Finite Group Databasebeta

← C11×#11279 #14588472

Subgroups — C11×#11279 #14588472

Order 2816.

850 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2315C211yesmaximal, characteristic
2C2×C11×#342C211yesmaximal, characteristic
3C2×C11×#342C211yesmaximal, characteristic
4C2×C11×#342C211yesmaximal, characteristic
5C2×C11×#342C211yesmaximal, characteristic
6C2×C11×#342C211yesmaximal, characteristic
7C2×C11×#342C211yesmaximal, characteristic
8C22×C11×C22⋊C4C2211yescharacteristic
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C11×C22⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C11×#385—22no—
16C11×#385—22no—
17C11×#380—22no—
18C11×#342—22no—
19C11×#342—22no—
20C11×#342—22no—
21C11×#342—22no—
22C11×#342—22no—
23C11×#342C414yescomplemented
24C25×C11C2311yescharacteristic
25C23×C4×C11—21no—
26C23×C4×C11—21no—
27C23×C4×C11—21no—
28C23×C4×C11—21no—
29C23×C4×C11—21no—
30C23×C4×C11—21no—
31C23×C4×C11Q812yes—
32C2×C11×C4⋊C4—24no—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4—21no—
54C2×C11×C22⋊C4—21no—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—21no—
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⋊C4C2×C412yes—
68C2×C11×C22⋊C4C2×C412yes—
69C2×C11×C22⋊C4C2×C412yes—
70C2×C11×C22⋊C4D412yes—
71C2×C11×C22⋊C4D412yes—
72C2×C11×C22⋊C4D412yes—
73C2×C11×C22⋊C4D412yes—
74C2×C11×C22⋊C4Q812yes—
75C11×#95—24no—
76#11279C1111yesmaximal, characteristic, direct product factor, Sylow
77C24×C11—82no—
78C24×C11C22×C411yescharacteristic
79C24×C11C2×D411yescharacteristic
80C24×C11C2×D411yescharacteristic
81C24×C11C2×D411yescharacteristic
82C24×C11C2×D411yescharacteristic
83C24×C11C2×Q811yescharacteristic
84C24×C11C2×Q811yescharacteristic
85C24×C11#4111yescharacteristic
86C24×C11#4111yescharacteristic
87C24×C11#4111yescharacteristic
88C24×C11#4111yescharacteristic
89C24×C11#4111yescharacteristic
90C24×C11#4111yescharacteristic
91C24×C11#4111yescharacteristic
92C24×C11#4111yescharacteristic
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
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—41no—
112C22×C4×C11—41no—
113C22×C4×C11—41no—
114C22×C4×C11—82no—
115C22×C4×C11—82no—
116C22×C4×C11—82no—
117C22×C4×C11—82no—
118C22×C4×C11—82no—
119C22×C4×C11—82no—
120C22×C4×C11—82no—
121C11×C4⋊C4—84no—
122C11×C22⋊C4—22no—
123C11×C22⋊C4—22no—
124C11×C22⋊C4—22no—
125C11×C22⋊C4—22no—
126C11×C22⋊C4—22no—
127C11×C22⋊C4—22no—
128C11×C22⋊C4—22no—
129C11×C22⋊C4—22no—
130C11×C22⋊C4—22no—
131C11×C22⋊C4—22no—
132C11×C22⋊C4—22no—
133C11×C22⋊C4—22no—
134C11×C22⋊C4—22no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—41no—
138C11×C22⋊C4—41no—
139C11×C22⋊C4—41no—
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—41no—
149C11×C22⋊C4C4⋊C414yes—
150#2315C2×C1111yescharacteristic
151C2×#342C2×C1111yescharacteristic
152C2×#342C2×C1111yescharacteristic
153C2×#342C2×C1111yescharacteristic
154C2×#342C2×C1111yescharacteristic
155C2×#342C2×C1111yescharacteristic
156C2×#342C2×C1111yescharacteristic
157C23×C11—42no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—81no—
165C23×C11—81no—
166C23×C11—81no—
167C23×C11—81no—
168C23×C11—81no—
169C23×C11—81no—
170C23×C11—81no—
171C23×C11—81no—
172C23×C11C2×C4⋊C411yescharacteristic
173C23×C11#11711yescharacteristic
174C23×C11#11711yescharacteristic
175C23×C11C4×D411yescharacteristic
176C23×C11C4×D411yescharacteristic
177C23×C11C4×D411yescharacteristic
178C23×C11C4×Q811yescharacteristic
179C23×C11#12011yescharacteristic
180C23×C11#12111yescharacteristic
181C23×C11#12111yescharacteristic
182C23×C11#12111yescharacteristic
183C23×C11C22⋊Q811yescharacteristic
184C23×C11C22⋊Q811yescharacteristic
185C23×C11C22⋊Q811yescharacteristic
186C23×C11C22⋊Q811yescharacteristic
187C23×C11C22⋊Q811yescharacteristic
188C23×C11#12311yescharacteristic
189C23×C11#12311yescharacteristic
190C23×C11#12311yescharacteristic
191C23×C11#12311yescharacteristic
192C23×C11#12311yescharacteristic
193C23×C11#12411yescharacteristic
194C23×C11#12411yescharacteristic
195C23×C11#12411yescharacteristic
196C23×C11#12411yescharacteristic
197C23×C11#12511yescharacteristic
198C23×C11#12511yescharacteristic
199C23×C11#12511yescharacteristic
200C23×C11#12511yescharacteristic
201C23×C11#12511yescharacteristic
202C23×C11#12611yescharacteristic
203C23×C11#12611yescharacteristic
204C23×C11#12611yescharacteristic
205C23×C11#12611yescharacteristic
206C23×C11C4⋊Q811yescharacteristic
207C2×C4×C11—24no—
208C2×C4×C11—44no—
209C2×C4×C11—44no—
210C2×C4×C11—44no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—82no—
218C2×C4×C11—82no—
219C2×C4×C11—82no—
220C2×C4×C11—82no—
221C2×C4×C11—82no—
222C2×C4×C11—82no—
223C2×C4×C11—82no—
224C2×C4×C11—82no—
225C2×C4×C11—82no—
226C2×C4×C11—82no—
227C2×C4×C11—82no—
228C2×C4×C11—82no—
229C2×C4×C11—82no—
230C2×C4×C11—82no—
231C2×C4×C11—82no—
232C2×C4×C11—82no—
233C2×C4×C11—82no—
234C2×C4×C11—82no—
235C22×C22⋊C4C22×C1111yescharacteristic
236C22×C22⋊C4C22×C1111yescharacteristic
237C22×C22⋊C4C22×C1111yescharacteristic
238C22×C22⋊C4C22×C1111yescharacteristic
239C22×C22⋊C4C22×C1111yescharacteristic
240C22×C22⋊C4C22×C1111yescharacteristic
241C22×C22⋊C4C22×C1111yescharacteristic
242#385—22no—
243#385—22no—
244#380—22no—
245#342—22no—
246#342—22no—
247#342—22no—
248#342—22no—
249#342—22no—
250#342C4×C1114yescomplemented
251C22×C11—22no—
252C22×C11—22no—
253C22×C11—22no—
254C22×C11—22no—
255C22×C11—22no—
256C22×C11—22no—
257C22×C11—22no—
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—41no—
267C22×C11—41no—
268C22×C11—41no—
269C22×C11—41no—
270C22×C11—41no—
271C22×C11—41no—
272C22×C11—41no—
273C22×C11—41no—
274C22×C11—41no—
275C22×C11—41no—
276C22×C11—41no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11—41no—
280C22×C11—41no—
281C22×C11—41no—
282C22×C11—41no—
283C22×C11—41no—
284C22×C11—41no—
285C22×C11—41no—
286C22×C11#38211yescharacteristic
287C22×C11#38511yescharacteristic
288C22×C11#38711yescharacteristic
289C22×C11#38711yescharacteristic
290C22×C11#38811yescharacteristic
291C22×C11#38811yescharacteristic
292C22×C11#38911yescharacteristic
293C22×C11#39311yescharacteristic
294C22×C11#39411yescharacteristic
295C22×C11#39711yescharacteristic
296C22×C11#39811yescharacteristic
297C22×C11#39811yescharacteristic
298C22×C11#40011yescharacteristic
299C22×C11#40011yescharacteristic
300C22×C11#40011yescharacteristic
301C4×C11—44no—
302C4×C11—82no—
303C4×C11—82no—
304C4×C11—82no—
305C4×C11—82no—
306C4×C11—82no—
307C4×C11—82no—
308C25C23×C1111yescharacteristic
309C23×C4—21no—
310C23×C4—21no—
311C23×C4—21no—
312C23×C4—21no—
313C23×C4—21no—
314C23×C4—21no—
315C23×C4Q8×C1112yes—
316C2×C4⋊C4—24no—
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—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4C2×C4×C1112yes—
352C2×C22⋊C4C2×C4×C1112yes—
353C2×C22⋊C4C2×C4×C1112yes—
354C2×C22⋊C4D4×C1112yes—
355C2×C22⋊C4D4×C1112yes—
356C2×C22⋊C4D4×C1112yes—
357C2×C22⋊C4D4×C1112yes—
358C2×C22⋊C4Q8×C1112yes—
359#95—24no—
360C2×C11—21no—
361C2×C11—21no—
362C2×C11—21no—
363C2×C11—21no—
364C2×C11—21no—
365C2×C11—21no—
366C2×C11—21no—
367C2×C11—21no—
368C2×C11—21no—
369C2×C11—21no—
370C2×C11—21no—
371C2×C11—21no—
372C2×C11—21no—
373C2×C11—21no—
374C2×C11#144211yescharacteristic
375C2×C11#203212yes—
376C24—82no—
377C24C22×C4×C1111yescharacteristic
378C24C2×D4×C1111yescharacteristic
379C24C2×D4×C1111yescharacteristic
380C24C2×D4×C1111yescharacteristic
381C24C2×D4×C1111yescharacteristic
382C24C2×Q8×C1111yescharacteristic
383C24C2×Q8×C1111yescharacteristic
384C24C11×#4111yescharacteristic
385C24C11×#4111yescharacteristic
386C24C11×#4111yescharacteristic
387C24C11×#4111yescharacteristic
388C24C11×#4111yescharacteristic
389C24C11×#4111yescharacteristic
390C24C11×#4111yescharacteristic
391C24C11×#4111yescharacteristic
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—82no—
414C22×C4—82no—
415C22×C4—82no—
416C22×C4—82no—
417C22×C4—82no—
418C22×C4—82no—
419C22×C4—82no—
420C4⋊C4—84no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—41no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4C11×C4⋊C414yes—
449C11#1127911yescharacteristic, direct product factor, Sylow
450C23—42no—
451C23—42no—
452C23—42no—
453C23—42no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23—81no—
458C23—81no—
459C23—81no—
460C23—81no—
461C23—81no—
462C23—81no—
463C23—81no—
464C23—81no—
465C23C2×C11×C4⋊C411yescharacteristic
466C23C11×#11711yescharacteristic
467C23C11×#11711yescharacteristic
468C23C4×D4×C1111yescharacteristic
469C23C4×D4×C1111yescharacteristic
470C23C4×D4×C1111yescharacteristic
471C23C4×Q8×C1111yescharacteristic
472C23C11×#12011yescharacteristic
473C23C11×#12111yescharacteristic
474C23C11×#12111yescharacteristic
475C23C11×#12111yescharacteristic
476C23C11×C22⋊Q811yescharacteristic
477C23C11×C22⋊Q811yescharacteristic
478C23C11×C22⋊Q811yescharacteristic
479C23C11×C22⋊Q811yescharacteristic
480C23C11×C22⋊Q811yescharacteristic
481C23C11×#12311yescharacteristic
482C23C11×#12311yescharacteristic
483C23C11×#12311yescharacteristic
484C23C11×#12311yescharacteristic
485C23C11×#12311yescharacteristic
486C23C11×#12411yescharacteristic
487C23C11×#12411yescharacteristic
488C23C11×#12411yescharacteristic
489C23C11×#12411yescharacteristic
490C23C11×#12511yescharacteristic
491C23C11×#12511yescharacteristic
492C23C11×#12511yescharacteristic
493C23C11×#12511yescharacteristic
494C23C11×#12511yescharacteristic
495C23C11×#12611yescharacteristic
496C23C11×#12611yescharacteristic
497C23C11×#12611yescharacteristic
498C23C11×#12611yescharacteristic
499C23C11×C4⋊Q811yescharacteristic
500C2×C4—24no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—82no—
511C2×C4—82no—
512C2×C4—82no—
513C2×C4—82no—
514C2×C4—82no—
515C2×C4—82no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4—82no—
524C2×C4—82no—
525C2×C4—82no—
526C2×C4—82no—
527C2×C4—82no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22C11×#38211yescharacteristic
564C22C11×#38511yescharacteristic
565C22C11×#38711yescharacteristic
566C22C11×#38711yescharacteristic
567C22C11×#38811yescharacteristic
568C22C11×#38811yescharacteristic
569C22C11×#38911yescharacteristic
570C22C11×#39311yescharacteristic
571C22C11×#39411yescharacteristic
572C22C11×#39711yescharacteristic
573C22C11×#39811yescharacteristic
574C22C11×#39811yescharacteristic
575C22C11×#40011yescharacteristic
576C22C11×#40011yescharacteristic
577C22C11×#40011yescharacteristic
578C4—44no—
579C4—82no—
580C4—82no—
581C4—82no—
582C4—82no—
583C4—82no—
584C4—82no—
585C2—21no—
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—21no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2C11×#144211yescharacteristic
600C2C11×#203212yes—
subgroupG/H
center, socleC22×C11#393
commutatorC24C22×C4×C11
Frattini, cosocleC25C23×C11
prime radicalC25×C11C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
23. C11×#342C4semidirect
76. #11279C11direct (N × H)
250. #342C4×C11semidirect
449. C11#11279direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23152
C2×C11×#3422
#1127911