Group #14564617 — subgroups

Subgroups — #14564617

Order 2432.

244 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 97 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	#11926568	C₂	1	1	yes	maximal, characteristic
2	#11926390	C₂	1	1	yes	maximal, characteristic
3	#11926303	C₂	1	4	yes	maximal
4	C₁₉×#533	C₂	1	1	yes	maximal, characteristic
5	C₁₉×C₄⋊Q₈	C₄	1	2	yes	complemented
6	C₁₉×#125	C₄	1	2	yes	complemented
7	C₁₉×C₂²⋊Q₈	—	2	2	no	—
8	C₄×Q₈×C₁₉	—	2	2	no	—
9	C₁₉×#117	C₂²	1	2	yes	—
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
12	C₂×#64520	C₂²	1	2	yes	—
13	C₁₉⋊#95	—	2	2	no	—
14	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
15	C₂×Q₈×C₁₉	—	2	2	no	—
16	C₂²×C₄×C₁₉	D₄	1	2	yes	—
17	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	C₂²×Dic₁₉	—	2	2	no	—
19	C₄⋊C₄×C₁₉	—	2	4	no	—
20	C₄⋊C₄×C₁₉	—	2	2	no	—
21	C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
22	C₂²⋊C₄×C₁₉	—	2	2	no	—
23	C₄²×C₁₉	—	2	2	no	—
24	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₄²×C₁₉	D₄	1	2	yes	—
27	C₄×Dic₁₉	—	2	2	no	—
28	C₄×Dic₁₉	Q₈	1	4	yes	complemented
29	#64520	—	2	4	no	—
30	C₂×C₁₉⋊C₈	—	2	2	no	—
31	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
32	Q₈×C₁₉	—	4	4	no	—
33	C₂×C₄×C₁₉	—	2	4	no	—
34	C₂×C₄×C₁₉	—	4	2	no	—
35	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
36	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
40	C₂×C₄×C₁₉	#41	1	2	yes	—
41	C₂×Dic₁₉	—	2	4	no	—
42	C₂×Dic₁₉	—	4	4	no	—
43	C₁₉⋊C₈	—	4	2	no	—
44	#1995	—	19	1	no	maximal, Sylow
45	C₂²×C₁₉	—	2	2	no	—
46	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₁₉	C₂²⋊Q₈	1	2	yes	—
48	C₄×C₁₉	—	2	2	no	—
49	C₄×C₁₉	—	2	2	no	—
50	C₄×C₁₉	—	4	4	no	—
51	C₄×C₁₉	C₄×Q₈	1	2	yes	—
52	C₄×C₁₉	#124	1	1	yes	characteristic
53	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
54	Dic₁₉	—	4	4	no	—
55	#533	D₁₉	1	1	yes	characteristic
56	#423	—	19	1	no	—
57	#376	—	19	1	no	—
58	#339	—	19	4	no	—
59	C₂×C₁₉	—	2	2	no	—
60	C₂×C₁₉	#391	1	1	yes	characteristic
61	C₂×C₁₉	#421	1	2	yes	—
62	C₂×M₁₆	—	19	2	no	—
63	C₄⋊Q₈	Dic₁₉	1	2	yes	complemented
64	#125	Dic₁₉	1	2	yes	complemented
65	C₂²⋊Q₈	—	2	2	no	—
66	C₄×Q₈	—	2	2	no	—
67	#117	C₂×D₁₉	1	2	yes	—
68	C₂×C₄²	—	19	2	no	—
69	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
70	C₄⋊C₈	—	38	2	no	—
71	#95	—	38	2	no	—
72	C₁₉	#1995	1	1	yes	characteristic, complemented, Sylow
73	C₂×Q₈	—	2	2	no	—
74	C₂²×C₄	—	38	2	no	—
75	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
76	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
77	M₁₆	—	38	4	no	—
78	C₂×C₈	—	38	2	no	—
79	C₄⋊C₄	—	2	4	no	—
80	C₄⋊C₄	—	2	2	no	—
81	C₄⋊C₄	C₂×Dic₁₉	1	4	yes	—
82	C₂²⋊C₄	—	2	2	no	—
83	C₄²	—	2	2	no	—
84	C₄²	—	19	4	no	—
85	C₄²	—	38	2	no	—
86	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
87	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
88	C₄²	C₂²⋊D₁₉	1	2	yes	—
89	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
90	Q₈	—	4	4	no	—
91	C₂×C₄	—	2	4	no	—
92	C₂×C₄	—	4	2	no	—
93	C₂×C₄	—	38	4	no	—
94	C₂×C₄	—	76	4	no	—
95	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
96	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
97	C₂×C₄	Q₈×D₁₉	1	2	yes	—
98	C₂×C₄	#64545	1	2	yes	—
99	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
100	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
101	C₈	—	76	2	no	—
102	C₂²	—	2	2	no	—
103	C₂²	#10597392	1	2	yes	—
104	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
105	C₄	—	2	2	no	—
106	C₄	—	2	2	no	—
107	C₄	—	4	4	no	—
108	C₄	—	76	4	no	—
109	C₄	#10597390	1	1	yes	characteristic
110	C₄	Q₈×Dic₁₉	1	2	yes	—
111	C₄	#10597393	1	1	yes	characteristic
112	C₂	—	2	2	no	—
113	C₂	#11926451	1	1	yes	characteristic
114	C₂	#11926561	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926568

C₂

yes

maximal, characteristic

#11926390

C₂

yes

maximal, characteristic

#11926303

C₂

yes

maximal

C₁₉×#533

C₂

yes

maximal, characteristic

C₁₉×C₄⋊Q₈

C₄

yes

complemented

C₁₉×#125

C₄

yes

complemented

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄×Dic₁₉

C₂²

yes

—

C₂×#64520

C₂²

yes

—

C₁₉⋊#95

—

C₄⋊(C₁₉⋊C₈)

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

D₄

yes

—

C₄×Dic₁₉

—

C₄×Dic₁₉

Q₈

yes

complemented

#64520

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂×D₄

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

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#1995

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×Q₈

yes

—

C₄×C₁₉

#124

yes

characteristic

C₄×C₁₉

C₄⋊Q₈

yes

characteristic

Dic₁₉

—

#533

D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

#391

yes

characteristic

C₂×C₁₉

#421

yes

—

C₂×M₁₆

—

C₄⋊Q₈

Dic₁₉

yes

complemented

#125

Dic₁₉

yes

complemented

C₂²⋊Q₈

—

C₄×Q₈

—

#117

C₂×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

#95

—

C₁₉

#1995

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×Dic₁₉

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×Dic₁₉

yes

characteristic

C₄²

C₂×Dic₁₉

yes

characteristic

C₄²

C₂²⋊D₁₉

yes

—

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊Dic₁₉

yes

—

C₂×C₄

C₂²⋊Dic₁₉

yes

—

C₂×C₄

Q₈×D₁₉

yes

—

C₂×C₄

#64545

yes

—

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

100

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

101

C₈

—

102

C₂²

—

103

C₂²

#10597392

yes

—

104

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

#10597390

yes

characteristic

110

C₄

Q₈×Dic₁₉

yes

—

111

C₄

#10597393

yes

characteristic

112

C₂

—

113

C₂

#11926451

yes

characteristic

114

C₂

#11926561

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#533	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#533	D₁₉
hypocenter	C₁₉	#1995
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #533

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#533

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #533

N	H ≅ G/N	type
5. C₁₉×C₄⋊Q₈	C₄	semidirect
6. C₁₉×#125	C₄	semidirect
28. C₄×Dic₁₉	Q₈	semidirect
63. C₄⋊Q₈	Dic₁₉	semidirect
64. #125	Dic₁₉	semidirect
72. C₁₉	#1995	semidirect

H ≅ G/N

type

5. C₁₉×C₄⋊Q₈

C₄

semidirect

6. C₁₉×#125

C₄

semidirect

28. C₄×Dic₁₉

Q₈

semidirect

63. C₄⋊Q₈

Dic₁₉

semidirect

64. #125

Dic₁₉

semidirect

72. C₁₉

#1995

semidirect

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

subgroup	index
#11926568	2
#11926390	2
#11926303	2
C₁₉×#533	2
#1995	19

subgroup

index

C₁₉×#533

Subgroups — #14564617

Conjugacy classes of subgroups

Complements

Maximal subgroups