Finite Group Databasebeta

← D11×#2582 #14925807

Subgroups — D11×#2582 #14925807

Order 2816.

2702 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D11C212yesmaximal
2#13073989C211yesmaximal, characteristic, complemented
3#13073988C214yesmaximal, complemented
4#13073987C214yesmaximal, complemented
5#13073986C212yesmaximal, complemented
6#13073985C214yesmaximal, complemented
7D11×#398C214yesmaximal
8D11×#391C214yesmaximal
9D11×#389C214yesmaximal
10D11×#384C211yesmaximal, characteristic
11C11×#2582C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2212yes—
13C2×C4×Q8×C11C2212yes—
14C2×Q8×Dic11C2212yes—
15C4×Q8×D11—216no—
16C2×C4⋊C4×D11C2214yes—
17C2×C4⋊C4×D11C2212yes—
18C2×C4⋊C4×D11C2214yes—
19C2×C4⋊C4×D11C2212yes—
20C2×C4⋊C4×D11C2214yes—
21C2×#66940C2214yes—
22C2×#66940C2212yes—
23C2×C42×D11C2214yes—
24C2×C42×D11C2211yescharacteristic
25C2×C4×Dic22C2212yes—
26C2×C4×Dic22C2214yes—
27C11×#398C2214yes—
28C11×#391C2214yes—
29C11×#389C2214yes—
30C11×#384C2211yescharacteristic
31#10622843C2214yes—
32#10622598C2214yes—
33#10622597C2218yes—
34#10622596C2214yes—
35#10622593C2214yes—
36#10622589C2212yes—
37#10622589C2214yes—
38#10622587C2214yes—
39#10622586C2214yes—
40#10622585C2218yes—
41#10622548C2211yescharacteristic
42#10622542C2214yes—
43#10622541C2214yes—
44D11×#95C2218yes—
45D11×#95C2214yes—
46#10622274C2214yes—
47#10622270C2218yes—
48#10622260C2218yes—
49#10622259C2218yes—
50#10622259C2218yes—
51C22×Q8×C11C2312yes—
52C2×Q8×D11—28no—
53C2×Q8×D11—28no—
54C2×Q8×D11Q8116yescomplemented
55C22×C4×D11C2314yes—
56C22×C4×D11C2314yes—
57C22×C4×D11C2311yescharacteristic
58C22×C4×D11C2314yes—
59C22×C4×D11C2312yes—
60C22×Dic22C2314yes—
61C22×Dic22C2312yes—
62C4×Q8×C11—28no—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2314yes—
65C2×C11×C4⋊C4C2314yes—
66C2×C11×C4⋊C4C2314yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C42×C11C2314yes—
69C2×C42×C11C2311yescharacteristic
70Q8×Dic11—28no—
71C2×C4⋊Dic11C2314yes—
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2314yes—
74C2×C4⋊Dic11C2314yes—
75C2×C4⋊Dic11C2312yes—
76C2×Dic11⋊C4C2314yes—
77C2×Dic11⋊C4C2314yes—
78C2×Dic11⋊C4C2314yes—
79C2×Dic11⋊C4C2318yes—
80C2×Dic11⋊C4C2318yes—
81C2×Dic11⋊C4C2314yes—
82C2×C4×Dic11C2314yes—
83C2×C4×Dic11C2314yes—
84C2×C4×Dic11C2314yes—
85C2×C4×Dic11C2312yes—
86C2×C4×Dic11C2311yescharacteristic
87C4⋊C4×D11—28no—
88C4⋊C4×D11—216no—
89C4⋊C4×D11—216no—
90C4⋊C4×D11—44no—
91C4⋊C4×D11—48no—
92#66940—28no—
93#66940—216no—
94C42×D11—216no—
95C42×D11D418yes—
96C4×Dic22—28no—
97C4×Dic22—216no—
98C11×#95C2314yes—
99C11×#95C2318yes—
100C11⋊#95C2318yes—
101C11⋊#95C2314yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C2×#2582—111nomaximal, Sylow
106C23×D11C2411yescharacteristic
107C2×Q8×C11—24no—
108C2×Q8×C11—24no—
109C2×Q8×C11C2×Q818yescomplemented
110C22×C4×C11C2414yes—
111C22×C4×C11C2414yes—
112C22×C4×C11C2411yescharacteristic
113C22×C4×C11C2414yes—
114C22×C4×C11C2412yes—
115C22×Dic11C2414yes—
116C22×Dic11C2414yes—
117C22×Dic11C2411yescharacteristic
118C22×Dic11C2414yes—
119C22×Dic11C2412yes—
120Q8×D11—264no—
121C2×C4×D11—28no—
122C2×C4×D11—28no—
123C2×C4×D11—28no—
124C2×C4×D11—216no—
125C2×C4×D11—22no—
126C2×C4×D11—28no—
127C2×C4×D11—28no—
128C2×C4×D11—22no—
129C2×C4×D11—28no—
130C2×C4×D11C2×D414yes—
131C2×C4×D11C2×D418yes—
132C2×C4×D11C2×Q8116yes—
133C2×C4×D11C2×Q818yes—
134C2×C4×D11#4118yes—
135C2×Dic22—28no—
136C2×Dic22—28no—
137C2×Dic22—24no—
138C2×Dic22—24no—
139C2×Dic22C2×Q8116yescomplemented
140C2×Dic22C2×Q818yescomplemented
141C11×C4⋊C4—28no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—28no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4—44no—
146C42×C11—28no—
147C42×C11C2×D414yes—
148C4⋊Dic11—28no—
149C4⋊Dic11—24no—
150C4⋊Dic11—28no—
151C4⋊Dic11—42no—
152C4⋊Dic11—44no—
153Dic11⋊C4—28no—
154Dic11⋊C4—28no—
155Dic11⋊C4—216no—
156Dic11⋊C4—28no—
157Dic11⋊C4—48no—
158Dic11⋊C4—44no—
159C4×Dic11—28no—
160C4×Dic11—28no—
161C4×Dic11—28no—
162C4×Dic11C2×D418yes—
163C4×Dic11C2×D414yes—
164C22×C4×Q8—112no—
165#2582—114no—
166#2582—114no—
167#2582—114no—
168#2582—111no—
169#2582—112no—
170#2582D1111yescharacteristic, direct product factor
171C2×#398—114no—
172C2×#391—114no—
173C2×#389—114no—
174C2×#384—111no—
175C23×C11C2511yescharacteristic
176C22×D11C22×D412yes—
177C22×D11C22×Q814yes—
178C22×D11C2×#4114yes—
179C22×D11H(5,𝔽2)12yes—
180C22×D112−1+412yes—
181Q8×C11—216no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—24no—
187C2×C4×C11—28no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—24no—
191C2×C4×C11C22×D412yes—
192C2×C4×C11C22×D414yes—
193C2×C4×C11C22×Q818yes—
194C2×C4×C11C22×Q814yes—
195C2×C4×C11C2×#4114yes—
196C2×Dic11—24no—
197C2×Dic11—24no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—24no—
201C2×Dic11—28no—
202C2×Dic11—24no—
203C2×Dic11—24no—
204C2×Dic11—24no—
205C2×Dic11C22×D412yes—
206C2×Dic11C22×D414yes—
207C2×Dic11C22×Q818yes—
208C2×Dic11C22×Q814yes—
209C2×Dic11C2×#4114yes—
210C4×D11—232no—
211C4×D11—28no—
212C4×D11—416no—
213C4×D11—416no—
214C4×D11C22⋊Q8132yes—
215Dic22—216no—
216Dic22—232no—
217C23×Q8—112no—
218C2×C4×Q8—112no—
219C2×C4×Q8—114no—
220C2×C4×Q8—112no—
221C2×C4×Q8—114no—
222C2×C4×Q8—112no—
223C2×C4×Q8—2216no—
224C2×C4×Q8C2×D1112yes—
225C22×C4⋊C4—114no—
226C22×C4⋊C4—112no—
227C22×C4⋊C4—114no—
228C22×C4⋊C4—112no—
229C22×C4⋊C4—114no—
230C22×C42—111no—
231C22×C42—114no—
232#398—114no—
233#398—114no—
234#398—118no—
235#398—118no—
236#398—114no—
237#398C2×D1114yes—
238#391—114no—
239#391—114no—
240#391—114no—
241#391—118no—
242#391—118no—
243#391C2×D1114yes—
244#389—118no—
245#389—114no—
246#389—114no—
247#389—114no—
248#389—118no—
249#389C2×D1114yes—
250#384—112no—
251#384—114no—
252#384—111no—
253#384C2×D1111yescharacteristic
254C2×#95—118no—
255C2×#95—114no—
256C22×C11C23×D411yescharacteristic
257C22×C11C23×Q812yes—
258C22×C11C22×#4112yes—
259C22×C11C2×H(5,𝔽2)11yescharacteristic
260C22×C11C2×2−1+411yescharacteristic
261C2×D11C2×C22⋊Q818yes—
262C2×D11#53714yes—
263C2×D11#55718yes—
264C2×D11Q8214yes—
265C2×D11#55914yes—
266C4×C11—28no—
267C4×C11—22no—
268C4×C11—44no—
269C4×C11—44no—
270C4×C11C2×C22⋊Q818yes—
271Dic11—28no—
272Dic11—22no—
273Dic11—44no—
274Dic11—44no—
275Dic11C2×C22⋊Q818yes—
276C22×Q8—1116no—
277C22×Q8—114no—
278C22×Q8—112no—
279C22×Q8—228no—
280C22×Q8—228no—
281C22×Q8C22×D1112yes—
282C23×C4—112no—
283C23×C4—111no—
284C23×C4—114no—
285C23×C4—114no—
286C23×C4—114no—
287C4×Q8—28no—
288C4×Q8—2216no—
289C4×Q8—228no—
290C4×Q8—2216no—
291C4×Q8—228no—
292C4×Q8—228no—
293C2×C4⋊C4—114no—
294C2×C4⋊C4—112no—
295C2×C4⋊C4—114no—
296C2×C4⋊C4—114no—
297C2×C4⋊C4—114no—
298C2×C4⋊C4—118no—
299C2×C4⋊C4—114no—
300C2×C4⋊C4—114no—
301C2×C4⋊C4—112no—
302C2×C4⋊C4—118no—
303C2×C4⋊C4—114no—
304C2×C4⋊C4—228no—
305C2×C4⋊C4—2216no—
306C2×C4⋊C4—2216no—
307C2×C4⋊C4—444no—
308C2×C4⋊C4—448no—
309C2×C4⋊C4C22×D1112yes—
310C2×C4⋊C4C22×D1114yes—
311C2×C4⋊C4C22×D1114yes—
312C2×C4⋊C4C22×D1112yes—
313C2×C4⋊C4C22×D1114yes—
314C2×C42—111no—
315C2×C42—112no—
316C2×C42—118no—
317C2×C42—114no—
318C2×C42—114no—
319C2×C42—114no—
320C2×C42—2216no—
321C2×C42C22×D1114yes—
322C2×C42C22×D1111yescharacteristic
323#95—118no—
324#95—118no—
325#95—118no—
326#95—114no—
327#95—118no—
328#95C22×D1118yes—
329#95C22×D1114yes—
330C2×C11C22×C22⋊Q812yes—
331C2×C11C2×#53711yescharacteristic
332C2×C11C2×#55712yes—
333C2×C11C2×Q8211yescharacteristic
334C2×C11C2×#55911yescharacteristic
335D11#258218yesdirect product factor
336C24—111no—
337C2×Q8—24no—
338C2×Q8—24no—
339C2×Q8—1116no—
340C2×Q8—118no—
341C2×Q8—228no—
342C2×Q8—228no—
343C2×Q8—2264no—
344C2×Q8—224no—
345C2×Q8—224no—
346C2×Q8Q8×D1118yescomplemented
347C22×C4—112no—
348C22×C4—118no—
349C22×C4—118no—
350C22×C4—118no—
351C22×C4—114no—
352C22×C4—111no—
353C22×C4—114no—
354C22×C4—1116no—
355C22×C4—114no—
356C22×C4—114no—
357C22×C4—228no—
358C22×C4—222no—
359C22×C4—228no—
360C22×C4—222no—
361C22×C4—228no—
362C22×C4—2216no—
363C22×C4—228no—
364C22×C4—228no—
365C22×C4—228no—
366C22×C4C23×D1114yes—
367C22×C4C23×D1114yes—
368C22×C4C23×D1111yescharacteristic
369C22×C4C23×D1114yes—
370C22×C4C23×D1112yes—
371C4⋊C4—28no—
372C4⋊C4—24no—
373C4⋊C4—28no—
374C4⋊C4—42no—
375C4⋊C4—44no—
376C4⋊C4—228no—
377C4⋊C4—228no—
378C4⋊C4—228no—
379C4⋊C4—2216no—
380C4⋊C4—228no—
381C4⋊C4—224no—
382C4⋊C4—228no—
383C4⋊C4—444no—
384C4⋊C4—448no—
385C4⋊C4—442no—
386C4⋊C4—444no—
387C42—28no—
388C42—114no—
389C42—118no—
390C42—228no—
391C42—228no—
392C42—228no—
393C42D4×D1114yes—
394C11C2×#258211yescharacteristic, complemented, Sylow
395C23—112no—
396C23—114no—
397C23—114no—
398C23—112no—
399C23—112no—
400C23C24×D1111yescharacteristic
401Q8—216no—
402Q8—2232no—
403Q8—2216no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—24no—
409C2×C4—28no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—114no—
414C2×C4—114no—
415C2×C4—114no—
416C2×C4—1132no—
417C2×C4—112no—
418C2×C4—118no—
419C2×C4—2232no—
420C2×C4—228no—
421C2×C4—224no—
422C2×C4—224no—
423C2×C4—221no—
424C2×C4—221no—
425C2×C4—224no—
426C2×C4—228no—
427C2×C4—224no—
428C2×C4—224no—
429C2×C4—224no—
430C2×C4—4416no—
431C2×C4—4416no—
432C2×C4C2×D4×D1112yes—
433C2×C4C2×D4×D1114yes—
434C2×C4C2×Q8×D1118yes—
435C2×C4C2×Q8×D1114yes—
436C2×C4#41×D1114yes—
437C22—118no—
438C22—114no—
439C22—114no—
440C22—114no—
441C22—118no—
442C22C22×D4×D1111yescharacteristic
443C22C22×Q8×D1112yes—
444C22C2×#41×D1112yes—
445C22D11×H(5,𝔽2)11yescharacteristic
446C22D11×2−1+411yescharacteristic
447C4—22no—
448C4—28no—
449C4—44no—
450C4—44no—
451C4—118no—
452C4—222no—
453C4—228no—
454C4—444no—
455C4—444no—
456C4D11×C22⋊Q818yes—
457C2—118no—
458C2C2×D11×C22⋊Q812yes—
459C2D11×#53711yescharacteristic
460C2D11×#55712yes—
461C2Q82×D1111yescharacteristic
462C2D11×#55911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2582C2
prime radicalC23×D11C24
hypercenter#2582D11
hypocenterC11C2×#2582
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2582

Complements

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

NH ≅ G/Ntype
2. #13073989C2semidirect
3. #13073988C2semidirect
4. #13073987C2semidirect
5. #13073986C2semidirect
6. #13073985C2semidirect
11. C11×#2582C2semidirect
54. C2×Q8×D11Q8semidirect
109. C2×Q8×C11C2×Q8semidirect
139. C2×Dic22C2×Q8semidirect
140. C2×Dic22C2×Q8semidirect
170. #2582D11direct (N × H)
335. D11#2582direct (N × H)
346. C2×Q8Q8×D11semidirect
394. C11C2×#2582semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D112
#130739892
#130739882
#130739872
#130739862
#130739852
D11×#3982
D11×#3912
D11×#3892
D11×#3842
C11×#25822
C2×#258211