Subgroups — #14563244

Order 2432.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926949	C₂	1	1	yes	maximal, characteristic
2	#11926896	C₂	1	2	yes	maximal
3	#11926894	C₂	1	2	yes	maximal
4	C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#500	C₂	1	1	yes	maximal, characteristic
6	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
7	#10597315	C₂²	1	2	yes	—
8	C₁₉×#107	—	2	2	no	—
9	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	#10597292	—	2	4	no	—
11	#10597275	—	2	2	no	—
12	#10597267	—	2	4	no	—
13	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₁₉	—	2	2	no	—
16	C₂×Dic₃₈	—	2	2	no	—
17	C₂×C₈×C₁₉	D₄	1	2	yes	—
18	C₄⋊C₄×C₁₉	—	2	2	no	—
19	C₄⋊C₄×C₁₉	—	2	2	no	—
20	C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	C₄⋊Dic₁₉	—	2	2	no	—
22	C₄⋊Dic₁₉	—	2	2	no	—
23	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
24	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
25	Q₈×C₁₉	—	4	4	no	—
26	C₂×C₄×C₁₉	—	4	2	no	—
27	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₁₉	—	4	2	no	—
31	Dic₃₈	—	4	4	no	—
32	C₈×C₁₉	Q₁₆	1	4	yes	—
33	C₁₉⋊C₈	—	2	2	no	—
34	C₁₉⋊C₈	—	2	2	no	—
35	#1710	—	19	1	no	maximal, Sylow
36	C₂²×C₁₉	#127	1	1	yes	characteristic
37	C₄×C₁₉	—	8	2	no	—
38	C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
39	C₄×C₁₉	#135	1	2	yes	—
40	C₄×C₁₉	#135	1	2	yes	—
41	Dic₁₉	—	8	2	no	—
42	#500	—	19	1	no	—
43	#500	D₁₉	1	1	yes	characteristic
44	#487	—	19	2	no	—
45	#487	—	19	2	no	—
46	C₈²	—	19	1	no	—
47	C₂×C₁₉	#494	1	1	yes	characteristic
48	C₂×C₁₉	#495	1	1	yes	characteristic
49	C₂×C₁₉	#495	1	1	yes	characteristic
50	C₄⋊Q₈	—	19	2	no	—
51	C₄⋊Q₈	C₂×D₁₉	1	2	yes	—
52	#107	—	2	2	no	—
53	#107	—	38	2	no	—
54	#103	—	38	4	no	—
55	#103	—	38	4	no	—
56	C₄×C₈	—	19	1	no	—
57	C₄×C₈	—	19	1	no	—
58	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
59	C₁₉	#1710	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₈	—	2	2	no	—
61	C₂×Q₈	—	38	2	no	—
62	C₂×C₈	—	19	2	no	—
63	C₂×C₈	—	19	2	no	—
64	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	—	2	2	no	—
67	C₄⋊C₄	—	38	2	no	—
68	C₄⋊C₄	—	38	2	no	—
69	C₄²	C₂²×D₁₉	1	1	yes	characteristic
70	Q₈	—	4	4	no	—
71	Q₈	—	76	4	no	—
72	C₂×C₄	—	4	2	no	—
73	C₂×C₄	—	76	2	no	—
74	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
75	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
76	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
77	C₈	—	38	2	no	—
78	C₈	—	38	2	no	—
79	C₈	#64528	1	4	yes	—
80	C₂²	#10597386	1	1	yes	characteristic
81	C₄	—	8	2	no	—
82	C₄	—	152	2	no	—
83	C₄	#10597358	1	2	yes	—
84	C₄	#10597365	1	2	yes	—
85	C₄	C₂×#64528	1	2	yes	—
86	C₂	#11926923	1	1	yes	characteristic
87	C₂	#11926927	1	1	yes	characteristic
88	C₂	#11926929	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10597386
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#500	C₂
socle, prime radical	C₂²×C₁₉	#127
hypercenter	#500	D₁₉
hypocenter	C₁₉	#1710
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #500

Complements

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

N	H ≅ G/N	type
59. C₁₉	#1710	semidirect

Maximal subgroups

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

subgroup	index
#11926949	2
#11926896	2
#11926894	2
C₈×C₁₉⋊C₈	2
C₁₉×#500	2
#1710	19