Subgroups — C₄⋊(C₃⋊#4223) #14520194

Order 1968.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊#4223	C₂	1	2	yes	maximal
2	C₃×C₄×D₄₁	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#4223	—	3	1	no	maximal, Hall
4	C₂×C₃×D₄₁	C₂²	1	1	yes	characteristic
5	C₃⋊#4223	—	2	2	no	—
6	C₃×C₄×C₄₁	C₄	1	1	yes	characteristic, complemented
7	C₃×Dic₄₁	C₄	1	1	yes	characteristic, complemented
8	C₂×#4223	—	3	2	no	—
9	C₄×D₄₁	D₃	1	1	yes	characteristic
10	C₂×C₃×C₄₁	C₂×C₄	1	1	yes	characteristic
11	C₃×D₄₁	D₄	1	1	yes	characteristic
12	C₃×D₄₁	Q₈	1	1	yes	characteristic
13	C₂×D₄₁	C₂×D₃	1	1	yes	characteristic
14	#4223	—	6	2	no	—
15	C₄×C₄₁	Dic₃	1	1	yes	characteristic, complemented
16	Dic₄₁	Dic₃	1	1	yes	characteristic, complemented
17	C₃×C₄₁	C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
18	C₂×C₄₁	C₂×Dic₃	1	1	yes	characteristic
19	D₄₁	Dic₆	1	1	yes	characteristic
20	D₄₁	D₁₂	1	1	yes	characteristic
21	C₄⋊Dic₃	—	41	1	no	maximal, Hall
22	C₄₁	C₄⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₃×C₄	—	41	1	no	—
24	C₂×Dic₃	—	41	2	no	—
25	C₄⋊C₄	—	123	1	no	Sylow
26	C₂²×C₃	—	41	1	no	—
27	C₃×C₄	—	41	1	no	—
28	C₃×C₄	#4223	1	1	yes	characteristic, complemented
29	Dic₃	—	82	2	no	—
30	C₂×C₄	—	41	1	no	—
31	C₂×C₄	—	123	2	no	—
32	C₂×C₃	—	41	1	no	—
33	C₂×C₃	—	41	1	no	—
34	C₂×C₃	C₂×#4223	1	1	yes	characteristic
35	C₂²	—	41	1	no	—
36	C₄	—	41	1	no	—
37	C₄	—	246	2	no	—
38	C₄	C₃⋊#4223	1	1	yes	characteristic, complemented
39	C₃	C₄⋊#4223	1	1	yes	characteristic, complemented, Sylow
40	C₂	—	41	1	no	—
41	C₂	—	41	1	no	—
42	C₂	C₂×C₃⋊#4223	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
6. C₃×C₄×C₄₁	C₄	semidirect
7. C₃×Dic₄₁	C₄	semidirect
15. C₄×C₄₁	Dic₃	semidirect
16. Dic₄₁	Dic₃	semidirect
17. C₃×C₄₁	C₄⋊C₄	semidirect
22. C₄₁	C₄⋊Dic₃	semidirect
28. C₃×C₄	#4223	semidirect
38. C₄	C₃⋊#4223	semidirect
39. C₃	C₄⋊#4223	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃⋊#4223	2
C₃×C₄×D₄₁	2
C₄⋊#4223	3
C₄⋊Dic₃	41

Subgroups — C4⋊(C3⋊#4223) #14520194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊(C₃⋊#4223) #14520194