Group #18070361 — subgroups

Subgroups — #18070361

Order 4864.

196 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 27 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	#14561802	C₂	1	1	yes	maximal, characteristic, complemented
2	#14561676	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1629	C₂	1	1	yes	maximal, characteristic
4	#11926365	—	2	1	no	—
5	#11926343	—	2	1	no	—
6	D₄²×C₁₉	C₄	1	1	yes	characteristic
7	C₁₉×#492	C₂²	1	1	yes	characteristic
8	C₁₉×#476	—	2	1	no	—
9	C₁₉×#331	C₄	1	1	yes	characteristic
10	C₁₉×D₄⋊C₈	—	2	1	no	—
11	C₂²×D₄×C₁₉	—	4	1	no	—
12	C₂×SD₁₆×C₁₉	—	4	1	no	—
13	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
14	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
15	C₁₉×#121	—	4	1	no	—
16	C₁₉×#120	—	4	1	no	—
17	C₄×D₄×C₁₉	—	2	1	no	—
18	C₁₉×#106	—	4	1	no	—
19	C₁₉×C₄⋊C₈	—	2	1	no	—
20	C₁₉×#102	—	4	1	no	—
21	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
22	#10597293	—	4	1	no	—
23	#10597269	—	4	1	no	—
24	C₂⁴×C₁₉	—	4	1	no	—
25	C₂×Q₈×C₁₉	—	2	1	no	—
26	C₂×D₄×C₁₉	—	2	1	no	—
27	C₂×D₄×C₁₉	—	2	1	no	—
28	C₂×D₄×C₁₉	—	4	1	no	—
29	C₂×D₄×C₁₉	—	4	2	no	—
30	C₂×D₄×C₁₉	—	8	2	no	—
31	C₂×D₄×C₁₉	—	8	2	no	—
32	C₂²×C₄×C₁₉	—	4	1	no	—
33	SD₁₆×C₁₉	—	8	1	no	—
34	SD₁₆×C₁₉	—	8	1	no	—
35	C₂×C₈×C₁₉	—	2	1	no	—
36	C₂×C₈×C₁₉	—	4	1	no	—
37	C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₄⋊C₄×C₁₉	—	4	1	no	—
39	C₂²⋊C₄×C₁₉	—	4	1	no	—
40	C₂²⋊C₄×C₁₉	—	4	1	no	—
41	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
42	#64520	—	8	1	no	—
43	C₁₉⋊C₁₆	—	8	1	no	—
44	#7517	—	19	1	no	maximal, Sylow
45	C₂³×C₁₉	—	4	1	no	—
46	C₂³×C₁₉	—	4	1	no	—
47	C₂³×C₁₉	—	8	4	no	—
48	C₂³×C₁₉	—	16	1	no	—
49	Q₈×C₁₉	—	8	1	no	—
50	D₄×C₁₉	—	2	2	no	—
51	D₄×C₁₉	—	4	1	no	—
52	D₄×C₁₉	—	8	1	no	—
53	D₄×C₁₉	—	8	1	no	—
54	D₄×C₁₉	—	8	1	no	—
55	D₄×C₁₉	—	8	4	no	—
56	C₂×C₄×C₁₉	—	2	1	no	—
57	C₂×C₄×C₁₉	—	4	1	no	—
58	C₂×C₄×C₁₉	—	4	1	no	—
59	C₂×C₄×C₁₉	—	8	1	no	—
60	C₂×C₄×C₁₉	—	8	1	no	—
61	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
62	C₈×C₁₉	—	2	1	no	—
63	C₈×C₁₉	—	2	1	no	—
64	C₈×C₁₉	—	8	1	no	—
65	C₁₉⋊C₈	—	16	1	no	—
66	#1629	D₁₉	1	1	yes	characteristic
67	#1410	—	19	1	no	—
68	#1359	—	19	1	no	—
69	C₂²×C₁₉	—	4	2	no	—
70	C₂²×C₁₉	—	8	1	no	—
71	C₂²×C₁₉	—	8	2	no	—
72	C₂²×C₁₉	—	8	1	no	—
73	C₂²×C₁₉	—	8	1	no	—
74	C₂²×C₁₉	—	16	2	no	—
75	C₂²×C₁₉	—	16	2	no	—
76	C₂²×C₁₉	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
77	C₄×C₁₉	—	2	1	no	—
78	C₄×C₁₉	—	2	1	no	—
79	C₄×C₁₉	—	2	1	no	—
80	C₄×C₁₉	—	8	1	no	—
81	C₄×C₁₉	—	8	1	no	—
82	D₄²	Dic₁₉	1	1	yes	characteristic
83	#492	C₂×D₁₉	1	1	yes	characteristic
84	#476	—	2	1	no	—
85	#364	—	38	1	no	—
86	#356	—	38	1	no	—
87	#331	Dic₁₉	1	1	yes	characteristic
88	D₄⋊C₈	—	2	1	no	—
89	C₂×C₁₉	—	2	1	no	—
90	C₂×C₁₉	—	8	2	no	—
91	C₂×C₁₉	—	16	1	no	—
92	C₂×C₁₉	#1402	1	1	yes	characteristic
93	C₂²×D₄	—	4	1	no	—
94	C₂×SD₁₆	—	4	1	no	—
95	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
96	#127	C₂×Dic₁₉	1	1	yes	characteristic
97	#121	—	4	1	no	—
98	#120	—	4	1	no	—
99	C₄×D₄	—	2	1	no	—
100	M₃₂	—	76	1	no	—
101	#106	—	4	1	no	—
102	C₄⋊C₈	—	2	1	no	—
103	#102	—	4	1	no	—
104	#101	—	76	1	no	—
105	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
106	C₁₉	#7517	1	1	yes	characteristic, complemented, Sylow
107	C₂⁴	—	4	1	no	—
108	C₂×Q₈	—	2	1	no	—
109	C₂×D₄	—	2	1	no	—
110	C₂×D₄	—	2	1	no	—
111	C₂×D₄	—	4	1	no	—
112	C₂×D₄	—	4	2	no	—
113	C₂×D₄	—	8	2	no	—
114	C₂×D₄	—	8	2	no	—
115	C₂²×C₄	—	4	1	no	—
116	SD₁₆	—	8	1	no	—
117	SD₁₆	—	8	1	no	—
118	M₁₆	—	152	1	no	—
119	C₂×C₈	—	2	1	no	—
120	C₂×C₈	—	4	1	no	—
121	C₄⋊C₄	—	2	1	no	—
122	C₄⋊C₄	—	4	1	no	—
123	C₂²⋊C₄	—	4	1	no	—
124	C₂²⋊C₄	—	4	1	no	—
125	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
126	C₁₆	—	152	1	no	—
127	C₂³	—	4	1	no	—
128	C₂³	—	4	1	no	—
129	C₂³	—	8	4	no	—
130	C₂³	—	16	1	no	—
131	Q₈	—	8	1	no	—
132	D₄	—	2	2	no	—
133	D₄	—	4	1	no	—
134	D₄	—	8	1	no	—
135	D₄	—	8	1	no	—
136	D₄	—	8	1	no	—
137	D₄	—	8	4	no	—
138	C₂×C₄	—	2	1	no	—
139	C₂×C₄	—	4	1	no	—
140	C₂×C₄	—	4	1	no	—
141	C₂×C₄	—	8	1	no	—
142	C₂×C₄	—	8	1	no	—
143	C₂×C₄	#10597291	1	1	yes	characteristic
144	C₈	—	2	1	no	—
145	C₈	—	2	1	no	—
146	C₈	—	8	1	no	—
147	C₈	—	304	1	no	—
148	C₂²	—	4	2	no	—
149	C₂²	—	8	1	no	—
150	C₂²	—	8	2	no	—
151	C₂²	—	8	1	no	—
152	C₂²	—	8	1	no	—
153	C₂²	—	16	2	no	—
154	C₂²	—	16	2	no	—
155	C₂²	#11926331	1	1	yes	characteristic
156	C₄	—	2	1	no	—
157	C₄	—	2	1	no	—
158	C₄	—	2	1	no	—
159	C₄	—	8	1	no	—
160	C₄	—	8	1	no	—
161	C₂	—	2	1	no	—
162	C₂	—	8	2	no	—
163	C₂	—	16	1	no	—
164	C₂	#14561780	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561802

C₂

yes

maximal, characteristic, complemented

#14561676

C₂

yes

maximal, characteristic, complemented

C₁₉×#1629

C₂

yes

maximal, characteristic

#11926365

—

#11926343

—

D₄²×C₁₉

C₄

yes

characteristic

C₁₉×#492

C₂²

yes

characteristic

C₁₉×#476

—

C₁₉×#331

C₄

yes

characteristic

C₁₉×D₄⋊C₈

—

C₂²×D₄×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

D₄

yes

characteristic

C₁₉×#127

C₂×C₄

yes

characteristic

C₁₉×#121

—

C₁₉×#120

—

C₄×D₄×C₁₉

—

C₁₉×#106

—

C₁₉×C₄⋊C₈

—

C₁₉×#102

—

C₄×C₈×C₁₉

D₄

yes

characteristic

#10597293

—

#10597269

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

SD₁₆×C₁₉

—

SD₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

#64520

—

C₁₉⋊C₁₆

—

#7517

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#99

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1629

D₁₉

yes

characteristic

#1410

—

#1359

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

AΣL(1,𝔽₁₆)

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

D₄²

Dic₁₉

yes

characteristic

#492

C₂×D₁₉

yes

—

—

—

Dic₁₉

yes

characteristic

D₄⋊C₈

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1402

yes

characteristic

C₂²×D₄

—

C₂×SD₁₆

—

C₄⋊Q₈

C₂²⋊D₁₉

yes

characteristic

#127

C₂×Dic₁₉

yes

characteristic

#121

—

#120

—

C₄×D₄

—

100

M₃₂

—

101

#106

—

102

C₄⋊C₈

—

103

#102

—

104

#101

—

105

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

106

C₁₉

#7517

yes

characteristic, complemented, Sylow

107

C₂⁴

—

108

C₂×Q₈

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂×D₄

—

112

C₂×D₄

—

113

C₂×D₄

—

114

C₂×D₄

—

115

C₂²×C₄

—

116

SD₁₆

—

117

SD₁₆

—

118

M₁₆

—

152

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₂²⋊C₄

—

124

C₂²⋊C₄

—

125

C₄²

C₂²⋊Dic₁₉

yes

characteristic

126

C₁₆

—

152

—

127

C₂³

—

128

C₂³

—

129

C₂³

—

130

C₂³

—

131

Q₈

—

132

D₄

—

133

D₄

—

134

D₄

—

135

D₄

—

136

D₄

—

137

D₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

#10597291

yes

characteristic

144

C₈

—

145

C₈

—

146

C₈

—

147

C₈

—

304

—

148

C₂²

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

#11926331

yes

characteristic

156

C₄

—

157

C₄

—

158

C₄

—

159

C₄

—

160

C₄

—

161

C₂

—

162

C₂

—

163

C₂

—

164

C₂

#14561780

yes

characteristic

	subgroup	G/H
center	C₂	#14561780
commutator	C₁₉×#127	C₂×C₄
Frattini	#492	C₂×D₁₉
Fitting	C₁₉×#1629	C₂
socle	C₂×C₁₉	#1402
prime radical	D₄²×C₁₉	C₄
cosocle	C₁₉×#492	C₂²
hypercenter	#1629	D₁₉
hypocenter	C₁₉	#7517
LCS	G ▷ C₁₉×#127 ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #492 ◁ #1629

subgroup

G/H

center

C₂

#14561780

commutator

C₁₉×#127

C₂×C₄

Frattini

#492

C₂×D₁₉

Fitting

C₁₉×#1629

C₂

socle

C₂×C₁₉

#1402

prime radical

D₄²×C₁₉

C₄

cosocle

C₁₉×#492

C₂²

D₁₉

C₁₉

G ▷ C₁₉×#127 ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #492 ◁ #1629

N	H ≅ G/N	type
1. #14561802	C₂	semidirect
2. #14561676	C₂	semidirect
106. C₁₉	#7517	semidirect

H ≅ G/N

type

1. #14561802

C₂

semidirect

2. #14561676

C₂

semidirect

106. C₁₉

#7517

semidirect

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

subgroup	index
#14561802	2
#14561676	2
C₁₉×#1629	2
#7517	19

subgroup

index

#14561802

#14561676

C₁₉×#1629

#7517

Subgroups — #18070361

Conjugacy classes of subgroups

Complements

Maximal subgroups