Group #18073893 — subgroups

Subgroups — #18073893

Order 4864.

810 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 171 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	#14563703	C₂	1	2	yes	maximal
2	C₂×#11926270	C₂	1	4	yes	maximal
3	C₂²×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
5	#11926299	—	2	4	no	—
6	#11926270	—	2	8	no	—
7	C₂×C₁₉×#125	—	2	8	no	—
8	C₂×C₁₉×#125	—	2	4	no	—
9	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
11	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
17	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
18	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₁₉×#125	—	2	32	no	—
20	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
21	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
22	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
23	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
24	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
25	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
29	C₂×C₄⋊C₄×C₁₉	D₄	1	8	yes	—
30	C₂×C₄²×C₁₉	—	2	4	no	—
31	C₂×C₄²×C₁₉	D₄	1	4	yes	—
32	C₂²×C₁₉⋊C₈	—	2	4	no	—
33	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
34	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	—	2	2	no	—
36	C₂²×C₄×C₁₉	—	2	4	no	—
37	C₂²×C₄×C₁₉	—	2	2	no	—
38	C₂²×C₄×C₁₉	—	2	2	no	—
39	C₂²×C₄×C₁₉	—	2	2	no	—
40	C₂²×C₄×C₁₉	—	2	2	no	—
41	C₂²×C₄×C₁₉	—	2	2	no	—
42	C₂²×C₄×C₁₉	—	2	4	no	—
43	C₂²×C₄×C₁₉	—	2	8	no	—
44	C₂²×C₄×C₁₉	—	4	2	no	—
45	C₂²×C₄×C₁₉	—	4	4	no	—
46	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
47	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
48	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
50	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
51	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
52	C₄⋊C₄×C₁₉	—	2	8	no	—
53	C₄⋊C₄×C₁₉	—	2	8	no	—
54	C₄⋊C₄×C₁₉	—	2	16	no	—
55	C₄⋊C₄×C₁₉	—	2	16	no	—
56	C₄²×C₁₉	—	2	8	no	—
57	C₂×C₁₉⋊C₈	—	4	8	no	—
58	C₂×C₁₉⋊C₈	—	4	4	no	—
59	#8306	—	19	1	no	maximal, Sylow
60	C₂³×C₁₉	—	2	2	no	—
61	C₂³×C₁₉	—	2	2	no	—
62	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
63	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
64	C₂³×C₁₉	#131	1	4	yes	—
65	C₂×C₄×C₁₉	—	2	8	no	—
66	C₂×C₄×C₁₉	—	2	2	no	—
67	C₂×C₄×C₁₉	—	2	4	no	—
68	C₂×C₄×C₁₉	—	2	2	no	—
69	C₂×C₄×C₁₉	—	2	2	no	—
70	C₂×C₄×C₁₉	—	2	4	no	—
71	C₂×C₄×C₁₉	—	2	4	no	—
72	C₂×C₄×C₁₉	—	2	8	no	—
73	C₂×C₄×C₁₉	—	2	4	no	—
74	C₂×C₄×C₁₉	—	4	4	no	—
75	C₂×C₄×C₁₉	—	4	4	no	—
76	C₂×C₄×C₁₉	—	4	4	no	—
77	C₂×C₄×C₁₉	—	4	4	no	—
78	C₂×C₄×C₁₉	—	4	4	no	—
79	C₂×C₄×C₁₉	—	4	4	no	—
80	C₂×C₄×C₁₉	—	4	4	no	—
81	C₂×C₄×C₁₉	#101	1	4	yes	—
82	C₂×C₄×C₁₉	#120	1	4	yes	—
83	C₁₉⋊C₈	—	8	4	no	—
84	C₂²×#125	D₁₉	1	1	yes	characteristic
85	#1817	—	19	2	no	—
86	C₂×#324	—	19	4	no	—
87	C₂²×C₁₉	—	2	8	no	—
88	C₂²×C₁₉	—	2	2	no	—
89	C₂²×C₁₉	—	2	2	no	—
90	C₂²×C₁₉	#379	1	1	yes	characteristic
91	C₂²×C₁₉	#408	1	4	yes	—
92	C₂²×C₁₉	#408	1	2	yes	—
93	C₂²×C₁₉	#410	1	2	yes	—
94	C₂²×C₁₉	C₂×#101	1	2	yes	—
95	C₄×C₁₉	—	2	4	no	—
96	C₄×C₁₉	—	2	4	no	—
97	C₄×C₁₉	—	4	2	no	—
98	C₄×C₁₉	—	4	4	no	—
99	C₄×C₁₉	—	4	4	no	—
100	C₂×#125	—	2	8	no	—
101	C₂×#125	—	2	4	no	—
102	C₂²×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
103	C₂²×C₄⋊C₄	Dic₁₉	1	2	yes	—
104	C₂²×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
105	C₂²×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
106	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
107	C₂×C₂²⋊C₈	—	19	4	no	—
108	#336	—	38	4	no	—
109	#324	—	38	8	no	—
110	C₂×C₁₉	—	2	4	no	—
111	C₂×C₁₉	#1470	1	4	yes	—
112	C₂×C₁₉	#1780	1	1	yes	characteristic
113	C₂×C₁₉	#1782	1	1	yes	characteristic
114	C₂×C₁₉	#1784	1	1	yes	characteristic
115	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
116	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
117	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
118	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
119	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
120	C₂²×C₈	—	38	4	no	—
121	#125	—	2	32	no	—
122	C₂×C₄⋊C₄	—	2	4	no	—
123	C₂×C₄⋊C₄	—	2	4	no	—
124	C₂×C₄⋊C₄	—	2	4	no	—
125	C₂×C₄⋊C₄	—	2	4	no	—
126	C₂×C₄⋊C₄	—	2	4	no	—
127	C₂×C₄⋊C₄	—	2	2	no	—
128	C₂×C₄⋊C₄	—	2	2	no	—
129	C₂×C₄⋊C₄	—	2	4	no	—
130	C₂×C₄⋊C₄	—	2	4	no	—
131	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	8	yes	—
132	C₂×C₄²	—	2	4	no	—
133	C₂×C₄²	C₂²⋊D₁₉	1	4	yes	—
134	C₂²⋊C₈	—	38	8	no	—
135	C₁₉	#8306	1	1	yes	characteristic, complemented, Sylow
136	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
137	C₂²×C₄	—	2	2	no	—
138	C₂²×C₄	—	2	4	no	—
139	C₂²×C₄	—	2	8	no	—
140	C₂²×C₄	—	2	4	no	—
141	C₂²×C₄	—	2	2	no	—
142	C₂²×C₄	—	2	2	no	—
143	C₂²×C₄	—	2	2	no	—
144	C₂²×C₄	—	2	2	no	—
145	C₂²×C₄	—	2	2	no	—
146	C₂²×C₄	—	4	2	no	—
147	C₂²×C₄	—	4	4	no	—
148	C₂²×C₄	C₂²⋊Dic₁₉	1	4	yes	—
149	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
150	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
151	C₂²×C₄	C₂²⋊Dic₁₉	1	4	yes	—
152	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
153	C₂²×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
154	C₂×C₈	—	76	8	no	—
155	C₂×C₈	—	76	4	no	—
156	C₄⋊C₄	—	2	8	no	—
157	C₄⋊C₄	—	2	8	no	—
158	C₄⋊C₄	—	2	16	no	—
159	C₄⋊C₄	—	2	16	no	—
160	C₄²	—	2	8	no	—
161	C₂³	—	2	2	no	—
162	C₂³	—	2	2	no	—
163	C₂³	#10597394	1	4	yes	—
164	C₂³	C₂×C₂²⋊Dic₁₉	1	2	yes	—
165	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
166	C₂×C₄	—	2	8	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	4	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	4	no	—
172	C₂×C₄	—	2	4	no	—
173	C₂×C₄	—	2	8	no	—
174	C₂×C₄	—	2	4	no	—
175	C₂×C₄	—	4	4	no	—
176	C₂×C₄	—	4	4	no	—
177	C₂×C₄	—	4	4	no	—
178	C₂×C₄	—	4	4	no	—
179	C₂×C₄	—	4	4	no	—
180	C₂×C₄	—	4	4	no	—
181	C₂×C₄	—	4	4	no	—
182	C₂×C₄	#10597293	1	4	yes	—
183	C₂×C₄	#10597399	1	4	yes	—
184	C₈	—	152	4	no	—
185	C₂²	—	2	8	no	—
186	C₂²	—	2	2	no	—
187	C₂²	—	2	2	no	—
188	C₂²	#11926400	1	1	yes	characteristic
189	C₂²	#11926511	1	4	yes	—
190	C₂²	#11926511	1	2	yes	—
191	C₂²	#11926518	1	2	yes	—
192	C₂²	C₂×#10597293	1	2	yes	—
193	C₄	—	2	4	no	—
194	C₄	—	2	4	no	—
195	C₄	—	4	2	no	—
196	C₄	—	4	4	no	—
197	C₄	—	4	4	no	—
198	C₂	—	2	4	no	—
199	C₂	#14561991	1	4	yes	—
200	C₂	#14563547	1	1	yes	characteristic
201	C₂	#14563553	1	1	yes	characteristic
202	C₂	#14563559	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563703

C₂

yes

maximal

C₂×#11926270

C₂

yes

maximal

C₂²×C₁₉×#125

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

#11926299

—

#11926270

—

C₂×C₁₉×#125

—

C₂×C₁₉×#125

—

C₂²×C₄⋊C₄×C₁₉

C₄

yes

characteristic

C₂²×C₄⋊C₄×C₁₉

C₄

yes

—

C₂²×C₄⋊C₄×C₁₉

C₄

yes

characteristic

C₂²×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₁₉×#125

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂²×C₁₉⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8306

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

#131

yes

—

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#101

yes

—

C₂×C₄×C₁₉

#120

yes

—

C₁₉⋊C₈

—

C₂²×#125

D₁₉

yes

characteristic

#1817

—

C₂×#324

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#379

yes

characteristic

C₂²×C₁₉

#408

yes

—

C₂²×C₁₉

#408

yes

—

C₂²×C₁₉

#410

yes

—

C₂²×C₁₉

C₂×#101

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

100

C₂×#125

—

101

C₂×#125

—

102

C₂²×C₄⋊C₄

Dic₁₉

yes

characteristic

103

C₂²×C₄⋊C₄

Dic₁₉

yes

—

104

C₂²×C₄⋊C₄

Dic₁₉

yes

characteristic

105

C₂²×C₄⋊C₄

C₂×D₁₉

yes

—

106

C₂²×C₄²

C₂×D₁₉

yes

characteristic

107

C₂×C₂²⋊C₈

—

108

#336

—

109

#324

—

110

C₂×C₁₉

—

111

C₂×C₁₉

#1470

yes

—

112

C₂×C₁₉

#1780

yes

characteristic

113

C₂×C₁₉

#1782

yes

characteristic

114

C₂×C₁₉

#1784

yes

characteristic

115

C₂³×C₄

C₂×Dic₁₉

yes

—

116

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

117

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

118

C₂³×C₄

C₂×Dic₁₉

yes

—

119

C₂³×C₄

C₂²×D₁₉

yes

characteristic

120

C₂²×C₈

—

121

#125

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

—

124

C₂×C₄⋊C₄

—

125

C₂×C₄⋊C₄

—

126

C₂×C₄⋊C₄

—

127

C₂×C₄⋊C₄

—

128

C₂×C₄⋊C₄

—

129

C₂×C₄⋊C₄

—

130

C₂×C₄⋊C₄

—

131

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

132

C₂×C₄²

—

133

C₂×C₄²

C₂²⋊D₁₉

yes

—

134

C₂²⋊C₈

—

135

C₁₉

#8306

yes

characteristic, complemented, Sylow

136

C₂⁴

C₂²×Dic₁₉

yes

characteristic

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

149

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

150

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

151

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

152

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

153

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

154

C₂×C₈

—

155

C₂×C₈

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄²

—

161

C₂³

—

162

C₂³

—

163

C₂³

#10597394

yes

—

164

C₂³

C₂×C₂²⋊Dic₁₉

yes

—

165

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

#10597293

yes

—

183

C₂×C₄

#10597399

yes

—

184

C₈

—

152

—

185

C₂²

—

186

C₂²

—

187

C₂²

—

188

C₂²

#11926400

yes

characteristic

189

C₂²

#11926511

yes

—

190

C₂²

#11926511

yes

—

191

C₂²

#11926518

yes

—

192

C₂²

C₂×#10597293

yes

—

193

C₄

—

194

C₄

—

195

C₄

—

196

C₄

—

197

C₄

—

198

C₂

—

199

C₂

#14561991

yes

—

200

C₂

#14563547

yes

characteristic

201

C₂

#14563553

yes

characteristic

202

C₂

#14563559

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator, prime radical	C₂⁴×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂²×C₁₉×#125	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×#125	D₁₉
hypocenter	C₁₉	#8306
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂²×#125

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator, prime radical

C₂⁴×C₁₉

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting

C₂²×C₁₉×#125

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂³×C₄×C₁₉

C₂³

hypercenter

C₂²×#125

D₁₉

hypocenter

C₁₉

#8306

LCS

G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂²×#125

N	H ≅ G/N	type
135. C₁₉	#8306	semidirect

H ≅ G/N

type

135. C₁₉

#8306

semidirect

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

subgroup	index
#14563703	2
C₂×#11926270	2
C₂²×C₁₉×#125	2
#8306	19

subgroup

index

#14563703

C₂×#11926270

C₂²×C₁₉×#125

#8306

Subgroups — #18073893

Conjugacy classes of subgroups

Complements

Maximal subgroups