Group #14571707 — subgroups

Subgroups — #14571707

Order 2432.

456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 133 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	C₂×#10597322	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926477	C₂	1	3	yes	maximal, complemented
3	#11926467	C₂	1	3	yes	maximal, complemented
4	#11926466	C₂	1	3	yes	maximal, complemented
5	#11926460	C₂	1	3	yes	maximal
6	#11926414	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#126	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#126	—	2	4	no	—
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
11	C₂×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Dic₁₉	C₂²	1	3	yes	—
14	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	3	yes	—
15	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	3	yes	—
16	C₂×C₄⋊Dic₁₉	C₂²	1	3	yes	—
17	C₂×C₄⋊Dic₁₉	C₂²	1	3	yes	—
18	C₂×Dic₁₉⋊C₄	C₂²	1	3	yes	—
19	C₂×Dic₁₉⋊C₄	C₂²	1	3	yes	—
20	#10597322	—	2	4	no	—
21	C₁₉⋊#95	C₂²	1	3	yes	—
22	C₁₉⋊#95	C₂²	1	3	yes	—
23	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
24	C₂³×D₁₉	C₂³	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
27	C₂×C₂²⋊D₁₉	—	4	3	no	—
28	C₂²×Dic₁₉	C₂³	1	3	yes	—
29	C₂²×Dic₁₉	C₂³	1	3	yes	—
30	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
31	C₄⋊C₄×C₁₉	—	2	6	no	—
32	C₂²⋊C₄×C₁₉	—	2	6	no	—
33	C₄²×C₁₉	D₄	1	4	yes	complemented
34	C₂²⋊Dic₁₉	—	4	3	no	—
35	(C₂×D₁₉)⋊C₄	—	2	6	no	—
36	(C₂×D₁₉)⋊C₄	—	4	3	no	—
37	C₄⋊Dic₁₉	—	4	3	no	—
38	C₄⋊Dic₁₉	—	4	3	no	—
39	Dic₁₉⋊C₄	—	2	6	no	—
40	Dic₁₉⋊C₄	—	4	3	no	—
41	C₂³×C₁₉	—	2	1	no	—
42	C₂³×C₁₉	—	2	3	no	—
43	C₂³×C₁₉	—	2	3	no	—
44	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
45	C₂²×D₁₉	—	2	1	no	—
46	C₂²×D₁₉	—	2	3	no	—
47	C₂²×D₁₉	—	2	3	no	—
48	C₂×C₄×C₁₉	—	2	3	no	—
49	C₂×C₄×C₁₉	—	2	3	no	—
50	C₂×C₄×C₁₉	—	2	3	no	—
51	C₂×C₄×C₁₉	—	2	3	no	—
52	C₂×C₄×C₁₉	—	2	3	no	—
53	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
54	C₂²⋊D₁₉	—	4	4	no	—
55	C₂×Dic₁₉	—	2	3	no	—
56	C₂×Dic₁₉	—	2	3	no	—
57	C₂×Dic₁₉	—	2	3	no	—
58	C₂×Dic₁₉	—	2	3	no	—
59	C₂×Dic₁₉	—	2	3	no	—
60	C₂×Dic₁₉	—	2	3	no	—
61	C₂×Dic₁₉	—	2	3	no	—
62	#2823	—	19	1	no	maximal, Sylow
63	C₂²×C₁₉	—	4	3	no	—
64	C₂²×C₁₉	—	4	1	no	—
65	C₂²×C₁₉	—	4	3	no	—
66	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
67	C₂²×C₁₉	H(5,𝔽₂)	1	3	yes	—
68	C₂²×C₁₉	2₋¹⁺⁴	1	3	yes	—
69	C₂×D₁₉	—	4	3	no	—
70	C₂×D₁₉	—	4	1	no	—
71	C₂×D₁₉	—	4	3	no	—
72	C₄×C₁₉	—	2	6	no	—
73	C₄×C₁₉	—	4	3	no	—
74	Dic₁₉	—	4	3	no	—
75	Dic₁₉	—	4	3	no	—
76	Dic₁₉	—	4	1	no	—
77	C₂×#126	—	19	1	no	—
78	C₂×#126	D₁₉	1	1	yes	characteristic, complemented
79	#398	—	19	3	no	—
80	#396	—	19	3	no	—
81	#396	—	19	3	no	—
82	#394	—	19	3	no	—
83	#384	—	19	1	no	—
84	C₂×C₁₉	—	8	1	no	—
85	C₂×C₁₉	#537	1	3	yes	—
86	C₂×C₁₉	#560	1	1	yes	characteristic
87	C₂×C₁₉	#563	1	3	yes	—
88	D₁₉	—	8	1	no	—
89	C₂²×D₄	—	19	1	no	—
90	#126	—	2	4	no	—
91	#126	—	38	4	no	—
92	C₂×C₄⋊C₄	—	19	3	no	—
93	C₂×C₄⋊C₄	—	19	3	no	—
94	C₂×C₄⋊C₄	—	19	3	no	—
95	C₂×C₄⋊C₄	—	19	3	no	—
96	C₂×C₄⋊C₄	C₂×D₁₉	1	3	yes	—
97	C₂×C₂²⋊C₄	—	19	3	no	—
98	C₂×C₂²⋊C₄	—	19	3	no	—
99	C₂×C₂²⋊C₄	—	19	3	no	—
100	C₂×C₂²⋊C₄	C₂×D₁₉	1	3	yes	—
101	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
102	#95	—	19	3	no	—
103	#95	—	19	3	no	—
104	C₁₉	#2823	1	1	yes	characteristic, complemented, Sylow
105	C₂⁴	—	19	1	no	—
106	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
107	C₂×D₄	—	76	3	no	—
108	C₂²×C₄	—	19	1	no	—
109	C₂²×C₄	—	19	3	no	—
110	C₂²×C₄	—	19	3	no	—
111	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
112	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
113	C₄⋊C₄	—	2	6	no	—
114	C₄⋊C₄	—	38	6	no	—
115	C₄⋊C₄	—	76	3	no	—
116	C₄⋊C₄	—	76	3	no	—
117	C₄⋊C₄	—	76	3	no	—
118	C₂²⋊C₄	—	2	6	no	—
119	C₂²⋊C₄	—	38	6	no	—
120	C₂²⋊C₄	—	76	3	no	—
121	C₂²⋊C₄	—	76	3	no	—
122	C₄²	C₂²⋊D₁₉	1	4	yes	complemented
123	C₂³	—	2	3	no	—
124	C₂³	—	2	3	no	—
125	C₂³	—	2	1	no	—
126	C₂³	—	38	3	no	—
127	C₂³	—	38	3	no	—
128	C₂³	—	38	1	no	—
129	C₂³	C₂³×D₁₉	1	1	yes	characteristic
130	D₄	—	76	4	no	—
131	C₂×C₄	—	2	3	no	—
132	C₂×C₄	—	2	3	no	—
133	C₂×C₄	—	2	3	no	—
134	C₂×C₄	—	2	3	no	—
135	C₂×C₄	—	2	3	no	—
136	C₂×C₄	—	38	3	no	—
137	C₂×C₄	—	38	3	no	—
138	C₂×C₄	—	38	3	no	—
139	C₂×C₄	—	38	3	no	—
140	C₂×C₄	—	38	3	no	—
141	C₂×C₄	—	38	3	no	—
142	C₂×C₄	—	38	3	no	—
143	C₂×C₄	C₂×C₂²⋊D₁₉	1	6	yes	—
144	C₂²	—	4	3	no	—
145	C₂²	—	4	3	no	—
146	C₂²	—	4	1	no	—
147	C₂²	—	76	3	no	—
148	C₂²	—	76	3	no	—
149	C₂²	—	76	1	no	—
150	C₂²	#10597435	1	3	yes	—
151	C₂²	#10597436	1	3	yes	—
152	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
153	C₄	—	2	6	no	—
154	C₄	—	4	3	no	—
155	C₄	—	76	3	no	—
156	C₄	—	76	1	no	—
157	C₄	—	76	3	no	—
158	C₂	—	8	1	no	—
159	C₂	—	152	1	no	—
160	C₂	#11927122	1	3	yes	—
161	C₂	#11927285	1	1	yes	characteristic
162	C₂	#11927296	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597322

C₂

yes

maximal, characteristic, complemented

#11926477

C₂

yes

maximal, complemented

#11926467

C₂

yes

maximal, complemented

#11926466

C₂

yes

maximal, complemented

#11926460

C₂

yes

maximal

#11926414

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#126

C₂

yes

maximal, characteristic, complemented

C₂²×C₂²⋊D₁₉

C₂²

yes

characteristic

C₁₉×#126

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

#10597322

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂³×D₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

complemented

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#2823

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×#126

—

C₂×#126

D₁₉

yes

characteristic, complemented

—

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

#537

yes

—

C₂×C₁₉

#560

yes

characteristic

C₂×C₁₉

#563

yes

—

D₁₉

—

C₂²×D₄

—

#126

—

#126

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

100

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

101

C₂×C₄²

C₂×D₁₉

yes

characteristic

102

#95

—

103

#95

—

104

C₁₉

#2823

yes

characteristic, complemented, Sylow

105

C₂⁴

—

106

C₂⁴

C₂²×D₁₉

yes

characteristic

107

C₂×D₄

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

C₂²×D₁₉

yes

—

112

C₂²×C₄

C₂²×D₁₉

yes

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₂²⋊C₄

—

119

C₂²⋊C₄

—

120

C₂²⋊C₄

—

121

C₂²⋊C₄

—

122

C₄²

C₂²⋊D₁₉

yes

complemented

123

C₂³

—

124

C₂³

—

125

C₂³

—

126

C₂³

—

127

C₂³

—

128

C₂³

—

129

C₂³

C₂³×D₁₉

yes

characteristic

130

D₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

#10597435

yes

—

151

C₂²

#10597436

yes

—

152

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

—

158

C₂

—

159

C₂

—

152

—

160

C₂

#11927122

yes

—

161

C₂

#11927285

yes

characteristic

162

C₂

#11927296

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₁₉×#126	C₂
prime radical	C₂²×C₂²⋊D₁₉	C₂²
hypercenter	C₂×#126	D₁₉
hypocenter	C₁₉	#2823
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×#126

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂×C₁₉×#126

C₂

prime radical

C₂²×C₂²⋊D₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×#126

N	H ≅ G/N	type
1. C₂×#10597322	C₂	semidirect
2. #11926477	C₂	semidirect
3. #11926467	C₂	semidirect
4. #11926466	C₂	semidirect
6. #11926414	C₂	semidirect
7. C₂×C₁₉×#126	C₂	semidirect
33. C₄²×C₁₉	D₄	semidirect
78. C₂×#126	D₁₉	semidirect
104. C₁₉	#2823	semidirect
122. C₄²	C₂²⋊D₁₉	semidirect

H ≅ G/N

type

1. C₂×#10597322

C₂

semidirect

2. #11926477

C₂

semidirect

3. #11926467

C₂

semidirect

4. #11926466

C₂

semidirect

6. #11926414

C₂

semidirect

7. C₂×C₁₉×#126

C₂

semidirect

33. C₄²×C₁₉

D₄

semidirect

78. C₂×#126

D₁₉

semidirect

104. C₁₉

#2823

semidirect

122. C₄²

C₂²⋊D₁₉

semidirect

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

subgroup	index
C₂×#10597322	2
#11926477	2
#11926467	2
#11926466	2
#11926460	2
#11926414	2
C₂×C₁₉×#126	2
#2823	19

subgroup

index

C₂×C₁₉×#126

Subgroups — #14571707

Conjugacy classes of subgroups

Complements

Maximal subgroups