Finite Group Databasebeta

← #19146197

Subgroups — #19146197

Order 5504.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#13063353C212yesmaximal, complemented
2#14583554C211yesmaximal, characteristic, complemented
3D4×D172C211yesmaximal, characteristic, complemented
4#14583272C211yesmaximal, characteristic, complemented
5#14583145C212yesmaximal, complemented
6#14583105C211yesmaximal, characteristic, complemented
7#14583095C211yesmaximal, characteristic, complemented
8#14583052C212yesmaximal, complemented
9#14583046C212yesmaximal, complemented
10C4×D344C211yesmaximal, characteristic, complemented
11C43×#436C211yesmaximal, characteristic, complemented
12C2×#10621898C2212yescomplemented
13C22×D172C2212yes—
14C2×D4×D43—21no—
15#13063353—28no—
16C2×#10621873C2212yes—
17C2×#10621873C2212yescomplemented
18C2×#10621873C2212yescomplemented
19C2×D344C2211yescharacteristic
20C2×D344C2212yescomplemented
21#13063325C2211yescharacteristic, complemented
22#13063322C2211yescharacteristic
23#13063307—22no—
24#13063304C2212yescomplemented
25#13063300—21no—
26#13063299C2212yes—
27#13063296—21no—
28#13063295—22no—
29C4×D172C2211yescharacteristic
30C4×D172C2211yescharacteristic, complemented
31C4⋊C4×D43—21no—
32#13063259C2211yescharacteristic, complemented
33#13063250C2212yescomplemented
34#13063247C2211yescharacteristic
35#13063247C2211yescharacteristic, complemented
36#13063247C2212yescomplemented
37C2×M16×C43C2212yescomplemented
38C4×D4×C43C2211yescharacteristic
39C4⋊C8×C43C2211yescharacteristic, complemented
40C22⋊C8×C43C2212yescomplemented
41C4×C8×C43C2211yescharacteristic, complemented
42C23×D43—22no—
43C2×D4×C43D411yescharacteristic
44C22×C4×C43C2312yes—
45C2×C22⋊D43—22no—
46C2×C22⋊D43—22no—
47D4×D43—44no—
48#10621898—24no—
49#10621898—42no—
50C2×D172—22no—
51C2×D172—21no—
52C2×D172—21no—
53C2×D172—24no—
54C2×D172—42no—
55C2×D172C2312yes—
56C2×D172C2311yescharacteristic
57C2×D172C2311yescharacteristic
58C2×C4×D43—21no—
59C2×C4×D43—22no—
60C2×C4×D43—21no—
61C2×Dic86C2312yes—
62M16×C43—24no—
63C2×C8×C43C2311yescharacteristic
64C2×C8×C43C2312yes—
65C2×C8×C43C2311yescharacteristic
66C4⋊C4×C43D411yescharacteristic
67C22⋊C4×C43D412yes—
68C42×C43C2311yescharacteristic
69C22⋊Dic43—22no—
70(C2×D43)⋊C4—21no—
71(C2×D43)⋊C4—21no—
72(C2×D43)⋊C4—22no—
73C4⋊Dic43—21no—
74C4⋊Dic43—21no—
75C4⋊Dic43C2311yescharacteristic
76C4⋊Dic43C2311yescharacteristic
77Dic43⋊C4—22no—
78D344—24no—
79D344D414yescomplemented
80#10621873—24no—
81#10621873—24no—
82#10621873—42no—
83C23×C43C2×D412yes—
84C22×D43—21no—
85C22×D43—21no—
86C22×D43—22no—
87C22×D43—44no—
88C22×D43—44no—
89C22×D43—82no—
90D4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43C2×D412yes—
94C2×C4×C43C2×D411yescharacteristic
95C2×C4×C43C2×D411yescharacteristic
96C2×C4×C43C2411yescharacteristic
97C22⋊D43—44no—
98C22⋊D43—44no—
99C2×Dic43—21no—
100C2×Dic43—22no—
101C2×Dic43—21no—
102D172—22no—
103D172—21no—
104D172—21no—
105D172—22no—
106D172—44no—
107D172—42no—
108D172—81no—
109D172C2×D412yes—
110D172C2×D412yescomplemented
111C4×D43—44no—
112C4×D43—42no—
113C4×D43—42no—
114Dic86—22no—
115Dic86—22no—
116C8×C43—22no—
117C8×C43—21no—
118C8×C43C2×D412yescomplemented
119C22×C43—22no—
120C22×C43—22no—
121C22×C43—22no—
122C22×C43C22×D411yescharacteristic
123C2×D43—22no—
124C2×D43—22no—
125C2×D43—41no—
126C2×D43—41no—
127C2×D43—41no—
128C2×D43—41no—
129C2×D43—42no—
130C2×D43—42no—
131C2×D43—42no—
132C2×D43—88no—
133C4×C43—22no—
134C4×C43—21no—
135C4×C43AGL(1,ℤ/8)12yescomplemented
136C4×C43C22×D411yescharacteristic
137C4×C43H(5,𝔽2)11yescharacteristic
138Dic43—42no—
139Dic43—41no—
140Dic43—41no—
141#3272—431nomaximal, Sylow
142C2×C43—42no—
143C2×C43D4211yescharacteristic
144C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
145C2×C43#57711yescharacteristic
146D43—42no—
147D43—42no—
148D43—82no—
149C2×AGL(1,ℤ/8)—432no—
150#547—431no—
151D42—431no—
152#492—431no—
153#468—432no—
154#461—431no—
155#459—431no—
156#450—432no—
157#449—432no—
158C4×D8—431no—
159#436D4311yescharacteristic, complemented
160C43#327211yescharacteristic, complemented, Sylow
161C2×#41—432no—
162C22×D4—432no—
163C22×D4—861no—
164AGL(1,ℤ/8)—868no—
165C2×SD16—432no—
166C2×SD16—432no—
167C2×SD16—432no—
168C2×D8—431no—
169C2×D8—432no—
170C2×M16C2×D4312yescomplemented
171C4⋊Q8—431no—
172#127—431no—
173#123—862no—
174C22⋊Q8—432no—
175#121—432no—
176#121—861no—
177#121—861no—
178#120—862no—
179C4×D4—431no—
180C4×D4—431no—
181C4×D4C2×D4311yescharacteristic
182C2×C4⋊C4—861no—
183#107—431no—
184C4⋊C8C2×D4311yescharacteristic, complemented
185#103—432no—
186#102—431no—
187#102—431no—
188#102—432no—
189C22⋊C8C2×D4312yescomplemented
190C4×C8C2×D4311yescharacteristic, complemented
191C24—862no—
192#41—864no—
193#41—1722no—
194C2×Q8—432no—
195C2×D4—431no—
196C2×D4—431no—
197C2×D4—432no—
198C2×D4—864no—
199C2×D4—862no—
200C2×D4—862no—
201C2×D4—861no—
202C2×D4—862no—
203C2×D4—861no—
204C2×D4—1722no—
205C2×D4—1724no—
206C2×D4D17211yescharacteristic
207C22×C4—861no—
208C22×C4—862no—
209C22×C4—861no—
210C22×C4C22×D4312yes—
211SD16—864no—
212SD16—864no—
213SD16—1722no—
214D8—434no—
215D8—864no—
216M16—24no—
217C2×C8C22×D4311yescharacteristic
218C2×C8C22×D4312yes—
219C2×C8C22×D4311yescharacteristic
220C4⋊C4—431no—
221C4⋊C4—431no—
222C4⋊C4—861no—
223C4⋊C4—862no—
224C4⋊C4—861no—
225C4⋊C4D17211yescharacteristic
226C22⋊C4—862no—
227C22⋊C4—861no—
228C22⋊C4—861no—
229C22⋊C4—862no—
230C22⋊C4D17212yes—
231C42C22×D4311yescharacteristic
232C23—861no—
233C23—861no—
234C23—862no—
235C23—3442no—
236C23—1724no—
237C23—1724no—
238C23C2×D17212yes—
239Q8—862no—
240Q8—862no—
241D4—22no—
242D4—432no—
243D4—432no—
244D4—862no—
245D4—861no—
246D4—861no—
247D4—862no—
248D4—3441no—
249D4—1724no—
250D4—1724no—
251D4—1724no—
252D4—1722no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—861no—
256C2×C4—861no—
257C2×C4—862no—
258C2×C4—1724no—
259C2×C4—1722no—
260C2×C4—1722no—
261C2×C4C2×D17211yescharacteristic
262C2×C4C2×D17212yes—
263C2×C4C2×D17211yescharacteristic
264C2×C4C23×D4311yescharacteristic
265C8—22no—
266C8—21no—
267C8D4×D4312yescomplemented
268C22—22no—
269C22—22no—
270C22—22no—
271C22—862no—
272C22—862no—
273C22—3448no—
274C22—1722no—
275C22—1722no—
276C22—1722no—
277C22—1721no—
278C22—1721no—
279C22—1721no—
280C22—1721no—
281C22C22×D17211yescharacteristic
282C4—21no—
283C4—22no—
284C4—1721no—
285C4—1721no—
286C4—1722no—
287C4#1306335312yescomplemented
288C4C2×D4×D4311yescharacteristic
289C4#1306337111yescharacteristic
290C2—42no—
291C2—3442no—
292C2—1722no—
293C2—1722no—
294C2D4×D17211yescharacteristic
295C2C2×#1306335311yescharacteristic
296C2#1458371111yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#436C2
socleC22×C43C22×D4
hypercenter#436D43
hypocenterC43#3272
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#13063353C2semidirect
2. #14583554C2semidirect
3. D4×D172C2semidirect
4. #14583272C2semidirect
5. #14583145C2semidirect
6. #14583105C2semidirect
7. #14583095C2semidirect
8. #14583052C2semidirect
9. #14583046C2semidirect
10. C4×D344C2semidirect
11. C43×#436C2semidirect
12. C2×#10621898C22semidirect
17. C2×#10621873C22semidirect
18. C2×#10621873C22semidirect
20. C2×D344C22semidirect
21. #13063325C22semidirect
24. #13063304C22semidirect
30. C4×D172C22semidirect
32. #13063259C22semidirect
33. #13063250C22semidirect
35. #13063247C22semidirect
36. #13063247C22semidirect
37. C2×M16×C43C22semidirect
39. C4⋊C8×C43C22semidirect
40. C22⋊C8×C43C22semidirect
41. C4×C8×C43C22semidirect
79. D344D4semidirect
110. D172C2×D4semidirect
118. C8×C43C2×D4semidirect
135. C4×C43AGL(1,ℤ/8)semidirect
159. #436D43semidirect
160. C43#3272semidirect
170. C2×M16C2×D43semidirect
184. C4⋊C8C2×D43semidirect
189. C22⋊C8C2×D43semidirect
190. C4×C8C2×D43semidirect
267. C8D4×D43semidirect
287. C4#13063353semidirect