Group #14561528 — subgroups

Subgroups — #14561528

Order 2432.

172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 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	#11926601	C₂	1	1	yes	maximal, characteristic
2	C₄×#64520	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#376	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄²×C₁₉	—	2	1	no	—
5	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
6	C₂×#64520	—	2	1	no	—
7	C₁₉×#95	—	2	1	no	—
8	C₁₉×#95	C₄	1	2	yes	—
9	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
10	C₄⋊(C₁₉⋊C₈)	C₄	1	2	yes	complemented
11	#10597260	—	2	1	no	—
12	#10597260	C₄	1	2	yes	complemented
13	C₄×C₁₉⋊C₈	—	2	1	no	—
14	C₂²×C₄×C₁₉	—	2	2	no	—
15	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
18	C₄²×C₁₉	—	2	4	no	—
19	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₄²×C₁₉	D₄	1	1	yes	characteristic
22	C₄²×C₁₉	Q₈	1	1	yes	characteristic
23	#64520	—	2	4	no	—
24	C₂×C₁₉⋊C₈	—	2	2	no	—
25	C₂×C₁₉⋊C₈	—	2	2	no	—
26	C₂³×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₁₉	—	2	2	no	—
28	C₂×C₄×C₁₉	—	2	2	no	—
29	C₂×C₄×C₁₉	—	2	4	no	—
30	C₂×C₄×C₁₉	—	4	1	no	—
31	C₂×C₄×C₁₉	—	4	2	no	—
32	C₂×C₄×C₁₉	—	4	2	no	—
33	C₂×C₄×C₁₉	C₄²	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	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
39	C₁₉⋊C₈	—	2	4	no	—
40	C₁₉⋊C₈	—	4	2	no	—
41	#1300	—	19	1	no	maximal, Sylow
42	C₂²×C₁₉	—	2	1	no	—
43	C₂²×C₁₉	—	2	1	no	—
44	C₂²×C₁₉	#95	1	1	yes	characteristic
45	C₂²×C₁₉	#104	1	2	yes	—
46	C₄×C₁₉	—	2	1	no	—
47	C₄×C₁₉	—	2	1	no	—
48	C₄×C₁₉	—	2	1	no	—
49	C₄×C₁₉	—	2	1	no	—
50	C₄×C₁₉	—	2	1	no	—
51	C₄×C₁₉	—	4	4	no	—
52	C₄×C₁₉	#104	1	2	yes	—
53	#432	—	19	1	no	—
54	C₄×M₁₆	—	19	1	no	—
55	#376	D₁₉	1	1	yes	characteristic
56	C₂×C₁₉	—	2	2	no	—
57	C₂×C₁₉	#339	1	1	yes	characteristic
58	C₂×C₁₉	#339	1	1	yes	characteristic
59	C₂×C₁₉	#344	1	1	yes	characteristic
60	C₂×M₁₆	—	38	1	no	—
61	C₂×C₄²	—	2	1	no	—
62	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
63	C₄⋊C₈	—	19	2	no	—
64	C₂²⋊C₈	—	38	1	no	—
65	#97	—	19	2	no	—
66	#97	—	38	1	no	—
67	C₄×C₈	—	38	1	no	—
68	#95	—	2	1	no	—
69	#95	Dic₁₉	1	2	yes	—
70	C₁₉	#1300	1	1	yes	characteristic, complemented, Sylow
71	C₂²×C₄	—	2	2	no	—
72	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
73	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
74	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
75	M₁₆	—	38	4	no	—
76	C₂×C₈	—	38	2	no	—
77	C₂×C₈	—	38	2	no	—
78	C₄²	—	2	4	no	—
79	C₄²	Dic₃₈	1	1	yes	characteristic
80	C₄²	C₄×D₁₉	1	1	yes	characteristic
81	C₄²	C₄×D₁₉	1	1	yes	characteristic
82	C₄²	D₇₆	1	1	yes	characteristic
83	C₂³	C₂²⋊Dic₁₉	1	1	yes	characteristic
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	4	1	no	—
88	C₂×C₄	—	4	2	no	—
89	C₂×C₄	—	4	2	no	—
90	C₂×C₄	C₄×Dic₁₉	1	1	yes	characteristic
91	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
92	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
93	C₂×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
94	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
95	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
96	C₈	—	38	4	no	—
97	C₈	—	76	2	no	—
98	C₂²	—	2	1	no	—
99	C₂²	—	2	1	no	—
100	C₂²	C₁₉⋊#95	1	1	yes	characteristic
101	C₂²	#10597294	1	2	yes	—
102	C₄	—	2	1	no	—
103	C₄	—	2	1	no	—
104	C₄	—	2	1	no	—
105	C₄	—	2	1	no	—
106	C₄	—	2	1	no	—
107	C₄	—	4	4	no	—
108	C₄	#10597262	1	2	yes	—
109	C₂	—	2	2	no	—
110	C₂	#11926303	1	1	yes	characteristic
111	C₂	#11926304	1	1	yes	characteristic
112	C₂	#11926314	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926601

C₂

yes

maximal, characteristic

C₄×#64520

C₂

yes

maximal, characteristic

C₁₉×#376

C₂

yes

maximal, characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×#64520

—

C₁₉×#95

—

C₁₉×#95

C₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₄

yes

complemented

#10597260

—

#10597260

C₄

yes

complemented

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

Q₈

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄²

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1300

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#95

yes

characteristic

C₂²×C₁₉

#104

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#104

yes

—

#432

—

C₄×M₁₆

—

#376

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

C₄×C₈

—

#95

—

#95

Dic₁₉

yes

—

C₁₉

#1300

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

Dic₃₈

yes

characteristic

C₄²

C₄×D₁₉

yes

characteristic

C₄²

C₄×D₁₉

yes

characteristic

C₄²

D₇₆

yes

characteristic

C₂³

C₂²⋊Dic₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₁₉

yes

characteristic

C₂×C₄

Dic₁₉⋊C₄

yes

characteristic

C₂×C₄

Dic₁₉⋊C₄

yes

characteristic

C₂×C₄

C₄⋊Dic₁₉

yes

characteristic

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

C₈

—

C₈

—

C₂²

—

C₂²

—

100

C₂²

C₁₉⋊#95

yes

characteristic

101

C₂²

#10597294

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

#10597262

yes

—

109

C₂

—

110

C₂

#11926303

yes

characteristic

111

C₂

#11926304

yes

characteristic

112

C₂

#11926314

yes

characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₁₉)⋊C₄
commutator	C₂×C₄×C₁₉	C₄²
Frattini	C₂×C₄²	C₂×D₁₉
Fitting	C₁₉×#376	C₂
socle	C₂²×C₁₉	#95
prime radical	C₂³×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂²
hypercenter	#376	D₁₉
hypocenter	C₁₉	#1300
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #376

subgroup

G/H

center

C₂×C₄

(C₂×D₁₉)⋊C₄

commutator

C₂×C₄×C₁₉

C₄²

Frattini

C₂×C₄²

C₂×D₁₉

Fitting

C₁₉×#376

C₂

socle

C₂²×C₁₉

#95

prime radical

C₂³×C₁₉

C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #376

N	H ≅ G/N	type
10. C₄⋊(C₁₉⋊C₈)	C₄	semidirect
12. #10597260	C₄	semidirect
70. C₁₉	#1300	semidirect

H ≅ G/N

type

10. C₄⋊(C₁₉⋊C₈)

C₄

semidirect

12. #10597260

C₄

semidirect

70. C₁₉

#1300

semidirect

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

subgroup	index
#11926601	2
C₄×#64520	2
C₁₉×#376	2
#1300	19

subgroup

index

#11926601

C₄×#64520

C₁₉×#376

#1300

Subgroups — #14561528

Conjugacy classes of subgroups

Complements

Maximal subgroups