Group #14563152 — subgroups

Subgroups — #14563152

Order 2432.

152 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 51 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	#11926947	C₂	1	1	yes	maximal, characteristic
2	#11926755	C₂	1	1	yes	maximal, characteristic
3	#11926751	C₂	1	1	yes	maximal, characteristic
4	#11926671	C₂	1	1	yes	maximal, characteristic
5	#11926294	C₂	1	1	yes	maximal, characteristic
6	#11926289	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#332	C₂	1	1	yes	maximal, characteristic
8	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂×#64528	—	2	1	no	—
10	C₂×Dic₇₆	—	2	1	no	—
11	#10597315	C₂²	1	1	yes	characteristic
12	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
13	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	#10597292	—	2	1	no	—
16	#10597273	—	2	1	no	—
17	#10597272	—	2	1	no	—
18	Dic₁₉⋊C₈	—	2	1	no	—
19	#10597264	—	2	1	no	—
20	#10597264	—	2	1	no	—
21	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
22	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₁₉	—	2	1	no	—
24	C₂×Dic₃₈	—	2	1	no	—
25	C₂×Dic₃₈	D₄	1	1	yes	characteristic
26	C₂×C₈×C₁₉	—	2	1	no	—
27	C₂×C₈×C₁₉	—	2	1	no	—
28	C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	#64528	—	4	2	no	—
32	C₄⋊Dic₁₉	—	2	1	no	—
33	C₄⋊Dic₁₉	—	2	1	no	—
34	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
35	Dic₁₉⋊C₄	—	2	1	no	—
36	C₄×Dic₁₉	—	2	1	no	—
37	C₂×C₁₉⋊C₈	—	2	1	no	—
38	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
39	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
40	Dic₇₆	—	4	2	no	—
41	Q₈×C₁₉	—	4	1	no	—
42	Q₈×C₁₉	—	4	1	no	—
43	C₂×C₄×C₁₉	—	4	1	no	—
44	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
47	C₂×Dic₁₉	—	2	1	no	—
48	C₂×Dic₁₉	—	2	1	no	—
49	C₂×Dic₁₉	—	4	1	no	—
50	Dic₃₈	—	2	1	no	—
51	Dic₃₈	—	2	1	no	—
52	Dic₃₈	—	4	1	no	—
53	Dic₃₈	—	4	1	no	—
54	C₈×C₁₉	—	4	1	no	—
55	C₈×C₁₉	—	4	1	no	—
56	C₁₉⋊C₈	—	2	1	no	—
57	C₁₉⋊C₈	—	4	1	no	—
58	C₁₉⋊C₈	Q₁₆	1	2	yes	complemented
59	#1694	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	#121	1	1	yes	characteristic
61	C₄×C₁₉	—	2	1	no	—
62	C₄×C₁₉	—	8	1	no	—
63	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
64	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
65	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
66	C₄×C₁₉	#137	1	1	yes	characteristic
67	Dic₁₉	—	4	1	no	—
68	Dic₁₉	—	4	1	no	—
69	Dic₁₉	—	8	1	no	—
70	#500	—	19	1	no	—
71	#462	—	19	1	no	—
72	#462	—	19	1	no	—
73	#446	—	19	1	no	—
74	#334	—	19	1	no	—
75	#332	—	19	1	no	—
76	#332	D₁₉	1	1	yes	characteristic
77	C₂×C₁₉	#462	1	1	yes	characteristic
78	C₂×C₁₉	#469	1	1	yes	characteristic
79	C₂×C₁₉	#473	1	1	yes	characteristic
80	C₂×Q₁₆	—	38	1	no	—
81	C₂×Q₁₆	—	38	1	no	—
82	C₄⋊Q₈	—	19	1	no	—
83	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
84	C₄×Q₈	—	19	1	no	—
85	#107	—	38	1	no	—
86	#107	—	38	1	no	—
87	C₄⋊C₈	—	19	1	no	—
88	C₄⋊C₈	—	38	1	no	—
89	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
90	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
91	#103	—	38	1	no	—
92	#103	—	38	1	no	—
93	#97	—	38	1	no	—
94	C₄×C₈	—	19	1	no	—
95	C₁₉	#1694	1	1	yes	characteristic, complemented, Sylow
96	C₂×Q₈	—	2	1	no	—
97	C₂×Q₈	—	19	1	no	—
98	C₂×Q₈	—	38	1	no	—
99	Q₁₆	—	76	2	no	—
100	Q₁₆	—	76	2	no	—
101	C₂×C₈	—	2	1	no	—
102	C₂×C₈	—	2	1	no	—
103	C₂×C₈	—	19	1	no	—
104	C₂×C₈	—	19	1	no	—
105	C₂×C₈	—	38	1	no	—
106	C₄⋊C₄	—	2	1	no	—
107	C₄⋊C₄	—	2	1	no	—
108	C₄⋊C₄	—	19	1	no	—
109	C₄⋊C₄	—	38	1	no	—
110	C₄⋊C₄	—	38	1	no	—
111	C₄⋊C₄	—	38	1	no	—
112	C₄²	—	38	1	no	—
113	C₄²	C₂²×D₁₉	1	1	yes	characteristic
114	Q₈	—	4	1	no	—
115	Q₈	—	4	1	no	—
116	Q₈	—	38	1	no	—
117	Q₈	—	38	1	no	—
118	Q₈	—	76	1	no	—
119	Q₈	—	76	1	no	—
120	C₂×C₄	—	4	1	no	—
121	C₂×C₄	—	38	1	no	—
122	C₂×C₄	—	38	1	no	—
123	C₂×C₄	—	76	1	no	—
124	C₂×C₄	#64541	1	1	yes	characteristic
125	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
126	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
127	C₈	—	4	1	no	—
128	C₈	—	4	1	no	—
129	C₈	—	19	2	no	—
130	C₈	—	38	1	no	—
131	C₈	—	76	1	no	—
132	C₂²	#10597330	1	1	yes	characteristic
133	C₄	—	2	1	no	—
134	C₄	—	8	1	no	—
135	C₄	—	76	1	no	—
136	C₄	—	76	1	no	—
137	C₄	—	152	1	no	—
138	C₄	#10597357	1	1	yes	characteristic
139	C₄	#10597360	1	1	yes	characteristic
140	C₄	#10597361	1	1	yes	characteristic
141	C₄	Q₁₆×D₁₉	1	1	yes	characteristic
142	C₂	#11926753	1	1	yes	characteristic
143	C₂	#11926796	1	1	yes	characteristic
144	C₂	#11926818	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926947

C₂

yes

maximal, characteristic

#11926755

C₂

yes

maximal, characteristic

#11926751

C₂

yes

maximal, characteristic

#11926671

C₂

yes

maximal, characteristic

#11926294

C₂

yes

maximal, characteristic

#11926289

C₂

yes

maximal, characteristic

C₁₉×#332

C₂

yes

maximal, characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×#64528

—

C₂×Dic₇₆

—

#10597315

C₂²

yes

characteristic

C₄×Dic₃₈

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

—

—

—

Dic₁₉⋊C₈

—

#10597264

—

#10597264

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

#64528

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

characteristic

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

Dic₇₆

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

Q₁₆

yes

—

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×Q₁₆

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

—

—

D₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

C₄×Q₈

—

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₁₉

yes

characteristic

C₄⋊C₈

C₂×D₁₉

yes

—

—

—

C₄×C₈

—

C₁₉

#1694

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

100

Q₁₆

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄²

—

113

C₄²

C₂²×D₁₉

yes

characteristic

114

Q₈

—

115

Q₈

—

116

Q₈

—

117

Q₈

—

118

Q₈

—

119

Q₈

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

#64541

yes

characteristic

125

C₂×C₄

D₄×D₁₉

yes

characteristic

126

C₂×C₄

D₄×D₁₉

yes

characteristic

127

C₈

—

128

C₈

—

129

C₈

—

130

C₈

—

131

C₈

—

132

C₂²

#10597330

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

152

—

138

C₄

#10597357

yes

characteristic

139

C₄

#10597360

yes

characteristic

140

C₄

#10597361

yes

characteristic

141

C₄

Q₁₆×D₁₉

yes

characteristic

142

C₂

#11926753

yes

characteristic

143

C₂

#11926796

yes

characteristic

144

C₂

#11926818

yes

characteristic

	subgroup	G/H
center	C₂²	#10597330
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#332	C₂
socle, prime radical	C₂²×C₁₉	#121
hypercenter	#332	D₁₉
hypocenter	C₁₉	#1694
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #332

subgroup

G/H

center

C₂²

#10597330

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#332

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #332

N	H ≅ G/N	type
58. C₁₉⋊C₈	Q₁₆	semidirect
95. C₁₉	#1694	semidirect

H ≅ G/N

type

58. C₁₉⋊C₈

Q₁₆

semidirect

95. C₁₉

#1694

semidirect

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

subgroup	index
#11926947	2
#11926755	2
#11926751	2
#11926671	2
#11926294	2
#11926289	2
C₁₉×#332	2
#1694	19

subgroup

index

C₁₉×#332

Subgroups — #14563152

Conjugacy classes of subgroups

Complements

Maximal subgroups