Finite Group Databasebeta

← C11×#18146 #14595339

Subgroups — C11×#18146 #14595339

Order 2816.

1186 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3460C211yesmaximal, characteristic
2C11×#3004C212yesmaximal, complemented
3C11×#2409C211yesmaximal, characteristic, complemented
4C11×#1606C214yesmaximal, complemented
5C11×#1605C212yesmaximal, complemented
6C11×#1604C212yesmaximal, complemented
7C11×#1513C212yesmaximal, complemented
8C11×#1465C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C2×C11×#137—22no—
11C11×#544C2211yescharacteristic
12C11×#542—22no—
13C11×#540—22no—
14C11×#538—21no—
15C11×#538C2212yes—
16C11×#537C2211yescharacteristic
17C11×#535—21no—
18C11×#532—22no—
19C11×#529—22no—
20C11×#525—21no—
21C11×#525C2212yes—
22C2×C11×C22⋊Q8—21no—
23C4×C11×#41—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C11×#451—22no—
26C11×#451C2214yes—
27C11×#448—22no—
28C11×#448C2214yes—
29C11×#419—22no—
30C11×#407C2212yes—
31C11×#395C2212yes—
32C11×#393C2212yes—
33C11×#391—21no—
34C11×#386—21no—
35C11×#385—21no—
36C11×#380C2211yescharacteristic
37C11×#328C2214yes—
38C11×#327C2214yes—
39C11×#324C2212yes—
40C11×#323C2212yes—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41D412yes—
44C22×Q8×C11—21no—
45C22×Q8×C11—22no—
46C22×Q8×C11—22no—
47C22×Q8×C11—44no—
48C22×Q8×C11C2312yes—
49C22×D4×C11D411yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C11×#137—48no—
54C2×C11×Q16—24no—
55C2×C11×SD16—24no—
56C2×C11×M16—22no—
57C11×C4⋊Q8—22no—
58C11×#127—22no—
59C11×#126—22no—
60C11×#126—22no—
61C11×#125—22no—
62C11×#124—22no—
63C11×#124—22no—
64C11×#124—22no—
65C11×#123—22no—
66C11×#123—22no—
67C11×#123—22no—
68C11×#123—22no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—44no—
73C11×C22⋊Q8D412yes—
74C11×C22⋊Q8C2312yes—
75C11×#121—21no—
76C11×#121—22no—
77C11×#121—22no—
78C11×#121—22no—
79C11×#121—22no—
80C11×#121—22no—
81C11×#121—21no—
82C11×#121D412yes—
83C11×#121C2312yes—
84C11×#120—22no—
85C11×#120—22no—
86C4×Q8×C11—21no—
87C4×Q8×C11—21no—
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C11×#117—22no—
97C11×#117—21no—
98C11×#117—21no—
99C11×#117D412yes—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—22no—
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4D411yescharacteristic
106C2×C11×C22⋊C4C2311yescharacteristic
107C2×C42×C11—22no—
108C2×C42×C11D411yescharacteristic
109C11×#103—24no—
110C11×#103—24no—
111C11×C22⋊C8—22no—
112C11×C22⋊C8C2314yes—
113C11×#95—22no—
114C11×#95—22no—
115C11×#95C2312yes—
116#18146C1111yesmaximal, characteristic, direct product factor, Sylow
117C24×C11C2×D411yescharacteristic
118C24×C11C2×D411yescharacteristic
119C11×#41—42no—
120C11×#41—44no—
121C11×#41—42no—
122C11×#41—82no—
123C2×Q8×C11—21no—
124C2×Q8×C11—24no—
125C2×Q8×C11—21no—
126C2×Q8×C11—28no—
127C2×Q8×C11—24no—
128C2×Q8×C11—44no—
129C2×Q8×C11—42no—
130C2×Q8×C11—44no—
131C2×Q8×C11—48no—
132C2×Q8×C11—41no—
133C2×Q8×C11—41no—
134C2×Q8×C11C2×D412yes—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—41no—
145C2×D4×C11C2×D412yes—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11—42no—
154C22×C4×C11—44no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2411yescharacteristic
164C11×Q16—48no—
165C11×SD16—48no—
166C11×M16—44no—
167C2×C8×C11—24no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4—44no—
179C11×C4⋊C4C2×D412yes—
180C11×C4⋊C4C2×D412yes—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—44no—
193C11×C22⋊C4—42no—
194C42×C11—22no—
195C42×C11—22no—
196C42×C11—21no—
197C42×C11—22no—
198C42×C11—21no—
199#3460C2×C1111yescharacteristic
200#3004C2×C1112yescomplemented
201#2409C2×C1111yescharacteristic, complemented
202#1606C2×C1114yescomplemented
203#1605C2×C1112yescomplemented
204#1604C2×C1112yescomplemented
205#1513C2×C1112yescomplemented
206#1465C2×C1111yescharacteristic, complemented
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—22no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11#12012yes—
218C23×C11C22×D411yescharacteristic
219Q8×C11—28no—
220Q8×C11—42no—
221Q8×C11—44no—
222Q8×C11—44no—
223Q8×C11—42no—
224Q8×C11—44no—
225Q8×C11—81no—
226D4×C11—44no—
227D4×C11—42no—
228D4×C11—42no—
229D4×C11—42no—
230D4×C11—42no—
231D4×C11—82no—
232D4×C11—82no—
233D4×C11—82no—
234D4×C11—81no—
235D4×C11—82no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—44no—
249C2×C4×C11—42no—
250C2×C4×C11—48no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—44no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—81no—
260C2×C4×C11—82no—
261C2×C4×C11#12011yescharacteristic
262C2×C4×C11#12011yescharacteristic
263C2×C4×C11#13712yescomplemented
264C2×C4×C11C22×D412yes—
265C8×C11—44no—
266C23×Q8C22×C1111yescharacteristic
267C2×#137—22no—
268#544C22×C1111yescharacteristic
269#542—22no—
270#540—22no—
271#538—21no—
272#538C22×C1112yes—
273#537C22×C1111yescharacteristic
274#535—21no—
275#532—22no—
276#529—22no—
277#525—21no—
278#525C22×C1112yes—
279C2×C22⋊Q8—21no—
280C4×#41—21no—
281C2×C4×D4C22×C1111yescharacteristic
282#451—22no—
283#451C22×C1114yes—
284#448—22no—
285#448C22×C1114yes—
286#419—22no—
287#407C22×C1112yes—
288#395C22×C1112yes—
289#393C22×C1112yes—
290#391—21no—
291#386—21no—
292#385—21no—
293#380C22×C1111yescharacteristic
294#328C22×C1114yes—
295#327C22×C1114yes—
296#324C22×C1112yes—
297#323C22×C1112yes—
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—22no—
301C22×C11—22no—
302C22×C11—22no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—41no—
308C22×C11—42no—
309C22×C11—41no—
310C22×C11—41no—
311C22×C11—42no—
312C22×C11—81no—
313C22×C11C2×#12011yescharacteristic
314C22×C11C2×#13711yescharacteristic
315C22×C11#57511yescharacteristic
316C4×C11—22no—
317C4×C11—21no—
318C4×C11—22no—
319C4×C11—42no—
320C4×C11—41no—
321C4×C11—42no—
322C4×C11—44no—
323C4×C11—41no—
324C4×C11—42no—
325C4×C11—82no—
326C4×C11B(4,𝔽2)12yes—
327C2×#41—21no—
328C2×#41—21no—
329C2×#41D4×C1112yes—
330C22×Q8—21no—
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8—44no—
334C22×Q8C23×C1112yes—
335C22×D4D4×C1111yescharacteristic
336C23×C4—21no—
337C23×C4D4×C1111yescharacteristic
338C23×C4C23×C1111yescharacteristic
339#137—48no—
340C2×Q16—24no—
341C2×SD16—24no—
342C2×M16—22no—
343C4⋊Q8—22no—
344#127—22no—
345#126—22no—
346#126—22no—
347#125—22no—
348#124—22no—
349#124—22no—
350#124—22no—
351#123—22no—
352#123—22no—
353#123—22no—
354#123—22no—
355C22⋊Q8—21no—
356C22⋊Q8—21no—
357C22⋊Q8—22no—
358C22⋊Q8—44no—
359C22⋊Q8D4×C1112yes—
360C22⋊Q8C23×C1112yes—
361#121—21no—
362#121—22no—
363#121—22no—
364#121—22no—
365#121—22no—
366#121—22no—
367#121—21no—
368#121D4×C1112yes—
369#121C23×C1112yes—
370#120—22no—
371#120—22no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—22no—
382#117—22no—
383#117—21no—
384#117—21no—
385#117D4×C1112yes—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4C23×C1111yescharacteristic
389C2×C22⋊C4—22no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4D4×C1111yescharacteristic
392C2×C22⋊C4C23×C1111yescharacteristic
393C2×C42—22no—
394C2×C42D4×C1111yescharacteristic
395#103—24no—
396#103—24no—
397C22⋊C8—22no—
398C22⋊C8C23×C1114yes—
399#95—22no—
400#95—22no—
401#95C23×C1112yes—
402C2×C11—21no—
403C2×C11—21no—
404C2×C11—42no—
405C2×C11—82no—
406C2×C11—81no—
407C2×C11#300711yescharacteristic
408C2×C11#302211yescharacteristic
409C2×C11C2×B(4,𝔽2)11yescharacteristic
410C24C2×D4×C1111yescharacteristic
411C24C2×D4×C1111yescharacteristic
412#41—42no—
413#41—44no—
414#41—42no—
415#41—82no—
416C2×Q8—21no—
417C2×Q8—24no—
418C2×Q8—21no—
419C2×Q8—28no—
420C2×Q8—24no—
421C2×Q8—44no—
422C2×Q8—42no—
423C2×Q8—44no—
424C2×Q8—48no—
425C2×Q8—41no—
426C2×Q8—41no—
427C2×Q8C2×D4×C1112yes—
428C2×D4—21no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—21no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—41no—
438C2×D4C2×D4×C1112yes—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—42no—
447C22×C4—44no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4C2×D4×C1111yescharacteristic
451C22×C4C2×D4×C1112yes—
452C22×C4C2×D4×C1111yescharacteristic
453C22×C4C2×D4×C1111yescharacteristic
454C22×C4C2×D4×C1111yescharacteristic
455C22×C4C2×D4×C1112yes—
456C22×C4C24×C1111yescharacteristic
457Q16—48no—
458SD16—48no—
459M16—44no—
460C2×C8—24no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—42no—
471C4⋊C4—44no—
472C4⋊C4C2×D4×C1112yes—
473C4⋊C4C2×D4×C1112yes—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—44no—
486C22⋊C4—42no—
487C42—22no—
488C42—22no—
489C42—21no—
490C42—22no—
491C42—21no—
492C11#1814611yescharacteristic, direct product factor, Sylow
493C23—21no—
494C23—21no—
495C23—21no—
496C23—22no—
497C23—21no—
498C23—21no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23C11×#12012yes—
504C23C22×D4×C1111yescharacteristic
505Q8—28no—
506Q8—42no—
507Q8—44no—
508Q8—44no—
509Q8—42no—
510Q8—44no—
511Q8—81no—
512D4—44no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—82no—
518D4—82no—
519D4—82no—
520D4—81no—
521D4—82no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—44no—
535C2×C4—42no—
536C2×C4—48no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—44no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—81no—
546C2×C4—82no—
547C2×C4C11×#12011yescharacteristic
548C2×C4C11×#12011yescharacteristic
549C2×C4C11×#13712yescomplemented
550C2×C4C22×D4×C1112yes—
551C8—44no—
552C22—21no—
553C22—21no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—41no—
562C22—42no—
563C22—41no—
564C22—41no—
565C22—42no—
566C22—81no—
567C22C2×C11×#12011yescharacteristic
568C22C2×C11×#13711yescharacteristic
569C22C11×#57511yescharacteristic
570C4—22no—
571C4—22no—
572C4—21no—
573C4—42no—
574C4—41no—
575C4—42no—
576C4—44no—
577C4—41no—
578C4—42no—
579C4—82no—
580C4C11×B(4,𝔽2)12yes—
581C2—21no—
582C2—21no—
583C2—42no—
584C2—81no—
585C2—82no—
586C2C11×#300711yescharacteristic
587C2C11×#302211yescharacteristic
588C2C2×C11×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3460C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C11×#3004C2semidirect
3. C11×#2409C2semidirect
4. C11×#1606C2semidirect
5. C11×#1605C2semidirect
6. C11×#1604C2semidirect
7. C11×#1513C2semidirect
8. C11×#1465C2semidirect
116. #18146C11direct (N × H)
200. #3004C2×C11semidirect
201. #2409C2×C11semidirect
202. #1606C2×C11semidirect
203. #1605C2×C11semidirect
204. #1604C2×C11semidirect
205. #1513C2×C11semidirect
206. #1465C2×C11semidirect
263. C2×C4×C11#137semidirect
492. C11#18146direct (N × H)
549. C2×C4C11×#137semidirect

Maximal subgroups

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

subgroupindex
C11×#34602
C11×#30042
C11×#24092
C11×#16062
C11×#16052
C11×#16042
C11×#15132
C11×#14652
#1814611