Subgroups — D₃×C₈×C₄₁ #14520126

Order 1968.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₃×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₃×C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×C₄₁	—	3	1	no	maximal, Hall
5	C₂×D₃×C₄₁	C₄	1	1	yes	characteristic
6	C₃×C₄×C₄₁	C₂²	1	1	yes	characteristic
7	Dic₃×C₄₁	C₄	1	1	yes	characteristic
8	C₂×C₄×C₄₁	—	3	1	no	—
9	C₈×C₄₁	—	3	1	no	—
10	C₈×C₄₁	D₃	1	1	yes	characteristic, direct product factor
11	C₂×C₃×C₄₁	C₂×C₄	1	1	yes	characteristic
12	D₃×C₄₁	C₈	1	2	yes	direct product factor
13	C₂²×C₄₁	—	3	1	no	—
14	C₄×C₄₁	—	3	1	no	—
15	C₄×C₄₁	C₂×D₃	1	1	yes	characteristic
16	C₃×C₄₁	C₂×C₈	1	1	yes	characteristic, complemented, Hall
17	C₂×C₄₁	—	3	2	no	—
18	C₂×C₄₁	C₄×D₃	1	1	yes	characteristic
19	D₃×C₈	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₄₁	D₃×C₈	1	1	yes	characteristic, direct product factor, Sylow
21	C₄×D₃	C₂×C₄₁	1	1	yes	characteristic
22	C₃×C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
23	C₃⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
24	C₂×C₈	—	3	1	no	Sylow
25	C₂×D₃	C₄×C₄₁	1	1	yes	characteristic
26	C₃×C₄	C₂²×C₄₁	1	1	yes	characteristic
27	Dic₃	C₄×C₄₁	1	1	yes	characteristic
28	C₂×C₄	—	3	1	no	—
29	C₈	—	3	1	no	—
30	C₈	D₃×C₄₁	1	1	yes	characteristic, direct product factor
31	C₂×C₃	C₂×C₄×C₄₁	1	1	yes	characteristic
32	D₃	C₈×C₄₁	1	2	yes	direct product factor
33	C₂²	—	3	1	no	—
34	C₄	—	3	1	no	—
35	C₄	C₂×D₃×C₄₁	1	1	yes	characteristic
36	C₃	C₂×C₈×C₄₁	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	3	2	no	—
38	C₂	C₄×D₃×C₄₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₈×C₄₁	D₃
commutator, hypocenter	C₃	C₂×C₈×C₄₁
Frattini	C₄	C₂×D₃×C₄₁
Fitting	C₃×C₈×C₄₁	C₂
socle	C₂×C₃×C₄₁	C₂×C₄
prime radical	C₂×D₃×C₄₁	C₄
cosocle	C₃×C₄	C₂²×C₄₁
LCS	G ▷ C₃
UCS	C₁ ◁ C₈×C₄₁

Complements

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

N	H ≅ G/N	type
2. C₃×C₈×C₄₁	C₂	semidirect
3. C₃⋊C₈×C₄₁	C₂	semidirect
10. C₈×C₄₁	D₃	direct (N × H)
12. D₃×C₄₁	C₈	direct (N × H)
16. C₃×C₄₁	C₂×C₈	semidirect
19. D₃×C₈	C₄₁	direct (N × H)
20. C₄₁	D₃×C₈	direct (N × H)
22. C₃×C₈	C₂×C₄₁	semidirect
23. C₃⋊C₈	C₂×C₄₁	semidirect
30. C₈	D₃×C₄₁	direct (N × H)
32. D₃	C₈×C₄₁	direct (N × H)
36. C₃	C₂×C₈×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₃×C₄₁	2
C₃×C₈×C₄₁	2
C₃⋊C₈×C₄₁	2
C₂×C₈×C₄₁	3
D₃×C₈	41

Subgroups — D3×C8×C41 #14520126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₈×C₄₁ #14520126