Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1136 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1136 conjugacy classes of subgroups — too many to draw. Only its 155 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×#17986729 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#17986184 | C2 | 1 | 2 | yes | maximal |
| 3 | C2×#17986181 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #22590371 | C2 | 1 | 8 | yes | maximal, direct product factor |
| 5 | C2×#17985797 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C2×#356×C71 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×#14556176 | C22 | 1 | 1 | yes | characteristic |
| 8 | C2×#14556161 | — | 2 | 2 | no | — |
| 9 | C2×#14556159 | — | 2 | 1 | no | — |
| 10 | #17986729 | — | 2 | 4 | no | — |
| 11 | #17986729 | — | 2 | 2 | no | — |
| 12 | #17986729 | C22 | 1 | 4 | yes | complemented |
| 13 | C2×#14556127 | — | 2 | 2 | no | — |
| 14 | C2×#14556126 | — | 2 | 1 | no | — |
| 15 | C2×#14556126 | C22 | 1 | 2 | yes | — |
| 16 | C2×C4×Dic142 | — | 2 | 1 | no | — |
| 17 | C2×#14556093 | — | 2 | 2 | no | — |
| 18 | #17986184 | — | 2 | 4 | no | — |
| 19 | #17986184 | C22 | 1 | 8 | yes | — |
| 20 | #17986181 | — | 2 | 2 | no | — |
| 21 | #17986181 | C22 | 1 | 4 | yes | — |
| 22 | C2×#14556056 | — | 2 | 1 | no | — |
| 23 | C2×#14556054 | — | 2 | 2 | no | — |
| 24 | C2×#14556047 | C22 | 1 | 1 | yes | characteristic |
| 25 | #17985797 | C22 | 1 | 8 | yes | complemented |
| 26 | C2×C4⋊Q8×C71 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#101×C71 | C22 | 1 | 2 | yes | — |
| 28 | #356×C71 | C22 | 1 | 4 | yes | complemented |
| 29 | #14556176 | — | 2 | 1 | no | — |
| 30 | #14556176 | — | 2 | 2 | no | — |
| 31 | #14556176 | — | 4 | 2 | no | — |
| 32 | #14556176 | C23 | 1 | 2 | yes | — |
| 33 | C2×#11765866 | — | 4 | 1 | no | — |
| 34 | C2×#11765865 | — | 2 | 2 | no | — |
| 35 | C2×#11765865 | — | 2 | 1 | no | — |
| 36 | C22×Dic142 | — | 2 | 1 | no | — |
| 37 | C22×Dic142 | — | 2 | 1 | no | — |
| 38 | C22×Dic142 | D4 | 1 | 2 | yes | — |
| 39 | C2×Q8×D71 | — | 4 | 1 | no | — |
| 40 | #14556161 | — | 2 | 8 | no | — |
| 41 | #14556161 | — | 4 | 4 | no | — |
| 42 | #14556159 | — | 2 | 4 | no | — |
| 43 | #14556159 | — | 4 | 2 | no | — |
| 44 | C2×Dic284 | — | 4 | 2 | no | — |
| 45 | C2×#11765855 | — | 4 | 1 | no | — |
| 46 | C2×#11765854 | — | 4 | 2 | no | — |
| 47 | C2×#11765852 | — | 4 | 1 | no | — |
| 48 | C2×#11765849 | — | 2 | 1 | no | — |
| 49 | #14556127 | — | 2 | 8 | no | — |
| 50 | #14556127 | — | 2 | 8 | no | — |
| 51 | #14556126 | — | 2 | 4 | no | — |
| 52 | #14556126 | — | 2 | 2 | no | — |
| 53 | #14556126 | — | 2 | 2 | no | — |
| 54 | #14556126 | — | 2 | 4 | no | — |
| 55 | #14556126 | D4 | 1 | 4 | yes | — |
| 56 | #14556126 | C23 | 1 | 4 | yes | — |
| 57 | C4×Dic142 | — | 2 | 4 | no | — |
| 58 | C4×Dic142 | — | 2 | 4 | no | — |
| 59 | #14556093 | — | 2 | 8 | no | — |
| 60 | #14556093 | — | 2 | 8 | no | — |
| 61 | C2×C4⋊Dic71 | — | 2 | 1 | no | — |
| 62 | C2×Dic71⋊C4 | — | 2 | 2 | no | — |
| 63 | C2×Dic71⋊C4 | — | 2 | 2 | no | — |
| 64 | C2×Dic71⋊C4 | — | 2 | 2 | no | — |
| 65 | C2×C4×Dic71 | — | 2 | 1 | no | — |
| 66 | C2×C4×Dic71 | — | 2 | 2 | no | — |
| 67 | C2×C4×Dic71 | D4 | 1 | 2 | yes | — |
| 68 | #14556056 | — | 2 | 4 | no | — |
| 69 | #14556054 | — | 2 | 8 | no | — |
| 70 | #14556047 | — | 2 | 1 | no | — |
| 71 | #14556047 | C23 | 1 | 2 | yes | — |
| 72 | C22×Q8×C71 | D4 | 1 | 1 | yes | characteristic |
| 73 | C22×Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×M16×C71 | — | 2 | 2 | no | — |
| 75 | C4⋊Q8×C71 | — | 2 | 2 | no | — |
| 76 | C4⋊Q8×C71 | D4 | 1 | 2 | yes | — |
| 77 | C4⋊Q8×C71 | C23 | 1 | 2 | yes | — |
| 78 | C2×C4⋊C4×C71 | — | 2 | 2 | no | — |
| 79 | C2×C42×C71 | D4 | 1 | 1 | yes | characteristic |
| 80 | #101×C71 | — | 2 | 2 | no | — |
| 81 | #101×C71 | C23 | 1 | 4 | yes | — |
| 82 | #11765866 | — | 4 | 2 | no | — |
| 83 | #11765866 | — | 4 | 2 | no | — |
| 84 | #11765866 | — | 4 | 4 | no | — |
| 85 | #11765865 | — | 2 | 4 | no | — |
| 86 | #11765865 | — | 2 | 2 | no | — |
| 87 | #11765865 | — | 2 | 4 | no | — |
| 88 | #11765865 | — | 2 | 2 | no | — |
| 89 | #11765865 | — | 4 | 2 | no | — |
| 90 | #11765865 | — | 4 | 1 | no | — |
| 91 | #11765865 | — | 4 | 1 | no | — |
| 92 | #11765865 | — | 4 | 2 | no | — |
| 93 | C2×Dic142 | — | 2 | 8 | no | — |
| 94 | C2×Dic142 | — | 2 | 4 | no | — |
| 95 | C2×Dic142 | — | 2 | 1 | no | — |
| 96 | C2×Dic142 | — | 2 | 2 | no | — |
| 97 | C2×Dic142 | — | 2 | 4 | no | — |
| 98 | C2×Dic142 | — | 2 | 2 | no | — |
| 99 | C2×Dic142 | — | 4 | 2 | no | — |
| 100 | C2×Dic142 | — | 4 | 2 | no | — |
| 101 | C2×Dic142 | — | 8 | 1 | no | — |
| 102 | C2×Dic142 | — | 8 | 1 | no | — |
| 103 | C2×Dic142 | C2×D4 | 1 | 4 | yes | — |
| 104 | Q8×D71 | — | 4 | 2 | no | — |
| 105 | Q8×D71 | — | 4 | 2 | no | — |
| 106 | Q8×D71 | — | 4 | 4 | no | — |
| 107 | C2×D284 | — | 2 | 1 | no | — |
| 108 | C2×D284 | — | 2 | 2 | no | — |
| 109 | C2×C22⋊D71 | — | 4 | 1 | no | — |
| 110 | C22×Dic71 | — | 2 | 2 | no | — |
| 111 | C22×Dic71 | — | 2 | 2 | no | — |
| 112 | C2×C4×D71 | — | 4 | 2 | no | — |
| 113 | C2×C4×D71 | — | 4 | 1 | no | — |
| 114 | Dic284 | — | 4 | 8 | no | — |
| 115 | #11765855 | — | 4 | 4 | no | — |
| 116 | #11765854 | — | 4 | 8 | no | — |
| 117 | #11765852 | — | 4 | 4 | no | — |
| 118 | #11765849 | — | 2 | 2 | no | — |
| 119 | #11765849 | — | 4 | 1 | no | — |
| 120 | C2×C71⋊C8 | — | 4 | 1 | no | — |
| 121 | C4⋊Dic71 | — | 2 | 4 | no | — |
| 122 | Dic71⋊C4 | — | 2 | 8 | no | — |
| 123 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 124 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 125 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 126 | Dic71⋊C4 | — | 2 | 4 | no | — |
| 127 | C4×Dic71 | — | 2 | 4 | no | — |
| 128 | C4×Dic71 | — | 2 | 8 | no | — |
| 129 | C4×Dic71 | — | 2 | 2 | no | — |
| 130 | C4×Dic71 | C2×D4 | 1 | 4 | yes | — |
| 131 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 132 | C2×Q8×C71 | — | 4 | 1 | no | — |
| 133 | C2×Q8×C71 | — | 4 | 1 | no | — |
| 134 | C2×Q8×C71 | — | 4 | 1 | no | — |
| 135 | C2×Q8×C71 | — | 4 | 1 | no | — |
| 136 | C2×Q8×C71 | C2×D4 | 1 | 2 | yes | — |
| 137 | C2×Q8×C71 | C2×D4 | 1 | 2 | yes | — |
| 138 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C2×Q8×C71 | C24 | 1 | 1 | yes | characteristic |
| 140 | C22×C4×C71 | — | 2 | 1 | no | — |
| 141 | C22×C4×C71 | — | 2 | 1 | no | — |
| 142 | C22×C4×C71 | C2×D4 | 1 | 2 | yes | — |
| 143 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | M16×C71 | — | 2 | 4 | no | — |
| 145 | M16×C71 | — | 4 | 2 | no | — |
| 146 | C2×C8×C71 | — | 4 | 2 | no | — |
| 147 | C4⋊C4×C71 | — | 2 | 4 | no | — |
| 148 | C4⋊C4×C71 | — | 2 | 4 | no | — |
| 149 | C42×C71 | — | 2 | 1 | no | — |
| 150 | C42×C71 | C2×D4 | 1 | 2 | yes | — |
| 151 | C23×C71 | #120 | 1 | 1 | yes | characteristic |
| 152 | C22×D71 | — | 4 | 1 | no | — |
| 153 | Q8×C71 | — | 4 | 2 | no | — |
| 154 | Q8×C71 | — | 4 | 1 | no | — |
| 155 | Q8×C71 | — | 4 | 1 | no | — |
| 156 | Q8×C71 | — | 4 | 2 | no | — |
| 157 | Q8×C71 | — | 8 | 1 | no | — |
| 158 | C2×C4×C71 | — | 2 | 4 | no | — |
| 159 | C2×C4×C71 | — | 2 | 2 | no | — |
| 160 | C2×C4×C71 | — | 2 | 2 | no | — |
| 161 | C2×C4×C71 | — | 2 | 2 | no | — |
| 162 | C2×C4×C71 | — | 2 | 1 | no | — |
| 163 | C2×C4×C71 | — | 2 | 1 | no | — |
| 164 | C2×C4×C71 | — | 2 | 2 | no | — |
| 165 | C2×C4×C71 | — | 4 | 1 | no | — |
| 166 | C2×C4×C71 | — | 4 | 1 | no | — |
| 167 | C2×C4×C71 | #120 | 1 | 1 | yes | characteristic |
| 168 | C2×C4×C71 | #120 | 1 | 2 | yes | — |
| 169 | C2×C4×C71 | C22×D4 | 1 | 2 | yes | — |
| 170 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 171 | C22⋊D71 | — | 4 | 2 | no | — |
| 172 | C22⋊D71 | — | 4 | 2 | no | — |
| 173 | C2×Dic71 | — | 2 | 8 | no | — |
| 174 | C2×Dic71 | — | 2 | 4 | no | — |
| 175 | C2×Dic71 | — | 2 | 4 | no | — |
| 176 | C2×Dic71 | — | 4 | 1 | no | — |
| 177 | C2×Dic71 | — | 4 | 2 | no | — |
| 178 | C2×Dic71 | — | 4 | 2 | no | — |
| 179 | D284 | — | 2 | 2 | no | — |
| 180 | D284 | — | 2 | 4 | no | — |
| 181 | D284 | — | 4 | 2 | no | — |
| 182 | D284 | — | 4 | 1 | no | — |
| 183 | C4×D71 | — | 4 | 2 | no | — |
| 184 | C4×D71 | — | 4 | 4 | no | — |
| 185 | C4×D71 | — | 4 | 4 | no | — |
| 186 | C4×D71 | — | 4 | 2 | no | — |
| 187 | Dic142 | — | 2 | 16 | no | — |
| 188 | Dic142 | — | 2 | 2 | no | — |
| 189 | Dic142 | — | 2 | 4 | no | — |
| 190 | Dic142 | — | 4 | 2 | no | — |
| 191 | Dic142 | — | 4 | 1 | no | — |
| 192 | Dic142 | — | 4 | 4 | no | — |
| 193 | Dic142 | — | 8 | 2 | no | — |
| 194 | Dic142 | — | 8 | 4 | no | — |
| 195 | C8×C71 | — | 4 | 4 | no | — |
| 196 | C71⋊C8 | — | 4 | 2 | no | — |
| 197 | C22×C71 | — | 2 | 2 | no | — |
| 198 | C22×C71 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 199 | C22×C71 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 200 | C22×C71 | C2×#120 | 1 | 1 | yes | characteristic |
| 201 | C2×D71 | — | 4 | 2 | no | — |
| 202 | C2×D71 | — | 8 | 2 | no | — |
| 203 | C4×C71 | — | 2 | 4 | no | — |
| 204 | C4×C71 | — | 2 | 1 | no | — |
| 205 | C4×C71 | — | 2 | 2 | no | — |
| 206 | C4×C71 | — | 2 | 2 | no | — |
| 207 | C4×C71 | — | 2 | 1 | no | — |
| 208 | C4×C71 | — | 4 | 2 | no | — |
| 209 | Dic71 | — | 2 | 8 | no | — |
| 210 | Dic71 | — | 4 | 2 | no | — |
| 211 | Dic71 | — | 4 | 4 | no | — |
| 212 | C2×#2205 | — | 71 | 1 | no | maximal, Sylow |
| 213 | C2×C71 | — | 2 | 1 | no | — |
| 214 | C2×C71 | — | 2 | 1 | no | — |
| 215 | C2×C71 | #2205 | 1 | 2 | yes | complemented |
| 216 | C2×C71 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 217 | D71 | — | 8 | 2 | no | — |
| 218 | C2×Q82 | — | 71 | 1 | no | — |
| 219 | C2×#456 | — | 71 | 2 | no | — |
| 220 | C2×#456 | — | 71 | 1 | no | — |
| 221 | #2205 | — | 71 | 8 | no | — |
| 222 | C2×#356 | — | 71 | 2 | no | — |
| 223 | C2×#356 | D71 | 1 | 1 | yes | characteristic, complemented |
| 224 | C71 | C2×#2205 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 225 | C2×2−1+4 | — | 71 | 1 | no | — |
| 226 | C2×#137 | — | 142 | 2 | no | — |
| 227 | C2×#137 | — | 142 | 1 | no | — |
| 228 | Q82 | — | 71 | 4 | no | — |
| 229 | Q82 | — | 142 | 4 | no | — |
| 230 | Q82 | — | 142 | 2 | no | — |
| 231 | C2×C4⋊Q8 | — | 71 | 2 | no | — |
| 232 | C2×C4⋊Q8 | — | 142 | 2 | no | — |
| 233 | C2×C4⋊Q8 | — | 142 | 1 | no | — |
| 234 | C2×C4⋊Q8 | C2×D71 | 1 | 1 | yes | characteristic |
| 235 | C2×C4×Q8 | — | 142 | 2 | no | — |
| 236 | C2×C4×Q8 | — | 142 | 1 | no | — |
| 237 | #456 | — | 71 | 4 | no | — |
| 238 | #456 | — | 71 | 8 | no | — |
| 239 | #456 | — | 142 | 4 | no | — |
| 240 | #456 | — | 142 | 2 | no | — |
| 241 | C2×#104 | — | 142 | 2 | no | — |
| 242 | C2×#104 | — | 142 | 1 | no | — |
| 243 | C2×#101 | — | 71 | 1 | no | — |
| 244 | C2×#101 | C2×D71 | 1 | 2 | yes | — |
| 245 | #356 | — | 71 | 8 | no | — |
| 246 | #356 | C2×D71 | 1 | 4 | yes | complemented |
| 247 | 2−1+4 | — | 284 | 2 | no | — |
| 248 | 2−1+4 | — | 71 | 2 | no | — |
| 249 | 2−1+4 | — | 142 | 2 | no | — |
| 250 | 2−1+4 | — | 142 | 1 | no | — |
| 251 | C2×#41 | — | 284 | 1 | no | — |
| 252 | C2×#41 | — | 142 | 2 | no | — |
| 253 | C2×#41 | — | 142 | 1 | no | — |
| 254 | C22×Q8 | — | 284 | 1 | no | — |
| 255 | C22×Q8 | — | 71 | 2 | no | — |
| 256 | C22×Q8 | — | 142 | 1 | no | — |
| 257 | C22×Q8 | — | 142 | 1 | no | — |
| 258 | C22×Q8 | D284 | 1 | 1 | yes | characteristic |
| 259 | C22×Q8 | C22×D71 | 1 | 1 | yes | characteristic |
| 260 | #137 | — | 284 | 4 | no | — |
| 261 | #137 | — | 284 | 2 | no | — |
| 262 | #137 | — | 142 | 8 | no | — |
| 263 | #137 | — | 142 | 4 | no | — |
| 264 | C2×Q16 | — | 284 | 2 | no | — |
| 265 | C2×Q16 | — | 284 | 1 | no | — |
| 266 | C2×SD16 | — | 284 | 2 | no | — |
| 267 | C2×SD16 | — | 284 | 1 | no | — |
| 268 | C2×M16 | — | 2 | 2 | no | — |
| 269 | C2×M16 | — | 142 | 1 | no | — |
| 270 | C4⋊Q8 | — | 2 | 2 | no | — |
| 271 | C4⋊Q8 | — | 71 | 4 | no | — |
| 272 | C4⋊Q8 | — | 71 | 4 | no | — |
| 273 | C4⋊Q8 | — | 142 | 8 | no | — |
| 274 | C4⋊Q8 | — | 142 | 8 | no | — |
| 275 | C4⋊Q8 | — | 142 | 4 | no | — |
| 276 | C4⋊Q8 | — | 142 | 2 | no | — |
| 277 | C4⋊Q8 | — | 142 | 2 | no | — |
| 278 | C4⋊Q8 | — | 142 | 4 | no | — |
| 279 | C4⋊Q8 | D284 | 1 | 2 | yes | — |
| 280 | C4⋊Q8 | C22×D71 | 1 | 2 | yes | — |
| 281 | C4×Q8 | — | 142 | 4 | no | — |
| 282 | C4×Q8 | — | 142 | 8 | no | — |
| 283 | C4×Q8 | — | 142 | 8 | no | — |
| 284 | C4×Q8 | — | 142 | 4 | no | — |
| 285 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 286 | C2×C4⋊C4 | — | 142 | 2 | no | — |
| 287 | C2×C4⋊C4 | — | 142 | 1 | no | — |
| 288 | C2×C4⋊C4 | — | 142 | 2 | no | — |
| 289 | C2×C4⋊C4 | — | 142 | 2 | no | — |
| 290 | C2×C42 | — | 71 | 2 | no | — |
| 291 | C2×C42 | — | 142 | 2 | no | — |
| 292 | C2×C42 | — | 142 | 1 | no | — |
| 293 | C2×C42 | D284 | 1 | 1 | yes | characteristic |
| 294 | #104 | — | 142 | 8 | no | — |
| 295 | #104 | — | 142 | 4 | no | — |
| 296 | #101 | — | 2 | 2 | no | — |
| 297 | #101 | — | 71 | 2 | no | — |
| 298 | #101 | — | 142 | 1 | no | — |
| 299 | #101 | C22×D71 | 1 | 4 | yes | — |
| 300 | #41 | — | 284 | 2 | no | — |
| 301 | #41 | — | 284 | 1 | no | — |
| 302 | #41 | — | 284 | 4 | no | — |
| 303 | #41 | — | 284 | 2 | no | — |
| 304 | #41 | — | 284 | 2 | no | — |
| 305 | #41 | — | 284 | 1 | no | — |
| 306 | #41 | — | 284 | 2 | no | — |
| 307 | #41 | — | 142 | 4 | no | — |
| 308 | #41 | — | 142 | 2 | no | — |
| 309 | #41 | — | 142 | 4 | no | — |
| 310 | #41 | — | 142 | 2 | no | — |
| 311 | C2×Q8 | — | 2 | 1 | no | — |
| 312 | C2×Q8 | — | 4 | 1 | no | — |
| 313 | C2×Q8 | — | 4 | 1 | no | — |
| 314 | C2×Q8 | — | 4 | 1 | no | — |
| 315 | C2×Q8 | — | 4 | 1 | no | — |
| 316 | C2×Q8 | — | 284 | 2 | no | — |
| 317 | C2×Q8 | — | 284 | 2 | no | — |
| 318 | C2×Q8 | — | 284 | 4 | no | — |
| 319 | C2×Q8 | — | 284 | 2 | no | — |
| 320 | C2×Q8 | — | 284 | 2 | no | — |
| 321 | C2×Q8 | — | 568 | 1 | no | — |
| 322 | C2×Q8 | — | 568 | 1 | no | — |
| 323 | C2×Q8 | — | 71 | 4 | no | — |
| 324 | C2×Q8 | — | 142 | 2 | no | — |
| 325 | C2×Q8 | — | 142 | 1 | no | — |
| 326 | C2×Q8 | — | 142 | 4 | no | — |
| 327 | C2×Q8 | — | 142 | 4 | no | — |
| 328 | C2×Q8 | — | 142 | 8 | no | — |
| 329 | C2×Q8 | — | 142 | 2 | no | — |
| 330 | C2×Q8 | D4×D71 | 1 | 2 | yes | — |
| 331 | C2×Q8 | C2×D284 | 1 | 2 | yes | — |
| 332 | C2×Q8 | C2×D284 | 1 | 1 | yes | characteristic |
| 333 | C2×Q8 | C23×D71 | 1 | 1 | yes | characteristic |
| 334 | C2×D4 | — | 284 | 1 | no | — |
| 335 | C2×D4 | — | 142 | 2 | no | — |
| 336 | C2×D4 | — | 142 | 1 | no | — |
| 337 | C22×C4 | — | 2 | 1 | no | — |
| 338 | C22×C4 | — | 2 | 1 | no | — |
| 339 | C22×C4 | — | 284 | 2 | no | — |
| 340 | C22×C4 | — | 284 | 1 | no | — |
| 341 | C22×C4 | — | 142 | 2 | no | — |
| 342 | C22×C4 | — | 142 | 2 | no | — |
| 343 | C22×C4 | D4×D71 | 1 | 2 | yes | — |
| 344 | C22×C4 | C2×D284 | 1 | 1 | yes | characteristic |
| 345 | Q16 | — | 284 | 8 | no | — |
| 346 | Q16 | — | 284 | 4 | no | — |
| 347 | SD16 | — | 284 | 8 | no | — |
| 348 | SD16 | — | 284 | 4 | no | — |
| 349 | M16 | — | 2 | 4 | no | — |
| 350 | M16 | — | 4 | 2 | no | — |
| 351 | M16 | — | 284 | 1 | no | — |
| 352 | M16 | — | 142 | 2 | no | — |
| 353 | C2×C8 | — | 4 | 2 | no | — |
| 354 | C2×C8 | — | 284 | 1 | no | — |
| 355 | C4⋊C4 | — | 2 | 4 | no | — |
| 356 | C4⋊C4 | — | 2 | 4 | no | — |
| 357 | C4⋊C4 | — | 142 | 8 | no | — |
| 358 | C4⋊C4 | — | 142 | 4 | no | — |
| 359 | C4⋊C4 | — | 142 | 4 | no | — |
| 360 | C4⋊C4 | — | 142 | 4 | no | — |
| 361 | C4⋊C4 | — | 142 | 4 | no | — |
| 362 | C4⋊C4 | — | 142 | 4 | no | — |
| 363 | C42 | — | 2 | 1 | no | — |
| 364 | C42 | — | 71 | 4 | no | — |
| 365 | C42 | — | 142 | 8 | no | — |
| 366 | C42 | — | 142 | 4 | no | — |
| 367 | C42 | — | 142 | 2 | no | — |
| 368 | C42 | C2×D284 | 1 | 2 | yes | — |
| 369 | C23 | — | 284 | 1 | no | — |
| 370 | C23 | #14556098 | 1 | 1 | yes | characteristic |
| 371 | Q8 | — | 4 | 2 | no | — |
| 372 | Q8 | — | 4 | 1 | no | — |
| 373 | Q8 | — | 4 | 1 | no | — |
| 374 | Q8 | — | 4 | 2 | no | — |
| 375 | Q8 | — | 8 | 1 | no | — |
| 376 | Q8 | — | 284 | 4 | no | — |
| 377 | Q8 | — | 284 | 1 | no | — |
| 378 | Q8 | — | 284 | 2 | no | — |
| 379 | Q8 | — | 568 | 2 | no | — |
| 380 | Q8 | — | 568 | 4 | no | — |
| 381 | Q8 | — | 142 | 4 | no | — |
| 382 | Q8 | — | 142 | 2 | no | — |
| 383 | Q8 | — | 142 | 16 | no | — |
| 384 | D4 | — | 284 | 1 | no | — |
| 385 | D4 | — | 284 | 2 | no | — |
| 386 | D4 | — | 284 | 2 | no | — |
| 387 | D4 | — | 284 | 2 | no | — |
| 388 | D4 | — | 142 | 4 | no | — |
| 389 | D4 | — | 142 | 2 | no | — |
| 390 | C2×C4 | — | 2 | 4 | no | — |
| 391 | C2×C4 | — | 2 | 2 | no | — |
| 392 | C2×C4 | — | 2 | 1 | no | — |
| 393 | C2×C4 | — | 2 | 2 | no | — |
| 394 | C2×C4 | — | 2 | 1 | no | — |
| 395 | C2×C4 | — | 2 | 2 | no | — |
| 396 | C2×C4 | — | 2 | 2 | no | — |
| 397 | C2×C4 | — | 4 | 1 | no | — |
| 398 | C2×C4 | — | 4 | 1 | no | — |
| 399 | C2×C4 | — | 284 | 4 | no | — |
| 400 | C2×C4 | — | 284 | 2 | no | — |
| 401 | C2×C4 | — | 284 | 2 | no | — |
| 402 | C2×C4 | — | 284 | 4 | no | — |
| 403 | C2×C4 | — | 284 | 2 | no | — |
| 404 | C2×C4 | — | 284 | 1 | no | — |
| 405 | C2×C4 | — | 284 | 2 | no | — |
| 406 | C2×C4 | — | 142 | 4 | no | — |
| 407 | C2×C4 | — | 142 | 8 | no | — |
| 408 | C2×C4 | — | 142 | 4 | no | — |
| 409 | C2×C4 | #14556098 | 1 | 1 | yes | characteristic |
| 410 | C2×C4 | #14556098 | 1 | 2 | yes | — |
| 411 | C2×C4 | C2×D4×D71 | 1 | 2 | yes | — |
| 412 | C2×C4 | C22×D284 | 1 | 1 | yes | characteristic |
| 413 | C8 | — | 4 | 4 | no | — |
| 414 | C8 | — | 284 | 2 | no | — |
| 415 | C22 | — | 2 | 2 | no | — |
| 416 | C22 | — | 284 | 2 | no | — |
| 417 | C22 | — | 568 | 2 | no | — |
| 418 | C22 | #17986187 | 1 | 1 | yes | characteristic |
| 419 | C22 | #17986187 | 1 | 1 | yes | characteristic |
| 420 | C22 | C2×#14556098 | 1 | 1 | yes | characteristic |
| 421 | C4 | — | 2 | 4 | no | — |
| 422 | C4 | — | 2 | 2 | no | — |
| 423 | C4 | — | 2 | 1 | no | — |
| 424 | C4 | — | 2 | 1 | no | — |
| 425 | C4 | — | 2 | 2 | no | — |
| 426 | C4 | — | 4 | 2 | no | — |
| 427 | C4 | — | 284 | 2 | no | — |
| 428 | C4 | — | 284 | 4 | no | — |
| 429 | C4 | — | 142 | 8 | no | — |
| 430 | C2 | — | 2 | 1 | no | — |
| 431 | C2 | — | 2 | 1 | no | — |
| 432 | C2 | — | 568 | 2 | no | — |
| 433 | C2 | #22590371 | 1 | 2 | yes | direct product factor |
| 434 | C2 | C2×#17986187 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#17986729 | C2 | semidirect |
| 4. #22590371 | C2 | direct (N × H) |
| 5. C2×#17985797 | C2 | semidirect |
| 6. C2×#356×C71 | C2 | semidirect |
| 12. #17986729 | C22 | semidirect |
| 25. #17985797 | C22 | semidirect |
| 28. #356×C71 | C22 | semidirect |
| 215. C2×C71 | #2205 | semidirect |
| 223. C2×#356 | D71 | semidirect |
| 224. C71 | C2×#2205 | semidirect |
| 246. #356 | C2×D71 | semidirect |
| 433. C2 | #22590371 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986729 | 2 |
| C2×#17986184 | 2 |
| C2×#17986181 | 2 |
| #22590371 | 2 |
| C2×#17985797 | 2 |
| C2×#356×C71 | 2 |
| C2×#2205 | 71 |