Group #18076328 — subgroups

Subgroups — #18076328

Order 4864.

438 conjugacy classes of subgroups; only the 227 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 227 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	#14563795	C₂	1	2	yes	maximal
2	#14563795	C₂	1	1	yes	maximal, characteristic
3	#14563792	C₂	1	1	yes	maximal, characteristic
4	#14563763	C₂	1	2	yes	maximal
5	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597275	—	2	4	no	—
7	C₂×#10597275	—	2	2	no	—
8	C₂×#10597274	—	2	2	no	—
9	#11926414	C₂²	1	1	yes	characteristic
10	#11926414	C₂²	1	2	yes	—
11	#11926414	C₂²	1	1	yes	characteristic
12	#11926307	—	2	4	no	—
13	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#322	C₄	1	4	yes	complemented
16	C₂²×C₈×C₁₉	D₄	1	4	yes	—
17	C₂²×C₈×C₁₉	D₄	1	2	yes	—
18	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
19	C₂×C₄⋊Dic₁₉	—	2	2	no	—
20	C₂×C₄⋊Dic₁₉	—	2	2	no	—
21	C₂×C₄⋊Dic₁₉	—	2	1	no	—
22	C₂×C₄⋊Dic₁₉	—	2	1	no	—
23	C₂×C₄⋊Dic₁₉	—	2	2	no	—
24	C₂×C₄⋊Dic₁₉	—	2	2	no	—
25	C₂×C₄⋊Dic₁₉	—	2	2	no	—
26	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
27	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
28	C₄×C₈×C₁₉	Q₈	1	4	yes	—
29	C₄×C₈×C₁₉	Q₈	1	2	yes	—
30	#10597275	—	4	8	no	—
31	#10597275	—	4	4	no	—
32	#10597274	—	4	4	no	—
33	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
35	C₂²×Dic₁₉	—	4	2	no	—
36	C₂²×Dic₁₉	—	4	1	no	—
37	C₂²×Dic₁₉	—	4	1	no	—
38	C₂×C₈×C₁₉	—	2	4	no	—
39	C₂×C₈×C₁₉	—	2	4	no	—
40	C₂×C₈×C₁₉	C₄⋊C₄	1	8	yes	—
41	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
42	C₂×C₈×C₁₉	D₈	1	4	yes	—
43	C₂×C₈×C₁₉	Q₁₆	1	4	yes	—
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	C₄⋊Dic₁₉	—	4	4	no	—
52	C₄⋊Dic₁₉	—	4	4	no	—
53	C₄⋊Dic₁₉	—	4	4	no	—
54	#8820	—	19	1	no	maximal, Sylow
55	C₂³×C₁₉	#127	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
58	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
59	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
60	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
61	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
62	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
63	C₂×C₄×C₁₉	#137	1	4	yes	—
64	C₂×Dic₁₉	—	8	1	no	—
65	C₂×Dic₁₉	—	8	2	no	—
66	C₂×Dic₁₉	—	8	1	no	—
67	C₂×Dic₁₉	—	8	2	no	—
68	C₂×Dic₁₉	—	8	2	no	—
69	C₂×Dic₁₉	—	8	2	no	—
70	C₂×Dic₁₉	—	8	2	no	—
71	C₈×C₁₉	—	2	8	no	—
72	C₈×C₁₉	#107	1	8	yes	complemented
73	#1845	—	19	1	no	—
74	#1845	—	19	2	no	—
75	#1844	—	19	1	no	—
76	#1834	—	19	2	no	—
77	C₂×#322	D₁₉	1	1	yes	characteristic
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	C₂×#107	1	2	yes	—
84	C₄×C₁₉	#428	1	4	yes	—
85	C₄×C₁₉	#500	1	2	yes	—
86	C₄×C₁₉	#501	1	4	yes	—
87	Dic₁₉	—	16	1	no	—
88	Dic₁₉	—	16	2	no	—
89	Dic₁₉	—	16	1	no	—
90	C₂×#107	—	38	4	no	—
91	C₂×#107	—	38	2	no	—
92	C₂×#106	—	38	2	no	—
93	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
94	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
95	#384	—	19	1	no	—
96	#384	—	19	2	no	—
97	#384	—	19	1	no	—
98	#340	—	38	4	no	—
99	#322	Dic₁₉	1	4	yes	complemented
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	D₇₆	1	4	yes	—
106	C₂²×C₈	D₇₆	1	2	yes	—
107	C₂×C₄⋊C₄	—	38	2	no	—
108	C₂×C₄⋊C₄	—	38	2	no	—
109	C₂×C₄⋊C₄	—	38	1	no	—
110	C₂×C₄⋊C₄	—	38	1	no	—
111	C₂×C₄⋊C₄	—	38	2	no	—
112	C₂×C₄⋊C₄	—	38	2	no	—
113	C₂×C₄⋊C₄	—	38	2	no	—
114	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
115	#107	—	76	8	no	—
116	#107	—	76	4	no	—
117	#106	—	76	4	no	—
118	C₄×C₈	Dic₃₈	1	4	yes	—
119	C₄×C₈	Dic₃₈	1	2	yes	—
120	C₄×C₈	C₂×Dic₁₉	1	4	yes	—
121	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
122	C₁₉	#8820	1	1	yes	characteristic, complemented, Sylow
123	C₂²×C₄	—	76	2	no	—
124	C₂²×C₄	—	76	1	no	—
125	C₂²×C₄	—	76	1	no	—
126	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
127	C₂²×C₄	C₂×D₇₆	1	2	yes	—
128	C₂×C₈	—	2	4	no	—
129	C₂×C₈	—	2	4	no	—
130	C₂×C₈	D₁₅₂	1	4	yes	—
131	C₂×C₈	Dic₇₆	1	4	yes	—
132	C₂×C₈	C₄⋊Dic₁₉	1	8	yes	—
133	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
134	C₄⋊C₄	—	76	2	no	—
135	C₄⋊C₄	—	76	2	no	—
136	C₄⋊C₄	—	76	4	no	—
137	C₄⋊C₄	—	76	4	no	—
138	C₄⋊C₄	—	76	4	no	—
139	C₄⋊C₄	—	76	4	no	—
140	C₄⋊C₄	—	76	4	no	—
141	C₄²	C₂×Dic₃₈	1	2	yes	—
142	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
143	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
144	C₂³	#10597320	1	1	yes	characteristic
145	C₂×C₄	—	152	1	no	—
146	C₂×C₄	—	152	2	no	—
147	C₂×C₄	—	152	1	no	—
148	C₂×C₄	—	152	2	no	—
149	C₂×C₄	—	152	2	no	—
150	C₂×C₄	—	152	2	no	—
151	C₂×C₄	—	152	2	no	—
152	C₂×C₄	#10597315	1	1	yes	characteristic
153	C₂×C₄	#10597315	1	2	yes	—
154	C₂×C₄	C₂×D₁₅₂	1	2	yes	—
155	C₂×C₄	C₂×Dic₇₆	1	2	yes	—
156	C₂×C₄	#10597354	1	4	yes	—
157	C₂×C₄	#10597355	1	4	yes	—
158	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
159	C₂×C₄	C₂×C₄⋊Dic₁₉	1	2	yes	—
160	C₈	—	2	8	no	—
161	C₈	#10597275	1	8	yes	complemented
162	C₂²	#11926414	1	1	yes	characteristic
163	C₂²	#11926921	1	1	yes	characteristic
164	C₂²	#11926924	1	1	yes	characteristic
165	C₂²	#11926933	1	2	yes	—
166	C₂²	#11926938	1	2	yes	—
167	C₄	—	304	1	no	—
168	C₄	—	304	2	no	—
169	C₄	—	304	1	no	—
170	C₄	C₂×#10597275	1	2	yes	—
171	C₄	#11926586	1	4	yes	—
172	C₄	#11926949	1	2	yes	—
173	C₄	#11926953	1	4	yes	—
174	C₂	#14563301	1	1	yes	characteristic
175	C₂	#14563306	1	1	yes	characteristic
176	C₂	#14563312	1	2	yes	—
177	C₂	#14563795	1	1	yes	characteristic
178	C₂	#14563803	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563795

C₂

yes

maximal

#14563795

C₂

yes

maximal, characteristic

#14563792

C₂

yes

maximal, characteristic

#14563763

C₂

yes

maximal

C₂×C₁₉×#322

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

characteristic

#11926414

C₂²

yes

—

#11926414

C₂²

yes

characteristic

#11926307

—

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#322

C₄

yes

complemented

C₂²×C₈×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

Q₈

yes

—

C₄×C₈×C₁₉

Q₈

yes

—

#10597275

—

#10597275

—

#10597274

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

D₈

yes

—

C₂×C₈×C₁₉

Q₁₆

yes

—

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

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

—

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

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

yes

—

—

—

—

D₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#497

yes

—

C₄×C₁₉

C₂×#107

yes

—

C₄×C₁₉

#428

yes

—

C₄×C₁₉

#500

yes

—

C₄×C₁₉

#501

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×#107

—

C₂×#107

—

C₂×#106

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

—

—

—

Dic₁₉

yes

complemented

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

D₇₆

yes

—

106

C₂²×C₈

D₇₆

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

Dic₃₈

yes

—

119

C₄×C₈

Dic₃₈

yes

—

120

C₄×C₈

C₂×Dic₁₉

yes

—

121

C₄×C₈

C₂×Dic₁₉

yes

—

122

C₁₉

#8820

yes

characteristic, complemented, Sylow

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

C₂×D₇₆

yes

characteristic

127

C₂²×C₄

C₂×D₇₆

yes

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

D₁₅₂

yes

—

131

C₂×C₈

Dic₇₆

yes

—

132

C₂×C₈

C₄⋊Dic₁₉

yes

—

133

C₂×C₈

C₄⋊Dic₁₉

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

—

142

C₄²

C₂×Dic₃₈

yes

characteristic

143

C₄²

C₂²×Dic₁₉

yes

characteristic

144

C₂³

#10597320

yes

characteristic

145

C₂×C₄

—

152

—

146

C₂×C₄

—

152

—

147

C₂×C₄

—

152

—

148

C₂×C₄

—

152

—

149

C₂×C₄

—

152

—

150

C₂×C₄

—

152

—

151

C₂×C₄

—

152

—

152

C₂×C₄

#10597315

yes

characteristic

153

C₂×C₄

#10597315

yes

—

154

C₂×C₄

C₂×D₁₅₂

yes

—

155

C₂×C₄

C₂×Dic₇₆

yes

—

156

C₂×C₄

#10597354

yes

—

157

C₂×C₄

#10597355

yes

—

158

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

159

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

—

160

C₈

—

161

C₈

#10597275

yes

complemented

162

C₂²

#11926414

yes

characteristic

163

C₂²

#11926921

yes

characteristic

164

C₂²

#11926924

yes

characteristic

165

C₂²

#11926933

yes

—

166

C₂²

#11926938

yes

—

167

C₄

—

304

—

168

C₄

—

304

—

169

C₄

—

304

—

170

C₄

C₂×#10597275

yes

—

171

C₄

#11926586

yes

—

172

C₄

#11926949

yes

—

173

C₄

#11926953

yes

—

174

C₂

#14563301

yes

characteristic

175

C₂

#14563306

yes

characteristic

176

C₂

#14563312

yes

—

177

C₂

#14563795

yes

characteristic

178

C₂

#14563803

yes

—

	subgroup	G/H
center	C₂³	#10597320
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#322	C₂
socle, prime radical	C₂³×C₁₉	#127
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#322	D₁₉
hypocenter	C₁₉	#8820
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#322

subgroup

G/H

center

C₂³

#10597320

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#322

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 ◁ C₂×#322

N	H ≅ G/N	type
15. C₁₉×#322	C₄	semidirect
72. C₈×C₁₉	#107	semidirect
99. #322	Dic₁₉	semidirect
122. C₁₉	#8820	semidirect
161. C₈	#10597275	semidirect

H ≅ G/N

type

15. C₁₉×#322

C₄

semidirect

72. C₈×C₁₉

#107

semidirect

99. #322

Dic₁₉

semidirect

122. C₁₉

#8820

semidirect

161. C₈

#10597275

semidirect

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

subgroup	index
#14563795	2
#14563792	2
#14563763	2
C₂×C₁₉×#322	2
#8820	19

subgroup

index

C₂×C₁₉×#322

Subgroups — #18076328

Conjugacy classes of subgroups

Complements

Maximal subgroups