Finite Group Databasebeta

← D11×#2834 #14959985

Subgroups — D11×#2834 #14959985

Order 2816.

1958 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076802C211yesmaximal, characteristic, complemented
2#13076801C213yesmaximal, complemented
3#13076800C212yesmaximal, complemented
4#13076799C213yesmaximal, complemented
5#13076798C216yesmaximal, complemented
6D11×#401C212yesmaximal, complemented
7D11×#399C211yesmaximal, characteristic
8D11×#398C216yesmaximal, complemented
9D11×#397C213yesmaximal
10D11×#385C213yesmaximal
11C11×#2834C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C2×C4⋊C4×D11C2216yes—
14C2×C4⋊C4×D11C2213yes—
15C2×C4⋊C4×D11C2213yes—
16C2×C22⋊C4×D11C2213yes—
17C2×C22⋊C4×D11C2213yes—
18C11×#401C2212yescomplemented
19C11×#399C2211yescharacteristic
20C11×#398C2216yescomplemented
21C11×#397C2213yes—
22C11×#385C2213yes—
23#10622823C2213yes—
24#10622606C2213yes—
25#10622605C2213yes—
26#10622602C2216yes—
27#10622597C2216yescomplemented
28#10622597C2216yescomplemented
29#10622596C2216yescomplemented
30#10622593C2216yescomplemented
31#10622566C2213yes—
32#10622565C2216yes—
33#10622563C2213yes—
34#10622562C2213yes—
35#10622559C2213yes—
36#10622290C2211yescharacteristic
37#10622288C2216yes—
38#10622287C2213yes—
39#10622281C2216yes—
40D11×#95C2211yescharacteristic
41D11×#95C2216yes—
42D11×#95C2216yes—
43D11×#95C2213yes—
44C11⋊#401C2216yescomplemented
45C11⋊#401C2216yescomplemented
46C11⋊#401C2212yescomplemented
47#10622274C2216yescomplemented
48#10622270C2216yescomplemented
49#10622270C2216yescomplemented
50C24×D11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×Dic11C2311yescharacteristic
53C22×C4×D11—46no—
54C22×C4×D11C2313yes—
55C22×C4×D11C2316yes—
56C22×C4×D11C2313yes—
57C22×C4×D11C2312yes—
58C22×C4×D11C2312yes—
59C2×C11×C4⋊C4C2316yes—
60C2×C11×C4⋊C4C2313yes—
61C2×C11×C4⋊C4C2313yes—
62C2×C11×C22⋊C4C2313yes—
63C2×C11×C22⋊C4C2313yes—
64C2×C22⋊Dic11C2313yes—
65C2×C22⋊Dic11C2313yes—
66C2×(C2×D11)⋊C4C2316yes—
67C2×(C2×D11)⋊C4C2313yes—
68C2×(C2×D11)⋊C4C2313yes—
69C2×C4⋊Dic11C2313yes—
70C2×C4⋊Dic11C2316yes—
71C2×C4⋊Dic11C2313yes—
72C2×Dic11⋊C4C2316yes—
73C2×Dic11⋊C4C2316yes—
74C2×Dic11⋊C4C2316yes—
75C2×Dic11⋊C4C2316yes—
76C4⋊C4×D11—46no—
77C4⋊C4×D11—46no—
78C4⋊C4×D11—412no—
79C22⋊C4×D11—212no—
80C22⋊C4×D11—46no—
81C11×#95C2313yes—
82C11×#95C2316yes—
83C11×#95C2316yes—
84C11×#95C2311yescharacteristic
85C11⋊#95C2316yes—
86C11⋊#95C2316yes—
87C11⋊#95C2316yes—
88C11⋊#95C2316yes—
89C11⋊#95C2316yes—
90C11⋊#95C2313yes—
91C11⋊#95C2316yes—
92C11⋊#95C2316yes—
93C11⋊#95C2313yes—
94C2×#2834—111nomaximal, Sylow
95C24×C11C2411yescharacteristic
96C23×D11—26no—
97C23×D11—26no—
98C23×D11#4114yes—
99C23×D11C2411yescharacteristic
100C23×D11C2411yescharacteristic
101C22×C4×C11—43no—
102C22×C4×C11C2413yes—
103C22×C4×C11C2416yes—
104C22×C4×C11C2412yes—
105C22×C4×C11C2413yes—
106C22×Dic11—43no—
107C22×Dic11C2413yes—
108C22×Dic11C2416yes—
109C22×Dic11C2412yes—
110C22×Dic11C2413yes—
111C2×C4×D11—212no—
112C2×C4×D11—26no—
113C2×C4×D11—26no—
114C2×C4×D11—212no—
115C2×C4×D11—212no—
116C2×C4×D11—212no—
117C2×C4×D11—212no—
118C2×C4×D11—212no—
119C2×C4×D11—46no—
120C2×C4×D11—416no—
121C11×C4⋊C4—43no—
122C11×C4⋊C4—46no—
123C11×C4⋊C4—43no—
124C11×C22⋊C4—26no—
125C11×C22⋊C4—43no—
126C22⋊Dic11—26no—
127C22⋊Dic11—43no—
128(C2×D11)⋊C4—212no—
129(C2×D11)⋊C4—43no—
130(C2×D11)⋊C4—43no—
131C4⋊Dic11—46no—
132C4⋊Dic11—43no—
133C4⋊Dic11—43no—
134Dic11⋊C4—46no—
135Dic11⋊C4—46no—
136Dic11⋊C4—46no—
137Dic11⋊C4—46no—
138#2834—112no—
139#2834—111no—
140#2834—116no—
141#2834—113no—
142#2834—113no—
143#2834D1111yescharacteristic, direct product factor
144C2×#401—112no—
145C2×#399—111no—
146C2×#398—116no—
147C2×#397—113no—
148C2×#385—113no—
149C23×C11—23no—
150C23×C11—23no—
151C23×C11C2×#4112yes—
152C23×C11C2511yescharacteristic
153C22×D11—23no—
154C22×D11—23no—
155C22×D11—224no—
156C22×D11—44no—
157C22×D11—412no—
158C22×D11C2×#4112yes—
159C22×D11C2×#4112yes—
160C22×D11H(5,𝔽2)16yes—
161C22×D112−1+416yes—
162C2×C4×C11—26no—
163C2×C4×C11—26no—
164C2×C4×C11—26no—
165C2×C4×C11—26no—
166C2×C4×C11—23no—
167C2×C4×C11—23no—
168C2×C4×C11—26no—
169C2×C4×C11—26no—
170C2×C4×C11—44no—
171C2×Dic11—26no—
172C2×Dic11—26no—
173C2×Dic11—26no—
174C2×Dic11—23no—
175C2×Dic11—23no—
176C2×Dic11—26no—
177C2×Dic11—26no—
178C2×Dic11—26no—
179C2×Dic11—44no—
180C4×D11—48no—
181C4×D11—424no—
182C4×D11—412no—
183C4×D11—48no—
184C4×D11—412no—
185C24×C4—111no—
186C22×C4⋊C4—113no—
187C22×C4⋊C4—113no—
188C22×C4⋊C4—116no—
189C22×C22⋊C4—113no—
190C22×C22⋊C4—113no—
191#401—112no—
192#401—116no—
193#401—116no—
194#401C2×D1112yescomplemented
195#399—113no—
196#399—113no—
197#399—111no—
198#399C2×D1111yescharacteristic
199#398—116no—
200#398—116no—
201#398—116no—
202#398—116no—
203#398—116no—
204#398—116no—
205#398—116no—
206#398C2×D1116yescomplemented
207#397—113no—
208#397—116no—
209#397—113no—
210#397—113no—
211#397—116no—
212#397C2×D1113yes—
213#385—113no—
214#385—116no—
215#385—113no—
216#385—113no—
217#385—116no—
218#385C2×D1113yes—
219C2×#95—113no—
220C2×#95—116no—
221C2×#95—116no—
222C2×#95—111no—
223C22×C11—26no—
224C22×C11—41no—
225C22×C11—43no—
226C22×C11C22×#4111yescharacteristic
227C22×C11C2×H(5,𝔽2)13yes—
228C22×C11C2×2−1+413yes—
229C2×D11—26no—
230C2×D11—41no—
231C2×D11—43no—
232C2×D11—416no—
233C2×D11#539112yes—
234C2×D11#56014yes—
235C2×D11#563112yes—
236C4×C11—46no—
237C4×C11—42no—
238C4×C11—43no—
239C4×C11—43no—
240Dic11—46no—
241Dic11—42no—
242Dic11—43no—
243Dic11—43no—
244C25—111no—
245C23×C4—111no—
246C23×C4—113no—
247C23×C4—116no—
248C23×C4—113no—
249C23×C4—112no—
250C23×C4—112no—
251C23×C4—446no—
252C23×C4C22×D1111yescharacteristic
253C2×C4⋊C4—116no—
254C2×C4⋊C4—116no—
255C2×C4⋊C4—116no—
256C2×C4⋊C4—116no—
257C2×C4⋊C4—113no—
258C2×C4⋊C4—116no—
259C2×C4⋊C4—113no—
260C2×C4⋊C4—446no—
261C2×C4⋊C4—446no—
262C2×C4⋊C4—4412no—
263C2×C4⋊C4C22×D1116yes—
264C2×C4⋊C4C22×D1113yes—
265C2×C4⋊C4C22×D1113yes—
266C2×C22⋊C4—113no—
267C2×C22⋊C4—116no—
268C2×C22⋊C4—113no—
269C2×C22⋊C4—113no—
270C2×C22⋊C4—113no—
271C2×C22⋊C4—2212no—
272C2×C22⋊C4—446no—
273C2×C22⋊C4C22×D1113yes—
274C2×C22⋊C4C22×D1113yes—
275#95—116no—
276#95—116no—
277#95—116no—
278#95—113no—
279#95—116no—
280#95—116no—
281#95—116no—
282#95—116no—
283#95—113no—
284#95C22×D1116yes—
285#95C22×D1113yes—
286#95C22×D1116yes—
287#95C22×D1111yescharacteristic
288C2×C11—42no—
289C2×C11C2×#53913yes—
290C2×C11C2×#56011yescharacteristic
291C2×C11C2×#56313yes—
292D11—42no—
293D11#283418yesdirect product factor
294C24—111no—
295C24—114no—
296C24—111no—
297C24—226no—
298C24—226no—
299C24C23×D1111yescharacteristic
300C22×C4—43no—
301C22×C4—113no—
302C22×C4—116no—
303C22×C4—112no—
304C22×C4—113no—
305C22×C4—2212no—
306C22×C4—226no—
307C22×C4—226no—
308C22×C4—2212no—
309C22×C4—2212no—
310C22×C4—2212no—
311C22×C4—2212no—
312C22×C4—2212no—
313C22×C4—446no—
314C22×C4—4416no—
315C22×C4—443no—
316C22×C4C23×D1113yes—
317C22×C4C23×D1116yes—
318C22×C4C23×D1112yes—
319C22×C4C23×D1113yes—
320C4⋊C4—43no—
321C4⋊C4—43no—
322C4⋊C4—46no—
323C4⋊C4—446no—
324C4⋊C4—446no—
325C4⋊C4—446no—
326C4⋊C4—446no—
327C4⋊C4—443no—
328C4⋊C4—443no—
329C4⋊C4—446no—
330C22⋊C4—26no—
331C22⋊C4—43no—
332C22⋊C4—2212no—
333C22⋊C4—226no—
334C22⋊C4—443no—
335C22⋊C4—443no—
336C22⋊C4—443no—
337C11C2×#283411yescharacteristic, complemented, Sylow
338C23—23no—
339C23—23no—
340C23—112no—
341C23—116no—
342C23—116no—
343C23—112no—
344C23—2224no—
345C23—223no—
346C23—223no—
347C23—444no—
348C23—4412no—
349C23#41×D1112yes—
350C23C24×D1111yescharacteristic
351C2×C4—26no—
352C2×C4—23no—
353C2×C4—23no—
354C2×C4—26no—
355C2×C4—26no—
356C2×C4—26no—
357C2×C4—26no—
358C2×C4—26no—
359C2×C4—44no—
360C2×C4—226no—
361C2×C4—223no—
362C2×C4—223no—
363C2×C4—226no—
364C2×C4—226no—
365C2×C4—226no—
366C2×C4—226no—
367C2×C4—226no—
368C2×C4—448no—
369C2×C4—4424no—
370C2×C4—4412no—
371C2×C4—4412no—
372C2×C4—448no—
373C2×C4—444no—
374C22—26no—
375C22—41no—
376C22—43no—
377C22—1112no—
378C22—114no—
379C22—1112no—
380C22—226no—
381C22—4416no—
382C22—441no—
383C22—443no—
384C22C2×#41×D1111yescharacteristic
385C22D11×H(5,𝔽2)13yes—
386C22D11×2−1+413yes—
387C4—46no—
388C4—42no—
389C4—43no—
390C4—43no—
391C4—446no—
392C4—442no—
393C4—443no—
394C4—443no—
395C2—42no—
396C2—118no—
397C2—442no—
398C2D11×#53913yes—
399C2D11×#56011yescharacteristic
400C2D11×#56313yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2834C2
prime radicalC24×D11C23
hypercenter#2834D11
hypocenterC11C2×#2834
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2834

Complements

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

NH ≅ G/Ntype
1. #13076802C2semidirect
2. #13076801C2semidirect
3. #13076800C2semidirect
4. #13076799C2semidirect
5. #13076798C2semidirect
6. D11×#401C2semidirect
8. D11×#398C2semidirect
11. C11×#2834C2semidirect
18. C11×#401C22semidirect
20. C11×#398C22semidirect
27. #10622597C22semidirect
28. #10622597C22semidirect
29. #10622596C22semidirect
30. #10622593C22semidirect
44. C11⋊#401C22semidirect
45. C11⋊#401C22semidirect
46. C11⋊#401C22semidirect
47. #10622274C22semidirect
48. #10622270C22semidirect
49. #10622270C22semidirect
143. #2834D11direct (N × H)
194. #401C2×D11semidirect
206. #398C2×D11semidirect
293. D11#2834direct (N × H)
337. C11C2×#2834semidirect

Maximal subgroups

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

subgroupindex
#130768022
#130768012
#130768002
#130767992
#130767982
D11×#4012
D11×#3992
D11×#3982
D11×#3972
D11×#3852
C11×#28342
C2×#283411