Subgroups — D₁₉×Q₆₄ #14565938

Order 2432.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₃₂×D₁₉	C₂	1	2	yes	maximal
2	Dic₃₀₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926384	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₁₆×D₁₉	—	2	2	no	—
7	C₁₉×Q₃₂	C₂²	1	2	yes	—
8	#10597286	—	2	2	no	—
9	Dic₁₅₂	C₂²	1	2	yes	—
10	C₁₆×D₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×C₃₂	C₂²	1	1	yes	characteristic
12	C₁₉⋊C₃₂	C₂²	1	1	yes	characteristic
13	Q₈×D₁₉	—	4	2	no	—
14	Q₁₆×C₁₉	—	2	2	no	—
15	#64528	—	4	2	no	—
16	Dic₇₆	—	2	2	no	—
17	C₈×D₁₉	D₄	1	1	yes	characteristic
18	C₁₆×C₁₉	C₂³	1	1	yes	characteristic
19	C₁₉⋊C₁₆	D₄	1	1	yes	characteristic
20	Q₈×C₁₉	—	4	2	no	—
21	C₄×D₁₉	—	8	2	no	—
22	C₄×D₁₉	D₈	1	1	yes	characteristic
23	Dic₃₈	—	4	2	no	—
24	Dic₃₈	—	8	2	no	—
25	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
26	C₁₉⋊C₈	D₈	1	1	yes	characteristic
27	C₂×Q₆₄	—	19	1	no	maximal, Sylow
28	C₂×D₁₉	D₁₆	1	1	yes	characteristic
29	C₄×C₁₉	—	8	2	no	—
30	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
31	Dic₁₉	—	8	2	no	—
32	Dic₁₉	D₁₆	1	1	yes	characteristic
33	C₂×Q₃₂	—	19	2	no	—
34	Q₆₄	—	19	2	no	—
35	Q₆₄	—	19	1	no	—
36	Q₆₄	D₁₉	1	1	yes	characteristic, direct product factor
37	C₂×C₃₂	—	19	1	no	—
38	C₂×C₁₉	C₂×D₁₆	1	1	yes	characteristic
39	D₁₉	Q₆₄	1	2	yes	direct product factor
40	C₂×Q₁₆	—	38	2	no	—
41	Q₃₂	—	19	2	no	—
42	Q₃₂	—	38	2	no	—
43	Q₃₂	C₂×D₁₉	1	2	yes	—
44	C₂×C₁₆	—	19	1	no	—
45	C₃₂	—	19	1	no	—
46	C₃₂	C₂×D₁₉	1	1	yes	characteristic
47	C₁₉	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
48	C₂×Q₈	—	76	2	no	—
49	Q₁₆	—	2	2	no	—
50	Q₁₆	—	38	2	no	—
51	Q₁₆	—	76	2	no	—
52	C₂×C₈	—	19	1	no	—
53	C₁₆	—	19	1	no	—
54	C₁₆	C₂²×D₁₉	1	1	yes	characteristic
55	Q₈	—	4	2	no	—
56	Q₈	—	76	2	no	—
57	Q₈	—	152	2	no	—
58	C₂×C₄	—	19	1	no	—
59	C₂×C₄	—	152	2	no	—
60	C₈	—	19	1	no	—
61	C₈	D₄×D₁₉	1	1	yes	characteristic
62	C₂²	—	19	1	no	—
63	C₄	—	8	2	no	—
64	C₄	—	19	1	no	—
65	C₄	—	152	2	no	—
66	C₄	D₈×D₁₉	1	1	yes	characteristic
67	C₂	—	19	2	no	—
68	C₂	D₁₆×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₁₉
commutator, cosocle	C₁₆×C₁₉	C₂³
Frattini	C₁₆	C₂²×D₁₉
Fitting	C₁₉×Q₆₄	C₂
socle	C₂×C₁₉	C₂×D₁₆
prime radical	C₂×D₁₉	D₁₆
hypercenter	Q₆₄	D₁₉
hypocenter	C₁₉	C₂×Q₆₄
LCS	G ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
2. Dic₃₀₄	C₂	semidirect
3. #11926384	C₂	semidirect
5. C₁₉×Q₆₄	C₂	semidirect
36. Q₆₄	D₁₉	direct (N × H)
39. D₁₉	Q₆₄	direct (N × H)
47. C₁₉	C₂×Q₆₄	semidirect

Maximal subgroups

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

subgroup	index
Q₃₂×D₁₉	2
Dic₃₀₄	2
#11926384	2
C₃₂×D₁₉	2
C₁₉×Q₆₄	2
C₂×Q₆₄	19

Subgroups — D19×Q64 #14565938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₉×Q₆₄ #14565938