Group #18076248 — subgroups

Subgroups — #18076248

Order 4864.

228 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 99 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	#14562398	C₂	1	1	yes	maximal, characteristic
2	#14561918	C₂	1	1	yes	maximal, characteristic
3	#14561498	C₂	1	2	yes	maximal
4	#14561496	C₂	1	2	yes	maximal
5	C₁₉×#1568	C₂	1	1	yes	maximal, characteristic
6	#11926601	C₂²	1	2	yes	—
7	#11926597	C₂²	1	1	yes	characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	#11926297	—	2	1	no	—
10	#11926295	—	2	1	no	—
11	#11926265	C₄	1	2	yes	—
12	C₈×C₁₉⋊C₈	C₄	1	2	yes	—
13	C₁₉×#432	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#335	—	2	1	no	—
16	C₁₉×#334	—	2	1	no	—
17	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
18	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
20	C₁₉×C₄⋊C₈	—	2	2	no	—
21	C₁₉×C₂²⋊C₈	—	2	2	no	—
22	C₁₉×#97	—	2	2	no	—
23	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
27	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
28	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
29	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
30	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
31	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
32	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
33	#10597260	—	2	2	no	—
34	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
35	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
36	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
39	C₂×C₈×C₁₉	—	2	2	no	—
40	C₂×C₈×C₁₉	—	2	2	no	—
41	C₂×C₈×C₁₉	—	4	2	no	—
42	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
46	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
47	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₄²×C₁₉	#41	1	1	yes	characteristic
49	C₄²×C₁₉	#41	1	1	yes	characteristic
50	C₂×C₁₉⋊C₈	—	2	2	no	—
51	C₂×C₁₉⋊C₈	—	2	2	no	—
52	C₂×C₁₉⋊C₈	—	4	2	no	—
53	#8797	—	19	1	no	maximal, Sylow
54	C₂³×C₁₉	#125	1	1	yes	characteristic
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	2	1	no	—
57	C₂×C₄×C₁₉	—	4	1	no	—
58	C₂×C₄×C₁₉	—	4	1	no	—
59	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
60	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
61	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
62	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
65	C₈×C₁₉	—	2	1	no	—
66	C₈×C₁₉	—	2	1	no	—
67	C₈×C₁₉	—	8	2	no	—
68	C₈×C₁₉	#108	1	2	yes	—
69	C₈×C₁₉	#108	1	2	yes	—
70	C₁₉⋊C₈	—	4	2	no	—
71	C₁₉⋊C₈	—	4	2	no	—
72	C₁₉⋊C₈	—	8	2	no	—
73	#1568	—	19	1	no	—
74	#1568	D₁₉	1	1	yes	characteristic
75	#1450	—	19	1	no	—
76	#1287	—	19	2	no	—
77	#1287	—	19	2	no	—
78	C₂²×C₁₉	—	2	1	no	—
79	C₂²×C₁₉	—	2	1	no	—
80	C₂²×C₁₉	—	2	1	no	—
81	C₂²×C₁₉	#382	1	1	yes	characteristic
82	C₄×C₁₉	—	2	1	no	—
83	C₄×C₁₉	—	2	1	no	—
84	C₄×C₁₉	—	2	1	no	—
85	C₄×C₁₉	—	2	1	no	—
86	C₄×C₁₉	—	2	1	no	—
87	C₄×C₁₉	C₂×#108	1	1	yes	characteristic
88	C₄×C₁₉	C₂×#108	1	1	yes	characteristic
89	#432	—	19	2	no	—
90	#432	C₂×D₁₉	1	2	yes	—
91	#431	—	19	1	no	—
92	#431	—	19	1	no	—
93	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
94	#335	—	2	1	no	—
95	#335	—	38	1	no	—
96	#334	—	2	1	no	—
97	#334	—	38	1	no	—
98	#322	—	19	2	no	—
99	C₈²	—	19	2	no	—
100	C₂×C₁₉	—	4	1	no	—
101	C₂×C₁₉	#1833	1	1	yes	characteristic
102	C₂×C₁₉	#1833	1	1	yes	characteristic
103	C₂×C₁₉	#1837	1	1	yes	characteristic
104	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
105	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
106	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
107	C₄⋊C₈	—	2	2	no	—
108	C₄⋊C₈	—	38	1	no	—
109	C₄⋊C₈	—	38	1	no	—
110	C₄⋊C₈	—	38	2	no	—
111	C₂²⋊C₈	—	2	2	no	—
112	C₂²⋊C₈	—	38	1	no	—
113	C₂²⋊C₈	—	38	1	no	—
114	C₂²⋊C₈	—	38	2	no	—
115	#97	—	2	2	no	—
116	#97	—	38	2	no	—
117	C₄×C₈	—	19	2	no	—
118	C₄×C₈	—	19	2	no	—
119	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
120	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
121	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
122	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
123	C₁₉	#8797	1	1	yes	characteristic, complemented, Sylow
124	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
125	C₂²×C₄	#64543	1	1	yes	characteristic
126	C₂²×C₄	#64545	1	1	yes	characteristic
127	C₂×C₈	—	2	2	no	—
128	C₂×C₈	—	2	2	no	—
129	C₂×C₈	—	4	2	no	—
130	C₂×C₈	—	38	2	no	—
131	C₂×C₈	—	38	2	no	—
132	C₂×C₈	—	76	2	no	—
133	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
134	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
135	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
136	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
137	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
138	C₄²	#64543	1	1	yes	characteristic
139	C₄²	#64545	1	1	yes	characteristic
140	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
141	C₂³	#10597336	1	1	yes	characteristic
142	C₂×C₄	—	2	1	no	—
143	C₂×C₄	—	2	1	no	—
144	C₂×C₄	—	4	1	no	—
145	C₂×C₄	—	4	1	no	—
146	C₂×C₄	#10597336	1	1	yes	characteristic
147	C₂×C₄	#10597338	1	1	yes	characteristic
148	C₂×C₄	#10597338	1	1	yes	characteristic
149	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
150	C₂×C₄	#10597382	1	1	yes	characteristic
151	C₂×C₄	#10597393	1	1	yes	characteristic
152	C₈	—	2	1	no	—
153	C₈	—	2	1	no	—
154	C₈	—	8	2	no	—
155	C₈	—	76	2	no	—
156	C₈	—	76	2	no	—
157	C₈	—	152	2	no	—
158	C₈	#10597279	1	2	yes	—
159	C₈	#10597279	1	2	yes	—
160	C₂²	—	2	1	no	—
161	C₂²	—	2	1	no	—
162	C₂²	—	2	1	no	—
163	C₂²	#11926409	1	1	yes	characteristic
164	C₄	—	2	1	no	—
165	C₄	—	2	1	no	—
166	C₄	—	2	1	no	—
167	C₄	—	2	1	no	—
168	C₄	—	2	1	no	—
169	C₄	C₂×#10597279	1	1	yes	characteristic
170	C₄	C₂×#10597279	1	1	yes	characteristic
171	C₂	—	4	1	no	—
172	C₂	#14563758	1	1	yes	characteristic
173	C₂	#14563760	1	1	yes	characteristic
174	C₂	#14563772	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14562398

C₂

yes

maximal, characteristic

#14561918

C₂

yes

maximal, characteristic

#14561498

C₂

yes

maximal

#14561496

C₂

yes

maximal

C₁₉×#1568

C₂

yes

maximal, characteristic

#11926601

C₂²

yes

—

#11926597

C₂²

yes

characteristic

#11926597

C₂²

yes

—

—

C₄

yes

—

C₈×C₁₉⋊C₈

C₄

yes

—

C₁₉×#432

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₁₉×#334

—

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×Q₈

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

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

#108

yes

—

C₈×C₁₉

#108

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1568

—

#1568

D₁₉

yes

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#382

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₂×D₁₉

yes

—

#431

—

#431

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

—

—

—

—

C₈²

—

100

C₂×C₁₉

—

101

C₂×C₁₉

#1833

yes

characteristic

102

C₂×C₁₉

#1833

yes

characteristic

103

C₂×C₁₉

#1837

yes

characteristic

104

C₂²×C₈

Dic₃₈

yes

characteristic

105

C₂²×C₈

Dic₃₈

yes

characteristic

106

C₂×C₄²

C₂²×D₁₉

yes

characteristic

107

C₄⋊C₈

—

108

C₄⋊C₈

—

109

C₄⋊C₈

—

110

C₄⋊C₈

—

111

C₂²⋊C₈

—

112

C₂²⋊C₈

—

113

C₂²⋊C₈

—

114

C₂²⋊C₈

—

115

#97

—

116

#97

—

117

C₄×C₈

—

118

C₄×C₈

—

119

C₄×C₈

C₄×D₁₉

yes

characteristic

120

C₄×C₈

C₄×D₁₉

yes

characteristic

121

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

122

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

123

C₁₉

#8797

yes

characteristic, complemented, Sylow

124

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

125

C₂²×C₄

#64543

yes

characteristic

126

C₂²×C₄

#64545

yes

characteristic

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

134

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

135

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

136

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

137

C₄²

C₂×C₄×D₁₉

yes

characteristic

138

C₄²

#64543

yes

characteristic

139

C₄²

#64545

yes

characteristic

140

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

141

C₂³

#10597336

yes

characteristic

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

#10597336

yes

characteristic

147

C₂×C₄

#10597338

yes

characteristic

148

C₂×C₄

#10597338

yes

characteristic

149

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

150

C₂×C₄

#10597382

yes

characteristic

151

C₂×C₄

#10597393

yes

characteristic

152

C₈

—

153

C₈

—

154

C₈

—

155

C₈

—

156

C₈

—

157

C₈

—

152

—

158

C₈

#10597279

yes

—

159

C₈

#10597279

yes

—

160

C₂²

—

161

C₂²

—

162

C₂²

—

163

C₂²

#11926409

yes

characteristic

164

C₄

—

165

C₄

—

166

C₄

—

167

C₄

—

168

C₄

—

169

C₄

C₂×#10597279

yes

characteristic

170

C₄

C₂×#10597279

yes

characteristic

171

C₂

—

172

C₂

#14563758

yes

characteristic

173

C₂

#14563760

yes

characteristic

174

C₂

#14563772

yes

characteristic

	subgroup	G/H
center	C₂²	#11926409
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1568	C₂
socle	C₂²×C₁₉	#382
prime radical	C₂³×C₁₉	#125
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1568	D₁₉
hypocenter	C₁₉	#8797
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

subgroup

G/H

center

C₂²

#11926409

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1568

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

N	H ≅ G/N	type
123. C₁₉	#8797	semidirect

H ≅ G/N

type

123. C₁₉

#8797

semidirect

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

subgroup	index
#14562398	2
#14561918	2
#14561498	2
#14561496	2
C₁₉×#1568	2
#8797	19

subgroup

index

C₁₉×#1568

Subgroups — #18076248

Conjugacy classes of subgroups

Complements

Maximal subgroups