Finite Group Databasebeta

← C11×#60643 #14637836

Subgroups — C11×#60643 #14637836

Order 2816.

3194 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#575C212yesmaximal, complemented
2C22×C11×#135C212yesmaximal, complemented
3C11×#3449C212yesmaximal, complemented
4C11×#3156C214yesmaximal, complemented
5C11×#3155C214yesmaximal, complemented
6C11×#3154C218yesmaximal, complemented
7C11×#3150C214yesmaximal, complemented
8C11×#3147C214yesmaximal, complemented
9C2×C11×#405C211yesmaximal, characteristic, complemented
10C22×C11×#41C2214yes—
11C11×#575—216no—
12C2×C11×#137C2218yescomplemented
13C2×C11×AGL(1,ℤ/8)C2218yescomplemented
14C2×C11×#135—216no—
15C2×C11×#135C2214yes—
16C2×C11×#135C2214yes—
17C2×C11×#135C2214yescomplemented
18C2×C11×#135C2218yescomplemented
19C2×C11×#135C2214yescomplemented
20C22×C11×Q16C2212yescomplemented
21C22×C11×SD16C2214yescomplemented
22C22×C11×D8C2212yescomplemented
23C22×C11×M16C2211yescharacteristic
24C23×C8×C11C2211yescharacteristic
25C11×#537—24no—
26C11×#536C2218yescomplemented
27C11×#535C2218yescomplemented
28C11×#534—24no—
29C11×#532C2218yescomplemented
30C11×#525—28no—
31C2×C11×#117C2211yescharacteristic
32C11×#497C22116yescomplemented
33C11×#496C22116yescomplemented
34C11×#495C2218yescomplemented
35C11×#495C2218yescomplemented
36C11×#494C2214yescomplemented
37C11×#493C2214yescomplemented
38C11×#492C2218yescomplemented
39C11×#405C2214yescomplemented
40C11×#405C2214yescomplemented
41C2×C11×#97C2212yescomplemented
42C2×C4×C8×C11C2212yescomplemented
43C2×C11×#41—24no—
44C2×C11×#41—24no—
45C2×C11×#41—216no—
46C2×C11×#41—216no—
47C2×C11×#41C2318yes—
48C2×C11×#41C2318yes—
49C22×Q8×C11C2314yes—
50C22×D4×C11—24no—
51C22×D4×C11C2314yes—
52C23×C4×C11—24no—
53C23×C4×C11C2311yescharacteristic
54C11×#137—232no—
55C11×AGL(1,ℤ/8)—232no—
56C11×#135—216no—
57C11×#135—216no—
58C11×#135—216no—
59C11×#135—216no—
60C11×#135—232no—
61C2×C11×Q16—28no—
62C2×C11×Q16C2314yes—
63C2×C11×Q16C2318yes—
64C2×C11×Q16C2314yes—
65C2×C11×SD16—216no—
66C2×C11×SD16C2318yes—
67C2×C11×SD16C23116yes—
68C2×C11×SD16C2318yes—
69C2×C11×D8—28no—
70C2×C11×D8C2314yes—
71C2×C11×D8C2318yes—
72C2×C11×D8C2314yes—
73C2×C11×M16D418yescomplemented
74C2×C11×M16C2314yes—
75C22×C8×C11D418yescomplemented
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2312yes—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2312yes—
80C22×C8×C11C2312yes—
81C11×C4⋊Q8C2318yes—
82C11×#127C2318yes—
83C11×#124C23116yes—
84C11×#123—216no—
85C11×C22⋊Q8—216no—
86C11×#121—216no—
87C11×#121—216no—
88C11×#120—216no—
89C4×D4×C11—216no—
90C11×#117D414yes—
91C11×#117C2314yes—
92C2×C11×C4⋊C4D412yes—
93C2×C11×C22⋊C4D412yes—
94C2×C42×C11C2312yes—
95C11×#97C2318yes—
96C4×C8×C11C2314yes—
97C4×C8×C11C2314yes—
98#60643C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11—24no—
100C24×C11C2×D411yescharacteristic
101C11×#41—216no—
102C11×#41—216no—
103C11×#41—216no—
104C11×#41—216no—
105C11×#41—416no—
106C11×#41—416no—
107C2×Q8×C11—24no—
108C2×Q8×C11—28no—
109C2×Q8×C11—28no—
110C2×Q8×C11C2418yes—
111C2×D4×C11—28no—
112C2×D4×C11—28no—
113C2×D4×C11—28no—
114C2×D4×C11—28no—
115C2×D4×C11—24no—
116C2×D4×C11—216no—
117C2×D4×C11—416no—
118C2×D4×C11C2418yes—
119C22×C4×C11—24no—
120C22×C4×C11—28no—
121C22×C4×C11—28no—
122C22×C4×C11—416no—
123C22×C4×C11C2×D414yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D414yes—
127C22×C4×C11C2×D414yes—
128C22×C4×C11C2412yes—
129C22×C4×C11C2411yescharacteristic
130C11×Q16—28no—
131C11×Q16—28no—
132C11×Q16—216no—
133C11×SD16—216no—
134C11×SD16—216no—
135C11×SD16—232no—
136C11×D8—28no—
137C11×D8—28no—
138C11×D8—216no—
139C11×M16C2×D4116yes—
140C2×C8×C11C2×D418yes—
141C2×C8×C11C2×D418yes—
142C2×C8×C11C2×D414yes—
143C2×C8×C11C2×D414yes—
144C2×C8×C11C2×D418yes—
145C2×C8×C11C2411yescharacteristic
146C2×C8×C11C2411yescharacteristic
147C2×C8×C11C2414yes—
148C2×C8×C11C2412yes—
149C11×C4⋊C4—216no—
150C11×C4⋊C4C2×D418yes—
151C11×C22⋊C4—232no—
152C11×C22⋊C4C2×D418yes—
153C42×C11C2×D414yes—
154C42×C11C2414yes—
155C2×#575C2×C1112yescomplemented
156C22×#135C2×C1112yescomplemented
157#3449C2×C1112yescomplemented
158#3156C2×C1114yescomplemented
159#3155C2×C1114yescomplemented
160#3154C2×C1118yescomplemented
161#3150C2×C1114yescomplemented
162#3147C2×C1114yescomplemented
163C2×#405C2×C1111yescharacteristic, complemented
164C23×C11—28no—
165C23×C11—42no—
166C23×C11—48no—
167C23×C11—88no—
168C23×C11#12714yes—
169C23×C11C22×D412yes—
170C23×C11C22×D411yescharacteristic
171Q8×C11—28no—
172Q8×C11—28no—
173Q8×C11—48no—
174D4×C11—28no—
175D4×C11—28no—
176D4×C11—416no—
177D4×C11—416no—
178D4×C11—48no—
179D4×C11—816no—
180C2×C4×C11—28no—
181C2×C4×C11—44no—
182C2×C4×C11—48no—
183C2×C4×C11—416no—
184C2×C4×C11—416no—
185C2×C4×C11#12718yes—
186C2×C4×C11#12714yes—
187C2×C4×C11C22×D418yes—
188C2×C4×C11C22×D412yes—
189C2×C4×C11C22×D414yes—
190C2×C4×C11C22×D412yes—
191C2×C4×C11C22×D412yes—
192C2×C4×C11C22×D414yes—
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C2511yescharacteristic
195C8×C11C22×D412yes—
196C8×C11C22×D414yes—
197C8×C11C22×D412yes—
198C8×C11C22×D418yes—
199C22×#41C22×C1114yes—
200#575—216no—
201C2×#137C22×C1118yescomplemented
202C2×AGL(1,ℤ/8)C22×C1118yescomplemented
203C2×#135—216no—
204C2×#135C22×C1114yes—
205C2×#135C22×C1114yes—
206C2×#135C22×C1114yescomplemented
207C2×#135C22×C1118yescomplemented
208C2×#135C22×C1114yescomplemented
209C22×Q16C22×C1112yescomplemented
210C22×SD16C22×C1114yescomplemented
211C22×D8C22×C1112yescomplemented
212C22×M16C22×C1111yescharacteristic
213C23×C8C22×C1111yescharacteristic
214#537—24no—
215#536C22×C1118yescomplemented
216#535C22×C1118yescomplemented
217#534—24no—
218#532C22×C1118yescomplemented
219#525—28no—
220C2×#117C22×C1111yescharacteristic
221#497C22×C11116yescomplemented
222#496C22×C11116yescomplemented
223#495C22×C1118yescomplemented
224#495C22×C1118yescomplemented
225#494C22×C1114yescomplemented
226#493C22×C1114yescomplemented
227#492C22×C1118yescomplemented
228#405C22×C1114yescomplemented
229#405C22×C1114yescomplemented
230C2×#97C22×C1112yescomplemented
231C2×C4×C8C22×C1112yescomplemented
232C22×C11—22no—
233C22×C11—24no—
234C22×C11—44no—
235C22×C11—416no—
236C22×C11—48no—
237C22×C11—816no—
238C22×C11C2×#12714yes—
239C22×C11C2×#12712yes—
240C22×C11C23×D411yescharacteristic
241C4×C11—28no—
242C4×C11—48no—
243C4×C11C2×#12712yes—
244C4×C11C2×#12714yes—
245C4×C11C23×D411yescharacteristic
246C4×C11C23×D411yescharacteristic
247C2×#41—24no—
248C2×#41—24no—
249C2×#41—216no—
250C2×#41—216no—
251C2×#41C23×C1118yes—
252C2×#41C23×C1118yes—
253C22×Q8C23×C1114yes—
254C22×D4—24no—
255C22×D4C23×C1114yes—
256C23×C4—24no—
257C23×C4C23×C1111yescharacteristic
258#137—232no—
259AGL(1,ℤ/8)—232no—
260#135—216no—
261#135—216no—
262#135—216no—
263#135—216no—
264#135—232no—
265C2×Q16—28no—
266C2×Q16C23×C1114yes—
267C2×Q16C23×C1114yes—
268C2×Q16C23×C1118yes—
269C2×SD16—216no—
270C2×SD16C23×C1118yes—
271C2×SD16C23×C1118yes—
272C2×SD16C23×C11116yes—
273C2×D8—28no—
274C2×D8C23×C1114yes—
275C2×D8C23×C1114yes—
276C2×D8C23×C1118yes—
277C2×M16D4×C1118yescomplemented
278C2×M16C23×C1114yes—
279C22×C8D4×C1118yescomplemented
280C22×C8C23×C1112yes—
281C22×C8C23×C1112yes—
282C22×C8C23×C1111yescharacteristic
283C22×C8C23×C1111yescharacteristic
284C22×C8C23×C1112yes—
285C4⋊Q8C23×C1118yes—
286#127C23×C1118yes—
287#124C23×C11116yes—
288#123—216no—
289C22⋊Q8—216no—
290#121—216no—
291#121—216no—
292#120—216no—
293C4×D4—216no—
294#117D4×C1114yes—
295#117C23×C1114yes—
296C2×C4⋊C4D4×C1112yes—
297C2×C22⋊C4D4×C1112yes—
298C2×C42C23×C1112yes—
299#97C23×C1118yes—
300C4×C8C23×C1114yes—
301C4×C8C23×C1114yes—
302C2×C11—24no—
303C2×C11—22no—
304C2×C11—88no—
305C2×C11C22×#12711yescharacteristic
306C2×C11#358412yes—
307C24—24no—
308C24C2×D4×C1111yescharacteristic
309#41—216no—
310#41—216no—
311#41—216no—
312#41—216no—
313#41—416no—
314#41—416no—
315C2×Q8—24no—
316C2×Q8—28no—
317C2×Q8—28no—
318C2×Q8C24×C1118yes—
319C2×D4—28no—
320C2×D4—28no—
321C2×D4—28no—
322C2×D4—28no—
323C2×D4—24no—
324C2×D4—216no—
325C2×D4—416no—
326C2×D4C24×C1118yes—
327C22×C4—24no—
328C22×C4—28no—
329C22×C4—28no—
330C22×C4—416no—
331C22×C4C2×D4×C1114yes—
332C22×C4C2×D4×C1111yescharacteristic
333C22×C4C2×D4×C1112yes—
334C22×C4C2×D4×C1114yes—
335C22×C4C2×D4×C1114yes—
336C22×C4C24×C1111yescharacteristic
337C22×C4C24×C1112yes—
338Q16—28no—
339Q16—28no—
340Q16—216no—
341SD16—216no—
342SD16—216no—
343SD16—232no—
344D8—28no—
345D8—28no—
346D8—216no—
347M16C2×D4×C11116yes—
348C2×C8C2×D4×C1118yes—
349C2×C8C2×D4×C1118yes—
350C2×C8C2×D4×C1114yes—
351C2×C8C2×D4×C1114yes—
352C2×C8C2×D4×C1118yes—
353C2×C8C24×C1111yescharacteristic
354C2×C8C24×C1111yescharacteristic
355C2×C8C24×C1114yes—
356C2×C8C24×C1112yes—
357C4⋊C4—216no—
358C4⋊C4C2×D4×C1118yes—
359C22⋊C4—232no—
360C22⋊C4C2×D4×C1118yes—
361C42C2×D4×C1114yes—
362C42C24×C1114yes—
363C11#6064311yescharacteristic, direct product factor, Sylow
364C23—28no—
365C23—42no—
366C23—48no—
367C23—88no—
368C23C11×#12714yes—
369C23C22×D4×C1112yes—
370C23C22×D4×C1111yescharacteristic
371Q8—28no—
372Q8—28no—
373Q8—48no—
374D4—28no—
375D4—28no—
376D4—416no—
377D4—416no—
378D4—48no—
379D4—816no—
380C2×C4—28no—
381C2×C4—44no—
382C2×C4—48no—
383C2×C4—416no—
384C2×C4—416no—
385C2×C4C11×#12718yes—
386C2×C4C11×#12714yes—
387C2×C4C22×D4×C1118yes—
388C2×C4C22×D4×C1112yes—
389C2×C4C22×D4×C1111yescharacteristic
390C2×C4C22×D4×C1114yes—
391C2×C4C22×D4×C1112yes—
392C2×C4C22×D4×C1112yes—
393C2×C4C22×D4×C1114yes—
394C2×C4C25×C1111yescharacteristic
395C8C22×D4×C1112yes—
396C8C22×D4×C1114yes—
397C8C22×D4×C1112yes—
398C8C22×D4×C1118yes—
399C22—22no—
400C22—24no—
401C22—44no—
402C22—48no—
403C22—416no—
404C22—816no—
405C22C2×C11×#12714yes—
406C22C2×C11×#12712yes—
407C22C23×D4×C1111yescharacteristic
408C4—28no—
409C4—48no—
410C4C2×C11×#12712yes—
411C4C2×C11×#12714yes—
412C4C23×D4×C1111yescharacteristic
413C4C23×D4×C1111yescharacteristic
414C2—24no—
415C2—22no—
416C2—88no—
417C2C22×C11×#12711yescharacteristic
418C2C11×#358412yes—
subgroupG/H
centerC2×C4×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
socleC22×C11C23×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#575C2semidirect
2. C22×C11×#135C2semidirect
3. C11×#3449C2semidirect
4. C11×#3156C2semidirect
5. C11×#3155C2semidirect
6. C11×#3154C2semidirect
7. C11×#3150C2semidirect
8. C11×#3147C2semidirect
9. C2×C11×#405C2semidirect
12. C2×C11×#137C22semidirect
13. C2×C11×AGL(1,ℤ/8)C22semidirect
17. C2×C11×#135C22semidirect
18. C2×C11×#135C22semidirect
19. C2×C11×#135C22semidirect
20. C22×C11×Q16C22semidirect
21. C22×C11×SD16C22semidirect
22. C22×C11×D8C22semidirect
26. C11×#536C22semidirect
27. C11×#535C22semidirect
29. C11×#532C22semidirect
32. C11×#497C22semidirect
33. C11×#496C22semidirect
34. C11×#495C22semidirect
35. C11×#495C22semidirect
36. C11×#494C22semidirect
37. C11×#493C22semidirect
38. C11×#492C22semidirect
39. C11×#405C22semidirect
40. C11×#405C22semidirect
41. C2×C11×#97C22semidirect
42. C2×C4×C8×C11C22semidirect
73. C2×C11×M16D4semidirect
75. C22×C8×C11D4semidirect
98. #60643C11direct (N × H)
155. C2×#575C2×C11semidirect
156. C22×#135C2×C11semidirect
157. #3449C2×C11semidirect
158. #3156C2×C11semidirect
159. #3155C2×C11semidirect
160. #3154C2×C11semidirect
161. #3150C2×C11semidirect
162. #3147C2×C11semidirect
163. C2×#405C2×C11semidirect
201. C2×#137C22×C11semidirect
202. C2×AGL(1,ℤ/8)C22×C11semidirect
206. C2×#135C22×C11semidirect
207. C2×#135C22×C11semidirect
208. C2×#135C22×C11semidirect
209. C22×Q16C22×C11semidirect
210. C22×SD16C22×C11semidirect
211. C22×D8C22×C11semidirect
215. #536C22×C11semidirect
216. #535C22×C11semidirect
218. #532C22×C11semidirect
221. #497C22×C11semidirect
222. #496C22×C11semidirect
223. #495C22×C11semidirect
224. #495C22×C11semidirect
225. #494C22×C11semidirect
226. #493C22×C11semidirect
227. #492C22×C11semidirect
228. #405C22×C11semidirect
229. #405C22×C11semidirect
230. C2×#97C22×C11semidirect
231. C2×C4×C8C22×C11semidirect
277. C2×M16D4×C11semidirect
279. C22×C8D4×C11semidirect
363. C11#60643direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5752
C22×C11×#1352
C11×#34492
C11×#31562
C11×#31552
C11×#31542
C11×#31502
C11×#31472
C2×C11×#4052
#6064311