Finite Group Databasebeta

← C11×#19050 #14596243

Subgroups — C11×#19050 #14596243

Order 2816.

1026 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3545C211yesmaximal, characteristic, complemented
2C11×#3217C212yesmaximal, complemented
3C2×C11×#496C211yesmaximal, characteristic, complemented
4C11×#1657C212yesmaximal, complemented
5C11×#1656C214yesmaximal, complemented
6C11×#1655C212yesmaximal, complemented
7C11×#1533C211yesmaximal, characteristic, complemented
8C11×#1532C212yesmaximal, complemented
9C22×C11×SD16—21no—
10C22×C11×D8—21no—
11C11×#563C2211yescharacteristic, complemented
12C11×#562C2212yescomplemented
13C11×H(3,𝔽4)C2211yescharacteristic, complemented
14C11×#555—21no—
15C11×#551—21no—
16C11×#551—22no—
17C11×#546—22no—
18C11×#542—22no—
19C11×#538—22no—
20C11×#536—21no—
21C11×#534—21no—
22C2×C11×#127C2211yescharacteristic, complemented
23C11×#529C2212yes—
24C2×C11×#124C2211yescharacteristic
25C11×#496—21no—
26C11×#496—21no—
27C11×#496C2212yes—
28C11×#496C2212yescomplemented
29C11×#496C2214yescomplemented
30C11×#490C2214yescomplemented
31C11×#460—22no—
32C11×#459—22no—
33C11×#450—22no—
34C11×#447—22no—
35C11×#432C2212yescomplemented
36C2×C11×#97C2211yescharacteristic, complemented
37C11×#330C2214yescomplemented
38C11×#329C2214yescomplemented
39C11×#329C2212yescomplemented
40C11×#329C2212yescomplemented
41C2×C11×#41—21no—
42C22×Q8×C11D411yescharacteristic
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11—22no—
46C22×D4×C11D411yescharacteristic
47C2×C11×SD16—22no—
48C2×C11×SD16—22no—
49C2×C11×SD16—24no—
50C2×C11×SD16—44no—
51C2×C11×D8—22no—
52C2×C11×D8—22no—
53C2×C11×D8—24no—
54C2×C11×D8—44no—
55C22×C8×C11—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C11×#127—21no—
59C11×#127—22no—
60C11×#127C2312yes—
61C11×#126—22no—
62C11×#126—22no—
63C11×#126—22no—
64C11×#125C2312yes—
65C11×#124—21no—
66C11×#124—22no—
67C11×#124—21no—
68C11×#124—22no—
69C11×#124—22no—
70C11×#124D411yescharacteristic
71C11×#124D411yescharacteristic
72C11×#124C2311yescharacteristic
73C11×#124C2311yescharacteristic
74C11×#124C2312yes—
75C11×#123—21no—
76C11×#123—22no—
77C11×#123—22no—
78C11×#123—21no—
79C11×#123—22no—
80C11×#123—22no—
81C11×#123—22no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8D412yes—
87C11×#121—22no—
88C11×#121—22no—
89C11×#121—22no—
90C11×#121—22no—
91C11×#121D412yes—
92C11×#120—21no—
93C11×#120—22no—
94C11×#120—21no—
95C11×#120—22no—
96C4×Q8×C11D412yes—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11D412yes—
101C11×#117—21no—
102C11×#117—22no—
103C11×#117—22no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C42×C11C2311yescharacteristic
108C11×C4⋊C8—22no—
109C11×#102—24no—
110C11×#102—24no—
111C11×C22⋊C8—22no—
112C11×#97—21no—
113C11×#97C2314yes—
114C11×#97C2312yes—
115#19050C1111yesmaximal, characteristic, direct product factor, Sylow
116C24×C11—21no—
117C24×C11—21no—
118C24×C11—41no—
119C11×#41—82no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—42no—
123C2×Q8×C11C2×D412yes—
124C2×Q8×C11C2×D411yescharacteristic
125C2×Q8×C11C2×D411yescharacteristic
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—21no—
130C2×D4×C11—22no—
131C2×D4×C11—21no—
132C2×D4×C11—24no—
133C2×D4×C11—22no—
134C2×D4×C11—42no—
135C2×D4×C11—42no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11—41no—
139C2×D4×C11—84no—
140C2×D4×C11—82no—
141C2×D4×C11C2×D412yes—
142C2×D4×C11C2×D411yescharacteristic
143C2×D4×C11C2×D411yescharacteristic
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C11×SD16—44no—
152C11×SD16—44no—
153C11×SD16—84no—
154C11×D8—44no—
155C11×D8—44no—
156C11×D8—84no—
157C2×C8×C11—24no—
158C2×C8×C11—22no—
159C2×C8×C11—24no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4C2×D412yes—
168C11×C4⋊C4C2×D412yes—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—21no—
171C11×C22⋊C4—21no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—22no—
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D412yes—
189C42×C11C2411yescharacteristic
190#3545C2×C1111yescharacteristic, complemented
191#3217C2×C1112yescomplemented
192C2×#496C2×C1111yescharacteristic, complemented
193#1657C2×C1112yescomplemented
194#1656C2×C1114yescomplemented
195#1655C2×C1112yescomplemented
196#1533C2×C1111yescharacteristic, complemented
197#1532C2×C1112yescomplemented
198C23×C11—21no—
199C23×C11—22no—
200C23×C11—21no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—82no—
204C23×C11—84no—
205C23×C11—81no—
206C23×C11—82no—
207C23×C11—82no—
208C23×C11#12011yescharacteristic
209Q8×C11—41no—
210Q8×C11—41no—
211Q8×C11—42no—
212Q8×C11—81no—
213Q8×C11—81no—
214D4×C11—41no—
215D4×C11—41no—
216D4×C11—42no—
217D4×C11—42no—
218D4×C11—44no—
219D4×C11—42no—
220D4×C11—44no—
221D4×C11—44no—
222D4×C11—81no—
223D4×C11—82no—
224D4×C11—84no—
225D4×C11—82no—
226D4×C11—82no—
227D4×C11—82no—
228D4×C11—81no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—21no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—82no—
238C2×C4×C11—82no—
239C2×C4×C11—81no—
240C2×C4×C11—82no—
241C2×C4×C11#12012yes—
242C2×C4×C11#12011yescharacteristic
243C2×C4×C11C22×D412yes—
244C2×C4×C11C22×D411yescharacteristic
245C8×C11—24no—
246C8×C11—44no—
247C22×SD16—21no—
248C22×D8—21no—
249#563C22×C1111yescharacteristic, complemented
250#562C22×C1112yescomplemented
251H(3,𝔽4)C22×C1111yescharacteristic, complemented
252#555—21no—
253#551—21no—
254#551—22no—
255#546—22no—
256#542—22no—
257#538—22no—
258#536—21no—
259#534—21no—
260C2×#127C22×C1111yescharacteristic, complemented
261#529C22×C1112yes—
262C2×#124C22×C1111yescharacteristic
263#496—21no—
264#496—21no—
265#496C22×C1112yes—
266#496C22×C1112yescomplemented
267#496C22×C1114yescomplemented
268#490C22×C1114yescomplemented
269#460—22no—
270#459—22no—
271#450—22no—
272#447—22no—
273#432C22×C1112yescomplemented
274C2×#97C22×C1111yescharacteristic, complemented
275#330C22×C1114yescomplemented
276#329C22×C1114yescomplemented
277#329C22×C1112yescomplemented
278#329C22×C1112yescomplemented
279C22×C11—22no—
280C22×C11—42no—
281C22×C11—41no—
282C22×C11—41no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—82no—
288C22×C11—84no—
289C22×C11—162no—
290C22×C11—164no—
291C22×C11—162no—
292C22×C11#45312yes—
293C22×C11C2×#12011yescharacteristic
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—22no—
297C4×C11—22no—
298C4×C11—41no—
299C4×C11—41no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—42no—
303C2×#41—21no—
304C22×Q8D4×C1111yescharacteristic
305C22×D4—21no—
306C22×D4—21no—
307C22×D4—22no—
308C22×D4D4×C1111yescharacteristic
309C2×SD16—22no—
310C2×SD16—22no—
311C2×SD16—24no—
312C2×SD16—44no—
313C2×D8—22no—
314C2×D8—22no—
315C2×D8—24no—
316C2×D8—44no—
317C22×C8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320#127—22no—
321#127—21no—
322#127C23×C1112yes—
323#126—22no—
324#126—22no—
325#126—22no—
326#125C23×C1112yes—
327#124—21no—
328#124—22no—
329#124—21no—
330#124—22no—
331#124—22no—
332#124D4×C1111yescharacteristic
333#124D4×C1111yescharacteristic
334#124C23×C1111yescharacteristic
335#124C23×C1111yescharacteristic
336#124C23×C1112yes—
337#123—21no—
338#123—22no—
339#123—22no—
340#123—21no—
341#123—22no—
342#123—22no—
343#123—22no—
344C22⋊Q8—22no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347C22⋊Q8—22no—
348C22⋊Q8D4×C1112yes—
349#121—22no—
350#121—22no—
351#121—22no—
352#121—22no—
353#121D4×C1112yes—
354#120—21no—
355#120—22no—
356#120—21no—
357#120—22no—
358C4×Q8D4×C1112yes—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4D4×C1112yes—
363#117—21no—
364#117—22no—
365#117—22no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C42C23×C1111yescharacteristic
370C4⋊C8—22no—
371#102—24no—
372#102—24no—
373C22⋊C8—22no—
374#97—21no—
375#97C23×C1114yes—
376#97C23×C1112yes—
377C2×C11—22no—
378C2×C11—82no—
379C2×C11—81no—
380C2×C11—81no—
381C2×C11—162no—
382C2×C11C2×#45311yescharacteristic
383C2×C11#302112yes—
384C24—21no—
385C24—21no—
386C24—41no—
387#41—82no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—42no—
391C2×Q8C2×D4×C1112yes—
392C2×Q8C2×D4×C1111yescharacteristic
393C2×Q8C2×D4×C1111yescharacteristic
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—21no—
398C2×D4—22no—
399C2×D4—21no—
400C2×D4—24no—
401C2×D4—22no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—42no—
406C2×D4—41no—
407C2×D4—84no—
408C2×D4—82no—
409C2×D4C2×D4×C1112yes—
410C2×D4C2×D4×C1111yescharacteristic
411C2×D4C2×D4×C1111yescharacteristic
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4C2×D4×C1111yescharacteristic
418C22×C4C2×D4×C1112yes—
419SD16—44no—
420SD16—44no—
421SD16—84no—
422D8—44no—
423D8—44no—
424D8—84no—
425C2×C8—24no—
426C2×C8—22no—
427C2×C8—24no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4C2×D4×C1112yes—
436C4⋊C4C2×D4×C1112yes—
437C22⋊C4—22no—
438C22⋊C4—21no—
439C22⋊C4—21no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C42—21no—
453C42—21no—
454C42—22no—
455C42C2×D4×C1111yescharacteristic
456C42C2×D4×C1112yes—
457C42C24×C1111yescharacteristic
458C11#1905011yescharacteristic, direct product factor, Sylow
459C23—21no—
460C23—22no—
461C23—21no—
462C23—42no—
463C23—42no—
464C23—82no—
465C23—84no—
466C23—81no—
467C23—82no—
468C23—82no—
469C23C11×#12011yescharacteristic
470Q8—41no—
471Q8—41no—
472Q8—42no—
473Q8—81no—
474Q8—81no—
475D4—41no—
476D4—41no—
477D4—42no—
478D4—42no—
479D4—44no—
480D4—42no—
481D4—44no—
482D4—44no—
483D4—81no—
484D4—82no—
485D4—84no—
486D4—82no—
487D4—82no—
488D4—82no—
489D4—81no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—81no—
501C2×C4—82no—
502C2×C4C11×#12012yes—
503C2×C4C11×#12011yescharacteristic
504C2×C4C22×D4×C1112yes—
505C2×C4C22×D4×C1111yescharacteristic
506C8—24no—
507C8—44no—
508C22—22no—
509C22—42no—
510C22—41no—
511C22—41no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—82no—
517C22—84no—
518C22—162no—
519C22—164no—
520C22—162no—
521C22C11×#45312yes—
522C22C2×C11×#12011yescharacteristic
523C4—21no—
524C4—21no—
525C4—22no—
526C4—22no—
527C4—41no—
528C4—41no—
529C4—42no—
530C4—42no—
531C4—42no—
532C2—22no—
533C2—81no—
534C2—82no—
535C2—81no—
536C2—162no—
537C2C2×C11×#45311yescharacteristic
538C2C11×#302112yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3545C2semidirect
2. C11×#3217C2semidirect
3. C2×C11×#496C2semidirect
4. C11×#1657C2semidirect
5. C11×#1656C2semidirect
6. C11×#1655C2semidirect
7. C11×#1533C2semidirect
8. C11×#1532C2semidirect
11. C11×#563C22semidirect
12. C11×#562C22semidirect
13. C11×H(3,𝔽4)C22semidirect
22. C2×C11×#127C22semidirect
28. C11×#496C22semidirect
29. C11×#496C22semidirect
30. C11×#490C22semidirect
35. C11×#432C22semidirect
36. C2×C11×#97C22semidirect
37. C11×#330C22semidirect
38. C11×#329C22semidirect
39. C11×#329C22semidirect
40. C11×#329C22semidirect
115. #19050C11direct (N × H)
190. #3545C2×C11semidirect
191. #3217C2×C11semidirect
192. C2×#496C2×C11semidirect
193. #1657C2×C11semidirect
194. #1656C2×C11semidirect
195. #1655C2×C11semidirect
196. #1533C2×C11semidirect
197. #1532C2×C11semidirect
249. #563C22×C11semidirect
250. #562C22×C11semidirect
251. H(3,𝔽4)C22×C11semidirect
260. C2×#127C22×C11semidirect
266. #496C22×C11semidirect
267. #496C22×C11semidirect
268. #490C22×C11semidirect
273. #432C22×C11semidirect
274. C2×#97C22×C11semidirect
275. #330C22×C11semidirect
276. #329C22×C11semidirect
277. #329C22×C11semidirect
278. #329C22×C11semidirect
458. C11#19050direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35452
C11×#32172
C2×C11×#4962
C11×#16572
C11×#16562
C11×#16552
C11×#15332
C11×#15322
#1905011