Monolithic groups
Groups with a unique minimal normal subgroup, the monolith they are built over.
| order | group | monolith | G/monolith |
|---|
| 2 | C2 #2 | simple |
| 3 | C3 #3 | simple |
| 4 | C4 #4 | C2 | C2 |
| 5 | C5 #6 | simple |
| 6 | D3 #7 | C3 | C2 |
| 7 | C7 #9 | simple |
| 8 | C8 #10 | C2 | C4 |
| 8 | D4 #12 | C2 | C22 |
| 8 | Q8 #13 | C2 | C22 |
| 9 | C9 #15 | C3 | C3 |
| 10 | D5 #17 | C5 | C2 |
| 11 | C11 #19 | simple |
| 12 | A4 #22 | C22 | C3 |
| 13 | C13 #25 | simple |
| 14 | D7 #26 | C7 | C2 |
| 16 | C16 #29 | C2 | C8 |
| 16 | M16 #34 | C2 | C2×C4 |
| 16 | D8 #35 | C2 | D4 |
| 16 | SD16 #36 | C2 | D4 |
| 16 | Q16 #37 | C2 | D4 |
| 16 | #41 | C2 | C23 |
| 17 | C17 #43 | simple |
| 18 | D9 #44 | C3 | D3 |
| 19 | C19 #49 | simple |
| 20 | AGL(1,𝔽5) #52 | C5 | C4 |
| 21 | ΓL(1,𝔽8) #55 | C7 | C3 |
| 22 | D11 #57 | C11 | C2 |
| 23 | C23 #59 | simple |
| 24 | SL(2,𝔽3) #62 | C2 | A4 |
| 24 | S4 #71 | C22 | D3 |
| 25 | C25 #75 | C5 | C5 |
| 26 | D13 #77 | C13 | C2 |
| 27 | C27 #79 | C3 | C9 |
| 27 | H(3,𝔽3) #81 | C3 | C32 |
| 27 | 3−1+2 #82 | C3 | C32 |
| 29 | C29 #88 | simple |
| 31 | C31 #93 | simple |
| 32 | C32 #94 | C2 | C16 |
| 32 | #99 | C2 | C22⋊C4 |
| 32 | #100 | C2 | C22⋊C4 |
| 32 | #101 | C2 | C22⋊C4 |
| 32 | #104 | C2 | C22⋊C4 |
| 32 | #108 | C2 | C4⋊C4 |
| 32 | M32 #110 | C2 | C2×C8 |
| 32 | D16 #111 | C2 | D8 |
| 32 | SD32 #112 | C2 | D8 |
| 32 | Q32 #113 | C2 | D8 |
| 32 | #131 | C2 | C22×C4 |
| 32 | #135 | C2 | C2×D4 |
| 32 | AGL(1,ℤ/8) #136 | C2 | C2×D4 |
| 32 | #137 | C2 | C2×D4 |
| 32 | H(5,𝔽2) #142 | C2 | C24 |
| 32 | 2−1+4 #143 | C2 | C24 |
| 34 | D17 #146 | C17 | C2 |
| 36 | #157 | C32 | C4 |
| 37 | C37 #163 | simple |
| 38 | D19 #164 | C19 | C2 |
| 39 | C13⋊C3 #166 | C13 | C3 |
| 41 | C41 #182 | simple |
| 42 | AGL(1,𝔽7) #183 | C7 | C2×C3 |
| 43 | C43 #189 | simple |
| 46 | D23 #196 | C23 | C2 |
| 47 | C47 #198 | simple |
| 48 | C42⋊C3 #201 | C22 | A4 |
| 48 | #226 | C2 | S4 |
| 48 | GL(2,𝔽3) #227 | C2 | S4 |
| 48 | #41⋊C3 #231 | C2 | C2×A4 |
| 49 | C49 #251 | C7 | C7 |
| 50 | D25 #253 | C5 | D5 |
| 52 | #261 | C13 | C4 |
| 53 | C53 #264 | simple |
| 54 | D27 #265 | C3 | D9 |
| 54 | (C3⋊D3)⋊C3 #269 | C3 | C3×D3 |
| 54 | AGL(1,ℤ/9) #270 | C3 | C3×D3 |
| 54 | #272 | C3 | C3⋊D3 |
| 55 | C11⋊C5 #280 | C11 | C5 |
| 56 | AGL(1,𝔽8) #292 | C23 | C7 |
| 57 | C19⋊C3 #295 | C19 | C3 |
| 58 | D29 #297 | C29 | C2 |
| 59 | C59 #299 | simple |
| 60 | A5 #304 | simple |
| 61 | C61 #313 | simple |
| 62 | D31 #314 | C31 | C2 |
| 64 | C64 #320 | C2 | C32 |
| 64 | H(3,ℤ/4) #337 | C2 | #95 |
| 64 | #338 | C2 | #95 |
| 64 | #344 | C2 | #95 |
| 64 | #347 | C2 | #97 |
| 64 | #349 | C2 | C22⋊C8 |
| 64 | #350 | C2 | C22⋊C8 |
| 64 | AΣL(1,𝔽16) #351 | C2 | #99 |
| 64 | #352 | C2 | #99 |
| 64 | #353 | C2 | #99 |
| 64 | #354 | C2 | #99 |
| 64 | #355 | C2 | #99 |
| 64 | #356 | C2 | #99 |
| 64 | #359 | C2 | #102 |
| 64 | #360 | C2 | #102 |
| 64 | #361 | C2 | #102 |
| 64 | #362 | C2 | #102 |
About monolithic groups →
Finite Group Databasebeta