Group #14574024 — subgroups

Subgroups — #14574024

Order 2432.

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

normal subgroups only

This group has 400 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×#10597321	C₂	1	1	yes	maximal, characteristic
2	#11926906	C₂	1	4	yes	maximal, complemented
3	#11926901	C₂	1	4	yes	maximal, complemented
4	#11926552	C₂	1	2	yes	maximal, complemented
5	#11926548	C₂	1	2	yes	maximal
6	C₄×#64520	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₇₆	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
10	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
11	C₁₉×#125	C₂²	1	2	yes	complemented
12	C₁₉×C₂²⋊Q₈	—	2	2	no	—
13	C₄×Q₈×C₁₉	—	2	2	no	—
14	C₁₉×#117	C₂²	1	2	yes	—
15	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
17	C₂×#64520	C₂²	1	2	yes	—
18	#10597321	—	2	2	no	—
19	#10597321	C₂²	1	2	yes	—
20	#10597321	C₂²	1	2	yes	—
21	#10597267	C₂²	1	8	yes	complemented
22	#10597266	C₂²	1	8	yes	—
23	#10597260	C₂²	1	2	yes	complemented
24	C₄×C₁₉⋊C₈	C₂²	1	2	yes	complemented
25	C₂³×D₁₉	—	2	1	no	—
26	C₂×Q₈×C₁₉	—	2	2	no	—
27	C₂²×C₄×C₁₉	D₄	1	2	yes	—
28	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×Dic₁₉	—	2	1	no	—
30	C₂×D₇₆	—	2	4	no	—
31	C₂×D₇₆	—	2	1	no	—
32	C₂×D₇₆	C₂³	1	2	yes	—
33	C₂×Dic₃₈	—	2	4	no	—
34	C₂×Dic₃₈	—	2	1	no	—
35	C₂×Dic₃₈	C₂³	1	2	yes	—
36	C₄⋊C₄×C₁₉	—	2	4	no	—
37	C₄⋊C₄×C₁₉	—	2	2	no	—
38	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
39	C₂²⋊C₄×C₁₉	—	2	2	no	—
40	C₄²×C₁₉	—	2	2	no	—
41	C₄²×C₁₉	D₄	1	2	yes	—
42	C₄²×C₁₉	C₂³	1	1	yes	characteristic
43	C₄²×C₁₉	C₂³	1	1	yes	characteristic
44	(C₂×D₁₉)⋊C₄	—	2	4	no	—
45	(C₂×D₁₉)⋊C₄	—	2	4	no	—
46	#64520	—	2	4	no	—
47	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
48	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×D₁₉	—	2	2	no	—
50	C₂²×D₁₉	—	4	4	no	—
51	C₂²×D₁₉	—	4	2	no	—
52	Q₈×C₁₉	—	4	4	no	—
53	C₂×C₄×C₁₉	—	2	4	no	—
54	C₂×C₄×C₁₉	—	4	2	no	—
55	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
56	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
57	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#41	1	4	yes	—
59	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
60	C₂×Dic₁₉	—	2	2	no	—
61	C₂×Dic₁₉	—	4	2	no	—
62	D₇₆	—	2	4	no	—
63	D₇₆	—	4	2	no	—
64	Dic₃₈	—	2	4	no	—
65	Dic₃₈	—	4	2	no	—
66	C₁₉⋊C₈	—	2	4	no	—
67	#3140	—	19	1	no	maximal, Sylow
68	C₂²×C₁₉	—	2	2	no	—
69	C₂²×C₁₉	#124	1	2	yes	—
70	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
71	C₂×D₁₉	—	4	2	no	—
72	C₂×D₁₉	—	4	4	no	—
73	C₂×D₁₉	—	8	4	no	—
74	C₄×C₁₉	—	2	2	no	—
75	C₄×C₁₉	—	2	2	no	—
76	C₄×C₁₉	—	4	4	no	—
77	C₄×C₁₉	#124	1	2	yes	—
78	C₄×C₁₉	C₂×#41	1	2	yes	—
79	Dic₁₉	—	4	2	no	—
80	#533	D₁₉	1	1	yes	characteristic, complemented
81	C₂×#124	—	19	1	no	—
82	#489	—	19	4	no	—
83	#488	—	19	4	no	—
84	#419	—	19	2	no	—
85	#418	—	19	2	no	—
86	C₄×M₁₆	—	19	1	no	—
87	C₂×C₁₉	—	2	2	no	—
88	C₂×C₁₉	C₂×#124	1	1	yes	characteristic
89	C₂×C₁₉	#575	1	2	yes	—
90	D₁₉	—	8	2	no	—
91	C₂²×Q₈	—	19	1	no	—
92	C₂²×D₄	—	19	1	no	—
93	C₂×M₁₆	—	19	2	no	—
94	C₄⋊Q₈	C₂×D₁₉	1	2	yes	complemented
95	#125	C₂×D₁₉	1	2	yes	complemented
96	#124	—	19	2	no	—
97	#124	—	19	2	no	—
98	#124	—	38	2	no	—
99	C₂²⋊Q₈	—	2	2	no	—
100	C₄×Q₈	—	2	2	no	—
101	#117	C₂×D₁₉	1	2	yes	—
102	C₂×C₂²⋊C₄	—	38	2	no	—
103	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
104	#103	—	19	8	no	—
105	#102	—	19	8	no	—
106	#97	—	19	2	no	—
107	C₄×C₈	—	19	2	no	—
108	C₁₉	#3140	1	1	yes	characteristic, complemented, Sylow
109	C₂⁴	—	38	1	no	—
110	C₂×Q₈	—	2	2	no	—
111	C₂×Q₈	—	19	2	no	—
112	C₂×Q₈	—	38	1	no	—
113	C₂×Q₈	—	38	4	no	—
114	C₂×D₄	—	19	2	no	—
115	C₂×D₄	—	38	4	no	—
116	C₂×D₄	—	38	1	no	—
117	C₂²×C₄	—	38	1	no	—
118	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
119	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
120	M₁₆	—	38	4	no	—
121	C₂×C₈	—	19	4	no	—
122	C₄⋊C₄	—	2	4	no	—
123	C₄⋊C₄	—	2	2	no	—
124	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
125	C₂²⋊C₄	—	2	2	no	—
126	C₂²⋊C₄	—	38	4	no	—
127	C₂²⋊C₄	—	38	4	no	—
128	C₄²	—	2	2	no	—
129	C₄²	C₂²⋊D₁₉	1	2	yes	—
130	C₄²	C₂²×D₁₉	1	1	yes	characteristic
131	C₄²	C₂²×D₁₉	1	1	yes	characteristic
132	C₂³	—	38	2	no	—
133	C₂³	—	76	4	no	—
134	C₂³	—	76	2	no	—
135	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
136	Q₈	—	4	4	no	—
137	Q₈	—	38	4	no	—
138	Q₈	—	76	2	no	—
139	D₄	—	38	4	no	—
140	D₄	—	76	2	no	—
141	C₂×C₄	—	2	4	no	—
142	C₂×C₄	—	4	2	no	—
143	C₂×C₄	—	38	2	no	—
144	C₂×C₄	—	76	2	no	—
145	C₂×C₄	#64545	1	4	yes	—
146	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
147	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
148	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
149	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
150	C₈	—	38	4	no	—
151	C₂²	—	2	2	no	—
152	C₂²	—	76	2	no	—
153	C₂²	—	76	4	no	—
154	C₂²	—	152	4	no	—
155	C₂²	#10597393	1	2	yes	—
156	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
157	C₄	—	2	2	no	—
158	C₄	—	2	2	no	—
159	C₄	—	4	4	no	—
160	C₄	—	76	2	no	—
161	C₄	#10597393	1	2	yes	—
162	C₄	C₂×#64545	1	2	yes	—
163	C₂	—	2	2	no	—
164	C₂	—	152	2	no	—
165	C₂	C₂×#10597393	1	1	yes	characteristic
166	C₂	#11927342	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597321

C₂

yes

maximal, characteristic

#11926906

C₂

yes

maximal, complemented

#11926901

C₂

yes

maximal, complemented

#11926552

C₂

yes

maximal, complemented

#11926548

C₂

yes

maximal

C₄×#64520

C₂

yes

maximal, characteristic, complemented

C₁₉×#533

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

complemented

C₁₉×#125

C₂²

yes

complemented

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

—

C₂×#64520

C₂²

yes

—

#10597321

—

#10597321

C₂²

yes

—

#10597321

C₂²

yes

—

#10597267

C₂²

yes

complemented

#10597266

C₂²

yes

—

#10597260

C₂²

yes

complemented

C₄×C₁₉⋊C₈

C₂²

yes

complemented

C₂³×D₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

#64520

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

Dic₃₈

—

Dic₃₈

—

C₁₉⋊C₈

—

#3140

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

#124

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#124

yes

—

C₄×C₁₉

C₂×#41

yes

—

Dic₁₉

—

#533

D₁₉

yes

characteristic, complemented

—

—

—

—

—

C₄×M₁₆

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#124

yes

characteristic

C₂×C₁₉

#575

yes

—

D₁₉

—

C₂²×Q₈

—

C₂²×D₄

—

C₂×M₁₆

—

C₄⋊Q₈

C₂×D₁₉

yes

complemented

#125

C₂×D₁₉

yes

—

—

—

C₂²⋊Q₈

—

100

C₄×Q₈

—

101

#117

C₂×D₁₉

yes

—

102

C₂×C₂²⋊C₄

—

103

C₂×C₄²

C₂×D₁₉

yes

characteristic

104

#103

—

105

#102

—

106

#97

—

107

C₄×C₈

—

108

C₁₉

#3140

yes

characteristic, complemented, Sylow

109

C₂⁴

—

110

C₂×Q₈

—

111

C₂×Q₈

—

112

C₂×Q₈

—

113

C₂×Q₈

—

114

C₂×D₄

—

115

C₂×D₄

—

116

C₂×D₄

—

117

C₂²×C₄

—

118

C₂²×C₄

C₂²⋊D₁₉

yes

—

119

C₂²×C₄

C₂²×D₁₉

yes

characteristic

120

M₁₆

—

121

C₂×C₈

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₄⋊C₄

C₂²×D₁₉

yes

—

125

C₂²⋊C₄

—

126

C₂²⋊C₄

—

127

C₂²⋊C₄

—

128

C₄²

—

129

C₄²

C₂²⋊D₁₉

yes

—

130

C₄²

C₂²×D₁₉

yes

characteristic

131

C₄²

C₂²×D₁₉

yes

characteristic

132

C₂³

—

133

C₂³

—

134

C₂³

—

135

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

136

Q₈

—

137

Q₈

—

138

Q₈

—

139

D₄

—

140

D₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

#64545

yes

—

146

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

147

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

148

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

149

C₂×C₄

C₂³×D₁₉

yes

characteristic

150

C₈

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

152

—

155

C₂²

#10597393

yes

—

156

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

157

C₄

—

158

C₄

—

159

C₄

—

160

C₄

—

161

C₄

#10597393

yes

—

162

C₄

C₂×#64545

yes

—

163

C₂

—

164

C₂

—

152

—

165

C₂

C₂×#10597393

yes

characteristic

166

C₂

#11927342

yes

—

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#533	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂²×D₇₆	C₂²
hypercenter	#533	D₁₉
hypocenter	C₁₉	#3140
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #533

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#533

C₂

socle

C₂²×C₁₉

C₂²×D₄

prime radical

C₂²×D₇₆

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #533

N	H ≅ G/N	type
2. #11926906	C₂	semidirect
3. #11926901	C₂	semidirect
4. #11926552	C₂	semidirect
6. C₄×#64520	C₂	semidirect
7. C₁₉×#533	C₂	semidirect
10. C₁₉×C₄⋊Q₈	C₂²	semidirect
11. C₁₉×#125	C₂²	semidirect
21. #10597267	C₂²	semidirect
23. #10597260	C₂²	semidirect
24. C₄×C₁₉⋊C₈	C₂²	semidirect
80. #533	D₁₉	semidirect
94. C₄⋊Q₈	C₂×D₁₉	semidirect
95. #125	C₂×D₁₉	semidirect
108. C₁₉	#3140	semidirect

H ≅ G/N

type

2. #11926906

C₂

semidirect

3. #11926901

C₂

semidirect

4. #11926552

C₂

semidirect

6. C₄×#64520

C₂

semidirect

7. C₁₉×#533

C₂

semidirect

10. C₁₉×C₄⋊Q₈

C₂²

semidirect

11. C₁₉×#125

C₂²

semidirect

21. #10597267

C₂²

semidirect

23. #10597260

C₂²

semidirect

24. C₄×C₁₉⋊C₈

C₂²

semidirect

80. #533

D₁₉

semidirect

94. C₄⋊Q₈

C₂×D₁₉

semidirect

95. #125

C₂×D₁₉

semidirect

108. C₁₉

#3140

semidirect

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

subgroup	index
C₂×#10597321	2
#11926906	2
#11926901	2
#11926552	2
#11926548	2
C₄×#64520	2
C₁₉×#533	2
#3140	19

subgroup

index

C₁₉×#533

Subgroups — #14574024

Conjugacy classes of subgroups

Complements

Maximal subgroups