Group #18087358 — subgroups

Subgroups — #18087358

Order 4864.

278 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 85 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	#14564609	C₂	1	1	yes	maximal, characteristic
2	#14563775	C₂	1	1	yes	maximal, characteristic
3	#14562316	C₂	1	1	yes	maximal, characteristic
4	#14561495	C₂	1	1	yes	maximal, characteristic
5	#14561494	C₂	1	1	yes	maximal, characteristic
6	#14561479	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1549	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	#11926568	C₂²	1	1	yes	characteristic
10	C₂×#10597260	C₂²	1	1	yes	characteristic
11	#11926410	C₂²	1	1	yes	characteristic
12	#11926308	—	2	1	no	—
13	#11926308	—	2	1	no	—
14	#11926306	—	2	1	no	—
15	#11926306	—	2	1	no	—
16	#11926293	—	2	2	no	—
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₁₉×#431	C₂²	1	1	yes	characteristic
19	C₁₉×#423	C₂²	1	1	yes	characteristic
20	C₁₉×#332	—	2	2	no	—
21	C₂²×Q₈×C₁₉	—	2	1	no	—
22	C₂×M₁₆×C₁₉	—	2	1	no	—
23	C₁₉×C₄⋊Q₈	—	2	1	no	—
24	C₁₉×C₄⋊Q₈	—	2	1	no	—
25	C₁₉×C₄⋊Q₈	—	2	1	no	—
26	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
27	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×C₄⋊Dic₁₉	—	2	1	no	—
31	C₂×#64520	—	2	1	no	—
32	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
33	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
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	—	2	1	no	—
39	C₁₉⋊#95	—	2	1	no	—
40	C₁₉⋊#95	—	2	1	no	—
41	C₂²⋊(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	#10597260	—	2	1	no	—
46	#10597260	—	2	1	no	—
47	C₄×C₁₉⋊C₈	—	2	1	no	—
48	C₂×Q₈×C₁₉	—	2	2	no	—
49	C₂×Q₈×C₁₉	—	4	1	no	—
50	C₂×Q₈×C₁₉	—	8	2	no	—
51	C₂²×C₄×C₁₉	—	4	1	no	—
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
55	C₂²×Dic₁₉	—	4	1	no	—
56	M₁₆×C₁₉	—	4	1	no	—
57	M₁₆×C₁₉	—	4	1	no	—
58	C₂×C₈×C₁₉	—	4	1	no	—
59	C₂×C₈×C₁₉	—	4	1	no	—
60	C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₄⋊C₄×C₁₉	—	4	1	no	—
63	C₄⋊C₄×C₁₉	—	4	1	no	—
64	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₁₉	#41	1	1	yes	characteristic
66	C₄²×C₁₉	#41	1	1	yes	characteristic
67	C₄²×C₁₉	#41	1	1	yes	characteristic
68	C₄⋊Dic₁₉	—	4	1	no	—
69	C₄⋊Dic₁₉	—	4	1	no	—
70	#64520	—	4	1	no	—
71	#64520	—	4	1	no	—
72	C₂×C₁₉⋊C₈	—	2	1	no	—
73	C₂×C₁₉⋊C₈	—	2	1	no	—
74	C₂×C₁₉⋊C₈	—	2	1	no	—
75	C₂×C₁₉⋊C₈	—	2	1	no	—
76	C₂×C₁₉⋊C₈	—	2	1	no	—
77	C₂×C₁₉⋊C₈	—	2	1	no	—
78	C₂×C₁₉⋊C₈	—	4	1	no	—
79	C₂×C₁₉⋊C₈	—	4	1	no	—
80	#10636	—	19	1	no	maximal, Sylow
81	C₂³×C₁₉	#124	1	1	yes	characteristic
82	Q₈×C₁₉	—	8	2	no	—
83	Q₈×C₁₉	—	8	2	no	—
84	C₂×C₄×C₁₉	—	4	1	no	—
85	C₂×C₄×C₁₉	—	4	1	no	—
86	C₂×C₄×C₁₉	—	4	2	no	—
87	C₂×C₄×C₁₉	—	8	2	no	—
88	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
89	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
98	C₂×Dic₁₉	—	8	1	no	—
99	C₂×Dic₁₉	—	8	1	no	—
100	C₂×Dic₁₉	—	8	1	no	—
101	C₈×C₁₉	—	8	1	no	—
102	C₈×C₁₉	—	8	1	no	—
103	C₁₉⋊C₈	—	4	1	no	—
104	C₁₉⋊C₈	—	4	1	no	—
105	C₁₉⋊C₈	—	8	1	no	—
106	C₁₉⋊C₈	—	8	1	no	—
107	#1993	—	19	1	no	—
108	#1838	—	19	1	no	—
109	#1549	D₁₉	1	1	yes	characteristic
110	#1548	—	19	1	no	—
111	#1286	—	19	1	no	—
112	#1286	—	19	1	no	—
113	#1281	—	19	1	no	—
114	C₂²×C₁₉	—	2	1	no	—
115	C₂²×C₁₉	—	2	1	no	—
116	C₂²×C₁₉	#397	1	1	yes	characteristic
117	C₂²×C₁₉	#488	1	1	yes	characteristic
118	C₂²×C₁₉	#491	1	1	yes	characteristic
119	C₄×C₁₉	—	2	1	no	—
120	C₄×C₁₉	—	2	1	no	—
121	C₄×C₁₉	—	2	1	no	—
122	C₄×C₁₉	—	2	1	no	—
123	C₄×C₁₉	—	8	2	no	—
124	C₄×C₁₉	#464	1	1	yes	characteristic
125	C₄×C₁₉	#464	1	1	yes	characteristic
126	C₄×C₁₉	#485	1	1	yes	characteristic
127	C₄×C₁₉	#485	1	1	yes	characteristic
128	Dic₁₉	—	16	1	no	—
129	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
130	#431	—	19	1	no	—
131	#431	C₂×D₁₉	1	1	yes	characteristic
132	#423	—	19	1	no	—
133	#423	C₂×D₁₉	1	1	yes	characteristic
134	C₂×#97	—	19	1	no	—
135	#382	—	19	1	no	—
136	#341	—	38	1	no	—
137	#341	—	38	1	no	—
138	#340	—	38	1	no	—
139	#340	—	38	1	no	—
140	#333	—	38	2	no	—
141	#332	—	2	2	no	—
142	C₂×C₁₉	—	2	1	no	—
143	C₂×C₁₉	—	2	1	no	—
144	C₂×C₁₉	#2074	1	1	yes	characteristic
145	C₂×C₁₉	#2081	1	1	yes	characteristic
146	C₂×C₁₉	#2082	1	1	yes	characteristic
147	C₂²×Q₈	—	2	1	no	—
148	C₂×M₁₆	—	2	1	no	—
149	C₂×M₁₆	—	38	1	no	—
150	C₂²×C₈	—	19	1	no	—
151	C₂²×C₈	—	19	1	no	—
152	C₄⋊Q₈	—	2	1	no	—
153	C₄⋊Q₈	—	2	1	no	—
154	C₄⋊Q₈	—	2	1	no	—
155	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
156	C₂×C₄⋊C₄	—	2	1	no	—
157	C₂×C₄⋊C₄	—	2	1	no	—
158	C₂×C₄⋊C₄	—	38	1	no	—
159	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
160	C₄⋊C₈	—	2	1	no	—
161	C₄⋊C₈	—	2	1	no	—
162	C₄⋊C₈	—	2	1	no	—
163	C₄⋊C₈	—	38	1	no	—
164	C₄⋊C₈	—	38	1	no	—
165	C₄⋊C₈	—	38	1	no	—
166	C₂²⋊C₈	—	2	1	no	—
167	C₂²⋊C₈	—	38	1	no	—
168	#97	—	38	1	no	—
169	#97	—	38	1	no	—
170	C₄×C₈	—	2	1	no	—
171	C₄×C₈	—	38	1	no	—
172	#95	—	38	1	no	—
173	#95	—	38	1	no	—
174	C₁₉	#10636	1	1	yes	characteristic, complemented, Sylow
175	C₂×Q₈	—	2	2	no	—
176	C₂×Q₈	—	4	1	no	—
177	C₂×Q₈	—	8	2	no	—
178	C₂²×C₄	—	4	1	no	—
179	C₂²×C₄	—	76	1	no	—
180	C₂²×C₄	#64541	1	1	yes	characteristic
181	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
182	C₂²×C₄	#64543	1	1	yes	characteristic
183	M₁₆	—	4	1	no	—
184	M₁₆	—	4	1	no	—
185	M₁₆	—	76	1	no	—
186	M₁₆	—	76	1	no	—
187	C₂×C₈	—	4	1	no	—
188	C₂×C₈	—	4	1	no	—
189	C₂×C₈	—	38	1	no	—
190	C₂×C₈	—	38	1	no	—
191	C₂×C₈	—	38	1	no	—
192	C₂×C₈	—	38	1	no	—
193	C₂×C₈	—	38	1	no	—
194	C₂×C₈	—	38	1	no	—
195	C₂×C₈	—	76	1	no	—
196	C₂×C₈	—	76	1	no	—
197	C₄⋊C₄	—	2	2	no	—
198	C₄⋊C₄	—	2	2	no	—
199	C₄⋊C₄	—	4	1	no	—
200	C₄⋊C₄	—	4	1	no	—
201	C₄⋊C₄	—	76	1	no	—
202	C₄⋊C₄	—	76	1	no	—
203	C₄²	#64541	1	1	yes	characteristic
204	C₄²	#64543	1	1	yes	characteristic
205	C₄²	#64543	1	1	yes	characteristic
206	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
207	C₂³	#10597331	1	1	yes	characteristic
208	Q₈	—	8	2	no	—
209	Q₈	—	8	2	no	—
210	C₂×C₄	—	4	1	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	—	8	2	no	—
214	C₂×C₄	—	152	1	no	—
215	C₂×C₄	—	152	1	no	—
216	C₂×C₄	—	152	1	no	—
217	C₂×C₄	#10597325	1	1	yes	characteristic
218	C₂×C₄	#10597325	1	1	yes	characteristic
219	C₂×C₄	#10597329	1	1	yes	characteristic
220	C₂×C₄	#10597361	1	1	yes	characteristic
221	C₂×C₄	#10597362	1	1	yes	characteristic
222	C₂×C₄	#10597364	1	1	yes	characteristic
223	C₂×C₄	#10597365	1	1	yes	characteristic
224	C₂×C₄	#10597375	1	1	yes	characteristic
225	C₂×C₄	#10597381	1	1	yes	characteristic
226	C₂×C₄	#10597385	1	1	yes	characteristic
227	C₈	—	8	1	no	—
228	C₈	—	8	1	no	—
229	C₈	—	76	1	no	—
230	C₈	—	76	1	no	—
231	C₈	—	152	1	no	—
232	C₈	—	152	1	no	—
233	C₂²	—	2	1	no	—
234	C₂²	—	2	1	no	—
235	C₂²	#11926472	1	1	yes	characteristic
236	C₂²	#11926900	1	1	yes	characteristic
237	C₂²	#11926911	1	1	yes	characteristic
238	C₄	—	2	1	no	—
239	C₄	—	2	1	no	—
240	C₄	—	2	1	no	—
241	C₄	—	2	1	no	—
242	C₄	—	8	2	no	—
243	C₄	—	304	1	no	—
244	C₄	#11926764	1	1	yes	characteristic
245	C₄	#11926768	1	1	yes	characteristic
246	C₄	#11926883	1	1	yes	characteristic
247	C₄	#11926884	1	1	yes	characteristic
248	C₂	—	2	1	no	—
249	C₂	—	2	1	no	—
250	C₂	#14565056	1	1	yes	characteristic
251	C₂	#14565096	1	1	yes	characteristic
252	C₂	#14565102	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564609

C₂

yes

maximal, characteristic

#14563775

C₂

yes

maximal, characteristic

#14562316

C₂

yes

maximal, characteristic

#14561495

C₂

yes

maximal, characteristic

#14561494

C₂

yes

maximal, characteristic

#14561479

C₂

yes

maximal, characteristic

C₁₉×#1549

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

characteristic

#11926568

C₂²

yes

characteristic

C₂×#10597260

C₂²

yes

characteristic

#11926410

C₂²

yes

—

—

—

—

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#332

—

C₂²×Q₈×C₁₉

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×#64520

—

C₂²×C₁₉⋊C₈

D₄

yes

characteristic

C₂²×C₁₉⋊C₈

D₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

100

C₂×Dic₁₉

—

101

C₈×C₁₉

—

102

C₈×C₁₉

—

103

C₁₉⋊C₈

—

104

C₁₉⋊C₈

—

105

C₁₉⋊C₈

—

106

C₁₉⋊C₈

—

107

#1993

—

108

#1838

—

109

#1549

D₁₉

yes

characteristic

110

#1548

—

111

#1286

—

112

#1286

—

113

#1281

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

#397

yes

characteristic

117

C₂²×C₁₉

#488

yes

characteristic

118

C₂²×C₁₉

#491

yes

characteristic

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

#464

yes

characteristic

125

C₄×C₁₉

#464

yes

characteristic

126

C₄×C₁₉

#485

yes

characteristic

127

C₄×C₁₉

#485

yes

characteristic

128

Dic₁₉

—

129

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

130

#431

—

131

#431

C₂×D₁₉

yes

characteristic

132

#423

—

133

#423

C₂×D₁₉

yes

characteristic

134

C₂×#97

—

135

#382

—

136

#341

—

137

#341

—

138

#340

—

139

#340

—

140

#333

—

141

#332

—

142

C₂×C₁₉

—

143

C₂×C₁₉

—

144

C₂×C₁₉

#2074

yes

characteristic

145

C₂×C₁₉

#2081

yes

characteristic

146

C₂×C₁₉

#2082

yes

characteristic

147

C₂²×Q₈

—

148

C₂×M₁₆

—

149

C₂×M₁₆

—

150

C₂²×C₈

—

151

C₂²×C₈

—

152

C₄⋊Q₈

—

153

C₄⋊Q₈

—

154

C₄⋊Q₈

—

155

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄²

C₂²×D₁₉

yes

characteristic

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

C₂²⋊C₈

—

167

C₂²⋊C₈

—

168

#97

—

169

#97

—

170

C₄×C₈

—

171

C₄×C₈

—

172

#95

—

173

#95

—

174

C₁₉

#10636

yes

characteristic, complemented, Sylow

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

#64541

yes

characteristic

181

C₂²×C₄

D₄×D₁₉

yes

characteristic

182

C₂²×C₄

#64543

yes

characteristic

183

M₁₆

—

184

M₁₆

—

185

M₁₆

—

186

M₁₆

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄²

#64541

yes

characteristic

204

C₄²

#64543

yes

characteristic

205

C₄²

#64543

yes

characteristic

206

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

207

C₂³

#10597331

yes

characteristic

208

Q₈

—

209

Q₈

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

152

—

215

C₂×C₄

—

152

—

216

C₂×C₄

—

152

—

217

C₂×C₄

#10597325

yes

characteristic

218

C₂×C₄

#10597325

yes

characteristic

219

C₂×C₄

#10597329

yes

characteristic

220

C₂×C₄

#10597361

yes

characteristic

221

C₂×C₄

#10597362

yes

characteristic

222

C₂×C₄

#10597364

yes

characteristic

223

C₂×C₄

#10597365

yes

characteristic

224

C₂×C₄

#10597375

yes

characteristic

225

C₂×C₄

#10597381

yes

characteristic

226

C₂×C₄

#10597385

yes

characteristic

227

C₈

—

228

C₈

—

229

C₈

—

230

C₈

—

231

C₈

—

152

—

232

C₈

—

152

—

233

C₂²

—

234

C₂²

—

235

C₂²

#11926472

yes

characteristic

236

C₂²

#11926900

yes

characteristic

237

C₂²

#11926911

yes

characteristic

238

C₄

—

239

C₄

—

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

304

—

244

C₄

#11926764

yes

characteristic

245

C₄

#11926768

yes

characteristic

246

C₄

#11926883

yes

characteristic

247

C₄

#11926884

yes

characteristic

248

C₂

—

249

C₂

—

250

C₂

#14565056

yes

characteristic

251

C₂

#14565096

yes

characteristic

252

C₂

#14565102

yes

characteristic

	subgroup	G/H
center	C₂²	#11926472
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1549	C₂
socle	C₂²×C₁₉	#397
prime radical	C₂³×C₁₉	#124
hypercenter	#1549	D₁₉
hypocenter	C₁₉	#10636
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1549

subgroup

G/H

center

C₂²

#11926472

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1549

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1549

N	H ≅ G/N	type
174. C₁₉	#10636	semidirect

H ≅ G/N

type

174. C₁₉

#10636

semidirect

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

subgroup	index
#14564609	2
#14563775	2
#14562316	2
#14561495	2
#14561494	2
#14561479	2
C₁₉×#1549	2
#10636	19

subgroup

index

C₁₉×#1549

Subgroups — #18087358

Conjugacy classes of subgroups

Complements

Maximal subgroups