Subgroups — C₂²×C₃⋊#4223 #14520273

Order 1968.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊#4223	C₂	1	6	yes	maximal, direct product factor
3	C₂²×#4223	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₄₁	C₄	1	1	yes	characteristic, complemented
5	C₂×C₃×D₄₁	C₄	1	3	yes	complemented
6	C₂×C₃×D₄₁	C₂²	1	3	yes	—
7	C₃⋊#4223	C₂²	1	4	yes	direct product factor
8	C₂²×D₄₁	D₃	1	1	yes	characteristic
9	C₂×#4223	—	3	6	no	—
10	C₂×C₃×C₄₁	C₂×C₄	1	3	yes	complemented
11	C₃×D₄₁	C₂×C₄	1	3	yes	complemented
12	C₃×D₄₁	C₂³	1	1	yes	characteristic
13	C₂²×C₄₁	Dic₃	1	1	yes	characteristic, complemented
14	C₂×D₄₁	Dic₃	1	3	yes	complemented
15	C₂×D₄₁	C₂×D₃	1	3	yes	—
16	#4223	—	3	4	no	—
17	C₃×C₄₁	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
18	C₂×C₄₁	C₂×Dic₃	1	3	yes	complemented
19	D₄₁	C₂×Dic₃	1	3	yes	complemented
20	D₄₁	C₂²×D₃	1	1	yes	characteristic
21	C₂²×Dic₃	—	41	1	no	maximal, Hall
22	C₄₁	C₂²×Dic₃	1	1	yes	characteristic, complemented, Sylow
23	C₂³×C₃	—	41	1	no	—
24	C₂×Dic₃	—	41	6	no	—
25	C₂²×C₄	—	123	1	no	Sylow
26	C₂²×C₃	—	41	3	no	—
27	C₂²×C₃	—	41	3	no	—
28	C₂²×C₃	#4223	1	1	yes	characteristic, complemented
29	Dic₃	—	41	4	no	—
30	C₂³	—	41	1	no	—
31	C₂×C₄	—	123	6	no	—
32	C₂×C₃	—	41	3	no	—
33	C₂×C₃	—	41	1	no	—
34	C₂×C₃	C₂×#4223	1	3	yes	complemented
35	C₂²	—	41	3	no	—
36	C₂²	—	41	3	no	—
37	C₂²	C₃⋊#4223	1	1	yes	characteristic, direct product factor
38	C₄	—	123	4	no	—
39	C₃	C₂²×#4223	1	1	yes	characteristic, complemented, Sylow
40	C₂	—	41	1	no	—
41	C₂	—	41	3	no	—
42	C₂	C₂×C₃⋊#4223	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	C₃⋊#4223
commutator, hypocenter	C₃×C₄₁	C₂²×C₄
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₄₁	C₄
prime radical	C₂²×C₃×D₄₁	C₂
cosocle	C₃×D₄₁	C₂³
LCS	G ▷ C₃×C₄₁
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. C₂×C₃⋊#4223	C₂	direct (N × H)
4. C₂²×C₃×C₄₁	C₄	semidirect
5. C₂×C₃×D₄₁	C₄	semidirect
7. C₃⋊#4223	C₂²	direct (N × H)
10. C₂×C₃×C₄₁	C₂×C₄	semidirect
11. C₃×D₄₁	C₂×C₄	semidirect
13. C₂²×C₄₁	Dic₃	semidirect
14. C₂×D₄₁	Dic₃	semidirect
17. C₃×C₄₁	C₂²×C₄	semidirect
18. C₂×C₄₁	C₂×Dic₃	semidirect
19. D₄₁	C₂×Dic₃	semidirect
22. C₄₁	C₂²×Dic₃	semidirect
28. C₂²×C₃	#4223	semidirect
34. C₂×C₃	C₂×#4223	semidirect
37. C₂²	C₃⋊#4223	direct (N × H)
39. C₃	C₂²×#4223	semidirect
42. C₂	C₂×C₃⋊#4223	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₄₁	2
C₂×C₃⋊#4223	2
C₂²×#4223	3
C₂²×Dic₃	41

Subgroups — C22×C3⋊#4223 #14520273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃⋊#4223 #14520273