Finite Group Databasebeta

← C11×#60639 #14637832

Subgroups — C11×#60639 #14637832

Order 2816.

3314 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#575C214yesmaximal, complemented
2C2×C11×#532C212yesmaximal, complemented
3C11×#3153C218yesmaximal, complemented
4C11×#3152C214yesmaximal, complemented
5C11×#3151C214yesmaximal, complemented
6C11×#3150C214yesmaximal, complemented
7C11×#3147C214yesmaximal, complemented
8C2×C4×C11×M16C211yesmaximal, characteristic, complemented
9C22×C11×#41C2214yes—
10C11×#575—232no—
11C2×C11×#137C22116yescomplemented
12C2×C11×AGL(1,ℤ/8)C22116yescomplemented
13C2×C11×#135C22116yescomplemented
14C22×C11×M16C2212yes—
15C11×#532—24no—
16C11×#532—24no—
17C11×#532C2214yes—
18C11×#532C2214yes—
19C11×#532C2214yescomplemented
20C11×#532C2214yescomplemented
21C2×C11×C4⋊Q8C2212yescomplemented
22C2×C11×#127C2212yescomplemented
23C2×C11×#124C2214yescomplemented
24C2×C11×#121—24no—
25C2×C4×D4×C11—24no—
26C22×C42×C11C2211yescharacteristic
27C11×#497C22116yescomplemented
28C11×#496C22116yescomplemented
29C11×#495C22116yescomplemented
30C11×#494C2214yescomplemented
31C11×#493C2214yescomplemented
32C11×#492C2218yescomplemented
33C4×C11×M16C2214yescomplemented
34C4×C11×M16C2214yescomplemented
35C2×C11×#97C2212yescomplemented
36C2×C4×C8×C11C2212yescomplemented
37C2×C11×#41—24no—
38C2×C11×#41—24no—
39C2×C11×#41—232no—
40C2×C11×#41C2318yes—
41C2×C11×#41C2318yes—
42C22×Q8×C11C2314yes—
43C22×D4×C11—24no—
44C22×D4×C11—24no—
45C22×D4×C11C2314yes—
46C23×C4×C11—24no—
47C23×C4×C11D412yes—
48C23×C4×C11C2311yescharacteristic
49C11×#137—264no—
50C11×AGL(1,ℤ/8)—264no—
51C11×#135—264no—
52C2×C11×Q16C23116yes—
53C2×C11×SD16C23132yes—
54C2×C11×D8C23116yes—
55C2×C11×M16D4116yescomplemented
56C2×C11×M16C2318yes—
57C22×C8×C11C2314yes—
58C11×C4⋊Q8—24no—
59C11×C4⋊Q8C2314yes—
60C11×C4⋊Q8C2314yes—
61C11×#127—24no—
62C11×#127C2314yes—
63C11×#127C2314yes—
64C11×#124—28no—
65C11×#124C2318yes—
66C11×#124C2318yes—
67C11×#121—28no—
68C11×#121—28no—
69C11×#121—28no—
70C11×#121—28no—
71C4×D4×C11—28no—
72C4×D4×C11—28no—
73C4×D4×C11—28no—
74C4×D4×C11—28no—
75C2×C11×C4⋊C4—24no—
76C2×C11×C22⋊C4—28no—
77C2×C42×C11D414yes—
78C2×C42×C11D412yes—
79C2×C42×C11C2312yes—
80C2×C42×C11C2312yes—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C11×#97C2318yes—
84C4×C8×C11C2314yes—
85C4×C8×C11C2314yes—
86#60639C1111yesmaximal, characteristic, direct product factor, Sylow
87C24×C11—24no—
88C24×C11C2×D411yescharacteristic
89C11×#41—232no—
90C11×#41—232no—
91C11×#41—416no—
92C11×#41—416no—
93C2×Q8×C11—24no—
94C2×Q8×C11—216no—
95C2×Q8×C11C2418yes—
96C2×D4×C11—28no—
97C2×D4×C11—28no—
98C2×D4×C11—216no—
99C2×D4×C11—28no—
100C2×D4×C11—28no—
101C2×D4×C11—24no—
102C2×D4×C11—416no—
103C2×D4×C11—416no—
104C2×D4×C11C2418yes—
105C22×C4×C11—24no—
106C22×C4×C11—28no—
107C22×C4×C11—28no—
108C22×C4×C11—44no—
109C22×C4×C11—416no—
110C22×C4×C11C2×D414yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D414yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D418yes—
117C22×C4×C11C2412yes—
118C22×C4×C11C2411yescharacteristic
119C11×Q16—232no—
120C11×SD16—264no—
121C11×D8—232no—
122C11×M16C2×D4132yescomplemented
123C2×C8×C11C2×D4116yescomplemented
124C2×C8×C11C2418yes—
125C11×C4⋊C4—28no—
126C11×C4⋊C4—28no—
127C11×C22⋊C4—216no—
128C11×C22⋊C4—216no—
129C42×C11C2×D414yes—
130C42×C11C2×D414yes—
131C42×C11C2×D412yes—
132C42×C11C2×D412yes—
133C42×C11C2411yescharacteristic
134C42×C11C2411yescharacteristic
135C42×C11C2412yes—
136C2×#575C2×C1114yescomplemented
137C2×#532C2×C1112yescomplemented
138#3153C2×C1118yescomplemented
139#3152C2×C1114yescomplemented
140#3151C2×C1114yescomplemented
141#3150C2×C1114yescomplemented
142#3147C2×C1114yescomplemented
143C2×C4×M16C2×C1111yescharacteristic, complemented
144C23×C11—28no—
145C23×C11—42no—
146C23×C11—416no—
147C23×C11—48no—
148C23×C11#12714yes—
149C23×C11C22×D412yes—
150C23×C11C22×D411yescharacteristic
151Q8×C11—216no—
152Q8×C11—48no—
153D4×C11—216no—
154D4×C11—416no—
155D4×C11—416no—
156D4×C11—416no—
157D4×C11—48no—
158D4×C11—416no—
159C2×C4×C11—24no—
160C2×C4×C11—28no—
161C2×C4×C11—28no—
162C2×C4×C11—44no—
163C2×C4×C11—42no—
164C2×C4×C11—48no—
165C2×C4×C11—416no—
166C2×C4×C11—416no—
167C2×C4×C11#12718yes—
168C2×C4×C11#12714yes—
169C2×C4×C11C22×D412yes—
170C2×C4×C11C22×D414yes—
171C2×C4×C11C22×D412yes—
172C2×C4×C11C22×D414yes—
173C2×C4×C11C22×D418yes—
174C2×C4×C11C22×D412yes—
175C2×C4×C11C22×D411yescharacteristic
176C2×C4×C11C2511yescharacteristic
177C8×C11C22×D4116yes—
178C22×#41C22×C1114yes—
179#575—232no—
180C2×#137C22×C11116yescomplemented
181C2×AGL(1,ℤ/8)C22×C11116yescomplemented
182C2×#135C22×C11116yescomplemented
183C22×M16C22×C1112yes—
184#532—24no—
185#532—24no—
186#532C22×C1114yes—
187#532C22×C1114yes—
188#532C22×C1114yescomplemented
189#532C22×C1114yescomplemented
190C2×C4⋊Q8C22×C1112yescomplemented
191C2×#127C22×C1112yescomplemented
192C2×#124C22×C1114yescomplemented
193C2×#121—24no—
194C2×C4×D4—24no—
195C22×C42C22×C1111yescharacteristic
196#497C22×C11116yescomplemented
197#496C22×C11116yescomplemented
198#495C22×C11116yescomplemented
199#494C22×C1114yescomplemented
200#493C22×C1114yescomplemented
201#492C22×C1118yescomplemented
202C4×M16C22×C1114yescomplemented
203C4×M16C22×C1114yescomplemented
204C2×#97C22×C1112yescomplemented
205C2×C4×C8C22×C1112yescomplemented
206C22×C11—24no—
207C22×C11—22no—
208C22×C11—44no—
209C22×C11—48no—
210C22×C11—416no—
211C22×C11—816no—
212C22×C11C2×#12714yes—
213C22×C11C2×#12712yes—
214C22×C11C23×D411yescharacteristic
215C4×C11—22no—
216C4×C11—24no—
217C4×C11—48no—
218C4×C11C2×#12712yes—
219C4×C11C2×#12714yes—
220C4×C11#57514yescomplemented
221C4×C11C23×D412yes—
222C2×#41—24no—
223C2×#41—24no—
224C2×#41—232no—
225C2×#41C23×C1118yes—
226C2×#41C23×C1118yes—
227C22×Q8C23×C1114yes—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4C23×C1114yes—
231C23×C4—24no—
232C23×C4D4×C1112yes—
233C23×C4C23×C1111yescharacteristic
234#137—264no—
235AGL(1,ℤ/8)—264no—
236#135—264no—
237C2×Q16C23×C11116yes—
238C2×SD16C23×C11132yes—
239C2×D8C23×C11116yes—
240C2×M16D4×C11116yescomplemented
241C2×M16C23×C1118yes—
242C22×C8C23×C1114yes—
243C4⋊Q8—24no—
244C4⋊Q8C23×C1114yes—
245C4⋊Q8C23×C1114yes—
246#127—24no—
247#127C23×C1114yes—
248#127C23×C1114yes—
249#124—28no—
250#124C23×C1118yes—
251#124C23×C1118yes—
252#121—28no—
253#121—28no—
254#121—28no—
255#121—28no—
256C4×D4—28no—
257C4×D4—28no—
258C4×D4—28no—
259C4×D4—28no—
260C2×C4⋊C4—24no—
261C2×C22⋊C4—28no—
262C2×C42D4×C1114yes—
263C2×C42D4×C1112yes—
264C2×C42C23×C1112yes—
265C2×C42C23×C1112yes—
266C2×C42C23×C1111yescharacteristic
267C2×C42C23×C1111yescharacteristic
268#97C23×C1118yes—
269C4×C8C23×C1114yes—
270C4×C8C23×C1114yes—
271C2×C11—24no—
272C2×C11—22no—
273C2×C11—88no—
274C2×C11C22×#12711yescharacteristic
275C2×C11C2×#57512yes—
276C24—24no—
277C24C2×D4×C1111yescharacteristic
278#41—232no—
279#41—232no—
280#41—416no—
281#41—416no—
282C2×Q8—24no—
283C2×Q8—216no—
284C2×Q8C24×C1118yes—
285C2×D4—28no—
286C2×D4—28no—
287C2×D4—216no—
288C2×D4—28no—
289C2×D4—28no—
290C2×D4—24no—
291C2×D4—416no—
292C2×D4—416no—
293C2×D4C24×C1118yes—
294C22×C4—24no—
295C22×C4—28no—
296C22×C4—28no—
297C22×C4—44no—
298C22×C4—416no—
299C22×C4C2×D4×C1114yes—
300C22×C4C2×D4×C1112yes—
301C22×C4C2×D4×C1114yes—
302C22×C4C2×D4×C1112yes—
303C22×C4C2×D4×C1112yes—
304C22×C4C2×D4×C1111yescharacteristic
305C22×C4C2×D4×C1118yes—
306C22×C4C24×C1111yescharacteristic
307C22×C4C24×C1112yes—
308Q16—232no—
309SD16—264no—
310D8—232no—
311M16C2×D4×C11132yescomplemented
312C2×C8C2×D4×C11116yescomplemented
313C2×C8C24×C1118yes—
314C4⋊C4—28no—
315C4⋊C4—28no—
316C22⋊C4—216no—
317C22⋊C4—216no—
318C42C2×D4×C1112yes—
319C42C2×D4×C1112yes—
320C42C2×D4×C1114yes—
321C42C2×D4×C1114yes—
322C42C24×C1111yescharacteristic
323C42C24×C1111yescharacteristic
324C42C24×C1112yes—
325C11#6063911yescharacteristic, direct product factor, Sylow
326C23—28no—
327C23—42no—
328C23—416no—
329C23—48no—
330C23C11×#12714yes—
331C23C22×D4×C1112yes—
332C23C22×D4×C1111yescharacteristic
333Q8—216no—
334Q8—48no—
335D4—216no—
336D4—416no—
337D4—416no—
338D4—416no—
339D4—48no—
340D4—416no—
341C2×C4—24no—
342C2×C4—28no—
343C2×C4—28no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—48no—
347C2×C4—416no—
348C2×C4—416no—
349C2×C4C11×#12718yes—
350C2×C4C11×#12714yes—
351C2×C4C22×D4×C1112yes—
352C2×C4C22×D4×C1114yes—
353C2×C4C22×D4×C1112yes—
354C2×C4C22×D4×C1111yescharacteristic
355C2×C4C22×D4×C1114yes—
356C2×C4C22×D4×C1118yes—
357C2×C4C22×D4×C1112yes—
358C2×C4C25×C1111yescharacteristic
359C8C22×D4×C11116yes—
360C22—24no—
361C22—22no—
362C22—44no—
363C22—48no—
364C22—416no—
365C22—816no—
366C22C2×C11×#12714yes—
367C22C2×C11×#12712yes—
368C22C23×D4×C1111yescharacteristic
369C4—24no—
370C4—22no—
371C4—48no—
372C4C2×C11×#12712yes—
373C4C2×C11×#12714yes—
374C4C11×#57514yescomplemented
375C4C23×D4×C1112yes—
376C2—24no—
377C2—22no—
378C2—88no—
379C2C22×C11×#12711yescharacteristic
380C2C2×C11×#57512yes—
subgroupG/H
centerC2×C4×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
socleC22×C11C23×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#575C2semidirect
2. C2×C11×#532C2semidirect
3. C11×#3153C2semidirect
4. C11×#3152C2semidirect
5. C11×#3151C2semidirect
6. C11×#3150C2semidirect
7. C11×#3147C2semidirect
8. C2×C4×C11×M16C2semidirect
11. C2×C11×#137C22semidirect
12. C2×C11×AGL(1,ℤ/8)C22semidirect
13. C2×C11×#135C22semidirect
19. C11×#532C22semidirect
20. C11×#532C22semidirect
21. C2×C11×C4⋊Q8C22semidirect
22. C2×C11×#127C22semidirect
23. C2×C11×#124C22semidirect
27. C11×#497C22semidirect
28. C11×#496C22semidirect
29. C11×#495C22semidirect
30. C11×#494C22semidirect
31. C11×#493C22semidirect
32. C11×#492C22semidirect
33. C4×C11×M16C22semidirect
34. C4×C11×M16C22semidirect
35. C2×C11×#97C22semidirect
36. C2×C4×C8×C11C22semidirect
55. C2×C11×M16D4semidirect
86. #60639C11direct (N × H)
122. C11×M16C2×D4semidirect
123. C2×C8×C11C2×D4semidirect
136. C2×#575C2×C11semidirect
137. C2×#532C2×C11semidirect
138. #3153C2×C11semidirect
139. #3152C2×C11semidirect
140. #3151C2×C11semidirect
141. #3150C2×C11semidirect
142. #3147C2×C11semidirect
143. C2×C4×M16C2×C11semidirect
180. C2×#137C22×C11semidirect
181. C2×AGL(1,ℤ/8)C22×C11semidirect
182. C2×#135C22×C11semidirect
188. #532C22×C11semidirect
189. #532C22×C11semidirect
190. C2×C4⋊Q8C22×C11semidirect
191. C2×#127C22×C11semidirect
192. C2×#124C22×C11semidirect
196. #497C22×C11semidirect
197. #496C22×C11semidirect
198. #495C22×C11semidirect
199. #494C22×C11semidirect
200. #493C22×C11semidirect
201. #492C22×C11semidirect
202. C4×M16C22×C11semidirect
203. C4×M16C22×C11semidirect
204. C2×#97C22×C11semidirect
205. C2×C4×C8C22×C11semidirect
220. C4×C11#575semidirect
240. C2×M16D4×C11semidirect
311. M16C2×D4×C11semidirect
312. C2×C8C2×D4×C11semidirect
325. C11#60639direct (N × H)
374. C4C11×#575semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5752
C2×C11×#5322
C11×#31532
C11×#31522
C11×#31512
C11×#31502
C11×#31472
C2×C4×C11×M162
#6063911