Group #18069250 — subgroups

Subgroups — #18069250

Order 4864.

180 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 49 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	#14565128	C₂	1	1	yes	maximal, characteristic
2	#14561575	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1292	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597275	C₄	1	1	yes	characteristic
5	#11926442	—	2	1	no	—
6	C₂²⋊(C₁₉⋊C₁₆)	—	2	1	no	—
7	#11926307	—	2	1	no	—
8	#11926307	C₄	1	1	yes	characteristic
9	C₁₉×#423	—	2	1	no	—
10	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×M₁₆×C₁₉	—	4	1	no	—
12	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
14	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
15	C₂×C₄⋊Dic₁₉	—	2	1	no	—
16	C₂×C₄⋊Dic₁₉	—	2	1	no	—
17	C₂×Dic₁₉⋊C₄	—	4	1	no	—
18	C₁₉×C₄⋊C₈	—	2	2	no	—
19	C₁₉×C₄⋊C₈	—	4	1	no	—
20	C₁₉×C₄⋊C₈	—	4	1	no	—
21	C₁₉⋊#95	—	4	1	no	—
22	#10597275	—	4	1	no	—
23	C₂×C₁₉⋊C₁₆	—	4	1	no	—
24	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
27	C₂²×Dic₁₉	—	4	1	no	—
28	C₂²×Dic₁₉	—	4	1	no	—
29	M₁₆×C₁₉	—	8	1	no	—
30	M₁₆×C₁₉	—	8	1	no	—
31	C₂×C₈×C₁₉	—	2	1	no	—
32	C₂×C₈×C₁₉	—	2	1	no	—
33	C₂×C₈×C₁₉	—	4	1	no	—
34	C₂×C₈×C₁₉	—	4	1	no	—
35	C₂×C₈×C₁₉	—	4	2	no	—
36	C₄²×C₁₉	—	2	1	no	—
37	C₄²×C₁₉	—	2	1	no	—
38	C₄⋊Dic₁₉	—	2	2	no	—
39	C₄⋊Dic₁₉	—	4	1	no	—
40	C₄⋊Dic₁₉	—	4	1	no	—
41	C₄⋊Dic₁₉	—	4	1	no	—
42	Dic₁₉⋊C₄	—	8	2	no	—
43	C₁₉⋊C₁₆	—	8	1	no	—
44	#7089	—	19	1	no	maximal, Sylow
45	C₂³×C₁₉	#102	1	1	yes	characteristic
46	C₂×C₄×C₁₉	—	2	1	no	—
47	C₂×C₄×C₁₉	—	2	1	no	—
48	C₂×C₄×C₁₉	—	2	1	no	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
53	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
54	C₂×C₄×C₁₉	SD₃₂	1	1	yes	characteristic
55	C₂×C₄×C₁₉	Q₃₂	1	1	yes	characteristic
56	C₂×Dic₁₉	—	4	2	no	—
57	C₂×Dic₁₉	—	8	1	no	—
58	C₂×Dic₁₉	—	8	1	no	—
59	C₂×Dic₁₉	—	8	1	no	—
60	C₂×Dic₁₉	—	8	1	no	—
61	C₂×Dic₁₉	—	8	1	no	—
62	C₈×C₁₉	—	4	1	no	—
63	C₈×C₁₉	—	4	1	no	—
64	C₈×C₁₉	—	8	2	no	—
65	#2087	—	19	1	no	—
66	#1322	—	19	1	no	—
67	#1292	D₁₉	1	1	yes	characteristic
68	C₂²×C₁₉	—	2	1	no	—
69	C₂²×C₁₉	—	2	1	no	—
70	C₂²×C₁₉	#327	1	1	yes	characteristic
71	C₂²×C₁₉	#358	1	1	yes	characteristic
72	C₂²×C₁₉	#360	1	1	yes	characteristic
73	C₄×C₁₉	—	2	1	no	—
74	C₄×C₁₉	—	2	1	no	—
75	C₄×C₁₉	—	2	1	no	—
76	C₄×C₁₉	—	4	1	no	—
77	C₄×C₁₉	#352	1	1	yes	characteristic
78	C₄×C₁₉	#356	1	1	yes	characteristic
79	Dic₁₉	—	8	2	no	—
80	Dic₁₉	—	16	1	no	—
81	C₂×#107	—	19	1	no	—
82	#423	—	2	1	no	—
83	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
84	#389	—	38	1	no	—
85	C₂²⋊C₁₆	—	38	1	no	—
86	#340	—	19	1	no	—
87	#340	—	38	1	no	—
88	C₂×C₁₉	—	2	1	no	—
89	C₂×C₁₉	—	2	1	no	—
90	C₂×C₁₉	#1341	1	1	yes	characteristic
91	C₂×C₁₉	#1346	1	1	yes	characteristic
92	C₂×C₁₉	#1348	1	1	yes	characteristic
93	C₂×M₁₆	—	4	1	no	—
94	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
95	C₂²×C₈	D₇₆	1	1	yes	characteristic
96	C₂×C₄⋊C₄	—	38	1	no	—
97	C₂×C₄⋊C₄	—	38	1	no	—
98	C₂×C₄⋊C₄	—	76	1	no	—
99	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
100	C₂×C₁₆	—	76	1	no	—
101	#107	—	76	1	no	—
102	C₄⋊C₈	—	2	2	no	—
103	C₄⋊C₈	—	4	1	no	—
104	C₄⋊C₈	—	4	1	no	—
105	#95	—	76	1	no	—
106	C₁₉	#7089	1	1	yes	characteristic, complemented, Sylow
107	C₂²×C₄	—	76	1	no	—
108	C₂²×C₄	—	76	1	no	—
109	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
110	C₂²×C₄	#64525	1	1	yes	characteristic
111	C₂²×C₄	#64527	1	1	yes	characteristic
112	M₁₆	—	8	1	no	—
113	M₁₆	—	8	1	no	—
114	C₂×C₈	—	2	1	no	—
115	C₂×C₈	—	2	1	no	—
116	C₂×C₈	—	4	1	no	—
117	C₂×C₈	—	4	1	no	—
118	C₂×C₈	—	4	2	no	—
119	C₄⋊C₄	—	38	2	no	—
120	C₄⋊C₄	—	76	1	no	—
121	C₄⋊C₄	—	76	1	no	—
122	C₄⋊C₄	—	76	1	no	—
123	C₄⋊C₄	—	152	2	no	—
124	C₄²	—	2	1	no	—
125	C₄²	—	2	1	no	—
126	C₁₆	—	152	1	no	—
127	C₂³	#10597266	1	1	yes	characteristic
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	2	1	no	—
131	C₂×C₄	—	2	1	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	4	1	no	—
134	C₂×C₄	—	76	2	no	—
135	C₂×C₄	—	152	1	no	—
136	C₂×C₄	—	152	1	no	—
137	C₂×C₄	—	152	1	no	—
138	C₂×C₄	—	152	1	no	—
139	C₂×C₄	—	152	1	no	—
140	C₂×C₄	#10597262	1	1	yes	characteristic
141	C₂×C₄	#10597263	1	1	yes	characteristic
142	C₂×C₄	#10597284	1	1	yes	characteristic
143	C₂×C₄	#10597286	1	1	yes	characteristic
144	C₈	—	4	1	no	—
145	C₈	—	4	1	no	—
146	C₈	—	8	2	no	—
147	C₂²	—	2	1	no	—
148	C₂²	—	2	1	no	—
149	C₂²	#11926277	1	1	yes	characteristic
150	C₂²	#11926347	1	1	yes	characteristic
151	C₂²	#11926353	1	1	yes	characteristic
152	C₄	—	2	1	no	—
153	C₄	—	2	1	no	—
154	C₄	—	2	1	no	—
155	C₄	—	4	1	no	—
156	C₄	—	304	1	no	—
157	C₄	—	152	2	no	—
158	C₄	#11926335	1	1	yes	characteristic
159	C₄	#11926342	1	1	yes	characteristic
160	C₂	—	2	1	no	—
161	C₂	—	2	1	no	—
162	C₂	#14561625	1	1	yes	characteristic
163	C₂	#14561640	1	1	yes	characteristic
164	C₂	#14561646	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565128

C₂

yes

maximal, characteristic

#14561575

C₂

yes

maximal, characteristic

C₁₉×#1292

C₂

yes

maximal, characteristic

C₂×#10597275

C₄

yes

characteristic

#11926442

—

C₂²⋊(C₁₉⋊C₁₆)

—

#11926307

—

#11926307

C₄

yes

characteristic

C₁₉×#423

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×Dic₁₉⋊C₄

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉⋊#95

—

#10597275

—

C₂×C₁₉⋊C₁₆

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₁₉⋊C₁₆

—

—

C₂³×C₁₉

yes

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×C₄×C₁₉

SD₃₂

yes

characteristic

C₂×C₄×C₁₉

Q₃₂

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#2087

—

#1322

—

#1292

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

C₂×#107

—

#423

—

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

#389

—

C₂²⋊C₁₆

—

#340

—

#340

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

—

C₂²×C₈

C₄×D₁₉

yes

characteristic

C₂²×C₈

D₇₆

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

100

C₂×C₁₆

—

101

#107

—

102

C₄⋊C₈

—

103

C₄⋊C₈

—

104

C₄⋊C₈

—

105

#95

—

106

C₁₉

#7089

yes

characteristic, complemented, Sylow

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

110

C₂²×C₄

#64525

yes

characteristic

111

C₂²×C₄

#64527

yes

characteristic

112

M₁₆

—

113

M₁₆

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

152

—

124

C₄²

—

125

C₄²

—

126

C₁₆

—

152

—

127

C₂³

#10597266

yes

characteristic

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

152

—

136

C₂×C₄

—

152

—

137

C₂×C₄

—

152

—

138

C₂×C₄

—

152

—

139

C₂×C₄

—

152

—

140

C₂×C₄

#10597262

yes

characteristic

141

C₂×C₄

#10597263

yes

characteristic

142

C₂×C₄

#10597284

yes

characteristic

143

C₂×C₄

#10597286

yes

characteristic

144

C₈

—

145

C₈

—

146

C₈

—

147

C₂²

—

148

C₂²

—

149

C₂²

#11926277

yes

characteristic

150

C₂²

#11926347

yes

characteristic

151

C₂²

#11926353

yes

characteristic

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

304

—

157

C₄

—

152

—

158

C₄

#11926335

yes

characteristic

159

C₄

#11926342

yes

characteristic

160

C₂

—

161

C₂

—

162

C₂

#14561625

yes

characteristic

163

C₂

#14561640

yes

characteristic

164

C₂

#14561646

yes

characteristic

	subgroup	G/H
center	C₂²	#11926277
commutator	C₂²×C₈×C₁₉	C₂×C₄
Frattini	C₂×C₄⋊C₈	C₂×D₁₉
Fitting	C₁₉×#1292	C₂
socle	C₂²×C₁₉	#327
prime radical	C₂³×C₁₉	#102
cosocle	C₂×C₁₉×C₄⋊C₈	C₂²
hypercenter	#1292	D₁₉
hypocenter	C₁₉	#7089
LCS	G ▷ C₂²×C₈×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #1292

subgroup

G/H

center

C₂²

#11926277

commutator

C₂²×C₈×C₁₉

C₂×C₄

Frattini

C₂×C₄⋊C₈

C₂×D₁₉

Fitting

C₁₉×#1292

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₁₉×C₄⋊C₈

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₈×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #1292

N	H ≅ G/N	type
106. C₁₉	#7089	semidirect

H ≅ G/N

type

106. C₁₉

#7089

semidirect

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

subgroup	index
#14565128	2
#14561575	2
C₁₉×#1292	2
#7089	19

subgroup

index

#14565128

#14561575

C₁₉×#1292

#7089

Subgroups — #18069250

Conjugacy classes of subgroups

Complements

Maximal subgroups