Finite Group Databasebeta

← D11×#2835 #14959991

Subgroups — D11×#2835 #14959991

Order 2816.

2022 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076807C211yesmaximal, characteristic, complemented
2#13076806C213yesmaximal, complemented
3#13076805C212yesmaximal, complemented
4#13076804C213yesmaximal, complemented
5#13076803C216yesmaximal, complemented
6D11×#400C216yesmaximal, complemented
7D11×#397C213yesmaximal
8D11×#395C212yesmaximal, complemented
9D11×#393C211yesmaximal, characteristic
10D11×#385C213yesmaximal
11C11×#2835C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C2×C4⋊C4×D11C2216yes—
15C2×C4⋊C4×D11C2213yes—
16C2×C22⋊C4×D11C2213yes—
17C2×C22⋊C4×D11C2213yes—
18C11×#400C2216yescomplemented
19C11×#397C2213yes—
20C11×#395C2212yescomplemented
21C11×#393C2211yescharacteristic
22C11×#385C2213yes—
23#10622844C2211yescharacteristic
24#10622842C2212yescomplemented
25#10622823C2213yes—
26#10622606C2213yes—
27#10622602C2216yes—
28#10622599C2216yescomplemented
29#10622595C2216yescomplemented
30#10622592C2216yescomplemented
31#10622566C2213yes—
32#10622565C2216yes—
33#10622563C2213yes—
34#10622560C2213yes—
35#10622559C2213yes—
36#10622288C2216yes—
37#10622287C2213yes—
38#10622286C2213yes—
39#10622281C2216yes—
40D11×#95C2216yes—
41D11×#95C2213yes—
42D11×#95C2216yes—
43D11×#95C2213yes—
44#10622273C2216yescomplemented
45#10622273C2216yescomplemented
46#10622272C2216yescomplemented
47#10622271C2216yescomplemented
48#10622271C2216yescomplemented
49#10622269C2216yescomplemented
50C24×D11C2311yescharacteristic
51C22×Q8×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×Dic11C2311yescharacteristic
54C2×Q8×D11—46no—
55C22×C4×D11—46no—
56C22×C4×D11C2316yes—
57C22×C4×D11C2313yes—
58C22×C4×D11C2313yes—
59C22×C4×D11C2312yes—
60C22×C4×D11C2312yes—
61C22×Dic22C2313yes—
62C2×C11×C4⋊C4C2316yes—
63C2×C11×C4⋊C4C2313yes—
64C2×C11×C22⋊C4C2313yes—
65C2×C11×C22⋊C4C2313yes—
66C2×C22⋊Dic11C2313yes—
67C2×C22⋊Dic11C2313yes—
68C2×(C2×D11)⋊C4C2316yes—
69C2×(C2×D11)⋊C4C2313yes—
70C2×(C2×D11)⋊C4C2313yes—
71C2×C4⋊Dic11C2316yes—
72C2×C4⋊Dic11C2313yes—
73C2×Dic11⋊C4C2316yes—
74C2×Dic11⋊C4C2316yes—
75C2×Dic11⋊C4C2316yes—
76C4⋊C4×D11—46no—
77C4⋊C4×D11—412no—
78C22⋊C4×D11—212no—
79C22⋊C4×D11—46no—
80C11×#95C2316yes—
81C11×#95C2316yes—
82C11×#95C2313yes—
83C11×#95C2313yes—
84C11⋊#95C2316yes—
85C11⋊#95C2316yes—
86C11⋊#95C2316yes—
87C11⋊#95C2313yes—
88C11⋊#95C2313yes—
89C11⋊#95C2316yes—
90C11⋊#95C2316yes—
91C11⋊#95C2316yes—
92C11⋊#95C2316yes—
93C11⋊#95C2316yes—
94C2×#2835—111nomaximal, Sylow
95C24×C11C2411yescharacteristic
96C23×D11—26no—
97C23×D11—26no—
98C23×D11#4114yes—
99C23×D11C2411yescharacteristic
100C23×D11C2411yescharacteristic
101C2×Q8×C11—43no—
102C22×C4×C11—43no—
103C22×C4×C11C2413yes—
104C22×C4×C11C2416yes—
105C22×C4×C11C2412yes—
106C22×C4×C11C2413yes—
107C22×Dic11—43no—
108C22×Dic11C2413yes—
109C22×Dic11C2416yes—
110C22×Dic11C2412yes—
111C22×Dic11C2413yes—
112Q8×D11—416no—
113C2×C4×D11—212no—
114C2×C4×D11—26no—
115C2×C4×D11—26no—
116C2×C4×D11—212no—
117C2×C4×D11—212no—
118C2×C4×D11—212no—
119C2×C4×D11—212no—
120C2×C4×D11—212no—
121C2×C4×D11—46no—
122C2×C4×D11—416no—
123C2×Dic22—46no—
124C2×Dic22—43no—
125C11×C4⋊C4—43no—
126C11×C4⋊C4—46no—
127C11×C22⋊C4—26no—
128C11×C22⋊C4—43no—
129C22⋊Dic11—26no—
130C22⋊Dic11—43no—
131(C2×D11)⋊C4—212no—
132(C2×D11)⋊C4—43no—
133(C2×D11)⋊C4—43no—
134C4⋊Dic11—46no—
135C4⋊Dic11—43no—
136Dic11⋊C4—46no—
137Dic11⋊C4—46no—
138Dic11⋊C4—46no—
139#2835—116no—
140#2835—113no—
141#2835—112no—
142#2835—111no—
143#2835—113no—
144#2835D1111yescharacteristic, direct product factor
145C2×#400—116no—
146C2×#397—113no—
147C2×#395—112no—
148C2×#393—111no—
149C2×#385—113no—
150C23×C11—23no—
151C23×C11—23no—
152C23×C11C2×#4112yes—
153C23×C11C2511yescharacteristic
154C22×D11—23no—
155C22×D11—23no—
156C22×D11—224no—
157C22×D11—44no—
158C22×D11—412no—
159C22×D11C2×#4112yes—
160C22×D11C2×#4112yes—
161C22×D11H(5,𝔽2)16yes—
162C22×D112−1+416yes—
163Q8×C11—44no—
164C2×C4×C11—26no—
165C2×C4×C11—26no—
166C2×C4×C11—26no—
167C2×C4×C11—26no—
168C2×C4×C11—23no—
169C2×C4×C11—23no—
170C2×C4×C11—26no—
171C2×C4×C11—26no—
172C2×C4×C11—44no—
173C2×Dic11—26no—
174C2×Dic11—26no—
175C2×Dic11—23no—
176C2×Dic11—26no—
177C2×Dic11—26no—
178C2×Dic11—23no—
179C2×Dic11—26no—
180C2×Dic11—26no—
181C2×Dic11—44no—
182C4×D11—48no—
183C4×D11—424no—
184C4×D11—48no—
185C4×D11—412no—
186C4×D11—412no—
187Dic22—412no—
188C23×Q8—111no—
189C24×C4—111no—
190C22×C4⋊C4—116no—
191C22×C4⋊C4—113no—
192C22×C22⋊C4—113no—
193C22×C22⋊C4—113no—
194#400—116no—
195#400—116no—
196#400—116no—
197#400—116no—
198#400—116no—
199#400—116no—
200#400—116no—
201#400C2×D1116yescomplemented
202#397—113no—
203#397—116no—
204#397—113no—
205#397—113no—
206#397—116no—
207#397C2×D1113yes—
208#395—112no—
209#395—116no—
210#395—116no—
211#395C2×D1112yescomplemented
212#393—111no—
213#393—113no—
214#393—113no—
215#393C2×D1111yescharacteristic
216#385—113no—
217#385—116no—
218#385—113no—
219#385—113no—
220#385—116no—
221#385C2×D1113yes—
222C2×#95—113no—
223C2×#95—116no—
224C2×#95—113no—
225C2×#95—116no—
226C22×C11—26no—
227C22×C11—41no—
228C22×C11—43no—
229C22×C11C22×#4111yescharacteristic
230C22×C11C2×H(5,𝔽2)13yes—
231C22×C11C2×2−1+413yes—
232C2×D11—26no—
233C2×D11—41no—
234C2×D11—43no—
235C2×D11—416no—
236C2×D11#539112yes—
237C2×D11H(3,𝔽4)14yes—
238C2×D11#563112yes—
239C4×C11—46no—
240C4×C11—42no—
241C4×C11—43no—
242C4×C11—43no—
243Dic11—46no—
244Dic11—43no—
245Dic11—42no—
246Dic11—43no—
247C25—111no—
248C22×Q8—113no—
249C22×Q8—446no—
250C22×Q8C22×D1111yescharacteristic
251C23×C4—111no—
252C23×C4—113no—
253C23×C4—116no—
254C23×C4—113no—
255C23×C4—112no—
256C23×C4—112no—
257C23×C4—446no—
258C23×C4C22×D1111yescharacteristic
259C2×C4⋊C4—116no—
260C2×C4⋊C4—116no—
261C2×C4⋊C4—116no—
262C2×C4⋊C4—116no—
263C2×C4⋊C4—113no—
264C2×C4⋊C4—446no—
265C2×C4⋊C4—4412no—
266C2×C4⋊C4C22×D1116yes—
267C2×C4⋊C4C22×D1113yes—
268C2×C22⋊C4—113no—
269C2×C22⋊C4—116no—
270C2×C22⋊C4—113no—
271C2×C22⋊C4—113no—
272C2×C22⋊C4—113no—
273C2×C22⋊C4—2212no—
274C2×C22⋊C4—446no—
275C2×C22⋊C4C22×D1113yes—
276C2×C22⋊C4C22×D1113yes—
277#95—116no—
278#95—116no—
279#95—116no—
280#95—113no—
281#95—116no—
282#95—116no—
283#95—116no—
284#95—116no—
285#95—116no—
286#95—113no—
287#95C22×D1116yes—
288#95C22×D1113yes—
289#95C22×D1116yes—
290#95C22×D1113yes—
291C2×C11—42no—
292C2×C11C2×#53913yes—
293C2×C11C2×H(3,𝔽4)11yescharacteristic
294C2×C11C2×#56313yes—
295D11—42no—
296D11#283518yesdirect product factor
297C24—111no—
298C24—114no—
299C24—111no—
300C24—226no—
301C24—226no—
302C24C23×D1111yescharacteristic
303C2×Q8—43no—
304C2×Q8—443no—
305C2×Q8—446no—
306C2×Q8—4416no—
307C22×C4—43no—
308C22×C4—113no—
309C22×C4—116no—
310C22×C4—113no—
311C22×C4—112no—
312C22×C4—2212no—
313C22×C4—226no—
314C22×C4—226no—
315C22×C4—2212no—
316C22×C4—2212no—
317C22×C4—2212no—
318C22×C4—2212no—
319C22×C4—2212no—
320C22×C4—446no—
321C22×C4—4416no—
322C22×C4—443no—
323C22×C4C23×D1113yes—
324C22×C4C23×D1116yes—
325C22×C4C23×D1113yes—
326C22×C4C23×D1112yes—
327C4⋊C4—43no—
328C4⋊C4—46no—
329C4⋊C4—446no—
330C4⋊C4—446no—
331C4⋊C4—446no—
332C4⋊C4—443no—
333C4⋊C4—446no—
334C22⋊C4—26no—
335C22⋊C4—43no—
336C22⋊C4—2212no—
337C22⋊C4—226no—
338C22⋊C4—443no—
339C22⋊C4—443no—
340C22⋊C4—443no—
341C11C2×#283511yescharacteristic, complemented, Sylow
342C23—23no—
343C23—23no—
344C23—112no—
345C23—116no—
346C23—116no—
347C23—112no—
348C23—2224no—
349C23—223no—
350C23—223no—
351C23—444no—
352C23—4412no—
353C23#41×D1112yes—
354C23C24×D1111yescharacteristic
355Q8—44no—
356Q8—4412no—
357C2×C4—26no—
358C2×C4—23no—
359C2×C4—23no—
360C2×C4—26no—
361C2×C4—26no—
362C2×C4—26no—
363C2×C4—26no—
364C2×C4—26no—
365C2×C4—44no—
366C2×C4—226no—
367C2×C4—223no—
368C2×C4—223no—
369C2×C4—226no—
370C2×C4—226no—
371C2×C4—226no—
372C2×C4—226no—
373C2×C4—226no—
374C2×C4—448no—
375C2×C4—4412no—
376C2×C4—4424no—
377C2×C4—4412no—
378C2×C4—448no—
379C2×C4—444no—
380C22—26no—
381C22—41no—
382C22—43no—
383C22—1112no—
384C22—114no—
385C22—1112no—
386C22—226no—
387C22—4416no—
388C22—441no—
389C22—443no—
390C22C2×#41×D1111yescharacteristic
391C22D11×H(5,𝔽2)13yes—
392C22D11×2−1+413yes—
393C4—46no—
394C4—42no—
395C4—43no—
396C4—43no—
397C4—446no—
398C4—442no—
399C4—443no—
400C4—443no—
401C2—42no—
402C2—118no—
403C2—442no—
404C2D11×#53913yes—
405C2D11×H(3,𝔽4)11yescharacteristic
406C2D11×#56313yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2835C2
prime radicalC24×D11C23
hypercenter#2835D11
hypocenterC11C2×#2835
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2835

Complements

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

NH ≅ G/Ntype
1. #13076807C2semidirect
2. #13076806C2semidirect
3. #13076805C2semidirect
4. #13076804C2semidirect
5. #13076803C2semidirect
6. D11×#400C2semidirect
8. D11×#395C2semidirect
11. C11×#2835C2semidirect
18. C11×#400C22semidirect
20. C11×#395C22semidirect
24. #10622842C22semidirect
28. #10622599C22semidirect
29. #10622595C22semidirect
30. #10622592C22semidirect
44. #10622273C22semidirect
45. #10622273C22semidirect
46. #10622272C22semidirect
47. #10622271C22semidirect
48. #10622271C22semidirect
49. #10622269C22semidirect
144. #2835D11direct (N × H)
201. #400C2×D11semidirect
211. #395C2×D11semidirect
296. D11#2835direct (N × H)
341. C11C2×#2835semidirect

Maximal subgroups

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

subgroupindex
#130768072
#130768062
#130768052
#130768042
#130768032
D11×#4002
D11×#3972
D11×#3952
D11×#3932
D11×#3852
C11×#28352
C2×#283511