Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1144 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 151 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 | #22574345 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22569601 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22562221 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22562215 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #22562209 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22561874 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #22561851 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C67×#3018 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #16864146 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | #16864145 | — | 2 | 1 | no | — |
| 11 | #16864141 | — | 2 | 2 | no | — |
| 12 | #16864140 | — | 2 | 1 | no | — |
| 13 | #16864138 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | #16864134 | — | 2 | 2 | no | — |
| 15 | #16864133 | C22 | 1 | 2 | yes | complemented |
| 16 | #16863942 | — | 2 | 1 | no | — |
| 17 | #16863930 | — | 2 | 1 | no | — |
| 18 | #16863926 | — | 2 | 2 | no | — |
| 19 | #16863905 | — | 2 | 2 | no | — |
| 20 | #16863903 | — | 2 | 2 | no | — |
| 21 | #16863903 | C22 | 1 | 2 | yes | — |
| 22 | #16863586 | — | 2 | 2 | no | — |
| 23 | #16863586 | C22 | 1 | 4 | yes | — |
| 24 | #16863583 | — | 2 | 2 | no | — |
| 25 | #16863583 | C22 | 1 | 4 | yes | — |
| 26 | #16863370 | — | 2 | 2 | no | — |
| 27 | #16863370 | C22 | 1 | 2 | yes | — |
| 28 | #16863191 | C22 | 1 | 2 | yes | complemented |
| 29 | #16863189 | C22 | 1 | 2 | yes | complemented |
| 30 | #16863187 | C22 | 1 | 4 | yes | complemented |
| 31 | #16863184 | C22 | 1 | 4 | yes | complemented |
| 32 | #585×C67 | C22 | 1 | 1 | yes | characteristic |
| 33 | #575×C67 | — | 2 | 1 | no | — |
| 34 | #532×C67 | C22 | 1 | 1 | yes | characteristic |
| 35 | #456×C67 | — | 2 | 1 | no | — |
| 36 | #455×C67 | C22 | 1 | 2 | yes | — |
| 37 | #454×C67 | — | 2 | 1 | no | — |
| 38 | #453×C67 | C22 | 1 | 2 | yes | — |
| 39 | C2×#104×C67 | — | 2 | 1 | no | — |
| 40 | #413×C67 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#11761628 | — | 2 | 1 | no | — |
| 42 | C22×C4×D67 | D4 | 1 | 2 | yes | complemented |
| 43 | #14524041 | — | 2 | 1 | no | — |
| 44 | #14524039 | — | 2 | 1 | no | — |
| 45 | #14524038 | — | 2 | 2 | no | — |
| 46 | #14524037 | — | 2 | 2 | no | — |
| 47 | #14524036 | — | 2 | 2 | no | — |
| 48 | #14524035 | — | 2 | 1 | no | — |
| 49 | #14524033 | — | 2 | 2 | no | — |
| 50 | #14524032 | — | 2 | 1 | no | — |
| 51 | #14524031 | — | 2 | 1 | no | — |
| 52 | #14524030 | — | 2 | 1 | no | — |
| 53 | #14524029 | — | 2 | 2 | no | — |
| 54 | #14524028 | — | 2 | 2 | no | — |
| 55 | #14524027 | — | 2 | 2 | no | — |
| 56 | #14524026 | — | 2 | 2 | no | — |
| 57 | #14524025 | — | 2 | 2 | no | — |
| 58 | #14524024 | — | 2 | 2 | no | — |
| 59 | #14524024 | — | 2 | 4 | no | — |
| 60 | #14524024 | D4 | 1 | 2 | yes | complemented |
| 61 | #14524024 | C23 | 1 | 2 | yes | — |
| 62 | #14524022 | — | 2 | 1 | no | — |
| 63 | #14524021 | — | 2 | 2 | no | — |
| 64 | #14524020 | — | 2 | 2 | no | — |
| 65 | #14524020 | — | 2 | 2 | no | — |
| 66 | #14524019 | — | 2 | 2 | no | — |
| 67 | #14524019 | — | 4 | 2 | no | — |
| 68 | #14524017 | — | 2 | 1 | no | — |
| 69 | #14524016 | — | 2 | 2 | no | — |
| 70 | #14524015 | — | 2 | 2 | no | — |
| 71 | #14524015 | — | 2 | 2 | no | — |
| 72 | #14524015 | — | 2 | 2 | no | — |
| 73 | #14524015 | — | 2 | 2 | no | — |
| 74 | #14524014 | — | 2 | 2 | no | — |
| 75 | #14524014 | — | 4 | 2 | no | — |
| 76 | #14524013 | — | 2 | 2 | no | — |
| 77 | #14524011 | — | 2 | 2 | no | — |
| 78 | #14524011 | — | 2 | 4 | no | — |
| 79 | #14524011 | D4 | 1 | 2 | yes | complemented |
| 80 | #14524011 | C23 | 1 | 2 | yes | — |
| 81 | C4×Dic134 | — | 2 | 1 | no | — |
| 82 | C4×D268 | — | 2 | 1 | no | — |
| 83 | C4×C22⋊D67 | — | 2 | 2 | no | — |
| 84 | C4×C22⋊D67 | — | 2 | 2 | no | — |
| 85 | C4×C22⋊D67 | — | 2 | 2 | no | — |
| 86 | C4×C22⋊D67 | — | 4 | 4 | no | — |
| 87 | #14524002 | — | 2 | 2 | no | — |
| 88 | #14524002 | D4 | 1 | 2 | yes | complemented |
| 89 | #14524000 | — | 2 | 2 | no | — |
| 90 | C2×C4×Dic67 | — | 2 | 1 | no | — |
| 91 | #14523958 | — | 2 | 4 | no | — |
| 92 | #14523958 | — | 2 | 4 | no | — |
| 93 | #14523958 | — | 2 | 2 | no | — |
| 94 | #14523958 | C23 | 1 | 4 | yes | — |
| 95 | 2−1+4×C67 | — | 2 | 1 | no | — |
| 96 | 2−1+4×C67 | — | 4 | 1 | no | — |
| 97 | H(5,𝔽2)×C67 | — | 2 | 2 | no | — |
| 98 | H(5,𝔽2)×C67 | — | 4 | 1 | no | — |
| 99 | H(5,𝔽2)×C67 | C23 | 1 | 2 | yes | — |
| 100 | C2×#41×C67 | — | 2 | 2 | no | — |
| 101 | C2×#41×C67 | — | 2 | 1 | no | — |
| 102 | C2×#41×C67 | — | 4 | 2 | no | — |
| 103 | C2×#41×C67 | D4 | 1 | 1 | yes | characteristic, complemented |
| 104 | C2×#41×C67 | C23 | 1 | 1 | yes | characteristic |
| 105 | #137×C67 | — | 2 | 2 | no | — |
| 106 | #137×C67 | — | 4 | 1 | no | — |
| 107 | AGL(1,ℤ/8)×C67 | — | 2 | 2 | no | — |
| 108 | AGL(1,ℤ/8)×C67 | — | 4 | 1 | no | — |
| 109 | #135×C67 | — | 4 | 2 | no | — |
| 110 | C2×M16×C67 | — | 2 | 1 | no | — |
| 111 | C4⋊Q8×C67 | D4 | 1 | 1 | yes | characteristic, complemented |
| 112 | #127×C67 | C23 | 1 | 1 | yes | characteristic |
| 113 | #124×C67 | D4 | 1 | 1 | yes | characteristic, complemented |
| 114 | #124×C67 | C23 | 1 | 1 | yes | characteristic |
| 115 | #121×C67 | — | 2 | 2 | no | — |
| 116 | C4×D4×C67 | — | 2 | 2 | no | — |
| 117 | C2×C42×C67 | D4 | 1 | 1 | yes | characteristic, complemented |
| 118 | #104×C67 | — | 2 | 2 | no | — |
| 119 | #104×C67 | — | 2 | 2 | no | — |
| 120 | #101×C67 | — | 2 | 1 | no | — |
| 121 | #100×C67 | C23 | 1 | 2 | yes | — |
| 122 | C23×D67 | C2×D4 | 1 | 2 | yes | — |
| 123 | #11761628 | — | 8 | 1 | no | — |
| 124 | #11761628 | — | 8 | 1 | no | — |
| 125 | C2×Dic134 | — | 2 | 1 | no | — |
| 126 | C2×Dic134 | — | 2 | 1 | no | — |
| 127 | C2×D268 | — | 2 | 1 | no | — |
| 128 | C2×D268 | — | 2 | 1 | no | — |
| 129 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 130 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 131 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 132 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 133 | C2×C22⋊D67 | — | 4 | 4 | no | — |
| 134 | C22×Dic67 | — | 2 | 2 | no | — |
| 135 | C22×Dic67 | C2×D4 | 1 | 2 | yes | — |
| 136 | C2×C4×D67 | — | 2 | 2 | no | — |
| 137 | C2×C4×D67 | — | 2 | 2 | no | — |
| 138 | C2×C4×D67 | — | 4 | 2 | no | — |
| 139 | C2×C4×D67 | — | 4 | 2 | no | — |
| 140 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 141 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 142 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 143 | C4⋊Dic67 | — | 4 | 2 | no | — |
| 144 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 145 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 146 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 147 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 148 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 149 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 150 | Dic67⋊C4 | — | 4 | 4 | no | — |
| 151 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 152 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 153 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 154 | C22⋊Dic67 | — | 2 | 4 | no | — |
| 155 | C22⋊Dic67 | — | 4 | 4 | no | — |
| 156 | C22⋊Dic67 | C2×D4 | 1 | 2 | yes | — |
| 157 | C22⋊Dic67 | C2×D4 | 1 | 2 | yes | — |
| 158 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 159 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 160 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 161 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 162 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 163 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 164 | (C2×D67)⋊C4 | — | 4 | 4 | no | — |
| 165 | C4×Dic67 | — | 2 | 1 | no | — |
| 166 | C4×Dic67 | — | 2 | 1 | no | — |
| 167 | C4×Dic67 | — | 2 | 2 | no | — |
| 168 | C4×Dic67 | — | 4 | 2 | no | — |
| 169 | #41×C67 | — | 2 | 2 | no | — |
| 170 | #41×C67 | — | 2 | 2 | no | — |
| 171 | #41×C67 | — | 4 | 1 | no | — |
| 172 | #41×C67 | — | 4 | 1 | no | — |
| 173 | #41×C67 | — | 4 | 2 | no | — |
| 174 | #41×C67 | — | 4 | 2 | no | — |
| 175 | #41×C67 | — | 4 | 1 | no | — |
| 176 | #41×C67 | — | 4 | 2 | no | — |
| 177 | #41×C67 | — | 4 | 4 | no | — |
| 178 | #41×C67 | — | 4 | 1 | no | — |
| 179 | #41×C67 | — | 4 | 1 | no | — |
| 180 | #41×C67 | — | 4 | 2 | no | — |
| 181 | #41×C67 | — | 4 | 1 | no | — |
| 182 | #41×C67 | — | 4 | 2 | no | — |
| 183 | C2×Q8×C67 | — | 2 | 2 | no | — |
| 184 | C2×Q8×C67 | — | 2 | 1 | no | — |
| 185 | C2×Q8×C67 | — | 4 | 2 | no | — |
| 186 | C2×Q8×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 187 | C2×Q8×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 188 | C2×D4×C67 | — | 2 | 1 | no | — |
| 189 | C2×D4×C67 | — | 2 | 2 | no | — |
| 190 | C2×D4×C67 | — | 2 | 4 | no | — |
| 191 | C2×D4×C67 | — | 2 | 1 | no | — |
| 192 | C2×D4×C67 | — | 2 | 2 | no | — |
| 193 | C2×D4×C67 | — | 4 | 2 | no | — |
| 194 | C2×D4×C67 | — | 4 | 4 | no | — |
| 195 | C2×D4×C67 | — | 4 | 1 | no | — |
| 196 | C2×D4×C67 | C2×D4 | 1 | 2 | yes | — |
| 197 | C2×D4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 198 | C2×D4×C67 | C24 | 1 | 1 | yes | characteristic |
| 199 | C22×C4×C67 | — | 2 | 4 | no | — |
| 200 | C22×C4×C67 | — | 2 | 1 | no | — |
| 201 | C22×C4×C67 | — | 2 | 1 | no | — |
| 202 | C22×C4×C67 | — | 4 | 1 | no | — |
| 203 | C22×C4×C67 | C2×D4 | 1 | 2 | yes | — |
| 204 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 205 | Q16×C67 | — | 4 | 2 | no | — |
| 206 | SD16×C67 | — | 4 | 2 | no | — |
| 207 | SD16×C67 | — | 4 | 2 | no | — |
| 208 | D8×C67 | — | 4 | 2 | no | — |
| 209 | M16×C67 | — | 2 | 2 | no | — |
| 210 | M16×C67 | — | 4 | 1 | no | — |
| 211 | C2×C8×C67 | — | 4 | 1 | no | — |
| 212 | C4⋊C4×C67 | — | 2 | 2 | no | — |
| 213 | C22⋊C4×C67 | — | 2 | 2 | no | — |
| 214 | C22⋊C4×C67 | — | 2 | 2 | no | — |
| 215 | C42×C67 | — | 2 | 1 | no | — |
| 216 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 217 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 218 | C23×C67 | — | 2 | 4 | no | — |
| 219 | C23×C67 | — | 2 | 1 | no | — |
| 220 | C23×C67 | — | 4 | 1 | no | — |
| 221 | C23×C67 | #120 | 1 | 1 | yes | characteristic |
| 222 | C23×C67 | C22×D4 | 1 | 2 | yes | — |
| 223 | C22×D67 | — | 2 | 2 | no | — |
| 224 | C22×D67 | — | 4 | 2 | no | — |
| 225 | C22×D67 | — | 8 | 2 | no | — |
| 226 | Q8×C67 | — | 2 | 2 | no | — |
| 227 | Q8×C67 | — | 4 | 1 | no | — |
| 228 | Q8×C67 | — | 4 | 1 | no | — |
| 229 | Q8×C67 | — | 4 | 2 | no | — |
| 230 | Q8×C67 | — | 4 | 1 | no | — |
| 231 | D4×C67 | — | 2 | 2 | no | — |
| 232 | D4×C67 | — | 4 | 2 | no | — |
| 233 | D4×C67 | — | 4 | 1 | no | — |
| 234 | D4×C67 | — | 4 | 1 | no | — |
| 235 | D4×C67 | — | 4 | 2 | no | — |
| 236 | D4×C67 | — | 4 | 4 | no | — |
| 237 | D4×C67 | — | 4 | 2 | no | — |
| 238 | D4×C67 | — | 4 | 2 | no | — |
| 239 | D4×C67 | — | 4 | 1 | no | — |
| 240 | D4×C67 | — | 8 | 1 | no | — |
| 241 | D4×C67 | — | 8 | 2 | no | — |
| 242 | C2×C4×C67 | — | 2 | 1 | no | — |
| 243 | C2×C4×C67 | — | 2 | 1 | no | — |
| 244 | C2×C4×C67 | — | 2 | 2 | no | — |
| 245 | C2×C4×C67 | — | 2 | 2 | no | — |
| 246 | C2×C4×C67 | — | 2 | 4 | no | — |
| 247 | C2×C4×C67 | — | 2 | 1 | no | — |
| 248 | C2×C4×C67 | — | 2 | 1 | no | — |
| 249 | C2×C4×C67 | — | 2 | 1 | no | — |
| 250 | C2×C4×C67 | — | 4 | 4 | no | — |
| 251 | C2×C4×C67 | — | 4 | 2 | no | — |
| 252 | C2×C4×C67 | — | 4 | 1 | no | — |
| 253 | C2×C4×C67 | — | 4 | 2 | no | — |
| 254 | C2×C4×C67 | — | 4 | 1 | no | — |
| 255 | C2×C4×C67 | — | 4 | 1 | no | — |
| 256 | C2×C4×C67 | — | 8 | 1 | no | — |
| 257 | C2×C4×C67 | #120 | 1 | 2 | yes | — |
| 258 | C2×C4×C67 | #120 | 1 | 1 | yes | characteristic |
| 259 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 260 | C22⋊D67 | — | 8 | 2 | no | — |
| 261 | C22⋊D67 | — | 8 | 2 | no | — |
| 262 | C22⋊D67 | — | 8 | 2 | no | — |
| 263 | C22⋊D67 | — | 8 | 2 | no | — |
| 264 | C22⋊D67 | — | 8 | 8 | no | — |
| 265 | C2×Dic67 | — | 2 | 2 | no | — |
| 266 | C2×Dic67 | — | 2 | 2 | no | — |
| 267 | C2×Dic67 | — | 2 | 2 | no | — |
| 268 | C2×Dic67 | — | 4 | 2 | no | — |
| 269 | C2×Dic67 | — | 4 | 4 | no | — |
| 270 | C2×Dic67 | — | 8 | 2 | no | — |
| 271 | D268 | — | 8 | 1 | no | — |
| 272 | D268 | — | 8 | 1 | no | — |
| 273 | C4×D67 | — | 4 | 2 | no | — |
| 274 | C4×D67 | — | 4 | 2 | no | — |
| 275 | C4×D67 | — | 8 | 2 | no | — |
| 276 | Dic134 | — | 8 | 1 | no | — |
| 277 | Dic134 | — | 8 | 1 | no | — |
| 278 | C8×C67 | — | 4 | 2 | no | — |
| 279 | C22×C67 | — | 2 | 2 | no | — |
| 280 | C22×C67 | — | 2 | 1 | no | — |
| 281 | C22×C67 | — | 4 | 1 | no | — |
| 282 | C22×C67 | — | 4 | 2 | no | — |
| 283 | C22×C67 | — | 4 | 2 | no | — |
| 284 | C22×C67 | — | 4 | 1 | no | — |
| 285 | C22×C67 | — | 4 | 2 | no | — |
| 286 | C22×C67 | — | 8 | 4 | no | — |
| 287 | C22×C67 | — | 16 | 1 | no | — |
| 288 | C22×C67 | C2×#120 | 1 | 1 | yes | characteristic |
| 289 | C2×D67 | — | 4 | 2 | no | — |
| 290 | C2×D67 | — | 4 | 2 | no | — |
| 291 | C2×D67 | — | 4 | 4 | no | — |
| 292 | C2×D67 | — | 4 | 2 | no | — |
| 293 | C2×D67 | — | 8 | 2 | no | — |
| 294 | C4×C67 | — | 2 | 1 | no | — |
| 295 | C4×C67 | — | 2 | 2 | no | — |
| 296 | C4×C67 | — | 4 | 1 | no | — |
| 297 | C4×C67 | — | 4 | 1 | no | — |
| 298 | C4×C67 | — | 4 | 1 | no | — |
| 299 | C4×C67 | — | 4 | 2 | no | — |
| 300 | C4×C67 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 301 | C4×C67 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 302 | Dic67 | — | 4 | 2 | no | — |
| 303 | Dic67 | — | 4 | 2 | no | — |
| 304 | Dic67 | — | 4 | 2 | no | — |
| 305 | Dic67 | — | 8 | 4 | no | — |
| 306 | #33550 | — | 67 | 1 | no | maximal, Sylow |
| 307 | C2×C67 | — | 2 | 1 | no | — |
| 308 | C2×C67 | — | 4 | 2 | no | — |
| 309 | C2×C67 | — | 4 | 1 | no | — |
| 310 | C2×C67 | — | 8 | 1 | no | — |
| 311 | C2×C67 | — | 8 | 2 | no | — |
| 312 | C2×C67 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 313 | D67 | — | 8 | 2 | no | — |
| 314 | #3529 | — | 67 | 1 | no | — |
| 315 | #3025 | — | 67 | 2 | no | — |
| 316 | #3018 | D67 | 1 | 1 | yes | characteristic, complemented |
| 317 | #2201 | — | 67 | 2 | no | — |
| 318 | #2200 | — | 67 | 4 | no | — |
| 319 | #2199 | — | 67 | 2 | no | — |
| 320 | #2126 | — | 67 | 1 | no | — |
| 321 | #2120 | — | 67 | 2 | no | — |
| 322 | C67 | #33550 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 323 | #585 | C2×D67 | 1 | 1 | yes | characteristic |
| 324 | #575 | — | 2 | 1 | no | — |
| 325 | #563 | — | 67 | 1 | no | — |
| 326 | #563 | — | 134 | 1 | no | — |
| 327 | #562 | — | 134 | 2 | no | — |
| 328 | #562 | — | 134 | 1 | no | — |
| 329 | H(3,𝔽4) | — | 67 | 1 | no | — |
| 330 | #560 | — | 67 | 2 | no | — |
| 331 | #560 | — | 134 | 2 | no | — |
| 332 | #532 | — | 134 | 1 | no | — |
| 333 | #532 | C2×D67 | 1 | 1 | yes | characteristic |
| 334 | #529 | — | 134 | 2 | no | — |
| 335 | #529 | — | 134 | 1 | no | — |
| 336 | #525 | — | 67 | 2 | no | — |
| 337 | #525 | — | 134 | 2 | no | — |
| 338 | #525 | — | 134 | 2 | no | — |
| 339 | #458 | — | 67 | 4 | no | — |
| 340 | #458 | — | 134 | 2 | no | — |
| 341 | B(4,𝔽2) | — | 67 | 4 | no | — |
| 342 | B(4,𝔽2) | — | 134 | 2 | no | — |
| 343 | #456 | — | 2 | 1 | no | — |
| 344 | #455 | C2×D67 | 1 | 2 | yes | — |
| 345 | #454 | — | 2 | 1 | no | — |
| 346 | #453 | C2×D67 | 1 | 2 | yes | — |
| 347 | C2×#104 | — | 2 | 1 | no | — |
| 348 | #413 | C2×D67 | 1 | 1 | yes | characteristic |
| 349 | #410 | — | 67 | 2 | no | — |
| 350 | #410 | — | 134 | 2 | no | — |
| 351 | #354 | — | 67 | 2 | no | — |
| 352 | #353 | — | 67 | 2 | no | — |
| 353 | #352 | — | 67 | 4 | no | — |
| 354 | AΣL(1,𝔽16) | — | 67 | 4 | no | — |
| 355 | 2−1+4 | — | 2 | 1 | no | — |
| 356 | 2−1+4 | — | 4 | 1 | no | — |
| 357 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 358 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 359 | H(5,𝔽2) | C22×D67 | 1 | 2 | yes | — |
| 360 | C2×#41 | — | 2 | 2 | no | — |
| 361 | C2×#41 | — | 2 | 1 | no | — |
| 362 | C2×#41 | — | 4 | 2 | no | — |
| 363 | C2×#41 | — | 134 | 1 | no | — |
| 364 | C2×#41 | C22⋊D67 | 1 | 1 | yes | characteristic, complemented |
| 365 | C2×#41 | C22×D67 | 1 | 1 | yes | characteristic |
| 366 | C23×C4 | — | 67 | 2 | no | — |
| 367 | #137 | — | 2 | 2 | no | — |
| 368 | #137 | — | 4 | 1 | no | — |
| 369 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 370 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 371 | #135 | — | 4 | 2 | no | — |
| 372 | C2×M16 | — | 2 | 1 | no | — |
| 373 | C4⋊Q8 | — | 134 | 1 | no | — |
| 374 | C4⋊Q8 | C22⋊D67 | 1 | 1 | yes | characteristic, complemented |
| 375 | #127 | — | 134 | 1 | no | — |
| 376 | #127 | C22×D67 | 1 | 1 | yes | characteristic |
| 377 | #126 | — | 134 | 2 | no | — |
| 378 | #126 | — | 134 | 2 | no | — |
| 379 | #126 | — | 134 | 2 | no | — |
| 380 | #125 | — | 134 | 2 | no | — |
| 381 | #125 | — | 134 | 1 | no | — |
| 382 | #124 | — | 134 | 2 | no | — |
| 383 | #124 | — | 134 | 1 | no | — |
| 384 | #124 | — | 134 | 1 | no | — |
| 385 | #124 | — | 134 | 1 | no | — |
| 386 | #124 | C22⋊D67 | 1 | 1 | yes | characteristic, complemented |
| 387 | #124 | C22×D67 | 1 | 1 | yes | characteristic |
| 388 | #123 | — | 67 | 2 | no | — |
| 389 | #123 | — | 67 | 2 | no | — |
| 390 | #123 | — | 134 | 2 | no | — |
| 391 | #123 | — | 134 | 2 | no | — |
| 392 | #123 | — | 134 | 4 | no | — |
| 393 | #123 | — | 134 | 2 | no | — |
| 394 | #123 | — | 134 | 2 | no | — |
| 395 | #123 | — | 134 | 2 | no | — |
| 396 | C22⋊Q8 | — | 268 | 2 | no | — |
| 397 | C22⋊Q8 | — | 134 | 2 | no | — |
| 398 | C22⋊Q8 | — | 134 | 2 | no | — |
| 399 | C22⋊Q8 | — | 134 | 2 | no | — |
| 400 | C22⋊Q8 | — | 134 | 1 | no | — |
| 401 | C22⋊Q8 | — | 134 | 2 | no | — |
| 402 | #121 | — | 2 | 2 | no | — |
| 403 | #121 | — | 268 | 2 | no | — |
| 404 | #121 | — | 134 | 2 | no | — |
| 405 | #121 | — | 134 | 2 | no | — |
| 406 | #121 | — | 134 | 1 | no | — |
| 407 | #121 | — | 134 | 2 | no | — |
| 408 | #121 | — | 134 | 2 | no | — |
| 409 | #121 | — | 134 | 2 | no | — |
| 410 | #121 | — | 134 | 2 | no | — |
| 411 | #120 | — | 67 | 2 | no | — |
| 412 | #120 | — | 67 | 2 | no | — |
| 413 | #120 | — | 134 | 2 | no | — |
| 414 | #120 | — | 134 | 4 | no | — |
| 415 | #120 | — | 134 | 2 | no | — |
| 416 | C4×Q8 | — | 134 | 1 | no | — |
| 417 | C4×D4 | — | 2 | 2 | no | — |
| 418 | C4×D4 | — | 268 | 4 | no | — |
| 419 | C4×D4 | — | 134 | 1 | no | — |
| 420 | C4×D4 | — | 134 | 2 | no | — |
| 421 | C4×D4 | — | 134 | 2 | no | — |
| 422 | C4×D4 | — | 134 | 2 | no | — |
| 423 | #117 | — | 67 | 2 | no | — |
| 424 | #117 | — | 134 | 2 | no | — |
| 425 | #117 | — | 134 | 2 | no | — |
| 426 | C2×C42 | — | 134 | 1 | no | — |
| 427 | C2×C42 | C22⋊D67 | 1 | 1 | yes | characteristic, complemented |
| 428 | #104 | — | 2 | 2 | no | — |
| 429 | #104 | — | 2 | 2 | no | — |
| 430 | #101 | — | 2 | 1 | no | — |
| 431 | #100 | C22×D67 | 1 | 2 | yes | — |
| 432 | #99 | — | 67 | 4 | no | — |
| 433 | #99 | — | 134 | 4 | no | — |
| 434 | #99 | — | 134 | 4 | no | — |
| 435 | #99 | — | 134 | 2 | no | — |
| 436 | C24 | — | 67 | 2 | no | — |
| 437 | #41 | — | 2 | 2 | no | — |
| 438 | #41 | — | 2 | 2 | no | — |
| 439 | #41 | — | 4 | 1 | no | — |
| 440 | #41 | — | 4 | 1 | no | — |
| 441 | #41 | — | 4 | 2 | no | — |
| 442 | #41 | — | 4 | 2 | no | — |
| 443 | #41 | — | 4 | 2 | no | — |
| 444 | #41 | — | 4 | 1 | no | — |
| 445 | #41 | — | 4 | 4 | no | — |
| 446 | #41 | — | 4 | 1 | no | — |
| 447 | #41 | — | 4 | 1 | no | — |
| 448 | #41 | — | 4 | 2 | no | — |
| 449 | #41 | — | 4 | 2 | no | — |
| 450 | #41 | — | 4 | 1 | no | — |
| 451 | #41 | — | 536 | 1 | no | — |
| 452 | #41 | — | 536 | 1 | no | — |
| 453 | C2×Q8 | — | 2 | 2 | no | — |
| 454 | C2×Q8 | — | 2 | 1 | no | — |
| 455 | C2×Q8 | — | 4 | 2 | no | — |
| 456 | C2×Q8 | — | 134 | 1 | no | — |
| 457 | C2×Q8 | — | 134 | 1 | no | — |
| 458 | C2×Q8 | C2×C22⋊D67 | 1 | 1 | yes | characteristic |
| 459 | C2×Q8 | C2×C22⋊D67 | 1 | 1 | yes | characteristic |
| 460 | C2×D4 | — | 2 | 1 | no | — |
| 461 | C2×D4 | — | 2 | 2 | no | — |
| 462 | C2×D4 | — | 2 | 4 | no | — |
| 463 | C2×D4 | — | 2 | 1 | no | — |
| 464 | C2×D4 | — | 2 | 2 | no | — |
| 465 | C2×D4 | — | 4 | 2 | no | — |
| 466 | C2×D4 | — | 4 | 4 | no | — |
| 467 | C2×D4 | — | 4 | 1 | no | — |
| 468 | C2×D4 | — | 268 | 4 | no | — |
| 469 | C2×D4 | — | 134 | 1 | no | — |
| 470 | C2×D4 | — | 134 | 1 | no | — |
| 471 | C2×D4 | — | 134 | 2 | no | — |
| 472 | C2×D4 | — | 134 | 2 | no | — |
| 473 | C2×D4 | — | 134 | 2 | no | — |
| 474 | C2×D4 | — | 134 | 2 | no | — |
| 475 | C2×D4 | D4×D67 | 1 | 2 | yes | — |
| 476 | C2×D4 | C2×C22⋊D67 | 1 | 1 | yes | characteristic |
| 477 | C2×D4 | C23×D67 | 1 | 1 | yes | characteristic |
| 478 | C22×C4 | — | 2 | 4 | no | — |
| 479 | C22×C4 | — | 2 | 1 | no | — |
| 480 | C22×C4 | — | 2 | 1 | no | — |
| 481 | C22×C4 | — | 4 | 1 | no | — |
| 482 | C22×C4 | — | 268 | 2 | no | — |
| 483 | C22×C4 | — | 268 | 2 | no | — |
| 484 | C22×C4 | — | 67 | 2 | no | — |
| 485 | C22×C4 | — | 134 | 2 | no | — |
| 486 | C22×C4 | — | 134 | 2 | no | — |
| 487 | C22×C4 | — | 134 | 2 | no | — |
| 488 | C22×C4 | D4×D67 | 1 | 2 | yes | — |
| 489 | C22×C4 | C2×C22⋊D67 | 1 | 1 | yes | characteristic |
| 490 | Q16 | — | 4 | 2 | no | — |
| 491 | SD16 | — | 4 | 2 | no | — |
| 492 | SD16 | — | 4 | 2 | no | — |
| 493 | D8 | — | 4 | 2 | no | — |
| 494 | M16 | — | 2 | 2 | no | — |
| 495 | M16 | — | 4 | 1 | no | — |
| 496 | C2×C8 | — | 4 | 1 | no | — |
| 497 | C4⋊C4 | — | 2 | 2 | no | — |
| 498 | C4⋊C4 | — | 268 | 2 | no | — |
| 499 | C4⋊C4 | — | 268 | 4 | no | — |
| 500 | C4⋊C4 | — | 134 | 2 | no | — |
| 501 | C4⋊C4 | — | 134 | 2 | no | — |
| 502 | C4⋊C4 | — | 134 | 2 | no | — |
| 503 | C4⋊C4 | — | 134 | 1 | no | — |
| 504 | C4⋊C4 | — | 134 | 2 | no | — |
| 505 | C4⋊C4 | — | 134 | 1 | no | — |
| 506 | C4⋊C4 | — | 134 | 2 | no | — |
| 507 | C4⋊C4 | — | 134 | 2 | no | — |
| 508 | C4⋊C4 | — | 134 | 2 | no | — |
| 509 | C22⋊C4 | — | 2 | 2 | no | — |
| 510 | C22⋊C4 | — | 2 | 2 | no | — |
| 511 | C22⋊C4 | — | 268 | 4 | no | — |
| 512 | C22⋊C4 | — | 268 | 4 | no | — |
| 513 | C22⋊C4 | — | 67 | 2 | no | — |
| 514 | C22⋊C4 | — | 67 | 2 | no | — |
| 515 | C22⋊C4 | — | 134 | 2 | no | — |
| 516 | C22⋊C4 | — | 134 | 2 | no | — |
| 517 | C22⋊C4 | — | 134 | 2 | no | — |
| 518 | C22⋊C4 | — | 134 | 2 | no | — |
| 519 | C22⋊C4 | — | 134 | 4 | no | — |
| 520 | C22⋊C4 | — | 134 | 2 | no | — |
| 521 | C22⋊C4 | — | 134 | 2 | no | — |
| 522 | C22⋊C4 | — | 134 | 2 | no | — |
| 523 | C22⋊C4 | — | 134 | 2 | no | — |
| 524 | C22⋊C4 | — | 134 | 2 | no | — |
| 525 | C42 | — | 2 | 1 | no | — |
| 526 | C42 | — | 268 | 2 | no | — |
| 527 | C42 | — | 134 | 1 | no | — |
| 528 | C42 | — | 134 | 1 | no | — |
| 529 | C42 | — | 134 | 2 | no | — |
| 530 | C42 | C2×C22⋊D67 | 1 | 1 | yes | characteristic |
| 531 | C42 | C2×C22⋊D67 | 1 | 1 | yes | characteristic |
| 532 | C23 | — | 2 | 4 | no | — |
| 533 | C23 | — | 2 | 1 | no | — |
| 534 | C23 | — | 4 | 1 | no | — |
| 535 | C23 | — | 268 | 2 | no | — |
| 536 | C23 | — | 536 | 2 | no | — |
| 537 | C23 | — | 134 | 2 | no | — |
| 538 | C23 | #14524011 | 1 | 1 | yes | characteristic |
| 539 | C23 | C2×D4×D67 | 1 | 2 | yes | — |
| 540 | Q8 | — | 2 | 2 | no | — |
| 541 | Q8 | — | 4 | 1 | no | — |
| 542 | Q8 | — | 4 | 1 | no | — |
| 543 | Q8 | — | 4 | 2 | no | — |
| 544 | Q8 | — | 4 | 1 | no | — |
| 545 | Q8 | — | 536 | 1 | no | — |
| 546 | Q8 | — | 536 | 1 | no | — |
| 547 | D4 | — | 2 | 2 | no | — |
| 548 | D4 | — | 4 | 2 | no | — |
| 549 | D4 | — | 4 | 1 | no | — |
| 550 | D4 | — | 4 | 1 | no | — |
| 551 | D4 | — | 4 | 2 | no | — |
| 552 | D4 | — | 4 | 4 | no | — |
| 553 | D4 | — | 4 | 2 | no | — |
| 554 | D4 | — | 4 | 2 | no | — |
| 555 | D4 | — | 4 | 1 | no | — |
| 556 | D4 | — | 8 | 1 | no | — |
| 557 | D4 | — | 8 | 2 | no | — |
| 558 | D4 | — | 536 | 1 | no | — |
| 559 | D4 | — | 536 | 1 | no | — |
| 560 | D4 | — | 536 | 2 | no | — |
| 561 | D4 | — | 536 | 2 | no | — |
| 562 | D4 | — | 536 | 2 | no | — |
| 563 | D4 | — | 536 | 2 | no | — |
| 564 | D4 | — | 536 | 8 | no | — |
| 565 | C2×C4 | — | 2 | 2 | no | — |
| 566 | C2×C4 | — | 2 | 1 | no | — |
| 567 | C2×C4 | — | 2 | 2 | no | — |
| 568 | C2×C4 | — | 2 | 1 | no | — |
| 569 | C2×C4 | — | 2 | 4 | no | — |
| 570 | C2×C4 | — | 2 | 1 | no | — |
| 571 | C2×C4 | — | 2 | 1 | no | — |
| 572 | C2×C4 | — | 2 | 1 | no | — |
| 573 | C2×C4 | — | 4 | 4 | no | — |
| 574 | C2×C4 | — | 4 | 2 | no | — |
| 575 | C2×C4 | — | 4 | 1 | no | — |
| 576 | C2×C4 | — | 4 | 1 | no | — |
| 577 | C2×C4 | — | 4 | 2 | no | — |
| 578 | C2×C4 | — | 4 | 1 | no | — |
| 579 | C2×C4 | — | 8 | 1 | no | — |
| 580 | C2×C4 | — | 268 | 2 | no | — |
| 581 | C2×C4 | — | 268 | 2 | no | — |
| 582 | C2×C4 | — | 268 | 2 | no | — |
| 583 | C2×C4 | — | 268 | 4 | no | — |
| 584 | C2×C4 | — | 536 | 2 | no | — |
| 585 | C2×C4 | — | 536 | 2 | no | — |
| 586 | C2×C4 | — | 134 | 2 | no | — |
| 587 | C2×C4 | — | 134 | 2 | no | — |
| 588 | C2×C4 | — | 134 | 2 | no | — |
| 589 | C2×C4 | #14524011 | 1 | 2 | yes | — |
| 590 | C2×C4 | #14524011 | 1 | 1 | yes | characteristic |
| 591 | C2×C4 | C22×C22⋊D67 | 1 | 1 | yes | characteristic |
| 592 | C8 | — | 4 | 2 | no | — |
| 593 | C22 | — | 2 | 2 | no | — |
| 594 | C22 | — | 2 | 1 | no | — |
| 595 | C22 | — | 4 | 1 | no | — |
| 596 | C22 | — | 4 | 2 | no | — |
| 597 | C22 | — | 4 | 2 | no | — |
| 598 | C22 | — | 4 | 2 | no | — |
| 599 | C22 | — | 4 | 1 | no | — |
| 600 | C22 | — | 8 | 4 | no | — |
| 601 | C22 | — | 268 | 2 | no | — |
| 602 | C22 | — | 268 | 2 | no | — |
| 603 | C22 | — | 268 | 4 | no | — |
| 604 | C22 | — | 268 | 2 | no | — |
| 605 | C22 | — | 16 | 1 | no | — |
| 606 | C22 | — | 536 | 2 | no | — |
| 607 | C22 | C2×#14524011 | 1 | 1 | yes | characteristic |
| 608 | C4 | — | 2 | 1 | no | — |
| 609 | C4 | — | 2 | 2 | no | — |
| 610 | C4 | — | 4 | 1 | no | — |
| 611 | C4 | — | 4 | 1 | no | — |
| 612 | C4 | — | 4 | 2 | no | — |
| 613 | C4 | — | 4 | 1 | no | — |
| 614 | C4 | — | 268 | 2 | no | — |
| 615 | C4 | — | 268 | 2 | no | — |
| 616 | C4 | — | 268 | 2 | no | — |
| 617 | C4 | — | 536 | 4 | no | — |
| 618 | C4 | #16863582 | 1 | 1 | yes | characteristic |
| 619 | C4 | #16863582 | 1 | 1 | yes | characteristic |
| 620 | C2 | — | 2 | 1 | no | — |
| 621 | C2 | — | 4 | 2 | no | — |
| 622 | C2 | — | 4 | 1 | no | — |
| 623 | C2 | — | 8 | 1 | no | — |
| 624 | C2 | — | 8 | 2 | no | — |
| 625 | C2 | — | 536 | 2 | no | — |
| 626 | C2 | C2×#16863582 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22574345 | C2 | semidirect |
| 2. #22569601 | C2 | semidirect |
| 3. #22562221 | C2 | semidirect |
| 4. #22562215 | C2 | semidirect |
| 5. #22562209 | C2 | semidirect |
| 6. #22561874 | C2 | semidirect |
| 7. #22561851 | C2 | semidirect |
| 8. C67×#3018 | C2 | semidirect |
| 9. #16864146 | C22 | semidirect |
| 13. #16864138 | C22 | semidirect |
| 15. #16864133 | C22 | semidirect |
| 28. #16863191 | C22 | semidirect |
| 29. #16863189 | C22 | semidirect |
| 30. #16863187 | C22 | semidirect |
| 31. #16863184 | C22 | semidirect |
| 42. C22×C4×D67 | D4 | semidirect |
| 60. #14524024 | D4 | semidirect |
| 79. #14524011 | D4 | semidirect |
| 88. #14524002 | D4 | semidirect |
| 103. C2×#41×C67 | D4 | semidirect |
| 111. C4⋊Q8×C67 | D4 | semidirect |
| 113. #124×C67 | D4 | semidirect |
| 117. C2×C42×C67 | D4 | semidirect |
| 316. #3018 | D67 | semidirect |
| 322. C67 | #33550 | semidirect |
| 364. C2×#41 | C22⋊D67 | semidirect |
| 374. C4⋊Q8 | C22⋊D67 | semidirect |
| 386. #124 | C22⋊D67 | semidirect |
| 427. C2×C42 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574345 | 2 |
| #22569601 | 2 |
| #22562221 | 2 |
| #22562215 | 2 |
| #22562209 | 2 |
| #22561874 | 2 |
| #22561851 | 2 |
| C67×#3018 | 2 |
| #33550 | 67 |