Group #14566221 — subgroups

Subgroups — #14566221

Order 2432.

784 conjugacy classes of subgroups; only the 309 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 309 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×#10597372	C₂	1	2	yes	maximal
2	#11926451	C₂	1	8	yes	maximal, complemented
3	#11926407	C₂	1	4	yes	maximal
4	C₂³×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₈×C₁₉	—	2	8	no	—
6	C₂²×Q₈×C₁₉	C₄	1	8	yes	complemented
7	C₂²×Q₈×C₁₉	C₂²	1	4	yes	—
8	C₂³×C₄×C₁₉	C₂²	1	2	yes	—
9	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
11	#10597372	—	2	8	no	—
12	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
13	C₂×C₄×Dic₁₉	C₂²	1	4	yes	—
14	C₁₉⋊#95	C₂²	1	16	yes	—
15	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
16	C₂×Q₈×C₁₉	—	2	32	no	—
17	C₂×Q₈×C₁₉	—	2	8	no	—
18	C₂×Q₈×C₁₉	—	2	8	no	—
19	C₂×Q₈×C₁₉	C₂×C₄	1	16	yes	—
20	C₂²×C₄×C₁₉	—	2	8	no	—
21	C₂²×C₄×C₁₉	C₂×C₄	1	8	yes	—
22	C₂²×C₄×C₁₉	C₂×C₄	1	4	yes	—
23	C₂²×C₄×C₁₉	D₄	1	8	yes	—
24	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
26	C₂²×Dic₁₉	C₂³	1	8	yes	—
27	C₂²⋊Dic₁₉	—	2	8	no	—
28	C₄⋊Dic₁₉	—	2	8	no	—
29	C₄×Dic₁₉	—	2	8	no	—
30	C₂³×C₁₉	—	2	4	no	—
31	C₂³×C₁₉	C₂²×C₄	1	2	yes	—
32	C₂³×C₁₉	C₂×D₄	1	4	yes	—
33	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
34	Q₈×C₁₉	—	2	32	no	—
35	C₂×C₄×C₁₉	—	2	16	no	—
36	C₂×C₄×C₁₉	—	2	8	no	—
37	C₂×C₄×C₁₉	C₂²⋊C₄	1	16	yes	—
38	C₂×C₄×C₁₉	C₂²×C₄	1	8	yes	—
39	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
40	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
41	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
42	C₂×Dic₁₉	—	2	8	no	—
43	C₂×Dic₁₉	—	2	16	no	—
44	#2310	—	19	1	no	maximal, Sylow
45	C₂²×C₁₉	—	2	4	no	—
46	C₂²×C₁₉	—	2	8	no	—
47	C₂²×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
48	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
49	C₂²×C₁₉	C₂²×D₄	1	2	yes	—
50	C₂²×C₁₉	2₋¹⁺⁴	1	4	yes	—
51	C₄×C₁₉	—	2	8	no	—
52	C₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
53	Dic₁₉	—	4	8	no	—
54	C₂³×Q₈	D₁₉	1	1	yes	characteristic
55	C₂×#117	—	19	2	no	—
56	#391	—	19	8	no	—
57	#381	—	19	4	no	—
58	C₂×C₁₉	—	2	4	no	—
59	C₂×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₁₉	#519	1	2	yes	—
61	C₂×C₁₉	#536	1	4	yes	—
62	C₂²×Q₈	—	2	8	no	—
63	C₂²×Q₈	Dic₁₉	1	8	yes	complemented
64	C₂²×Q₈	C₂×D₁₉	1	4	yes	—
65	C₂³×C₄	C₂×D₁₉	1	2	yes	—
66	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
67	#117	—	38	8	no	—
68	C₂×C₄⋊C₄	—	19	4	no	—
69	C₂×C₂²⋊C₄	—	19	4	no	—
70	C₂×C₄²	—	19	4	no	—
71	#95	—	19	16	no	—
72	C₁₉	#2310	1	1	yes	characteristic, complemented, Sylow
73	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
74	C₂×Q₈	—	2	32	no	—
75	C₂×Q₈	—	2	8	no	—
76	C₂×Q₈	—	2	8	no	—
77	C₂×Q₈	C₂×Dic₁₉	1	16	yes	—
78	C₂²×C₄	—	2	8	no	—
79	C₂²×C₄	—	19	8	no	—
80	C₂²×C₄	C₂×Dic₁₉	1	8	yes	—
81	C₂²×C₄	C₂×Dic₁₉	1	4	yes	—
82	C₂²×C₄	C₂²⋊D₁₉	1	8	yes	—
83	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
84	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
85	C₄⋊C₄	—	38	8	no	—
86	C₂²⋊C₄	—	38	8	no	—
87	C₄²	—	38	8	no	—
88	C₂³	—	2	4	no	—
89	C₂³	C₂²×Dic₁₉	1	2	yes	—
90	C₂³	C₂×C₂²⋊D₁₉	1	4	yes	—
91	C₂³	C₂³×D₁₉	1	1	yes	characteristic
92	Q₈	—	2	32	no	—
93	C₂×C₄	—	2	16	no	—
94	C₂×C₄	—	2	8	no	—
95	C₂×C₄	—	38	16	no	—
96	C₂×C₄	—	38	8	no	—
97	C₂×C₄	C₂²⋊Dic₁₉	1	16	yes	—
98	C₂×C₄	C₂²×Dic₁₉	1	8	yes	—
99	C₂×C₄	C₂²×Dic₁₉	1	4	yes	—
100	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
101	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
102	C₂²	—	2	8	no	—
103	C₂²	—	2	4	no	—
104	C₂²	C₂×C₂²⋊Dic₁₉	1	4	yes	—
105	C₂²	#10597433	1	4	yes	—
106	C₂²	C₂³×Dic₁₉	1	1	yes	characteristic
107	C₂²	C₂²×C₂²⋊D₁₉	1	2	yes	—
108	C₄	—	2	8	no	—
109	C₄	—	76	8	no	—
110	C₄	C₂×C₂²⋊Dic₁₉	1	8	yes	—
111	C₂	—	2	4	no	—
112	C₂	C₂²×C₂²⋊Dic₁₉	1	1	yes	characteristic
113	C₂	#11927022	1	2	yes	—
114	C₂	#11927118	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597372

C₂

yes

maximal

#11926451

C₂

yes

maximal, complemented

#11926407

C₂

yes

maximal

C₂³×Q₈×C₁₉

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

C₄

yes

complemented

C₂²×Q₈×C₁₉

C₂²

yes

—

C₂³×C₄×C₁₉

C₂²

yes

—

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

#10597372

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²×C₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#2310

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

—

C₂²×C₁₉

C₂³×C₄

yes

characteristic

C₂²×C₁₉

C₂²×D₄

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

—

Dic₁₉

—

C₂³×Q₈

D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

C₂²×C₂²⋊C₄

yes

characteristic

C₂×C₁₉

#519

yes

—

C₂×C₁₉

#536

yes

—

C₂²×Q₈

—

C₂²×Q₈

Dic₁₉

yes

complemented

C₂²×Q₈

C₂×D₁₉

yes

—

C₂³×C₄

C₂×D₁₉

yes

—

C₂³×C₄

C₂×D₁₉

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

#95

—

C₁₉

#2310

yes

characteristic, complemented, Sylow

C₂⁴

C₂²×D₁₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂×Dic₁₉

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂²⋊D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

—

C₂³

C₂²×Dic₁₉

yes

—

C₂³

C₂×C₂²⋊D₁₉

yes

—

C₂³

C₂³×D₁₉

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊Dic₁₉

yes

—

C₂×C₄

C₂²×Dic₁₉

yes

—

C₂×C₄

C₂²×Dic₁₉

yes

—

100

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

101

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

102

C₂²

—

103

C₂²

—

104

C₂²

C₂×C₂²⋊Dic₁₉

yes

—

105

C₂²

#10597433

yes

—

106

C₂²

C₂³×Dic₁₉

yes

characteristic

107

C₂²

C₂²×C₂²⋊D₁₉

yes

—

108

C₄

—

109

C₄

—

110

C₄

C₂×C₂²⋊Dic₁₉

yes

—

111

C₂

—

112

C₂

C₂²×C₂²⋊Dic₁₉

yes

characteristic

113

C₂

#11927022

yes

—

114

C₂

#11927118

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator	C₂²×C₁₉	C₂³×C₄
Fitting	C₂³×Q₈×C₁₉	C₂
socle, cosocle	C₂³×C₁₉	C₂⁴
prime radical	C₂⁴×C₁₉	C₂³
hypercenter	C₂³×Q₈	D₁₉
hypocenter	C₁₉	#2310
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator

C₂²×C₁₉

C₂³×C₄

Fitting

C₂³×Q₈×C₁₉

C₂

socle, cosocle

C₂³×C₁₉

C₂⁴

prime radical

C₂⁴×C₁₉

C₂³

hypercenter

C₂³×Q₈

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂³×Q₈

N	H ≅ G/N	type
2. #11926451	C₂	semidirect
6. C₂²×Q₈×C₁₉	C₄	semidirect
63. C₂²×Q₈	Dic₁₉	semidirect
72. C₁₉	#2310	semidirect

H ≅ G/N

type

2. #11926451

C₂

semidirect

6. C₂²×Q₈×C₁₉

C₄

semidirect

63. C₂²×Q₈

Dic₁₉

semidirect

72. C₁₉

#2310

semidirect

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

subgroup	index
C₂×#10597372	2
#11926451	2
#11926407	2
C₂³×Q₈×C₁₉	2
#2310	19

subgroup

index

C₂³×Q₈×C₁₉

Subgroups — #14566221

Conjugacy classes of subgroups

Complements

Maximal subgroups