Group #24993977 — subgroups

Subgroups — #24993977

Order 11008.

470 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 135 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	#19139807	C₂	1	1	yes	maximal, characteristic
2	#19134591	C₂	1	1	yes	maximal, characteristic
3	#19133279	C₂	1	2	yes	maximal
4	#19132497	C₂	1	2	yes	maximal
5	C₄₃×#2982	C₂	1	1	yes	maximal, characteristic
6	C₂×#13063325	C₂²	1	1	yes	characteristic
7	#14582923	C₂²	1	2	yes	—
8	C₂×#13063244	—	2	1	no	—
9	#14582838	C₄	1	4	yes	—
10	#14582806	—	2	1	no	—
11	#14582805	—	2	2	no	—
12	#14582764	—	2	1	no	—
13	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
14	#14582668	—	2	1	no	—
15	#14582646	—	2	4	no	—
16	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₈×Q₈×C₄₃	—	2	4	no	—
18	C₄₃×#431	—	2	2	no	—
19	C₄₃×#431	C₂²	1	2	yes	—
20	C₂²×Dic₈₆	—	2	1	no	—
21	C₂×#10621877	—	2	2	no	—
22	#13063325	—	2	2	no	—
23	#13063325	—	2	2	no	—
24	C₂×C₄⋊Dic₄₃	—	2	1	no	—
25	C₂×C₄⋊Dic₄₃	—	2	1	no	—
26	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
27	C₂×C₄×Dic₄₃	—	2	1	no	—
28	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
29	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
30	#13063244	—	4	2	no	—
31	C₄₃⋊#95	—	2	4	no	—
32	C₄₃⋊#95	—	2	4	no	—
33	C₄₃⋊#95	C₂×C₄	1	2	yes	—
34	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
35	C₄×Q₈×C₄₃	—	2	2	no	—
36	C₄×Q₈×C₄₃	—	2	2	no	—
37	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
38	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₄₃	D₄	1	2	yes	—
40	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
41	C₄⋊C₈×C₄₃	—	2	4	no	—
42	C₄⋊C₈×C₄₃	D₄	1	4	yes	—
43	C₂²⋊C₈×C₄₃	—	2	2	no	—
44	C₄×C₈×C₄₃	—	2	4	no	—
45	C₄×C₈×C₄₃	—	2	2	no	—
46	C₂×Q₈×C₄₃	—	2	2	no	—
47	C₂×Q₈×C₄₃	—	2	2	no	—
48	C₂×Q₈×C₄₃	SD₁₆	1	2	yes	—
49	C₂×Q₈×C₄₃	Q₁₆	1	2	yes	—
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	C₂×C₈×C₄₃	—	2	4	no	—
61	C₄⋊C₄×C₄₃	—	2	4	no	—
62	C₄⋊C₄×C₄₃	—	2	2	no	—
63	C₄²×C₄₃	—	2	2	no	—
64	C₄²×C₄₃	—	2	2	no	—
65	C₄²×C₄₃	C₂×D₄	1	2	yes	—
66	C₄²×C₄₃	#41	1	2	yes	—
67	C₄⋊Dic₄₃	—	2	4	no	—
68	C₄⋊Dic₄₃	—	4	2	no	—
69	C₄⋊Dic₄₃	—	4	2	no	—
70	C₄×Dic₄₃	—	4	2	no	—
71	#10621877	—	4	2	no	—
72	#10621877	—	4	2	no	—
73	C₂×C₄₃⋊C₈	—	4	2	no	—
74	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	Q₈×C₄₃	—	2	4	no	—
76	Q₈×C₄₃	—	2	4	no	—
77	C₂×C₄×C₄₃	—	2	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	—	4	1	no	—
82	C₂×C₄×C₄₃	—	4	2	no	—
83	C₂×C₄×C₄₃	#103	1	4	yes	—
84	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
85	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
86	C₂×C₄×C₄₃	#121	1	2	yes	—
87	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
88	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
89	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
90	C₂×C₄×C₄₃	#135	1	2	yes	—
91	C₂×Dic₄₃	—	4	2	no	—
92	C₂×Dic₄₃	—	4	4	no	—
93	C₂×Dic₄₃	—	4	2	no	—
94	C₂×Dic₄₃	—	4	2	no	—
95	C₂×Dic₄₃	—	4	2	no	—
96	Dic₈₆	—	8	2	no	—
97	Dic₈₆	—	8	2	no	—
98	C₈×C₄₃	—	4	4	no	—
99	C₄₃⋊C₈	—	8	2	no	—
100	#9396	—	43	1	no	maximal, Sylow
101	C₂²×C₄₃	—	2	1	no	—
102	C₂²×C₄₃	—	2	1	no	—
103	C₂²×C₄₃	#386	1	1	yes	characteristic
104	C₂²×C₄₃	C₂×#103	1	1	yes	characteristic
105	C₂²×C₄₃	#416	1	1	yes	characteristic
106	C₄×C₄₃	—	2	1	no	—
107	C₄×C₄₃	—	2	4	no	—
108	C₄×C₄₃	—	2	2	no	—
109	C₄×C₄₃	—	4	2	no	—
110	C₄×C₄₃	#454	1	2	yes	—
111	C₄×C₄₃	#465	1	2	yes	—
112	C₄×C₄₃	#467	1	2	yes	—
113	Dic₄₃	—	8	2	no	—
114	Dic₄₃	—	8	2	no	—
115	#2982	D₄₃	1	1	yes	characteristic
116	#2568	—	43	1	no	—
117	#1801	—	43	1	no	—
118	#1549	—	43	2	no	—
119	#1303	—	43	2	no	—
120	C₂×C₄₃	—	2	1	no	—
121	C₂×C₄₃	—	2	1	no	—
122	C₂×C₄₃	#1888	1	1	yes	characteristic
123	C₂×C₄₃	#1892	1	1	yes	characteristic
124	C₂×C₄₃	#1915	1	1	yes	characteristic
125	C₂×C₄⋊Q₈	—	43	1	no	—
126	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
127	C₈×Q₈	—	2	4	no	—
128	#431	—	2	2	no	—
129	#431	C₂×D₄₃	1	2	yes	—
130	#423	—	43	2	no	—
131	C₂×#101	—	86	1	no	—
132	#400	—	43	4	no	—
133	#391	—	86	1	no	—
134	#391	—	86	2	no	—
135	#382	—	86	1	no	—
136	C₄×C₄⋊C₄	—	43	1	no	—
137	#343	—	86	1	no	—
138	#332	—	86	4	no	—
139	C₄₃	#9396	1	1	yes	characteristic, complemented, Sylow
140	C₂²×Q₈	—	86	1	no	—
141	C₂²×Q₈	D₁₇₂	1	1	yes	characteristic
142	C₂×M₁₆	—	86	2	no	—
143	C₄⋊Q₈	—	86	2	no	—
144	C₄⋊Q₈	—	86	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	C₂×C₄⋊C₄	—	43	2	no	—
148	C₂×C₄⋊C₄	—	86	1	no	—
149	C₂×C₄⋊C₄	—	86	1	no	—
150	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
151	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
152	C₂×C₄²	—	86	1	no	—
153	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
154	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
155	C₄⋊C₈	—	2	4	no	—
156	C₄⋊C₈	—	86	2	no	—
157	C₄⋊C₈	—	86	2	no	—
158	C₄⋊C₈	C₂²⋊D₄₃	1	4	yes	—
159	#101	—	172	2	no	—
160	C₂²⋊C₈	—	2	2	no	—
161	C₄×C₈	—	2	4	no	—
162	C₄×C₈	—	2	2	no	—
163	#95	—	43	2	no	—
164	#95	—	86	4	no	—
165	#95	—	86	4	no	—
166	C₂×Q₈	—	2	2	no	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	172	4	no	—
169	C₂×Q₈	—	172	1	no	—
170	C₂×Q₈	—	172	1	no	—
171	C₂×Q₈	#10621873	1	2	yes	—
172	C₂×Q₈	Dic₁₇₂	1	2	yes	—
173	C₂²×C₄	—	86	2	no	—
174	C₂²×C₄	—	86	2	no	—
175	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
176	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
177	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
178	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
179	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
180	M₁₆	—	172	2	no	—
181	M₁₆	—	172	2	no	—
182	C₂×C₈	—	2	4	no	—
183	C₂×C₈	—	172	2	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	—	86	4	no	—
187	C₄⋊C₄	—	172	2	no	—
188	C₄⋊C₄	—	172	2	no	—
189	C₄²	—	2	2	no	—
190	C₄²	—	2	2	no	—
191	C₄²	—	172	2	no	—
192	C₄²	#10621898	1	2	yes	—
193	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
194	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
195	Q₈	—	2	4	no	—
196	Q₈	—	2	4	no	—
197	Q₈	—	344	2	no	—
198	Q₈	—	344	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	4	1	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	172	2	no	—
206	C₂×C₄	—	172	4	no	—
207	C₂×C₄	—	172	2	no	—
208	C₂×C₄	—	172	2	no	—
209	C₂×C₄	—	172	2	no	—
210	C₂×C₄	#13063250	1	4	yes	—
211	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
212	C₂×C₄	#13063294	1	1	yes	characteristic
213	C₂×C₄	#13063299	1	2	yes	—
214	C₂×C₄	#13063308	1	1	yes	characteristic
215	C₂×C₄	C₂×#10621873	1	1	yes	characteristic
216	C₂×C₄	C₂×Dic₁₇₂	1	1	yes	characteristic
217	C₂×C₄	#13063347	1	2	yes	—
218	C₈	—	4	4	no	—
219	C₈	—	344	2	no	—
220	C₂²	—	2	1	no	—
221	C₂²	—	2	1	no	—
222	C₂²	#14582778	1	1	yes	characteristic
223	C₂²	C₂×#13063250	1	1	yes	characteristic
224	C₂²	#14582896	1	1	yes	characteristic
225	C₄	—	2	1	no	—
226	C₄	—	2	4	no	—
227	C₄	—	2	2	no	—
228	C₄	—	4	2	no	—
229	C₄	—	344	2	no	—
230	C₄	—	344	2	no	—
231	C₄	#14583072	1	2	yes	—
232	C₄	#14583128	1	2	yes	—
233	C₄	#14583140	1	2	yes	—
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	#19134998	1	1	yes	characteristic
237	C₂	#19135018	1	1	yes	characteristic
238	C₂	#19135147	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19139807

C₂

yes

maximal, characteristic

#19134591

C₂

yes

maximal, characteristic

#19133279

C₂

yes

maximal

#19132497

C₂

yes

maximal

C₄₃×#2982

C₂

yes

maximal, characteristic

C₂×#13063325

C₂²

yes

characteristic

#14582923

C₂²

yes

—

C₂×#13063244

—

#14582838

C₄

yes

—

#14582806

—

#14582805

—

#14582764

—

C₄×C₄⋊Dic₄₃

C₂²

yes

characteristic

#14582668

—

#14582646

—

C₂×C₄×Q₈×C₄₃

C₂²

yes

characteristic

C₈×Q₈×C₄₃

—

C₄₃×#431

—

C₄₃×#431

C₂²

yes

—

C₂²×Dic₈₆

—

C₂×#10621877

—

#13063325

—

#13063325

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂×C₄

yes

—

C₂×C₄×Dic₄₃

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

#13063244

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₄₃⋊#95

C₂×C₄

yes

—

C₂²×Q₈×C₄₃

D₄

yes

characteristic

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

D₄

yes

—

C₂²⋊C₈×C₄₃

—

C₄×C₈×C₄₃

—

C₄×C₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

SD₁₆

yes

—

C₂×Q₈×C₄₃

Q₁₆

yes

—

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

—

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

—

#10621877

—

#10621877

—

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

#103

yes

—

C₂×C₄×C₄₃

C₄×D₄

yes

—

C₂×C₄×C₄₃

#120

yes

characteristic

C₂×C₄×C₄₃

#121

yes

—

C₂×C₄×C₄₃

#123

yes

characteristic

C₂×C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₄₃

#135

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

100

#9396

—

maximal, Sylow

101

C₂²×C₄₃

—

102

C₂²×C₄₃

—

103

C₂²×C₄₃

#386

yes

characteristic

104

C₂²×C₄₃

C₂×#103

yes

characteristic

105

C₂²×C₄₃

#416

yes

characteristic

106

C₄×C₄₃

—

107

C₄×C₄₃

—

108

C₄×C₄₃

—

109

C₄×C₄₃

—

110

C₄×C₄₃

#454

yes

—

111

C₄×C₄₃

#465

yes

—

112

C₄×C₄₃

#467

yes

—

113

Dic₄₃

—

114

Dic₄₃

—

115

#2982

D₄₃

yes

characteristic

116

#2568

—

117

#1801

—

118

#1549

—

119

#1303

—

120

C₂×C₄₃

—

121

C₂×C₄₃

—

122

C₂×C₄₃

#1888

yes

characteristic

123

C₂×C₄₃

#1892

yes

characteristic

124

C₂×C₄₃

#1915

yes

characteristic

125

C₂×C₄⋊Q₈

—

126

C₂×C₄×Q₈

C₂×D₄₃

yes

characteristic

127

C₈×Q₈

—

128

#431

—

129

#431

C₂×D₄₃

yes

—

130

#423

—

131

C₂×#101

—

132

#400

—

133

#391

—

134

#391

—

135

#382

—

136

C₄×C₄⋊C₄

—

137

#343

—

138

#332

—

139

C₄₃

#9396

yes

characteristic, complemented, Sylow

140

C₂²×Q₈

—

141

C₂²×Q₈

D₁₇₂

yes

characteristic

142

C₂×M₁₆

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

C₄×Q₈

—

146

C₄×Q₈

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

C₄×D₄₃

yes

—

151

C₂×C₄⋊C₄

D₁₇₂

yes

characteristic

152

C₂×C₄²

—

153

C₂×C₄²

C₂²⋊D₄₃

yes

—

154

C₂×C₄²

C₂²×D₄₃

yes

characteristic

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

C₂²⋊D₄₃

yes

—

159

#101

—

172

—

160

C₂²⋊C₈

—

161

C₄×C₈

—

162

C₄×C₈

—

163

#95

—

164

#95

—

165

#95

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

172

—

169

C₂×Q₈

—

172

—

170

C₂×Q₈

—

172

—

171

C₂×Q₈

#10621873

yes

—

172

C₂×Q₈

Dic₁₇₂

yes

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

176

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

177

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

178

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

179

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

180

M₁₆

—

172

—

181

M₁₆

—

172

—

182

C₂×C₈

—

183

C₂×C₈

—

172

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

172

—

188

C₄⋊C₄

—

172

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

172

—

192

C₄²

#10621898

yes

—

193

C₄²

C₂×C₂²⋊D₄₃

yes

—

194

C₂³

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

195

Q₈

—

196

Q₈

—

197

Q₈

—

344

—

198

Q₈

—

344

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

172

—

206

C₂×C₄

—

172

—

207

C₂×C₄

—

172

—

208

C₂×C₄

—

172

—

209

C₂×C₄

—

172

—

210

C₂×C₄

#13063250

yes

—

211

C₂×C₄

C₄×C₂²⋊D₄₃

yes

—

212

C₂×C₄

#13063294

yes

characteristic

213

C₂×C₄

#13063299

yes

—

214

C₂×C₄

#13063308

yes

characteristic

215

C₂×C₄

C₂×#10621873

yes

characteristic

216

C₂×C₄

C₂×Dic₁₇₂

yes

characteristic

217

C₂×C₄

#13063347

yes

—

218

C₈

—

219

C₈

—

344

—

220

C₂²

—

221

C₂²

—

222

C₂²

#14582778

yes

characteristic

223

C₂²

C₂×#13063250

yes

characteristic

224

C₂²

#14582896

yes

characteristic

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

344

—

230

C₄

—

344

—

231

C₄

#14583072

yes

—

232

C₄

#14583128

yes

—

233

C₄

#14583140

yes

—

234

C₂

—

235

C₂

—

236

C₂

#19134998

yes

characteristic

237

C₂

#19135018

yes

characteristic

238

C₂

#19135147

yes

characteristic

	subgroup	G/H
center	C₂²	#14582778
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#2982	C₂
socle	C₂²×C₄₃	#386
prime radical	C₂³×C₄₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#2982	D₄₃
hypocenter	C₄₃	#9396
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2982

subgroup

G/H

center

C₂²

#14582778

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#2982

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 ◁ #2982

N	H ≅ G/N	type
139. C₄₃	#9396	semidirect

H ≅ G/N

type

139. C₄₃

#9396

semidirect

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

subgroup	index
#19139807	2
#19134591	2
#19133279	2
#19132497	2
C₄₃×#2982	2
#9396	43

subgroup

index

C₄₃×#2982

Subgroups — #24993977

Conjugacy classes of subgroups

Complements

Maximal subgroups