Finite Group Databasebeta

← #19145609

Subgroups — #19145609

Order 5504.

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

normal subgroups only

This group has 490 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#127×D43C211yesmaximal, characteristic, complemented
2#14583428C211yesmaximal, characteristic, complemented
3#14583289C211yesmaximal, characteristic, complemented
4#14583264C211yesmaximal, characteristic, complemented
5#14583263C211yesmaximal, characteristic, complemented
6#14583097C212yesmaximal, complemented
7#14583092C212yesmaximal, complemented
8#14583048C212yesmaximal, complemented
9#14583031C212yesmaximal, complemented
10#14582954C211yesmaximal, characteristic, complemented
11C43×#496C211yesmaximal, characteristic, complemented
12C2×D4×D43—21no—
13C2×D4×D43—21no—
14C2×D4×D43C2212yes—
15C2×#10621884C2212yescomplemented
16C2×#10621882C2212yescomplemented
17#13063322C2211yescharacteristic
18#13063321—21no—
19#13063321—21no—
20#13063321C2212yes—
21#13063318—21no—
22#13063317C2211yescharacteristic, complemented
23#13063307—21no—
24#13063301C2211yescharacteristic
25#13063296C2211yescharacteristic
26Q8×Dic43C2211yescharacteristic, complemented
27D4×Dic43C2211yescharacteristic, complemented
28(C22⋊D43)⋊C4—21no—
29#13063281—21no—
30C42×D43C2211yescharacteristic
31Dic43⋊C8C2212yescomplemented
32#13063247C2212yescomplemented
33#13063247C2212yescomplemented
34#13063246C2212yescomplemented
35#13063246C2212yescomplemented
36(C2×D43)⋊C8C2212yes—
37#13063236C2211yescharacteristic, complemented
38C2×SD16×C43C2212yescomplemented
39C2×D8×C43C2212yescomplemented
40#127×C43C2211yescharacteristic
41#124×C43C2211yescharacteristic, complemented
42#97×C43C2211yescharacteristic, complemented
43C23×D43—22no—
44C2×Q8×C43C2311yescharacteristic
45C2×D4×C43—21no—
46C2×D4×C43—21no—
47C2×D4×C43C2311yescharacteristic
48C2×D4×C43C2312yes—
49C2×C22⋊D43—22no—
50C2×C22⋊D43—22no—
51C2×C22⋊D43—22no—
52C2×C22⋊D43—21no—
53C22×Dic43—21no—
54D4×D43—42no—
55D4×D43—42no—
56D4×D43—44no—
57D4×D43—44no—
58C2×D172—21no—
59C2×D172—21no—
60C2×D172C2312yes—
61C2×C4×D43D411yescharacteristic
62C2×C4×D43D411yescharacteristic
63C2×C4×D43C2311yescharacteristic
64SD16×C43—42no—
65D8×C43—42no—
66C2×C8×C43C2312yes—
67C22⋊C4×C43—21no—
68C22⋊C4×C43—21no—
69C42×C43C2311yescharacteristic
70C22⋊Dic43—21no—
71C22⋊Dic43—21no—
72#10621884—42no—
73#10621882—42no—
74(C2×D43)⋊C4—21no—
75C4⋊Dic43—21no—
76C4⋊Dic43C2311yescharacteristic
77C4⋊Dic43C2311yescharacteristic
78Dic43⋊C4—21no—
79Dic43⋊C4—21no—
80Dic43⋊C4—21no—
81C4×Dic43—21no—
82C4×Dic43D411yescharacteristic
83C4×Dic43D411yescharacteristic
84C4×Dic43C2311yescharacteristic
85C2×C43⋊C8C2312yes—
86C23×C43—21no—
87C23×C43—22no—
88C22×D43—22no—
89C22×D43—44no—
90C22×D43—44no—
91C22×D43—44no—
92C22×D43C2×D411yescharacteristic
93Q8×C43—22no—
94D4×C43—22no—
95D4×C43—22no—
96D4×C43—22no—
97D4×C43—42no—
98D4×C43—42no—
99C2×C4×C43—21no—
100C2×C4×C43C2×D411yescharacteristic
101C2×C4×C43C2×D411yescharacteristic
102C2×C4×C43C2411yescharacteristic
103C22⋊D43—44no—
104C22⋊D43—44no—
105C22⋊D43—42no—
106C22⋊D43—44no—
107C2×Dic43—21no—
108C2×Dic43—21no—
109C2×Dic43—42no—
110C2×Dic43C2×D411yescharacteristic
111C2×Dic43C2×D411yescharacteristic
112C2×Dic43C2×D411yescharacteristic
113D172—22no—
114D172—22no—
115D172—42no—
116D172—42no—
117C4×D43—22no—
118C4×D43—22no—
119C4×D43—22no—
120C8×C43—22no—
121C43⋊C8—22no—
122C22×C43—42no—
123C22×C43—41no—
124C22×C43—42no—
125C22×C43—42no—
126C22×C43—41no—
127C22×C43—41no—
128C22×C43C22×D411yescharacteristic
129C2×D43—21no—
130C2×D43—21no—
131C2×D43—42no—
132C2×D43—42no—
133C2×D43—42no—
134C2×D43—88no—
135C2×D43AGL(1,ℤ/8)12yes—
136C4×C43—21no—
137C4×C43—21no—
138C4×C43—41no—
139C4×C43H(5,𝔽2)12yes—
140Dic43—21no—
141Dic43—21no—
142Dic43—41no—
143Dic43—41no—
144Dic43AGL(1,ℤ/8)12yes—
145#3217—431nomaximal, Sylow
146C2×C43—82no—
147C2×C43—81no—
148C2×C43#53511yescharacteristic
149C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
150C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
151D43—22no—
152D43—82no—
153C2×#127—431no—
154#529—431no—
155#496—431no—
156#496D4311yescharacteristic, complemented
157#490—431no—
158#490—431no—
159#460—432no—
160#459—432no—
161#450—432no—
162#447—432no—
163#432—431no—
164C43#321711yescharacteristic, complemented, Sylow
165C22×D4—432no—
166C22×D4—861no—
167C22×D4—861no—
168C2×SD16—432no—
169C2×SD16C2×D4312yescomplemented
170C2×D8—432no—
171C2×D8C2×D4312yescomplemented
172#127—432no—
173#127—431no—
174#127—861no—
175#127—861no—
176#127C2×D4311yescharacteristic
177#126—861no—
178#125—431no—
179#124C2×D4311yescharacteristic, complemented
180#123—861no—
181C22⋊Q8—431no—
182#121—431no—
183C4×Q8—431no—
184C4×D4—431no—
185C4×D4—861no—
186#117—861no—
187C2×C42—431no—
188C4⋊C8—432no—
189#102—432no—
190#102—432no—
191#102—432no—
192#102—432no—
193C22⋊C8—432no—
194#97—431no—
195#97C2×D4311yescharacteristic, complemented
196C24—862no—
197C2×Q8C22×D4311yescharacteristic
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—432no—
201C2×D4—862no—
202C2×D4—862no—
203C2×D4—862no—
204C2×D4—861no—
205C2×D4—861no—
206C2×D4—861no—
207C2×D4—1722no—
208C2×D4—1722no—
209C2×D4—1724no—
210C2×D4—1724no—
211C2×D4C22×D4312yes—
212C2×D4C22×D4311yescharacteristic
213C22×C4—431no—
214C22×C4—431no—
215C22×C4—431no—
216C22×C4—861no—
217SD16—42no—
218SD16—1722no—
219D8—42no—
220D8—1722no—
221C2×C8—432no—
222C2×C8C22×D4312yes—
223C4⋊C4—431no—
224C4⋊C4—431no—
225C4⋊C4—861no—
226C4⋊C4—861no—
227C4⋊C4—861no—
228C4⋊C4—861no—
229C22⋊C4—21no—
230C22⋊C4—21no—
231C22⋊C4—861no—
232C22⋊C4—861no—
233C22⋊C4—861no—
234C42—431no—
235C42—431no—
236C42—431no—
237C42—861no—
238C42C22×D4311yescharacteristic
239C23—21no—
240C23—22no—
241C23—431no—
242C23—862no—
243C23—1724no—
244C23—1724no—
245C23—1724no—
246Q8—22no—
247D4—22no—
248D4—22no—
249D4—22no—
250D4—42no—
251D4—42no—
252D4—862no—
253D4—862no—
254D4—1722no—
255D4—1722no—
256D4—1724no—
257D4—1724no—
258D4—1724no—
259D4—1722no—
260C2×C4—21no—
261C2×C4—431no—
262C2×C4—431no—
263C2×C4—431no—
264C2×C4—862no—
265C2×C4—862no—
266C2×C4—862no—
267C2×C4—861no—
268C2×C4—861no—
269C2×C4—1722no—
270C2×C4D4×D4311yescharacteristic
271C2×C4D4×D4311yescharacteristic
272C2×C4C23×D4311yescharacteristic
273C8—22no—
274C8—862no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—41no—
279C22—42no—
280C22—41no—
281C22—432no—
282C22—861no—
283C22—861no—
284C22—3448no—
285C22—1722no—
286C22—1722no—
287C22—1722no—
288C22C2×D4×D4311yescharacteristic
289C4—21no—
290C4—21no—
291C4—41no—
292C4—432no—
293C4—861no—
294C4—861no—
295C4—1721no—
296C4—1721no—
297C4#1306337012yes—
298C2—82no—
299C2—81no—
300C2—862no—
301C2—3442no—
302C2#1458346211yescharacteristic
303C2AGL(1,ℤ/8)×D4311yescharacteristic
304C2AGL(1,ℤ/8)×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#496C2
socleC22×C43C22×D4
hypercenter#496D43
hypocenterC43#3217
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #127×D43C2semidirect
2. #14583428C2semidirect
3. #14583289C2semidirect
4. #14583264C2semidirect
5. #14583263C2semidirect
6. #14583097C2semidirect
7. #14583092C2semidirect
8. #14583048C2semidirect
9. #14583031C2semidirect
10. #14582954C2semidirect
11. C43×#496C2semidirect
15. C2×#10621884C22semidirect
16. C2×#10621882C22semidirect
22. #13063317C22semidirect
26. Q8×Dic43C22semidirect
27. D4×Dic43C22semidirect
31. Dic43⋊C8C22semidirect
32. #13063247C22semidirect
33. #13063247C22semidirect
34. #13063246C22semidirect
35. #13063246C22semidirect
37. #13063236C22semidirect
38. C2×SD16×C43C22semidirect
39. C2×D8×C43C22semidirect
41. #124×C43C22semidirect
42. #97×C43C22semidirect
156. #496D43semidirect
164. C43#3217semidirect
169. C2×SD16C2×D43semidirect
171. C2×D8C2×D43semidirect
179. #124C2×D43semidirect
195. #97C2×D43semidirect