Finite Group Databasebeta

← C11×#36572 #14613765

Subgroups — C11×#36572 #14613765

Order 2816.

2446 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2848C213yesmaximal, complemented
2C11×#2564C213yesmaximal, complemented
3C11×#2549C213yesmaximal, complemented
4C11×#2505C216yesmaximal, complemented
5C11×#2450C216yesmaximal, complemented
6C11×#2368C213yesmaximal, complemented
7C11×#2349C213yesmaximal, complemented
8C4×C11×#120C213yesmaximal
9C22×C11×#95C211yesmaximal, characteristic, complemented
10C24×C4×C11C2213yes—
11C2×C11×C22⋊Q8C2213yes—
12C2×C11×C22⋊Q8C2216yes—
13C2×C11×#120C2211yescharacteristic
14C2×C4×D4×C11C2213yes—
15C2×C4×D4×C11C2216yes—
16C11×#400C2216yescomplemented
17C11×#400C2213yescomplemented
18C11×#399C2211yescharacteristic, complemented
19C11×#398C2216yescomplemented
20C11×#396C2212yescomplemented
21C11×#395C2213yescomplemented
22C11×#393C2213yescomplemented
23C11×#391C2216yescomplemented
24C11×#389C2216yescomplemented
25C11×#387C2216yescomplemented
26C11×#387C2216yescomplemented
27C11×#386C2213yes—
28C11×#386C2216yes—
29C11×#385C2216yes—
30C11×#385C2216yes—
31C11×#385C2213yes—
32C11×#385C2216yes—
33C11×#385C2216yes—
34C11×#385C2216yescomplemented
35C11×#382C2213yescomplemented
36C11×#380C2216yes—
37C11×#380C2213yes—
38C11×#380C2213yescomplemented
39C11×#379C2213yes—
40C4×C11×C4⋊C4C2213yescomplemented
41C4×C11×C22⋊C4C2216yes—
42C4×C11×C22⋊C4C2213yes—
43C2×C11×#95C2216yes—
44C2×C11×#95C2213yes—
45C2×C11×#95C2213yes—
46C2×C11×#95C2211yescharacteristic, complemented
47C25×C11C2311yescharacteristic
48C22×Q8×C11C2313yes—
49C22×D4×C11C2313yes—
50C23×C4×C11—212no—
51C23×C4×C11—412no—
52C23×C4×C11C2316yes—
53C23×C4×C11C2316yes—
54C23×C4×C11C2313yes—
55C23×C4×C11C2313yes—
56C23×C4×C11C2313yes—
57C11×C22⋊Q8—212no—
58C11×C22⋊Q8—412no—
59C11×#120Q818yescomplemented
60C4×D4×C11—212no—
61C4×D4×C11—412no—
62C2×C11×C4⋊C4C2313yes—
63C2×C11×C4⋊C4C2316yes—
64C2×C11×C4⋊C4C2313yes—
65C2×C11×C4⋊C4C2316yes—
66C2×C11×C4⋊C4C2316yes—
67C2×C11×C4⋊C4C2316yes—
68C2×C11×C4⋊C4C2316yes—
69C2×C11×C22⋊C4C2316yes—
70C2×C11×C22⋊C4C2313yes—
71C2×C11×C22⋊C4C2313yes—
72C2×C11×C22⋊C4C2316yes—
73C2×C11×C22⋊C4C2313yes—
74C2×C11×C22⋊C4C2316yes—
75C2×C11×C22⋊C4C2313yes—
76C2×C42×C11C2313yes—
77C2×C42×C11C2316yes—
78C11×#95C2311yescharacteristic
79C11×#95C2313yes—
80C11×#95C2316yes—
81C11×#95C2313yes—
82C11×#95C2311yescharacteristic
83C11×#95C2312yes—
84C11×#95C2313yes—
85C11×#95C2316yes—
86C11×#95C2316yes—
87C11×#95C2316yes—
88C11×#95C2313yes—
89C11×#95C2316yes—
90C11×#95C2316yes—
91#36572C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11—26no—
93C24×C11—26no—
94C24×C11C2×Q814yes—
95C24×C11C2411yescharacteristic
96C24×C11C2413yes—
97C2×Q8×C11—26no—
98C2×Q8×C11—46no—
99C2×D4×C11—26no—
100C2×D4×C11—26no—
101C2×D4×C11C2×Q8112yes—
102C22×C4×C11—26no—
103C22×C4×C11—212no—
104C22×C4×C11—212no—
105C22×C4×C11—212no—
106C22×C4×C11—212no—
107C22×C4×C11—26no—
108C22×C4×C11—46no—
109C22×C4×C11—46no—
110C22×C4×C11—46no—
111C22×C4×C11—46no—
112C22×C4×C11—46no—
113C22×C4×C11—448no—
114C22×C4×C11#41112yes—
115C22×C4×C11C2416yes—
116C22×C4×C11C2413yes—
117C22×C4×C11C2416yes—
118C22×C4×C11C2413yes—
119C22×C4×C11C2413yes—
120C22×C4×C11C2413yes—
121C22×C4×C11C2413yes—
122C11×C4⋊C4—26no—
123C11×C4⋊C4—26no—
124C11×C4⋊C4—212no—
125C11×C4⋊C4—46no—
126C11×C4⋊C4—46no—
127C11×C4⋊C4—46no—
128C11×C4⋊C4—46no—
129C11×C22⋊C4—26no—
130C11×C22⋊C4—212no—
131C11×C22⋊C4—212no—
132C11×C22⋊C4—26no—
133C11×C22⋊C4—26no—
134C11×C22⋊C4—46no—
135C11×C22⋊C4C2×Q8112yes—
136C42×C11—26no—
137C42×C11—46no—
138#2848C2×C1113yescomplemented
139#2564C2×C1113yescomplemented
140#2549C2×C1113yescomplemented
141#2505C2×C1116yescomplemented
142#2450C2×C1116yescomplemented
143#2368C2×C1113yescomplemented
144#2349C2×C1113yescomplemented
145C4×#120C2×C1113yes—
146C22×#95C2×C1111yescharacteristic, complemented
147C23×C11—224no—
148C23×C11—28no—
149C23×C11—224no—
150C23×C11—26no—
151C23×C11—26no—
152C23×C11—23no—
153C23×C11—23no—
154C23×C11C22×Q812yes—
155C23×C11C22×Q816yes—
156C23×C11C2×#4116yes—
157C23×C11H(5,𝔽2)16yes—
158C23×C11C2511yescharacteristic
159Q8×C11—86no—
160D4×C11—224no—
161C2×C4×C11—23no—
162C2×C4×C11—23no—
163C2×C4×C11—26no—
164C2×C4×C11—26no—
165C2×C4×C11—23no—
166C2×C4×C11—26no—
167C2×C4×C11—23no—
168C2×C4×C11—26no—
169C2×C4×C11—26no—
170C2×C4×C11—26no—
171C2×C4×C11—26no—
172C2×C4×C11—26no—
173C2×C4×C11—26no—
174C2×C4×C11—26no—
175C2×C4×C11—412no—
176C2×C4×C11—424no—
177C2×C4×C11—424no—
178C2×C4×C11—412no—
179C2×C4×C11—86no—
180C2×C4×C11C22×Q816yes—
181C2×C4×C11C2×#4116yes—
182C2×C4×C11C2×#4116yes—
183C24×C4C22×C1113yes—
184C2×C22⋊Q8C22×C1113yes—
185C2×C22⋊Q8C22×C1116yes—
186C2×#120C22×C1111yescharacteristic
187C2×C4×D4C22×C1113yes—
188C2×C4×D4C22×C1116yes—
189#400C22×C1113yescomplemented
190#400C22×C1116yescomplemented
191#399C22×C1111yescharacteristic, complemented
192#398C22×C1116yescomplemented
193#396C22×C1112yescomplemented
194#395C22×C1113yescomplemented
195#393C22×C1113yescomplemented
196#391C22×C1116yescomplemented
197#389C22×C1116yescomplemented
198#387C22×C1116yescomplemented
199#387C22×C1116yescomplemented
200#386C22×C1116yes—
201#386C22×C1113yes—
202#385C22×C1116yes—
203#385C22×C1116yes—
204#385C22×C1116yes—
205#385C22×C1113yes—
206#385C22×C1116yes—
207#385C22×C1116yescomplemented
208#382C22×C1113yescomplemented
209#380C22×C1116yes—
210#380C22×C1113yes—
211#380C22×C1113yescomplemented
212#379C22×C1113yes—
213C4×C4⋊C4C22×C1113yescomplemented
214C4×C22⋊C4C22×C1116yes—
215C4×C22⋊C4C22×C1113yes—
216C2×#95C22×C1113yes—
217C2×#95C22×C1113yes—
218C2×#95C22×C1116yes—
219C2×#95C22×C1111yescharacteristic, complemented
220C22×C11—232no—
221C22×C11—26no—
222C22×C11—212no—
223C22×C11—26no—
224C22×C11—212no—
225C22×C11—26no—
226C22×C11—41no—
227C22×C11—43no—
228C22×C11#554112yes—
229C22×C11C23×Q811yescharacteristic
230C22×C11C22×#4113yes—
231C22×C11C2×H(5,𝔽2)13yes—
232C4×C11—26no—
233C4×C11—26no—
234C4×C11—26no—
235C4×C11—43no—
236C4×C11—46no—
237C4×C11—43no—
238C4×C11—46no—
239C25C23×C1111yescharacteristic
240C22×Q8C23×C1113yes—
241C22×D4C23×C1113yes—
242C23×C4—212no—
243C23×C4—412no—
244C23×C4C23×C1116yes—
245C23×C4C23×C1116yes—
246C23×C4C23×C1113yes—
247C23×C4C23×C1113yes—
248C23×C4C23×C1113yes—
249C22⋊Q8—212no—
250C22⋊Q8—412no—
251#120Q8×C1118yescomplemented
252C4×D4—212no—
253C4×D4—412no—
254C2×C4⋊C4C23×C1113yes—
255C2×C4⋊C4C23×C1116yes—
256C2×C4⋊C4C23×C1113yes—
257C2×C4⋊C4C23×C1116yes—
258C2×C4⋊C4C23×C1116yes—
259C2×C4⋊C4C23×C1116yes—
260C2×C4⋊C4C23×C1116yes—
261C2×C22⋊C4C23×C1116yes—
262C2×C22⋊C4C23×C1113yes—
263C2×C22⋊C4C23×C1113yes—
264C2×C22⋊C4C23×C1113yes—
265C2×C22⋊C4C23×C1116yes—
266C2×C22⋊C4C23×C1116yes—
267C2×C22⋊C4C23×C1113yes—
268C2×C42C23×C1113yes—
269C2×C42C23×C1116yes—
270#95C23×C1111yescharacteristic
271#95C23×C1113yes—
272#95C23×C1116yes—
273#95C23×C1113yes—
274#95C23×C1111yescharacteristic
275#95C23×C1112yes—
276#95C23×C1113yes—
277#95C23×C1116yes—
278#95C23×C1116yes—
279#95C23×C1116yes—
280#95C23×C1113yes—
281#95C23×C1116yes—
282#95C23×C1116yes—
283C2×C11—212no—
284C2×C11—42no—
285C2×C11#344411yescharacteristic
286C2×C11C2×#55413yes—
287C2×C11#349013yes—
288C24—26no—
289C24—26no—
290C24C2×Q8×C1114yes—
291C24C24×C1111yescharacteristic
292C24C24×C1113yes—
293C2×Q8—26no—
294C2×Q8—46no—
295C2×D4—26no—
296C2×D4—26no—
297C2×D4C2×Q8×C11112yes—
298C22×C4—26no—
299C22×C4—212no—
300C22×C4—212no—
301C22×C4—212no—
302C22×C4—212no—
303C22×C4—26no—
304C22×C4—46no—
305C22×C4—46no—
306C22×C4—46no—
307C22×C4—46no—
308C22×C4—46no—
309C22×C4—448no—
310C22×C4C11×#41112yes—
311C22×C4C24×C1116yes—
312C22×C4C24×C1113yes—
313C22×C4C24×C1116yes—
314C22×C4C24×C1113yes—
315C22×C4C24×C1113yes—
316C22×C4C24×C1113yes—
317C22×C4C24×C1113yes—
318C4⋊C4—26no—
319C4⋊C4—26no—
320C4⋊C4—212no—
321C4⋊C4—46no—
322C4⋊C4—46no—
323C4⋊C4—46no—
324C4⋊C4—46no—
325C22⋊C4—26no—
326C22⋊C4—212no—
327C22⋊C4—212no—
328C22⋊C4—26no—
329C22⋊C4—26no—
330C22⋊C4—46no—
331C22⋊C4C2×Q8×C11112yes—
332C42—26no—
333C42—46no—
334C11#3657211yescharacteristic, direct product factor, Sylow
335C23—224no—
336C23—28no—
337C23—224no—
338C23—26no—
339C23—26no—
340C23—23no—
341C23—23no—
342C23C22×Q8×C1112yes—
343C23C22×Q8×C1116yes—
344C23C2×C11×#4116yes—
345C23C11×H(5,𝔽2)16yes—
346C23C25×C1111yescharacteristic
347Q8—86no—
348D4—224no—
349C2×C4—23no—
350C2×C4—23no—
351C2×C4—26no—
352C2×C4—26no—
353C2×C4—23no—
354C2×C4—26no—
355C2×C4—23no—
356C2×C4—26no—
357C2×C4—26no—
358C2×C4—26no—
359C2×C4—26no—
360C2×C4—26no—
361C2×C4—26no—
362C2×C4—26no—
363C2×C4—412no—
364C2×C4—424no—
365C2×C4—424no—
366C2×C4—412no—
367C2×C4—86no—
368C2×C4C22×Q8×C1116yes—
369C2×C4C2×C11×#4116yes—
370C2×C4C2×C11×#4116yes—
371C22—232no—
372C22—26no—
373C22—212no—
374C22—26no—
375C22—212no—
376C22—26no—
377C22—41no—
378C22—43no—
379C22C11×#554112yes—
380C22C23×Q8×C1111yescharacteristic
381C22C22×C11×#4113yes—
382C22C2×C11×H(5,𝔽2)13yes—
383C4—26no—
384C4—26no—
385C4—26no—
386C4—43no—
387C4—46no—
388C4—43no—
389C4—46no—
390C2—212no—
391C2—42no—
392C2C11×#344411yescharacteristic
393C2C2×C11×#55413yes—
394C2C11×#349013yes—
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
prime radicalC2×C11×#120C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2848C2semidirect
2. C11×#2564C2semidirect
3. C11×#2549C2semidirect
4. C11×#2505C2semidirect
5. C11×#2450C2semidirect
6. C11×#2368C2semidirect
7. C11×#2349C2semidirect
9. C22×C11×#95C2semidirect
16. C11×#400C22semidirect
17. C11×#400C22semidirect
18. C11×#399C22semidirect
19. C11×#398C22semidirect
20. C11×#396C22semidirect
21. C11×#395C22semidirect
22. C11×#393C22semidirect
23. C11×#391C22semidirect
24. C11×#389C22semidirect
25. C11×#387C22semidirect
26. C11×#387C22semidirect
34. C11×#385C22semidirect
35. C11×#382C22semidirect
38. C11×#380C22semidirect
40. C4×C11×C4⋊C4C22semidirect
46. C2×C11×#95C22semidirect
59. C11×#120Q8semidirect
91. #36572C11direct (N × H)
138. #2848C2×C11semidirect
139. #2564C2×C11semidirect
140. #2549C2×C11semidirect
141. #2505C2×C11semidirect
142. #2450C2×C11semidirect
143. #2368C2×C11semidirect
144. #2349C2×C11semidirect
146. C22×#95C2×C11semidirect
189. #400C22×C11semidirect
190. #400C22×C11semidirect
191. #399C22×C11semidirect
192. #398C22×C11semidirect
193. #396C22×C11semidirect
194. #395C22×C11semidirect
195. #393C22×C11semidirect
196. #391C22×C11semidirect
197. #389C22×C11semidirect
198. #387C22×C11semidirect
199. #387C22×C11semidirect
207. #385C22×C11semidirect
208. #382C22×C11semidirect
211. #380C22×C11semidirect
213. C4×C4⋊C4C22×C11semidirect
219. C2×#95C22×C11semidirect
251. #120Q8×C11semidirect
334. C11#36572direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28482
C11×#25642
C11×#25492
C11×#25052
C11×#24502
C11×#23682
C11×#23492
C4×C11×#1202
C22×C11×#952
#3657211