Group #19133086 — subgroups

Subgroups — #19133086

Order 5504.

304 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₂×C₂²⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₂²⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582636	C₂	1	2	yes	maximal, complemented
4	#14582633	C₂	1	2	yes	maximal, complemented
5	C₄₃×#525	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₃⋊C₈	—	2	1	no	—
7	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
8	C₂×C₄×Dic₄₃	—	2	1	no	—
9	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
10	C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
11	C₄₃⋊#95	C₂²	1	2	yes	—
12	C₂×#41×C₄₃	C₄	1	1	yes	characteristic, complemented
13	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
14	#123×C₄₃	—	2	1	no	—
15	C₂²⋊Q₈×C₄₃	C₄	1	1	yes	characteristic, complemented
16	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
17	#121×C₄₃	C₄	1	1	yes	characteristic, complemented
18	#121×C₄₃	C₂²	1	1	yes	characteristic
19	#120×C₄₃	—	2	1	no	—
20	C₄×D₄×C₄₃	—	2	1	no	—
21	C₄×D₄×C₄₃	—	2	1	no	—
22	#117×C₄₃	C₄	1	1	yes	characteristic, complemented
23	C₂⁴×C₄₃	D₄	1	1	yes	characteristic
24	#41×C₄₃	—	4	2	no	—
25	C₂×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
26	C₂×D₄×C₄₃	—	2	1	no	—
27	C₂×D₄×C₄₃	—	2	1	no	—
28	C₂×D₄×C₄₃	—	2	1	no	—
29	C₂×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₄₃	—	2	1	no	—
31	C₂²×C₄×C₄₃	—	4	2	no	—
32	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
35	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
36	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
37	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
38	C₂²×Dic₄₃	—	2	2	no	—
39	C₄⋊C₄×C₄₃	—	2	1	no	—
40	C₄⋊C₄×C₄₃	—	2	1	no	—
41	C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
42	C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
43	C₂²⋊C₄×C₄₃	—	2	1	no	—
44	C₂²⋊C₄×C₄₃	—	2	1	no	—
45	C₂²⋊C₄×C₄₃	—	2	1	no	—
46	C₂²⋊C₄×C₄₃	—	2	1	no	—
47	C₂²⋊C₄×C₄₃	—	2	1	no	—
48	C₄²×C₄₃	—	2	1	no	—
49	C₂²⋊Dic₄₃	—	2	4	no	—
50	C₄×Dic₄₃	—	4	2	no	—
51	C₂×C₄₃⋊C₈	—	2	2	no	—
52	C₂×C₄₃⋊C₈	—	4	2	no	—
53	C₂³×C₄₃	—	2	2	no	—
54	C₂³×C₄₃	—	2	2	no	—
55	C₂³×C₄₃	—	2	1	no	—
56	C₂³×C₄₃	—	4	1	no	—
57	C₂³×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
58	C₂³×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
59	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
60	Q₈×C₄₃	—	4	1	no	—
61	D₄×C₄₃	—	4	1	no	—
62	D₄×C₄₃	—	4	2	no	—
63	D₄×C₄₃	—	4	2	no	—
64	D₄×C₄₃	—	4	2	no	—
65	C₂×C₄×C₄₃	—	2	2	no	—
66	C₂×C₄×C₄₃	—	2	2	no	—
67	C₂×C₄×C₄₃	—	2	2	no	—
68	C₂×C₄×C₄₃	—	2	1	no	—
69	C₂×C₄×C₄₃	—	2	1	no	—
70	C₂×C₄×C₄₃	—	2	1	no	—
71	C₂×C₄×C₄₃	—	4	1	no	—
72	C₂×C₄×C₄₃	—	4	1	no	—
73	C₂×C₄×C₄₃	—	4	1	no	—
74	C₂×C₄×C₄₃	—	4	2	no	—
75	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
79	C₂×Dic₄₃	—	2	4	no	—
80	C₂×Dic₄₃	—	4	2	no	—
81	C₂×Dic₄₃	—	4	2	no	—
82	C₄₃⋊C₈	—	4	2	no	—
83	C₂²×C₄₃	—	2	1	no	—
84	C₂²×C₄₃	—	2	1	no	—
85	C₂²×C₄₃	—	2	1	no	—
86	C₂²×C₄₃	—	2	1	no	—
87	C₂²×C₄₃	—	2	1	no	—
88	C₂²×C₄₃	—	2	1	no	—
89	C₂²×C₄₃	—	2	1	no	—
90	C₂²×C₄₃	—	4	4	no	—
91	C₂²×C₄₃	—	4	1	no	—
92	C₂²×C₄₃	—	4	1	no	—
93	C₂²×C₄₃	—	4	1	no	—
94	C₂²×C₄₃	#104	1	2	yes	—
95	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄₃	#135	1	2	yes	—
97	C₄×C₄₃	—	2	1	no	—
98	C₄×C₄₃	—	2	1	no	—
99	C₄×C₄₃	—	2	1	no	—
100	C₄×C₄₃	—	4	1	no	—
101	C₄×C₄₃	—	4	1	no	—
102	C₄×C₄₃	—	4	1	no	—
103	C₄×C₄₃	#99	1	2	yes	—
104	Dic₄₃	—	4	4	no	—
105	#1501	—	43	1	no	maximal, Sylow
106	C₂×C₄₃	—	2	2	no	—
107	C₂×C₄₃	—	2	2	no	—
108	C₂×C₄₃	—	4	1	no	—
109	C₂×C₄₃	—	8	1	no	—
110	C₂×C₄₃	C₂×#99	1	1	yes	characteristic
111	C₂×C₄₃	#416	1	1	yes	characteristic
112	C₂×C₄₃	C₂×#104	1	1	yes	characteristic
113	#525	D₄₃	1	1	yes	characteristic
114	C₂×C₂²⋊C₈	—	43	1	no	—
115	C₄×C₂²⋊C₄	—	43	1	no	—
116	#328	—	43	2	no	—
117	#327	—	43	2	no	—
118	C₄₃	#1501	1	1	yes	characteristic, complemented, Sylow
119	C₂×#41	Dic₄₃	1	1	yes	characteristic, complemented
120	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
121	C₂²×C₈	—	86	1	no	—
122	#123	—	2	1	no	—
123	C₂²⋊Q₈	Dic₄₃	1	1	yes	characteristic, complemented
124	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
125	#121	Dic₄₃	1	1	yes	characteristic, complemented
126	#121	C₂×D₄₃	1	1	yes	characteristic
127	#120	—	2	1	no	—
128	C₄×D₄	—	2	1	no	—
129	C₄×D₄	—	2	1	no	—
130	#117	Dic₄₃	1	1	yes	characteristic, complemented
131	C₂×C₂²⋊C₄	—	86	1	no	—
132	C₂×C₄²	—	86	1	no	—
133	C₂²⋊C₈	—	43	2	no	—
134	C₂²⋊C₈	—	86	1	no	—
135	#95	—	43	2	no	—
136	C₂⁴	C₂²⋊D₄₃	1	1	yes	characteristic
137	#41	—	4	2	no	—
138	C₂×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
139	C₂×D₄	—	2	1	no	—
140	C₂×D₄	—	2	1	no	—
141	C₂×D₄	—	2	1	no	—
142	C₂×D₄	C₂×Dic₄₃	1	1	yes	characteristic
143	C₂²×C₄	—	2	1	no	—
144	C₂²×C₄	—	4	2	no	—
145	C₂²×C₄	—	86	2	no	—
146	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
147	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
148	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
149	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
150	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
151	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
152	C₂×C₈	—	86	2	no	—
153	C₂×C₈	—	172	2	no	—
154	C₄⋊C₄	—	2	1	no	—
155	C₄⋊C₄	—	2	1	no	—
156	C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
157	C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
158	C₂²⋊C₄	—	2	1	no	—
159	C₂²⋊C₄	—	2	1	no	—
160	C₂²⋊C₄	—	2	1	no	—
161	C₂²⋊C₄	—	2	1	no	—
162	C₂²⋊C₄	—	2	1	no	—
163	C₂²⋊C₄	—	86	4	no	—
164	C₄²	—	2	1	no	—
165	C₄²	—	172	2	no	—
166	C₂³	—	2	2	no	—
167	C₂³	—	2	2	no	—
168	C₂³	—	2	1	no	—
169	C₂³	—	4	1	no	—
170	C₂³	C₂²⋊Dic₄₃	1	1	yes	characteristic
171	C₂³	C₂²⋊Dic₄₃	1	1	yes	characteristic
172	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
173	Q₈	—	4	1	no	—
174	D₄	—	4	1	no	—
175	D₄	—	4	2	no	—
176	D₄	—	4	2	no	—
177	D₄	—	4	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	1	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	4	1	no	—
185	C₂×C₄	—	4	1	no	—
186	C₂×C₄	—	4	1	no	—
187	C₂×C₄	—	4	2	no	—
188	C₂×C₄	—	86	4	no	—
189	C₂×C₄	—	172	2	no	—
190	C₂×C₄	—	172	2	no	—
191	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
192	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
193	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
194	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
195	C₈	—	172	2	no	—
196	C₂²	—	2	1	no	—
197	C₂²	—	2	1	no	—
198	C₂²	—	2	1	no	—
199	C₂²	—	2	1	no	—
200	C₂²	—	2	1	no	—
201	C₂²	—	2	1	no	—
202	C₂²	—	2	1	no	—
203	C₂²	—	4	4	no	—
204	C₂²	—	4	1	no	—
205	C₂²	—	4	1	no	—
206	C₂²	—	4	1	no	—
207	C₂²	#13063252	1	2	yes	—
208	C₂²	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
209	C₂²	#13063345	1	2	yes	—
210	C₄	—	2	1	no	—
211	C₄	—	2	1	no	—
212	C₄	—	2	1	no	—
213	C₄	—	4	1	no	—
214	C₄	—	4	1	no	—
215	C₄	—	4	1	no	—
216	C₄	—	172	4	no	—
217	C₄	#13063240	1	2	yes	—
218	C₂	—	2	2	no	—
219	C₂	—	2	2	no	—
220	C₂	—	4	1	no	—
221	C₂	—	8	1	no	—
222	C₂	C₂×#13063240	1	1	yes	characteristic
223	C₂	#14582895	1	1	yes	characteristic
224	C₂	C₂×#13063252	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₂²⋊(C₄₃⋊C₈)

C₂

yes

maximal, characteristic, complemented

C₄×C₂²⋊Dic₄₃

C₂

yes

maximal, characteristic, complemented

#14582636

C₂

yes

maximal, complemented

#14582633

C₂

yes

maximal, complemented

C₄₃×#525

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

—

C₂×C₂²⋊Dic₄₃

—

C₂×C₄×Dic₄₃

—

C₂²⋊(C₄₃⋊C₈)

—

C₂²⋊(C₄₃⋊C₈)

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂×#41×C₄₃

C₄

yes

characteristic, complemented

C₂³×C₄×C₄₃

C₂²

yes

characteristic

#123×C₄₃

—

C₂²⋊Q₈×C₄₃

C₄

yes

characteristic, complemented

C₂²⋊Q₈×C₄₃

C₂²

yes

characteristic

#121×C₄₃

C₄

yes

characteristic, complemented

#121×C₄₃

C₂²

yes

characteristic

#120×C₄₃

—

C₄×D₄×C₄₃

—

C₄×D₄×C₄₃

—

#117×C₄₃

C₄

yes

characteristic, complemented

C₂⁴×C₄₃

D₄

yes

characteristic

#41×C₄₃

—

C₂×Q₈×C₄₃

C₂×C₄

yes

characteristic

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

C₂×C₄

yes

characteristic

C₄⋊C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₂²⋊Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂²⋊C₄

yes

characteristic

C₂³×C₄₃

C₂²⋊C₄

yes

characteristic

C₂³×C₄₃

C₂×D₄

yes

characteristic

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×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

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#104

yes

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₃

#135

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

100

C₄×C₄₃

—

101

C₄×C₄₃

—

102

C₄×C₄₃

—

103

C₄×C₄₃

#99

yes

—

104

Dic₄₃

—

105

#1501

—

maximal, Sylow

106

C₂×C₄₃

—

107

C₂×C₄₃

—

108

C₂×C₄₃

—

109

C₂×C₄₃

—

110

C₂×C₄₃

C₂×#99

yes

characteristic

111

C₂×C₄₃

#416

yes

characteristic

112

C₂×C₄₃

C₂×#104

yes

characteristic

113

#525

D₄₃

yes

characteristic

114

C₂×C₂²⋊C₈

—

115

C₄×C₂²⋊C₄

—

116

#328

—

117

#327

—

118

C₄₃

#1501

yes

characteristic, complemented, Sylow

119

C₂×#41

Dic₄₃

yes

characteristic, complemented

120

C₂³×C₄

C₂×D₄₃

yes

characteristic

121

C₂²×C₈

—

122

#123

—

123

C₂²⋊Q₈

Dic₄₃

yes

characteristic, complemented

124

C₂²⋊Q₈

C₂×D₄₃

yes

characteristic

125

#121

Dic₄₃

yes

characteristic, complemented

126

#121

C₂×D₄₃

yes

characteristic

127

#120

—

128

C₄×D₄

—

129

C₄×D₄

—

130

#117

Dic₄₃

yes

characteristic, complemented

131

C₂×C₂²⋊C₄

—

132

C₂×C₄²

—

133

C₂²⋊C₈

—

134

C₂²⋊C₈

—

135

#95

—

136

C₂⁴

C₂²⋊D₄₃

yes

characteristic

137

#41

—

138

C₂×Q₈

C₂×Dic₄₃

yes

characteristic

139

C₂×D₄

—

140

C₂×D₄

—

141

C₂×D₄

—

142

C₂×D₄

C₂×Dic₄₃

yes

characteristic

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

147

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

148

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

149

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

150

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

151

C₂²×C₄

C₂²×D₄₃

yes

characteristic

152

C₂×C₈

—

153

C₂×C₈

—

172

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

C₂×Dic₄₃

yes

characteristic

157

C₄⋊C₄

C₂×Dic₄₃

yes

characteristic

158

C₂²⋊C₄

—

159

C₂²⋊C₄

—

160

C₂²⋊C₄

—

161

C₂²⋊C₄

—

162

C₂²⋊C₄

—

163

C₂²⋊C₄

—

164

C₄²

—

165

C₄²

—

172

—

166

C₂³

—

167

C₂³

—

168

C₂³

—

169

C₂³

—

170

C₂³

C₂²⋊Dic₄₃

yes

characteristic

171

C₂³

C₂²⋊Dic₄₃

yes

characteristic

172

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

173

Q₈

—

174

D₄

—

175

D₄

—

176

D₄

—

177

D₄

—

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

—

172

—

190

C₂×C₄

—

172

—

191

C₂×C₄

C₂²⋊Dic₄₃

yes

characteristic

192

C₂×C₄

C₂²⋊Dic₄₃

yes

characteristic

193

C₂×C₄

C₂²×Dic₄₃

yes

characteristic

194

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

195

C₈

—

172

—

196

C₂²

—

197

C₂²

—

198

C₂²

—

199

C₂²

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

—

204

C₂²

—

205

C₂²

—

206

C₂²

—

207

C₂²

#13063252

yes

—

208

C₂²

C₂×C₂²⋊Dic₄₃

yes

characteristic

209

C₂²

#13063345

yes

—

210

C₄

—

211

C₄

—

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

172

—

217

C₄

#13063240

yes

—

218

C₂

—

219

C₂

—

220

C₂

—

221

C₂

—

222

C₂

C₂×#13063240

yes

characteristic

223

C₂

#14582895

yes

characteristic

224

C₂

C₂×#13063252

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#525	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₄
hypercenter	#525	D₄₃
hypocenter	C₄₃	#1501
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #525

subgroup

G/H

center

C₂×C₄

C₂²⋊Dic₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#525

C₂

socle

C₂²×C₄₃

C₂×C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #525

N	H ≅ G/N	type
1. C₂×C₂²⋊(C₄₃⋊C₈)	C₂	semidirect
2. C₄×C₂²⋊Dic₄₃	C₂	semidirect
3. #14582636	C₂	semidirect
4. #14582633	C₂	semidirect
12. C₂×#41×C₄₃	C₄	semidirect
15. C₂²⋊Q₈×C₄₃	C₄	semidirect
17. #121×C₄₃	C₄	semidirect
22. #117×C₄₃	C₄	semidirect
118. C₄₃	#1501	semidirect
119. C₂×#41	Dic₄₃	semidirect
123. C₂²⋊Q₈	Dic₄₃	semidirect
125. #121	Dic₄₃	semidirect
130. #117	Dic₄₃	semidirect

H ≅ G/N

type

1. C₂×C₂²⋊(C₄₃⋊C₈)

C₂

semidirect

2. C₄×C₂²⋊Dic₄₃

C₂

semidirect

3. #14582636

C₂

semidirect

4. #14582633

C₂

semidirect

12. C₂×#41×C₄₃

C₄

semidirect

15. C₂²⋊Q₈×C₄₃

C₄

semidirect

17. #121×C₄₃

C₄

semidirect

22. #117×C₄₃

C₄

semidirect

118. C₄₃

#1501

semidirect

119. C₂×#41

Dic₄₃

semidirect

123. C₂²⋊Q₈

Dic₄₃

semidirect

125. #121

Dic₄₃

semidirect

130. #117

Dic₄₃

semidirect

Subgroups — #19133086

Conjugacy classes of subgroups

Complements