Group #14563202 — subgroups

Subgroups — #14563202

Order 2432.

162 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 49 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	#11926890	C₂	1	1	yes	maximal, characteristic
2	#11926755	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926741	C₂	1	1	yes	maximal, characteristic
4	#11926671	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926294	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926289	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#331	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#127	C₂²	1	1	yes	characteristic
9	C₂×#64526	—	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	#10597289	—	2	1	no	—
16	#10597289	—	2	1	no	—
17	#10597289	—	2	1	no	—
18	#10597273	—	2	1	no	—
19	#10597272	—	2	1	no	—
20	Dic₁₉⋊C₈	—	2	1	no	—
21	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
22	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×D₄×C₁₉	—	2	1	no	—
24	C₂×D₄×C₁₉	—	2	1	no	—
25	C₂×D₄×C₁₉	—	2	1	no	—
26	C₂×Dic₃₈	—	2	1	no	—
27	C₂×Dic₃₈	D₄	1	1	yes	characteristic
28	C₂×C₈×C₁₉	—	2	1	no	—
29	C₂×C₈×C₁₉	—	2	1	no	—
30	C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	#64526	—	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	C₂³×C₁₉	—	4	1	no	—
42	D₄×C₁₉	—	4	1	no	—
43	D₄×C₁₉	—	4	1	no	—
44	D₄×C₁₉	—	4	1	no	—
45	D₄×C₁₉	—	4	1	no	—
46	D₄×C₁₉	—	8	1	no	—
47	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
50	C₂×Dic₁₉	—	2	1	no	—
51	C₂×Dic₁₉	—	2	1	no	—
52	C₂×Dic₁₉	—	4	1	no	—
53	Dic₃₈	—	2	1	no	—
54	Dic₃₈	—	2	1	no	—
55	Dic₃₈	—	4	1	no	—
56	Dic₃₈	—	4	1	no	—
57	C₈×C₁₉	—	4	1	no	—
58	C₈×C₁₉	—	4	1	no	—
59	C₁₉⋊C₈	—	2	1	no	—
60	C₁₉⋊C₈	—	2	1	no	—
61	C₁₉⋊C₈	—	4	1	no	—
62	#1702	—	19	1	no	maximal, Sylow
63	C₂²×C₁₉	—	8	1	no	—
64	C₂²×C₁₉	—	8	1	no	—
65	C₂²×C₁₉	—	8	1	no	—
66	C₂²×C₁₉	#121	1	1	yes	characteristic
67	C₄×C₁₉	—	2	1	no	—
68	C₄×C₁₉	#135	1	1	yes	characteristic
69	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
70	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
71	C₄×C₁₉	#137	1	1	yes	characteristic
72	Dic₁₉	—	4	1	no	—
73	Dic₁₉	—	4	1	no	—
74	Dic₁₉	—	8	1	no	—
75	#486	—	19	1	no	—
76	#462	—	19	1	no	—
77	#460	—	19	1	no	—
78	#446	—	19	1	no	—
79	#334	—	19	1	no	—
80	#332	—	19	1	no	—
81	#331	D₁₉	1	1	yes	characteristic
82	C₂×C₁₉	—	16	1	no	—
83	C₂×C₁₉	#464	1	1	yes	characteristic
84	C₂×C₁₉	#469	1	1	yes	characteristic
85	C₂×C₁₉	#471	1	1	yes	characteristic
86	C₂×Q₁₆	—	38	1	no	—
87	C₂×SD₁₆	—	38	1	no	—
88	C₄⋊Q₈	—	19	1	no	—
89	#127	C₂×D₁₉	1	1	yes	characteristic
90	C₄×Q₈	—	19	1	no	—
91	C₄⋊C₈	—	19	1	no	—
92	C₄⋊C₈	—	38	1	no	—
93	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
94	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
95	#103	—	38	1	no	—
96	#102	—	38	1	no	—
97	#102	—	38	1	no	—
98	#102	—	38	1	no	—
99	#97	—	38	1	no	—
100	C₄×C₈	—	19	1	no	—
101	C₁₉	#1702	1	1	yes	characteristic, complemented, Sylow
102	C₂×Q₈	—	19	1	no	—
103	C₂×Q₈	—	38	1	no	—
104	C₂×D₄	—	2	1	no	—
105	C₂×D₄	—	2	1	no	—
106	C₂×D₄	—	2	1	no	—
107	Q₁₆	—	76	2	no	—
108	SD₁₆	—	76	2	no	—
109	C₂×C₈	—	2	1	no	—
110	C₂×C₈	—	2	1	no	—
111	C₂×C₈	—	19	1	no	—
112	C₂×C₈	—	19	1	no	—
113	C₂×C₈	—	38	1	no	—
114	C₄⋊C₄	—	19	1	no	—
115	C₄⋊C₄	—	38	1	no	—
116	C₄⋊C₄	—	38	1	no	—
117	C₄⋊C₄	—	38	1	no	—
118	C₄²	—	38	1	no	—
119	C₄²	C₂²×D₁₉	1	1	yes	characteristic
120	C₂³	—	4	1	no	—
121	Q₈	—	38	1	no	—
122	Q₈	—	38	1	no	—
123	Q₈	—	76	1	no	—
124	Q₈	—	76	1	no	—
125	D₄	—	4	1	no	—
126	D₄	—	4	1	no	—
127	D₄	—	4	1	no	—
128	D₄	—	4	1	no	—
129	D₄	—	8	1	no	—
130	C₂×C₄	—	38	1	no	—
131	C₂×C₄	—	38	1	no	—
132	C₂×C₄	—	76	1	no	—
133	C₂×C₄	#64541	1	1	yes	characteristic
134	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
135	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
136	C₈	—	4	1	no	—
137	C₈	—	4	1	no	—
138	C₈	—	38	1	no	—
139	C₈	—	38	1	no	—
140	C₈	—	76	1	no	—
141	C₂²	—	8	1	no	—
142	C₂²	—	8	1	no	—
143	C₂²	—	8	1	no	—
144	C₂²	#10597330	1	1	yes	characteristic
145	C₄	—	2	1	no	—
146	C₄	—	76	1	no	—
147	C₄	—	76	1	no	—
148	C₄	—	152	1	no	—
149	C₄	#10597357	1	1	yes	characteristic
150	C₄	#10597358	1	1	yes	characteristic
151	C₄	#10597360	1	1	yes	characteristic
152	C₄	#10597361	1	1	yes	characteristic
153	C₂	—	16	1	no	—
154	C₂	#11926765	1	1	yes	characteristic
155	C₂	#11926796	1	1	yes	characteristic
156	C₂	#11926806	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926890

C₂

yes

maximal, characteristic

#11926755

C₂

yes

maximal, characteristic, complemented

#11926741

C₂

yes

maximal, characteristic

#11926671

C₂

yes

maximal, characteristic, complemented

#11926294

C₂

yes

maximal, characteristic, complemented

#11926289

C₂

yes

maximal, characteristic, complemented

C₁₉×#331

C₂

yes

maximal, characteristic

C₁₉×#127

C₂²

yes

characteristic

C₂×#64526

—

C₂×Dic₇₆

—

#10597315

C₂²

yes

characteristic

C₄×Dic₃₈

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

—

—

—

—

—

Dic₁₉⋊C₈

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

#64526

—

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

—

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×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

—

#1702

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#121

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

—

—

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₂×SD₁₆

—

C₄⋊Q₈

—

#127

C₂×D₁₉

yes

characteristic

C₄×Q₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₁₉

yes

characteristic

C₄⋊C₈

C₂×D₁₉

yes

—

—

—

—

—

100

C₄×C₈

—

101

C₁₉

#1702

yes

characteristic, complemented, Sylow

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂×D₄

—

107

Q₁₆

—

108

SD₁₆

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄²

—

119

C₄²

C₂²×D₁₉

yes

characteristic

120

C₂³

—

121

Q₈

—

122

Q₈

—

123

Q₈

—

124

Q₈

—

125

D₄

—

126

D₄

—

127

D₄

—

128

D₄

—

129

D₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

#64541

yes

characteristic

134

C₂×C₄

D₄×D₁₉

yes

characteristic

135

C₂×C₄

D₄×D₁₉

yes

characteristic

136

C₈

—

137

C₈

—

138

C₈

—

139

C₈

—

140

C₈

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

#10597330

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

152

—

149

C₄

#10597357

yes

characteristic

150

C₄

#10597358

yes

characteristic

151

C₄

#10597360

yes

characteristic

152

C₄

#10597361

yes

characteristic

153

C₂

—

154

C₂

#11926765

yes

characteristic

155

C₂

#11926796

yes

characteristic

156

C₂

#11926806

yes

characteristic

	subgroup	G/H
center	C₂²	#10597330
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#331	C₂
socle	C₂²×C₁₉	#121
prime radical	C₁₉×#127	C₂²
hypercenter	#331	D₁₉
hypocenter	C₁₉	#1702
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #331

subgroup

G/H

center

C₂²

#10597330

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#331

C₂

socle

C₂²×C₁₉

#121

prime radical

C₁₉×#127

C₂²

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #331

N	H ≅ G/N	type
2. #11926755	C₂	semidirect
4. #11926671	C₂	semidirect
5. #11926294	C₂	semidirect
6. #11926289	C₂	semidirect
101. C₁₉	#1702	semidirect

H ≅ G/N

type

2. #11926755

C₂

semidirect

4. #11926671

C₂

semidirect

5. #11926294

C₂

semidirect

6. #11926289

C₂

semidirect

101. C₁₉

#1702

semidirect

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

subgroup	index
#11926890	2
#11926755	2
#11926741	2
#11926671	2
#11926294	2
#11926289	2
C₁₉×#331	2
#1702	19

subgroup

index

C₁₉×#331

Subgroups — #14563202

Conjugacy classes of subgroups

Complements

Maximal subgroups