Group #18075561 — subgroups

Subgroups — #18075561

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	#14562391	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	#11926295	—	2	2	no	—
7	#11926295	—	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	#8637	—	19	1	no	maximal, Sylow
55	C₂³×C₁₉	#117	1	1	yes	characteristic
56	Q₈×C₁₉	—	4	4	no	—
57	C₂×C₄×C₁₉	—	2	1	no	—
58	C₂×C₄×C₁₉	—	2	1	no	—
59	C₂×C₄×C₁₉	—	2	4	no	—
60	C₂×C₄×C₁₉	—	2	4	no	—
61	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#121	1	2	yes	—
64	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
65	C₈×C₁₉	—	2	1	no	—
66	C₈×C₁₉	—	2	2	no	—
67	C₈×C₁₉	—	4	2	no	—
68	C₈×C₁₉	#101	1	2	yes	—
69	C₁₉⋊C₈	—	8	4	no	—
70	#2960	D₁₉	1	1	yes	characteristic
71	#1566	—	19	2	no	—
72	#1561	—	19	2	no	—
73	#1309	—	19	2	no	—
74	C₂²×C₁₉	—	2	1	no	—
75	C₂²×C₁₉	—	2	2	no	—
76	C₂²×C₁₉	#380	1	1	yes	characteristic
77	C₄×C₁₉	—	2	1	no	—
78	C₄×C₁₉	—	2	2	no	—
79	C₄×C₁₉	—	4	4	no	—
80	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
81	C₄×C₁₉	#413	1	1	yes	characteristic
82	C₄×C₁₉	#471	1	4	yes	—
83	#533	C₂×D₁₉	1	1	yes	characteristic
84	#446	—	2	2	no	—
85	C₈×Q₈	—	2	2	no	—
86	#424	Dic₁₉	1	2	yes	—
87	#423	—	19	4	no	—
88	#423	C₂×D₁₉	1	1	yes	characteristic
89	#405	Dic₁₉	1	2	yes	—
90	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
91	#334	—	38	2	no	—
92	#334	—	38	2	no	—
93	#332	—	38	4	no	—
94	C₂×C₁₉	—	4	1	no	—
95	C₂×C₁₉	#1801	1	1	yes	characteristic
96	C₂×C₁₉	#1815	1	2	yes	—
97	C₂×M₁₆	—	38	4	no	—
98	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
99	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
100	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
101	C₄⋊Q₈	D₇₆	1	2	yes	—
102	#125	Dic₃₈	1	2	yes	—
103	C₂²⋊Q₈	—	2	2	no	—
104	C₄×Q₈	—	2	2	no	—
105	#117	C₂×Dic₁₉	1	2	yes	—
106	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
107	C₄⋊C₈	—	2	4	no	—
108	C₄⋊C₈	—	2	2	no	—
109	C₄⋊C₈	—	38	4	no	—
110	C₄⋊C₈	—	38	4	no	—
111	#97	—	2	2	no	—
112	C₄×C₈	—	2	2	no	—
113	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
114	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
115	C₁₉	#8637	1	1	yes	characteristic, complemented, Sylow
116	C₂×Q₈	—	2	2	no	—
117	C₂²×C₄	#64541	1	2	yes	—
118	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
119	M₁₆	—	4	2	no	—
120	M₁₆	—	152	4	no	—
121	C₂×C₈	—	2	2	no	—
122	C₂×C₈	—	2	2	no	—
123	C₂×C₈	—	4	1	no	—
124	C₂×C₈	—	76	4	no	—
125	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
126	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
127	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
128	C₄⋊C₄	—	2	2	no	—
129	C₄⋊C₄	—	2	4	no	—
130	C₄⋊C₄	C₄⋊Dic₁₉	1	4	yes	—
131	C₂²⋊C₄	—	2	2	no	—
132	C₄²	—	2	2	no	—
133	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
134	C₄²	C₂×D₇₆	1	1	yes	characteristic
135	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
136	C₂³	#10597372	1	1	yes	characteristic
137	Q₈	—	4	4	no	—
138	C₂×C₄	—	2	1	no	—
139	C₂×C₄	—	2	4	no	—
140	C₂×C₄	—	2	1	no	—
141	C₂×C₄	—	2	4	no	—
142	C₂×C₄	#10597370	1	2	yes	—
143	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
144	C₂×C₄	#10597376	1	2	yes	—
145	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
146	C₈	—	2	2	no	—
147	C₈	—	2	1	no	—
148	C₈	—	4	2	no	—
149	C₈	—	152	4	no	—
150	C₈	#10597293	1	2	yes	—
151	C₂²	—	2	1	no	—
152	C₂²	—	2	2	no	—
153	C₂²	#11926404	1	1	yes	characteristic
154	C₄	—	2	1	no	—
155	C₄	—	2	2	no	—
156	C₄	—	4	4	no	—
157	C₄	C₂×#10597293	1	1	yes	characteristic
158	C₄	#11926528	1	1	yes	characteristic
159	C₄	#11926807	1	4	yes	—
160	C₂	—	4	1	no	—
161	C₂	#14563631	1	1	yes	characteristic
162	C₂	#14563694	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14562391

C₂

yes

maximal

#14562373

C₂

yes

maximal

C₁₉⋊#1309

C₂

yes

maximal

C₁₉×#2960

C₂

yes

maximal, characteristic

#11926568

C₂²

yes

—

#11926295

—

#11926295

—

#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

—

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

—

#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

#1815

yes

—

C₂×M₁₆

—

C₂×M₁₆

C₂×Dic₁₉

yes

—

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

100

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

101

C₄⋊Q₈

D₇₆

yes

—

102

#125

Dic₃₈

yes

—

103

C₂²⋊Q₈

—

104

C₄×Q₈

—

105

#117

C₂×Dic₁₉

yes

—

106

C₂×C₄²

C₂²×D₁₉

yes

characteristic

107

C₄⋊C₈

—

108

C₄⋊C₈

—

109

C₄⋊C₈

—

110

C₄⋊C₈

—

111

#97

—

112

C₄×C₈

—

113

C₄×C₈

C₂²⋊D₁₉

yes

—

114

C₄×C₈

C₂²⋊D₁₉

yes

—

115

C₁₉

#8637

yes

characteristic, complemented, Sylow

116

C₂×Q₈

—

117

C₂²×C₄

#64541

yes

—

118

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

119

M₁₆

—

120

M₁₆

—

152

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

126

C₂×C₈

C₂²⋊Dic₁₉

yes

—

127

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

128

C₄⋊C₄

—

129

C₄⋊C₄

—

130

C₄⋊C₄

C₄⋊Dic₁₉

yes

—

131

C₂²⋊C₄

—

132

C₄²

—

133

C₄²

C₂×Dic₃₈

yes

characteristic

134

C₄²

C₂×D₇₆

yes

characteristic

135

C₄²

C₂×C₂²⋊D₁₉

yes

—

136

C₂³

#10597372

yes

characteristic

137

Q₈

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

#10597370

yes

—

143

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

144

C₂×C₄

#10597376

yes

—

145

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

146

C₈

—

147

C₈

—

148

C₈

—

149

C₈

—

152

—

150

C₈

#10597293

yes

—

151

C₂²

—

152

C₂²

—

153

C₂²

#11926404

yes

characteristic

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

C₂×#10597293

yes

characteristic

158

C₄

#11926528

yes

characteristic

159

C₄

#11926807

yes

—

160

C₂

—

161

C₂

#14563631

yes

characteristic

162

C₂

#14563694

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	#8637
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
115. C₁₉	#8637	semidirect

H ≅ G/N

type

115. C₁₉

#8637

semidirect

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

subgroup	index
#14562391	2
#14562373	2
C₁₉⋊#1309	2
C₁₉×#2960	2
#8637	19

subgroup

index

#14562391

#14562373

C₁₉⋊#1309

C₁₉×#2960

#8637

Subgroups — #18075561

Conjugacy classes of subgroups

Complements

Maximal subgroups