Subgroups — #18070209

Order 4864.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561703	C₂	1	1	yes	maximal, characteristic
2	#14561701	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1398	C₂	1	1	yes	maximal, characteristic
4	#11926365	—	2	1	no	—
5	#11926295	—	2	1	no	—
6	C₁₉×M₆₄	C₄	1	1	yes	characteristic
7	C₁₉×M₆₄	C₄	1	1	yes	characteristic
8	C₁₉×#346	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₂×C₁₆×C₁₉	Q₈	1	1	yes	characteristic
11	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
12	#10597269	—	4	1	no	—
13	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
14	C₁₉×C₃₂	—	2	1	no	—
15	C₁₉×C₃₂	C₈	1	2	yes	complemented
16	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
18	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
19	C₂×C₁₉⋊C₈	—	8	1	no	—
20	C₁₆×C₁₉	—	2	1	no	—
21	C₁₆×C₁₉	C₂×C₈	1	1	yes	characteristic
22	C₁₆×C₁₉	M₁₆	1	1	yes	characteristic
23	C₁₉⋊C₁₆	—	8	1	no	—
24	#7457	—	19	1	no	maximal, Sylow
25	C₂×C₄×C₁₉	—	2	1	no	—
26	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
27	C₈×C₁₉	—	2	1	no	—
28	C₈×C₁₉	C₄⋊C₈	1	1	yes	characteristic
29	C₈×C₁₉	#108	1	1	yes	characteristic
30	C₁₉⋊C₈	—	16	1	no	—
31	#1398	D₁₉	1	1	yes	characteristic
32	#1369	—	19	1	no	—
33	#1368	—	19	1	no	—
34	C₂²×C₁₉	#365	1	1	yes	characteristic
35	C₄×C₁₉	—	4	1	no	—
36	C₄×C₁₉	#334	1	1	yes	characteristic
37	C₄×C₁₉	#365	1	1	yes	characteristic
38	M₆₄	Dic₁₉	1	1	yes	characteristic
39	M₆₄	Dic₁₉	1	1	yes	characteristic
40	#364	—	38	1	no	—
41	#346	C₂×D₁₉	1	1	yes	characteristic
42	#334	—	38	1	no	—
43	C₂×C₁₉	—	2	1	no	—
44	C₂×C₁₉	#1368	1	1	yes	characteristic
45	M₃₂	—	76	1	no	—
46	C₂×C₁₆	Dic₃₈	1	1	yes	characteristic
47	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
48	C₄⋊C₈	—	76	1	no	—
49	C₄×C₈	D₇₆	1	1	yes	characteristic
50	C₃₂	—	2	1	no	—
51	C₃₂	C₁₉⋊C₈	1	2	yes	complemented
52	C₁₉	#7457	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₈	—	152	1	no	—
54	C₂×C₈	#64516	1	1	yes	characteristic
55	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
56	C₄²	#64516	1	1	yes	characteristic
57	C₁₆	—	2	1	no	—
58	C₁₆	—	152	1	no	—
59	C₁₆	C₂×C₁₉⋊C₈	1	1	yes	characteristic
60	C₁₆	#64520	1	1	yes	characteristic
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	#10597274	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	304	1	no	—
65	C₈	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
66	C₈	#10597276	1	1	yes	characteristic
67	C₂²	#11926367	1	1	yes	characteristic
68	C₄	—	4	1	no	—
69	C₄	#11926295	1	1	yes	characteristic
70	C₄	#11926367	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#14561701	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14561701
commutator	C₁₆×C₁₉	C₂×C₈
Frattini	#346	C₂×D₁₉
Fitting	C₁₉×#1398	C₂
socle	C₂×C₁₉	#1368
prime radical	C₂²×C₁₉	#365
cosocle	C₁₉×#346	C₂²
hypercenter	#1398	D₁₉
hypocenter	C₁₉	#7457
LCS	G ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #346 ◁ #1398

Complements

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

N	H ≅ G/N	type
15. C₁₉×C₃₂	C₈	semidirect
51. C₃₂	C₁₉⋊C₈	semidirect
52. C₁₉	#7457	semidirect

Maximal subgroups

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

subgroup	index
#14561703	2
#14561701	2
C₁₉×#1398	2
#7457	19