Finite Group Databasebeta

← #19145457

Subgroups — #19145457

Order 5504.

442 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 109 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#14583465C212yesmaximal, complemented
2#14583225C212yesmaximal, complemented
3#14583222C212yesmaximal, complemented
4#14583152C211yesmaximal, characteristic, complemented
5#14583133C212yesmaximal, complemented
6#14583034C212yesmaximal, complemented
7#14583031C212yesmaximal, complemented
8#14582867C211yesmaximal, characteristic, complemented
9C43×#469C211yesmaximal, characteristic, complemented
10C2×#10621898C2211yescharacteristic
11C2×D4×D43C2212yescomplemented
12C2×D344C2211yescharacteristic
13C2×#10621882C2212yes—
14C22×C43⋊C8C2211yescharacteristic, complemented
15#13063321—22no—
16#13063311—22no—
17#13063300C2212yes—
18#13063299C2212yescomplemented
19#13063296C2212yes—
20#13063295—22no—
21#13063293—22no—
22#13063283C2212yescomplemented
23#13063258C2212yescomplemented
24#13063257C2211yescharacteristic, complemented
25#13063247C2212yescomplemented
26#13063246C2212yescomplemented
27#13063245C2212yescomplemented
28(C2×D43)⋊C8C2212yescomplemented
29(C2×D43)⋊C8C2212yescomplemented
30C2×D8×C43C2211yescharacteristic
31C2×M16×C43C2211yescharacteristic, complemented
32#121×C43C2212yescomplemented
33#106×C43C2211yescharacteristic, complemented
34#102×C43C2212yescomplemented
35C23×D43—22no—
36C2×D4×C43—22no—
37C2×D4×C43C2312yes—
38C22×C4×C43C2311yescharacteristic
39C2×C22⋊D43—22no—
40C2×C22⋊D43—22no—
41C2×C22⋊D43—22no—
42C2×C22⋊D43D412yes—
43D4×D43—42no—
44D4×D43—42no—
45#10621898—41no—
46#10621898—41no—
47C2×D172—22no—
48C2×D172D411yescharacteristic
49C2×D172C2312yes—
50C2×C4×D43C2312yes—
51C2×Dic86D411yescharacteristic
52D8×C43—41no—
53M16×C43—41no—
54C2×C8×C43C2311yescharacteristic
55C2×C8×C43C2311yescharacteristic
56C4⋊C4×C43C2312yes—
57C22⋊C4×C43—22no—
58C22⋊Dic43—22no—
59#10621882—42no—
60(C2×D43)⋊C4—22no—
61(C2×D43)⋊C4—22no—
62(C2×D43)⋊C4—22no—
63C4⋊Dic43C2312yes—
64C4×Dic43—22no—
65C2×C43⋊C8—41no—
66C2×C43⋊C8C2312yes—
67D344—41no—
68C23×C43—22no—
69C23×C43C2×D411yescharacteristic
70C22×D43—22no—
71C22×D43—44no—
72C22×D43—82no—
73C22×D43—82no—
74C22×D43C2×D412yes—
75D4×C43—22no—
76D4×C43—22no—
77D4×C43—82no—
78C2×C4×C43—21no—
79C2×C4×C43—21no—
80C2×C4×C43—22no—
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43C2411yescharacteristic
83C22⋊D43—42no—
84C22⋊D43—44no—
85C22⋊D43—82no—
86C22⋊D43—82no—
87C2×Dic43—22no—
88C2×Dic43C2×D412yes—
89D172—22no—
90D172—22no—
91D172—41no—
92D172—82no—
93C4×D43—22no—
94C4×D43—22no—
95Dic86—41no—
96C8×C43—21no—
97C8×C43—21no—
98C43⋊C8—22no—
99C22×C43—21no—
100C22×C43—22no—
101C22×C43—42no—
102C22×C43—42no—
103C22×C43—42no—
104C22×C43C22×D411yescharacteristic
105C2×D43—22no—
106C2×D43—22no—
107C2×D43—22no—
108C2×D43—42no—
109C2×D43—42no—
110C2×D43—42no—
111C2×D43—88no—
112C4×C43—21no—
113C4×C43—42no—
114C4×C43H(5,𝔽2)11yescharacteristic
115C4×C43H(5,𝔽2)11yescharacteristic
116Dic43—22no—
117Dic43—42no—
118#3199—431nomaximal, Sylow
119C2×C43—41no—
120C2×C43—82no—
121C2×C43#53411yescharacteristic
122C2×C43#57612yes—
123D43—42no—
124D43—82no—
125#535—432no—
126#482—432no—
127#482—432no—
128#469—431no—
129#469D4311yescharacteristic, complemented
130#466—432no—
131#447—432no—
132#447—432no—
133#408—431no—
134C43#319911yescharacteristic, complemented, Sylow
135C2×#41—431no—
136C22×D4—432no—
137C2×D8—432no—
138C2×D8—431no—
139C2×D8C2×D4311yescharacteristic
140C2×M16C2×D4311yescharacteristic, complemented
141C22×C8—431no—
142#127—862no—
143#124—862no—
144#121—432no—
145#121—432no—
146#121—432no—
147#121C2×D4312yescomplemented
148#120—862no—
149#120—862no—
150#117—432no—
151#107—432no—
152#106—431no—
153#106C2×D4311yescharacteristic, complemented
154#102—432no—
155#102—432no—
156#102—432no—
157#102C2×D4312yescomplemented
158C22⋊C8—432no—
159C22⋊C8—432no—
160C24—862no—
161#41—1721no—
162#41—1721no—
163C2×Q8—431no—
164C2×D4—22no—
165C2×D4—432no—
166C2×D4—431no—
167C2×D4—432no—
168C2×D4—862no—
169C2×D4—862no—
170C2×D4—862no—
171C2×D4—862no—
172C2×D4—1722no—
173C2×D4—1722no—
174C2×D4C22×D4312yes—
175C22×C4—432no—
176C22×C4C22×D4311yescharacteristic
177D8—41no—
178D8—1721no—
179D8—1722no—
180M16—41no—
181C2×C8—432no—
182C2×C8—1721no—
183C2×C8C22×D4311yescharacteristic
184C2×C8C22×D4311yescharacteristic
185C4⋊C4—432no—
186C4⋊C4C22×D4312yes—
187C22⋊C4—22no—
188C22⋊C4—862no—
189C22⋊C4—862no—
190C22⋊C4—862no—
191C22⋊C4—862no—
192C42—862no—
193C23—22no—
194C23—432no—
195C23—862no—
196C23—3442no—
197C23—3442no—
198C23—1724no—
199C23D4×D4311yescharacteristic
200Q8—1721no—
201D4—22no—
202D4—22no—
203D4—82no—
204D4—862no—
205D4—862no—
206D4—3442no—
207D4—3442no—
208D4—3442no—
209D4—1721no—
210D4—1722no—
211D4—1724no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—432no—
216C2×C4—862no—
217C2×C4—862no—
218C2×C4—862no—
219C2×C4D4×D4311yescharacteristic
220C2×C4C23×D4311yescharacteristic
221C8—21no—
222C8—21no—
223C8—862no—
224C22—22no—
225C22—21no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—862no—
230C22—862no—
231C22—862no—
232C22—3448no—
233C22—1722no—
234C22—1722no—
235C22—1722no—
236C22C2×D4×D4311yescharacteristic
237C4—21no—
238C4—42no—
239C4—862no—
240C4—1722no—
241C4#1306337011yescharacteristic
242C4#1306337111yescharacteristic
243C2—41no—
244C2—82no—
245C2—3442no—
246C2—1722no—
247C2#1458345711yescharacteristic
248C2#1458370312yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#469C2
socleC22×C43C22×D4
hypercenter#469D43
hypocenterC43#3199
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #14583465C2semidirect
2. #14583225C2semidirect
3. #14583222C2semidirect
4. #14583152C2semidirect
5. #14583133C2semidirect
6. #14583034C2semidirect
7. #14583031C2semidirect
8. #14582867C2semidirect
9. C43×#469C2semidirect
11. C2×D4×D43C22semidirect
14. C22×C43⋊C8C22semidirect
18. #13063299C22semidirect
22. #13063283C22semidirect
23. #13063258C22semidirect
24. #13063257C22semidirect
25. #13063247C22semidirect
26. #13063246C22semidirect
27. #13063245C22semidirect
28. (C2×D43)⋊C8C22semidirect
29. (C2×D43)⋊C8C22semidirect
31. C2×M16×C43C22semidirect
32. #121×C43C22semidirect
33. #106×C43C22semidirect
34. #102×C43C22semidirect
129. #469D43semidirect
134. C43#3199semidirect
140. C2×M16C2×D43semidirect
147. #121C2×D43semidirect
153. #106C2×D43semidirect
157. #102C2×D43semidirect