Subgroups — D₃×Q₈×C₁₉ #11744978

Order 912.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₃×C₁₉	C₂	1	3	yes	maximal
3	C₁₉×Dic₆	C₂	1	3	yes	maximal, complemented
4	C₂×Q₈×C₁₉	—	3	1	no	maximal, Hall
5	C₂×D₃×C₁₉	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₁₉	C₂²	1	3	yes	—
7	Dic₃×C₁₉	C₂²	1	3	yes	—
8	Q₈×C₁₉	—	3	3	no	—
9	Q₈×C₁₉	D₃	1	1	yes	characteristic, direct product factor
10	C₂×C₄×C₁₉	—	3	3	no	—
11	C₂×C₃×C₁₉	C₂³	1	1	yes	characteristic
12	D₃×C₁₉	Q₈	1	2	yes	direct product factor
13	C₂²×C₁₉	—	3	1	no	—
14	C₄×C₁₉	—	3	3	no	—
15	C₄×C₁₉	C₂×D₃	1	3	yes	—
16	C₃×C₁₉	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
17	D₃×Q₈	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂×C₁₉	—	3	2	no	—
19	C₂×C₁₉	C₂²×D₃	1	1	yes	characteristic
20	C₃×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
21	C₄×D₃	C₂×C₁₉	1	3	yes	—
22	Dic₆	C₂×C₁₉	1	3	yes	complemented
23	C₁₉	D₃×Q₈	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×Q₈	—	3	1	no	Sylow
25	C₂×D₃	C₂²×C₁₉	1	1	yes	characteristic
26	C₃×C₄	C₂²×C₁₉	1	3	yes	—
27	Dic₃	C₂²×C₁₉	1	3	yes	—
28	Q₈	—	3	3	no	—
29	Q₈	D₃×C₁₉	1	1	yes	characteristic, direct product factor
30	C₂×C₄	—	3	3	no	—
31	C₂×C₃	C₂³×C₁₉	1	1	yes	characteristic
32	D₃	Q₈×C₁₉	1	2	yes	direct product factor
33	C₂²	—	3	1	no	—
34	C₄	—	3	3	no	—
35	C₄	C₂×D₃×C₁₉	1	3	yes	—
36	C₃	C₂×Q₈×C₁₉	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	3	2	no	—
38	C₂	C₂²×D₃×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₉	C₂²×D₃
commutator, cosocle	C₂×C₃	C₂³×C₁₉
Frattini	C₂	C₂²×D₃×C₁₉
Fitting	C₃×Q₈×C₁₉	C₂
socle	C₂×C₃×C₁₉	C₂³
prime radical	C₂×D₃×C₁₉	C₂²
hypercenter	Q₈×C₁₉	D₃
hypocenter	C₃	C₂×Q₈×C₁₉
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₁₉ ◁ Q₈×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×Q₈×C₁₉	C₂	semidirect
3. C₁₉×Dic₆	C₂	semidirect
9. Q₈×C₁₉	D₃	direct (N × H)
12. D₃×C₁₉	Q₈	direct (N × H)
16. C₃×C₁₉	C₂×Q₈	semidirect
17. D₃×Q₈	C₁₉	direct (N × H)
20. C₃×Q₈	C₂×C₁₉	semidirect
22. Dic₆	C₂×C₁₉	semidirect
23. C₁₉	D₃×Q₈	direct (N × H)
29. Q₈	D₃×C₁₉	direct (N × H)
32. D₃	Q₈×C₁₉	direct (N × H)
36. C₃	C₂×Q₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×Q₈×C₁₉	2
C₄×D₃×C₁₉	2
C₁₉×Dic₆	2
C₂×Q₈×C₁₉	3
D₃×Q₈	19

Subgroups — D3×Q8×C19 #11744978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×Q₈×C₁₉ #11744978