Finite Group Databasebeta

← D11×#485 #13078504

Subgroups — D11×#485 #13078504

Order 1408.

416 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×C22⋊Q8C211yesmaximal, characteristic
2D11×#117C211yesmaximal, characteristic
3C11×#485C211yesmaximal, characteristic, complemented
4#10622658C211yesmaximal, characteristic, complemented
5#10622609C211yesmaximal, characteristic, complemented
6#10622501C211yesmaximal, characteristic, complemented
7D11×#107C211yesmaximal, characteristic, complemented
8#10622480C211yesmaximal, characteristic, complemented
9D11×#106C211yesmaximal, characteristic, complemented
10#10622428C211yesmaximal, characteristic, complemented
11#10622427C211yesmaximal, characteristic, complemented
12D11×#103C211yesmaximal, characteristic, complemented
13D11×#103C211yesmaximal, characteristic, complemented
14D11×C22⋊C8C211yesmaximal, characteristic
15#10622336C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C22×C4×D11C2211yescharacteristic
18C11×C22⋊Q8C2211yescharacteristic
19C11×#117C2211yescharacteristic
20#66999C2211yescharacteristic
21#66979C2211yescharacteristic
22#66977C2211yescharacteristic
23C2×C8×D11C2211yescharacteristic
24C2×C8×D11C2211yescharacteristic
25#66950C2211yescharacteristic
26#66949—21no—
27#66945C2211yescharacteristic
28#66945C2211yescharacteristic
29C4⋊C4×D11—21no—
30C4⋊C4×D11C2211yescharacteristic
31C4⋊C4×D11C2211yescharacteristic
32C4⋊C4×D11C2211yescharacteristic
33C22⋊C4×D11—21no—
34C22⋊C4×D11—21no—
35#66931—21no—
36#66930—21no—
37#66925—21no—
38C42×D11—21no—
39C11×#107C2211yescharacteristic, complemented
40C11×#106C2211yescharacteristic, complemented
41C11×#103C2211yescharacteristic, complemented
42C11×#103C2211yescharacteristic, complemented
43C11×C22⋊C8C2211yescharacteristic
44#66899C2211yescharacteristic, complemented
45#66899C2211yescharacteristic, complemented
46C22⋊(C11⋊C8)C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49#66882C2211yescharacteristic, complemented
50#66881C2211yescharacteristic, complemented
51#66880C2211yescharacteristic, complemented
52#66880C2211yescharacteristic, complemented
53#66874C2211yescharacteristic, complemented
54#66874C2211yescharacteristic, complemented
55#66872C2211yescharacteristic, complemented
56#66872C2211yescharacteristic, complemented
57#66871C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C23×D11D411yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×Dic11D411yescharacteristic
63Q8×D11—22no—
64Q8×D11—22no—
65C2×C4×D11—22no—
66C2×C4×D11—22no—
67C2×C4×D11—21no—
68C2×C4×D11—21no—
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×C4×D11D411yescharacteristic
72C2×C4×D11D411yescharacteristic
73C2×C4×D11C2311yescharacteristic
74C2×C4×D11C2311yescharacteristic
75C2×Dic22—21no—
76C2×Dic22C2311yescharacteristic
77C2×C8×C11C2311yescharacteristic
78C2×C8×C11C2311yescharacteristic
79C11×C4⋊C4—21no—
80C11×C4⋊C4C2311yescharacteristic
81C11×C4⋊C4C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C42×C11—21no—
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106C8×D11—22no—
107C8×D11—22no—
108C2×#485—111nomaximal, Sylow
109C23×C11C2×D411yescharacteristic
110C22×D11—22no—
111C22×D11—22no—
112C22×D11—22no—
113C22×D11C2×D411yescharacteristic
114C22×D11C2×D411yescharacteristic
115Q8×C11—21no—
116Q8×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2411yescharacteristic
125C2×Dic11—22no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132C4×D11—22no—
133C4×D11—21no—
134C4×D11—21no—
135C4×D11—22no—
136C4×D11—42no—
137C4×D11—42no—
138C4×D11—42no—
139C4×D11—42no—
140C4×D11#4112yes—
141C4×D11#4112yes—
142Dic22—21no—
143Dic22—21no—
144Dic22—42no—
145C8×C11—21no—
146C8×C11—21no—
147C11⋊C8—21no—
148C11⋊C8—21no—
149C2×C22⋊Q8—111no—
150C2×#117—111no—
151#485—111no—
152#485—111no—
153#485—111no—
154#485—111no—
155#485—111no—
156#485—111no—
157#485—111no—
158#485D1111yescharacteristic, direct product factor
159C2×#107—111no—
160C2×#106—111no—
161C2×#103—111no—
162C2×#103—111no—
163C2×C22⋊C8—111no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11C22×D411yescharacteristic
168C2×D11—21no—
169C2×D11—21no—
170C2×D11—21no—
171C2×D11—44no—
172C2×D11#12312yes—
173C2×D11#13512yes—
174C2×D11#13712yes—
175C4×C11—21no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11C2×#4111yescharacteristic
181C4×C11C2×#4111yescharacteristic
182Dic11—21no—
183Dic11—41no—
184Dic11—41no—
185Dic11—41no—
186Dic11—41no—
187Dic11#12312yes—
188C22×Q8—111no—
189C23×C4—111no—
190C22×C8—111no—
191C22×C8—111no—
192C22⋊Q8—111no—
193C22⋊Q8—111no—
194C22⋊Q8—111no—
195C22⋊Q8—221no—
196C22⋊Q8—221no—
197C22⋊Q8C2×D1111yescharacteristic
198#117—111no—
199#117—111no—
200#117—111no—
201#117—221no—
202#117—221no—
203#117C2×D1111yescharacteristic
204C2×C4⋊C4—111no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—221no—
208C2×C22⋊C4—221no—
209C2×C22⋊C4—221no—
210C2×C42—221no—
211#107—111no—
212#107—111no—
213#107—111no—
214#107C2×D1111yescharacteristic, complemented
215#106—111no—
216#106—111no—
217#106—111no—
218#106C2×D1111yescharacteristic, complemented
219#103—111no—
220#103—111no—
221#103—111no—
222#103—111no—
223#103—111no—
224#103—111no—
225#103C2×D1111yescharacteristic, complemented
226#103C2×D1111yescharacteristic, complemented
227C22⋊C8—111no—
228C22⋊C8—111no—
229C22⋊C8—111no—
230C22⋊C8C2×D1111yescharacteristic
231C2×C11—41no—
232C2×C11C2×#12311yescharacteristic
233C2×C11C2×#13511yescharacteristic
234C2×C11C2×#13711yescharacteristic
235D11—41no—
236D11#48514yesdirect product factor
237C24—111no—
238C2×Q8—111no—
239C2×Q8—221no—
240C2×Q8—222no—
241C2×Q8—222no—
242C2×Q8C22×D1111yescharacteristic
243C22×C4—111no—
244C22×C4—111no—
245C22×C4—111no—
246C22×C4—111no—
247C22×C4—111no—
248C22×C4—222no—
249C22×C4—222no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4C22×D1111yescharacteristic
255C2×C8—111no—
256C2×C8—111no—
257C2×C8—222no—
258C2×C8—222no—
259C2×C8C22×D1111yescharacteristic
260C2×C8C22×D1111yescharacteristic
261C4⋊C4—21no—
262C4⋊C4—111no—
263C4⋊C4—111no—
264C4⋊C4—111no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4C22×D1111yescharacteristic
272C4⋊C4C22×D1111yescharacteristic
273C4⋊C4C22×D1111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C42—21no—
283C42—221no—
284C42—221no—
285C42—221no—
286C11C2×#48511yescharacteristic, complemented, Sylow
287C23—111no—
288C23—111no—
289C23—222no—
290C23—222no—
291C23—222no—
292C23D4×D1111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—221no—
296Q8—221no—
297Q8—442no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—111no—
305C2×C4—112no—
306C2×C4—112no—
307C2×C4—111no—
308C2×C4—222no—
309C2×C4—222no—
310C2×C4—222no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—442no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4—442no—
321C2×C4D4×D1111yescharacteristic
322C2×C4C23×D1111yescharacteristic
323C8—21no—
324C8—21no—
325C8—221no—
326C8—221no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—112no—
331C22—112no—
332C22—112no—
333C22—221no—
334C22—221no—
335C22—221no—
336C22—444no—
337C22C2×D4×D1111yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—112no—
344C4—221no—
345C4—441no—
346C4—441no—
347C4—441no—
348C4—441no—
349C4#41×D1111yescharacteristic
350C4#41×D1111yescharacteristic
351C2—41no—
352C2—114no—
353C2—441no—
354C2D11×#12311yescharacteristic
355C2D11×#13511yescharacteristic
356C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#485C2
socleC22×C11C22×D4
prime radicalC23×D11D4
hypercenter#485D11
hypocenterC11C2×#485
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. C11×#485C2semidirect
4. #10622658C2semidirect
5. #10622609C2semidirect
6. #10622501C2semidirect
7. D11×#107C2semidirect
8. #10622480C2semidirect
9. D11×#106C2semidirect
10. #10622428C2semidirect
11. #10622427C2semidirect
12. D11×#103C2semidirect
13. D11×#103C2semidirect
15. #10622336C2semidirect
39. C11×#107C22semidirect
40. C11×#106C22semidirect
41. C11×#103C22semidirect
42. C11×#103C22semidirect
44. #66899C22semidirect
45. #66899C22semidirect
49. #66882C22semidirect
50. #66881C22semidirect
51. #66880C22semidirect
52. #66880C22semidirect
53. #66874C22semidirect
54. #66874C22semidirect
55. #66872C22semidirect
56. #66872C22semidirect
57. #66871C22semidirect
58. #66871C22semidirect
158. #485D11direct (N × H)
214. #107C2×D11semidirect
218. #106C2×D11semidirect
225. #103C2×D11semidirect
226. #103C2×D11semidirect
236. D11#485direct (N × H)
286. C11C2×#485semidirect

Maximal subgroups

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

subgroupindex
D11×C22⋊Q82
D11×#1172
C11×#4852
#106226582
#106226092
#106225012
D11×#1072
#106224802
D11×#1062
#106224282
#106224272
D11×#1032
D11×C22⋊C82
#106223362
C2×#48511