Supersolvable but not nilpotent groups

Groups with a normal series of cyclic factors but no central series. Each is shown with its largest nilpotent normal subgroup F(G), the part of it that is nilpotent, and the quotient over it.

order	group	F(G)	G/F(G)
6	D₃ #7	C₃	C₂
10	D₅ #17	C₅	C₂
12	Dic₃ #20	C₂×C₃	C₂
12	C₂×D₃ #23	C₂×C₃	C₂
14	D₇ #26	C₇	C₂
18	D₉ #44	C₉	C₂
18	C₃×D₃ #46	C₃²	C₂
18	C₃⋊D₃ #47	C₃²	C₂
20	Dic₅ #50	C₂×C₅	C₂
20	AGL(1,𝔽₅) #52	C₅	C₄
20	C₂×D₅ #53	C₂×C₅	C₂
21	ΓL(1,𝔽₈) #55	C₇	C₃
22	D₁₁ #57	C₁₁	C₂
24	C₃⋊C₈ #60	C₃×C₄	C₂
24	Dic₆ #63	C₃×C₄	C₂
24	C₄×D₃ #64	C₃×C₄	C₂
24	D₁₂ #65	C₃×C₄	C₂
24	C₂×Dic₃ #66	C₂²×C₃	C₂
24	#67	C₂²×C₃	C₂
24	C₂²×D₃ #73	C₂²×C₃	C₂
26	D₁₃ #77	C₁₃	C₂
28	Dic₇ #84	C₂×C₇	C₂
28	C₂×D₇ #86	C₂×C₇	C₂
30	C₅×D₃ #89	C₃×C₅	C₂
30	C₃×D₅ #90	C₃×C₅	C₂
30	D₁₅ #91	C₃×C₅	C₂
34	D₁₇ #146	C₁₇	C₂
36	Dic₉ #149	C₂×C₉	C₂
36	C₂×D₉ #152	C₂×C₉	C₂
36	C₃×Dic₃ #154	C₂×C₃²	C₂
36	C₃⋊Dic₃ #155	C₂×C₃²	C₂
36	D₃² #158	C₃²	C₂²
36	C₂×C₃×D₃ #160	C₂×C₃²	C₂
36	C₂×C₃⋊D₃ #161	C₂×C₃²	C₂
38	D₁₉ #164	C₁₉	C₂
39	C₁₃⋊C₃ #166	C₁₃	C₃
40	#168	C₄×C₅	C₂
40	#170	C₂×C₅	C₄
40	Dic₁₀ #171	C₄×C₅	C₂
40	C₄×D₅ #172	C₄×C₅	C₂
40	D₂₀ #173	C₄×C₅	C₂
40	C₂×Dic₅ #174	C₂²×C₅	C₂
40	C₂²⋊D₅ #175	C₂²×C₅	C₂
40	C₂×AGL(1,𝔽₅) #179	C₂×C₅	C₄
40	C₂²×D₅ #180	C₂²×C₅	C₂
42	AGL(1,𝔽₇) #183	C₇	C₂×C₃
42	C₂×ΓL(1,𝔽₈) #184	C₂×C₇	C₃
42	D₃×C₇ #185	C₃×C₇	C₂
42	C₃×D₇ #186	C₃×C₇	C₂
42	D₂₁ #187	C₃×C₇	C₂
44	Dic₁₁ #190	C₂×C₁₁	C₂
44	C₂×D₁₁ #192	C₂×C₁₁	C₂
46	D₂₃ #196	C₂₃	C₂
48	C₃⋊C₁₆ #199	C₃×C₈	C₂
48	D₃×C₈ #202	C₃×C₈	C₂
48	ΓL(1,𝔽₂₅) #203	C₃×C₈	C₂
48	#204	C₃×C₈	C₂
48	D₂₄ #205	C₃×C₈	C₂
48	Dic₁₂ #206	C₃×C₈	C₂
48	C₂×C₃⋊C₈ #207	C₂×C₃×C₄	C₂
48	#208	C₂×C₃×C₄	C₂
48	C₄×Dic₃ #209	C₂×C₃×C₄	C₂
48	Dic₃⋊C₄ #210	C₂×C₃×C₄	C₂
48	C₄⋊Dic₃ #211	C₂×C₃×C₄	C₂
48	(C₂×D₃)⋊C₄ #212	C₂×C₃×C₄	C₂
48	#213	C₃×D₄	C₂
48	#214	C₃×D₄	C₂
48	#215	C₃×Q₈	C₂
48	#216	C₃×Q₈	C₂
48	#217	C₂³×C₃	C₂
48	C₂×Dic₆ #232	C₂×C₃×C₄	C₂
48	C₂×C₄×D₃ #233	C₂×C₃×C₄	C₂
48	C₂×D₁₂ #234	C₂×C₃×C₄	C₂
48	#235	C₂×C₃×C₄	C₂
48	D₃×D₄ #236	C₃×D₄	C₂
48	#237	C₃×D₄	C₂
48	D₃×Q₈ #238	C₃×Q₈	C₂
48	#239	C₃×Q₈	C₂
48	C₂²×Dic₃ #240	C₂³×C₃	C₂
48	C₂×#67 #241	C₂³×C₃	C₂
48	C₂³×D₃ #249	C₂³×C₃	C₂
50	D₂₅ #253	C₂₅	C₂
50	C₅×D₅ #255	C₅²	C₂
50	C₅⋊D₅ #256	C₅²	C₂
52	Dic₁₃ #259	C₂×C₁₃	C₂
52	#261	C₁₃	C₄
52	C₂×D₁₃ #262	C₂×C₁₃	C₂
54	D₂₇ #265	C₂₇	C₂
54	C₃×D₉ #267	C₃×C₉	C₂
54	D₃×C₉ #268	C₃×C₉	C₂
54	(C₃⋊D₃)⋊C₃ #269	H(3,𝔽₃)	C₂
54	AGL(1,ℤ/9) #270	3₋¹⁺²	C₂
54	C₃⋊D₉ #271	C₃×C₉	C₂
54	#272	H(3,𝔽₃)	C₂
54	C₃²×D₃ #276	C₃³	C₂
54	C₃×C₃⋊D₃ #277	C₃³	C₂
54	C₃⋊(C₃⋊D₃) #278	C₃³	C₂
55	C₁₁⋊C₅ #280	C₁₁	C₅
56	C₇⋊C₈ #282	C₄×C₇	C₂
56	Dic₁₄ #284	C₄×C₇	C₂

About supersolvable but not nilpotent groups →