Group #14576349 — subgroups

Subgroups — #14576349

Order 2432.

372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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	Q₈×D₇₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926903	C₂	1	2	yes	maximal, complemented
3	#11926894	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926839	C₂	1	2	yes	maximal, complemented
5	#11926824	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926756	C₂	1	2	yes	maximal
7	#11926746	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926675	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926642	C₂	1	2	yes	maximal, complemented
10	C₄×#64525	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#556	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₈×D₁₉	—	2	1	no	—
13	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₁₉×#126	—	2	2	no	—
15	C₁₉×#124	C₂²	1	2	yes	—
16	C₁₉×C₂²⋊Q₈	—	2	1	no	—
17	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
18	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#117	—	2	1	no	—
21	C₂×#64527	C₂²	1	2	yes	—
22	C₂×#64525	C₂²	1	1	yes	characteristic
23	#10597343	—	2	1	no	—
24	#10597343	—	2	2	no	—
25	C₄×D₇₆	C₂²	1	1	yes	characteristic
26	C₄×D₇₆	C₂²	1	2	yes	—
27	#10597315	C₂²	1	1	yes	characteristic
28	#10597315	C₂²	1	2	yes	—
29	#10597292	C₂²	1	2	yes	—
30	#10597292	C₂²	1	2	yes	—
31	#10597292	C₂²	1	2	yes	—
32	#10597289	C₂²	1	2	yes	—
33	#10597289	C₂²	1	1	yes	characteristic
34	#10597266	C₂²	1	1	yes	characteristic
35	#10597264	C₂²	1	2	yes	—
36	#10597264	C₂²	1	1	yes	characteristic
37	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
38	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
39	#10597260	C₂²	1	2	yes	—
40	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×Q₈×C₁₉	D₄	1	1	yes	characteristic
42	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
43	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	—	2	1	no	—
45	Q₈×D₁₉	—	4	4	no	—
46	C₂×D₇₆	C₂³	1	1	yes	characteristic
47	C₂×C₄×D₁₉	—	2	2	no	—
48	C₂×C₄×D₁₉	—	2	1	no	—
49	C₂×Dic₃₈	—	2	2	no	—
50	C₂×Dic₃₈	—	2	1	no	—
51	C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
55	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
56	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²⋊C₄×C₁₉	—	2	2	no	—
58	C₂²⋊C₄×C₁₉	—	2	1	no	—
59	C₂²⋊C₄×C₁₉	—	2	2	no	—
60	C₄²×C₁₉	—	2	2	no	—
61	C₄²×C₁₉	C₂³	1	1	yes	characteristic
62	C₄²×C₁₉	C₂³	1	2	yes	—
63	#64527	—	2	4	no	—
64	#64525	—	2	2	no	—
65	(C₂×D₁₉)⋊C₄	—	2	2	no	—
66	(C₂×D₁₉)⋊C₄	—	2	1	no	—
67	C₄⋊Dic₁₉	—	2	2	no	—
68	C₄⋊Dic₁₉	—	2	1	no	—
69	C₄⋊Dic₁₉	C₂³	1	2	yes	—
70	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
71	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
72	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
73	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
74	C₂³×C₁₉	—	2	1	no	—
75	C₂²×D₁₉	—	2	1	no	—
76	Q₈×C₁₉	—	2	2	no	—
77	Q₈×C₁₉	—	2	2	no	—
78	Q₈×C₁₉	—	2	2	no	—
79	D₄×C₁₉	—	2	1	no	—
80	D₄×C₁₉	—	2	1	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	4	2	no	—
84	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
85	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
87	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
89	C₂×Dic₁₉	—	2	1	no	—
90	C₂×Dic₁₉	—	2	2	no	—
91	D₇₆	—	2	1	no	—
92	D₇₆	#41	1	2	yes	—
93	C₄×D₁₉	—	4	4	no	—
94	C₄×D₁₉	—	4	2	no	—
95	Dic₃₈	—	4	4	no	—
96	Dic₃₈	—	4	2	no	—
97	C₁₉⋊C₈	—	2	1	no	—
98	C₁₉⋊C₈	—	2	2	no	—
99	C₁₉⋊C₈	—	2	1	no	—
100	#3367	—	19	1	no	maximal, Sylow
101	C₂²×C₁₉	—	4	1	no	—
102	C₂²×C₁₉	—	4	1	no	—
103	C₂²×C₁₉	—	4	1	no	—
104	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
105	C₂×D₁₉	—	2	2	no	—
106	C₂×D₁₉	—	4	1	no	—
107	C₂×D₁₉	—	4	1	no	—
108	C₄×C₁₉	—	2	2	no	—
109	C₄×C₁₉	—	2	2	no	—
110	C₄×C₁₉	—	2	1	no	—
111	C₄×C₁₉	—	4	2	no	—
112	C₄×C₁₉	—	4	1	no	—
113	C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
114	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
115	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
116	Dic₁₉	—	4	1	no	—
117	Dic₁₉	—	4	2	no	—
118	#556	D₁₉	1	1	yes	characteristic, complemented
119	D₄×Q₈	—	19	1	no	—
120	#489	—	19	2	no	—
121	#487	—	19	1	no	—
122	#477	—	19	2	no	—
123	#474	—	19	1	no	—
124	#463	—	19	2	no	—
125	#461	—	19	1	no	—
126	#446	—	19	1	no	—
127	#440	—	19	2	no	—
128	C₄×D₈	—	19	1	no	—
129	C₂×C₁₉	—	8	1	no	—
130	C₂×C₁₉	#548	1	1	yes	characteristic
131	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
132	C₂×C₁₉	#578	1	1	yes	characteristic
133	D₁₉	—	4	2	no	—
134	C₂²×Q₈	—	38	1	no	—
135	C₂×SD₁₆	—	19	2	no	—
136	C₂×D₈	—	19	1	no	—
137	C₄⋊Q₈	—	19	1	no	—
138	C₄⋊Q₈	—	19	2	no	—
139	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
140	#126	—	2	2	no	—
141	#124	C₂×D₁₉	1	2	yes	—
142	C₂²⋊Q₈	—	2	1	no	—
143	C₂²⋊Q₈	—	38	1	no	—
144	C₂²⋊Q₈	—	38	2	no	—
145	C₄×Q₈	C₂×D₁₉	1	2	yes	—
146	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
147	C₄×D₄	—	19	1	no	—
148	C₄×D₄	—	19	2	no	—
149	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
150	#117	—	2	1	no	—
151	#107	—	19	1	no	—
152	#107	—	19	2	no	—
153	C₄⋊C₈	—	19	1	no	—
154	C₄⋊C₈	—	19	2	no	—
155	#103	—	19	2	no	—
156	#103	—	19	2	no	—
157	#103	—	19	2	no	—
158	#102	—	19	1	no	—
159	#102	—	19	2	no	—
160	#102	—	19	1	no	—
161	#97	—	19	2	no	—
162	C₄×C₈	—	19	1	no	—
163	C₁₉	#3367	1	1	yes	characteristic, complemented, Sylow
164	C₂×Q₈	—	38	2	no	—
165	C₂×Q₈	—	38	1	no	—
166	C₂×Q₈	—	76	4	no	—
167	C₂×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
168	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
169	C₂×D₄	—	19	1	no	—
170	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
171	C₂²×C₄	—	2	1	no	—
172	C₂²×C₄	—	38	2	no	—
173	C₂²×C₄	—	38	1	no	—
174	SD₁₆	—	38	4	no	—
175	D₈	—	38	2	no	—
176	C₂×C₈	—	19	1	no	—
177	C₂×C₈	—	19	1	no	—
178	C₂×C₈	—	19	2	no	—
179	C₄⋊C₄	—	2	1	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	2	1	no	—
182	C₄⋊C₄	—	19	1	no	—
183	C₄⋊C₄	—	19	2	no	—
184	C₄⋊C₄	—	38	2	no	—
185	C₄⋊C₄	—	38	1	no	—
186	C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
187	C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
188	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
189	C₂²⋊C₄	—	2	2	no	—
190	C₂²⋊C₄	—	2	1	no	—
191	C₂²⋊C₄	—	2	2	no	—
192	C₂²⋊C₄	—	38	2	no	—
193	C₂²⋊C₄	—	38	1	no	—
194	C₄²	—	2	2	no	—
195	C₄²	C₂²×D₁₉	1	1	yes	characteristic
196	C₄²	C₂²×D₁₉	1	2	yes	—
197	C₂³	—	2	1	no	—
198	C₂³	—	38	1	no	—
199	Q₈	—	2	2	no	—
200	Q₈	—	2	2	no	—
201	Q₈	—	2	2	no	—
202	Q₈	—	76	4	no	—
203	Q₈	—	76	2	no	—
204	D₄	—	2	1	no	—
205	D₄	—	2	1	no	—
206	D₄	—	19	2	no	—
207	D₄	—	38	1	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	38	2	no	—
212	C₂×C₄	—	38	1	no	—
213	C₂×C₄	—	76	4	no	—
214	C₂×C₄	—	76	2	no	—
215	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
216	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
217	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
218	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
219	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
220	C₈	—	38	1	no	—
221	C₈	—	38	2	no	—
222	C₈	—	38	1	no	—
223	C₂²	—	4	1	no	—
224	C₂²	—	4	1	no	—
225	C₂²	—	4	1	no	—
226	C₂²	—	38	2	no	—
227	C₂²	—	76	1	no	—
228	C₂²	—	76	1	no	—
229	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
230	C₄	—	2	2	no	—
231	C₄	—	2	2	no	—
232	C₄	—	2	1	no	—
233	C₄	—	4	1	no	—
234	C₄	—	4	2	no	—
235	C₄	—	76	2	no	—
236	C₄	—	76	1	no	—
237	C₄	#10597395	1	2	yes	—
238	C₄	#41×D₁₉	1	1	yes	characteristic
239	C₄	#10597436	1	1	yes	characteristic
240	C₂	—	8	1	no	—
241	C₂	—	76	2	no	—
242	C₂	#11927201	1	1	yes	characteristic
243	C₂	C₂×#10597395	1	1	yes	characteristic
244	C₂	#11927359	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₈×D₇₆

C₂

yes

maximal, characteristic, complemented

#11926903

C₂

yes

maximal, complemented

#11926894

C₂

yes

maximal, characteristic, complemented

#11926839

C₂

yes

maximal, complemented

#11926824

C₂

yes

maximal, characteristic, complemented

#11926756

C₂

yes

maximal

#11926746

C₂

yes

maximal, characteristic, complemented

#11926675

C₂

yes

maximal, characteristic, complemented

#11926642

C₂

yes

maximal, complemented

C₄×#64525

C₂

yes

maximal, characteristic

C₁₉×#556

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₁₉

—

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#126

—

C₁₉×#124

C₂²

yes

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

C₂²

yes

—

C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#117

—

C₂×#64527

C₂²

yes

—

C₂×#64525

C₂²

yes

characteristic

#10597343

—

#10597343

—

C₄×D₇₆

C₂²

yes

characteristic

C₄×D₇₆

C₂²

yes

—

#10597315

C₂²

yes

characteristic

#10597315

C₂²

yes

—

#10597292

C₂²

yes

—

#10597292

C₂²

yes

—

#10597292

C₂²

yes

—

#10597289

C₂²

yes

—

#10597289

C₂²

yes

characteristic

#10597266

C₂²

yes

characteristic

#10597264

C₂²

yes

—

#10597264

C₂²

yes

characteristic

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#10597260

C₂²

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

D₄

yes

characteristic

C₂×Q₈×C₁₉

C₂³

yes

—

C₂×D₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

—

Q₈×D₁₉

—

C₂×D₇₆

C₂³

yes

characteristic

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

C₂³

yes

characteristic

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂³

yes

—

#64527

—

#64525

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

C₄⋊Dic₁₉

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂×C₁₉⋊C₈

C₂³

yes

characteristic

C₂³×C₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

#41

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

100

#3367

—

maximal, Sylow

101

C₂²×C₁₉

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

C₂²×D₄

yes

characteristic

105

C₂×D₁₉

—

106

C₂×D₁₉

—

107

C₂×D₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

114

C₄×C₁₉

C₂×#41

yes

characteristic

115

C₄×C₁₉

2₋¹⁺⁴

yes

characteristic

116

Dic₁₉

—

117

Dic₁₉

—

118

#556

D₁₉

yes

characteristic, complemented

119

D₄×Q₈

—

120

#489

—

121

#487

—

122

#477

—

123

#474

—

124

#463

—

125

#461

—

126

#446

—

127

#440

—

128

C₄×D₈

—

129

C₂×C₁₉

—

130

C₂×C₁₉

#548

yes

characteristic

131

C₂×C₁₉

C₂×AGL(1,ℤ/8)

yes

characteristic

132

C₂×C₁₉

#578

yes

characteristic

133

D₁₉

—

134

C₂²×Q₈

—

135

C₂×SD₁₆

—

136

C₂×D₈

—

137

C₄⋊Q₈

—

138

C₄⋊Q₈

—

139

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

140

#126

—

141

#124

C₂×D₁₉

yes

—

142

C₂²⋊Q₈

—

143

C₂²⋊Q₈

—

144

C₂²⋊Q₈

—

145

C₄×Q₈

C₂×D₁₉

yes

—

146

C₄×Q₈

C₂×D₁₉

yes

characteristic

147

C₄×D₄

—

148

C₄×D₄

—

149

C₄×D₄

C₂×D₁₉

yes

characteristic

150

#117

—

151

#107

—

152

#107

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

#103

—

156

#103

—

157

#103

—

158

#102

—

159

#102

—

160

#102

—

161

#97

—

162

C₄×C₈

—

163

C₁₉

#3367

yes

characteristic, complemented, Sylow

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

C₂²⋊D₁₉

yes

characteristic

168

C₂×Q₈

C₂²×D₁₉

yes

—

169

C₂×D₄

—

170

C₂×D₄

C₂²×D₁₉

yes

characteristic

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

SD₁₆

—

175

D₈

—

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

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

187

C₄⋊C₄

C₂²⋊D₁₉

yes

—

188

C₄⋊C₄

C₂²×D₁₉

yes

characteristic

189

C₂²⋊C₄

—

190

C₂²⋊C₄

—

191

C₂²⋊C₄

—

192

C₂²⋊C₄

—

193

C₂²⋊C₄

—

194

C₄²

—

195

C₄²

C₂²×D₁₉

yes

characteristic

196

C₄²

C₂²×D₁₉

yes

—

197

C₂³

—

198

C₂³

—

199

Q₈

—

200

Q₈

—

201

Q₈

—

202

Q₈

—

203

Q₈

—

204

D₄

—

205

D₄

—

206

D₄

—

207

D₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

216

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

217

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

218

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

219

C₂×C₄

C₂³×D₁₉

yes

characteristic

220

C₈

—

221

C₈

—

222

C₈

—

223

C₂²

—

224

C₂²

—

225

C₂²

—

226

C₂²

—

227

C₂²

—

228

C₂²

—

229

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

#10597395

yes

—

238

C₄

#41×D₁₉

yes

characteristic

239

C₄

#10597436

yes

characteristic

240

C₂

—

241

C₂

—

242

C₂

#11927201

yes

characteristic

243

C₂

C₂×#10597395

yes

characteristic

244

C₂

#11927359

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#556	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂×#64525	C₂²
hypercenter	#556	D₁₉
hypocenter	C₁₉	#3367
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #556

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#556

C₂

socle

C₂²×C₁₉

C₂²×D₄

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #556

N	H ≅ G/N	type
1. Q₈×D₇₆	C₂	semidirect
2. #11926903	C₂	semidirect
3. #11926894	C₂	semidirect
4. #11926839	C₂	semidirect
5. #11926824	C₂	semidirect
7. #11926746	C₂	semidirect
8. #11926675	C₂	semidirect
9. #11926642	C₂	semidirect
11. C₁₉×#556	C₂	semidirect
118. #556	D₁₉	semidirect
163. C₁₉	#3367	semidirect

H ≅ G/N

type

1. Q₈×D₇₆

C₂

semidirect

2. #11926903

C₂

semidirect

3. #11926894

C₂

semidirect

4. #11926839

C₂

semidirect

5. #11926824

C₂

semidirect

7. #11926746

C₂

semidirect

8. #11926675

C₂

semidirect

9. #11926642

C₂

semidirect

11. C₁₉×#556

C₂

semidirect

118. #556

D₁₉

semidirect

163. C₁₉

#3367

semidirect

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

subgroup	index
Q₈×D₇₆	2
#11926903	2
#11926894	2
#11926839	2
#11926824	2
#11926756	2
#11926746	2
#11926675	2
#11926642	2
C₄×#64525	2
C₁₉×#556	2
#3367	19

subgroup

index

Q₈×D₇₆

C₁₉×#556

Subgroups — #14576349

Conjugacy classes of subgroups

Complements

Maximal subgroups