Group #14562672 — subgroups

Subgroups — #14562672

Order 2432.

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

normal subgroups only

This group has 246 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	#11926860	C₂	1	2	yes	maximal, complemented
2	#11926483	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926278	C₂	1	2	yes	maximal, complemented
4	#11926270	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#537	C₂	1	1	yes	maximal, characteristic
6	C₂×#41×C₁₉	—	2	1	no	—
7	C₁₉×C₂²⋊Q₈	—	2	2	no	—
8	C₁₉×#121	—	2	2	no	—
9	C₁₉×#121	—	2	1	no	—
10	C₁₉×#121	C₂²	1	2	yes	—
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	#10597289	—	2	2	no	—
14	C₁₉⋊#95	—	2	1	no	—
15	C₁₉⋊#95	—	2	1	no	—
16	C₁₉⋊#95	C₂²	1	1	yes	characteristic
17	C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
18	#10597265	—	2	2	no	—
19	#41×C₁₉	—	4	2	no	—
20	#41×C₁₉	—	4	2	no	—
21	C₂×Q₈×C₁₉	—	2	1	no	—
22	C₂×D₄×C₁₉	—	2	1	no	—
23	C₂×D₄×C₁₉	—	2	2	no	—
24	C₂×D₄×C₁₉	—	2	1	no	—
25	C₂×D₄×C₁₉	D₄	1	2	yes	—
26	C₂²×C₄×C₁₉	—	2	2	no	—
27	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₂²×Dic₁₉	—	2	1	no	—
31	C₂²×Dic₁₉	—	2	1	no	—
32	C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₄⋊C₄×C₁₉	—	2	2	no	—
34	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
35	C₂²⋊C₄×C₁₉	—	2	2	no	—
36	C₂²⋊C₄×C₁₉	—	2	2	no	—
37	C₄⋊Dic₁₉	—	2	2	no	—
38	C₂×C₁₉⋊C₈	—	2	2	no	—
39	C₂³×C₁₉	—	2	2	no	—
40	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
41	Q₈×C₁₉	—	4	2	no	—
42	D₄×C₁₉	—	4	2	no	—
43	D₄×C₁₉	—	4	2	no	—
44	D₄×C₁₉	—	4	2	no	—
45	D₄×C₁₉	—	4	2	no	—
46	D₄×C₁₉	—	8	1	no	—
47	C₂×C₄×C₁₉	—	2	1	no	—
48	C₂×C₄×C₁₉	—	2	1	no	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	—	4	4	no	—
53	C₂×C₄×C₁₉	—	4	1	no	—
54	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
55	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
56	C₂×Dic₁₉	—	4	1	no	—
57	C₂×Dic₁₉	—	4	1	no	—
58	C₂×Dic₁₉	—	4	2	no	—
59	C₂×Dic₁₉	—	4	1	no	—
60	C₂×Dic₁₉	—	4	1	no	—
61	C₁₉⋊C₈	—	4	2	no	—
62	#1616	—	19	1	no	maximal, Sylow
63	C₂²×C₁₉	—	2	1	no	—
64	C₂²×C₁₉	—	2	1	no	—
65	C₂²×C₁₉	—	4	2	no	—
66	C₂²×C₁₉	—	4	2	no	—
67	C₂²×C₁₉	—	4	2	no	—
68	C₂²×C₁₉	#120	1	1	yes	characteristic
69	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
70	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
71	C₄×C₁₉	—	2	2	no	—
72	C₄×C₁₉	—	2	2	no	—
73	C₄×C₁₉	—	4	2	no	—
74	C₄×C₁₉	—	4	1	no	—
75	Dic₁₉	—	8	1	no	—
76	Dic₁₉	—	8	1	no	—
77	#537	D₁₉	1	1	yes	characteristic
78	#481	—	19	2	no	—
79	#400	—	19	1	no	—
80	#327	—	19	2	no	—
81	#324	—	19	1	no	—
82	C₂×C₁₉	—	2	1	no	—
83	C₂×C₁₉	—	2	1	no	—
84	C₂×C₁₉	—	8	2	no	—
85	C₂×C₁₉	#450	1	1	yes	characteristic
86	C₂×C₁₉	#454	1	1	yes	characteristic
87	C₂×C₁₉	#458	1	1	yes	characteristic
88	C₂×#41	—	2	1	no	—
89	C₂²⋊Q₈	—	2	2	no	—
90	#121	—	2	2	no	—
91	#121	—	2	1	no	—
92	#121	C₂×D₁₉	1	2	yes	—
93	C₂×C₄⋊C₄	—	19	1	no	—
94	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
95	#106	—	38	2	no	—
96	#102	—	38	2	no	—
97	C₂²⋊C₈	—	19	2	no	—
98	#95	—	19	1	no	—
99	#95	—	38	1	no	—
100	#95	—	38	1	no	—
101	C₁₉	#1616	1	1	yes	characteristic, complemented, Sylow
102	#41	—	4	2	no	—
103	#41	—	4	2	no	—
104	C₂×Q₈	—	2	1	no	—
105	C₂×D₄	—	2	1	no	—
106	C₂×D₄	—	2	2	no	—
107	C₂×D₄	—	2	1	no	—
108	C₂×D₄	C₂²⋊D₁₉	1	2	yes	—
109	C₂²×C₄	—	2	2	no	—
110	C₂²×C₄	—	38	1	no	—
111	C₂²×C₄	—	38	1	no	—
112	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
113	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
114	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
115	C₂×C₈	—	38	2	no	—
116	C₄⋊C₄	—	2	1	no	—
117	C₄⋊C₄	—	2	2	no	—
118	C₄⋊C₄	—	38	2	no	—
119	C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
120	C₂²⋊C₄	—	2	2	no	—
121	C₂²⋊C₄	—	2	2	no	—
122	C₂³	—	2	2	no	—
123	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
124	Q₈	—	4	2	no	—
125	D₄	—	4	2	no	—
126	D₄	—	4	2	no	—
127	D₄	—	4	2	no	—
128	D₄	—	4	2	no	—
129	D₄	—	8	1	no	—
130	C₂×C₄	—	2	1	no	—
131	C₂×C₄	—	2	1	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	4	1	no	—
135	C₂×C₄	—	4	4	no	—
136	C₂×C₄	—	4	1	no	—
137	C₂×C₄	—	76	1	no	—
138	C₂×C₄	—	76	1	no	—
139	C₂×C₄	—	76	2	no	—
140	C₂×C₄	—	76	1	no	—
141	C₂×C₄	—	76	1	no	—
142	C₂×C₄	#64526	1	2	yes	—
143	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
144	C₈	—	76	2	no	—
145	C₂²	—	2	1	no	—
146	C₂²	—	2	1	no	—
147	C₂²	—	4	2	no	—
148	C₂²	—	4	2	no	—
149	C₂²	—	4	2	no	—
150	C₂²	#10597378	1	1	yes	characteristic
151	C₂²	C₂×#64526	1	1	yes	characteristic
152	C₂²	#10597399	1	1	yes	characteristic
153	C₄	—	2	2	no	—
154	C₄	—	2	2	no	—
155	C₄	—	4	2	no	—
156	C₄	—	4	1	no	—
157	C₄	—	152	1	no	—
158	C₄	—	152	1	no	—
159	C₂	—	2	1	no	—
160	C₂	—	2	1	no	—
161	C₂	—	8	2	no	—
162	C₂	#11926695	1	1	yes	characteristic
163	C₂	#11926717	1	1	yes	characteristic
164	C₂	#11926734	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926860

C₂

yes

maximal, complemented

#11926483

C₂

yes

maximal, characteristic, complemented

#11926278

C₂

yes

maximal, complemented

#11926270

C₂

yes

maximal, characteristic, complemented

C₁₉×#537

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

—

C₁₉×C₂²⋊Q₈

—

C₁₉×#121

—

C₁₉×#121

—

C₁₉×#121

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

#10597289

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

C₂²

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

#10597265

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#1616

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#120

yes

characteristic

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₂²×C₁₉

AGL(1,ℤ/8)

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

#537

D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×#41

—

C₂²⋊Q₈

—

#121

—

#121

—

#121

C₂×D₁₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

#106

—

#102

—

C₂²⋊C₈

—

#95

—

#95

—

100

#95

—

101

C₁₉

#1616

yes

characteristic, complemented, Sylow

102

#41

—

103

#41

—

104

C₂×Q₈

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

C₂²⋊D₁₉

yes

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

113

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

114

C₂²×C₄

C₂²×D₁₉

yes

characteristic

115

C₂×C₈

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

C₂²⋊D₁₉

yes

—

120

C₂²⋊C₄

—

121

C₂²⋊C₄

—

122

C₂³

—

123

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

124

Q₈

—

125

D₄

—

126

D₄

—

127

D₄

—

128

D₄

—

129

D₄

—

130

C₂×C₄

—

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

#64526

yes

—

143

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

144

C₈

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

#10597378

yes

characteristic

151

C₂²

C₂×#64526

yes

characteristic

152

C₂²

#10597399

yes

characteristic

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

—

152

—

158

C₄

—

152

—

159

C₂

—

160

C₂

—

161

C₂

—

162

C₂

#11926695

yes

characteristic

163

C₂

#11926717

yes

characteristic

164

C₂

#11926734

yes

characteristic

	subgroup	G/H
center	C₂²	#10597399
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting, prime radical	C₁₉×#537	C₂
socle	C₂²×C₁₉	#120
hypercenter	#537	D₁₉
hypocenter	C₁₉	#1616
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #537

subgroup

G/H

center

C₂²

#10597399

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting, prime radical

C₁₉×#537

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #537

N	H ≅ G/N	type
1. #11926860	C₂	semidirect
2. #11926483	C₂	semidirect
3. #11926278	C₂	semidirect
4. #11926270	C₂	semidirect
101. C₁₉	#1616	semidirect

H ≅ G/N

type

1. #11926860

C₂

semidirect

2. #11926483

C₂

semidirect

3. #11926278

C₂

semidirect

4. #11926270

C₂

semidirect

101. C₁₉

#1616

semidirect

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

subgroup	index
#11926860	2
#11926483	2
#11926278	2
#11926270	2
C₁₉×#537	2
#1616	19

subgroup

index

C₁₉×#537

Subgroups — #14562672

Conjugacy classes of subgroups

Complements

Maximal subgroups