Group #18070137 — subgroups

Subgroups — #18070137

Order 4864.

210 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 37 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	#14565151	C₂	1	1	yes	maximal, characteristic
2	#14561520	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1320	C₂	1	1	yes	maximal, characteristic
4	#11926593	C₄	1	1	yes	characteristic, complemented
5	#11926592	—	2	1	no	—
6	#11926508	—	2	1	no	—
7	C₄×C₂²⋊Dic₁₉	—	2	1	no	—
8	C₁₉⋊#338	C₄	1	1	yes	characteristic, complemented
9	C₁₉×#407	C₂²	1	1	yes	characteristic
10	C₁₉×#349	—	2	1	no	—
11	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
12	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
14	C₂×C₂²⋊Dic₁₉	—	4	1	no	—
15	C₂×C₄×Dic₁₉	—	4	1	no	—
16	C₂×#64520	—	2	1	no	—
17	C₂×#64520	—	2	1	no	—
18	C₁₉×M₃₂	—	4	1	no	—
19	C₁₉×C₂²⋊C₈	—	4	1	no	—
20	C₁₉⋊#95	—	2	2	no	—
21	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
22	#10597279	—	4	2	no	—
23	#10597276	—	4	1	no	—
24	C₂⁴×C₁₉	SD₁₆	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	—	2	1	no	—
26	C₂²×C₄×C₁₉	—	2	1	no	—
27	C₂²×C₄×C₁₉	—	4	1	no	—
28	C₂²×C₄×C₁₉	—	4	1	no	—
29	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
31	C₂²×Dic₁₉	—	4	2	no	—
32	M₁₆×C₁₉	—	4	1	no	—
33	M₁₆×C₁₉	—	4	1	no	—
34	C₂×C₈×C₁₉	—	2	1	no	—
35	C₂×C₈×C₁₉	—	2	1	no	—
36	C₂²⋊Dic₁₉	—	4	4	no	—
37	C₄×Dic₁₉	—	8	1	no	—
38	C₄×Dic₁₉	—	8	1	no	—
39	#64520	—	4	1	no	—
40	#64520	—	4	1	no	—
41	#64520	—	4	1	no	—
42	#64520	—	4	1	no	—
43	C₂×C₁₉⋊C₈	—	2	2	no	—
44	C₂×C₁₉⋊C₈	—	4	1	no	—
45	C₁₆×C₁₉	—	8	1	no	—
46	#7432	—	19	1	no	maximal, Sylow
47	C₂³×C₁₉	—	2	1	no	—
48	C₂³×C₁₉	—	4	2	no	—
49	C₂³×C₁₉	—	4	1	no	—
50	C₂³×C₁₉	#103	1	1	yes	characteristic
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	2	1	no	—
54	C₂×C₄×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	—	4	1	no	—
56	C₂×C₄×C₁₉	—	4	1	no	—
57	C₂×C₄×C₁₉	—	8	1	no	—
58	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
59	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
60	C₂×Dic₁₉	—	4	4	no	—
61	C₂×Dic₁₉	—	8	2	no	—
62	C₂×Dic₁₉	—	8	2	no	—
63	C₈×C₁₉	—	4	1	no	—
64	C₈×C₁₉	—	4	1	no	—
65	C₁₉⋊C₈	—	4	2	no	—
66	C₁₉⋊C₈	—	8	1	no	—
67	#2091	—	19	1	no	—
68	#1320	D₁₉	1	1	yes	characteristic
69	#1297	—	19	1	no	—
70	C₂²×C₁₉	—	2	2	no	—
71	C₂²×C₁₉	—	2	1	no	—
72	C₂²×C₁₉	—	4	1	no	—
73	C₂²×C₁₉	—	4	1	no	—
74	C₂²×C₁₉	—	4	2	no	—
75	C₂²×C₁₉	—	4	1	no	—
76	C₂²×C₁₉	—	8	1	no	—
77	C₂²×C₁₉	#328	1	1	yes	characteristic
78	C₄×C₁₉	—	2	1	no	—
79	C₄×C₁₉	—	4	1	no	—
80	C₄×C₁₉	#352	1	1	yes	characteristic
81	C₄×C₁₉	#353	1	1	yes	characteristic
82	Dic₁₉	—	8	4	no	—
83	#430	—	19	1	no	—
84	#430	—	38	1	no	—
85	#407	—	38	1	no	—
86	#407	C₂×D₁₉	1	1	yes	characteristic
87	C₄×C₂²⋊C₄	—	38	1	no	—
88	#349	—	2	1	no	—
89	#338	—	19	1	no	—
90	C₂×C₁₉	—	2	1	no	—
91	C₂×C₁₉	—	4	2	no	—
92	C₂×C₁₉	—	4	1	no	—
93	C₂×C₁₉	#1352	1	1	yes	characteristic
94	C₂³×C₄	D₇₆	1	1	yes	characteristic
95	C₂×M₁₆	—	38	1	no	—
96	C₂×M₁₆	—	38	1	no	—
97	C₂×M₁₆	C₄×D₁₉	1	1	yes	characteristic
98	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
99	C₂×C₂²⋊C₄	—	76	1	no	—
100	C₂×C₄²	—	76	1	no	—
101	M₃₂	—	4	1	no	—
102	#108	—	76	1	no	—
103	#108	—	76	2	no	—
104	C₂²⋊C₈	—	4	1	no	—
105	C₂²⋊C₈	—	76	2	no	—
106	#95	—	38	2	no	—
107	C₁₉	#7432	1	1	yes	characteristic, complemented, Sylow
108	C₂⁴	#64516	1	1	yes	characteristic
109	C₂²×C₄	—	2	1	no	—
110	C₂²×C₄	—	2	1	no	—
111	C₂²×C₄	—	4	1	no	—
112	C₂²×C₄	—	4	1	no	—
113	C₂²×C₄	—	76	2	no	—
114	C₂²×C₄	Dic₇₆	1	1	yes	characteristic
115	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
116	M₁₆	—	4	1	no	—
117	M₁₆	—	4	1	no	—
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	—	38	2	no	—
125	C₂×C₈	—	76	1	no	—
126	C₂²⋊C₄	—	76	4	no	—
127	C₄²	—	152	1	no	—
128	C₄²	—	152	1	no	—
129	C₁₆	—	8	1	no	—
130	C₂³	—	2	1	no	—
131	C₂³	—	4	2	no	—
132	C₂³	—	4	1	no	—
133	C₂³	#10597273	1	1	yes	characteristic
134	C₂×C₄	—	2	1	no	—
135	C₂×C₄	—	2	1	no	—
136	C₂×C₄	—	2	1	no	—
137	C₂×C₄	—	4	1	no	—
138	C₂×C₄	—	4	1	no	—
139	C₂×C₄	—	4	1	no	—
140	C₂×C₄	—	8	1	no	—
141	C₂×C₄	—	76	4	no	—
142	C₂×C₄	—	152	2	no	—
143	C₂×C₄	—	152	2	no	—
144	C₂×C₄	#10597263	1	1	yes	characteristic
145	C₂×C₄	#10597282	1	1	yes	characteristic
146	C₈	—	4	1	no	—
147	C₈	—	4	1	no	—
148	C₈	—	76	2	no	—
149	C₈	—	152	1	no	—
150	C₂²	—	2	2	no	—
151	C₂²	—	2	1	no	—
152	C₂²	—	4	1	no	—
153	C₂²	—	4	1	no	—
154	C₂²	—	4	2	no	—
155	C₂²	—	4	1	no	—
156	C₂²	—	8	1	no	—
157	C₂²	#11926282	1	1	yes	characteristic
158	C₄	—	2	1	no	—
159	C₄	—	4	1	no	—
160	C₄	—	152	4	no	—
161	C₄	#11926335	1	1	yes	characteristic
162	C₄	#11926336	1	1	yes	characteristic
163	C₂	—	2	1	no	—
164	C₂	—	4	2	no	—
165	C₂	—	4	1	no	—
166	C₂	#14561660	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565151

C₂

yes

maximal, characteristic

#14561520

C₂

yes

maximal, characteristic

C₁₉×#1320

C₂

yes

maximal, characteristic

#11926593

C₄

yes

characteristic, complemented

#11926592

—

#11926508

—

C₄×C₂²⋊Dic₁₉

—

C₁₉⋊#338

C₄

yes

characteristic, complemented

C₁₉×#407

C₂²

yes

characteristic

C₁₉×#349

—

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂×#64520

—

C₂×#64520

—

C₁₉×M₃₂

—

C₁₉×C₂²⋊C₈

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

#10597279

—

#10597276

—

C₂⁴×C₁₉

SD₁₆

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

Q₁₆

yes

characteristic

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂²⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

—

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

#7432

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#103

yes

characteristic

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

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2091

—

#1320

D₁₉

yes

characteristic

#1297

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#328

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

—

—

—

C₂×D₁₉

yes

characteristic

C₄×C₂²⋊C₄

—

#349

—

#338

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1352

yes

characteristic

C₂³×C₄

D₇₆

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₄×D₁₉

yes

characteristic

C₂×M₁₆

C₂²⋊D₁₉

yes

characteristic

C₂×C₂²⋊C₄

—

100

C₂×C₄²

—

101

M₃₂

—

102

#108

—

103

#108

—

104

C₂²⋊C₈

—

105

C₂²⋊C₈

—

106

#95

—

107

C₁₉

#7432

yes

characteristic, complemented, Sylow

108

C₂⁴

#64516

yes

characteristic

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

Dic₇₆

yes

characteristic

115

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

116

M₁₆

—

117

M₁₆

—

118

M₁₆

—

119

M₁₆

—

120

M₁₆

—

121

M₁₆

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂²⋊C₄

—

127

C₄²

—

152

—

128

C₄²

—

152

—

129

C₁₆

—

130

C₂³

—

131

C₂³

—

132

C₂³

—

133

C₂³

#10597273

yes

characteristic

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

—

152

—

143

C₂×C₄

—

152

—

144

C₂×C₄

#10597263

yes

characteristic

145

C₂×C₄

#10597282

yes

characteristic

146

C₈

—

147

C₈

—

148

C₈

—

149

C₈

—

152

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

#11926282

yes

characteristic

158

C₄

—

159

C₄

—

160

C₄

—

152

—

161

C₄

#11926335

yes

characteristic

162

C₄

#11926336

yes

characteristic

163

C₂

—

164

C₂

—

165

C₂

—

166

C₂

#14561660

yes

characteristic

	subgroup	G/H
center	C₄	#11926336
commutator	C₂×M₁₆×C₁₉	C₂×C₄
Frattini	#407	C₂×D₁₉
Fitting	C₁₉×#1320	C₂
socle	C₂×C₁₉	#1352
prime radical	C₂⁴×C₁₉	SD₁₆
cosocle	C₁₉×#407	C₂²
hypercenter	#1320	D₁₉
hypocenter	C₁₉	#7432
LCS	G ▷ C₂×M₁₆×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #407 ◁ #1320

subgroup

G/H

center

C₄

#11926336

commutator

C₂×M₁₆×C₁₉

C₂×C₄

Frattini

#407

C₂×D₁₉

Fitting

C₁₉×#1320

C₂

socle

C₂×C₁₉

#1352

prime radical

C₂⁴×C₁₉

SD₁₆

cosocle

C₁₉×#407

C₂²

D₁₉

C₁₉

G ▷ C₂×M₁₆×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #407 ◁ #1320

N	H ≅ G/N	type
4. #11926593	C₄	semidirect
8. C₁₉⋊#338	C₄	semidirect
107. C₁₉	#7432	semidirect

H ≅ G/N

type

4. #11926593

C₄

semidirect

8. C₁₉⋊#338

C₄

semidirect

107. C₁₉

#7432

semidirect

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

subgroup	index
#14565151	2
#14561520	2
C₁₉×#1320	2
#7432	19

subgroup

index

#14565151

#14561520

C₁₉×#1320

#7432

Subgroups — #18070137

Conjugacy classes of subgroups

Complements

Maximal subgroups