Group #24993955 — subgroups

Subgroups — #24993955

Order 11008.

486 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 131 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	#19143676	C₂	1	1	yes	maximal, characteristic
2	#19139800	C₂	1	1	yes	maximal, characteristic
3	#19133277	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	Q₈×C₄₃⋊C₈	—	2	4	no	—
8	#14582952	—	2	2	no	—
9	#14582952	C₂²	1	2	yes	—
10	#14582819	C₄	1	4	yes	—
11	#14582806	—	2	1	no	—
12	#14582797	—	2	2	no	—
13	#14582768	—	2	1	no	—
14	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
15	#14582647	—	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	C₂×C₄	1	2	yes	—
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	—	2	1	no	—
26	C₂×Dic₄₃⋊C₄	—	2	4	no	—
27	C₂×C₄×Dic₄₃	—	2	1	no	—
28	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
29	C₄⋊(C₄₃⋊C₈)	D₄	1	4	yes	—
30	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
31	C₄×C₄₃⋊C₈	—	2	4	no	—
32	C₄×C₄₃⋊C₈	—	2	2	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	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	—	2	4	no	—
58	C₂×Dic₈₆	—	8	2	no	—
59	M₁₆×C₄₃	—	4	2	no	—
60	M₁₆×C₄₃	—	4	2	no	—
61	C₂×C₈×C₄₃	—	4	2	no	—
62	C₄⋊C₄×C₄₃	—	2	4	no	—
63	C₄⋊C₄×C₄₃	—	2	2	no	—
64	C₄²×C₄₃	—	2	2	no	—
65	C₄²×C₄₃	—	2	2	no	—
66	C₄²×C₄₃	C₂×D₄	1	2	yes	—
67	C₄²×C₄₃	#41	1	2	yes	—
68	C₄⋊Dic₄₃	—	2	4	no	—
69	C₄⋊Dic₄₃	—	4	1	no	—
70	C₄⋊Dic₄₃	—	4	2	no	—
71	C₄⋊Dic₄₃	—	4	1	no	—
72	Dic₄₃⋊C₄	—	8	4	no	—
73	C₄×Dic₄₃	—	4	2	no	—
74	C₂×C₄₃⋊C₈	—	2	4	no	—
75	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	Q₈×C₄₃	—	2	4	no	—
77	Q₈×C₄₃	—	2	4	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	—	4	1	no	—
83	C₂×C₄×C₄₃	—	4	2	no	—
84	C₂×C₄×C₄₃	#103	1	4	yes	—
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	C₂×SD₁₆	1	1	yes	characteristic
90	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
91	C₂×C₄×C₄₃	#135	1	2	yes	—
92	C₂×Dic₄₃	—	2	4	no	—
93	C₂×Dic₄₃	—	4	2	no	—
94	C₂×Dic₄₃	—	4	2	no	—
95	C₂×Dic₄₃	—	4	4	no	—
96	C₂×Dic₄₃	—	4	2	no	—
97	Dic₈₆	—	8	4	no	—
98	C₈×C₄₃	—	8	2	no	—
99	C₄₃⋊C₈	—	4	4	no	—
100	#9392	—	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	#456	1	2	yes	—
111	C₄×C₄₃	#465	1	2	yes	—
112	C₄×C₄₃	#467	1	2	yes	—
113	Dic₄₃	—	4	4	no	—
114	Dic₄₃	—	8	2	no	—
115	#2982	—	43	1	no	—
116	#2567	—	43	1	no	—
117	#1801	D₄₃	1	1	yes	characteristic
118	#1548	—	43	2	no	—
119	#1303	—	43	2	no	—
120	C₂×C₄₃	—	2	1	no	—
121	C₂×C₄₃	—	2	1	no	—
122	C₂×C₄₃	#1886	1	1	yes	characteristic
123	C₂×C₄₃	#1892	1	1	yes	characteristic
124	C₂×C₄₃	#1914	1	1	yes	characteristic
125	C₂×C₄⋊Q₈	—	43	1	no	—
126	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
127	C₈×Q₈	—	86	4	no	—
128	#431	—	43	2	no	—
129	#431	—	86	2	no	—
130	#423	C₂×D₄₃	1	2	yes	—
131	C₂×#101	—	2	1	no	—
132	#395	—	43	4	no	—
133	#391	—	86	1	no	—
134	#389	—	86	2	no	—
135	#384	—	86	1	no	—
136	C₄×C₄⋊C₄	—	43	1	no	—
137	#343	—	2	1	no	—
138	#333	—	86	4	no	—
139	C₄₃	#9392	1	1	yes	characteristic, complemented, Sylow
140	C₂²×Q₈	—	43	2	no	—
141	C₂²×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
142	C₂×M₁₆	—	2	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	—	86	1	no	—
148	C₂×C₄⋊C₄	—	86	4	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	C₄×C₈	—	86	4	no	—
163	C₄×C₈	—	86	2	no	—
164	#95	—	43	2	no	—
165	#95	—	86	4	no	—
166	C₂×Q₈	—	2	2	no	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	86	4	no	—
169	C₂×Q₈	—	344	2	no	—
170	C₂×Q₈	#10621883	1	2	yes	—
171	C₂×Q₈	#10621885	1	2	yes	—
172	C₂²×C₄	—	86	2	no	—
173	C₂²×C₄	—	86	2	no	—
174	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
175	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
176	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
177	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
178	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
179	M₁₆	—	4	2	no	—
180	M₁₆	—	4	2	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	86	4	no	—
183	C₄⋊C₄	—	2	4	no	—
184	C₄⋊C₄	—	2	2	no	—
185	C₄⋊C₄	—	86	4	no	—
186	C₄⋊C₄	—	344	4	no	—
187	C₄⋊C₄	—	172	1	no	—
188	C₄⋊C₄	—	172	2	no	—
189	C₄⋊C₄	—	172	1	no	—
190	C₄²	—	2	2	no	—
191	C₄²	—	2	2	no	—
192	C₄²	—	172	2	no	—
193	C₄²	D₄×D₄₃	1	2	yes	—
194	C₄²	#10621900	1	2	yes	—
195	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
196	Q₈	—	2	4	no	—
197	Q₈	—	2	4	no	—
198	Q₈	—	344	4	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	—	86	4	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	#13063248	1	4	yes	—
211	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
212	C₂×C₄	#13063295	1	1	yes	characteristic
213	C₂×C₄	#13063297	1	2	yes	—
214	C₂×C₄	#13063309	1	1	yes	characteristic
215	C₂×C₄	C₂×#10621883	1	1	yes	characteristic
216	C₂×C₄	C₂×#10621885	1	1	yes	characteristic
217	C₂×C₄	#13063345	1	2	yes	—
218	C₈	—	8	2	no	—
219	C₈	—	172	4	no	—
220	C₂²	—	2	1	no	—
221	C₂²	—	2	1	no	—
222	C₂²	#14582776	1	1	yes	characteristic
223	C₂²	C₂×#13063248	1	1	yes	characteristic
224	C₂²	#14582893	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	—	172	4	no	—
231	C₄	#14583084	1	2	yes	—
232	C₄	#14583126	1	2	yes	—
233	C₄	#14583138	1	2	yes	—
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	#19134986	1	1	yes	characteristic
237	C₂	#19135016	1	1	yes	characteristic
238	C₂	#19135140	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19143676

C₂

yes

maximal, characteristic

#19139800

C₂

yes

maximal, characteristic

#19133277

C₂

yes

maximal

#19132496

C₂

yes

maximal

C₄₃×#1801

C₂

yes

maximal, characteristic

C₂×#13063325

C₂²

yes

characteristic

Q₈×C₄₃⋊C₈

—

#14582952

—

#14582952

C₂²

yes

—

#14582819

C₄

yes

—

#14582806

—

#14582797

—

#14582768

—

C₄×C₄⋊Dic₄₃

C₂²

yes

characteristic

#14582647

—

C₂×C₄×Q₈×C₄₃

C₂²

yes

characteristic

C₄₃×#423

C₂²

yes

—

C₂×#101×C₄₃

—

C₄₃×#343

—

C₂²×Dic₈₆

C₂×C₄

yes

—

#13063325

—

#13063325

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×Dic₄₃⋊C₄

—

C₂×C₄×Dic₄₃

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

D₄

yes

—

C₂²⋊(C₄₃⋊C₈)

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

—

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

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

—

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

—

Dic₄₃⋊C₄

—

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

#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

—

C₈×C₄₃

—

C₄₃⋊C₈

—

100

#9392

—

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

#456

yes

—

111

C₄×C₄₃

#465

yes

—

112

C₄×C₄₃

#467

yes

—

113

Dic₄₃

—

114

Dic₄₃

—

115

#2982

—

116

#2567

—

117

#1801

D₄₃

yes

characteristic

118

#1548

—

119

#1303

—

120

C₂×C₄₃

—

121

C₂×C₄₃

—

122

C₂×C₄₃

#1886

yes

characteristic

123

C₂×C₄₃

#1892

yes

characteristic

124

C₂×C₄₃

#1914

yes

characteristic

125

C₂×C₄⋊Q₈

—

126

C₂×C₄×Q₈

C₂×D₄₃

yes

characteristic

127

C₈×Q₈

—

128

#431

—

129

#431

—

130

#423

C₂×D₄₃

yes

—

131

C₂×#101

—

132

#395

—

133

#391

—

134

#389

—

135

#384

—

136

C₄×C₄⋊C₄

—

137

#343

—

138

#333

—

139

C₄₃

#9392

yes

characteristic, complemented, Sylow

140

C₂²×Q₈

—

141

C₂²×Q₈

C₂²⋊D₄₃

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

—

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

C₄×C₈

—

163

C₄×C₈

—

164

#95

—

165

#95

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

344

—

170

C₂×Q₈

#10621883

yes

—

171

C₂×Q₈

#10621885

yes

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

175

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

176

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

177

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

178

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

179

M₁₆

—

180

M₁₆

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

344

—

187

C₄⋊C₄

—

172

—

188

C₄⋊C₄

—

172

—

189

C₄⋊C₄

—

172

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

172

—

193

C₄²

D₄×D₄₃

yes

—

194

C₄²

#10621900

yes

—

195

C₂³

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

196

Q₈

—

197

Q₈

—

198

Q₈

—

344

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

172

—

207

C₂×C₄

—

172

—

208

C₂×C₄

—

172

—

209

C₂×C₄

—

172

—

210

C₂×C₄

#13063248

yes

—

211

C₂×C₄

(C₂²⋊D₄₃)⋊C₄

yes

—

212

C₂×C₄

#13063295

yes

characteristic

213

C₂×C₄

#13063297

yes

—

214

C₂×C₄

#13063309

yes

characteristic

215

C₂×C₄

C₂×#10621883

yes

characteristic

216

C₂×C₄

C₂×#10621885

yes

characteristic

217

C₂×C₄

#13063345

yes

—

218

C₈

—

219

C₈

—

172

—

220

C₂²

—

221

C₂²

—

222

C₂²

#14582776

yes

characteristic

223

C₂²

C₂×#13063248

yes

characteristic

224

C₂²

#14582893

yes

characteristic

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

344

—

230

C₄

—

172

—

231

C₄

#14583084

yes

—

232

C₄

#14583126

yes

—

233

C₄

#14583138

yes

—

234

C₂

—

235

C₂

—

236

C₂

#19134986

yes

characteristic

237

C₂

#19135016

yes

characteristic

238

C₂

#19135140

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	#9392
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
139. C₄₃	#9392	semidirect

H ≅ G/N

type

139. C₄₃

#9392

semidirect

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

subgroup	index
#19143676	2
#19139800	2
#19133277	2
#19132496	2
C₄₃×#1801	2
#9392	43

subgroup

index

C₄₃×#1801

Subgroups — #24993955

Conjugacy classes of subgroups

Complements

Maximal subgroups