Group #18071797 — subgroups

Subgroups — #18071797

Order 4864.

698 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 95 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	#14565168	C₂	1	3	yes	maximal, complemented
2	#14561456	C₂	1	3	yes	maximal, complemented
3	C₁₉×#2679	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597265	—	2	3	no	—
5	C₂×#10597289	—	2	3	no	—
6	#11926414	C₂²	1	1	yes	characteristic, complemented
7	#11926299	C₂²	1	3	yes	complemented
8	C₂×C₁₉×#120	—	2	3	no	—
9	C₁₉×#394	—	2	3	no	—
10	C₁₉×#390	C₂²	1	3	yes	—
11	C₂⁵×C₁₉	—	2	1	no	—
12	C₂²×D₄×C₁₉	—	2	3	no	—
13	C₂²×D₄×C₁₉	D₄	1	3	yes	—
14	C₁₉×#120	—	4	6	no	—
15	C₁₉×#120	—	4	6	no	—
16	C₂×C₄⋊C₄×C₁₉	D₄	1	3	yes	—
17	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
18	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
19	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
20	C₂×C₄⋊Dic₁₉	—	2	3	no	—
21	C₂²×C₁₉⋊C₈	—	2	3	no	—
22	C₁₉×#95	—	2	1	no	—
23	#10597289	—	4	6	no	—
24	#10597265	—	4	6	no	—
25	C₂⁴×C₁₉	—	2	3	no	—
26	C₂⁴×C₁₉	—	4	6	no	—
27	C₂⁴×C₁₉	—	8	3	no	—
28	C₂⁴×C₁₉	—	8	1	no	—
29	C₂×D₄×C₁₉	—	2	3	no	—
30	C₂×D₄×C₁₉	—	4	3	no	—
31	C₂×D₄×C₁₉	—	4	3	no	—
32	C₂×D₄×C₁₉	—	4	12	no	—
33	C₂×D₄×C₁₉	—	8	3	no	—
34	C₂×D₄×C₁₉	SD₁₆	1	6	yes	—
35	C₂²×C₄×C₁₉	—	2	3	no	—
36	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
37	C₂²×Dic₁₉	—	4	1	no	—
38	C₄⋊C₄×C₁₉	—	4	3	no	—
39	C₂²⋊C₄×C₁₉	—	4	6	no	—
40	C₂²⋊C₄×C₁₉	—	4	6	no	—
41	C₂²⋊C₄×C₁₉	—	4	6	no	—
42	C₄²×C₁₉	—	4	1	no	—
43	C₄⋊Dic₁₉	—	4	3	no	—
44	C₄⋊Dic₁₉	—	4	3	no	—
45	C₂×C₁₉⋊C₈	—	2	6	no	—
46	C₂×C₁₉⋊C₈	—	4	3	no	—
47	C₂×C₁₉⋊C₈	—	4	3	no	—
48	#7822	—	19	1	no	maximal, Sylow
49	C₂³×C₁₉	—	2	6	no	—
50	C₂³×C₁₉	—	4	6	no	—
51	C₂³×C₁₉	—	4	3	no	—
52	C₂³×C₁₉	—	4	6	no	—
53	C₂³×C₁₉	—	4	3	no	—
54	C₂³×C₁₉	—	8	12	no	—
55	C₂³×C₁₉	—	8	12	no	—
56	C₂³×C₁₉	—	8	4	no	—
57	C₂³×C₁₉	#120	1	1	yes	characteristic
58	D₄×C₁₉	—	4	6	no	—
59	D₄×C₁₉	—	8	3	no	—
60	D₄×C₁₉	—	8	12	no	—
61	C₂×C₄×C₁₉	—	2	3	no	—
62	C₂×C₄×C₁₉	—	2	3	no	—
63	C₂×C₄×C₁₉	—	4	6	no	—
64	C₂×C₄×C₁₉	—	4	3	no	—
65	C₂×C₄×C₁₉	C₂×SD₁₆	1	3	yes	—
66	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	3	yes	—
67	C₂×Dic₁₉	—	8	3	no	—
68	C₁₉⋊C₈	—	4	6	no	—
69	#2679	D₁₉	1	1	yes	characteristic
70	#2094	—	19	3	no	—
71	#1270	—	19	3	no	—
72	C₂²×C₁₉	—	4	6	no	—
73	C₂²×C₁₉	—	4	12	no	—
74	C₂²×C₁₉	—	8	16	no	—
75	C₂²×C₁₉	—	8	6	no	—
76	C₂²×C₁₉	—	8	3	no	—
77	C₂²×C₁₉	—	8	3	no	—
78	C₂²×C₁₉	#450	1	3	yes	—
79	C₂²×C₁₉	#453	1	3	yes	—
80	C₂²×C₁₉	#458	1	1	yes	characteristic
81	C₄×C₁₉	—	2	3	no	—
82	C₄×C₁₉	—	2	3	no	—
83	C₄×C₁₉	—	8	3	no	—
84	Dic₁₉	—	16	1	no	—
85	C₂×#120	—	2	3	no	—
86	C₂×#106	—	38	3	no	—
87	C₂×#102	—	38	3	no	—
88	#394	—	2	3	no	—
89	#390	C₂×D₁₉	1	3	yes	—
90	#384	—	19	1	no	—
91	#336	—	19	3	no	—
92	C₂×C₁₉	—	8	6	no	—
93	C₂×C₁₉	#1613	1	3	yes	—
94	C₂×C₁₉	#1629	1	3	yes	—
95	C₂×C₁₉	#1655	1	1	yes	characteristic
96	C₂⁵	—	2	1	no	—
97	C₂²×D₄	—	2	3	no	—
98	C₂²×D₄	C₂²⋊D₁₉	1	3	yes	—
99	C₂²×C₈	—	38	3	no	—
100	#120	—	4	6	no	—
101	#120	—	4	6	no	—
102	C₂×C₄⋊C₄	—	38	3	no	—
103	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	3	yes	—
104	C₂×C₂²⋊C₄	—	2	3	no	—
105	C₂×C₂²⋊C₄	—	2	6	no	—
106	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
107	#106	—	76	6	no	—
108	#102	—	76	6	no	—
109	#95	—	2	1	no	—
110	C₁₉	#7822	1	1	yes	characteristic, complemented, Sylow
111	C₂⁴	—	2	3	no	—
112	C₂⁴	—	4	6	no	—
113	C₂⁴	—	8	3	no	—
114	C₂⁴	—	8	1	no	—
115	C₂×D₄	—	2	3	no	—
116	C₂×D₄	—	4	3	no	—
117	C₂×D₄	—	4	3	no	—
118	C₂×D₄	—	4	12	no	—
119	C₂×D₄	—	8	3	no	—
120	C₂×D₄	#64526	1	6	yes	—
121	C₂²×C₄	—	2	3	no	—
122	C₂²×C₄	—	76	1	no	—
123	C₂²×C₄	C₂×C₂²⋊D₁₉	1	3	yes	—
124	C₂×C₈	—	38	6	no	—
125	C₂×C₈	—	76	3	no	—
126	C₂×C₈	—	76	3	no	—
127	C₄⋊C₄	—	4	3	no	—
128	C₄⋊C₄	—	76	3	no	—
129	C₄⋊C₄	—	76	3	no	—
130	C₂²⋊C₄	—	4	6	no	—
131	C₂²⋊C₄	—	4	6	no	—
132	C₂²⋊C₄	—	4	6	no	—
133	C₄²	—	4	1	no	—
134	C₂³	—	2	6	no	—
135	C₂³	—	4	6	no	—
136	C₂³	—	4	3	no	—
137	C₂³	—	4	6	no	—
138	C₂³	—	4	3	no	—
139	C₂³	—	8	12	no	—
140	C₂³	—	8	12	no	—
141	C₂³	—	8	4	no	—
142	C₂³	#10597399	1	1	yes	characteristic
143	D₄	—	4	6	no	—
144	D₄	—	8	3	no	—
145	D₄	—	8	12	no	—
146	C₂×C₄	—	2	3	no	—
147	C₂×C₄	—	2	3	no	—
148	C₂×C₄	—	4	6	no	—
149	C₂×C₄	—	4	3	no	—
150	C₂×C₄	—	152	3	no	—
151	C₂×C₄	#10597378	1	3	yes	—
152	C₂×C₄	C₂×#64526	1	3	yes	—
153	C₈	—	76	6	no	—
154	C₂²	—	4	6	no	—
155	C₂²	—	4	12	no	—
156	C₂²	—	8	16	no	—
157	C₂²	—	8	6	no	—
158	C₂²	—	8	3	no	—
159	C₂²	—	8	3	no	—
160	C₂²	#11926695	1	3	yes	—
161	C₂²	#11926712	1	3	yes	—
162	C₂²	#11926734	1	1	yes	characteristic
163	C₄	—	2	3	no	—
164	C₄	—	2	3	no	—
165	C₄	—	8	3	no	—
166	C₄	—	304	1	no	—
167	C₂	—	8	6	no	—
168	C₂	#14562655	1	3	yes	—
169	C₂	#14562751	1	3	yes	—
170	C₂	#14562924	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565168

C₂

yes

maximal, complemented

#14561456

C₂

yes

maximal, complemented

C₁₉×#2679

C₂

yes

maximal, characteristic

C₂×#10597265

—

C₂×#10597289

—

#11926414

C₂²

yes

characteristic, complemented

#11926299

C₂²

yes

complemented

C₂×C₁₉×#120

—

C₁₉×#394

—

C₁₉×#390

C₂²

yes

—

C₂⁵×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

D₄

yes

—

C₁₉×#120

—

C₁₉×#120

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

#10597289

—

#10597265

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

SD₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7822

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#120

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#2679

D₁₉

yes

characteristic

#2094

—

#1270

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#450

yes

—

C₂²×C₁₉

#453

yes

—

C₂²×C₁₉

#458

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

—

—

—

—

C₂×D₁₉

yes

—

#384

—

#336

—

C₂×C₁₉

—

C₂×C₁₉

#1613

yes

—

C₂×C₁₉

#1629

yes

—

C₂×C₁₉

#1655

yes

characteristic

C₂⁵

—

C₂²×D₄

—

C₂²×D₄

C₂²⋊D₁₉

yes

—

C₂²×C₈

—

100

#120

—

101

#120

—

102

C₂×C₄⋊C₄

—

103

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

104

C₂×C₂²⋊C₄

—

105

C₂×C₂²⋊C₄

—

106

C₂×C₄²

C₂²×D₁₉

yes

characteristic

107

#106

—

108

#102

—

109

#95

—

110

C₁₉

#7822

yes

characteristic, complemented, Sylow

111

C₂⁴

—

112

C₂⁴

—

113

C₂⁴

—

114

C₂⁴

—

115

C₂×D₄

—

116

C₂×D₄

—

117

C₂×D₄

—

118

C₂×D₄

—

119

C₂×D₄

—

120

C₂×D₄

#64526

yes

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₄⋊C₄

—

128

C₄⋊C₄

—

129

C₄⋊C₄

—

130

C₂²⋊C₄

—

131

C₂²⋊C₄

—

132

C₂²⋊C₄

—

133

C₄²

—

134

C₂³

—

135

C₂³

—

136

C₂³

—

137

C₂³

—

138

C₂³

—

139

C₂³

—

140

C₂³

—

141

C₂³

—

142

C₂³

#10597399

yes

characteristic

143

D₄

—

144

D₄

—

145

D₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

152

—

151

C₂×C₄

#10597378

yes

—

152

C₂×C₄

C₂×#64526

yes

—

153

C₈

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

159

C₂²

—

160

C₂²

#11926695

yes

—

161

C₂²

#11926712

yes

—

162

C₂²

#11926734

yes

characteristic

163

C₄

—

164

C₄

—

165

C₄

—

166

C₄

—

304

—

167

C₂

—

168

C₂

#14562655

yes

—

169

C₂

#14562751

yes

—

170

C₂

#14562924

yes

characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#2679	C₂
socle	C₂³×C₁₉	#120
hypercenter	#2679	D₁₉
hypocenter	C₁₉	#7822
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2679

subgroup

G/H

center

C₂³

#10597399

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting, prime radical

C₁₉×#2679

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂³×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2679

N	H ≅ G/N	type
1. #14565168	C₂	semidirect
2. #14561456	C₂	semidirect
6. #11926414	C₂²	semidirect
7. #11926299	C₂²	semidirect
110. C₁₉	#7822	semidirect

H ≅ G/N

type

1. #14565168

C₂

semidirect

2. #14561456

C₂

semidirect

6. #11926414

C₂²

semidirect

7. #11926299

C₂²

semidirect

110. C₁₉

#7822

semidirect

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

subgroup	index
#14565168	2
#14561456	2
C₁₉×#2679	2
#7822	19

subgroup

index

#14565168

#14561456

C₁₉×#2679

#7822

Subgroups — #18071797

Conjugacy classes of subgroups

Complements

Maximal subgroups