Group #18013207 — subgroups

Subgroups — C₁₉×#7248 #18013207

Order 4864.

244 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 78 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	C₁₉×#1984	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1467	C₂	1	2	yes	maximal
3	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
4	C₁₉×#432	—	2	2	no	—
5	C₂×C₁₉×C₄⋊C₈	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
7	C₁₉×#336	—	2	2	no	—
8	C₁₉×#324	—	2	2	no	—
9	C₁₉×#324	C₄	1	4	yes	—
10	C₂²×Q₈×C₁₉	Q₈	1	1	yes	characteristic
11	C₂²×C₈×C₁₉	—	2	1	no	—
12	C₂²×C₈×C₁₉	—	2	1	no	—
13	C₄×Q₈×C₁₉	—	4	1	no	—
14	C₄×Q₈×C₁₉	—	4	1	no	—
15	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
16	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	D₄	1	2	yes	—
19	C₁₉×C₄⋊C₈	—	4	2	no	—
20	C₁₉×C₄⋊C₈	—	4	1	no	—
21	C₁₉×C₂²⋊C₈	—	2	4	no	—
22	C₁₉×#97	—	4	2	no	—
23	C₄×C₈×C₁₉	—	4	1	no	—
24	C₂×Q₈×C₁₉	—	2	2	no	—
25	C₂×Q₈×C₁₉	—	4	1	no	—
26	C₂×Q₈×C₁₉	—	4	1	no	—
27	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
29	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
31	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₈×C₁₉	—	2	2	no	—
33	C₂×C₈×C₁₉	—	4	1	no	—
34	C₂×C₈×C₁₉	—	4	1	no	—
35	C₂×C₈×C₁₉	—	4	2	no	—
36	C₂×C₈×C₁₉	—	4	4	no	—
37	C₂×C₈×C₁₉	—	4	1	no	—
38	C₄⋊C₄×C₁₉	—	4	2	no	—
39	C₄⋊C₄×C₁₉	—	4	1	no	—
40	C₄²×C₁₉	—	2	1	no	—
41	C₄²×C₁₉	—	2	1	no	—
42	C₄²×C₁₉	—	2	2	no	—
43	C₄²×C₁₉	—	2	2	no	—
44	#7248	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂³×C₁₉	#95	1	1	yes	characteristic
46	Q₈×C₁₉	—	4	4	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	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	2	1	no	—
55	C₂×C₄×C₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	—	4	1	no	—
57	C₂×C₄×C₁₉	—	4	2	no	—
58	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
59	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
60	C₂×C₄×C₁₉	#108	1	2	yes	—
61	C₈×C₁₉	—	4	2	no	—
62	C₈×C₁₉	—	8	4	no	—
63	C₈×C₁₉	—	8	1	no	—
64	#1984	C₂×C₁₉	1	1	yes	characteristic
65	#1467	C₂×C₁₉	1	2	yes	—
66	C₂²×C₁₉	—	2	1	no	—
67	C₂²×C₁₉	—	2	1	no	—
68	C₂²×C₁₉	#338	1	1	yes	characteristic
69	C₂²×C₁₉	#341	1	1	yes	characteristic
70	C₂²×C₁₉	#342	1	1	yes	characteristic
71	C₄×C₁₉	—	2	2	no	—
72	C₄×C₁₉	—	2	1	no	—
73	C₄×C₁₉	—	4	2	no	—
74	C₄×C₁₉	—	4	2	no	—
75	C₄×C₁₉	—	4	1	no	—
76	C₄×C₁₉	#355	1	1	yes	characteristic
77	C₄×C₁₉	#356	1	1	yes	characteristic
78	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
79	#432	—	2	2	no	—
80	C₂×C₄⋊C₈	C₄×C₁₉	1	1	yes	characteristic
81	C₂×C₄×C₈	C₄×C₁₉	1	1	yes	characteristic
82	#336	—	2	2	no	—
83	#324	—	2	2	no	—
84	#324	C₄×C₁₉	1	4	yes	—
85	C₂×C₁₉	—	2	1	no	—
86	C₂×C₁₉	—	2	1	no	—
87	C₂×C₁₉	#1293	1	1	yes	characteristic
88	C₂×C₁₉	#1391	1	1	yes	characteristic
89	C₂×C₁₉	#1394	1	1	yes	characteristic
90	C₂²×Q₈	Q₈×C₁₉	1	1	yes	characteristic
91	C₂²×C₈	—	2	1	no	—
92	C₂²×C₈	—	2	1	no	—
93	C₄×Q₈	—	4	1	no	—
94	C₄×Q₈	—	4	1	no	—
95	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
96	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
97	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
98	C₂×C₄²	D₄×C₁₉	1	2	yes	—
99	C₄⋊C₈	—	4	1	no	—
100	C₄⋊C₈	—	4	2	no	—
101	C₂²⋊C₈	—	2	4	no	—
102	#97	—	4	2	no	—
103	C₄×C₈	—	4	1	no	—
104	C₁₉	#7248	1	1	yes	characteristic, direct product factor, Sylow
105	C₂×Q₈	—	2	2	no	—
106	C₂×Q₈	—	4	1	no	—
107	C₂×Q₈	—	4	1	no	—
108	C₂²×C₄	C₄²×C₁₉	1	1	yes	characteristic
109	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
110	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
111	C₂²×C₄	C₄⋊C₄×C₁₉	1	2	yes	—
112	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
113	C₂×C₈	—	2	2	no	—
114	C₂×C₈	—	4	1	no	—
115	C₂×C₈	—	4	1	no	—
116	C₂×C₈	—	4	4	no	—
117	C₂×C₈	—	4	2	no	—
118	C₂×C₈	—	4	1	no	—
119	C₄⋊C₄	—	4	2	no	—
120	C₄⋊C₄	—	4	1	no	—
121	C₄²	—	2	1	no	—
122	C₄²	—	2	2	no	—
123	C₄²	—	2	1	no	—
124	C₄²	—	2	2	no	—
125	C₂³	C₁₉×#95	1	1	yes	characteristic
126	Q₈	—	4	4	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	2	1	no	—
131	C₂×C₄	—	2	2	no	—
132	C₂×C₄	—	2	2	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	2	2	no	—
136	C₂×C₄	—	4	1	no	—
137	C₂×C₄	—	4	2	no	—
138	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
139	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
140	C₂×C₄	C₁₉×#108	1	2	yes	—
141	C₈	—	4	2	no	—
142	C₈	—	8	4	no	—
143	C₈	—	8	1	no	—
144	C₂²	—	2	1	no	—
145	C₂²	—	2	1	no	—
146	C₂²	C₁₉×#338	1	1	yes	characteristic
147	C₂²	C₁₉×#341	1	1	yes	characteristic
148	C₂²	C₁₉×#342	1	1	yes	characteristic
149	C₄	—	2	1	no	—
150	C₄	—	2	2	no	—
151	C₄	—	4	2	no	—
152	C₄	—	4	1	no	—
153	C₄	—	4	2	no	—
154	C₄	C₁₉×#355	1	1	yes	characteristic
155	C₄	C₁₉×#356	1	1	yes	characteristic
156	C₂	—	2	1	no	—
157	C₂	—	2	1	no	—
158	C₂	C₁₉×#1293	1	1	yes	characteristic
159	C₂	C₁₉×#1391	1	1	yes	characteristic
160	C₂	C₁₉×#1394	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#1984

C₂

yes

maximal, characteristic

C₁₉×#1467

C₂

yes

maximal

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#432

—

C₂×C₁₉×C₄⋊C₈

C₄

yes

characteristic

C₂×C₄×C₈×C₁₉

C₄

yes

characteristic

C₁₉×#336

—

C₁₉×#324

—

C₁₉×#324

C₄

yes

—

C₂²×Q₈×C₁₉

Q₈

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

#7248

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#95

yes

characteristic

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

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

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#1984

C₂×C₁₉

yes

characteristic

#1467

C₂×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×C₄×Q₈

C₂²×C₁₉

yes

characteristic

#432

—

C₂×C₄⋊C₈

C₄×C₁₉

yes

characteristic

C₂×C₄×C₈

C₄×C₁₉

yes

—

—

C₄×C₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

Q₈×C₁₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

—

C₂×C₄⋊C₄

D₄×C₁₉

yes

characteristic

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

C₂×C₄²

D₄×C₁₉

yes

—

C₄⋊C₈

—

100

C₄⋊C₈

—

101

C₂²⋊C₈

—

102

#97

—

103

C₄×C₈

—

104

C₁₉

#7248

yes

characteristic, direct product factor, Sylow

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

—

108

C₂²×C₄

C₄²×C₁₉

yes

characteristic

109

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

110

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

111

C₂²×C₄

C₄⋊C₄×C₁₉

yes

—

112

C₂²×C₄

C₄⋊C₄×C₁₉

yes

characteristic

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄²

—

122

C₄²

—

123

C₄²

—

124

C₄²

—

125

C₂³

C₁₉×#95

yes

characteristic

126

Q₈

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

C₁₉×#99

yes

characteristic

139

C₂×C₄

C₁₉×#99

yes

characteristic

140

C₂×C₄

C₁₉×#108

yes

—

141

C₈

—

142

C₈

—

143

C₈

—

144

C₂²

—

145

C₂²

—

146

C₂²

C₁₉×#338

yes

characteristic

147

C₂²

C₁₉×#341

yes

characteristic

148

C₂²

C₁₉×#342

yes

characteristic

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

C₁₉×#355

yes

characteristic

155

C₄

C₁₉×#356

yes

characteristic

156

C₂

—

157

C₂

—

158

C₂

C₁₉×#1293

yes

characteristic

159

C₂

C₁₉×#1391

yes

characteristic

160

C₂

C₁₉×#1394

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#342
commutator	C₂²×C₄	C₄²×C₁₉
Frattini, cosocle	C₂×C₄×Q₈	C₂²×C₁₉
prime radical	C₂³×C₁₉	#95
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#342

commutator

C₂²×C₄

C₄²×C₁₉

Frattini, cosocle

C₂×C₄×Q₈

C₂²×C₁₉

prime radical

C₂³×C₁₉

#95

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

N	H ≅ G/N	type
44. #7248	C₁₉	direct (N × H)
104. C₁₉	#7248	direct (N × H)

H ≅ G/N

type

44. #7248

C₁₉

direct (N × H)

104. C₁₉

#7248

direct (N × H)

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

subgroup	index
C₁₉×#1984	2
C₁₉×#1467	2
#7248	19

subgroup

index

C₁₉×#1984

C₁₉×#1467

#7248

Subgroups — C₁₉×#7248 #18013207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7248 #18013207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7248 #18013207