Finite Group Databasebeta

← #19145342

Subgroups — #19145342

Order 5504.

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

normal subgroups only

This group has 520 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#121×D43C212yesmaximal, complemented
2#14583214C212yesmaximal, complemented
3#14583211C212yesmaximal, complemented
4#14583135C211yesmaximal, characteristic, complemented
5#14583133C212yesmaximal, complemented
6#14583034C212yesmaximal, complemented
7#14583031C212yesmaximal, complemented
8C2×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
9C43×#466C211yesmaximal, characteristic, complemented
10C2×D4×D43—22no—
11C2×D4×D43C2212yescomplemented
12C22×C4×D43C2211yescharacteristic
13C2×D344C2211yescharacteristic, complemented
14C2×#10621882C2212yescomplemented
15C22×C43⋊C8C2211yescharacteristic, complemented
16#13063300C2212yes—
17#13063299C2212yescomplemented
18#13063298—22no—
19#13063297—22no—
20#13063296C2212yes—
21C4⋊C4×D43C2212yescomplemented
22C22⋊C4×D43—22no—
23#13063259C2211yescharacteristic, complemented
24#13063258C2212yescomplemented
25#13063247C2212yescomplemented
26#13063246C2212yescomplemented
27#13063245C2212yescomplemented
28(C2×D43)⋊C8C2212yescomplemented
29(C2×D43)⋊C8C2212yescomplemented
30C2×D8×C43C2211yescharacteristic, complemented
31C22×C8×C43C2211yescharacteristic, complemented
32#121×C43C2212yescomplemented
33#107×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—42no—
45D4×D43—42no—
46D4×D43—48no—
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—
55C2×C8×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—
66C2×C43⋊C8—41no—
67C2×C43⋊C8C2312yes—
68D344—41no—
69C23×C43—22no—
70C23×C43C2×D411yescharacteristic
71C22×D43—22no—
72C22×D43—41no—
73C22×D43—41no—
74C22×D43—44no—
75C22×D43—44no—
76C22×D43—44no—
77C22×D43D814yescomplemented
78C22×D43C2×D412yes—
79D4×C43—22no—
80D4×C43—22no—
81D4×C43—44no—
82C2×C4×C43—21no—
83C2×C4×C43—21no—
84C2×C4×C43—22no—
85C2×C4×C43C2×D411yescharacteristic
86C2×C4×C43C2411yescharacteristic
87C22⋊D43—44no—
88C22⋊D43—44no—
89C22⋊D43—44no—
90C2×Dic43—22no—
91C2×Dic43—41no—
92C2×Dic43C2×D412yes—
93D172—22no—
94D172—22no—
95D172—44no—
96C4×D43—22no—
97C4×D43—22no—
98C4×D43—42no—
99C4×D43—44no—
100C8×C43—21no—
101C8×C43—21no—
102C43⋊C8—22no—
103C22×C43—21no—
104C22×C43—21no—
105C22×C43—42no—
106C22×C43—42no—
107C22×C43—42no—
108C22×C43C2×D812yes—
109C22×C43C22×D411yescharacteristic
110C2×D43—22no—
111C2×D43—22no—
112C2×D43—44no—
113C2×D43—42no—
114C2×D43—42no—
115C2×D43—42no—
116C2×D43—88no—
117C2×D43C2×D814yes—
118C4×C43—21no—
119C4×C43—42no—
120C4×C43H(5,𝔽2)11yescharacteristic
121C4×C43H(5,𝔽2)11yescharacteristic
122Dic43—22no—
123Dic43—42no—
124#3186—431nomaximal, Sylow
125C2×C43—22no—
126C2×C43—82no—
127C2×C43#53411yescharacteristic
128C2×C43C22×D811yescharacteristic
129C2×C43#57511yescharacteristic
130D43—24no—
131D43—82no—
132C2×#121—432no—
133#480—432no—
134#480—432no—
135#466—431no—
136#466—432no—
137#466D4311yescharacteristic, complemented
138#447—432no—
139#447—432no—
140C2×C22⋊C8—431no—
141C43#318611yescharacteristic, complemented, Sylow
142C22×D4—432no—
143C22×D4—862no—
144C23×C4—431no—
145C2×D8—432no—
146C2×D8—431no—
147C2×D8C2×D4311yescharacteristic, complemented
148C22×C8—431no—
149C22×C8C2×D4311yescharacteristic, complemented
150#121—432no—
151#121—432no—
152#121—432no—
153#121—862no—
154#121—862no—
155#121C2×D4312yescomplemented
156C2×C4⋊C4—432no—
157C2×C22⋊C4—862no—
158#107—431no—
159#107—432no—
160#107C2×D4311yescharacteristic, complemented
161#102—432no—
162#102—432no—
163#102—432no—
164#102C2×D4312yescomplemented
165C22⋊C8—432no—
166C22⋊C8—432no—
167C24—431no—
168C24—862no—
169C2×D4—22no—
170C2×D4—432no—
171C2×D4—862no—
172C2×D4—862no—
173C2×D4—862no—
174C2×D4—862no—
175C2×D4—1722no—
176C2×D4—1722no—
177C2×D4—1728no—
178C2×D4C22×D4312yes—
179C22×C4—431no—
180C22×C4—432no—
181C22×C4—432no—
182C22×C4—862no—
183C22×C4—1721no—
184C22×C4—1721no—
185C22×C4C22×D4311yescharacteristic
186D8—41no—
187D8—1721no—
188D8—1722no—
189C2×C8—41no—
190C2×C8—432no—
191C2×C8—1721no—
192C2×C8C22×D4311yescharacteristic
193C2×C8C22×D4311yescharacteristic
194C4⋊C4—432no—
195C4⋊C4—862no—
196C4⋊C4C22×D4312yes—
197C22⋊C4—22no—
198C22⋊C4—862no—
199C22⋊C4—862no—
200C22⋊C4—862no—
201C23—22no—
202C23—432no—
203C23—434no—
204C23—862no—
205C23—1721no—
206C23—1721no—
207C23—1724no—
208C23—1724no—
209C23—1724no—
210C23D4×D4311yescharacteristic
211D4—22no—
212D4—22no—
213D4—44no—
214D4—862no—
215D4—862no—
216D4—1724no—
217D4—1724no—
218D4—1724no—
219D4—1724no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—432no—
224C2×C4—862no—
225C2×C4—862no—
226C2×C4—862no—
227C2×C4—1722no—
228C2×C4—1724no—
229C2×C4—1721no—
230C2×C4D4×D4311yescharacteristic
231C2×C4C23×D4311yescharacteristic
232C8—21no—
233C8—21no—
234C8—862no—
235C22—21no—
236C22—21no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—434no—
241C22—862no—
242C22—862no—
243C22—3448no—
244C22—1724no—
245C22—1722no—
246C22—1722no—
247C22—1722no—
248C22D8×D4312yes—
249C22C2×D4×D4311yescharacteristic
250C4—21no—
251C4—42no—
252C4—862no—
253C4—1722no—
254C4#1306337011yescharacteristic
255C4#1306337111yescharacteristic
256C2—22no—
257C2—82no—
258C2—864no—
259C2—3442no—
260C2#1458345711yescharacteristic
261C2C2×D8×D4311yescharacteristic
262C2#1458369611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#466C2
socleC22×C43C22×D4
hypercenter#466D43
hypocenterC43#3186
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #121×D43C2semidirect
2. #14583214C2semidirect
3. #14583211C2semidirect
4. #14583135C2semidirect
5. #14583133C2semidirect
6. #14583034C2semidirect
7. #14583031C2semidirect
8. C2×(C2×D43)⋊C8C2semidirect
9. C43×#466C2semidirect
11. C2×D4×D43C22semidirect
13. C2×D344C22semidirect
14. C2×#10621882C22semidirect
15. C22×C43⋊C8C22semidirect
17. #13063299C22semidirect
21. C4⋊C4×D43C22semidirect
23. #13063259C22semidirect
24. #13063258C22semidirect
25. #13063247C22semidirect
26. #13063246C22semidirect
27. #13063245C22semidirect
28. (C2×D43)⋊C8C22semidirect
29. (C2×D43)⋊C8C22semidirect
30. C2×D8×C43C22semidirect
31. C22×C8×C43C22semidirect
32. #121×C43C22semidirect
33. #107×C43C22semidirect
34. #102×C43C22semidirect
77. C22×D43D8semidirect
137. #466D43semidirect
141. C43#3186semidirect
147. C2×D8C2×D43semidirect
149. C22×C8C2×D43semidirect
155. #121C2×D43semidirect
160. #107C2×D43semidirect
164. #102C2×D43semidirect