Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
412 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 55 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 | #11733917 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C7×#2027 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11729656 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11729653 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11725446 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11725302 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11725299 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C7×#544 | C22 | 1 | 1 | yes | characteristic |
| 9 | C7×#418 | — | 2 | 1 | no | — |
| 10 | C7×#390 | C22 | 1 | 1 | yes | characteristic |
| 11 | #89995 | — | 2 | 1 | no | — |
| 12 | #89818 | — | 2 | 1 | no | — |
| 13 | #89816 | — | 2 | 1 | no | — |
| 14 | #89763 | C22 | 1 | 1 | yes | characteristic |
| 15 | #89758 | C22 | 1 | 1 | yes | characteristic |
| 16 | #89733 | — | 2 | 1 | no | — |
| 17 | #89732 | — | 2 | 1 | no | — |
| 18 | #89731 | — | 2 | 1 | no | — |
| 19 | #89724 | — | 2 | 1 | no | — |
| 20 | #89712 | — | 2 | 1 | no | — |
| 21 | C7×#343 | C22 | 1 | 1 | yes | characteristic |
| 22 | C7×#339 | — | 2 | 1 | no | — |
| 23 | #89333 | — | 2 | 1 | no | — |
| 24 | #89333 | — | 2 | 1 | no | — |
| 25 | #89323 | C22 | 1 | 1 | yes | characteristic |
| 26 | #89323 | C22 | 1 | 1 | yes | characteristic |
| 27 | #12274 | — | 7 | 1 | no | maximal, Sylow |
| 28 | C22×C7×D4 | D4 | 1 | 1 | yes | characteristic |
| 29 | C22×C22⋊D7 | — | 2 | 1 | no | — |
| 30 | C22×C22⋊D7 | — | 2 | 1 | no | — |
| 31 | C22×D28 | D4 | 1 | 1 | yes | characteristic |
| 32 | C2×C7×M16 | — | 2 | 1 | no | — |
| 33 | C7×C4⋊Q8 | — | 4 | 1 | no | — |
| 34 | C7×#125 | — | 4 | 1 | no | — |
| 35 | C7×C22⋊Q8 | — | 2 | 1 | no | — |
| 36 | C7×C22⋊Q8 | — | 2 | 1 | no | — |
| 37 | C7×#117 | — | 2 | 1 | no | — |
| 38 | C2×C7×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 39 | C2×C7×C22⋊C4 | — | 2 | 1 | no | — |
| 40 | C2×C7×C22⋊C4 | — | 2 | 1 | no | — |
| 41 | C2×C42×C7 | D4 | 1 | 1 | yes | characteristic |
| 42 | C2×C22⋊Dic7 | — | 2 | 1 | no | — |
| 43 | C2×C22⋊Dic7 | — | 2 | 1 | no | — |
| 44 | C2×#1143 | — | 4 | 1 | no | — |
| 45 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 46 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 47 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 48 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 49 | C2×C4⋊Dic7 | D4 | 1 | 1 | yes | characteristic |
| 50 | C2×Dic7⋊C4 | — | 2 | 1 | no | — |
| 51 | C7×#102 | — | 4 | 1 | no | — |
| 52 | C7×#102 | — | 4 | 1 | no | — |
| 53 | #6409 | — | 4 | 1 | no | — |
| 54 | C7⋊#95 | — | 2 | 1 | no | — |
| 55 | C7⋊#95 | — | 2 | 1 | no | — |
| 56 | C7⋊#95 | — | 2 | 1 | no | — |
| 57 | C7⋊#95 | D4 | 1 | 1 | yes | characteristic |
| 58 | C7⋊#95 | D4 | 1 | 1 | yes | characteristic |
| 59 | C22⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 60 | C22⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 61 | #6383 | — | 4 | 1 | no | — |
| 62 | #6381 | — | 4 | 1 | no | — |
| 63 | #2828 | — | 7 | 1 | no | — |
| 64 | #2027 | D7 | 1 | 1 | yes | characteristic, complemented |
| 65 | #1617 | — | 7 | 1 | no | — |
| 66 | #1599 | — | 7 | 1 | no | — |
| 67 | #1353 | — | 7 | 1 | no | — |
| 68 | #1345 | — | 7 | 1 | no | — |
| 69 | #1318 | — | 7 | 1 | no | — |
| 70 | C24×C7 | — | 2 | 1 | no | — |
| 71 | C23×D7 | — | 2 | 1 | no | — |
| 72 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 73 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 74 | C2×C7×D4 | — | 2 | 1 | no | — |
| 75 | C2×C7×D4 | — | 2 | 1 | no | — |
| 76 | C2×C7×D4 | — | 4 | 1 | no | — |
| 77 | C2×C7×D4 | — | 4 | 1 | no | — |
| 78 | C22×C4×C7 | — | 2 | 1 | no | — |
| 79 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 80 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 81 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 82 | C2×C22⋊D7 | — | 8 | 1 | no | — |
| 83 | C2×C22⋊D7 | — | 8 | 1 | no | — |
| 84 | C2×C22⋊D7 | — | 8 | 1 | no | — |
| 85 | C2×C22⋊D7 | — | 8 | 1 | no | — |
| 86 | C2×C22⋊D7 | — | 8 | 1 | no | — |
| 87 | C2×C22⋊D7 | — | 8 | 1 | no | — |
| 88 | C22×Dic7 | — | 2 | 1 | no | — |
| 89 | C22×Dic7 | — | 2 | 1 | no | — |
| 90 | C22×Dic7 | — | 2 | 1 | no | — |
| 91 | C2×D28 | — | 4 | 1 | no | — |
| 92 | C2×D28 | — | 8 | 1 | no | — |
| 93 | C7×M16 | — | 4 | 1 | no | — |
| 94 | C7×M16 | — | 4 | 1 | no | — |
| 95 | C2×C7×C8 | — | 4 | 1 | no | — |
| 96 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 97 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 98 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 99 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 100 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 101 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 102 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 103 | C7×C22⋊C4 | — | 4 | 1 | no | — |
| 104 | C7×C22⋊C4 | — | 8 | 1 | no | — |
| 105 | C7×C22⋊C4 | — | 8 | 1 | no | — |
| 106 | C42×C7 | — | 4 | 1 | no | — |
| 107 | C42×C7 | — | 4 | 1 | no | — |
| 108 | C22⋊Dic7 | — | 8 | 1 | no | — |
| 109 | C22⋊Dic7 | — | 8 | 1 | no | — |
| 110 | #1143 | — | 8 | 2 | no | — |
| 111 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 112 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 113 | (C2×D7)⋊C4 | — | 8 | 1 | no | — |
| 114 | (C2×D7)⋊C4 | — | 8 | 1 | no | — |
| 115 | (C2×D7)⋊C4 | — | 8 | 1 | no | — |
| 116 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 117 | Dic7⋊C4 | — | 8 | 1 | no | — |
| 118 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 119 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 120 | #544 | C2×D7 | 1 | 1 | yes | characteristic |
| 121 | #484 | — | 14 | 1 | no | — |
| 122 | #450 | — | 14 | 1 | no | — |
| 123 | #418 | — | 2 | 1 | no | — |
| 124 | #400 | — | 7 | 1 | no | — |
| 125 | #397 | — | 14 | 1 | no | — |
| 126 | #394 | — | 7 | 1 | no | — |
| 127 | #394 | — | 14 | 1 | no | — |
| 128 | #394 | — | 14 | 1 | no | — |
| 129 | #392 | — | 14 | 1 | no | — |
| 130 | #392 | — | 14 | 1 | no | — |
| 131 | #390 | C2×D7 | 1 | 1 | yes | characteristic |
| 132 | #388 | — | 14 | 1 | no | — |
| 133 | #343 | C2×D7 | 1 | 1 | yes | characteristic |
| 134 | #339 | — | 2 | 1 | no | — |
| 135 | #328 | — | 14 | 1 | no | — |
| 136 | #328 | — | 14 | 1 | no | — |
| 137 | #324 | — | 7 | 1 | no | — |
| 138 | #324 | — | 7 | 1 | no | — |
| 139 | C23×C7 | — | 4 | 1 | no | — |
| 140 | C23×C7 | — | 4 | 1 | no | — |
| 141 | C23×C7 | — | 4 | 1 | no | — |
| 142 | C23×C7 | — | 4 | 1 | no | — |
| 143 | C23×C7 | — | 4 | 1 | no | — |
| 144 | C23×C7 | — | 4 | 1 | no | — |
| 145 | C23×C7 | — | 4 | 1 | no | — |
| 146 | C23×C7 | #120 | 1 | 1 | yes | characteristic |
| 147 | C22×D7 | — | 4 | 1 | no | — |
| 148 | C22×D7 | — | 4 | 1 | no | — |
| 149 | C22×D7 | — | 4 | 1 | no | — |
| 150 | C22×D7 | — | 4 | 1 | no | — |
| 151 | C22×D7 | — | 4 | 1 | no | — |
| 152 | C22×D7 | — | 4 | 1 | no | — |
| 153 | C22×D7 | — | 4 | 1 | no | — |
| 154 | C7×Q8 | — | 8 | 1 | no | — |
| 155 | C7×Q8 | — | 8 | 1 | no | — |
| 156 | C7×D4 | — | 4 | 2 | no | — |
| 157 | C7×D4 | — | 8 | 1 | no | — |
| 158 | C2×C4×C7 | — | 2 | 1 | no | — |
| 159 | C2×C4×C7 | — | 2 | 1 | no | — |
| 160 | C2×C4×C7 | — | 2 | 1 | no | — |
| 161 | C2×C4×C7 | — | 2 | 1 | no | — |
| 162 | C2×C4×C7 | — | 4 | 1 | no | — |
| 163 | C2×C4×C7 | — | 4 | 1 | no | — |
| 164 | C2×C4×C7 | — | 4 | 1 | no | — |
| 165 | C2×C4×C7 | — | 4 | 1 | no | — |
| 166 | C2×C4×C7 | — | 4 | 1 | no | — |
| 167 | C2×C4×C7 | — | 4 | 1 | no | — |
| 168 | C2×C4×C7 | — | 4 | 1 | no | — |
| 169 | C2×C4×C7 | #135 | 1 | 1 | yes | characteristic |
| 170 | C2×C4×C7 | #137 | 1 | 1 | yes | characteristic |
| 171 | C22⋊D7 | — | 8 | 4 | no | — |
| 172 | C22⋊D7 | — | 8 | 4 | no | — |
| 173 | C2×Dic7 | — | 4 | 1 | no | — |
| 174 | C2×Dic7 | — | 4 | 1 | no | — |
| 175 | C2×Dic7 | — | 4 | 1 | no | — |
| 176 | C2×Dic7 | — | 4 | 1 | no | — |
| 177 | C2×Dic7 | — | 4 | 1 | no | — |
| 178 | C2×Dic7 | — | 4 | 1 | no | — |
| 179 | C2×Dic7 | — | 4 | 1 | no | — |
| 180 | C2×Dic7 | — | 4 | 1 | no | — |
| 181 | C2×Dic7 | — | 4 | 1 | no | — |
| 182 | D28 | — | 4 | 2 | no | — |
| 183 | D28 | — | 8 | 1 | no | — |
| 184 | C7×C8 | — | 8 | 1 | no | — |
| 185 | C7⋊C8 | — | 8 | 1 | no | — |
| 186 | C7⋊C8 | — | 8 | 1 | no | — |
| 187 | C22×D4 | — | 7 | 1 | no | — |
| 188 | C22×D4 | — | 14 | 1 | no | — |
| 189 | C22×D4 | — | 14 | 1 | no | — |
| 190 | C22×D4 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 191 | C2×SD16 | — | 28 | 1 | no | — |
| 192 | C2×M16 | — | 2 | 1 | no | — |
| 193 | C4⋊Q8 | — | 4 | 1 | no | — |
| 194 | #125 | — | 4 | 1 | no | — |
| 195 | C22⋊Q8 | — | 2 | 1 | no | — |
| 196 | C22⋊Q8 | — | 2 | 1 | no | — |
| 197 | #117 | — | 2 | 1 | no | — |
| 198 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 199 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 200 | C2×C4⋊C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 201 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 202 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 203 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 204 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 205 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 206 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 207 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 208 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 209 | C2×C42 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 210 | #107 | — | 28 | 1 | no | — |
| 211 | #103 | — | 28 | 1 | no | — |
| 212 | #102 | — | 4 | 1 | no | — |
| 213 | #102 | — | 4 | 1 | no | — |
| 214 | #102 | — | 28 | 1 | no | — |
| 215 | C22⋊C8 | — | 14 | 1 | no | — |
| 216 | C22⋊C8 | — | 14 | 1 | no | — |
| 217 | #95 | — | 7 | 1 | no | — |
| 218 | #95 | — | 7 | 1 | no | — |
| 219 | #95 | — | 14 | 1 | no | — |
| 220 | #95 | — | 14 | 1 | no | — |
| 221 | #95 | — | 14 | 1 | no | — |
| 222 | C22×C7 | — | 2 | 1 | no | — |
| 223 | C22×C7 | — | 2 | 1 | no | — |
| 224 | C22×C7 | — | 8 | 1 | no | — |
| 225 | C22×C7 | — | 8 | 1 | no | — |
| 226 | C22×C7 | — | 8 | 1 | no | — |
| 227 | C22×C7 | — | 8 | 1 | no | — |
| 228 | C22×C7 | — | 8 | 1 | no | — |
| 229 | C22×C7 | — | 8 | 1 | no | — |
| 230 | C22×C7 | — | 8 | 1 | no | — |
| 231 | C22×C7 | #452 | 1 | 1 | yes | characteristic |
| 232 | C22×C7 | #455 | 1 | 1 | yes | characteristic |
| 233 | C22×C7 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 234 | C2×D7 | — | 8 | 1 | no | — |
| 235 | C2×D7 | — | 8 | 1 | no | — |
| 236 | C2×D7 | — | 8 | 1 | no | — |
| 237 | C2×D7 | — | 8 | 1 | no | — |
| 238 | C2×D7 | — | 8 | 1 | no | — |
| 239 | C2×D7 | — | 8 | 1 | no | — |
| 240 | C2×D7 | — | 8 | 1 | no | — |
| 241 | C4×C7 | — | 2 | 1 | no | — |
| 242 | C4×C7 | — | 2 | 1 | no | — |
| 243 | C4×C7 | — | 4 | 1 | no | — |
| 244 | C4×C7 | — | 4 | 1 | no | — |
| 245 | C4×C7 | — | 8 | 1 | no | — |
| 246 | C4×C7 | — | 8 | 1 | no | — |
| 247 | C4×C7 | — | 8 | 1 | no | — |
| 248 | Dic7 | — | 8 | 1 | no | — |
| 249 | Dic7 | — | 8 | 1 | no | — |
| 250 | Dic7 | — | 8 | 1 | no | — |
| 251 | C24 | — | 2 | 1 | no | — |
| 252 | C24 | — | 14 | 1 | no | — |
| 253 | C2×Q8 | — | 2 | 1 | no | — |
| 254 | C2×Q8 | — | 2 | 1 | no | — |
| 255 | C2×D4 | — | 2 | 1 | no | — |
| 256 | C2×D4 | — | 2 | 1 | no | — |
| 257 | C2×D4 | — | 4 | 1 | no | — |
| 258 | C2×D4 | — | 4 | 1 | no | — |
| 259 | C2×D4 | — | 28 | 1 | no | — |
| 260 | C2×D4 | — | 56 | 1 | no | — |
| 261 | C2×D4 | — | 56 | 1 | no | — |
| 262 | C2×D4 | — | 56 | 1 | no | — |
| 263 | C2×D4 | — | 56 | 1 | no | — |
| 264 | C2×D4 | — | 56 | 1 | no | — |
| 265 | C2×D4 | — | 56 | 1 | no | — |
| 266 | C2×D4 | — | 56 | 1 | no | — |
| 267 | C22×C4 | — | 2 | 1 | no | — |
| 268 | C22×C4 | — | 14 | 1 | no | — |
| 269 | C22×C4 | — | 14 | 1 | no | — |
| 270 | C22×C4 | — | 14 | 1 | no | — |
| 271 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 272 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 273 | C22×C4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 274 | SD16 | — | 56 | 2 | no | — |
| 275 | M16 | — | 4 | 1 | no | — |
| 276 | M16 | — | 4 | 1 | no | — |
| 277 | C2×C8 | — | 4 | 1 | no | — |
| 278 | C2×C8 | — | 28 | 1 | no | — |
| 279 | C2×C8 | — | 28 | 1 | no | — |
| 280 | C4⋊C4 | — | 2 | 1 | no | — |
| 281 | C4⋊C4 | — | 2 | 1 | no | — |
| 282 | C4⋊C4 | — | 2 | 1 | no | — |
| 283 | C4⋊C4 | — | 2 | 1 | no | — |
| 284 | C4⋊C4 | — | 4 | 1 | no | — |
| 285 | C4⋊C4 | — | 4 | 1 | no | — |
| 286 | C4⋊C4 | — | 4 | 1 | no | — |
| 287 | C4⋊C4 | — | 28 | 1 | no | — |
| 288 | C4⋊C4 | — | 56 | 1 | no | — |
| 289 | C22⋊C4 | — | 4 | 1 | no | — |
| 290 | C22⋊C4 | — | 8 | 1 | no | — |
| 291 | C22⋊C4 | — | 8 | 1 | no | — |
| 292 | C22⋊C4 | — | 28 | 1 | no | — |
| 293 | C22⋊C4 | — | 28 | 1 | no | — |
| 294 | C22⋊C4 | — | 56 | 1 | no | — |
| 295 | C22⋊C4 | — | 56 | 1 | no | — |
| 296 | C22⋊C4 | — | 56 | 1 | no | — |
| 297 | C22⋊C4 | — | 56 | 1 | no | — |
| 298 | C22⋊C4 | — | 56 | 1 | no | — |
| 299 | C42 | — | 4 | 1 | no | — |
| 300 | C42 | — | 4 | 1 | no | — |
| 301 | C2×C7 | — | 2 | 1 | no | — |
| 302 | C2×C7 | — | 2 | 1 | no | — |
| 303 | C2×C7 | — | 16 | 1 | no | — |
| 304 | C2×C7 | #1606 | 1 | 1 | yes | characteristic |
| 305 | C2×C7 | #2200 | 1 | 1 | yes | characteristic |
| 306 | C2×C7 | #2202 | 1 | 1 | yes | characteristic |
| 307 | D7 | — | 16 | 1 | no | — |
| 308 | C23 | — | 4 | 1 | no | — |
| 309 | C23 | — | 4 | 1 | no | — |
| 310 | C23 | — | 4 | 1 | no | — |
| 311 | C23 | — | 4 | 1 | no | — |
| 312 | C23 | — | 4 | 1 | no | — |
| 313 | C23 | — | 4 | 1 | no | — |
| 314 | C23 | — | 4 | 1 | no | — |
| 315 | C23 | — | 28 | 1 | no | — |
| 316 | C23 | — | 28 | 1 | no | — |
| 317 | C23 | — | 28 | 1 | no | — |
| 318 | C23 | — | 28 | 1 | no | — |
| 319 | C23 | — | 28 | 1 | no | — |
| 320 | C23 | — | 28 | 1 | no | — |
| 321 | C23 | — | 28 | 1 | no | — |
| 322 | C23 | #6500 | 1 | 1 | yes | characteristic |
| 323 | Q8 | — | 8 | 1 | no | — |
| 324 | Q8 | — | 8 | 1 | no | — |
| 325 | D4 | — | 4 | 2 | no | — |
| 326 | D4 | — | 8 | 1 | no | — |
| 327 | D4 | — | 28 | 2 | no | — |
| 328 | D4 | — | 56 | 1 | no | — |
| 329 | D4 | — | 56 | 4 | no | — |
| 330 | D4 | — | 56 | 4 | no | — |
| 331 | C2×C4 | — | 2 | 1 | no | — |
| 332 | C2×C4 | — | 2 | 1 | no | — |
| 333 | C2×C4 | — | 2 | 1 | no | — |
| 334 | C2×C4 | — | 2 | 1 | no | — |
| 335 | C2×C4 | — | 4 | 1 | no | — |
| 336 | C2×C4 | — | 4 | 1 | no | — |
| 337 | C2×C4 | — | 4 | 1 | no | — |
| 338 | C2×C4 | — | 4 | 1 | no | — |
| 339 | C2×C4 | — | 4 | 1 | no | — |
| 340 | C2×C4 | — | 4 | 1 | no | — |
| 341 | C2×C4 | — | 4 | 1 | no | — |
| 342 | C2×C4 | — | 28 | 1 | no | — |
| 343 | C2×C4 | — | 28 | 1 | no | — |
| 344 | C2×C4 | — | 28 | 1 | no | — |
| 345 | C2×C4 | — | 28 | 1 | no | — |
| 346 | C2×C4 | — | 28 | 1 | no | — |
| 347 | C2×C4 | — | 28 | 1 | no | — |
| 348 | C2×C4 | — | 28 | 1 | no | — |
| 349 | C2×C4 | — | 28 | 1 | no | — |
| 350 | C2×C4 | — | 28 | 1 | no | — |
| 351 | C2×C4 | #6505 | 1 | 1 | yes | characteristic |
| 352 | C2×C4 | #6513 | 1 | 1 | yes | characteristic |
| 353 | C8 | — | 8 | 1 | no | — |
| 354 | C8 | — | 56 | 1 | no | — |
| 355 | C8 | — | 56 | 1 | no | — |
| 356 | C7 | #12274 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 357 | C22 | — | 2 | 1 | no | — |
| 358 | C22 | — | 2 | 1 | no | — |
| 359 | C22 | — | 8 | 1 | no | — |
| 360 | C22 | — | 8 | 1 | no | — |
| 361 | C22 | — | 8 | 1 | no | — |
| 362 | C22 | — | 8 | 1 | no | — |
| 363 | C22 | — | 8 | 1 | no | — |
| 364 | C22 | — | 8 | 1 | no | — |
| 365 | C22 | — | 8 | 1 | no | — |
| 366 | C22 | — | 56 | 1 | no | — |
| 367 | C22 | — | 56 | 1 | no | — |
| 368 | C22 | — | 56 | 1 | no | — |
| 369 | C22 | — | 56 | 1 | no | — |
| 370 | C22 | — | 56 | 1 | no | — |
| 371 | C22 | — | 56 | 1 | no | — |
| 372 | C22 | — | 56 | 1 | no | — |
| 373 | C22 | #89804 | 1 | 1 | yes | characteristic |
| 374 | C22 | #89819 | 1 | 1 | yes | characteristic |
| 375 | C22 | #89833 | 1 | 1 | yes | characteristic |
| 376 | C4 | — | 2 | 1 | no | — |
| 377 | C4 | — | 2 | 1 | no | — |
| 378 | C4 | — | 4 | 1 | no | — |
| 379 | C4 | — | 4 | 1 | no | — |
| 380 | C4 | — | 8 | 1 | no | — |
| 381 | C4 | — | 8 | 1 | no | — |
| 382 | C4 | — | 8 | 1 | no | — |
| 383 | C4 | — | 56 | 1 | no | — |
| 384 | C4 | — | 56 | 1 | no | — |
| 385 | C4 | — | 56 | 1 | no | — |
| 386 | C2 | — | 2 | 1 | no | — |
| 387 | C2 | — | 2 | 1 | no | — |
| 388 | C2 | — | 16 | 1 | no | — |
| 389 | C2 | — | 112 | 1 | no | — |
| 390 | C2 | #11727454 | 1 | 1 | yes | characteristic |
| 391 | C2 | #11728739 | 1 | 1 | yes | characteristic |
| 392 | C2 | #11728741 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#2027 | C2 | semidirect |
| 3. #11729656 | C2 | semidirect |
| 4. #11729653 | C2 | semidirect |
| 5. #11725446 | C2 | semidirect |
| 6. #11725302 | C2 | semidirect |
| 7. #11725299 | C2 | semidirect |
| 64. #2027 | D7 | semidirect |
| 356. C7 | #12274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11733917 | 2 |
| C7×#2027 | 2 |
| #11729656 | 2 |
| #11729653 | 2 |
| #11725446 | 2 |
| #11725302 | 2 |
| #11725299 | 2 |
| #12274 | 7 |