Group #18069913 — subgroups

Subgroups — #18069913

Order 4864.

178 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 39 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	#14563716	C₂	1	1	yes	maximal, characteristic
2	#14561571	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1320	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597372	C₄	1	1	yes	characteristic
5	#11926508	C₄	1	1	yes	characteristic
6	#11926326	—	2	1	no	—
7	#11926312	—	2	1	no	—
8	#11926312	—	2	1	no	—
9	C₁₉×#407	C₂²	1	1	yes	characteristic
10	C₁₉×#349	—	2	1	no	—
11	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
13	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
14	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
15	#10597372	—	4	1	no	—
16	#10597372	—	4	1	no	—
17	C₂×C₄⋊Dic₁₉	—	2	1	no	—
18	C₂×C₄×Dic₁₉	C₈	1	2	yes	—
19	C₂×#64520	—	2	1	no	—
20	C₁₉×M₃₂	—	4	1	no	—
21	C₁₉×C₂²⋊C₈	—	4	1	no	—
22	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
23	#10597269	—	4	1	no	—
24	C₂⁴×C₁₉	M₁₆	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	—	2	1	no	—
26	C₂²×C₄×C₁₉	—	2	1	no	—
27	C₂²×C₄×C₁₉	—	4	1	no	—
28	C₂²×C₄×C₁₉	—	4	1	no	—
29	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
31	C₂²×Dic₁₉	—	2	2	no	—
32	M₁₆×C₁₉	—	4	1	no	—
33	M₁₆×C₁₉	—	4	1	no	—
34	C₂×C₈×C₁₉	—	2	1	no	—
35	C₂×C₈×C₁₉	—	2	1	no	—
36	C₂²⋊Dic₁₉	—	4	2	no	—
37	C₄⋊Dic₁₉	—	4	1	no	—
38	C₄⋊Dic₁₉	—	4	1	no	—
39	C₄×Dic₁₉	—	4	2	no	—
40	#64520	—	4	1	no	—
41	#64520	—	4	1	no	—
42	C₂×C₁₉⋊C₈	—	4	1	no	—
43	C₁₆×C₁₉	—	8	1	no	—
44	C₁₉⋊C₁₆	—	8	1	no	—
45	#7350	—	19	1	no	maximal, Sylow
46	C₂³×C₁₉	—	2	1	no	—
47	C₂³×C₁₉	—	4	1	no	—
48	C₂³×C₁₉	—	8	1	no	—
49	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	4	2	no	—
54	C₂×C₄×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	—	4	1	no	—
56	C₂×C₄×C₁₉	—	4	1	no	—
57	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
59	C₂×Dic₁₉	—	4	2	no	—
60	C₂×Dic₁₉	—	8	2	no	—
61	C₈×C₁₉	—	4	1	no	—
62	C₈×C₁₉	—	4	1	no	—
63	C₁₉⋊C₈	—	8	1	no	—
64	#1822	—	19	1	no	—
65	#1320	—	19	1	no	—
66	#1320	D₁₉	1	1	yes	characteristic
67	C₂²×C₁₉	—	2	1	no	—
68	C₂²×C₁₉	—	4	1	no	—
69	C₂²×C₁₉	—	4	2	no	—
70	C₂²×C₁₉	—	4	1	no	—
71	C₂²×C₁₉	—	8	2	no	—
72	C₂²×C₁₉	#323	1	1	yes	characteristic
73	C₄×C₁₉	—	2	1	no	—
74	C₄×C₁₉	—	4	1	no	—
75	C₄×C₁₉	#352	1	1	yes	characteristic
76	C₄×C₁₉	#352	1	1	yes	characteristic
77	Dic₁₉	—	8	2	no	—
78	C₂×#117	—	19	1	no	—
79	#407	—	19	1	no	—
80	#407	C₂×D₁₉	1	1	yes	characteristic
81	#349	—	2	1	no	—
82	#349	—	38	1	no	—
83	#343	—	38	1	no	—
84	#343	—	38	1	no	—
85	C₂×C₁₉	—	2	1	no	—
86	C₂×C₁₉	—	4	1	no	—
87	C₂×C₁₉	—	8	1	no	—
88	C₂×C₁₉	#1317	1	1	yes	characteristic
89	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
90	C₂×M₁₆	—	38	1	no	—
91	C₂×M₁₆	D₇₆	1	1	yes	characteristic
92	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
93	#117	—	76	1	no	—
94	#117	—	76	1	no	—
95	C₂×C₄⋊C₄	—	38	1	no	—
96	C₂×C₂²⋊C₄	—	38	1	no	—
97	C₂×C₄²	—	19	2	no	—
98	M₃₂	—	4	1	no	—
99	M₃₂	—	76	1	no	—
100	C₂²⋊C₈	—	4	1	no	—
101	C₂²⋊C₈	—	76	1	no	—
102	C₁₉	#7350	1	1	yes	characteristic, complemented, Sylow
103	C₂⁴	#64515	1	1	yes	characteristic
104	C₂²×C₄	—	2	1	no	—
105	C₂²×C₄	—	2	1	no	—
106	C₂²×C₄	—	4	1	no	—
107	C₂²×C₄	—	4	1	no	—
108	C₂²×C₄	—	38	2	no	—
109	C₂²×C₄	C₈×D₁₉	1	1	yes	characteristic
110	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
111	M₁₆	—	4	1	no	—
112	M₁₆	—	4	1	no	—
113	M₁₆	—	76	1	no	—
114	M₁₆	—	76	1	no	—
115	C₂×C₈	—	2	1	no	—
116	C₂×C₈	—	2	1	no	—
117	C₂×C₈	—	76	1	no	—
118	C₄⋊C₄	—	76	1	no	—
119	C₄⋊C₄	—	76	1	no	—
120	C₂²⋊C₄	—	76	2	no	—
121	C₄²	—	76	2	no	—
122	C₁₆	—	8	1	no	—
123	C₁₆	—	152	1	no	—
124	C₂³	—	2	1	no	—
125	C₂³	—	4	1	no	—
126	C₂³	—	8	1	no	—
127	C₂³	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	2	1	no	—
131	C₂×C₄	—	4	2	no	—
132	C₂×C₄	—	4	1	no	—
133	C₂×C₄	—	4	1	no	—
134	C₂×C₄	—	4	1	no	—
135	C₂×C₄	—	76	2	no	—
136	C₂×C₄	—	152	2	no	—
137	C₂×C₄	#10597263	1	1	yes	characteristic
138	C₂×C₄	#10597280	1	1	yes	characteristic
139	C₈	—	4	1	no	—
140	C₈	—	4	1	no	—
141	C₈	—	152	1	no	—
142	C₂²	—	2	1	no	—
143	C₂²	—	4	1	no	—
144	C₂²	—	4	2	no	—
145	C₂²	—	4	1	no	—
146	C₂²	—	8	2	no	—
147	C₂²	#11926267	1	1	yes	characteristic
148	C₄	—	2	1	no	—
149	C₄	—	4	1	no	—
150	C₄	—	152	2	no	—
151	C₄	#11926333	1	1	yes	characteristic
152	C₄	#11926335	1	1	yes	characteristic
153	C₂	—	2	1	no	—
154	C₂	—	4	1	no	—
155	C₂	—	8	1	no	—
156	C₂	#14561564	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563716

C₂

yes

maximal, characteristic

#14561571

C₂

yes

maximal, characteristic

C₁₉×#1320

C₂

yes

maximal, characteristic

C₂×#10597372

C₄

yes

characteristic

#11926508

C₄

yes

—

—

—

C₁₉×#407

C₂²

yes

characteristic

C₁₉×#349

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

#10597372

—

#10597372

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄×Dic₁₉

C₈

yes

—

C₂×#64520

—

C₁₉×M₃₂

—

C₁₉×C₂²⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

#10597269

—

C₂⁴×C₁₉

M₁₆

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

#7350

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₈

yes

characteristic

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×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1822

—

#1320

—

#1320

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#323

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂×#117

—

#407

—

#407

C₂×D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1317

yes

characteristic

C₂³×C₄

C₄×D₁₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

D₇₆

yes

characteristic

C₂×M₁₆

C₂²⋊D₁₉

yes

characteristic

#117

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

M₃₂

—

M₃₂

—

100

C₂²⋊C₈

—

101

C₂²⋊C₈

—

102

C₁₉

#7350

yes

characteristic, complemented, Sylow

103

C₂⁴

#64515

yes

characteristic

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

C₈×D₁₉

yes

characteristic

110

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

111

M₁₆

—

112

M₁₆

—

113

M₁₆

—

114

M₁₆

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₂²⋊C₄

—

121

C₄²

—

122

C₁₆

—

123

C₁₆

—

152

—

124

C₂³

—

125

C₂³

—

126

C₂³

—

127

C₂³

(C₂×D₁₉)⋊C₈

yes

characteristic

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

—

152

—

137

C₂×C₄

#10597263

yes

characteristic

138

C₂×C₄

#10597280

yes

characteristic

139

C₈

—

140

C₈

—

141

C₈

—

152

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

147

C₂²

#11926267

yes

characteristic

148

C₄

—

149

C₄

—

150

C₄

—

152

—

151

C₄

#11926333

yes

characteristic

152

C₄

#11926335

yes

characteristic

153

C₂

—

154

C₂

—

155

C₂

—

156

C₂

#14561564

yes

characteristic

	subgroup	G/H
center	C₂	#14561564
commutator	C₂²×C₄×C₁₉	C₂×C₈
Frattini	#407	C₂×D₁₉
Fitting	C₁₉×#1320	C₂
socle	C₂×C₁₉	#1317
prime radical	C₂⁴×C₁₉	M₁₆
cosocle	C₁₉×#407	C₂²
hypercenter	#1320	D₁₉
hypocenter	C₁₉	#7350
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #407 ◁ #1320

subgroup

G/H

center

C₂

#14561564

commutator

C₂²×C₄×C₁₉

C₂×C₈

Frattini

#407

C₂×D₁₉

Fitting

C₁₉×#1320

C₂

socle

C₂×C₁₉

#1317

prime radical

C₂⁴×C₁₉

M₁₆

cosocle

C₁₉×#407

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #407 ◁ #1320

N	H ≅ G/N	type
102. C₁₉	#7350	semidirect

H ≅ G/N

type

102. C₁₉

#7350

semidirect

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

subgroup	index
#14563716	2
#14561571	2
C₁₉×#1320	2
#7350	19

subgroup

index

#14563716

#14561571

C₁₉×#1320

#7350

Subgroups — #18069913

Conjugacy classes of subgroups

Complements

Maximal subgroups