Subgroups — #18070190

Order 4864.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₁₉⋊C₃₂)	C₂	1	1	yes	maximal, characteristic
2	#14561707	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2252	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉⋊C₃₂	—	2	1	no	—
5	#11926297	—	2	1	no	—
6	C₁₉×#500	—	2	1	no	—
7	C₁₉×#366	—	2	1	no	—
8	C₁₉×#366	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	C₄⋊(C₁₉⋊C₈)	—	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	SD₁₆	1	1	yes	characteristic
21	C₄⋊C₄×C₁₉	—	4	2	no	—
22	C₄⋊C₄×C₁₉	—	8	1	no	—
23	C₄²×C₁₉	D₈	1	1	yes	characteristic
24	C₂×C₁₉⋊C₈	—	8	1	no	—
25	C₁₆×C₁₉	—	2	1	no	—
26	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
27	C₁₆×C₁₉	Q₁₆	1	1	yes	characteristic
28	#7450	—	19	1	no	maximal, Sylow
29	Q₈×C₁₉	—	16	1	no	—
30	Q₈×C₁₉	—	16	1	no	—
31	C₂×C₄×C₁₉	—	8	2	no	—
32	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
33	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
34	C₂×C₄×C₁₉	SD₃₂	1	1	yes	characteristic
35	C₈×C₁₉	—	2	1	no	—
36	C₈×C₁₉	#101	1	1	yes	characteristic
37	C₈×C₁₉	#103	1	1	yes	characteristic
38	C₁₉⋊C₈	—	16	1	no	—
39	#2252	D₁₉	1	1	yes	characteristic
40	C₄⋊C₃₂	—	19	1	no	—
41	#1371	—	19	1	no	—
42	C₂²×C₁₉	#357	1	1	yes	characteristic
43	C₄×C₁₉	—	2	1	no	—
44	C₄×C₁₉	—	16	2	no	—
45	C₄×C₁₉	#332	1	1	yes	characteristic
46	C₄×C₁₉	#362	1	1	yes	characteristic
47	C₄×C₁₉	D₃₂	1	1	yes	characteristic
48	C₄×C₁₉	SD₆₄	1	1	yes	characteristic
49	#500	—	2	1	no	—
50	C₂×C₃₂	—	38	1	no	—
51	#366	—	2	1	no	—
52	#366	Dic₁₉	1	2	yes	—
53	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
54	#335	—	38	1	no	—
55	C₂×C₁₉	#1364	1	1	yes	characteristic
56	C₂×C₁₉	#1415	1	1	yes	characteristic
57	C₂×C₁₉	#1420	1	1	yes	characteristic
58	C₄⋊Q₈	—	4	1	no	—
59	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
60	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
61	#107	—	2	2	no	—
62	#107	—	4	1	no	—
63	C₄⋊C₈	—	76	1	no	—
64	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
65	C₃₂	—	76	1	no	—
66	C₁₉	#7450	1	1	yes	characteristic, complemented, Sylow
67	C₂×Q₈	—	8	1	no	—
68	C₂×C₈	—	152	1	no	—
69	C₂×C₈	#64526	1	1	yes	characteristic
70	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
71	C₄⋊C₄	—	4	2	no	—
72	C₄⋊C₄	—	8	1	no	—
73	C₄²	#64525	1	1	yes	characteristic
74	C₁₆	—	2	1	no	—
75	C₁₆	#64527	1	1	yes	characteristic
76	C₁₆	#64528	1	1	yes	characteristic
77	Q₈	—	16	1	no	—
78	Q₈	—	16	1	no	—
79	C₂×C₄	—	8	2	no	—
80	C₂×C₄	#10597283	1	1	yes	characteristic
81	C₂×C₄	#10597284	1	1	yes	characteristic
82	C₂×C₄	#10597289	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	304	1	no	—
85	C₈	#10597292	1	1	yes	characteristic
86	C₈	#10597293	1	1	yes	characteristic
87	C₂²	#11926345	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	16	2	no	—
90	C₄	#11926290	1	1	yes	characteristic
91	C₄	#11926360	1	1	yes	characteristic
92	C₄	#11926379	1	1	yes	characteristic
93	C₄	#11926382	1	1	yes	characteristic
94	C₂	#14561690	1	1	yes	characteristic
95	C₂	#14561813	1	1	yes	characteristic
96	C₂	#14561828	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926345
commutator	C₂×C₁₆×C₁₉	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting	C₁₉×#2252	C₂
socle, prime radical	C₂²×C₁₉	#357
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	#2252	D₁₉
hypocenter	C₁₉	#7450
LCS	G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2252

Complements

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

N	H ≅ G/N	type
66. C₁₉	#7450	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊(C₁₉⋊C₃₂)	2
#14561707	2
C₁₉×#2252	2
#7450	19