Finite Group Databasebeta

← C11×#18427 #14595620

Subgroups — C11×#18427 #14595620

Order 2816.

996 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×#3558C211yesmaximal, characteristic
2C11×#3218C211yesmaximal, characteristic, complemented
3C11×#3206C211yesmaximal, characteristic, complemented
4C11×#2640C211yesmaximal, characteristic, complemented
5C11×#1606C214yesmaximal, complemented
6C11×#1601C214yesmaximal, complemented
7C11×#1505C211yesmaximal, characteristic, complemented
8C11×#1500C211yesmaximal, characteristic, complemented
9C11×#1469C211yesmaximal, characteristic, complemented
10C11×#562—21no—
11C11×H(3,𝔽4)—21no—
12C11×#559—21no—
13C11×#548—21no—
14C11×#546—21no—
15C11×#546—22no—
16D42×C11—21no—
17C11×#542—21no—
18C11×#538—22no—
19C11×#538C2212yes—
20C11×#535—21no—
21C11×#534C2212yes—
22C11×#532C2211yescharacteristic
23C2×C11×C4⋊Q8C2211yescharacteristic, complemented
24C11×#529C2211yescharacteristic
25C2×C11×#124C2211yescharacteristic
26C11×#497—21no—
27C11×#492—21no—
28C11×#491—21no—
29C11×#487—21no—
30C11×#462—21no—
31C11×#461—22no—
32C11×#461—21no—
33C11×#451C2212yescomplemented
34C11×#448C2212yes—
35C11×#448C2214yescomplemented
36C11×#432C2211yescharacteristic, complemented
37C11×#431C2211yescharacteristic, complemented
38C11×#397—22no—
39C11×#393C2214yescomplemented
40C11×#391—21no—
41C11×#390—21no—
42C11×#376C2211yescharacteristic, complemented
43C11×#328C2212yescomplemented
44C11×#327C2212yes—
45C11×#327C2214yescomplemented
46C11×#323C2214yescomplemented
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C22×Q8×C11D411yescharacteristic
50C22×Q8×C11C2312yes—
51C22×D4×C11—21no—
52C22×D4×C11—22no—
53C22×D4×C11D411yescharacteristic
54C2×C11×Q16—22no—
55C2×C11×SD16—24no—
56C2×C11×SD16—22no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8D411yescharacteristic
62C11×#127—21no—
63C11×#127D411yescharacteristic
64C11×#126—22no—
65C11×#126—21no—
66C11×#125D411yescharacteristic
67C11×#124—21no—
68C11×#124—22no—
69C11×#124—22no—
70C11×#124—22no—
71C11×#124—21no—
72C11×#124—21no—
73C11×#124—21no—
74C11×#124—21no—
75C11×#124—21no—
76C11×#124D411yescharacteristic
77C11×#123—22no—
78C11×#123—21no—
79C11×#123—22no—
80C11×#123—22no—
81C11×#123—22no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8C2311yescharacteristic
86C11×#121—22no—
87C11×#121—22no—
88C11×#121—22no—
89C11×#121—21no—
90C11×#121—22no—
91C11×#121—21no—
92C11×#121—22no—
93C11×#121C2311yescharacteristic
94C11×#121C2312yes—
95C11×#120—22no—
96C11×#120—22no—
97C11×#120—22no—
98C11×#120—22no—
99C11×#120—22no—
100C4×Q8×C11—21no—
101C4×Q8×C11D411yescharacteristic
102C4×D4×C11—22no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C4×D4×C11—22no—
106C4×D4×C11—21no—
107C4×D4×C11D411yescharacteristic
108C4×D4×C11D412yes—
109C11×#117—21no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4—24no—
114C2×C11×C22⋊C4D412yes—
115C2×C11×C22⋊C4C2312yes—
116C2×C42×C11—21no—
117C2×C42×C11C2311yescharacteristic
118C11×C4⋊C8—21no—
119C11×C4⋊C8—21no—
120C11×#103—22no—
121C11×#103—22no—
122C11×#103—24no—
123C11×C22⋊C8C2312yes—
124C11×C22⋊C8C2312yes—
125C11×#97—21no—
126C4×C8×C11—21no—
127C11×#95—21no—
128C11×#95—24no—
129C11×#95C2312yes—
130#18427C1111yesmaximal, characteristic, direct product factor, Sylow
131C24×C11—22no—
132C24×C11C2×D412yes—
133C11×#41—82no—
134C11×#41—82no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—22no—
139C2×Q8×C11—22no—
140C2×Q8×C11—42no—
141C2×Q8×C11—82no—
142C2×Q8×C11C2×D411yescharacteristic
143C2×D4×C11—22no—
144C2×D4×C11—21no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—21no—
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—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—21no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2411yescharacteristic
169C11×Q16—82no—
170C11×SD16—84no—
171C11×SD16—82no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—41no—
182C11×C4⋊C4—41no—
183C11×C4⋊C4—41no—
184C11×C4⋊C4—41no—
185C11×C4⋊C4C2×D412yes—
186C11×C4⋊C4C2×D411yescharacteristic
187C11×C4⋊C4C2×D411yescharacteristic
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—21no—
194C11×C22⋊C4—21no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—21no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—21no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—84no—
205C42×C11—22no—
206C42×C11—21no—
207C42×C11—42no—
208C42×C11C2×D411yescharacteristic
209C42×C11C2×D411yescharacteristic
210C42×C11C2×D411yescharacteristic
211C42×C11C2×D411yescharacteristic
212#3558C2×C1111yescharacteristic
213#3218C2×C1111yescharacteristic, complemented
214#3206C2×C1111yescharacteristic, complemented
215#2640C2×C1111yescharacteristic, complemented
216#1606C2×C1114yescomplemented
217#1601C2×C1114yescomplemented
218#1505C2×C1111yescharacteristic, complemented
219#1500C2×C1111yescharacteristic, complemented
220#1469C2×C1111yescharacteristic, complemented
221C23×C11—22no—
222C23×C11—21no—
223C23×C11—22no—
224C23×C11—24no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—82no—
228C23×C11—82no—
229C23×C11—82no—
230C23×C11C22×D411yescharacteristic
231Q8×C11—41no—
232Q8×C11—44no—
233Q8×C11—42no—
234Q8×C11—42no—
235Q8×C11—42no—
236Q8×C11—81no—
237Q8×C11—81no—
238D4×C11—42no—
239D4×C11—41no—
240D4×C11—42no—
241D4×C11—44no—
242D4×C11—42no—
243D4×C11—42no—
244D4×C11—81no—
245D4×C11—81no—
246D4×C11—82no—
247D4×C11—82no—
248D4×C11—82no—
249D4×C11—82no—
250D4×C11—82no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—41no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—44no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—82no—
267C2×C4×C11—82no—
268C2×C4×C11—82no—
269C2×C4×C11#12011yescharacteristic
270C2×C4×C11#12011yescharacteristic
271C2×C4×C11#12011yescharacteristic
272C2×C4×C11#12011yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C8×C11—42no—
276C8×C11—42no—
277#562—21no—
278H(3,𝔽4)—21no—
279#559—21no—
280#548—21no—
281#546—21no—
282#546—22no—
283D42—21no—
284#542—21no—
285#538—22no—
286#538C22×C1112yes—
287#535—21no—
288#534C22×C1112yes—
289#532C22×C1111yescharacteristic
290C2×C4⋊Q8C22×C1111yescharacteristic, complemented
291#529C22×C1111yescharacteristic
292C2×#124C22×C1111yescharacteristic
293#497—21no—
294#492—21no—
295#491—21no—
296#487—21no—
297#462—21no—
298#461—22no—
299#461—21no—
300#451C22×C1112yescomplemented
301#448C22×C1112yes—
302#448C22×C1114yescomplemented
303#432C22×C1111yescharacteristic, complemented
304#431C22×C1111yescharacteristic, complemented
305#397—22no—
306#393C22×C1114yescomplemented
307#391—21no—
308#390—21no—
309#376C22×C1111yescharacteristic, complemented
310#328C22×C1112yescomplemented
311#327C22×C1112yes—
312#327C22×C1114yescomplemented
313#323C22×C1114yescomplemented
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—41no—
324C22×C11—42no—
325C22×C11—84no—
326C22×C11—164no—
327C22×C11C2×#12011yescharacteristic
328C22×C11#57712yes—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—41no—
335C4×C11—42no—
336C4×C11—41no—
337C4×C11—42no—
338C4×C11—41no—
339C4×C11—82no—
340C4×C11—82no—
341C4×C11#45512yes—
342C2×#41—21no—
343C2×#41—21no—
344C22×Q8D4×C1111yescharacteristic
345C22×Q8C23×C1112yes—
346C22×D4—21no—
347C22×D4—22no—
348C22×D4D4×C1111yescharacteristic
349C2×Q16—22no—
350C2×SD16—22no—
351C2×SD16—24no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—21no—
355C4⋊Q8—21no—
356C4⋊Q8D4×C1111yescharacteristic
357#127—21no—
358#127D4×C1111yescharacteristic
359#126—22no—
360#126—21no—
361#125D4×C1111yescharacteristic
362#124—21no—
363#124—22no—
364#124—22no—
365#124—22no—
366#124—21no—
367#124—21no—
368#124—21no—
369#124—21no—
370#124—21no—
371#124D4×C1111yescharacteristic
372#123—22no—
373#123—21no—
374#123—22no—
375#123—22no—
376#123—22no—
377C22⋊Q8—22no—
378C22⋊Q8—21no—
379C22⋊Q8—22no—
380C22⋊Q8C23×C1111yescharacteristic
381#121—22no—
382#121—22no—
383#121—22no—
384#121—21no—
385#121—22no—
386#121—21no—
387#121—22no—
388#121C23×C1111yescharacteristic
389#121C23×C1112yes—
390#120—22no—
391#120—22no—
392#120—22no—
393#120—22no—
394#120—22no—
395C4×Q8—21no—
396C4×Q8D4×C1111yescharacteristic
397C4×D4—22no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—22no—
401C4×D4—21no—
402C4×D4D4×C1111yescharacteristic
403C4×D4D4×C1112yes—
404#117—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4D4×C1112yes—
410C2×C22⋊C4C23×C1112yes—
411C2×C42—21no—
412C2×C42C23×C1111yescharacteristic
413C4⋊C8—21no—
414C4⋊C8—21no—
415#103—22no—
416#103—24no—
417#103—22no—
418C22⋊C8C23×C1112yes—
419C22⋊C8C23×C1112yes—
420#97—21no—
421C4×C8—21no—
422#95—21no—
423#95—24no—
424#95C23×C1112yes—
425C2×C11—22no—
426C2×C11—82no—
427C2×C11—82no—
428C2×C11—81no—
429C2×C11#300911yescharacteristic
430C2×C11C2×#45511yescharacteristic
431C2×C11#302711yescharacteristic
432C24—22no—
433C24C2×D4×C1112yes—
434#41—82no—
435#41—82no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—42no—
442C2×Q8—82no—
443C2×Q8C2×D4×C1111yescharacteristic
444C2×D4—22no—
445C2×D4—21no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—42no—
456C2×D4—82no—
457C2×D4—84no—
458C2×D4C2×D4×C1111yescharacteristic
459C2×D4C2×D4×C1112yes—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C2×D4×C1111yescharacteristic
468C22×C4C2×D4×C1112yes—
469C22×C4C24×C1111yescharacteristic
470Q16—82no—
471SD16—84no—
472SD16—82no—
473C2×C8—22no—
474C2×C8—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4C2×D4×C1112yes—
487C4⋊C4C2×D4×C1111yescharacteristic
488C4⋊C4C2×D4×C1111yescharacteristic
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—21no—
504C22⋊C4—22no—
505C22⋊C4—84no—
506C42—22no—
507C42—21no—
508C42—42no—
509C42C2×D4×C1111yescharacteristic
510C42C2×D4×C1111yescharacteristic
511C42C2×D4×C1111yescharacteristic
512C42C2×D4×C1111yescharacteristic
513C11#1842711yescharacteristic, direct product factor, Sylow
514C23—22no—
515C23—21no—
516C23—22no—
517C23—24no—
518C23—42no—
519C23—42no—
520C23—82no—
521C23—82no—
522C23—82no—
523C23C22×D4×C1111yescharacteristic
524Q8—41no—
525Q8—44no—
526Q8—42no—
527Q8—42no—
528Q8—42no—
529Q8—81no—
530Q8—81no—
531D4—42no—
532D4—41no—
533D4—42no—
534D4—44no—
535D4—42no—
536D4—42no—
537D4—81no—
538D4—81no—
539D4—82no—
540D4—82no—
541D4—82no—
542D4—82no—
543D4—82no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—44no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4C11×#12011yescharacteristic
563C2×C4C11×#12011yescharacteristic
564C2×C4C11×#12011yescharacteristic
565C2×C4C11×#12011yescharacteristic
566C2×C4C22×D4×C1111yescharacteristic
567C2×C4C22×D4×C1111yescharacteristic
568C8—42no—
569C8—42no—
570C22—21no—
571C22—21no—
572C22—42no—
573C22—42no—
574C22—41no—
575C22—41no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—41no—
580C22—42no—
581C22—84no—
582C22—164no—
583C22C2×C11×#12011yescharacteristic
584C22C11×#57712yes—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—41no—
591C4—42no—
592C4—41no—
593C4—42no—
594C4—41no—
595C4—82no—
596C4—82no—
597C4C11×#45512yes—
598C2—22no—
599C2—82no—
600C2—81no—
601C2—82no—
602C2C11×#300911yescharacteristic
603C2C2×C11×#45511yescharacteristic
604C2C11×#302711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3558C2
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×#3218C2semidirect
3. C11×#3206C2semidirect
4. C11×#2640C2semidirect
5. C11×#1606C2semidirect
6. C11×#1601C2semidirect
7. C11×#1505C2semidirect
8. C11×#1500C2semidirect
9. C11×#1469C2semidirect
23. C2×C11×C4⋊Q8C22semidirect
33. C11×#451C22semidirect
35. C11×#448C22semidirect
36. C11×#432C22semidirect
37. C11×#431C22semidirect
39. C11×#393C22semidirect
42. C11×#376C22semidirect
43. C11×#328C22semidirect
45. C11×#327C22semidirect
46. C11×#323C22semidirect
130. #18427C11direct (N × H)
213. #3218C2×C11semidirect
214. #3206C2×C11semidirect
215. #2640C2×C11semidirect
216. #1606C2×C11semidirect
217. #1601C2×C11semidirect
218. #1505C2×C11semidirect
219. #1500C2×C11semidirect
220. #1469C2×C11semidirect
290. C2×C4⋊Q8C22×C11semidirect
300. #451C22×C11semidirect
302. #448C22×C11semidirect
303. #432C22×C11semidirect
304. #431C22×C11semidirect
306. #393C22×C11semidirect
309. #376C22×C11semidirect
310. #328C22×C11semidirect
312. #327C22×C11semidirect
313. #323C22×C11semidirect
513. C11#18427direct (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×#32182
C11×#32062
C11×#26402
C11×#16062
C11×#16012
C11×#15052
C11×#15002
C11×#14692
#1842711