Group #14574861 — subgroups

Subgroups — #14574861

Order 2432.

362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 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	C₄⋊Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927073	C₂	1	1	yes	maximal, characteristic
3	#11926953	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926950	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926903	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926878	C₂	1	2	yes	maximal, complemented
7	#11926861	C₂	1	2	yes	maximal
8	#11926827	C₂	1	2	yes	maximal, complemented
9	#11926822	C₂	1	2	yes	maximal, complemented
10	#11926599	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#489	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×#124	C₂²	1	1	yes	characteristic
15	#10597392	C₂²	1	1	yes	characteristic
16	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic
17	#10597390	—	2	1	no	—
18	#10597384	C₂²	1	1	yes	characteristic
19	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
20	C₄⋊C₄×D₁₉	—	2	1	no	—
21	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
22	#10597334	—	2	1	no	—
23	#10597334	C₂²	1	2	yes	—
24	#10597329	—	2	1	no	—
25	(C₂²⋊D₁₉)⋊C₄	—	2	1	no	—
26	#10597325	—	2	1	no	—
27	#10597323	—	2	1	no	—
28	C₄²×D₁₉	C₂²	1	1	yes	characteristic
29	#10597316	C₂²	1	1	yes	characteristic
30	#10597315	C₂²	1	1	yes	characteristic
31	C₁₉×#103	C₂²	1	2	yes	—
32	C₁₉×#102	C₂²	1	2	yes	—
33	C₁₉×#97	C₂²	1	1	yes	characteristic
34	#10597292	C₂²	1	2	yes	—
35	#10597289	C₂²	1	2	yes	—
36	(C₂×D₁₉)⋊C₈	C₂²	1	2	yes	—
37	#10597275	C₂²	1	2	yes	—
38	#10597274	C₂²	1	2	yes	—
39	Dic₁₉⋊C₈	C₂²	1	2	yes	—
40	#10597265	C₂²	1	2	yes	—
41	#10597264	C₂²	1	2	yes	—
42	#10597260	C₂²	1	1	yes	characteristic
43	C₂×Q₈×C₁₉	—	2	1	no	—
44	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂×C₂²⋊D₁₉	—	2	1	no	—
47	C₂²×Dic₁₉	—	2	1	no	—
48	Q₈×D₁₉	—	4	4	no	—
49	C₂×C₄×D₁₉	—	2	2	no	—
50	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
51	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
52	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
53	C₂×Dic₃₈	—	2	1	no	—
54	C₂×Dic₃₈	—	2	2	no	—
55	C₂×C₈×C₁₉	C₂³	1	2	yes	—
56	C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
58	C₂²⋊C₄×C₁₉	—	2	1	no	—
59	C₂²⋊C₄×C₁₉	—	2	1	no	—
60	C₄²×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²⋊Dic₁₉	—	2	1	no	—
62	C₂²⋊Dic₁₉	—	2	1	no	—
63	(C₂×D₁₉)⋊C₄	—	2	1	no	—
64	C₄⋊Dic₁₉	—	2	1	no	—
65	C₄⋊Dic₁₉	—	2	1	no	—
66	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
67	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
68	C₄⋊Dic₁₉	C₂³	1	2	yes	—
69	Dic₁₉⋊C₄	—	2	1	no	—
70	Dic₁₉⋊C₄	—	2	1	no	—
71	Dic₁₉⋊C₄	—	2	2	no	—
72	Dic₁₉⋊C₄	—	2	2	no	—
73	Dic₁₉⋊C₄	—	2	1	no	—
74	C₄×Dic₁₉	—	2	1	no	—
75	C₄×Dic₁₉	D₄	1	1	yes	characteristic
76	C₄×Dic₁₉	D₄	1	1	yes	characteristic
77	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
78	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
79	C₂³×C₁₉	—	2	1	no	—
80	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
81	Q₈×C₁₉	—	2	2	no	—
82	Q₈×C₁₉	—	4	2	no	—
83	D₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	2	1	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
89	C₂²⋊D₁₉	—	4	2	no	—
90	C₂×Dic₁₉	—	2	1	no	—
91	C₂×Dic₁₉	—	2	1	no	—
92	C₂×Dic₁₉	—	2	2	no	—
93	C₂×Dic₁₉	—	4	2	no	—
94	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
97	C₄×D₁₉	—	2	2	no	—
98	C₄×D₁₉	—	2	2	no	—
99	C₄×D₁₉	—	2	2	no	—
100	C₄×D₁₉	—	4	4	no	—
101	Dic₃₈	—	4	2	no	—
102	Dic₃₈	—	4	4	no	—
103	C₈×C₁₉	—	2	2	no	—
104	C₁₉⋊C₈	—	2	2	no	—
105	#3239	—	19	1	no	maximal, Sylow
106	C₂²×C₁₉	—	4	1	no	—
107	C₂²×C₁₉	—	4	1	no	—
108	C₂²×C₁₉	—	4	1	no	—
109	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
110	C₂×D₁₉	—	2	1	no	—
111	C₂×D₁₉	—	2	1	no	—
112	C₂×D₁₉	#137	1	2	yes	—
113	C₄×C₁₉	—	2	1	no	—
114	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	—	4	1	no	—
116	C₄×C₁₉	—	4	2	no	—
117	C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
118	Dic₁₉	—	2	1	no	—
119	Dic₁₉	—	2	1	no	—
120	Dic₁₉	—	4	2	no	—
121	Dic₁₉	—	4	1	no	—
122	Dic₁₉	—	4	1	no	—
123	Dic₁₉	AGL(1,ℤ/8)	1	2	yes	—
124	C₂×C₄⋊Q₈	—	19	1	no	—
125	#529	—	19	1	no	—
126	#501	—	19	1	no	—
127	#501	—	19	1	no	—
128	#489	—	19	1	no	—
129	#489	D₁₉	1	1	yes	characteristic, complemented
130	#484	—	19	2	no	—
131	#481	—	19	2	no	—
132	#475	—	19	2	no	—
133	#474	—	19	2	no	—
134	#432	—	19	1	no	—
135	C₂×C₁₉	—	8	1	no	—
136	C₂×C₁₉	#536	1	1	yes	characteristic
137	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
138	C₂×C₁₉	C₂×#137	1	1	yes	characteristic
139	D₁₉	—	2	2	no	—
140	C₂²×Q₈	—	38	1	no	—
141	C₄⋊Q₈	—	19	2	no	—
142	C₄⋊Q₈	—	19	1	no	—
143	C₄⋊Q₈	—	38	1	no	—
144	C₄⋊Q₈	—	38	1	no	—
145	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
146	#126	—	38	1	no	—
147	#125	—	19	1	no	—
148	#124	C₂×D₁₉	1	1	yes	characteristic
149	#123	—	38	1	no	—
150	C₂²⋊Q₈	—	19	1	no	—
151	#121	—	19	1	no	—
152	C₄×Q₈	—	19	1	no	—
153	C₄×D₄	—	19	1	no	—
154	C₄×D₄	—	38	1	no	—
155	#117	—	38	1	no	—
156	C₂×C₄⋊C₄	—	19	2	no	—
157	C₂×C₄⋊C₄	—	38	1	no	—
158	C₂×C₄²	—	19	1	no	—
159	#107	—	19	2	no	—
160	#107	—	19	2	no	—
161	#106	—	19	2	no	—
162	#106	—	19	2	no	—
163	C₄⋊C₈	—	19	2	no	—
164	#103	—	19	2	no	—
165	#103	C₂×D₁₉	1	2	yes	—
166	#102	—	19	2	no	—
167	#102	C₂×D₁₉	1	2	yes	—
168	C₂²⋊C₈	—	19	2	no	—
169	#97	—	19	1	no	—
170	#97	C₂×D₁₉	1	1	yes	characteristic
171	C₁₉	#3239	1	1	yes	characteristic, complemented, Sylow
172	C₂×Q₈	—	2	1	no	—
173	C₂×Q₈	—	38	2	no	—
174	C₂×Q₈	—	38	1	no	—
175	C₂×Q₈	—	76	4	no	—
176	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
177	C₂×D₄	—	38	1	no	—
178	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
179	C₂²×C₄	—	19	1	no	—
180	C₂²×C₄	—	19	1	no	—
181	C₂²×C₄	—	19	1	no	—
182	C₂²×C₄	—	38	2	no	—
183	C₂²×C₄	—	38	1	no	—
184	C₂×C₈	—	19	2	no	—
185	C₂×C₈	C₂²×D₁₉	1	2	yes	—
186	C₄⋊C₄	—	2	1	no	—
187	C₄⋊C₄	—	19	2	no	—
188	C₄⋊C₄	—	19	1	no	—
189	C₄⋊C₄	—	19	1	no	—
190	C₄⋊C₄	—	38	2	no	—
191	C₄⋊C₄	—	38	2	no	—
192	C₄⋊C₄	—	38	1	no	—
193	C₄⋊C₄	—	38	1	no	—
194	C₄⋊C₄	—	38	1	no	—
195	C₄⋊C₄	—	38	1	no	—
196	C₄⋊C₄	—	38	1	no	—
197	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
198	C₂²⋊C₄	—	2	1	no	—
199	C₂²⋊C₄	—	2	1	no	—
200	C₂²⋊C₄	—	38	1	no	—
201	C₂²⋊C₄	—	38	1	no	—
202	C₂²⋊C₄	—	38	1	no	—
203	C₄²	—	19	1	no	—
204	C₄²	—	19	1	no	—
205	C₄²	—	19	1	no	—
206	C₄²	—	38	1	no	—
207	C₄²	C₂²×D₁₉	1	1	yes	characteristic
208	C₂³	—	2	1	no	—
209	C₂³	—	19	1	no	—
210	Q₈	—	2	2	no	—
211	Q₈	—	4	2	no	—
212	Q₈	—	76	2	no	—
213	Q₈	—	76	4	no	—
214	D₄	—	2	2	no	—
215	D₄	—	76	2	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	19	1	no	—
219	C₂×C₄	—	19	1	no	—
220	C₂×C₄	—	19	1	no	—
221	C₂×C₄	—	38	2	no	—
222	C₂×C₄	—	38	2	no	—
223	C₂×C₄	—	38	2	no	—
224	C₂×C₄	—	38	1	no	—
225	C₂×C₄	—	38	1	no	—
226	C₂×C₄	—	38	2	no	—
227	C₂×C₄	—	76	4	no	—
228	C₂×C₄	—	76	2	no	—
229	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
230	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
231	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
232	C₈	—	2	2	no	—
233	C₈	—	38	2	no	—
234	C₂²	—	4	1	no	—
235	C₂²	—	4	1	no	—
236	C₂²	—	4	1	no	—
237	C₂²	—	19	2	no	—
238	C₂²	—	38	1	no	—
239	C₂²	—	38	1	no	—
240	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
241	C₄	—	2	1	no	—
242	C₄	—	2	1	no	—
243	C₄	—	4	2	no	—
244	C₄	—	4	1	no	—
245	C₄	—	19	2	no	—
246	C₄	—	38	1	no	—
247	C₄	—	38	1	no	—
248	C₄	—	76	2	no	—
249	C₄	—	76	1	no	—
250	C₄	—	76	1	no	—
251	C₄	#10597436	1	2	yes	—
252	C₂	—	8	1	no	—
253	C₂	—	38	2	no	—
254	C₂	#11927114	1	1	yes	characteristic
255	C₂	AGL(1,ℤ/8)×D₁₉	1	1	yes	characteristic
256	C₂	#137×D₁₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊Q₈×D₁₉

C₂

yes

maximal, characteristic, complemented

#11927073

C₂

yes

maximal, characteristic

#11926953

C₂

yes

maximal, characteristic, complemented

#11926950

C₂

yes

maximal, characteristic, complemented

#11926903

C₂

yes

maximal, characteristic, complemented

#11926878

C₂

yes

maximal, complemented

#11926861

C₂

yes

maximal

#11926827

C₂

yes

maximal, complemented

#11926822

C₂

yes

maximal, complemented

#11926599

C₂

yes

maximal, characteristic, complemented

C₁₉×#489

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₁₉

—

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#124

C₂²

yes

characteristic

#10597392

C₂²

yes

characteristic

Q₈×Dic₁₉

C₂²

yes

characteristic

#10597390

—

#10597384

C₂²

yes

characteristic

D₄×Dic₁₉

C₂²

yes

characteristic

C₄⋊C₄×D₁₉

—

C₄⋊C₄×D₁₉

C₂²

yes

—

#10597334

—

#10597334

C₂²

yes

—

#10597329

—

(C₂²⋊D₁₉)⋊C₄

—

#10597325

—

#10597323

—

C₄²×D₁₉

C₂²

yes

characteristic

#10597316

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₁₉×#103

C₂²

yes

—

C₁₉×#102

C₂²

yes

—

C₁₉×#97

C₂²

yes

characteristic

#10597292

C₂²

yes

—

#10597289

C₂²

yes

—

(C₂×D₁₉)⋊C₈

C₂²

yes

—

#10597275

C₂²

yes

—

#10597274

C₂²

yes

—

Dic₁₉⋊C₈

C₂²

yes

—

#10597265

C₂²

yes

—

#10597264

C₂²

yes

—

#10597260

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂³

yes

characteristic

C₂×D₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

—

Q₈×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

D₄

yes

characteristic

C₂×C₄×D₁₉

D₄

yes

characteristic

C₂×C₄×D₁₉

C₂³

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

characteristic

C₄⋊Dic₁₉

C₂³

yes

characteristic

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

characteristic

C₄×Dic₁₉

D₄

yes

characteristic

C₄×Dic₁₉

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

—

C₂²×D₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

100

C₄×D₁₉

—

101

Dic₃₈

—

102

Dic₃₈

—

103

C₈×C₁₉

—

104

C₁₉⋊C₈

—

105

#3239

—

maximal, Sylow

106

C₂²×C₁₉

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

C₂²×D₄

yes

characteristic

110

C₂×D₁₉

—

111

C₂×D₁₉

—

112

C₂×D₁₉

#137

yes

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

2₋¹⁺⁴

yes

—

118

Dic₁₉

—

119

Dic₁₉

—

120

Dic₁₉

—

121

Dic₁₉

—

122

Dic₁₉

—

123

Dic₁₉

AGL(1,ℤ/8)

yes

—

124

C₂×C₄⋊Q₈

—

125

#529

—

126

#501

—

127

#501

—

128

#489

—

129

#489

D₁₉

yes

characteristic, complemented

130

#484

—

131

#481

—

132

#475

—

133

#474

—

134

#432

—

135

C₂×C₁₉

—

136

C₂×C₁₉

#536

yes

characteristic

137

C₂×C₁₉

C₂×AGL(1,ℤ/8)

yes

characteristic

138

C₂×C₁₉

C₂×#137

yes

characteristic

139

D₁₉

—

140

C₂²×Q₈

—

141

C₄⋊Q₈

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

146

#126

—

147

#125

—

148

#124

C₂×D₁₉

yes

characteristic

149

#123

—

150

C₂²⋊Q₈

—

151

#121

—

152

C₄×Q₈

—

153

C₄×D₄

—

154

C₄×D₄

—

155

#117

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄²

—

159

#107

—

160

#107

—

161

#106

—

162

#106

—

163

C₄⋊C₈

—

164

#103

—

165

#103

C₂×D₁₉

yes

—

166

#102

—

167

#102

C₂×D₁₉

yes

—

168

C₂²⋊C₈

—

169

#97

—

170

#97

C₂×D₁₉

yes

characteristic

171

C₁₉

#3239

yes

characteristic, complemented, Sylow

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

C₂²×D₁₉

yes

characteristic

177

C₂×D₄

—

178

C₂×D₄

C₂²×D₁₉

yes

characteristic

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂×C₈

—

185

C₂×C₈

C₂²×D₁₉

yes

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

C₂²×D₁₉

yes

—

198

C₂²⋊C₄

—

199

C₂²⋊C₄

—

200

C₂²⋊C₄

—

201

C₂²⋊C₄

—

202

C₂²⋊C₄

—

203

C₄²

—

204

C₄²

—

205

C₄²

—

206

C₄²

—

207

C₄²

C₂²×D₁₉

yes

characteristic

208

C₂³

—

209

C₂³

—

210

Q₈

—

211

Q₈

—

212

Q₈

—

213

Q₈

—

214

D₄

—

215

D₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

D₄×D₁₉

yes

characteristic

230

C₂×C₄

D₄×D₁₉

yes

characteristic

231

C₂×C₄

C₂³×D₁₉

yes

characteristic

232

C₈

—

233

C₈

—

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

C₂×D₄×D₁₉

yes

characteristic

241

C₄

—

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

#10597436

yes

—

252

C₂

—

253

C₂

—

254

C₂

#11927114

yes

characteristic

255

C₂

AGL(1,ℤ/8)×D₁₉

yes

characteristic

256

C₂

#137×D₁₉

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#489	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	#10597384	C₂²
hypercenter	#489	D₁₉
hypocenter	C₁₉	#3239
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #489

subgroup

G/H

center

C₂²

C₂×D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#489

C₂

socle

C₂²×C₁₉

C₂²×D₄

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #489

N	H ≅ G/N	type
1. C₄⋊Q₈×D₁₉	C₂	semidirect
3. #11926953	C₂	semidirect
4. #11926950	C₂	semidirect
5. #11926903	C₂	semidirect
6. #11926878	C₂	semidirect
8. #11926827	C₂	semidirect
9. #11926822	C₂	semidirect
10. #11926599	C₂	semidirect
11. C₁₉×#489	C₂	semidirect
129. #489	D₁₉	semidirect
171. C₁₉	#3239	semidirect

H ≅ G/N

type

1. C₄⋊Q₈×D₁₉

C₂

semidirect

3. #11926953

C₂

semidirect

4. #11926950

C₂

semidirect

5. #11926903

C₂

semidirect

6. #11926878

C₂

semidirect

8. #11926827

C₂

semidirect

9. #11926822

C₂

semidirect

10. #11926599

C₂

semidirect

11. C₁₉×#489

C₂

semidirect

129. #489

D₁₉

semidirect

171. C₁₉

#3239

semidirect

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

subgroup	index
C₄⋊Q₈×D₁₉	2
#11927073	2
#11926953	2
#11926950	2
#11926903	2
#11926878	2
#11926861	2
#11926827	2
#11926822	2
#11926599	2
C₁₉×#489	2
#3239	19

subgroup

index

C₄⋊Q₈×D₁₉

C₁₉×#489

Subgroups — #14574861

Conjugacy classes of subgroups

Complements

Maximal subgroups