Group #25015063 — subgroups

Subgroups — #25015063

Order 11008.

598 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 159 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×#14583276	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582701	C₂	1	4	yes	maximal, complemented
3	C₄×#13063259	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₃₄₄	—	2	1	no	—
6	C₂²×D₃₄₄	C₂²	1	2	yes	—
7	C₂×#13063322	—	2	1	no	—
8	#14583276	—	2	2	no	—
9	#14583276	C₄	1	4	yes	complemented
10	C₂×#13063259	C₂²	1	2	yes	—
11	C₄×C₄⋊Dic₄₃	—	2	1	no	—
12	#14582701	—	2	8	no	—
13	#14582662	—	2	1	no	—
14	C₂²×C₁₆×C₄₃	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×C₄⋊C₁₆	—	2	2	no	—
17	C₂²×D₁₇₂	—	2	2	no	—
18	C₂²×D₁₇₂	—	4	1	no	—
19	C₂²×D₁₇₂	—	4	1	no	—
20	C₂×D₃₄₄	—	2	4	no	—
21	C₂×D₃₄₄	—	2	4	no	—
22	C₂×D₃₄₄	—	2	4	no	—
23	C₂×D₃₄₄	—	2	2	no	—
24	C₂×D₃₄₄	—	4	4	no	—
25	C₂×D₃₄₄	C₂×C₄	1	4	yes	—
26	#13063322	—	2	4	no	—
27	#13063322	—	4	2	no	—
28	C₂×C₄⋊Dic₄₃	—	2	2	no	—
29	C₂×C₄×Dic₄₃	—	4	1	no	—
30	#13063259	—	2	2	no	—
31	#13063259	D₄	1	4	yes	complemented
32	C₄₃⋊#95	—	4	1	no	—
33	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
34	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
35	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
36	C₂×C₁₆×C₄₃	—	2	2	no	—
37	C₂×C₁₆×C₄₃	—	2	4	no	—
38	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
39	C₄×C₈×C₄₃	D₄	1	2	yes	—
40	C₂³×D₄₃	—	4	2	no	—
41	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
42	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
43	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
44	C₂²×Dic₄₃	—	4	2	no	—
45	C₂×D₁₇₂	—	2	4	no	—
46	C₂×D₁₇₂	—	4	4	no	—
47	C₂×D₁₇₂	—	4	4	no	—
48	C₂×D₁₇₂	—	4	2	no	—
49	C₂×D₁₇₂	—	4	4	no	—
50	C₂×D₁₇₂	—	4	4	no	—
51	C₂×D₁₇₂	—	8	4	no	—
52	C₂×D₁₇₂	—	8	2	no	—
53	C₂×D₁₇₂	—	8	2	no	—
54	C₂×C₈×C₄₃	—	2	2	no	—
55	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
56	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
58	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
59	C₂×C₈×C₄₃	#41	1	2	yes	—
60	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
61	C₄²×C₄₃	SD₁₆	1	2	yes	—
62	C₄⋊Dic₄₃	—	2	4	no	—
63	C₄⋊Dic₄₃	—	4	2	no	—
64	C₄×Dic₄₃	—	8	2	no	—
65	D₃₄₄	—	2	8	no	—
66	D₃₄₄	—	4	8	no	—
67	D₃₄₄	—	4	2	no	—
68	D₃₄₄	—	4	2	no	—
69	C₁₆×C₄₃	—	4	2	no	—
70	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
71	C₂²×D₄₃	—	4	4	no	—
72	C₂²×D₄₃	—	8	4	no	—
73	C₂²×D₄₃	—	8	2	no	—
74	C₂²×D₄₃	—	8	2	no	—
75	C₂²×D₄₃	—	8	4	no	—
76	C₂×C₄×C₄₃	—	2	2	no	—
77	C₂×C₄×C₄₃	#102	1	2	yes	—
78	C₂×C₄×C₄₃	#102	1	2	yes	—
79	C₂×C₄×C₄₃	D₁₆	1	2	yes	—
80	C₂×C₄×C₄₃	SD₃₂	1	2	yes	—
81	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₄₃	#121	1	2	yes	—
83	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
84	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
85	C₂×Dic₄₃	—	4	4	no	—
86	C₂×Dic₄₃	—	8	2	no	—
87	C₂×Dic₄₃	—	8	2	no	—
88	D₁₇₂	—	4	4	no	—
89	D₁₇₂	—	4	4	no	—
90	D₁₇₂	—	8	8	no	—
91	D₁₇₂	—	8	8	no	—
92	D₁₇₂	—	8	4	no	—
93	C₈×C₄₃	—	2	2	no	—
94	C₈×C₄₃	C₄×D₄	1	2	yes	—
95	C₈×C₄₃	#124	1	1	yes	characteristic
96	C₈×C₄₃	#127	1	1	yes	characteristic
97	#13252	—	43	1	no	maximal, Sylow
98	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
99	C₂²×C₄₃	#459	1	2	yes	—
100	C₂²×C₄₃	C₂×D₁₆	1	1	yes	characteristic
101	C₂²×C₄₃	C₂×SD₃₂	1	1	yes	characteristic
102	C₂²×C₄₃	#509	1	2	yes	—
103	C₂×D₄₃	—	8	4	no	—
104	C₂×D₄₃	—	8	4	no	—
105	C₂×D₄₃	—	8	4	no	—
106	C₂×D₄₃	—	16	4	no	—
107	C₂×D₄₃	—	16	4	no	—
108	C₄×C₄₃	—	2	2	no	—
109	C₄×C₄₃	#357	1	4	yes	complemented
110	C₄×C₄₃	#390	1	1	yes	characteristic
111	C₄×C₄₃	#418	1	1	yes	characteristic
112	C₄×C₄₃	#460	1	2	yes	—
113	Dic₄₃	—	8	4	no	—
114	C₂×#493	—	43	1	no	—
115	C₂×C₄⋊C₁₆	D₄₃	1	1	yes	characteristic, complemented
116	C₂×#357	—	43	4	no	—
117	C₄×#107	—	43	1	no	—
118	C₂×C₄₃	#1982	1	1	yes	characteristic
119	C₂×C₄₃	C₂×#357	1	1	yes	characteristic
120	C₂×C₄₃	#2140	1	1	yes	characteristic
121	C₂×C₄₃	#2206	1	2	yes	—
122	C₂×C₄₃	#2207	1	2	yes	—
123	D₄₃	—	16	4	no	—
124	C₂²×D₈	—	43	2	no	—
125	C₂²×D₈	—	86	1	no	—
126	C₂×#127	—	86	1	no	—
127	C₂²×C₁₆	C₂×D₄₃	1	2	yes	—
128	#493	—	43	4	no	—
129	#493	—	86	2	no	—
130	C₂×#107	—	43	2	no	—
131	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
132	C₄×C₄⋊C₄	—	86	1	no	—
133	C₄⋊C₁₆	—	2	2	no	—
134	#357	—	86	8	no	—
135	#340	—	86	1	no	—
136	C₄₃	#13252	1	1	yes	characteristic, complemented, Sylow
137	C₂²×D₄	—	86	2	no	—
138	C₂²×D₄	—	172	1	no	—
139	C₂²×D₄	—	172	1	no	—
140	C₂×D₈	—	43	4	no	—
141	C₂×D₈	—	86	4	no	—
142	C₂×D₈	—	86	4	no	—
143	C₂×D₈	—	86	4	no	—
144	C₂×D₈	—	86	2	no	—
145	C₂×D₈	—	172	4	no	—
146	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
147	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
148	#127	—	86	4	no	—
149	#127	—	172	2	no	—
150	C₂×C₄⋊C₄	—	86	2	no	—
151	C₂×C₄²	—	172	1	no	—
152	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
153	C₂×C₁₆	—	2	4	no	—
154	C₂×C₁₆	—	2	2	no	—
155	#107	—	43	4	no	—
156	#107	—	86	2	no	—
157	C₄×C₈	C₄×D₄₃	1	2	yes	—
158	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
159	#95	—	172	1	no	—
160	C₂⁴	—	172	2	no	—
161	C₂×D₄	—	86	4	no	—
162	C₂×D₄	—	344	4	no	—
163	C₂×D₄	—	344	2	no	—
164	C₂×D₄	—	344	2	no	—
165	C₂×D₄	—	172	4	no	—
166	C₂×D₄	—	172	4	no	—
167	C₂×D₄	—	172	4	no	—
168	C₂×D₄	—	172	2	no	—
169	C₂×D₄	—	172	4	no	—
170	C₂²×C₄	—	172	2	no	—
171	C₂²×C₄	D₃₄₄	1	1	yes	characteristic
172	C₂²×C₄	D₃₄₄	1	1	yes	characteristic
173	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
174	D₈	—	86	8	no	—
175	D₈	—	172	8	no	—
176	D₈	—	172	2	no	—
177	D₈	—	172	2	no	—
178	C₂×C₈	—	2	2	no	—
179	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
180	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
181	C₂×C₈	D₄×D₄₃	1	2	yes	—
182	C₂×C₈	#10621902	1	2	yes	—
183	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
184	C₄⋊C₄	—	86	4	no	—
185	C₄⋊C₄	—	172	2	no	—
186	C₄²	—	344	2	no	—
187	C₄²	#10621873	1	2	yes	—
188	C₄²	(C₂×D₄₃)⋊C₄	1	2	yes	—
189	C₁₆	—	4	2	no	—
190	C₂³	—	344	2	no	—
191	C₂³	—	344	2	no	—
192	C₂³	—	344	4	no	—
193	C₂³	—	344	4	no	—
194	C₂³	—	172	4	no	—
195	C₂³	C₂×D₃₄₄	1	1	yes	characteristic
196	D₄	—	344	8	no	—
197	D₄	—	344	4	no	—
198	D₄	—	344	8	no	—
199	D₄	—	172	4	no	—
200	D₄	—	172	4	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	344	2	no	—
203	C₂×C₄	—	344	2	no	—
204	C₂×C₄	—	172	4	no	—
205	C₂×C₄	#13063247	1	2	yes	—
206	C₂×C₄	#13063247	1	2	yes	—
207	C₂×C₄	D₆₈₈	1	2	yes	—
208	C₂×C₄	#13063270	1	2	yes	—
209	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
210	C₂×C₄	#13063300	1	2	yes	—
211	C₂×C₄	C₂×#10621873	1	1	yes	characteristic
212	C₂×C₄	#13063353	1	2	yes	—
213	C₈	—	2	2	no	—
214	C₈	#13063287	1	2	yes	—
215	C₈	#13063314	1	1	yes	characteristic
216	C₈	#13063321	1	1	yes	characteristic
217	C₂²	—	344	4	no	—
218	C₂²	—	344	4	no	—
219	C₂²	—	344	4	no	—
220	C₂²	—	688	4	no	—
221	C₂²	—	688	4	no	—
222	C₂²	C₂×#13063247	1	1	yes	characteristic
223	C₂²	#14583095	1	2	yes	—
224	C₂²	C₂×D₆₈₈	1	1	yes	characteristic
225	C₂²	C₂×#13063270	1	1	yes	characteristic
226	C₂²	#14583337	1	2	yes	—
227	C₄	—	2	2	no	—
228	C₄	—	344	4	no	—
229	C₄	#14582701	1	4	yes	complemented
230	C₄	#14582800	1	1	yes	characteristic
231	C₄	#14582905	1	1	yes	characteristic
232	C₄	#14583100	1	2	yes	—
233	C₂	—	688	4	no	—
234	C₂	#19135521	1	1	yes	characteristic
235	C₂	C₂×#14582701	1	1	yes	characteristic
236	C₂	#19136312	1	1	yes	characteristic
237	C₂	#19136631	1	2	yes	—
238	C₂	#19136636	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14583276

C₂

yes

maximal, characteristic

C₂×#14582701

C₂

yes

maximal, complemented

C₄×#13063259

C₂

yes

maximal, characteristic, complemented

C₂×C₄₃×C₄⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂²×D₃₄₄

—

C₂²×D₃₄₄

C₂²

yes

—

C₂×#13063322

—

#14583276

—

#14583276

C₄

yes

complemented

C₂×#13063259

C₂²

yes

—

C₄×C₄⋊Dic₄₃

—

#14582701

—

#14582662

—

C₂²×C₁₆×C₄₃

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×C₄⋊C₁₆

—

C₂²×D₁₇₂

—

C₂²×D₁₇₂

—

C₂²×D₁₇₂

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

C₂×C₄

yes

—

#13063322

—

#13063322

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄×Dic₄₃

—

#13063259

—

#13063259

D₄

yes

complemented

C₄₃⋊#95

—

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

D₄

yes

—

C₂³×D₄₃

—

C₂²×C₄×C₄₃

D₈

yes

characteristic

C₂²×C₄×C₄₃

D₈

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

#41

yes

—

C₄²×C₄₃

C₂²⋊C₄

yes

—

C₄²×C₄₃

SD₁₆

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

C₁₆×C₄₃

—

C₂³×C₄₃

C₂×D₈

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#102

yes

—

C₂×C₄×C₄₃

#102

yes

—

C₂×C₄×C₄₃

D₁₆

yes

—

C₂×C₄×C₄₃

SD₃₂

yes

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

#121

yes

—

C₂×C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

—

C₈×C₄₃

C₄×D₄

yes

—

C₈×C₄₃

yes

C₈×C₄₃

yes

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

100

C₂²×C₄₃

C₂×D₁₆

yes

characteristic

101

C₂²×C₄₃

C₂×SD₃₂

yes

characteristic

102

C₂²×C₄₃

#509

yes

—

103

C₂×D₄₃

—

104

C₂×D₄₃

—

105

C₂×D₄₃

—

106

C₂×D₄₃

—

107

C₂×D₄₃

—

108

C₄×C₄₃

—

109

C₄×C₄₃

#357

yes

complemented

110

C₄×C₄₃

#390

yes

characteristic

111

C₄×C₄₃

#418

yes

characteristic

112

C₄×C₄₃

#460

yes

—

113

Dic₄₃

—

114

C₂×#493

—

115

C₂×C₄⋊C₁₆

D₄₃

yes

characteristic, complemented

116

C₂×#357

—

117

C₄×#107

—

118

C₂×C₄₃

#1982

yes

characteristic

119

C₂×C₄₃

C₂×#357

yes

characteristic

120

C₂×C₄₃

#2140

yes

characteristic

121

C₂×C₄₃

#2206

yes

—

122

C₂×C₄₃

#2207

yes

—

123

D₄₃

—

124

C₂²×D₈

—

125

C₂²×D₈

—

126

C₂×#127

—

127

C₂²×C₁₆

C₂×D₄₃

yes

—

128

#493

—

129

#493

—

130

C₂×#107

—

131

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

132

C₄×C₄⋊C₄

—

133

C₄⋊C₁₆

—

134

#357

—

135

#340

—

136

C₄₃

#13252

yes

characteristic, complemented, Sylow

137

C₂²×D₄

—

138

C₂²×D₄

—

172

—

139

C₂²×D₄

—

172

—

140

C₂×D₈

—

141

C₂×D₈

—

142

C₂×D₈

—

143

C₂×D₈

—

144

C₂×D₈

—

145

C₂×D₈

—

172

—

146

C₂²×C₈

D₁₇₂

yes

characteristic

147

C₂²×C₈

C₂²×D₄₃

yes

characteristic

148

#127

—

149

#127

—

172

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄²

—

172

—

152

C₂×C₄²

D₁₇₂

yes

characteristic

153

C₂×C₁₆

—

154

C₂×C₁₆

—

155

#107

—

156

#107

—

157

C₄×C₈

C₄×D₄₃

yes

—

158

C₄×C₈

C₂²⋊D₄₃

yes

—

159

#95

—

172

—

160

C₂⁴

—

172

—

161

C₂×D₄

—

162

C₂×D₄

—

344

—

163

C₂×D₄

—

344

—

164

C₂×D₄

—

344

—

165

C₂×D₄

—

172

—

166

C₂×D₄

—

172

—

167

C₂×D₄

—

172

—

168

C₂×D₄

—

172

—

169

C₂×D₄

—

172

—

170

C₂²×C₄

—

172

—

171

C₂²×C₄

D₃₄₄

yes

characteristic

172

C₂²×C₄

D₃₄₄

yes

characteristic

173

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

174

D₈

—

175

D₈

—

172

—

176

D₈

—

172

—

177

D₈

—

172

—

178

C₂×C₈

—

179

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

—

180

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

181

C₂×C₈

D₄×D₄₃

yes

—

182

C₂×C₈

#10621902

yes

—

183

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

184

C₄⋊C₄

—

185

C₄⋊C₄

—

172

—

186

C₄²

—

344

—

187

C₄²

#10621873

yes

—

188

C₄²

(C₂×D₄₃)⋊C₄

yes

—

189

C₁₆

—

190

C₂³

—

344

—

191

C₂³

—

344

—

192

C₂³

—

344

—

193

C₂³

—

344

—

194

C₂³

—

172

—

195

C₂³

C₂×D₃₄₄

yes

characteristic

196

D₄

—

344

—

197

D₄

—

344

—

198

D₄

—

344

—

199

D₄

—

172

—

200

D₄

—

172

—

201

C₂×C₄

—

202

C₂×C₄

—

344

—

203

C₂×C₄

—

344

—

204

C₂×C₄

—

172

—

205

C₂×C₄

#13063247

yes

—

206

C₂×C₄

#13063247

yes

—

207

C₂×C₄

D₆₈₈

yes

—

208

C₂×C₄

#13063270

yes

—

209

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

210

C₂×C₄

#13063300

yes

—

211

C₂×C₄

C₂×#10621873

yes

characteristic

212

C₂×C₄

#13063353

yes

—

213

C₈

—

214

C₈

#13063287

yes

—

215

C₈

#13063314

yes

characteristic

216

C₈

#13063321

yes

characteristic

217

C₂²

—

344

—

218

C₂²

—

344

—

219

C₂²

—

344

—

220

C₂²

—

688

—

221

C₂²

—

688

—

222

C₂²

C₂×#13063247

yes

characteristic

223

C₂²

#14583095

yes

—

224

C₂²

C₂×D₆₈₈

yes

characteristic

225

C₂²

C₂×#13063270

yes

characteristic

226

C₂²

#14583337

yes

—

227

C₄

—

228

C₄

—

344

—

229

C₄

#14582701

yes

complemented

230

C₄

#14582800

yes

characteristic

231

C₄

#14582905

yes

characteristic

232

C₄

#14583100

yes

—

233

C₂

—

688

—

234

C₂

#19135521

yes

characteristic

235

C₂

C₂×#14582701

yes

characteristic

236

C₂

#19136312

yes

characteristic

237

C₂

#19136631

yes

—

238

C₂

#19136636

yes

—

	subgroup	G/H
center	C₂³	C₂×D₃₄₄
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂×C₄₃×C₄⋊C₁₆	C₂
socle	C₂³×C₄₃	C₂×D₈
prime radical	C₂×#14583276	C₂
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×C₄⋊C₁₆	D₄₃
hypocenter	C₄₃	#13252
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

subgroup

G/H

center

C₂³

C₂×D₃₄₄

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₂×C₄₃×C₄⋊C₁₆

C₂

socle

C₂³×C₄₃

C₂×D₈

prime radical

C₂×#14583276

C₂

cosocle

C₂²×C₈×C₄₃

C₂³

hypercenter

C₂×C₄⋊C₁₆

D₄₃

hypocenter

C₄₃

#13252

LCS

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

N	H ≅ G/N	type
2. C₂×#14582701	C₂	semidirect
3. C₄×#13063259	C₂	semidirect
4. C₂×C₄₃×C₄⋊C₁₆	C₂	semidirect
9. #14583276	C₄	semidirect
31. #13063259	D₄	semidirect
109. C₄×C₄₃	#357	semidirect
115. C₂×C₄⋊C₁₆	D₄₃	semidirect
136. C₄₃	#13252	semidirect
229. C₄	#14582701	semidirect

H ≅ G/N

type

2. C₂×#14582701

C₂

semidirect

3. C₄×#13063259

C₂

semidirect

4. C₂×C₄₃×C₄⋊C₁₆

C₂

semidirect

9. #14583276

C₄

semidirect

31. #13063259

D₄

semidirect

109. C₄×C₄₃

#357

semidirect

115. C₂×C₄⋊C₁₆

D₄₃

semidirect

136. C₄₃

#13252

semidirect

229. C₄

#14582701

semidirect

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

subgroup	index
C₂×#14583276	2
C₂×#14582701	2
C₄×#13063259	2
C₂×C₄₃×C₄⋊C₁₆	2
#13252	43

subgroup

index

C₂×C₄₃×C₄⋊C₁₆

Subgroups — #25015063

Conjugacy classes of subgroups

Complements

Maximal subgroups