Group #18075569 — subgroups

Subgroups — #18075569

Order 4864.

336 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 127 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	#14562394	C₂	1	2	yes	maximal
2	#14562373	C₂	1	2	yes	maximal
3	C₁₉⋊#1309	C₂	1	2	yes	maximal
4	C₁₉×#2960	C₂	1	1	yes	maximal, characteristic
5	#11926568	C₂²	1	4	yes	—
6	#11926297	—	2	2	no	—
7	#11926297	—	2	2	no	—
8	#11926290	—	2	4	no	—
9	C₁₉×#533	C₂²	1	1	yes	characteristic
10	C₁₉×#446	—	2	2	no	—
11	C₈×Q₈×C₁₉	—	2	2	no	—
12	C₁₉×#424	C₄	1	2	yes	—
13	C₁₉×#423	C₂²	1	1	yes	characteristic
14	C₁₉×#405	C₄	1	2	yes	—
15	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
17	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
20	C₁₉×#125	Q₈	1	2	yes	—
21	C₁₉×C₂²⋊Q₈	—	2	2	no	—
22	C₄×Q₈×C₁₉	—	2	2	no	—
23	C₁₉×#117	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
25	C₂×#64520	—	2	4	no	—
26	C₁₉×C₄⋊C₈	—	2	4	no	—
27	C₁₉×C₄⋊C₈	—	2	2	no	—
28	C₁₉×#97	—	2	2	no	—
29	C₄×C₈×C₁₉	—	2	2	no	—
30	C₄×C₈×C₁₉	D₄	1	2	yes	—
31	C₄×C₈×C₁₉	D₄	1	2	yes	—
32	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
33	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
34	C₂×Q₈×C₁₉	—	2	2	no	—
35	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₉	#41	1	2	yes	—
37	M₁₆×C₁₉	—	4	2	no	—
38	C₂×C₈×C₁₉	—	2	2	no	—
39	C₂×C₈×C₁₉	—	2	2	no	—
40	C₂×C₈×C₁₉	—	4	1	no	—
41	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
43	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
44	C₄⋊C₄×C₁₉	—	2	2	no	—
45	C₄⋊C₄×C₁₉	—	2	4	no	—
46	C₄⋊C₄×C₁₉	C₄⋊C₄	1	4	yes	—
47	C₂²⋊C₄×C₁₉	—	2	2	no	—
48	C₄²×C₁₉	—	2	2	no	—
49	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₄²×C₁₉	C₂×D₄	1	2	yes	—
51	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
52	#64520	—	8	4	no	—
53	C₂×C₁₉⋊C₈	—	4	4	no	—
54	#8639	—	19	1	no	maximal, Sylow
55	C₂³×C₁₉	#117	1	1	yes	characteristic
56	Q₈×C₁₉	—	4	2	no	—
57	Q₈×C₁₉	—	4	2	no	—
58	C₂×C₄×C₁₉	—	2	1	no	—
59	C₂×C₄×C₁₉	—	2	1	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	—	2	4	no	—
63	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#121	1	2	yes	—
66	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
67	C₈×C₁₉	—	2	1	no	—
68	C₈×C₁₉	—	2	2	no	—
69	C₈×C₁₉	—	4	2	no	—
70	C₈×C₁₉	#101	1	2	yes	—
71	C₁₉⋊C₈	—	8	4	no	—
72	#2960	D₁₉	1	1	yes	characteristic
73	#1567	—	19	2	no	—
74	#1561	—	19	2	no	—
75	#1309	—	19	2	no	—
76	C₂²×C₁₉	—	2	1	no	—
77	C₂²×C₁₉	—	2	2	no	—
78	C₂²×C₁₉	#380	1	1	yes	characteristic
79	C₄×C₁₉	—	2	1	no	—
80	C₄×C₁₉	—	2	2	no	—
81	C₄×C₁₉	—	4	4	no	—
82	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
83	C₄×C₁₉	#413	1	1	yes	characteristic
84	C₄×C₁₉	#472	1	2	yes	—
85	C₄×C₁₉	#473	1	2	yes	—
86	#533	C₂×D₁₉	1	1	yes	characteristic
87	#446	—	2	2	no	—
88	C₈×Q₈	—	2	2	no	—
89	#424	Dic₁₉	1	2	yes	—
90	#423	—	19	4	no	—
91	#423	C₂×D₁₉	1	1	yes	characteristic
92	#405	Dic₁₉	1	2	yes	—
93	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
94	#335	—	38	2	no	—
95	#335	—	38	2	no	—
96	#332	—	38	4	no	—
97	C₂×C₁₉	—	4	1	no	—
98	C₂×C₁₉	#1801	1	1	yes	characteristic
99	C₂×C₁₉	#1816	1	2	yes	—
100	C₂×M₁₆	—	38	4	no	—
101	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
102	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
103	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
104	C₄⋊Q₈	D₇₆	1	2	yes	—
105	#125	Dic₃₈	1	2	yes	—
106	C₂²⋊Q₈	—	2	2	no	—
107	C₄×Q₈	—	2	2	no	—
108	#117	C₂×Dic₁₉	1	2	yes	—
109	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
110	C₄⋊C₈	—	2	4	no	—
111	C₄⋊C₈	—	2	2	no	—
112	C₄⋊C₈	—	38	4	no	—
113	C₄⋊C₈	—	38	4	no	—
114	#97	—	2	2	no	—
115	C₄×C₈	—	2	2	no	—
116	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
117	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
118	C₁₉	#8639	1	1	yes	characteristic, complemented, Sylow
119	C₂×Q₈	—	2	2	no	—
120	C₂²×C₄	#64541	1	2	yes	—
121	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
122	M₁₆	—	4	2	no	—
123	M₁₆	—	152	4	no	—
124	C₂×C₈	—	2	2	no	—
125	C₂×C₈	—	2	2	no	—
126	C₂×C₈	—	4	1	no	—
127	C₂×C₈	—	76	4	no	—
128	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
129	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
130	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
131	C₄⋊C₄	—	2	2	no	—
132	C₄⋊C₄	—	2	4	no	—
133	C₄⋊C₄	C₄⋊Dic₁₉	1	4	yes	—
134	C₂²⋊C₄	—	2	2	no	—
135	C₄²	—	2	2	no	—
136	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
137	C₄²	C₂×D₇₆	1	1	yes	characteristic
138	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
139	C₂³	#10597372	1	1	yes	characteristic
140	Q₈	—	4	2	no	—
141	Q₈	—	4	2	no	—
142	C₂×C₄	—	2	1	no	—
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	—	2	1	no	—
146	C₂×C₄	—	2	4	no	—
147	C₂×C₄	#10597370	1	2	yes	—
148	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
149	C₂×C₄	#10597376	1	2	yes	—
150	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
151	C₈	—	2	2	no	—
152	C₈	—	2	1	no	—
153	C₈	—	4	2	no	—
154	C₈	—	152	4	no	—
155	C₈	#10597293	1	2	yes	—
156	C₂²	—	2	1	no	—
157	C₂²	—	2	2	no	—
158	C₂²	#11926404	1	1	yes	characteristic
159	C₄	—	2	1	no	—
160	C₄	—	2	2	no	—
161	C₄	—	4	4	no	—
162	C₄	C₂×#10597293	1	1	yes	characteristic
163	C₄	#11926528	1	1	yes	characteristic
164	C₄	#11926814	1	2	yes	—
165	C₄	#11926819	1	2	yes	—
166	C₂	—	4	1	no	—
167	C₂	#14563631	1	1	yes	characteristic
168	C₂	#14563699	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14562394

C₂

yes

maximal

#14562373

C₂

yes

maximal

C₁₉⋊#1309

C₂

yes

maximal

C₁₉×#2960

C₂

yes

maximal, characteristic

#11926568

C₂²

yes

—

#11926297

—

#11926297

—

#11926290

—

C₁₉×#533

C₂²

yes

characteristic

C₁₉×#446

—

C₈×Q₈×C₁₉

—

C₁₉×#424

C₄

yes

—

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#405

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#125

Q₈

yes

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₄⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#101

yes

—

C₁₉⋊C₈

—

#2960

D₁₉

yes

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#380

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₄×C₁₉

#473

yes

—

#533

C₂×D₁₉

yes

characteristic

#446

—

C₈×Q₈

—

#424

Dic₁₉

yes

—

#423

—

#423

C₂×D₁₉

yes

characteristic

#405

Dic₁₉

yes

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

#1801

yes

characteristic

C₂×C₁₉

#1816

yes

—

100

C₂×M₁₆

—

101

C₂×M₁₆

C₂×Dic₁₉

yes

—

102

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

103

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

104

C₄⋊Q₈

D₇₆

yes

—

105

#125

Dic₃₈

yes

—

106

C₂²⋊Q₈

—

107

C₄×Q₈

—

108

#117

C₂×Dic₁₉

yes

—

109

C₂×C₄²

C₂²×D₁₉

yes

characteristic

110

C₄⋊C₈

—

111

C₄⋊C₈

—

112

C₄⋊C₈

—

113

C₄⋊C₈

—

114

#97

—

115

C₄×C₈

—

116

C₄×C₈

C₂²⋊D₁₉

yes

—

117

C₄×C₈

C₂²⋊D₁₉

yes

—

118

C₁₉

#8639

yes

characteristic, complemented, Sylow

119

C₂×Q₈

—

120

C₂²×C₄

#64541

yes

—

121

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

122

M₁₆

—

123

M₁₆

—

152

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

129

C₂×C₈

C₂²⋊Dic₁₉

yes

—

130

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₄⋊C₄

C₄⋊Dic₁₉

yes

—

134

C₂²⋊C₄

—

135

C₄²

—

136

C₄²

C₂×Dic₃₈

yes

characteristic

137

C₄²

C₂×D₇₆

yes

characteristic

138

C₄²

C₂×C₂²⋊D₁₉

yes

—

139

C₂³

#10597372

yes

characteristic

140

Q₈

—

141

Q₈

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

#10597370

yes

—

148

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

149

C₂×C₄

#10597376

yes

—

150

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

151

C₈

—

152

C₈

—

153

C₈

—

154

C₈

—

152

—

155

C₈

#10597293

yes

—

156

C₂²

—

157

C₂²

—

158

C₂²

#11926404

yes

characteristic

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

C₂×#10597293

yes

characteristic

163

C₄

#11926528

yes

characteristic

164

C₄

#11926814

yes

—

165

C₄

#11926819

yes

—

166

C₂

—

167

C₂

#14563631

yes

characteristic

168

C₂

#14563699

yes

—

	subgroup	G/H
center	C₂²	#11926404
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2960	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2960	D₁₉
hypocenter	C₁₉	#8639
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2960

subgroup

G/H

center

C₂²

#11926404

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2960

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2960

N	H ≅ G/N	type
118. C₁₉	#8639	semidirect

H ≅ G/N

type

118. C₁₉

#8639

semidirect

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

subgroup	index
#14562394	2
#14562373	2
C₁₉⋊#1309	2
C₁₉×#2960	2
#8639	19

subgroup

index

#14562394

#14562373

C₁₉⋊#1309

C₁₉×#2960

#8639

Subgroups — #18075569

Conjugacy classes of subgroups

Complements

Maximal subgroups