Subgroups — #18070199

Order 4864.

102 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	#14561711	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2254	C₂	1	1	yes	maximal, characteristic
4	#11926378	—	2	1	no	—
5	#11926365	—	2	1	no	—
6	C₁₉×#500	—	2	1	no	—
7	C₁₉×#367	—	2	1	no	—
8	C₁₉×#367	C₄	1	2	yes	—
9	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×C₄⋊Q₈	—	4	1	no	—
11	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
13	C₁₉×#107	—	2	2	no	—
14	C₁₉×#107	—	4	1	no	—
15	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
16	#10597269	—	4	1	no	—
17	C₁₉⋊C₃₂	—	4	1	no	—
18	C₂×Q₈×C₁₉	—	8	1	no	—
19	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
21	C₄⋊C₄×C₁₉	—	4	2	no	—
22	C₄⋊C₄×C₁₉	—	8	1	no	—
23	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
24	C₁₆×C₁₉	—	2	1	no	—
25	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
26	C₁₆×C₁₉	Q₁₆	1	1	yes	characteristic
27	C₁₉⋊C₁₆	—	8	1	no	—
28	#7453	—	19	1	no	maximal, Sylow
29	Q₈×C₁₉	—	16	2	no	—
30	C₂×C₄×C₁₉	—	2	1	no	—
31	C₂×C₄×C₁₉	—	8	2	no	—
32	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
33	C₈×C₁₉	#101	1	1	yes	characteristic
34	C₈×C₁₉	#103	1	1	yes	characteristic
35	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
36	C₈×C₁₉	Q₃₂	1	1	yes	characteristic
37	#2254	D₁₉	1	1	yes	characteristic
38	#1422	—	19	1	no	—
39	#1373	—	19	1	no	—
40	C₂²×C₁₉	#361	1	1	yes	characteristic
41	C₄×C₁₉	—	2	2	no	—
42	C₄×C₁₉	—	16	2	no	—
43	C₄×C₁₉	#332	1	1	yes	characteristic
44	C₄×C₁₉	#358	1	1	yes	characteristic
45	#500	—	2	1	no	—
46	M₆₄	—	38	1	no	—
47	#367	—	2	1	no	—
48	#367	Dic₁₉	1	2	yes	—
49	#364	—	38	1	no	—
50	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
51	C₂×C₁₉	—	2	1	no	—
52	C₂×C₁₉	#1365	1	1	yes	characteristic
53	C₄⋊Q₈	—	4	1	no	—
54	M₃₂	—	76	1	no	—
55	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
56	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
57	#107	—	2	2	no	—
58	#107	—	4	1	no	—
59	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
60	C₃₂	—	76	1	no	—
61	C₁₉	#7453	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₈	—	8	1	no	—
63	C₂×C₈	#64525	1	1	yes	characteristic
64	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
65	C₄⋊C₄	—	4	2	no	—
66	C₄⋊C₄	—	8	1	no	—
67	C₄²	#64526	1	1	yes	characteristic
68	C₁₆	—	2	1	no	—
69	C₁₆	—	152	1	no	—
70	C₁₆	#64527	1	1	yes	characteristic
71	C₁₆	#64528	1	1	yes	characteristic
72	Q₈	—	16	2	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	8	2	no	—
75	C₂×C₄	#10597289	1	1	yes	characteristic
76	C₈	#10597285	1	1	yes	characteristic
77	C₈	#10597286	1	1	yes	characteristic
78	C₈	#10597292	1	1	yes	characteristic
79	C₈	#10597293	1	1	yes	characteristic
80	C₂²	#11926357	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	16	2	no	—
83	C₄	#11926290	1	1	yes	characteristic
84	C₄	#11926348	1	1	yes	characteristic
85	C₂	—	2	1	no	—
86	C₂	#14561693	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14561693
commutator	C₂×C₁₆×C₁₉	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting	C₁₉×#2254	C₂
socle	C₂×C₁₉	#1365
prime radical	C₂²×C₁₉	#361
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	#2254	D₁₉
hypocenter	C₁₉	#7453
LCS	G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2254

Complements

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

N	H ≅ G/N	type
61. C₁₉	#7453	semidirect

Maximal subgroups

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

subgroup	index
#14561833	2
#14561711	2
C₁₉×#2254	2
#7453	19