Subgroups — #18070201

Order 4864.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14565914	C₂	1	1	yes	maximal, characteristic
2	#14561711	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1422	C₂	1	1	yes	maximal, characteristic
4	#11926946	—	2	1	no	—
5	#11926372	C₄	1	2	yes	—
6	#11926370	—	2	1	no	—
7	#11926365	—	2	1	no	—
8	C₁₉×M₆₄	—	2	1	no	—
9	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	#10597316	—	4	1	no	—
11	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
13	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
14	#10597275	—	2	2	no	—
15	#10597274	—	4	1	no	—
16	#10597269	—	4	1	no	—
17	C₁₉×C₃₂	—	4	1	no	—
18	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
20	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
21	C₄⋊Dic₁₉	—	4	2	no	—
22	Dic₁₉⋊C₄	—	8	2	no	—
23	C₁₆×C₁₉	—	2	1	no	—
24	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
25	C₁₆×C₁₉	Q₁₆	1	1	yes	characteristic
26	C₁₉⋊C₁₆	—	8	1	no	—
27	#7454	—	19	1	no	maximal, Sylow
28	C₂×C₄×C₁₉	—	2	1	no	—
29	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
30	C₂×Dic₁₉	—	8	2	no	—
31	C₈×C₁₉	#101	1	1	yes	characteristic
32	C₈×C₁₉	#103	1	1	yes	characteristic
33	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
34	C₈×C₁₉	Q₃₂	1	1	yes	characteristic
35	#2253	—	19	1	no	—
36	#1422	D₁₉	1	1	yes	characteristic
37	#1373	—	19	1	no	—
38	C₂²×C₁₉	#361	1	1	yes	characteristic
39	C₄×C₁₉	—	4	1	no	—
40	C₄×C₁₉	#332	1	1	yes	characteristic
41	C₄×C₁₉	#358	1	1	yes	characteristic
42	Dic₁₉	—	16	2	no	—
43	#499	—	38	1	no	—
44	M₆₄	—	2	1	no	—
45	#367	—	19	2	no	—
46	#366	—	38	1	no	—
47	#364	—	38	1	no	—
48	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
49	C₂×C₁₉	—	2	1	no	—
50	C₂×C₁₉	#1365	1	1	yes	characteristic
51	#125	—	76	1	no	—
52	M₃₂	—	76	1	no	—
53	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
54	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
55	#107	—	38	2	no	—
56	#106	—	76	1	no	—
57	C₄×C₈	D₇₆	1	1	yes	characteristic
58	C₃₂	—	4	1	no	—
59	C₁₉	#7454	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₈	D₁₅₂	1	1	yes	characteristic
61	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
62	C₄⋊C₄	—	76	2	no	—
63	C₄⋊C₄	—	152	2	no	—
64	C₄²	#64516	1	1	yes	characteristic
65	C₁₆	—	2	1	no	—
66	C₁₆	—	152	1	no	—
67	C₁₆	#64526	1	1	yes	characteristic
68	C₁₆	#64528	1	1	yes	characteristic
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	152	2	no	—
71	C₂×C₄	#10597278	1	1	yes	characteristic
72	C₈	#10597257	1	1	yes	characteristic
73	C₈	Dic₁₅₂	1	1	yes	characteristic
74	C₈	#10597267	1	1	yes	characteristic
75	C₈	#10597281	1	1	yes	characteristic
76	C₂²	#11926358	1	1	yes	characteristic
77	C₄	—	4	1	no	—
78	C₄	—	304	2	no	—
79	C₄	#11926289	1	1	yes	characteristic
80	C₄	#11926349	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	#14561692	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14561692
commutator	C₂×C₁₆×C₁₉	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting	C₁₉×#1422	C₂
socle	C₂×C₁₉	#1365
prime radical	C₂²×C₁₉	#361
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	#1422	D₁₉
hypocenter	C₁₉	#7454
LCS	G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1422

Complements

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

N	H ≅ G/N	type
59. C₁₉	#7454	semidirect

Maximal subgroups

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

subgroup	index
#14565914	2
#14561711	2
C₁₉×#1422	2
#7454	19