Group #14562796 — subgroups

Subgroups — #14562796

Order 2432.

188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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	#11927273	C₂	1	1	yes	maximal, characteristic
2	#11926895	C₂	1	1	yes	maximal, characteristic
3	#11926840	C₂	1	1	yes	maximal, characteristic
4	#11926839	C₂	1	1	yes	maximal, characteristic
5	#11926291	C₂	1	1	yes	maximal, characteristic
6	#11926276	C₂	1	1	yes	maximal, characteristic
7	C₁₉×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic
8	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	Q₈×Dic₁₉	—	2	1	no	—
10	#10597336	—	2	1	no	—
11	#10597336	—	2	2	no	—
12	#10597315	—	2	1	no	—
13	#10597315	C₂²	1	1	yes	characteristic
14	#10597315	C₂²	1	1	yes	characteristic
15	C₄×Dic₃₈	—	2	1	no	—
16	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
17	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	#10597292	—	2	1	no	—
20	#10597275	—	2	1	no	—
21	#10597273	—	2	1	no	—
22	#10597273	—	2	2	no	—
23	#10597264	—	2	1	no	—
24	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×Q₈×C₁₉	D₄	1	1	yes	characteristic
26	C₂×Dic₃₈	—	2	1	no	—
27	C₂×Dic₃₈	—	2	1	no	—
28	C₂×Dic₃₈	D₄	1	1	yes	characteristic
29	C₂×C₈×C₁₉	—	2	1	no	—
30	C₂×C₈×C₁₉	—	2	1	no	—
31	C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
33	C₄²×C₁₉	—	2	1	no	—
34	C₄²×C₁₉	C₂³	1	1	yes	characteristic
35	C₄⋊Dic₁₉	—	2	2	no	—
36	C₄⋊Dic₁₉	—	2	2	no	—
37	C₄⋊Dic₁₉	—	2	1	no	—
38	C₄⋊Dic₁₉	—	2	1	no	—
39	C₄⋊Dic₁₉	—	2	1	no	—
40	C₄⋊Dic₁₉	D₄	1	2	yes	—
41	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
42	Dic₁₉⋊C₄	—	2	2	no	—
43	Dic₁₉⋊C₄	—	2	1	no	—
44	C₄×Dic₁₉	—	2	2	no	—
45	C₄×Dic₁₉	—	2	1	no	—
46	C₂×C₁₉⋊C₈	—	2	1	no	—
47	Q₈×C₁₉	—	2	1	no	—
48	Q₈×C₁₉	Q₁₆	1	2	yes	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂×Dic₁₉	—	2	1	no	—
55	C₂×Dic₁₉	—	2	1	no	—
56	C₂×Dic₁₉	—	2	2	no	—
57	C₂×Dic₁₉	—	4	1	no	—
58	Dic₃₈	—	2	1	no	—
59	Dic₃₈	—	2	1	no	—
60	Dic₃₈	—	4	1	no	—
61	Dic₃₈	—	4	1	no	—
62	Dic₃₈	—	4	2	no	—
63	C₈×C₁₉	—	4	1	no	—
64	C₈×C₁₉	—	4	1	no	—
65	C₁₉⋊C₈	—	4	1	no	—
66	#1636	—	19	1	no	maximal, Sylow
67	C₂²×C₁₉	#120	1	1	yes	characteristic
68	C₄×C₁₉	—	2	2	no	—
69	C₄×C₁₉	—	2	1	no	—
70	C₄×C₁₉	—	4	1	no	—
71	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
72	C₄×C₁₉	#135	1	1	yes	characteristic
73	C₄×C₁₉	#137	1	1	yes	characteristic
74	C₄×C₁₉	#137	1	1	yes	characteristic
75	Dic₁₉	—	4	1	no	—
76	Dic₁₉	—	4	2	no	—
77	Dic₁₉	—	4	1	no	—
78	Dic₁₉	—	8	1	no	—
79	#557	—	19	1	no	—
80	#487	—	19	1	no	—
81	#477	—	19	1	no	—
82	#477	—	19	1	no	—
83	#332	—	19	1	no	—
84	Q₈⋊C₈	—	19	1	no	—
85	Q₈⋊C₈	D₁₉	1	1	yes	characteristic
86	C₂×C₁₉	#451	1	1	yes	characteristic
87	C₂×C₁₉	#452	1	1	yes	characteristic
88	C₂×C₁₉	#454	1	1	yes	characteristic
89	C₄⋊Q₈	—	19	1	no	—
90	C₄⋊Q₈	—	19	1	no	—
91	C₄⋊Q₈	—	38	1	no	—
92	#125	—	38	2	no	—
93	#125	—	38	1	no	—
94	C₄×Q₈	—	19	1	no	—
95	C₄×Q₈	—	38	1	no	—
96	C₄×Q₈	—	38	1	no	—
97	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
98	#107	—	38	1	no	—
99	#107	—	38	1	no	—
100	C₄⋊C₈	—	19	1	no	—
101	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
102	#103	—	38	2	no	—
103	#103	—	38	1	no	—
104	#103	—	38	1	no	—
105	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
106	C₁₉	#1636	1	1	yes	characteristic, complemented, Sylow
107	C₂×Q₈	—	19	1	no	—
108	C₂×Q₈	—	38	1	no	—
109	C₂×Q₈	—	38	1	no	—
110	C₂×Q₈	D₇₆	1	1	yes	characteristic
111	C₂×C₈	—	2	1	no	—
112	C₂×C₈	—	2	1	no	—
113	C₂×C₈	—	38	1	no	—
114	C₄⋊C₄	—	2	1	no	—
115	C₄⋊C₄	—	19	2	no	—
116	C₄⋊C₄	—	19	1	no	—
117	C₄⋊C₄	—	38	2	no	—
118	C₄⋊C₄	—	38	2	no	—
119	C₄⋊C₄	—	38	2	no	—
120	C₄⋊C₄	—	38	1	no	—
121	C₄⋊C₄	—	38	1	no	—
122	C₄⋊C₄	—	38	1	no	—
123	C₄⋊C₄	—	38	1	no	—
124	C₄⋊C₄	D₇₆	1	1	yes	characteristic
125	C₄²	—	2	1	no	—
126	C₄²	—	38	2	no	—
127	C₄²	—	38	1	no	—
128	C₄²	C₂²×D₁₉	1	1	yes	characteristic
129	Q₈	—	2	1	no	—
130	Q₈	—	38	1	no	—
131	Q₈	—	38	1	no	—
132	Q₈	—	76	2	no	—
133	Q₈	—	76	1	no	—
134	Q₈	—	76	1	no	—
135	Q₈	Dic₇₆	1	2	yes	—
136	C₂×C₄	—	2	1	no	—
137	C₂×C₄	—	2	1	no	—
138	C₂×C₄	—	38	1	no	—
139	C₂×C₄	—	38	2	no	—
140	C₂×C₄	—	38	1	no	—
141	C₂×C₄	—	76	1	no	—
142	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
143	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
144	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
145	C₈	—	4	1	no	—
146	C₈	—	4	1	no	—
147	C₈	—	76	1	no	—
148	C₂²	#10597328	1	1	yes	characteristic
149	C₄	—	2	2	no	—
150	C₄	—	2	1	no	—
151	C₄	—	4	1	no	—
152	C₄	—	76	1	no	—
153	C₄	—	76	2	no	—
154	C₄	—	76	1	no	—
155	C₄	—	152	1	no	—
156	C₄	C₂×Dic₇₆	1	1	yes	characteristic
157	C₄	#10597355	1	1	yes	characteristic
158	C₄	#10597362	1	1	yes	characteristic
159	C₄	#10597364	1	1	yes	characteristic
160	C₂	#11926702	1	1	yes	characteristic
161	C₂	#11926709	1	1	yes	characteristic
162	C₂	#11926718	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927273

C₂

yes

maximal, characteristic

#11926895

C₂

yes

maximal, characteristic

#11926840

C₂

yes

maximal, characteristic

#11926839

C₂

yes

maximal, characteristic

#11926291

C₂

yes

maximal, characteristic

#11926276

C₂

yes

maximal, characteristic

C₁₉×Q₈⋊C₈

C₂

yes

maximal, characteristic

C₄×Q₈×C₁₉

C₂²

yes

characteristic

Q₈×Dic₁₉

—

—

—

—

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

—

—

—

—

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×Q₈×C₁₉

D₄

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

C₄⋊Dic₁₉

D₄

yes

characteristic

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

Q₈×C₁₉

—

Q₈×C₁₉

Q₁₆

yes

—

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

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

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

—

—

—

—

—

—

Q₈⋊C₈

—

Q₈⋊C₈

D₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

#125

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

C₂×D₁₉

yes

characteristic

#107

—

#107

—

100

C₄⋊C₈

—

101

C₄⋊C₈

C₂×D₁₉

yes

characteristic

102

#103

—

103

#103

—

104

#103

—

105

C₄×C₈

C₂×D₁₉

yes

characteristic

106

C₁₉

#1636

yes

characteristic, complemented, Sylow

107

C₂×Q₈

—

108

C₂×Q₈

—

109

C₂×Q₈

—

110

C₂×Q₈

D₇₆

yes

characteristic

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₄⋊C₄

D₇₆

yes

characteristic

125

C₄²

—

126

C₄²

—

127

C₄²

—

128

C₄²

C₂²×D₁₉

yes

characteristic

129

Q₈

—

130

Q₈

—

131

Q₈

—

132

Q₈

—

133

Q₈

—

134

Q₈

—

135

Q₈

Dic₇₆

yes

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

C₂×D₇₆

yes

characteristic

143

C₂×C₄

D₄×D₁₉

yes

characteristic

144

C₂×C₄

D₄×D₁₉

yes

characteristic

145

C₈

—

146

C₈

—

147

C₈

—

148

C₂²

#10597328

yes

characteristic

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

152

—

156

C₄

C₂×Dic₇₆

yes

characteristic

157

C₄

#10597355

yes

characteristic

158

C₄

#10597362

yes

characteristic

159

C₄

#10597364

yes

characteristic

160

C₂

#11926702

yes

characteristic

161

C₂

#11926709

yes

characteristic

162

C₂

#11926718

yes

characteristic

	subgroup	G/H
center	C₂²	#10597328
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×Q₈⋊C₈	C₂
socle, prime radical	C₂²×C₁₉	#120
hypercenter	Q₈⋊C₈	D₁₉
hypocenter	C₁₉	#1636
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ Q₈⋊C₈

subgroup

G/H

center

C₂²

#10597328

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×Q₈⋊C₈

C₂

socle, prime radical

C₂²×C₁₉

#120

hypercenter

Q₈⋊C₈

D₁₉

hypocenter

C₁₉

#1636

LCS

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ Q₈⋊C₈

N	H ≅ G/N	type
106. C₁₉	#1636	semidirect

H ≅ G/N

type

106. C₁₉

#1636

semidirect

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

subgroup	index
#11927273	2
#11926895	2
#11926840	2
#11926839	2
#11926291	2
#11926276	2
C₁₉×Q₈⋊C₈	2
#1636	19

subgroup

index

C₁₉×Q₈⋊C₈

Subgroups — #14562796

Conjugacy classes of subgroups

Complements

Maximal subgroups