Finite Group Databasebeta

← C11×#9920 #14587113

Subgroups — C11×#9920 #14587113

Order 2816.

856 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#481C211yesmaximal, characteristic, complemented
2C11×#2617C211yesmaximal, characteristic
3C2×C11×#399C211yesmaximal, characteristic, complemented
4C11×#1824C211yesmaximal, characteristic, complemented
5C2×C11×#327C211yesmaximal, characteristic, complemented
6C2×C11×#323C211yesmaximal, characteristic, complemented
7C11×#1294C211yesmaximal, characteristic, complemented
8C2×C11×#121C2211yescharacteristic
9C2×C11×#120—21no—
10C22×C11×C4⋊C4—21no—
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4—21no—
13C22×C11×C22⋊C4C2211yescharacteristic
14C11×#481—22no—
15C11×#481—22no—
16C2×C11×#106—21no—
17C2×C11×#102—21no—
18C2×C11×C22⋊C8C2211yescharacteristic
19C2×C11×C22⋊C8C2211yescharacteristic
20C11×#399—22no—
21C11×#399—22no—
22C11×#397—21no—
23C11×#394—22no—
24C11×#392—21no—
25C11×#386—21no—
26C11×#380C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C11×#340—22no—
29C11×#327—22no—
30C11×#323—22no—
31C25×C11D411yescharacteristic
32C22×D4×C11—21no—
33C22×D4×C11—22no—
34C22×D4×C11D411yescharacteristic
35C23×C4×C11—21no—
36C23×C4×C11—21no—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C22×C8×C11—21no—
40C22×C8×C11—21no—
41C11×#121—21no—
42C11×#121—21no—
43C11×#121—21no—
44C11×#121—21no—
45C11×#120—42no—
46C11×#120—42no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—24no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—44no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4D412yescomplemented
57C2×C11×C22⋊C4—24no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4—21no—
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—44no—
69C11×#106—24no—
70C11×#102—24no—
71C11×C22⋊C8—21no—
72C11×C22⋊C8—21no—
73C11×C22⋊C8—21no—
74C11×C22⋊C8D412yescomplemented
75C11×#95—22no—
76C11×#95—21no—
77C11×#95—21no—
78C11×#95D412yescomplemented
79#9920C1111yesmaximal, characteristic, direct product factor, Sylow
80C24×C11—21no—
81C24×C11—21no—
82C24×C11—21no—
83C24×C11—21no—
84C24×C11—21no—
85C24×C11—21no—
86C24×C11—21no—
87C24×C11—42no—
88C24×C11—42no—
89C24×C11SD1612yes—
90C24×C11C2×D411yescharacteristic
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—42no—
94C2×D4×C11—44no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—82no—
102C2×D4×C11—82no—
103C22×C4×C11—24no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11—41no—
114C22×C4×C11—41no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11—41no—
119C22×C4×C11—41no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C2×C8×C11—22no—
127C2×C8×C11—42no—
128C2×C8×C11—42no—
129C2×C8×C11—41no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—48no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4—41no—
137C11×C4⋊C4—41no—
138C11×C22⋊C4—48no—
139C11×C22⋊C4—44no—
140C11×C22⋊C4—41no—
141C11×C22⋊C4—41no—
142C11×C22⋊C4—41no—
143C11×C22⋊C4—41no—
144C11×C22⋊C4—41no—
145C11×C22⋊C4—41no—
146C11×C22⋊C4—41no—
147C11×C22⋊C4—41no—
148C11×C22⋊C4—82no—
149C2×#481C2×C1111yescharacteristic, complemented
150#2617C2×C1111yescharacteristic
151C2×#399C2×C1111yescharacteristic, complemented
152#1824C2×C1111yescharacteristic, complemented
153C2×#327C2×C1111yescharacteristic, complemented
154C2×#323C2×C1111yescharacteristic, complemented
155#1294C2×C1111yescharacteristic, complemented
156C23×C11—22no—
157C23×C11—22no—
158C23×C11—22no—
159C23×C11—22no—
160C23×C11—22no—
161C23×C11—44no—
162C23×C11—42no—
163C23×C11—44no—
164C23×C11—42no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—82no—
177C23×C11—82no—
178C23×C11—81no—
179C23×C11—81no—
180C23×C11#12011yescharacteristic
181C23×C11#12011yescharacteristic
182C23×C11#12111yescharacteristic
183C23×C11C2×SD1611yescharacteristic
184C23×C11#13511yescharacteristic
185C23×C11AGL(1,ℤ/8)11yescharacteristic
186C23×C11#13711yescharacteristic
187D4×C11—42no—
188D4×C11—81no—
189D4×C11—88no—
190D4×C11—81no—
191D4×C11—81no—
192D4×C11—81no—
193D4×C11—81no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—44no—
202C2×C4×C11—44no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—82no—
218C2×C4×C11—82no—
219C2×C4×C11—81no—
220C2×C4×C11#12011yescharacteristic
221C2×C4×C11#12111yescharacteristic
222C2×C4×C11#12111yescharacteristic
223C2×C4×C11#12711yescharacteristic
224C8×C11—42no—
225C8×C11—81no—
226C2×#121C22×C1111yescharacteristic
227C2×#120—21no—
228C22×C4⋊C4—21no—
229C22×C4⋊C4C22×C1111yescharacteristic
230C22×C22⋊C4—21no—
231C22×C22⋊C4C22×C1111yescharacteristic
232#481—22no—
233#481—22no—
234C2×#106—21no—
235C2×#102—21no—
236C2×C22⋊C8C22×C1111yescharacteristic
237C2×C22⋊C8C22×C1111yescharacteristic
238#399—22no—
239#399—22no—
240#397—21no—
241#394—22no—
242#392—21no—
243#386—21no—
244#380C22×C1111yescharacteristic
245C2×#95C22×C1111yescharacteristic
246#340—22no—
247#327—22no—
248#323—22no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—22no—
252C22×C11—22no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—44no—
258C22×C11—44no—
259C22×C11—42no—
260C22×C11—82no—
261C22×C11—82no—
262C22×C11—82no—
263C22×C11—82no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11—82no—
267C22×C11—82no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11#39211yescharacteristic
272C22×C11#44811yescharacteristic
273C22×C11#44911yescharacteristic
274C22×C11#45011yescharacteristic
275C22×C11#45211yescharacteristic
276C22×C11#45312yes—
277C22×C11#45812yes—
278C22×C11#46511yescharacteristic
279C22×C11#46811yescharacteristic
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—44no—
285C4×C11—82no—
286C4×C11—81no—
287C4×C11—81no—
288C4×C11—82no—
289C25D4×C1111yescharacteristic
290C22×D4—21no—
291C22×D4—22no—
292C22×D4D4×C1111yescharacteristic
293C23×C4—21no—
294C23×C4—21no—
295C23×C4D4×C1111yescharacteristic
296C23×C4C23×C1111yescharacteristic
297C22×C8—21no—
298C22×C8—21no—
299#121—21no—
300#121—21no—
301#121—21no—
302#121—21no—
303#120—42no—
304#120—42no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4D4×C1111yescharacteristic
313C2×C4⋊C4D4×C1112yes—
314C2×C4⋊C4D4×C1112yescomplemented
315C2×C22⋊C4—24no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—44no—
327#106—24no—
328#102—24no—
329C22⋊C8—21no—
330C22⋊C8—21no—
331C22⋊C8—21no—
332C22⋊C8D4×C1112yescomplemented
333#95—22no—
334#95—21no—
335#95—21no—
336#95D4×C1112yescomplemented
337C2×C11—21no—
338C2×C11—21no—
339C2×C11—21no—
340C2×C11—21no—
341C2×C11—82no—
342C2×C11—161no—
343C2×C11#161312yes—
344C2×C11#161812yes—
345C2×C11#200011yescharacteristic
346C2×C11#200211yescharacteristic
347C2×C11#202211yescharacteristic
348C24—21no—
349C24—21no—
350C24—21no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24—21no—
355C24—42no—
356C24—42no—
357C24C11×SD1612yes—
358C24C2×D4×C1111yescharacteristic
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—42no—
362C2×D4—44no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—82no—
370C2×D4—82no—
371C22×C4—24no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4C2×D4×C1111yescharacteristic
389C22×C4C2×D4×C1111yescharacteristic
390C22×C4C2×D4×C1111yescharacteristic
391C22×C4C2×D4×C1111yescharacteristic
392C22×C4C2×D4×C1111yescharacteristic
393C22×C4C11×#4111yescharacteristic
394C2×C8—22no—
395C2×C8—42no—
396C2×C8—42no—
397C2×C8—41no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—42no—
403C4⋊C4—48no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C22⋊C4—48no—
407C22⋊C4—44no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—82no—
417C11#992011yescharacteristic, direct product factor, Sylow
418C23—22no—
419C23—22no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—44no—
424C23—42no—
425C23—44no—
426C23—42no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—42no—
431C23—42no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—42no—
437C23—42no—
438C23—82no—
439C23—82no—
440C23—81no—
441C23—81no—
442C23C11×#12011yescharacteristic
443C23C11×#12011yescharacteristic
444C23C11×#12111yescharacteristic
445C23C2×C11×SD1611yescharacteristic
446C23C11×#13511yescharacteristic
447C23C11×AGL(1,ℤ/8)11yescharacteristic
448C23C11×#13711yescharacteristic
449D4—42no—
450D4—81no—
451D4—88no—
452D4—81no—
453D4—81no—
454D4—81no—
455D4—81no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—44no—
464C2×C4—44no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4—81no—
482C2×C4C11×#12011yescharacteristic
483C2×C4C11×#12111yescharacteristic
484C2×C4C11×#12111yescharacteristic
485C2×C4C11×#12711yescharacteristic
486C8—42no—
487C8—81no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—44no—
497C22—44no—
498C22—42no—
499C22—82no—
500C22—82no—
501C22—82no—
502C22—82no—
503C22—81no—
504C22—81no—
505C22—82no—
506C22—82no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22C11×#39211yescharacteristic
511C22C11×#44811yescharacteristic
512C22C11×#44911yescharacteristic
513C22C11×#45011yescharacteristic
514C22C11×#45211yescharacteristic
515C22C11×#45312yes—
516C22C11×#45812yes—
517C22C11×#46511yescharacteristic
518C22C11×#46811yescharacteristic
519C4—21no—
520C4—21no—
521C4—21no—
522C4—21no—
523C4—44no—
524C4—82no—
525C4—81no—
526C4—81no—
527C4—82no—
528C2—21no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—82no—
533C2—161no—
534C2C11×#161312yes—
535C2C11×#161812yes—
536C2C11×#200011yescharacteristic
537C2C11×#200211yescharacteristic
538C2C11×#202211yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC23×C4C23×C11
prime radicalC11×#2617C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#481C2semidirect
3. C2×C11×#399C2semidirect
4. C11×#1824C2semidirect
5. C2×C11×#327C2semidirect
6. C2×C11×#323C2semidirect
7. C11×#1294C2semidirect
56. C2×C11×C4⋊C4D4semidirect
74. C11×C22⋊C8D4semidirect
78. C11×#95D4semidirect
79. #9920C11direct (N × H)
149. C2×#481C2×C11semidirect
151. C2×#399C2×C11semidirect
152. #1824C2×C11semidirect
153. C2×#327C2×C11semidirect
154. C2×#323C2×C11semidirect
155. #1294C2×C11semidirect
314. C2×C4⋊C4D4×C11semidirect
332. C22⋊C8D4×C11semidirect
336. #95D4×C11semidirect
417. C11#9920direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4812
C11×#26172
C2×C11×#3992
C11×#18242
C2×C11×#3272
C2×C11×#3232
C11×#12942
#992011