Finite Group Databasebeta

← #19145614

Subgroups — #19145614

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#14583434C211yesmaximal, characteristic, complemented
3#14583288C211yesmaximal, characteristic, complemented
4#14583286C211yesmaximal, characteristic, complemented
5#14583265C211yesmaximal, characteristic, complemented
6#14583098C212yesmaximal, complemented
7#14583093C212yesmaximal, complemented
8#14583051C212yesmaximal, complemented
9#14583034C212yesmaximal, complemented
10#14582954C211yesmaximal, characteristic, complemented
11C43×#490C211yesmaximal, characteristic, complemented
12C2×D4×D43—21no—
13C2×D4×D43—21no—
14C2×D4×D43C2212yes—
15C2×#10621873C2212yescomplemented
16C2×#10621883C2212yescomplemented
17C2×D344C2212yescomplemented
18C2×#10621882C2212yescomplemented
19#13063322C2211yescharacteristic
20#13063321—21no—
21#13063321—21no—
22#13063321C2212yes—
23#13063320—21no—
24#13063313C2211yescharacteristic, complemented
25#13063310—21no—
26#13063305C2211yescharacteristic
27#13063300C2211yescharacteristic
28#13063290C2211yescharacteristic, complemented
29#13063287—21no—
30#13063287C2211yescharacteristic, complemented
31#13063283—21no—
32C42×D43C2211yescharacteristic
33Dic43⋊C8C2212yescomplemented
34#13063245C2212yescomplemented
35#13063245C2212yescomplemented
36(C2×D43)⋊C8C2212yes—
37#13063236C2211yescharacteristic, complemented
38#127×C43C2211yescharacteristic
39#125×C43C2211yescharacteristic, complemented
40#102×C43C2212yescomplemented
41#102×C43C2212yescomplemented
42#97×C43C2211yescharacteristic, complemented
43C23×D43—22no—
44C2×D4×C43—21no—
45C2×D4×C43—21no—
46C2×D4×C43C2312yes—
47C2×C22⋊D43—22no—
48C2×C22⋊D43—22no—
49C2×C22⋊D43—22no—
50D4×D43—42no—
51D4×D43—42no—
52D4×D43—44no—
53D4×D43—44no—
54C2×D172—21no—
55C2×D172—21no—
56C2×D172—21no—
57C2×D172C2312yes—
58C2×D172C2311yescharacteristic
59C2×C4×D43—21no—
60C2×C4×D43D411yescharacteristic
61C2×C4×D43D411yescharacteristic
62C2×C4×D43C2311yescharacteristic
63C2×Dic86C2311yescharacteristic
64C2×C8×C43C2312yes—
65C4⋊C4×C43—21no—
66C4⋊C4×C43—21no—
67C4⋊C4×C43C2311yescharacteristic
68C4⋊C4×C43C2311yescharacteristic
69C42×C43C2311yescharacteristic
70#10621883—42no—
71#10621882—42no—
72(C2×D43)⋊C4—21no—
73(C2×D43)⋊C4—21no—
74(C2×D43)⋊C4—21no—
75(C2×D43)⋊C4—21no—
76(C2×D43)⋊C4—21no—
77C4⋊Dic43—21no—
78Dic43⋊C4—21no—
79C4×Dic43—21no—
80C4×Dic43D411yescharacteristic
81C4×Dic43D411yescharacteristic
82C4×Dic43C2311yescharacteristic
83C2×C43⋊C8C2312yes—
84D344—42no—
85#10621873—42no—
86C23×C43—22no—
87C22×D43—21no—
88C22×D43—22no—
89C22×D43—44no—
90C22×D43—44no—
91C22×D43—44no—
92C22×D43C2×D411yescharacteristic
93D4×C43—22no—
94D4×C43—22no—
95D4×C43—42no—
96D4×C43—42no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43C2×D411yescharacteristic
100C2×C4×C43C2×D411yescharacteristic
101C2×C4×C43C2411yescharacteristic
102C22⋊D43—44no—
103C22⋊D43—44no—
104C22⋊D43—44no—
105C2×Dic43—21no—
106C2×Dic43C2×D411yescharacteristic
107C2×Dic43C2×D411yescharacteristic
108C2×Dic43C2×D411yescharacteristic
109D172—22no—
110D172—22no—
111D172—22no—
112D172—42no—
113D172—42no—
114D172—42no—
115C4×D43—22no—
116C4×D43—22no—
117C4×D43—22no—
118C4×D43—42no—
119Dic86—22no—
120C8×C43—22no—
121C43⋊C8—22no—
122C22×C43—42no—
123C22×C43—42no—
124C22×C43—42no—
125C22×C43C22×D411yescharacteristic
126C2×D43—21no—
127C2×D43—21no—
128C2×D43—42no—
129C2×D43—41no—
130C2×D43—42no—
131C2×D43—42no—
132C2×D43—41no—
133C2×D43—41no—
134C2×D43—88no—
135C2×D43AGL(1,ℤ/8)12yes—
136C4×C43—21no—
137C4×C43—21no—
138C4×C43—41no—
139C4×C43—41no—
140C4×C43H(5,𝔽2)12yes—
141Dic43—21no—
142Dic43—21no—
143Dic43—41no—
144Dic43AGL(1,ℤ/8)12yes—
145#3217—431nomaximal, Sylow
146C2×C43—82no—
147C2×C43#53511yescharacteristic
148C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
149C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
150D43—22no—
151D43—81no—
152D43—82no—
153C2×#127—431no—
154#529—431no—
155#496—431no—
156#496—431no—
157#490—431no—
158#490D4311yescharacteristic, complemented
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×SD16—432no—
170C2×D8—432no—
171C2×D8—432no—
172#127—432no—
173#127—431no—
174#127—861no—
175#127—861no—
176#127C2×D4311yescharacteristic
177#126—861no—
178#125C2×D4311yescharacteristic, complemented
179#124—431no—
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#102C2×D4312yescomplemented
192#102C2×D4312yescomplemented
193C22⋊C8—432no—
194#97—431no—
195#97C2×D4311yescharacteristic, complemented
196C24—862no—
197C2×Q8—431no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—432no—
201C2×D4—431no—
202C2×D4—861no—
203C2×D4—862no—
204C2×D4—862no—
205C2×D4—862no—
206C2×D4—861no—
207C2×D4—861no—
208C2×D4—1722no—
209C2×D4—1722no—
210C2×D4—1724no—
211C2×D4—1724no—
212C2×D4C22×D4312yes—
213C22×C4—431no—
214C22×C4—431no—
215C22×C4—431no—
216C22×C4—861no—
217SD16—1722no—
218SD16—1722no—
219D8—1722no—
220D8—1722no—
221C2×C8—432no—
222C2×C8C22×D4312yes—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—861no—
226C4⋊C4—861no—
227C4⋊C4C22×D4311yescharacteristic
228C4⋊C4C22×D4311yescharacteristic
229C22⋊C4—861no—
230C22⋊C4—861no—
231C22⋊C4—861no—
232C22⋊C4—861no—
233C22⋊C4—861no—
234C42—431no—
235C42—431no—
236C42—431no—
237C42—861no—
238C42C22×D4311yescharacteristic
239C23—22no—
240C23—431no—
241C23—861no—
242C23—862no—
243C23—1724no—
244C23—1724no—
245C23—1724no—
246Q8—862no—
247D4—22no—
248D4—22no—
249D4—42no—
250D4—42no—
251D4—862no—
252D4—862no—
253D4—862no—
254D4—1722no—
255D4—1722no—
256D4—1722no—
257D4—1724no—
258D4—1724no—
259D4—1724no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—431no—
263C2×C4—431no—
264C2×C4—431no—
265C2×C4—862no—
266C2×C4—862no—
267C2×C4—862no—
268C2×C4—861no—
269C2×C4—1722no—
270C2×C4D4×D4311yescharacteristic
271C2×C4D4×D4311yescharacteristic
272C2×C4C23×D4311yescharacteristic
273C8—22no—
274C8—862no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—432no—
279C22—861no—
280C22—861no—
281C22—3448no—
282C22—1721no—
283C22—1722no—
284C22—1722no—
285C22—1721no—
286C22—1722no—
287C22—1721no—
288C22C2×D4×D4311yescharacteristic
289C4—21no—
290C4—21no—
291C4—41no—
292C4—41no—
293C4—432no—
294C4—861no—
295C4—861no—
296C4—1721no—
297C4#1306337112yes—
298C2—82no—
299C2—862no—
300C2—3442no—
301C2—3441no—
302C2#1458346711yescharacteristic
303C2AGL(1,ℤ/8)×D4311yescharacteristic
304C2AGL(1,ℤ/8)×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#490C2
socleC22×C43C22×D4
hypercenter#490D43
hypocenterC43#3217
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #127×D43C2semidirect
2. #14583434C2semidirect
3. #14583288C2semidirect
4. #14583286C2semidirect
5. #14583265C2semidirect
6. #14583098C2semidirect
7. #14583093C2semidirect
8. #14583051C2semidirect
9. #14583034C2semidirect
10. #14582954C2semidirect
11. C43×#490C2semidirect
15. C2×#10621873C22semidirect
16. C2×#10621883C22semidirect
17. C2×D344C22semidirect
18. C2×#10621882C22semidirect
24. #13063313C22semidirect
28. #13063290C22semidirect
30. #13063287C22semidirect
33. Dic43⋊C8C22semidirect
34. #13063245C22semidirect
35. #13063245C22semidirect
37. #13063236C22semidirect
39. #125×C43C22semidirect
40. #102×C43C22semidirect
41. #102×C43C22semidirect
42. #97×C43C22semidirect
158. #490D43semidirect
164. C43#3217semidirect
178. #125C2×D43semidirect
191. #102C2×D43semidirect
192. #102C2×D43semidirect
195. #97C2×D43semidirect