Finite Group Databasebeta

← C11×#18209 #14595402

Subgroups — C11×#18209 #14595402

Order 2816.

938 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3491C211yesmaximal, characteristic
2C11×#3108C212yesmaximal, complemented
3C11×#2599C211yesmaximal, characteristic, complemented
4C11×#1609C212yesmaximal, complemented
5C11×#1608C211yesmaximal, characteristic, complemented
6C11×#1607C211yesmaximal, characteristic
7C11×#1603C212yesmaximal, complemented
8C11×#1602C211yesmaximal, characteristic, complemented
9C11×#1601C211yesmaximal, characteristic
10C11×#1521C212yesmaximal, complemented
11C11×#1458C211yesmaximal, characteristic, complemented
12C11×#552—22no—
13C11×#552—22no—
14C11×#551—22no—
15C11×#551—22no—
16C11×#543C2211yescharacteristic
17C11×#539—21no—
18C11×#539C2212yes—
19C11×#534C2211yescharacteristic
20C11×#529—21no—
21C11×#529C2212yes—
22C2×C11×#123—21no—
23C11×#518—21no—
24C2×C4×Q8×C11C2211yescharacteristic, complemented
25C2×C11×#117C2211yescharacteristic
26C11×#483C2212yescomplemented
27C11×#480C2212yes—
28C11×#479—22no—
29C11×#464—22no—
30C11×#451C2212yescomplemented
31C11×#448C2212yes—
32C4×C11×Q16—22no—
33C4×C11×SD16—22no—
34C11×#431C2212yescomplemented
35C11×#398C2211yescharacteristic, complemented
36C11×#397C2211yescharacteristic
37C11×#395C2211yescharacteristic, complemented
38C11×#393C2211yescharacteristic
39C11×#388—21no—
40C11×#387—21no—
41C11×#387—21no—
42C11×#385—21no—
43C11×#383C2211yescharacteristic, complemented
44C11×#328C2212yescomplemented
45C11×#328C2212yescomplemented
46C11×#327C2212yes—
47C11×#327C2212yes—
48C11×#324C2212yescomplemented
49C11×#323C2211yescharacteristic
50C11×#323C2211yescharacteristic
51C22×Q8×C11C2311yescharacteristic
52C22×D4×C11—21no—
53C23×C4×C11D411yescharacteristic
54C2×C11×Q16—22no—
55C2×C11×SD16—22no—
56C11×#126—22no—
57C11×#126—22no—
58C11×#126—22no—
59C11×#126—22no—
60C11×#125—21no—
61C11×#125—22no—
62C11×#125—22no—
63C11×#125D412yes—
64C11×#124—21no—
65C11×#124D412yes—
66C11×#123—22no—
67C11×#123—22no—
68C11×#123—22no—
69C11×#123—22no—
70C11×#123—22no—
71C11×#123—22no—
72C11×#123—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8C2312yes—
79C11×#121—21no—
80C11×#121C2312yes—
81C11×#120—22no—
82C4×Q8×C11—21no—
83C4×Q8×C11—22no—
84C4×Q8×C11—22no—
85C4×Q8×C11D412yes—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—21no—
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11D412yes—
92C11×#117—22no—
93C11×#117—22no—
94C11×#117—22no—
95C11×#117—22no—
96C11×#117—22no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4D411yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4D411yescharacteristic
112C2×C11×C22⋊C4C2311yescharacteristic
113C2×C42×C11—21no—
114C2×C42×C11D411yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C11×#107—22no—
117C11×#106—22no—
118C11×C4⋊C8—22no—
119C11×#103—22no—
120C11×#103—22no—
121C11×#103—22no—
122C11×#102—22no—
123C11×C22⋊C8C2312yes—
124C11×C22⋊C8C2312yes—
125C4×C8×C11—22no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95C2311yescharacteristic
133C11×#95C2311yescharacteristic
134#18209C1111yesmaximal, characteristic, direct product factor, Sylow
135C24×C11—21no—
136C24×C11C2×D411yescharacteristic
137C2×Q8×C11—21no—
138C2×Q8×C11—22no—
139C2×Q8×C11—42no—
140C2×Q8×C11C2×D412yes—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—21no—
144C2×D4×C11—42no—
145C2×D4×C11—42no—
146C2×D4×C11C2×D412yes—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—22no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—41no—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2411yescharacteristic
166C11×Q16—44no—
167C11×SD16—44no—
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—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4—41no—
186C11×C4⋊C4—41no—
187C11×C4⋊C4C2×D412yes—
188C11×C4⋊C4C2×D412yes—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—42no—
202C11×C22⋊C4—42no—
203C42×C11—22no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—22no—
207C42×C11—42no—
208C42×C11C2×D412yes—
209C42×C11C2×D412yes—
210#3491C2×C1111yescharacteristic
211#3108C2×C1112yescomplemented
212#2599C2×C1111yescharacteristic, complemented
213#1609C2×C1112yescomplemented
214#1608C2×C1111yescharacteristic, complemented
215#1607C2×C1111yescharacteristic
216#1603C2×C1112yescomplemented
217#1602C2×C1111yescharacteristic, complemented
218#1601C2×C1111yescharacteristic
219#1521C2×C1112yescomplemented
220#1458C2×C1111yescharacteristic, complemented
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—22no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—42no—
227C23×C11—81no—
228C23×C11—81no—
229C23×C11#13512yes—
230C23×C11C22×D411yescharacteristic
231Q8×C11—24no—
232Q8×C11—42no—
233Q8×C11—42no—
234Q8×C11—81no—
235D4×C11—42no—
236D4×C11—44no—
237D4×C11—42no—
238D4×C11—42no—
239D4×C11—81no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—82no—
270C2×C4×C11—81no—
271C2×C4×C11—82no—
272C2×C4×C11—81no—
273C2×C4×C11#12012yes—
274C2×C4×C11#12011yescharacteristic
275C2×C4×C11#12011yescharacteristic
276C2×C4×C11C22×D412yes—
277C8×C11—42no—
278C8×C11—42no—
279#552—22no—
280#552—22no—
281#551—22no—
282#551—22no—
283#543C22×C1111yescharacteristic
284#539—21no—
285#539C22×C1112yes—
286#534C22×C1111yescharacteristic
287#529—21no—
288#529C22×C1112yes—
289C2×#123—21no—
290#518—21no—
291C2×C4×Q8C22×C1111yescharacteristic, complemented
292C2×#117C22×C1111yescharacteristic
293#483C22×C1112yescomplemented
294#480C22×C1112yes—
295#479—22no—
296#464—22no—
297#451C22×C1112yescomplemented
298#448C22×C1112yes—
299C4×Q16—22no—
300C4×SD16—22no—
301#431C22×C1112yescomplemented
302#398C22×C1111yescharacteristic, complemented
303#397C22×C1111yescharacteristic
304#395C22×C1111yescharacteristic, complemented
305#393C22×C1111yescharacteristic
306#388—21no—
307#387—21no—
308#387—21no—
309#385—21no—
310#383C22×C1111yescharacteristic, complemented
311#328C22×C1112yescomplemented
312#328C22×C1112yescomplemented
313#327C22×C1112yes—
314#327C22×C1112yes—
315#324C22×C1112yescomplemented
316#323C22×C1111yescharacteristic
317#323C22×C1111yescharacteristic
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—22no—
321C22×C11—42no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—81no—
328C22×C11—162no—
329C22×C11C2×#12011yescharacteristic
330C22×C11C2×#13511yescharacteristic
331C22×C11#57511yescharacteristic
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—41no—
337C4×C11—42no—
338C4×C11—41no—
339C4×C11—42no—
340C4×C11—42no—
341C4×C11—41no—
342C4×C11—42no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11—81no—
346C22×Q8C23×C1111yescharacteristic
347C22×D4—21no—
348C23×C4D4×C1111yescharacteristic
349C2×Q16—22no—
350C2×SD16—22no—
351#126—22no—
352#126—22no—
353#126—22no—
354#126—22no—
355#125—21no—
356#125—22no—
357#125—22no—
358#125D4×C1112yes—
359#124—21no—
360#124D4×C1112yes—
361#123—22no—
362#123—22no—
363#123—22no—
364#123—22no—
365#123—22no—
366#123—22no—
367#123—22no—
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—21no—
372C22⋊Q8—22no—
373C22⋊Q8C23×C1112yes—
374#121—21no—
375#121C23×C1112yes—
376#120—22no—
377C4×Q8—21no—
378C4×Q8—22no—
379C4×Q8—22no—
380C4×Q8D4×C1112yes—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—21no—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4D4×C1112yes—
387#117—22no—
388#117—22no—
389#117—22no—
390#117—22no—
391#117—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4D4×C1111yescharacteristic
398C2×C4⋊C4C23×C1111yescharacteristic
399C2×C4⋊C4C23×C1111yescharacteristic
400C2×C22⋊C4—22no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4D4×C1111yescharacteristic
407C2×C22⋊C4C23×C1111yescharacteristic
408C2×C42—21no—
409C2×C42D4×C1111yescharacteristic
410C2×C42C23×C1111yescharacteristic
411#107—22no—
412#106—22no—
413C4⋊C8—22no—
414#103—22no—
415#103—22no—
416#103—22no—
417#102—22no—
418C22⋊C8C23×C1112yes—
419C22⋊C8C23×C1112yes—
420C4×C8—22no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95C23×C1111yescharacteristic
428#95C23×C1111yescharacteristic
429C2×C11—21no—
430C2×C11—21no—
431C2×C11—42no—
432C2×C11—82no—
433C2×C11#300211yescharacteristic
434C2×C11#302211yescharacteristic
435C2×C11#302511yescharacteristic
436C24—21no—
437C24C2×D4×C1111yescharacteristic
438C2×Q8—21no—
439C2×Q8—22no—
440C2×Q8—42no—
441C2×Q8C2×D4×C1112yes—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—21no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4C2×D4×C1112yes—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—41no—
461C22×C4C2×D4×C1111yescharacteristic
462C22×C4C2×D4×C1111yescharacteristic
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C2×D4×C1111yescharacteristic
465C22×C4C2×D4×C1111yescharacteristic
466C22×C4C24×C1111yescharacteristic
467Q16—44no—
468SD16—44no—
469C2×C8—22no—
470C2×C8—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—42no—
485C4⋊C4—42no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4C2×D4×C1112yes—
489C4⋊C4C2×D4×C1112yes—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—42no—
503C22⋊C4—42no—
504C42—22no—
505C42—21no—
506C42—21no—
507C42—22no—
508C42—42no—
509C42C2×D4×C1112yes—
510C42C2×D4×C1112yes—
511C11#1820911yescharacteristic, direct product factor, Sylow
512C23—21no—
513C23—21no—
514C23—22no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—81no—
519C23—81no—
520C23C11×#13512yes—
521C23C22×D4×C1111yescharacteristic
522Q8—24no—
523Q8—42no—
524Q8—42no—
525Q8—81no—
526D4—42no—
527D4—44no—
528D4—42no—
529D4—42no—
530D4—81no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—82no—
561C2×C4—81no—
562C2×C4—82no—
563C2×C4—81no—
564C2×C4C11×#12012yes—
565C2×C4C11×#12011yescharacteristic
566C2×C4C11×#12011yescharacteristic
567C2×C4C22×D4×C1112yes—
568C8—42no—
569C8—42no—
570C22—21no—
571C22—21no—
572C22—22no—
573C22—42no—
574C22—41no—
575C22—41no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—81no—
580C22—162no—
581C22C2×C11×#12011yescharacteristic
582C22C2×C11×#13511yescharacteristic
583C22C11×#57511yescharacteristic
584C4—21no—
585C4—21no—
586C4—22no—
587C4—22no—
588C4—41no—
589C4—42no—
590C4—41no—
591C4—42no—
592C4—42no—
593C4—41no—
594C4—42no—
595C4—81no—
596C4—81no—
597C4—81no—
598C2—21no—
599C2—21no—
600C2—42no—
601C2—82no—
602C2C11×#300211yescharacteristic
603C2C11×#302211yescharacteristic
604C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#534C22
LCSG ▷ C22×C4 ▷ 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×#3108C2semidirect
3. C11×#2599C2semidirect
4. C11×#1609C2semidirect
5. C11×#1608C2semidirect
7. C11×#1603C2semidirect
8. C11×#1602C2semidirect
10. C11×#1521C2semidirect
11. C11×#1458C2semidirect
24. C2×C4×Q8×C11C22semidirect
26. C11×#483C22semidirect
30. C11×#451C22semidirect
34. C11×#431C22semidirect
35. C11×#398C22semidirect
37. C11×#395C22semidirect
43. C11×#383C22semidirect
44. C11×#328C22semidirect
45. C11×#328C22semidirect
48. C11×#324C22semidirect
134. #18209C11direct (N × H)
211. #3108C2×C11semidirect
212. #2599C2×C11semidirect
213. #1609C2×C11semidirect
214. #1608C2×C11semidirect
216. #1603C2×C11semidirect
217. #1602C2×C11semidirect
219. #1521C2×C11semidirect
220. #1458C2×C11semidirect
291. C2×C4×Q8C22×C11semidirect
293. #483C22×C11semidirect
297. #451C22×C11semidirect
301. #431C22×C11semidirect
302. #398C22×C11semidirect
304. #395C22×C11semidirect
310. #383C22×C11semidirect
311. #328C22×C11semidirect
312. #328C22×C11semidirect
315. #324C22×C11semidirect
511. C11#18209direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34912
C11×#31082
C11×#25992
C11×#16092
C11×#16082
C11×#16072
C11×#16032
C11×#16022
C11×#16012
C11×#15212
C11×#14582
#1820911