Group #14562611 — subgroups

Subgroups — #14562611

Order 2432.

238 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 53 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	#11927175	C₂	1	1	yes	maximal, characteristic
2	#11926702	C₂	1	2	yes	maximal
3	#11926464	C₂	1	1	yes	maximal, characteristic
4	#11926282	C₂	1	2	yes	maximal
5	C₁₉×#324	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
8	#10597372	—	2	1	no	—
9	#10597370	—	2	1	no	—
10	#10597370	C₂²	1	2	yes	—
11	C₂×Dic₁₉⋊C₄	—	2	1	no	—
12	C₂×Dic₇₆	—	2	2	no	—
13	#10597336	—	2	2	no	—
14	#10597334	—	2	2	no	—
15	C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
16	C₁₉⋊#95	—	2	1	no	—
17	C₁₉⋊#95	C₂²	1	1	yes	characteristic
18	#10597273	—	2	2	no	—
19	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂²×Dic₁₉	—	2	1	no	—
23	C₂²×Dic₁₉	—	2	1	no	—
24	C₂×Dic₃₈	—	2	2	no	—
25	C₂×Dic₃₈	—	2	1	no	—
26	C₂×Dic₃₈	—	4	2	no	—
27	C₂×Dic₃₈	D₄	1	2	yes	—
28	C₂×C₈×C₁₉	—	2	2	no	—
29	C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₂²⋊Dic₁₉	—	2	2	no	—
31	C₄⋊Dic₁₉	—	2	1	no	—
32	C₄⋊Dic₁₉	—	2	1	no	—
33	C₄⋊Dic₁₉	—	2	1	no	—
34	C₄⋊Dic₁₉	D₄	1	2	yes	—
35	Dic₁₉⋊C₄	—	2	2	no	—
36	Dic₁₉⋊C₄	—	2	2	no	—
37	Dic₁₉⋊C₄	—	4	2	no	—
38	C₄×Dic₁₉	—	2	2	no	—
39	Dic₇₆	—	4	4	no	—
40	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₁₉	—	2	1	no	—
42	C₂×C₄×C₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	4	1	no	—
45	C₂×C₄×C₁₉	—	4	1	no	—
46	C₂×C₄×C₁₉	Q₁₆	1	2	yes	complemented
47	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
48	C₂×Dic₁₉	—	2	2	no	—
49	C₂×Dic₁₉	—	2	2	no	—
50	C₂×Dic₁₉	—	2	2	no	—
51	C₂×Dic₁₉	—	2	2	no	—
52	C₂×Dic₁₉	—	4	1	no	—
53	C₂×Dic₁₉	—	4	1	no	—
54	C₂×Dic₁₉	—	4	1	no	—
55	C₂×Dic₁₉	—	4	1	no	—
56	Dic₃₈	—	2	4	no	—
57	Dic₃₈	—	4	2	no	—
58	Dic₃₈	—	4	2	no	—
59	Dic₃₈	—	8	1	no	—
60	C₈×C₁₉	—	4	2	no	—
61	#1605	—	19	1	no	maximal, Sylow
62	C₂²×C₁₉	—	2	1	no	—
63	C₂²×C₁₉	—	2	1	no	—
64	C₂²×C₁₉	#120	1	1	yes	characteristic
65	C₂²×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
66	C₂²×C₁₉	#137	1	1	yes	characteristic
67	C₄×C₁₉	—	2	2	no	—
68	C₄×C₁₉	—	2	2	no	—
69	C₄×C₁₉	—	4	1	no	—
70	Dic₁₉	—	4	2	no	—
71	Dic₁₉	—	4	2	no	—
72	Dic₁₉	—	4	2	no	—
73	Dic₁₉	—	4	2	no	—
74	#544	—	19	1	no	—
75	#451	—	19	2	no	—
76	#395	—	19	1	no	—
77	#328	—	19	2	no	—
78	#324	D₁₉	1	1	yes	characteristic
79	C₂×C₁₉	—	2	1	no	—
80	C₂×C₁₉	—	2	1	no	—
81	C₂×C₁₉	#451	1	1	yes	characteristic
82	C₂×C₁₉	#456	1	1	yes	characteristic
83	C₂×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
84	C₂²×Q₈	—	19	1	no	—
85	C₂×Q₁₆	—	38	2	no	—
86	C₄⋊Q₈	—	38	2	no	—
87	#125	—	38	2	no	—
88	C₂²⋊Q₈	—	19	2	no	—
89	C₂²⋊Q₈	—	38	1	no	—
90	#117	—	38	1	no	—
91	C₂×C₄⋊C₄	—	38	1	no	—
92	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
93	#103	—	38	2	no	—
94	C₂²⋊C₈	C₂×D₁₉	1	2	yes	—
95	#95	—	19	1	no	—
96	#95	—	38	1	no	—
97	C₁₉	#1605	1	1	yes	characteristic, complemented, Sylow
98	C₂×Q₈	—	19	2	no	—
99	C₂×Q₈	—	38	1	no	—
100	C₂×Q₈	—	38	2	no	—
101	C₂×Q₈	—	76	2	no	—
102	C₂²×C₄	—	38	1	no	—
103	C₂²×C₄	—	38	1	no	—
104	C₂²×C₄	D₇₆	1	1	yes	characteristic
105	C₂²×C₄	D₇₆	1	1	yes	characteristic
106	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
107	Q₁₆	—	76	4	no	—
108	C₂×C₈	—	2	2	no	—
109	C₄⋊C₄	—	2	2	no	—
110	C₄⋊C₄	—	19	2	no	—
111	C₄⋊C₄	—	38	2	no	—
112	C₄⋊C₄	—	38	1	no	—
113	C₄⋊C₄	—	38	1	no	—
114	C₄⋊C₄	—	38	1	no	—
115	C₄⋊C₄	—	38	2	no	—
116	C₄⋊C₄	—	76	2	no	—
117	C₂²⋊C₄	—	38	2	no	—
118	C₄²	—	38	2	no	—
119	C₂³	C₂×D₇₆	1	1	yes	characteristic
120	Q₈	—	38	4	no	—
121	Q₈	—	76	2	no	—
122	Q₈	—	76	2	no	—
123	Q₈	—	152	1	no	—
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	2	1	no	—
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	—	4	1	no	—
128	C₂×C₄	—	4	1	no	—
129	C₂×C₄	—	38	2	no	—
130	C₂×C₄	—	38	2	no	—
131	C₂×C₄	—	38	2	no	—
132	C₂×C₄	—	38	2	no	—
133	C₂×C₄	—	76	1	no	—
134	C₂×C₄	—	76	1	no	—
135	C₂×C₄	—	76	1	no	—
136	C₂×C₄	—	76	1	no	—
137	C₂×C₄	Dic₇₆	1	2	yes	complemented
138	C₂×C₄	D₄×D₁₉	1	2	yes	—
139	C₈	—	4	2	no	—
140	C₂²	—	2	1	no	—
141	C₂²	—	2	1	no	—
142	C₂²	#10597328	1	1	yes	characteristic
143	C₂²	C₂×Dic₇₆	1	1	yes	characteristic
144	C₂²	#10597355	1	1	yes	characteristic
145	C₄	—	2	2	no	—
146	C₄	—	2	2	no	—
147	C₄	—	4	1	no	—
148	C₄	—	76	2	no	—
149	C₄	—	76	2	no	—
150	C₄	—	76	2	no	—
151	C₄	—	76	2	no	—
152	C₂	—	2	1	no	—
153	C₂	—	2	1	no	—
154	C₂	#11926702	1	1	yes	characteristic
155	C₂	#11926729	1	1	yes	characteristic
156	C₂	#11926732	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927175

C₂

yes

maximal, characteristic

#11926702

C₂

yes

maximal

#11926464

C₂

yes

maximal, characteristic

#11926282

C₂

yes

maximal

C₁₉×#324

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

—

C₂²

yes

—

C₂×Dic₁₉⋊C₄

—

C₂×Dic₇₆

—

#10597336

—

#10597334

—

C₁₉×C₂²⋊C₈

C₂²

yes

—

C₁₉⋊#95

—

C₁₉⋊#95

C₂²

yes

characteristic

#10597273

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

Dic₇₆

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

Q₁₆

yes

complemented

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

#1605

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#120

yes

characteristic

C₂²×C₁₉

C₂×Q₁₆

yes

characteristic

C₂²×C₁₉

#137

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

—

C₂×Q₁₆

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

#103

—

C₂²⋊C₈

C₂×D₁₉

yes

—

#95

—

#95

—

C₁₉

#1605

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

100

C₂×Q₈

—

101

C₂×Q₈

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

D₇₆

yes

characteristic

105

C₂²×C₄

D₇₆

yes

characteristic

106

C₂²×C₄

C₂²×D₁₉

yes

characteristic

107

Q₁₆

—

108

C₂×C₈

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₂²⋊C₄

—

118

C₄²

—

119

C₂³

C₂×D₇₆

yes

characteristic

120

Q₈

—

121

Q₈

—

122

Q₈

—

123

Q₈

—

152

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

Dic₇₆

yes

complemented

138

C₂×C₄

D₄×D₁₉

yes

—

139

C₈

—

140

C₂²

—

141

C₂²

—

142

C₂²

#10597328

yes

characteristic

143

C₂²

C₂×Dic₇₆

yes

characteristic

144

C₂²

#10597355

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₂

—

153

C₂

—

154

C₂

#11926702

yes

characteristic

155

C₂

#11926729

yes

characteristic

156

C₂

#11926732

yes

characteristic

	subgroup	G/H
center	C₂²	#10597328
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#324	C₂
socle	C₂²×C₁₉	#120
prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#324	D₁₉
hypocenter	C₁₉	#1605
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #324

subgroup

G/H

center

C₂²

#10597328

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#324

C₂

socle

C₂²×C₁₉

#120

prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #324

N	H ≅ G/N	type
46. C₂×C₄×C₁₉	Q₁₆	semidirect
97. C₁₉	#1605	semidirect
137. C₂×C₄	Dic₇₆	semidirect

H ≅ G/N

type

46. C₂×C₄×C₁₉

Q₁₆

semidirect

97. C₁₉

#1605

semidirect

137. C₂×C₄

Dic₇₆

semidirect

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

subgroup	index
#11927175	2
#11926702	2
#11926464	2
#11926282	2
C₁₉×#324	2
#1605	19

subgroup

index

C₁₉×#324

Subgroups — #14562611

Conjugacy classes of subgroups

Complements

Maximal subgroups