Subgroups — #14561587

Order 2432.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926572	C₂	1	1	yes	maximal, characteristic
2	#11926326	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#349	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
5	#10597372	C₄	1	1	yes	characteristic
6	C₂²×C₁₉⋊C₈	C₄	1	1	yes	characteristic
7	C₁₉×M₃₂	—	2	1	no	—
8	Dic₁₉⋊C₈	—	2	1	no	—
9	Dic₁₉⋊C₈	—	2	1	no	—
10	#10597269	—	2	1	no	—
11	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
12	M₁₆×C₁₉	—	4	1	no	—
13	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
14	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
15	C₂²⋊Dic₁₉	C₈	1	2	yes	—
16	C₄⋊Dic₁₉	—	2	1	no	—
17	C₄×Dic₁₉	—	2	1	no	—
18	C₂×C₁₉⋊C₈	—	2	1	no	—
19	C₂×C₁₉⋊C₈	—	4	1	no	—
20	C₁₆×C₁₉	—	4	1	no	—
21	C₁₉⋊C₁₆	—	4	1	no	—
22	C₂³×C₁₉	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₁₉	—	2	1	no	—
24	C₂×C₄×C₁₉	—	2	1	no	—
25	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₉	M₁₆	1	1	yes	characteristic
27	C₂×Dic₁₉	—	2	2	no	—
28	C₈×C₁₉	—	2	1	no	—
29	C₈×C₁₉	—	2	1	no	—
30	C₁₉⋊C₈	—	4	1	no	—
31	#1328	—	19	1	no	maximal, Sylow
32	C₂²×C₁₉	—	2	1	no	—
33	C₂²×C₁₉	—	4	1	no	—
34	C₂²×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
35	C₄×C₁₉	—	2	1	no	—
36	C₄×C₁₉	#99	1	1	yes	characteristic
37	C₄×C₁₉	#101	1	1	yes	characteristic
38	Dic₁₉	—	4	2	no	—
39	#424	—	19	1	no	—
40	#349	—	19	1	no	—
41	#349	D₁₉	1	1	yes	characteristic
42	C₂×C₁₉	—	2	1	no	—
43	C₂×C₁₉	—	4	1	no	—
44	C₂×C₁₉	#324	1	1	yes	characteristic
45	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
46	C₂²×C₈	—	19	1	no	—
47	#117	—	19	1	no	—
48	M₃₂	—	2	1	no	—
49	M₃₂	—	38	1	no	—
50	C₄⋊C₈	—	38	1	no	—
51	C₄⋊C₈	—	38	1	no	—
52	C₁₉	#1328	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
54	M₁₆	—	4	1	no	—
55	C₂×C₈	—	38	1	no	—
56	C₂×C₈	—	76	1	no	—
57	C₂×C₈	D₇₆	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
59	C₄⋊C₄	—	38	1	no	—
60	C₂²⋊C₄	—	19	2	no	—
61	C₄²	—	38	1	no	—
62	C₁₆	—	4	1	no	—
63	C₁₆	—	76	1	no	—
64	C₂³	C₈×D₁₉	1	1	yes	characteristic
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	38	2	no	—
68	C₂×C₄	#64515	1	1	yes	characteristic
69	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
70	C₈	—	2	1	no	—
71	C₈	—	2	1	no	—
72	C₈	—	76	1	no	—
73	C₂²	—	2	1	no	—
74	C₂²	—	4	1	no	—
75	C₂²	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	76	2	no	—
78	C₄	#10597263	1	1	yes	characteristic
79	C₄	#10597281	1	1	yes	characteristic
80	C₂	—	2	1	no	—
81	C₂	—	4	1	no	—
82	C₂	#11926269	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10597263
commutator, prime radical	C₂³×C₁₉	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₁₉
Fitting	C₁₉×#349	C₂
socle	C₂×C₁₉	#324
cosocle	C₂×M₁₆×C₁₉	C₂²
hypercenter	#349	D₁₉
hypocenter	C₁₉	#1328
LCS	G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

Complements

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

N	H ≅ G/N	type
52. C₁₉	#1328	semidirect

Maximal subgroups

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

subgroup	index
#11926572	2
#11926326	2
C₁₉×#349	2
#1328	19