Group #18085649 — subgroups

Subgroups — #18085649

Order 4864.

364 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 93 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	#14564612	C₂	1	1	yes	maximal, characteristic
2	#14562198	C₂	1	2	yes	maximal
3	#14561493	C₂	1	2	yes	maximal
4	#14561468	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2864	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	1	yes	characteristic
7	#11926597	C₂²	1	2	yes	—
8	#11926568	C₂²	1	1	yes	characteristic
9	#11926304	—	2	2	no	—
10	#11926280	—	2	4	no	—
11	C₁₉×#389	—	2	2	no	—
12	C₁₉×#387	—	2	4	no	—
13	C₁₉×#382	C₂²	1	2	yes	—
14	C₄³×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
16	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
17	C₂×C₄²×C₁₉	—	2	2	no	—
18	C₂×C₄²×C₁₉	D₄	1	2	yes	—
19	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
20	#10597372	—	2	1	no	—
21	#10597370	—	2	2	no	—
22	C₂×#64520	—	2	1	no	—
23	#10597316	—	2	1	no	—
24	#10597315	Q₈	1	2	yes	—
25	C₄×Dic₃₈	—	2	2	no	—
26	C₁₉×#95	—	2	4	no	—
27	C₁₉×#95	—	2	2	no	—
28	C₁₉×#95	D₄	1	4	yes	—
29	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
30	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
31	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
32	C₄×C₁₉⋊C₈	—	2	2	no	—
33	C₂²×C₄×C₁₉	—	2	2	no	—
34	C₂²×C₄×C₁₉	—	2	4	no	—
35	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
36	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₂×Dic₃₈	—	2	2	no	—
38	C₄⋊C₄×C₁₉	—	4	8	no	—
39	C₄⋊C₄×C₁₉	—	4	2	no	—
40	C₄⋊C₄×C₁₉	—	4	2	no	—
41	C₄²×C₁₉	—	2	2	no	—
42	C₄²×C₁₉	—	2	2	no	—
43	C₄²×C₁₉	—	4	4	no	—
44	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
45	C₄²×C₁₉	#41	1	1	yes	characteristic
46	C₄²×C₁₉	#41	1	2	yes	—
47	C₂²⋊Dic₁₉	—	4	1	no	—
48	C₄⋊Dic₁₉	—	2	2	no	—
49	C₄⋊Dic₁₉	—	2	2	no	—
50	Dic₁₉⋊C₄	—	4	2	no	—
51	C₄×Dic₁₉	—	4	1	no	—
52	#64520	—	4	2	no	—
53	C₂×C₁₉⋊C₈	—	4	2	no	—
54	C₂×C₁₉⋊C₈	—	4	1	no	—
55	#10367	—	19	1	no	maximal, Sylow
56	C₂³×C₁₉	#120	1	1	yes	characteristic
57	C₂×C₄×C₁₉	—	2	4	no	—
58	C₂×C₄×C₁₉	—	4	2	no	—
59	C₂×C₄×C₁₉	—	4	2	no	—
60	C₂×C₄×C₁₉	—	4	2	no	—
61	C₂×C₄×C₁₉	—	4	8	no	—
62	C₂×C₄×C₁₉	—	4	4	no	—
63	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
64	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#124	1	2	yes	—
66	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#135	1	2	yes	—
68	C₂×C₄×C₁₉	#137	1	2	yes	—
69	C₂×Dic₁₉	—	4	2	no	—
70	Dic₃₈	—	8	2	no	—
71	C₁₉⋊C₈	—	8	2	no	—
72	C₁₉⋊C₈	—	8	1	no	—
73	#2864	D₁₉	1	1	yes	characteristic
74	#1994	—	19	1	no	—
75	#1518	—	19	2	no	—
76	#1286	—	19	2	no	—
77	#1276	—	19	1	no	—
78	C₂²×C₁₉	—	2	2	no	—
79	C₂²×C₁₉	#393	1	1	yes	characteristic
80	C₂²×C₁₉	#452	1	2	yes	—
81	C₄×C₁₉	—	2	2	no	—
82	C₄×C₁₉	—	2	2	no	—
83	C₄×C₁₉	—	4	4	no	—
84	C₄×C₁₉	—	8	4	no	—
85	C₄×C₁₉	#479	1	2	yes	—
86	C₄×C₁₉	#488	1	1	yes	characteristic
87	C₄×C₁₉	#491	1	1	yes	characteristic
88	Dic₁₉	—	8	2	no	—
89	#533	—	19	1	no	—
90	#431	—	19	2	no	—
91	#423	—	19	1	no	—
92	#389	—	2	2	no	—
93	#387	—	2	4	no	—
94	#382	C₂×D₁₉	1	2	yes	—
95	C₄³	C₂×D₁₉	1	1	yes	characteristic
96	#339	—	38	2	no	—
97	#328	—	38	4	no	—
98	C₂×C₁₉	—	2	2	no	—
99	C₂×C₁₉	#2026	1	1	yes	characteristic
100	C₂×C₁₉	#2031	1	2	yes	—
101	C₂×M₁₆	—	38	1	no	—
102	C₄⋊Q₈	—	19	2	no	—
103	#125	—	38	1	no	—
104	C₂²⋊Q₈	—	38	2	no	—
105	C₄×Q₈	—	38	2	no	—
106	#117	—	38	1	no	—
107	C₂×C₄⋊C₄	—	2	4	no	—
108	C₂×C₄⋊C₄	—	2	2	no	—
109	C₂×C₄²	—	2	2	no	—
110	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
111	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
112	C₄⋊C₈	—	38	2	no	—
113	C₄⋊C₈	—	38	2	no	—
114	C₂²⋊C₈	—	38	2	no	—
115	C₄×C₈	—	38	2	no	—
116	#95	—	2	4	no	—
117	#95	—	2	2	no	—
118	#95	C₂²⋊D₁₉	1	4	yes	—
119	C₁₉	#10367	1	1	yes	characteristic, complemented, Sylow
120	C₂×Q₈	—	38	2	no	—
121	C₂²×C₄	—	2	2	no	—
122	C₂²×C₄	—	2	4	no	—
123	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
124	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
125	M₁₆	—	76	2	no	—
126	C₂×C₈	—	76	2	no	—
127	C₂×C₈	—	76	1	no	—
128	C₄⋊C₄	—	4	8	no	—
129	C₄⋊C₄	—	4	2	no	—
130	C₄⋊C₄	—	4	2	no	—
131	C₄⋊C₄	—	38	2	no	—
132	C₄⋊C₄	—	38	2	no	—
133	C₄⋊C₄	—	76	2	no	—
134	C₂²⋊C₄	—	76	1	no	—
135	C₄²	—	2	2	no	—
136	C₄²	—	2	2	no	—
137	C₄²	—	4	4	no	—
138	C₄²	—	76	1	no	—
139	C₄²	Q₈×D₁₉	1	1	yes	characteristic
140	C₄²	#64545	1	1	yes	characteristic
141	C₄²	#64545	1	2	yes	—
142	C₂³	#10597399	1	1	yes	characteristic
143	Q₈	—	152	2	no	—
144	C₂×C₄	—	2	4	no	—
145	C₂×C₄	—	4	2	no	—
146	C₂×C₄	—	4	2	no	—
147	C₂×C₄	—	4	2	no	—
148	C₂×C₄	—	4	8	no	—
149	C₂×C₄	—	4	4	no	—
150	C₂×C₄	—	76	2	no	—
151	C₂×C₄	#10597392	1	2	yes	—
152	C₂×C₄	#10597392	1	1	yes	characteristic
153	C₂×C₄	#10597393	1	2	yes	—
154	C₂×C₄	#10597393	1	1	yes	characteristic
155	C₂×C₄	#10597396	1	2	yes	—
156	C₂×C₄	#10597397	1	2	yes	—
157	C₈	—	152	2	no	—
158	C₈	—	152	1	no	—
159	C₂²	—	2	2	no	—
160	C₂²	#11926455	1	1	yes	characteristic
161	C₂²	#11926706	1	2	yes	—
162	C₄	—	2	2	no	—
163	C₄	—	2	2	no	—
164	C₄	—	4	4	no	—
165	C₄	—	8	4	no	—
166	C₄	—	152	2	no	—
167	C₄	#11926848	1	2	yes	—
168	C₄	#11926901	1	1	yes	characteristic
169	C₄	#11926914	1	1	yes	characteristic
170	C₂	—	2	2	no	—
171	C₂	#14564783	1	1	yes	characteristic
172	C₂	#14564804	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564612

C₂

yes

maximal, characteristic

#14562198

C₂

yes

maximal

#14561493

C₂

yes

maximal

#14561468

C₂

yes

maximal, characteristic

C₁₉×#2864

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

characteristic

#11926597

C₂²

yes

—

#11926568

C₂²

yes

characteristic

#11926304

—

#11926280

—

C₁₉×#389

—

C₁₉×#387

—

C₁₉×#382

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

—

Q₈

yes

—

C₄×Dic₃₈

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

D₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×Q₈

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

#124

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

Dic₃₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2864

D₁₉

yes

—

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

#393

yes

characteristic

C₂²×C₁₉

#452

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#479

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

—

—

—

—

—

C₂×D₁₉

yes

—

C₄³

C₂×D₁₉

yes

characteristic

#339

—

#328

—

C₂×C₁₉

—

C₂×C₁₉

#2026

yes

characteristic

100

C₂×C₁₉

#2031

yes

—

101

C₂×M₁₆

—

102

C₄⋊Q₈

—

103

#125

—

104

C₂²⋊Q₈

—

105

C₄×Q₈

—

106

#117

—

107

C₂×C₄⋊C₄

—

108

C₂×C₄⋊C₄

—

109

C₂×C₄²

—

110

C₂×C₄²

C₂²⋊D₁₉

yes

—

111

C₂×C₄²

C₂²×D₁₉

yes

characteristic

112

C₄⋊C₈

—

113

C₄⋊C₈

—

114

C₂²⋊C₈

—

115

C₄×C₈

—

116

#95

—

117

#95

—

118

#95

C₂²⋊D₁₉

yes

—

119

C₁₉

#10367

yes

characteristic, complemented, Sylow

120

C₂×Q₈

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

124

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

125

M₁₆

—

126

C₂×C₈

—

127

C₂×C₈

—

128

C₄⋊C₄

—

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₄⋊C₄

—

134

C₂²⋊C₄

—

135

C₄²

—

136

C₄²

—

137

C₄²

—

138

C₄²

—

139

C₄²

Q₈×D₁₉

yes

characteristic

140

C₄²

#64545

yes

characteristic

141

C₄²

#64545

yes

—

142

C₂³

#10597399

yes

characteristic

143

Q₈

—

152

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

#10597392

yes

—

152

C₂×C₄

#10597392

yes

characteristic

153

C₂×C₄

#10597393

yes

—

154

C₂×C₄

#10597393

yes

characteristic

155

C₂×C₄

#10597396

yes

—

156

C₂×C₄

#10597397

yes

—

157

C₈

—

152

—

158

C₈

—

152

—

159

C₂²

—

160

C₂²

#11926455

yes

characteristic

161

C₂²

#11926706

yes

—

162

C₄

—

163

C₄

—

164

C₄

—

165

C₄

—

166

C₄

—

152

—

167

C₄

#11926848

yes

—

168

C₄

#11926901

yes

characteristic

169

C₄

#11926914

yes

characteristic

170

C₂

—

171

C₂

#14564783

yes

characteristic

172

C₂

#14564804

yes

—

	subgroup	G/H
center	C₂²	#11926455
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2864	C₂
socle	C₂²×C₁₉	#393
prime radical	C₂³×C₁₉	#120
hypercenter	#2864	D₁₉
hypocenter	C₁₉	#10367
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2864

subgroup

G/H

center

C₂²

#11926455

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2864

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2864

N	H ≅ G/N	type
119. C₁₉	#10367	semidirect

H ≅ G/N

type

119. C₁₉

#10367

semidirect

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

subgroup	index
#14564612	2
#14562198	2
#14561493	2
#14561468	2
C₁₉×#2864	2
#10367	19

subgroup

index

C₁₉×#2864

Subgroups — #18085649

Conjugacy classes of subgroups

Complements

Maximal subgroups