Finite Group Databasebeta

← C11×#18959 #14596152

Subgroups — C11×#18959 #14596152

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3554C211yesmaximal, characteristic
2C11×#3238C211yesmaximal, characteristic, complemented
3C11×#3230C211yesmaximal, characteristic, complemented
4C11×#3206C211yesmaximal, characteristic, complemented
5C11×#1637C212yesmaximal, complemented
6C11×#1636C212yesmaximal, complemented
7C11×#1631C212yesmaximal, complemented
8C11×#1630C212yesmaximal, complemented
9C11×#1553C211yesmaximal, characteristic, complemented
10C11×#1497C211yesmaximal, characteristic, complemented
11C11×#1482C211yesmaximal, characteristic, complemented
12C11×#562—22no—
13C11×#559—21no—
14C11×#559C2211yescharacteristic
15C11×#557C2211yescharacteristic
16C11×#554—21no—
17C11×#550C2211yescharacteristic
18D4×Q8×C11C2211yescharacteristic
19C11×#548—21no—
20C11×#547—21no—
21C11×#542—21no—
22C11×#542—21no—
23C11×#540—21no—
24C11×#539—22no—
25C11×#536—21no—
26C11×#533C2211yescharacteristic
27C11×#532C2211yescharacteristic
28C2×C11×C4⋊Q8C2211yescharacteristic
29C11×#529C2211yescharacteristic
30C11×#501—21no—
31C11×#500—21no—
32C11×#492C2212yes—
33C11×#489—21no—
34C11×#487—21no—
35C11×#487C2212yes—
36C11×#484—21no—
37C11×#484—21no—
38C11×#483—21no—
39C11×#480—21no—
40C11×#477C2212yes—
41C11×#477C2212yes—
42C11×#477C2212yes—
43C11×#476C2212yes—
44C11×#461—22no—
45C11×#448—22no—
46C11×#432C2211yescharacteristic
47C11×#431C2211yescharacteristic
48C11×#431C2211yescharacteristic
49C11×#332C2212yes—
50C11×#331C2212yes—
51C11×Q8⋊C8C2212yes—
52C11×Q8⋊C8C2212yes—
53C11×Q8⋊C8C2212yes—
54C11×D4⋊C8C2212yes—
55C2×C11×#41—21no—
56C2×C11×#41—21no—
57C22×Q8×C11—21no—
58C22×Q8×C11—21no—
59C2×C11×SD16—24no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8D411yescharacteristic
66C11×C4⋊Q8D411yescharacteristic
67C11×C4⋊Q8C2312yes—
68C11×C4⋊Q8C2311yescharacteristic
69C11×#127—21no—
70C11×#127C2311yescharacteristic
71C11×#126—22no—
72C11×#126—21no—
73C11×#125—22no—
74C11×#125—21no—
75C11×#125—21no—
76C11×#125D411yescharacteristic
77C11×#124—22no—
78C11×#124—22no—
79C11×#124—21no—
80C11×#124—21no—
81C11×#124—21no—
82C11×#124D411yescharacteristic
83C11×#123—22no—
84C11×#123—22no—
85C11×#123—22no—
86C11×#123—22no—
87C11×#123—22no—
88C11×#123—22no—
89C11×#123—21no—
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8—22no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8—21no—
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8—21no—
97C11×C22⋊Q8D411yescharacteristic
98C11×C22⋊Q8D411yescharacteristic
99C11×C22⋊Q8D411yescharacteristic
100C11×#121—22no—
101C11×#121—22no—
102C11×#121—22no—
103C11×#121—21no—
104C11×#121—21no—
105C11×#121D411yescharacteristic
106C11×#121D412yes—
107C4×Q8×C11—21no—
108C4×Q8×C11—21no—
109C4×Q8×C11—21no—
110C4×Q8×C11C2311yescharacteristic
111C4×Q8×C11C2311yescharacteristic
112C4×Q8×C11C2311yescharacteristic
113C4×D4×C11—22no—
114C4×D4×C11—21no—
115C4×D4×C11—21no—
116C4×D4×C11—21no—
117C4×D4×C11—21no—
118C4×D4×C11—21no—
119C4×D4×C11—21no—
120C4×D4×C11D412yes—
121C4×D4×C11C2311yescharacteristic
122C11×#117—21no—
123C11×#117—21no—
124C2×C11×C4⋊C4—22no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C42×C11C2311yescharacteristic
128C11×#107—22no—
129C11×#107—22no—
130C11×#107—22no—
131C11×#106—22no—
132C11×C4⋊C8—21no—
133C11×C4⋊C8C2312yes—
134C11×C4⋊C8C2312yes—
135C11×#103—22no—
136C11×#103—22no—
137C11×#103—22no—
138C11×#103—24no—
139C11×#102—22no—
140C11×C22⋊C8—21no—
141C11×C22⋊C8—21no—
142C11×C22⋊C8—21no—
143C11×#97—21no—
144C4×C8×C11—21no—
145C4×C8×C11C2312yes—
146#18959C1111yesmaximal, characteristic, direct product factor, Sylow
147C11×#41—82no—
148C11×#41—82no—
149C2×Q8×C11—22no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—22no—
153C2×Q8×C11—41no—
154C2×Q8×C11—82no—
155C2×Q8×C11—82no—
156C2×Q8×C11C2×D411yescharacteristic
157C2×Q8×C11C2×D411yescharacteristic
158C2×Q8×C11C2×D411yescharacteristic
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—21no—
162C2×D4×C11—22no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11C2×D411yescharacteristic
166C2×D4×C11C2×D412yes—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—21no—
171C22×C4×C11—22no—
172C22×C4×C11—41no—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C11×SD16—84no—
177C2×C8×C11—22no—
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—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
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—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—41no—
199C11×C4⋊C4—41no—
200C11×C4⋊C4C2×D412yes—
201C11×C4⋊C4C2×D411yescharacteristic
202C11×C4⋊C4C2×D411yescharacteristic
203C11×C4⋊C4C2×D411yescharacteristic
204C11×C4⋊C4C2×D411yescharacteristic
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—21no—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—21no—
213C11×C22⋊C4—21no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—21no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—21no—
219C42×C11—22no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11C2×D411yescharacteristic
224C42×C11C2×D411yescharacteristic
225C42×C11C2×D411yescharacteristic
226C42×C11C2411yescharacteristic
227#3554C2×C1111yescharacteristic
228#3238C2×C1111yescharacteristic, complemented
229#3230C2×C1111yescharacteristic, complemented
230#3206C2×C1111yescharacteristic, complemented
231#1637C2×C1112yescomplemented
232#1636C2×C1112yescomplemented
233#1631C2×C1112yescomplemented
234#1630C2×C1112yescomplemented
235#1553C2×C1111yescharacteristic, complemented
236#1497C2×C1111yescharacteristic, complemented
237#1482C2×C1111yescharacteristic, complemented
238C23×C11—21no—
239C23×C11—22no—
240C23×C11#12011yescharacteristic
241Q8×C11—22no—
242Q8×C11—22no—
243Q8×C11—22no—
244Q8×C11—44no—
245Q8×C11—42no—
246Q8×C11—81no—
247Q8×C11—82no—
248Q8×C11—82no—
249D4×C11—22no—
250D4×C11—42no—
251D4×C11—42no—
252D4×C11—42no—
253D4×C11—81no—
254D4×C11—82no—
255D4×C11—82no—
256D4×C11—82no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—41no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—82no—
271C2×C4×C11—82no—
272C2×C4×C11—82no—
273C2×C4×C11—82no—
274C2×C4×C11—82no—
275C2×C4×C11#12011yescharacteristic
276C2×C4×C11#12011yescharacteristic
277C2×C4×C11#12011yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C8×C11—42no—
282C8×C11—42no—
283C8×C11—42no—
284#562—22no—
285#559—21no—
286#559C22×C1111yescharacteristic
287#557C22×C1111yescharacteristic
288#554—21no—
289#550C22×C1111yescharacteristic
290D4×Q8C22×C1111yescharacteristic
291#548—21no—
292#547—21no—
293#542—21no—
294#542—21no—
295#540—21no—
296#539—22no—
297#536—21no—
298#533C22×C1111yescharacteristic
299#532C22×C1111yescharacteristic
300C2×C4⋊Q8C22×C1111yescharacteristic
301#529C22×C1111yescharacteristic
302#501—21no—
303#500—21no—
304#492C22×C1112yes—
305#489—21no—
306#487—21no—
307#487C22×C1112yes—
308#484—21no—
309#484—21no—
310#483—21no—
311#480—21no—
312#477C22×C1112yes—
313#477C22×C1112yes—
314#477C22×C1112yes—
315#476C22×C1112yes—
316#461—22no—
317#448—22no—
318#432C22×C1111yescharacteristic
319#431C22×C1111yescharacteristic
320#431C22×C1111yescharacteristic
321#332C22×C1112yes—
322#331C22×C1112yes—
323Q8⋊C8C22×C1112yes—
324Q8⋊C8C22×C1112yes—
325Q8⋊C8C22×C1112yes—
326D4⋊C8C22×C1112yes—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—41no—
331C22×C11—42no—
332C22×C11—41no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—41no—
336C22×C11C2×#12011yescharacteristic
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—42no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—82no—
350C4×C11#57712yes—
351C4×C11#57812yes—
352C2×#41—21no—
353C2×#41—21no—
354C22×Q8—21no—
355C22×Q8—21no—
356C2×SD16—24no—
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8D4×C1111yescharacteristic
363C4⋊Q8D4×C1111yescharacteristic
364C4⋊Q8C23×C1112yes—
365C4⋊Q8C23×C1111yescharacteristic
366#127—21no—
367#127C23×C1111yescharacteristic
368#126—22no—
369#126—21no—
370#125—22no—
371#125—21no—
372#125—21no—
373#125D4×C1111yescharacteristic
374#124—22no—
375#124—22no—
376#124—21no—
377#124—21no—
378#124—21no—
379#124D4×C1111yescharacteristic
380#123—22no—
381#123—22no—
382#123—22no—
383#123—22no—
384#123—22no—
385#123—22no—
386#123—21no—
387C22⋊Q8—22no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8—21no—
392C22⋊Q8—22no—
393C22⋊Q8—21no—
394C22⋊Q8D4×C1111yescharacteristic
395C22⋊Q8D4×C1111yescharacteristic
396C22⋊Q8D4×C1111yescharacteristic
397#121—22no—
398#121—22no—
399#121—22no—
400#121—21no—
401#121—21no—
402#121D4×C1111yescharacteristic
403#121D4×C1112yes—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8C23×C1111yescharacteristic
408C4×Q8C23×C1111yescharacteristic
409C4×Q8C23×C1111yescharacteristic
410C4×D4—22no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4D4×C1112yes—
418C4×D4C23×C1111yescharacteristic
419#117—21no—
420#117—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C42C23×C1111yescharacteristic
425#107—22no—
426#107—22no—
427#107—22no—
428#106—22no—
429C4⋊C8—21no—
430C4⋊C8C23×C1112yes—
431C4⋊C8C23×C1112yes—
432#103—22no—
433#103—22no—
434#103—22no—
435#103—24no—
436#102—22no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—21no—
440#97—21no—
441C4×C8—21no—
442C4×C8C23×C1112yes—
443C2×C11—41no—
444C2×C11—81no—
445C2×C11—82no—
446C2×C11#300911yescharacteristic
447C2×C11#301111yescharacteristic
448C2×C11#302111yescharacteristic
449#41—82no—
450#41—82no—
451C2×Q8—22no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—22no—
455C2×Q8—41no—
456C2×Q8—82no—
457C2×Q8—82no—
458C2×Q8C2×D4×C1111yescharacteristic
459C2×Q8C2×D4×C1111yescharacteristic
460C2×Q8C2×D4×C1111yescharacteristic
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4C2×D4×C1111yescharacteristic
468C2×D4C2×D4×C1112yes—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—41no—
475C22×C4C2×D4×C1111yescharacteristic
476C22×C4C2×D4×C1111yescharacteristic
477C22×C4C2×D4×C1111yescharacteristic
478SD16—84no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4C2×D4×C1112yes—
503C4⋊C4C2×D4×C1111yescharacteristic
504C4⋊C4C2×D4×C1111yescharacteristic
505C4⋊C4C2×D4×C1111yescharacteristic
506C4⋊C4C2×D4×C1111yescharacteristic
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—21no—
521C42—22no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42C2×D4×C1111yescharacteristic
526C42C2×D4×C1111yescharacteristic
527C42C2×D4×C1111yescharacteristic
528C42C24×C1111yescharacteristic
529C11#1895911yescharacteristic, direct product factor, Sylow
530C23—21no—
531C23—22no—
532C23C11×#12011yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—22no—
536Q8—44no—
537Q8—42no—
538Q8—81no—
539Q8—82no—
540Q8—82no—
541D4—22no—
542D4—42no—
543D4—42no—
544D4—42no—
545D4—81no—
546D4—82no—
547D4—82no—
548D4—82no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4—82no—
566C2×C4—82no—
567C2×C4C11×#12011yescharacteristic
568C2×C4C11×#12011yescharacteristic
569C2×C4C11×#12011yescharacteristic
570C2×C4C22×D4×C1111yescharacteristic
571C2×C4C22×D4×C1111yescharacteristic
572C2×C4C22×D4×C1111yescharacteristic
573C8—42no—
574C8—42no—
575C8—42no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—41no—
580C22—42no—
581C22—41no—
582C22—42no—
583C22—42no—
584C22—41no—
585C22C2×C11×#12011yescharacteristic
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—41no—
591C4—41no—
592C4—42no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—82no—
599C4C11×#57712yes—
600C4C11×#57812yes—
601C2—41no—
602C2—81no—
603C2—82no—
604C2C11×#300911yescharacteristic
605C2C11×#301111yescharacteristic
606C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3554C2
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×#3230C2semidirect
4. C11×#3206C2semidirect
5. C11×#1637C2semidirect
6. C11×#1636C2semidirect
7. C11×#1631C2semidirect
8. C11×#1630C2semidirect
9. C11×#1553C2semidirect
10. C11×#1497C2semidirect
11. C11×#1482C2semidirect
146. #18959C11direct (N × H)
228. #3238C2×C11semidirect
229. #3230C2×C11semidirect
230. #3206C2×C11semidirect
231. #1637C2×C11semidirect
232. #1636C2×C11semidirect
233. #1631C2×C11semidirect
234. #1630C2×C11semidirect
235. #1553C2×C11semidirect
236. #1497C2×C11semidirect
237. #1482C2×C11semidirect
529. C11#18959direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35542
C11×#32382
C11×#32302
C11×#32062
C11×#16372
C11×#16362
C11×#16312
C11×#16302
C11×#15532
C11×#14972
C11×#14822
#1895911