Subgroups — Dic₃×Dic₄₁ #14520102

Order 1968.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₃×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×Dic₄₁	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₄₁	—	3	1	no	maximal, Hall
5	C₂²×C₃×C₄₁	C₂²	1	1	yes	characteristic
6	Dic₁₂₃	C₄	1	2	yes	complemented
7	C₃×Dic₄₁	C₄	1	2	yes	complemented
8	Dic₃×C₄₁	C₄	1	2	yes	complemented
9	C₂×C₄×C₄₁	—	3	1	no	—
10	C₂×Dic₄₁	—	3	1	no	—
11	C₂×Dic₄₁	D₃	1	1	yes	characteristic
12	C₂×C₃×C₄₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃×C₄₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₃×C₄₁	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄₁	C₂×D₃	1	1	yes	characteristic
16	C₄×C₄₁	—	3	2	no	—
17	Dic₄₁	—	3	2	no	—
18	Dic₄₁	Dic₃	1	2	yes	direct product factor
19	C₃×C₄₁	C₄²	1	1	yes	characteristic, complemented, Hall
20	C₂×C₄₁	C₄×D₃	1	1	yes	characteristic
21	C₂×C₄₁	C₄×D₃	1	1	yes	characteristic
22	C₂×C₄₁	C₂×Dic₃	1	1	yes	characteristic
23	C₄×Dic₃	—	41	1	no	maximal, Hall
24	C₄₁	C₄×Dic₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃×C₄	—	41	1	no	—
26	C₂×Dic₃	—	41	1	no	—
27	C₂×Dic₃	D₄₁	1	1	yes	characteristic
28	C₄²	—	123	1	no	Sylow
29	C₂²×C₃	C₂×D₄₁	1	1	yes	characteristic
30	C₃×C₄	—	41	2	no	—
31	Dic₃	—	41	2	no	—
32	Dic₃	Dic₄₁	1	2	yes	direct product factor
33	C₂×C₄	—	3	1	no	—
34	C₂×C₄	—	41	1	no	—
35	C₂×C₄	—	123	1	no	—
36	C₂×C₃	C₄×D₄₁	1	1	yes	characteristic
37	C₂×C₃	C₄×D₄₁	1	1	yes	characteristic
38	C₂×C₃	C₂×Dic₄₁	1	1	yes	characteristic
39	C₂²	D₃×D₄₁	1	1	yes	characteristic
40	C₄	—	3	2	no	—
41	C₄	—	41	2	no	—
42	C₄	—	123	2	no	—
43	C₃	C₄×Dic₄₁	1	1	yes	characteristic, complemented, Sylow
44	C₂	Dic₃×D₄₁	1	1	yes	characteristic
45	C₂	D₃×Dic₄₁	1	1	yes	characteristic
46	C₂	#11758295	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₃×D₄₁
commutator, hypocenter	C₃×C₄₁	C₄²
Fitting, socle, prime radical, cosocle	C₂²×C₃×C₄₁	C₂²
LCS	G ▷ C₃×C₄₁
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
6. Dic₁₂₃	C₄	semidirect
7. C₃×Dic₄₁	C₄	semidirect
8. Dic₃×C₄₁	C₄	semidirect
18. Dic₄₁	Dic₃	direct (N × H)
19. C₃×C₄₁	C₄²	semidirect
24. C₄₁	C₄×Dic₃	semidirect
32. Dic₃	Dic₄₁	direct (N × H)
43. C₃	C₄×Dic₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₂₃	2
C₂×Dic₃×C₄₁	2
C₂×C₃×Dic₄₁	2
C₄×Dic₄₁	3
C₄×Dic₃	41

Subgroups — Dic3×Dic41 #14520102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃×Dic₄₁ #14520102