Group #14563743 — subgroups

Subgroups — #14563743

Order 2432.

296 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 89 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×#10597291	C₂	1	2	yes	maximal
2	#11926310	C₂	1	4	yes	maximal, complemented
3	C₁₉×#518	C₂	1	1	yes	maximal, characteristic
4	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
5	C₄×D₄×C₁₉	—	2	4	no	—
6	C₁₉×#117	C₄	1	2	yes	complemented
7	C₂×C₂²⋊C₄×C₁₉	C₄	1	2	yes	complemented
8	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
10	#10597291	—	2	4	no	—
11	C₂⁴×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
13	C₂×D₄×C₁₉	—	2	4	no	—
14	C₂×D₄×C₁₉	D₄	1	4	yes	—
15	C₂²×C₄×C₁₉	—	2	2	no	—
16	C₂²×C₄×C₁₉	—	2	2	no	—
17	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₁₉	—	2	4	no	—
19	C₄⋊C₄×C₁₉	—	2	2	no	—
20	C₂²⋊C₄×C₁₉	—	2	2	no	—
21	C₂²⋊C₄×C₁₉	—	2	2	no	—
22	C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
23	C₄²×C₁₉	—	2	2	no	—
24	C₂²⋊Dic₁₉	—	2	4	no	—
25	C₂²⋊Dic₁₉	—	2	4	no	—
26	C₂³×C₁₉	—	2	2	no	—
27	C₂³×C₁₉	—	8	1	no	—
28	C₂³×C₁₉	—	8	1	no	—
29	C₂³×C₁₉	C₂²⋊C₄	1	2	yes	—
30	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
31	C₂³×C₁₉	C₂×D₄	1	2	yes	—
32	C₂³×C₁₉	#41	1	4	yes	—
33	D₄×C₁₉	—	2	8	no	—
34	C₂×C₄×C₁₉	—	2	2	no	—
35	C₂×C₄×C₁₉	—	2	4	no	—
36	C₂×C₄×C₁₉	—	8	2	no	—
37	C₂×C₄×C₁₉	—	8	2	no	—
38	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
39	C₂×Dic₁₉	—	4	4	no	—
40	C₂×Dic₁₉	—	8	4	no	—
41	#1828	—	19	1	no	maximal, Sylow
42	C₂²×C₁₉	—	2	2	no	—
43	C₂²×C₁₉	—	4	4	no	—
44	C₂²×C₁₉	—	4	2	no	—
45	C₂²×C₁₉	—	4	1	no	—
46	C₂²×C₁₉	—	4	2	no	—
47	C₂²×C₁₉	—	8	2	no	—
48	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₁₉	#117	1	2	yes	—
50	C₂²×C₁₉	#123	1	4	yes	—
51	C₄×C₁₉	—	2	2	no	—
52	C₄×C₁₉	—	4	4	no	—
53	Dic₁₉	—	8	4	no	—
54	#518	D₁₉	1	1	yes	characteristic
55	C₂×#99	—	19	2	no	—
56	#342	—	19	4	no	—
57	C₂×C₁₉	—	2	4	no	—
58	C₂×C₁₉	—	2	1	no	—
59	C₂×C₁₉	—	2	2	no	—
60	C₂×C₁₉	—	4	2	no	—
61	C₂×C₁₉	#381	1	1	yes	characteristic
62	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
63	C₄×D₄	—	2	4	no	—
64	#117	Dic₁₉	1	2	yes	complemented
65	C₂×C₂²⋊C₄	—	19	4	no	—
66	C₂×C₂²⋊C₄	Dic₁₉	1	2	yes	complemented
67	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
68	#99	—	38	4	no	—
69	C₁₉	#1828	1	1	yes	characteristic, complemented, Sylow
70	C₂⁴	C₂×Dic₁₉	1	1	yes	characteristic
71	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
72	C₂×D₄	—	2	4	no	—
73	C₂×D₄	C₂²⋊D₁₉	1	4	yes	—
74	C₂²×C₄	—	2	2	no	—
75	C₂²×C₄	—	2	2	no	—
76	C₂²×C₄	—	38	4	no	—
77	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
78	C₄⋊C₄	—	2	2	no	—
79	C₂²⋊C₄	—	2	2	no	—
80	C₂²⋊C₄	—	2	2	no	—
81	C₂²⋊C₄	—	38	4	no	—
82	C₂²⋊C₄	—	38	4	no	—
83	C₂²⋊C₄	C₂×Dic₁₉	1	4	yes	—
84	C₄²	—	2	2	no	—
85	C₂³	—	2	2	no	—
86	C₂³	—	8	1	no	—
87	C₂³	—	8	1	no	—
88	C₂³	C₂²⋊Dic₁₉	1	2	yes	—
89	C₂³	#64541	1	4	yes	—
90	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
91	C₂³	C₂×C₂²⋊D₁₉	1	2	yes	—
92	D₄	—	2	8	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	4	no	—
95	C₂×C₄	—	8	2	no	—
96	C₂×C₄	—	8	2	no	—
97	C₂×C₄	—	76	4	no	—
98	C₂×C₄	—	152	4	no	—
99	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
100	C₂²	—	2	2	no	—
101	C₂²	—	4	2	no	—
102	C₂²	—	4	4	no	—
103	C₂²	—	4	1	no	—
104	C₂²	—	4	2	no	—
105	C₂²	—	8	2	no	—
106	C₂²	#10597372	1	2	yes	—
107	C₂²	#10597375	1	4	yes	—
108	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
109	C₄	—	2	2	no	—
110	C₄	—	4	4	no	—
111	C₄	—	152	4	no	—
112	C₂	—	2	1	no	—
113	C₂	—	2	4	no	—
114	C₂	—	2	2	no	—
115	C₂	—	4	2	no	—
116	C₂	#11926407	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597291

C₂

yes

maximal

#11926310

C₂

yes

maximal, complemented

C₁₉×#518

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₄×D₄×C₁₉

—

C₁₉×#117

C₄

yes

complemented

C₂×C₂²⋊C₄×C₁₉

C₄

yes

complemented

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

#10597291

—

C₂⁴×C₁₉

C₂×C₄

yes

characteristic

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₄

yes

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

#41

yes

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#1828

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

#117

yes

—

C₂²×C₁₉

#123

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

#518

D₁₉

yes

characteristic

C₂×#99

—

#342

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#381

yes

characteristic

C₂²×D₄

C₂×D₁₉

yes

characteristic

C₄×D₄

—

#117

Dic₁₉

yes

complemented

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

Dic₁₉

yes

complemented

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

#99

—

C₁₉

#1828

yes

characteristic, complemented, Sylow

C₂⁴

C₂×Dic₁₉

yes

characteristic

C₂⁴

C₂²×D₁₉

yes

characteristic

C₂×D₄

—

C₂×D₄

C₂²⋊D₁₉

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

C₂×Dic₁₉

yes

—

C₄²

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂²⋊Dic₁₉

yes

—

C₂³

#64541

yes

—

C₂³

C₂²×Dic₁₉

yes

characteristic

C₂³

C₂×C₂²⋊D₁₉

yes

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

152

—

C₂×C₄

C₂²⋊Dic₁₉

yes

—

100

C₂²

—

101

C₂²

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

#10597372

yes

—

107

C₂²

#10597375

yes

—

108

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

152

—

112

C₂

—

113

C₂

—

114

C₂

—

115

C₂

—

116

C₂

#11926407

yes

characteristic

	subgroup	G/H
center	C₂	#11926407
commutator	C₂³×C₁₉	C₂²×C₄
Frattini	C₂⁴	C₂²×D₁₉
Fitting	C₁₉×#518	C₂
socle	C₂×C₁₉	#381
prime radical	C₂²×D₄×C₁₉	C₂²
cosocle	C₂⁴×C₁₉	C₂³
hypercenter	#518	D₁₉
hypocenter	C₁₉	#1828
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ #518

subgroup

G/H

center

C₂

#11926407

commutator

C₂³×C₁₉

C₂²×C₄

Frattini

C₂⁴

C₂²×D₁₉

Fitting

C₁₉×#518

C₂

socle

C₂×C₁₉

#381

prime radical

C₂²×D₄×C₁₉

C₂²

cosocle

C₂⁴×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂⁴ ◁ #518

N	H ≅ G/N	type
2. #11926310	C₂	semidirect
6. C₁₉×#117	C₄	semidirect
7. C₂×C₂²⋊C₄×C₁₉	C₄	semidirect
64. #117	Dic₁₉	semidirect
66. C₂×C₂²⋊C₄	Dic₁₉	semidirect
69. C₁₉	#1828	semidirect

H ≅ G/N

type

2. #11926310

C₂

semidirect

6. C₁₉×#117

C₄

semidirect

7. C₂×C₂²⋊C₄×C₁₉

C₄

semidirect

64. #117

Dic₁₉

semidirect

66. C₂×C₂²⋊C₄

Dic₁₉

semidirect

69. C₁₉

#1828

semidirect

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

subgroup	index
C₂×#10597291	2
#11926310	2
C₁₉×#518	2
#1828	19

subgroup

index

C₂×#10597291

#11926310

C₁₉×#518

#1828

Subgroups — #14563743

Conjugacy classes of subgroups

Complements

Maximal subgroups