Group #14574435 — subgroups

Subgroups — #14574435

Order 2432.

514 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 125 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×#10597376	C₂	1	2	yes	maximal, complemented
2	#11926863	C₂	1	4	yes	maximal, complemented
3	#11926797	C₂	1	4	yes	maximal, complemented
4	#11926680	C₂	1	4	yes	maximal, complemented
5	C₁₉×#407	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₂²⋊D₁₉	—	2	2	no	—
8	C₂²×D₇₆	C₂²	1	2	yes	complemented
9	C₂×M₁₆×C₁₉	C₂²	1	2	yes	complemented
10	#10597376	—	2	2	no	—
11	#10597376	—	2	2	no	—
12	#10597376	C₂²	1	4	yes	—
13	#10597376	C₂²	1	4	yes	complemented
14	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
15	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	complemented
16	C₂×D₁₅₂	C₂²	1	4	yes	complemented
17	C₁₉×C₂²⋊C₈	C₂²	1	4	yes	complemented
18	#10597278	C₂²	1	8	yes	complemented
19	#10597274	C₂²	1	4	yes	complemented
20	C₂⁴×C₁₉	D₄	1	1	yes	characteristic
21	C₂³×D₁₉	—	2	2	no	—
22	C₂²×C₄×C₁₉	—	4	2	no	—
23	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	D₄	1	2	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×C₂²⋊D₁₉	—	2	4	no	—
28	C₂×C₂²⋊D₁₉	—	2	4	no	—
29	C₂×C₂²⋊D₁₉	—	4	8	no	—
30	C₂²×Dic₁₉	—	2	2	no	—
31	C₂×D₇₆	—	2	2	no	—
32	C₂×D₇₆	—	4	4	no	—
33	C₂×D₇₆	C₂³	1	4	yes	—
34	M₁₆×C₁₉	—	4	2	no	—
35	C₂×C₈×C₁₉	C₂³	1	4	yes	—
36	(C₂×D₁₉)⋊C₄	—	2	4	no	—
37	(C₂×D₁₉)⋊C₄	—	2	4	no	—
38	C₄⋊Dic₁₉	—	2	2	no	—
39	C₄⋊Dic₁₉	C₂³	1	4	yes	—
40	D₁₅₂	—	4	4	no	—
41	C₂³×C₁₉	—	2	4	no	—
42	C₂³×C₁₉	—	4	1	no	—
43	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂³×C₁₉	C₂×D₄	1	2	yes	—
45	C₂²×D₁₉	—	2	4	no	—
46	C₂²×D₁₉	—	4	4	no	—
47	C₂²×D₁₉	—	4	4	no	—
48	C₂²×D₁₉	—	4	4	no	—
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	2	4	no	—
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	—	4	2	no	—
53	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
56	C₂²⋊D₁₉	—	4	8	no	—
57	C₂²⋊D₁₉	—	4	8	no	—
58	C₂×Dic₁₉	—	2	4	no	—
59	C₂×Dic₁₉	—	4	4	no	—
60	D₇₆	—	2	8	no	—
61	D₇₆	—	4	4	no	—
62	C₈×C₁₉	—	2	4	no	—
63	#3192	—	19	1	no	maximal, Sylow
64	C₂²×C₁₉	—	2	2	no	—
65	C₂²×C₁₉	—	2	2	no	—
66	C₂²×C₁₉	—	2	1	no	—
67	C₂²×C₁₉	—	2	2	no	—
68	C₂²×C₁₉	—	4	4	no	—
69	C₂²×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
70	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
71	C₂×D₁₉	—	4	4	no	—
72	C₂×D₁₉	—	4	4	no	—
73	C₂×D₁₉	—	4	4	no	—
74	C₂×D₁₉	—	8	8	no	—
75	C₄×C₁₉	—	2	2	no	—
76	C₄×C₁₉	—	2	1	no	—
77	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
78	Dic₁₉	—	4	4	no	—
79	C₂×#121	—	19	2	no	—
80	#481	—	19	4	no	—
81	#469	—	19	4	no	—
82	#447	—	19	4	no	—
83	#407	D₁₉	1	1	yes	characteristic, complemented
84	C₂×C₁₉	—	2	4	no	—
85	C₂×C₁₉	—	4	1	no	—
86	C₂×C₁₉	#534	1	1	yes	characteristic
87	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
88	D₁₉	—	8	4	no	—
89	C₂²×D₄	—	19	2	no	—
90	C₂²×D₄	—	38	2	no	—
91	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
92	C₂×D₈	—	19	4	no	—
93	C₂×M₁₆	C₂×D₁₉	1	2	yes	complemented
94	#121	—	19	4	no	—
95	#121	—	19	4	no	—
96	#121	—	38	2	no	—
97	#121	—	38	2	no	—
98	C₂×C₄⋊C₄	—	19	2	no	—
99	C₂×C₂²⋊C₄	—	38	2	no	—
100	#106	—	19	4	no	—
101	#102	—	19	8	no	—
102	C₂²⋊C₈	C₂×D₁₉	1	4	yes	complemented
103	C₁₉	#3192	1	1	yes	characteristic, complemented, Sylow
104	C₂⁴	—	38	2	no	—
105	C₂⁴	D₇₆	1	1	yes	characteristic
106	C₂×D₄	—	19	4	no	—
107	C₂×D₄	—	38	4	no	—
108	C₂×D₄	—	38	4	no	—
109	C₂×D₄	—	38	2	no	—
110	C₂×D₄	—	76	4	no	—
111	C₂×D₄	—	76	8	no	—
112	C₂²×C₄	—	4	2	no	—
113	C₂²×C₄	—	38	2	no	—
114	C₂²×C₄	D₇₆	1	2	yes	—
115	C₂²×C₄	D₇₆	1	1	yes	characteristic
116	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
117	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
118	D₈	—	76	4	no	—
119	M₁₆	—	4	2	no	—
120	C₂×C₈	C₂²×D₁₉	1	4	yes	—
121	C₄⋊C₄	—	19	4	no	—
122	C₄⋊C₄	—	38	2	no	—
123	C₂²⋊C₄	—	38	4	no	—
124	C₂²⋊C₄	—	38	4	no	—
125	C₂³	—	2	4	no	—
126	C₂³	—	4	1	no	—
127	C₂³	—	38	4	no	—
128	C₂³	—	76	4	no	—
129	C₂³	—	76	4	no	—
130	C₂³	—	76	4	no	—
131	C₂³	C₂×D₇₆	1	1	yes	characteristic
132	C₂³	C₂×D₇₆	1	2	yes	—
133	D₄	—	38	8	no	—
134	D₄	—	76	4	no	—
135	D₄	—	76	8	no	—
136	D₄	—	76	8	no	—
137	C₂×C₄	—	2	2	no	—
138	C₂×C₄	—	2	4	no	—
139	C₂×C₄	—	4	1	no	—
140	C₂×C₄	—	4	2	no	—
141	C₂×C₄	—	38	4	no	—
142	C₂×C₄	—	76	4	no	—
143	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
144	C₂×C₄	C₂×D₇₆	1	2	yes	—
145	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
146	C₈	—	2	4	no	—
147	C₂²	—	2	2	no	—
148	C₂²	—	2	2	no	—
149	C₂²	—	2	2	no	—
150	C₂²	—	2	1	no	—
151	C₂²	—	4	4	no	—
152	C₂²	—	76	4	no	—
153	C₂²	—	76	4	no	—
154	C₂²	—	76	4	no	—
155	C₂²	—	152	8	no	—
156	C₂²	#10597354	1	4	yes	—
157	C₂²	C₂²×D₇₆	1	1	yes	characteristic
158	C₄	—	2	2	no	—
159	C₄	—	2	1	no	—
160	C₄	—	76	4	no	—
161	C₄	#10597430	1	2	yes	—
162	C₂	—	2	4	no	—
163	C₂	—	4	1	no	—
164	C₂	—	152	4	no	—
165	C₂	#11927106	1	1	yes	characteristic
166	C₂	C₂×#10597354	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597376

C₂

yes

maximal, complemented

#11926863

C₂

yes

maximal, complemented

#11926797

C₂

yes

maximal, complemented

#11926680

C₂

yes

maximal, complemented

C₁₉×#407

C₂

yes

maximal, characteristic, complemented

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂²×C₂²⋊D₁₉

—

C₂²×D₇₆

C₂²

yes

complemented

C₂×M₁₆×C₁₉

C₂²

yes

—

—

C₂²

yes

—

#10597376

C₂²

yes

complemented

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

C₂²

yes

complemented

C₂×D₁₅₂

C₂²

yes

complemented

C₁₉×C₂²⋊C₈

C₂²

yes

complemented

#10597278

C₂²

yes

complemented

#10597274

C₂²

yes

complemented

C₂⁴×C₁₉

D₄

yes

characteristic

C₂³×D₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂×C₂²⋊D₁₉

—

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂³

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

D₁₅₂

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂³×C₁₉

C₂×D₄

yes

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

#3192

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

AGL(1,ℤ/8)

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

H(5,𝔽₂)

yes

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#534

yes

characteristic

C₂×C₁₉

C₂×AGL(1,ℤ/8)

yes

—

D₁₉

—

C₂²×D₄

—

C₂²×D₄

—

C₂³×C₄

C₂×D₁₉

yes

characteristic

C₂×D₈

—

C₂×M₁₆

C₂×D₁₉

yes

—

—

—

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

100

#106

—

101

#102

—

102

C₂²⋊C₈

C₂×D₁₉

yes

complemented

103

C₁₉

#3192

yes

characteristic, complemented, Sylow

104

C₂⁴

—

105

C₂⁴

D₇₆

yes

characteristic

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂×D₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

D₇₆

yes

—

115

C₂²×C₄

D₇₆

yes

characteristic

116

C₂²×C₄

C₂²×D₁₉

yes

—

117

C₂²×C₄

C₂²×D₁₉

yes

characteristic

118

D₈

—

119

M₁₆

—

120

C₂×C₈

C₂²×D₁₉

yes

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₂²⋊C₄

—

124

C₂²⋊C₄

—

125

C₂³

—

126

C₂³

—

127

C₂³

—

128

C₂³

—

129

C₂³

—

130

C₂³

—

131

C₂³

C₂×D₇₆

yes

characteristic

132

C₂³

C₂×D₇₆

yes

—

133

D₄

—

134

D₄

—

135

D₄

—

136

D₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

C₂×D₇₆

yes

characteristic

144

C₂×C₄

C₂×D₇₆

yes

—

145

C₂×C₄

C₂³×D₁₉

yes

characteristic

146

C₈

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

152

—

156

C₂²

#10597354

yes

—

157

C₂²

C₂²×D₇₆

yes

characteristic

158

C₄

—

159

C₄

—

160

C₄

—

161

C₄

#10597430

yes

—

162

C₂

—

163

C₂

—

164

C₂

—

152

—

165

C₂

#11927106

yes

characteristic

166

C₂

C₂×#10597354

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₇₆
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#407	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	#407	D₁₉
hypocenter	C₁₉	#3192
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #407

subgroup

G/H

center

C₂²

C₂²×D₇₆

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#407

C₂

socle

C₂²×C₁₉

C₂²×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #407

N	H ≅ G/N	type
1. C₂×#10597376	C₂	semidirect
2. #11926863	C₂	semidirect
3. #11926797	C₂	semidirect
4. #11926680	C₂	semidirect
5. C₁₉×#407	C₂	semidirect
8. C₂²×D₇₆	C₂²	semidirect
9. C₂×M₁₆×C₁₉	C₂²	semidirect
13. #10597376	C₂²	semidirect
15. C₂×C₄⋊Dic₁₉	C₂²	semidirect
16. C₂×D₁₅₂	C₂²	semidirect
17. C₁₉×C₂²⋊C₈	C₂²	semidirect
18. #10597278	C₂²	semidirect
19. #10597274	C₂²	semidirect
83. #407	D₁₉	semidirect
93. C₂×M₁₆	C₂×D₁₉	semidirect
102. C₂²⋊C₈	C₂×D₁₉	semidirect
103. C₁₉	#3192	semidirect

H ≅ G/N

type

1. C₂×#10597376

C₂

semidirect

2. #11926863

C₂

semidirect

3. #11926797

C₂

semidirect

4. #11926680

C₂

semidirect

5. C₁₉×#407

C₂

semidirect

8. C₂²×D₇₆

C₂²

semidirect

9. C₂×M₁₆×C₁₉

C₂²

semidirect

13. #10597376

C₂²

semidirect

15. C₂×C₄⋊Dic₁₉

C₂²

semidirect

16. C₂×D₁₅₂

C₂²

semidirect

17. C₁₉×C₂²⋊C₈

C₂²

semidirect

18. #10597278

C₂²

semidirect

19. #10597274

C₂²

semidirect

83. #407

D₁₉

semidirect

93. C₂×M₁₆

C₂×D₁₉

semidirect

102. C₂²⋊C₈

C₂×D₁₉

semidirect

103. C₁₉

#3192

semidirect

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

subgroup	index
C₂×#10597376	2
#11926863	2
#11926797	2
#11926680	2
C₁₉×#407	2
#3192	19

subgroup

index

C₁₉×#407

Subgroups — #14574435

Conjugacy classes of subgroups

Complements

Maximal subgroups