Finite Group Databasebeta

← D11×#2551 #14925522

Subgroups — D11×#2551 #14925522

Order 2816.

3182 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C214yesmaximal
2#13073645C211yesmaximal, characteristic, complemented
3#13073644C214yesmaximal, complemented
4#13073643C214yesmaximal, complemented
5#13073642C212yesmaximal, complemented
6#13073641C214yesmaximal, complemented
7D11×#395C214yesmaximal
8D11×#389C214yesmaximal
9D11×#384C211yesmaximal, characteristic
10C4×C4⋊C4×D11C212yesmaximal
11C11×#2551C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2214yes—
13C2×C11×C4⋊Q8C2214yes—
14C2×#66997C2218yes—
15D11×C4⋊Q8—232no—
16C2×C4⋊C4×D11C2214yes—
17C2×C4⋊C4×D11C2218yes—
18C2×C4⋊C4×D11C2212yes—
19C2×C4⋊C4×D11C2212yes—
20C2×C4⋊C4×D11C2212yes—
21C2×#66941C2218yes—
22C2×#66941C2214yes—
23C2×#66941C2214yes—
24C2×C42×D11C2214yes—
25C2×C42×D11C2211yescharacteristic
26C2×#66922C2214yes—
27C11×#395C2214yes—
28C11×#389C2214yes—
29C11×#384C2211yescharacteristic
30C4×C11×C4⋊C4C2212yes—
31#10622842C2214yes—
32#10622598C2214yes—
33#10622592C2214yes—
34#10622592C2218yes—
35#10622589C2212yes—
36#10622589C2214yes—
37C4⋊C4×Dic11C2212yes—
38C4⋊C4×Dic11C2212yes—
39#10622586C2214yes—
40#10622585C2218yes—
41#10622548C2211yescharacteristic
42C4×C4⋊Dic11C2212yes—
43C4×Dic11⋊C4C2214yes—
44#10622541C2214yes—
45D11×#95C2214yes—
46D11×#95C2214yes—
47#10622269C2218yes—
48#10622269C2214yes—
49#10622262C2214yes—
50#10622260C2218yes—
51C22×Q8×C11C2314yes—
52C2×Q8×D11—232no—
53C2×Q8×D11—48no—
54C22×C4×D11C2314yes—
55C22×C4×D11C2314yes—
56C22×C4×D11C2314yes—
57C22×C4×D11C2311yescharacteristic
58C22×C4×D11C2312yes—
59C22×Dic22C2318yes—
60C22×Dic22C2314yes—
61C11×C4⋊Q8—216no—
62C2×C11×C4⋊C4C2318yes—
63C2×C11×C4⋊C4C2314yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C42×C11C2314yes—
68C2×C42×C11C2311yescharacteristic
69#66997—232no—
70C2×C4⋊Dic11C2318yes—
71C2×C4⋊Dic11C2314yes—
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2312yes—
75C2×Dic11⋊C4C2318yes—
76C2×Dic11⋊C4C2318yes—
77C2×Dic11⋊C4C2318yes—
78C2×Dic11⋊C4C2314yes—
79C2×Dic11⋊C4C2314yes—
80C2×Dic11⋊C4C2314yes—
81C2×C4×Dic11C2314yes—
82C2×C4×Dic11C2314yes—
83C2×C4×Dic11C2314yes—
84C2×C4×Dic11C2311yescharacteristic
85C2×C4×Dic11C2312yes—
86C4⋊C4×D11—216no—
87C4⋊C4×D11—232no—
88C4⋊C4×D11—44no—
89C4⋊C4×D11D4116yes—
90C4⋊C4×D11Q8116yescomplemented
91#66941—216no—
92#66941—216no—
93#66941—232no—
94C42×D11—216no—
95C42×D11Q818yescomplemented
96#66922—216no—
97C11×#95C2314yes—
98C11×#95C2314yes—
99C11⋊#95C2318yes—
100C11⋊#95C2314yes—
101C11⋊#95C2314yes—
102C11⋊#95C2314yes—
103C11⋊#95C2314yes—
104C2×#2551—111nomaximal, Sylow
105C23×D11C2411yescharacteristic
106C2×Q8×C11—216no—
107C2×Q8×C11—44no—
108C22×C4×C11C2414yes—
109C22×C4×C11C2414yes—
110C22×C4×C11C2411yescharacteristic
111C22×C4×C11C2414yes—
112C22×C4×C11C2412yes—
113C22×Dic11C2414yes—
114C22×Dic11C2414yes—
115C22×Dic11C2411yescharacteristic
116C22×Dic11C2414yes—
117C22×Dic11C2412yes—
118Q8×D11—464no—
119C2×C4×D11—28no—
120C2×C4×D11—28no—
121C2×C4×D11—216no—
122C2×C4×D11—22no—
123C2×C4×D11—28no—
124C2×C4×D11—28no—
125C2×C4×D11—22no—
126C2×C4×D11—28no—
127C2×C4×D11C2×D4116yes—
128C2×C4×D11C2×D418yes—
129C2×C4×D11C2×Q814yes—
130C2×C4×D11C2×Q8116yes—
131C2×C4×D11C2×Q818yes—
132C2×C4×D11C2×Q818yes—
133C2×Dic22—216no—
134C2×Dic22—216no—
135C2×Dic22—216no—
136C2×Dic22—48no—
137C2×Dic22—44no—
138C11×C4⋊C4—216no—
139C11×C4⋊C4—28no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4C2×D418yes—
142C11×C4⋊C4C2×Q818yescomplemented
143C42×C11—28no—
144C42×C11C2×Q814yescomplemented
145C4⋊Dic11—216no—
146C4⋊Dic11—28no—
147C4⋊Dic11—42no—
148C4⋊Dic11C2×D418yes—
149C4⋊Dic11C2×Q818yescomplemented
150Dic11⋊C4—216no—
151Dic11⋊C4—216no—
152Dic11⋊C4—216no—
153Dic11⋊C4—44no—
154Dic11⋊C4C2×D4116yes—
155Dic11⋊C4C2×Q8116yescomplemented
156C4×Dic11—28no—
157C4×Dic11—28no—
158C4×Dic11—28no—
159C4×Dic11C2×Q814yescomplemented
160C4×Dic11C2×Q818yescomplemented
161C22×C4⋊Q8—114no—
162#2551—114no—
163#2551—114no—
164#2551—111no—
165#2551—112no—
166#2551—114no—
167#2551D1111yescharacteristic, direct product factor
168C2×#395—114no—
169C2×#389—114no—
170C2×#384—111no—
171C2×C4×C4⋊C4—112no—
172C23×C11C2511yescharacteristic
173C22×D11C22×D414yes—
174C22×D11C22×Q812yes—
175C22×D11C22×Q814yes—
176C22×D11H(5,𝔽2)12yes—
177C22×D112−1+412yes—
178Q8×C11—416no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—21no—
182C2×C4×C11—24no—
183C2×C4×C11—21no—
184C2×C4×C11—24no—
185C2×C4×C11—28no—
186C2×C4×C11—24no—
187C2×C4×C11C22×D418yes—
188C2×C4×C11C22×D414yes—
189C2×C4×C11C22×Q812yes—
190C2×C4×C11C22×Q818yes—
191C2×C4×C11C22×Q814yes—
192C2×C4×C11C22×Q814yes—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—21no—
196C2×Dic11—24no—
197C2×Dic11—21no—
198C2×Dic11—24no—
199C2×Dic11—28no—
200C2×Dic11—24no—
201C2×Dic11C22×D418yes—
202C2×Dic11C22×D414yes—
203C2×Dic11C22×Q812yes—
204C2×Dic11C22×Q818yes—
205C2×Dic11C22×Q814yes—
206C2×Dic11C22×Q814yes—
207C4×D11—28no—
208C4×D11—232no—
209C4×D11—232no—
210C4×D11—416no—
211C4×D11C4⋊Q8132yescomplemented
212Dic22—416no—
213Dic22—432no—
214C23×Q8—114no—
215C2×C4⋊Q8—118no—
216C2×C4⋊Q8—118no—
217C2×C4⋊Q8—114no—
218C2×C4⋊Q8—114no—
219C2×C4⋊Q8—114no—
220C2×C4⋊Q8—2232no—
221C2×C4⋊Q8C2×D1114yes—
222C22×C4⋊C4—112no—
223C22×C4⋊C4—112no—
224C22×C4⋊C4—118no—
225C22×C4⋊C4—114no—
226C22×C4⋊C4—112no—
227C22×C42—111no—
228C22×C42—114no—
229#395—114no—
230#395—114no—
231#395—118no—
232#395—114no—
233#395—118no—
234#395C2×D1114yes—
235#389—118no—
236#389—114no—
237#389—114no—
238#389—114no—
239#389—118no—
240#389C2×D1114yes—
241#384—112no—
242#384—114no—
243#384—111no—
244#384C2×D1111yescharacteristic
245C4×C4⋊C4—112no—
246C4×C4⋊C4—112no—
247C4×C4⋊C4—114no—
248C4×C4⋊C4—112no—
249C4×C4⋊C4—114no—
250C4×C4⋊C4C2×D1112yes—
251C2×#95—114no—
252C2×#95—114no—
253C22×C11C23×D412yes—
254C22×C11C23×Q811yescharacteristic
255C22×C11C23×Q812yes—
256C22×C11C2×H(5,𝔽2)11yescharacteristic
257C22×C11C2×2−1+411yescharacteristic
258C2×D11C2×C4⋊Q818yes—
259C2×D11#54414yes—
260C2×D11D4214yes—
261C2×D11D4×Q818yes—
262C2×D11Q8214yes—
263C4×C11—22no—
264C4×C11—28no—
265C4×C11—28no—
266C4×C11—44no—
267C4×C11C2×C4⋊Q818yescomplemented
268Dic11—22no—
269Dic11—28no—
270Dic11—28no—
271Dic11—44no—
272Dic11C2×C4⋊Q818yescomplemented
273C22×Q8—114no—
274C22×Q8—118no—
275C22×Q8—2232no—
276C22×Q8—448no—
277C22×Q8C22×D1114yes—
278C23×C4—112no—
279C23×C4—114no—
280C23×C4—114no—
281C23×C4—111no—
282C23×C4—114no—
283C4⋊Q8—216no—
284C4⋊Q8—2216no—
285C4⋊Q8—2232no—
286C4⋊Q8—2216no—
287C4⋊Q8—2232no—
288C4⋊Q8—2216no—
289C2×C4⋊C4—114no—
290C2×C4⋊C4—112no—
291C2×C4⋊C4—114no—
292C2×C4⋊C4—112no—
293C2×C4⋊C4—1116no—
294C2×C4⋊C4—1116no—
295C2×C4⋊C4—118no—
296C2×C4⋊C4—114no—
297C2×C4⋊C4—118no—
298C2×C4⋊C4—118no—
299C2×C4⋊C4—118no—
300C2×C4⋊C4—114no—
301C2×C4⋊C4—112no—
302C2×C4⋊C4—2216no—
303C2×C4⋊C4—2232no—
304C2×C4⋊C4—444no—
305C2×C4⋊C4C22×D1114yes—
306C2×C4⋊C4C22×D1118yes—
307C2×C4⋊C4C22×D1112yes—
308C2×C4⋊C4C22×D1112yes—
309C2×C4⋊C4C22×D1112yes—
310C2×C42—111no—
311C2×C42—112no—
312C2×C42—118no—
313C2×C42—114no—
314C2×C42—114no—
315C2×C42—114no—
316C2×C42—2216no—
317C2×C42C22×D1114yes—
318C2×C42C22×D1111yescharacteristic
319#95—114no—
320#95—114no—
321#95—114no—
322#95—114no—
323#95—118no—
324#95C22×D1114yes—
325#95C22×D1114yes—
326C2×C11C22×C4⋊Q812yes—
327C2×C11C2×#54411yescharacteristic
328C2×C11C2×D4211yescharacteristic
329C2×C11C2×D4×Q812yes—
330C2×C11C2×Q8211yescharacteristic
331D11#255118yesdirect product factor
332C24—111no—
333C2×Q8—216no—
334C2×Q8—44no—
335C2×Q8—2216no—
336C2×Q8—2216no—
337C2×Q8—2216no—
338C2×Q8—448no—
339C2×Q8—444no—
340C2×Q8—4464no—
341C22×C4—112no—
342C22×C4—118no—
343C22×C4—118no—
344C22×C4—118no—
345C22×C4—111no—
346C22×C4—114no—
347C22×C4—114no—
348C22×C4—1116no—
349C22×C4—114no—
350C22×C4—1116no—
351C22×C4—114no—
352C22×C4—228no—
353C22×C4—228no—
354C22×C4—222no—
355C22×C4—228no—
356C22×C4—228no—
357C22×C4—222no—
358C22×C4—2216no—
359C22×C4—228no—
360C22×C4C23×D1114yes—
361C22×C4C23×D1114yes—
362C22×C4C23×D1111yescharacteristic
363C22×C4C23×D1114yes—
364C22×C4C23×D1112yes—
365C4⋊C4—216no—
366C4⋊C4—28no—
367C4⋊C4—42no—
368C4⋊C4—1116no—
369C4⋊C4—118no—
370C4⋊C4—1116no—
371C4⋊C4—118no—
372C4⋊C4—2216no—
373C4⋊C4—2216no—
374C4⋊C4—2216no—
375C4⋊C4—2216no—
376C4⋊C4—228no—
377C4⋊C4—444no—
378C4⋊C4—442no—
379C4⋊C4D4×D1118yes—
380C4⋊C4Q8×D1118yescomplemented
381C42—28no—
382C42—114no—
383C42—118no—
384C42—228no—
385C42—228no—
386C42—228no—
387C42Q8×D1114yescomplemented
388C11C2×#255111yescharacteristic, complemented, Sylow
389C23—114no—
390C23—112no—
391C23—114no—
392C23—112no—
393C23—112no—
394C23C24×D1111yescharacteristic
395Q8—416no—
396Q8—4432no—
397Q8—4416no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—21no—
401C2×C4—24no—
402C2×C4—21no—
403C2×C4—24no—
404C2×C4—28no—
405C2×C4—24no—
406C2×C4—114no—
407C2×C4—114no—
408C2×C4—114no—
409C2×C4—1132no—
410C2×C4—118no—
411C2×C4—112no—
412C2×C4—118no—
413C2×C4—2232no—
414C2×C4—228no—
415C2×C4—2232no—
416C2×C4—224no—
417C2×C4—224no—
418C2×C4—221no—
419C2×C4—224no—
420C2×C4—221no—
421C2×C4—224no—
422C2×C4—228no—
423C2×C4—224no—
424C2×C4—4416no—
425C2×C4C2×D4×D1118yes—
426C2×C4C2×D4×D1114yes—
427C2×C4C2×Q8×D1112yes—
428C2×C4C2×Q8×D1118yes—
429C2×C4C2×Q8×D1114yes—
430C2×C4C2×Q8×D1114yes—
431C22—118no—
432C22—114no—
433C22—114no—
434C22—114no—
435C22—118no—
436C22C22×D4×D1112yes—
437C22C22×Q8×D1111yescharacteristic
438C22C22×Q8×D1112yes—
439C22D11×H(5,𝔽2)11yescharacteristic
440C22D11×2−1+411yescharacteristic
441C4—22no—
442C4—28no—
443C4—28no—
444C4—44no—
445C4—118no—
446C4—222no—
447C4—228no—
448C4—228no—
449C4—444no—
450C4D11×C4⋊Q818yescomplemented
451C2—118no—
452C2C2×D11×C4⋊Q812yes—
453C2D11×#54411yescharacteristic
454C2D42×D1111yescharacteristic
455C2D4×Q8×D1112yes—
456C2Q82×D1111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2551C2
prime radicalC23×D11C24
hypercenter#2551D11
hypocenterC11C2×#2551
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2551

Complements

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

NH ≅ G/Ntype
2. #13073645C2semidirect
3. #13073644C2semidirect
4. #13073643C2semidirect
5. #13073642C2semidirect
6. #13073641C2semidirect
11. C11×#2551C2semidirect
90. C4⋊C4×D11Q8semidirect
95. C42×D11Q8semidirect
142. C11×C4⋊C4C2×Q8semidirect
144. C42×C11C2×Q8semidirect
149. C4⋊Dic11C2×Q8semidirect
155. Dic11⋊C4C2×Q8semidirect
159. C4×Dic11C2×Q8semidirect
160. C4×Dic11C2×Q8semidirect
167. #2551D11direct (N × H)
211. C4×D11C4⋊Q8semidirect
267. C4×C11C2×C4⋊Q8semidirect
272. Dic11C2×C4⋊Q8semidirect
331. D11#2551direct (N × H)
380. C4⋊C4Q8×D11semidirect
387. C42Q8×D11semidirect
388. C11C2×#2551semidirect
450. C4D11×C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
#130736452
#130736442
#130736432
#130736422
#130736412
D11×#3952
D11×#3892
D11×#3842
C4×C4⋊C4×D112
C11×#25512
C2×#255111