Finite Group Databasebeta

← D11×#2843 #14960363

Subgroups — D11×#2843 #14960363

Order 2816.

1806 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076886C213yesmaximal, complemented
2#13076885C211yesmaximal, characteristic, complemented
3#13076884C216yesmaximal, complemented
4#13076883C212yesmaximal, complemented
5#13076882C213yesmaximal, complemented
6D11×#400C213yesmaximal
7D11×#398C216yesmaximal
8D11×#395C213yesmaximal
9D11×#384C211yesmaximal, characteristic
10D11×#383C212yesmaximal
11C11×#2843C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2211yescharacteristic
13C2×C4⋊C4×D11C2213yes—
14C2×C4⋊C4×D11C2213yes—
15C2×C4⋊C4×D11C2216yes—
16C2×C4⋊C4×D11C2213yes—
17C2×C42×D11C2211yescharacteristic
18C11×#400C2213yes—
19C11×#398C2216yes—
20C11×#395C2213yes—
21C11×#384C2211yescharacteristic
22C11×#383C2212yes—
23#10622842C2213yes—
24#10622599C2213yes—
25#10622597C2216yes—
26#10622597C2216yes—
27#10622596C2216yes—
28#10622595C2213yes—
29#10622593C2216yes—
30#10622592C2216yes—
31#10622592C2213yes—
32#10622589C2213yes—
33#10622589C2213yes—
34#10622550C2212yes—
35#10622548C2211yescharacteristic
36D11×#95C2216yes—
37D11×#95C2216yes—
38D11×#95C2213yes—
39D11×#95C2213yes—
40#10622274C2216yes—
41#10622273C2216yes—
42#10622272C2213yes—
43#10622271C2216yes—
44#10622270C2216yes—
45#10622270C2216yes—
46#10622269C2216yes—
47#10622269C2213yes—
48#10622264C2216yes—
49#10622264C2216yes—
50C22×Q8×C11C2311yescharacteristic
51C2×Q8×D11—46no—
52C22×C4×D11C2313yes—
53C22×C4×D11C2311yescharacteristic
54C22×C4×D11C2312yes—
55C22×C4×D11C2316yes—
56C22×C4×D11C2313yes—
57C22×Dic22C2312yes—
58C22×Dic22C2311yescharacteristic
59C2×C11×C4⋊C4C2313yes—
60C2×C11×C4⋊C4C2313yes—
61C2×C11×C4⋊C4C2316yes—
62C2×C11×C4⋊C4C2313yes—
63C2×C42×C11C2311yescharacteristic
64C2×C4⋊Dic11C2316yes—
65C2×C4⋊Dic11C2313yes—
66C2×C4⋊Dic11C2313yes—
67C2×C4⋊Dic11C2313yes—
68C2×Dic11⋊C4C2316yes—
69C2×Dic11⋊C4C2313yes—
70C2×Dic11⋊C4C2316yes—
71C2×Dic11⋊C4C2316yes—
72C2×Dic11⋊C4C2316yes—
73C2×Dic11⋊C4C2313yes—
74C2×C4×Dic11C2313yes—
75C4⋊C4×D11—46no—
76C4⋊C4×D11—46no—
77C4⋊C4×D11—46no—
78C4⋊C4×D11—412no—
79C42×D11Q818yescomplemented
80C11×#95C2316yes—
81C11×#95C2316yes—
82C11×#95C2313yes—
83C11×#95C2313yes—
84C11⋊#95C2316yes—
85C11⋊#95C2316yes—
86C11⋊#95C2316yes—
87C11⋊#95C2316yes—
88C11⋊#95C2316yes—
89C11⋊#95C2316yes—
90C11⋊#95C2316yes—
91C11⋊#95C2316yes—
92C11⋊#95C2313yes—
93C11⋊#95C2313yes—
94C2×#2843—111nomaximal, Sylow
95C23×D11C2411yescharacteristic
96C2×Q8×C11—43no—
97C22×C4×C11C2416yes—
98C22×C4×C11C2412yes—
99C22×C4×C11C2411yescharacteristic
100C22×C4×C11C2413yes—
101C22×C4×C11C2413yes—
102C22×Dic11C2416yes—
103C22×Dic11C2412yes—
104C22×Dic11C2411yescharacteristic
105C22×Dic11C2413yes—
106C22×Dic11C2413yes—
107Q8×D11—416no—
108C2×C4×D11—26no—
109C2×C4×D11—212no—
110C2×C4×D11—26no—
111C2×C4×D11—212no—
112C2×C4×D11—26no—
113C2×C4×D11—212no—
114C2×C4×D11—26no—
115C2×C4×D11—224no—
116C2×C4×D11C2×Q8112yes—
117C2×Dic22—46no—
118C2×Dic22—43no—
119C11×C4⋊C4—43no—
120C11×C4⋊C4—43no—
121C11×C4⋊C4—46no—
122C11×C4⋊C4—43no—
123C42×C11C2×Q814yescomplemented
124C4⋊Dic11—43no—
125C4⋊Dic11—43no—
126C4⋊Dic11—43no—
127C4⋊Dic11—46no—
128Dic11⋊C4—46no—
129Dic11⋊C4—46no—
130Dic11⋊C4—43no—
131Dic11⋊C4—46no—
132Dic11⋊C4—43no—
133Dic11⋊C4—46no—
134C4×Dic11C2×Q8112yescomplemented
135#2843—113no—
136#2843—116no—
137#2843—113no—
138#2843—111no—
139#2843—112no—
140#2843D1111yescharacteristic, direct product factor
141C2×#400—113no—
142C2×#398—116no—
143C2×#395—113no—
144C2×#384—111no—
145C2×#383—112no—
146C23×C11C2511yescharacteristic
147C22×D11C22×Q812yes—
148C22×D11H(5,𝔽2)16yes—
149C22×D112−1+416yes—
150Q8×C11—44no—
151C2×C4×C11—23no—
152C2×C4×C11—23no—
153C2×C4×C11—26no—
154C2×C4×C11—23no—
155C2×C4×C11—26no—
156C2×C4×C11—23no—
157C2×C4×C11—26no—
158C2×C4×C11—212no—
159C2×C4×C11C22×Q816yes—
160C2×Dic11—23no—
161C2×Dic11—23no—
162C2×Dic11—23no—
163C2×Dic11—26no—
164C2×Dic11—26no—
165C2×Dic11—26no—
166C2×Dic11—23no—
167C2×Dic11—212no—
168C2×Dic11C22×Q816yes—
169C4×D11—224no—
170C4×D11—412no—
171C4×D11—44no—
172C4×D11—48no—
173C4×D11—424no—
174Dic22—48no—
175Dic22—44no—
176C23×Q8—111no—
177C22×C4⋊C4—116no—
178C22×C4⋊C4—113no—
179C22×C4⋊C4—113no—
180C22×C4⋊C4—113no—
181C22×C42—111no—
182#400—113no—
183#400—113no—
184#400—116no—
185#400—113no—
186#400—116no—
187#400C2×D1113yes—
188#398—116no—
189#398—116no—
190#398—116no—
191#398—116no—
192#398—116no—
193#398—116no—
194#398—116no—
195#398C2×D1116yes—
196#395—113no—
197#395—116no—
198#395—113no—
199#395—113no—
200#395—116no—
201#395C2×D1113yes—
202#384—113no—
203#384—113no—
204#384—111no—
205#384C2×D1111yescharacteristic
206#383—112no—
207#383—116no—
208#383—116no—
209#383C2×D1112yes—
210C2×#95—116no—
211C2×#95—113no—
212C2×#95—113no—
213C2×#95—116no—
214C22×C11C23×Q811yescharacteristic
215C22×C11C2×H(5,𝔽2)13yes—
216C22×C11C2×2−1+413yes—
217C2×D11#544112yes—
218C2×D11#56014yes—
219C2×D11#563112yes—
220C4×C11—26no—
221C4×C11—41no—
222C4×C11—42no—
223C4×C11—43no—
224C4×C11—46no—
225Dic11—26no—
226Dic11—42no—
227Dic11—41no—
228Dic11—43no—
229Dic11—46no—
230C22×Q8—111no—
231C22×Q8—112no—
232C22×Q8—446no—
233C22×Q8C22×D1111yescharacteristic
234C23×C4—113no—
235C23×C4—113no—
236C23×C4—112no—
237C23×C4—111no—
238C23×C4—116no—
239C2×C4⋊C4—113no—
240C2×C4⋊C4—113no—
241C2×C4⋊C4—113no—
242C2×C4⋊C4—116no—
243C2×C4⋊C4—113no—
244C2×C4⋊C4—116no—
245C2×C4⋊C4—116no—
246C2×C4⋊C4—116no—
247C2×C4⋊C4—116no—
248C2×C4⋊C4—113no—
249C2×C4⋊C4—446no—
250C2×C4⋊C4—446no—
251C2×C4⋊C4—446no—
252C2×C4⋊C4—4412no—
253C2×C4⋊C4C22×D1113yes—
254C2×C4⋊C4C22×D1113yes—
255C2×C4⋊C4C22×D1116yes—
256C2×C4⋊C4C22×D1113yes—
257C2×C42—113no—
258C2×C42—118no—
259C2×C42C22×D1111yescharacteristic
260#95—116no—
261#95—116no—
262#95—116no—
263#95—116no—
264#95—116no—
265#95—116no—
266#95—113no—
267#95—116no—
268#95—113no—
269#95—116no—
270#95C22×D1116yes—
271#95C22×D1116yes—
272#95C22×D1113yes—
273#95C22×D1113yes—
274C2×C11C2×#54413yes—
275C2×C11C2×#56011yescharacteristic
276C2×C11C2×#56313yes—
277D11#284318yesdirect product factor
278C24—111no—
279C2×Q8—43no—
280C2×Q8—443no—
281C2×Q8—446no—
282C2×Q8—4416no—
283C22×C4—113no—
284C22×C4—1112no—
285C22×C4—116no—
286C22×C4—112no—
287C22×C4—111no—
288C22×C4—113no—
289C22×C4—226no—
290C22×C4—226no—
291C22×C4—2212no—
292C22×C4—226no—
293C22×C4—2212no—
294C22×C4—226no—
295C22×C4—2212no—
296C22×C4—2224no—
297C22×C4C23×D1116yes—
298C22×C4C23×D1112yes—
299C22×C4C23×D1111yescharacteristic
300C22×C4C23×D1113yes—
301C22×C4C23×D1113yes—
302C4⋊C4—43no—
303C4⋊C4—43no—
304C4⋊C4—43no—
305C4⋊C4—46no—
306C4⋊C4—446no—
307C4⋊C4—443no—
308C4⋊C4—446no—
309C4⋊C4—446no—
310C4⋊C4—443no—
311C4⋊C4—446no—
312C4⋊C4—443no—
313C4⋊C4—443no—
314C4⋊C4—443no—
315C4⋊C4—446no—
316C42—1112no—
317C42Q8×D1114yescomplemented
318C11C2×#284311yescharacteristic, complemented, Sylow
319C23—112no—
320C23—116no—
321C23—116no—
322C23C24×D1111yescharacteristic
323Q8—44no—
324Q8—444no—
325Q8—448no—
326C2×C4—23no—
327C2×C4—23no—
328C2×C4—26no—
329C2×C4—23no—
330C2×C4—26no—
331C2×C4—23no—
332C2×C4—26no—
333C2×C4—212no—
334C2×C4—116no—
335C2×C4—2224no—
336C2×C4—223no—
337C2×C4—223no—
338C2×C4—223no—
339C2×C4—226no—
340C2×C4—226no—
341C2×C4—223no—
342C2×C4—226no—
343C2×C4—2212no—
344C2×C4—444no—
345C2×C4—448no—
346C2×C4—4412no—
347C2×C4—4424no—
348C2×C4C2×Q8×D1116yes—
349C22—114no—
350C22—1112no—
351C22—1112no—
352C22C22×Q8×D1111yescharacteristic
353C22D11×H(5,𝔽2)13yes—
354C22D11×2−1+413yes—
355C4—26no—
356C4—41no—
357C4—42no—
358C4—43no—
359C4—46no—
360C4—226no—
361C4—441no—
362C4—442no—
363C4—443no—
364C4—446no—
365C2—118no—
366C2D11×#54413yes—
367C2D11×#56011yescharacteristic
368C2D11×#56313yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2843C2
prime radicalC23×D11C24
hypercenter#2843D11
hypocenterC11C2×#2843
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2843

Complements

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

NH ≅ G/Ntype
1. #13076886C2semidirect
2. #13076885C2semidirect
3. #13076884C2semidirect
4. #13076883C2semidirect
5. #13076882C2semidirect
11. C11×#2843C2semidirect
79. C42×D11Q8semidirect
123. C42×C11C2×Q8semidirect
134. C4×Dic11C2×Q8semidirect
140. #2843D11direct (N × H)
277. D11#2843direct (N × H)
317. C42Q8×D11semidirect
318. C11C2×#2843semidirect

Maximal subgroups

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

subgroupindex
#130768862
#130768852
#130768842
#130768832
#130768822
D11×#4002
D11×#3982
D11×#3952
D11×#3842
D11×#3832
C11×#28432
C2×#284311