Finite Group Databasebeta

← #19145332

Subgroups — #19145332

Order 5504.

446 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583450C211yesmaximal, characteristic, complemented
2#14583447C211yesmaximal, characteristic, complemented
3#14583295C211yesmaximal, characteristic, complemented
4#14583275C211yesmaximal, characteristic, complemented
5#14583246C211yesmaximal, characteristic, complemented
6#14583151C214yesmaximal, complemented
7#14583008C214yesmaximal, complemented
8C4×#10621872C211yesmaximal, characteristic, complemented
9C43×#486C211yesmaximal, characteristic, complemented
10C2×#10621902—21no—
11C2×#10621900—21no—
12C2×#10621882C2214yes—
13C2×#10621872C2212yes—
14#13063325C2211yescharacteristic
15#13063322C2211yescharacteristic
16#13063314—21no—
17#13063312—21no—
18#13063300—21no—
19#13063300C2212yes—
20#13063296—21no—
21#13063296C2212yes—
22D4×Dic43—21no—
23D4×Dic43C2212yes—
24#13063287—21no—
25#13063287C2212yes—
26C42×D43C2211yescharacteristic
27#13063256C2214yes—
28#13063247C2214yes—
29#13063235C2212yes—
30C4×C43⋊C8C2211yescharacteristic
31C4⋊Q8×C43C2211yescharacteristic
32#127×C43C2211yescharacteristic
33#102×C43C2214yes—
34C4×C8×C43C2211yescharacteristic
35C2×Q8×C43—21no—
36C2×D4×C43—21no—
37C2×D4×C43—21no—
38C2×D4×C43C2312yes—
39C2×C22⋊D43—22no—
40C22×Dic43—22no—
41#10621902—44no—
42#10621900—44no—
43C2×D172—21no—
44C2×D172—21no—
45C2×D172—22no—
46C2×D172C2312yes—
47C2×C4×D43—22no—
48C2×C4×D43D411yescharacteristic
49C2×C4×D43D411yescharacteristic
50C2×C4×D43C2311yescharacteristic
51C2×Dic86—21no—
52C2×C8×C43C2312yes—
53C4⋊C4×C43—21no—
54C4⋊C4×C43C2312yes—
55C42×C43C2311yescharacteristic
56C22⋊Dic43—22no—
57C22⋊Dic43—22no—
58#10621882—28no—
59(C2×D43)⋊C4—22no—
60(C2×D43)⋊C4—22no—
61C4⋊Dic43—21no—
62C4⋊Dic43C2312yes—
63C4×Dic43D411yescharacteristic
64C4×Dic43D411yescharacteristic
65C4×Dic43C2311yescharacteristic
66C2×C43⋊C8C2312yes—
67#10621872—24no—
68C23×C43—22no—
69C22×D43—22no—
70C22×D43C2×D411yescharacteristic
71Q8×C43—42no—
72D4×C43—24no—
73D4×C43—42no—
74D4×C43—42no—
75C2×C4×C43—22no—
76C2×C4×C43C2×D411yescharacteristic
77C2×C4×C43C2×D411yescharacteristic
78C2×C4×C43C2411yescharacteristic
79C22⋊D43—44no—
80C2×Dic43—22no—
81C2×Dic43—44no—
82C2×Dic43C2×D411yescharacteristic
83C2×Dic43C2×D411yescharacteristic
84C2×Dic43C2×D411yescharacteristic
85D172—24no—
86D172—44no—
87D172—42no—
88D172—42no—
89C4×D43—22no—
90C4×D43—22no—
91C4×D43—22no—
92C4×D43—44no—
93Dic86—42no—
94C8×C43—22no—
95C43⋊C8#4114yescomplemented
96C22×C43—42no—
97C22×C43—42no—
98C22×C43—42no—
99C22×C43C22×D411yescharacteristic
100C2×D43—21no—
101C2×D43—21no—
102C2×D43—21no—
103C2×D43—42no—
104C2×D43—42no—
105C2×D43—42no—
106C4×C43—42no—
107C4×C43AGL(1,ℤ/8)12yes—
108C4×C43AGL(1,ℤ/8)12yes—
109C4×C43C2×#4112yes—
110Dic43—21no—
111Dic43—21no—
112Dic43—21no—
113Dic43—42no—
114#3184—431nomaximal, Sylow
115C2×C43—82no—
116C2×C43#53211yescharacteristic
117C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
118C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
119D43—41no—
120D43—82no—
121#532—431no—
122#532—431no—
123#498—431no—
124#493—431no—
125#486—431no—
126#486D4311yescharacteristic, complemented
127#469—434no—
128#442—434no—
129C4×M16—431no—
130C43#318411yescharacteristic, complemented, Sylow
131C2×#41—861no—
132C2×#41—861no—
133C2×D8—434no—
134C2×M16—432no—
135C4⋊Q8—431no—
136C4⋊Q8C2×D4311yescharacteristic
137#127—431no—
138#127C2×D4311yescharacteristic
139#124—861no—
140#124—861no—
141#121—432no—
142#121—432no—
143#121—861no—
144#121—861no—
145C4×D4—432no—
146C4×D4—432no—
147C4×D4—861no—
148C4×D4—861no—
149C2×C42—431no—
150#106—434no—
151#102—434no—
152#102C2×D4314yes—
153#97—432no—
154C4×C8—431no—
155C4×C8C2×D4311yescharacteristic
156#41—1724no—
157#41—1724no—
158C2×Q8—21no—
159C2×Q8—861no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—432no—
163C2×D4—862no—
164C2×D4—862no—
165C2×D4—861no—
166C2×D4—861no—
167C2×D4C22×D4312yes—
168C22×C4—431no—
169C22×C4—431no—
170C22×C4—431no—
171C22×C4—862no—
172C22×C4—862no—
173D8—868no—
174M16—864no—
175C2×C8—432no—
176C2×C8C22×D4312yes—
177C4⋊C4—21no—
178C4⋊C4—432no—
179C4⋊C4—861no—
180C4⋊C4C22×D4312yes—
181C22⋊C4—862no—
182C22⋊C4—862no—
183C22⋊C4—862no—
184C22⋊C4—862no—
185C42—431no—
186C42—431no—
187C42—431no—
188C42C22×D4311yescharacteristic
189C23—22no—
190C23—431no—
191C23—862no—
192Q8—42no—
193Q8—1722no—
194D4—24no—
195D4—42no—
196D4—42no—
197D4—864no—
198D4—1724no—
199D4—1724no—
200D4—1722no—
201D4—1722no—
202C2×C4—22no—
203C2×C4—431no—
204C2×C4—431no—
205C2×C4—431no—
206C2×C4—862no—
207C2×C4—862no—
208C2×C4—862no—
209C2×C4—862no—
210C2×C4—1724no—
211C2×C4—1724no—
212C2×C4D4×D4311yescharacteristic
213C2×C4D4×D4311yescharacteristic
214C2×C4C23×D4311yescharacteristic
215C8—22no—
216C8—434no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—861no—
221C22—861no—
222C22—861no—
223C22—1722no—
224C22—1722no—
225C22—1722no—
226C22C2×D4×D4311yescharacteristic
227C4—42no—
228C4—861no—
229C4—861no—
230C4—861no—
231C4—1722no—
232C4#1306334912yes—
233C4#1306335212yes—
234C4#41×D4312yes—
235C2—82no—
236C2—3442no—
237C2—1721no—
238C2#1458344811yescharacteristic
239C2C2×#1306334911yescharacteristic
240C2C2×#1306335211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#486C2
socleC22×C43C22×D4
hypercenter#486D43
hypocenterC43#3184
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14583450C2semidirect
2. #14583447C2semidirect
3. #14583295C2semidirect
4. #14583275C2semidirect
5. #14583246C2semidirect
6. #14583151C2semidirect
7. #14583008C2semidirect
8. C4×#10621872C2semidirect
9. C43×#486C2semidirect
95. C43⋊C8#41semidirect
126. #486D43semidirect
130. C43#3184semidirect