Finite Group Databasebeta

← C11×#19015 #14596208

Subgroups — C11×#19015 #14596208

Order 2816.

1012 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3558C211yesmaximal, characteristic
2C11×#3238C211yesmaximal, characteristic, complemented
3C11×#3152C211yesmaximal, characteristic, complemented
4C2×C11×#489C211yesmaximal, characteristic, complemented
5C11×#1661C214yesmaximal, complemented
6C11×#1659C214yesmaximal, complemented
7C11×#1530C211yesmaximal, characteristic, complemented
8C11×#1527C211yesmaximal, characteristic, complemented
9C11×#1524C211yesmaximal, characteristic, complemented
10C2×C11×#137—22no—
11C11×#562C2212yes—
12C11×H(3,𝔽4)C2212yes—
13C11×#559—21no—
14C11×#548—21no—
15C11×#546—22no—
16C11×#546—21no—
17D42×C11—21no—
18C11×#542—21no—
19C11×#538—22no—
20C11×#538—21no—
21C11×#535—21no—
22C11×#534—21no—
23C11×#532C2211yescharacteristic
24C2×C11×C4⋊Q8C2211yescharacteristic, complemented
25C11×#529C2211yescharacteristic
26C2×C11×#124C2211yescharacteristic
27C11×#501C2212yescomplemented
28C11×#497C2214yescomplemented
29C11×#494—21no—
30C11×#492—21no—
31C11×#489—22no—
32C11×#489C2212yescomplemented
33C11×#489C2214yescomplemented
34C11×#483—21no—
35C11×#480—21no—
36C11×#477—21no—
37C11×#476—21no—
38C11×#432C2211yescharacteristic, complemented
39C2×C11×#103—21no—
40C2×C11×#102—21no—
41C4×C11×M16C2211yescharacteristic, complemented
42C2×C11×#97C2211yescharacteristic, complemented
43C11×#330C2212yescomplemented
44C11×#329C2212yescomplemented
45C11×#329C2214yescomplemented
46C11×#329C2214yescomplemented
47C2×C11×#41—21no—
48C2×C11×#41D412yes—
49C22×Q8×C11—21no—
50C22×Q8×C11D411yescharacteristic
51C22×D4×C11—22no—
52C22×D4×C11—21no—
53C22×D4×C11D411yescharacteristic
54C11×#137—48no—
55C2×C11×Q16—24no—
56C2×C11×SD16—24no—
57C2×C11×M16—21no—
58C22×C8×C11—21no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8D411yescharacteristic
63C11×C4⋊Q8C2312yes—
64C11×#127—21no—
65C11×#127D411yescharacteristic
66C11×#126—22no—
67C11×#126—21no—
68C11×#125C2311yescharacteristic
69C11×#124—21no—
70C11×#124—22no—
71C11×#124—22no—
72C11×#124—22no—
73C11×#124—21no—
74C11×#124—21no—
75C11×#124D412yes—
76C11×#124C2312yes—
77C11×#124C2311yescharacteristic
78C11×#124C2312yes—
79C11×#123—22no—
80C11×#123—22no—
81C11×#123—21no—
82C11×#123—22no—
83C11×#123—22no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8D411yescharacteristic
88C11×#121—22no—
89C11×#121—22no—
90C11×#121—22no—
91C11×#121—21no—
92C11×#121—22no—
93C11×#121—22no—
94C11×#121—21no—
95C11×#121—21no—
96C11×#121D411yescharacteristic
97C11×#120—22no—
98C11×#120—22no—
99C11×#120—22no—
100C11×#120—22no—
101C11×#120—22no—
102C4×Q8×C11—21no—
103C4×Q8×C11D411yescharacteristic
104C4×D4×C11—22no—
105C4×D4×C11—22no—
106C4×D4×C11—21no—
107C4×D4×C11—21no—
108C4×D4×C11—21no—
109C4×D4×C11—21no—
110C4×D4×C11D411yescharacteristic
111C11×#117—21no—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4—21no—
114C2×C11×C22⋊C4—22no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C42×C11C2311yescharacteristic
118C11×#107—22no—
119C11×#106—22no—
120C11×C4⋊C8—21no—
121C11×#103—24no—
122C11×#103—22no—
123C11×#102—24no—
124C11×#102—22no—
125C11×C22⋊C8—21no—
126C11×#97—21no—
127C11×#97C2312yes—
128C11×#97C2312yes—
129C11×#97C2312yes—
130C4×C8×C11—21no—
131#19015C1111yesmaximal, characteristic, direct product factor, Sylow
132C24×C11—22no—
133C24×C11—21no—
134C11×#41—44no—
135C11×#41—82no—
136C2×Q8×C11—21no—
137C2×Q8×C11—22no—
138C2×Q8×C11—42no—
139C2×Q8×C11—44no—
140C2×Q8×C11—41no—
141C2×Q8×C11C2×D411yescharacteristic
142C2×Q8×C11C2×D412yes—
143C2×Q8×C11C2×D412yes—
144C2×D4×C11—22no—
145C2×D4×C11—21no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—42no—
155C2×D4×C11—82no—
156C2×D4×C11—84no—
157C2×D4×C11C2×D411yescharacteristic
158C2×D4×C11C2×D412yes—
159C2×D4×C11C2×D412yes—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—22no—
165C22×C4×C11—41no—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C11×Q16—48no—
170C11×SD16—48no—
171C11×M16—24no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—42no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—41no—
187C11×C4⋊C4—41no—
188C11×C4⋊C4C2×D411yescharacteristic
189C11×C4⋊C4C2×D411yescharacteristic
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—21no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—21no—
203C11×C22⋊C4—21no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C42×C11—22no—
207C42×C11—21no—
208C42×C11C2×D411yescharacteristic
209C42×C11C2×D411yescharacteristic
210C42×C11C2×D411yescharacteristic
211C42×C11C2411yescharacteristic
212#3558C2×C1111yescharacteristic
213#3238C2×C1111yescharacteristic, complemented
214#3152C2×C1111yescharacteristic, complemented
215C2×#489C2×C1111yescharacteristic, complemented
216#1661C2×C1114yescomplemented
217#1659C2×C1114yescomplemented
218#1530C2×C1111yescharacteristic, complemented
219#1527C2×C1111yescharacteristic, complemented
220#1524C2×C1111yescharacteristic, complemented
221C23×C11—22no—
222C23×C11—21no—
223C23×C11—22no—
224C23×C11—42no—
225C23×C11—81no—
226C23×C11—81no—
227C23×C11—82no—
228C23×C11—82no—
229C23×C11—82no—
230C23×C11#12011yescharacteristic
231Q8×C11—42no—
232Q8×C11—42no—
233Q8×C11—41no—
234Q8×C11—44no—
235Q8×C11—42no—
236Q8×C11—82no—
237D4×C11—42no—
238D4×C11—42no—
239D4×C11—41no—
240D4×C11—42no—
241D4×C11—44no—
242D4×C11—42no—
243D4×C11—42no—
244D4×C11—81no—
245D4×C11—82no—
246D4×C11—82no—
247D4×C11—82no—
248D4×C11—82no—
249D4×C11—82no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—41no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—82no—
261C2×C4×C11—81no—
262C2×C4×C11—82no—
263C2×C4×C11—82no—
264C2×C4×C11—82no—
265C2×C4×C11#12011yescharacteristic
266C2×C4×C11#12011yescharacteristic
267C2×C4×C11#12011yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C8×C11—24no—
272C8×C11—42no—
273C8×C11—42no—
274C2×#137—22no—
275#562C22×C1112yes—
276H(3,𝔽4)C22×C1112yes—
277#559—21no—
278#548—21no—
279#546—22no—
280#546—21no—
281D42—21no—
282#542—21no—
283#538—22no—
284#538—21no—
285#535—21no—
286#534—21no—
287#532C22×C1111yescharacteristic
288C2×C4⋊Q8C22×C1111yescharacteristic, complemented
289#529C22×C1111yescharacteristic
290C2×#124C22×C1111yescharacteristic
291#501C22×C1112yescomplemented
292#497C22×C1114yescomplemented
293#494—21no—
294#492—21no—
295#489—22no—
296#489C22×C1114yescomplemented
297#489C22×C1112yescomplemented
298#483—21no—
299#480—21no—
300#477—21no—
301#476—21no—
302#432C22×C1111yescharacteristic, complemented
303C2×#103—21no—
304C2×#102—21no—
305C4×M16C22×C1111yescharacteristic, complemented
306C2×#97C22×C1111yescharacteristic, complemented
307#330C22×C1112yescomplemented
308#329C22×C1112yescomplemented
309#329C22×C1114yescomplemented
310#329C22×C1114yescomplemented
311C22×C11—21no—
312C22×C11—21no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—41no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—162no—
323C22×C11—164no—
324C22×C11#45312yes—
325C22×C11C2×#12011yescharacteristic
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—41no—
332C4×C11—42no—
333C4×C11—41no—
334C4×C11—42no—
335C4×C11—41no—
336C4×C11—82no—
337C4×C11#45512yes—
338C2×#41—21no—
339C2×#41D4×C1112yes—
340C22×Q8—21no—
341C22×Q8D4×C1111yescharacteristic
342C22×D4—22no—
343C22×D4—21no—
344C22×D4D4×C1111yescharacteristic
345#137—48no—
346C2×Q16—24no—
347C2×SD16—24no—
348C2×M16—21no—
349C22×C8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8D4×C1111yescharacteristic
354C4⋊Q8C23×C1112yes—
355#127—21no—
356#127D4×C1111yescharacteristic
357#126—22no—
358#126—21no—
359#125C23×C1111yescharacteristic
360#124—21no—
361#124—22no—
362#124—22no—
363#124—22no—
364#124—21no—
365#124—21no—
366#124D4×C1112yes—
367#124C23×C1112yes—
368#124C23×C1111yescharacteristic
369#124C23×C1112yes—
370#123—22no—
371#123—22no—
372#123—21no—
373#123—22no—
374#123—22no—
375C22⋊Q8—21no—
376C22⋊Q8—22no—
377C22⋊Q8—22no—
378C22⋊Q8D4×C1111yescharacteristic
379#121—22no—
380#121—22no—
381#121—22no—
382#121—21no—
383#121—22no—
384#121—22no—
385#121—21no—
386#121—21no—
387#121D4×C1111yescharacteristic
388#120—22no—
389#120—22no—
390#120—22no—
391#120—22no—
392#120—22no—
393C4×Q8—21no—
394C4×Q8D4×C1111yescharacteristic
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4D4×C1111yescharacteristic
402#117—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C42C23×C1111yescharacteristic
409#107—22no—
410#106—22no—
411C4⋊C8—21no—
412#103—24no—
413#103—22no—
414#102—24no—
415#102—22no—
416C22⋊C8—21no—
417#97—21no—
418#97C23×C1112yes—
419#97C23×C1112yes—
420#97C23×C1112yes—
421C4×C8—21no—
422C2×C11—22no—
423C2×C11—82no—
424C2×C11—82no—
425C2×C11—81no—
426C2×C11C2×#45311yescharacteristic
427C2×C11C2×#45511yescharacteristic
428C2×C11#302211yescharacteristic
429C24—22no—
430C24—21no—
431#41—44no—
432#41—82no—
433C2×Q8—21no—
434C2×Q8—22no—
435C2×Q8—42no—
436C2×Q8—44no—
437C2×Q8—41no—
438C2×Q8C2×D4×C1111yescharacteristic
439C2×Q8C2×D4×C1112yes—
440C2×Q8C2×D4×C1112yes—
441C2×D4—22no—
442C2×D4—21no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—42no—
452C2×D4—82no—
453C2×D4—84no—
454C2×D4C2×D4×C1111yescharacteristic
455C2×D4C2×D4×C1112yes—
456C2×D4C2×D4×C1112yes—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—41no—
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C2×D4×C1111yescharacteristic
465C22×C4C2×D4×C1111yescharacteristic
466Q16—48no—
467SD16—48no—
468M16—24no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—42no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4C2×D4×C1111yescharacteristic
486C4⋊C4C2×D4×C1111yescharacteristic
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—21no—
493C22⋊C4—22no—
494C22⋊C4—21no—
495C22⋊C4—22no—
496C22⋊C4—21no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C42—22no—
504C42—21no—
505C42C2×D4×C1111yescharacteristic
506C42C2×D4×C1111yescharacteristic
507C42C2×D4×C1111yescharacteristic
508C42C24×C1111yescharacteristic
509C11#1901511yescharacteristic, direct product factor, Sylow
510C23—22no—
511C23—21no—
512C23—22no—
513C23—42no—
514C23—81no—
515C23—81no—
516C23—82no—
517C23—82no—
518C23—82no—
519C23C11×#12011yescharacteristic
520Q8—42no—
521Q8—42no—
522Q8—41no—
523Q8—44no—
524Q8—42no—
525Q8—82no—
526D4—42no—
527D4—42no—
528D4—41no—
529D4—42no—
530D4—44no—
531D4—42no—
532D4—42no—
533D4—81no—
534D4—82no—
535D4—82no—
536D4—82no—
537D4—82no—
538D4—82no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—82no—
550C2×C4—81no—
551C2×C4—82no—
552C2×C4—82no—
553C2×C4—82no—
554C2×C4C11×#12011yescharacteristic
555C2×C4C11×#12011yescharacteristic
556C2×C4C11×#12011yescharacteristic
557C2×C4C22×D4×C1111yescharacteristic
558C2×C4C22×D4×C1111yescharacteristic
559C2×C4C22×D4×C1111yescharacteristic
560C8—24no—
561C8—42no—
562C8—42no—
563C22—21no—
564C22—21no—
565C22—42no—
566C22—42no—
567C22—41no—
568C22—41no—
569C22—42no—
570C22—42no—
571C22—41no—
572C22—42no—
573C22—42no—
574C22—162no—
575C22—164no—
576C22C11×#45312yes—
577C22C2×C11×#12011yescharacteristic
578C4—21no—
579C4—21no—
580C4—21no—
581C4—21no—
582C4—21no—
583C4—41no—
584C4—42no—
585C4—41no—
586C4—42no—
587C4—41no—
588C4—82no—
589C4C11×#45512yes—
590C2—22no—
591C2—82no—
592C2—81no—
593C2—82no—
594C2C2×C11×#45311yescharacteristic
595C2C2×C11×#45511yescharacteristic
596C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3558C2
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
2. C11×#3238C2semidirect
3. C11×#3152C2semidirect
4. C2×C11×#489C2semidirect
5. C11×#1661C2semidirect
6. C11×#1659C2semidirect
7. C11×#1530C2semidirect
8. C11×#1527C2semidirect
9. C11×#1524C2semidirect
24. C2×C11×C4⋊Q8C22semidirect
27. C11×#501C22semidirect
28. C11×#497C22semidirect
32. C11×#489C22semidirect
33. C11×#489C22semidirect
38. C11×#432C22semidirect
41. C4×C11×M16C22semidirect
42. C2×C11×#97C22semidirect
43. C11×#330C22semidirect
44. C11×#329C22semidirect
45. C11×#329C22semidirect
46. C11×#329C22semidirect
131. #19015C11direct (N × H)
213. #3238C2×C11semidirect
214. #3152C2×C11semidirect
215. C2×#489C2×C11semidirect
216. #1661C2×C11semidirect
217. #1659C2×C11semidirect
218. #1530C2×C11semidirect
219. #1527C2×C11semidirect
220. #1524C2×C11semidirect
288. C2×C4⋊Q8C22×C11semidirect
291. #501C22×C11semidirect
292. #497C22×C11semidirect
296. #489C22×C11semidirect
297. #489C22×C11semidirect
302. #432C22×C11semidirect
305. C4×M16C22×C11semidirect
306. C2×#97C22×C11semidirect
307. #330C22×C11semidirect
308. #329C22×C11semidirect
309. #329C22×C11semidirect
310. #329C22×C11semidirect
509. C11#19015direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35582
C11×#32382
C11×#31522
C2×C11×#4892
C11×#16612
C11×#16592
C11×#15302
C11×#15272
C11×#15242
#1901511