Group #18081578 — subgroups

Subgroups — #18081578

Order 4864.

478 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 163 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	#14572013	C₂	1	1	yes	maximal, characteristic
2	#14563752	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926292	C₂	1	2	yes	maximal
4	C₂×#11926289	C₂	1	2	yes	maximal
5	C₄×C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	C₂×#10597315	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
9	#11926450	—	2	2	no	—
10	#11926450	C₄	1	4	yes	—
11	#11926410	—	2	1	no	—
12	#11926410	—	2	1	no	—
13	#11926299	—	2	2	no	—
14	#11926292	—	2	4	no	—
15	#11926289	—	2	4	no	—
16	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₁₉	—	2	1	no	—
18	C₄³×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#336	—	2	1	no	—
20	C₂²×Dic₃₈	—	2	1	no	—
21	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
22	C₂²×C₈×C₁₉	—	2	2	no	—
23	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₉	D₄	1	2	yes	—
25	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₉	—	2	1	no	—
29	C₂×C₄⋊Dic₁₉	—	2	1	no	—
30	C₂×C₄⋊Dic₁₉	—	2	1	no	—
31	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
32	C₂²×C₁₉⋊C₈	—	2	2	no	—
33	#10597315	—	2	2	no	—
34	#10597315	—	2	2	no	—
35	#10597315	—	2	2	no	—
36	#10597315	—	2	2	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉×C₄⋊C₈	D₄	1	4	yes	—
39	C₄×C₈×C₁₉	—	4	2	no	—
40	C₁₉⋊#95	—	2	4	no	—
41	C₁₉⋊#95	—	2	4	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
45	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
46	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×Dic₁₉	—	2	2	no	—
50	C₂²×Dic₁₉	—	2	2	no	—
51	C₂×Dic₃₈	—	2	4	no	—
52	C₂×Dic₃₈	—	4	1	no	—
53	C₂×Dic₃₈	—	4	1	no	—
54	C₂×Dic₃₈	—	4	4	no	—
55	C₂×Dic₃₈	—	4	4	no	—
56	C₂×C₈×C₁₉	—	2	4	no	—
57	C₂×C₈×C₁₉	—	4	2	no	—
58	C₂×C₈×C₁₉	—	4	2	no	—
59	C₄²×C₁₉	—	2	4	no	—
60	C₄²×C₁₉	—	2	2	no	—
61	C₄²×C₁₉	—	4	2	no	—
62	C₄²×C₁₉	SD₁₆	1	2	yes	—
63	C₄²×C₁₉	Q₁₆	1	2	yes	—
64	C₄²×C₁₉	C₂×D₄	1	2	yes	—
65	C₄²×C₁₉	#41	1	2	yes	—
66	C₄⋊Dic₁₉	—	2	4	no	—
67	C₄⋊Dic₁₉	—	4	2	no	—
68	C₄⋊Dic₁₉	—	4	2	no	—
69	C₄⋊Dic₁₉	—	4	1	no	—
70	C₄⋊Dic₁₉	—	4	1	no	—
71	C₂×C₁₉⋊C₈	—	4	2	no	—
72	C₂×C₁₉⋊C₈	—	4	4	no	—
73	#9693	—	19	1	no	maximal, Sylow
74	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	#103	1	4	yes	—
82	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
83	C₂×C₄×C₁₉	#121	1	2	yes	—
84	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
85	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
86	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
87	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#135	1	4	yes	—
89	C₂×C₄×C₁₉	#137	1	2	yes	—
90	C₂×Dic₁₉	—	4	2	no	—
91	C₂×Dic₁₉	—	4	2	no	—
92	C₂×Dic₁₉	—	4	4	no	—
93	C₂×Dic₁₉	—	4	4	no	—
94	Dic₃₈	—	8	2	no	—
95	Dic₃₈	—	8	2	no	—
96	Dic₃₈	—	8	4	no	—
97	C₈×C₁₉	—	4	4	no	—
98	C₁₉⋊C₈	—	8	2	no	—
99	#2862	—	19	1	no	—
100	#1831	—	19	1	no	—
101	C₄×C₄⋊C₈	D₁₉	1	1	yes	characteristic
102	C₂×#333	—	19	2	no	—
103	C₂×#332	—	19	2	no	—
104	C₂²×C₁₉	#390	1	1	yes	characteristic
105	C₂²×C₁₉	#413	1	2	yes	—
106	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
107	C₂²×C₁₉	#416	1	2	yes	—
108	C₂²×C₁₉	#419	1	1	yes	characteristic
109	C₄×C₁₉	—	2	4	no	—
110	C₄×C₁₉	—	2	2	no	—
111	C₄×C₁₉	—	4	2	no	—
112	C₄×C₁₉	#461	1	2	yes	—
113	C₄×C₁₉	#462	1	2	yes	—
114	C₄×C₁₉	#488	1	2	yes	—
115	C₄×C₁₉	#495	1	2	yes	—
116	Dic₁₉	—	8	2	no	—
117	Dic₁₉	—	8	2	no	—
118	C₂×C₄⋊Q₈	—	19	1	no	—
119	C₂×C₄⋊Q₈	—	19	1	no	—
120	C₂×C₄⋊C₈	—	19	2	no	—
121	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
122	C₂×C₄×C₈	—	2	1	no	—
123	#391	—	19	4	no	—
124	#391	—	38	2	no	—
125	#382	—	38	1	no	—
126	#382	—	38	1	no	—
127	C₄³	C₂×D₁₉	1	1	yes	characteristic
128	#336	—	2	1	no	—
129	#336	—	38	2	no	—
130	#333	—	38	4	no	—
131	#332	—	38	4	no	—
132	C₂×C₁₉	#1542	1	2	yes	—
133	C₂×C₁₉	#1554	1	2	yes	—
134	C₂×C₁₉	#1958	1	1	yes	characteristic
135	C₂×C₁₉	#1967	1	1	yes	characteristic
136	C₂×C₁₉	#1981	1	1	yes	characteristic
137	C₂²×Q₈	—	19	2	no	—
138	C₂²×Q₈	—	38	1	no	—
139	C₂²×C₈	—	2	2	no	—
140	C₂²×C₈	—	38	2	no	—
141	C₄⋊Q₈	—	38	2	no	—
142	C₄⋊Q₈	—	38	2	no	—
143	C₄⋊Q₈	—	38	2	no	—
144	C₄⋊Q₈	—	38	2	no	—
145	C₂×C₄⋊C₄	—	19	2	no	—
146	C₂×C₄⋊C₄	—	38	1	no	—
147	C₂×C₄⋊C₄	—	38	1	no	—
148	C₂×C₄⋊C₄	—	38	1	no	—
149	C₂×C₄²	C₄×D₁₉	1	2	yes	—
150	C₂×C₄²	D₇₆	1	2	yes	—
151	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
152	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
153	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
154	C₄⋊C₈	—	2	2	no	—
155	C₄⋊C₈	—	38	2	no	—
156	C₄⋊C₈	—	38	2	no	—
157	C₄⋊C₈	D₇₆	1	4	yes	—
158	C₄×C₈	—	4	2	no	—
159	#95	—	38	4	no	—
160	#95	—	38	4	no	—
161	C₁₉	#9693	1	1	yes	characteristic, complemented, Sylow
162	C₂×Q₈	—	38	4	no	—
163	C₂×Q₈	—	76	4	no	—
164	C₂×Q₈	—	76	1	no	—
165	C₂×Q₈	—	76	1	no	—
166	C₂×Q₈	—	76	4	no	—
167	C₂²×C₄	—	38	2	no	—
168	C₂²×C₄	—	38	2	no	—
169	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
170	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
171	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
172	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
173	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
174	C₂×C₈	—	2	4	no	—
175	C₂×C₈	—	4	2	no	—
176	C₂×C₈	—	4	2	no	—
177	C₂×C₈	—	76	2	no	—
178	C₂×C₈	—	76	4	no	—
179	C₄⋊C₄	—	38	4	no	—
180	C₄⋊C₄	—	76	2	no	—
181	C₄⋊C₄	—	76	2	no	—
182	C₄⋊C₄	—	76	1	no	—
183	C₄⋊C₄	—	76	1	no	—
184	C₄²	—	2	2	no	—
185	C₄²	—	2	4	no	—
186	C₄²	—	4	2	no	—
187	C₄²	#64526	1	2	yes	—
188	C₄²	#64528	1	2	yes	—
189	C₄²	C₂×D₇₆	1	2	yes	—
190	C₄²	#64541	1	2	yes	—
191	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
192	Q₈	—	152	4	no	—
193	Q₈	—	152	2	no	—
194	Q₈	—	152	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	76	4	no	—
202	C₂×C₄	—	76	2	no	—
203	C₂×C₄	—	76	2	no	—
204	C₂×C₄	—	76	4	no	—
205	C₂×C₄	#10597267	1	4	yes	—
206	C₂×C₄	C₄×D₇₆	1	2	yes	—
207	C₂×C₄	#10597320	1	1	yes	characteristic
208	C₂×C₄	#10597321	1	1	yes	characteristic
209	C₂×C₄	#10597350	1	4	yes	—
210	C₂×C₄	#10597376	1	2	yes	—
211	C₂×C₄	C₂×#64526	1	1	yes	characteristic
212	C₂×C₄	C₂×#64528	1	1	yes	characteristic
213	C₂×C₄	#10597397	1	2	yes	—
214	C₈	—	4	4	no	—
215	C₈	—	152	2	no	—
216	C₂²	#11926446	1	1	yes	characteristic
217	C₂²	#11926526	1	2	yes	—
218	C₂²	C₂×#10597267	1	1	yes	characteristic
219	C₂²	#11926541	1	2	yes	—
220	C₂²	#11926552	1	1	yes	characteristic
221	C₄	—	2	2	no	—
222	C₄	—	2	4	no	—
223	C₄	—	4	2	no	—
224	C₄	—	152	2	no	—
225	C₄	—	152	2	no	—
226	C₄	#11926749	1	2	yes	—
227	C₄	#11926754	1	2	yes	—
228	C₄	#11926899	1	2	yes	—
229	C₄	#11926928	1	2	yes	—
230	C₂	#14562293	1	2	yes	—
231	C₂	#14562343	1	2	yes	—
232	C₂	#14564446	1	1	yes	characteristic
233	C₂	#14564484	1	1	yes	characteristic
234	C₂	#14564558	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572013

C₂

yes

maximal, characteristic

#14563752

C₂

yes

maximal, characteristic

C₂×#11926292

C₂

yes

maximal

C₂×#11926289

C₂

yes

maximal

C₄×C₁₉×C₄⋊C₈

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

characteristic

C₂×#10597315

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#11926450

—

#11926450

C₄

yes

—

—

—

—

—

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₂×C₄×C₈×C₁₉

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₂²×Dic₃₈

—

C₂²×Dic₃₈

C₂×C₄

yes

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

—

—

—

—

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₄×C₈×C₁₉

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

Q₁₆

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9693

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#103

yes

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2862

—

100

#1831

—

101

C₄×C₄⋊C₈

D₁₉

yes

characteristic

102

C₂×#333

—

103

C₂×#332

—

104

C₂²×C₁₉

#390

yes

characteristic

105

C₂²×C₁₉

#413

yes

—

106

C₂²×C₁₉

C₂×#103

yes

characteristic

107

C₂²×C₁₉

#416

yes

—

108

C₂²×C₁₉

#419

yes

characteristic

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

#461

yes

—

113

C₄×C₁₉

#462

yes

—

114

C₄×C₁₉

#488

yes

—

115

C₄×C₁₉

#495

yes

—

116

Dic₁₉

—

117

Dic₁₉

—

118

C₂×C₄⋊Q₈

—

119

C₂×C₄⋊Q₈

—

120

C₂×C₄⋊C₈

—

121

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

122

C₂×C₄×C₈

—

123

#391

—

124

#391

—

125

#382

—

126

#382

—

127

C₄³

C₂×D₁₉

yes

characteristic

128

#336

—

129

#336

—

130

#333

—

131

#332

—

132

C₂×C₁₉

#1542

yes

—

133

C₂×C₁₉

#1554

yes

—

134

C₂×C₁₉

#1958

yes

characteristic

135

C₂×C₁₉

#1967

yes

characteristic

136

C₂×C₁₉

#1981

yes

characteristic

137

C₂²×Q₈

—

138

C₂²×Q₈

—

139

C₂²×C₈

—

140

C₂²×C₈

—

141

C₄⋊Q₈

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄²

C₄×D₁₉

yes

—

150

C₂×C₄²

D₇₆

yes

—

151

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

152

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

153

C₂×C₄²

C₂²×D₁₉

yes

characteristic

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

D₇₆

yes

—

158

C₄×C₈

—

159

#95

—

160

#95

—

161

C₁₉

#9693

yes

characteristic, complemented, Sylow

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

170

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

171

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

172

C₂²×C₄

C₂×D₇₆

yes

characteristic

173

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

#64526

yes

—

188

C₄²

#64528

yes

—

189

C₄²

C₂×D₇₆

yes

—

190

C₄²

#64541

yes

—

191

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

192

Q₈

—

152

—

193

Q₈

—

152

—

194

Q₈

—

152

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

#10597267

yes

—

206

C₂×C₄

C₄×D₇₆

yes

—

207

C₂×C₄

#10597320

yes

characteristic

208

C₂×C₄

#10597321

yes

characteristic

209

C₂×C₄

#10597350

yes

—

210

C₂×C₄

#10597376

yes

—

211

C₂×C₄

C₂×#64526

yes

characteristic

212

C₂×C₄

C₂×#64528

yes

characteristic

213

C₂×C₄

#10597397

yes

—

214

C₈

—

215

C₈

—

152

—

216

C₂²

#11926446

yes

characteristic

217

C₂²

#11926526

yes

—

218

C₂²

C₂×#10597267

yes

characteristic

219

C₂²

#11926541

yes

—

220

C₂²

#11926552

yes

characteristic

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

—

152

—

225

C₄

—

152

—

226

C₄

#11926749

yes

—

227

C₄

#11926754

yes

—

228

C₄

#11926899

yes

—

229

C₄

#11926928

yes

—

230

C₂

#14562293

yes

—

231

C₂

#14562343

yes

—

232

C₂

#14564446

yes

characteristic

233

C₂

#14564484

yes

characteristic

234

C₂

#14564558

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×C₄⋊C₈	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×C₄⋊C₈	D₁₉
hypocenter	C₁₉	#9693
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×C₄⋊C₈

subgroup

G/H

center

C₂³

C₂×(C₂×D₁₉)⋊C₄

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×C₄⋊C₈

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

hypercenter

C₄×C₄⋊C₈

D₁₉

hypocenter

C₁₉

#9693

LCS

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×C₄⋊C₈

N	H ≅ G/N	type
161. C₁₉	#9693	semidirect

H ≅ G/N

type

161. C₁₉

#9693

semidirect

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

subgroup	index
#14572013	2
#14563752	2
C₂×#11926292	2
C₂×#11926289	2
C₄×C₁₉×C₄⋊C₈	2
#9693	19

subgroup

index

C₄×C₁₉×C₄⋊C₈

Subgroups — #18081578

Conjugacy classes of subgroups

Complements

Maximal subgroups