Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1436 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 1436 conjugacy classes of subgroups — too many to draw. Only its 124 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 | C22×#157⋊D3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×D3×GO+(4,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11724440 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11724330 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C3×#64242 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #67×#157 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11724124 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11724118 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11724116 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11724113 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #11724111 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | D4×GO+(4,𝔽2) | — | 3 | 1 | no | maximal |
| 13 | C22×#1113 | C22 | 1 | 2 | yes | complemented |
| 14 | C22×C3×#157 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C2×D33 | C22 | 1 | 2 | yes | complemented |
| 16 | C2×#157⋊D3 | — | 2 | 4 | no | — |
| 17 | C2×#157⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#157⋊D3 | C22 | 1 | 2 | yes | complemented |
| 19 | C2×#157⋊D3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C2×D32⋊D3 | C22 | 1 | 2 | yes | complemented |
| 21 | C2×D32⋊D3 | C22 | 1 | 2 | yes | complemented |
| 22 | C2×C3×GO+(4,𝔽2) | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C2×D3×#157 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | D3×GO+(4,𝔽2) | — | 2 | 4 | no | — |
| 25 | C3⋊D3×#67 | — | 2 | 2 | no | — |
| 26 | C3⋊D3×#67 | C22 | 1 | 1 | yes | characteristic |
| 27 | C3×#3811 | — | 2 | 2 | no | — |
| 28 | C3×#3811 | C22 | 1 | 2 | yes | complemented |
| 29 | #88994 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #88955 | — | 2 | 2 | no | — |
| 31 | #88955 | C22 | 1 | 2 | yes | complemented |
| 32 | #88953 | — | 2 | 2 | no | — |
| 33 | #88953 | C22 | 1 | 2 | yes | complemented |
| 34 | #88949 | C22 | 1 | 2 | yes | complemented |
| 35 | #88932 | C22 | 1 | 2 | yes | complemented |
| 36 | #88932 | C22 | 1 | 2 | yes | complemented |
| 37 | C3×#3773 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | C3×D32⋊C4 | C22 | 1 | 2 | yes | complemented |
| 39 | Dic3⋊#157 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | (C2×D3)⋊#157 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | Dic3×#157 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | C22×GO+(4,𝔽2) | — | 3 | 1 | no | — |
| 43 | C22×GO+(4,𝔽2) | — | 3 | 1 | no | — |
| 44 | D32×D4 | — | 3 | 2 | no | — |
| 45 | D32×D4 | — | 6 | 2 | no | — |
| 46 | D4×#157 | — | 3 | 1 | no | — |
| 47 | #64242 | — | 3 | 1 | no | — |
| 48 | #64242 | D3 | 1 | 1 | yes | characteristic, complemented |
| 49 | #64241 | — | 3 | 2 | no | — |
| 50 | #64241 | — | 3 | 2 | no | — |
| 51 | #64231 | — | 3 | 1 | no | — |
| 52 | #64230 | — | 3 | 2 | no | — |
| 53 | C4×GO+(4,𝔽2) | — | 3 | 1 | no | — |
| 54 | C22×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 55 | C22×C3×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 56 | C2×#1113 | — | 2 | 4 | no | — |
| 57 | C2×#1113 | — | 2 | 2 | no | — |
| 58 | C2×#1113 | — | 4 | 2 | no | — |
| 59 | C2×#1113 | C23 | 1 | 2 | yes | — |
| 60 | C2×#1113 | C23 | 1 | 2 | yes | — |
| 61 | C2×D3×C3⋊D3 | — | 2 | 2 | no | — |
| 62 | C2×D3×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 63 | C2×C3×D32 | — | 2 | 2 | no | — |
| 64 | C2×C3×D32 | C23 | 1 | 2 | yes | — |
| 65 | C2×C3⋊#157 | C23 | 1 | 1 | yes | characteristic |
| 66 | C2×C3⋊#157 | C23 | 1 | 1 | yes | characteristic |
| 67 | C2×C3×#157 | — | 2 | 2 | no | — |
| 68 | C2×C3×#157 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×C3×#157 | C23 | 1 | 1 | yes | characteristic |
| 70 | D33 | — | 2 | 4 | no | — |
| 71 | D33 | — | 4 | 2 | no | — |
| 72 | #157⋊D3 | — | 2 | 4 | no | — |
| 73 | #157⋊D3 | — | 2 | 2 | no | — |
| 74 | #157⋊D3 | D4 | 1 | 4 | yes | complemented |
| 75 | D32⋊D3 | — | 2 | 4 | no | — |
| 76 | D32⋊D3 | — | 4 | 2 | no | — |
| 77 | C3×GO+(4,𝔽2) | — | 2 | 2 | no | — |
| 78 | D3×#157 | — | 2 | 2 | no | — |
| 79 | #6312 | D4 | 1 | 1 | yes | characteristic, complemented |
| 80 | C32×#67 | — | 2 | 2 | no | — |
| 81 | C32×#67 | D4 | 1 | 1 | yes | characteristic, complemented |
| 82 | #6292 | — | 2 | 2 | no | — |
| 83 | #6292 | D4 | 1 | 1 | yes | characteristic, complemented |
| 84 | #6290 | — | 2 | 2 | no | — |
| 85 | #6290 | D4 | 1 | 1 | yes | characteristic, complemented |
| 86 | Dic3×C3⋊D3 | — | 2 | 2 | no | — |
| 87 | Dic3×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 88 | C3×#626 | — | 2 | 2 | no | — |
| 89 | C3×#626 | — | 2 | 2 | no | — |
| 90 | C3×#626 | — | 2 | 2 | no | — |
| 91 | C3×#624 | — | 2 | 2 | no | — |
| 92 | C3×#624 | C23 | 1 | 2 | yes | — |
| 93 | #5609 | — | 9 | 1 | no | maximal |
| 94 | C22×D32 | — | 3 | 2 | no | — |
| 95 | C22×D32 | — | 3 | 2 | no | — |
| 96 | C22×D32 | — | 6 | 2 | no | — |
| 97 | C22×D32 | — | 6 | 2 | no | — |
| 98 | C22×#157 | — | 3 | 1 | no | — |
| 99 | C22×#157 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 100 | C2×GO+(4,𝔽2) | — | 3 | 1 | no | — |
| 101 | C2×GO+(4,𝔽2) | — | 3 | 2 | no | — |
| 102 | C2×GO+(4,𝔽2) | — | 3 | 2 | no | — |
| 103 | C2×GO+(4,𝔽2) | — | 3 | 1 | no | — |
| 104 | C2×GO+(4,𝔽2) | — | 3 | 2 | no | — |
| 105 | C2×GO+(4,𝔽2) | — | 6 | 4 | no | — |
| 106 | C2×GO+(4,𝔽2) | — | 6 | 4 | no | — |
| 107 | C2×GO+(4,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 108 | D4×C3⋊D3 | — | 3 | 1 | no | — |
| 109 | D4×C3⋊D3 | — | 6 | 2 | no | — |
| 110 | C3×D3×D4 | — | 6 | 2 | no | — |
| 111 | C3×D3×D4 | — | 6 | 2 | no | — |
| 112 | C3×D3×D4 | — | 6 | 2 | no | — |
| 113 | #3811 | — | 2 | 2 | no | — |
| 114 | #3811 | — | 3 | 2 | no | — |
| 115 | #3811 | — | 6 | 2 | no | — |
| 116 | #3811 | C2×D3 | 1 | 2 | yes | complemented |
| 117 | D3×#67 | — | 6 | 2 | no | — |
| 118 | D3×#67 | — | 6 | 2 | no | — |
| 119 | D3×#67 | — | 6 | 2 | no | — |
| 120 | D3×#67 | — | 6 | 2 | no | — |
| 121 | D3×#67 | — | 6 | 2 | no | — |
| 122 | D3×#67 | — | 6 | 2 | no | — |
| 123 | D3×#67 | — | 12 | 2 | no | — |
| 124 | #3802 | — | 3 | 2 | no | — |
| 125 | #3802 | — | 6 | 2 | no | — |
| 126 | D3×D12 | — | 6 | 2 | no | — |
| 127 | D3×D12 | — | 6 | 2 | no | — |
| 128 | D3×D12 | — | 6 | 2 | no | — |
| 129 | C4×D32 | — | 3 | 2 | no | — |
| 130 | C4×D32 | — | 6 | 2 | no | — |
| 131 | C22⋊#157 | — | 3 | 1 | no | — |
| 132 | C22⋊#157 | — | 3 | 1 | no | — |
| 133 | C4⋊#157 | — | 3 | 1 | no | — |
| 134 | C4×#157 | — | 3 | 1 | no | — |
| 135 | #3773 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 136 | D32⋊C4 | — | 3 | 2 | no | — |
| 137 | D32⋊C4 | — | 3 | 2 | no | — |
| 138 | D32⋊C4 | C2×D3 | 1 | 2 | yes | complemented |
| 139 | C22×C33 | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 140 | C2×C3⋊(C3⋊D3) | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 141 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 142 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 143 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 144 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 145 | C2×C3×C3⋊D3 | — | 4 | 4 | no | — |
| 146 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 147 | C2×C3×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 148 | C2×C32×D3 | — | 2 | 2 | no | — |
| 149 | C2×C32×D3 | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 150 | #1113 | — | 2 | 2 | no | — |
| 151 | #1113 | — | 2 | 2 | no | — |
| 152 | #1113 | — | 2 | 2 | no | — |
| 153 | #1113 | — | 4 | 4 | no | — |
| 154 | #1113 | C2×D4 | 1 | 4 | yes | complemented |
| 155 | D3×C3⋊D3 | — | 2 | 1 | no | — |
| 156 | D3×C3⋊D3 | — | 2 | 1 | no | — |
| 157 | D3×C3⋊D3 | — | 4 | 4 | no | — |
| 158 | C3×D32 | — | 2 | 2 | no | — |
| 159 | C3×D32 | — | 2 | 2 | no | — |
| 160 | C3×D32 | — | 4 | 4 | no | — |
| 161 | C3⋊#157 | — | 2 | 1 | no | — |
| 162 | C3⋊#157 | — | 2 | 1 | no | — |
| 163 | C3×#157 | — | 2 | 1 | no | — |
| 164 | C3×#157 | C2×D4 | 1 | 2 | yes | complemented |
| 165 | C3⋊(C3⋊Dic3) | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 166 | C32×Dic3 | — | 2 | 2 | no | — |
| 167 | C32×Dic3 | C2×D4 | 1 | 1 | yes | characteristic, complemented |
| 168 | C2×D3×D4 | — | 9 | 2 | no | — |
| 169 | C2×D3×D4 | — | 9 | 1 | no | — |
| 170 | C2×D3×D4 | — | 18 | 2 | no | — |
| 171 | C22×D12 | — | 9 | 1 | no | — |
| 172 | C3×#121 | — | 9 | 1 | no | — |
| 173 | #940 | — | 9 | 1 | no | — |
| 174 | #937 | — | 9 | 2 | no | — |
| 175 | C4×#67 | — | 9 | 1 | no | — |
| 176 | #895 | — | 9 | 1 | no | — |
| 177 | #893 | — | 9 | 1 | no | — |
| 178 | #884 | — | 9 | 2 | no | — |
| 179 | #882 | — | 9 | 2 | no | — |
| 180 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 181 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 182 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 183 | C22×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 184 | C22×C3×D3 | — | 6 | 2 | no | — |
| 185 | C22×C3×D3 | — | 6 | 2 | no | — |
| 186 | C22×C3×D3 | — | 6 | 2 | no | — |
| 187 | C22×C3×D3 | — | 6 | 2 | no | — |
| 188 | C22×C3×D3 | — | 6 | 2 | no | — |
| 189 | C22×C3×D3 | — | 6 | 2 | no | — |
| 190 | C22×C3×D3 | — | 12 | 2 | no | — |
| 191 | C2×D32 | — | 2 | 2 | no | — |
| 192 | C2×D32 | — | 3 | 2 | no | — |
| 193 | C2×D32 | — | 3 | 2 | no | — |
| 194 | C2×D32 | — | 6 | 2 | no | — |
| 195 | C2×D32 | — | 6 | 2 | no | — |
| 196 | C2×D32 | — | 6 | 2 | no | — |
| 197 | C2×D32 | — | 6 | 2 | no | — |
| 198 | C2×D32 | — | 6 | 2 | no | — |
| 199 | C2×D32 | — | 6 | 2 | no | — |
| 200 | C2×D32 | — | 6 | 2 | no | — |
| 201 | C2×D32 | — | 6 | 2 | no | — |
| 202 | C2×D32 | — | 6 | 4 | no | — |
| 203 | C2×D32 | — | 6 | 4 | no | — |
| 204 | C2×D32 | — | 12 | 4 | no | — |
| 205 | C2×D32 | — | 12 | 4 | no | — |
| 206 | C2×D32 | — | 12 | 2 | no | — |
| 207 | C2×D32 | — | 12 | 2 | no | — |
| 208 | C2×D32 | — | 12 | 4 | no | — |
| 209 | C2×D32 | — | 12 | 2 | no | — |
| 210 | C2×D32 | — | 12 | 4 | no | — |
| 211 | C2×D32 | C22×D3 | 1 | 2 | yes | — |
| 212 | C2×#157 | — | 2 | 2 | no | — |
| 213 | C2×#157 | — | 3 | 1 | no | — |
| 214 | C2×#157 | — | 3 | 1 | no | — |
| 215 | C2×#157 | — | 6 | 2 | no | — |
| 216 | C2×#157 | C22×D3 | 1 | 1 | yes | characteristic |
| 217 | C2×#157 | C22×D3 | 1 | 1 | yes | characteristic |
| 218 | GO+(4,𝔽2) | — | 2 | 2 | no | — |
| 219 | GO+(4,𝔽2) | — | 3 | 4 | no | — |
| 220 | GO+(4,𝔽2) | — | 6 | 4 | no | — |
| 221 | GO+(4,𝔽2) | — | 6 | 4 | no | — |
| 222 | GO+(4,𝔽2) | — | 6 | 2 | no | — |
| 223 | GO+(4,𝔽2) | — | 12 | 2 | no | — |
| 224 | C32×D4 | — | 3 | 1 | no | — |
| 225 | C32×D4 | — | 6 | 2 | no | — |
| 226 | #638 | — | 3 | 1 | no | — |
| 227 | #638 | — | 3 | 1 | no | — |
| 228 | #638 | — | 6 | 2 | no | — |
| 229 | #638 | — | 6 | 2 | no | — |
| 230 | #638 | — | 12 | 2 | no | — |
| 231 | C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 232 | C4⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 233 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 234 | C4×C3⋊D3 | — | 6 | 2 | no | — |
| 235 | C3×#67 | — | 2 | 2 | no | — |
| 236 | C3×#67 | — | 2 | 2 | no | — |
| 237 | C3×#67 | — | 2 | 2 | no | — |
| 238 | C3×#67 | — | 4 | 2 | no | — |
| 239 | C3×#67 | — | 6 | 2 | no | — |
| 240 | C3×#67 | — | 6 | 2 | no | — |
| 241 | C3×#67 | — | 6 | 2 | no | — |
| 242 | C3×D12 | — | 6 | 2 | no | — |
| 243 | C3×D12 | — | 6 | 2 | no | — |
| 244 | C3×D12 | — | 6 | 2 | no | — |
| 245 | C3×C4×D3 | — | 6 | 2 | no | — |
| 246 | C3×C4×D3 | — | 6 | 2 | no | — |
| 247 | C3×C4×D3 | — | 6 | 2 | no | — |
| 248 | #626 | — | 2 | 2 | no | — |
| 249 | #626 | — | 2 | 2 | no | — |
| 250 | #626 | — | 2 | 2 | no | — |
| 251 | #626 | — | 6 | 2 | no | — |
| 252 | #626 | — | 6 | 2 | no | — |
| 253 | #626 | — | 6 | 2 | no | — |
| 254 | #626 | — | 12 | 2 | no | — |
| 255 | #625 | — | 6 | 2 | no | — |
| 256 | #625 | — | 6 | 2 | no | — |
| 257 | #625 | — | 6 | 2 | no | — |
| 258 | #625 | — | 12 | 2 | no | — |
| 259 | #624 | — | 2 | 2 | no | — |
| 260 | #624 | C22×D3 | 1 | 2 | yes | — |
| 261 | D3×Dic3 | — | 6 | 2 | no | — |
| 262 | D3×Dic3 | — | 6 | 2 | no | — |
| 263 | D3×Dic3 | — | 6 | 2 | no | — |
| 264 | D3×Dic3 | — | 12 | 2 | no | — |
| 265 | D42 | — | 27 | 1 | no | Sylow |
| 266 | C2×C33 | — | 2 | 1 | no | — |
| 267 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 268 | C3⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 269 | C3×C3⋊D3 | — | 2 | 4 | no | — |
| 270 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 271 | C3×C3⋊D3 | — | 4 | 2 | no | — |
| 272 | C3×C3⋊D3 | C22×D4 | 1 | 1 | yes | characteristic |
| 273 | C3×C3⋊D3 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 274 | C32×D3 | — | 2 | 1 | no | — |
| 275 | C32×D3 | — | 4 | 2 | no | — |
| 276 | C23×D3 | — | 9 | 2 | no | — |
| 277 | C23×D3 | — | 9 | 2 | no | — |
| 278 | C23×D3 | — | 18 | 2 | no | — |
| 279 | C23×D3 | — | 18 | 2 | no | — |
| 280 | C2×C3×D4 | — | 9 | 2 | no | — |
| 281 | C2×C3×D4 | — | 9 | 1 | no | — |
| 282 | C2×C3×D4 | — | 18 | 2 | no | — |
| 283 | C22×C3×C4 | — | 9 | 1 | no | — |
| 284 | C2×#67 | — | 9 | 2 | no | — |
| 285 | C2×#67 | — | 9 | 1 | no | — |
| 286 | C2×#67 | — | 9 | 2 | no | — |
| 287 | C2×#67 | — | 9 | 2 | no | — |
| 288 | C2×#67 | — | 18 | 2 | no | — |
| 289 | C2×#67 | — | 18 | 2 | no | — |
| 290 | D3×D4 | — | 6 | 2 | no | — |
| 291 | D3×D4 | — | 6 | 2 | no | — |
| 292 | D3×D4 | — | 6 | 2 | no | — |
| 293 | D3×D4 | — | 18 | 2 | no | — |
| 294 | D3×D4 | — | 18 | 2 | no | — |
| 295 | D3×D4 | — | 18 | 2 | no | — |
| 296 | D3×D4 | — | 18 | 2 | no | — |
| 297 | D3×D4 | — | 18 | 2 | no | — |
| 298 | D3×D4 | — | 18 | 2 | no | — |
| 299 | D3×D4 | — | 18 | 2 | no | — |
| 300 | D3×D4 | — | 18 | 4 | no | — |
| 301 | D3×D4 | — | 18 | 2 | no | — |
| 302 | D3×D4 | — | 18 | 2 | no | — |
| 303 | D3×D4 | — | 36 | 2 | no | — |
| 304 | C2×D12 | — | 9 | 2 | no | — |
| 305 | C2×D12 | — | 9 | 1 | no | — |
| 306 | C2×D12 | — | 9 | 2 | no | — |
| 307 | C2×D12 | — | 9 | 1 | no | — |
| 308 | C2×D12 | — | 18 | 2 | no | — |
| 309 | C2×D12 | — | 18 | 4 | no | — |
| 310 | C2×C4×D3 | — | 9 | 2 | no | — |
| 311 | C2×C4×D3 | — | 9 | 1 | no | — |
| 312 | C2×C4×D3 | — | 18 | 2 | no | — |
| 313 | C3×C4⋊C4 | — | 9 | 1 | no | — |
| 314 | C3×C22⋊C4 | — | 9 | 2 | no | — |
| 315 | #217 | — | 9 | 1 | no | — |
| 316 | (C2×D3)⋊C4 | — | 9 | 1 | no | — |
| 317 | (C2×D3)⋊C4 | — | 9 | 2 | no | — |
| 318 | (C2×D3)⋊C4 | — | 9 | 2 | no | — |
| 319 | Dic3⋊C4 | — | 9 | 1 | no | — |
| 320 | C4×Dic3 | — | 9 | 1 | no | — |
| 321 | C22×C32 | — | 2 | 2 | no | — |
| 322 | C22×C32 | — | 3 | 1 | no | — |
| 323 | C22×C32 | — | 4 | 2 | no | — |
| 324 | C22×C32 | — | 6 | 2 | no | — |
| 325 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic, complemented |
| 326 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 327 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 328 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 329 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 330 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 331 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 332 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 333 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 334 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 335 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 336 | C2×C3⋊D3 | — | 12 | 4 | no | — |
| 337 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic, complemented |
| 338 | C2×C3⋊D3 | C23×D3 | 1 | 1 | yes | characteristic |
| 339 | C2×C3×D3 | — | 2 | 2 | no | — |
| 340 | C2×C3×D3 | — | 2 | 2 | no | — |
| 341 | C2×C3×D3 | — | 2 | 2 | no | — |
| 342 | C2×C3×D3 | — | 4 | 2 | no | — |
| 343 | C2×C3×D3 | — | 6 | 2 | no | — |
| 344 | C2×C3×D3 | — | 6 | 2 | no | — |
| 345 | C2×C3×D3 | — | 6 | 2 | no | — |
| 346 | C2×C3×D3 | — | 6 | 2 | no | — |
| 347 | C2×C3×D3 | — | 6 | 2 | no | — |
| 348 | C2×C3×D3 | — | 6 | 2 | no | — |
| 349 | C2×C3×D3 | — | 12 | 2 | no | — |
| 350 | C2×C3×D3 | — | 12 | 2 | no | — |
| 351 | C2×C3×D3 | — | 12 | 2 | no | — |
| 352 | C2×C3×D3 | — | 12 | 2 | no | — |
| 353 | C2×C3×D3 | — | 12 | 2 | no | — |
| 354 | C2×C3×D3 | — | 12 | 2 | no | — |
| 355 | C2×C3×D3 | — | 12 | 4 | no | — |
| 356 | C2×C3×D3 | — | 12 | 4 | no | — |
| 357 | C2×C3×D3 | — | 12 | 4 | no | — |
| 358 | C2×C3×D3 | — | 12 | 4 | no | — |
| 359 | C2×C3×D3 | — | 24 | 4 | no | — |
| 360 | D32 | — | 2 | 2 | no | — |
| 361 | D32 | — | 2 | 2 | no | — |
| 362 | D32 | — | 3 | 4 | no | — |
| 363 | D32 | — | 4 | 4 | no | — |
| 364 | D32 | — | 6 | 4 | no | — |
| 365 | D32 | — | 6 | 4 | no | — |
| 366 | D32 | — | 6 | 2 | no | — |
| 367 | D32 | — | 6 | 2 | no | — |
| 368 | D32 | — | 6 | 2 | no | — |
| 369 | D32 | — | 12 | 2 | no | — |
| 370 | D32 | — | 12 | 2 | no | — |
| 371 | D32 | — | 12 | 2 | no | — |
| 372 | D32 | — | 12 | 2 | no | — |
| 373 | D32 | — | 12 | 4 | no | — |
| 374 | D32 | — | 12 | 4 | no | — |
| 375 | D32 | — | 12 | 4 | no | — |
| 376 | D32 | — | 12 | 4 | no | — |
| 377 | D32 | — | 12 | 4 | no | — |
| 378 | D32 | — | 24 | 4 | no | — |
| 379 | #157 | — | 2 | 1 | no | — |
| 380 | #157 | — | 6 | 1 | no | — |
| 381 | #157 | — | 6 | 1 | no | — |
| 382 | #157 | D3×D4 | 1 | 2 | yes | complemented |
| 383 | C32×C4 | — | 3 | 1 | no | — |
| 384 | C32×C4 | — | 6 | 2 | no | — |
| 385 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 386 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 387 | C3⋊Dic3 | — | 12 | 2 | no | — |
| 388 | C3×Dic3 | — | 2 | 2 | no | — |
| 389 | C3×Dic3 | — | 2 | 2 | no | — |
| 390 | C3×Dic3 | — | 2 | 2 | no | — |
| 391 | C3×Dic3 | — | 4 | 2 | no | — |
| 392 | C22×D4 | — | 27 | 1 | no | — |
| 393 | C22×D4 | — | 27 | 2 | no | — |
| 394 | C22×D4 | — | 27 | 1 | no | — |
| 395 | #127 | — | 27 | 1 | no | — |
| 396 | #121 | — | 9 | 1 | no | — |
| 397 | #121 | — | 27 | 2 | no | — |
| 398 | #121 | — | 27 | 1 | no | — |
| 399 | #120 | — | 27 | 2 | no | — |
| 400 | #120 | — | 27 | 2 | no | — |
| 401 | C4×D4 | — | 27 | 1 | no | — |
| 402 | C4×D4 | — | 27 | 1 | no | — |
| 403 | C33 | D42 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 404 | C23×C3 | — | 9 | 2 | no | — |
| 405 | C23×C3 | — | 9 | 1 | no | — |
| 406 | C23×C3 | — | 18 | 2 | no | — |
| 407 | C23×C3 | — | 18 | 2 | no | — |
| 408 | C22×D3 | — | 6 | 2 | no | — |
| 409 | C22×D3 | — | 6 | 2 | no | — |
| 410 | C22×D3 | — | 6 | 2 | no | — |
| 411 | C22×D3 | — | 6 | 2 | no | — |
| 412 | C22×D3 | — | 6 | 2 | no | — |
| 413 | C22×D3 | — | 6 | 2 | no | — |
| 414 | C22×D3 | — | 9 | 2 | no | — |
| 415 | C22×D3 | — | 9 | 2 | no | — |
| 416 | C22×D3 | — | 9 | 1 | no | — |
| 417 | C22×D3 | — | 12 | 2 | no | — |
| 418 | C22×D3 | — | 18 | 2 | no | — |
| 419 | C22×D3 | — | 18 | 2 | no | — |
| 420 | C22×D3 | — | 18 | 2 | no | — |
| 421 | C22×D3 | — | 18 | 2 | no | — |
| 422 | C22×D3 | — | 18 | 2 | no | — |
| 423 | C22×D3 | — | 18 | 2 | no | — |
| 424 | C22×D3 | — | 18 | 2 | no | — |
| 425 | C22×D3 | — | 18 | 2 | no | — |
| 426 | C22×D3 | — | 18 | 2 | no | — |
| 427 | C22×D3 | — | 18 | 4 | no | — |
| 428 | C22×D3 | — | 18 | 4 | no | — |
| 429 | C22×D3 | — | 36 | 4 | no | — |
| 430 | C22×D3 | — | 36 | 4 | no | — |
| 431 | C22×D3 | — | 36 | 2 | no | — |
| 432 | C22×D3 | — | 36 | 2 | no | — |
| 433 | C22×D3 | — | 36 | 2 | no | — |
| 434 | C22×D3 | — | 36 | 4 | no | — |
| 435 | C22×D3 | — | 36 | 4 | no | — |
| 436 | C3×D4 | — | 6 | 2 | no | — |
| 437 | C3×D4 | — | 6 | 2 | no | — |
| 438 | C3×D4 | — | 6 | 2 | no | — |
| 439 | C3×D4 | — | 12 | 2 | no | — |
| 440 | C3×D4 | — | 18 | 2 | no | — |
| 441 | C3×D4 | — | 18 | 2 | no | — |
| 442 | C3×D4 | — | 18 | 2 | no | — |
| 443 | C3×D4 | — | 18 | 2 | no | — |
| 444 | C2×C3×C4 | — | 9 | 2 | no | — |
| 445 | C2×C3×C4 | — | 9 | 1 | no | — |
| 446 | C2×C3×C4 | — | 9 | 1 | no | — |
| 447 | C2×C3×C4 | — | 18 | 2 | no | — |
| 448 | C2×C3×C4 | — | 18 | 2 | no | — |
| 449 | #67 | — | 2 | 2 | no | — |
| 450 | #67 | — | 6 | 2 | no | — |
| 451 | #67 | — | 6 | 2 | no | — |
| 452 | #67 | — | 6 | 2 | no | — |
| 453 | #67 | — | 9 | 1 | no | — |
| 454 | #67 | — | 9 | 1 | no | — |
| 455 | #67 | — | 9 | 1 | no | — |
| 456 | #67 | — | 18 | 2 | no | — |
| 457 | #67 | — | 18 | 2 | no | — |
| 458 | #67 | — | 18 | 2 | no | — |
| 459 | #67 | — | 18 | 2 | no | — |
| 460 | #67 | — | 18 | 2 | no | — |
| 461 | #67 | — | 18 | 2 | no | — |
| 462 | #67 | — | 18 | 4 | no | — |
| 463 | #67 | — | 36 | 2 | no | — |
| 464 | #67 | — | 36 | 2 | no | — |
| 465 | #67 | — | 36 | 2 | no | — |
| 466 | #67 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 467 | C2×Dic3 | — | 9 | 1 | no | — |
| 468 | C2×Dic3 | — | 9 | 1 | no | — |
| 469 | C2×Dic3 | — | 9 | 1 | no | — |
| 470 | C2×Dic3 | — | 18 | 2 | no | — |
| 471 | D12 | — | 6 | 2 | no | — |
| 472 | D12 | — | 6 | 2 | no | — |
| 473 | D12 | — | 6 | 2 | no | — |
| 474 | D12 | — | 9 | 4 | no | — |
| 475 | D12 | — | 18 | 2 | no | — |
| 476 | D12 | — | 18 | 2 | no | — |
| 477 | D12 | — | 18 | 2 | no | — |
| 478 | D12 | — | 18 | 2 | no | — |
| 479 | D12 | — | 18 | 4 | no | — |
| 480 | D12 | — | 36 | 2 | no | — |
| 481 | C4×D3 | — | 6 | 2 | no | — |
| 482 | C4×D3 | — | 6 | 2 | no | — |
| 483 | C4×D3 | — | 6 | 2 | no | — |
| 484 | C4×D3 | — | 18 | 2 | no | — |
| 485 | C4×D3 | — | 18 | 2 | no | — |
| 486 | C4×D3 | — | 18 | 2 | no | — |
| 487 | C4×D3 | — | 18 | 2 | no | — |
| 488 | C4×D3 | — | 36 | 2 | no | — |
| 489 | C2×C32 | — | 2 | 2 | no | — |
| 490 | C2×C32 | — | 2 | 1 | no | — |
| 491 | C2×C32 | — | 4 | 2 | no | — |
| 492 | C2×C32 | — | 4 | 2 | no | — |
| 493 | C2×C32 | — | 6 | 1 | no | — |
| 494 | C2×C32 | — | 8 | 2 | no | — |
| 495 | C2×C32 | — | 12 | 2 | no | — |
| 496 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 497 | C3⋊D3 | — | 2 | 4 | no | — |
| 498 | C3⋊D3 | — | 2 | 1 | no | — |
| 499 | C3⋊D3 | — | 4 | 2 | no | — |
| 500 | C3⋊D3 | — | 6 | 1 | no | — |
| 501 | C3⋊D3 | — | 12 | 2 | no | — |
| 502 | C3⋊D3 | — | 24 | 2 | no | — |
| 503 | C3⋊D3 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 504 | C3⋊D3 | #1009 | 1 | 1 | yes | characteristic |
| 505 | C3×D3 | — | 4 | 2 | no | — |
| 506 | C3×D3 | — | 4 | 2 | no | — |
| 507 | C3×D3 | — | 4 | 2 | no | — |
| 508 | C3×D3 | — | 6 | 2 | no | — |
| 509 | C3×D3 | — | 6 | 2 | no | — |
| 510 | C3×D3 | — | 6 | 4 | no | — |
| 511 | C3×D3 | — | 6 | 4 | no | — |
| 512 | C3×D3 | — | 8 | 2 | no | — |
| 513 | C3×D3 | — | 12 | 2 | no | — |
| 514 | C3×D3 | — | 12 | 4 | no | — |
| 515 | C3×D3 | — | 12 | 2 | no | — |
| 516 | C3×D3 | — | 12 | 2 | no | — |
| 517 | C3×D3 | — | 24 | 2 | no | — |
| 518 | C24 | — | 27 | 2 | no | — |
| 519 | C24 | — | 27 | 2 | no | — |
| 520 | C2×D4 | — | 9 | 2 | no | — |
| 521 | C2×D4 | — | 9 | 1 | no | — |
| 522 | C2×D4 | — | 18 | 2 | no | — |
| 523 | C2×D4 | — | 27 | 2 | no | — |
| 524 | C2×D4 | — | 27 | 1 | no | — |
| 525 | C2×D4 | — | 27 | 2 | no | — |
| 526 | C2×D4 | — | 27 | 1 | no | — |
| 527 | C2×D4 | — | 27 | 1 | no | — |
| 528 | C2×D4 | — | 27 | 2 | no | — |
| 529 | C2×D4 | — | 27 | 2 | no | — |
| 530 | C2×D4 | — | 27 | 2 | no | — |
| 531 | C2×D4 | — | 54 | 2 | no | — |
| 532 | C2×D4 | — | 54 | 4 | no | — |
| 533 | C2×D4 | — | 54 | 2 | no | — |
| 534 | C2×D4 | — | 54 | 2 | no | — |
| 535 | C2×D4 | — | 54 | 4 | no | — |
| 536 | C22×C4 | — | 9 | 1 | no | — |
| 537 | C22×C4 | — | 27 | 2 | no | — |
| 538 | C22×C4 | — | 27 | 1 | no | — |
| 539 | C4⋊C4 | — | 9 | 1 | no | — |
| 540 | C4⋊C4 | — | 27 | 1 | no | — |
| 541 | C22⋊C4 | — | 9 | 2 | no | — |
| 542 | C22⋊C4 | — | 27 | 2 | no | — |
| 543 | C22⋊C4 | — | 27 | 1 | no | — |
| 544 | C22⋊C4 | — | 27 | 2 | no | — |
| 545 | C22⋊C4 | — | 27 | 1 | no | — |
| 546 | C42 | — | 27 | 1 | no | — |
| 547 | C22×C3 | — | 2 | 2 | no | — |
| 548 | C22×C3 | — | 4 | 2 | no | — |
| 549 | C22×C3 | — | 6 | 2 | no | — |
| 550 | C22×C3 | — | 6 | 2 | no | — |
| 551 | C22×C3 | — | 6 | 2 | no | — |
| 552 | C22×C3 | — | 9 | 1 | no | — |
| 553 | C22×C3 | — | 9 | 1 | no | — |
| 554 | C22×C3 | — | 12 | 2 | no | — |
| 555 | C22×C3 | — | 18 | 1 | no | — |
| 556 | C22×C3 | — | 18 | 1 | no | — |
| 557 | C22×C3 | — | 18 | 2 | no | — |
| 558 | C22×C3 | — | 18 | 2 | no | — |
| 559 | C22×C3 | — | 18 | 2 | no | — |
| 560 | C22×C3 | — | 18 | 2 | no | — |
| 561 | C22×C3 | — | 36 | 4 | no | — |
| 562 | C22×C3 | — | 36 | 4 | no | — |
| 563 | C22×C3 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 564 | C2×D3 | — | 2 | 2 | no | — |
| 565 | C2×D3 | — | 6 | 2 | no | — |
| 566 | C2×D3 | — | 6 | 2 | no | — |
| 567 | C2×D3 | — | 6 | 2 | no | — |
| 568 | C2×D3 | — | 6 | 2 | no | — |
| 569 | C2×D3 | — | 6 | 2 | no | — |
| 570 | C2×D3 | — | 6 | 2 | no | — |
| 571 | C2×D3 | — | 9 | 4 | no | — |
| 572 | C2×D3 | — | 9 | 1 | no | — |
| 573 | C2×D3 | — | 12 | 2 | no | — |
| 574 | C2×D3 | — | 12 | 2 | no | — |
| 575 | C2×D3 | — | 12 | 2 | no | — |
| 576 | C2×D3 | — | 12 | 2 | no | — |
| 577 | C2×D3 | — | 12 | 2 | no | — |
| 578 | C2×D3 | — | 12 | 2 | no | — |
| 579 | C2×D3 | — | 12 | 4 | no | — |
| 580 | C2×D3 | — | 12 | 4 | no | — |
| 581 | C2×D3 | — | 12 | 4 | no | — |
| 582 | C2×D3 | — | 12 | 4 | no | — |
| 583 | C2×D3 | — | 18 | 4 | no | — |
| 584 | C2×D3 | — | 18 | 2 | no | — |
| 585 | C2×D3 | — | 18 | 1 | no | — |
| 586 | C2×D3 | — | 18 | 1 | no | — |
| 587 | C2×D3 | — | 18 | 2 | no | — |
| 588 | C2×D3 | — | 18 | 4 | no | — |
| 589 | C2×D3 | — | 18 | 2 | no | — |
| 590 | C2×D3 | — | 18 | 2 | no | — |
| 591 | C2×D3 | — | 24 | 4 | no | — |
| 592 | C2×D3 | — | 36 | 2 | no | — |
| 593 | C2×D3 | — | 36 | 2 | no | — |
| 594 | C2×D3 | — | 36 | 2 | no | — |
| 595 | C2×D3 | — | 36 | 2 | no | — |
| 596 | C2×D3 | — | 36 | 2 | no | — |
| 597 | C2×D3 | — | 36 | 4 | no | — |
| 598 | C2×D3 | — | 36 | 4 | no | — |
| 599 | C2×D3 | — | 36 | 4 | no | — |
| 600 | C2×D3 | — | 36 | 4 | no | — |
| 601 | C2×D3 | — | 36 | 4 | no | — |
| 602 | C2×D3 | — | 36 | 4 | no | — |
| 603 | C2×D3 | — | 72 | 4 | no | — |
| 604 | C2×D3 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 605 | C3×C4 | — | 6 | 2 | no | — |
| 606 | C3×C4 | — | 6 | 2 | no | — |
| 607 | C3×C4 | — | 6 | 2 | no | — |
| 608 | C3×C4 | — | 9 | 2 | no | — |
| 609 | C3×C4 | — | 12 | 2 | no | — |
| 610 | C3×C4 | — | 18 | 1 | no | — |
| 611 | Dic3 | — | 2 | 2 | no | — |
| 612 | Dic3 | — | 9 | 1 | no | — |
| 613 | Dic3 | — | 18 | 2 | no | — |
| 614 | Dic3 | — | 18 | 1 | no | — |
| 615 | Dic3 | — | 18 | 1 | no | — |
| 616 | Dic3 | — | 36 | 2 | no | — |
| 617 | Dic3 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 618 | C32 | — | 2 | 2 | no | — |
| 619 | C32 | — | 4 | 2 | no | — |
| 620 | C32 | #5609 | 1 | 1 | yes | characteristic, complemented |
| 621 | C23 | — | 9 | 2 | no | — |
| 622 | C23 | — | 9 | 1 | no | — |
| 623 | C23 | — | 18 | 2 | no | — |
| 624 | C23 | — | 18 | 2 | no | — |
| 625 | C23 | — | 27 | 1 | no | — |
| 626 | C23 | — | 27 | 2 | no | — |
| 627 | C23 | — | 27 | 2 | no | — |
| 628 | C23 | — | 54 | 2 | no | — |
| 629 | C23 | — | 54 | 2 | no | — |
| 630 | C23 | — | 54 | 4 | no | — |
| 631 | C23 | — | 54 | 4 | no | — |
| 632 | C23 | — | 108 | 2 | no | — |
| 633 | C23 | — | 108 | 2 | no | — |
| 634 | D4 | — | 3 | 1 | no | — |
| 635 | D4 | — | 6 | 2 | no | — |
| 636 | D4 | — | 18 | 2 | no | — |
| 637 | D4 | — | 18 | 2 | no | — |
| 638 | D4 | — | 18 | 2 | no | — |
| 639 | D4 | — | 18 | 2 | no | — |
| 640 | D4 | — | 27 | 1 | no | — |
| 641 | D4 | — | 27 | 4 | no | — |
| 642 | D4 | — | 27 | 1 | no | — |
| 643 | D4 | — | 27 | 1 | no | — |
| 644 | D4 | — | 54 | 2 | no | — |
| 645 | D4 | — | 54 | 2 | no | — |
| 646 | D4 | — | 54 | 4 | no | — |
| 647 | D4 | — | 54 | 2 | no | — |
| 648 | D4 | — | 54 | 4 | no | — |
| 649 | D4 | — | 108 | 2 | no | — |
| 650 | C2×C4 | — | 9 | 2 | no | — |
| 651 | C2×C4 | — | 9 | 1 | no | — |
| 652 | C2×C4 | — | 9 | 1 | no | — |
| 653 | C2×C4 | — | 18 | 2 | no | — |
| 654 | C2×C4 | — | 18 | 2 | no | — |
| 655 | C2×C4 | — | 27 | 1 | no | — |
| 656 | C2×C4 | — | 27 | 1 | no | — |
| 657 | C2×C4 | — | 27 | 1 | no | — |
| 658 | C2×C4 | — | 54 | 2 | no | — |
| 659 | C2×C4 | — | 54 | 2 | no | — |
| 660 | C2×C3 | — | 2 | 1 | no | — |
| 661 | C2×C3 | — | 2 | 2 | no | — |
| 662 | C2×C3 | — | 4 | 2 | no | — |
| 663 | C2×C3 | — | 4 | 2 | no | — |
| 664 | C2×C3 | — | 8 | 2 | no | — |
| 665 | C2×C3 | — | 9 | 1 | no | — |
| 666 | C2×C3 | — | 9 | 1 | no | — |
| 667 | C2×C3 | — | 12 | 2 | no | — |
| 668 | C2×C3 | — | 12 | 2 | no | — |
| 669 | C2×C3 | — | 12 | 2 | no | — |
| 670 | C2×C3 | — | 18 | 4 | no | — |
| 671 | C2×C3 | — | 18 | 1 | no | — |
| 672 | C2×C3 | — | 24 | 2 | no | — |
| 673 | C2×C3 | — | 36 | 2 | no | — |
| 674 | C2×C3 | C22×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 675 | D3 | — | 2 | 1 | no | — |
| 676 | D3 | — | 4 | 2 | no | — |
| 677 | D3 | — | 6 | 2 | no | — |
| 678 | D3 | — | 6 | 2 | no | — |
| 679 | D3 | — | 6 | 4 | no | — |
| 680 | D3 | — | 6 | 4 | no | — |
| 681 | D3 | — | 12 | 2 | no | — |
| 682 | D3 | — | 12 | 4 | no | — |
| 683 | D3 | — | 12 | 2 | no | — |
| 684 | D3 | — | 12 | 2 | no | — |
| 685 | D3 | — | 18 | 1 | no | — |
| 686 | D3 | — | 24 | 2 | no | — |
| 687 | D3 | — | 36 | 2 | no | — |
| 688 | D3 | — | 72 | 2 | no | — |
| 689 | C22 | — | 3 | 1 | no | — |
| 690 | C22 | — | 6 | 2 | no | — |
| 691 | C22 | — | 9 | 1 | no | — |
| 692 | C22 | — | 9 | 1 | no | — |
| 693 | C22 | — | 18 | 1 | no | — |
| 694 | C22 | — | 18 | 1 | no | — |
| 695 | C22 | — | 18 | 2 | no | — |
| 696 | C22 | — | 18 | 2 | no | — |
| 697 | C22 | — | 18 | 2 | no | — |
| 698 | C22 | — | 18 | 2 | no | — |
| 699 | C22 | — | 27 | 4 | no | — |
| 700 | C22 | — | 27 | 1 | no | — |
| 701 | C22 | — | 36 | 4 | no | — |
| 702 | C22 | — | 36 | 4 | no | — |
| 703 | C22 | — | 54 | 1 | no | — |
| 704 | C22 | — | 54 | 1 | no | — |
| 705 | C22 | — | 54 | 2 | no | — |
| 706 | C22 | — | 54 | 2 | no | — |
| 707 | C22 | — | 54 | 2 | no | — |
| 708 | C22 | — | 108 | 4 | no | — |
| 709 | C22 | — | 108 | 4 | no | — |
| 710 | C22 | D3×GO+(4,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 711 | C4 | — | 3 | 1 | no | — |
| 712 | C4 | — | 6 | 2 | no | — |
| 713 | C4 | — | 9 | 2 | no | — |
| 714 | C4 | — | 18 | 1 | no | — |
| 715 | C4 | — | 27 | 1 | no | — |
| 716 | C4 | — | 54 | 1 | no | — |
| 717 | C4 | — | 54 | 1 | no | — |
| 718 | C3 | — | 2 | 2 | no | — |
| 719 | C3 | — | 4 | 2 | no | — |
| 720 | C3 | D4×GO+(4,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 721 | C2 | — | 2 | 1 | no | — |
| 722 | C2 | — | 6 | 1 | no | — |
| 723 | C2 | — | 9 | 1 | no | — |
| 724 | C2 | — | 9 | 1 | no | — |
| 725 | C2 | — | 12 | 2 | no | — |
| 726 | C2 | — | 18 | 1 | no | — |
| 727 | C2 | — | 18 | 4 | no | — |
| 728 | C2 | — | 36 | 2 | no | — |
| 729 | C2 | — | 54 | 1 | no | — |
| 730 | C2 | C2×D3×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D3×GO+(4,𝔽2) |
| commutator, cosocle | C2×C3×C3⋊D3 | C24 |
| Fitting | C22×C33 | C2×D4 |
| socle | C2×C33 | C22×D4 |
| hypercenter | C22 | D3×GO+(4,𝔽2) |
| hypocenter | C33 | D42 |
| LCS | G ▷ C2×C3×C3⋊D3 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#157⋊D3 | C2 | semidirect |
| 2. C2×D3×GO+(4,𝔽2) | C2 | semidirect |
| 3. #11724440 | C2 | semidirect |
| 4. #11724330 | C2 | semidirect |
| 5. C3×#64242 | C2 | semidirect |
| 6. #67×#157 | C2 | semidirect |
| 7. #11724124 | C2 | semidirect |
| 8. #11724118 | C2 | semidirect |
| 9. #11724116 | C2 | semidirect |
| 10. #11724113 | C2 | semidirect |
| 11. #11724111 | C2 | semidirect |
| 13. C22×#1113 | C22 | semidirect |
| 14. C22×C3×#157 | C22 | semidirect |
| 15. C2×D33 | C22 | semidirect |
| 18. C2×#157⋊D3 | C22 | semidirect |
| 19. C2×#157⋊D3 | C22 | semidirect |
| 20. C2×D32⋊D3 | C22 | semidirect |
| 21. C2×D32⋊D3 | C22 | semidirect |
| 22. C2×C3×GO+(4,𝔽2) | C22 | semidirect |
| 23. C2×D3×#157 | C22 | semidirect |
| 28. C3×#3811 | C22 | semidirect |
| 29. #88994 | C22 | semidirect |
| 31. #88955 | C22 | semidirect |
| 33. #88953 | C22 | semidirect |
| 34. #88949 | C22 | semidirect |
| 35. #88932 | C22 | semidirect |
| 36. #88932 | C22 | semidirect |
| 37. C3×#3773 | C22 | semidirect |
| 38. C3×D32⋊C4 | C22 | semidirect |
| 39. Dic3⋊#157 | C22 | semidirect |
| 40. (C2×D3)⋊#157 | C22 | semidirect |
| 41. Dic3×#157 | C22 | semidirect |
| 48. #64242 | D3 | semidirect |
| 74. #157⋊D3 | D4 | semidirect |
| 79. #6312 | D4 | semidirect |
| 81. C32×#67 | D4 | semidirect |
| 83. #6292 | D4 | semidirect |
| 85. #6290 | D4 | semidirect |
| 99. C22×#157 | C2×D3 | semidirect |
| 107. C2×GO+(4,𝔽2) | C2×D3 | semidirect |
| 116. #3811 | C2×D3 | semidirect |
| 135. #3773 | C2×D3 | semidirect |
| 138. D32⋊C4 | C2×D3 | semidirect |
| 139. C22×C33 | C2×D4 | semidirect |
| 140. C2×C3⋊(C3⋊D3) | C2×D4 | semidirect |
| 146. C2×C3×C3⋊D3 | C2×D4 | semidirect |
| 149. C2×C32×D3 | C2×D4 | semidirect |
| 154. #1113 | C2×D4 | semidirect |
| 164. C3×#157 | C2×D4 | semidirect |
| 165. C3⋊(C3⋊Dic3) | C2×D4 | semidirect |
| 167. C32×Dic3 | C2×D4 | semidirect |
| 325. C22×C32 | D3×D4 | semidirect |
| 337. C2×C3⋊D3 | D3×D4 | semidirect |
| 382. #157 | D3×D4 | semidirect |
| 403. C33 | D42 | semidirect |
| 466. #67 | GO+(4,𝔽2) | semidirect |
| 563. C22×C3 | C2×GO+(4,𝔽2) | semidirect |
| 604. C2×D3 | C2×GO+(4,𝔽2) | semidirect |
| 617. Dic3 | C2×GO+(4,𝔽2) | semidirect |
| 620. C32 | #5609 | semidirect |
| 710. C22 | D3×GO+(4,𝔽2) | semidirect |
| 720. C3 | D4×GO+(4,𝔽2) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#157⋊D3 | 2 |
| C2×D3×GO+(4,𝔽2) | 2 |
| #11724440 | 2 |
| #11724330 | 2 |
| C3×#64242 | 2 |
| #67×#157 | 2 |
| #11724124 | 2 |
| #11724118 | 2 |
| #11724116 | 2 |
| #11724113 | 2 |
| #11724111 | 2 |
| D4×GO+(4,𝔽2) | 3 |
| #5609 | 9 |