Group #25014474 — subgroups

Subgroups — #25014474

Order 11008.

320 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 99 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×#14582723	C₂	1	1	yes	maximal, characteristic
2	#19136315	C₂	1	1	yes	maximal, characteristic
3	#19135467	C₂	1	1	yes	maximal, characteristic
4	#19134482	C₂	1	1	yes	maximal, characteristic
5	#19132701	C₂	1	1	yes	maximal, characteristic
6	#19132674	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄₃×#362	C₂	1	1	yes	maximal, characteristic
8	C₂×#13063265	C₂²	1	1	yes	characteristic
9	#14582937	C₂²	1	1	yes	characteristic
10	C₂×#13063257	C₂²	1	1	yes	characteristic
11	C₂×#13063249	—	2	1	no	—
12	#14582857	—	2	1	no	—
13	C₂×#13063235	C₂²	1	1	yes	characteristic
14	#14582806	—	2	1	no	—
15	#14582723	—	2	2	no	—
16	#14582703	C₄	1	4	yes	complemented
17	#14582660	—	2	1	no	—
18	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×M₃₂×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
21	C₄₃×#362	—	2	2	no	—
22	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
23	#13063284	—	2	1	no	—
24	C₂×C₄⋊Dic₄₃	—	2	1	no	—
25	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
26	#13063265	—	2	1	no	—
27	#13063265	—	2	1	no	—
28	C₂×C₄₃⋊C₁₆	C₂×C₄	1	2	yes	—
29	#13063259	C₂×C₄	1	2	yes	—
30	#13063257	—	2	1	no	—
31	#13063257	—	2	1	no	—
32	#13063257	—	2	1	no	—
33	#13063249	—	4	2	no	—
34	#13063235	—	2	1	no	—
35	#13063235	—	2	1	no	—
36	#13063235	—	4	1	no	—
37	C₈×Dic₄₃	—	4	1	no	—
38	C₄₃⋊#95	—	4	2	no	—
39	C₂²×Q₈×C₄₃	—	2	1	no	—
40	C₂×Q₁₆×C₄₃	—	2	1	no	—
41	C₂×Q₁₆×C₄₃	—	2	1	no	—
42	C₂×Q₁₆×C₄₃	—	2	1	no	—
43	C₂×Q₁₆×C₄₃	—	2	1	no	—
44	C₂×Q₁₆×C₄₃	—	2	1	no	—
45	C₂×Q₁₆×C₄₃	C₂×C₄	1	2	yes	—
46	C₂×M₁₆×C₄₃	—	2	1	no	—
47	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
48	M₃₂×C₄₃	—	2	1	no	—
49	M₃₂×C₄₃	—	2	1	no	—
50	C₂×C₁₆×C₄₃	—	2	1	no	—
51	#108×C₄₃	—	2	1	no	—
52	#108×C₄₃	D₄	1	2	yes	—
53	C₂×Q₈×C₄₃	—	2	2	no	—
54	C₂×Q₈×C₄₃	—	4	1	no	—
55	C₂×Q₈×C₄₃	—	4	1	no	—
56	C₂×Q₈×C₄₃	—	4	1	no	—
57	C₂×Q₈×C₄₃	—	4	1	no	—
58	C₂×Q₈×C₄₃	—	4	1	no	—
59	C₂²×C₄×C₄₃	—	4	1	no	—
60	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
61	C₂²×Dic₄₃	—	2	1	no	—
62	C₂²×Dic₄₃	—	4	1	no	—
63	Q₁₆×C₄₃	—	2	2	no	—
64	Q₁₆×C₄₃	—	2	2	no	—
65	Q₁₆×C₄₃	—	4	1	no	—
66	Q₁₆×C₄₃	—	4	1	no	—
67	M₁₆×C₄₃	—	2	2	no	—
68	M₁₆×C₄₃	—	4	1	no	—
69	C₂×C₈×C₄₃	—	4	1	no	—
70	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
73	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
74	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
75	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
76	C₂²⋊Dic₄₃	—	4	1	no	—
77	C₄⋊Dic₄₃	—	2	2	no	—
78	C₄⋊Dic₄₃	—	4	1	no	—
79	C₄⋊Dic₄₃	—	4	1	no	—
80	C₄×Dic₄₃	—	2	1	no	—
81	C₄×Dic₄₃	—	2	1	no	—
82	C₄×Dic₄₃	—	4	1	no	—
83	C₂×C₄₃⋊C₈	—	2	1	no	—
84	C₂×C₄₃⋊C₈	—	2	1	no	—
85	C₂×C₄₃⋊C₈	SD₁₆	1	2	yes	—
86	C₁₆×C₄₃	—	4	1	no	—
87	C₄₃⋊C₁₆	—	2	2	no	—
88	C₂³×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
89	Q₈×C₄₃	—	4	2	no	—
90	Q₈×C₄₃	—	4	2	no	—
91	Q₈×C₄₃	—	8	1	no	—
92	Q₈×C₄₃	—	8	1	no	—
93	C₂×C₄×C₄₃	—	4	2	no	—
94	C₂×C₄×C₄₃	—	8	1	no	—
95	C₂×C₄×C₄₃	—	8	1	no	—
96	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
97	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
98	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
99	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
100	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
101	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
102	C₂×Dic₄₃	—	4	2	no	—
103	C₂×Dic₄₃	—	4	2	no	—
104	C₂×Dic₄₃	—	4	1	no	—
105	C₂×Dic₄₃	—	8	2	no	—
106	C₂×Dic₄₃	—	8	1	no	—
107	C₈×C₄₃	—	4	2	no	—
108	C₈×C₄₃	#117	1	1	yes	characteristic
109	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
110	C₈×C₄₃	#124	1	1	yes	characteristic
111	C₈×C₄₃	#126	1	1	yes	characteristic
112	C₄₃⋊C₈	—	2	2	no	—
113	#13141	—	43	1	no	maximal, Sylow
114	C₂²×C₄₃	—	2	2	no	—
115	C₂²×C₄₃	#442	1	1	yes	characteristic
116	C₂²×C₄₃	#460	1	1	yes	characteristic
117	C₂²×C₄₃	#482	1	1	yes	characteristic
118	C₄×C₄₃	—	8	2	no	—
119	C₄×C₄₃	#388	1	1	yes	characteristic
120	C₄×C₄₃	C₄×SD₁₆	1	1	yes	characteristic
121	C₄×C₄₃	#463	1	1	yes	characteristic
122	C₄×C₄₃	#481	1	1	yes	characteristic
123	Dic₄₃	—	8	1	no	—
124	Dic₄₃	—	8	2	no	—
125	Dic₄₃	—	16	1	no	—
126	C₂×#365	—	43	1	no	—
127	C₂×#362	D₄₃	1	1	yes	characteristic
128	#2141	—	43	1	no	—
129	#1971	—	43	1	no	—
130	#1773	—	43	1	no	—
131	#1386	—	43	1	no	—
132	#1375	—	43	1	no	—
133	C₂×C₄₃	—	2	1	no	—
134	C₂×C₄₃	—	2	1	no	—
135	C₂×C₄₃	#1926	1	1	yes	characteristic
136	C₂×C₄₃	#2180	1	2	yes	—
137	C₂²×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
138	C₂×M₃₂	—	43	1	no	—
139	C₂×M₃₂	C₂×D₄₃	1	1	yes	characteristic
140	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
141	#427	—	43	1	no	—
142	C₂×#106	—	43	1	no	—
143	C₂×#103	—	86	1	no	—
144	#405	—	86	1	no	—
145	C₂×#97	—	43	1	no	—
146	#391	—	86	1	no	—
147	#365	—	86	2	no	—
148	#362	—	2	2	no	—
149	#358	—	43	4	no	—
150	#339	—	86	1	no	—
151	C₄₃	#13141	1	1	yes	characteristic, complemented, Sylow
152	C₂²×Q₈	—	2	1	no	—
153	C₂×Q₁₆	—	2	1	no	—
154	C₂×Q₁₆	—	2	1	no	—
155	C₂×Q₁₆	—	2	1	no	—
156	C₂×Q₁₆	—	2	1	no	—
157	C₂×Q₁₆	—	2	1	no	—
158	C₂×Q₁₆	C₄×D₄₃	1	2	yes	—
159	C₂×M₁₆	—	2	1	no	—
160	C₂²×C₈	—	43	1	no	—
161	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
162	#117	—	86	1	no	—
163	C₂×C₄⋊C₄	—	86	1	no	—
164	C₂×C₄²	—	43	1	no	—
165	M₃₂	—	2	1	no	—
166	M₃₂	—	2	1	no	—
167	M₃₂	—	86	1	no	—
168	M₃₂	—	86	1	no	—
169	C₂×C₁₆	—	2	1	no	—
170	C₂×C₁₆	—	43	2	no	—
171	#108	—	2	1	no	—
172	#108	C₂²⋊D₄₃	1	2	yes	—
173	#107	—	43	2	no	—
174	#106	—	86	1	no	—
175	#106	—	86	1	no	—
176	#106	—	86	1	no	—
177	#103	—	172	2	no	—
178	#97	—	86	1	no	—
179	#97	—	86	1	no	—
180	#97	—	172	1	no	—
181	C₄×C₈	—	172	1	no	—
182	#95	—	172	2	no	—
183	C₂×Q₈	—	2	2	no	—
184	C₂×Q₈	—	4	1	no	—
185	C₂×Q₈	—	4	1	no	—
186	C₂×Q₈	—	4	1	no	—
187	C₂×Q₈	—	4	1	no	—
188	C₂×Q₈	—	4	1	no	—
189	C₂²×C₄	—	4	1	no	—
190	C₂²×C₄	—	86	1	no	—
191	C₂²×C₄	—	172	1	no	—
192	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
193	Q₁₆	—	2	2	no	—
194	Q₁₆	—	2	2	no	—
195	Q₁₆	—	4	1	no	—
196	Q₁₆	—	4	1	no	—
197	M₁₆	—	2	2	no	—
198	M₁₆	—	4	1	no	—
199	C₂×C₈	—	4	1	no	—
200	C₂×C₈	—	43	2	no	—
201	C₂×C₈	—	86	1	no	—
202	C₂×C₈	—	86	1	no	—
203	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
204	C₂×C₈	#10621898	1	1	yes	characteristic
205	C₂×C₈	#10621900	1	1	yes	characteristic
206	C₂×C₈	#10621900	1	1	yes	characteristic
207	C₂×C₈	#10621900	1	1	yes	characteristic
208	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
209	C₄⋊C₄	—	86	2	no	—
210	C₄⋊C₄	—	172	1	no	—
211	C₄⋊C₄	—	172	1	no	—
212	C₂²⋊C₄	—	172	1	no	—
213	C₄²	—	86	1	no	—
214	C₄²	—	86	1	no	—
215	C₄²	—	172	1	no	—
216	C₁₆	—	4	1	no	—
217	C₁₆	—	86	2	no	—
218	C₂³	#13063352	1	1	yes	characteristic
219	Q₈	—	4	2	no	—
220	Q₈	—	4	2	no	—
221	Q₈	—	8	1	no	—
222	Q₈	—	8	1	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	8	1	no	—
225	C₂×C₄	—	8	1	no	—
226	C₂×C₄	—	344	2	no	—
227	C₂×C₄	—	344	1	no	—
228	C₂×C₄	—	172	2	no	—
229	C₂×C₄	—	172	1	no	—
230	C₂×C₄	—	172	2	no	—
231	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
232	C₂×C₄	#13063297	1	1	yes	characteristic
233	C₂×C₄	#13063307	1	1	yes	characteristic
234	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
235	C₂×C₄	#13063344	1	1	yes	characteristic
236	C₂×C₄	#13063349	1	1	yes	characteristic
237	C₈	—	4	2	no	—
238	C₈	—	86	2	no	—
239	C₈	#13063281	1	1	yes	characteristic
240	C₈	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
241	C₈	#13063312	1	1	yes	characteristic
242	C₈	#13063318	1	1	yes	characteristic
243	C₂²	—	2	2	no	—
244	C₂²	#14583008	1	1	yes	characteristic
245	C₂²	#14583097	1	1	yes	characteristic
246	C₂²	#14583221	1	1	yes	characteristic
247	C₄	—	8	2	no	—
248	C₄	—	344	1	no	—
249	C₄	—	344	2	no	—
250	C₄	—	688	1	no	—
251	C₄	#14582793	1	1	yes	characteristic
252	C₄	#14582990	1	1	yes	characteristic
253	C₄	#14583112	1	1	yes	characteristic
254	C₄	#14583216	1	1	yes	characteristic
255	C₂	—	2	1	no	—
256	C₂	—	2	1	no	—
257	C₂	#19135225	1	1	yes	characteristic
258	C₂	#19136489	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14582723

C₂

yes

maximal, characteristic

#19136315

C₂

yes

maximal, characteristic

#19135467

C₂

yes

maximal, characteristic

#19134482

C₂

yes

maximal, characteristic

#19132701

C₂

yes

maximal, characteristic

#19132674

C₂

yes

maximal, characteristic

C₂×C₄₃×#362

C₂

yes

maximal, characteristic

C₂×#13063265

C₂²

yes

characteristic

#14582937

C₂²

yes

characteristic

C₂×#13063257

C₂²

yes

—

—

C₂²

yes

—

—

C₄

yes

complemented

#14582660

—

C₂²×Q₁₆×C₄₃

C₂²

yes

characteristic

C₂×M₃₂×C₄₃

C₂²

yes

characteristic

C₂×#108×C₄₃

C₂²

yes

characteristic

C₄₃×#362

—

C₂²×C₄₃⋊C₈

D₄

yes

characteristic

#13063284

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄×Dic₄₃

D₄

yes

characteristic

#13063265

—

#13063265

—

C₂×C₄₃⋊C₁₆

C₂×C₄

yes

—

#13063259

C₂×C₄

yes

—

—

—

—

—

—

—

—

C₈×Dic₄₃

—

C₄₃⋊#95

—

C₂²×Q₈×C₄₃

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

C₂×C₄

yes

—

C₂×M₁₆×C₄₃

—

C₂²×C₈×C₄₃

C₂³

yes

characteristic

M₃₂×C₄₃

—

M₃₂×C₄₃

—

C₂×C₁₆×C₄₃

—

#108×C₄₃

—

#108×C₄₃

D₄

yes

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

C₂×C₈×C₄₃

yes

C₂×C₈×C₄₃

yes

C₂×C₈×C₄₃

yes

C₂×C₈×C₄₃

yes

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

SD₁₆

yes

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

AGL(1,ℤ/8)

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄×D₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

C₂×SD₁₆

yes

characteristic

100

C₂×C₄×C₄₃

#135

yes

characteristic

101

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

characteristic

102

C₂×Dic₄₃

—

103

C₂×Dic₄₃

—

104

C₂×Dic₄₃

—

105

C₂×Dic₄₃

—

106

C₂×Dic₄₃

—

107

C₈×C₄₃

—

108

C₈×C₄₃

#117

yes

characteristic

109

C₈×C₄₃

C₄×D₄

yes

characteristic

110

C₈×C₄₃

#124

yes

characteristic

111

C₈×C₄₃

#126

yes

characteristic

112

C₄₃⋊C₈

—

113

#13141

—

maximal, Sylow

114

C₂²×C₄₃

—

115

C₂²×C₄₃

#442

yes

characteristic

116

C₂²×C₄₃

#460

yes

characteristic

117

C₂²×C₄₃

#482

yes

characteristic

118

C₄×C₄₃

—

119

C₄×C₄₃

#388

yes

characteristic

120

C₄×C₄₃

C₄×SD₁₆

yes

characteristic

121

C₄×C₄₃

#463

yes

characteristic

122

C₄×C₄₃

#481

yes

characteristic

123

Dic₄₃

—

124

Dic₄₃

—

125

Dic₄₃

—

126

C₂×#365

—

127

C₂×#362

D₄₃

yes

characteristic

128

#2141

—

129

#1971

—

130

#1773

—

131

#1386

—

132

#1375

—

133

C₂×C₄₃

—

134

C₂×C₄₃

—

135

C₂×C₄₃

#1926

yes

characteristic

136

C₂×C₄₃

#2180

yes

—

137

C₂²×Q₁₆

C₂×D₄₃

yes

characteristic

138

C₂×M₃₂

—

139

C₂×M₃₂

C₂×D₄₃

yes

characteristic

140

C₂×#108

C₂×D₄₃

yes

characteristic

141

#427

—

142

C₂×#106

—

143

C₂×#103

—

144

#405

—

145

C₂×#97

—

146

#391

—

147

#365

—

148

#362

—

149

#358

—

150

#339

—

151

C₄₃

#13141

yes

characteristic, complemented, Sylow

152

C₂²×Q₈

—

153

C₂×Q₁₆

—

154

C₂×Q₁₆

—

155

C₂×Q₁₆

—

156

C₂×Q₁₆

—

157

C₂×Q₁₆

—

158

C₂×Q₁₆

C₄×D₄₃

yes

—

159

C₂×M₁₆

—

160

C₂²×C₈

—

161

C₂²×C₈

C₂²×D₄₃

yes

characteristic

162

#117

—

163

C₂×C₄⋊C₄

—

164

C₂×C₄²

—

165

M₃₂

—

166

M₃₂

—

167

M₃₂

—

168

M₃₂

—

169

C₂×C₁₆

—

170

C₂×C₁₆

—

171

#108

—

172

#108

C₂²⋊D₄₃

yes

—

173

#107

—

174

#106

—

175

#106

—

176

#106

—

177

#103

—

172

—

178

#97

—

179

#97

—

180

#97

—

172

—

181

C₄×C₈

—

172

—

182

#95

—

172

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

172

—

192

C₂²×C₄

D₄×D₄₃

yes

characteristic

193

Q₁₆

—

194

Q₁₆

—

195

Q₁₆

—

196

Q₁₆

—

197

M₁₆

—

198

M₁₆

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

204

C₂×C₈

#10621898

yes

characteristic

205

C₂×C₈

#10621900

yes

characteristic

206

C₂×C₈

#10621900

yes

characteristic

207

C₂×C₈

#10621900

yes

characteristic

208

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

209

C₄⋊C₄

—

210

C₄⋊C₄

—

172

—

211

C₄⋊C₄

—

172

—

212

C₂²⋊C₄

—

172

—

213

C₄²

—

214

C₄²

—

215

C₄²

—

172

—

216

C₁₆

—

217

C₁₆

—

218

C₂³

#13063352

yes

characteristic

219

Q₈

—

220

Q₈

—

221

Q₈

—

222

Q₈

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

344

—

227

C₂×C₄

—

344

—

228

C₂×C₄

—

172

—

229

C₂×C₄

—

172

—

230

C₂×C₄

—

172

—

231

C₂×C₄

(C₂²⋊D₄₃)⋊C₄

yes

characteristic

232

C₂×C₄

#13063297

yes

characteristic

233

C₂×C₄

#13063307

yes

characteristic

234

C₂×C₄

SD₁₆×D₄₃

yes

characteristic

235

C₂×C₄

#13063344

yes

characteristic

236

C₂×C₄

#13063349

yes

characteristic

237

C₈

—

238

C₈

—

239

C₈

#13063281

yes

characteristic

240

C₈

C₄×C₂²⋊D₄₃

yes

characteristic

241

C₈

#13063312

yes

characteristic

242

C₈

#13063318

yes

characteristic

243

C₂²

—

244

C₂²

#14583008

yes

characteristic

245

C₂²

#14583097

yes

characteristic

246

C₂²

#14583221

yes

characteristic

247

C₄

—

248

C₄

—

344

—

249

C₄

—

344

—

250

C₄

—

688

—

251

C₄

#14582793

yes

characteristic

252

C₄

#14582990

yes

characteristic

253

C₄

#14583112

yes

characteristic

254

C₄

#14583216

yes

characteristic

255

C₂

—

256

C₂

—

257

C₂

#19135225

yes

characteristic

258

C₂

#19136489

yes

—

	subgroup	G/H
center	C₂²	#14583008
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂×C₄₃×#362	C₂
socle	C₂²×C₄₃	#442
prime radical	C₂³×C₄₃	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×#362	D₄₃
hypocenter	C₄₃	#13141
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#362

subgroup

G/H

center

C₂²

#14583008

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₂×C₄₃×#362

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#362

N	H ≅ G/N	type
16. #14582703	C₄	semidirect
151. C₄₃	#13141	semidirect

H ≅ G/N

type

16. #14582703

C₄

semidirect

151. C₄₃

#13141

semidirect

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

subgroup	index
C₂×#14582723	2
#19136315	2
#19135467	2
#19134482	2
#19132701	2
#19132674	2
C₂×C₄₃×#362	2
#13141	43

subgroup

index

C₂×C₄₃×#362

Subgroups — #25014474

Conjugacy classes of subgroups

Complements

Maximal subgroups