Finite Group Databasebeta

← C11×#18973 #14596166

Subgroups — C11×#18973 #14596166

Order 2816.

818 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3555C211yesmaximal, characteristic
2C11×#3230C211yesmaximal, characteristic, complemented
3C11×#3229C211yesmaximal, characteristic, complemented
4C11×#3218C211yesmaximal, characteristic
5C11×#1650C212yesmaximal, complemented
6C11×#1648C212yesmaximal, complemented
7C11×#1645C212yesmaximal, complemented
8C11×#1643C212yesmaximal, complemented
9C11×#1554C211yesmaximal, characteristic, complemented
10C11×#1497C211yesmaximal, characteristic, complemented
11C11×#1482C211yesmaximal, characteristic
12C11×#563—22no—
13Q82×C11C2211yescharacteristic
14C11×#557—21no—
15C11×#557C2211yescharacteristic
16C11×#556—21no—
17C11×#556—21no—
18C11×#556C2211yescharacteristic
19C11×#554C2211yescharacteristic
20C11×#552—21no—
21C11×#544—21no—
22C11×#542—21no—
23C11×#541—21no—
24C11×#541—21no—
25C11×#541—22no—
26C11×#533C2211yescharacteristic
27C11×#533C2211yescharacteristic
28C2×C11×C4⋊Q8C2211yescharacteristic
29C11×#529C2211yescharacteristic
30C11×#500C2212yes—
31C11×#498—21no—
32C11×#497—21no—
33C11×#491—21no—
34C11×#487—21no—
35C11×#487C2212yes—
36C11×#484—22no—
37C11×#483—21no—
38C11×#483—21no—
39C11×#477—22no—
40C11×#475C2212yes—
41C11×#475C2212yes—
42C11×#462C2212yes—
43C11×#461C2212yes—
44C11×#451—21no—
45C11×#448—21no—
46C11×#432C2211yescharacteristic
47C11×#431C2211yescharacteristic
48C11×#431C2211yescharacteristic
49C11×#333C2212yes—
50C11×#332C2212yes—
51C11×Q8⋊C8C2212yes—
52C11×Q8⋊C8C2212yes—
53C11×Q8⋊C8C2212yes—
54C11×D4⋊C8C2212yes—
55C22×Q8×C11—21no—
56C2×C11×Q16—22no—
57C2×C11×SD16—22no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8—21no—
66C11×C4⋊Q8D411yescharacteristic
67C11×C4⋊Q8D411yescharacteristic
68C11×C4⋊Q8C2312yes—
69C11×C4⋊Q8C2311yescharacteristic
70C11×C4⋊Q8C2311yescharacteristic
71C11×#126—22no—
72C11×#126—22no—
73C11×#126—22no—
74C11×#126—22no—
75C11×#126—22no—
76C11×#126—22no—
77C11×#126—21no—
78C11×#125—22no—
79C11×#125—22no—
80C11×#125—22no—
81C11×#125—22no—
82C11×#125—21no—
83C11×#125—22no—
84C11×#125—21no—
85C11×#125—21no—
86C11×#125—21no—
87C11×#125D411yescharacteristic
88C11×#124—22no—
89C11×#124—21no—
90C11×#124D411yescharacteristic
91C11×#123—22no—
92C11×#123—21no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8—21no—
96C11×C22⋊Q8—21no—
97C11×C22⋊Q8—22no—
98C11×C22⋊Q8—21no—
99C11×C22⋊Q8—21no—
100C11×C22⋊Q8D411yescharacteristic
101C11×C22⋊Q8D411yescharacteristic
102C11×C22⋊Q8D411yescharacteristic
103C11×C22⋊Q8D412yes—
104C11×#121D411yescharacteristic
105C4×Q8×C11—22no—
106C4×Q8×C11—21no—
107C4×Q8×C11—21no—
108C4×Q8×C11—21no—
109C4×Q8×C11—21no—
110C4×Q8×C11—21no—
111C4×Q8×C11—21no—
112C4×Q8×C11—21no—
113C4×Q8×C11D412yes—
114C4×Q8×C11C2311yescharacteristic
115C4×Q8×C11C2311yescharacteristic
116C4×Q8×C11C2311yescharacteristic
117C4×D4×C11—21no—
118C4×D4×C11—21no—
119C4×D4×C11C2311yescharacteristic
120C11×#117—22no—
121C11×#117—21no—
122C11×#117—21no—
123C11×#117—21no—
124C11×#117—21no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C42×C11C2311yescharacteristic
129C11×#107—24no—
130C11×#106—22no—
131C11×#106—22no—
132C11×C4⋊C8—21no—
133C11×C4⋊C8C2312yes—
134C11×C4⋊C8C2312yes—
135C11×#103—22no—
136C11×#103—22no—
137C11×#103—24no—
138C11×#103—22no—
139C11×#103—22no—
140C11×C22⋊C8—21no—
141C11×C22⋊C8—21no—
142C11×C22⋊C8—21no—
143C11×#97—21no—
144C4×C8×C11—21no—
145C4×C8×C11C2312yes—
146#18973C1111yesmaximal, characteristic, direct product factor, Sylow
147C2×Q8×C11—22no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—22no—
151C2×Q8×C11—41no—
152C2×Q8×C11—82no—
153C2×Q8×C11C2×D411yescharacteristic
154C2×Q8×C11C2×D411yescharacteristic
155C2×Q8×C11C2×D411yescharacteristic
156C2×Q8×C11C2×D412yes—
157C2×D4×C11—21no—
158C2×D4×C11C2×D411yescharacteristic
159C22×C4×C11—22no—
160C22×C4×C11—21no—
161C22×C4×C11—41no—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C11×Q16—82no—
166C11×SD16—82no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
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—21no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—41no—
197C11×C4⋊C4—41no—
198C11×C4⋊C4C2×D411yescharacteristic
199C11×C4⋊C4C2×D411yescharacteristic
200C11×C4⋊C4C2×D411yescharacteristic
201C11×C4⋊C4C2×D411yescharacteristic
202C11×C4⋊C4C2×D412yes—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—21no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—21no—
209C11×C22⋊C4—21no—
210C11×C22⋊C4—21no—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—21no—
213C11×C22⋊C4—21no—
214C42×C11—22no—
215C42×C11—22no—
216C42×C11—22no—
217C42×C11—22no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11C2×D411yescharacteristic
222C42×C11C2×D411yescharacteristic
223C42×C11C2×D411yescharacteristic
224C42×C11C2411yescharacteristic
225#3555C2×C1111yescharacteristic
226#3230C2×C1111yescharacteristic, complemented
227#3229C2×C1111yescharacteristic, complemented
228#3218C2×C1111yescharacteristic
229#1650C2×C1112yescomplemented
230#1648C2×C1112yescomplemented
231#1645C2×C1112yescomplemented
232#1643C2×C1112yescomplemented
233#1554C2×C1111yescharacteristic, complemented
234#1497C2×C1111yescharacteristic, complemented
235#1482C2×C1111yescharacteristic
236C23×C11—21no—
237C23×C11#12011yescharacteristic
238Q8×C11—22no—
239Q8×C11—22no—
240Q8×C11—22no—
241Q8×C11—42no—
242Q8×C11—42no—
243Q8×C11—42no—
244Q8×C11—42no—
245Q8×C11—81no—
246Q8×C11—82no—
247Q8×C11—82no—
248D4×C11—22no—
249D4×C11—81no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—41no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—82no—
265C2×C4×C11—82no—
266C2×C4×C11#12011yescharacteristic
267C2×C4×C11#12011yescharacteristic
268C2×C4×C11#12011yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C8×C11—42no—
273C8×C11—42no—
274C8×C11—42no—
275#563—22no—
276Q82C22×C1111yescharacteristic
277#557—21no—
278#557C22×C1111yescharacteristic
279#556—21no—
280#556—21no—
281#556C22×C1111yescharacteristic
282#554C22×C1111yescharacteristic
283#552—21no—
284#544—21no—
285#542—21no—
286#541—21no—
287#541—21no—
288#541—22no—
289#533C22×C1111yescharacteristic
290#533C22×C1111yescharacteristic
291C2×C4⋊Q8C22×C1111yescharacteristic
292#529C22×C1111yescharacteristic
293#500C22×C1112yes—
294#498—21no—
295#497—21no—
296#491—21no—
297#487—21no—
298#487C22×C1112yes—
299#484—22no—
300#483—21no—
301#483—21no—
302#477—22no—
303#475C22×C1112yes—
304#475C22×C1112yes—
305#462C22×C1112yes—
306#461C22×C1112yes—
307#451—21no—
308#448—21no—
309#432C22×C1111yescharacteristic
310#431C22×C1111yescharacteristic
311#431C22×C1111yescharacteristic
312#333C22×C1112yes—
313#332C22×C1112yes—
314Q8⋊C8C22×C1112yes—
315Q8⋊C8C22×C1112yes—
316Q8⋊C8C22×C1112yes—
317D4⋊C8C22×C1112yes—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11C2×#12011yescharacteristic
325C4×C11—21no—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—41no—
330C4×C11—42no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—42no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—82no—
339C4×C11#57712yes—
340C4×C11#57812yes—
341C22×Q8—21no—
342C2×Q16—22no—
343C2×SD16—22no—
344C4⋊Q8—22no—
345C4⋊Q8—21no—
346C4⋊Q8—22no—
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8D4×C1111yescharacteristic
353C4⋊Q8D4×C1111yescharacteristic
354C4⋊Q8C23×C1112yes—
355C4⋊Q8C23×C1111yescharacteristic
356C4⋊Q8C23×C1111yescharacteristic
357#126—22no—
358#126—22no—
359#126—22no—
360#126—22no—
361#126—22no—
362#126—22no—
363#126—21no—
364#125—22no—
365#125—22no—
366#125—22no—
367#125—22no—
368#125—21no—
369#125—22no—
370#125—21no—
371#125—21no—
372#125—21no—
373#125D4×C1111yescharacteristic
374#124—22no—
375#124—21no—
376#124D4×C1111yescharacteristic
377#123—22no—
378#123—21no—
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383C22⋊Q8—22no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8D4×C1111yescharacteristic
387C22⋊Q8D4×C1111yescharacteristic
388C22⋊Q8D4×C1111yescharacteristic
389C22⋊Q8D4×C1112yes—
390#121D4×C1111yescharacteristic
391C4×Q8—22no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8D4×C1112yes—
400C4×Q8C23×C1111yescharacteristic
401C4×Q8C23×C1111yescharacteristic
402C4×Q8C23×C1111yescharacteristic
403C4×D4—21no—
404C4×D4—21no—
405C4×D4C23×C1111yescharacteristic
406#117—22no—
407#117—21no—
408#117—21no—
409#117—21no—
410#117—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C42C23×C1111yescharacteristic
415#107—24no—
416#106—22no—
417#106—22no—
418C4⋊C8—21no—
419C4⋊C8C23×C1112yes—
420C4⋊C8C23×C1112yes—
421#103—22no—
422#103—22no—
423#103—24no—
424#103—22no—
425#103—22no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429#97—21no—
430C4×C8—21no—
431C4×C8C23×C1112yes—
432C2×C11—41no—
433C2×C11—81no—
434C2×C11#301011yescharacteristic
435C2×C11#301111yescharacteristic
436C2×C11#302211yescharacteristic
437C2×Q8—22no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—22no—
441C2×Q8—41no—
442C2×Q8—82no—
443C2×Q8C2×D4×C1111yescharacteristic
444C2×Q8C2×D4×C1111yescharacteristic
445C2×Q8C2×D4×C1111yescharacteristic
446C2×Q8C2×D4×C1112yes—
447C2×D4—21no—
448C2×D4C2×D4×C1111yescharacteristic
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—41no—
452C22×C4C2×D4×C1111yescharacteristic
453C22×C4C2×D4×C1111yescharacteristic
454C22×C4C2×D4×C1111yescharacteristic
455Q16—82no—
456SD16—82no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—22no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4C2×D4×C1111yescharacteristic
489C4⋊C4C2×D4×C1111yescharacteristic
490C4⋊C4C2×D4×C1111yescharacteristic
491C4⋊C4C2×D4×C1111yescharacteristic
492C4⋊C4C2×D4×C1112yes—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—21no—
497C22⋊C4—22no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C42—22no—
505C42—22no—
506C42—22no—
507C42—22no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42C2×D4×C1111yescharacteristic
512C42C2×D4×C1111yescharacteristic
513C42C2×D4×C1111yescharacteristic
514C42C24×C1111yescharacteristic
515C11#1897311yescharacteristic, direct product factor, Sylow
516C23—21no—
517C23C11×#12011yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—22no—
521Q8—42no—
522Q8—42no—
523Q8—42no—
524Q8—42no—
525Q8—81no—
526Q8—82no—
527Q8—82no—
528D4—22no—
529D4—81no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4C11×#12011yescharacteristic
547C2×C4C11×#12011yescharacteristic
548C2×C4C11×#12011yescharacteristic
549C2×C4C22×D4×C1111yescharacteristic
550C2×C4C22×D4×C1111yescharacteristic
551C2×C4C22×D4×C1111yescharacteristic
552C8—42no—
553C8—42no—
554C8—42no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22C2×C11×#12011yescharacteristic
562C4—21no—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—41no—
567C4—42no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—42no—
573C4—41no—
574C4—41no—
575C4—82no—
576C4C11×#57712yes—
577C4C11×#57812yes—
578C2—41no—
579C2—81no—
580C2C11×#301011yescharacteristic
581C2C11×#301111yescharacteristic
582C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#121D4
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×#3230C2semidirect
3. C11×#3229C2semidirect
5. C11×#1650C2semidirect
6. C11×#1648C2semidirect
7. C11×#1645C2semidirect
8. C11×#1643C2semidirect
9. C11×#1554C2semidirect
10. C11×#1497C2semidirect
146. #18973C11direct (N × H)
226. #3230C2×C11semidirect
227. #3229C2×C11semidirect
229. #1650C2×C11semidirect
230. #1648C2×C11semidirect
231. #1645C2×C11semidirect
232. #1643C2×C11semidirect
233. #1554C2×C11semidirect
234. #1497C2×C11semidirect
515. C11#18973direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35552
C11×#32302
C11×#32292
C11×#32182
C11×#16502
C11×#16482
C11×#16452
C11×#16432
C11×#15542
C11×#14972
C11×#14822
#1897311