Finite Group Databasebeta

← C11×#11318 #14588511

Subgroups — C11×#11318 #14588511

Order 2816.

782 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#342C211yesmaximal, 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×#342—22no—
16C11×#342—22no—
17C11×#342—22no—
18C11×#342—22no—
19C11×#342—22no—
20C11×#342—22no—
21C11×#342C414yescomplemented
22C25×C11C2311yescharacteristic
23C23×C4×C11—21no—
24C23×C4×C11—21no—
25C23×C4×C11—21no—
26C23×C4×C11—21no—
27C23×C4×C11—21no—
28C23×C4×C11—21no—
29C23×C4×C11—21no—
30C2×C11×C22⋊C4—21no—
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4—21no—
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⋊C4C2×C412yes—
66C2×C11×C22⋊C4C2×C412yes—
67C2×C11×C22⋊C4C2×C412yes—
68C2×C11×C22⋊C4D412yes—
69C2×C11×C22⋊C4D412yes—
70C2×C11×C22⋊C4D412yes—
71C2×C11×C22⋊C4Q812yes—
72#11318C1111yesmaximal, characteristic, direct product factor, Sylow
73C24×C11—82no—
74C24×C11C22×C411yescharacteristic
75C24×C11C2×D411yescharacteristic
76C24×C11C2×D411yescharacteristic
77C24×C11C2×D411yescharacteristic
78C24×C11C2×Q811yescharacteristic
79C24×C11#4111yescharacteristic
80C24×C11#4111yescharacteristic
81C24×C11#4111yescharacteristic
82C24×C11#4111yescharacteristic
83C24×C11#4111yescharacteristic
84C24×C11#4111yescharacteristic
85C24×C11#4111yescharacteristic
86C24×C11#4111yescharacteristic
87C24×C11#4111yescharacteristic
88C24×C11#4111yescharacteristic
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
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—82no—
111C22×C4×C11—82no—
112C22×C4×C11—82no—
113C22×C4×C11—82no—
114C22×C4×C11—82no—
115C22×C4×C11—82no—
116C22×C4×C11—82no—
117C11×C22⋊C4—22no—
118C11×C22⋊C4—22no—
119C11×C22⋊C4—22no—
120C11×C22⋊C4—22no—
121C11×C22⋊C4—22no—
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—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
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—
145C2×#342C2×C1111yescharacteristic
146C2×#342C2×C1111yescharacteristic
147C2×#342C2×C1111yescharacteristic
148C2×#342C2×C1111yescharacteristic
149C2×#342C2×C1111yescharacteristic
150C2×#342C2×C1111yescharacteristic
151C2×#342C2×C1111yescharacteristic
152C23×C11—42no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11—42no—
156C23×C11—42no—
157C23×C11—42no—
158C23×C11—42no—
159C23×C11—81no—
160C23×C11—81no—
161C23×C11—81no—
162C23×C11—81no—
163C23×C11—81no—
164C23×C11—81no—
165C23×C11—81no—
166C23×C11—81no—
167C23×C11#11711yescharacteristic
168C23×C11#11711yescharacteristic
169C23×C11#11711yescharacteristic
170C23×C11C4×D411yescharacteristic
171C23×C11C4×D411yescharacteristic
172C23×C11C4×D411yescharacteristic
173C23×C11C4×Q811yescharacteristic
174C23×C11#12111yescharacteristic
175C23×C11#12111yescharacteristic
176C23×C11#12111yescharacteristic
177C23×C11C22⋊Q811yescharacteristic
178C23×C11C22⋊Q811yescharacteristic
179C23×C11C22⋊Q811yescharacteristic
180C23×C11#12311yescharacteristic
181C23×C11#12311yescharacteristic
182C23×C11#12311yescharacteristic
183C23×C11#12311yescharacteristic
184C23×C11#12311yescharacteristic
185C23×C11#12311yescharacteristic
186C23×C11#12411yescharacteristic
187C23×C11#12411yescharacteristic
188C23×C11#12411yescharacteristic
189C23×C11#12511yescharacteristic
190C23×C11#12511yescharacteristic
191C23×C11#12511yescharacteristic
192C23×C11#12611yescharacteristic
193C23×C11#12611yescharacteristic
194C23×C11#12611yescharacteristic
195C23×C11#12611yescharacteristic
196C23×C11#12611yescharacteristic
197C23×C11#12611yescharacteristic
198C23×C11#12611yescharacteristic
199C23×C11#12611yescharacteristic
200C23×C11#12611yescharacteristic
201C23×C11#12611yescharacteristic
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—82no—
210C2×C4×C11—82no—
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—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—
230C22×C22⋊C4C22×C1111yescharacteristic
231C22×C22⋊C4C22×C1111yescharacteristic
232C22×C22⋊C4C22×C1111yescharacteristic
233C22×C22⋊C4C22×C1111yescharacteristic
234C22×C22⋊C4C22×C1111yescharacteristic
235C22×C22⋊C4C22×C1111yescharacteristic
236C22×C22⋊C4C22×C1111yescharacteristic
237#342—22no—
238#342—22no—
239#342—22no—
240#342—22no—
241#342—22no—
242#342—22no—
243#342C4×C1114yescomplemented
244C22×C11—22no—
245C22×C11—22no—
246C22×C11—22no—
247C22×C11—22no—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—41no—
252C22×C11—41no—
253C22×C11—41no—
254C22×C11—41no—
255C22×C11—41no—
256C22×C11—41no—
257C22×C11—41no—
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#38311yescharacteristic
280C22×C11#38711yescharacteristic
281C22×C11#38711yescharacteristic
282C22×C11#38711yescharacteristic
283C22×C11#38811yescharacteristic
284C22×C11#38811yescharacteristic
285C22×C11#38811yescharacteristic
286C22×C11#39611yescharacteristic
287C22×C11#39711yescharacteristic
288C22×C11#39711yescharacteristic
289C22×C11#39711yescharacteristic
290C22×C11#40011yescharacteristic
291C22×C11#40011yescharacteristic
292C22×C11#40011yescharacteristic
293C22×C11#40111yescharacteristic
294C4×C11—82no—
295C4×C11—82no—
296C4×C11—82no—
297C4×C11—82no—
298C4×C11—82no—
299C4×C11—82no—
300C4×C11—82no—
301C25C23×C1111yescharacteristic
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4—21no—
307C23×C4—21no—
308C23×C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
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⋊C4C2×C4×C1112yes—
345C2×C22⋊C4C2×C4×C1112yes—
346C2×C22⋊C4C2×C4×C1112yes—
347C2×C22⋊C4D4×C1112yes—
348C2×C22⋊C4D4×C1112yes—
349C2×C22⋊C4D4×C1112yes—
350C2×C22⋊C4Q8×C1112yes—
351C2×C11—21no—
352C2×C11—21no—
353C2×C11—21no—
354C2×C11—21no—
355C2×C11—21no—
356C2×C11—21no—
357C2×C11—21no—
358C2×C11—21no—
359C2×C11—21no—
360C2×C11—21no—
361C2×C11—21no—
362C2×C11—21no—
363C2×C11—21no—
364C2×C11—21no—
365C2×C11#144311yescharacteristic
366C2×C11#210412yes—
367C24—82no—
368C24C22×C4×C1111yescharacteristic
369C24C2×D4×C1111yescharacteristic
370C24C2×D4×C1111yescharacteristic
371C24C2×D4×C1111yescharacteristic
372C24C2×Q8×C1111yescharacteristic
373C24C11×#4111yescharacteristic
374C24C11×#4111yescharacteristic
375C24C11×#4111yescharacteristic
376C24C11×#4111yescharacteristic
377C24C11×#4111yescharacteristic
378C24C11×#4111yescharacteristic
379C24C11×#4111yescharacteristic
380C24C11×#4111yescharacteristic
381C24C11×#4111yescharacteristic
382C24C11×#4111yescharacteristic
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—82no—
405C22×C4—82no—
406C22×C4—82no—
407C22×C4—82no—
408C22×C4—82no—
409C22×C4—82no—
410C22×C4—82no—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C11#1131811yescharacteristic, direct product factor, Sylow
440C23—42no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—81no—
448C23—81no—
449C23—81no—
450C23—81no—
451C23—81no—
452C23—81no—
453C23—81no—
454C23—81no—
455C23C11×#11711yescharacteristic
456C23C11×#11711yescharacteristic
457C23C11×#11711yescharacteristic
458C23C4×D4×C1111yescharacteristic
459C23C4×D4×C1111yescharacteristic
460C23C4×D4×C1111yescharacteristic
461C23C4×Q8×C1111yescharacteristic
462C23C11×#12111yescharacteristic
463C23C11×#12111yescharacteristic
464C23C11×#12111yescharacteristic
465C23C11×C22⋊Q811yescharacteristic
466C23C11×C22⋊Q811yescharacteristic
467C23C11×C22⋊Q811yescharacteristic
468C23C11×#12311yescharacteristic
469C23C11×#12311yescharacteristic
470C23C11×#12311yescharacteristic
471C23C11×#12311yescharacteristic
472C23C11×#12311yescharacteristic
473C23C11×#12311yescharacteristic
474C23C11×#12411yescharacteristic
475C23C11×#12411yescharacteristic
476C23C11×#12411yescharacteristic
477C23C11×#12511yescharacteristic
478C23C11×#12511yescharacteristic
479C23C11×#12511yescharacteristic
480C23C11×#12611yescharacteristic
481C23C11×#12611yescharacteristic
482C23C11×#12611yescharacteristic
483C23C11×#12611yescharacteristic
484C23C11×#12611yescharacteristic
485C23C11×#12611yescharacteristic
486C23C11×#12611yescharacteristic
487C23C11×#12611yescharacteristic
488C23C11×#12611yescharacteristic
489C23C11×#12611yescharacteristic
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—82no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4—82no—
504C2×C4—82no—
505C2×C4—82no—
506C2×C4—82no—
507C2×C4—82no—
508C2×C4—82no—
509C2×C4—82no—
510C2×C4—82no—
511C2×C4—82no—
512C2×C4—82no—
513C2×C4—82no—
514C2×C4—82no—
515C2×C4—82no—
516C2×C4—82no—
517C2×C4—82no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—22no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—41no—
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—
553C22C11×#38311yescharacteristic
554C22C11×#38711yescharacteristic
555C22C11×#38711yescharacteristic
556C22C11×#38711yescharacteristic
557C22C11×#38811yescharacteristic
558C22C11×#38811yescharacteristic
559C22C11×#38811yescharacteristic
560C22C11×#39611yescharacteristic
561C22C11×#39711yescharacteristic
562C22C11×#39711yescharacteristic
563C22C11×#39711yescharacteristic
564C22C11×#40011yescharacteristic
565C22C11×#40011yescharacteristic
566C22C11×#40011yescharacteristic
567C22C11×#40111yescharacteristic
568C4—82no—
569C4—82no—
570C4—82no—
571C4—82no—
572C4—82no—
573C4—82no—
574C4—82no—
575C2—21no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—21no—
580C2—21no—
581C2—21no—
582C2—21no—
583C2—21no—
584C2—21no—
585C2—21no—
586C2—21no—
587C2—21no—
588C2—21no—
589C2C11×#144311yescharacteristic
590C2C11×#210412yes—
subgroupG/H
center, socleC22×C11#401
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
21. C11×#342C4semidirect
72. #11318C11direct (N × H)
243. #342C4×C11semidirect
439. C11#11318direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3422
#1131811