Finite Group Databasebeta

← C11×#61933 #14639126

Subgroups — C11×#61933 #14639126

Order 2816.

1754 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3556C211yesmaximal, characteristic, complemented
2C11×#3508C211yesmaximal, characteristic
3C11×#3400C214yesmaximal, complemented
4C11×#3392C214yesmaximal, complemented
5C11×#3368C214yesmaximal, complemented
6C11×#3365C214yesmaximal, complemented
7C11×#3222C214yesmaximal, complemented
8C11×#3208C212yesmaximal, complemented
9C11×#3123C214yesmaximal, complemented
10C11×#3107C212yesmaximal, complemented
11C11×#2986C211yesmaximal, characteristic, complemented
12C11×#564—22no—
13C11×#559C2214yes—
14C11×#557—22no—
15C11×#557C2214yescomplemented
16C11×#557C2214yescomplemented
17C11×#550C2214yes—
18C11×#546—24no—
19C11×#541—24no—
20C11×#541C2214yes—
21C11×#540—22no—
22C11×#535C2212yes—
23C11×#533C2212yes—
24C11×#533C2211yescharacteristic
25C11×#532—22no—
26C2×C11×#127C2211yescharacteristic
27C11×#518C2212yes—
28C4×C11×#41C2211yescharacteristic
29C11×#497C2214yescomplemented
30C11×#492C2214yes—
31C11×#492C2214yescomplemented
32C11×#490C2214yescomplemented
33C11×#488C2214yescomplemented
34C11×#486C2214yes—
35C11×#485C2214yes—
36C11×#478C2218yescomplemented
37C11×#475C2212yescomplemented
38C11×#474C2212yescomplemented
39C11×#464C2218yescomplemented
40C11×#462C2212yescomplemented
41C11×#461C2212yescomplemented
42C11×#461C2218yescomplemented
43C11×#460C2214yes—
44C11×#460C2214yes—
45C11×#460C2218yescomplemented
46C11×#452C2214yes—
47C11×#450C2218yes—
48C11×#446C2214yescomplemented
49C8×Q8×C11C2214yescomplemented
50C11×#440C2218yescomplemented
51C4×C11×Q16C2214yescomplemented
52C4×C11×SD16C2214yescomplemented
53C4×C11×SD16C2218yescomplemented
54C11×#433C2214yes—
55C11×#431C2212yes—
56C2×C11×#41—24no—
57C2×C11×#41C2311yescharacteristic
58C22×D4×C11—22no—
59C22×D4×C11C2312yes—
60C2×C11×Q16C2314yes—
61C2×C11×SD16C2318yes—
62C2×C11×SD16C2318yes—
63C2×C11×SD16C2314yes—
64C11×C4⋊Q8—24no—
65C11×C4⋊Q8D412yes—
66C11×C4⋊Q8C2312yes—
67C11×C4⋊Q8C2314yes—
68C11×C4⋊Q8C2312yes—
69C11×#127—21no—
70C11×#127—21no—
71C11×#127C2314yes—
72C11×#127C2314yes—
73C11×#126—28no—
74C11×#125—24no—
75C11×#125—28no—
76C11×#125—28no—
77C11×#125—28no—
78C11×#125—22no—
79C11×#125D412yes—
80C11×#125C2314yes—
81C11×#124—24no—
82C11×#124C2314yes—
83C11×#123—28no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8D414yes—
86C11×C22⋊Q8C2314yes—
87C11×#121—24no—
88C11×#121—24no—
89C11×#121—28no—
90C11×#120—24no—
91C4×Q8×C11—24no—
92C4×Q8×C11—24no—
93C4×Q8×C11—22no—
94C4×Q8×C11C2312yes—
95C4×Q8×C11C2314yes—
96C4×Q8×C11C2318yes—
97C4×Q8×C11C2314yes—
98C4×D4×C11—22no—
99C4×D4×C11—24no—
100C4×D4×C11—24no—
101C4×D4×C11C2312yes—
102C4×D4×C11C2318yes—
103C11×#117—22no—
104C11×#117—21no—
105C11×#117C2311yescharacteristic
106C11×#117C2312yes—
107C2×C11×C22⋊C4—24no—
108C2×C42×C11—21no—
109C2×C42×C11C2311yescharacteristic
110C11×#107C2314yes—
111C11×#106C2314yes—
112C11×C4⋊C8C2312yes—
113C11×C4⋊C8C2312yes—
114C11×C4⋊C8C2318yes—
115C11×#103C2314yes—
116C11×#103C2314yes—
117C11×#103C2314yes—
118C11×#102C2314yes—
119C11×#102C2318yes—
120C11×#102C2318yes—
121C11×C22⋊C8C2314yes—
122C11×#97C2314yes—
123C4×C8×C11C2314yes—
124C4×C8×C11C2314yes—
125#61933C1111yesmaximal, characteristic, direct product factor, Sylow
126C24×C11—22no—
127C11×#41—42no—
128C11×#41—88no—
129C2×Q8×C11—22no—
130C2×Q8×C11C2×D414yes—
131C2×Q8×C11C2411yescharacteristic
132C2×Q8×C11C2414yes—
133C2×D4×C11—21no—
134C2×D4×C11—22no—
135C2×D4×C11—24no—
136C2×D4×C11—28no—
137C2×D4×C11—24no—
138C2×D4×C11—44no—
139C2×D4×C11—84no—
140C2×D4×C11C2414yes—
141C2×D4×C11C2411yescharacteristic
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—28no—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2411yescharacteristic
147C11×Q16—44no—
148C11×SD16—48no—
149C11×SD16—48no—
150C11×SD16—44no—
151C2×C8×C11C2414yes—
152C2×C8×C11C2414yes—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—28no—
159C11×C4⋊C4—28no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—28no—
162C11×C4⋊C4C2×D414yes—
163C11×C4⋊C4C2×D414yes—
164C11×C4⋊C4C2×D418yes—
165C11×C4⋊C4C2414yes—
166C11×C4⋊C4C2412yes—
167C11×C22⋊C4—21no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—28no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—28no—
172C11×C22⋊C4C2×D414yes—
173C42×C11—21no—
174C42×C11—22no—
175C42×C11—24no—
176C42×C11—28no—
177C42×C11C2×D411yescharacteristic
178C42×C11C2×D411yescharacteristic
179C42×C11C2412yes—
180C42×C11C2414yes—
181#3556C2×C1111yescharacteristic, complemented
182#3508C2×C1111yescharacteristic
183#3400C2×C1114yescomplemented
184#3392C2×C1114yescomplemented
185#3368C2×C1114yescomplemented
186#3365C2×C1114yescomplemented
187#3222C2×C1114yescomplemented
188#3208C2×C1112yescomplemented
189#3123C2×C1114yescomplemented
190#3107C2×C1112yescomplemented
191#2986C2×C1111yescharacteristic, complemented
192C23×C11—24no—
193C23×C11—21no—
194C23×C11—44no—
195C23×C11—84no—
196C23×C11C22×D411yescharacteristic
197Q8×C11—28no—
198Q8×C11—24no—
199Q8×C11—24no—
200Q8×C11—22no—
201Q8×C11—44no—
202D4×C11—28no—
203D4×C11—22no—
204D4×C11—44no—
205D4×C11—42no—
206D4×C11—48no—
207D4×C11—84no—
208D4×C11—88no—
209C2×C4×C11—24no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—21no—
214C2×C4×C11—22no—
215C2×C4×C11—42no—
216C2×C4×C11—44no—
217C2×C4×C11—88no—
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×D418yes—
220C2×C4×C11C22×D412yes—
221C2×C4×C11C22×D412yes—
222C2×C4×C11C2511yescharacteristic
223C8×C11—24no—
224C8×C11—24no—
225#564—22no—
226#559C22×C1114yes—
227#557—22no—
228#557C22×C1114yescomplemented
229#557C22×C1114yescomplemented
230#550C22×C1114yes—
231#546—24no—
232#541—24no—
233#541C22×C1114yes—
234#540—22no—
235#535C22×C1112yes—
236#533C22×C1112yes—
237#533C22×C1111yescharacteristic
238#532—22no—
239C2×#127C22×C1111yescharacteristic
240#518C22×C1112yes—
241C4×#41C22×C1111yescharacteristic
242#497C22×C1114yescomplemented
243#492C22×C1114yes—
244#492C22×C1114yescomplemented
245#490C22×C1114yescomplemented
246#488C22×C1114yescomplemented
247#486C22×C1114yes—
248#485C22×C1114yes—
249#478C22×C1118yescomplemented
250#475C22×C1112yescomplemented
251#474C22×C1112yescomplemented
252#464C22×C1118yescomplemented
253#462C22×C1112yescomplemented
254#461C22×C1112yescomplemented
255#461C22×C1118yescomplemented
256#460C22×C1114yes—
257#460C22×C1114yes—
258#460C22×C1118yescomplemented
259#452C22×C1114yes—
260#450C22×C1118yes—
261#446C22×C1114yescomplemented
262C8×Q8C22×C1114yescomplemented
263#440C22×C1118yescomplemented
264C4×Q16C22×C1114yescomplemented
265C4×SD16C22×C1114yescomplemented
266C4×SD16C22×C1118yescomplemented
267#433C22×C1114yes—
268#431C22×C1112yes—
269C22×C11—21no—
270C22×C11—22no—
271C22×C11—41no—
272C22×C11—44no—
273C22×C11—42no—
274C22×C11—48no—
275C22×C11—164no—
276C22×C11C23×D411yescharacteristic
277C4×C11—21no—
278C4×C11—22no—
279C4×C11—28no—
280C4×C11—41no—
281C4×C11—44no—
282C4×C11—42no—
283C4×C11—44no—
284C4×C11#57714yes—
285C4×C11#58512yes—
286C2×#41—24no—
287C2×#41C23×C1111yescharacteristic
288C22×D4—22no—
289C22×D4C23×C1112yes—
290C2×Q16C23×C1114yes—
291C2×SD16C23×C1118yes—
292C2×SD16C23×C1114yes—
293C2×SD16C23×C1118yes—
294C4⋊Q8—24no—
295C4⋊Q8D4×C1112yes—
296C4⋊Q8C23×C1112yes—
297C4⋊Q8C23×C1114yes—
298C4⋊Q8C23×C1112yes—
299#127—21no—
300#127—21no—
301#127C23×C1114yes—
302#127C23×C1114yes—
303#126—28no—
304#125—24no—
305#125—28no—
306#125—28no—
307#125—28no—
308#125—22no—
309#125D4×C1112yes—
310#125C23×C1114yes—
311#124—24no—
312#124C23×C1114yes—
313#123—28no—
314C22⋊Q8—22no—
315C22⋊Q8D4×C1114yes—
316C22⋊Q8C23×C1114yes—
317#121—24no—
318#121—24no—
319#121—28no—
320#120—24no—
321C4×Q8—24no—
322C4×Q8—24no—
323C4×Q8—22no—
324C4×Q8C23×C1112yes—
325C4×Q8C23×C1114yes—
326C4×Q8C23×C1118yes—
327C4×Q8C23×C1114yes—
328C4×D4—22no—
329C4×D4—24no—
330C4×D4—24no—
331C4×D4C23×C1112yes—
332C4×D4C23×C1118yes—
333#117—22no—
334#117—21no—
335#117C23×C1111yescharacteristic
336#117C23×C1112yes—
337C2×C22⋊C4—24no—
338C2×C42—21no—
339C2×C42C23×C1111yescharacteristic
340#107C23×C1114yes—
341#106C23×C1114yes—
342C4⋊C8C23×C1112yes—
343C4⋊C8C23×C1112yes—
344C4⋊C8C23×C1118yes—
345#103C23×C1114yes—
346#103C23×C1114yes—
347#103C23×C1114yes—
348#102C23×C1118yes—
349#102C23×C1114yes—
350#102C23×C1118yes—
351C22⋊C8C23×C1114yes—
352#97C23×C1114yes—
353C4×C8C23×C1114yes—
354C4×C8C23×C1114yes—
355C2×C11—41no—
356C2×C11—81no—
357C2×C11—84no—
358C2×C11#348711yescharacteristic
359C2×C11C2×#57712yes—
360C24—22no—
361#41—42no—
362#41—88no—
363C2×Q8—22no—
364C2×Q8C2×D4×C1114yes—
365C2×Q8C24×C1111yescharacteristic
366C2×Q8C24×C1114yes—
367C2×D4—21no—
368C2×D4—22no—
369C2×D4—24no—
370C2×D4—28no—
371C2×D4—24no—
372C2×D4—44no—
373C2×D4—84no—
374C2×D4C24×C1114yes—
375C2×D4C24×C1111yescharacteristic
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—28no—
379C22×C4C2×D4×C1112yes—
380C22×C4C24×C1111yescharacteristic
381Q16—44no—
382SD16—48no—
383SD16—44no—
384SD16—48no—
385C2×C8C24×C1114yes—
386C2×C8C24×C1114yes—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—24no—
392C4⋊C4—28no—
393C4⋊C4—28no—
394C4⋊C4—24no—
395C4⋊C4—28no—
396C4⋊C4C2×D4×C1114yes—
397C4⋊C4C2×D4×C1114yes—
398C4⋊C4C2×D4×C1118yes—
399C4⋊C4C24×C1114yes—
400C4⋊C4C24×C1112yes—
401C22⋊C4—21no—
402C22⋊C4—24no—
403C22⋊C4—28no—
404C22⋊C4—22no—
405C22⋊C4—28no—
406C22⋊C4C2×D4×C1114yes—
407C42—21no—
408C42—22no—
409C42—24no—
410C42—28no—
411C42C2×D4×C1111yescharacteristic
412C42C2×D4×C1111yescharacteristic
413C42C24×C1112yes—
414C42C24×C1114yes—
415C11#6193311yescharacteristic, direct product factor, Sylow
416C23—24no—
417C23—21no—
418C23—44no—
419C23—84no—
420C23C22×D4×C1111yescharacteristic
421Q8—28no—
422Q8—24no—
423Q8—24no—
424Q8—22no—
425Q8—44no—
426D4—28no—
427D4—22no—
428D4—44no—
429D4—42no—
430D4—48no—
431D4—84no—
432D4—88no—
433C2×C4—24no—
434C2×C4—22no—
435C2×C4—24no—
436C2×C4—24no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—42no—
440C2×C4—44no—
441C2×C4—88no—
442C2×C4C22×D4×C1111yescharacteristic
443C2×C4C22×D4×C1118yes—
444C2×C4C22×D4×C1112yes—
445C2×C4C22×D4×C1112yes—
446C2×C4C25×C1111yescharacteristic
447C8—24no—
448C8—24no—
449C22—21no—
450C22—22no—
451C22—41no—
452C22—44no—
453C22—42no—
454C22—48no—
455C22—164no—
456C22C23×D4×C1111yescharacteristic
457C4—21no—
458C4—22no—
459C4—28no—
460C4—41no—
461C4—44no—
462C4—42no—
463C4—44no—
464C4C11×#57714yes—
465C4C11×#58512yes—
466C2—41no—
467C2—84no—
468C2—81no—
469C2C11×#348711yescharacteristic
470C2C2×C11×#57712yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3508C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3556C2semidirect
3. C11×#3400C2semidirect
4. C11×#3392C2semidirect
5. C11×#3368C2semidirect
6. C11×#3365C2semidirect
7. C11×#3222C2semidirect
8. C11×#3208C2semidirect
9. C11×#3123C2semidirect
10. C11×#3107C2semidirect
11. C11×#2986C2semidirect
15. C11×#557C22semidirect
16. C11×#557C22semidirect
29. C11×#497C22semidirect
31. C11×#492C22semidirect
32. C11×#490C22semidirect
33. C11×#488C22semidirect
36. C11×#478C22semidirect
37. C11×#475C22semidirect
38. C11×#474C22semidirect
39. C11×#464C22semidirect
40. C11×#462C22semidirect
41. C11×#461C22semidirect
42. C11×#461C22semidirect
45. C11×#460C22semidirect
48. C11×#446C22semidirect
49. C8×Q8×C11C22semidirect
50. C11×#440C22semidirect
51. C4×C11×Q16C22semidirect
52. C4×C11×SD16C22semidirect
53. C4×C11×SD16C22semidirect
125. #61933C11direct (N × H)
181. #3556C2×C11semidirect
183. #3400C2×C11semidirect
184. #3392C2×C11semidirect
185. #3368C2×C11semidirect
186. #3365C2×C11semidirect
187. #3222C2×C11semidirect
188. #3208C2×C11semidirect
189. #3123C2×C11semidirect
190. #3107C2×C11semidirect
191. #2986C2×C11semidirect
228. #557C22×C11semidirect
229. #557C22×C11semidirect
242. #497C22×C11semidirect
244. #492C22×C11semidirect
245. #490C22×C11semidirect
246. #488C22×C11semidirect
249. #478C22×C11semidirect
250. #475C22×C11semidirect
251. #474C22×C11semidirect
252. #464C22×C11semidirect
253. #462C22×C11semidirect
254. #461C22×C11semidirect
255. #461C22×C11semidirect
258. #460C22×C11semidirect
261. #446C22×C11semidirect
262. C8×Q8C22×C11semidirect
263. #440C22×C11semidirect
264. C4×Q16C22×C11semidirect
265. C4×SD16C22×C11semidirect
266. C4×SD16C22×C11semidirect
415. C11#61933direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35562
C11×#35082
C11×#34002
C11×#33922
C11×#33682
C11×#33652
C11×#32222
C11×#32082
C11×#31232
C11×#31072
C11×#29862
#6193311