Finite Group Databasebeta

← C11×#11095 #14588288

Subgroups — C11×#11095 #14588288

Order 2816.

1230 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#106C211yesmaximal, characteristic, complemented
2C22×C11×C22⋊C8C211yesmaximal, characteristic
3C2×C11×#380C212yesmaximal
4C2×C11×#340C211yesmaximal, characteristic, complemented
5C2×C11×#340C212yesmaximal, complemented
6C24×C4×C11C2211yescharacteristic
7C23×C8×C11C2211yescharacteristic
8C23×C8×C11C2211yescharacteristic
9C22×C11×C4⋊C4C2212yes—
10C22×C11×C4⋊C4C2212yes—
11C22×C11×C22⋊C4—22no—
12C2×C11×#106—22no—
13C2×C11×#106—24no—
14C2×C11×C22⋊C8—22no—
15C2×C11×C22⋊C8—22no—
16C2×C11×C22⋊C8C414yescomplemented
17C11×#380—24no—
18C11×#380—24no—
19C2×C11×#95—22no—
20C11×#340—22no—
21C11×#340—24no—
22C25×C11D411yescharacteristic
23C23×C4×C11—22no—
24C23×C4×C11—22no—
25C23×C4×C11—21no—
26C23×C4×C11—21no—
27C23×C4×C11—21no—
28C23×C4×C11—21no—
29C23×C4×C11—22no—
30C23×C4×C11—22no—
31C23×C4×C11—22no—
32C23×C4×C11—22no—
33C23×C4×C11C2×C412yes—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11Q812yes—
36C23×C4×C11C2311yescharacteristic
37C22×C8×C11—22no—
38C22×C8×C11—22no—
39C22×C8×C11—22no—
40C22×C8×C11—21no—
41C22×C8×C11—21no—
42C22×C8×C11—22no—
43C22×C8×C11C2×C412yes—
44C22×C8×C11C2×C412yes—
45C22×C8×C11D412yes—
46C22×C8×C11D412yes—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4D414yes—
58C2×C11×C4⋊C4D414yes—
59C2×C11×C22⋊C4—28no—
60C2×C11×C22⋊C4—44no—
61C2×C11×C22⋊C4—44no—
62C11×#106—28no—
63C11×C22⋊C8—28no—
64C11×#95—28no—
65#11095C1111yesmaximal, characteristic, direct product factor, Sylow
66C24×C11—22no—
67C24×C11—21no—
68C24×C11—21no—
69C24×C11—22no—
70C24×C11—22no—
71C24×C11—22no—
72C24×C11—22no—
73C24×C11C4⋊C412yes—
74C24×C11SD1614yes—
75C24×C11C2×D411yescharacteristic
76C22×C4×C11—22no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—24no—
83C22×C4×C11—24no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—24no—
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—24no—
90C22×C4×C11—41no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11—41no—
96C22×C4×C11—42no—
97C22×C4×C11—41no—
98C22×C4×C11—42no—
99C22×C4×C11—41no—
100C22×C4×C11—42no—
101C22×C4×C11—42no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11C4⋊C412yes—
113C22×C4×C11C22×C411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×Q811yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C22×C4×C11#4111yescharacteristic
121C22×C4×C11#4112yes—
122C22×C4×C11#4112yes—
123C2×C8×C11—22no—
124C2×C8×C11—24no—
125C2×C8×C11—24no—
126C2×C8×C11—22no—
127C2×C8×C11—24no—
128C2×C8×C11—22no—
129C2×C8×C11—42no—
130C2×C8×C11—41no—
131C2×C8×C11—41no—
132C2×C8×C11C22⋊C414yescomplemented
133C11×C4⋊C4—24no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4—42no—
140C11×C4⋊C4—42no—
141C11×C22⋊C4—416no—
142C22×#106C2×C1111yescharacteristic, complemented
143C22×C22⋊C8C2×C1111yescharacteristic
144C2×#380C2×C1112yes—
145C2×#340C2×C1112yescomplemented
146C2×#340C2×C1111yescharacteristic, complemented
147C23×C11—22no—
148C23×C11—24no—
149C23×C11—22no—
150C23×C11—24no—
151C23×C11—24no—
152C23×C11—24no—
153C23×C11—24no—
154C23×C11—24no—
155C23×C11—24no—
156C23×C11—24no—
157C23×C11—41no—
158C23×C11—42no—
159C23×C11—41no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11#10614yescomplemented
168C23×C11C2×C4⋊C411yescharacteristic
169C23×C11#12012yes—
170C23×C11#12111yescharacteristic
171C23×C11#12111yescharacteristic
172C23×C11#12312yes—
173C23×C11C2×SD1612yes—
174C23×C11#13512yes—
175C23×C11AGL(1,ℤ/8)12yes—
176C23×C11#13712yes—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—44no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—44no—
187C2×C4×C11—42no—
188C2×C4×C11—44no—
189C2×C4×C11—44no—
190C2×C4×C11—44no—
191C2×C4×C11—44no—
192C2×C4×C11—44no—
193C2×C4×C11—44no—
194C2×C4×C11—82no—
195C2×C4×C11—82no—
196C2×C4×C11—82no—
197C2×C4×C11—82no—
198C2×C4×C11—82no—
199C2×C4×C11—82no—
200C2×C4×C11—82no—
201C2×C4×C11—82no—
202C2×C4×C11C2×C22⋊C411yescharacteristic
203C2×C4×C11#11711yescharacteristic
204C2×C4×C11C4×D412yes—
205C2×C4×C11C4×D412yes—
206C2×C4×C11#12011yescharacteristic
207C2×C4×C11#12112yes—
208C2×C4×C11#12112yes—
209C2×C4×C11#12112yes—
210C2×C4×C11C22⋊Q812yes—
211C2×C4×C11C22⋊Q811yescharacteristic
212C2×C4×C11C22⋊Q811yescharacteristic
213C2×C4×C11C22⋊Q812yes—
214C2×C4×C11#12311yescharacteristic
215C2×C4×C11#12312yes—
216C2×C4×C11#12412yes—
217C2×C4×C11#12411yescharacteristic
218C2×C4×C11#12612yes—
219C2×C4×C11#12711yescharacteristic
220C8×C11—24no—
221C8×C11—42no—
222C24×C4C22×C1111yescharacteristic
223C23×C8C22×C1111yescharacteristic
224C23×C8C22×C1111yescharacteristic
225C22×C4⋊C4C22×C1112yes—
226C22×C4⋊C4C22×C1112yes—
227C22×C22⋊C4—22no—
228C2×#106—22no—
229C2×#106—24no—
230C2×C22⋊C8—22no—
231C2×C22⋊C8—22no—
232C2×C22⋊C8C4×C1114yescomplemented
233#380—24no—
234#380—24no—
235C2×#95—22no—
236#340—22no—
237#340—24no—
238C22×C11—24no—
239C22×C11—28no—
240C22×C11—42no—
241C22×C11—44no—
242C22×C11—44no—
243C22×C11—42no—
244C22×C11—44no—
245C22×C11—44no—
246C22×C11—44no—
247C22×C11#38011yescharacteristic
248C22×C11#38512yes—
249C22×C11#39211yescharacteristic
250C22×C11#39412yes—
251C22×C11#39711yescharacteristic
252C22×C11C2×#10611yescharacteristic
253C22×C11#42711yescharacteristic
254C22×C11#42812yes—
255C22×C11#44812yes—
256C22×C11#44912yes—
257C22×C11#45012yes—
258C22×C11#45212yes—
259C22×C11#46512yes—
260C22×C11#46512yes—
261C22×C11#46812yes—
262C22×C11#46911yescharacteristic
263C22×C11#47011yescharacteristic
264C22×C11#48112yes—
265C22×C11#48212yes—
266C22×C11#48312yes—
267C22×C11#48512yes—
268C4×C11—42no—
269C4×C11—84no—
270C4×C11—84no—
271C4×C11#38611yescharacteristic
272C4×C11#38812yes—
273C4×C11#39011yescharacteristic
274C4×C11#39311yescharacteristic
275C4×C11#39612yes—
276C4×C11#39911yescharacteristic
277C25D4×C1111yescharacteristic
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4C2×C4×C1112yes—
289C23×C4D4×C1111yescharacteristic
290C23×C4Q8×C1112yes—
291C23×C4C23×C1111yescharacteristic
292C22×C8—22no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—21no—
296C22×C8—21no—
297C22×C8—22no—
298C22×C8C2×C4×C1112yes—
299C22×C8C2×C4×C1112yes—
300C22×C8D4×C1112yes—
301C22×C8D4×C1112yes—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4D4×C1114yes—
313C2×C4⋊C4D4×C1114yes—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—44no—
316C2×C22⋊C4—44no—
317#106—28no—
318C22⋊C8—28no—
319#95—28no—
320C2×C11—44no—
321C2×C11#143911yescharacteristic
322C2×C11#180711yescharacteristic
323C2×C11#180911yescharacteristic
324C2×C11#185312yes—
325C2×C11#185412yes—
326C2×C11#200012yes—
327C2×C11#203412yes—
328C2×C11#203512yes—
329C2×C11#207712yes—
330C24—22no—
331C24—21no—
332C24—21no—
333C24—22no—
334C24—22no—
335C24—22no—
336C24—22no—
337C24C11×C4⋊C412yes—
338C24C11×SD1614yes—
339C24C2×D4×C1111yescharacteristic
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—41no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—41no—
360C22×C4—42no—
361C22×C4—41no—
362C22×C4—42no—
363C22×C4—41no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4C11×C4⋊C412yes—
377C22×C4C22×C4×C1111yescharacteristic
378C22×C4C2×D4×C1111yescharacteristic
379C22×C4C2×D4×C1111yescharacteristic
380C22×C4C2×D4×C1112yes—
381C22×C4C2×D4×C1112yes—
382C22×C4C2×Q8×C1111yescharacteristic
383C22×C4C11×#4111yescharacteristic
384C22×C4C11×#4111yescharacteristic
385C22×C4C11×#4112yes—
386C22×C4C11×#4112yes—
387C2×C8—24no—
388C2×C8—22no—
389C2×C8—24no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—24no—
393C2×C8—42no—
394C2×C8—41no—
395C2×C8—41no—
396C2×C8C11×C22⋊C414yescomplemented
397C4⋊C4—24no—
398C4⋊C4—24no—
399C4⋊C4—24no—
400C4⋊C4—24no—
401C4⋊C4—42no—
402C4⋊C4—42no—
403C4⋊C4—42no—
404C4⋊C4—42no—
405C22⋊C4—416no—
406C11#1109511yescharacteristic, direct product factor, Sylow
407C23—22no—
408C23—24no—
409C23—22no—
410C23—24no—
411C23—24no—
412C23—24no—
413C23—24no—
414C23—24no—
415C23—24no—
416C23—24no—
417C23—41no—
418C23—42no—
419C23—41no—
420C23—42no—
421C23—42no—
422C23—42no—
423C23—41no—
424C23—41no—
425C23—42no—
426C23—42no—
427C23C11×#10614yescomplemented
428C23C2×C11×C4⋊C411yescharacteristic
429C23C11×#12012yes—
430C23C11×#12111yescharacteristic
431C23C11×#12111yescharacteristic
432C23C11×#12312yes—
433C23C2×C11×SD1612yes—
434C23C11×#13512yes—
435C23C11×AGL(1,ℤ/8)12yes—
436C23C11×#13712yes—
437C2×C4—22no—
438C2×C4—24no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—42no—
443C2×C4—44no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—44no—
447C2×C4—42no—
448C2×C4—44no—
449C2×C4—44no—
450C2×C4—44no—
451C2×C4—44no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—82no—
457C2×C4—82no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4—82no—
461C2×C4—82no—
462C2×C4C2×C11×C22⋊C411yescharacteristic
463C2×C4C11×#11711yescharacteristic
464C2×C4C4×D4×C1112yes—
465C2×C4C4×D4×C1112yes—
466C2×C4C11×#12011yescharacteristic
467C2×C4C11×#12112yes—
468C2×C4C11×#12112yes—
469C2×C4C11×#12112yes—
470C2×C4C11×C22⋊Q812yes—
471C2×C4C11×C22⋊Q811yescharacteristic
472C2×C4C11×C22⋊Q811yescharacteristic
473C2×C4C11×C22⋊Q812yes—
474C2×C4C11×#12311yescharacteristic
475C2×C4C11×#12312yes—
476C2×C4C11×#12412yes—
477C2×C4C11×#12411yescharacteristic
478C2×C4C11×#12612yes—
479C2×C4C11×#12711yescharacteristic
480C8—24no—
481C8—42no—
482C22—24no—
483C22—28no—
484C22—42no—
485C22—44no—
486C22—44no—
487C22—44no—
488C22—42no—
489C22—44no—
490C22—44no—
491C22C11×#38011yescharacteristic
492C22C11×#38512yes—
493C22C11×#39211yescharacteristic
494C22C11×#39412yes—
495C22C11×#39711yescharacteristic
496C22C2×C11×#10611yescharacteristic
497C22C11×#42711yescharacteristic
498C22C11×#42812yes—
499C22C11×#44812yes—
500C22C11×#44912yes—
501C22C11×#45012yes—
502C22C11×#45212yes—
503C22C11×#46512yes—
504C22C11×#46512yes—
505C22C11×#46812yes—
506C22C11×#46911yescharacteristic
507C22C11×#47011yescharacteristic
508C22C11×#48112yes—
509C22C11×#48212yes—
510C22C11×#48312yes—
511C22C11×#48512yes—
512C4—42no—
513C4—84no—
514C4—84no—
515C4C11×#38611yescharacteristic
516C4C11×#38812yes—
517C4C11×#39011yescharacteristic
518C4C11×#39311yescharacteristic
519C4C11×#39612yes—
520C4C11×#39911yescharacteristic
521C2—44no—
522C2C11×#143911yescharacteristic
523C2C11×#180711yescharacteristic
524C2C11×#180911yescharacteristic
525C2C11×#185312yes—
526C2C11×#185412yes—
527C2C11×#200012yes—
528C2C11×#203412yes—
529C2C11×#203512yes—
530C2C11×#207712yes—
subgroupG/H
center, socleC24×C11C2×D4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC25×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#106C2semidirect
4. C2×C11×#340C2semidirect
5. C2×C11×#340C2semidirect
16. C2×C11×C22⋊C8C4semidirect
65. #11095C11direct (N × H)
132. C2×C8×C11C22⋊C4semidirect
142. C22×#106C2×C11semidirect
145. C2×#340C2×C11semidirect
146. C2×#340C2×C11semidirect
167. C23×C11#106semidirect
232. C2×C22⋊C8C4×C11semidirect
396. C2×C8C11×C22⋊C4semidirect
406. C11#11095direct (N × H)
427. C23C11×#106semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1062
C22×C11×C22⋊C82
C2×C11×#3802
C2×C11×#3402
#1109511