Subgroups — C₂³×C₃×D₄₁ #14520277

Order 1968.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₄₁	C₂	1	14	yes	maximal, direct product factor
3	C₂³×D₄₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₃×C₄₁	C₂²	1	7	yes	complemented
5	C₂×C₃×D₄₁	C₂²	1	28	yes	direct product factor
6	C₂³×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂²×D₄₁	C₂×C₃	1	14	yes	direct product factor
8	C₂×C₃×C₄₁	C₂³	1	7	yes	complemented
9	C₃×D₄₁	C₂³	1	8	yes	direct product factor
10	C₂²×C₄₁	C₂²×C₃	1	7	yes	complemented
11	C₂×D₄₁	C₂²×C₃	1	28	yes	direct product factor
12	C₃×C₄₁	C₂⁴	1	1	yes	characteristic, complemented, Hall
13	C₂×C₄₁	C₂³×C₃	1	7	yes	complemented
14	D₄₁	C₂³×C₃	1	8	yes	direct product factor
15	C₂⁴×C₃	—	41	1	no	maximal, Hall
16	C₄₁	C₂⁴×C₃	1	1	yes	characteristic, complemented, Sylow
17	C₂³×C₃	—	41	14	no	—
18	C₂³×C₃	D₄₁	1	1	yes	characteristic, direct product factor
19	C₂⁴	—	41	1	no	Sylow
20	C₂²×C₃	—	41	28	no	—
21	C₂²×C₃	C₂×D₄₁	1	7	yes	direct product factor
22	C₂³	—	41	14	no	—
23	C₂³	C₃×D₄₁	1	1	yes	characteristic, direct product factor
24	C₂×C₃	—	41	8	no	—
25	C₂×C₃	C₂²×D₄₁	1	7	yes	direct product factor
26	C₂²	—	41	28	no	—
27	C₂²	C₂×C₃×D₄₁	1	7	yes	direct product factor
28	C₃	C₂³×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	41	8	no	—
30	C₂	C₂²×C₃×D₄₁	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³×C₃	D₄₁
commutator, cosocle, hypocenter	C₄₁	C₂⁴×C₃
Frattini	C₁	G
Fitting, socle	C₂³×C₃×C₄₁	C₂
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₂³×C₃

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.