Finite Group Databasebeta

← #19145391

Subgroups — #19145391

Order 5504.

514 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 113 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#121×D43C212yesmaximal, complemented
2#14583219C212yesmaximal, complemented
3#14583216C212yesmaximal, complemented
4#14583152C211yesmaximal, characteristic, complemented
5#14583150C212yesmaximal, complemented
6#14583034C212yesmaximal, complemented
7#14583031C212yesmaximal, complemented
8#14582862C211yesmaximal, characteristic, complemented
9C43×#469C211yesmaximal, characteristic, complemented
10C2×D4×D43—22no—
11C2×D4×D43C2212yescomplemented
12C22×C4×D43C2211yescharacteristic
13C2×D344C2211yescharacteristic, complemented
14C2×#10621882C2212yescomplemented
15C2×#10621877C2211yescharacteristic, complemented
16#13063300C2212yes—
17#13063299C2212yescomplemented
18#13063298—22no—
19#13063297—22no—
20#13063296C2212yes—
21C4⋊C4×D43C2212yescomplemented
22C22⋊C4×D43—22no—
23#13063257C2211yescharacteristic, complemented
24#13063256C2212yescomplemented
25#13063247C2212yescomplemented
26#13063246C2212yescomplemented
27#13063245C2212yescomplemented
28(C2×D43)⋊C8C2212yescomplemented
29(C2×D43)⋊C8C2212yescomplemented
30C2×D8×C43C2211yescharacteristic, complemented
31C2×M16×C43C2211yescharacteristic, complemented
32#121×C43C2212yescomplemented
33#106×C43C2211yescharacteristic, complemented
34#102×C43C2212yescomplemented
35C23×D43—22no—
36C23×D43D411yescharacteristic
37C2×D4×C43—22no—
38C2×D4×C43C2312yes—
39C22×C4×C43C2311yescharacteristic
40C2×C22⋊D43—22no—
41C2×C22⋊D43—22no—
42C2×C22⋊D43—22no—
43C22×Dic43D411yescharacteristic
44D4×D43—48no—
45D4×D43—42no—
46D4×D43—42no—
47C2×D172—22no—
48C2×D172C2312yes—
49C2×C4×D43—22no—
50C2×C4×D43—41no—
51C2×C4×D43—41no—
52C2×C4×D43D412yes—
53C2×C4×D43C2312yes—
54D8×C43—41no—
55M16×C43—41no—
56C2×C8×C43C2311yescharacteristic
57C2×C8×C43C2311yescharacteristic
58C4⋊C4×C43C2312yes—
59C22⋊C4×C43—22no—
60C22⋊Dic43—22no—
61#10621882—42no—
62(C2×D43)⋊C4—22no—
63(C2×D43)⋊C4—22no—
64C4⋊Dic43C2312yes—
65Dic43⋊C4—22no—
66#10621877—41no—
67C2×C43⋊C8C2312yes—
68D344—41no—
69C23×C43—22no—
70C23×C43C2×D411yescharacteristic
71C22×D43—24no—
72C22×D43—22no—
73C22×D43—41no—
74C22×D43—44no—
75C22×D43—44no—
76C22×D43—44no—
77C22×D43C2×D412yes—
78D4×C43—22no—
79D4×C43—22no—
80D4×C43—44no—
81C2×C4×C43—21no—
82C2×C4×C43—21no—
83C2×C4×C43—22no—
84C2×C4×C43C2×D411yescharacteristic
85C2×C4×C43C2411yescharacteristic
86C22⋊D43—44no—
87C22⋊D43—44no—
88C22⋊D43—44no—
89C2×Dic43—22no—
90C2×Dic43—41no—
91C2×Dic43C2×D412yes—
92D172—22no—
93D172—22no—
94D172—44no—
95C4×D43—22no—
96C4×D43—22no—
97C4×D43—42no—
98C4×D43—44no—
99C8×C43—21no—
100C8×C43—21no—
101C43⋊C8—22no—
102C22×C43—21no—
103C22×C43—22no—
104C22×C43—42no—
105C22×C43—42no—
106C22×C43—42no—
107C22×C43C22×D411yescharacteristic
108C2×D43—22no—
109C2×D43—22no—
110C2×D43—44no—
111C2×D43—42no—
112C2×D43—42no—
113C2×D43—42no—
114C2×D43—88no—
115C2×D43AGL(1,ℤ/8)14yes—
116C4×C43—21no—
117C4×C43—42no—
118C4×C43H(5,𝔽2)11yescharacteristic
119C4×C43H(5,𝔽2)11yescharacteristic
120Dic43—22no—
121Dic43—42no—
122#3192—431nomaximal, Sylow
123C2×C43—41no—
124C2×C43—82no—
125C2×C43#53411yescharacteristic
126C2×C43C2×AGL(1,ℤ/8)12yes—
127D43—24no—
128D43—82no—
129C2×#121—432no—
130#481—432no—
131#481—432no—
132#469—431no—
133#469—432no—
134#469D4311yescharacteristic, complemented
135#447—432no—
136#447—432no—
137#407—431no—
138C43#319211yescharacteristic, complemented, Sylow
139C22×D4—432no—
140C22×D4—862no—
141C23×C4—431no—
142C2×D8—432no—
143C2×D8—431no—
144C2×D8C2×D4311yescharacteristic, complemented
145C2×M16—431no—
146C2×M16C2×D4311yescharacteristic, complemented
147#121—432no—
148#121—432no—
149#121—432no—
150#121—862no—
151#121—862no—
152#121C2×D4312yescomplemented
153C2×C4⋊C4—432no—
154C2×C22⋊C4—862no—
155#106—431no—
156#106—432no—
157#106C2×D4311yescharacteristic, complemented
158#102—432no—
159#102—432no—
160#102—432no—
161#102C2×D4312yescomplemented
162C22⋊C8—432no—
163C22⋊C8—432no—
164C24—431no—
165C24—862no—
166C2×D4—22no—
167C2×D4—432no—
168C2×D4—862no—
169C2×D4—862no—
170C2×D4—862no—
171C2×D4—862no—
172C2×D4—1722no—
173C2×D4—1722no—
174C2×D4—1728no—
175C2×D4C22×D4312yes—
176C22×C4—431no—
177C22×C4—432no—
178C22×C4—432no—
179C22×C4—862no—
180C22×C4—1721no—
181C22×C4—1721no—
182C22×C4C22×D4311yescharacteristic
183D8—41no—
184D8—1721no—
185D8—1722no—
186M16—41no—
187M16—1721no—
188C2×C8—432no—
189C2×C8C22×D4311yescharacteristic
190C2×C8C22×D4311yescharacteristic
191C4⋊C4—432no—
192C4⋊C4—862no—
193C4⋊C4C22×D4312yes—
194C22⋊C4—22no—
195C22⋊C4—862no—
196C22⋊C4—862no—
197C22⋊C4—862no—
198C23—22no—
199C23—432no—
200C23—864no—
201C23—862no—
202C23—1721no—
203C23—1724no—
204C23—1724no—
205C23—1724no—
206C23D4×D4311yescharacteristic
207D4—22no—
208D4—22no—
209D4—44no—
210D4—862no—
211D4—862no—
212D4—1724no—
213D4—1724no—
214D4—1724no—
215D4—1724no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—432no—
220C2×C4—862no—
221C2×C4—862no—
222C2×C4—862no—
223C2×C4—1722no—
224C2×C4—1724no—
225C2×C4—1721no—
226C2×C4D4×D4311yescharacteristic
227C2×C4C23×D4311yescharacteristic
228C8—21no—
229C8—21no—
230C8—862no—
231C22—22no—
232C22—21no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—434no—
237C22—862no—
238C22—862no—
239C22—3448no—
240C22—1724no—
241C22—1722no—
242C22—1722no—
243C22—1722no—
244C22C2×D4×D4311yescharacteristic
245C4—21no—
246C4—42no—
247C4—862no—
248C4—1722no—
249C4#1306337011yescharacteristic
250C4#1306337111yescharacteristic
251C2—41no—
252C2—82no—
253C2—864no—
254C2—3442no—
255C2#1458345711yescharacteristic
256C2AGL(1,ℤ/8)×D4312yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#469C2
socleC22×C43C22×D4
hypercenter#469D43
hypocenterC43#3192
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. #121×D43C2semidirect
2. #14583219C2semidirect
3. #14583216C2semidirect
4. #14583152C2semidirect
5. #14583150C2semidirect
6. #14583034C2semidirect
7. #14583031C2semidirect
8. #14582862C2semidirect
9. C43×#469C2semidirect
11. C2×D4×D43C22semidirect
13. C2×D344C22semidirect
14. C2×#10621882C22semidirect
15. C2×#10621877C22semidirect
17. #13063299C22semidirect
21. C4⋊C4×D43C22semidirect
23. #13063257C22semidirect
24. #13063256C22semidirect
25. #13063247C22semidirect
26. #13063246C22semidirect
27. #13063245C22semidirect
28. (C2×D43)⋊C8C22semidirect
29. (C2×D43)⋊C8C22semidirect
30. C2×D8×C43C22semidirect
31. C2×M16×C43C22semidirect
32. #121×C43C22semidirect
33. #106×C43C22semidirect
34. #102×C43C22semidirect
134. #469D43semidirect
138. C43#3192semidirect
144. C2×D8C2×D43semidirect
146. C2×M16C2×D43semidirect
152. #121C2×D43semidirect
157. #106C2×D43semidirect
161. #102C2×D43semidirect