Group #14561725 — subgroups

Subgroups — #14561725

Order 2432.

136 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 77 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	C₂²×C₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#11926499	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×M₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
5	#10597372	C₄	1	1	yes	characteristic
6	C₂×#64520	C₄	1	1	yes	characteristic
7	C₁₉×M₃₂	—	2	1	no	—
8	C₁₉×M₃₂	C₄	1	2	yes	complemented
9	C₂×C₁₆×C₁₉	—	2	1	no	—
10	#10597272	—	2	1	no	—
11	C₈×Dic₁₉	—	2	1	no	—
12	C₂×C₁₉⋊C₁₆	—	2	1	no	—
13	C₂×C₁₉⋊C₁₆	—	2	1	no	—
14	C₂×C₁₉⋊C₁₆	C₄	1	2	yes	complemented
15	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
19	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	Q₈	1	1	yes	characteristic
22	C₂²⋊Dic₁₉	—	2	1	no	—
23	C₄⋊Dic₁₉	C₈	1	2	yes	—
24	C₄×Dic₁₉	—	2	1	no	—
25	#64520	—	2	1	no	—
26	#64520	C₈	1	2	yes	—
27	C₂×C₁₉⋊C₈	—	2	1	no	—
28	C₁₆×C₁₉	—	2	2	no	—
29	C₁₉⋊C₁₆	—	2	2	no	—
30	C₂³×C₁₉	M₁₆	1	1	yes	characteristic
31	C₂×C₄×C₁₉	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×C₁₉	M₁₆	1	1	yes	characteristic
37	C₂×Dic₁₉	—	2	2	no	—
38	C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
39	C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
40	C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
41	C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
42	C₁₉⋊C₈	—	2	2	no	—
43	#1379	—	19	1	no	maximal, Sylow
44	C₂²×C₁₉	—	2	2	no	—
45	C₂²×C₁₉	#97	1	1	yes	characteristic
46	C₂²×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
47	C₂²×C₁₉	C₄⋊C₈	1	1	yes	characteristic
48	C₄×C₁₉	#95	1	1	yes	characteristic
49	C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
50	C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
51	C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
52	Dic₁₉	—	4	2	no	—
53	C₂×M₃₂	D₁₉	1	1	yes	characteristic
54	C₂²×C₁₆	—	19	1	no	—
55	#405	—	19	1	no	—
56	C₂×C₁₉	—	2	1	no	—
57	C₂×C₁₉	—	2	1	no	—
58	C₂×C₁₉	#336	1	1	yes	characteristic
59	C₂×C₁₉	#350	1	2	yes	—
60	C₂×M₁₆	—	19	1	no	—
61	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
62	#117	—	19	1	no	—
63	M₃₂	—	2	1	no	—
64	M₃₂	Dic₁₉	1	2	yes	complemented
65	C₂×C₁₆	—	2	1	no	—
66	C₂×C₁₆	—	19	2	no	—
67	C₂×C₁₆	—	38	1	no	—
68	C₂×C₁₆	—	38	1	no	—
69	#97	—	38	1	no	—
70	C₄×C₈	—	38	1	no	—
71	C₁₉	#1379	1	1	yes	characteristic, complemented, Sylow
72	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
73	M₁₆	—	19	2	no	—
74	M₁₆	—	38	1	no	—
75	C₂×C₈	—	38	1	no	—
76	C₂×C₈	Dic₃₈	1	1	yes	characteristic
77	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
78	C₂×C₈	D₇₆	1	1	yes	characteristic
79	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
80	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
81	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
82	C₄⋊C₄	—	19	2	no	—
83	C₂²⋊C₄	—	38	1	no	—
84	C₄²	—	38	1	no	—
85	C₁₆	—	2	2	no	—
86	C₁₆	—	38	2	no	—
87	C₂³	#64515	1	1	yes	characteristic
88	C₂×C₄	—	38	2	no	—
89	C₂×C₄	C₈×D₁₉	1	1	yes	characteristic
90	C₂×C₄	C₈×D₁₉	1	1	yes	characteristic
91	C₂×C₄	#64515	1	1	yes	characteristic
92	C₂×C₄	C₄×Dic₁₉	1	1	yes	characteristic
93	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
94	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
95	C₈	—	38	2	no	—
96	C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
97	C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
98	C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
99	C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
100	C₂²	—	2	2	no	—
101	C₂²	Dic₁₉⋊C₈	1	1	yes	characteristic
102	C₂²	#10597272	1	1	yes	characteristic
103	C₂²	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
104	C₄	—	76	2	no	—
105	C₄	C₈×Dic₁₉	1	1	yes	characteristic
106	C₄	Dic₁₉⋊C₈	1	1	yes	characteristic
107	C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
108	C₄	C₁₉⋊#95	1	1	yes	characteristic
109	C₂	—	2	1	no	—
110	C₂	—	2	1	no	—
111	C₂	#11926298	1	1	yes	characteristic
112	C₂	#11926329	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₁₉⋊C₁₆

C₂

yes

maximal, characteristic

#11926499

C₂

yes

maximal, characteristic

C₂×C₁₉×M₃₂

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

#10597372

C₄

yes

characteristic

C₂×#64520

C₄

yes

characteristic

C₁₉×M₃₂

—

C₁₉×M₃₂

C₄

yes

complemented

C₂×C₁₆×C₁₉

—

#10597272

—

C₈×Dic₁₉

—

C₂×C₁₉⋊C₁₆

—

C₂×C₁₉⋊C₁₆

—

C₂×C₁₉⋊C₁₆

C₄

yes

complemented

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

Q₈

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

C₈

yes

—

C₄×Dic₁₉

—

#64520

—

#64520

C₈

yes

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

M₁₆

yes

characteristic

C₂×C₄×C₁₉

C₄²

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

M₁₆

yes

characteristic

C₂×Dic₁₉

—

C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₁₉⋊C₈

—

#1379

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

#97

yes

characteristic

C₂²×C₁₉

C₂²⋊C₈

yes

characteristic

C₂²×C₁₉

C₄⋊C₈

yes

characteristic

C₄×C₁₉

#95

yes

characteristic

C₄×C₁₉

C₄×C₈

yes

characteristic

C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₄×C₁₉

C₄⋊C₈

yes

characteristic

Dic₁₉

—

C₂×M₃₂

D₁₉

yes

characteristic

C₂²×C₁₆

—

#405

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#336

yes

characteristic

C₂×C₁₉

#350

yes

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

#117

—

M₃₂

—

M₃₂

Dic₁₉

yes

complemented

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

C₄×C₈

—

C₁₉

#1379

yes

characteristic, complemented, Sylow

C₂²×C₄

C₄×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

Dic₃₈

yes

characteristic

C₂×C₈

C₄×D₁₉

yes

characteristic

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

C₁₆

—

C₂³

#64515

yes

characteristic

C₂×C₄

—

C₂×C₄

C₈×D₁₉

yes

characteristic

C₂×C₄

C₈×D₁₉

yes

characteristic

C₂×C₄

#64515

yes

characteristic

C₂×C₄

C₄×Dic₁₉

yes

characteristic

C₂×C₄

Dic₁₉⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

C₈

—

C₈

Dic₁₉⋊C₄

yes

characteristic

C₈

C₄⋊Dic₁₉

yes

characteristic

C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

C₈

C₂²⋊Dic₁₉

yes

characteristic

100

C₂²

—

101

C₂²

Dic₁₉⋊C₈

yes

characteristic

102

C₂²

#10597272

yes

characteristic

103

C₂²

(C₂×D₁₉)⋊C₈

yes

characteristic

104

C₄

—

105

C₄

C₈×Dic₁₉

yes

characteristic

106

C₄

Dic₁₉⋊C₈

yes

characteristic

107

C₄

(C₂×D₁₉)⋊C₈

yes

characteristic

108

C₄

C₁₉⋊#95

yes

characteristic

109

C₂

—

110

C₂

—

111

C₂

#11926298

yes

characteristic

112

C₂

#11926329

yes

—

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₁₉
commutator	C₄×C₁₉	C₄×C₈
Frattini	C₂²×C₈	C₂×D₁₉
Fitting	C₂×C₁₉×M₃₂	C₂
socle	C₂²×C₁₉	C₂²⋊C₈
prime radical	C₂³×C₁₉	M₁₆
cosocle	C₂²×C₈×C₁₉	C₂²
hypercenter	C₂×M₃₂	D₁₉
hypocenter	C₁₉	#1379
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂×C₈

C₂²⋊D₁₉

commutator

C₄×C₁₉

C₄×C₈

Frattini

C₂²×C₈

C₂×D₁₉

Fitting

C₂×C₁₉×M₃₂

C₂

socle

C₂²×C₁₉

C₂²⋊C₈

prime radical

C₂³×C₁₉

M₁₆

cosocle

C₂²×C₈×C₁₉

C₂²

hypercenter

C₂×M₃₂

D₁₉

hypocenter

C₁₉

#1379

LCS

G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
8. C₁₉×M₃₂	C₄	semidirect
14. C₂×C₁₉⋊C₁₆	C₄	semidirect
64. M₃₂	Dic₁₉	semidirect
71. C₁₉	#1379	semidirect

H ≅ G/N

type

8. C₁₉×M₃₂

C₄

semidirect

14. C₂×C₁₉⋊C₁₆

C₄

semidirect

64. M₃₂

Dic₁₉

semidirect

71. C₁₉

#1379

semidirect

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

subgroup	index
C₂²×C₁₉⋊C₁₆	2
#11926499	2
C₂×C₁₉×M₃₂	2
#1379	19

subgroup

index

C₂²×C₁₉⋊C₁₆

#11926499

C₂×C₁₉×M₃₂

#1379

Subgroups — #14561725

Conjugacy classes of subgroups

Complements

Maximal subgroups