Group #18082405 — subgroups

Subgroups — #18082405

Order 4864.

626 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 195 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	C₂×#11926917	C₂	1	1	yes	maximal, characteristic
2	#14564596	C₂	1	2	yes	maximal, complemented
3	#14564441	C₂	1	2	yes	maximal
4	#14563795	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#64516	—	2	2	no	—
7	C₂×#10597315	C₂²	1	1	yes	characteristic
8	C₂×#10597320	C₂²	1	1	yes	characteristic
9	#11926917	—	2	2	no	—
10	#11926917	C₄	1	4	yes	complemented
11	C₂×#10597275	—	2	2	no	—
12	C₂×#10597278	—	2	4	no	—
13	#11926414	C₂²	1	2	yes	—
14	#11926307	—	2	4	no	—
15	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#322	—	2	2	no	—
18	C₂²×D₇₆	—	2	2	no	—
19	C₂²×D₇₆	—	2	1	no	—
20	C₂²×Dic₃₈	—	2	1	no	—
21	C₂²×C₈×C₁₉	D₄	1	4	yes	—
22	C₂²×C₈×C₁₉	D₄	1	2	yes	—
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₉	—	2	2	no	—
25	C₂×C₄⋊Dic₁₉	—	2	2	no	—
26	C₂×C₄⋊Dic₁₉	—	2	2	no	—
27	C₂×C₄⋊Dic₁₉	—	2	2	no	—
28	C₂×#64516	—	2	8	no	—
29	C₂×#64516	—	4	4	no	—
30	C₂×#64516	—	4	4	no	—
31	#10597320	—	2	1	no	—
32	#10597320	—	2	2	no	—
33	#10597320	C₂×C₄	1	2	yes	—
34	#10597315	—	2	2	no	—
35	#10597315	—	2	1	no	—
36	#10597315	C₂×C₄	1	2	yes	—
37	C₄×C₈×C₁₉	—	2	2	no	—
38	C₄×C₈×C₁₉	—	2	2	no	—
39	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
40	C₄×C₈×C₁₉	D₄	1	2	yes	—
41	#10597278	—	4	8	no	—
42	#10597275	—	4	4	no	—
43	C₂³×D₁₉	—	4	1	no	—
44	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
46	C₂²×Dic₁₉	—	4	1	no	—
47	C₂²×Dic₁₉	—	4	2	no	—
48	C₂×D₇₆	—	2	2	no	—
49	C₂×D₇₆	—	2	4	no	—
50	C₂×D₇₆	—	4	2	no	—
51	C₂×D₇₆	—	4	2	no	—
52	C₂×D₇₆	—	4	4	no	—
53	C₂×D₇₆	—	4	4	no	—
54	C₂×D₇₆	—	4	2	no	—
55	C₂×D₇₆	—	4	1	no	—
56	C₂×Dic₃₈	—	2	2	no	—
57	C₂×Dic₃₈	—	4	2	no	—
58	C₂×Dic₃₈	—	4	2	no	—
59	C₂×Dic₃₈	—	4	1	no	—
60	C₂×C₈×C₁₉	—	2	4	no	—
61	C₂×C₈×C₁₉	—	2	4	no	—
62	C₂×C₈×C₁₉	—	2	4	no	—
63	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
64	C₂×C₈×C₁₉	D₈	1	4	yes	—
65	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
66	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
67	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₄²×C₁₉	#41	1	2	yes	—
69	C₄⋊Dic₁₉	—	2	4	no	—
70	C₄⋊Dic₁₉	—	4	2	no	—
71	C₄⋊Dic₁₉	—	4	4	no	—
72	C₄⋊Dic₁₉	—	4	4	no	—
73	C₄⋊Dic₁₉	—	4	4	no	—
74	#64516	—	4	16	no	—
75	#9842	—	19	1	no	maximal, Sylow
76	C₂³×C₁₉	#127	1	1	yes	characteristic
77	C₂²×D₁₉	—	4	2	no	—
78	C₂²×D₁₉	—	8	1	no	—
79	C₂²×D₁₉	—	8	1	no	—
80	C₂²×D₁₉	—	8	2	no	—
81	C₂²×D₁₉	—	8	2	no	—
82	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
84	C₂×C₄×C₁₉	#121	1	2	yes	—
85	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
86	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
87	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
88	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
89	C₂×C₄×C₁₉	#137	1	4	yes	—
90	C₂×Dic₁₉	—	4	2	no	—
91	C₂×Dic₁₉	—	8	1	no	—
92	C₂×Dic₁₉	—	8	1	no	—
93	C₂×Dic₁₉	—	8	2	no	—
94	C₂×Dic₁₉	—	8	2	no	—
95	C₂×Dic₁₉	—	8	2	no	—
96	D₇₆	—	4	4	no	—
97	D₇₆	—	4	8	no	—
98	D₇₆	—	8	4	no	—
99	D₇₆	—	8	2	no	—
100	Dic₃₈	—	4	4	no	—
101	Dic₃₈	—	8	2	no	—
102	C₈×C₁₉	—	4	4	no	—
103	C₈×C₁₉	#102	1	8	yes	complemented
104	C₂×#492	—	19	1	no	—
105	#1990	—	19	2	no	—
106	#1957	—	19	2	no	—
107	#1845	—	19	1	no	—
108	C₂×#322	D₁₉	1	1	yes	characteristic, complemented
109	C₂²×C₁₉	#390	1	1	yes	characteristic
110	C₂²×C₁₉	#492	1	1	yes	characteristic
111	C₂²×C₁₉	#493	1	1	yes	characteristic
112	C₂²×C₁₉	#496	1	2	yes	—
113	C₂²×C₁₉	#497	1	2	yes	—
114	C₂×D₁₉	—	8	2	no	—
115	C₂×D₁₉	—	8	4	no	—
116	C₂×D₁₉	—	16	2	no	—
117	C₂×D₁₉	—	16	1	no	—
118	C₂×D₁₉	—	16	1	no	—
119	C₄×C₁₉	C₂×#102	1	2	yes	—
120	C₄×C₁₉	#440	1	4	yes	—
121	C₄×C₁₉	#468	1	4	yes	—
122	C₄×C₁₉	#486	1	2	yes	—
123	Dic₁₉	—	8	2	no	—
124	Dic₁₉	—	16	2	no	—
125	C₂²×SD₁₆	—	38	2	no	—
126	C₂×C₄⋊Q₈	—	19	1	no	—
127	C₂×#127	—	19	1	no	—
128	#492	—	19	4	no	—
129	#492	—	38	2	no	—
130	C₂×#107	—	38	2	no	—
131	C₂×#102	—	38	4	no	—
132	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
133	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
134	#384	—	19	2	no	—
135	#340	—	38	4	no	—
136	#322	—	2	2	no	—
137	C₂×C₁₉	#1714	1	2	yes	—
138	C₂×C₁₉	#1721	1	1	yes	characteristic
139	C₂×C₁₉	#1722	1	1	yes	characteristic
140	C₂×C₁₉	#1957	1	1	yes	characteristic
141	C₂×C₁₉	#1973	1	2	yes	—
142	D₁₉	—	16	2	no	—
143	C₂²×Q₈	—	38	1	no	—
144	C₂²×D₄	—	38	1	no	—
145	C₂²×D₄	—	38	2	no	—
146	C₂×SD₁₆	—	38	8	no	—
147	C₂×SD₁₆	—	76	4	no	—
148	C₂×SD₁₆	—	76	4	no	—
149	C₂²×C₈	D₇₆	1	4	yes	—
150	C₂²×C₈	D₇₆	1	2	yes	—
151	C₄⋊Q₈	—	19	2	no	—
152	C₄⋊Q₈	—	38	2	no	—
153	C₄⋊Q₈	—	38	1	no	—
154	#127	—	19	2	no	—
155	#127	—	38	2	no	—
156	#127	—	38	1	no	—
157	C₂×C₄⋊C₄	—	38	2	no	—
158	C₂×C₄⋊C₄	—	38	2	no	—
159	C₂×C₄⋊C₄	—	38	2	no	—
160	C₂×C₄⋊C₄	—	38	2	no	—
161	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
162	#107	—	76	4	no	—
163	#102	—	76	8	no	—
164	C₄×C₈	—	2	2	no	—
165	C₄×C₈	—	2	2	no	—
166	C₄×C₈	C₄×D₁₉	1	2	yes	—
167	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
168	C₁₉	#9842	1	1	yes	characteristic, complemented, Sylow
169	C₂⁴	—	76	1	no	—
170	C₂×Q₈	—	38	2	no	—
171	C₂×Q₈	—	76	1	no	—
172	C₂×Q₈	—	76	2	no	—
173	C₂×Q₈	—	76	2	no	—
174	C₂×D₄	—	38	4	no	—
175	C₂×D₄	—	38	2	no	—
176	C₂×D₄	—	76	2	no	—
177	C₂×D₄	—	76	1	no	—
178	C₂×D₄	—	76	2	no	—
179	C₂×D₄	—	76	2	no	—
180	C₂×D₄	—	76	4	no	—
181	C₂×D₄	—	76	4	no	—
182	C₂²×C₄	—	76	1	no	—
183	C₂²×C₄	—	76	2	no	—
184	C₂²×C₄	C₂×D₇₆	1	2	yes	—
185	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
186	SD₁₆	—	76	16	no	—
187	C₂×C₈	—	2	4	no	—
188	C₂×C₈	—	2	4	no	—
189	C₂×C₈	—	2	4	no	—
190	C₂×C₈	#64516	1	4	yes	—
191	C₂×C₈	D₁₅₂	1	4	yes	—
192	C₂×C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
193	C₄⋊C₄	—	38	4	no	—
194	C₄⋊C₄	—	76	2	no	—
195	C₄⋊C₄	—	76	4	no	—
196	C₄⋊C₄	—	76	4	no	—
197	C₄⋊C₄	—	76	4	no	—
198	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
199	C₄²	#64541	1	2	yes	—
200	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
201	C₂³	—	76	2	no	—
202	C₂³	—	152	1	no	—
203	C₂³	—	152	1	no	—
204	C₂³	—	152	2	no	—
205	C₂³	—	152	2	no	—
206	C₂³	#10597320	1	1	yes	characteristic
207	Q₈	—	76	4	no	—
208	Q₈	—	152	2	no	—
209	D₄	—	76	4	no	—
210	D₄	—	76	8	no	—
211	D₄	—	152	4	no	—
212	D₄	—	152	2	no	—
213	C₂×C₄	—	76	2	no	—
214	C₂×C₄	—	152	2	no	—
215	C₂×C₄	—	152	2	no	—
216	C₂×C₄	—	152	2	no	—
217	C₂×C₄	—	152	1	no	—
218	C₂×C₄	—	152	1	no	—
219	C₂×C₄	C₄×D₇₆	1	2	yes	—
220	C₂×C₄	#10597321	1	1	yes	characteristic
221	C₂×C₄	C₂×#64516	1	2	yes	—
222	C₂×C₄	C₂×D₁₅₂	1	2	yes	—
223	C₂×C₄	#10597354	1	4	yes	—
224	C₂×C₄	#10597355	1	4	yes	—
225	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
226	C₂×C₄	#10597376	1	2	yes	—
227	C₈	—	4	4	no	—
228	C₈	#10597278	1	8	yes	complemented
229	C₂²	—	304	2	no	—
230	C₂²	—	304	1	no	—
231	C₂²	—	304	1	no	—
232	C₂²	—	152	2	no	—
233	C₂²	—	152	4	no	—
234	C₂²	#11926446	1	1	yes	characteristic
235	C₂²	#11926917	1	1	yes	characteristic
236	C₂²	#11926921	1	1	yes	characteristic
237	C₂²	#11926933	1	2	yes	—
238	C₂²	#11926938	1	2	yes	—
239	C₄	—	304	2	no	—
240	C₄	—	152	2	no	—
241	C₄	C₂×#10597278	1	2	yes	—
242	C₄	#11926646	1	4	yes	—
243	C₄	#11926790	1	4	yes	—
244	C₄	#11926891	1	2	yes	—
245	C₂	—	304	2	no	—
246	C₂	#14563257	1	2	yes	—
247	C₂	#14563301	1	1	yes	characteristic
248	C₂	#14563306	1	1	yes	characteristic
249	C₂	#14564441	1	1	yes	characteristic
250	C₂	#14564516	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926917

C₂

yes

maximal, characteristic

#14564596

C₂

yes

maximal, complemented

#14564441

C₂

yes

maximal

#14563795

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#322

C₂

yes

maximal, characteristic, complemented

C₂²×#64516

—

C₂×#10597315

C₂²

yes

characteristic

C₂×#10597320

C₂²

yes

characteristic

#11926917

—

#11926917

C₄

yes

—

—

C₂²

yes

—

#11926307

—

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#322

—

C₂²×D₇₆

—

C₂²×D₇₆

—

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

—

—

—

—

—

C₂×C₄

yes

—

#10597315

—

#10597315

—

#10597315

C₂×C₄

yes

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

#10597278

—

#10597275

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

D₈

yes

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

100

Dic₃₈

—

101

Dic₃₈

—

102

C₈×C₁₉

—

103

C₈×C₁₉

#102

yes

complemented

104

C₂×#492

—

105

#1990

—

106

#1957

—

107

#1845

—

108

C₂×#322

D₁₉

yes

characteristic, complemented

109

C₂²×C₁₉

#390

yes

characteristic

110

C₂²×C₁₉

#492

yes

characteristic

111

C₂²×C₁₉

#493

yes

characteristic

112

C₂²×C₁₉

#496

yes

—

113

C₂²×C₁₉

#497

yes

—

114

C₂×D₁₉

—

115

C₂×D₁₉

—

116

C₂×D₁₉

—

117

C₂×D₁₉

—

118

C₂×D₁₉

—

119

C₄×C₁₉

C₂×#102

yes

—

120

C₄×C₁₉

#440

yes

—

121

C₄×C₁₉

#468

yes

—

122

C₄×C₁₉

#486

yes

—

123

Dic₁₉

—

124

Dic₁₉

—

125

C₂²×SD₁₆

—

126

C₂×C₄⋊Q₈

—

127

C₂×#127

—

128

#492

—

129

#492

—

130

C₂×#107

—

131

C₂×#102

—

132

C₂×C₄×C₈

C₂×D₁₉

yes

—

133

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

134

#384

—

135

#340

—

136

#322

—

137

C₂×C₁₉

#1714

yes

—

138

C₂×C₁₉

#1721

yes

characteristic

139

C₂×C₁₉

#1722

yes

characteristic

140

C₂×C₁₉

#1957

yes

characteristic

141

C₂×C₁₉

#1973

yes

—

142

D₁₉

—

143

C₂²×Q₈

—

144

C₂²×D₄

—

145

C₂²×D₄

—

146

C₂×SD₁₆

—

147

C₂×SD₁₆

—

148

C₂×SD₁₆

—

149

C₂²×C₈

D₇₆

yes

—

150

C₂²×C₈

D₇₆

yes

—

151

C₄⋊Q₈

—

152

C₄⋊Q₈

—

153

C₄⋊Q₈

—

154

#127

—

155

#127

—

156

#127

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄²

C₂²×D₁₉

yes

characteristic

162

#107

—

163

#102

—

164

C₄×C₈

—

165

C₄×C₈

—

166

C₄×C₈

C₄×D₁₉

yes

—

167

C₄×C₈

C₂²⋊D₁₉

yes

—

168

C₁₉

#9842

yes

characteristic, complemented, Sylow

169

C₂⁴

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

C₂×D₇₆

yes

—

185

C₂²×C₄

C₂×D₇₆

yes

characteristic

186

SD₁₆

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

#64516

yes

—

191

C₂×C₈

D₁₅₂

yes

—

192

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄²

C₂×C₄×D₁₉

yes

characteristic

199

C₄²

#64541

yes

—

200

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

201

C₂³

—

202

C₂³

—

152

—

203

C₂³

—

152

—

204

C₂³

—

152

—

205

C₂³

—

152

—

206

C₂³

#10597320

yes

characteristic

207

Q₈

—

208

Q₈

—

152

—

209

D₄

—

210

D₄

—

211

D₄

—

152

—

212

D₄

—

152

—

213

C₂×C₄

—

214

C₂×C₄

—

152

—

215

C₂×C₄

—

152

—

216

C₂×C₄

—

152

—

217

C₂×C₄

—

152

—

218

C₂×C₄

—

152

—

219

C₂×C₄

C₄×D₇₆

yes

—

220

C₂×C₄

#10597321

yes

characteristic

221

C₂×C₄

C₂×#64516

yes

—

222

C₂×C₄

C₂×D₁₅₂

yes

—

223

C₂×C₄

#10597354

yes

—

224

C₂×C₄

#10597355

yes

—

225

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

226

C₂×C₄

#10597376

yes

—

227

C₈

—

228

C₈

#10597278

yes

complemented

229

C₂²

—

304

—

230

C₂²

—

304

—

231

C₂²

—

304

—

232

C₂²

—

152

—

233

C₂²

—

152

—

234

C₂²

#11926446

yes

characteristic

235

C₂²

#11926917

yes

characteristic

236

C₂²

#11926921

yes

characteristic

237

C₂²

#11926933

yes

—

238

C₂²

#11926938

yes

—

239

C₄

—

304

—

240

C₄

—

152

—

241

C₄

C₂×#10597278

yes

—

242

C₄

#11926646

yes

—

243

C₄

#11926790

yes

—

244

C₄

#11926891

yes

—

245

C₂

—

304

—

246

C₂

#14563257

yes

—

247

C₂

#14563301

yes

characteristic

248

C₂

#14563306

yes

characteristic

249

C₂

#14564441

yes

characteristic

250

C₂

#14564516

yes

—

	subgroup	G/H
center	C₂³	#10597320
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#322	C₂
socle	C₂³×C₁₉	#127
prime radical	C₂×#10597320	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#322	D₁₉
hypocenter	C₁₉	#9842
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#322

subgroup

G/H

center

C₂³

#10597320

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#322

C₂

C₂³×C₁₉

C₂²

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#322

N	H ≅ G/N	type
2. #14564596	C₂	semidirect
4. #14563795	C₂	semidirect
5. C₂×C₁₉×#322	C₂	semidirect
10. #11926917	C₄	semidirect
103. C₈×C₁₉	#102	semidirect
108. C₂×#322	D₁₉	semidirect
168. C₁₉	#9842	semidirect
228. C₈	#10597278	semidirect

H ≅ G/N

type

2. #14564596

C₂

semidirect

4. #14563795

C₂

semidirect

5. C₂×C₁₉×#322

C₂

semidirect

10. #11926917

C₄

semidirect

103. C₈×C₁₉

#102

semidirect

108. C₂×#322

D₁₉

semidirect

168. C₁₉

#9842

semidirect

228. C₈

#10597278

semidirect

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

subgroup	index
C₂×#11926917	2
#14564596	2
#14564441	2
#14563795	2
C₂×C₁₉×#322	2
#9842	19

subgroup

index

C₂×C₁₉×#322

Subgroups — #18082405

Conjugacy classes of subgroups

Complements

Maximal subgroups