Group #24928745 — subgroups

Subgroups — C₄₃×#8728 #24928745

Order 11008.

514 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 166 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	C₄₃×#2285	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#1797	C₂	1	2	yes	maximal
3	C₄₃×#1296	C₂	1	2	yes	maximal, complemented
4	C₄₃×#1296	C₂	1	2	yes	maximal, complemented
5	C₂×#117×C₄₃	C₄	1	2	yes	—
6	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₈×C₄₃	C₂²	1	4	yes	—
8	C₂×C₂²⋊C₈×C₄₃	—	2	2	no	—
9	C₄₃×#384	C₂²	1	1	yes	characteristic
10	C₄₃×#384	C₂²	1	1	yes	characteristic
11	C₄₃×#382	C₄	1	2	yes	—
12	C₄₃×#380	—	2	2	no	—
13	C₄×C₄⋊C₄×C₄₃	—	2	2	no	—
14	C₄₃×#336	—	2	2	no	—
15	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂³×C₄×C₄₃	D₄	1	2	yes	—
17	C₂²×C₈×C₄₃	—	2	4	no	—
18	#117×C₄₃	—	4	4	no	—
19	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
20	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
21	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
22	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
23	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
24	C₂×C₄²×C₄₃	—	2	4	no	—
25	C₂×C₄²×C₄₃	—	2	2	no	—
26	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₄₃	D₄	1	2	yes	—
28	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
29	C₄⋊C₈×C₄₃	—	2	8	no	—
30	C₂²⋊C₈×C₄₃	—	4	4	no	—
31	#95×C₄₃	—	2	4	no	—
32	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
33	C₂²×C₄×C₄₃	—	2	2	no	—
34	C₂²×C₄×C₄₃	—	2	2	no	—
35	C₂²×C₄×C₄₃	—	2	4	no	—
36	C₂²×C₄×C₄₃	—	2	4	no	—
37	C₂²×C₄×C₄₃	—	2	2	no	—
38	C₂²×C₄×C₄₃	—	2	2	no	—
39	C₂²×C₄×C₄₃	—	2	2	no	—
40	C₂²×C₄×C₄₃	—	2	2	no	—
41	C₂²×C₄×C₄₃	—	2	2	no	—
42	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
43	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
44	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
45	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
46	C₂×C₈×C₄₃	—	4	4	no	—
47	C₂×C₈×C₄₃	—	4	4	no	—
48	C₂×C₈×C₄₃	—	4	4	no	—
49	C₄⋊C₄×C₄₃	—	4	2	no	—
50	C₄⋊C₄×C₄₃	—	4	2	no	—
51	C₄⋊C₄×C₄₃	—	4	4	no	—
52	C₄⋊C₄×C₄₃	—	4	2	no	—
53	C₄⋊C₄×C₄₃	—	4	2	no	—
54	C₂²⋊C₄×C₄₃	—	4	4	no	—
55	C₄²×C₄₃	—	2	2	no	—
56	C₄²×C₄₃	—	2	4	no	—
57	C₄²×C₄₃	—	4	4	no	—
58	C₄²×C₄₃	#41	1	4	yes	—
59	C₂³×C₄₃	—	2	1	no	—
60	C₂³×C₄₃	—	2	1	no	—
61	C₂³×C₄₃	—	2	2	no	—
62	C₂³×C₄₃	—	2	2	no	—
63	C₂³×C₄₃	#101	1	2	yes	—
64	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₄×C₄₃	—	2	8	no	—
66	C₂×C₄×C₄₃	—	2	1	no	—
67	C₂×C₄×C₄₃	—	2	1	no	—
68	C₂×C₄×C₄₃	—	2	1	no	—
69	C₂×C₄×C₄₃	—	2	1	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	—	4	4	no	—
74	C₂×C₄×C₄₃	—	4	4	no	—
75	C₂×C₄×C₄₃	—	4	2	no	—
76	C₂×C₄×C₄₃	—	4	2	no	—
77	C₂×C₄×C₄₃	—	4	4	no	—
78	C₂×C₄×C₄₃	—	4	4	no	—
79	C₂×C₄×C₄₃	#100	1	2	yes	—
80	C₂×C₄×C₄₃	#117	1	2	yes	—
81	C₂×C₄×C₄₃	#123	1	4	yes	—
82	C₂×C₄×C₄₃	#135	1	4	yes	—
83	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
84	C₂×C₄×C₄₃	#137	1	2	yes	—
85	C₈×C₄₃	—	8	4	no	—
86	#8728	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂²×C₄₃	—	2	4	no	—
88	C₂²×C₄₃	—	2	2	no	—
89	C₂²×C₄₃	—	4	1	no	—
90	C₂²×C₄₃	—	4	1	no	—
91	C₂²×C₄₃	—	4	2	no	—
92	C₂²×C₄₃	#381	1	1	yes	characteristic
93	C₂²×C₄₃	C₂×#100	1	1	yes	characteristic
94	C₂²×C₄₃	C₂×#101	1	1	yes	characteristic
95	C₂²×C₄₃	#416	1	2	yes	—
96	C₂²×C₄₃	#417	1	2	yes	—
97	C₄×C₄₃	—	2	2	no	—
98	C₄×C₄₃	—	2	2	no	—
99	C₄×C₄₃	—	4	2	no	—
100	C₄×C₄₃	—	8	2	no	—
101	C₄×C₄₃	—	8	2	no	—
102	C₄×C₄₃	#482	1	4	yes	—
103	C₄×C₄₃	#485	1	4	yes	—
104	#2285	C₂×C₄₃	1	1	yes	characteristic
105	#1797	C₂×C₄₃	1	2	yes	—
106	#1296	C₂×C₄₃	1	2	yes	complemented
107	#1296	C₂×C₄₃	1	2	yes	complemented
108	C₂×C₄₃	—	4	2	no	—
109	C₂×C₄₃	#1543	1	1	yes	characteristic
110	C₂×C₄₃	#1552	1	2	yes	—
111	C₂×C₄₃	#1560	1	1	yes	characteristic
112	C₂×C₄₃	#1821	1	1	yes	characteristic
113	C₂×C₄₃	#1825	1	2	yes	—
114	C₂×#117	C₄×C₄₃	1	2	yes	—
115	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
116	C₂×C₄⋊C₈	C₂²×C₄₃	1	4	yes	—
117	C₂×C₂²⋊C₈	—	2	2	no	—
118	#384	C₂²×C₄₃	1	1	yes	characteristic
119	#384	C₂²×C₄₃	1	1	yes	characteristic
120	#382	C₄×C₄₃	1	2	yes	—
121	#380	—	2	2	no	—
122	C₄×C₄⋊C₄	—	2	2	no	—
123	#336	—	2	2	no	—
124	C₄₃	#8728	1	1	yes	characteristic, direct product factor, Sylow
125	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
126	C₂³×C₄	D₄×C₄₃	1	2	yes	—
127	C₂²×C₈	—	2	4	no	—
128	#117	—	4	4	no	—
129	C₂×C₄⋊C₄	—	2	2	no	—
130	C₂×C₄⋊C₄	—	2	2	no	—
131	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
132	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
133	C₂×C₂²⋊C₄	—	2	2	no	—
134	C₂×C₄²	—	2	4	no	—
135	C₂×C₄²	—	2	2	no	—
136	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
137	C₂×C₄²	D₄×C₄₃	1	2	yes	—
138	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
139	C₄⋊C₈	—	2	8	no	—
140	C₂²⋊C₈	—	4	4	no	—
141	#95	—	2	4	no	—
142	C₂⁴	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
143	C₂²×C₄	—	2	2	no	—
144	C₂²×C₄	—	2	2	no	—
145	C₂²×C₄	—	2	2	no	—
146	C₂²×C₄	—	2	4	no	—
147	C₂²×C₄	—	2	4	no	—
148	C₂²×C₄	—	2	2	no	—
149	C₂²×C₄	—	2	2	no	—
150	C₂²×C₄	—	2	2	no	—
151	C₂²×C₄	—	2	2	no	—
152	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
153	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
154	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
155	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
156	C₂×C₈	—	4	4	no	—
157	C₂×C₈	—	4	4	no	—
158	C₂×C₈	—	4	4	no	—
159	C₄⋊C₄	—	4	2	no	—
160	C₄⋊C₄	—	4	2	no	—
161	C₄⋊C₄	—	4	4	no	—
162	C₄⋊C₄	—	4	2	no	—
163	C₄⋊C₄	—	4	2	no	—
164	C₂²⋊C₄	—	4	4	no	—
165	C₄²	—	2	2	no	—
166	C₄²	—	2	4	no	—
167	C₄²	—	4	4	no	—
168	C₄²	#41×C₄₃	1	4	yes	—
169	C₂³	—	2	1	no	—
170	C₂³	—	2	1	no	—
171	C₂³	—	2	2	no	—
172	C₂³	—	2	2	no	—
173	C₂³	#101×C₄₃	1	2	yes	—
174	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
175	C₂×C₄	—	2	8	no	—
176	C₂×C₄	—	2	1	no	—
177	C₂×C₄	—	2	1	no	—
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	—	2	1	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	4	4	no	—
184	C₂×C₄	—	4	4	no	—
185	C₂×C₄	—	4	2	no	—
186	C₂×C₄	—	4	2	no	—
187	C₂×C₄	—	4	4	no	—
188	C₂×C₄	—	4	4	no	—
189	C₂×C₄	#100×C₄₃	1	2	yes	—
190	C₂×C₄	#117×C₄₃	1	2	yes	—
191	C₂×C₄	#123×C₄₃	1	4	yes	—
192	C₂×C₄	#135×C₄₃	1	4	yes	—
193	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
194	C₂×C₄	#137×C₄₃	1	2	yes	—
195	C₈	—	8	4	no	—
196	C₂²	—	2	4	no	—
197	C₂²	—	2	2	no	—
198	C₂²	—	4	1	no	—
199	C₂²	—	4	2	no	—
200	C₂²	—	4	1	no	—
201	C₂²	C₄₃×#381	1	1	yes	characteristic
202	C₂²	C₂×#100×C₄₃	1	1	yes	characteristic
203	C₂²	C₂×#101×C₄₃	1	1	yes	characteristic
204	C₂²	C₄₃×#416	1	2	yes	—
205	C₂²	C₄₃×#417	1	2	yes	—
206	C₄	—	2	2	no	—
207	C₄	—	2	2	no	—
208	C₄	—	4	2	no	—
209	C₄	—	8	2	no	—
210	C₄	—	8	2	no	—
211	C₄	C₄₃×#482	1	4	yes	—
212	C₄	C₄₃×#485	1	4	yes	—
213	C₂	—	4	2	no	—
214	C₂	C₄₃×#1543	1	1	yes	characteristic
215	C₂	C₄₃×#1552	1	2	yes	—
216	C₂	C₄₃×#1560	1	1	yes	characteristic
217	C₂	C₄₃×#1821	1	1	yes	characteristic
218	C₂	C₄₃×#1825	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄₃×#2285

C₂

yes

maximal, characteristic

C₄₃×#1797

C₂

yes

maximal

C₄₃×#1296

C₂

yes

maximal, complemented

C₄₃×#1296

C₂

yes

maximal, complemented

C₂×#117×C₄₃

C₄

yes

—

C₂²×C₄²×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₄₃

C₂²

yes

—

C₂×C₂²⋊C₈×C₄₃

—

C₄₃×#384

C₂²

yes

characteristic

C₄₃×#384

C₂²

yes

characteristic

C₄₃×#382

C₄

yes

—

C₄₃×#380

—

C₄×C₄⋊C₄×C₄₃

—

C₄₃×#336

—

C₂³×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₃

D₄

yes

—

C₂²×C₈×C₄₃

—

#117×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₄₃

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²⋊C₈×C₄₃

—

#95×C₄₃

—

C₂⁴×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

#41

yes

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

#101

yes

—

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

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#100

yes

—

C₂×C₄×C₄₃

#117

yes

—

C₂×C₄×C₄₃

#123

yes

—

C₂×C₄×C₄₃

#135

yes

—

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₈×C₄₃

—

#8728

C₄₃

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₂²×C₄₃

#417

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

100

C₄×C₄₃

—

101

C₄×C₄₃

—

102

C₄×C₄₃

#482

yes

—

103

C₄×C₄₃

#485

yes

—

104

#2285

C₂×C₄₃

yes

characteristic

105

#1797

C₂×C₄₃

yes

—

106

#1296

C₂×C₄₃

yes

complemented

107

#1296

C₂×C₄₃

yes

complemented

108

C₂×C₄₃

—

109

C₂×C₄₃

#1543

yes

characteristic

110

C₂×C₄₃

#1552

yes

—

111

C₂×C₄₃

#1560

yes

characteristic

112

C₂×C₄₃

#1821

yes

characteristic

113

C₂×C₄₃

#1825

yes

—

114

C₂×#117

C₄×C₄₃

yes

—

115

C₂²×C₄²

C₂²×C₄₃

yes

characteristic

116

C₂×C₄⋊C₈

C₂²×C₄₃

yes

—

117

C₂×C₂²⋊C₈

—

118

#384

C₂²×C₄₃

yes

characteristic

119

#384

C₂²×C₄₃

yes

characteristic

120

#382

C₄×C₄₃

yes

—

121

#380

—

122

C₄×C₄⋊C₄

—

123

#336

—

124

C₄₃

#8728

yes

characteristic, direct product factor, Sylow

125

C₂³×C₄

C₂×C₄×C₄₃

yes

characteristic

126

C₂³×C₄

D₄×C₄₃

yes

—

127

C₂²×C₈

—

128

#117

—

129

C₂×C₄⋊C₄

—

130

C₂×C₄⋊C₄

—

131

C₂×C₄⋊C₄

C₂×C₄×C₄₃

yes

—

132

C₂×C₄⋊C₄

C₂×C₄×C₄₃

yes

—

133

C₂×C₂²⋊C₄

—

134

C₂×C₄²

—

135

C₂×C₄²

—

136

C₂×C₄²

C₂×C₄×C₄₃

yes

characteristic

137

C₂×C₄²

D₄×C₄₃

yes

—

138

C₂×C₄²

C₂³×C₄₃

yes

characteristic

139

C₄⋊C₈

—

140

C₂²⋊C₈

—

141

#95

—

142

C₂⁴

C₂²⋊C₄×C₄₃

yes

characteristic

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

—

151

C₂²×C₄

—

152

C₂²×C₄

C₂²⋊C₄×C₄₃

yes

—

153

C₂²×C₄

C₂²⋊C₄×C₄₃

yes

characteristic

154

C₂²×C₄

C₂²×C₄×C₄₃

yes

characteristic

155

C₂²×C₄

C₂×D₄×C₄₃

yes

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₄⋊C₄

—

160

C₄⋊C₄

—

161

C₄⋊C₄

—

162

C₄⋊C₄

—

163

C₄⋊C₄

—

164

C₂²⋊C₄

—

165

C₄²

—

166

C₄²

—

167

C₄²

—

168

C₄²

#41×C₄₃

yes

—

169

C₂³

—

170

C₂³

—

171

C₂³

—

172

C₂³

—

173

C₂³

#101×C₄₃

yes

—

174

C₂³

C₂×C₂²⋊C₄×C₄₃

yes

characteristic

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

#100×C₄₃

yes

—

190

C₂×C₄

#117×C₄₃

yes

—

191

C₂×C₄

#123×C₄₃

yes

—

192

C₂×C₄

#135×C₄₃

yes

—

193

C₂×C₄

AGL(1,ℤ/8)×C₄₃

yes

—

194

C₂×C₄

#137×C₄₃

yes

—

195

C₈

—

196

C₂²

—

197

C₂²

—

198

C₂²

—

199

C₂²

—

200

C₂²

—

201

C₂²

C₄₃×#381

yes

characteristic

202

C₂²

C₂×#100×C₄₃

yes

characteristic

203

C₂²

C₂×#101×C₄₃

yes

characteristic

204

C₂²

C₄₃×#416

yes

—

205

C₂²

C₄₃×#417

yes

—

206

C₄

—

207

C₄

—

208

C₄

—

209

C₄

—

210

C₄

—

211

C₄

C₄₃×#482

yes

—

212

C₄

C₄₃×#485

yes

—

213

C₂

—

214

C₂

C₄₃×#1543

yes

characteristic

215

C₂

C₄₃×#1552

yes

—

216

C₂

C₄₃×#1560

yes

characteristic

217

C₂

C₄₃×#1821

yes

characteristic

218

C₂

C₄₃×#1825

yes

—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₄₃
Frattini, cosocle	C₂×C₄²	C₂³×C₄₃
prime radical	C₂⁴×C₄₃	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

subgroup

G/H

center, socle

C₂³×C₄₃

C₂×C₂²⋊C₄

commutator

C₂²×C₄

C₂²×C₄×C₄₃

Frattini, cosocle

C₂×C₄²

C₂³×C₄₃

prime radical

C₂⁴×C₄₃

C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

N	H ≅ G/N	type
3. C₄₃×#1296	C₂	semidirect
4. C₄₃×#1296	C₂	semidirect
86. #8728	C₄₃	direct (N × H)
106. #1296	C₂×C₄₃	semidirect
107. #1296	C₂×C₄₃	semidirect
124. C₄₃	#8728	direct (N × H)

H ≅ G/N

type

3. C₄₃×#1296

C₂

semidirect

4. C₄₃×#1296

C₂

semidirect

86. #8728

C₄₃

direct (N × H)

106. #1296

C₂×C₄₃

semidirect

107. #1296

C₂×C₄₃

semidirect

124. C₄₃

#8728

direct (N × H)

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

subgroup	index
C₄₃×#2285	2
C₄₃×#1797	2
C₄₃×#1296	2
#8728	43

subgroup

index

C₄₃×#2285

C₄₃×#1797

C₄₃×#1296

#8728

Subgroups — C₄₃×#8728 #24928745

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C43×#8728 #24928745

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#8728 #24928745