Subgroups — D₃×C₁₉⋊C₈ #11744813

Order 912.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₃×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉⋊C₈	—	3	1	no	maximal, Hall
5	C₂×D₃×C₁₉	C₄	1	1	yes	characteristic
6	C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	Dic₃×C₁₉	C₄	1	1	yes	characteristic
8	C₂×C₄×C₁₉	—	3	1	no	—
9	C₁₉⋊C₈	—	3	1	no	—
10	C₁₉⋊C₈	D₃	1	1	yes	characteristic, direct product factor
11	C₂×C₃×C₁₉	C₂×C₄	1	1	yes	characteristic
12	D₃×C₁₉	C₈	1	2	yes	complemented
13	C₂²×C₁₉	—	3	1	no	—
14	C₄×C₁₉	—	3	1	no	—
15	C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
16	C₃×C₁₉	C₂×C₈	1	1	yes	characteristic, complemented, Hall
17	D₃×C₈	—	19	1	no	maximal, Hall
18	C₂×C₁₉	—	3	2	no	—
19	C₂×C₁₉	C₄×D₃	1	1	yes	characteristic
20	C₄×D₃	D₁₉	1	1	yes	characteristic
21	C₃×C₈	—	19	1	no	—
22	C₃⋊C₈	—	19	1	no	—
23	C₁₉	D₃×C₈	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₈	—	57	1	no	Sylow
25	C₂×D₃	Dic₁₉	1	1	yes	characteristic
26	C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
27	Dic₃	Dic₁₉	1	1	yes	characteristic
28	C₂×C₄	—	3	1	no	—
29	C₈	—	19	1	no	—
30	C₈	—	57	1	no	—
31	C₂×C₃	C₂×Dic₁₉	1	1	yes	characteristic
32	D₃	C₁₉⋊C₈	1	2	yes	direct product factor
33	C₂²	—	3	1	no	—
34	C₄	—	3	1	no	—
35	C₄	D₃×D₁₉	1	1	yes	characteristic
36	C₃	C₂×C₁₉⋊C₈	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	3	2	no	—
38	C₂	D₃×Dic₁₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₃×D₁₉
commutator, hypocenter	C₃×C₁₉	C₂×C₈
Fitting, cosocle	C₃×C₄×C₁₉	C₂²
socle	C₂×C₃×C₁₉	C₂×C₄
prime radical	C₂×D₃×C₁₉	C₄
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₁₉⋊C₈)	C₂	semidirect
3. C₃×C₁₉⋊C₈	C₂	semidirect
10. C₁₉⋊C₈	D₃	direct (N × H)
12. D₃×C₁₉	C₈	semidirect
16. C₃×C₁₉	C₂×C₈	semidirect
23. C₁₉	D₃×C₈	semidirect
32. D₃	C₁₉⋊C₈	direct (N × H)
36. C₃	C₂×C₁₉⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₃×C₁₉	2
C₃⋊(C₁₉⋊C₈)	2
C₃×C₁₉⋊C₈	2
C₂×C₁₉⋊C₈	3
D₃×C₈	19

Subgroups — D3×C19⋊C8 #11744813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₉⋊C₈ #11744813