Group #14562874 — subgroups

Subgroups — #14562874

Order 2432.

194 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 55 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	#11927269	C₂	1	1	yes	maximal, characteristic
2	#11926826	C₂	1	1	yes	maximal, characteristic
3	#11926751	C₂	1	1	yes	maximal, characteristic
4	#11926290	C₂	1	1	yes	maximal, characteristic
5	#11926276	C₂	1	1	yes	maximal, characteristic
6	#11926276	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#500	C₂	1	1	yes	maximal, characteristic
8	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	Q₈×Dic₁₉	—	2	1	no	—
11	#10597390	—	2	1	no	—
12	C₂×#64528	—	2	1	no	—
13	#10597336	—	2	1	no	—
14	#10597335	—	2	2	no	—
15	#10597333	—	2	1	no	—
16	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
17	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
18	C₁₉×#107	—	2	2	no	—
19	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	#10597292	—	2	1	no	—
21	#10597267	—	2	1	no	—
22	#10597265	—	2	1	no	—
23	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
24	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×Q₈×C₁₉	—	2	1	no	—
26	C₂×Q₈×C₁₉	—	2	1	no	—
27	C₂×Dic₃₈	D₄	1	1	yes	characteristic
28	C₂×Dic₃₈	D₄	1	1	yes	characteristic
29	C₂×C₈×C₁₉	—	2	1	no	—
30	C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
34	C₄²×C₁₉	C₂³	1	1	yes	characteristic
35	#64528	—	4	2	no	—
36	C₄⋊Dic₁₉	—	2	2	no	—
37	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
38	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
39	Dic₁₉⋊C₄	—	2	2	no	—
40	Dic₁₉⋊C₄	—	2	2	no	—
41	Dic₁₉⋊C₄	—	2	1	no	—
42	Dic₁₉⋊C₄	—	2	1	no	—
43	C₄×Dic₁₉	—	2	2	no	—
44	C₄×Dic₁₉	—	2	1	no	—
45	C₄×Dic₁₉	—	2	1	no	—
46	C₂×C₁₉⋊C₈	—	2	1	no	—
47	C₂×C₁₉⋊C₈	—	2	1	no	—
48	Q₈×C₁₉	—	4	1	no	—
49	Q₈×C₁₉	—	4	1	no	—
50	Q₈×C₁₉	—	4	1	no	—
51	Q₈×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	4	1	no	—
54	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂×Dic₁₉	—	2	1	no	—
58	C₂×Dic₁₉	—	2	1	no	—
59	C₂×Dic₁₉	—	2	1	no	—
60	C₂×Dic₁₉	—	2	1	no	—
61	Dic₃₈	—	2	1	no	—
62	Dic₃₈	—	2	1	no	—
63	Dic₃₈	—	2	1	no	—
64	Dic₃₈	Q₁₆	1	2	yes	complemented
65	C₈×C₁₉	—	2	2	no	—
66	C₁₉⋊C₈	—	4	1	no	—
67	C₁₉⋊C₈	—	4	1	no	—
68	#1648	—	19	1	no	maximal, Sylow
69	C₂²×C₁₉	#120	1	1	yes	characteristic
70	C₄×C₁₉	—	2	1	no	—
71	C₄×C₁₉	—	4	2	no	—
72	C₄×C₁₉	—	8	1	no	—
73	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
74	C₄×C₁₉	#135	1	1	yes	characteristic
75	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
76	C₄×C₁₉	#137	1	1	yes	characteristic
77	Dic₁₉	—	2	2	no	—
78	Dic₁₉	—	4	1	no	—
79	Dic₁₉	—	4	1	no	—
80	Dic₁₉	—	4	1	no	—
81	#557	—	19	1	no	—
82	#500	D₁₉	1	1	yes	characteristic
83	#475	—	19	1	no	—
84	#462	—	19	1	no	—
85	#332	—	19	1	no	—
86	Q₈⋊C₈	—	19	1	no	—
87	Q₈⋊C₈	—	19	1	no	—
88	C₂×C₁₉	#449	1	1	yes	characteristic
89	C₂×C₁₉	#451	1	1	yes	characteristic
90	C₂×C₁₉	#456	1	1	yes	characteristic
91	C₂×Q₁₆	—	38	1	no	—
92	C₄⋊Q₈	—	38	1	no	—
93	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
94	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
95	#125	—	38	1	no	—
96	#125	—	38	2	no	—
97	C₄×Q₈	—	19	1	no	—
98	C₄×Q₈	—	19	1	no	—
99	C₄×Q₈	—	38	1	no	—
100	C₄×Q₈	—	38	1	no	—
101	#107	—	2	2	no	—
102	#106	—	38	1	no	—
103	C₄⋊C₈	—	19	1	no	—
104	C₄⋊C₈	—	19	1	no	—
105	#103	—	38	1	no	—
106	#103	—	38	1	no	—
107	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
108	C₁₉	#1648	1	1	yes	characteristic, complemented, Sylow
109	C₂×Q₈	—	2	1	no	—
110	C₂×Q₈	—	2	1	no	—
111	C₂×Q₈	—	19	1	no	—
112	C₂×Q₈	—	19	1	no	—
113	Q₁₆	—	76	2	no	—
114	C₂×C₈	—	2	1	no	—
115	C₂×C₈	—	38	1	no	—
116	C₂×C₈	—	38	1	no	—
117	C₄⋊C₄	—	2	1	no	—
118	C₄⋊C₄	—	2	1	no	—
119	C₄⋊C₄	—	2	1	no	—
120	C₄⋊C₄	—	19	1	no	—
121	C₄⋊C₄	—	19	1	no	—
122	C₄⋊C₄	—	38	2	no	—
123	C₄⋊C₄	—	38	2	no	—
124	C₄⋊C₄	—	38	2	no	—
125	C₄⋊C₄	—	38	1	no	—
126	C₄⋊C₄	—	38	1	no	—
127	C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
128	C₄²	—	38	2	no	—
129	C₄²	—	38	1	no	—
130	C₄²	—	38	1	no	—
131	C₄²	C₂²×D₁₉	1	1	yes	characteristic
132	Q₈	—	4	1	no	—
133	Q₈	—	4	1	no	—
134	Q₈	—	4	1	no	—
135	Q₈	—	4	1	no	—
136	Q₈	—	19	2	no	—
137	Q₈	—	38	1	no	—
138	Q₈	—	38	1	no	—
139	Q₈	—	38	1	no	—
140	C₂×C₄	—	2	2	no	—
141	C₂×C₄	—	4	1	no	—
142	C₂×C₄	—	38	1	no	—
143	C₂×C₄	—	38	1	no	—
144	C₂×C₄	—	38	1	no	—
145	C₂×C₄	—	38	1	no	—
146	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
147	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
148	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
149	C₈	—	2	2	no	—
150	C₈	—	76	1	no	—
151	C₈	—	76	1	no	—
152	C₂²	#10597383	1	1	yes	characteristic
153	C₄	—	2	1	no	—
154	C₄	—	4	2	no	—
155	C₄	—	8	1	no	—
156	C₄	—	38	2	no	—
157	C₄	—	76	1	no	—
158	C₄	—	76	1	no	—
159	C₄	—	76	1	no	—
160	C₄	#10597357	1	1	yes	characteristic
161	C₄	#10597358	1	1	yes	characteristic
162	C₄	Q₁₆×D₁₉	1	1	yes	characteristic
163	C₄	#10597364	1	1	yes	characteristic
164	C₂	#11926686	1	1	yes	characteristic
165	C₂	#11926698	1	1	yes	characteristic
166	C₂	#11926726	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927269

C₂

yes

maximal, characteristic

#11926826

C₂

yes

maximal, characteristic

#11926751

C₂

yes

maximal, characteristic

#11926290

C₂

yes

maximal, characteristic

#11926276

C₂

yes

maximal, characteristic

#11926276

C₂

yes

maximal, characteristic

C₁₉×#500

C₂

yes

maximal, characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

Q₈×Dic₁₉

—

—

—

—

—

—

C₄×Dic₃₈

C₂²

yes

characteristic

C₄×Dic₃₈

C₂²

yes

characteristic

C₁₉×#107

—

C₄×C₈×C₁₉

C₂²

yes

—

—

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Dic₃₈

D₄

yes

characteristic

C₂×Dic₃₈

D₄

yes

characteristic

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

#64528

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

D₄

yes

characteristic

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

Q₁₆

yes

complemented

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×Q₁₆

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

#557

—

#500

D₁₉

yes

—

—

—

Q₈⋊C₈

—

Q₈⋊C₈

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

#125

—

#125

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

100

C₄×Q₈

—

101

#107

—

102

#106

—

103

C₄⋊C₈

—

104

C₄⋊C₈

—

105

#103

—

106

#103

—

107

C₄×C₈

C₂×D₁₉

yes

characteristic

108

C₁₉

#1648

yes

characteristic, complemented, Sylow

109

C₂×Q₈

—

110

C₂×Q₈

—

111

C₂×Q₈

—

112

C₂×Q₈

—

113

Q₁₆

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₄⋊C₄

—

127

C₄⋊C₄

C₂²⋊D₁₉

yes

—

128

C₄²

—

129

C₄²

—

130

C₄²

—

131

C₄²

C₂²×D₁₉

yes

characteristic

132

Q₈

—

133

Q₈

—

134

Q₈

—

135

Q₈

—

136

Q₈

—

137

Q₈

—

138

Q₈

—

139

Q₈

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

D₄×D₁₉

yes

characteristic

147

C₂×C₄

D₄×D₁₉

yes

characteristic

148

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

149

C₈

—

150

C₈

—

151

C₈

—

152

C₂²

#10597383

yes

characteristic

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

—

158

C₄

—

159

C₄

—

160

C₄

#10597357

yes

characteristic

161

C₄

#10597358

yes

characteristic

162

C₄

Q₁₆×D₁₉

yes

characteristic

163

C₄

#10597364

yes

characteristic

164

C₂

#11926686

yes

characteristic

165

C₂

#11926698

yes

characteristic

166

C₂

#11926726

yes

characteristic

	subgroup	G/H
center	C₂²	#10597383
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#500	C₂
socle, prime radical	C₂²×C₁₉	#120
hypercenter	#500	D₁₉
hypocenter	C₁₉	#1648
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #500

subgroup

G/H

center

C₂²

#10597383

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#500

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #500

N	H ≅ G/N	type
64. Dic₃₈	Q₁₆	semidirect
108. C₁₉	#1648	semidirect

H ≅ G/N

type

64. Dic₃₈

Q₁₆

semidirect

108. C₁₉

#1648

semidirect

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

subgroup	index
#11927269	2
#11926826	2
#11926751	2
#11926290	2
#11926276	2
C₁₉×#500	2
#1648	19

subgroup

index

C₁₉×#500

Subgroups — #14562874

Conjugacy classes of subgroups

Complements

Maximal subgroups