Finite Group Databasebeta

← D11×#2571 #14925726

Subgroups — D11×#2571 #14925726

Order 2816.

1966 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073858C211yesmaximal, characteristic, complemented
2#13073857C214yesmaximal, complemented
3#13073856C214yesmaximal, complemented
4#13073855C212yesmaximal, complemented
5#13073854C214yesmaximal, complemented
6D11×#400C214yesmaximal
7D11×#389C214yesmaximal
8D11×#384C211yesmaximal, characteristic
9D11×#382C214yesmaximal
10C4×C4⋊C4×D11C212yesmaximal
11C11×#2571C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×D11C2212yes—
13C2×C4⋊C4×D11C2212yes—
14C2×C4⋊C4×D11C2214yes—
15C2×C4⋊C4×D11C2212yes—
16C2×C4⋊C4×D11C2214yes—
17C2×C42×D11C2214yes—
18C2×C42×D11C2211yescharacteristic
19C11×#400C2214yes—
20C11×#389C2214yes—
21C11×#384C2211yescharacteristic
22C11×#382C2214yes—
23C4×C11×C4⋊C4C2212yes—
24#10622599C2214yes—
25#10622598C2214yes—
26#10622595C2214yes—
27#10622590C2214yes—
28#10622590C2214yes—
29#10622589C2212yes—
30#10622589C2214yes—
31C4⋊C4×Dic11C2212yes—
32C4⋊C4×Dic11C2212yes—
33#10622586C2214yes—
34#10622585C2218yes—
35#10622549C2214yes—
36#10622548C2211yescharacteristic
37C4×C4⋊Dic11C2212yes—
38C4×Dic11⋊C4C2214yes—
39#10622541C2214yes—
40D11×#95C2214yes—
41D11×#95C2214yes—
42D11×#95C2218yes—
43#10622273C2218yes—
44#10622272C2214yes—
45#10622271C2218yes—
46#10622263C2218yes—
47#10622263C2218yes—
48#10622262C2214yes—
49#10622260C2218yes—
50C22×C4×D11C2314yes—
51C22×C4×D11C2314yes—
52C22×C4×D11C2314yes—
53C22×C4×D11C2311yescharacteristic
54C22×C4×D11C2312yes—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2314yes—
58C2×C11×C4⋊C4C2314yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C42×C11C2314yes—
61C2×C42×C11C2311yescharacteristic
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2314yes—
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2314yes—
66C2×C4⋊Dic11C2312yes—
67C2×Dic11⋊C4C2314yes—
68C2×Dic11⋊C4C2318yes—
69C2×Dic11⋊C4C2314yes—
70C2×Dic11⋊C4C2318yes—
71C2×Dic11⋊C4C2314yes—
72C2×C4×Dic11C2314yes—
73C2×C4×Dic11C2314yes—
74C2×C4×Dic11C2314yes—
75C2×C4×Dic11C2311yescharacteristic
76C2×C4×Dic11C2312yes—
77C4⋊C4×D11—28no—
78C4⋊C4×D11—28no—
79C4⋊C4×D11—216no—
80C4⋊C4×D11—44no—
81C4⋊C4×D11—48no—
82C42×D11—216no—
83C42×D11Q818yes—
84C11×#95C2318yes—
85C11×#95C2314yes—
86C11×#95C2314yes—
87C11⋊#95C2318yes—
88C11⋊#95C2314yes—
89C11⋊#95C2318yes—
90C11⋊#95C2314yes—
91C11⋊#95C2318yes—
92C11⋊#95C2318yes—
93C11⋊#95C2314yes—
94C11⋊#95C2314yes—
95C2×#2571—111nomaximal, Sylow
96C23×D11C2411yescharacteristic
97C22×C4×C11C2414yes—
98C22×C4×C11C2414yes—
99C22×C4×C11C2414yes—
100C22×C4×C11C2411yescharacteristic
101C22×C4×C11C2412yes—
102C22×Dic11C2414yes—
103C22×Dic11C2414yes—
104C22×Dic11C2414yes—
105C22×Dic11C2411yescharacteristic
106C22×Dic11C2412yes—
107C2×C4×D11—28no—
108C2×C4×D11—28no—
109C2×C4×D11—28no—
110C2×C4×D11—28no—
111C2×C4×D11—216no—
112C2×C4×D11—22no—
113C2×C4×D11—28no—
114C2×C4×D11—28no—
115C2×C4×D11—22no—
116C2×C4×D11—28no—
117C2×C4×D11C2×Q814yes—
118C2×C4×D11C2×Q818yes—
119C2×C4×D11#4118yes—
120C2×C4×D11#4118yes—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—24no—
123C11×C4⋊C4—28no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4—44no—
126C42×C11—28no—
127C42×C11C2×Q814yes—
128C4⋊Dic11—24no—
129C4⋊Dic11—28no—
130C4⋊Dic11—24no—
131C4⋊Dic11—42no—
132C4⋊Dic11—44no—
133Dic11⋊C4—28no—
134Dic11⋊C4—216no—
135Dic11⋊C4—28no—
136Dic11⋊C4—48no—
137Dic11⋊C4—44no—
138C4×Dic11—28no—
139C4×Dic11—28no—
140C4×Dic11—28no—
141C4×Dic11C2×Q814yes—
142C4×Dic11C2×Q818yes—
143#2571—114no—
144#2571—114no—
145#2571—111no—
146#2571—114no—
147#2571—112no—
148#2571D1111yescharacteristic, direct product factor
149C2×#400—114no—
150C2×#389—114no—
151C2×#384—111no—
152C2×#382—114no—
153C2×C4×C4⋊C4—112no—
154C23×C11C2511yescharacteristic
155C22×D11C22×Q812yes—
156C22×D11C2×#4114yes—
157C22×D11C2×#4114yes—
158C22×D11H(5,𝔽2)12yes—
159C22×D112−1+412yes—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—28no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11C22×Q812yes—
171C2×C4×C11C22×Q814yes—
172C2×C4×C11C2×#4114yes—
173C2×C4×C11C2×#4114yes—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—24no—
177C2×Dic11—24no—
178C2×Dic11—24no—
179C2×Dic11—24no—
180C2×Dic11—28no—
181C2×Dic11—24no—
182C2×Dic11—24no—
183C2×Dic11—24no—
184C2×Dic11C22×Q812yes—
185C2×Dic11C22×Q814yes—
186C2×Dic11C2×#4114yes—
187C2×Dic11C2×#4114yes—
188C4×D11—28no—
189C4×D11—416no—
190C4×D11—416no—
191C4×D11—416no—
192C4×D11#125132yes—
193C22×C4⋊C4—112no—
194C22×C4⋊C4—112no—
195C22×C4⋊C4—114no—
196C22×C4⋊C4—112no—
197C22×C4⋊C4—114no—
198C22×C42—111no—
199C22×C42—114no—
200#400—114no—
201#400—114no—
202#400—118no—
203#400—114no—
204#400—118no—
205#400C2×D1114yes—
206#389—118no—
207#389—114no—
208#389—114no—
209#389—114no—
210#389—118no—
211#389C2×D1114yes—
212#384—112no—
213#384—114no—
214#384—111no—
215#384C2×D1111yescharacteristic
216#382—114no—
217#382—114no—
218#382—114no—
219#382—118no—
220#382—118no—
221#382C2×D1114yes—
222C4×C4⋊C4—112no—
223C4×C4⋊C4—112no—
224C4×C4⋊C4—114no—
225C4×C4⋊C4—112no—
226C4×C4⋊C4—114no—
227C4×C4⋊C4C2×D1112yes—
228C2×#95—114no—
229C2×#95—114no—
230C2×#95—118no—
231C22×C11C23×Q811yescharacteristic
232C22×C11C22×#4112yes—
233C22×C11C22×#4112yes—
234C22×C11C2×H(5,𝔽2)11yescharacteristic
235C22×C11C2×2−1+411yescharacteristic
236C2×D11C2×#12518yes—
237C2×D11#54414yes—
238C2×D11#55514yes—
239C2×D11#55618yes—
240C2×D11#55914yes—
241C4×C11—22no—
242C4×C11—44no—
243C4×C11—44no—
244C4×C11—44no—
245C4×C11C2×#12518yes—
246Dic11—22no—
247Dic11—44no—
248Dic11—44no—
249Dic11—44no—
250Dic11C2×#12518yes—
251C23×C4—112no—
252C23×C4—111no—
253C23×C4—114no—
254C23×C4—114no—
255C23×C4—114no—
256C2×C4⋊C4—114no—
257C2×C4⋊C4—112no—
258C2×C4⋊C4—114no—
259C2×C4⋊C4—112no—
260C2×C4⋊C4—118no—
261C2×C4⋊C4—114no—
262C2×C4⋊C4—114no—
263C2×C4⋊C4—112no—
264C2×C4⋊C4—118no—
265C2×C4⋊C4—114no—
266C2×C4⋊C4—228no—
267C2×C4⋊C4—228no—
268C2×C4⋊C4—2216no—
269C2×C4⋊C4—444no—
270C2×C4⋊C4—448no—
271C2×C4⋊C4C22×D1112yes—
272C2×C4⋊C4C22×D1112yes—
273C2×C4⋊C4C22×D1114yes—
274C2×C4⋊C4C22×D1112yes—
275C2×C4⋊C4C22×D1114yes—
276C2×C42—111no—
277C2×C42—112no—
278C2×C42—118no—
279C2×C42—114no—
280C2×C42—114no—
281C2×C42—114no—
282C2×C42—2216no—
283C2×C42C22×D1114yes—
284C2×C42C22×D1111yescharacteristic
285#95—114no—
286#95—114no—
287#95—114no—
288#95—114no—
289#95—118no—
290#95—118no—
291#95—118no—
292#95—118no—
293#95C22×D1114yes—
294#95C22×D1114yes—
295#95C22×D1118yes—
296C2×C11C22×#12512yes—
297C2×C11C2×#54411yescharacteristic
298C2×C11C2×#55511yescharacteristic
299C2×C11C2×#55612yes—
300C2×C11C2×#55911yescharacteristic
301D11#257118yesdirect product factor
302C24—111no—
303C22×C4—112no—
304C22×C4—118no—
305C22×C4—118no—
306C22×C4—118no—
307C22×C4—111no—
308C22×C4—114no—
309C22×C4—114no—
310C22×C4—114no—
311C22×C4—114no—
312C22×C4—222no—
313C22×C4—222no—
314C22×C4—228no—
315C22×C4—228no—
316C22×C4—2216no—
317C22×C4—228no—
318C22×C4—228no—
319C22×C4—228no—
320C22×C4—228no—
321C22×C4—228no—
322C22×C4C23×D1114yes—
323C22×C4C23×D1114yes—
324C22×C4C23×D1114yes—
325C22×C4C23×D1111yescharacteristic
326C22×C4C23×D1112yes—
327C4⋊C4—24no—
328C4⋊C4—24no—
329C4⋊C4—28no—
330C4⋊C4—42no—
331C4⋊C4—44no—
332C4⋊C4—228no—
333C4⋊C4—228no—
334C4⋊C4—2216no—
335C4⋊C4—224no—
336C4⋊C4—224no—
337C4⋊C4—228no—
338C4⋊C4—444no—
339C4⋊C4—448no—
340C4⋊C4—442no—
341C4⋊C4—444no—
342C42—28no—
343C42—114no—
344C42—118no—
345C42—228no—
346C42—228no—
347C42—228no—
348C42Q8×D1114yes—
349C11C2×#257111yescharacteristic, complemented, Sylow
350C23—112no—
351C23—114no—
352C23—114no—
353C23—112no—
354C23—112no—
355C23C24×D1111yescharacteristic
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—28no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—114no—
367C2×C4—114no—
368C2×C4—114no—
369C2×C4—1132no—
370C2×C4—112no—
371C2×C4—228no—
372C2×C4—221no—
373C2×C4—221no—
374C2×C4—224no—
375C2×C4—224no—
376C2×C4—224no—
377C2×C4—224no—
378C2×C4—228no—
379C2×C4—224no—
380C2×C4—224no—
381C2×C4—224no—
382C2×C4—4416no—
383C2×C4—4416no—
384C2×C4—4416no—
385C2×C4C2×Q8×D1112yes—
386C2×C4C2×Q8×D1114yes—
387C2×C4#41×D1114yes—
388C2×C4#41×D1114yes—
389C22—118no—
390C22—114no—
391C22—118no—
392C22—114no—
393C22—114no—
394C22C22×Q8×D1111yescharacteristic
395C22C2×#41×D1112yes—
396C22C2×#41×D1112yes—
397C22D11×H(5,𝔽2)11yescharacteristic
398C22D11×2−1+411yescharacteristic
399C4—22no—
400C4—44no—
401C4—44no—
402C4—44no—
403C4—118no—
404C4—222no—
405C4—444no—
406C4—444no—
407C4—444no—
408C4D11×#12518yes—
409C2—118no—
410C2C2×D11×#12512yes—
411C2D11×#54411yescharacteristic
412C2D11×#55511yescharacteristic
413C2D11×#55612yes—
414C2D11×#55911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2571C2
prime radicalC23×D11C24
hypercenter#2571D11
hypocenterC11C2×#2571
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2571

Complements

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

NH ≅ G/Ntype
1. #13073858C2semidirect
2. #13073857C2semidirect
3. #13073856C2semidirect
4. #13073855C2semidirect
5. #13073854C2semidirect
11. C11×#2571C2semidirect
148. #2571D11direct (N × H)
301. D11#2571direct (N × H)
349. C11C2×#2571semidirect

Maximal subgroups

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

subgroupindex
#130738582
#130738572
#130738562
#130738552
#130738542
D11×#4002
D11×#3892
D11×#3842
D11×#3822
C4×C4⋊C4×D112
C11×#25712
C2×#257111