Group #18087530 — subgroups

Subgroups — #18087530

Order 4864.

320 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 95 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	#14564576	C₂	1	1	yes	maximal, characteristic
2	#14563809	C₂	1	1	yes	maximal, characteristic
3	#14562407	C₂	1	1	yes	maximal, characteristic
4	#14562406	C₂	1	1	yes	maximal, characteristic
5	#14562064	C₂	1	1	yes	maximal, characteristic
6	#14561465	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1487	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	C₂×#10597279	—	2	2	no	—
10	#11926568	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×#10597260	C₂²	1	1	yes	characteristic
13	#11926299	—	2	2	no	—
14	#11926295	—	2	2	no	—
15	#11926294	—	2	2	no	—
16	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
17	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#431	C₂²	1	1	yes	characteristic
19	C₁₉×#423	C₂²	1	1	yes	characteristic
20	C₁₉×Q₈⋊C₈	—	2	2	no	—
21	C₂²×Q₈×C₁₉	Q₈	1	1	yes	characteristic
22	C₂×M₁₆×C₁₉	—	2	1	no	—
23	C₄×Q₈×C₁₉	—	2	1	no	—
24	C₄×Q₈×C₁₉	—	2	1	no	—
25	C₄×Q₈×C₁₉	—	2	1	no	—
26	C₄×Q₈×C₁₉	—	2	1	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
29	C₂×C₄²×C₁₉	—	2	1	no	—
30	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×#64520	—	2	1	no	—
32	C₂²×C₁₉⋊C₈	—	2	1	no	—
33	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
34	C₁₉×C₄⋊C₈	—	2	1	no	—
35	C₁₉×C₄⋊C₈	—	2	1	no	—
36	C₁₉×C₄⋊C₈	—	2	1	no	—
37	C₁₉×C₂²⋊C₈	—	2	1	no	—
38	C₄×C₈×C₁₉	D₄	1	2	yes	—
39	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
40	#10597279	—	4	4	no	—
41	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
45	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
46	#10597260	—	2	1	no	—
47	#10597260	—	2	1	no	—
48	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
49	C₂×Q₈×C₁₉	—	2	1	no	—
50	C₂×Q₈×C₁₉	—	2	1	no	—
51	C₂×Q₈×C₁₉	—	4	2	no	—
52	C₂²×C₄×C₁₉	—	2	1	no	—
53	C₂²×C₄×C₁₉	—	2	1	no	—
54	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
57	M₁₆×C₁₉	—	4	2	no	—
58	C₂×C₈×C₁₉	—	2	2	no	—
59	C₂×C₈×C₁₉	—	4	1	no	—
60	C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₄⋊C₄×C₁₉	—	4	1	no	—
63	C₄⋊C₄×C₁₉	—	4	1	no	—
64	C₄²×C₁₉	—	4	1	no	—
65	C₄²×C₁₉	—	4	1	no	—
66	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₄²×C₁₉	#41	1	1	yes	characteristic
69	C₄²×C₁₉	#41	1	1	yes	characteristic
70	#64520	—	4	2	no	—
71	C₂×C₁₉⋊C₈	—	2	2	no	—
72	C₂×C₁₉⋊C₈	—	2	2	no	—
73	C₂×C₁₉⋊C₈	—	2	2	no	—
74	C₂×C₁₉⋊C₈	—	4	1	no	—
75	C₂×C₁₉⋊C₈	—	4	1	no	—
76	C₂×C₁₉⋊C₈	—	4	2	no	—
77	C₂×C₁₉⋊C₈	SD₁₆	1	4	yes	—
78	#10663	—	19	1	no	maximal, Sylow
79	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
80	Q₈×C₁₉	—	2	2	no	—
81	Q₈×C₁₉	—	2	2	no	—
82	Q₈×C₁₉	—	4	1	no	—
83	Q₈×C₁₉	—	4	1	no	—
84	C₂×C₄×C₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	—	4	1	no	—
86	C₂×C₄×C₁₉	—	4	1	no	—
87	C₂×C₄×C₁₉	—	4	1	no	—
88	C₂×C₄×C₁₉	—	4	1	no	—
89	C₂×C₄×C₁₉	—	4	2	no	—
90	C₂×C₄×C₁₉	—	4	1	no	—
91	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
92	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
97	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
98	C₂×C₄×C₁₉	#137	1	2	yes	—
99	C₈×C₁₉	—	4	2	no	—
100	C₈×C₁₉	—	8	1	no	—
101	C₁₉⋊C₈	—	2	4	no	—
102	C₁₉⋊C₈	—	4	2	no	—
103	C₁₉⋊C₈	—	8	1	no	—
104	C₁₉⋊C₈	—	8	1	no	—
105	#1985	—	19	1	no	—
106	#1849	—	19	1	no	—
107	#1570	—	19	1	no	—
108	#1570	—	19	1	no	—
109	#1487	—	19	1	no	—
110	#1487	D₁₉	1	1	yes	characteristic
111	#1275	—	19	1	no	—
112	C₂²×C₁₉	—	2	1	no	—
113	C₂²×C₁₉	—	2	1	no	—
114	C₂²×C₁₉	#399	1	1	yes	characteristic
115	C₂²×C₁₉	#475	1	2	yes	—
116	C₄×C₁₉	—	2	1	no	—
117	C₄×C₁₉	—	2	1	no	—
118	C₄×C₁₉	—	2	1	no	—
119	C₄×C₁₉	—	2	1	no	—
120	C₄×C₁₉	—	4	2	no	—
121	C₄×C₁₉	—	8	1	no	—
122	C₄×C₁₉	#483	1	2	yes	—
123	C₄×C₁₉	#492	1	1	yes	characteristic
124	C₄×C₁₉	#497	1	1	yes	characteristic
125	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
126	#431	—	19	1	no	—
127	#431	C₂×D₁₉	1	1	yes	characteristic
128	C₂×#108	—	38	2	no	—
129	#423	—	19	1	no	—
130	#423	C₂×D₁₉	1	1	yes	characteristic
131	C₂×C₄⋊C₈	—	19	1	no	—
132	C₂×#97	—	19	1	no	—
133	#336	—	38	2	no	—
134	#334	—	38	2	no	—
135	#334	—	38	2	no	—
136	Q₈⋊C₈	—	2	2	no	—
137	Q₈⋊C₈	—	38	2	no	—
138	C₂×C₁₉	—	2	2	no	—
139	C₂×C₁₉	#2091	1	1	yes	characteristic
140	C₂×C₁₉	#2096	1	1	yes	characteristic
141	C₂×C₁₉	#2098	1	1	yes	characteristic
142	C₂²×Q₈	Dic₃₈	1	1	yes	characteristic
143	C₂×M₁₆	—	2	1	no	—
144	C₂×M₁₆	—	38	1	no	—
145	C₂²×C₈	—	19	2	no	—
146	C₂²×C₈	—	38	1	no	—
147	C₄×Q₈	—	2	1	no	—
148	C₄×Q₈	—	2	1	no	—
149	C₄×Q₈	—	2	1	no	—
150	C₄×Q₈	—	2	1	no	—
151	C₂×C₄⋊C₄	—	2	1	no	—
152	C₂×C₄⋊C₄	Dic₃₈	1	1	yes	characteristic
153	C₂×C₄²	—	2	1	no	—
154	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
155	#108	—	76	4	no	—
156	C₄⋊C₈	—	2	1	no	—
157	C₄⋊C₈	—	2	1	no	—
158	C₄⋊C₈	—	2	1	no	—
159	C₄⋊C₈	—	38	1	no	—
160	C₄⋊C₈	—	38	1	no	—
161	C₄⋊C₈	—	38	1	no	—
162	C₄⋊C₈	—	38	1	no	—
163	C₄⋊C₈	—	38	1	no	—
164	C₂²⋊C₈	—	2	1	no	—
165	C₂²⋊C₈	—	38	1	no	—
166	#97	—	38	1	no	—
167	#97	—	38	1	no	—
168	C₄×C₈	—	19	2	no	—
169	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
170	C₁₉	#10663	1	1	yes	characteristic, complemented, Sylow
171	C₂×Q₈	—	2	1	no	—
172	C₂×Q₈	—	2	1	no	—
173	C₂×Q₈	—	4	2	no	—
174	C₂²×C₄	—	2	1	no	—
175	C₂²×C₄	—	2	1	no	—
176	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
177	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
178	C₂²×C₄	#64543	1	1	yes	characteristic
179	M₁₆	—	4	2	no	—
180	M₁₆	—	76	2	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	4	1	no	—
183	C₂×C₈	—	19	4	no	—
184	C₂×C₈	—	38	2	no	—
185	C₂×C₈	—	38	2	no	—
186	C₂×C₈	—	38	2	no	—
187	C₂×C₈	—	76	1	no	—
188	C₂×C₈	—	76	1	no	—
189	C₂×C₈	—	76	2	no	—
190	C₄⋊C₄	—	2	1	no	—
191	C₄⋊C₄	—	2	1	no	—
192	C₄⋊C₄	—	4	1	no	—
193	C₄⋊C₄	—	4	1	no	—
194	C₄²	—	4	1	no	—
195	C₄²	—	4	1	no	—
196	C₄²	#64541	1	1	yes	characteristic
197	C₄²	D₄×D₁₉	1	1	yes	characteristic
198	C₄²	#64543	1	1	yes	characteristic
199	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
200	C₂³	#10597324	1	1	yes	characteristic
201	Q₈	—	2	2	no	—
202	Q₈	—	2	2	no	—
203	Q₈	—	4	1	no	—
204	Q₈	—	4	1	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	#10597324	1	1	yes	characteristic
213	C₂×C₄	#10597329	1	1	yes	characteristic
214	C₂×C₄	#10597329	1	1	yes	characteristic
215	C₂×C₄	SD₁₆×D₁₉	1	2	yes	—
216	C₂×C₄	#10597364	1	2	yes	—
217	C₂×C₄	#10597370	1	1	yes	characteristic
218	C₂×C₄	#10597381	1	1	yes	characteristic
219	C₂×C₄	#10597386	1	1	yes	characteristic
220	C₈	—	4	2	no	—
221	C₈	—	8	1	no	—
222	C₈	—	38	4	no	—
223	C₈	—	76	2	no	—
224	C₈	—	152	1	no	—
225	C₈	—	152	1	no	—
226	C₂²	—	2	1	no	—
227	C₂²	—	2	1	no	—
228	C₂²	#11926480	1	1	yes	characteristic
229	C₂²	#11926827	1	2	yes	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	4	2	no	—
235	C₄	—	8	1	no	—
236	C₄	#11926873	1	2	yes	—
237	C₄	#11926915	1	1	yes	characteristic
238	C₄	#11926937	1	1	yes	characteristic
239	C₂	—	2	2	no	—
240	C₂	#14565151	1	1	yes	characteristic
241	C₂	#14565176	1	1	yes	characteristic
242	C₂	#14565190	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564576

C₂

yes

maximal, characteristic

#14563809

C₂

yes

maximal, characteristic

#14562407

C₂

yes

maximal, characteristic

#14562406

C₂

yes

maximal, characteristic

#14562064

C₂

yes

maximal, characteristic

#14561465

C₂

yes

maximal, characteristic

C₁₉×#1487

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

characteristic

C₂×#10597279

—

#11926568

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×#10597260

C₂²

yes

—

—

—

Q₈⋊(C₁₉⋊C₈)

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₁₉×Q₈⋊C₈

—

C₂²×Q₈×C₁₉

Q₈

yes

characteristic

C₂×M₁₆×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

#10597279

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

SD₁₆

yes

—

#10663

—

maximal, Sylow

C₂³×C₁₉

C₂²⋊Q₈

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×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

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₈×C₁₉

—

100

C₈×C₁₉

—

101

C₁₉⋊C₈

—

102

C₁₉⋊C₈

—

103

C₁₉⋊C₈

—

104

C₁₉⋊C₈

—

105

#1985

—

106

#1849

—

107

#1570

—

108

#1570

—

109

#1487

—

110

#1487

D₁₉

yes

characteristic

111

#1275

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

#399

yes

characteristic

115

C₂²×C₁₉

#475

yes

—

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

—

122

C₄×C₁₉

#483

yes

—

123

C₄×C₁₉

#492

yes

characteristic

124

C₄×C₁₉

#497

yes

characteristic

125

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

126

#431

—

127

#431

C₂×D₁₉

yes

characteristic

128

C₂×#108

—

129

#423

—

130

#423

C₂×D₁₉

yes

characteristic

131

C₂×C₄⋊C₈

—

132

C₂×#97

—

133

#336

—

134

#334

—

135

#334

—

136

Q₈⋊C₈

—

137

Q₈⋊C₈

—

138

C₂×C₁₉

—

139

C₂×C₁₉

#2091

yes

characteristic

140

C₂×C₁₉

#2096

yes

characteristic

141

C₂×C₁₉

#2098

yes

characteristic

142

C₂²×Q₈

Dic₃₈

yes

characteristic

143

C₂×M₁₆

—

144

C₂×M₁₆

—

145

C₂²×C₈

—

146

C₂²×C₈

—

147

C₄×Q₈

—

148

C₄×Q₈

—

149

C₄×Q₈

—

150

C₄×Q₈

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

Dic₃₈

yes

characteristic

153

C₂×C₄²

—

154

C₂×C₄²

C₂²×D₁₉

yes

characteristic

155

#108

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₂²⋊C₈

—

165

C₂²⋊C₈

—

166

#97

—

167

#97

—

168

C₄×C₈

—

169

C₄×C₈

C₂²⋊D₁₉

yes

—

170

C₁₉

#10663

yes

characteristic, complemented, Sylow

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

177

C₂²×C₄

D₄×D₁₉

yes

characteristic

178

C₂²×C₄

#64543

yes

characteristic

179

M₁₆

—

180

M₁₆

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄²

—

195

C₄²

—

196

C₄²

#64541

yes

characteristic

197

C₄²

D₄×D₁₉

yes

characteristic

198

C₄²

#64543

yes

characteristic

199

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

200

C₂³

#10597324

yes

characteristic

201

Q₈

—

202

Q₈

—

203

Q₈

—

204

Q₈

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

#10597324

yes

characteristic

213

C₂×C₄

#10597329

yes

characteristic

214

C₂×C₄

#10597329

yes

characteristic

215

C₂×C₄

SD₁₆×D₁₉

yes

—

216

C₂×C₄

#10597364

yes

—

217

C₂×C₄

#10597370

yes

characteristic

218

C₂×C₄

#10597381

yes

characteristic

219

C₂×C₄

#10597386

yes

characteristic

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

224

C₈

—

152

—

225

C₈

—

152

—

226

C₂²

—

227

C₂²

—

228

C₂²

#11926480

yes

characteristic

229

C₂²

#11926827

yes

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

#11926873

yes

—

237

C₄

#11926915

yes

characteristic

238

C₄

#11926937

yes

characteristic

239

C₂

—

240

C₂

#14565151

yes

characteristic

241

C₂

#14565176

yes

characteristic

242

C₂

#14565190

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1487	C₂
socle	C₂²×C₁₉	#399
prime radical	C₂³×C₁₉	C₂²⋊Q₈
hypercenter	#1487	D₁₉
hypocenter	C₁₉	#10663
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1487

subgroup

G/H

center

C₂×C₄

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1487

C₂

socle

C₂²×C₁₉

#399

prime radical

C₂³×C₁₉

C₂²⋊Q₈

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1487

N	H ≅ G/N	type
170. C₁₉	#10663	semidirect

H ≅ G/N

type

170. C₁₉

#10663

semidirect

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

subgroup	index
#14564576	2
#14563809	2
#14562407	2
#14562406	2
#14562064	2
#14561465	2
C₁₉×#1487	2
#10663	19

subgroup

index

C₁₉×#1487

Subgroups — #18087530

Conjugacy classes of subgroups

Complements

Maximal subgroups