Group #18069896 — subgroups

Subgroups — #18069896

Order 4864.

324 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 43 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	#14561571	C₂	1	2	yes	maximal
2	C₁₉×#1784	C₂	1	1	yes	maximal, characteristic
3	#11926326	—	2	2	no	—
4	C₂³×Q₈×C₁₉	C₄	1	1	yes	characteristic
5	C₂×C₁₉×#101	—	2	2	no	—
6	C₁₉×#407	C₄	1	1	yes	characteristic
7	C₁₉×#407	C₂²	1	1	yes	characteristic
8	C₂²×Q₈×C₁₉	—	2	1	no	—
9	C₂²×Q₈×C₁₉	—	4	1	no	—
10	C₂²×Q₈×C₁₉	—	4	1	no	—
11	C₂²×Q₈×C₁₉	—	4	4	no	—
12	C₂²×Q₈×C₁₉	C₈	1	2	yes	—
13	C₂³×C₄×C₁₉	—	2	1	no	—
14	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂×M₁₆×C₁₉	—	2	1	no	—
16	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
17	C₁₉×#101	—	4	4	no	—
18	C₁₉×C₂²⋊C₈	—	4	1	no	—
19	C₁₉×C₂²⋊C₈	—	4	1	no	—
20	#10597269	—	4	2	no	—
21	C₂⁴×C₁₉	M₁₆	1	1	yes	characteristic
22	C₂×Q₈×C₁₉	—	2	4	no	—
23	C₂×Q₈×C₁₉	—	4	4	no	—
24	C₂×Q₈×C₁₉	—	4	2	no	—
25	C₂×Q₈×C₁₉	—	4	2	no	—
26	C₂×Q₈×C₁₉	—	4	4	no	—
27	C₂×Q₈×C₁₉	—	4	8	no	—
28	C₂×Q₈×C₁₉	—	4	4	no	—
29	C₂×Q₈×C₁₉	—	4	1	no	—
30	C₂×Q₈×C₁₉	—	4	1	no	—
31	C₂²×C₄×C₁₉	—	2	2	no	—
32	C₂²×C₄×C₁₉	—	2	1	no	—
33	C₂²×C₄×C₁₉	—	2	1	no	—
34	C₂²×C₄×C₁₉	—	4	4	no	—
35	C₂²×C₄×C₁₉	—	4	2	no	—
36	C₂²×C₄×C₁₉	—	4	2	no	—
37	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
39	M₁₆×C₁₉	—	4	2	no	—
40	M₁₆×C₁₉	—	4	2	no	—
41	C₂×C₈×C₁₉	—	2	2	no	—
42	C₂×C₈×C₁₉	—	4	1	no	—
43	C₁₉⋊C₁₆	—	8	2	no	—
44	#7343	—	19	1	no	maximal, Sylow
45	C₂³×C₁₉	—	2	1	no	—
46	C₂³×C₁₉	—	4	1	no	—
47	C₂³×C₁₉	—	4	2	no	—
48	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
49	Q₈×C₁₉	—	4	4	no	—
50	Q₈×C₁₉	—	4	4	no	—
51	Q₈×C₁₉	—	4	4	no	—
52	Q₈×C₁₉	—	4	4	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	2	4	no	—
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	4	2	no	—
57	C₂×C₄×C₁₉	—	4	2	no	—
58	C₂×C₄×C₁₉	—	4	8	no	—
59	C₂×C₄×C₁₉	—	4	2	no	—
60	C₂×C₄×C₁₉	—	4	2	no	—
61	C₂×C₄×C₁₉	—	4	1	no	—
62	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
64	C₈×C₁₉	—	4	2	no	—
65	C₈×C₁₉	—	8	1	no	—
66	#1784	D₁₉	1	1	yes	characteristic
67	#1320	—	19	2	no	—
68	C₂²×C₁₉	—	2	2	no	—
69	C₂²×C₁₉	—	2	1	no	—
70	C₂²×C₁₉	—	4	1	no	—
71	C₂²×C₁₉	—	4	1	no	—
72	C₂²×C₁₉	—	4	2	no	—
73	C₂²×C₁₉	—	4	2	no	—
74	C₂²×C₁₉	—	4	1	no	—
75	C₂²×C₁₉	#323	1	1	yes	characteristic
76	C₄×C₁₉	—	2	1	no	—
77	C₄×C₁₉	—	4	4	no	—
78	C₄×C₁₉	—	4	1	no	—
79	C₄×C₁₉	AΣL(1,𝔽₁₆)	1	2	yes	—
80	C₂³×Q₈	Dic₁₉	1	1	yes	characteristic
81	C₂×#101	—	2	2	no	—
82	#407	Dic₁₉	1	1	yes	characteristic
83	#407	C₂×D₁₉	1	1	yes	characteristic
84	#349	—	38	2	no	—
85	C₂×C₁₉	—	2	1	no	—
86	C₂×C₁₉	—	4	2	no	—
87	C₂×C₁₉	—	4	1	no	—
88	C₂×C₁₉	#1316	1	1	yes	characteristic
89	C₂²×Q₈	—	2	1	no	—
90	C₂²×Q₈	—	4	1	no	—
91	C₂²×Q₈	—	4	1	no	—
92	C₂²×Q₈	—	4	4	no	—
93	C₂²×Q₈	C₁₉⋊C₈	1	2	yes	—
94	C₂³×C₄	—	2	1	no	—
95	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
96	C₂×M₁₆	—	2	1	no	—
97	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
98	M₃₂	—	76	2	no	—
99	#101	—	4	4	no	—
100	C₂²⋊C₈	—	4	1	no	—
101	C₂²⋊C₈	—	4	1	no	—
102	C₁₉	#7343	1	1	yes	characteristic, complemented, Sylow
103	C₂⁴	#64520	1	1	yes	characteristic
104	C₂×Q₈	—	2	4	no	—
105	C₂×Q₈	—	4	4	no	—
106	C₂×Q₈	—	4	2	no	—
107	C₂×Q₈	—	4	2	no	—
108	C₂×Q₈	—	4	4	no	—
109	C₂×Q₈	—	4	8	no	—
110	C₂×Q₈	—	4	4	no	—
111	C₂×Q₈	—	4	1	no	—
112	C₂×Q₈	—	4	1	no	—
113	C₂²×C₄	—	2	2	no	—
114	C₂²×C₄	—	2	1	no	—
115	C₂²×C₄	—	2	1	no	—
116	C₂²×C₄	—	4	4	no	—
117	C₂²×C₄	—	4	2	no	—
118	C₂²×C₄	—	4	2	no	—
119	C₂²×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
120	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
121	M₁₆	—	4	2	no	—
122	M₁₆	—	4	2	no	—
123	C₂×C₈	—	2	2	no	—
124	C₂×C₈	—	4	1	no	—
125	C₁₆	—	152	2	no	—
126	C₂³	—	2	1	no	—
127	C₂³	—	4	1	no	—
128	C₂³	—	4	2	no	—
129	C₂³	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
130	Q₈	—	4	4	no	—
131	Q₈	—	4	4	no	—
132	Q₈	—	4	4	no	—
133	Q₈	—	4	4	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	2	4	no	—
136	C₂×C₄	—	2	1	no	—
137	C₂×C₄	—	4	2	no	—
138	C₂×C₄	—	4	2	no	—
139	C₂×C₄	—	4	8	no	—
140	C₂×C₄	—	4	2	no	—
141	C₂×C₄	—	4	2	no	—
142	C₂×C₄	—	4	1	no	—
143	C₂×C₄	#10597290	1	1	yes	characteristic
144	C₂×C₄	#10597291	1	1	yes	characteristic
145	C₈	—	4	2	no	—
146	C₈	—	8	1	no	—
147	C₂²	—	2	2	no	—
148	C₂²	—	2	1	no	—
149	C₂²	—	4	1	no	—
150	C₂²	—	4	1	no	—
151	C₂²	—	4	2	no	—
152	C₂²	—	4	2	no	—
153	C₂²	—	4	1	no	—
154	C₂²	#11926268	1	1	yes	characteristic
155	C₄	—	2	1	no	—
156	C₄	—	4	4	no	—
157	C₄	—	4	1	no	—
158	C₄	#11926331	1	2	yes	—
159	C₂	—	2	1	no	—
160	C₂	—	4	2	no	—
161	C₂	—	4	1	no	—
162	C₂	#14561563	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561571

C₂

yes

maximal

C₁₉×#1784

C₂

yes

maximal, characteristic

#11926326

—

C₂³×Q₈×C₁₉

C₄

yes

characteristic

C₂×C₁₉×#101

—

C₁₉×#407

C₄

yes

characteristic

C₁₉×#407

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

C₈

yes

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

D₄

yes

—

C₁₉×#101

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

#10597269

—

C₂⁴×C₁₉

M₁₆

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₁₉⋊C₁₆

—

#7343

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₈

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×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

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

#1784

D₁₉

yes

characteristic

#1320

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#323

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

AΣL(1,𝔽₁₆)

yes

—

C₂³×Q₈

Dic₁₉

yes

characteristic

C₂×#101

—

#407

Dic₁₉

yes

characteristic

#407

C₂×D₁₉

yes

characteristic

#349

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1316

yes

characteristic

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×Q₈

C₁₉⋊C₈

yes

—

C₂³×C₄

—

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂²⋊D₁₉

yes

—

M₃₂

—

#101

—

100

C₂²⋊C₈

—

101

C₂²⋊C₈

—

102

C₁₉

#7343

yes

characteristic, complemented, Sylow

103

C₂⁴

#64520

yes

characteristic

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

—

108

C₂×Q₈

—

109

C₂×Q₈

—

110

C₂×Q₈

—

111

C₂×Q₈

—

112

C₂×Q₈

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

C₂×C₁₉⋊C₈

yes

characteristic

120

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

121

M₁₆

—

122

M₁₆

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₁₆

—

152

—

126

C₂³

—

127

C₂³

—

128

C₂³

—

129

C₂³

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

130

Q₈

—

131

Q₈

—

132

Q₈

—

133

Q₈

—

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

—

143

C₂×C₄

#10597290

yes

characteristic

144

C₂×C₄

#10597291

yes

characteristic

145

C₈

—

146

C₈

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

#11926268

yes

characteristic

155

C₄

—

156

C₄

—

157

C₄

—

158

C₄

#11926331

yes

—

159

C₂

—

160

C₂

—

161

C₂

—

162

C₂

#14561563

yes

characteristic

	subgroup	G/H
center	C₂	#14561563
commutator	C₂²×C₄×C₁₉	C₂×C₈
Frattini	#407	C₂×D₁₉
Fitting	C₁₉×#1784	C₂
socle	C₂×C₁₉	#1316
prime radical	C₂⁴×C₁₉	M₁₆
cosocle	C₁₉×#407	C₂²
hypercenter	#1784	D₁₉
hypocenter	C₁₉	#7343
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #407 ◁ #1784

subgroup

G/H

center

C₂

#14561563

commutator

C₂²×C₄×C₁₉

C₂×C₈

Frattini

#407

C₂×D₁₉

Fitting

C₁₉×#1784

C₂

socle

C₂×C₁₉

#1316

prime radical

C₂⁴×C₁₉

M₁₆

cosocle

C₁₉×#407

C₂²

D₁₉

C₁₉

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

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #407 ◁ #1784

N	H ≅ G/N	type
102. C₁₉	#7343	semidirect

H ≅ G/N

type

102. C₁₉

#7343

semidirect

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

subgroup	index
#14561571	2
C₁₉×#1784	2
#7343	19

subgroup

index

#14561571

C₁₉×#1784

#7343

Subgroups — #18069896

Conjugacy classes of subgroups

Complements

Maximal subgroups