Finite Group Databasebeta

← C11×#11064 #14588257

Subgroups — C11×#11064 #14588257

Order 2816.

958 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#419C211yesmaximal, characteristic
2C2×C11×#419C211yesmaximal, characteristic
3C11×#2317C211yesmaximal, characteristic
4C2×C11×#391C211yesmaximal, characteristic
5C2×C11×#343C211yesmaximal, characteristic
6C2×C11×#339C211yesmaximal, characteristic
7C2×C11×#339C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C11×#419—22no—
16C11×#419—22no—
17C11×#419—22no—
18C11×#419C414yescomplemented
19C2×C11×#103—21no—
20C2×C11×#103—21no—
21C2×C11×#103—22no—
22C11×#391—22no—
23C11×#391—22no—
24C11×#389—22no—
25C11×#385—22no—
26C11×#384—21no—
27C11×#382—21no—
28C2×C11×#95—22no—
29C11×#343—22no—
30C11×#339—22no—
31C11×#339—22no—
32C22×Q8×C11—21no—
33C22×Q8×C11—21no—
34C22×Q8×C11—21no—
35C22×Q8×C11—21no—
36C22×Q8×C11—21no—
37C22×Q8×C11—21no—
38C22×Q8×C11—21no—
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11—21no—
42C22×Q8×C11—21no—
43C22×Q8×C11C2×C412yes—
44C22×Q8×C11D412yes—
45C22×Q8×C11Q812yes—
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C23×C4×C11D412yes—
49C23×C4×C11C2311yescharacteristic
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16—21no—
60C2×C11×M16C2×C412yes—
61C2×C11×M16D412yes—
62C22×C8×C11—21no—
63C22×C8×C11—21no—
64C11×#117—21no—
65C11×#117—21no—
66C11×#117—21no—
67C11×#117—21no—
68C11×#117—21no—
69C11×#117—21no—
70C11×#117C2×C412yes—
71C11×#117D412yes—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4D412yes—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11D412yes—
92C11×#103—24no—
93C11×#103—24no—
94C11×#103—28no—
95C11×#95—28no—
96C11×#95—24no—
97#11064C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11C2×D411yescharacteristic
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—41no—
115C2×Q8×C11—41no—
116C2×Q8×C11—41no—
117C2×Q8×C11—41no—
118C2×Q8×C11—41no—
119C2×Q8×C11—41no—
120C2×Q8×C11—41no—
121C2×Q8×C11—41no—
122C2×Q8×C11—41no—
123C2×Q8×C11—41no—
124C2×Q8×C11—41no—
125C2×Q8×C11—41no—
126C2×Q8×C11C4⋊C414yescomplemented
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—42no—
139C22×C4×C11—41no—
140C22×C4×C11—41no—
141C22×C4×C11—41no—
142C22×C4×C11—41no—
143C22×C4×C11—41no—
144C22×C4×C11—41no—
145C22×C4×C11—44no—
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×Q811yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16—41no—
165C11×M16—41no—
166C11×M16—41no—
167C11×M16—41no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—41no—
171C2×C8×C11—41no—
172C2×C8×C11—41no—
173C2×C8×C11—41no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4—41no—
181C11×C4⋊C4—41no—
182C11×C4⋊C4—41no—
183C11×C4⋊C4—84no—
184C11×C4⋊C4C22⋊C414yes—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—41no—
188C11×C22⋊C4—41no—
189C42×C11—22no—
190C42×C11—22no—
191C42×C11—22no—
192C42×C11—22no—
193C42×C11—41no—
194C42×C11—41no—
195C42×C11—41no—
196C42×C11—41no—
197C2×#419C2×C1111yescharacteristic
198C2×#419C2×C1111yescharacteristic
199#2317C2×C1111yescharacteristic
200C2×#391C2×C1111yescharacteristic
201C2×#343C2×C1111yescharacteristic
202C2×#339C2×C1111yescharacteristic
203C2×#339C2×C1111yescharacteristic
204C23×C11—22no—
205C23×C11—22no—
206C23×C11C4×D411yescharacteristic
207C23×C11#12011yescharacteristic
208C23×C11#12011yescharacteristic
209C23×C11#12111yescharacteristic
210C23×C11#12111yescharacteristic
211C23×C11C22⋊Q811yescharacteristic
212C23×C11#12411yescharacteristic
213Q8×C11—24no—
214Q8×C11—24no—
215Q8×C11—42no—
216Q8×C11—42no—
217Q8×C11—42no—
218Q8×C11—42no—
219Q8×C11—42no—
220Q8×C11—42no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—44no—
225C2×C4×C11—42no—
226C2×C4×C11—44no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—44no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—44no—
242C2×C4×C11—42no—
243C2×C4×C11—82no—
244C2×C4×C11C2×C22⋊C411yescharacteristic
245C2×C4×C11C2×C4⋊C411yescharacteristic
246C2×C4×C11#11711yescharacteristic
247C2×C4×C11C4×D411yescharacteristic
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11#12011yescharacteristic
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11C22⋊Q811yescharacteristic
258C2×C4×C11C22⋊Q811yescharacteristic
259C2×C4×C11C22⋊Q811yescharacteristic
260C2×C4×C11C22⋊Q811yescharacteristic
261C2×C4×C11C22⋊Q811yescharacteristic
262C2×C4×C11#12311yescharacteristic
263C2×C4×C11#12311yescharacteristic
264C2×C4×C11#12311yescharacteristic
265C2×C4×C11#12311yescharacteristic
266C2×C4×C11#12311yescharacteristic
267C2×C4×C11#12411yescharacteristic
268C2×C4×C11#12411yescharacteristic
269C2×C4×C11#12611yescharacteristic
270C2×C4×C11#12611yescharacteristic
271C2×C4×C11#12711yescharacteristic
272C8×C11—42no—
273C8×C11—42no—
274C23×Q8C22×C1111yescharacteristic
275C22×M16C22×C1111yescharacteristic
276C22×M16C22×C1111yescharacteristic
277C2×#117C22×C1111yescharacteristic
278C2×#117C22×C1111yescharacteristic
279C22×C4⋊C4C22×C1111yescharacteristic
280C22×C42C22×C1111yescharacteristic
281#419—22no—
282#419—22no—
283#419—22no—
284#419C4×C1114yescomplemented
285C2×#103—21no—
286C2×#103—21no—
287C2×#103—22no—
288#391—22no—
289#391—22no—
290#389—22no—
291#385—22no—
292#384—21no—
293#382—21no—
294C2×#95—22no—
295#343—22no—
296#339—22no—
297#339—22no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—22no—
305C22×C11—22no—
306C22×C11#38511yescharacteristic
307C22×C11#38611yescharacteristic
308C22×C11#38811yescharacteristic
309C22×C11#39211yescharacteristic
310C22×C11#39311yescharacteristic
311C22×C11#39411yescharacteristic
312C22×C11#39611yescharacteristic
313C22×C11#45512yes—
314C22×C11#45612yes—
315C4×C11—44no—
316C4×C11—44no—
317C4×C11—44no—
318C4×C11—81no—
319C4×C11—82no—
320C4×C11—81no—
321C4×C11#38011yescharacteristic
322C4×C11#38511yescharacteristic
323C4×C11#38811yescharacteristic
324C4×C11#39011yescharacteristic
325C4×C11#39411yescharacteristic
326C4×C11#39611yescharacteristic
327C4×C11#39711yescharacteristic
328C4×C11#39911yescharacteristic
329C22×Q8—21no—
330C22×Q8—21no—
331C22×Q8—21no—
332C22×Q8—21no—
333C22×Q8—21no—
334C22×Q8—21no—
335C22×Q8—21no—
336C22×Q8—21no—
337C22×Q8—21no—
338C22×Q8—21no—
339C22×Q8—21no—
340C22×Q8C2×C4×C1112yes—
341C22×Q8D4×C1112yes—
342C22×Q8Q8×C1112yes—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4D4×C1112yes—
346C23×C4C23×C1111yescharacteristic
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16C2×C4×C1112yes—
358C2×M16D4×C1112yes—
359C22×C8—21no—
360C22×C8—21no—
361#117—21no—
362#117—21no—
363#117—21no—
364#117—21no—
365#117—21no—
366#117—21no—
367#117C2×C4×C1112yes—
368#117D4×C1112yes—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4D4×C1111yescharacteristic
377C2×C4⋊C4D4×C1111yescharacteristic
378C2×C4⋊C4D4×C1112yes—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42D4×C1112yes—
389#103—24no—
390#103—24no—
391#103—28no—
392#95—28no—
393#95—24no—
394C2×C11—21no—
395C2×C11—21no—
396C2×C11—21no—
397C2×C11—21no—
398C2×C11#143911yescharacteristic
399C2×C11#188212yes—
400C2×C11#200411yescharacteristic
401C2×C11#200511yescharacteristic
402C2×C11#202812yes—
403C24C2×D4×C1111yescharacteristic
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—41no—
420C2×Q8—41no—
421C2×Q8—41no—
422C2×Q8—41no—
423C2×Q8—41no—
424C2×Q8—41no—
425C2×Q8—41no—
426C2×Q8—41no—
427C2×Q8—41no—
428C2×Q8—41no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8C11×C4⋊C414yescomplemented
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—42no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—44no—
451C22×C4C22×C4×C1111yescharacteristic
452C22×C4C2×D4×C1111yescharacteristic
453C22×C4C2×D4×C1111yescharacteristic
454C22×C4C2×D4×C1111yescharacteristic
455C22×C4C2×D4×C1111yescharacteristic
456C22×C4C2×D4×C1111yescharacteristic
457C22×C4C2×D4×C1111yescharacteristic
458C22×C4C2×Q8×C1111yescharacteristic
459C22×C4C11×#4111yescharacteristic
460C22×C4C11×#4111yescharacteristic
461C22×C4C11×#4111yescharacteristic
462C22×C4C11×#4111yescharacteristic
463C22×C4C11×#4111yescharacteristic
464C22×C4C11×#4111yescharacteristic
465M16—22no—
466M16—22no—
467M16—22no—
468M16—22no—
469M16—41no—
470M16—41no—
471M16—41no—
472M16—41no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C4⋊C4—22no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—84no—
489C4⋊C4C11×C22⋊C414yes—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C42—22no—
495C42—22no—
496C42—22no—
497C42—22no—
498C42—41no—
499C42—41no—
500C42—41no—
501C42—41no—
502C11#1106411yescharacteristic, direct product factor, Sylow
503C23—22no—
504C23—22no—
505C23C4×D4×C1111yescharacteristic
506C23C11×#12011yescharacteristic
507C23C11×#12011yescharacteristic
508C23C11×#12111yescharacteristic
509C23C11×#12111yescharacteristic
510C23C11×C22⋊Q811yescharacteristic
511C23C11×#12411yescharacteristic
512Q8—24no—
513Q8—24no—
514Q8—42no—
515Q8—42no—
516Q8—42no—
517Q8—42no—
518Q8—42no—
519Q8—42no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4—44no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—44no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—44no—
541C2×C4—42no—
542C2×C4—82no—
543C2×C4C2×C11×C22⋊C411yescharacteristic
544C2×C4C2×C11×C4⋊C411yescharacteristic
545C2×C4C11×#11711yescharacteristic
546C2×C4C4×D4×C1111yescharacteristic
547C2×C4C4×D4×C1111yescharacteristic
548C2×C4C4×D4×C1111yescharacteristic
549C2×C4C11×#12011yescharacteristic
550C2×C4C11×#12111yescharacteristic
551C2×C4C11×#12111yescharacteristic
552C2×C4C11×#12111yescharacteristic
553C2×C4C11×#12111yescharacteristic
554C2×C4C11×#12111yescharacteristic
555C2×C4C11×#12111yescharacteristic
556C2×C4C11×C22⋊Q811yescharacteristic
557C2×C4C11×C22⋊Q811yescharacteristic
558C2×C4C11×C22⋊Q811yescharacteristic
559C2×C4C11×C22⋊Q811yescharacteristic
560C2×C4C11×C22⋊Q811yescharacteristic
561C2×C4C11×#12311yescharacteristic
562C2×C4C11×#12311yescharacteristic
563C2×C4C11×#12311yescharacteristic
564C2×C4C11×#12311yescharacteristic
565C2×C4C11×#12311yescharacteristic
566C2×C4C11×#12411yescharacteristic
567C2×C4C11×#12411yescharacteristic
568C2×C4C11×#12611yescharacteristic
569C2×C4C11×#12611yescharacteristic
570C2×C4C11×#12711yescharacteristic
571C8—42no—
572C8—42no—
573C22—22no—
574C22—22no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—22no—
580C22—22no—
581C22C11×#38511yescharacteristic
582C22C11×#38611yescharacteristic
583C22C11×#38811yescharacteristic
584C22C11×#39211yescharacteristic
585C22C11×#39311yescharacteristic
586C22C11×#39411yescharacteristic
587C22C11×#39611yescharacteristic
588C22C11×#45512yes—
589C22C11×#45612yes—
590C4—44no—
591C4—44no—
592C4—44no—
593C4—82no—
594C4—81no—
595C4—81no—
596C4C11×#38011yescharacteristic
597C4C11×#38511yescharacteristic
598C4C11×#38811yescharacteristic
599C4C11×#39011yescharacteristic
600C4C11×#39411yescharacteristic
601C4C11×#39611yescharacteristic
602C4C11×#39711yescharacteristic
603C4C11×#39911yescharacteristic
604C2—21no—
605C2—21no—
606C2—21no—
607C2—21no—
608C2C11×#143911yescharacteristic
609C2C11×#188212yes—
610C2C11×#200411yescharacteristic
611C2C11×#200511yescharacteristic
612C2C11×#202812yes—
subgroupG/H
center, socleC23×C11#120
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
18. C11×#419C4semidirect
97. #11064C11direct (N × H)
126. C2×Q8×C11C4⋊C4semidirect
284. #419C4×C11semidirect
431. C2×Q8C11×C4⋊C4semidirect
502. C11#11064direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4192
C11×#23172
C2×C11×#3912
C2×C11×#3432
C2×C11×#3392
#1106411