Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1612 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 1612 conjugacy classes of subgroups — too many to draw. Only its 204 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×#5966 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10595154 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #10592942 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#5244 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10591534 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #10591530 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #10591528 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #84125 | — | 3 | 1 | no | maximal |
| 9 | #80304 | — | 3 | 1 | no | maximal |
| 10 | C32×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 11 | C3×#1010 | — | 2 | 3 | no | — |
| 12 | C3×D3×#41 | — | 2 | 3 | no | — |
| 13 | C3×#1004 | — | 2 | 3 | no | — |
| 14 | C3×#1004 | C22 | 1 | 3 | yes | — |
| 15 | C2×C3×#237 | — | 2 | 3 | no | — |
| 16 | C2×C3×#237 | C22 | 1 | 3 | yes | — |
| 17 | C22×D3×Dic3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #64144 | C22 | 1 | 3 | yes | complemented |
| 19 | C3×#937 | C22 | 1 | 3 | yes | complemented |
| 20 | #63976 | C22 | 1 | 3 | yes | complemented |
| 21 | Dic3×#67 | — | 2 | 3 | no | — |
| 22 | #63970 | — | 2 | 3 | no | — |
| 23 | #63962 | C22 | 1 | 3 | yes | complemented |
| 24 | #63955 | C22 | 1 | 3 | yes | complemented |
| 25 | #63887 | — | 2 | 3 | no | — |
| 26 | #63879 | — | 2 | 3 | no | — |
| 27 | #63661 | C22 | 1 | 3 | yes | complemented |
| 28 | C3×#834 | C22 | 1 | 3 | yes | complemented |
| 29 | #63580 | C22 | 1 | 6 | yes | complemented |
| 30 | C3×#585 | — | 3 | 1 | no | — |
| 31 | #5966 | D3 | 1 | 1 | yes | characteristic, complemented |
| 32 | #5828 | — | 3 | 3 | no | — |
| 33 | #5586 | — | 3 | 3 | no | — |
| 34 | C3×B(4,𝔽2) | — | 3 | 1 | no | — |
| 35 | #5244 | — | 3 | 3 | no | — |
| 36 | #5244 | D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | #5243 | — | 3 | 1 | no | — |
| 38 | #5243 | — | 3 | 1 | no | — |
| 39 | #5243 | — | 3 | 3 | no | — |
| 40 | #5243 | — | 6 | 1 | no | — |
| 41 | #5240 | — | 3 | 3 | no | — |
| 42 | #5032 | — | 3 | 3 | no | — |
| 43 | #4742 | — | 3 | 3 | no | — |
| 44 | #4740 | — | 3 | 3 | no | — |
| 45 | C23×C3×D3 | C23 | 1 | 1 | yes | characteristic |
| 46 | C32×#41 | — | 2 | 3 | no | — |
| 47 | C2×C32×D4 | — | 2 | 3 | no | — |
| 48 | C2×C32×D4 | C23 | 1 | 3 | yes | — |
| 49 | C22×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 50 | C2×C3×#67 | — | 2 | 3 | no | — |
| 51 | C2×C3×#67 | — | 2 | 3 | no | — |
| 52 | C2×C3×#67 | — | 2 | 3 | no | — |
| 53 | C2×C3×#67 | D4 | 1 | 3 | yes | complemented |
| 54 | C2×C3×#67 | C23 | 1 | 3 | yes | — |
| 55 | C22×C3×Dic3 | — | 2 | 1 | no | — |
| 56 | C22×C3×Dic3 | D4 | 1 | 3 | yes | complemented |
| 57 | C22×C3×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 58 | C3×#239 | — | 2 | 1 | no | — |
| 59 | C3×D3×Q8 | — | 2 | 3 | no | — |
| 60 | C3×#237 | — | 2 | 3 | no | — |
| 61 | C3×#237 | — | 2 | 6 | no | — |
| 62 | C3×#237 | — | 2 | 6 | no | — |
| 63 | C3×#237 | — | 2 | 6 | no | — |
| 64 | C3×#237 | — | 2 | 6 | no | — |
| 65 | C3×D3×D4 | — | 2 | 3 | no | — |
| 66 | C3×D3×D4 | — | 2 | 6 | no | — |
| 67 | C3×#235 | — | 2 | 6 | no | — |
| 68 | C3×#235 | — | 2 | 3 | no | — |
| 69 | C2×C3×C4×D3 | — | 2 | 3 | no | — |
| 70 | C2×C3×C4×D3 | D4 | 1 | 3 | yes | complemented |
| 71 | C2×C3×Dic6 | — | 2 | 3 | no | — |
| 72 | C2×C3×Dic6 | D4 | 1 | 3 | yes | complemented |
| 73 | C2×#625 | — | 2 | 3 | no | — |
| 74 | C2×D3×Dic3 | — | 2 | 3 | no | — |
| 75 | C2×D3×Dic3 | — | 2 | 3 | no | — |
| 76 | #3757 | — | 2 | 3 | no | — |
| 77 | #3757 | C23 | 1 | 3 | yes | — |
| 78 | #3750 | — | 2 | 3 | no | — |
| 79 | C3×#217 | C23 | 1 | 3 | yes | — |
| 80 | C3×(C2×D3)⋊C4 | — | 2 | 3 | no | — |
| 81 | Dic3⋊Dic3 | — | 2 | 3 | no | — |
| 82 | Dic3⋊Dic3 | — | 2 | 3 | no | — |
| 83 | (C2×D3)⋊Dic3 | — | 2 | 3 | no | — |
| 84 | (C2×D3)⋊Dic3 | — | 2 | 3 | no | — |
| 85 | Dic32 | — | 2 | 3 | no | — |
| 86 | #3025 | — | 9 | 1 | no | Sylow |
| 87 | C3×2−1+4 | — | 6 | 3 | no | — |
| 88 | C3×H(5,𝔽2) | — | 2 | 1 | no | — |
| 89 | C3×H(5,𝔽2) | — | 3 | 3 | no | — |
| 90 | C3×H(5,𝔽2) | — | 6 | 3 | no | — |
| 91 | C3×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 92 | C3×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 93 | C2×C3×#41 | — | 3 | 3 | no | — |
| 94 | C2×C3×#41 | — | 6 | 3 | no | — |
| 95 | C2×C3×#41 | — | 6 | 3 | no | — |
| 96 | C23×Dic3 | — | 3 | 1 | no | — |
| 97 | #1010 | — | 2 | 3 | no | — |
| 98 | D3×#41 | — | 2 | 3 | no | — |
| 99 | #1004 | — | 2 | 3 | no | — |
| 100 | #1004 | C2×D3 | 1 | 3 | yes | — |
| 101 | C2×#237 | — | 2 | 3 | no | — |
| 102 | C2×#237 | C2×D3 | 1 | 3 | yes | — |
| 103 | C22×C4×D3 | — | 3 | 1 | no | — |
| 104 | C3×#120 | — | 3 | 3 | no | — |
| 105 | #953 | — | 3 | 3 | no | — |
| 106 | #946 | — | 6 | 3 | no | — |
| 107 | #939 | — | 6 | 3 | no | — |
| 108 | #938 | — | 6 | 3 | no | — |
| 109 | #937 | — | 3 | 3 | no | — |
| 110 | #937 | C2×D3 | 1 | 3 | yes | complemented |
| 111 | #935 | — | 3 | 3 | no | — |
| 112 | #935 | — | 3 | 3 | no | — |
| 113 | #935 | — | 3 | 3 | no | — |
| 114 | #935 | — | 6 | 3 | no | — |
| 115 | D4×Dic3 | — | 6 | 3 | no | — |
| 116 | C4×#67 | — | 6 | 3 | no | — |
| 117 | C4×#67 | — | 6 | 3 | no | — |
| 118 | #926 | — | 3 | 3 | no | — |
| 119 | #886 | — | 3 | 3 | no | — |
| 120 | #67⋊C4 | — | 6 | 3 | no | — |
| 121 | #878 | — | 6 | 3 | no | — |
| 122 | #877 | — | 3 | 3 | no | — |
| 123 | C3×#99 | — | 3 | 3 | no | — |
| 124 | #834 | — | 3 | 3 | no | — |
| 125 | #834 | — | 3 | 3 | no | — |
| 126 | #834 | — | 3 | 6 | no | — |
| 127 | #834 | — | 6 | 3 | no | — |
| 128 | #834 | C2×D3 | 1 | 3 | yes | complemented |
| 129 | #806 | — | 3 | 6 | no | — |
| 130 | C23×C32 | — | 2 | 1 | no | — |
| 131 | C23×C32 | C2×D4 | 1 | 3 | yes | — |
| 132 | C23×C32 | C24 | 1 | 1 | yes | characteristic |
| 133 | C22×C3×D3 | — | 2 | 3 | no | — |
| 134 | C22×C3×D3 | — | 2 | 3 | no | — |
| 135 | C22×C3×D3 | — | 4 | 2 | no | — |
| 136 | C22×C3×D3 | C2×D4 | 1 | 3 | yes | — |
| 137 | C32×Q8 | — | 2 | 1 | no | — |
| 138 | C32×D4 | — | 2 | 3 | no | — |
| 139 | C32×D4 | — | 2 | 6 | no | — |
| 140 | C2×C32×C4 | — | 2 | 3 | no | — |
| 141 | C2×C32×C4 | C2×D4 | 1 | 3 | yes | — |
| 142 | C2×C3⋊Dic3 | — | 2 | 3 | no | — |
| 143 | C2×C3⋊Dic3 | — | 2 | 3 | no | — |
| 144 | C3×#67 | — | 2 | 6 | no | — |
| 145 | C3×#67 | — | 2 | 6 | no | — |
| 146 | C3×#67 | — | 2 | 6 | no | — |
| 147 | C3×#67 | — | 4 | 6 | no | — |
| 148 | C2×C3×Dic3 | — | 2 | 3 | no | — |
| 149 | C2×C3×Dic3 | — | 2 | 3 | no | — |
| 150 | C2×C3×Dic3 | — | 2 | 3 | no | — |
| 151 | C2×C3×Dic3 | — | 2 | 3 | no | — |
| 152 | C2×C3×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 153 | C2×C3×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 154 | C2×C3×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 155 | C3×D12 | — | 2 | 3 | no | — |
| 156 | C3×C4×D3 | — | 2 | 6 | no | — |
| 157 | C3×C4×D3 | — | 2 | 3 | no | — |
| 158 | C3×C4×D3 | — | 2 | 3 | no | — |
| 159 | C3×Dic6 | — | 2 | 3 | no | — |
| 160 | C3×Dic6 | — | 2 | 6 | no | — |
| 161 | #625 | — | 4 | 6 | no | — |
| 162 | D3×Dic3 | — | 4 | 3 | no | — |
| 163 | D3×Dic3 | — | 4 | 1 | no | — |
| 164 | #585 | — | 3 | 1 | no | — |
| 165 | #525 | — | 9 | 3 | no | — |
| 166 | #458 | — | 9 | 3 | no | — |
| 167 | #458 | — | 9 | 1 | no | — |
| 168 | B(4,𝔽2) | — | 3 | 1 | no | — |
| 169 | B(4,𝔽2) | — | 9 | 3 | no | — |
| 170 | #410 | — | 9 | 3 | no | — |
| 171 | C24×C3 | — | 3 | 1 | no | — |
| 172 | C23×D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 173 | C3×#41 | — | 2 | 3 | no | — |
| 174 | C3×#41 | — | 2 | 3 | no | — |
| 175 | C3×#41 | — | 4 | 3 | no | — |
| 176 | C3×#41 | — | 6 | 6 | no | — |
| 177 | C3×#41 | — | 6 | 6 | no | — |
| 178 | C3×#41 | — | 6 | 6 | no | — |
| 179 | C3×#41 | — | 6 | 6 | no | — |
| 180 | C3×#41 | — | 6 | 3 | no | — |
| 181 | C3×#41 | — | 6 | 6 | no | — |
| 182 | C3×#41 | — | 6 | 1 | no | — |
| 183 | C3×#41 | — | 6 | 3 | no | — |
| 184 | C2×C3×Q8 | — | 3 | 3 | no | — |
| 185 | C2×C3×Q8 | — | 6 | 3 | no | — |
| 186 | C2×C3×Q8 | — | 6 | 3 | no | — |
| 187 | C2×C3×D4 | — | 2 | 3 | no | — |
| 188 | C2×C3×D4 | — | 2 | 3 | no | — |
| 189 | C2×C3×D4 | — | 2 | 3 | no | — |
| 190 | C2×C3×D4 | — | 3 | 3 | no | — |
| 191 | C2×C3×D4 | — | 3 | 3 | no | — |
| 192 | C2×C3×D4 | — | 4 | 3 | no | — |
| 193 | C2×C3×D4 | — | 6 | 6 | no | — |
| 194 | C2×C3×D4 | — | 6 | 3 | no | — |
| 195 | C2×C3×D4 | — | 6 | 3 | no | — |
| 196 | C2×C3×D4 | — | 6 | 3 | no | — |
| 197 | C2×C3×D4 | — | 6 | 3 | no | — |
| 198 | C2×C3×D4 | C22×D3 | 1 | 3 | yes | — |
| 199 | C2×C3×D4 | C22×D3 | 1 | 3 | yes | — |
| 200 | C22×C3×C4 | — | 3 | 1 | no | — |
| 201 | C22×C3×C4 | — | 3 | 3 | no | — |
| 202 | C22×C3×C4 | — | 3 | 3 | no | — |
| 203 | C22×C3×C4 | — | 6 | 3 | no | — |
| 204 | C22×C3×C4 | — | 6 | 1 | no | — |
| 205 | C2×#67 | — | 2 | 3 | no | — |
| 206 | C2×#67 | — | 2 | 3 | no | — |
| 207 | C2×#67 | — | 2 | 3 | no | — |
| 208 | C2×#67 | — | 6 | 3 | no | — |
| 209 | C2×#67 | — | 6 | 3 | no | — |
| 210 | C2×#67 | #67 | 1 | 3 | yes | complemented |
| 211 | C2×#67 | C22×D3 | 1 | 3 | yes | — |
| 212 | C22×Dic3 | — | 2 | 1 | no | — |
| 213 | C22×Dic3 | — | 3 | 1 | no | — |
| 214 | C22×Dic3 | — | 3 | 1 | no | — |
| 215 | C22×Dic3 | — | 6 | 1 | no | — |
| 216 | C22×Dic3 | — | 6 | 3 | no | — |
| 217 | C22×Dic3 | — | 6 | 3 | no | — |
| 218 | C22×Dic3 | #67 | 1 | 3 | yes | complemented |
| 219 | C22×Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 220 | #239 | — | 2 | 1 | no | — |
| 221 | D3×Q8 | — | 2 | 3 | no | — |
| 222 | #237 | — | 2 | 3 | no | — |
| 223 | #237 | — | 2 | 6 | no | — |
| 224 | #237 | — | 2 | 6 | no | — |
| 225 | #237 | — | 2 | 6 | no | — |
| 226 | #237 | — | 2 | 6 | no | — |
| 227 | D3×D4 | — | 2 | 3 | no | — |
| 228 | D3×D4 | — | 2 | 6 | no | — |
| 229 | #235 | — | 2 | 6 | no | — |
| 230 | #235 | — | 2 | 3 | no | — |
| 231 | C2×C4×D3 | — | 2 | 3 | no | — |
| 232 | C2×C4×D3 | — | 6 | 3 | no | — |
| 233 | C2×C4×D3 | — | 6 | 3 | no | — |
| 234 | C2×C4×D3 | #67 | 1 | 3 | yes | complemented |
| 235 | C2×Dic6 | — | 2 | 3 | no | — |
| 236 | C2×Dic6 | #67 | 1 | 3 | yes | complemented |
| 237 | C3×C22⋊C4 | — | 3 | 3 | no | — |
| 238 | C3×C22⋊C4 | — | 6 | 3 | no | — |
| 239 | #217 | — | 3 | 3 | no | — |
| 240 | #217 | — | 3 | 3 | no | — |
| 241 | #217 | — | 6 | 3 | no | — |
| 242 | #217 | — | 6 | 3 | no | — |
| 243 | #217 | — | 6 | 3 | no | — |
| 244 | #217 | — | 6 | 3 | no | — |
| 245 | #217 | — | 6 | 3 | no | — |
| 246 | #217 | — | 12 | 3 | no | — |
| 247 | #217 | C22×D3 | 1 | 3 | yes | — |
| 248 | (C2×D3)⋊C4 | — | 2 | 3 | no | — |
| 249 | (C2×D3)⋊C4 | — | 6 | 3 | no | — |
| 250 | (C2×D3)⋊C4 | — | 6 | 3 | no | — |
| 251 | C4⋊Dic3 | — | 6 | 3 | no | — |
| 252 | C4⋊Dic3 | — | 6 | 3 | no | — |
| 253 | Dic3⋊C4 | — | 6 | 3 | no | — |
| 254 | Dic3⋊C4 | — | 6 | 3 | no | — |
| 255 | Dic3⋊C4 | — | 6 | 3 | no | — |
| 256 | Dic3⋊C4 | — | 6 | 3 | no | — |
| 257 | Dic3⋊C4 | — | 12 | 3 | no | — |
| 258 | C4×Dic3 | — | 6 | 3 | no | — |
| 259 | C4×Dic3 | — | 6 | 3 | no | — |
| 260 | C22×C32 | — | 2 | 3 | no | — |
| 261 | C22×C32 | — | 4 | 1 | no | — |
| 262 | C22×C32 | — | 4 | 3 | no | — |
| 263 | C22×C32 | — | 8 | 1 | no | — |
| 264 | C22×C32 | C22×D4 | 1 | 3 | yes | — |
| 265 | C2×C3×D3 | — | 2 | 6 | no | — |
| 266 | C2×C3×D3 | — | 2 | 3 | no | — |
| 267 | C2×C3×D3 | — | 4 | 3 | no | — |
| 268 | C2×C3×D3 | — | 4 | 1 | no | — |
| 269 | C2×C3×D3 | — | 4 | 3 | no | — |
| 270 | C2×C3×D3 | — | 8 | 3 | no | — |
| 271 | C32×C4 | — | 2 | 3 | no | — |
| 272 | C3⋊Dic3 | — | 4 | 3 | no | — |
| 273 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 274 | C3×Dic3 | — | 2 | 3 | no | — |
| 275 | C3×Dic3 | — | 4 | 3 | no | — |
| 276 | C3×Dic3 | #120 | 1 | 3 | yes | — |
| 277 | C3×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 278 | 2−1+4 | — | 6 | 3 | no | — |
| 279 | H(5,𝔽2) | — | 3 | 3 | no | — |
| 280 | H(5,𝔽2) | — | 6 | 3 | no | — |
| 281 | H(5,𝔽2) | D32 | 1 | 1 | yes | characteristic |
| 282 | C2×#41 | — | 3 | 3 | no | — |
| 283 | C2×#41 | — | 6 | 3 | no | — |
| 284 | C2×#41 | — | 6 | 3 | no | — |
| 285 | C23×C4 | — | 9 | 1 | no | — |
| 286 | #123 | — | 9 | 3 | no | — |
| 287 | #123 | — | 9 | 3 | no | — |
| 288 | C22⋊Q8 | — | 18 | 3 | no | — |
| 289 | #121 | — | 18 | 3 | no | — |
| 290 | #120 | — | 3 | 3 | no | — |
| 291 | #120 | — | 9 | 3 | no | — |
| 292 | C4×D4 | — | 18 | 3 | no | — |
| 293 | C4×D4 | — | 18 | 3 | no | — |
| 294 | #117 | — | 9 | 3 | no | — |
| 295 | #99 | — | 3 | 3 | no | — |
| 296 | #99 | — | 9 | 6 | no | — |
| 297 | #99 | — | 9 | 3 | no | — |
| 298 | C23×C3 | — | 2 | 1 | no | — |
| 299 | C23×C3 | — | 2 | 1 | no | — |
| 300 | C23×C3 | — | 2 | 1 | no | — |
| 301 | C23×C3 | — | 2 | 3 | no | — |
| 302 | C23×C3 | — | 3 | 3 | no | — |
| 303 | C23×C3 | — | 4 | 1 | no | — |
| 304 | C23×C3 | — | 6 | 3 | no | — |
| 305 | C23×C3 | — | 6 | 3 | no | — |
| 306 | C23×C3 | — | 12 | 2 | no | — |
| 307 | C23×C3 | D3×D4 | 1 | 3 | yes | — |
| 308 | C23×C3 | C2×#67 | 1 | 3 | yes | — |
| 309 | C23×C3 | C23×D3 | 1 | 1 | yes | characteristic |
| 310 | C23×C3 | C23×D3 | 1 | 1 | yes | characteristic |
| 311 | C22×D3 | — | 2 | 3 | no | — |
| 312 | C22×D3 | — | 2 | 3 | no | — |
| 313 | C22×D3 | — | 4 | 2 | no | — |
| 314 | C22×D3 | C2×#67 | 1 | 3 | yes | — |
| 315 | C3×Q8 | — | 2 | 1 | no | — |
| 316 | C3×Q8 | — | 2 | 1 | no | — |
| 317 | C3×Q8 | — | 4 | 1 | no | — |
| 318 | C3×Q8 | — | 6 | 6 | no | — |
| 319 | C3×Q8 | — | 6 | 3 | no | — |
| 320 | C3×D4 | — | 2 | 3 | no | — |
| 321 | C3×D4 | — | 2 | 3 | no | — |
| 322 | C3×D4 | — | 2 | 6 | no | — |
| 323 | C3×D4 | — | 2 | 6 | no | — |
| 324 | C3×D4 | — | 4 | 6 | no | — |
| 325 | C3×D4 | — | 4 | 3 | no | — |
| 326 | C3×D4 | — | 6 | 3 | no | — |
| 327 | C3×D4 | — | 6 | 6 | no | — |
| 328 | C3×D4 | — | 6 | 6 | no | — |
| 329 | C3×D4 | — | 6 | 6 | no | — |
| 330 | C3×D4 | — | 12 | 6 | no | — |
| 331 | C2×C3×C4 | — | 2 | 3 | no | — |
| 332 | C2×C3×C4 | — | 2 | 3 | no | — |
| 333 | C2×C3×C4 | — | 2 | 3 | no | — |
| 334 | C2×C3×C4 | — | 3 | 3 | no | — |
| 335 | C2×C3×C4 | — | 3 | 3 | no | — |
| 336 | C2×C3×C4 | — | 3 | 3 | no | — |
| 337 | C2×C3×C4 | — | 4 | 3 | no | — |
| 338 | C2×C3×C4 | — | 6 | 3 | no | — |
| 339 | C2×C3×C4 | — | 6 | 3 | no | — |
| 340 | C2×C3×C4 | — | 6 | 6 | no | — |
| 341 | C2×C3×C4 | — | 6 | 3 | no | — |
| 342 | C2×C3×C4 | — | 6 | 3 | no | — |
| 343 | C2×C3×C4 | — | 6 | 3 | no | — |
| 344 | C2×C3×C4 | — | 6 | 3 | no | — |
| 345 | C2×C3×C4 | D3×D4 | 1 | 3 | yes | — |
| 346 | C2×C3×C4 | C2×#67 | 1 | 3 | yes | — |
| 347 | #67 | — | 2 | 6 | no | — |
| 348 | #67 | — | 2 | 6 | no | — |
| 349 | #67 | — | 2 | 6 | no | — |
| 350 | #67 | — | 4 | 6 | no | — |
| 351 | #67 | — | 12 | 6 | no | — |
| 352 | #67 | — | 12 | 6 | no | — |
| 353 | C2×Dic3 | — | 2 | 3 | no | — |
| 354 | C2×Dic3 | — | 2 | 3 | no | — |
| 355 | C2×Dic3 | — | 2 | 3 | no | — |
| 356 | C2×Dic3 | — | 2 | 3 | no | — |
| 357 | C2×Dic3 | — | 6 | 3 | no | — |
| 358 | C2×Dic3 | — | 6 | 3 | no | — |
| 359 | C2×Dic3 | — | 6 | 3 | no | — |
| 360 | C2×Dic3 | — | 6 | 3 | no | — |
| 361 | C2×Dic3 | — | 12 | 3 | no | — |
| 362 | C2×Dic3 | — | 12 | 3 | no | — |
| 363 | C2×Dic3 | — | 12 | 3 | no | — |
| 364 | C2×Dic3 | — | 12 | 1 | no | — |
| 365 | C2×Dic3 | C2×#67 | 1 | 3 | yes | — |
| 366 | C2×Dic3 | C2×#67 | 1 | 3 | yes | — |
| 367 | C2×Dic3 | C2×#67 | 1 | 3 | yes | — |
| 368 | D12 | — | 2 | 3 | no | — |
| 369 | C4×D3 | — | 2 | 6 | no | — |
| 370 | C4×D3 | — | 2 | 3 | no | — |
| 371 | C4×D3 | — | 2 | 3 | no | — |
| 372 | C4×D3 | — | 12 | 1 | no | — |
| 373 | C4×D3 | — | 12 | 3 | no | — |
| 374 | Dic6 | — | 2 | 3 | no | — |
| 375 | Dic6 | — | 2 | 6 | no | — |
| 376 | C2×C32 | — | 2 | 3 | no | — |
| 377 | C2×C32 | — | 4 | 3 | no | — |
| 378 | C2×C32 | C2×#120 | 1 | 1 | yes | characteristic |
| 379 | C3×D3 | — | 4 | 2 | no | — |
| 380 | C3×D3 | — | 4 | 3 | no | — |
| 381 | C24 | — | 3 | 1 | no | — |
| 382 | #41 | — | 2 | 3 | no | — |
| 383 | #41 | — | 6 | 6 | no | — |
| 384 | #41 | — | 6 | 6 | no | — |
| 385 | #41 | — | 6 | 6 | no | — |
| 386 | #41 | — | 6 | 6 | no | — |
| 387 | #41 | — | 6 | 3 | no | — |
| 388 | #41 | — | 6 | 6 | no | — |
| 389 | #41 | — | 6 | 1 | no | — |
| 390 | #41 | — | 6 | 3 | no | — |
| 391 | C2×Q8 | — | 3 | 3 | no | — |
| 392 | C2×Q8 | — | 6 | 3 | no | — |
| 393 | C2×Q8 | — | 6 | 3 | no | — |
| 394 | C2×D4 | — | 2 | 3 | no | — |
| 395 | C2×D4 | — | 3 | 3 | no | — |
| 396 | C2×D4 | — | 3 | 3 | no | — |
| 397 | C2×D4 | — | 6 | 6 | no | — |
| 398 | C2×D4 | — | 6 | 3 | no | — |
| 399 | C2×D4 | — | 6 | 3 | no | — |
| 400 | C2×D4 | — | 6 | 3 | no | — |
| 401 | C2×D4 | — | 6 | 3 | no | — |
| 402 | C2×D4 | — | 18 | 3 | no | — |
| 403 | C2×D4 | C2×D32 | 1 | 3 | yes | — |
| 404 | C22×C4 | — | 3 | 1 | no | — |
| 405 | C22×C4 | — | 3 | 3 | no | — |
| 406 | C22×C4 | — | 3 | 3 | no | — |
| 407 | C22×C4 | — | 6 | 3 | no | — |
| 408 | C22×C4 | — | 6 | 1 | no | — |
| 409 | C22×C4 | — | 9 | 1 | no | — |
| 410 | C22×C4 | — | 18 | 3 | no | — |
| 411 | C22×C4 | — | 18 | 3 | no | — |
| 412 | C4⋊C4 | — | 18 | 3 | no | — |
| 413 | C4⋊C4 | — | 18 | 3 | no | — |
| 414 | C4⋊C4 | — | 18 | 3 | no | — |
| 415 | C22⋊C4 | — | 3 | 3 | no | — |
| 416 | C22⋊C4 | — | 6 | 3 | no | — |
| 417 | C22⋊C4 | — | 9 | 3 | no | — |
| 418 | C22⋊C4 | — | 18 | 3 | no | — |
| 419 | C22⋊C4 | — | 18 | 3 | no | — |
| 420 | C22⋊C4 | — | 18 | 3 | no | — |
| 421 | C42 | — | 18 | 3 | no | — |
| 422 | C22×C3 | — | 2 | 3 | no | — |
| 423 | C22×C3 | — | 2 | 3 | no | — |
| 424 | C22×C3 | — | 2 | 3 | no | — |
| 425 | C22×C3 | — | 4 | 3 | no | — |
| 426 | C22×C3 | — | 4 | 1 | no | — |
| 427 | C22×C3 | — | 4 | 1 | no | — |
| 428 | C22×C3 | — | 4 | 3 | no | — |
| 429 | C22×C3 | — | 4 | 3 | no | — |
| 430 | C22×C3 | — | 6 | 6 | no | — |
| 431 | C22×C3 | — | 6 | 3 | no | — |
| 432 | C22×C3 | — | 8 | 1 | no | — |
| 433 | C22×C3 | — | 8 | 3 | no | — |
| 434 | C22×C3 | — | 8 | 1 | no | — |
| 435 | C22×C3 | — | 8 | 1 | no | — |
| 436 | C22×C3 | — | 12 | 3 | no | — |
| 437 | C22×C3 | — | 12 | 3 | no | — |
| 438 | C22×C3 | — | 12 | 1 | no | — |
| 439 | C22×C3 | — | 16 | 1 | no | — |
| 440 | C22×C3 | — | 24 | 3 | no | — |
| 441 | C22×C3 | C2×D3×D4 | 1 | 3 | yes | — |
| 442 | C22×C3 | C22×#67 | 1 | 3 | yes | — |
| 443 | C2×D3 | — | 2 | 6 | no | — |
| 444 | C2×D3 | — | 2 | 3 | no | — |
| 445 | C2×D3 | — | 4 | 3 | no | — |
| 446 | C2×D3 | — | 4 | 1 | no | — |
| 447 | C2×D3 | — | 4 | 3 | no | — |
| 448 | C2×D3 | — | 8 | 3 | no | — |
| 449 | C3×C4 | — | 2 | 3 | no | — |
| 450 | C3×C4 | — | 2 | 3 | no | — |
| 451 | C3×C4 | — | 3 | 1 | no | — |
| 452 | C3×C4 | — | 3 | 3 | no | — |
| 453 | C3×C4 | — | 4 | 3 | no | — |
| 454 | C3×C4 | — | 6 | 3 | no | — |
| 455 | C3×C4 | — | 12 | 3 | no | — |
| 456 | Dic3 | — | 2 | 3 | no | — |
| 457 | Dic3 | — | 4 | 3 | no | — |
| 458 | Dic3 | — | 12 | 3 | no | — |
| 459 | Dic3 | — | 12 | 3 | no | — |
| 460 | Dic3 | — | 12 | 1 | no | — |
| 461 | Dic3 | — | 12 | 1 | no | — |
| 462 | Dic3 | — | 24 | 1 | no | — |
| 463 | Dic3 | — | 24 | 3 | no | — |
| 464 | Dic3 | #953 | 1 | 3 | yes | — |
| 465 | Dic3 | #953 | 1 | 1 | yes | characteristic |
| 466 | C32 | #3025 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 467 | C23 | — | 2 | 1 | no | — |
| 468 | C23 | — | 3 | 3 | no | — |
| 469 | C23 | — | 6 | 3 | no | — |
| 470 | C23 | — | 6 | 3 | no | — |
| 471 | C23 | — | 12 | 2 | no | — |
| 472 | C23 | D3×#67 | 1 | 3 | yes | — |
| 473 | C23 | C22×D32 | 1 | 1 | yes | characteristic |
| 474 | Q8 | — | 2 | 1 | no | — |
| 475 | Q8 | — | 6 | 6 | no | — |
| 476 | Q8 | — | 6 | 3 | no | — |
| 477 | D4 | — | 2 | 3 | no | — |
| 478 | D4 | — | 2 | 6 | no | — |
| 479 | D4 | — | 6 | 3 | no | — |
| 480 | D4 | — | 6 | 6 | no | — |
| 481 | D4 | — | 6 | 6 | no | — |
| 482 | D4 | — | 6 | 6 | no | — |
| 483 | D4 | — | 12 | 6 | no | — |
| 484 | D4 | — | 36 | 6 | no | — |
| 485 | C2×C4 | — | 2 | 3 | no | — |
| 486 | C2×C4 | — | 3 | 3 | no | — |
| 487 | C2×C4 | — | 3 | 3 | no | — |
| 488 | C2×C4 | — | 3 | 3 | no | — |
| 489 | C2×C4 | — | 6 | 3 | no | — |
| 490 | C2×C4 | — | 6 | 3 | no | — |
| 491 | C2×C4 | — | 6 | 6 | no | — |
| 492 | C2×C4 | — | 6 | 3 | no | — |
| 493 | C2×C4 | — | 6 | 3 | no | — |
| 494 | C2×C4 | — | 6 | 3 | no | — |
| 495 | C2×C4 | — | 6 | 3 | no | — |
| 496 | C2×C4 | — | 18 | 3 | no | — |
| 497 | C2×C4 | — | 18 | 3 | no | — |
| 498 | C2×C4 | — | 36 | 1 | no | — |
| 499 | C2×C4 | — | 36 | 3 | no | — |
| 500 | C2×C4 | D3×#67 | 1 | 3 | yes | — |
| 501 | C2×C3 | — | 2 | 3 | no | — |
| 502 | C2×C3 | — | 2 | 3 | no | — |
| 503 | C2×C3 | — | 2 | 1 | no | — |
| 504 | C2×C3 | — | 4 | 3 | no | — |
| 505 | C2×C3 | — | 4 | 3 | no | — |
| 506 | C2×C3 | — | 4 | 3 | no | — |
| 507 | C2×C3 | — | 8 | 3 | no | — |
| 508 | C2×C3 | — | 12 | 2 | no | — |
| 509 | C2×C3 | — | 12 | 3 | no | — |
| 510 | C2×C3 | D3×#120 | 1 | 1 | yes | characteristic |
| 511 | C2×C3 | C2×#953 | 1 | 1 | yes | characteristic |
| 512 | D3 | — | 4 | 3 | no | — |
| 513 | D3 | — | 4 | 2 | no | — |
| 514 | C22 | — | 2 | 3 | no | — |
| 515 | C22 | — | 4 | 1 | no | — |
| 516 | C22 | — | 4 | 3 | no | — |
| 517 | C22 | — | 6 | 6 | no | — |
| 518 | C22 | — | 6 | 3 | no | — |
| 519 | C22 | — | 8 | 1 | no | — |
| 520 | C22 | — | 12 | 3 | no | — |
| 521 | C22 | — | 12 | 3 | no | — |
| 522 | C22 | — | 12 | 1 | no | — |
| 523 | C22 | — | 24 | 3 | no | — |
| 524 | C22 | C2×D3×#67 | 1 | 3 | yes | — |
| 525 | C4 | — | 2 | 3 | no | — |
| 526 | C4 | — | 3 | 1 | no | — |
| 527 | C4 | — | 3 | 3 | no | — |
| 528 | C4 | — | 6 | 3 | no | — |
| 529 | C4 | — | 12 | 3 | no | — |
| 530 | C4 | — | 36 | 3 | no | — |
| 531 | C4 | — | 36 | 1 | no | — |
| 532 | C3 | — | 2 | 1 | no | — |
| 533 | C3 | #80304 | 1 | 1 | yes | characteristic, complemented |
| 534 | C3 | #84125 | 1 | 1 | yes | characteristic, complemented |
| 535 | C2 | — | 2 | 3 | no | — |
| 536 | C2 | — | 4 | 3 | no | — |
| 537 | C2 | — | 12 | 2 | no | — |
| 538 | C2 | — | 12 | 3 | no | — |
| 539 | C2 | D3×#953 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#5966 | C2 | semidirect |
| 2. #10595154 | C2 | semidirect |
| 3. #10592942 | C2 | semidirect |
| 4. C3×#5244 | C2 | semidirect |
| 5. #10591534 | C2 | semidirect |
| 6. #10591530 | C2 | semidirect |
| 7. #10591528 | C2 | semidirect |
| 17. C22×D3×Dic3 | C22 | semidirect |
| 18. #64144 | C22 | semidirect |
| 19. C3×#937 | C22 | semidirect |
| 20. #63976 | C22 | semidirect |
| 23. #63962 | C22 | semidirect |
| 24. #63955 | C22 | semidirect |
| 27. #63661 | C22 | semidirect |
| 28. C3×#834 | C22 | semidirect |
| 29. #63580 | C22 | semidirect |
| 31. #5966 | D3 | semidirect |
| 36. #5244 | D3 | semidirect |
| 53. C2×C3×#67 | D4 | semidirect |
| 56. C22×C3×Dic3 | D4 | semidirect |
| 70. C2×C3×C4×D3 | D4 | semidirect |
| 72. C2×C3×Dic6 | D4 | semidirect |
| 110. #937 | C2×D3 | semidirect |
| 128. #834 | C2×D3 | semidirect |
| 210. C2×#67 | #67 | semidirect |
| 218. C22×Dic3 | #67 | semidirect |
| 234. C2×C4×D3 | #67 | semidirect |
| 236. C2×Dic6 | #67 | semidirect |
| 466. C32 | #3025 | semidirect |
| 533. C3 | #80304 | semidirect |
| 534. C3 | #84125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5966 | 2 |
| #10595154 | 2 |
| #10592942 | 2 |
| C3×#5244 | 2 |
| #10591534 | 2 |
| #10591530 | 2 |
| #10591528 | 2 |
| #84125 | 3 |
| #80304 | 3 |