Finite Group Databasebeta

← D11×#2822 #14960309

Subgroups — D11×#2822 #14960309

Order 2816.

2046 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#125C212yesmaximal
2#13076686C214yesmaximal, complemented
3#13076685C214yesmaximal, complemented
4#13076684C211yesmaximal, characteristic, complemented
5#13076683C212yesmaximal, complemented
6#13076682C214yesmaximal, complemented
7D11×#400C214yesmaximal
8D11×#398C214yesmaximal
9D11×#398C214yesmaximal
10D11×#382C211yesmaximal, characteristic
11C11×#2822C211yesmaximal, characteristic, complemented
12C2×C11×#125C2212yes—
13D11×#125—216no—
14C2×C4⋊C4×D11C2214yes—
15C2×C4⋊C4×D11C2212yes—
16C2×C4⋊C4×D11C2214yes—
17C2×C4⋊C4×D11C2212yes—
18C2×C4⋊C4×D11C2212yes—
19C2×C4⋊C4×D11C2214yes—
20C2×#66943C2212yes—
21C2×#66943C2212yes—
22C2×#66942C2214yes—
23C2×#66942C2214yes—
24C2×C42×D11C2211yescharacteristic
25C2×#66923C2212yes—
26C11×#400C2214yes—
27C11×#398C2214yes—
28C11×#398C2214yes—
29C11×#382C2211yescharacteristic
30#10622599C2214yes—
31#10622597C2218yes—
32#10622597C2218yes—
33#10622596C2214yes—
34#10622596C2214yes—
35#10622595C2214yes—
36#10622593C2214yes—
37#10622593C2214yes—
38#10622590C2212yes—
39#10622549C2211yescharacteristic
40D11×#95C2214yes—
41D11×#95C2218yes—
42D11×#95C2214yes—
43#10622274C2214yes—
44#10622274C2214yes—
45#10622273C2218yes—
46#10622272C2214yes—
47#10622271C2218yes—
48#10622270C2218yes—
49#10622270C2218yes—
50#10622263C2214yes—
51C22×C4×D11C2314yes—
52C22×C4×D11C2314yes—
53C22×C4×D11C2314yes—
54C22×C4×D11C2311yescharacteristic
55C22×C4×D11C2312yes—
56C11×#125—28no—
57C2×C11×C4⋊C4C2314yes—
58C2×C11×C4⋊C4C2314yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2314yes—
63C2×C42×C11C2311yescharacteristic
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2312yes—
66C2×C4⋊Dic11C2314yes—
67C2×C4⋊Dic11C2314yes—
68C2×C4⋊Dic11C2314yes—
69C2×C4⋊Dic11C2312yes—
70C2×Dic11⋊C4C2314yes—
71C2×Dic11⋊C4C2314yes—
72C2×Dic11⋊C4C2314yes—
73C2×Dic11⋊C4C2314yes—
74C2×Dic11⋊C4C2314yes—
75C2×Dic11⋊C4C2314yes—
76C2×Dic11⋊C4C2314yes—
77C2×Dic11⋊C4C2318yes—
78C2×C4×Dic11C2311yescharacteristic
79C2×C4×Dic11C2312yes—
80C4⋊C4×D11—28no—
81C4⋊C4×D11—28no—
82C4⋊C4×D11—216no—
83C4⋊C4×D11—216no—
84C4⋊C4×D11—44no—
85C4⋊C4×D11—48no—
86#66943—28no—
87#66943—28no—
88#66942—216no—
89#66942—216no—
90C42×D11D418yes—
91#66923—28no—
92C11×#95C2314yes—
93C11×#95C2318yes—
94C11×#95C2314yes—
95C11⋊#95C2318yes—
96C11⋊#95C2314yes—
97C11⋊#95C2318yes—
98C11⋊#95C2318yes—
99C11⋊#95C2318yes—
100C11⋊#95C2314yes—
101C11⋊#95C2318yes—
102C2×#2822—111nomaximal, Sylow
103C23×D11C2411yescharacteristic
104C22×C4×C11C2414yes—
105C22×C4×C11C2414yes—
106C22×C4×C11C2414yes—
107C22×C4×C11C2412yes—
108C22×C4×C11C2411yescharacteristic
109C22×Dic11C2414yes—
110C22×Dic11C2414yes—
111C22×Dic11C2414yes—
112C22×Dic11C2412yes—
113C22×Dic11C2411yescharacteristic
114C2×C4×D11—28no—
115C2×C4×D11—28no—
116C2×C4×D11—22no—
117C2×C4×D11—28no—
118C2×C4×D11—28no—
119C2×C4×D11—28no—
120C2×C4×D11—22no—
121C2×C4×D11—216no—
122C2×C4×D11—216no—
123C2×C4×D11—28no—
124C2×C4×D11C2×D414yes—
125C2×C4×D11C2×D418yes—
126C11×C4⋊C4—28no—
127C11×C4⋊C4—28no—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—42no—
131C11×C4⋊C4—44no—
132C42×C11C2×D414yes—
133C4⋊Dic11—28no—
134C4⋊Dic11—28no—
135C4⋊Dic11—24no—
136C4⋊Dic11—24no—
137C4⋊Dic11—42no—
138C4⋊Dic11—44no—
139Dic11⋊C4—28no—
140Dic11⋊C4—28no—
141Dic11⋊C4—28no—
142Dic11⋊C4—28no—
143Dic11⋊C4—28no—
144Dic11⋊C4—28no—
145Dic11⋊C4—48no—
146Dic11⋊C4—44no—
147C4×Dic11C2×D414yes—
148C4×Dic11C2×D418yes—
149C22×#125—112no—
150#2822—114no—
151#2822—114no—
152#2822—114no—
153#2822—111no—
154#2822—112no—
155#2822D1111yescharacteristic, direct product factor
156C2×#400—114no—
157C2×#398—114no—
158C2×#398—114no—
159C2×#382—111no—
160C23×C11C2511yescharacteristic
161C22×D11C22×D412yes—
162C22×D11H(5,𝔽2)12yes—
163C22×D112−1+418yes—
164C22×D112−1+412yes—
165C2×C4×C11—21no—
166C2×C4×C11—24no—
167C2×C4×C11—21no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—28no—
173C2×C4×C11—24no—
174C2×C4×C11—28no—
175C2×C4×C11C22×D412yes—
176C2×C4×C11C22×D414yes—
177C2×Dic11—21no—
178C2×Dic11—24no—
179C2×Dic11—21no—
180C2×Dic11—24no—
181C2×Dic11—24no—
182C2×Dic11—24no—
183C2×Dic11—24no—
184C2×Dic11—28no—
185C2×Dic11—24no—
186C2×Dic11—28no—
187C2×Dic11C22×D414yes—
188C2×Dic11C22×D412yes—
189C4×D11—216no—
190C4×D11—28no—
191C4×D11—416no—
192C4×D11—416no—
193C4×D11—416no—
194C2×#125—114no—
195C2×#125—114no—
196C2×#125—112no—
197C2×#125—112no—
198C2×#125—112no—
199C2×#125—2216no—
200C2×#125C2×D1112yes—
201C22×C4⋊C4—114no—
202C22×C4⋊C4—112no—
203C22×C4⋊C4—114no—
204C22×C4⋊C4—112no—
205C22×C4⋊C4—114no—
206C22×C4⋊C4—112no—
207C22×C42—111no—
208#400—114no—
209#400—114no—
210#400—118no—
211#400—114no—
212#400—118no—
213#400C2×D1114yes—
214#398—114no—
215#398—114no—
216#398—114no—
217#398—114no—
218#398—118no—
219#398—118no—
220#398—118no—
221#398—118no—
222#398—114no—
223#398—114no—
224#398C2×D1114yes—
225#398C2×D1114yes—
226#382—112no—
227#382—111no—
228#382—114no—
229#382C2×D1111yescharacteristic
230C2×#95—118no—
231C2×#95—114no—
232C2×#95—114no—
233C22×C11C23×D411yescharacteristic
234C22×C11C2×H(5,𝔽2)11yescharacteristic
235C22×C11C2×2−1+414yes—
236C22×C11C2×2−1+411yescharacteristic
237C2×D11#53618yes—
238C2×D11#53714yes—
239C2×D11#56318yes—
240C2×D11#56418yes—
241C4×C11—24no—
242C4×C11—22no—
243C4×C11—44no—
244C4×C11—44no—
245C4×C11—44no—
246Dic11—24no—
247Dic11—22no—
248Dic11—44no—
249Dic11—44no—
250Dic11—44no—
251C23×C4—111no—
252C23×C4—112no—
253C23×C4—114no—
254C23×C4—114no—
255C23×C4—114no—
256#125—28no—
257#125—2216no—
258#125—2216no—
259#125—228no—
260#125—228no—
261#125—228no—
262C2×C4⋊C4—114no—
263C2×C4⋊C4—114no—
264C2×C4⋊C4—114no—
265C2×C4⋊C4—114no—
266C2×C4⋊C4—112no—
267C2×C4⋊C4—114no—
268C2×C4⋊C4—114no—
269C2×C4⋊C4—114no—
270C2×C4⋊C4—114no—
271C2×C4⋊C4—112no—
272C2×C4⋊C4—114no—
273C2×C4⋊C4—112no—
274C2×C4⋊C4—118no—
275C2×C4⋊C4—114no—
276C2×C4⋊C4—228no—
277C2×C4⋊C4—228no—
278C2×C4⋊C4—2216no—
279C2×C4⋊C4—2216no—
280C2×C4⋊C4—444no—
281C2×C4⋊C4—448no—
282C2×C4⋊C4C22×D1114yes—
283C2×C4⋊C4C22×D1112yes—
284C2×C4⋊C4C22×D1114yes—
285C2×C4⋊C4C22×D1112yes—
286C2×C4⋊C4C22×D1112yes—
287C2×C4⋊C4C22×D1114yes—
288C2×C42—111no—
289C2×C42—112no—
290C2×C42—118no—
291C2×C42C22×D1111yescharacteristic
292#95—118no—
293#95—114no—
294#95—118no—
295#95—118no—
296#95—118no—
297#95—118no—
298#95—114no—
299#95C22×D1114yes—
300#95C22×D1118yes—
301#95C22×D1114yes—
302C2×C11C2×#53612yes—
303C2×C11C2×#53711yescharacteristic
304C2×C11C2×#56312yes—
305C2×C11C2×#56412yes—
306D11#282218yesdirect product factor
307C24—111no—
308C22×C4—112no—
309C22×C4—111no—
310C22×C4—114no—
311C22×C4—118no—
312C22×C4—114no—
313C22×C4—114no—
314C22×C4—114no—
315C22×C4—222no—
316C22×C4—222no—
317C22×C4—228no—
318C22×C4—228no—
319C22×C4—228no—
320C22×C4—228no—
321C22×C4—228no—
322C22×C4—228no—
323C22×C4—2216no—
324C22×C4—2216no—
325C22×C4C23×D1114yes—
326C22×C4C23×D1114yes—
327C22×C4C23×D1114yes—
328C22×C4C23×D1112yes—
329C22×C4C23×D1111yescharacteristic
330C4⋊C4—28no—
331C4⋊C4—24no—
332C4⋊C4—28no—
333C4⋊C4—24no—
334C4⋊C4—42no—
335C4⋊C4—44no—
336C4⋊C4—228no—
337C4⋊C4—228no—
338C4⋊C4—228no—
339C4⋊C4—228no—
340C4⋊C4—228no—
341C4⋊C4—228no—
342C4⋊C4—228no—
343C4⋊C4—228no—
344C4⋊C4—224no—
345C4⋊C4—224no—
346C4⋊C4—444no—
347C4⋊C4—448no—
348C4⋊C4—442no—
349C4⋊C4—444no—
350C42—114no—
351C42—118no—
352C42D4×D1114yes—
353C11C2×#282211yescharacteristic, complemented, Sylow
354C23—112no—
355C23—112no—
356C23—118no—
357C23—112no—
358C23C24×D1111yescharacteristic
359C2×C4—21no—
360C2×C4—24no—
361C2×C4—21no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—28no—
367C2×C4—24no—
368C2×C4—28no—
369C2×C4—114no—
370C2×C4—112no—
371C2×C4—2216no—
372C2×C4—228no—
373C2×C4—221no—
374C2×C4—224no—
375C2×C4—221no—
376C2×C4—224no—
377C2×C4—224no—
378C2×C4—224no—
379C2×C4—224no—
380C2×C4—228no—
381C2×C4—224no—
382C2×C4—228no—
383C2×C4—4416no—
384C2×C4—4416no—
385C2×C4—4416no—
386C2×C4C2×D4×D1114yes—
387C2×C4C2×D4×D1112yes—
388C22—118no—
389C22—114no—
390C22—118no—
391C22—118no—
392C22C22×D4×D1111yescharacteristic
393C22D11×H(5,𝔽2)11yescharacteristic
394C22D11×2−1+414yes—
395C22D11×2−1+411yescharacteristic
396C4—24no—
397C4—22no—
398C4—44no—
399C4—44no—
400C4—44no—
401C4—224no—
402C4—222no—
403C4—444no—
404C4—444no—
405C4—444no—
406C2—118no—
407C2D11×#53612yes—
408C2D11×#53711yescharacteristic
409C2D11×#56312yes—
410C2D11×#56412yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2822C2
prime radicalC23×D11C24
hypercenter#2822D11
hypocenterC11C2×#2822
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2822

Complements

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

NH ≅ G/Ntype
2. #13076686C2semidirect
3. #13076685C2semidirect
4. #13076684C2semidirect
5. #13076683C2semidirect
6. #13076682C2semidirect
11. C11×#2822C2semidirect
155. #2822D11direct (N × H)
306. D11#2822direct (N × H)
353. C11C2×#2822semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1252
#130766862
#130766852
#130766842
#130766832
#130766822
D11×#4002
D11×#3982
D11×#3822
C11×#28222
C2×#282211