Group #14563543 — subgroups

Subgroups — #14563543

Order 2432.

220 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597276	C₂	1	1	yes	maximal, characteristic
2	M₁₆×Dic₁₉	C₂	1	2	yes	maximal
3	C₂×#10597272	C₂	1	1	yes	maximal, characteristic
4	#11926308	C₂	1	2	yes	maximal
5	C₂×C₁₉×#108	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
9	C₂×#64520	C₂²	1	2	yes	—
10	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₁₉×#108	C₄	1	4	yes	complemented
12	#10597276	C₄	1	4	yes	complemented
13	#10597272	—	2	2	no	—
14	#10597272	C₄	1	4	yes	—
15	C₈×Dic₁₉	—	2	2	no	—
16	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
17	C₂²×Dic₁₉	Q₈	1	2	yes	—
18	M₁₆×C₁₉	—	2	2	no	—
19	M₁₆×C₁₉	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₁₉	—	2	2	no	—
21	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
23	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
24	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
25	C₄×Dic₁₉	D₄	1	2	yes	—
26	#64520	—	2	2	no	—
27	#64520	C₂×C₄	1	4	yes	—
28	C₂×C₁₉⋊C₈	—	2	2	no	—
29	C₂×C₁₉⋊C₈	—	2	1	no	—
30	C₂×C₁₉⋊C₈	—	2	1	no	—
31	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
32	C₂³×C₁₉	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
38	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
39	C₂×Dic₁₉	—	4	2	no	—
40	C₂×Dic₁₉	C₄⋊C₄	1	4	yes	—
41	C₈×C₁₉	—	2	4	no	—
42	C₈×C₁₉	C₄²	1	4	yes	—
43	C₁₉⋊C₈	—	2	2	no	—
44	C₁₉⋊C₈	—	2	4	no	—
45	#1778	—	19	1	no	maximal, Sylow
46	C₂²×C₁₉	—	2	2	no	—
47	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂²×C₁₉	C₄×Q₈	1	1	yes	characteristic
49	C₂²×C₁₉	C₄×Q₈	1	1	yes	characteristic
50	C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
51	C₄×C₁₉	#117	1	1	yes	characteristic
52	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
53	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
54	Dic₁₉	—	2	4	no	—
55	C₂×#108	—	19	1	no	—
56	C₂×#108	D₁₉	1	1	yes	characteristic
57	C₄×M₁₆	—	19	2	no	—
58	C₂×#97	—	19	1	no	—
59	#341	—	19	2	no	—
60	C₂×C₁₉	—	2	1	no	—
61	C₂×C₁₉	—	2	1	no	—
62	C₂×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₁₉	#430	1	2	yes	—
64	C₂×M₁₆	—	19	2	no	—
65	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
66	C₂²×C₈	—	19	1	no	—
67	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
68	C₂×C₄²	—	19	1	no	—
69	#108	—	19	4	no	—
70	#108	Dic₁₉	1	4	yes	complemented
71	#97	—	19	4	no	—
72	#97	—	38	2	no	—
73	C₄×C₈	—	38	2	no	—
74	C₁₉	#1778	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₄	—	19	2	no	—
76	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
77	M₁₆	—	2	2	no	—
78	M₁₆	—	19	4	no	—
79	M₁₆	—	38	2	no	—
80	M₁₆	C₂×Dic₁₉	1	4	yes	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	19	2	no	—
83	C₂×C₈	—	38	2	no	—
84	C₂×C₈	—	38	1	no	—
85	C₂×C₈	—	38	1	no	—
86	C₂×C₈	C₄×D₁₉	1	2	yes	—
87	C₂×C₈	C₄×D₁₉	1	2	yes	—
88	C₂×C₈	C₂×Dic₁₉	1	2	yes	—
89	C₄²	—	19	2	no	—
90	C₄²	—	19	2	no	—
91	C₂³	Q₈×D₁₉	1	1	yes	characteristic
92	C₂×C₄	—	19	4	no	—
93	C₂×C₄	—	76	2	no	—
94	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
95	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
96	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
97	C₂×C₄	#64543	1	1	yes	characteristic
98	C₂×C₄	#64545	1	1	yes	characteristic
99	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
100	C₈	—	2	4	no	—
101	C₈	—	38	2	no	—
102	C₈	—	38	4	no	—
103	C₈	C₄×Dic₁₉	1	4	yes	—
104	C₂²	—	2	2	no	—
105	C₂²	#10597333	1	1	yes	characteristic
106	C₂²	C₄⋊C₄×D₁₉	1	1	yes	characteristic
107	C₂²	Q₈×Dic₁₉	1	1	yes	characteristic
108	C₄	—	38	4	no	—
109	C₄	#10597338	1	1	yes	characteristic
110	C₄	#10597339	1	1	yes	characteristic
111	C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
112	C₄	D₄×Dic₁₉	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
116	C₂	#11926591	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597276

C₂

yes

maximal, characteristic

M₁₆×Dic₁₉

C₂

yes

maximal

C₂×#10597272

C₂

yes

maximal, characteristic

#11926308

C₂

yes

maximal

C₂×C₁₉×#108

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#108

C₄

yes

complemented

#10597276

C₄

yes

complemented

#10597272

—

#10597272

C₄

yes

—

C₈×Dic₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

Q₈

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₄×Dic₁₉

C₂×C₄

yes

—

C₄×Dic₁₉

D₄

yes

—

#64520

—

#64520

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂³×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

C₄⋊C₄

yes

—

C₈×C₁₉

—

C₈×C₁₉

C₄²

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1778

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

C₄×Q₈

yes

characteristic

C₂²×C₁₉

C₄×Q₈

yes

characteristic

C₄×C₁₉

C₂×C₄²

yes

characteristic

C₄×C₁₉

#117

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

characteristic

Dic₁₉

—

C₂×#108

—

C₂×#108

D₁₉

yes

characteristic

C₄×M₁₆

—

C₂×#97

—

#341

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₄×C₄⋊C₄

yes

characteristic

C₂×C₁₉

#430

yes

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄²

—

#108

—

#108

Dic₁₉

yes

complemented

#97

—

#97

—

C₄×C₈

—

C₁₉

#1778

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

C₂×Dic₁₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₁₉

yes

—

C₂×C₈

C₄×D₁₉

yes

—

C₂×C₈

C₂×Dic₁₉

yes

—

C₄²

—

C₄²

—

C₂³

Q₈×D₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

C₂×C₄

D₄×D₁₉

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

100

C₈

—

101

C₈

—

102

C₈

—

103

C₈

C₄×Dic₁₉

yes

—

104

C₂²

—

105

C₂²

#10597333

yes

characteristic

106

C₂²

C₄⋊C₄×D₁₉

yes

characteristic

107

C₂²

Q₈×Dic₁₉

yes

characteristic

108

C₄

—

109

C₄

#10597338

yes

characteristic

110

C₄

#10597339

yes

characteristic

111

C₄

C₂×C₄×Dic₁₉

yes

characteristic

112

C₄

D₄×Dic₁₉

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

C₄⋊C₄×Dic₁₉

yes

characteristic

116

C₂

#11926591

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₁₉
commutator	C₄×C₁₉	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#108	C₂
socle	C₂²×C₁₉	C₂×C₄⋊C₄
prime radical	C₂³×C₁₉	C₂×Q₈
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#108	D₁₉
hypocenter	C₁₉	#1778
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₁₉

commutator

C₄×C₁₉

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#108

C₂

socle

C₂²×C₁₉

C₂×C₄⋊C₄

prime radical

C₂³×C₁₉

C₂×Q₈

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
11. C₁₉×#108	C₄	semidirect
12. #10597276	C₄	semidirect
70. #108	Dic₁₉	semidirect
74. C₁₉	#1778	semidirect

H ≅ G/N

type

11. C₁₉×#108

C₄

semidirect

12. #10597276

C₄

semidirect

70. #108

Dic₁₉

semidirect

74. C₁₉

#1778

semidirect

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

subgroup	index
C₂×#10597276	2
M₁₆×Dic₁₉	2
C₂×#10597272	2
#11926308	2
C₂×C₁₉×#108	2
#1778	19

subgroup

index

M₁₆×Dic₁₉

C₂×C₁₉×#108

Subgroups — #14563543

Conjugacy classes of subgroups

Complements

Maximal subgroups