Finite Group Databasebeta

← C11×#18889 #14596082

Subgroups — C11×#18889 #14596082

Order 2816.

910 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3511C211yesmaximal, characteristic
2C11×#3246C211yesmaximal, characteristic, complemented
3C11×#3230C211yesmaximal, characteristic, complemented
4C11×#3076C211yesmaximal, characteristic, complemented
5C11×#1650C212yesmaximal, complemented
6C11×#1647C212yesmaximal, complemented
7C11×#1638C212yesmaximal, complemented
8C11×#1635C212yesmaximal, complemented
9C2×C11×#332C211yesmaximal, characteristic, complemented
10C11×#1480C211yesmaximal, characteristic, complemented
11C11×#1477C211yesmaximal, characteristic, complemented
12C11×#556C2212yes—
13C11×#555—21no—
14C11×#554—21no—
15C11×#553—22no—
16C11×#548—22no—
17C11×#547C2212yes—
18C11×#542—22no—
19C11×#537—21no—
20C11×#533—21no—
21C11×#533C2211yescharacteristic
22C11×#532—21no—
23C11×#532C2211yescharacteristic
24C2×C11×C4⋊Q8C2211yescharacteristic
25C11×#520—21no—
26C4×C11×#41C2211yescharacteristic
27C11×#500C2212yes—
28C11×#487C2212yes—
29C11×#484—22no—
30C11×#479—21no—
31C11×#478—21no—
32C11×#477—22no—
33C11×#477C2211yescharacteristic
34C11×#476C2211yescharacteristic
35C11×#476C2212yes—
36C11×#475—21no—
37C11×#475C2211yescharacteristic
38C11×#474C2211yescharacteristic
39C11×#465—22no—
40C11×#461C2212yes—
41C11×#460—21no—
42C11×#431C2211yescharacteristic
43C11×#427—21no—
44C2×C11×C4⋊C8C2211yescharacteristic
45C2×C11×C4⋊C8C2211yescharacteristic
46C11×#416—21no—
47C11×#332C2212yes—
48C11×#332C2212yes—
49C11×Q8⋊C8C2212yes—
50C11×D4⋊C8C2212yes—
51C11×D4⋊C8C2212yes—
52C11×D4⋊C8C2212yes—
53C2×C11×#41—22no—
54C2×C11×#41—21no—
55C2×C11×#41D411yescharacteristic
56C22×Q8×C11—21no—
57C2×C11×SD16—22no—
58C22×C8×C11—21no—
59C22×C8×C11—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8D412yes—
63C11×C4⋊Q8D411yescharacteristic
64C11×C4⋊Q8C2311yescharacteristic
65C11×C4⋊Q8C2311yescharacteristic
66C11×C4⋊Q8C2312yes—
67C11×#127D411yescharacteristic
68C11×#126—24no—
69C11×#125—22no—
70C11×#125—21no—
71C11×#124—24no—
72C11×#124—22no—
73C11×#124—21no—
74C11×#123—24no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—24no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×#121—22no—
82C11×#121—22no—
83C11×#121—24no—
84C11×#121—22no—
85C11×#121—21no—
86C11×#121D412yes—
87C4×Q8×C11—22no—
88C4×Q8×C11—22no—
89C4×Q8×C11—21no—
90C4×Q8×C11—21no—
91C4×Q8×C11D411yescharacteristic
92C4×Q8×C11C2311yescharacteristic
93C4×D4×C11—22no—
94C4×D4×C11—24no—
95C4×D4×C11—22no—
96C4×D4×C11—21no—
97C4×D4×C11—21no—
98C4×D4×C11—21no—
99C4×D4×C11D411yescharacteristic
100C4×D4×C11C2311yescharacteristic
101C4×D4×C11C2312yes—
102C11×#117—22no—
103C11×#117—22no—
104C11×#117—21no—
105C11×#117—21no—
106C11×#117D411yescharacteristic
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—22no—
109C2×C11×C4⋊C4D412yes—
110C2×C42×C11—21no—
111C2×C42×C11C2311yescharacteristic
112C11×#107—24no—
113C11×#107—21no—
114C11×#107—21no—
115C11×#106—21no—
116C11×#106—21no—
117C11×#106—22no—
118C11×C4⋊C8—21no—
119C11×C4⋊C8—21no—
120C11×C4⋊C8—21no—
121C11×C4⋊C8C2311yescharacteristic
122C11×C4⋊C8C2311yescharacteristic
123C11×C4⋊C8C2312yes—
124C11×#103—21no—
125C11×#103—21no—
126C11×#103—22no—
127C11×#103—24no—
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—22no—
131C11×C22⋊C8—21no—
132C4×C8×C11C2312yes—
133#18889C1111yesmaximal, characteristic, direct product factor, Sylow
134C11×#41—22no—
135C11×#41—22no—
136C11×#41—42no—
137C11×#41—42no—
138C11×#41—82no—
139C11×#41—82no—
140C2×Q8×C11—21no—
141C2×Q8×C11—22no—
142C2×Q8×C11—22no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—81no—
146C2×Q8×C11—81no—
147C2×Q8×C11C2×D411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11—22no—
150C2×D4×C11—24no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11C2×D411yescharacteristic
154C2×D4×C11C2×D412yes—
155C22×C4×C11—24no—
156C22×C4×C11—22no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—22no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C11×SD16—82no—
165C2×C8×C11—22no—
166C2×C8×C11—21no—
167C2×C8×C11—22no—
168C2×C8×C11—21no—
169C2×C8×C11—42no—
170C2×C8×C11—81no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
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—41no—
184C11×C4⋊C4—41no—
185C11×C4⋊C4C2×D412yes—
186C11×C4⋊C4C2×D414yes—
187C11×C4⋊C4C2×D411yescharacteristic
188C11×C4⋊C4C2×D411yescharacteristic
189C11×C22⋊C4—24no—
190C11×C22⋊C4—24no—
191C11×C22⋊C4—24no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4—21no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—41no—
198C42×C11—24no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—41no—
203C42×C11C2×D411yescharacteristic
204C42×C11C2×D411yescharacteristic
205C42×C11C2×D411yescharacteristic
206C42×C11C2411yescharacteristic
207#3511C2×C1111yescharacteristic
208#3246C2×C1111yescharacteristic, complemented
209#3230C2×C1111yescharacteristic, complemented
210#3076C2×C1111yescharacteristic, complemented
211#1650C2×C1112yescomplemented
212#1647C2×C1112yescomplemented
213#1638C2×C1112yescomplemented
214#1635C2×C1112yescomplemented
215C2×#332C2×C1111yescharacteristic, complemented
216#1480C2×C1111yescharacteristic, complemented
217#1477C2×C1111yescharacteristic, complemented
218C23×C11—21no—
219C23×C11—22no—
220C23×C11#12011yescharacteristic
221Q8×C11—21no—
222Q8×C11—21no—
223Q8×C11—42no—
224Q8×C11—42no—
225Q8×C11—42no—
226Q8×C11—42no—
227Q8×C11—41no—
228Q8×C11—41no—
229Q8×C11—82no—
230D4×C11—21no—
231D4×C11—21no—
232D4×C11—22no—
233D4×C11—22no—
234D4×C11—42no—
235D4×C11—42no—
236D4×C11—44no—
237D4×C11—42no—
238D4×C11—84no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—24no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—42no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—82no—
256C2×C4×C11—84no—
257C2×C4×C11#12011yescharacteristic
258C2×C4×C11#12011yescharacteristic
259C2×C4×C11#12011yescharacteristic
260C2×C4×C11#13512yes—
261C2×C4×C11#13712yes—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C8×C11—42no—
266C8×C11—41no—
267C8×C11—41no—
268C8×C11—42no—
269#556C22×C1112yes—
270#555—21no—
271#554—21no—
272#553—22no—
273#548—22no—
274#547C22×C1112yes—
275#542—22no—
276#537—21no—
277#533—21no—
278#533C22×C1111yescharacteristic
279#532—21no—
280#532C22×C1111yescharacteristic
281C2×C4⋊Q8C22×C1111yescharacteristic
282#520—21no—
283C4×#41C22×C1111yescharacteristic
284#500C22×C1112yes—
285#487C22×C1112yes—
286#484—22no—
287#479—21no—
288#478—21no—
289#477—22no—
290#477C22×C1111yescharacteristic
291#476C22×C1111yescharacteristic
292#476C22×C1112yes—
293#475—21no—
294#475C22×C1111yescharacteristic
295#474C22×C1111yescharacteristic
296#465—22no—
297#461C22×C1112yes—
298#460—21no—
299#431C22×C1111yescharacteristic
300#427—21no—
301C2×C4⋊C8C22×C1111yescharacteristic
302C2×C4⋊C8C22×C1111yescharacteristic
303#416—21no—
304#332C22×C1112yes—
305#332C22×C1112yes—
306Q8⋊C8C22×C1112yes—
307D4⋊C8C22×C1112yes—
308D4⋊C8C22×C1112yes—
309D4⋊C8C22×C1112yes—
310C22×C11—21no—
311C22×C11—21no—
312C22×C11—41no—
313C22×C11—42no—
314C22×C11—41no—
315C22×C11—42no—
316C22×C11—41no—
317C22×C11—42no—
318C22×C11#45212yes—
319C22×C11C2×#12011yescharacteristic
320C4×C11—21no—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—41no—
324C4×C11—42no—
325C4×C11—41no—
326C4×C11—44no—
327C4×C11—41no—
328C4×C11—81no—
329C4×C11—81no—
330C4×C11#45212yes—
331C4×C11C2×#13511yescharacteristic
332C4×C11C2×#13711yescharacteristic
333C4×C11#57611yescharacteristic
334C4×C11#57711yescharacteristic
335C2×#41—22no—
336C2×#41—21no—
337C2×#41D4×C1111yescharacteristic
338C22×Q8—21no—
339C2×SD16—22no—
340C22×C8—21no—
341C22×C8—21no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8D4×C1112yes—
345C4⋊Q8D4×C1111yescharacteristic
346C4⋊Q8C23×C1111yescharacteristic
347C4⋊Q8C23×C1111yescharacteristic
348C4⋊Q8C23×C1112yes—
349#127D4×C1111yescharacteristic
350#126—24no—
351#125—22no—
352#125—21no—
353#124—24no—
354#124—22no—
355#124—21no—
356#123—24no—
357C22⋊Q8—22no—
358C22⋊Q8—24no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363#121—22no—
364#121—22no—
365#121—24no—
366#121—22no—
367#121—21no—
368#121D4×C1112yes—
369C4×Q8—22no—
370C4×Q8—22no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8D4×C1111yescharacteristic
374C4×Q8C23×C1111yescharacteristic
375C4×D4—22no—
376C4×D4—24no—
377C4×D4—22no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4D4×C1111yescharacteristic
382C4×D4C23×C1111yescharacteristic
383C4×D4C23×C1112yes—
384#117—22no—
385#117—22no—
386#117—21no—
387#117—21no—
388#117D4×C1111yescharacteristic
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4D4×C1112yes—
392C2×C42—21no—
393C2×C42C23×C1111yescharacteristic
394#107—21no—
395#107—21no—
396#107—24no—
397#106—21no—
398#106—21no—
399#106—22no—
400C4⋊C8—21no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8C23×C1111yescharacteristic
404C4⋊C8C23×C1111yescharacteristic
405C4⋊C8C23×C1112yes—
406#103—21no—
407#103—21no—
408#103—22no—
409#103—24no—
410#102—21no—
411#102—21no—
412#102—22no—
413C22⋊C8—21no—
414C4×C8C23×C1112yes—
415C2×C11—22no—
416C2×C11—81no—
417C2×C11—82no—
418C2×C11C2×#45211yescharacteristic
419C2×C11#301211yescharacteristic
420C2×C11#302011yescharacteristic
421#41—22no—
422#41—22no—
423#41—42no—
424#41—42no—
425#41—82no—
426#41—82no—
427C2×Q8—21no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—81no—
433C2×Q8—81no—
434C2×Q8C2×D4×C1111yescharacteristic
435C2×D4—21no—
436C2×D4—22no—
437C2×D4—24no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C2×D4×C1111yescharacteristic
441C2×D4C2×D4×C1112yes—
442C22×C4—24no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4C2×D4×C1111yescharacteristic
449C22×C4C2×D4×C1111yescharacteristic
450C22×C4C2×D4×C1111yescharacteristic
451SD16—82no—
452C2×C8—22no—
453C2×C8—21no—
454C2×C8—22no—
455C2×C8—21no—
456C2×C8—42no—
457C2×C8—81no—
458C4⋊C4—24no—
459C4⋊C4—24no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—22no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4C2×D4×C1112yes—
473C4⋊C4C2×D4×C1114yes—
474C4⋊C4C2×D4×C1111yescharacteristic
475C4⋊C4C2×D4×C1111yescharacteristic
476C22⋊C4—24no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—22no—
482C22⋊C4—21no—
483C22⋊C4—22no—
484C22⋊C4—41no—
485C42—24no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—41no—
490C42C2×D4×C1111yescharacteristic
491C42C2×D4×C1111yescharacteristic
492C42C2×D4×C1111yescharacteristic
493C42C24×C1111yescharacteristic
494C11#1888911yescharacteristic, direct product factor, Sylow
495C23—21no—
496C23—22no—
497C23C11×#12011yescharacteristic
498Q8—21no—
499Q8—21no—
500Q8—42no—
501Q8—42no—
502Q8—42no—
503Q8—42no—
504Q8—41no—
505Q8—41no—
506Q8—82no—
507D4—21no—
508D4—21no—
509D4—22no—
510D4—22no—
511D4—42no—
512D4—42no—
513D4—44no—
514D4—42no—
515D4—84no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—24no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—82no—
533C2×C4—84no—
534C2×C4C11×#12011yescharacteristic
535C2×C4C11×#12011yescharacteristic
536C2×C4C11×#12011yescharacteristic
537C2×C4C11×#13512yes—
538C2×C4C11×#13712yes—
539C2×C4C22×D4×C1111yescharacteristic
540C2×C4C22×D4×C1111yescharacteristic
541C2×C4C22×D4×C1111yescharacteristic
542C8—42no—
543C8—41no—
544C8—41no—
545C8—42no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—42no—
550C22—41no—
551C22—42no—
552C22—41no—
553C22—42no—
554C22C11×#45212yes—
555C22C2×C11×#12011yescharacteristic
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—42no—
561C4—41no—
562C4—44no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4C11×#45212yes—
567C4C2×C11×#13511yescharacteristic
568C4C2×C11×#13711yescharacteristic
569C4C11×#57611yescharacteristic
570C4C11×#57711yescharacteristic
571C2—22no—
572C2—81no—
573C2—82no—
574C2C2×C11×#45211yescharacteristic
575C2C11×#301211yescharacteristic
576C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3511C2
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×#3246C2semidirect
3. C11×#3230C2semidirect
4. C11×#3076C2semidirect
5. C11×#1650C2semidirect
6. C11×#1647C2semidirect
7. C11×#1638C2semidirect
8. C11×#1635C2semidirect
9. C2×C11×#332C2semidirect
10. C11×#1480C2semidirect
11. C11×#1477C2semidirect
133. #18889C11direct (N × H)
208. #3246C2×C11semidirect
209. #3230C2×C11semidirect
210. #3076C2×C11semidirect
211. #1650C2×C11semidirect
212. #1647C2×C11semidirect
213. #1638C2×C11semidirect
214. #1635C2×C11semidirect
215. C2×#332C2×C11semidirect
216. #1480C2×C11semidirect
217. #1477C2×C11semidirect
494. C11#18889direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35112
C11×#32462
C11×#32302
C11×#30762
C11×#16502
C11×#16472
C11×#16382
C11×#16352
C2×C11×#3322
C11×#14802
C11×#14772
#1888911