Subgroups — #18070193

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	#7451	—	19	1	no	maximal, Sylow
29	Q₈×C₁₉	—	16	2	no	—
30	C₂×C₄×C₁₉	—	8	2	no	—
31	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
32	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
33	C₂×C₄×C₁₉	SD₃₂	1	1	yes	characteristic
34	C₈×C₁₉	—	2	1	no	—
35	C₈×C₁₉	#101	1	1	yes	characteristic
36	C₈×C₁₉	#103	1	1	yes	characteristic
37	C₁₉⋊C₈	—	16	1	no	—
38	#2252	D₁₉	1	1	yes	characteristic
39	C₄⋊C₃₂	—	19	1	no	—
40	#1371	—	19	1	no	—
41	C₂²×C₁₉	#357	1	1	yes	characteristic
42	C₄×C₁₉	—	2	1	no	—
43	C₄×C₁₉	—	16	2	no	—
44	C₄×C₁₉	#332	1	1	yes	characteristic
45	C₄×C₁₉	#362	1	1	yes	characteristic
46	C₄×C₁₉	SD₆₄	1	1	yes	characteristic
47	C₄×C₁₉	Q₆₄	1	1	yes	characteristic
48	#500	—	2	1	no	—
49	C₂×C₃₂	—	38	1	no	—
50	#366	—	2	1	no	—
51	#366	Dic₁₉	1	2	yes	—
52	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
53	#335	—	38	1	no	—
54	C₂×C₁₉	#1364	1	1	yes	characteristic
55	C₂×C₁₉	#1416	1	1	yes	characteristic
56	C₂×C₁₉	#1419	1	1	yes	characteristic
57	C₄⋊Q₈	—	4	1	no	—
58	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
59	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
60	#107	—	2	2	no	—
61	#107	—	4	1	no	—
62	C₄⋊C₈	—	76	1	no	—
63	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
64	C₃₂	—	76	1	no	—
65	C₁₉	#7451	1	1	yes	characteristic, complemented, Sylow
66	C₂×Q₈	—	8	1	no	—
67	C₂×C₈	—	152	1	no	—
68	C₂×C₈	#64526	1	1	yes	characteristic
69	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
70	C₄⋊C₄	—	4	2	no	—
71	C₄⋊C₄	—	8	1	no	—
72	C₄²	#64525	1	1	yes	characteristic
73	C₁₆	—	2	1	no	—
74	C₁₆	#64527	1	1	yes	characteristic
75	C₁₆	#64528	1	1	yes	characteristic
76	Q₈	—	16	2	no	—
77	C₂×C₄	—	8	2	no	—
78	C₂×C₄	#10597283	1	1	yes	characteristic
79	C₂×C₄	#10597284	1	1	yes	characteristic
80	C₂×C₄	#10597289	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	304	1	no	—
83	C₈	#10597292	1	1	yes	characteristic
84	C₈	#10597293	1	1	yes	characteristic
85	C₂²	#11926345	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	16	2	no	—
88	C₄	#11926290	1	1	yes	characteristic
89	C₄	#11926360	1	1	yes	characteristic
90	C₄	#11926381	1	1	yes	characteristic
91	C₄	#11926384	1	1	yes	characteristic
92	C₂	#14561690	1	1	yes	characteristic
93	C₂	#14561816	1	1	yes	characteristic
94	C₂	#14561825	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	#7451
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
65. C₁₉	#7451	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
#7451	19