Group #24995387 — subgroups

Subgroups — #24995387

Order 11008.

530 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 171 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	C₄×#13063325	C₂	1	1	yes	maximal, characteristic
2	#19134712	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582631	C₂	1	4	yes	maximal
4	C₄₃×#1744	C₂	1	1	yes	maximal, characteristic
5	C₂×#13063325	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₈₆	C₂²	1	2	yes	—
7	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
8	#14582805	C₄	1	2	yes	—
9	#14582797	—	2	2	no	—
10	#14582769	C₄	1	1	yes	characteristic
11	C₄×C₄⋊Dic₄₃	—	2	2	no	—
12	#14582654	—	2	2	no	—
13	#14582631	—	2	8	no	—
14	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
15	C₄³×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×#336	—	2	2	no	—
17	C₂²×Dic₈₆	C₂×C₄	1	2	yes	—
18	C₂²×C₄₃⋊C₈	—	2	2	no	—
19	#13063325	—	2	2	no	—
20	#13063325	C₈	1	4	yes	complemented
21	C₄×Dic₈₆	—	2	4	no	—
22	C₄×Dic₈₆	—	2	4	no	—
23	C₂×C₄⋊Dic₄₃	—	2	2	no	—
24	C₂×C₄⋊Dic₄₃	—	2	2	no	—
25	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
26	C₂×Dic₄₃⋊C₄	—	2	2	no	—
27	C₂×C₄×Dic₄₃	—	2	2	no	—
28	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
29	C₄₃⋊#95	—	2	4	no	—
30	C₂²×C₈×C₄₃	—	2	2	no	—
31	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₄₃	D₄	1	2	yes	—
34	C₂×C₄²×C₄₃	D₄	1	2	yes	—
35	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
36	C₄×C₈×C₄₃	—	2	2	no	—
37	C₄×C₈×C₄₃	D₄	1	4	yes	—
38	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
39	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
40	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
43	C₂²×Dic₄₃	—	2	2	no	—
44	C₂²×Dic₄₃	—	2	2	no	—
45	C₂×Dic₈₆	—	2	4	no	—
46	C₂×Dic₈₆	—	2	4	no	—
47	C₂×Dic₈₆	—	2	2	no	—
48	C₂×Dic₈₆	C₂×C₈	1	4	yes	—
49	C₂×C₈×C₄₃	—	2	4	no	—
50	C₂×C₈×C₄₃	—	4	4	no	—
51	C₄²×C₄₃	—	2	2	no	—
52	C₄²×C₄₃	—	2	4	no	—
53	C₄²×C₄₃	—	4	2	no	—
54	C₄²×C₄₃	C₂×C₈	1	2	yes	—
55	C₄²×C₄₃	M₁₆	1	2	yes	—
56	C₄²×C₄₃	C₂×D₄	1	2	yes	—
57	C₄²×C₄₃	#41	1	2	yes	—
58	C₄⋊Dic₄₃	—	2	8	no	—
59	C₄⋊Dic₄₃	—	2	4	no	—
60	C₄⋊Dic₄₃	—	4	4	no	—
61	Dic₄₃⋊C₄	—	4	4	no	—
62	C₄×Dic₄₃	—	4	2	no	—
63	C₄×Dic₄₃	—	4	2	no	—
64	C₂×C₄₃⋊C₈	—	4	2	no	—
65	C₂×C₄₃⋊C₈	—	4	4	no	—
66	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₄₃	—	2	2	no	—
68	C₂×C₄×C₄₃	—	2	2	no	—
69	C₂×C₄×C₄₃	—	2	2	no	—
70	C₂×C₄×C₄₃	—	2	2	no	—
71	C₂×C₄×C₄₃	—	2	2	no	—
72	C₂×C₄×C₄₃	—	2	2	no	—
73	C₂×C₄×C₄₃	C₂²⋊C₈	1	4	yes	—
74	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
75	C₂×C₄×C₄₃	#121	1	2	yes	—
76	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
77	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
78	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
79	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
80	C₂×C₄×C₄₃	#131	1	2	yes	—
81	C₂×C₄×C₄₃	#137	1	4	yes	—
82	C₂×Dic₄₃	—	2	4	no	—
83	C₂×Dic₄₃	—	4	2	no	—
84	C₂×Dic₄₃	—	4	2	no	—
85	C₂×Dic₄₃	—	4	2	no	—
86	C₂×Dic₄₃	—	4	4	no	—
87	Dic₈₆	—	2	8	no	—
88	Dic₈₆	—	4	4	no	—
89	C₈×C₄₃	—	4	4	no	—
90	C₄₃⋊C₈	—	8	2	no	—
91	#9641	—	43	1	no	maximal, Sylow
92	C₂²×C₄₃	#390	1	1	yes	characteristic
93	C₂²×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
94	C₂²×C₄₃	#408	1	1	yes	characteristic
95	C₂²×C₄₃	#419	1	2	yes	—
96	C₂²×C₄₃	#421	1	2	yes	—
97	C₄×C₄₃	—	2	2	no	—
98	C₄×C₄₃	—	2	4	no	—
99	C₄×C₄₃	—	4	2	no	—
100	C₄×C₄₃	C₈×D₄	1	2	yes	—
101	C₄×C₄₃	#436	1	2	yes	—
102	C₄×C₄₃	#491	1	2	yes	—
103	C₄×C₄₃	#497	1	2	yes	—
104	Dic₄₃	—	4	4	no	—
105	Dic₄₃	—	8	2	no	—
106	C₄×C₄⋊Q₈	—	43	1	no	—
107	#1831	—	43	1	no	—
108	#1744	D₄₃	1	1	yes	characteristic
109	C₂×Q₈⋊C₈	—	43	4	no	—
110	C₂×C₄₃	#1479	1	2	yes	—
111	C₂×C₄₃	#1497	1	2	yes	—
112	C₂×C₄₃	#1954	1	1	yes	characteristic
113	C₂×C₄₃	#1960	1	1	yes	characteristic
114	C₂×C₄₃	#1963	1	1	yes	characteristic
115	C₂×C₄⋊Q₈	—	43	1	no	—
116	C₂×C₄×Q₈	—	43	2	no	—
117	C₂×C₄⋊C₈	—	43	2	no	—
118	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
119	#391	—	43	2	no	—
120	#389	—	86	2	no	—
121	#384	—	43	1	no	—
122	C₄×C₄⋊C₄	—	86	2	no	—
123	C₄³	C₂×D₄₃	1	1	yes	characteristic
124	#336	—	2	2	no	—
125	#336	—	86	2	no	—
126	Q₈⋊C₈	—	86	8	no	—
127	C₄₃	#9641	1	1	yes	characteristic, complemented, Sylow
128	C₂²×Q₈	—	43	2	no	—
129	C₂²×C₈	—	2	2	no	—
130	C₂²×C₈	—	86	2	no	—
131	C₄⋊Q₈	—	43	4	no	—
132	C₄⋊Q₈	—	86	2	no	—
133	C₄×Q₈	—	86	4	no	—
134	C₄×Q₈	—	86	4	no	—
135	C₂×C₄⋊C₄	—	43	2	no	—
136	C₂×C₄⋊C₄	—	86	2	no	—
137	C₂×C₄⋊C₄	—	86	2	no	—
138	C₂×C₄⋊C₄	—	86	2	no	—
139	C₂×C₄²	—	86	2	no	—
140	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
141	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
142	C₂×C₄²	D₁₇₂	1	2	yes	—
143	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
144	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
145	C₄⋊C₈	—	86	4	no	—
146	C₄×C₈	—	2	2	no	—
147	C₄×C₈	D₁₇₂	1	4	yes	—
148	#95	—	86	4	no	—
149	C₂×Q₈	—	43	4	no	—
150	C₂×Q₈	—	86	2	no	—
151	C₂×Q₈	—	86	4	no	—
152	C₂×Q₈	—	86	4	no	—
153	C₂²×C₄	—	86	2	no	—
154	C₂²×C₄	—	86	2	no	—
155	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
156	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
157	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
158	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
159	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
160	C₂×C₈	—	2	4	no	—
161	C₂×C₈	—	4	4	no	—
162	C₂×C₈	—	172	2	no	—
163	C₂×C₈	—	172	4	no	—
164	C₄⋊C₄	—	86	8	no	—
165	C₄⋊C₄	—	86	4	no	—
166	C₄⋊C₄	—	172	4	no	—
167	C₄⋊C₄	—	172	4	no	—
168	C₄²	—	2	2	no	—
169	C₄²	—	2	4	no	—
170	C₄²	—	4	2	no	—
171	C₄²	—	172	2	no	—
172	C₄²	—	172	2	no	—
173	C₄²	C₈×D₄₃	1	2	yes	—
174	C₄²	#10621872	1	2	yes	—
175	C₄²	C₂×D₁₇₂	1	2	yes	—
176	C₄²	#10621898	1	2	yes	—
177	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
178	Q₈	—	86	8	no	—
179	Q₈	—	172	4	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	86	4	no	—
187	C₂×C₄	—	172	2	no	—
188	C₂×C₄	—	172	4	no	—
189	C₂×C₄	—	172	2	no	—
190	C₂×C₄	—	172	2	no	—
191	C₂×C₄	(C₂×D₄₃)⋊C₈	1	4	yes	—
192	C₂×C₄	C₄×D₁₇₂	1	2	yes	—
193	C₂×C₄	#13063299	1	2	yes	—
194	C₂×C₄	#13063313	1	1	yes	characteristic
195	C₂×C₄	#13063322	1	1	yes	characteristic
196	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
197	C₂×C₄	C₂×#10621872	1	1	yes	characteristic
198	C₂×C₄	#13063331	1	2	yes	—
199	C₂×C₄	#13063358	1	4	yes	—
200	C₈	—	4	4	no	—
201	C₈	—	344	2	no	—
202	C₂²	#14582801	1	1	yes	characteristic
203	C₂²	C₂×(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
204	C₂²	#14582865	1	1	yes	characteristic
205	C₂²	#14582909	1	2	yes	—
206	C₂²	#14582917	1	2	yes	—
207	C₄	—	2	4	no	—
208	C₄	—	2	2	no	—
209	C₄	—	4	2	no	—
210	C₄	—	344	2	no	—
211	C₄	—	172	4	no	—
212	C₄	C₈×D₁₇₂	1	2	yes	—
213	C₄	#14582978	1	2	yes	—
214	C₄	#14583268	1	2	yes	—
215	C₄	#14583293	1	2	yes	—
216	C₂	#19132991	1	2	yes	—
217	C₂	#19133069	1	2	yes	—
218	C₂	#19135389	1	1	yes	characteristic
219	C₂	#19135415	1	1	yes	characteristic
220	C₂	#19135427	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#13063325

C₂

yes

maximal, characteristic

#19134712

C₂

yes

maximal, characteristic

C₂×#14582631

C₂

yes

maximal

C₄₃×#1744

C₂

yes

maximal, characteristic

C₂×#13063325

C₄

yes

characteristic

C₂×C₄×Dic₈₆

C₂²

yes

—

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

#14582805

C₄

yes

—

#14582797

—

#14582769

C₄

yes

characteristic

C₄×C₄⋊Dic₄₃

—

#14582654

—

#14582631

—

C₂×C₄×C₈×C₄₃

C₂²

yes

—

C₄³×C₄₃

C₂²

yes

characteristic

C₄₃×#336

—

C₂²×Dic₈₆

C₂×C₄

yes

—

C₂²×C₄₃⋊C₈

—

#13063325

—

#13063325

C₈

yes

complemented

C₄×Dic₈₆

—

C₄×Dic₈₆

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂×C₄

yes

—

C₂×Dic₄₃⋊C₄

—

C₂×C₄×Dic₄₃

—

C₄⋊(C₄₃⋊C₈)

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

—

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄×C₈×C₄₃

—

C₄×C₈×C₄₃

D₄

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×Dic₈₆

C₂×C₈

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×C₈

yes

—

C₄²×C₄₃

M₁₆

yes

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

#41

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₈

yes

—

C₂×C₄×C₄₃

C₄×D₄

yes

—

C₂×C₄×C₄₃

#121

yes

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₄₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₄₃

#131

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

—

C₂²×C₄₃

yes

C₂²×C₄₃

C₂×C₂²⋊C₈

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₂²×C₄₃

#421

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

100

C₄×C₄₃

C₈×D₄

yes

—

101

C₄×C₄₃

#436

yes

—

102

C₄×C₄₃

#491

yes

—

103

C₄×C₄₃

#497

yes

—

104

Dic₄₃

—

105

Dic₄₃

—

106

C₄×C₄⋊Q₈

—

107

#1831

—

108

#1744

D₄₃

yes

characteristic

109

C₂×Q₈⋊C₈

—

110

C₂×C₄₃

#1479

yes

—

111

C₂×C₄₃

#1497

yes

—

112

C₂×C₄₃

#1954

yes

characteristic

113

C₂×C₄₃

#1960

yes

characteristic

114

C₂×C₄₃

#1963

yes

characteristic

115

C₂×C₄⋊Q₈

—

116

C₂×C₄×Q₈

—

117

C₂×C₄⋊C₈

—

118

C₂×C₄×C₈

C₂×D₄₃

yes

—

119

#391

—

120

#389

—

121

#384

—

122

C₄×C₄⋊C₄

—

123

C₄³

C₂×D₄₃

yes

characteristic

124

#336

—

125

#336

—

126

Q₈⋊C₈

—

127

C₄₃

#9641

yes

characteristic, complemented, Sylow

128

C₂²×Q₈

—

129

C₂²×C₈

—

130

C₂²×C₈

—

131

C₄⋊Q₈

—

132

C₄⋊Q₈

—

133

C₄×Q₈

—

134

C₄×Q₈

—

135

C₂×C₄⋊C₄

—

136

C₂×C₄⋊C₄

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄²

—

140

C₂×C₄²

C₄×D₄₃

yes

characteristic

141

C₂×C₄²

C₄×D₄₃

yes

characteristic

142

C₂×C₄²

D₁₇₂

yes

—

143

C₂×C₄²

C₂²⋊D₄₃

yes

—

144

C₂×C₄²

C₂²×D₄₃

yes

characteristic

145

C₄⋊C₈

—

146

C₄×C₈

—

147

C₄×C₈

D₁₇₂

yes

—

148

#95

—

149

C₂×Q₈

—

150

C₂×Q₈

—

151

C₂×Q₈

—

152

C₂×Q₈

—

153

C₂²×C₄

—

154

C₂²×C₄

—

155

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

156

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

157

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

158

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

159

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

—

172

—

163

C₂×C₈

—

172

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

172

—

167

C₄⋊C₄

—

172

—

168

C₄²

—

169

C₄²

—

170

C₄²

—

171

C₄²

—

172

—

172

C₄²

—

172

—

173

C₄²

C₈×D₄₃

yes

—

174

C₄²

#10621872

yes

—

175

C₄²

C₂×D₁₇₂

yes

—

176

C₄²

#10621898

yes

—

177

C₂³

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

178

Q₈

—

179

Q₈

—

172

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

172

—

188

C₂×C₄

—

172

—

189

C₂×C₄

—

172

—

190

C₂×C₄

—

172

—

191

C₂×C₄

(C₂×D₄₃)⋊C₈

yes

—

192

C₂×C₄

C₄×D₁₇₂

yes

—

193

C₂×C₄

#13063299

yes

—

194

C₂×C₄

#13063313

yes

characteristic

195

C₂×C₄

#13063322

yes

characteristic

196

C₂×C₄

C₂×C₈×D₄₃

yes

characteristic

197

C₂×C₄

C₂×#10621872

yes

characteristic

198

C₂×C₄

#13063331

yes

—

199

C₂×C₄

#13063358

yes

—

200

C₈

—

201

C₈

—

344

—

202

C₂²

#14582801

yes

characteristic

203

C₂²

C₂×(C₂×D₄₃)⋊C₈

yes

characteristic

204

C₂²

#14582865

yes

characteristic

205

C₂²

#14582909

yes

—

206

C₂²

#14582917

yes

—

207

C₄

—

208

C₄

—

209

C₄

—

210

C₄

—

344

—

211

C₄

—

172

—

212

C₄

C₈×D₁₇₂

yes

—

213

C₄

#14582978

yes

—

214

C₄

#14583268

yes

—

215

C₄

#14583293

yes

—

216

C₂

#19132991

yes

—

217

C₂

#19133069

yes

—

218

C₂

#19135389

yes

characteristic

219

C₂

#19135415

yes

characteristic

220

C₂

#19135427

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1744	C₂
socle, prime radical	C₂³×C₄₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1744	D₄₃
hypocenter	C₄₃	#9641
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1744

subgroup

G/H

center

C₂²×C₄

C₂×D₁₇₂

commutator

C₂×C₄×C₄₃

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1744

C₂

socle, prime radical

C₂³×C₄₃

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1744

N	H ≅ G/N	type
20. #13063325	C₈	semidirect
127. C₄₃	#9641	semidirect

H ≅ G/N

type

20. #13063325

C₈

semidirect

127. C₄₃

#9641

semidirect

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

subgroup	index
C₄×#13063325	2
#19134712	2
C₂×#14582631	2
C₄₃×#1744	2
#9641	43

subgroup

index

C₄₃×#1744

Subgroups — #24995387

Conjugacy classes of subgroups

Complements

Maximal subgroups