Group #24996480 — subgroups

Subgroups — #24996480

Order 11008.

478 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 139 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	#19145181	C₂	1	1	yes	maximal, characteristic
2	#19135572	C₂	1	2	yes	maximal
3	#19133354	C₂	1	1	yes	maximal, characteristic
4	#19133051	C₂	1	2	yes	maximal
5	C₄²×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
6	#14583456	C₂²	1	2	yes	—
7	#14583304	C₄	1	1	yes	characteristic, complemented
8	#14583279	C₄	1	1	yes	characteristic, complemented
9	#14583250	C₄	1	2	yes	complemented
10	#14583140	—	2	2	no	—
11	C₄×Dic₁₇₂	—	2	2	no	—
12	#14582923	C₂²	1	2	yes	—
13	#14582659	—	2	4	no	—
14	#14582652	—	2	2	no	—
15	#14582631	—	2	4	no	—
16	C₂×C₄×C₈×C₄₃	—	2	2	no	—
17	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₄³×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×Dic₁₇₂	—	2	2	no	—
21	C₂×#10621877	—	2	2	no	—
22	#13063325	C₂×C₄	1	2	yes	—
23	#13063325	C₂×C₄	1	2	yes	—
24	#13063317	—	2	2	no	—
25	#13063304	—	2	2	no	—
26	#13063304	—	2	2	no	—
27	C₄×Dic₈₆	—	2	2	no	—
28	C₄×Dic₈₆	—	2	2	no	—
29	#13063284	—	2	2	no	—
30	#13063259	—	2	2	no	—
31	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
32	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
33	#13063250	—	2	4	no	—
34	C₂²×C₈×C₄₃	—	2	1	no	—
35	C₂²×C₈×C₄₃	D₄	1	2	yes	—
36	C₂×C₄²×C₄₃	—	2	1	no	—
37	C₂×C₄²×C₄₃	—	2	1	no	—
38	C₂×C₄²×C₄₃	D₄	1	2	yes	—
39	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
40	C₄×C₈×C₄₃	—	2	8	no	—
41	C₄×C₈×C₄₃	—	2	1	no	—
42	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₄₃	D₄	1	2	yes	—
45	C₄×C₈×C₄₃	D₄	1	2	yes	—
46	C₂²×C₄×C₄₃	—	2	2	no	—
47	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
50	C₂×Dic₈₆	—	2	2	no	—
51	C₂×Dic₈₆	—	2	2	no	—
52	C₂×C₈×C₄₃	—	2	4	no	—
53	C₂×C₈×C₄₃	—	2	2	no	—
54	C₂×C₈×C₄₃	—	2	4	no	—
55	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
56	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
57	C₄²×C₄₃	—	2	4	no	—
58	C₄²×C₄₃	—	2	4	no	—
59	C₄²×C₄₃	—	2	2	no	—
60	C₄²×C₄₃	Q₁₆	1	4	yes	complemented
61	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
62	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
63	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
64	C₄²×C₄₃	#41	1	1	yes	characteristic
65	C₂²⋊Dic₄₃	—	4	2	no	—
66	C₄⋊Dic₄₃	—	2	2	no	—
67	C₄⋊Dic₄₃	—	2	2	no	—
68	C₄⋊Dic₄₃	—	2	2	no	—
69	C₄⋊Dic₄₃	—	2	2	no	—
70	Dic₄₃⋊C₄	—	4	2	no	—
71	Dic₄₃⋊C₄	—	4	2	no	—
72	C₄×Dic₄₃	—	4	2	no	—
73	#10621877	—	4	4	no	—
74	C₂×C₄₃⋊C₈	—	4	2	no	—
75	Dic₁₇₂	—	4	4	no	—
76	C₂³×C₄₃	#121	1	1	yes	characteristic
77	C₂×C₄×C₄₃	—	2	4	no	—
78	C₂×C₄×C₄₃	—	2	4	no	—
79	C₂×C₄×C₄₃	—	2	4	no	—
80	C₂×C₄×C₄₃	—	2	2	no	—
81	C₂×C₄×C₄₃	—	2	2	no	—
82	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
84	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
86	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
87	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
88	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
89	C₂×C₄×C₄₃	#135	1	2	yes	—
90	C₂×Dic₄₃	—	4	2	no	—
91	C₂×Dic₄₃	—	4	2	no	—
92	Dic₈₆	—	4	4	no	—
93	Dic₈₆	—	4	4	no	—
94	C₈×C₄₃	—	2	4	no	—
95	C₈×C₄₃	—	2	2	no	—
96	C₈×C₄₃	#104	1	4	yes	—
97	C₄₃⋊C₈	—	8	2	no	—
98	#9845	—	43	1	no	maximal, Sylow
99	C₂²×C₄₃	—	2	1	no	—
100	C₂²×C₄₃	—	2	1	no	—
101	C₂²×C₄₃	#390	1	1	yes	characteristic
102	C₂²×C₄₃	#467	1	2	yes	—
103	C₄×C₄₃	—	2	8	no	—
104	C₄×C₄₃	—	2	1	no	—
105	C₄×C₄₃	—	2	1	no	—
106	C₄×C₄₃	C₂×#104	1	2	yes	—
107	C₄×C₄₃	C₄×Q₁₆	1	2	yes	—
108	C₄×C₄₃	#443	1	2	yes	—
109	C₄×C₄₃	#494	1	1	yes	characteristic
110	C₄×C₄₃	#495	1	1	yes	characteristic
111	Dic₄₃	—	8	2	no	—
112	Dic₄₃	—	8	2	no	—
113	#3170	—	43	1	no	—
114	#1994	—	43	2	no	—
115	C₄²×C₈	D₄₃	1	1	yes	characteristic
116	#1567	—	43	1	no	—
117	#1493	—	43	2	no	—
118	C₂×C₄₃	—	2	2	no	—
119	C₂×C₄₃	#1962	1	1	yes	characteristic
120	C₂×C₄₃	#1969	1	1	yes	characteristic
121	C₂×C₄₃	#1974	1	1	yes	characteristic
122	#533	—	43	2	no	—
123	#500	—	43	1	no	—
124	#494	—	43	1	no	—
125	#487	—	43	2	no	—
126	#467	—	86	2	no	—
127	C₄×Q₁₆	—	86	2	no	—
128	#423	—	43	2	no	—
129	C₂×C₄×C₈	—	2	2	no	—
130	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
131	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
132	C₄³	C₂×D₄₃	1	1	yes	characteristic
133	#339	—	86	4	no	—
134	#335	—	86	2	no	—
135	Q₈⋊C₈	—	86	4	no	—
136	C₄₃	#9845	1	1	yes	characteristic, complemented, Sylow
137	C₂×Q₁₆	—	86	2	no	—
138	C₂×M₁₆	—	86	2	no	—
139	C₂²×C₈	—	2	1	no	—
140	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
141	C₄⋊Q₈	—	43	2	no	—
142	C₄⋊Q₈	—	43	2	no	—
143	#125	—	86	2	no	—
144	C₂²⋊Q₈	—	86	2	no	—
145	C₂²⋊Q₈	—	86	2	no	—
146	C₄×Q₈	—	86	2	no	—
147	C₄×Q₈	—	86	2	no	—
148	#117	—	86	2	no	—
149	C₂×C₄²	—	2	1	no	—
150	C₂×C₄²	—	2	1	no	—
151	C₂×C₄²	D₁₇₂	1	2	yes	—
152	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
153	#107	—	86	2	no	—
154	C₄⋊C₈	—	86	2	no	—
155	C₄⋊C₈	—	86	2	no	—
156	#103	—	86	4	no	—
157	C₄×C₈	—	2	8	no	—
158	C₄×C₈	—	2	1	no	—
159	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
160	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
161	C₄×C₈	D₁₇₂	1	2	yes	—
162	C₄×C₈	D₁₇₂	1	2	yes	—
163	C₂×Q₈	—	86	2	no	—
164	C₂×Q₈	—	86	2	no	—
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
167	C₂²×C₄	#10621898	1	1	yes	characteristic
168	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
169	Q₁₆	—	172	4	no	—
170	M₁₆	—	172	4	no	—
171	C₂×C₈	—	2	4	no	—
172	C₂×C₈	—	2	2	no	—
173	C₂×C₈	—	2	4	no	—
174	C₂×C₈	—	172	2	no	—
175	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
176	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
177	C₄⋊C₄	—	86	2	no	—
178	C₄⋊C₄	—	86	2	no	—
179	C₄⋊C₄	—	86	2	no	—
180	C₄⋊C₄	—	86	2	no	—
181	C₄⋊C₄	—	172	2	no	—
182	C₄⋊C₄	—	172	2	no	—
183	C₂²⋊C₄	—	172	2	no	—
184	C₄²	—	2	4	no	—
185	C₄²	—	2	4	no	—
186	C₄²	—	2	2	no	—
187	C₄²	—	172	2	no	—
188	C₄²	Dic₁₇₂	1	4	yes	complemented
189	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
190	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
191	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
192	C₄²	#10621898	1	1	yes	characteristic
193	C₂³	#13063299	1	1	yes	characteristic
194	Q₈	—	172	4	no	—
195	Q₈	—	172	4	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	172	2	no	—
202	C₂×C₄	—	172	2	no	—
203	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
204	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
205	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
206	C₂×C₄	#13063299	1	1	yes	characteristic
207	C₂×C₄	#13063313	1	1	yes	characteristic
208	C₂×C₄	#13063322	1	1	yes	characteristic
209	C₂×C₄	C₂×Dic₁₇₂	1	2	yes	—
210	C₂×C₄	#13063347	1	2	yes	—
211	C₈	—	2	4	no	—
212	C₈	—	2	2	no	—
213	C₈	—	344	2	no	—
214	C₈	#13063253	1	4	yes	—
215	C₂²	—	2	1	no	—
216	C₂²	—	2	1	no	—
217	C₂²	#14582801	1	1	yes	characteristic
218	C₂²	#14583140	1	2	yes	—
219	C₄	—	2	8	no	—
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	—	344	2	no	—
223	C₄	—	344	2	no	—
224	C₄	C₂×#13063253	1	2	yes	—
225	C₄	C₄×Dic₁₇₂	1	2	yes	—
226	C₄	#14583017	1	2	yes	—
227	C₄	#14583279	1	1	yes	characteristic
228	C₄	#14583283	1	1	yes	characteristic
229	C₂	—	2	2	no	—
230	C₂	#19135423	1	1	yes	characteristic
231	C₂	#19135456	1	1	yes	characteristic
232	C₂	#19135483	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19145181

C₂

yes

maximal, characteristic

#19135572

C₂

yes

maximal

#19133354

C₂

yes

maximal, characteristic

#19133051

C₂

yes

maximal

C₄²×C₈×C₄₃

C₂

yes

maximal, characteristic

#14583456

C₂²

yes

—

#14583304

C₄

yes

characteristic, complemented

#14583279

C₄

yes

characteristic, complemented

#14583250

C₄

yes

complemented

#14583140

—

C₄×Dic₁₇₂

—

#14582923

C₂²

yes

—

#14582659

—

#14582652

—

#14582631

—

C₂×C₄×C₈×C₄₃

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄³×C₄₃

C₂²

yes

characteristic

C₂×Dic₁₇₂

—

C₂×#10621877

—

#13063325

C₂×C₄

yes

—

#13063325

C₂×C₄

yes

—

#13063317

—

#13063304

—

#13063304

—

C₄×Dic₈₆

—

C₄×Dic₈₆

—

#13063284

—

#13063259

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

#13063250

—

C₂²×C₈×C₄₃

—

C₂²×C₈×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄×C₈×C₄₃

—

C₄×C₈×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

—

C₄×C₈×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

Q₁₆

yes

complemented

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

#41

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

#10621877

—

C₂×C₄₃⋊C₈

—

Dic₁₇₂

—

C₂³×C₄₃

#121

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄×D₄

yes

characteristic

C₂×C₄×C₄₃

C₄×D₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

C₂×Q₁₆

yes

—

C₂×C₄×C₄₃

#135

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

#104

yes

—

C₄₃⋊C₈

—

#9845

—

maximal, Sylow

C₂²×C₄₃

—

100

C₂²×C₄₃

—

101

C₂²×C₄₃

#390

yes

characteristic

102

C₂²×C₄₃

#467

yes

—

103

C₄×C₄₃

—

104

C₄×C₄₃

—

105

C₄×C₄₃

—

106

C₄×C₄₃

C₂×#104

yes

—

107

C₄×C₄₃

C₄×Q₁₆

yes

—

108

C₄×C₄₃

#443

yes

—

109

C₄×C₄₃

#494

yes

characteristic

110

C₄×C₄₃

#495

yes

characteristic

111

Dic₄₃

—

112

Dic₄₃

—

113

#3170

—

114

#1994

—

115

C₄²×C₈

D₄₃

yes

characteristic

116

#1567

—

117

#1493

—

118

C₂×C₄₃

—

119

C₂×C₄₃

#1962

yes

characteristic

120

C₂×C₄₃

#1969

yes

characteristic

121

C₂×C₄₃

#1974

yes

characteristic

122

#533

—

123

#500

—

124

#494

—

125

#487

—

126

#467

—

127

C₄×Q₁₆

—

128

#423

—

129

C₂×C₄×C₈

—

130

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

131

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

132

C₄³

C₂×D₄₃

yes

characteristic

133

#339

—

134

#335

—

135

Q₈⋊C₈

—

136

C₄₃

#9845

yes

characteristic, complemented, Sylow

137

C₂×Q₁₆

—

138

C₂×M₁₆

—

139

C₂²×C₈

—

140

C₂²×C₈

C₂²⋊D₄₃

yes

—

141

C₄⋊Q₈

—

142

C₄⋊Q₈

—

143

#125

—

144

C₂²⋊Q₈

—

145

C₂²⋊Q₈

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

#117

—

149

C₂×C₄²

—

150

C₂×C₄²

—

151

C₂×C₄²

D₁₇₂

yes

—

152

C₂×C₄²

C₂²×D₄₃

yes

characteristic

153

#107

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

#103

—

157

C₄×C₈

—

158

C₄×C₈

—

159

C₄×C₈

C₄×D₄₃

yes

characteristic

160

C₄×C₈

C₄×D₄₃

yes

characteristic

161

C₄×C₈

D₁₇₂

yes

—

162

C₄×C₈

D₁₇₂

yes

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂²×C₄

—

166

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

167

C₂²×C₄

#10621898

yes

characteristic

168

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

169

Q₁₆

—

172

—

170

M₁₆

—

172

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

172

—

175

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

—

176

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

172

—

182

C₄⋊C₄

—

172

—

183

C₂²⋊C₄

—

172

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

172

—

188

C₄²

Dic₁₇₂

yes

complemented

189

C₄²

C₂×C₄×D₄₃

yes

characteristic

190

C₄²

C₂×D₁₇₂

yes

characteristic

191

C₄²

C₂×D₁₇₂

yes

characteristic

192

C₄²

#10621898

yes

characteristic

193

C₂³

#13063299

yes

characteristic

194

Q₈

—

172

—

195

Q₈

—

172

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

172

—

202

C₂×C₄

—

172

—

203

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

204

C₂×C₄

C₄×D₁₇₂

yes

characteristic

205

C₂×C₄

C₄×D₁₇₂

yes

characteristic

206

C₂×C₄

#13063299

yes

characteristic

207

C₂×C₄

#13063313

yes

characteristic

208

C₂×C₄

#13063322

yes

characteristic

209

C₂×C₄

C₂×Dic₁₇₂

yes

—

210

C₂×C₄

#13063347

yes

—

211

C₈

—

212

C₈

—

213

C₈

—

344

—

214

C₈

#13063253

yes

—

215

C₂²

—

216

C₂²

—

217

C₂²

#14582801

yes

characteristic

218

C₂²

#14583140

yes

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

344

—

223

C₄

—

344

—

224

C₄

C₂×#13063253

yes

—

225

C₄

C₄×Dic₁₇₂

yes

—

226

C₄

#14583017

yes

—

227

C₄

#14583279

yes

characteristic

228

C₄

#14583283

yes

characteristic

229

C₂

—

230

C₂

#19135423

yes

characteristic

231

C₂

#19135456

yes

characteristic

232

C₂

#19135483

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13063322
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄²×C₈×C₄₃	C₂
socle	C₂²×C₄₃	#390
prime radical	C₂³×C₄₃	#121
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₄²×C₈	D₄₃
hypocenter	C₄₃	#9845
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄²×C₈

subgroup

G/H

center

C₂×C₄

#13063322

commutator

C₄²×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄²×C₈×C₄₃

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×C₄²×C₄₃

C₂³

hypercenter

C₄²×C₈

D₄₃

hypocenter

C₄₃

#9845

LCS

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄²×C₈

N	H ≅ G/N	type
7. #14583304	C₄	semidirect
8. #14583279	C₄	semidirect
9. #14583250	C₄	semidirect
60. C₄²×C₄₃	Q₁₆	semidirect
136. C₄₃	#9845	semidirect
188. C₄²	Dic₁₇₂	semidirect

H ≅ G/N

type

7. #14583304

C₄

semidirect

8. #14583279

C₄

semidirect

9. #14583250

C₄

semidirect

60. C₄²×C₄₃

Q₁₆

semidirect

136. C₄₃

#9845

semidirect

188. C₄²

Dic₁₇₂

semidirect

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

subgroup	index
#19145181	2
#19135572	2
#19133354	2
#19133051	2
C₄²×C₈×C₄₃	2
#9845	43

subgroup

index

C₄²×C₈×C₄₃

Subgroups — #24996480

Conjugacy classes of subgroups

Complements

Maximal subgroups