Subgroups — #14561842

Order 2432.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926378	C₂	1	1	yes	maximal, characteristic
2	#11926372	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#368	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
5	C₁₉×#108	—	2	1	no	—
6	#10597275	—	2	1	no	—
7	C₁₉⋊C₃₂	C₄	1	2	yes	complemented
8	M₁₆×C₁₉	—	4	1	no	—
9	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
10	C₄⋊Dic₁₉	—	4	1	no	—
11	C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₉	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
14	C₂×Dic₁₉	—	8	1	no	—
15	C₈×C₁₉	—	8	1	no	—
16	C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₉	Q₁₆	1	1	yes	characteristic
18	#1426	—	19	1	no	maximal, Sylow
19	C₂²×C₁₉	SD₃₂	1	1	yes	characteristic
20	C₄×C₁₉	#107	1	1	yes	characteristic
21	C₄×C₁₉	SD₃₂	1	1	yes	characteristic
22	Dic₁₉	—	16	1	no	—
23	M₆₄	—	19	1	no	—
24	#368	D₁₉	1	1	yes	characteristic
25	#367	—	19	1	no	—
26	C₂×C₁₉	—	2	1	no	—
27	C₂×C₁₉	#367	1	1	yes	characteristic
28	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
29	#108	—	2	1	no	—
30	#107	—	38	1	no	—
31	C₃₂	—	19	2	no	—
32	C₁₉	#1426	1	1	yes	characteristic, complemented, Sylow
33	M₁₆	—	4	1	no	—
34	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
35	C₄⋊C₄	—	76	1	no	—
36	C₁₆	Dic₃₈	1	1	yes	characteristic
37	C₁₆	C₄×D₁₉	1	1	yes	characteristic
38	C₂×C₄	—	152	1	no	—
39	C₂×C₄	#64525	1	1	yes	characteristic
40	C₈	—	8	1	no	—
41	C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
42	C₈	#64528	1	1	yes	characteristic
43	C₂²	#10597285	1	1	yes	characteristic
44	C₄	—	304	1	no	—
45	C₄	#10597264	1	1	yes	characteristic
46	C₄	#10597284	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#11926371	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11926371
commutator	C₁₆×C₁₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₉
Fitting	C₁₉×#368	C₂
socle	C₂×C₁₉	#367
prime radical	C₂²×C₁₉	SD₃₂
cosocle	C₂×C₁₆×C₁₉	C₂²
hypercenter	#368	D₁₉
hypocenter	C₁₉	#1426
LCS	G ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
7. C₁₉⋊C₃₂	C₄	semidirect
32. C₁₉	#1426	semidirect

Maximal subgroups

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

subgroup	index
#11926378	2
#11926372	2
C₁₉×#368	2
#1426	19