Subgroups — Q₃₂×Dic₁₉ #14565494

Order 2432.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×Dic₁₉	C₂	1	2	yes	maximal
2	#11926370	C₂	1	1	yes	maximal, characteristic
3	#11926348	C₂	1	2	yes	maximal
4	C₁₆×Dic₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×Q₃₂	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆×C₁₉	C₂²	1	2	yes	—
7	Q₈×Dic₁₉	—	2	2	no	—
8	C₁₉×Q₃₂	C₄	1	4	yes	complemented
9	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	#10597292	—	2	2	no	—
11	#10597275	C₂²	1	2	yes	—
12	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
14	C₂×Q₈×C₁₉	—	2	2	no	—
15	Q₁₆×C₁₉	—	2	2	no	—
16	Q₁₆×C₁₉	C₂×C₄	1	4	yes	—
17	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
18	C₄⋊Dic₁₉	—	2	2	no	—
19	C₄⋊Dic₁₉	—	4	2	no	—
20	C₄×Dic₁₉	—	4	2	no	—
21	C₄×Dic₁₉	D₄	1	1	yes	characteristic
22	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
23	C₁₆×C₁₉	C₂×C₄	1	2	yes	—
24	C₁₉⋊C₁₆	—	2	1	no	—
25	Q₈×C₁₉	—	2	4	no	—
26	Q₈×C₁₉	—	4	2	no	—
27	C₂×C₄×C₁₉	—	4	2	no	—
28	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₁₉	—	4	2	no	—
30	C₂×Dic₁₉	D₈	1	1	yes	characteristic
31	C₂×Dic₁₉	D₈	1	1	yes	characteristic
32	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₁₉	#41	1	1	yes	characteristic
34	C₁₉⋊C₈	—	2	1	no	—
35	C₄×Q₃₂	—	19	1	no	maximal, Sylow
36	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
37	C₄×C₁₉	—	4	4	no	—
38	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
39	C₄×C₁₉	#135	1	1	yes	characteristic
40	Dic₁₉	—	2	1	no	—
41	Dic₁₉	—	8	2	no	—
42	Dic₁₉	Q₃₂	1	2	yes	direct product factor
43	C₂×Q₃₂	D₁₉	1	1	yes	characteristic
44	C₄×Q₁₆	—	19	2	no	—
45	#366	—	19	1	no	—
46	#358	—	19	2	no	—
47	C₄×C₁₆	—	19	1	no	—
48	C₂×C₁₉	C₄×D₈	1	1	yes	characteristic
49	C₂×C₁₉	C₂×Q₃₂	1	1	yes	characteristic
50	C₂×C₁₉	#508	1	1	yes	characteristic
51	C₂×Q₁₆	C₂×D₁₉	1	2	yes	—
52	C₄×Q₈	—	38	2	no	—
53	Q₃₂	Dic₁₉	1	4	yes	direct product factor
54	C₂×C₁₆	—	19	1	no	—
55	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
56	#107	—	19	2	no	—
57	#103	—	38	2	no	—
58	C₄×C₈	—	19	1	no	—
59	C₁₉	C₄×Q₃₂	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₈	—	2	2	no	—
61	Q₁₆	—	2	2	no	—
62	Q₁₆	C₂×Dic₁₉	1	4	yes	—
63	C₂×C₈	—	19	1	no	—
64	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
65	C₄⋊C₄	—	38	2	no	—
66	C₄⋊C₄	—	76	2	no	—
67	C₄²	—	19	1	no	—
68	C₄²	—	76	2	no	—
69	C₁₆	—	38	1	no	—
70	C₁₆	C₂×Dic₁₉	1	2	yes	—
71	Q₈	—	2	4	no	—
72	Q₈	—	4	2	no	—
73	C₂×C₄	—	4	2	no	—
74	C₂×C₄	—	19	1	no	—
75	C₂×C₄	—	19	1	no	—
76	C₂×C₄	—	76	2	no	—
77	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
78	C₈	—	38	1	no	—
79	C₈	#64543	1	1	yes	characteristic
80	C₈	C₂²×Dic₁₉	1	1	yes	characteristic
81	C₂²	D₈×D₁₉	1	1	yes	characteristic
82	C₄	—	4	4	no	—
83	C₄	—	19	2	no	—
84	C₄	—	38	1	no	—
85	C₄	—	152	2	no	—
86	C₄	#10597358	1	1	yes	characteristic
87	C₄	D₄×Dic₁₉	1	1	yes	characteristic
88	C₂	D₈×Dic₁₉	1	1	yes	characteristic
89	C₂	Q₃₂×D₁₉	1	1	yes	characteristic
90	C₂	#11926977	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈×D₁₉
commutator	C₈×C₁₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₂×C₁₉×Q₃₂	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₈
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	C₂×Q₃₂	D₁₉
hypocenter	C₁₉	C₄×Q₃₂
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
8. C₁₉×Q₃₂	C₄	semidirect
42. Dic₁₉	Q₃₂	direct (N × H)
53. Q₃₂	Dic₁₉	direct (N × H)
59. C₁₉	C₄×Q₃₂	semidirect

Maximal subgroups

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

subgroup	index
Q₁₆×Dic₁₉	2
#11926370	2
#11926348	2
C₁₆×Dic₁₉	2
C₂×C₁₉×Q₃₂	2
C₄×Q₃₂	19

Subgroups — Q32×Dic19 #14565494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₃₂×Dic₁₉ #14565494