Finite Group Databasebeta

← #19145455

Subgroups — #19145455

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#14583226C212yesmaximal, complemented
3#14583221C212yesmaximal, complemented
4#14583150C212yesmaximal, complemented
5#14583135C211yesmaximal, characteristic, complemented
6#14583034C212yesmaximal, complemented
7#14583031C212yesmaximal, complemented
8#14582865C211yesmaximal, characteristic, complemented
9C43×#466C211yesmaximal, characteristic, complemented
10C2×#10621898C2211yescharacteristic
11C2×D4×D43C2212yescomplemented
12C2×D344C2211yescharacteristic
13C2×#10621882C2212yes—
14C2×#10621877C2211yescharacteristic, complemented
15#13063321—22no—
16#13063311—22no—
17#13063300C2212yes—
18#13063299C2212yescomplemented
19#13063296C2212yes—
20#13063295—22no—
21#13063293—22no—
22#13063283C2212yescomplemented
23#13063259C2211yescharacteristic, complemented
24#13063256C2212yescomplemented
25#13063247C2212yescomplemented
26#13063246C2212yescomplemented
27#13063245C2212yescomplemented
28(C2×D43)⋊C8C2212yescomplemented
29(C2×D43)⋊C8C2212yescomplemented
30C2×D8×C43C2211yescharacteristic
31C22×C8×C43C2211yescharacteristic, complemented
32#121×C43C2212yescomplemented
33#107×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—
53C2×C8×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—
65#10621877—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—21no—
101C22×C43—21no—
102C22×C43—42no—
103C22×C43—42no—
104C22×C43—42no—
105C22×C43C22×D411yescharacteristic
106C2×D43—22no—
107C2×D43—22no—
108C2×D43—22no—
109C2×D43—42no—
110C2×D43—42no—
111C2×D43—42no—
112C2×D43—88no—
113C4×C43—21no—
114C4×C43—42no—
115C4×C43H(5,𝔽2)11yescharacteristic
116C4×C43H(5,𝔽2)11yescharacteristic
117Dic43—22no—
118Dic43—42no—
119#3199—431nomaximal, Sylow
120C2×C43—41no—
121C2×C43—82no—
122C2×C43#53411yescharacteristic
123C2×C43#57611yescharacteristic
124C2×C43#57611yescharacteristic
125D43—42no—
126D43—82no—
127#535—432no—
128#482—432no—
129#482—432no—
130#469—432no—
131#466—431no—
132#466D4311yescharacteristic, complemented
133#447—432no—
134#447—432no—
135#408—431no—
136C43#319911yescharacteristic, complemented, Sylow
137C2×#41—431no—
138C22×D4—432no—
139C2×D8—432no—
140C2×D8—431no—
141C2×D8C2×D4311yescharacteristic
142C2×M16—431no—
143C22×C8C2×D4311yescharacteristic, complemented
144#127—862no—
145#124—862no—
146#121—432no—
147#121—432no—
148#121—432no—
149#121C2×D4312yescomplemented
150#120—862no—
151#120—862no—
152#117—432no—
153#107—431no—
154#107C2×D4311yescharacteristic, complemented
155#106—432no—
156#102—432no—
157#102—432no—
158#102—432no—
159#102C2×D4312yescomplemented
160C22⋊C8—432no—
161C22⋊C8—432no—
162C24—862no—
163#41—1721no—
164#41—1721no—
165C2×Q8—431no—
166C2×D4—22no—
167C2×D4—432no—
168C2×D4—431no—
169C2×D4—432no—
170C2×D4—862no—
171C2×D4—862no—
172C2×D4—862no—
173C2×D4—862no—
174C2×D4—1722no—
175C2×D4—1722no—
176C2×D4C22×D4312yes—
177C22×C4—432no—
178C22×C4C22×D4311yescharacteristic
179D8—41no—
180D8—1721no—
181D8—1722no—
182M16—1721no—
183C2×C8—41no—
184C2×C8—432no—
185C2×C8C22×D4311yescharacteristic
186C2×C8C22×D4311yescharacteristic
187C4⋊C4—432no—
188C4⋊C4C22×D4312yes—
189C22⋊C4—22no—
190C22⋊C4—862no—
191C22⋊C4—862no—
192C22⋊C4—862no—
193C22⋊C4—862no—
194C42—862no—
195C23—22no—
196C23—432no—
197C23—862no—
198C23—3442no—
199C23—3442no—
200C23—1724no—
201C23D4×D4311yescharacteristic
202Q8—1721no—
203D4—22no—
204D4—22no—
205D4—82no—
206D4—862no—
207D4—862no—
208D4—3442no—
209D4—3442no—
210D4—3442no—
211D4—1721no—
212D4—1722no—
213D4—1724no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—432no—
218C2×C4—862no—
219C2×C4—862no—
220C2×C4—862no—
221C2×C4D4×D4311yescharacteristic
222C2×C4C23×D4311yescharacteristic
223C8—21no—
224C8—21no—
225C8—862no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22—862no—
233C22—862no—
234C22—862no—
235C22—3448no—
236C22—1722no—
237C22—1722no—
238C22—1722no—
239C22C2×D4×D4311yescharacteristic
240C4—21no—
241C4—42no—
242C4—862no—
243C4—1722no—
244C4#1306337011yescharacteristic
245C4#1306337111yescharacteristic
246C2—41no—
247C2—82no—
248C2—3442no—
249C2—1722no—
250C2#1458345711yescharacteristic
251C2#1458370011yescharacteristic
252C2#1458370111yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#466C2
socleC22×C43C22×D4
hypercenter#466D43
hypocenterC43#3199
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. #14583465C2semidirect
2. #14583226C2semidirect
3. #14583221C2semidirect
4. #14583150C2semidirect
5. #14583135C2semidirect
6. #14583034C2semidirect
7. #14583031C2semidirect
8. #14582865C2semidirect
9. C43×#466C2semidirect
11. C2×D4×D43C22semidirect
14. C2×#10621877C22semidirect
18. #13063299C22semidirect
22. #13063283C22semidirect
23. #13063259C22semidirect
24. #13063256C22semidirect
25. #13063247C22semidirect
26. #13063246C22semidirect
27. #13063245C22semidirect
28. (C2×D43)⋊C8C22semidirect
29. (C2×D43)⋊C8C22semidirect
31. C22×C8×C43C22semidirect
32. #121×C43C22semidirect
33. #107×C43C22semidirect
34. #102×C43C22semidirect
132. #466D43semidirect
136. C43#3199semidirect
143. C22×C8C2×D43semidirect
149. #121C2×D43semidirect
154. #107C2×D43semidirect
159. #102C2×D43semidirect