Group #18069843 — subgroups

Subgroups — #18069843

Order 4864.

456 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 67 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	#14563563	C₂	1	2	yes	maximal
2	C₁₉×#1782	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597293	—	2	2	no	—
4	C₂×#10597290	—	2	2	no	—
5	#11926508	C₄	1	4	yes	complemented
6	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×#99	—	2	2	no	—
8	C₁₉×#381	C₄	1	2	yes	—
9	C₂×#41×C₁₉	—	4	2	no	—
10	C₂×#41×C₁₉	—	4	4	no	—
11	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
12	C₂²×D₄×C₁₉	D₄	1	2	yes	—
13	C₂²×D₄×C₁₉	Q₈	1	1	yes	characteristic
14	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
15	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
17	C₂×#64520	—	2	4	no	—
18	C₁₉×#99	—	4	4	no	—
19	C₁₉×#95	—	4	2	no	—
20	#10597293	—	4	4	no	—
21	#10597290	—	4	4	no	—
22	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
23	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	—
25	#41×C₁₉	—	4	16	no	—
26	C₂×Q₈×C₁₉	—	2	4	no	—
27	C₂×Q₈×C₁₉	—	4	1	no	—
28	C₂×D₄×C₁₉	—	2	4	no	—
29	C₂×D₄×C₁₉	—	2	4	no	—
30	C₂×D₄×C₁₉	—	4	2	no	—
31	C₂×D₄×C₁₉	—	4	1	no	—
32	C₂×D₄×C₁₉	—	4	2	no	—
33	C₂²×C₄×C₁₉	—	2	2	no	—
34	C₂²×C₄×C₁₉	—	2	4	no	—
35	C₂²×C₄×C₁₉	—	4	2	no	—
36	C₂²×C₄×C₁₉	—	4	2	no	—
37	C₂²×C₄×C₁₉	—	4	2	no	—
38	C₂²×C₄×C₁₉	—	4	2	no	—
39	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
41	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
42	C₂²⋊C₄×C₁₉	—	4	4	no	—
43	#64520	—	4	4	no	—
44	#64520	—	4	4	no	—
45	C₂×C₁₉⋊C₈	—	4	4	no	—
46	#7319	—	19	1	no	maximal, Sylow
47	C₂³×C₁₉	—	2	2	no	—
48	C₂³×C₁₉	—	2	2	no	—
49	C₂³×C₁₉	—	2	2	no	—
50	C₂³×C₁₉	—	2	2	no	—
51	C₂³×C₁₉	—	8	1	no	—
52	C₂³×C₁₉	—	8	2	no	—
53	C₂³×C₁₉	#95	1	1	yes	characteristic
54	C₂³×C₁₉	#99	1	2	yes	—
55	Q₈×C₁₉	—	4	4	no	—
56	D₄×C₁₉	—	4	8	no	—
57	D₄×C₁₉	—	4	4	no	—
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	2	1	no	—
62	C₂×C₄×C₁₉	—	2	1	no	—
63	C₂×C₄×C₁₉	—	2	2	no	—
64	C₂×C₄×C₁₉	—	4	8	no	—
65	C₂×C₄×C₁₉	—	4	4	no	—
66	C₂×C₄×C₁₉	—	8	2	no	—
67	C₂×C₄×C₁₉	—	8	4	no	—
68	C₂×C₄×C₁₉	#99	1	4	yes	—
69	C₁₉⋊C₈	—	8	4	no	—
70	#1785	—	19	2	no	—
71	#1782	D₁₉	1	1	yes	characteristic
72	C₂²×C₁₉	—	2	2	no	—
73	C₂²×C₁₉	—	4	1	no	—
74	C₂²×C₁₉	—	4	2	no	—
75	C₂²×C₁₉	—	4	4	no	—
76	C₂²×C₁₉	—	4	2	no	—
77	C₂²×C₁₉	—	8	2	no	—
78	C₂²×C₁₉	—	8	2	no	—
79	C₂²×C₁₉	—	8	2	no	—
80	C₂²×C₁₉	#342	1	2	yes	—
81	C₂²×C₁₉	#342	1	1	yes	characteristic
82	C₄×C₁₉	—	2	4	no	—
83	C₄×C₁₉	—	4	1	no	—
84	C₄×C₁₉	—	4	1	no	—
85	C₄×C₁₉	—	16	2	no	—
86	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
87	C₂×#101	—	38	2	no	—
88	C₂×#100	—	38	2	no	—
89	C₂×#99	—	2	2	no	—
90	#407	—	19	4	no	—
91	#381	Dic₁₉	1	2	yes	—
92	C₂×C₁₉	—	2	2	no	—
93	C₂×C₁₉	—	2	1	no	—
94	C₂×C₁₉	—	4	2	no	—
95	C₂×C₁₉	—	8	2	no	—
96	C₂×C₁₉	#1304	1	1	yes	characteristic
97	C₂×#41	—	4	2	no	—
98	C₂×#41	—	4	4	no	—
99	C₂²×Q₈	D₇₆	1	1	yes	characteristic
100	C₂²×D₄	Dic₃₈	1	1	yes	characteristic
101	C₂²×D₄	C₂²⋊D₁₉	1	2	yes	—
102	C₂³×C₄	C₄×D₁₉	1	2	yes	—
103	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
104	C₂×M₁₆	—	38	4	no	—
105	C₂×C₂²⋊C₄	—	2	2	no	—
106	#101	—	76	4	no	—
107	#100	—	76	4	no	—
108	#99	—	4	4	no	—
109	C₂²⋊C₈	—	76	4	no	—
110	#95	—	4	2	no	—
111	C₁₉	#7319	1	1	yes	characteristic, complemented, Sylow
112	C₂⁴	Dic₁₉⋊C₄	1	2	yes	—
113	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
114	#41	—	4	16	no	—
115	C₂×Q₈	—	2	4	no	—
116	C₂×Q₈	—	4	1	no	—
117	C₂×D₄	—	2	4	no	—
118	C₂×D₄	—	2	4	no	—
119	C₂×D₄	—	4	2	no	—
120	C₂×D₄	—	4	1	no	—
121	C₂×D₄	—	4	2	no	—
122	C₂²×C₄	—	2	2	no	—
123	C₂²×C₄	—	2	4	no	—
124	C₂²×C₄	—	4	2	no	—
125	C₂²×C₄	—	4	2	no	—
126	C₂²×C₄	—	4	2	no	—
127	C₂²×C₄	—	4	2	no	—
128	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
129	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
130	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
131	M₁₆	—	76	4	no	—
132	M₁₆	—	76	4	no	—
133	C₂×C₈	—	76	4	no	—
134	C₂²⋊C₄	—	4	4	no	—
135	C₂³	—	2	2	no	—
136	C₂³	—	2	2	no	—
137	C₂³	—	2	2	no	—
138	C₂³	—	2	2	no	—
139	C₂³	—	8	2	no	—
140	C₂³	—	8	1	no	—
141	C₂³	C₁₉⋊#95	1	1	yes	characteristic
142	C₂³	#10597291	1	2	yes	—
143	Q₈	—	4	4	no	—
144	D₄	—	4	8	no	—
145	D₄	—	4	4	no	—
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	2	no	—
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	—	2	1	no	—
151	C₂×C₄	—	2	1	no	—
152	C₂×C₄	—	4	8	no	—
153	C₂×C₄	—	4	4	no	—
154	C₂×C₄	—	8	2	no	—
155	C₂×C₄	—	8	4	no	—
156	C₂×C₄	#10597263	1	4	yes	—
157	C₈	—	152	4	no	—
158	C₂²	—	2	2	no	—
159	C₂²	—	4	1	no	—
160	C₂²	—	4	2	no	—
161	C₂²	—	4	4	no	—
162	C₂²	—	4	2	no	—
163	C₂²	—	8	2	no	—
164	C₂²	—	8	2	no	—
165	C₂²	—	8	2	no	—
166	C₂²	#11926310	1	2	yes	—
167	C₂²	#11926311	1	1	yes	characteristic
168	C₄	—	2	4	no	—
169	C₄	—	4	1	no	—
170	C₄	—	4	1	no	—
171	C₄	—	16	2	no	—
172	C₂	—	2	2	no	—
173	C₂	—	2	1	no	—
174	C₂	—	4	2	no	—
175	C₂	—	8	2	no	—
176	C₂	C₁₉⋊#1304	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563563

C₂

yes

maximal

C₁₉×#1782

C₂

yes

maximal, characteristic

C₂×#10597293

—

C₂×#10597290

—

#11926508

C₄

yes

complemented

C₂²×#41×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#99

—

C₁₉×#381

C₄

yes

—

C₂×#41×C₁₉

—

C₂×#41×C₁₉

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂²×D₄×C₁₉

D₄

yes

—

C₂²×D₄×C₁₉

Q₈

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×#64520

—

C₁₉×#99

—

C₁₉×#95

—

#10597293

—

#10597290

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂⁴×C₁₉

C₄⋊C₄

yes

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²⋊C₄×C₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

#7319

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#95

yes

characteristic

C₂³×C₁₉

#99

yes

—

Q₈×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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#99

yes

—

C₁₉⋊C₈

—

#1785

—

#1782

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#342

yes

—

C₂²×C₁₉

#342

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂²×#41

C₂×D₁₉

yes

characteristic

C₂×#101

—

C₂×#100

—

C₂×#99

—

#407

—

#381

Dic₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1304

yes

characteristic

C₂×#41

—

C₂×#41

—

C₂²×Q₈

D₇₆

yes

characteristic

100

C₂²×D₄

Dic₃₈

yes

characteristic

101

C₂²×D₄

C₂²⋊D₁₉

yes

—

102

C₂³×C₄

C₄×D₁₉

yes

—

103

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

104

C₂×M₁₆

—

105

C₂×C₂²⋊C₄

—

106

#101

—

107

#100

—

108

#99

—

109

C₂²⋊C₈

—

110

#95

—

111

C₁₉

#7319

yes

characteristic, complemented, Sylow

112

C₂⁴

Dic₁₉⋊C₄

yes

—

113

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

114

#41

—

115

C₂×Q₈

—

116

C₂×Q₈

—

117

C₂×D₄

—

118

C₂×D₄

—

119

C₂×D₄

—

120

C₂×D₄

—

121

C₂×D₄

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

—

127

C₂²×C₄

—

128

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

129

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

130

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

131

M₁₆

—

132

M₁₆

—

133

C₂×C₈

—

134

C₂²⋊C₄

—

135

C₂³

—

136

C₂³

—

137

C₂³

—

138

C₂³

—

139

C₂³

—

140

C₂³

—

141

C₂³

C₁₉⋊#95

yes

characteristic

142

C₂³

#10597291

yes

—

143

Q₈

—

144

D₄

—

145

D₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

#10597263

yes

—

157

C₈

—

152

—

158

C₂²

—

159

C₂²

—

160

C₂²

—

161

C₂²

—

162

C₂²

—

163

C₂²

—

164

C₂²

—

165

C₂²

—

166

C₂²

#11926310

yes

—

167

C₂²

#11926311

yes

characteristic

168

C₄

—

169

C₄

—

170

C₄

—

171

C₄

—

172

C₂

—

173

C₂

—

174

C₂

—

175

C₂

—

176

C₂

C₁₉⋊#1304

yes

characteristic

	subgroup	G/H
center	C₂	C₁₉⋊#1304
commutator	C₂²×C₄×C₁₉	C₄²
Frattini	C₂²×#41	C₂×D₁₉
Fitting	C₁₉×#1782	C₂
socle	C₂×C₁₉	#1304
prime radical, cosocle	C₂²×#41×C₁₉	C₂²
hypercenter	#1782	D₁₉
hypocenter	C₁₉	#7319
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂²×#41 ◁ #1782

subgroup

G/H

center

C₂

C₁₉⋊#1304

commutator

C₂²×C₄×C₁₉

C₄²

Frattini

C₂²×#41

C₂×D₁₉

Fitting

C₁₉×#1782

C₂

socle

C₂×C₁₉

#1304

prime radical, cosocle

C₂²×#41×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂³ ◁ C₂²×#41 ◁ #1782

N	H ≅ G/N	type
5. #11926508	C₄	semidirect
111. C₁₉	#7319	semidirect

H ≅ G/N

type

5. #11926508

C₄

semidirect

111. C₁₉

#7319

semidirect

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

subgroup	index
#14563563	2
C₁₉×#1782	2
#7319	19

subgroup

index

#14563563

C₁₉×#1782

#7319

Subgroups — #18069843

Conjugacy classes of subgroups

Complements

Maximal subgroups