Group #14564900 — subgroups

Subgroups — #14564900

Order 2432.

256 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 71 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	#11926570	C₂	1	1	yes	maximal, characteristic
2	#11926553	C₂	1	2	yes	maximal
3	C₂×#10597293	C₂	1	2	yes	maximal
4	#11926309	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₉	C₂²	1	2	yes	—
7	C₂×Q₁₆×C₁₉	—	2	4	no	—
8	C₂×Q₁₆×C₁₉	—	2	2	no	—
9	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	#10597372	C₂²	1	1	yes	characteristic
11	C₂×#64520	C₂²	1	2	yes	—
12	C₂×#64520	C₂²	1	1	yes	characteristic
13	#10597293	—	2	4	no	—
14	#10597292	—	2	4	no	—
15	Dic₁₉⋊C₈	—	2	2	no	—
16	C₂×Q₈×C₁₉	—	2	2	no	—
17	C₂×Q₈×C₁₉	—	2	2	no	—
18	C₂×Q₈×C₁₉	—	2	2	no	—
19	C₂×Q₈×C₁₉	—	2	2	no	—
20	C₂×Q₈×C₁₉	—	2	2	no	—
21	C₂×Q₈×C₁₉	D₄	1	4	yes	—
22	C₂²×C₄×C₁₉	—	2	2	no	—
23	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	Q₁₆×C₁₉	—	2	8	no	—
25	C₂×C₈×C₁₉	—	2	2	no	—
26	C₂×C₈×C₁₉	D₄	1	2	yes	—
27	C₂²⋊Dic₁₉	—	2	1	no	—
28	C₄⋊Dic₁₉	D₄	1	2	yes	—
29	C₄×Dic₁₉	—	2	1	no	—
30	#64520	—	2	2	no	—
31	#64520	—	2	2	no	—
32	#64520	—	2	2	no	—
33	C₂×C₁₉⋊C₈	—	2	1	no	—
34	C₂×C₁₉⋊C₈	—	2	2	no	—
35	C₂³×C₁₉	#41	1	1	yes	characteristic
36	Q₈×C₁₉	—	2	4	no	—
37	Q₈×C₁₉	—	2	4	no	—
38	Q₈×C₁₉	—	4	2	no	—
39	Q₈×C₁₉	—	4	2	no	—
40	C₂×C₄×C₁₉	—	2	4	no	—
41	C₂×C₄×C₁₉	—	4	2	no	—
42	C₂×C₄×C₁₉	—	4	2	no	—
43	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
45	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	#41	1	2	yes	—
47	C₂×Dic₁₉	—	2	2	no	—
48	C₈×C₁₉	—	2	2	no	—
49	C₁₉⋊C₈	—	4	1	no	—
50	C₁₉⋊C₈	—	4	2	no	—
51	#2047	—	19	1	no	maximal, Sylow
52	C₂²×C₁₉	—	2	2	no	—
53	C₂²×C₁₉	#121	1	1	yes	characteristic
54	C₂²×C₁₉	#123	1	2	yes	—
55	C₄×C₁₉	—	4	4	no	—
56	C₄×C₁₉	#120	1	1	yes	characteristic
57	C₄×C₁₉	#121	1	2	yes	—
58	C₄×C₁₉	#124	1	1	yes	characteristic
59	Dic₁₉	—	4	2	no	—
60	C₂²×Q₁₆	D₁₉	1	1	yes	characteristic
61	#424	—	19	1	no	—
62	#419	—	19	2	no	—
63	C₂×#101	—	19	2	no	—
64	#341	—	19	1	no	—
65	C₂×C₁₉	—	2	2	no	—
66	C₂×C₁₉	#394	1	1	yes	characteristic
67	C₂×C₁₉	#473	1	2	yes	—
68	C₂²×Q₈	C₂×D₁₉	1	2	yes	—
69	C₂×Q₁₆	—	2	4	no	—
70	C₂×Q₁₆	—	2	2	no	—
71	C₂×M₁₆	—	19	2	no	—
72	C₂×M₁₆	—	19	1	no	—
73	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
74	#117	—	19	1	no	—
75	C₄⋊C₈	—	38	2	no	—
76	#103	—	38	4	no	—
77	#101	—	38	4	no	—
78	C₁₉	#2047	1	1	yes	characteristic, complemented, Sylow
79	C₂×Q₈	—	2	2	no	—
80	C₂×Q₈	—	2	2	no	—
81	C₂×Q₈	—	2	2	no	—
82	C₂×Q₈	—	2	2	no	—
83	C₂×Q₈	—	2	2	no	—
84	C₂×Q₈	C₂²⋊D₁₉	1	4	yes	—
85	C₂²×C₄	—	2	2	no	—
86	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
87	Q₁₆	—	2	8	no	—
88	M₁₆	—	38	2	no	—
89	M₁₆	—	38	2	no	—
90	M₁₆	—	38	2	no	—
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	38	2	no	—
93	C₂×C₈	—	38	1	no	—
94	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
95	C₄⋊C₄	—	19	2	no	—
96	C₂²⋊C₄	—	38	1	no	—
97	C₄²	—	38	1	no	—
98	C₂³	#64543	1	1	yes	characteristic
99	Q₈	—	2	4	no	—
100	Q₈	—	2	4	no	—
101	Q₈	—	4	2	no	—
102	Q₈	—	4	2	no	—
103	C₂×C₄	—	2	4	no	—
104	C₂×C₄	—	4	2	no	—
105	C₂×C₄	—	4	2	no	—
106	C₂×C₄	—	38	2	no	—
107	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
108	C₂×C₄	#64543	1	2	yes	—
109	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
110	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
111	C₈	—	2	2	no	—
112	C₈	—	76	2	no	—
113	C₈	—	76	1	no	—
114	C₂²	—	2	2	no	—
115	C₂²	#10597381	1	2	yes	—
116	C₂²	#10597384	1	1	yes	characteristic
117	C₄	—	4	4	no	—
118	C₄	—	76	2	no	—
119	C₄	#10597382	1	1	yes	characteristic
120	C₄	#10597385	1	2	yes	—
121	C₄	#10597399	1	1	yes	characteristic
122	C₂	—	2	2	no	—
123	C₂	#11926458	1	1	yes	characteristic
124	C₂	#11926816	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926570

C₂

yes

maximal, characteristic

#11926553

C₂

yes

maximal

C₂×#10597293

C₂

yes

maximal

#11926309

C₂

yes

maximal, characteristic

C₂²×Q₁₆×C₁₉

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

#10597372

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

C₂×#64520

C₂²

yes

characteristic

#10597293

—

#10597292

—

Dic₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

C₄×Dic₁₉

—

#64520

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

#41

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2047

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

#121

yes

characteristic

C₂²×C₁₉

#123

yes

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

characteristic

C₄×C₁₉

#121

yes

—

C₄×C₁₉

#124

yes

characteristic

Dic₁₉

—

C₂²×Q₁₆

D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

#394

yes

characteristic

C₂×C₁₉

#473

yes

—

C₂²×Q₈

C₂×D₁₉

yes

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

#117

—

C₄⋊C₈

—

#103

—

#101

—

C₁₉

#2047

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²⋊D₁₉

yes

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

Q₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₉

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

#64543

yes

characteristic

Q₈

—

100

Q₈

—

101

Q₈

—

102

Q₈

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

D₄×D₁₉

yes

characteristic

108

C₂×C₄

#64543

yes

—

109

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

110

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

111

C₈

—

112

C₈

—

113

C₈

—

114

C₂²

—

115

C₂²

#10597381

yes

—

116

C₂²

#10597384

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

#10597382

yes

characteristic

120

C₄

#10597385

yes

—

121

C₄

#10597399

yes

characteristic

122

C₂

—

123

C₂

#11926458

yes

characteristic

124

C₂

#11926816

yes

—

	subgroup	G/H
center	C₂²	#10597384
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂²×Q₁₆×C₁₉	C₂
socle	C₂²×C₁₉	#121
prime radical	C₂³×C₁₉	#41
hypercenter	C₂²×Q₁₆	D₁₉
hypocenter	C₁₉	#2047
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₁₆

subgroup

G/H

center

C₂²

#10597384

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂²×Q₁₆×C₁₉

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂²×Q₁₆

D₁₉

hypocenter

C₁₉

#2047

LCS

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₁₆

N	H ≅ G/N	type
78. C₁₉	#2047	semidirect

H ≅ G/N

type

78. C₁₉

#2047

semidirect

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

subgroup	index
#11926570	2
#11926553	2
C₂×#10597293	2
#11926309	2
C₂²×Q₁₆×C₁₉	2
#2047	19

subgroup

index

C₂²×Q₁₆×C₁₉

Subgroups — #14564900

Conjugacy classes of subgroups

Complements

Maximal subgroups