Group #18070319 — subgroups

Subgroups — #18070319

Order 4864.

272 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 63 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	C₂×#11926343	C₂	1	2	yes	maximal
2	C₁₉×#1956	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597293	—	2	2	no	—
4	#11926343	—	2	2	no	—
5	#11926343	C₄	1	4	yes	complemented
6	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×#103	—	2	2	no	—
8	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
9	C₁₉×#384	C₄	1	1	yes	characteristic
10	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
11	C₂²×C₈×C₁₉	—	2	1	no	—
12	C₁₉×C₄⋊Q₈	—	4	1	no	—
13	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
14	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
15	C₁₉×C₄⋊Q₈	Q₈	1	1	yes	characteristic
16	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
17	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
18	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
19	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×#64520	—	4	2	no	—
21	C₁₉×#103	—	4	4	no	—
22	C₄×C₈×C₁₉	—	4	1	no	—
23	#10597293	—	2	4	no	—
24	#10597293	—	4	2	no	—
25	C₂×Q₈×C₁₉	—	2	2	no	—
26	C₂×Q₈×C₁₉	—	4	2	no	—
27	C₂×Q₈×C₁₉	—	4	2	no	—
28	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
29	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
30	C₂²×C₄×C₁₉	—	2	1	no	—
31	C₂²×C₄×C₁₉	—	2	2	no	—
32	C₂²×C₄×C₁₉	—	4	1	no	—
33	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₈×C₁₉	—	2	2	no	—
35	C₂×C₈×C₁₉	—	4	1	no	—
36	C₂×C₈×C₁₉	—	4	1	no	—
37	C₄⋊C₄×C₁₉	—	4	2	no	—
38	C₄⋊C₄×C₁₉	—	4	1	no	—
39	C₄⋊C₄×C₁₉	—	4	1	no	—
40	C₄⋊C₄×C₁₉	—	4	2	no	—
41	C₄⋊C₄×C₁₉	—	8	2	no	—
42	C₄²×C₁₉	—	2	1	no	—
43	C₄²×C₁₉	C₄²	1	1	yes	characteristic
44	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
45	#64520	—	4	4	no	—
46	#64520	—	8	2	no	—
47	C₂×C₁₉⋊C₈	—	8	2	no	—
48	#7499	—	19	1	no	maximal, Sylow
49	C₂³×C₁₉	#99	1	1	yes	characteristic
50	Q₈×C₁₉	—	4	2	no	—
51	Q₈×C₁₉	—	4	2	no	—
52	Q₈×C₁₉	—	8	2	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	2	1	no	—
57	C₂×C₄×C₁₉	—	2	1	no	—
58	C₂×C₄×C₁₉	—	2	1	no	—
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	4	2	no	—
62	C₂×C₄×C₁₉	—	4	2	no	—
63	C₂×C₄×C₁₉	—	8	2	no	—
64	C₂×C₄×C₁₉	—	8	1	no	—
65	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
67	C₈×C₁₉	—	4	2	no	—
68	C₁₉⋊C₈	—	8	4	no	—
69	C₂×#356	—	19	2	no	—
70	#1956	D₁₉	1	1	yes	characteristic
71	C₂²×C₁₉	—	2	1	no	—
72	C₂²×C₁₉	—	2	1	no	—
73	C₂²×C₁₉	#342	1	1	yes	characteristic
74	C₂²×C₁₉	#353	1	1	yes	characteristic
75	C₂²×C₁₉	#354	1	1	yes	characteristic
76	C₄×C₁₉	—	2	2	no	—
77	C₄×C₁₉	—	2	2	no	—
78	C₄×C₁₉	—	2	1	no	—
79	C₄×C₁₉	—	2	1	no	—
80	C₄×C₁₉	—	4	2	no	—
81	C₄×C₁₉	—	4	2	no	—
82	C₄×C₁₉	—	16	1	no	—
83	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
84	C₂×#103	—	2	2	no	—
85	C₂×#101	—	38	2	no	—
86	C₂×C₄×C₈	Dic₁₉	1	1	yes	characteristic
87	#384	Dic₁₉	1	1	yes	characteristic
88	#356	—	19	4	no	—
89	#356	—	38	2	no	—
90	C₂×C₁₉	—	2	1	no	—
91	C₂×C₁₉	—	2	1	no	—
92	C₂×C₁₉	#1393	1	1	yes	characteristic
93	C₂×C₁₉	#1410	1	1	yes	characteristic
94	C₂×C₁₉	#1411	1	1	yes	characteristic
95	C₂²×Q₈	C₂²⋊D₁₉	1	2	yes	—
96	C₂×M₁₆	—	76	2	no	—
97	C₂²×C₈	—	2	1	no	—
98	C₄⋊Q₈	—	4	1	no	—
99	C₄⋊Q₈	Dic₃₈	1	1	yes	characteristic
100	C₄⋊Q₈	C₄×D₁₉	1	2	yes	—
101	C₄⋊Q₈	D₇₆	1	1	yes	characteristic
102	C₂×C₄⋊C₄	—	2	1	no	—
103	C₂×C₄⋊C₄	—	4	1	no	—
104	C₂×C₄⋊C₄	—	4	1	no	—
105	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
106	#103	—	4	4	no	—
107	#101	—	38	4	no	—
108	#101	—	76	2	no	—
109	C₄×C₈	—	4	1	no	—
110	C₁₉	#7499	1	1	yes	characteristic, complemented, Sylow
111	C₂×Q₈	—	2	2	no	—
112	C₂×Q₈	—	4	2	no	—
113	C₂×Q₈	—	4	2	no	—
114	C₂×Q₈	Dic₁₉⋊C₄	1	2	yes	—
115	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
116	C₂²×C₄	—	2	1	no	—
117	C₂²×C₄	—	2	2	no	—
118	C₂²×C₄	—	4	1	no	—
119	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
120	M₁₆	—	76	4	no	—
121	M₁₆	—	152	2	no	—
122	C₂×C₈	—	2	2	no	—
123	C₂×C₈	—	4	1	no	—
124	C₂×C₈	—	4	1	no	—
125	C₂×C₈	—	152	2	no	—
126	C₄⋊C₄	—	4	1	no	—
127	C₄⋊C₄	—	4	2	no	—
128	C₄⋊C₄	—	4	1	no	—
129	C₄⋊C₄	—	4	2	no	—
130	C₄⋊C₄	—	8	2	no	—
131	C₄²	—	2	1	no	—
132	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
133	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
134	C₂³	#10597291	1	1	yes	characteristic
135	Q₈	—	4	2	no	—
136	Q₈	—	4	2	no	—
137	Q₈	—	8	2	no	—
138	C₂×C₄	—	2	2	no	—
139	C₂×C₄	—	2	2	no	—
140	C₂×C₄	—	2	1	no	—
141	C₂×C₄	—	2	1	no	—
142	C₂×C₄	—	2	1	no	—
143	C₂×C₄	—	2	1	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	4	2	no	—
147	C₂×C₄	—	4	2	no	—
148	C₂×C₄	—	8	2	no	—
149	C₂×C₄	—	8	1	no	—
150	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
151	C₂×C₄	#10597291	1	1	yes	characteristic
152	C₈	—	4	2	no	—
153	C₈	—	152	4	no	—
154	C₂²	—	2	1	no	—
155	C₂²	—	2	1	no	—
156	C₂²	#11926311	1	1	yes	characteristic
157	C₂²	#11926337	1	1	yes	characteristic
158	C₂²	#11926339	1	1	yes	characteristic
159	C₄	—	2	2	no	—
160	C₄	—	2	2	no	—
161	C₄	—	2	1	no	—
162	C₄	—	2	1	no	—
163	C₄	—	4	2	no	—
164	C₄	—	4	2	no	—
165	C₄	—	16	1	no	—
166	C₂	—	2	1	no	—
167	C₂	—	2	1	no	—
168	C₂	#14561760	1	1	yes	characteristic
169	C₂	#14561802	1	1	yes	characteristic
170	C₂	#14561804	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926343

C₂

yes

maximal

C₁₉×#1956

C₂

yes

maximal, characteristic

C₂×#10597293

—

#11926343

—

#11926343

C₄

yes

complemented

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₉×#103

—

C₂×C₄×C₈×C₁₉

C₄

yes

characteristic

C₁₉×#384

C₄

yes

characteristic

C₂²×Q₈×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

characteristic

C₁₉×C₄⋊Q₈

Q₈

yes

characteristic

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×#64520

—

C₁₉×#103

—

C₄×C₈×C₁₉

—

#10597293

—

#10597293

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂×Q₈×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₄²

yes

characteristic

C₄²×C₁₉

C₄⋊C₄

yes

characteristic

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

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

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₁₉⋊C₈

—

C₂×#356

—

#1956

D₁₉

yes

characteristic

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

—

C₄×C₁₉

—

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

C₂×#103

—

C₂×#101

—

C₂×C₄×C₈

Dic₁₉

yes

characteristic

#384

Dic₁₉

yes

characteristic

#356

—

#356

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

C₂²⋊D₁₉

yes

—

C₂×M₁₆

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

Dic₃₈

yes

characteristic

100

C₄⋊Q₈

C₄×D₁₉

yes

—

101

C₄⋊Q₈

D₇₆

yes

characteristic

102

C₂×C₄⋊C₄

—

103

C₂×C₄⋊C₄

—

104

C₂×C₄⋊C₄

—

105

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

106

#103

—

107

#101

—

108

#101

—

109

C₄×C₈

—

110

C₁₉

#7499

yes

characteristic, complemented, Sylow

111

C₂×Q₈

—

112

C₂×Q₈

—

113

C₂×Q₈

—

114

C₂×Q₈

Dic₁₉⋊C₄

yes

—

115

C₂×Q₈

(C₂×D₁₉)⋊C₄

yes

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

120

M₁₆

—

121

M₁₆

—

152

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

—

152

—

126

C₄⋊C₄

—

127

C₄⋊C₄

—

128

C₄⋊C₄

—

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄²

—

132

C₄²

C₄×Dic₁₉

yes

characteristic

133

C₄²

C₄⋊Dic₁₉

yes

characteristic

134

C₂³

#10597291

yes

characteristic

135

Q₈

—

136

Q₈

—

137

Q₈

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

C₁₉⋊#95

yes

characteristic

151

C₂×C₄

#10597291

yes

characteristic

152

C₈

—

153

C₈

—

152

—

154

C₂²

—

155

C₂²

—

156

C₂²

#11926311

yes

characteristic

157

C₂²

#11926337

yes

characteristic

158

C₂²

#11926339

yes

characteristic

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

—

163

C₄

—

164

C₄

—

165

C₄

—

166

C₂

—

167

C₂

—

168

C₂

#14561760

yes

characteristic

169

C₂

#14561802

yes

characteristic

170

C₂

#14561804

yes

characteristic

	subgroup	G/H
center	C₂²	#11926337
commutator	C₄²×C₁₉	C₄²
Frattini	C₂×C₄⋊Q₈	C₂×D₁₉
Fitting	C₁₉×#1956	C₂
socle	C₂²×C₁₉	#353
prime radical	C₂³×C₁₉	#99
cosocle	C₂×C₁₉×C₄⋊Q₈	C₂²
hypercenter	#1956	D₁₉
hypocenter	C₁₉	#7499
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊Q₈ ◁ #1956

subgroup

G/H

center

C₂²

#11926337

commutator

C₄²×C₁₉

C₄²

Frattini

C₂×C₄⋊Q₈

C₂×D₁₉

Fitting

C₁₉×#1956

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₁₉×C₄⋊Q₈

C₂²

D₁₉

C₁₉

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

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊Q₈ ◁ #1956

N	H ≅ G/N	type
5. #11926343	C₄	semidirect
110. C₁₉	#7499	semidirect

H ≅ G/N

type

5. #11926343

C₄

semidirect

110. C₁₉

#7499

semidirect

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

subgroup	index
C₂×#11926343	2
C₁₉×#1956	2
#7499	19

subgroup

index

C₂×#11926343

C₁₉×#1956

#7499

Subgroups — #18070319

Conjugacy classes of subgroups

Complements

Maximal subgroups