Finite Group Databasebeta

← #483×D53 #20284589

Subgroups — #483×D53 #20284589

Order 6784.

460 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 135 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
1C22⋊Q8×D53C211yesmaximal, characteristic
2C2×C4⋊C4×D53C211yesmaximal, characteristic
3#16810955C212yesmaximal, complemented
4#16810954C211yesmaximal, characteristic, complemented
5#16810953C211yesmaximal, characteristic, complemented
6#16810952C212yesmaximal, complemented
7#16810951C211yesmaximal, characteristic, complemented
8#106×D53C212yesmaximal, complemented
9#103×D53C212yesmaximal, complemented
10C22⋊C8×D53C211yesmaximal, characteristic
11C53×#483C211yesmaximal, characteristic, complemented
12C2×Q8×D53C2211yescharacteristic
13C22×C4×D53—21no—
14C22×C4×D53C2211yescharacteristic
15C2×C8×D53C2212yes—
16#13133197C2211yescharacteristic
17#13133196C2211yescharacteristic
18#13133195—21no—
19#13133194—21no—
20#13133193C2211yescharacteristic
21C2×C4⋊Dic53C2211yescharacteristic
22C2×#11719919—21no—
23C4⋊C4×D53—21no—
24C4⋊C4×D53—21no—
25C4⋊C4×D53—21no—
26C4⋊C4×D53C2212yes—
27C4⋊C4×D53C2212yes—
28C4⋊C4×D53C2211yescharacteristic
29C22⋊C4×D53—21no—
30#13133149C2212yescomplemented
31#13133148C2212yescomplemented
32#13133148C2212yescomplemented
33#13133142C2212yescomplemented
34#13133141C2212yescomplemented
35#13133140C2212yescomplemented
36C22⋊#88322C2211yescharacteristic
37#13133129C2212yes—
38C22⋊Q8×C53C2211yescharacteristic
39C2×C4⋊C4×C53C2211yescharacteristic
40#106×C53C2212yescomplemented
41#103×C53C2212yescomplemented
42C22⋊C8×C53C2211yescharacteristic
43C23×D53D411yescharacteristic
44C2×Q8×C53C2311yescharacteristic
45C22×C4×C53—21no—
46C22×C4×C53C2311yescharacteristic
47C22×Dic53—21no—
48C22×Dic53D411yescharacteristic
49Q8×D53—24no—
50C2×C4×D53—24no—
51C2×C4×D53—21no—
52C2×C4×D53—21no—
53C2×C4×D53—22no—
54C2×C4×D53—22no—
55C2×C4×D53—44no—
56C2×C4×D53D411yescharacteristic
57C2×C4×D53D411yescharacteristic
58C2×C4×D53C2311yescharacteristic
59C2×C4×D53C2311yescharacteristic
60C2×Dic106—21no—
61C2×Dic106C2311yescharacteristic
62C2×C8×C53C2312yes—
63C4⋊C4×C53—21no—
64C4⋊C4×C53—21no—
65C4⋊C4×C53C2312yes—
66C4⋊C4×C53C2311yescharacteristic
67C22⋊C4×C53—21no—
68C22⋊Dic53—21no—
69#11719921—21no—
70#11719921—21no—
71C4⋊Dic53—21no—
72C4⋊Dic53—21no—
73C4⋊Dic53C2312yes—
74C4⋊Dic53C2311yescharacteristic
75#11719919—21no—
76#11719919—22no—
77#11719919—22no—
78#11719919—21no—
79#11719919—21no—
80C2×#88322C2312yes—
81C8×D53—24no—
82C23×C53C2×D411yescharacteristic
83C22×D53—22no—
84C22×D53—22no—
85C22×D53SD1614yes—
86C22×D53C2×D411yescharacteristic
87C22×D53C2×D411yescharacteristic
88Q8×C53—22no—
89C2×C4×C53—22no—
90C2×C4×C53—21no—
91C2×C4×C53—22no—
92C2×C4×C53—21no—
93C2×C4×C53—42no—
94C2×C4×C53C2×D411yescharacteristic
95C2×C4×C53C2411yescharacteristic
96C2×Dic53—22no—
97C2×Dic53—21no—
98C2×Dic53—22no—
99C2×Dic53—21no—
100C2×Dic53—42no—
101C2×Dic53C2×D411yescharacteristic
102C2×Dic53C2×D411yescharacteristic
103C4×D53—22no—
104C4×D53—22no—
105C4×D53—22no—
106C4×D53—42no—
107C4×D53—44no—
108C4×D53—44no—
109C4×D53—42no—
110C4×D53#4114yes—
111Dic106—22no—
112Dic106—42no—
113C8×C53—22no—
114#88322—22no—
115C22×C53—21no—
116C22×C53—21no—
117C22×C53C2×SD1612yes—
118C22×C53C22×D411yescharacteristic
119C2×D53—21no—
120C2×D53—21no—
121C2×D53—28no—
122C2×D53#12312yes—
123C2×D53C2×SD1612yes—
124C2×D53C2×SD1612yes—
125C2×D53#13712yes—
126C4×C53—21no—
127C4×C53—41no—
128C4×C53—42no—
129C4×C53—41no—
130C4×C53C2×#4112yes—
131Dic53—21no—
132Dic53—41no—
133Dic53—42no—
134Dic53—41no—
135Dic53#12312yes—
136C2×#483—531nomaximal, Sylow
137C2×C53—22no—
138C2×C53C2×#12311yescharacteristic
139C2×C53C22×SD1611yescharacteristic
140C2×C53C2×#13711yescharacteristic
141D53—22no—
142D53#48314yesdirect product factor
143C2×C22⋊Q8—531no—
144C22×C4⋊C4—531no—
145#483—531no—
146#483—531no—
147#483—532no—
148#483—532no—
149#483—531no—
150#483D5311yescharacteristic, direct product factor
151C2×#106—532no—
152C2×#103—532no—
153C2×C22⋊C8—531no—
154C53C2×#48311yescharacteristic, complemented, Sylow
155C22×Q8—531no—
156C23×C4—531no—
157C23×C4—1061no—
158C22×C8—532no—
159C22⋊Q8—531no—
160C22⋊Q8—531no—
161C22⋊Q8—531no—
162C22⋊Q8—1061no—
163C22⋊Q8—1061no—
164C22⋊Q8C2×D5311yescharacteristic
165C2×C4⋊C4—531no—
166C2×C4⋊C4—532no—
167C2×C4⋊C4—532no—
168C2×C4⋊C4—531no—
169C2×C4⋊C4—1061no—
170C2×C4⋊C4—1061no—
171C2×C4⋊C4—1061no—
172C2×C4⋊C4—1061no—
173C2×C4⋊C4C2×D5311yescharacteristic
174C2×C22⋊C4—1061no—
175#106—532no—
176#106—532no—
177#106—532no—
178#106C2×D5312yescomplemented
179#103—532no—
180#103—532no—
181#103—532no—
182#103C2×D5312yescomplemented
183C22⋊C8—531no—
184C22⋊C8—532no—
185C22⋊C8C2×D5311yescharacteristic
186C24—531no—
187C2×Q8—531no—
188C2×Q8—1061no—
189C2×Q8—1064no—
190C2×Q8C22×D5311yescharacteristic
191C22×C4—21no—
192C22×C4—531no—
193C22×C4—531no—
194C22×C4—531no—
195C22×C4—531no—
196C22×C4—531no—
197C22×C4—1064no—
198C22×C4—1061no—
199C22×C4—1061no—
200C22×C4—1062no—
201C22×C4—1062no—
202C22×C4—1061no—
203C22×C4—2124no—
204C22×C4C22×D5311yescharacteristic
205C2×C8—532no—
206C2×C8—1064no—
207C2×C8C22×D5312yes—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—532no—
211C4⋊C4—531no—
212C4⋊C4—1062no—
213C4⋊C4—1062no—
214C4⋊C4—1061no—
215C4⋊C4—1061no—
216C4⋊C4—1061no—
217C4⋊C4—1061no—
218C4⋊C4—1061no—
219C4⋊C4C22×D5312yes—
220C4⋊C4C22×D5311yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—1061no—
223C22⋊C4—1061no—
224C22⋊C4—1061no—
225C23—531no—
226C23—534no—
227C23—531no—
228C23—1062no—
229C23—1062no—
230C23D4×D5311yescharacteristic
231Q8—22no—
232Q8—1062no—
233Q8—2122no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—531no—
240C2×C4—534no—
241C2×C4—531no—
242C2×C4—1062no—
243C2×C4—1062no—
244C2×C4—1062no—
245C2×C4—1062no—
246C2×C4—1061no—
247C2×C4—1061no—
248C2×C4—1062no—
249C2×C4—2122no—
250C2×C4—2124no—
251C2×C4—2124no—
252C2×C4—2122no—
253C2×C4—2122no—
254C2×C4D4×D5311yescharacteristic
255C2×C4C23×D5311yescharacteristic
256C8—22no—
257C8—1062no—
258C22—21no—
259C22—21no—
260C22—532no—
261C22—532no—
262C22—532no—
263C22—532no—
264C22—1068no—
265C22—1061no—
266C22—1061no—
267C22SD16×D5312yes—
268C22C2×D4×D5311yescharacteristic
269C4—21no—
270C4—41no—
271C4—42no—
272C4—41no—
273C4—532no—
274C4—1061no—
275C4—2121no—
276C4—2122no—
277C4—2121no—
278C4#41×D5312yes—
279C2—22no—
280C2—534no—
281C2—1062no—
282C2#123×D5311yescharacteristic
283C2C2×SD16×D5311yescharacteristic
284C2#137×D5311yescharacteristic
subgroupG/H
centerC22C2×D4×D53
commutatorC2×C4×C53C24
FrattiniC2×C4C23×D53
FittingC53×#483C2
socleC22×C53C22×D4
hypercenter#483D53
hypocenterC53C2×#483
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #16810955C2semidirect
4. #16810954C2semidirect
5. #16810953C2semidirect
6. #16810952C2semidirect
7. #16810951C2semidirect
8. #106×D53C2semidirect
9. #103×D53C2semidirect
11. C53×#483C2semidirect
30. #13133149C22semidirect
31. #13133148C22semidirect
32. #13133148C22semidirect
33. #13133142C22semidirect
34. #13133141C22semidirect
35. #13133140C22semidirect
40. #106×C53C22semidirect
41. #103×C53C22semidirect
142. D53#483direct (N × H)
150. #483D53direct (N × H)
154. C53C2×#483semidirect
178. #106C2×D53semidirect
182. #103C2×D53semidirect