Finite Group Databasebeta

← #19145537

Subgroups — #19145537

Order 5504.

488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 125 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#14583454C211yesmaximal, characteristic, complemented
2#127×D43C211yesmaximal, characteristic
3#14583272C211yesmaximal, characteristic, complemented
4#14583271C211yesmaximal, characteristic, complemented
5#14583247C211yesmaximal, characteristic, complemented
6#14583098C214yesmaximal, complemented
7#14583051C214yesmaximal, complemented
8#14582950C211yesmaximal, characteristic, complemented
9C43×#486C211yesmaximal, characteristic, complemented
10C2×D4×D43—21no—
11C2×D4×D43—21no—
12C2×D4×D43C2212yes—
13C2×#10621873C2214yescomplemented
14C2×#10621883C2214yescomplemented
15#13063325C2211yescharacteristic, complemented
16#13063322C2211yescharacteristic
17#13063321—21no—
18#13063321—21no—
19#13063321C2212yes—
20#13063316—21no—
21#13063305C2212yes—
22#13063301—21no—
23Q8×Dic43—21no—
24#13063290C2212yescomplemented
25#13063283—21no—
26C42×D43C2211yescharacteristic
27Dic43⋊C8C2212yescomplemented
28#13063245C2214yescomplemented
29(C2×D43)⋊C8C2212yes—
30C4×C43⋊C8C2211yescharacteristic, complemented
31C4⋊Q8×C43C2211yescharacteristic, complemented
32#127×C43C2211yescharacteristic
33#102×C43C2214yescomplemented
34C4×C8×C43C2211yescharacteristic, complemented
35C23×D43—22no—
36C2×Q8×C43—21no—
37C2×D4×C43—21no—
38C2×D4×C43—21no—
39C2×D4×C43C2312yes—
40C2×C22⋊D43—22no—
41C2×C22⋊D43—22no—
42C2×C22⋊D43—22no—
43D4×D43—44no—
44D4×D43—44no—
45D4×D43—44no—
46C2×D172—21no—
47C2×D172—21no—
48C2×D172C2312yes—
49C2×C4×D43D411yescharacteristic
50C2×C4×D43D411yescharacteristic
51C2×C4×D43C2311yescharacteristic
52C2×Dic86C2312yes—
53C2×C8×C43C2312yes—
54C4⋊C4×C43—21no—
55C4⋊C4×C43C2312yes—
56C42×C43C2311yescharacteristic
57#10621883—44no—
58(C2×D43)⋊C4—22no—
59C4⋊Dic43—21no—
60C4⋊Dic43—21no—
61C4⋊Dic43—22no—
62Dic43⋊C4—22no—
63C4×Dic43—22no—
64C4×Dic43D411yescharacteristic
65C4×Dic43D411yescharacteristic
66C4×Dic43C2311yescharacteristic
67C2×C43⋊C8C2312yes—
68#10621873—44no—
69C23×C43—22no—
70C22×D43—22no—
71C22×D43—44no—
72C22×D43—44no—
73C22×D43—44no—
74C22×D43C2×D411yescharacteristic
75Q8×C43—42no—
76D4×C43—24no—
77D4×C43—42no—
78D4×C43—42no—
79C2×C4×C43—22no—
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43C2411yescharacteristic
83C22⋊D43—44no—
84C22⋊D43—44no—
85C22⋊D43—44no—
86C2×Dic43—22no—
87C2×Dic43C2×D411yescharacteristic
88C2×Dic43C2×D411yescharacteristic
89C2×Dic43C2×D411yescharacteristic
90D172—24no—
91D172—42no—
92D172—42no—
93C4×D43—22no—
94C4×D43—22no—
95C4×D43SD1614yescomplemented
96Dic86—24no—
97C8×C43—22no—
98C43⋊C8—22no—
99C22×C43—42no—
100C22×C43—42no—
101C22×C43—42no—
102C22×C43C22×D411yescharacteristic
103C2×D43—21no—
104C2×D43—21no—
105C2×D43—42no—
106C2×D43—42no—
107C2×D43—42no—
108C2×D43—88no—
109C2×D43C2×SD1612yes—
110C4×C43—42no—
111C4×C43C2×SD1612yes—
112C4×C43AGL(1,ℤ/8)12yes—
113C4×C43H(5,𝔽2)12yes—
114Dic43—21no—
115Dic43—21no—
116Dic43—42no—
117Dic43C2×SD1612yes—
118#3208—431nomaximal, Sylow
119C2×C43—82no—
120C2×C43#53511yescharacteristic
121C2×C43C22×SD1611yescharacteristic
122C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
123D43—22no—
124D43—82no—
125#533—431no—
126C2×#127—431no—
127#492—431no—
128#492—431no—
129#486—431no—
130#486D4311yescharacteristic, complemented
131#460—434no—
132#450—434no—
133#431—431no—
134C43#320811yescharacteristic, complemented, Sylow
135C22×D4—432no—
136C22×D4—861no—
137C22×D4—861no—
138C2×SD16—434no—
139C2×SD16—434no—
140C4⋊Q8—431no—
141C4⋊Q8C2×D4311yescharacteristic, complemented
142#127—432no—
143#127—431no—
144#127—861no—
145#127—861no—
146#127C2×D4311yescharacteristic
147#125—861no—
148C22⋊Q8—432no—
149C22⋊Q8—861no—
150C4×Q8—432no—
151C4×Q8—861no—
152#117—861no—
153C2×C42—431no—
154C4⋊C8—432no—
155#102—434no—
156#102C2×D4314yescomplemented
157C22⋊C8—432no—
158C4×C8—431no—
159C4×C8C2×D4311yescharacteristic, complemented
160C24—862no—
161C2×Q8—21no—
162C2×Q8—432no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—432no—
166C2×D4—862no—
167C2×D4—862no—
168C2×D4—862no—
169C2×D4—861no—
170C2×D4—861no—
171C2×D4—1724no—
172C2×D4—1724no—
173C2×D4—1724no—
174C2×D4C22×D4312yes—
175C22×C4—431no—
176C22×C4—431no—
177C22×C4—431no—
178SD16—1724no—
179SD16—1724no—
180C2×C8—432no—
181C2×C8C22×D4312yes—
182C4⋊C4—21no—
183C4⋊C4—862no—
184C4⋊C4—862no—
185C4⋊C4—861no—
186C4⋊C4—861no—
187C4⋊C4C22×D4312yes—
188C22⋊C4—862no—
189C42—431no—
190C42—431no—
191C42—431no—
192C42—862no—
193C42C22×D4311yescharacteristic
194C23—22no—
195C23—431no—
196C23—862no—
197C23—1724no—
198C23—1724no—
199C23—1724no—
200Q8—42no—
201Q8—864no—
202D4—24no—
203D4—42no—
204D4—42no—
205D4—864no—
206D4—1724no—
207D4—1724no—
208D4—1724no—
209D4—1722no—
210D4—1722no—
211C2×C4—22no—
212C2×C4—431no—
213C2×C4—434no—
214C2×C4—431no—
215C2×C4—431no—
216C2×C4—862no—
217C2×C4—862no—
218C2×C4—862no—
219C2×C4D4×D4311yescharacteristic
220C2×C4D4×D4311yescharacteristic
221C2×C4C23×D4311yescharacteristic
222C8—22no—
223C8—862no—
224C22—42no—
225C22—42no—
226C22—42no—
227C22—432no—
228C22—861no—
229C22—861no—
230C22—3448no—
231C22—1722no—
232C22—1722no—
233C22—1722no—
234C22C2×D4×D4311yescharacteristic
235C4—42no—
236C4—432no—
237C4—861no—
238C4—861no—
239C4—1722no—
240C4SD16×D4312yes—
241C4#1306334912yes—
242C4#1306337112yes—
243C2—82no—
244C2—862no—
245C2—3442no—
246C2#1458346711yescharacteristic
247C2C2×SD16×D4311yescharacteristic
248C2C2×#1306334911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#486C2
socleC22×C43C22×D4
hypercenter#486D43
hypocenterC43#3208
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. #14583454C2semidirect
3. #14583272C2semidirect
4. #14583271C2semidirect
5. #14583247C2semidirect
6. #14583098C2semidirect
7. #14583051C2semidirect
8. #14582950C2semidirect
9. C43×#486C2semidirect
13. C2×#10621873C22semidirect
14. C2×#10621883C22semidirect
15. #13063325C22semidirect
24. #13063290C22semidirect
27. Dic43⋊C8C22semidirect
28. #13063245C22semidirect
30. C4×C43⋊C8C22semidirect
31. C4⋊Q8×C43C22semidirect
33. #102×C43C22semidirect
34. C4×C8×C43C22semidirect
95. C4×D43SD16semidirect
130. #486D43semidirect
134. C43#3208semidirect
141. C4⋊Q8C2×D43semidirect
156. #102C2×D43semidirect
159. C4×C8C2×D43semidirect