Finite Group Databasebeta

← C11×#19089 #14596282

Subgroups — C11×#19089 #14596282

Order 2816.

850 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3559C211yesmaximal, characteristic
2C11×#3240C211yesmaximal, characteristic, complemented
3C11×#3236C211yesmaximal, characteristic, complemented
4C11×#3216C211yesmaximal, characteristic, complemented
5C11×#1664C212yesmaximal, complemented
6C11×#1662C212yesmaximal, complemented
7C11×#1661C212yesmaximal, complemented
8C11×#1660C212yesmaximal, complemented
9C11×#1536C211yesmaximal, characteristic, complemented
10C11×#1535C211yesmaximal, characteristic, complemented
11C11×#1534C211yesmaximal, characteristic, complemented
12C11×#563C2212yes—
13C11×#562C2212yes—
14C11×#554—21no—
15C11×#553—21no—
16C11×#553—21no—
17C11×#547—22no—
18C11×#547—21no—
19C11×#544—21no—
20C11×#540—21no—
21C11×#539—22no—
22C11×#539—21no—
23C11×#537—21no—
24C11×#533C2211yescharacteristic
25C11×#532C2211yescharacteristic
26C11×#529C2211yescharacteristic
27C2×C11×#125C2211yescharacteristic
28C11×#501C2211yescharacteristic
29C11×#501C2212yes—
30C11×#501C2211yescharacteristic
31C11×#497C2212yes—
32C11×#491C2212yes—
33C11×#489C2211yescharacteristic
34C11×#489C2211yescharacteristic
35C11×#489C2212yes—
36C11×#485—21no—
37C11×#484—21no—
38C11×#483—21no—
39C11×#482—21no—
40C11×#479—22no—
41C11×#479—21no—
42C11×#478—21no—
43C11×#462—21no—
44C11×#460—21no—
45C11×#452—22no—
46C11×#432C2211yescharacteristic
47C11×#432C2211yescharacteristic
48C11×#432C2211yescharacteristic
49C11×#330C2212yes—
50C11×#330C2212yes—
51C11×#330C2212yes—
52C11×#329C2212yes—
53C11×#329C2212yes—
54C11×#329C2212yes—
55C2×C11×#41—22no—
56C2×C11×#41D412yes—
57C2×C11×Q16—22no—
58C2×C11×SD16—22no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8D411yescharacteristic
62C11×C4⋊Q8C2311yescharacteristic
63C11×C4⋊Q8C2311yescharacteristic
64C11×#127D411yescharacteristic
65C11×#126—22no—
66C11×#126—22no—
67C11×#126—21no—
68C11×#125—22no—
69C11×#125—21no—
70C11×#125—21no—
71C11×#125—21no—
72C11×#125—21no—
73C11×#125D412yes—
74C11×#125C2312yes—
75C11×#125C2311yescharacteristic
76C11×#124C2311yescharacteristic
77C11×#124C2312yes—
78C11×#123—22no—
79C11×#123—22no—
80C11×#123—22no—
81C11×#123—22no—
82C11×#123—21no—
83C11×#123—22no—
84C11×#123—22no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8—21no—
92C11×C22⋊Q8—21no—
93C11×C22⋊Q8D411yescharacteristic
94C11×#121—22no—
95C11×#121—22no—
96C11×#121—21no—
97C11×#121—21no—
98C11×#121—22no—
99C11×#121—22no—
100C11×#121—21no—
101C11×#121—21no—
102C11×#121D411yescharacteristic
103C4×Q8×C11—21no—
104C4×Q8×C11—21no—
105C4×Q8×C11D411yescharacteristic
106C4×D4×C11—22no—
107C4×D4×C11—22no—
108C4×D4×C11—21no—
109C4×D4×C11—21no—
110C4×D4×C11—21no—
111C4×D4×C11—21no—
112C4×D4×C11—21no—
113C4×D4×C11D411yescharacteristic
114C11×#117—21no—
115C11×#117—21no—
116C11×#117—21no—
117C2×C11×C4⋊C4—22no—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4D411yescharacteristic
122C2×C11×C4⋊C4D411yescharacteristic
123C2×C42×C11C2311yescharacteristic
124C11×#107—21no—
125C11×#107—21no—
126C11×#107—22no—
127C11×#106—21no—
128C11×#106—21no—
129C11×#106—22no—
130C11×C4⋊C8—21no—
131C11×C4⋊C8—21no—
132C11×C4⋊C8—21no—
133C11×#103—22no—
134C11×#103—21no—
135C11×#103—21no—
136C11×#103—22no—
137C11×#103—22no—
138C11×#102—22no—
139C11×#102—21no—
140C11×#102—21no—
141C11×C22⋊C8—21no—
142C11×C22⋊C8—21no—
143C11×C22⋊C8—21no—
144C11×#97C2311yescharacteristic
145C11×#97C2311yescharacteristic
146C11×#97C2312yes—
147C11×#97C2312yes—
148#19089C1111yesmaximal, characteristic, direct product factor, Sylow
149C11×#41—84no—
150C11×#41—82no—
151C2×Q8×C11—22no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11C2×D411yescharacteristic
155C2×Q8×C11C2×D412yes—
156C2×D4×C11—22no—
157C2×D4×C11—21no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11C2×D411yescharacteristic
163C2×D4×C11C2×D412yes—
164C22×C4×C11—21no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—22no—
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C11×Q16—82no—
175C11×SD16—82no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—41no—
201C11×C4⋊C4—41no—
202C11×C4⋊C4C2×D412yes—
203C11×C4⋊C4C2×D412yes—
204C11×C4⋊C4C2×D411yescharacteristic
205C11×C4⋊C4C2×D411yescharacteristic
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—21no—
213C11×C22⋊C4—21no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—41no—
219C42×C11—22no—
220C42×C11—21no—
221C42×C11—41no—
222C42×C11C2×D411yescharacteristic
223C42×C11C2×D411yescharacteristic
224C42×C11C2×D411yescharacteristic
225C42×C11C2411yescharacteristic
226#3559C2×C1111yescharacteristic
227#3240C2×C1111yescharacteristic, complemented
228#3236C2×C1111yescharacteristic, complemented
229#3216C2×C1111yescharacteristic, complemented
230#1664C2×C1112yescomplemented
231#1662C2×C1112yescomplemented
232#1661C2×C1112yescomplemented
233#1660C2×C1112yescomplemented
234#1536C2×C1111yescharacteristic, complemented
235#1535C2×C1111yescharacteristic, complemented
236#1534C2×C1111yescharacteristic, complemented
237C23×C11—22no—
238C23×C11—21no—
239C23×C11#12011yescharacteristic
240Q8×C11—42no—
241Q8×C11—41no—
242Q8×C11—41no—
243Q8×C11—41no—
244Q8×C11—42no—
245Q8×C11—82no—
246D4×C11—42no—
247D4×C11—41no—
248D4×C11—42no—
249D4×C11—44no—
250D4×C11—42no—
251D4×C11—81no—
252D4×C11—82no—
253D4×C11—82no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—82no—
268C2×C4×C11—81no—
269C2×C4×C11—82no—
270C2×C4×C11—82no—
271C2×C4×C11—82no—
272C2×C4×C11#12011yescharacteristic
273C2×C4×C11#12011yescharacteristic
274C2×C4×C11#12011yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C8×C11—42no—
279C8×C11—41no—
280C8×C11—41no—
281C8×C11—42no—
282#563C22×C1112yes—
283#562C22×C1112yes—
284#554—21no—
285#553—21no—
286#553—21no—
287#547—22no—
288#547—21no—
289#544—21no—
290#540—21no—
291#539—22no—
292#539—21no—
293#537—21no—
294#533C22×C1111yescharacteristic
295#532C22×C1111yescharacteristic
296#529C22×C1111yescharacteristic
297C2×#125C22×C1111yescharacteristic
298#501C22×C1111yescharacteristic
299#501C22×C1112yes—
300#501C22×C1111yescharacteristic
301#497C22×C1112yes—
302#491C22×C1112yes—
303#489C22×C1111yescharacteristic
304#489C22×C1111yescharacteristic
305#489C22×C1112yes—
306#485—21no—
307#484—21no—
308#483—21no—
309#482—21no—
310#479—22no—
311#479—21no—
312#478—21no—
313#462—21no—
314#460—21no—
315#452—22no—
316#432C22×C1111yescharacteristic
317#432C22×C1111yescharacteristic
318#432C22×C1111yescharacteristic
319#330C22×C1112yes—
320#330C22×C1112yes—
321#330C22×C1112yes—
322#329C22×C1112yes—
323#329C22×C1112yes—
324#329C22×C1112yes—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—42no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—41no—
334C22×C11C2×#12011yescharacteristic
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—42no—
342C4×C11—42no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—42no—
346C4×C11—41no—
347C4×C11—81no—
348C4×C11—81no—
349C2×#41—22no—
350C2×#41D4×C1112yes—
351C2×Q16—22no—
352C2×SD16—22no—
353C4⋊Q8—21no—
354C4⋊Q8—22no—
355C4⋊Q8D4×C1111yescharacteristic
356C4⋊Q8C23×C1111yescharacteristic
357C4⋊Q8C23×C1111yescharacteristic
358#127D4×C1111yescharacteristic
359#126—22no—
360#126—22no—
361#126—21no—
362#125—22no—
363#125—21no—
364#125—21no—
365#125—21no—
366#125—21no—
367#125D4×C1112yes—
368#125C23×C1112yes—
369#125C23×C1111yescharacteristic
370#124C23×C1111yescharacteristic
371#124C23×C1112yes—
372#123—22no—
373#123—22no—
374#123—22no—
375#123—22no—
376#123—21no—
377#123—22no—
378#123—22no—
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382C22⋊Q8—22no—
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8D4×C1111yescharacteristic
388#121—22no—
389#121—22no—
390#121—21no—
391#121—21no—
392#121—22no—
393#121—22no—
394#121—21no—
395#121—21no—
396#121D4×C1111yescharacteristic
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8D4×C1111yescharacteristic
400C4×D4—22no—
401C4×D4—22no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4D4×C1111yescharacteristic
408#117—21no—
409#117—21no—
410#117—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4D4×C1111yescharacteristic
416C2×C4⋊C4D4×C1111yescharacteristic
417C2×C42C23×C1111yescharacteristic
418#107—21no—
419#107—21no—
420#107—22no—
421#106—21no—
422#106—21no—
423#106—22no—
424C4⋊C8—21no—
425C4⋊C8—21no—
426C4⋊C8—21no—
427#103—22no—
428#103—21no—
429#103—21no—
430#103—22no—
431#103—22no—
432#102—22no—
433#102—21no—
434#102—21no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438#97C23×C1112yes—
439#97C23×C1111yescharacteristic
440#97C23×C1111yescharacteristic
441#97C23×C1112yes—
442C2×C11—41no—
443C2×C11—82no—
444C2×C11—81no—
445C2×C11#301911yescharacteristic
446C2×C11#302011yescharacteristic
447C2×C11#302211yescharacteristic
448#41—84no—
449#41—82no—
450C2×Q8—22no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8C2×D4×C1111yescharacteristic
454C2×Q8C2×D4×C1112yes—
455C2×D4—22no—
456C2×D4—21no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4C2×D4×C1111yescharacteristic
462C2×D4C2×D4×C1112yes—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4C2×D4×C1111yescharacteristic
471C22×C4C2×D4×C1111yescharacteristic
472C22×C4C2×D4×C1111yescharacteristic
473Q16—82no—
474SD16—82no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—22no—
478C2×C8—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—22no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4C2×D4×C1112yes—
502C4⋊C4C2×D4×C1112yes—
503C4⋊C4C2×D4×C1111yescharacteristic
504C4⋊C4C2×D4×C1111yescharacteristic
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—21no—
517C22⋊C4—41no—
518C42—22no—
519C42—21no—
520C42—41no—
521C42C2×D4×C1111yescharacteristic
522C42C2×D4×C1111yescharacteristic
523C42C2×D4×C1111yescharacteristic
524C42C24×C1111yescharacteristic
525C11#1908911yescharacteristic, direct product factor, Sylow
526C23—22no—
527C23—21no—
528C23C11×#12011yescharacteristic
529Q8—42no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533Q8—42no—
534Q8—82no—
535D4—42no—
536D4—41no—
537D4—42no—
538D4—44no—
539D4—42no—
540D4—81no—
541D4—82no—
542D4—82no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—82no—
557C2×C4—81no—
558C2×C4—82no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4C11×#12011yescharacteristic
562C2×C4C11×#12011yescharacteristic
563C2×C4C11×#12011yescharacteristic
564C2×C4C22×D4×C1111yescharacteristic
565C2×C4C22×D4×C1111yescharacteristic
566C2×C4C22×D4×C1111yescharacteristic
567C8—42no—
568C8—42no—
569C8—41no—
570C8—41no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—42no—
575C22—41no—
576C22—41no—
577C22—42no—
578C22—42no—
579C22—41no—
580C22C2×C11×#12011yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—42no—
588C4—42no—
589C4—41no—
590C4—41no—
591C4—42no—
592C4—41no—
593C4—81no—
594C4—81no—
595C2—41no—
596C2—82no—
597C2—81no—
598C2C11×#301911yescharacteristic
599C2C11×#302011yescharacteristic
600C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3559C2
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×#3240C2semidirect
3. C11×#3236C2semidirect
4. C11×#3216C2semidirect
5. C11×#1664C2semidirect
6. C11×#1662C2semidirect
7. C11×#1661C2semidirect
8. C11×#1660C2semidirect
9. C11×#1536C2semidirect
10. C11×#1535C2semidirect
11. C11×#1534C2semidirect
148. #19089C11direct (N × H)
227. #3240C2×C11semidirect
228. #3236C2×C11semidirect
229. #3216C2×C11semidirect
230. #1664C2×C11semidirect
231. #1662C2×C11semidirect
232. #1661C2×C11semidirect
233. #1660C2×C11semidirect
234. #1536C2×C11semidirect
235. #1535C2×C11semidirect
236. #1534C2×C11semidirect
525. C11#19089direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35592
C11×#32402
C11×#32362
C11×#32162
C11×#16642
C11×#16622
C11×#16612
C11×#16602
C11×#15362
C11×#15352
C11×#15342
#1908911