Group #14564613 — subgroups

Subgroups — #14564613

Order 2432.

284 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 105 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	C₄²×Dic₁₉	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	—	2	2	no	—
12	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
13	C₂×#64520	C₂²	1	2	yes	—
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	8	no	—
28	C₄×Dic₁₉	—	2	2	no	—
29	C₄×Dic₁₉	Q₈	1	4	yes	complemented
30	#64520	—	2	4	no	—
31	C₂×C₁₉⋊C₈	—	2	2	no	—
32	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
33	Q₈×C₁₉	—	4	4	no	—
34	C₂×C₄×C₁₉	—	2	4	no	—
35	C₂×C₄×C₁₉	—	2	4	no	—
36	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
38	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
41	C₂×C₄×C₁₉	#41	1	2	yes	—
42	C₂×Dic₁₉	—	2	8	no	—
43	C₂×Dic₁₉	—	2	4	no	—
44	C₁₉⋊C₈	—	4	2	no	—
45	#1994	—	19	1	no	maximal, Sylow
46	C₂²×C₁₉	—	2	2	no	—
47	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₁₉	C₂²⋊Q₈	1	2	yes	—
49	C₄×C₁₉	—	2	2	no	—
50	C₄×C₁₉	—	4	4	no	—
51	C₄×C₁₉	#104	1	4	yes	—
52	C₄×C₁₉	C₄×Q₈	1	2	yes	—
53	C₄×C₁₉	#124	1	1	yes	characteristic
54	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
55	Dic₁₉	—	2	8	no	—
56	#533	D₁₉	1	1	yes	characteristic
57	#423	—	19	1	no	—
58	C₄³	—	19	1	no	—
59	#339	—	19	4	no	—
60	C₂×C₁₉	—	2	2	no	—
61	C₂×C₁₉	#391	1	1	yes	characteristic
62	C₂×C₁₉	C₂×#104	1	2	yes	—
63	C₂×M₁₆	—	19	2	no	—
64	C₄⋊Q₈	Dic₁₉	1	2	yes	complemented
65	#125	Dic₁₉	1	2	yes	complemented
66	C₂²⋊Q₈	—	2	2	no	—
67	C₄×Q₈	—	2	2	no	—
68	#117	C₂×D₁₉	1	2	yes	—
69	C₂×C₄²	—	19	2	no	—
70	C₂×C₄²	—	38	2	no	—
71	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
72	C₄⋊C₈	—	38	2	no	—
73	C₁₉	#1994	1	1	yes	characteristic, complemented, Sylow
74	C₂×Q₈	—	2	2	no	—
75	C₂²×C₄	—	38	2	no	—
76	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
77	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
78	M₁₆	—	38	4	no	—
79	C₂×C₈	—	38	2	no	—
80	C₄⋊C₄	—	2	4	no	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	C₂×Dic₁₉	1	4	yes	—
83	C₂²⋊C₄	—	2	2	no	—
84	C₄²	—	2	2	no	—
85	C₄²	—	19	4	no	—
86	C₄²	—	38	8	no	—
87	C₄²	—	38	2	no	—
88	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
89	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
90	C₄²	C₂²⋊D₁₉	1	2	yes	—
91	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
92	Q₈	—	4	4	no	—
93	C₂×C₄	—	2	4	no	—
94	C₂×C₄	—	2	4	no	—
95	C₂×C₄	—	38	8	no	—
96	C₂×C₄	—	38	4	no	—
97	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
98	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
99	C₂×C₄	Q₈×D₁₉	1	2	yes	—
100	C₂×C₄	#64545	1	2	yes	—
101	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
102	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
103	C₈	—	76	2	no	—
104	C₂²	—	2	2	no	—
105	C₂²	#10597392	1	2	yes	—
106	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
107	C₄	—	2	2	no	—
108	C₄	—	4	4	no	—
109	C₄	—	38	8	no	—
110	C₄	#10597294	1	4	yes	—
111	C₄	#10597390	1	1	yes	characteristic
112	C₄	Q₈×Dic₁₉	1	2	yes	—
113	C₄	#10597393	1	1	yes	characteristic
114	C₂	—	2	2	no	—
115	C₂	#11926451	1	1	yes	characteristic
116	C₂	C₂×#10597294	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926568

C₂

yes

maximal, characteristic

C₄²×Dic₁₉

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

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₂×#64520

C₂²

yes

—

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

—

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

—

#1994

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#104

yes

—

C₄×C₁₉

C₄×Q₈

yes

—

C₄×C₁₉

#124

yes

characteristic

C₄×C₁₉

C₄⋊Q₈

yes

characteristic

Dic₁₉

—

#533

D₁₉

yes

characteristic

#423

—

C₄³

—

#339

—

C₂×C₁₉

—

C₂×C₁₉

#391

yes

characteristic

C₂×C₁₉

C₂×#104

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×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₁₉

#1994

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

—

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

—

100

C₂×C₄

#64545

yes

—

101

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

102

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

103

C₈

—

104

C₂²

—

105

C₂²

#10597392

yes

—

106

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

#10597294

yes

—

111

C₄

#10597390

yes

characteristic

112

C₄

Q₈×Dic₁₉

yes

—

113

C₄

#10597393

yes

characteristic

114

C₂

—

115

C₂

#11926451

yes

characteristic

116

C₂

C₂×#10597294

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	#1994
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
29. C₄×Dic₁₉	Q₈	semidirect
64. C₄⋊Q₈	Dic₁₉	semidirect
65. #125	Dic₁₉	semidirect
73. C₁₉	#1994	semidirect

H ≅ G/N

type

5. C₁₉×C₄⋊Q₈

C₄

semidirect

6. C₁₉×#125

C₄

semidirect

29. C₄×Dic₁₉

Q₈

semidirect

64. C₄⋊Q₈

Dic₁₉

semidirect

65. #125

Dic₁₉

semidirect

73. C₁₉

#1994

semidirect

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

subgroup	index
#11926568	2
C₄²×Dic₁₉	2
#11926303	2
C₁₉×#533	2
#1994	19

subgroup

index

#11926568

C₄²×Dic₁₉

#11926303

C₁₉×#533

#1994

Subgroups — #14564613

Conjugacy classes of subgroups

Complements

Maximal subgroups