Subgroups — Q₈×Dic₃×C₁₉ #14269694

Order 1824.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₄⋊Dic₃	C₂	1	3	yes	maximal
3	C₄×Dic₃×C₁₉	C₂	1	3	yes	maximal
4	C₄×Q₈×C₁₉	—	3	1	no	maximal, Hall
5	C₃×Q₈×C₁₉	C₄	1	4	yes	complemented
6	C₂×C₃×C₄×C₁₉	C₂²	1	3	yes	—
7	C₂×Dic₃×C₁₉	C₂²	1	3	yes	—
8	C₂×Dic₃×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×Q₈×C₁₉	D₃	1	1	yes	characteristic
10	C₄⋊C₄×C₁₉	—	3	3	no	—
11	C₄²×C₁₉	—	3	3	no	—
12	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
13	C₃×C₄×C₁₉	C₂×C₄	1	6	yes	—
14	Dic₃×C₁₉	—	2	3	no	—
15	Dic₃×C₁₉	Q₈	1	2	yes	direct product factor
16	Q₈×C₁₉	Dic₃	1	4	yes	direct product factor
17	C₂×C₄×C₁₉	—	3	1	no	—
18	C₂×C₄×C₁₉	—	3	3	no	—
19	C₂×C₄×C₁₉	C₂×D₃	1	3	yes	—
20	C₂×C₃×C₁₉	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₃×C₁₉	C₂×Q₈	1	1	yes	characteristic
22	C₂×C₃×C₁₉	#41	1	1	yes	characteristic
23	Q₈×Dic₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
25	C₄×C₁₉	—	3	2	no	—
26	C₄×C₁₉	—	6	3	no	—
27	C₄×C₁₉	C₂×Dic₃	1	6	yes	—
28	C₃×C₁₉	C₄×Q₈	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×Q₈	C₂×C₁₉	1	1	yes	characteristic
30	C₄⋊Dic₃	C₂×C₁₉	1	3	yes	—
31	C₄×Dic₃	C₂×C₁₉	1	3	yes	—
32	C₂×C₁₉	D₃×Q₈	1	1	yes	characteristic
33	C₂×C₁₉	#239	1	1	yes	characteristic
34	C₂×C₁₉	C₂²×Dic₃	1	1	yes	characteristic
35	C₄×Q₈	—	3	1	no	Sylow
36	C₃×Q₈	C₄×C₁₉	1	4	yes	complemented
37	C₂×C₃×C₄	C₂²×C₁₉	1	3	yes	—
38	C₂×Dic₃	C₂²×C₁₉	1	3	yes	—
39	C₂×Dic₃	C₂²×C₁₉	1	1	yes	characteristic
40	C₁₉	Q₈×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×Q₈	D₃×C₁₉	1	1	yes	characteristic
42	C₄⋊C₄	—	3	3	no	—
43	C₄²	—	3	3	no	—
44	C₂²×C₃	C₂³×C₁₉	1	1	yes	characteristic
45	C₃×C₄	C₂×C₄×C₁₉	1	6	yes	—
46	Dic₃	—	2	3	no	—
47	Dic₃	Q₈×C₁₉	1	2	yes	direct product factor
48	Q₈	Dic₃×C₁₉	1	4	yes	direct product factor
49	C₂×C₄	—	3	1	no	—
50	C₂×C₄	—	3	3	no	—
51	C₂×C₄	C₂×D₃×C₁₉	1	3	yes	—
52	C₂×C₃	C₂²×C₄×C₁₉	1	1	yes	characteristic
53	C₂×C₃	C₂×Q₈×C₁₉	1	1	yes	characteristic
54	C₂×C₃	#41×C₁₉	1	1	yes	characteristic
55	C₂²	C₂²×D₃×C₁₉	1	1	yes	characteristic
56	C₄	—	3	2	no	—
57	C₄	—	6	3	no	—
58	C₄	C₂×Dic₃×C₁₉	1	6	yes	—
59	C₃	C₄×Q₈×C₁₉	1	1	yes	characteristic, complemented, Sylow
60	C₂	D₃×Q₈×C₁₉	1	1	yes	characteristic
61	C₂	C₁₉×#239	1	1	yes	characteristic
62	C₂	C₂²×Dic₃×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₉	C₂²×D₃
commutator	C₂×C₃	C₂²×C₄×C₁₉
Frattini	C₂²	C₂²×D₃×C₁₉
Fitting	C₂×C₃×Q₈×C₁₉	C₂
socle, prime radical	C₂²×C₃×C₁₉	C₂³
cosocle	C₂²×C₃	C₂³×C₁₉
hypercenter	C₂×Q₈×C₁₉	D₃
hypocenter	C₃	C₄×Q₈×C₁₉
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×Q₈×C₁₉

Complements

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

N	H ≅ G/N	type
5. C₃×Q₈×C₁₉	C₄	semidirect
15. Dic₃×C₁₉	Q₈	direct (N × H)
16. Q₈×C₁₉	Dic₃	direct (N × H)
23. Q₈×Dic₃	C₁₉	direct (N × H)
28. C₃×C₁₉	C₄×Q₈	semidirect
36. C₃×Q₈	C₄×C₁₉	semidirect
40. C₁₉	Q₈×Dic₃	direct (N × H)
47. Dic₃	Q₈×C₁₉	direct (N × H)
48. Q₈	Dic₃×C₁₉	direct (N × H)
59. C₃	C₄×Q₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×Q₈×C₁₉	2
C₁₉×C₄⋊Dic₃	2
C₄×Dic₃×C₁₉	2
C₄×Q₈×C₁₉	3
Q₈×Dic₃	19

Subgroups — Q8×Dic3×C19 #14269694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×Dic₃×C₁₉ #14269694