Group #24994015 — subgroups

Subgroups — #24994015

Order 11008.

450 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 115 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	#19143680	C₂	1	1	yes	maximal, characteristic
2	#19139807	C₂	1	1	yes	maximal, characteristic
3	#19133281	C₂	1	2	yes	maximal
4	#19132496	C₂	1	2	yes	maximal
5	C₄₃×#1801	C₂	1	1	yes	maximal, characteristic
6	C₂×#13063325	C₂²	1	1	yes	characteristic
7	#14583030	—	2	4	no	—
8	#14582956	—	2	2	no	—
9	#14582952	C₂²	1	2	yes	—
10	#14582838	C₄	1	4	yes	—
11	#14582806	—	2	1	no	—
12	#14582805	—	2	2	no	—
13	#14582764	—	2	1	no	—
14	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
15	#14582644	—	2	4	no	—
16	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₄₃×#423	C₂²	1	2	yes	—
18	C₂×#101×C₄₃	—	2	1	no	—
19	C₄₃×#343	—	2	1	no	—
20	C₂²×Dic₈₆	—	2	1	no	—
21	#13063325	—	2	2	no	—
22	#13063325	—	2	2	no	—
23	C₂×C₄⋊Dic₄₃	—	2	1	no	—
24	C₂×C₄⋊Dic₄₃	—	2	1	no	—
25	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
26	C₂×C₄×Dic₄₃	—	2	1	no	—
27	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
28	C₄⋊(C₄₃⋊C₈)	D₄	1	4	yes	—
29	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
30	#13063236	—	2	4	no	—
31	C₄×C₄₃⋊C₈	—	2	2	no	—
32	C₄₃⋊#95	—	2	4	no	—
33	C₄₃⋊#95	—	2	4	no	—
34	C₄₃⋊#95	C₂×C₄	1	2	yes	—
35	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
36	C₂×M₁₆×C₄₃	—	2	2	no	—
37	C₄×Q₈×C₄₃	—	2	2	no	—
38	C₄×Q₈×C₄₃	—	2	2	no	—
39	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
40	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₄₃	D₄	1	2	yes	—
42	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₄₃	—	2	2	no	—
44	C₄⋊C₈×C₄₃	—	2	2	no	—
45	#101×C₄₃	—	4	2	no	—
46	C₂×Q₈×C₄₃	—	2	2	no	—
47	C₂×Q₈×C₄₃	—	2	1	no	—
48	C₂×Q₈×C₄₃	—	2	2	no	—
49	C₂×Q₈×C₄₃	—	2	1	no	—
50	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
51	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
52	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
55	C₂²×Dic₄₃	—	2	2	no	—
56	C₂²×Dic₄₃	—	2	2	no	—
57	C₂×Dic₈₆	—	4	4	no	—
58	C₂×Dic₈₆	—	4	1	no	—
59	C₂×Dic₈₆	—	4	1	no	—
60	M₁₆×C₄₃	—	4	2	no	—
61	M₁₆×C₄₃	—	4	2	no	—
62	C₂×C₈×C₄₃	—	4	2	no	—
63	C₄⋊C₄×C₄₃	—	2	4	no	—
64	C₄⋊C₄×C₄₃	—	2	2	no	—
65	C₄²×C₄₃	—	2	2	no	—
66	C₄²×C₄₃	—	2	2	no	—
67	C₄²×C₄₃	C₂×D₄	1	2	yes	—
68	C₄²×C₄₃	#41	1	2	yes	—
69	C₄⋊Dic₄₃	—	2	4	no	—
70	C₄⋊Dic₄₃	—	4	2	no	—
71	C₄⋊Dic₄₃	—	4	2	no	—
72	C₄×Dic₄₃	—	4	1	no	—
73	C₄×Dic₄₃	—	4	1	no	—
74	C₂×C₄₃⋊C₈	—	2	4	no	—
75	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	Q₈×C₄₃	—	4	2	no	—
77	Q₈×C₄₃	—	4	2	no	—
78	C₂×C₄×C₄₃	—	2	2	no	—
79	C₂×C₄×C₄₃	—	2	2	no	—
80	C₂×C₄×C₄₃	—	2	2	no	—
81	C₂×C₄×C₄₃	—	2	2	no	—
82	C₂×C₄×C₄₃	—	2	2	no	—
83	C₂×C₄×C₄₃	—	4	1	no	—
84	C₂×C₄×C₄₃	—	4	2	no	—
85	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
86	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
87	C₂×C₄×C₄₃	#121	1	2	yes	—
88	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
89	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
90	C₂×C₄×C₄₃	#137	1	2	yes	—
91	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
92	C₂×Dic₄₃	—	4	2	no	—
93	C₂×Dic₄₃	—	4	4	no	—
94	C₂×Dic₄₃	—	4	2	no	—
95	C₂×Dic₄₃	—	4	2	no	—
96	C₂×Dic₄₃	—	4	2	no	—
97	Dic₈₆	—	8	2	no	—
98	Dic₈₆	—	8	2	no	—
99	C₈×C₄₃	—	8	2	no	—
100	C₄₃⋊C₈	—	4	4	no	—
101	#9404	—	43	1	no	maximal, Sylow
102	C₂²×C₄₃	—	2	1	no	—
103	C₂²×C₄₃	—	2	1	no	—
104	C₂²×C₄₃	#386	1	1	yes	characteristic
105	C₂²×C₄₃	#417	1	1	yes	characteristic
106	C₂²×C₄₃	#419	1	1	yes	characteristic
107	C₄×C₄₃	—	2	1	no	—
108	C₄×C₄₃	—	2	2	no	—
109	C₄×C₄₃	—	4	2	no	—
110	C₄×C₄₃	—	4	2	no	—
111	C₄×C₄₃	#454	1	2	yes	—
112	C₄×C₄₃	#468	1	2	yes	—
113	C₄×C₄₃	#470	1	2	yes	—
114	Dic₄₃	—	8	2	no	—
115	Dic₄₃	—	8	2	no	—
116	#2983	—	43	1	no	—
117	#2568	—	43	1	no	—
118	#1801	D₄₃	1	1	yes	characteristic
119	#1549	—	43	2	no	—
120	#1303	—	43	2	no	—
121	C₂×C₄₃	—	2	1	no	—
122	C₂×C₄₃	—	2	1	no	—
123	C₂×C₄₃	#1888	1	1	yes	characteristic
124	C₂×C₄₃	#1894	1	1	yes	characteristic
125	C₂×C₄₃	#1915	1	1	yes	characteristic
126	C₂×C₄⋊Q₈	—	43	1	no	—
127	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
128	#446	—	86	4	no	—
129	#432	—	86	2	no	—
130	#431	—	43	2	no	—
131	#423	C₂×D₄₃	1	2	yes	—
132	C₂×#101	—	2	1	no	—
133	#400	—	43	4	no	—
134	#391	—	86	1	no	—
135	#391	—	86	2	no	—
136	#382	—	86	1	no	—
137	C₄×C₄⋊C₄	—	43	1	no	—
138	#343	—	2	1	no	—
139	#332	—	86	4	no	—
140	C₄₃	#9404	1	1	yes	characteristic, complemented, Sylow
141	C₂²×Q₈	—	86	1	no	—
142	C₂²×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
143	C₂×M₁₆	—	2	2	no	—
144	C₄⋊Q₈	—	86	2	no	—
145	C₄⋊Q₈	—	86	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	C₄×Q₈	—	2	2	no	—
148	C₂×C₄⋊C₄	—	43	2	no	—
149	C₂×C₄⋊C₄	—	86	1	no	—
150	C₂×C₄⋊C₄	—	86	1	no	—
151	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
152	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
153	C₂×C₄²	—	86	1	no	—
154	C₂×C₄²	D₁₇₂	1	2	yes	—
155	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
156	C₄⋊C₈	—	2	2	no	—
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	43	4	no	—
159	C₄⋊C₈	—	86	4	no	—
160	#101	—	4	2	no	—
161	C₂²⋊C₈	—	86	2	no	—
162	#97	—	86	4	no	—
163	C₄×C₈	—	86	2	no	—
164	#95	—	43	2	no	—
165	#95	—	86	4	no	—
166	#95	—	86	4	no	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	1	no	—
169	C₂×Q₈	—	2	2	no	—
170	C₂×Q₈	—	2	1	no	—
171	C₂×Q₈	—	172	4	no	—
172	C₂×Q₈	—	172	1	no	—
173	C₂×Q₈	—	172	1	no	—
174	C₂²×C₄	—	86	2	no	—
175	C₂²×C₄	—	86	2	no	—
176	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
177	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
178	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
179	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
180	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
181	M₁₆	—	4	2	no	—
182	M₁₆	—	4	2	no	—
183	C₂×C₈	—	4	2	no	—
184	C₂×C₈	—	86	4	no	—
185	C₄⋊C₄	—	2	4	no	—
186	C₄⋊C₄	—	2	2	no	—
187	C₄⋊C₄	—	86	4	no	—
188	C₄⋊C₄	—	172	2	no	—
189	C₄⋊C₄	—	172	2	no	—
190	C₄²	—	2	2	no	—
191	C₄²	—	2	2	no	—
192	C₄²	—	172	1	no	—
193	C₄²	—	172	1	no	—
194	C₄²	D₄×D₄₃	1	2	yes	—
195	C₄²	#10621900	1	2	yes	—
196	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
197	Q₈	—	4	2	no	—
198	Q₈	—	4	2	no	—
199	Q₈	—	344	2	no	—
200	Q₈	—	344	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	172	2	no	—
209	C₂×C₄	—	172	4	no	—
210	C₂×C₄	—	172	2	no	—
211	C₂×C₄	—	172	2	no	—
212	C₂×C₄	—	172	2	no	—
213	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
214	C₂×C₄	#13063295	1	1	yes	characteristic
215	C₂×C₄	#13063297	1	2	yes	—
216	C₂×C₄	#13063309	1	1	yes	characteristic
217	C₂×C₄	#13063351	1	1	yes	characteristic
218	C₂×C₄	#13063355	1	2	yes	—
219	C₂×C₄	#13063356	1	1	yes	characteristic
220	C₈	—	8	2	no	—
221	C₈	—	172	4	no	—
222	C₂²	—	2	1	no	—
223	C₂²	—	2	1	no	—
224	C₂²	#14582776	1	1	yes	characteristic
225	C₂²	#14582898	1	1	yes	characteristic
226	C₂²	#14582907	1	1	yes	characteristic
227	C₄	—	2	1	no	—
228	C₄	—	2	2	no	—
229	C₄	—	4	2	no	—
230	C₄	—	4	2	no	—
231	C₄	—	344	2	no	—
232	C₄	—	344	2	no	—
233	C₄	#14583074	1	2	yes	—
234	C₄	#14583143	1	2	yes	—
235	C₄	#14583155	1	2	yes	—
236	C₂	—	2	1	no	—
237	C₂	—	2	1	no	—
238	C₂	#19134996	1	1	yes	characteristic
239	C₂	#19135026	1	1	yes	characteristic
240	C₂	#19135145	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19143680

C₂

yes

maximal, characteristic

#19139807

C₂

yes

maximal, characteristic

#19133281

C₂

yes

maximal

#19132496

C₂

yes

maximal

C₄₃×#1801

C₂

yes

maximal, characteristic

C₂×#13063325

C₂²

yes

—

—

C₂²

yes

—

#14582838

C₄

yes

—

#14582806

—

#14582805

—

#14582764

—

C₄×C₄⋊Dic₄₃

C₂²

yes

characteristic

#14582644

—

C₂×C₄×Q₈×C₄₃

C₂²

yes

characteristic

C₄₃×#423

C₂²

yes

—

C₂×#101×C₄₃

—

C₄₃×#343

—

C₂²×Dic₈₆

—

#13063325

—

#13063325

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂×C₄

yes

—

C₂×C₄×Dic₄₃

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

D₄

yes

—

C₂²⋊(C₄₃⋊C₈)

—

#13063236

—

C₄×C₄₃⋊C₈

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₄₃⋊#95

C₂×C₄

yes

—

C₂²×Q₈×C₄₃

D₄

yes

characteristic

C₂×M₁₆×C₄₃

—

C₄×Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

#101×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

#41

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄×D₄

yes

—

C₂×C₄×C₄₃

#120

yes

characteristic

C₂×C₄×C₄₃

#121

yes

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

—

C₂×C₄×C₄₃

#137

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

100

C₄₃⋊C₈

—

101

#9404

—

maximal, Sylow

102

C₂²×C₄₃

—

103

C₂²×C₄₃

—

104

C₂²×C₄₃

#386

yes

characteristic

105

C₂²×C₄₃

#417

yes

characteristic

106

C₂²×C₄₃

#419

yes

characteristic

107

C₄×C₄₃

—

108

C₄×C₄₃

—

109

C₄×C₄₃

—

110

C₄×C₄₃

—

111

C₄×C₄₃

#454

yes

—

112

C₄×C₄₃

#468

yes

—

113

C₄×C₄₃

#470

yes

—

114

Dic₄₃

—

115

Dic₄₃

—

116

#2983

—

117

#2568

—

118

#1801

D₄₃

yes

characteristic

119

#1549

—

120

#1303

—

121

C₂×C₄₃

—

122

C₂×C₄₃

—

123

C₂×C₄₃

#1888

yes

characteristic

124

C₂×C₄₃

#1894

yes

characteristic

125

C₂×C₄₃

#1915

yes

characteristic

126

C₂×C₄⋊Q₈

—

127

C₂×C₄×Q₈

C₂×D₄₃

yes

characteristic

128

#446

—

129

#432

—

130

#431

—

131

#423

C₂×D₄₃

yes

—

132

C₂×#101

—

133

#400

—

134

#391

—

135

#391

—

136

#382

—

137

C₄×C₄⋊C₄

—

138

#343

—

139

#332

—

140

C₄₃

#9404

yes

characteristic, complemented, Sylow

141

C₂²×Q₈

—

142

C₂²×Q₈

C₂²⋊D₄₃

yes

characteristic

143

C₂×M₁₆

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

C₄×D₄₃

yes

—

152

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

characteristic

153

C₂×C₄²

—

154

C₂×C₄²

D₁₇₂

yes

—

155

C₂×C₄²

C₂²×D₄₃

yes

characteristic

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

#101

—

161

C₂²⋊C₈

—

162

#97

—

163

C₄×C₈

—

164

#95

—

165

#95

—

166

#95

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

—

172

C₂×Q₈

—

172

—

173

C₂×Q₈

—

172

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

177

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

178

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

179

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

180

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

181

M₁₆

—

182

M₁₆

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

172

—

189

C₄⋊C₄

—

172

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

172

—

193

C₄²

—

172

—

194

C₄²

D₄×D₄₃

yes

—

195

C₄²

#10621900

yes

—

196

C₂³

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

197

Q₈

—

198

Q₈

—

199

Q₈

—

344

—

200

Q₈

—

344

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

172

—

209

C₂×C₄

—

172

—

210

C₂×C₄

—

172

—

211

C₂×C₄

—

172

—

212

C₂×C₄

—

172

—

213

C₂×C₄

(C₂²⋊D₄₃)⋊C₄

yes

—

214

C₂×C₄

#13063295

yes

characteristic

215

C₂×C₄

#13063297

yes

—

216

C₂×C₄

#13063309

yes

characteristic

217

C₂×C₄

#13063351

yes

characteristic

218

C₂×C₄

#13063355

yes

—

219

C₂×C₄

#13063356

yes

characteristic

220

C₈

—

221

C₈

—

172

—

222

C₂²

—

223

C₂²

—

224

C₂²

#14582776

yes

characteristic

225

C₂²

#14582898

yes

characteristic

226

C₂²

#14582907

yes

characteristic

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

344

—

232

C₄

—

344

—

233

C₄

#14583074

yes

—

234

C₄

#14583143

yes

—

235

C₄

#14583155

yes

—

236

C₂

—

237

C₂

—

238

C₂

#19134996

yes

characteristic

239

C₂

#19135026

yes

characteristic

240

C₂

#19135145

yes

characteristic

	subgroup	G/H
center	C₂²	#14582776
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1801	C₂
socle	C₂²×C₄₃	#386
prime radical	C₂³×C₄₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1801	D₄₃
hypocenter	C₄₃	#9404
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

subgroup

G/H

center

C₂²

#14582776

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1801

C₂

socle

C₂²×C₄₃

#386

prime radical

C₂³×C₄₃

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

N	H ≅ G/N	type
140. C₄₃	#9404	semidirect

H ≅ G/N

type

140. C₄₃

#9404

semidirect

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

subgroup	index
#19143680	2
#19139807	2
#19133281	2
#19132496	2
C₄₃×#1801	2
#9404	43

subgroup

index

C₄₃×#1801

Subgroups — #24994015

Conjugacy classes of subgroups

Complements

Maximal subgroups