Group #18069709 — subgroups

Subgroups — #18069709

Order 4864.

196 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 75 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×#11926322	C₂	1	1	yes	maximal, characteristic
2	#14563776	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#347	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597269	—	2	1	no	—
5	#11926568	C₄	1	1	yes	characteristic
6	#11926568	C₄	1	1	yes	characteristic
7	#11926322	—	2	1	no	—
8	#11926322	C₄	1	2	yes	—
9	#11926309	—	2	1	no	—
10	#11926309	—	2	1	no	—
11	C₂×C₁₉×M₃₂	—	2	1	no	—
12	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
13	C₁₉×#347	—	2	1	no	—
14	C₁₉×#347	C₄	1	2	yes	—
15	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×#64520	—	2	1	no	—
19	C₂×#64520	—	2	1	no	—
20	C₁₉×M₃₂	—	2	2	no	—
21	C₁₉×M₃₂	—	2	2	no	—
22	C₂×C₁₆×C₁₉	—	2	2	no	—
23	C₁₉×#97	C₂×C₄	1	1	yes	characteristic
24	C₁₉×#97	C₂×C₄	1	1	yes	characteristic
25	C₁₉×#97	D₄	1	1	yes	characteristic
26	C₁₉×#97	Q₈	1	1	yes	characteristic
27	#10597269	—	2	2	no	—
28	#10597269	—	2	2	no	—
29	C₂×C₁₉⋊C₁₆	—	2	2	no	—
30	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
31	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
32	C₂²×C₄×C₁₉	—	2	1	no	—
33	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₈×C₁₉	—	2	1	no	—
35	C₂×C₈×C₁₉	—	2	1	no	—
36	C₂×C₈×C₁₉	—	2	1	no	—
37	C₂×C₈×C₁₉	—	2	1	no	—
38	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
42	C₄²×C₁₉	—	2	1	no	—
43	C₄²×C₁₉	C₄²	1	1	yes	characteristic
44	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
45	#64520	—	4	1	no	—
46	#64520	—	4	1	no	—
47	#64520	—	4	1	no	—
48	#64520	—	4	1	no	—
49	C₂×C₁₉⋊C₈	—	4	1	no	—
50	C₂×C₁₉⋊C₈	—	4	1	no	—
51	C₁₆×C₁₉	—	2	4	no	—
52	C₁₉⋊C₁₆	—	2	4	no	—
53	#7267	—	19	1	no	maximal, Sylow
54	C₂³×C₁₉	#101	1	1	yes	characteristic
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	2	1	no	—
57	C₂×C₄×C₁₉	—	8	1	no	—
58	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
59	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
60	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
61	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
62	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
64	C₈×C₁₉	—	2	1	no	—
65	C₈×C₁₉	—	2	1	no	—
66	C₈×C₁₉	—	2	1	no	—
67	C₈×C₁₉	—	2	1	no	—
68	C₁₉⋊C₈	—	8	1	no	—
69	C₁₉⋊C₈	—	8	1	no	—
70	C₂×#347	—	19	1	no	—
71	C₂×#347	D₁₉	1	1	yes	characteristic
72	#1838	—	19	1	no	—
73	C₂²×C₁₉	—	4	1	no	—
74	C₂²×C₁₉	#330	1	1	yes	characteristic
75	C₂²×C₁₉	#330	1	1	yes	characteristic
76	C₂²×C₁₉	#343	1	1	yes	characteristic
77	C₄×C₁₉	—	4	1	no	—
78	C₄×C₁₉	—	4	1	no	—
79	C₄×C₁₉	#329	1	1	yes	characteristic
80	C₄×C₁₉	#329	1	1	yes	characteristic
81	C₄×C₁₉	#339	1	1	yes	characteristic
82	C₄×C₁₉	#339	1	1	yes	characteristic
83	C₂×M₃₂	—	2	1	no	—
84	C₂×M₃₂	—	38	1	no	—
85	#423	—	19	1	no	—
86	#423	—	19	1	no	—
87	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
88	#347	—	2	1	no	—
89	#347	—	19	2	no	—
90	#347	—	38	1	no	—
91	#347	Dic₁₉	1	2	yes	—
92	#341	—	38	1	no	—
93	#341	—	38	1	no	—
94	C₂×C₁₉	—	2	1	no	—
95	C₂×C₁₉	—	2	1	no	—
96	C₂×C₁₉	—	2	1	no	—
97	C₂×C₁₉	#1295	1	1	yes	characteristic
98	C₂×M₁₆	—	38	1	no	—
99	C₂×M₁₆	—	38	1	no	—
100	C₂²×C₈	D₇₆	1	1	yes	characteristic
101	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
102	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
103	M₃₂	—	2	2	no	—
104	M₃₂	—	2	2	no	—
105	M₃₂	—	38	2	no	—
106	M₃₂	—	38	2	no	—
107	C₂×C₁₆	—	2	2	no	—
108	C₂×C₁₆	—	38	2	no	—
109	C₄⋊C₈	—	76	1	no	—
110	C₄⋊C₈	—	76	1	no	—
111	#97	Dic₃₈	1	1	yes	characteristic
112	#97	C₄×D₁₉	1	1	yes	characteristic
113	#97	C₂×Dic₁₉	1	1	yes	characteristic
114	#97	C₂²⋊D₁₉	1	1	yes	characteristic
115	C₁₉	#7267	1	1	yes	characteristic, complemented, Sylow
116	C₂²×C₄	—	2	1	no	—
117	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
118	M₁₆	—	76	1	no	—
119	M₁₆	—	76	1	no	—
120	M₁₆	—	76	1	no	—
121	M₁₆	—	76	1	no	—
122	C₂×C₈	—	2	1	no	—
123	C₂×C₈	—	2	1	no	—
124	C₂×C₈	—	2	1	no	—
125	C₂×C₈	—	2	1	no	—
126	C₂×C₈	—	76	1	no	—
127	C₂×C₈	—	76	1	no	—
128	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
129	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
130	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
131	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
132	C₄²	—	2	1	no	—
133	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
134	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
135	C₁₆	—	2	4	no	—
136	C₁₆	—	38	4	no	—
137	C₂³	#10597281	1	1	yes	characteristic
138	C₂×C₄	—	2	1	no	—
139	C₂×C₄	—	2	1	no	—
140	C₂×C₄	—	8	1	no	—
141	C₂×C₄	#10597262	1	1	yes	characteristic
142	C₂×C₄	#10597262	1	1	yes	characteristic
143	C₂×C₄	#10597280	1	1	yes	characteristic
144	C₂×C₄	#10597282	1	1	yes	characteristic
145	C₂×C₄	#10597282	1	1	yes	characteristic
146	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
147	C₈	—	2	1	no	—
148	C₈	—	2	1	no	—
149	C₈	—	2	1	no	—
150	C₈	—	2	1	no	—
151	C₈	—	152	1	no	—
152	C₈	—	152	1	no	—
153	C₂²	—	4	1	no	—
154	C₂²	#11926285	1	1	yes	characteristic
155	C₂²	#11926285	1	1	yes	characteristic
156	C₂²	#11926312	1	1	yes	characteristic
157	C₄	—	4	1	no	—
158	C₄	—	4	1	no	—
159	C₄	#11926283	1	1	yes	characteristic
160	C₄	#11926283	1	1	yes	characteristic
161	C₄	#11926304	1	1	yes	characteristic
162	C₄	#11926305	1	1	yes	characteristic
163	C₂	—	2	1	no	—
164	C₂	—	2	1	no	—
165	C₂	—	2	1	no	—
166	C₂	#14561517	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926322

C₂

yes

maximal, characteristic

#14563776

C₂

yes

maximal, characteristic

C₂×C₁₉×#347

C₂

yes

maximal, characteristic

C₂×#10597269

—

#11926568

C₄

yes

characteristic

#11926568

C₄

yes

characteristic

#11926322

—

#11926322

C₄

yes

—

#11926309

—

#11926309

—

C₂×C₁₉×M₃₂

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₁₉×#347

—

C₁₉×#347

C₄

yes

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×#64520

—

C₂×#64520

—

C₁₉×M₃₂

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₁₉×#97

C₂×C₄

yes

characteristic

C₁₉×#97

C₂×C₄

yes

characteristic

C₁₉×#97

D₄

yes

characteristic

C₁₉×#97

Q₈

yes

characteristic

#10597269

—

#10597269

—

C₂×C₁₉⋊C₁₆

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

C₄²

yes

characteristic

C₄²×C₁₉

C₄⋊C₄

yes

—

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₂×#347

—

C₂×#347

D₁₉

yes

characteristic

#1838

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×M₃₂

—

C₂×M₃₂

—

#423

—

#423

—

C₂×#97

C₂×D₁₉

yes

—

—

—

Dic₁₉

yes

—

#341

—

#341

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1295

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

100

C₂²×C₈

D₇₆

yes

characteristic

101

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

102

C₂×C₄²

C₄×D₁₉

yes

characteristic

103

M₃₂

—

104

M₃₂

—

105

M₃₂

—

106

M₃₂

—

107

C₂×C₁₆

—

108

C₂×C₁₆

—

109

C₄⋊C₈

—

110

C₄⋊C₈

—

111

#97

Dic₃₈

yes

characteristic

112

#97

C₄×D₁₉

yes

characteristic

113

#97

C₂×Dic₁₉

yes

characteristic

114

#97

C₂²⋊D₁₉

yes

characteristic

115

C₁₉

#7267

yes

characteristic, complemented, Sylow

116

C₂²×C₄

—

117

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

118

M₁₆

—

119

M₁₆

—

120

M₁₆

—

121

M₁₆

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

129

C₂×C₈

C₄⋊Dic₁₉

yes

characteristic

130

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

131

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

132

C₄²

—

133

C₄²

C₄×Dic₁₉

yes

characteristic

134

C₄²

Dic₁₉⋊C₄

yes

characteristic

135

C₁₆

—

136

C₁₆

—

137

C₂³

#10597281

yes

characteristic

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

#10597262

yes

characteristic

142

C₂×C₄

#10597262

yes

characteristic

143

C₂×C₄

#10597280

yes

characteristic

144

C₂×C₄

#10597282

yes

characteristic

145

C₂×C₄

#10597282

yes

characteristic

146

C₂×C₄

C₁₉⋊#95

yes

characteristic

147

C₈

—

148

C₈

—

149

C₈

—

150

C₈

—

151

C₈

—

152

—

152

C₈

—

152

—

153

C₂²

—

154

C₂²

#11926285

yes

characteristic

155

C₂²

#11926285

yes

characteristic

156

C₂²

#11926312

yes

characteristic

157

C₄

—

158

C₄

—

159

C₄

#11926283

yes

characteristic

160

C₄

#11926283

yes

characteristic

161

C₄

#11926304

yes

characteristic

162

C₄

#11926305

yes

characteristic

163

C₂

—

164

C₂

—

165

C₂

—

166

C₂

#14561517

yes

characteristic

	subgroup	G/H
center	C₄	#11926283
commutator	C₄²×C₁₉	C₄²
Frattini	C₂×#97	C₂×D₁₉
Fitting	C₂×C₁₉×#347	C₂
socle	C₂×C₁₉	#1295
prime radical	C₂³×C₁₉	#101
cosocle	C₂×C₁₉×#97	C₂²
hypercenter	C₂×#347	D₁₉
hypocenter	C₁₉	#7267
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#97 ◁ C₂×#347

subgroup

G/H

center

C₄

#11926283

commutator

C₄²×C₁₉

C₄²

Frattini

C₂×#97

C₂×D₁₉

Fitting

C₂×C₁₉×#347

C₂

C₂×C₁₉

C₂³×C₁₉

C₂×C₁₉×#97

C₂²

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#97 ◁ C₂×#347

N	H ≅ G/N	type
115. C₁₉	#7267	semidirect

H ≅ G/N

type

115. C₁₉

#7267

semidirect

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

subgroup	index
C₂×#11926322	2
#14563776	2
C₂×C₁₉×#347	2
#7267	19

subgroup

index

C₂×#11926322

#14563776

C₂×C₁₉×#347

#7267

Subgroups — #18069709

Conjugacy classes of subgroups

Complements

Maximal subgroups