 4 | no | — |
| 345 | C2×C8 | — | 18 | 1 | no | — |
| 346 | C22×C3 | — | 2 | 1 | no | — |
| 347 | C22×C3 | — | 2 | 1 | no | — |
| 348 | C22×C3 | — | 4 | 2 | no | — |
| 349 | C22×C3 | — | 4 | 2 | no | — |
| 350 | C22×C3 | — | 8 | 2 | no | — |
| 351 | C22×C3 | — | 8 | 2 | no | — |
| 352 | C22×C3 | — | 12 | 2 | no | — |
| 353 | C22×C3 | — | 24 | 2 | no | — |
| 354 | C2×D3 | — | 4 | 2 | no | — |
| 355 | C2×D3 | — | 6 | 1 | no | — |
| 356 | C2×D3 | — | 6 | 1 | no | — |
| 357 | C2×D3 | — | 6 | 1 | no | — |
| 358 | C2×D3 | — | 6 | 1 | no | — |
| 359 | C2×D3 | — | 8 | 2 | no | — |
| 360 | C2×D3 | — | 12 | 2 | no | — |
| 361 | C2×D3 | — | 12 | 2 | no | — |
| 362 | C2×D3 | — | 24 | 4 | no | — |
| 363 | C2×D3 | — | 24 | 4 | no | — |
| 364 | C3×C4 | — | 2 | 1 | no | — |
| 365 | C3×C4 | — | 2 | 1 | no | — |
| 366 | C3×C4 | — | 2 | 1 | no | — |
| 367 | C3×C4 | — | 2 | 1 | no | — |
| 368 | C3×C4 | — | 12 | 2 | no | — |
| 369 | Dic3 | — | 4 | 2 | no | — |
| 370 | Dic3 | — | 6 | 1 | no | — |
| 371 | Dic3 | — | 6 | 1 | no | — |
| 372 | Dic3 | — | 6 | 1 | no | — |
| 373 | Dic3 | — | 6 | 1 | no | — |
| 374 | Dic3 | — | 12 | 2 | no | — |
| 375 | Dic3 | — | 12 | 2 | no | — |
| 376 | C32 | C2×#471 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 377 | C23 | — | 2 | 1 | no | — |
| 378 | C23 | — | 9 | 1 | no | — |
| 379 | C23 | — | 12 | 1 | no | — |
| 380 | C23 | — | 18 | 2 | no | — |
| 381 | C23 | — | 36 | 1 | no | — |
| 382 | C23 | — | 72 | 2 | no | — |
| 383 | Q8 | — | 6 | 2 | no | — |
| 384 | Q8 | — | 9 | 2 | no | — |
| 385 | Q8 | — | 12 | 1 | no | — |
| 386 | Q8 | — | 18 | 2 | no | — |
| 387 | Q8 | — | 18 | 1 | no | — |
| 388 | Q8 | — | 36 | 1 | no | — |
| 389 | D4 | — | 2 | 1 | no | — |
| 390 | D4 | — | 6 | 2 | no | — |
| 391 | D4 | — | 12 | 1 | no | — |
| 392 | D4 | — | 18 | 2 | no | — |
| 393 | D4 | — | 18 | 2 | no | — |
| 394 | D4 | — | 18 | 2 | no | — |
| 395 | D4 | — | 36 | 1 | no | — |
| 396 | D4 | C2×GO+(4,𝔽2) | 1 | 2 | yes | — |
| 397 | C2×C4 | — | 9 | 1 | no | — |
| 398 | C2×C4 | — | 9 | 1 | no | — |
| 399 | C2×C4 | — | 9 | 1 | no | — |
| 400 | C2×C4 | — | 9 | 1 | no | — |
| 401 | C2×C4 | — | 9 | 1 | no | — |
| 402 | C2×C4 | — | 12 | 1 | no | — |
| 403 | C2×C4 | — | 18 | 2 | no | — |
| 404 | C2×C4 | — | 18 | 2 | no | — |
| 405 | C2×C4 | — | 18 | 2 | no | — |
| 406 | C2×C4 | — | 18 | 1 | no | — |
| 407 | C2×C4 | — | 36 | 1 | no | — |
| 408 | C2×C4 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 409 | C8 | — | 6 | 2 | no | — |
| 410 | C8 | — | 6 | 2 | no | — |
| 411 | C8 | — | 9 | 2 | no | — |
| 412 | C8 | — | 9 | 2 | no | — |
| 413 | C8 | — | 18 | 2 | no | — |
| 414 | C2×C3 | — | 2 | 1 | no | — |
| 415 | C2×C3 | — | 2 | 1 | no | — |
| 416 | C2×C3 | — | 2 | 2 | no | — |
| 417 | C2×C3 | — | 2 | 2 | no | — |
| 418 | C2×C3 | — | 8 | 2 | no | — |
| 419 | C2×C3 | — | 8 | 2 | no | — |
| 420 | C2×C3 | — | 24 | 2 | no | — |
| 421 | D3 | — | 8 | 2 | no | — |
| 422 | D3 | — | 12 | 1 | no | — |
| 423 | D3 | — | 12 | 1 | no | — |
| 424 | D3 | — | 12 | 1 | no | — |
| 425 | D3 | — | 12 | 1 | no | — |
| 426 | C22 | — | 2 | 2 | no | — |
| 427 | C22 | — | 4 | 2 | no | — |
| 428 | C22 | — | 9 | 1 | no | — |
| 429 | C22 | — | 9 | 1 | no | — |
| 430 | C22 | — | 12 | 2 | no | — |
| 431 | C22 | — | 18 | 2 | no | — |
| 432 | C22 | — | 24 | 2 | no | — |
| 433 | C22 | — | 72 | 2 | no | — |
| 434 | C22 | — | 72 | 2 | no | — |
| 435 | C22 | #64242 | 1 | 1 | yes | characteristic |
| 436 | C4 | — | 9 | 1 | no | — |
| 437 | C4 | — | 9 | 1 | no | — |
| 438 | C4 | — | 12 | 2 | no | — |
| 439 | C4 | — | 18 | 2 | no | — |
| 440 | C4 | #64242 | 1 | 1 | yes | characteristic |
| 441 | C4 | C22×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 442 | C3 | — | 2 | 1 | no | — |
| 443 | C3 | — | 2 | 1 | no | — |
| 444 | C2 | — | 4 | 2 | no | — |
| 445 | C2 | — | 18 | 1 | no | — |
| 446 | C2 | — | 18 | 1 | no | — |
| 447 | C2 | — | 24 | 2 | no | — |
| 448 | C2 | #10593467 | 1 | 2 | yes | direct product factor |
| 449 | C2 | C2×#64242 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#64287 | C2 | semidirect |
| 2. C2×#64227 | C2 | semidirect |
| 3. C2×#63931 | C2 | semidirect |
| 5. #10593467 | C2 | direct (N × H) |
| 6. C2×#63733 | C2 | semidirect |
| 7. C2×#63728 | C2 | semidirect |
| 8. C2×#63727 | C2 | semidirect |
| 15. #64287 | C22 | semidirect |
| 21. #64227 | C22 | semidirect |
| 25. #63931 | C22 | semidirect |
| 32. #63733 | C22 | semidirect |
| 33. #63728 | C22 | semidirect |
| 34. #63727 | C22 | semidirect |
| 297. C2×C32 | #471 | semidirect |
| 376. C32 | C2×#471 | semidirect |
| 448. C2 | #10593467 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64287 | 2 |
| C2×#64227 | 2 |
| C2×#63931 | 2 |
| C2×#63927 | 2 |
| #10593467 | 2 |
| C2×#63733 | 2 |
| C2×#63728 | 2 |
| C2×#63727 | 2 |
| C2×#471 | 9 |