Group #14562674 — subgroups

Subgroups — #14562674

Order 2432.

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

normal subgroups only

This group has 246 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	#11927125	C₂	1	1	yes	maximal, characteristic
2	#11926863	C₂	1	2	yes	maximal, complemented
3	#11926483	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926279	C₂	1	2	yes	maximal, complemented
5	C₁₉×#324	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64541	—	2	1	no	—
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
8	#10597376	—	2	1	no	—
9	#10597376	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	#10597343	—	2	2	no	—
12	#10597341	—	2	2	no	—
13	C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
14	C₁₉⋊#95	—	2	1	no	—
15	C₁₉⋊#95	—	2	1	no	—
16	C₁₉⋊#95	C₂²	1	1	yes	characteristic
17	#10597278	—	2	2	no	—
18	#10597274	—	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	C₂×C₂²⋊D₁₉	—	2	2	no	—
23	C₂²×Dic₁₉	—	2	1	no	—
24	C₂²×Dic₁₉	—	2	1	no	—
25	#64541	—	4	2	no	—
26	#64541	—	4	2	no	—
27	C₂×D₇₆	—	2	1	no	—
28	C₂×D₇₆	—	2	1	no	—
29	C₂×D₇₆	D₄	1	2	yes	—
30	C₂×C₄×D₁₉	—	2	2	no	—
31	C₂×Dic₃₈	—	2	1	no	—
32	C₂×C₈×C₁₉	—	2	2	no	—
33	C₄⋊C₄×C₁₉	—	2	2	no	—
34	(C₂×D₁₉)⋊C₄	—	2	2	no	—
35	(C₂×D₁₉)⋊C₄	—	2	2	no	—
36	C₄⋊Dic₁₉	—	2	1	no	—
37	C₄⋊Dic₁₉	—	2	2	no	—
38	C₄⋊Dic₁₉	D₄	1	2	yes	—
39	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂²×D₁₉	—	2	2	no	—
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	SD₁₆	1	2	yes	—
47	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
48	C₂²⋊D₁₉	—	4	2	no	—
49	C₂²⋊D₁₉	—	4	2	no	—
50	C₂×Dic₁₉	—	2	2	no	—
51	C₂×Dic₁₉	—	4	1	no	—
52	C₂×Dic₁₉	—	4	1	no	—
53	C₂×Dic₁₉	—	4	2	no	—
54	C₂×Dic₁₉	—	4	1	no	—
55	C₂×Dic₁₉	—	4	1	no	—
56	D₇₆	—	4	2	no	—
57	D₇₆	—	4	2	no	—
58	D₇₆	—	8	1	no	—
59	C₄×D₁₉	—	4	4	no	—
60	Dic₃₈	—	4	2	no	—
61	C₈×C₁₉	—	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	#120	1	1	yes	characteristic
66	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
67	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
68	C₂×D₁₉	—	4	2	no	—
69	C₂×D₁₉	—	4	2	no	—
70	C₂×D₁₉	—	4	2	no	—
71	C₄×C₁₉	—	2	2	no	—
72	C₄×C₁₉	—	2	2	no	—
73	C₄×C₁₉	—	4	1	no	—
74	Dic₁₉	—	4	2	no	—
75	Dic₁₉	—	8	1	no	—
76	Dic₁₉	—	8	1	no	—
77	#537	—	19	1	no	—
78	#481	—	19	2	no	—
79	#400	—	19	1	no	—
80	#327	—	19	2	no	—
81	#324	D₁₉	1	1	yes	characteristic, complemented
82	C₂×C₁₉	—	2	1	no	—
83	C₂×C₁₉	—	2	1	no	—
84	C₂×C₁₉	#450	1	1	yes	characteristic
85	C₂×C₁₉	#454	1	1	yes	characteristic
86	C₂×C₁₉	#458	1	1	yes	characteristic
87	D₁₉	—	8	2	no	—
88	C₂×#41	—	38	1	no	—
89	C₂²⋊Q₈	—	38	2	no	—
90	#121	—	19	2	no	—
91	#121	—	38	2	no	—
92	#121	—	38	1	no	—
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	C₂×D₁₉	1	2	yes	—
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	—	76	2	no	—
103	#41	—	76	2	no	—
104	C₂×Q₈	—	38	1	no	—
105	C₂×D₄	—	19	2	no	—
106	C₂×D₄	—	38	1	no	—
107	C₂×D₄	—	38	1	no	—
108	C₂×D₄	—	38	2	no	—
109	C₂²×C₄	—	38	2	no	—
110	C₂²×C₄	—	38	1	no	—
111	C₂²×C₄	—	38	1	no	—
112	C₂²×C₄	D₇₆	1	1	yes	characteristic
113	C₂²×C₄	D₇₆	1	1	yes	characteristic
114	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
115	C₂×C₈	—	2	2	no	—
116	C₄⋊C₄	—	2	2	no	—
117	C₄⋊C₄	—	19	2	no	—
118	C₄⋊C₄	—	38	1	no	—
119	C₄⋊C₄	—	38	2	no	—
120	C₂²⋊C₄	—	38	2	no	—
121	C₂²⋊C₄	—	38	2	no	—
122	C₂³	—	38	2	no	—
123	C₂³	C₂×D₇₆	1	1	yes	characteristic
124	Q₈	—	76	2	no	—
125	D₄	—	76	2	no	—
126	D₄	—	76	2	no	—
127	D₄	—	76	2	no	—
128	D₄	—	76	2	no	—
129	D₄	—	152	1	no	—
130	C₂×C₄	—	2	1	no	—
131	C₂×C₄	—	2	1	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	4	1	no	—
134	C₂×C₄	—	4	1	no	—
135	C₂×C₄	—	38	2	no	—
136	C₂×C₄	—	76	4	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	#64516	1	2	yes	—
143	C₂×C₄	D₄×D₁₉	1	2	yes	—
144	C₈	—	4	2	no	—
145	C₂²	—	2	1	no	—
146	C₂²	—	2	1	no	—
147	C₂²	—	76	2	no	—
148	C₂²	—	76	2	no	—
149	C₂²	—	76	2	no	—
150	C₂²	#10597328	1	1	yes	characteristic
151	C₂²	C₂×#64516	1	1	yes	characteristic
152	C₂²	#10597354	1	1	yes	characteristic
153	C₄	—	2	2	no	—
154	C₄	—	2	2	no	—
155	C₄	—	4	1	no	—
156	C₄	—	76	2	no	—
157	C₄	—	152	1	no	—
158	C₄	—	152	1	no	—
159	C₂	—	2	1	no	—
160	C₂	—	2	1	no	—
161	C₂	—	152	2	no	—
162	C₂	#11926697	1	1	yes	characteristic
163	C₂	#11926719	1	1	yes	characteristic
164	C₂	#11926735	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927125

C₂

yes

maximal, characteristic

#11926863

C₂

yes

maximal, complemented

#11926483

C₂

yes

maximal, characteristic, complemented

#11926279

C₂

yes

maximal, complemented

C₁₉×#324

C₂

yes

maximal, characteristic, complemented

C₂×#64541

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

#10597376

—

#10597376

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

#10597343

—

#10597341

—

C₁₉×C₂²⋊C₈

C₂²

yes

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

C₂²

yes

characteristic

#10597278

—

#10597274

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

D₄

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

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

—

C₂²⋊D₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

#1616

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#120

yes

characteristic

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₂²×C₁₉

AGL(1,ℤ/8)

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂×#41

—

C₂²⋊Q₈

—

#121

—

#121

—

#121

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

#106

—

#102

—

C₂²⋊C₈

C₂×D₁₉

yes

—

#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

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

D₇₆

yes

characteristic

113

C₂²×C₄

D₇₆

yes

characteristic

114

C₂²×C₄

C₂²×D₁₉

yes

characteristic

115

C₂×C₈

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₂²⋊C₄

—

121

C₂²⋊C₄

—

122

C₂³

—

123

C₂³

C₂×D₇₆

yes

characteristic

124

Q₈

—

125

D₄

—

126

D₄

—

127

D₄

—

128

D₄

—

129

D₄

—

152

—

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

#64516

yes

—

143

C₂×C₄

D₄×D₁₉

yes

—

144

C₈

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

#10597328

yes

characteristic

151

C₂²

C₂×#64516

yes

characteristic

152

C₂²

#10597354

yes

characteristic

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

—

152

—

158

C₄

—

152

—

159

C₂

—

160

C₂

—

161

C₂

—

152

—

162

C₂

#11926697

yes

characteristic

163

C₂

#11926719

yes

characteristic

164

C₂

#11926735

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	#11927125	C₂
hypercenter	#324	D₁₉
hypocenter	C₁₉	#1616
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

C₂²×C₁₉

C₂

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #324

N	H ≅ G/N	type
2. #11926863	C₂	semidirect
3. #11926483	C₂	semidirect
4. #11926279	C₂	semidirect
5. C₁₉×#324	C₂	semidirect
81. #324	D₁₉	semidirect
101. C₁₉	#1616	semidirect

H ≅ G/N

type

2. #11926863

C₂

semidirect

3. #11926483

C₂

semidirect

4. #11926279

C₂

semidirect

5. C₁₉×#324

C₂

semidirect

81. #324

D₁₉

semidirect

101. C₁₉

#1616

semidirect

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

subgroup	index
#11927125	2
#11926863	2
#11926483	2
#11926279	2
C₁₉×#324	2
#1616	19

subgroup

index

C₁₉×#324

Subgroups — #14562674

Conjugacy classes of subgroups

Complements

Maximal subgroups