Group #18076329 — subgroups

Subgroups — #18076329

Order 4864.

438 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 203 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	#14563794	C₂	1	2	yes	maximal
2	#14563792	C₂	1	1	yes	maximal, characteristic
3	#14563762	C₂	1	2	yes	maximal
4	C₂×#11926265	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1845	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597264	—	2	4	no	—
7	C₂×#10597274	—	2	2	no	—
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
9	#11926414	C₂²	1	1	yes	characteristic
10	#11926414	C₂²	1	1	yes	characteristic
11	#11926306	—	2	4	no	—
12	#11926265	C₄	1	4	yes	complemented
13	C₂×C₁₉×#107	—	2	2	no	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#384	C₂²	1	2	yes	—
16	C₂²×C₈×C₁₉	D₄	1	2	yes	—
17	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
18	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
19	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×C₄⋊Dic₁₉	—	2	2	no	—
22	C₂×C₄⋊Dic₁₉	—	2	1	no	—
23	C₂×C₄⋊Dic₁₉	—	2	1	no	—
24	C₂×C₄⋊Dic₁₉	—	2	2	no	—
25	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
26	C₁₉×#107	—	4	4	no	—
27	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
28	C₄×C₈×C₁₉	Q₈	1	2	yes	—
29	#10597274	—	4	4	no	—
30	#10597264	—	4	8	no	—
31	C₄×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
32	C₄×C₁₉⋊C₈	Q₈	1	4	yes	—
33	C₂²×C₄×C₁₉	—	4	2	no	—
34	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
35	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
36	C₂²×Dic₁₉	—	4	1	no	—
37	C₂²×Dic₁₉	—	4	1	no	—
38	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
39	C₂×C₈×C₁₉	D₈	1	4	yes	—
40	C₂×C₈×C₁₉	Q₁₆	1	4	yes	—
41	C₄⋊C₄×C₁₉	—	4	4	no	—
42	C₄⋊C₄×C₁₉	—	4	4	no	—
43	C₄⋊C₄×C₁₉	—	4	4	no	—
44	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
45	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
46	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
47	C₄⋊Dic₁₉	—	4	2	no	—
48	C₄⋊Dic₁₉	—	4	2	no	—
49	C₄⋊Dic₁₉	—	4	4	no	—
50	C₄⋊Dic₁₉	—	4	4	no	—
51	C₂×C₁₉⋊C₈	—	2	4	no	—
52	C₂×C₁₉⋊C₈	—	2	4	no	—
53	C₂×C₁₉⋊C₈	C₄⋊C₄	1	8	yes	—
54	#8820	—	19	1	no	maximal, Sylow
55	C₂³×C₁₉	#127	1	1	yes	characteristic
56	C₂×C₄×C₁₉	—	8	2	no	—
57	C₂×C₄×C₁₉	—	8	2	no	—
58	C₂×C₄×C₁₉	—	8	2	no	—
59	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
60	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
62	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
63	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
64	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
65	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
66	C₂×C₄×C₁₉	#137	1	4	yes	—
67	C₂×Dic₁₉	—	8	1	no	—
68	C₂×Dic₁₉	—	8	1	no	—
69	C₂×Dic₁₉	—	8	2	no	—
70	C₂×Dic₁₉	—	8	2	no	—
71	C₈×C₁₉	#107	1	8	yes	complemented
72	C₁₉⋊C₈	—	2	8	no	—
73	#1845	—	19	2	no	—
74	#1845	D₁₉	1	1	yes	characteristic
75	#1844	—	19	1	no	—
76	#1834	—	19	2	no	—
77	C₂×#322	—	19	1	no	—
78	C₂²×C₁₉	#384	1	1	yes	characteristic
79	C₂²×C₁₉	#493	1	1	yes	characteristic
80	C₂²×C₁₉	#494	1	1	yes	characteristic
81	C₂²×C₁₉	#496	1	2	yes	—
82	C₂²×C₁₉	#497	1	2	yes	—
83	C₄×C₁₉	—	16	2	no	—
84	C₄×C₁₉	C₂×#107	1	2	yes	—
85	C₄×C₁₉	#428	1	4	yes	—
86	C₄×C₁₉	#500	1	2	yes	—
87	C₄×C₁₉	#501	1	4	yes	—
88	Dic₁₉	—	16	1	no	—
89	Dic₁₉	—	16	1	no	—
90	C₂×#107	—	2	2	no	—
91	C₂×#107	—	38	4	no	—
92	C₂×#106	—	38	2	no	—
93	C₂×C₄×C₈	—	19	2	no	—
94	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
95	#384	—	19	1	no	—
96	#384	—	19	1	no	—
97	#384	C₂×D₁₉	1	2	yes	—
98	#340	—	38	4	no	—
99	#322	—	19	4	no	—
100	C₂×C₁₉	#1721	1	1	yes	characteristic
101	C₂×C₁₉	#1722	1	1	yes	characteristic
102	C₂×C₁₉	#1723	1	2	yes	—
103	C₂×C₁₉	#1845	1	1	yes	characteristic
104	C₂×C₁₉	#1847	1	2	yes	—
105	C₂²×C₈	—	19	4	no	—
106	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
107	C₂×C₄⋊C₄	—	2	2	no	—
108	C₂×C₄⋊C₄	—	2	2	no	—
109	C₂×C₄⋊C₄	—	2	2	no	—
110	C₂×C₄⋊C₄	—	38	2	no	—
111	C₂×C₄⋊C₄	—	38	2	no	—
112	C₂×C₄⋊C₄	—	38	1	no	—
113	C₂×C₄⋊C₄	—	38	1	no	—
114	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
115	#107	—	4	4	no	—
116	#107	—	76	8	no	—
117	#106	—	76	4	no	—
118	C₄×C₈	—	19	4	no	—
119	C₄×C₈	—	19	4	no	—
120	C₄×C₈	Dic₃₈	1	2	yes	—
121	C₄×C₈	C₄×D₁₉	1	2	yes	—
122	C₁₉	#8820	1	1	yes	characteristic, complemented, Sylow
123	C₂²×C₄	—	4	2	no	—
124	C₂²×C₄	—	76	1	no	—
125	C₂²×C₄	—	76	1	no	—
126	C₂²×C₄	D₄×D₁₉	1	2	yes	—
127	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
128	C₂×C₈	—	19	8	no	—
129	C₂×C₈	—	38	4	no	—
130	C₂×C₈	—	38	4	no	—
131	C₂×C₈	Dic₁₉⋊C₄	1	4	yes	—
132	C₂×C₈	#64525	1	4	yes	—
133	C₂×C₈	#64528	1	4	yes	—
134	C₄⋊C₄	—	4	4	no	—
135	C₄⋊C₄	—	4	4	no	—
136	C₄⋊C₄	—	4	4	no	—
137	C₄⋊C₄	—	76	2	no	—
138	C₄⋊C₄	—	76	2	no	—
139	C₄⋊C₄	—	76	4	no	—
140	C₄⋊C₄	—	76	4	no	—
141	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
142	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
143	C₄²	Q₈×D₁₉	1	2	yes	—
144	C₂³	#10597386	1	1	yes	characteristic
145	C₂×C₄	—	8	2	no	—
146	C₂×C₄	—	8	2	no	—
147	C₂×C₄	—	8	2	no	—
148	C₂×C₄	—	152	1	no	—
149	C₂×C₄	—	152	1	no	—
150	C₂×C₄	—	152	2	no	—
151	C₂×C₄	—	152	2	no	—
152	C₂×C₄	#10597334	1	2	yes	—
153	C₂×C₄	C₄⋊C₄×D₁₉	1	2	yes	—
154	C₂×C₄	#10597357	1	4	yes	—
155	C₂×C₄	#10597364	1	4	yes	—
156	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
157	C₂×C₄	C₂×#64525	1	2	yes	—
158	C₂×C₄	C₂×#64528	1	2	yes	—
159	C₂×C₄	#10597390	1	1	yes	characteristic
160	C₈	—	38	8	no	—
161	C₈	#10597264	1	8	yes	complemented
162	C₂²	#11926413	1	1	yes	characteristic
163	C₂²	#11926920	1	1	yes	characteristic
164	C₂²	#11926923	1	1	yes	characteristic
165	C₂²	#11926932	1	2	yes	—
166	C₂²	#11926937	1	2	yes	—
167	C₄	—	16	2	no	—
168	C₄	—	304	1	no	—
169	C₄	—	304	1	no	—
170	C₄	C₂×#10597264	1	2	yes	—
171	C₄	#11926585	1	4	yes	—
172	C₄	#11926947	1	2	yes	—
173	C₄	#11926952	1	4	yes	—
174	C₂	#14563302	1	1	yes	characteristic
175	C₂	#14563307	1	1	yes	characteristic
176	C₂	#14563313	1	2	yes	—
177	C₂	#14563794	1	1	yes	characteristic
178	C₂	#14563802	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563794

C₂

yes

maximal

#14563792

C₂

yes

maximal, characteristic

#14563762

C₂

yes

maximal

C₂×#11926265

C₂

yes

maximal, characteristic

C₁₉×#1845

C₂

yes

maximal, characteristic

C₂×#10597264

—

C₂×#10597274

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926414

C₂²

yes

characteristic

#11926414

C₂²

yes

characteristic

#11926306

—

#11926265

C₄

yes

complemented

C₂×C₁₉×#107

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#384

C₂²

yes

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

D₄

yes

—

C₁₉×#107

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

Q₈

yes

—

#10597274

—

#10597264

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

Q₈

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

D₈

yes

—

C₂×C₈×C₁₉

Q₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

#107

yes

complemented

C₁₉⋊C₈

—

#1845

—

#1845

D₁₉

yes

—

—

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#497

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₂×#107

yes

—

C₄×C₁₉

#428

yes

—

C₄×C₁₉

#500

yes

—

C₄×C₁₉

#501

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×#107

—

C₂×#107

—

C₂×#106

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

—

C₂×D₁₉

yes

—

#340

—

#322

—

100

C₂×C₁₉

#1721

yes

characteristic

101

C₂×C₁₉

#1722

yes

characteristic

102

C₂×C₁₉

#1723

yes

—

103

C₂×C₁₉

#1845

yes

characteristic

104

C₂×C₁₉

#1847

yes

—

105

C₂²×C₈

—

106

C₂²×C₈

C₂²⋊D₁₉

yes

—

107

C₂×C₄⋊C₄

—

108

C₂×C₄⋊C₄

—

109

C₂×C₄⋊C₄

—

110

C₂×C₄⋊C₄

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄²

C₂²×D₁₉

yes

characteristic

115

#107

—

116

#107

—

117

#106

—

118

C₄×C₈

—

119

C₄×C₈

—

120

C₄×C₈

Dic₃₈

yes

—

121

C₄×C₈

C₄×D₁₉

yes

—

122

C₁₉

#8820

yes

characteristic, complemented, Sylow

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

D₄×D₁₉

yes

—

127

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

Dic₁₉⋊C₄

yes

—

132

C₂×C₈

#64525

yes

—

133

C₂×C₈

#64528

yes

—

134

C₄⋊C₄

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₄⋊C₄

—

139

C₄⋊C₄

—

140

C₄⋊C₄

—

141

C₄²

C₂×Dic₃₈

yes

characteristic

142

C₄²

C₂×C₄×D₁₉

yes

characteristic

143

C₄²

Q₈×D₁₉

yes

—

144

C₂³

#10597386

yes

characteristic

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

152

—

149

C₂×C₄

—

152

—

150

C₂×C₄

—

152

—

151

C₂×C₄

—

152

—

152

C₂×C₄

#10597334

yes

—

153

C₂×C₄

C₄⋊C₄×D₁₉

yes

—

154

C₂×C₄

#10597357

yes

—

155

C₂×C₄

#10597364

yes

—

156

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

157

C₂×C₄

C₂×#64525

yes

—

158

C₂×C₄

C₂×#64528

yes

—

159

C₂×C₄

#10597390

yes

characteristic

160

C₈

—

161

C₈

#10597264

yes

complemented

162

C₂²

#11926413

yes

characteristic

163

C₂²

#11926920

yes

characteristic

164

C₂²

#11926923

yes

characteristic

165

C₂²

#11926932

yes

—

166

C₂²

#11926937

yes

—

167

C₄

—

168

C₄

—

304

—

169

C₄

—

304

—

170

C₄

C₂×#10597264

yes

—

171

C₄

#11926585

yes

—

172

C₄

#11926947

yes

—

173

C₄

#11926952

yes

—

174

C₂

#14563302

yes

characteristic

175

C₂

#14563307

yes

characteristic

176

C₂

#14563313

yes

—

177

C₂

#14563794

yes

characteristic

178

C₂

#14563802

yes

—

	subgroup	G/H
center	C₂³	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1845	C₂
socle, prime radical	C₂³×C₁₉	#127
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1845	D₁₉
hypocenter	C₁₉	#8820
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

subgroup

G/H

center

C₂³

#10597386

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1845

C₂

socle, prime radical

C₂³×C₁₉

#127

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

N	H ≅ G/N	type
12. #11926265	C₄	semidirect
71. C₈×C₁₉	#107	semidirect
122. C₁₉	#8820	semidirect
161. C₈	#10597264	semidirect

H ≅ G/N

type

12. #11926265

C₄

semidirect

71. C₈×C₁₉

#107

semidirect

122. C₁₉

#8820

semidirect

161. C₈

#10597264

semidirect

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

subgroup	index
#14563794	2
#14563792	2
#14563762	2
C₂×#11926265	2
C₁₉×#1845	2
#8820	19

subgroup

index

C₁₉×#1845

Subgroups — #18076329

Conjugacy classes of subgroups

Complements

Maximal subgroups