Finite Group Databasebeta

← D11×#483 #13078490

Subgroups — D11×#483 #13078490

Order 1408.

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
1D11×C22⋊Q8C211yesmaximal, characteristic
2C2×C4⋊C4×D11C211yesmaximal, characteristic
3C11×#483C211yesmaximal, characteristic, complemented
4#10622656C211yesmaximal, characteristic, complemented
5#10622584C211yesmaximal, characteristic, complemented
6#10622475C212yesmaximal, complemented
7D11×#106C212yesmaximal, complemented
8#10622418C212yesmaximal, complemented
9D11×#103C212yesmaximal, complemented
10D11×C22⋊C8C211yesmaximal, characteristic
11#10622334C211yesmaximal, characteristic, complemented
12C2×Q8×D11C2211yescharacteristic
13C22×C4×D11—21no—
14C22×C4×D11C2211yescharacteristic
15C11×C22⋊Q8C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17#66999C2211yescharacteristic
18C2×C4⋊Dic11C2211yescharacteristic
19#66977C2211yescharacteristic
20C2×Dic11⋊C4—21no—
21C2×C8×D11C2212yes—
22#66950C2211yescharacteristic
23#66949—21no—
24C4⋊C4×D11—21no—
25C4⋊C4×D11—21no—
26C4⋊C4×D11—21no—
27C4⋊C4×D11C2211yescharacteristic
28C4⋊C4×D11C2212yes—
29C4⋊C4×D11C2212yes—
30C22⋊C4×D11—21no—
31#66931—21no—
32C11×#106C2212yescomplemented
33C11×#103C2212yescomplemented
34C11×C22⋊C8C2211yescharacteristic
35#66899C2212yescomplemented
36C22⋊(C11⋊C8)C2211yescharacteristic
37(C2×D11)⋊C8C2212yes—
38#66881C2212yescomplemented
39#66880C2212yescomplemented
40#66874C2212yescomplemented
41#66872C2212yescomplemented
42#66872C2212yescomplemented
43C23×D11D411yescharacteristic
44C2×Q8×C11C2311yescharacteristic
45C22×C4×C11—21no—
46C22×C4×C11C2311yescharacteristic
47C22×Dic11—21no—
48C22×Dic11D411yescharacteristic
49Q8×D11—24no—
50C2×C4×D11—24no—
51C2×C4×D11—21no—
52C2×C4×D11—21no—
53C2×C4×D11—22no—
54C2×C4×D11—22no—
55C2×C4×D11—44no—
56C2×C4×D11D411yescharacteristic
57C2×C4×D11D411yescharacteristic
58C2×C4×D11C2311yescharacteristic
59C2×C4×D11C2311yescharacteristic
60C2×Dic22—21no—
61C2×Dic22C2311yescharacteristic
62C2×C8×C11C2312yes—
63C11×C4⋊C4—21no—
64C11×C4⋊C4—21no—
65C11×C4⋊C4C2311yescharacteristic
66C11×C4⋊C4C2312yes—
67C11×C22⋊C4—21no—
68C22⋊Dic11—21no—
69(C2×D11)⋊C4—21no—
70(C2×D11)⋊C4—21no—
71C4⋊Dic11—21no—
72C4⋊Dic11—21no—
73C4⋊Dic11C2311yescharacteristic
74C4⋊Dic11C2312yes—
75Dic11⋊C4—21no—
76Dic11⋊C4—21no—
77Dic11⋊C4—22no—
78Dic11⋊C4—22no—
79Dic11⋊C4—21no—
80C2×C11⋊C8C2312yes—
81C8×D11—24no—
82C2×#483—111nomaximal, Sylow
83C23×C11C2×D411yescharacteristic
84C22×D11—22no—
85C22×D11—22no—
86C22×D11SD1614yes—
87C22×D11C2×D411yescharacteristic
88C22×D11C2×D411yescharacteristic
89Q8×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—42no—
95C2×C4×C11C2×D411yescharacteristic
96C2×C4×C11C2411yescharacteristic
97C2×Dic11—22no—
98C2×Dic11—21no—
99C2×Dic11—22no—
100C2×Dic11—21no—
101C2×Dic11—42no—
102C2×Dic11C2×D411yescharacteristic
103C2×Dic11C2×D411yescharacteristic
104C4×D11—22no—
105C4×D11—22no—
106C4×D11—22no—
107C4×D11—42no—
108C4×D11—44no—
109C4×D11—44no—
110C4×D11—42no—
111C4×D11#4114yes—
112Dic22—22no—
113Dic22—42no—
114C8×C11—22no—
115C11⋊C8—22no—
116C2×C22⋊Q8—111no—
117C22×C4⋊C4—111no—
118#483—111no—
119#483—111no—
120#483—112no—
121#483—112no—
122#483—111no—
123#483D1111yescharacteristic, direct product factor
124C2×#106—112no—
125C2×#103—112no—
126C2×C22⋊C8—111no—
127C22×C11—21no—
128C22×C11—21no—
129C22×C11C2×SD1612yes—
130C22×C11C22×D411yescharacteristic
131C2×D11—21no—
132C2×D11—21no—
133C2×D11—28no—
134C2×D11#12312yes—
135C2×D11C2×SD1612yes—
136C2×D11C2×SD1612yes—
137C2×D11#13712yes—
138C4×C11—21no—
139C4×C11—41no—
140C4×C11—42no—
141C4×C11—41no—
142C4×C11C2×#4112yes—
143Dic11—21no—
144Dic11—41no—
145Dic11—42no—
146Dic11—41no—
147Dic11#12312yes—
148C22×Q8—111no—
149C23×C4—111no—
150C23×C4—221no—
151C22×C8—112no—
152C22⋊Q8—111no—
153C22⋊Q8—111no—
154C22⋊Q8—111no—
155C22⋊Q8—221no—
156C22⋊Q8—221no—
157C22⋊Q8C2×D1111yescharacteristic
158C2×C4⋊C4—111no—
159C2×C4⋊C4—112no—
160C2×C4⋊C4—112no—
161C2×C4⋊C4—111no—
162C2×C4⋊C4—221no—
163C2×C4⋊C4—221no—
164C2×C4⋊C4—221no—
165C2×C4⋊C4—221no—
166C2×C4⋊C4C2×D1111yescharacteristic
167C2×C22⋊C4—221no—
168#106—112no—
169#106—112no—
170#106—112no—
171#106C2×D1112yescomplemented
172#103—112no—
173#103—112no—
174#103—112no—
175#103C2×D1112yescomplemented
176C22⋊C8—111no—
177C22⋊C8—112no—
178C22⋊C8C2×D1111yescharacteristic
179C2×C11—22no—
180C2×C11C2×#12311yescharacteristic
181C2×C11C22×SD1611yescharacteristic
182C2×C11C2×#13711yescharacteristic
183D11—22no—
184D11#48314yesdirect product factor
185C24—111no—
186C2×Q8—111no—
187C2×Q8—221no—
188C2×Q8—224no—
189C2×Q8C22×D1111yescharacteristic
190C22×C4—21no—
191C22×C4—111no—
192C22×C4—111no—
193C22×C4—111no—
194C22×C4—111no—
195C22×C4—111no—
196C22×C4—224no—
197C22×C4—221no—
198C22×C4—221no—
199C22×C4—222no—
200C22×C4—222no—
201C22×C4—221no—
202C22×C4—444no—
203C22×C4C22×D1111yescharacteristic
204C2×C8—112no—
205C2×C8—224no—
206C2×C8C22×D1112yes—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—112no—
210C4⋊C4—111no—
211C4⋊C4—222no—
212C4⋊C4—222no—
213C4⋊C4—221no—
214C4⋊C4—221no—
215C4⋊C4—221no—
216C4⋊C4—221no—
217C4⋊C4—221no—
218C4⋊C4C22×D1112yes—
219C4⋊C4C22×D1111yescharacteristic
220C22⋊C4—21no—
221C22⋊C4—221no—
222C22⋊C4—221no—
223C22⋊C4—221no—
224C11C2×#48311yescharacteristic, complemented, Sylow
225C23—111no—
226C23—114no—
227C23—111no—
228C23—222no—
229C23—222no—
230C23D4×D1111yescharacteristic
231Q8—22no—
232Q8—222no—
233Q8—442no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—111no—
240C2×C4—114no—
241C2×C4—111no—
242C2×C4—222no—
243C2×C4—222no—
244C2×C4—222no—
245C2×C4—222no—
246C2×C4—221no—
247C2×C4—221no—
248C2×C4—222no—
249C2×C4—444no—
250C2×C4—444no—
251C2×C4—442no—
252C2×C4—442no—
253C2×C4—442no—
254C2×C4D4×D1111yescharacteristic
255C2×C4C23×D1111yescharacteristic
256C8—22no—
257C8—222no—
258C22—21no—
259C22—21no—
260C22—112no—
261C22—112no—
262C22—112no—
263C22—112no—
264C22—228no—
265C22—221no—
266C22—221no—
267C22SD16×D1112yes—
268C22C2×D4×D1111yescharacteristic
269C4—21no—
270C4—42no—
271C4—41no—
272C4—41no—
273C4—112no—
274C4—221no—
275C4—442no—
276C4—441no—
277C4—441no—
278C4#41×D1112yes—
279C2—22no—
280C2—114no—
281C2—222no—
282C2D11×#12311yescharacteristic
283C2C2×SD16×D1111yescharacteristic
284C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#483C2
socleC22×C11C22×D4
prime radicalC23×D11D4
hypercenter#483D11
hypocenterC11C2×#483
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. C11×#483C2semidirect
4. #10622656C2semidirect
5. #10622584C2semidirect
6. #10622475C2semidirect
7. D11×#106C2semidirect
8. #10622418C2semidirect
9. D11×#103C2semidirect
11. #10622334C2semidirect
32. C11×#106C22semidirect
33. C11×#103C22semidirect
35. #66899C22semidirect
38. #66881C22semidirect
39. #66880C22semidirect
40. #66874C22semidirect
41. #66872C22semidirect
42. #66872C22semidirect
123. #483D11direct (N × H)
171. #106C2×D11semidirect
175. #103C2×D11semidirect
184. D11#483direct (N × H)
224. C11C2×#483semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D11×C22⋊Q82
C2×C4⋊C4×D112
C11×#4832
#106226562
#106225842
#106224752
D11×#1062
#106224182
D11×#1032
D11×C22⋊C82
#106223342
C2×#48311