Group #18069837 — subgroups

Subgroups — #18069837

Order 4864.

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

normal subgroups only

This group has 432 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	#14563559	C₂	1	2	yes	maximal
2	C₁₉×#1784	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597293	—	2	2	no	—
4	C₂×#10597293	C₄	1	4	yes	—
5	#11926508	—	2	2	no	—
6	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×#101	—	2	2	no	—
8	C₁₉×#407	C₄	1	2	yes	—
9	C₂²×Q₈×C₁₉	—	4	2	no	—
10	C₂²×Q₈×C₁₉	—	4	4	no	—
11	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
12	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
13	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	Q₈	1	1	yes	characteristic
16	C₂×M₁₆×C₁₉	—	2	2	no	—
17	C₂×#64520	—	2	4	no	—
18	C₁₉×#101	—	4	4	no	—
19	C₁₉×C₂²⋊C₈	—	4	2	no	—
20	#10597293	—	4	4	no	—
21	#10597293	—	4	4	no	—
22	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
23	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
24	C₂×Q₈×C₁₉	—	2	4	no	—
25	C₂×Q₈×C₁₉	—	2	4	no	—
26	C₂×Q₈×C₁₉	—	2	4	no	—
27	C₂×Q₈×C₁₉	—	4	2	no	—
28	C₂×Q₈×C₁₉	—	4	2	no	—
29	C₂×Q₈×C₁₉	—	4	2	no	—
30	C₂×Q₈×C₁₉	—	4	16	no	—
31	C₂²×C₄×C₁₉	—	2	2	no	—
32	C₂²×C₄×C₁₉	—	2	4	no	—
33	C₂²×C₄×C₁₉	—	4	2	no	—
34	C₂²×C₄×C₁₉	—	4	1	no	—
35	C₂²×C₄×C₁₉	—	4	2	no	—
36	C₂²×C₄×C₁₉	—	4	1	no	—
37	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
39	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
41	M₁₆×C₁₉	—	4	4	no	—
42	C₂×C₈×C₁₉	—	4	2	no	—
43	#64520	—	4	4	no	—
44	#64520	—	4	4	no	—
45	C₂×C₁₉⋊C₈	—	4	4	no	—
46	#7315	—	19	1	no	maximal, Sylow
47	C₂³×C₁₉	—	2	2	no	—
48	C₂³×C₁₉	—	2	1	no	—
49	C₂³×C₁₉	—	4	2	no	—
50	C₂³×C₁₉	#95	1	1	yes	characteristic
51	Q₈×C₁₉	—	4	8	no	—
52	Q₈×C₁₉	—	4	8	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	—	2	1	no	—
57	C₂×C₄×C₁₉	—	2	2	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	—	4	4	no	—
62	C₂×C₄×C₁₉	—	4	4	no	—
63	C₂×C₄×C₁₉	—	4	4	no	—
64	C₂×C₄×C₁₉	#99	1	4	yes	—
65	C₂×C₄×C₁₉	#99	1	2	yes	—
66	C₈×C₁₉	—	8	2	no	—
67	C₁₉⋊C₈	—	8	4	no	—
68	#1784	—	19	2	no	—
69	#1784	D₁₉	1	1	yes	characteristic
70	C₂²×C₁₉	—	2	4	no	—
71	C₂²×C₁₉	—	2	2	no	—
72	C₂²×C₁₉	—	4	1	no	—
73	C₂²×C₁₉	—	4	2	no	—
74	C₂²×C₁₉	—	4	1	no	—
75	C₂²×C₁₉	—	4	1	no	—
76	C₂²×C₁₉	#342	1	2	yes	—
77	C₂²×C₁₉	#342	1	1	yes	characteristic
78	C₄×C₁₉	—	2	4	no	—
79	C₄×C₁₉	—	2	2	no	—
80	C₄×C₁₉	—	4	1	no	—
81	C₄×C₁₉	—	4	2	no	—
82	C₂³×Q₈	C₂×D₁₉	1	1	yes	characteristic
83	C₂×#101	—	2	2	no	—
84	C₂×#101	—	19	4	no	—
85	C₂×#101	—	38	2	no	—
86	#407	—	38	2	no	—
87	#407	Dic₁₉	1	2	yes	—
88	C₂×C₁₉	—	2	2	no	—
89	C₂×C₁₉	—	2	1	no	—
90	C₂×C₁₉	—	4	2	no	—
91	C₂×C₁₉	#1304	1	1	yes	characteristic
92	C₂²×Q₈	—	4	4	no	—
93	C₂²×Q₈	—	4	2	no	—
94	C₂²×Q₈	C₄×D₁₉	1	2	yes	—
95	C₂²×Q₈	C₂²⋊D₁₉	1	2	yes	—
96	C₂³×C₄	Dic₃₈	1	1	yes	characteristic
97	C₂³×C₄	D₇₆	1	1	yes	characteristic
98	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
99	C₂×M₁₆	—	2	2	no	—
100	C₂×M₁₆	—	38	4	no	—
101	#101	—	4	4	no	—
102	#101	—	76	4	no	—
103	#101	—	76	4	no	—
104	C₂²⋊C₈	—	4	2	no	—
105	C₂²⋊C₈	—	76	4	no	—
106	C₁₉	#7315	1	1	yes	characteristic, complemented, Sylow
107	C₂⁴	C₄⋊Dic₁₉	1	1	yes	characteristic
108	C₂×Q₈	—	2	4	no	—
109	C₂×Q₈	—	2	4	no	—
110	C₂×Q₈	—	2	4	no	—
111	C₂×Q₈	—	4	2	no	—
112	C₂×Q₈	—	4	2	no	—
113	C₂×Q₈	—	4	2	no	—
114	C₂×Q₈	—	4	16	no	—
115	C₂²×C₄	—	2	4	no	—
116	C₂²×C₄	—	2	2	no	—
117	C₂²×C₄	—	4	2	no	—
118	C₂²×C₄	—	4	1	no	—
119	C₂²×C₄	—	4	1	no	—
120	C₂²×C₄	—	4	2	no	—
121	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
122	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
123	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
124	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
125	M₁₆	—	4	4	no	—
126	M₁₆	—	76	4	no	—
127	M₁₆	—	76	4	no	—
128	C₂×C₈	—	4	2	no	—
129	C₂×C₈	—	76	4	no	—
130	C₂³	—	2	2	no	—
131	C₂³	—	2	1	no	—
132	C₂³	—	4	2	no	—
133	C₂³	C₁₉⋊#95	1	1	yes	characteristic
134	Q₈	—	4	8	no	—
135	Q₈	—	4	8	no	—
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	—	2	2	no	—
138	C₂×C₄	—	2	2	no	—
139	C₂×C₄	—	2	2	no	—
140	C₂×C₄	—	2	2	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	2	1	no	—
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	—	4	4	no	—
145	C₂×C₄	—	4	4	no	—
146	C₂×C₄	—	4	4	no	—
147	C₂×C₄	#10597263	1	4	yes	—
148	C₂×C₄	#10597291	1	2	yes	—
149	C₈	—	8	2	no	—
150	C₈	—	152	4	no	—
151	C₂²	—	2	4	no	—
152	C₂²	—	2	2	no	—
153	C₂²	—	4	1	no	—
154	C₂²	—	4	2	no	—
155	C₂²	—	4	1	no	—
156	C₂²	—	4	1	no	—
157	C₂²	#11926310	1	2	yes	—
158	C₂²	#11926311	1	1	yes	characteristic
159	C₄	—	2	2	no	—
160	C₄	—	2	4	no	—
161	C₄	—	4	1	no	—
162	C₄	—	4	2	no	—
163	C₂	—	2	2	no	—
164	C₂	—	2	1	no	—
165	C₂	—	4	2	no	—
166	C₂	C₁₉⋊#1304	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563559

C₂

yes

maximal

C₁₉×#1784

C₂

yes

maximal, characteristic

C₂×#10597293

—

C₂×#10597293

C₄

yes

—

#11926508

—

C₂³×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#101

—

C₁₉×#407

C₄

yes

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

—

C₂²×Q₈×C₁₉

D₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

Q₈

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×#64520

—

C₁₉×#101

—

C₁₉×C₂²⋊C₈

—

#10597293

—

#10597293

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₄⋊C₄

yes

characteristic

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

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

#7315

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#95

yes

characteristic

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#99

yes

—

C₂×C₄×C₁₉

#99

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1784

—

#1784

D₁₉

yes

characteristic

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

—

C₂³×Q₈

C₂×D₁₉

yes

—

—

—

—

Dic₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1304

yes

characteristic

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×Q₈

C₄×D₁₉

yes

—

C₂²×Q₈

C₂²⋊D₁₉

yes

—

C₂³×C₄

Dic₃₈

yes

characteristic

C₂³×C₄

D₇₆

yes

characteristic

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

C₂×M₁₆

—

100

C₂×M₁₆

—

101

#101

—

102

#101

—

103

#101

—

104

C₂²⋊C₈

—

105

C₂²⋊C₈

—

106

C₁₉

#7315

yes

characteristic, complemented, Sylow

107

C₂⁴

C₄⋊Dic₁₉

yes

characteristic

108

C₂×Q₈

—

109

C₂×Q₈

—

110

C₂×Q₈

—

111

C₂×Q₈

—

112

C₂×Q₈

—

113

C₂×Q₈

—

114

C₂×Q₈

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

122

C₂²×C₄

Dic₁₉⋊C₄

yes

—

123

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

124

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

125

M₁₆

—

126

M₁₆

—

127

M₁₆

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂³

—

131

C₂³

—

132

C₂³

—

133

C₂³

C₁₉⋊#95

yes

characteristic

134

Q₈

—

135

Q₈

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

#10597263

yes

—

148

C₂×C₄

#10597291

yes

—

149

C₈

—

150

C₈

—

152

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

#11926310

yes

—

158

C₂²

#11926311

yes

characteristic

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

—

163

C₂

—

164

C₂

—

165

C₂

—

166

C₂

C₁₉⋊#1304

yes

characteristic

	subgroup	G/H
center	C₂	C₁₉⋊#1304
commutator	C₂²×C₄×C₁₉	C₄²
Frattini	C₂³×Q₈	C₂×D₁₉
Fitting	C₁₉×#1784	C₂
socle	C₂×C₁₉	#1304
prime radical	C₂⁴×C₁₉	C₄⋊C₄
cosocle	C₂³×Q₈×C₁₉	C₂²
hypercenter	#1784	D₁₉
hypocenter	C₁₉	#7315
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂³×Q₈ ◁ #1784

subgroup

G/H

center

C₂

C₁₉⋊#1304

commutator

C₂²×C₄×C₁₉

C₄²

Frattini

C₂³×Q₈

C₂×D₁₉

Fitting

C₁₉×#1784

C₂

socle

C₂×C₁₉

#1304

prime radical

C₂⁴×C₁₉

C₄⋊C₄

cosocle

C₂³×Q₈×C₁₉

C₂²

D₁₉

C₁₉

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

UCS

C₁ ◁ C₂ ◁ C₂³ ◁ C₂³×Q₈ ◁ #1784

N	H ≅ G/N	type
106. C₁₉	#7315	semidirect

H ≅ G/N

type

106. C₁₉

#7315

semidirect

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

subgroup	index
#14563559	2
C₁₉×#1784	2
#7315	19

subgroup

index

#14563559

C₁₉×#1784

#7315

Subgroups — #18069837

Conjugacy classes of subgroups

Complements

Maximal subgroups