Subgroups — #14561703

Order 2432.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926365	C₂	1	2	yes	maximal
2	C₁₉×#346	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₉	C₄	1	1	yes	characteristic
4	C₂×C₁₆×C₁₉	C₄	1	1	yes	characteristic
5	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
6	#10597269	—	2	2	no	—
7	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
8	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
9	C₄²×C₁₉	Q₈	1	1	yes	characteristic
10	C₁₆×C₁₉	—	2	1	no	—
11	C₁₆×C₁₉	C₈	1	2	yes	—
12	C₁₉⋊C₁₆	—	4	2	no	—
13	C₂×C₄×C₁₉	—	2	1	no	—
14	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
15	C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
16	C₈×C₁₉	M₁₆	1	1	yes	characteristic
17	C₈×C₁₉	SD₁₆	1	2	yes	—
18	#1369	—	19	1	no	maximal, Sylow
19	C₂²×C₁₉	#108	1	1	yes	characteristic
20	C₄×C₁₉	—	4	1	no	—
21	C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₁₉	#106	1	1	yes	characteristic
23	#364	—	19	2	no	—
24	#346	D₁₉	1	1	yes	characteristic
25	C₂×C₁₉	—	2	1	no	—
26	C₂×C₁₉	#334	1	1	yes	characteristic
27	M₃₂	—	38	2	no	—
28	C₂×C₁₆	Dic₁₉	1	1	yes	characteristic
29	C₂×C₁₆	Dic₁₉	1	1	yes	characteristic
30	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
31	C₁₉	#1369	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₈	D₇₆	1	1	yes	characteristic
33	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
34	C₄²	Dic₃₈	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₁₆	—	76	2	no	—
37	C₁₆	C₁₉⋊C₈	1	2	yes	—
38	C₂×C₄	—	2	1	no	—
39	C₂×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
40	C₈	#64516	1	2	yes	—
41	C₈	C₂×C₁₉⋊C₈	1	1	yes	characteristic
42	C₈	#64520	1	1	yes	characteristic
43	C₂²	#10597276	1	1	yes	characteristic
44	C₄	—	4	1	no	—
45	C₄	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
46	C₄	#10597274	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#11926295	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10597274
commutator	C₈×C₁₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#346	C₂
socle	C₂×C₁₉	#334
prime radical	C₂²×C₁₉	#108
cosocle	C₄×C₈×C₁₉	C₂²
hypercenter	#346	D₁₉
hypocenter	C₁₉	#1369
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
31. 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
C₁₉×#346	2
#1369	19