Finite Group Databasebeta

← C11×#11076 #14588269

Subgroups — C11×#11076 #14588269

Order 2816.

1266 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C4⋊C8C211yesmaximal, characteristic, complemented
2C22×C11×#102C212yesmaximal
3C2×C11×#390C211yesmaximal, characteristic
4C2×C11×#340C212yesmaximal, complemented
5C11×C4⋊#95C211yesmaximal, characteristic, complemented
6C23×D4×C11C2211yescharacteristic
7C23×C8×C11C2212yes—
8C22×C11×C4⋊C4C2211yescharacteristic
9C22×C11×C4⋊C4C2212yes—
10C22×C11×C22⋊C4—21no—
11C22×C11×C22⋊C4—21no—
12C22×C42×C11C2211yescharacteristic
13C2×C11×C4⋊C8—24no—
14C2×C11×C4⋊C8—22no—
15C2×C11×#102—24no—
16C2×C11×#102—24no—
17C2×C11×#102—24no—
18C11×#390—22no—
19C11×#390C414yescomplemented
20C2×C11×#95—21no—
21C2×C11×#95—21no—
22C11×#340—24no—
23C25×C11—21no—
24C22×D4×C11—22no—
25C22×D4×C11—22no—
26C22×D4×C11—21no—
27C22×D4×C11—22no—
28C22×D4×C11—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11C2×C412yes—
32C22×D4×C11D412yes—
33C22×D4×C11Q812yes—
34C23×C4×C11—21no—
35C23×C4×C11—22no—
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C22×C8×C11—22no—
40C22×C8×C11—22no—
41C22×C8×C11—22no—
42C22×C8×C11—22no—
43C22×C8×C11—22no—
44C22×C8×C11—22no—
45C22×C8×C11D414yes—
46C2×C11×C4⋊C4—22no—
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—21no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4C2×C412yes—
55C2×C11×C4⋊C4D414yes—
56C2×C11×C22⋊C4—24no—
57C2×C11×C22⋊C4—24no—
58C2×C11×C22⋊C4—44no—
59C2×C11×C22⋊C4—42no—
60C2×C11×C22⋊C4—42no—
61C2×C42×C11—22no—
62C2×C42×C11—22no—
63C2×C42×C11C2×C412yes—
64C2×C42×C11D412yes—
65C11×C4⋊C8—28no—
66C11×#102—216no—
67C11×#95—42no—
68C11×#95—42no—
69#11076C1111yesmaximal, characteristic, direct product factor, Sylow
70C24×C11—22no—
71C24×C11—22no—
72C24×C11—22no—
73C24×C11—42no—
74C24×C11—42no—
75C24×C11—41no—
76C24×C11—41no—
77C24×C11—42no—
78C24×C11—42no—
79C24×C11—41no—
80C24×C11—41no—
81C24×C11C2×D411yescharacteristic
82C2×D4×C11—22no—
83C2×D4×C11—24no—
84C2×D4×C11—24no—
85C2×D4×C11—24no—
86C2×D4×C11—22no—
87C2×D4×C11—24no—
88C2×D4×C11—24no—
89C2×D4×C11—22no—
90C2×D4×C11—24no—
91C2×D4×C11—41no—
92C2×D4×C11—42no—
93C2×D4×C11—42no—
94C2×D4×C11—41no—
95C2×D4×C11—42no—
96C2×D4×C11—41no—
97C2×D4×C11—42no—
98C2×D4×C11—41no—
99C2×D4×C11C4⋊C414yes—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—24no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11—41no—
113C22×C4×C11—41no—
114C22×C4×C11—42no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11C22⋊C412yes—
119C22×C4×C11C22⋊C412yes—
120C22×C4×C11D812yes—
121C22×C4×C11SD1612yes—
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×Q811yescharacteristic
128C22×C4×C11#4111yescharacteristic
129C22×C4×C11#4111yescharacteristic
130C22×C4×C11#4112yes—
131C22×C4×C11#4112yes—
132C2×C8×C11—24no—
133C2×C8×C11—24no—
134C2×C8×C11—24no—
135C2×C8×C11—42no—
136C2×C8×C11—42no—
137C2×C8×C11—42no—
138C2×C8×C11—42no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4—41no—
146C11×C22⋊C4—48no—
147C11×C22⋊C4—48no—
148C42×C11—24no—
149C42×C11—22no—
150C42×C11—22no—
151C22×C4⋊C8C2×C1111yescharacteristic, complemented
152C22×#102C2×C1112yes—
153C2×#390C2×C1111yescharacteristic
154C2×#340C2×C1112yescomplemented
155C4⋊#95C2×C1111yescharacteristic, complemented
156C23×C11—24no—
157C23×C11—42no—
158C23×C11—42no—
159C23×C11—44no—
160C23×C11—44no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11—44no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—44no—
171C23×C11—82no—
172C23×C11—82no—
173C23×C11—82no—
174C23×C11—82no—
175C23×C11—82no—
176C23×C11—82no—
177C23×C11—82no—
178C23×C11—82no—
179C23×C11C2×C22⋊C411yescharacteristic
180C23×C11#12111yescharacteristic
181C23×C11#12112yes—
182C23×C11#12112yes—
183C23×C11C22⋊Q811yescharacteristic
184C23×C11C2×D811yescharacteristic
185C23×C11C2×SD1611yescharacteristic
186C23×C11#13512yes—
187C23×C11AGL(1,ℤ/8)11yescharacteristic
188C23×C11AGL(1,ℤ/8)12yes—
189C23×C11#13711yescharacteristic
190D4×C11—28no—
191D4×C11—44no—
192D4×C11—42no—
193D4×C11—42no—
194D4×C11—42no—
195D4×C11—42no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—44no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—44no—
210C2×C4×C11—44no—
211C2×C4×C11—82no—
212C2×C4×C11—82no—
213C2×C4×C11—82no—
214C2×C4×C11—82no—
215C2×C4×C11—82no—
216C2×C4×C11—82no—
217C2×C4×C11#10214yescomplemented
218C2×C4×C11C2×C4⋊C411yescharacteristic
219C2×C4×C11#11711yescharacteristic
220C2×C4×C11C4×D412yes—
221C2×C4×C11C4×D412yes—
222C2×C4×C11#12012yes—
223C2×C4×C11#12011yescharacteristic
224C2×C4×C11#12112yes—
225C2×C4×C11#12111yescharacteristic
226C2×C4×C11C22⋊Q812yes—
227C2×C4×C11C22⋊Q812yes—
228C2×C4×C11C22⋊Q811yescharacteristic
229C2×C4×C11#12312yes—
230C2×C4×C11#12312yes—
231C2×C4×C11#12311yescharacteristic
232C2×C4×C11#12412yes—
233C2×C4×C11#12411yescharacteristic
234C2×C4×C11#12612yes—
235C2×C4×C11#12711yescharacteristic
236C8×C11—44no—
237C23×D4C22×C1111yescharacteristic
238C23×C8C22×C1112yes—
239C22×C4⋊C4C22×C1111yescharacteristic
240C22×C4⋊C4C22×C1112yes—
241C22×C22⋊C4—21no—
242C22×C22⋊C4—21no—
243C22×C42C22×C1111yescharacteristic
244C2×C4⋊C8—24no—
245C2×C4⋊C8—22no—
246C2×#102—24no—
247C2×#102—24no—
248C2×#102—24no—
249#390—22no—
250#390C4×C1114yescomplemented
251C2×#95—21no—
252C2×#95—21no—
253#340—24no—
254C22×C11—44no—
255C22×C11—44no—
256C22×C11—44no—
257C22×C11—84no—
258C22×C11—84no—
259C22×C11—84no—
260C22×C11—84no—
261C22×C11—82no—
262C22×C11—82no—
263C22×C11—82no—
264C22×C11—82no—
265C22×C11#38011yescharacteristic
266C22×C11#38611yescharacteristic
267C22×C11#39011yescharacteristic
268C22×C11#39412yes—
269C22×C11#39612yes—
270C22×C11C2×#10211yescharacteristic
271C22×C11#41611yescharacteristic
272C22×C11#41711yescharacteristic
273C22×C11#41811yescharacteristic
274C22×C11#45911yescharacteristic
275C22×C11#45912yes—
276C22×C11#46012yes—
277C22×C11#46111yescharacteristic
278C22×C11#46312yes—
279C22×C11#46312yes—
280C22×C11#46412yes—
281C22×C11#46512yes—
282C22×C11#46612yes—
283C22×C11#46812yes—
284C22×C11#46912yes—
285C22×C11#47411yescharacteristic
286C22×C11#47611yescharacteristic
287C22×C11#47812yes—
288C4×C11—24no—
289C4×C11—42no—
290C4×C11—84no—
291C4×C11—82no—
292C4×C11#38512yes—
293C4×C11#38812yes—
294C4×C11#39211yescharacteristic
295C4×C11#39311yescharacteristic
296C4×C11#39711yescharacteristic
297C4×C11#39911yescharacteristic
298C25—21no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—21no—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4C2×C4×C1112yes—
307C22×D4D4×C1112yes—
308C22×D4Q8×C1112yes—
309C23×C4—21no—
310C23×C4—22no—
311C23×C4D4×C1111yescharacteristic
312C23×C4D4×C1111yescharacteristic
313C23×C4C23×C1111yescharacteristic
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8D4×C1114yes—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4C2×C4×C1112yes—
330C2×C4⋊C4D4×C1114yes—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C42—22no—
337C2×C42—22no—
338C2×C42C2×C4×C1112yes—
339C2×C42D4×C1112yes—
340C4⋊C8—28no—
341#102—216no—
342#95—42no—
343#95—42no—
344C2×C11—84no—
345C2×C11#143911yescharacteristic
346C2×C11#180211yescharacteristic
347C2×C11#180411yescharacteristic
348C2×C11#189311yescharacteristic
349C2×C11#189511yescharacteristic
350C2×C11#198211yescharacteristic
351C2×C11#198311yescharacteristic
352C2×C11#205412yes—
353C2×C11#205512yes—
354C2×C11#206512yes—
355C2×C11#206712yes—
356C24—22no—
357C24—22no—
358C24—22no—
359C24—42no—
360C24—42no—
361C24—41no—
362C24—41no—
363C24—42no—
364C24—42no—
365C24—41no—
366C24—41no—
367C24C2×D4×C1111yescharacteristic
368C2×D4—22no—
369C2×D4—24no—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4—22no—
373C2×D4—24no—
374C2×D4—24no—
375C2×D4—22no—
376C2×D4—24no—
377C2×D4—41no—
378C2×D4—42no—
379C2×D4—42no—
380C2×D4—41no—
381C2×D4—42no—
382C2×D4—41no—
383C2×D4—42no—
384C2×D4—41no—
385C2×D4C11×C4⋊C414yes—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—24no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4C11×C22⋊C412yes—
405C22×C4C11×C22⋊C412yes—
406C22×C4C11×D812yes—
407C22×C4C11×SD1612yes—
408C22×C4C22×C4×C1111yescharacteristic
409C22×C4C2×D4×C1111yescharacteristic
410C22×C4C2×D4×C1112yes—
411C22×C4C2×D4×C1112yes—
412C22×C4C2×D4×C1111yescharacteristic
413C22×C4C2×Q8×C1111yescharacteristic
414C22×C4C11×#4111yescharacteristic
415C22×C4C11×#4111yescharacteristic
416C22×C4C11×#4112yes—
417C22×C4C11×#4112yes—
418C2×C8—24no—
419C2×C8—24no—
420C2×C8—24no—
421C2×C8—42no—
422C2×C8—42no—
423C2×C8—42no—
424C2×C8—42no—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—42no—
429C4⋊C4—41no—
430C4⋊C4—42no—
431C4⋊C4—41no—
432C22⋊C4—48no—
433C22⋊C4—48no—
434C42—24no—
435C42—22no—
436C42—22no—
437C11#1107611yescharacteristic, direct product factor, Sylow
438C23—24no—
439C23—42no—
440C23—42no—
441C23—44no—
442C23—44no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—44no—
450C23—42no—
451C23—42no—
452C23—44no—
453C23—82no—
454C23—82no—
455C23—82no—
456C23—82no—
457C23—82no—
458C23—82no—
459C23—82no—
460C23—82no—
461C23C2×C11×C22⋊C411yescharacteristic
462C23C11×#12111yescharacteristic
463C23C11×#12112yes—
464C23C11×#12112yes—
465C23C11×C22⋊Q811yescharacteristic
466C23C2×C11×D811yescharacteristic
467C23C2×C11×SD1611yescharacteristic
468C23C11×#13512yes—
469C23C11×AGL(1,ℤ/8)11yescharacteristic
470C23C11×AGL(1,ℤ/8)12yes—
471C23C11×#13711yescharacteristic
472D4—28no—
473D4—44no—
474D4—42no—
475D4—42no—
476D4—42no—
477D4—42no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—44no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—44no—
492C2×C4—44no—
493C2×C4—82no—
494C2×C4—82no—
495C2×C4—82no—
496C2×C4—82no—
497C2×C4—82no—
498C2×C4—82no—
499C2×C4C11×#10214yescomplemented
500C2×C4C2×C11×C4⋊C411yescharacteristic
501C2×C4C11×#11711yescharacteristic
502C2×C4C4×D4×C1112yes—
503C2×C4C4×D4×C1112yes—
504C2×C4C11×#12012yes—
505C2×C4C11×#12011yescharacteristic
506C2×C4C11×#12112yes—
507C2×C4C11×#12111yescharacteristic
508C2×C4C11×C22⋊Q812yes—
509C2×C4C11×C22⋊Q812yes—
510C2×C4C11×C22⋊Q811yescharacteristic
511C2×C4C11×#12312yes—
512C2×C4C11×#12312yes—
513C2×C4C11×#12311yescharacteristic
514C2×C4C11×#12412yes—
515C2×C4C11×#12411yescharacteristic
516C2×C4C11×#12612yes—
517C2×C4C11×#12711yescharacteristic
518C8—44no—
519C22—44no—
520C22—44no—
521C22—44no—
522C22—82no—
523C22—82no—
524C22—82no—
525C22—82no—
526C22—84no—
527C22—84no—
528C22—84no—
529C22—84no—
530C22C11×#38011yescharacteristic
531C22C11×#38611yescharacteristic
532C22C11×#39011yescharacteristic
533C22C11×#39412yes—
534C22C11×#39612yes—
535C22C2×C11×#10211yescharacteristic
536C22C11×#41611yescharacteristic
537C22C11×#41711yescharacteristic
538C22C11×#41811yescharacteristic
539C22C11×#45912yes—
540C22C11×#45911yescharacteristic
541C22C11×#46012yes—
542C22C11×#46111yescharacteristic
543C22C11×#46312yes—
544C22C11×#46312yes—
545C22C11×#46412yes—
546C22C11×#46512yes—
547C22C11×#46612yes—
548C22C11×#46812yes—
549C22C11×#46912yes—
550C22C11×#47411yescharacteristic
551C22C11×#47611yescharacteristic
552C22C11×#47812yes—
553C4—24no—
554C4—42no—
555C4—82no—
556C4—84no—
557C4C11×#38512yes—
558C4C11×#38812yes—
559C4C11×#39211yescharacteristic
560C4C11×#39311yescharacteristic
561C4C11×#39711yescharacteristic
562C4C11×#39911yescharacteristic
563C2—84no—
564C2C11×#143911yescharacteristic
565C2C11×#180211yescharacteristic
566C2C11×#180411yescharacteristic
567C2C11×#189311yescharacteristic
568C2C11×#189511yescharacteristic
569C2C11×#198211yescharacteristic
570C2C11×#198311yescharacteristic
571C2C11×#205412yes—
572C2C11×#205512yes—
573C2C11×#206512yes—
574C2C11×#206712yes—
subgroupG/H
center, socleC24×C11C2×D4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×C4⋊C8C2semidirect
4. C2×C11×#340C2semidirect
5. C11×C4⋊#95C2semidirect
19. C11×#390C4semidirect
69. #11076C11direct (N × H)
151. C22×C4⋊C8C2×C11semidirect
154. C2×#340C2×C11semidirect
155. C4⋊#95C2×C11semidirect
217. C2×C4×C11#102semidirect
250. #390C4×C11semidirect
437. C11#11076direct (N × H)
499. C2×C4C11×#102semidirect

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊C82
C22×C11×#1022
C2×C11×#3902
C2×C11×#3402
C11×C4⋊#952
#1107611