Finite Group Databasebeta

← C11×#9085 #14586278

Subgroups — C11×#9085 #14586278

Order 2816.

928 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#407C211yesmaximal, characteristic
2C2×C11×#385C211yesmaximal, characteristic
3C11×#1779C211yesmaximal, characteristic
4C2×C11×#324C212yesmaximal, complemented
5C11×#1280C212yesmaximal, complemented
6C24×C4×C11C2211yescharacteristic
7C22×C11×M16—21no—
8C22×C11×C4⋊C4C411yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C22×C11×C22⋊C4C411yescharacteristic
11C22×C11×C22⋊C4C411yescharacteristic
12C11×#407—24no—
13C2×C11×C22⋊C8—21no—
14C2×C11×C22⋊C8—21no—
15C2×C11×C22⋊C8—21no—
16C2×C11×C22⋊C8C2212yes—
17C2×C11×C22⋊C8C2212yes—
18C11×#385—21no—
19C11×#385—21no—
20C11×#385—21no—
21C11×#385—21no—
22C2×C11×#95C411yescharacteristic
23C2×C11×#95C2211yescharacteristic
24C11×#324—24no—
25C25×C11C2×C411yescharacteristic
26C23×C4×C11—22no—
27C23×C4×C11—22no—
28C23×C4×C11—42no—
29C23×C4×C11—42no—
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C2×C11×M16—24no—
41C2×C11×M16—42no—
42C2×C11×M16—42no—
43C22×C8×C11—22no—
44C22×C8×C11—22no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—42no—
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4—21no—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—42no—
59C11×C22⋊C8—24no—
60C11×C22⋊C8—22no—
61C11×C22⋊C8—22no—
62C11×C22⋊C8—22no—
63C11×C22⋊C8—42no—
64C11×C22⋊C8—42no—
65C11×C22⋊C8D414yes—
66C11×#95—21no—
67C11×#95—21no—
68C11×#95—21no—
69C11×#95—21no—
70#9085C1111yesmaximal, characteristic, direct product factor, Sylow
71C24×C11—22no—
72C24×C11—22no—
73C24×C11—21no—
74C24×C11—21no—
75C24×C11—22no—
76C24×C11—22no—
77C24×C11—41no—
78C24×C11—41no—
79C24×C11C22⋊C411yescharacteristic
80C24×C11C22⋊C411yescharacteristic
81C24×C11C22×C411yescharacteristic
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—22no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11—41no—
111C22×C4×C11—48no—
112C22×C4×C11—48no—
113C22×C4×C11—41no—
114C22×C4×C11—41no—
115C22×C4×C11—41no—
116C22×C4×C11—41no—
117C22×C4×C11—41no—
118C22×C4×C11—41no—
119C22×C4×C11C22⋊C411yescharacteristic
120C22×C4×C11C22⋊C411yescharacteristic
121C22×C4×C11M1612yescomplemented
122C22×C4×C11M1612yescomplemented
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D412yes—
126C22×C4×C11#4112yes—
127C11×M16—48no—
128C2×C8×C11—24no—
129C2×C8×C11—42no—
130C2×C8×C11—42no—
131C2×C8×C11—42no—
132C2×C8×C11—42no—
133C2×C8×C11—42no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4—41no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4—41no—
139C11×C22⋊C4—24no—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—42no—
142C11×C22⋊C4—42no—
143C2×#407C2×C1111yescharacteristic
144C2×#385C2×C1111yescharacteristic
145#1779C2×C1111yescharacteristic
146C2×#324C2×C1112yescomplemented
147#1280C2×C1112yescomplemented
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11—21no—
152C23×C11—24no—
153C23×C11—24no—
154C23×C11—21no—
155C23×C11—21no—
156C23×C11—21no—
157C23×C11—21no—
158C23×C11—21no—
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—44no—
167C23×C11—44no—
168C23×C11—44no—
169C23×C11—44no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11#9912yes—
175C23×C11#10112yes—
176C23×C11C2×C22⋊C411yescharacteristic
177C23×C11C4×D412yes—
178C23×C11C2×M1611yescharacteristic
179C23×C11C2×M1611yescharacteristic
180C23×C11#13112yes—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—24no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—44no—
198C2×C4×C11—44no—
199C2×C4×C11—44no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—82no—
216C2×C4×C11—82no—
217C2×C4×C11#9912yes—
218C2×C4×C11#12011yescharacteristic
219C2×C4×C11#12112yes—
220C2×C4×C11#12311yescharacteristic
221C8×C11—44no—
222C8×C11—82no—
223C24×C4C22×C1111yescharacteristic
224C22×M16—21no—
225C22×C4⋊C4C4×C1111yescharacteristic
226C22×C4⋊C4C22×C1111yescharacteristic
227C22×C22⋊C4C4×C1111yescharacteristic
228C22×C22⋊C4C4×C1111yescharacteristic
229#407—24no—
230C2×C22⋊C8—21no—
231C2×C22⋊C8—21no—
232C2×C22⋊C8—21no—
233C2×C22⋊C8C22×C1112yes—
234C2×C22⋊C8C22×C1112yes—
235#385—21no—
236#385—21no—
237#385—21no—
238#385—21no—
239C2×#95C4×C1111yescharacteristic
240C2×#95C22×C1111yescharacteristic
241#324—24no—
242C22×C11—22no—
243C22×C11—22no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—22no—
252C22×C11—22no—
253C22×C11—22no—
254C22×C11—22no—
255C22×C11—22no—
256C22×C11—48no—
257C22×C11—48no—
258C22×C11—41no—
259C22×C11—41no—
260C22×C11—41no—
261C22×C11—41no—
262C22×C11—41no—
263C22×C11—41no—
264C22×C11—41no—
265C22×C11—41no—
266C22×C11#38611yescharacteristic
267C22×C11#40711yescharacteristic
268C22×C11#40811yescharacteristic
269C22×C11C2×#9911yescharacteristic
270C22×C11C2×#9911yescharacteristic
271C22×C11C2×#10111yescharacteristic
272C22×C11#41311yescharacteristic
273C22×C11#43512yes—
274C22×C11#43612yes—
275C4×C11—22no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—22no—
279C4×C11—42no—
280C4×C11—41no—
281C4×C11—42no—
282C4×C11—81no—
283C4×C11—81no—
284C25C2×C4×C1111yescharacteristic
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4C2×C4×C1111yescharacteristic
290C23×C4C2×C4×C1111yescharacteristic
291C23×C4C2×C4×C1111yescharacteristic
292C23×C4C2×C4×C1111yescharacteristic
293C23×C4C2×C4×C1111yescharacteristic
294C23×C4D4×C1111yescharacteristic
295C23×C4D4×C1111yescharacteristic
296C23×C4D4×C1111yescharacteristic
297C23×C4D4×C1111yescharacteristic
298C23×C4C23×C1111yescharacteristic
299C2×M16—24no—
300C2×M16—42no—
301C2×M16—42no—
302C22×C8—22no—
303C22×C8—22no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—42no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—42no—
318C22⋊C8—24no—
319C22⋊C8—22no—
320C22⋊C8—22no—
321C22⋊C8—22no—
322C22⋊C8—42no—
323C22⋊C8—42no—
324C22⋊C8D4×C1114yes—
325#95—21no—
326#95—21no—
327#95—21no—
328#95—21no—
329C2×C11—22no—
330C2×C11—22no—
331C2×C11—42no—
332C2×C11—42no—
333C2×C11#146311yescharacteristic
334C2×C11#146511yescharacteristic
335C2×C11#146811yescharacteristic
336C2×C11#147211yescharacteristic
337C2×C11#187011yescharacteristic
338C2×C11#189811yescharacteristic
339C2×C11#190111yescharacteristic
340C24—22no—
341C24—22no—
342C24—21no—
343C24—21no—
344C24—22no—
345C24—22no—
346C24—41no—
347C24—41no—
348C24C11×C22⋊C411yescharacteristic
349C24C11×C22⋊C411yescharacteristic
350C24C22×C4×C1111yescharacteristic
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—48no—
381C22×C4—48no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4C11×C22⋊C411yescharacteristic
389C22×C4C11×C22⋊C411yescharacteristic
390C22×C4C11×M1612yescomplemented
391C22×C4C11×M1612yescomplemented
392C22×C4C2×D4×C1111yescharacteristic
393C22×C4C2×D4×C1111yescharacteristic
394C22×C4C2×D4×C1112yes—
395C22×C4C11×#4112yes—
396M16—48no—
397C2×C8—24no—
398C2×C8—42no—
399C2×C8—42no—
400C2×C8—42no—
401C2×C8—42no—
402C2×C8—42no—
403C4⋊C4—42no—
404C4⋊C4—42no—
405C4⋊C4—41no—
406C4⋊C4—42no—
407C4⋊C4—41no—
408C22⋊C4—24no—
409C22⋊C4—24no—
410C22⋊C4—42no—
411C22⋊C4—42no—
412C11#908511yescharacteristic, direct product factor, Sylow
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—24no—
418C23—24no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—44no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—42no—
439C23C11×#9912yes—
440C23C11×#10112yes—
441C23C2×C11×C22⋊C411yescharacteristic
442C23C4×D4×C1112yes—
443C23C2×C11×M1611yescharacteristic
444C23C2×C11×M1611yescharacteristic
445C23C11×#13112yes—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—24no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—44no—
463C2×C4—44no—
464C2×C4—44no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4C11×#9912yes—
483C2×C4C11×#12011yescharacteristic
484C2×C4C11×#12112yes—
485C2×C4C11×#12311yescharacteristic
486C8—44no—
487C8—82no—
488C22—22no—
489C22—22no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—22no—
501C22—22no—
502C22—48no—
503C22—48no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22C11×#38611yescharacteristic
513C22C11×#40711yescharacteristic
514C22C11×#40811yescharacteristic
515C22C2×C11×#9911yescharacteristic
516C22C2×C11×#9911yescharacteristic
517C22C2×C11×#10111yescharacteristic
518C22C11×#41311yescharacteristic
519C22C11×#43512yes—
520C22C11×#43612yes—
521C4—21no—
522C4—22no—
523C4—22no—
524C4—21no—
525C4—42no—
526C4—41no—
527C4—42no—
528C4—81no—
529C4—81no—
530C2—22no—
531C2—22no—
532C2—42no—
533C2—42no—
534C2C11×#146311yescharacteristic
535C2C11×#146511yescharacteristic
536C2C11×#146811yescharacteristic
537C2C11×#147211yescharacteristic
538C2C11×#187011yescharacteristic
539C2C11×#189811yescharacteristic
540C2C11×#190111yescharacteristic
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC24C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC25×C11C2×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C11×#324C2semidirect
5. C11×#1280C2semidirect
70. #9085C11direct (N × H)
121. C22×C4×C11M16semidirect
122. C22×C4×C11M16semidirect
146. C2×#324C2×C11semidirect
147. #1280C2×C11semidirect
390. C22×C4C11×M16semidirect
391. C22×C4C11×M16semidirect
412. C11#9085direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4072
C2×C11×#3852
C11×#17792
C2×C11×#3242
C11×#12802
#908511