Group #18087338 — subgroups

Subgroups — #18087338

Order 4864.

294 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 93 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	#14564608	C₂	1	1	yes	maximal, characteristic
2	#14562321	C₂	1	1	yes	maximal, characteristic
3	#14562317	C₂	1	1	yes	maximal, characteristic
4	#14561495	C₂	1	1	yes	maximal, characteristic
5	#14561495	C₂	1	1	yes	maximal, characteristic
6	#14561480	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1849	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597315	C₂²	1	1	yes	characteristic
9	#11926597	C₂²	1	1	yes	characteristic
10	#11926597	C₂²	1	1	yes	characteristic
11	#11926410	C₂²	1	1	yes	characteristic
12	#11926307	—	2	1	no	—
13	#11926307	—	2	1	no	—
14	#11926292	—	2	2	no	—
15	#11926289	—	2	2	no	—
16	C₂×C₁₉×#108	—	2	1	no	—
17	C₂×C₁₉×#108	—	2	1	no	—
18	C₁₉×#423	C₂²	1	1	yes	characteristic
19	C₁₉×#423	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
21	C₂²×Dic₃₈	—	2	1	no	—
22	C₂×M₁₆×C₁₉	—	2	1	no	—
23	C₂×M₁₆×C₁₉	—	2	1	no	—
24	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×C₄⋊Dic₁₉	—	2	1	no	—
28	C₂×C₄⋊Dic₁₉	—	2	1	no	—
29	C₂×C₄⋊Dic₁₉	—	2	1	no	—
30	#10597315	—	2	1	no	—
31	#10597315	—	2	1	no	—
32	#10597315	—	2	1	no	—
33	#10597315	D₄	1	2	yes	—
34	C₁₉×#108	—	4	2	no	—
35	C₁₉×#108	—	4	2	no	—
36	C₁₉×C₄⋊C₈	—	2	1	no	—
37	C₁₉×C₄⋊C₈	—	2	1	no	—
38	C₁₉×C₄⋊C₈	—	2	1	no	—
39	C₁₉×C₄⋊C₈	—	2	1	no	—
40	C₁₉×#97	—	2	1	no	—
41	C₁₉×#97	—	2	1	no	—
42	C₁₉⋊#95	—	2	1	no	—
43	C₁₉⋊#95	—	2	1	no	—
44	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
45	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
48	C₄×C₁₉⋊C₈	—	2	1	no	—
49	C₄×C₁₉⋊C₈	—	2	1	no	—
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
53	C₂²×Dic₁₉	—	4	1	no	—
54	C₂²×Dic₁₉	—	4	1	no	—
55	C₂×Dic₃₈	—	2	2	no	—
56	C₂×Dic₃₈	—	4	1	no	—
57	C₂×Dic₃₈	—	8	2	no	—
58	M₁₆×C₁₉	—	4	1	no	—
59	M₁₆×C₁₉	—	4	1	no	—
60	M₁₆×C₁₉	—	4	1	no	—
61	M₁₆×C₁₉	—	4	1	no	—
62	C₂×C₈×C₁₉	—	2	1	no	—
63	C₂×C₈×C₁₉	—	2	1	no	—
64	C₂×C₈×C₁₉	—	2	1	no	—
65	C₂×C₈×C₁₉	—	2	1	no	—
66	C₂×C₈×C₁₉	—	4	1	no	—
67	C₂×C₈×C₁₉	—	4	1	no	—
68	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
69	C₂×C₈×C₁₉	Q₁₆	1	2	yes	—
70	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₁₉	#41	1	1	yes	characteristic
72	C₄²×C₁₉	#41	1	1	yes	characteristic
73	C₄²×C₁₉	#41	1	1	yes	characteristic
74	C₄⋊Dic₁₉	—	2	2	no	—
75	C₄⋊Dic₁₉	—	2	2	no	—
76	C₄⋊Dic₁₉	—	4	1	no	—
77	C₄⋊Dic₁₉	—	4	1	no	—
78	C₄⋊Dic₁₉	—	4	1	no	—
79	C₄⋊Dic₁₉	—	4	1	no	—
80	C₂×C₁₉⋊C₈	—	4	1	no	—
81	C₂×C₁₉⋊C₈	—	4	1	no	—
82	#10633	—	19	1	no	maximal, Sylow
83	C₂³×C₁₉	#124	1	1	yes	characteristic
84	C₂×C₄×C₁₉	—	4	1	no	—
85	C₂×C₄×C₁₉	—	4	1	no	—
86	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
89	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
92	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
93	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
94	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
96	C₂×Dic₁₉	—	4	2	no	—
97	C₂×Dic₁₉	—	8	2	no	—
98	C₂×Dic₁₉	—	8	1	no	—
99	C₂×Dic₁₉	—	8	1	no	—
100	C₂×Dic₁₉	—	8	1	no	—
101	Dic₃₈	—	8	2	no	—
102	Dic₃₈	—	8	2	no	—
103	C₈×C₁₉	—	2	2	no	—
104	C₈×C₁₉	—	2	2	no	—
105	C₈×C₁₉	—	8	1	no	—
106	C₈×C₁₉	—	8	1	no	—
107	C₁₉⋊C₈	—	8	1	no	—
108	C₁₉⋊C₈	—	8	1	no	—
109	#1993	—	19	1	no	—
110	#1849	D₁₉	1	1	yes	characteristic
111	#1549	—	19	1	no	—
112	#1548	—	19	1	no	—
113	#1286	—	19	1	no	—
114	#1286	—	19	1	no	—
115	#1281	—	19	1	no	—
116	C₂²×C₁₉	—	2	1	no	—
117	C₂²×C₁₉	—	2	1	no	—
118	C₂²×C₁₉	#397	1	1	yes	characteristic
119	C₂²×C₁₉	#487	1	1	yes	characteristic
120	C₂²×C₁₉	#489	1	1	yes	characteristic
121	C₄×C₁₉	—	2	1	no	—
122	C₄×C₁₉	—	2	1	no	—
123	C₄×C₁₉	—	2	1	no	—
124	C₄×C₁₉	—	2	1	no	—
125	C₄×C₁₉	#460	1	1	yes	characteristic
126	C₄×C₁₉	#462	1	1	yes	characteristic
127	C₄×C₁₉	#483	1	1	yes	characteristic
128	C₄×C₁₉	#484	1	1	yes	characteristic
129	Dic₁₉	—	8	2	no	—
130	Dic₁₉	—	16	1	no	—
131	C₂×C₄⋊Q₈	—	19	1	no	—
132	#431	—	19	1	no	—
133	#431	—	19	1	no	—
134	C₂×#108	—	2	1	no	—
135	C₂×#108	—	2	1	no	—
136	#423	C₂×D₁₉	1	1	yes	characteristic
137	#423	C₂×D₁₉	1	1	yes	characteristic
138	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
139	#382	—	19	1	no	—
140	#340	—	38	1	no	—
141	#340	—	38	1	no	—
142	#333	—	38	2	no	—
143	#332	—	38	2	no	—
144	C₂×C₁₉	—	2	1	no	—
145	C₂×C₁₉	—	2	1	no	—
146	C₂×C₁₉	#2072	1	1	yes	characteristic
147	C₂×C₁₉	#2081	1	1	yes	characteristic
148	C₂×C₁₉	#2082	1	1	yes	characteristic
149	C₂²×Q₈	—	38	1	no	—
150	C₂×M₁₆	—	2	1	no	—
151	C₂×M₁₆	—	2	1	no	—
152	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
153	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
154	C₄⋊Q₈	—	19	2	no	—
155	C₄⋊Q₈	—	38	1	no	—
156	C₄⋊Q₈	—	38	1	no	—
157	C₄⋊Q₈	—	38	1	no	—
158	C₂×C₄⋊C₄	—	38	1	no	—
159	C₂×C₄⋊C₄	—	38	1	no	—
160	C₂×C₄⋊C₄	—	38	1	no	—
161	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
162	#108	—	4	2	no	—
163	#108	—	4	2	no	—
164	C₄⋊C₈	—	2	1	no	—
165	C₄⋊C₈	—	2	1	no	—
166	C₄⋊C₈	—	2	1	no	—
167	C₄⋊C₈	—	2	1	no	—
168	C₄⋊C₈	—	38	1	no	—
169	C₄⋊C₈	—	38	1	no	—
170	C₂²⋊C₈	—	38	1	no	—
171	C₂²⋊C₈	—	38	1	no	—
172	#97	—	2	1	no	—
173	#97	—	2	1	no	—
174	C₄×C₈	—	38	1	no	—
175	C₄×C₈	—	38	1	no	—
176	#95	—	38	1	no	—
177	#95	—	38	1	no	—
178	C₁₉	#10633	1	1	yes	characteristic, complemented, Sylow
179	C₂×Q₈	—	38	2	no	—
180	C₂×Q₈	—	76	1	no	—
181	C₂×Q₈	—	152	2	no	—
182	C₂²×C₄	—	76	1	no	—
183	C₂²×C₄	—	76	1	no	—
184	C₂²×C₄	#64545	1	1	yes	characteristic
185	C₂²×C₄	#64545	1	1	yes	characteristic
186	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
187	M₁₆	—	4	1	no	—
188	M₁₆	—	4	1	no	—
189	M₁₆	—	4	1	no	—
190	M₁₆	—	4	1	no	—
191	C₂×C₈	—	2	1	no	—
192	C₂×C₈	—	2	1	no	—
193	C₂×C₈	—	2	1	no	—
194	C₂×C₈	—	2	1	no	—
195	C₂×C₈	—	4	1	no	—
196	C₂×C₈	—	4	1	no	—
197	C₂×C₈	—	76	1	no	—
198	C₂×C₈	—	76	1	no	—
199	C₂×C₈	#64526	1	2	yes	—
200	C₂×C₈	#64528	1	2	yes	—
201	C₄⋊C₄	—	38	2	no	—
202	C₄⋊C₄	—	38	2	no	—
203	C₄⋊C₄	—	76	1	no	—
204	C₄⋊C₄	—	76	1	no	—
205	C₄⋊C₄	—	76	1	no	—
206	C₄⋊C₄	—	76	1	no	—
207	C₄²	#64541	1	1	yes	characteristic
208	C₄²	#64541	1	1	yes	characteristic
209	C₄²	D₄×D₁₉	1	1	yes	characteristic
210	C₄²	#64543	1	1	yes	characteristic
211	C₂³	#10597393	1	1	yes	characteristic
212	Q₈	—	152	2	no	—
213	Q₈	—	152	2	no	—
214	C₂×C₄	—	4	1	no	—
215	C₂×C₄	—	4	1	no	—
216	C₂×C₄	—	76	2	no	—
217	C₂×C₄	—	152	1	no	—
218	C₂×C₄	—	152	1	no	—
219	C₂×C₄	—	152	1	no	—
220	C₂×C₄	—	152	2	no	—
221	C₂×C₄	#10597340	1	1	yes	characteristic
222	C₂×C₄	#10597340	1	1	yes	characteristic
223	C₂×C₄	#10597344	1	1	yes	characteristic
224	C₂×C₄	#10597344	1	1	yes	characteristic
225	C₂×C₄	#10597375	1	1	yes	characteristic
226	C₂×C₄	#10597378	1	1	yes	characteristic
227	C₂×C₄	C₂×#64526	1	1	yes	characteristic
228	C₂×C₄	#10597384	1	1	yes	characteristic
229	C₂×C₄	#10597388	1	1	yes	characteristic
230	C₂×C₄	C₂×#64528	1	1	yes	characteristic
231	C₈	—	2	2	no	—
232	C₈	—	2	2	no	—
233	C₈	—	8	1	no	—
234	C₈	—	8	1	no	—
235	C₈	—	152	1	no	—
236	C₈	—	152	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	1	no	—
239	C₂²	#11926470	1	1	yes	characteristic
240	C₂²	#11926896	1	1	yes	characteristic
241	C₂²	#11926906	1	1	yes	characteristic
242	C₄	—	2	1	no	—
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	2	1	no	—
246	C₄	—	304	1	no	—
247	C₄	—	152	2	no	—
248	C₄	#11926741	1	1	yes	characteristic
249	C₄	#11926751	1	1	yes	characteristic
250	C₄	#11926874	1	1	yes	characteristic
251	C₄	#11926879	1	1	yes	characteristic
252	C₂	—	2	1	no	—
253	C₂	—	2	1	no	—
254	C₂	#14565044	1	1	yes	characteristic
255	C₂	#14565093	1	1	yes	characteristic
256	C₂	#14565100	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564608

C₂

yes

maximal, characteristic

#14562321

C₂

yes

maximal, characteristic

#14562317

C₂

yes

maximal, characteristic

#14561495

C₂

yes

maximal, characteristic

#14561495

C₂

yes

maximal, characteristic

#14561480

C₂

yes

maximal, characteristic

C₁₉×#1849

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

characteristic

#11926597

C₂²

yes

characteristic

#11926597

C₂²

yes

characteristic

#11926410

C₂²

yes

—

—

—

—

C₂×C₁₉×#108

—

C₂×C₁₉×#108

—

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂²×Dic₃₈

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

—

—

—

D₄

yes

—

C₁₉×#108

—

C₁₉×#108

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#97

—

C₁₉×#97

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂×D₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₂×C₈×C₁₉

Q₁₆

yes

—

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

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

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₁₆

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

100

C₂×Dic₁₉

—

101

Dic₃₈

—

102

Dic₃₈

—

103

C₈×C₁₉

—

104

C₈×C₁₉

—

105

C₈×C₁₉

—

106

C₈×C₁₉

—

107

C₁₉⋊C₈

—

108

C₁₉⋊C₈

—

109

#1993

—

110

#1849

D₁₉

yes

characteristic

111

#1549

—

112

#1548

—

113

#1286

—

114

#1286

—

115

#1281

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

#397

yes

characteristic

119

C₂²×C₁₉

#487

yes

characteristic

120

C₂²×C₁₉

#489

yes

characteristic

121

C₄×C₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

#460

yes

characteristic

126

C₄×C₁₉

#462

yes

characteristic

127

C₄×C₁₉

#483

yes

characteristic

128

C₄×C₁₉

#484

yes

characteristic

129

Dic₁₉

—

130

Dic₁₉

—

131

C₂×C₄⋊Q₈

—

132

#431

—

133

#431

—

134

C₂×#108

—

135

C₂×#108

—

136

#423

C₂×D₁₉

yes

characteristic

137

#423

C₂×D₁₉

yes

characteristic

138

C₂×#97

C₂×D₁₉

yes

characteristic

139

#382

—

140

#340

—

141

#340

—

142

#333

—

143

#332

—

144

C₂×C₁₉

—

145

C₂×C₁₉

—

146

C₂×C₁₉

#2072

yes

characteristic

147

C₂×C₁₉

#2081

yes

characteristic

148

C₂×C₁₉

#2082

yes

characteristic

149

C₂²×Q₈

—

150

C₂×M₁₆

—

151

C₂×M₁₆

—

152

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

153

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

154

C₄⋊Q₈

—

155

C₄⋊Q₈

—

156

C₄⋊Q₈

—

157

C₄⋊Q₈

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄²

C₂²×D₁₉

yes

characteristic

162

#108

—

163

#108

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

C₄⋊C₈

—

168

C₄⋊C₈

—

169

C₄⋊C₈

—

170

C₂²⋊C₈

—

171

C₂²⋊C₈

—

172

#97

—

173

#97

—

174

C₄×C₈

—

175

C₄×C₈

—

176

#95

—

177

#95

—

178

C₁₉

#10633

yes

characteristic, complemented, Sylow

179

C₂×Q₈

—

180

C₂×Q₈

—

181

C₂×Q₈

—

152

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

#64545

yes

characteristic

185

C₂²×C₄

#64545

yes

characteristic

186

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

187

M₁₆

—

188

M₁₆

—

189

M₁₆

—

190

M₁₆

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

#64526

yes

—

200

C₂×C₈

#64528

yes

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄²

#64541

yes

characteristic

208

C₄²

#64541

yes

characteristic

209

C₄²

D₄×D₁₉

yes

characteristic

210

C₄²

#64543

yes

characteristic

211

C₂³

#10597393

yes

characteristic

212

Q₈

—

152

—

213

Q₈

—

152

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

152

—

218

C₂×C₄

—

152

—

219

C₂×C₄

—

152

—

220

C₂×C₄

—

152

—

221

C₂×C₄

#10597340

yes

characteristic

222

C₂×C₄

#10597340

yes

characteristic

223

C₂×C₄

#10597344

yes

characteristic

224

C₂×C₄

#10597344

yes

characteristic

225

C₂×C₄

#10597375

yes

characteristic

226

C₂×C₄

#10597378

yes

characteristic

227

C₂×C₄

C₂×#64526

yes

characteristic

228

C₂×C₄

#10597384

yes

characteristic

229

C₂×C₄

#10597388

yes

characteristic

230

C₂×C₄

C₂×#64528

yes

characteristic

231

C₈

—

232

C₈

—

233

C₈

—

234

C₈

—

235

C₈

—

152

—

236

C₈

—

152

—

237

C₂²

—

238

C₂²

—

239

C₂²

#11926470

yes

characteristic

240

C₂²

#11926896

yes

characteristic

241

C₂²

#11926906

yes

characteristic

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

304

—

247

C₄

—

152

—

248

C₄

#11926741

yes

characteristic

249

C₄

#11926751

yes

characteristic

250

C₄

#11926874

yes

characteristic

251

C₄

#11926879

yes

characteristic

252

C₂

—

253

C₂

—

254

C₂

#14565044

yes

characteristic

255

C₂

#14565093

yes

characteristic

256

C₂

#14565100

yes

characteristic

	subgroup	G/H
center	C₂²	#11926470
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1849	C₂
socle	C₂²×C₁₉	#397
prime radical	C₂³×C₁₉	#124
hypercenter	#1849	D₁₉
hypocenter	C₁₉	#10633
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1849

subgroup

G/H

center

C₂²

#11926470

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1849

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1849

N	H ≅ G/N	type
178. C₁₉	#10633	semidirect

H ≅ G/N

type

178. C₁₉

#10633

semidirect

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

subgroup	index
#14564608	2
#14562321	2
#14562317	2
#14561495	2
#14561480	2
C₁₉×#1849	2
#10633	19

subgroup

index

C₁₉×#1849

Subgroups — #18087338

Conjugacy classes of subgroups

Complements

Maximal subgroups