Subgroups — #18070206

Order 4864.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561833	C₂	1	1	yes	maximal, characteristic
2	#14561551	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1422	C₂	1	1	yes	maximal, characteristic
4	#11926378	—	2	1	no	—
5	C₄×C₁₉⋊C₁₆	C₄	1	1	yes	characteristic
6	C₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic
7	C₁₉×M₆₄	—	2	1	no	—
8	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
10	C₂×C₁₆×C₁₉	Q₈	1	1	yes	characteristic
11	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₉⋊C₁₆	C₈	1	1	yes	characteristic
13	C₂×C₁₉⋊C₁₆	C₈	1	1	yes	characteristic
14	C₄×C₁₉⋊C₈	—	2	1	no	—
15	C₁₉×C₃₂	—	4	1	no	—
16	C₁₉⋊C₃₂	—	4	1	no	—
17	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
19	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
20	C₂×C₁₉⋊C₈	—	2	2	no	—
21	C₁₆×C₁₉	—	2	1	no	—
22	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
23	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
24	C₁₉⋊C₁₆	—	2	1	no	—
25	C₁₉⋊C₁₆	C₁₆	1	2	yes	—
26	#7456	—	19	1	no	maximal, Sylow
27	C₂×C₄×C₁₉	—	2	1	no	—
28	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
29	C₈×C₁₉	#106	1	1	yes	characteristic
30	C₈×C₁₉	#108	1	1	yes	characteristic
31	C₈×C₁₉	C₂×C₁₆	1	1	yes	characteristic
32	C₈×C₁₉	M₃₂	1	1	yes	characteristic
33	C₁₉⋊C₈	—	4	2	no	—
34	#1422	—	19	1	no	—
35	#1422	D₁₉	1	1	yes	characteristic
36	#1311	—	19	1	no	—
37	C₂²×C₁₉	#364	1	1	yes	characteristic
38	C₄×C₁₉	—	2	2	no	—
39	C₄×C₁₉	#334	1	1	yes	characteristic
40	C₄×C₁₉	C₄⋊C₁₆	1	1	yes	characteristic
41	M₆₄	—	2	1	no	—
42	M₆₄	—	38	1	no	—
43	C₄×C₁₆	—	19	1	no	—
44	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
45	C₈²	—	19	1	no	—
46	C₂×C₁₉	—	2	1	no	—
47	C₂×C₁₉	#1367	1	1	yes	characteristic
48	C₂×C₁₆	—	19	1	no	—
49	C₂×C₁₆	—	19	1	no	—
50	C₂×C₁₆	Dic₃₈	1	1	yes	characteristic
51	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
52	C₄×C₈	—	38	1	no	—
53	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
54	C₃₂	—	4	1	no	—
55	C₃₂	—	76	1	no	—
56	C₁₉	#7456	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₈	—	38	2	no	—
58	C₂×C₈	C₈×D₁₉	1	1	yes	characteristic
59	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
60	C₄²	#64515	1	1	yes	characteristic
61	C₁₆	—	2	1	no	—
62	C₁₆	—	19	2	no	—
63	C₁₆	—	38	1	no	—
64	C₁₆	#64526	1	1	yes	characteristic
65	C₁₆	#64527	1	1	yes	characteristic
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	Dic₁₉⋊C₈	1	1	yes	characteristic
68	C₈	—	76	2	no	—
69	C₈	C₁₆×D₁₉	1	1	yes	characteristic
70	C₈	#10597255	1	1	yes	characteristic
71	C₈	#10597265	1	1	yes	characteristic
72	C₈	#10597279	1	1	yes	characteristic
73	C₂²	#11926364	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	#11926294	1	1	yes	characteristic
76	C₄	Dic₁₉⋊C₁₆	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	#14561698	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#10597265
commutator	C₈×C₁₉	C₂×C₁₆
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting	C₁₉×#1422	C₂
socle	C₂×C₁₉	#1367
prime radical	C₂²×C₁₉	#364
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	#1422	D₁₉
hypocenter	C₁₉	#7456
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ C₄×C₁₆ ◁ #1422

Complements

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

N	H ≅ G/N	type
56. C₁₉	#7456	semidirect

Maximal subgroups

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

subgroup	index
#14561833	2
#14561551	2
C₁₉×#1422	2
#7456	19