Subgroups — #14561702

Order 2432.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926365	C₂	1	1	yes	maximal, characteristic
2	#11926320	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#364	C₂	1	1	yes	maximal, characteristic
4	C₁₉×M₃₂	—	2	1	no	—
5	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
6	#10597269	—	2	1	no	—
7	C₂×C₁₉⋊C₁₆	C₄	1	1	yes	characteristic
8	C₂×C₁₉⋊C₁₆	C₄	1	1	yes	characteristic
9	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
11	C₄²×C₁₉	Q₈	1	1	yes	characteristic
12	C₁₆×C₁₉	—	4	1	no	—
13	C₁₉⋊C₁₆	—	2	1	no	—
14	C₁₉⋊C₁₆	—	4	1	no	—
15	C₁₉⋊C₁₆	C₈	1	2	yes	—
16	C₂×C₄×C₁₉	—	2	1	no	—
17	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
19	C₈×C₁₉	M₁₆	1	1	yes	characteristic
20	C₈×C₁₉	SD₁₆	1	1	yes	characteristic
21	C₈×C₁₉	SD₁₆	1	1	yes	characteristic
22	#1369	—	19	1	no	maximal, Sylow
23	C₂²×C₁₉	#108	1	1	yes	characteristic
24	C₄×C₁₉	—	4	1	no	—
25	C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
26	C₄×C₁₉	#106	1	1	yes	characteristic
27	#364	—	19	1	no	—
28	#364	D₁₉	1	1	yes	characteristic
29	#346	—	19	1	no	—
30	C₂×C₁₉	—	2	1	no	—
31	C₂×C₁₉	#334	1	1	yes	characteristic
32	M₃₂	—	2	1	no	—
33	M₃₂	—	38	1	no	—
34	C₂×C₁₆	—	19	1	no	—
35	C₂×C₁₆	—	19	1	no	—
36	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
37	C₁₉	#1369	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
39	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
40	C₄²	Dic₃₈	1	1	yes	characteristic
41	C₁₆	—	4	1	no	—
42	C₁₆	—	19	2	no	—
43	C₁₆	—	38	1	no	—
44	C₁₆	—	76	1	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
47	C₈	C₈×D₁₉	1	1	yes	characteristic
48	C₈	#64515	1	1	yes	characteristic
49	C₈	#64526	1	1	yes	characteristic
50	C₈	#64527	1	1	yes	characteristic
51	C₂²	#10597279	1	1	yes	characteristic
52	C₄	—	4	1	no	—
53	C₄	#10597265	1	1	yes	characteristic
54	C₄	Dic₁₉⋊C₈	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#11926294	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10597265
commutator	C₈×C₁₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#364	C₂
socle	C₂×C₁₉	#334
prime radical	C₂²×C₁₉	#108
cosocle	C₄×C₈×C₁₉	C₂²
hypercenter	#364	D₁₉
hypocenter	C₁₉	#1369
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
37. C₁₉	#1369	semidirect

Maximal subgroups

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

subgroup	index
#11926365	2
#11926320	2
C₁₉×#364	2
#1369	19