Finite Group Databasebeta

← C11×#11078 #14588271

Subgroups — C11×#11078 #14588271

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#104C211yesmaximal, characteristic
2C2×C11×#417C211yesmaximal, characteristic
3C11×#2311C211yesmaximal, characteristic
4C2×C11×#384C211yesmaximal, characteristic, complemented
5C2×C11×#343C211yesmaximal, characteristic, complemented
6C11×#1736C211yesmaximal, characteristic, complemented
7C2×C11×#339C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C22×C11×C4⋊C4—22no—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C2×C11×#104—22no—
17C2×C11×#104—22no—
18C2×C11×#104C414yescomplemented
19C11×#417—22no—
20C11×#417—22no—
21C2×C11×#103—21no—
22C2×C11×#102—21no—
23C11×#391—21no—
24C11×#390—21no—
25C11×#386—22no—
26C11×#384—22no—
27C11×#384—22no—
28C11×#380—22no—
29C11×#343—22no—
30C11×#340—22no—
31C11×#339—22no—
32C2×C11×#41—21no—
33C2×C11×#41—21no—
34C2×C11×#41—21no—
35C2×C11×#41—21no—
36C2×C11×#41—21no—
37C2×C11×#41—21no—
38C2×C11×#41—21no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41C2×C412yes—
43C2×C11×#41Q812yes—
44C22×Q8×C11D411yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11D411yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11—21no—
50C23×C4×C11D412yes—
51C23×C4×C11C2311yescharacteristic
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×M16—21no—
61C2×C11×M16—21no—
62C2×C11×M16C2×C412yes—
63C2×C11×M16D412yes—
64C22×C8×C11—21no—
65C22×C8×C11—21no—
66C11×#117—21no—
67C11×#117—21no—
68C11×#117—21no—
69C11×#117—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—28no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—48no—
83C2×C11×C4⋊C4D412yes—
84C2×C11×C4⋊C4D412yes—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—24no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11C2×C412yes—
92C2×C42×C11D412yes—
93C2×C42×C11D412yes—
94C11×#104—28no—
95C11×#103—24no—
96C11×#102—24no—
97C11×#95—24no—
98#11078C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11—21no—
100C24×C11C2×D411yescharacteristic
101C11×#41—22no—
102C11×#41—22no—
103C11×#41—22no—
104C11×#41—22no—
105C11×#41—22no—
106C11×#41—22no—
107C11×#41—22no—
108C11×#41—22no—
109C11×#41—41no—
110C11×#41—41no—
111C11×#41—41no—
112C11×#41—41no—
113C11×#41—41no—
114C11×#41—41no—
115C11×#41—41no—
116C11×#41—41no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11C4⋊C412yescomplemented
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C2×D4×C11—41no—
133C2×D4×C11—41no—
134C2×D4×C11C4⋊C412yescomplemented
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—41no—
152C22×C4×C11—44no—
153C22×C4×C11—44no—
154C22×C4×C11—41no—
155C22×C4×C11—41no—
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×Q811yescharacteristic
164C22×C4×C11#4111yescharacteristic
165C22×C4×C11#4111yescharacteristic
166C22×C4×C11#4111yescharacteristic
167C22×C4×C11#4111yescharacteristic
168C22×C4×C11#4111yescharacteristic
169C22×C4×C11#4111yescharacteristic
170C11×M16—22no—
171C11×M16—22no—
172C11×M16—22no—
173C11×M16—22no—
174C11×M16—41no—
175C11×M16—41no—
176C11×M16—41no—
177C11×M16—41no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—41no—
181C2×C8×C11—41no—
182C2×C8×C11—41no—
183C2×C8×C11—41no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—416no—
189C11×C4⋊C4—41no—
190C11×C4⋊C4—41no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4—41no—
193C11×C4⋊C4—41no—
194C11×C4⋊C4—41no—
195C11×C22⋊C4—41no—
196C11×C22⋊C4—41no—
197C11×C22⋊C4—84no—
198C42×C11—22no—
199C42×C11—22no—
200C42×C11—22no—
201C42×C11—41no—
202C42×C11—41no—
203C42×C11C22⋊C414yescomplemented
204C22×#104C2×C1111yescharacteristic
205C2×#417C2×C1111yescharacteristic
206#2311C2×C1111yescharacteristic
207C2×#384C2×C1111yescharacteristic, complemented
208C2×#343C2×C1111yescharacteristic, complemented
209#1736C2×C1111yescharacteristic, complemented
210C2×#339C2×C1111yescharacteristic, complemented
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11C4×D411yescharacteristic
219C23×C11#12011yescharacteristic
220C23×C11#12011yescharacteristic
221C23×C11#12111yescharacteristic
222C23×C11#12111yescharacteristic
223C23×C11C22⋊Q811yescharacteristic
224C23×C11#12411yescharacteristic
225Q8×C11—22no—
226Q8×C11—22no—
227Q8×C11—41no—
228Q8×C11—41no—
229D4×C11—22no—
230D4×C11—22no—
231D4×C11—42no—
232D4×C11—42no—
233D4×C11—42no—
234D4×C11—42no—
235D4×C11—41no—
236D4×C11—41no—
237C2×C4×C11—24no—
238C2×C4×C11—28no—
239C2×C4×C11—24no—
240C2×C4×C11—28no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—44no—
250C2×C4×C11—44no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—44no—
256C2×C4×C11—42no—
257C2×C4×C11—82no—
258C2×C4×C11—82no—
259C2×C4×C11—82no—
260C2×C4×C11C2×C22⋊C411yescharacteristic
261C2×C4×C11C2×C4⋊C411yescharacteristic
262C2×C4×C11#11711yescharacteristic
263C2×C4×C11C4×D411yescharacteristic
264C2×C4×C11C4×D411yescharacteristic
265C2×C4×C11C4×D411yescharacteristic
266C2×C4×C11#12011yescharacteristic
267C2×C4×C11#12111yescharacteristic
268C2×C4×C11#12111yescharacteristic
269C2×C4×C11#12111yescharacteristic
270C2×C4×C11#12111yescharacteristic
271C2×C4×C11#12111yescharacteristic
272C2×C4×C11#12111yescharacteristic
273C2×C4×C11C22⋊Q811yescharacteristic
274C2×C4×C11C22⋊Q811yescharacteristic
275C2×C4×C11C22⋊Q811yescharacteristic
276C2×C4×C11C22⋊Q811yescharacteristic
277C2×C4×C11C22⋊Q811yescharacteristic
278C2×C4×C11#12311yescharacteristic
279C2×C4×C11#12311yescharacteristic
280C2×C4×C11#12311yescharacteristic
281C2×C4×C11#12311yescharacteristic
282C2×C4×C11#12311yescharacteristic
283C2×C4×C11#12411yescharacteristic
284C2×C4×C11#12411yescharacteristic
285C2×C4×C11#12611yescharacteristic
286C2×C4×C11#12611yescharacteristic
287C2×C4×C11#12711yescharacteristic
288C8×C11—42no—
289C8×C11—42no—
290C22×#41C22×C1111yescharacteristic
291C22×M16C22×C1111yescharacteristic
292C22×M16C22×C1111yescharacteristic
293C2×#117C22×C1111yescharacteristic
294C22×C4⋊C4—22no—
295C22×C4⋊C4C22×C1111yescharacteristic
296C22×C4⋊C4C22×C1111yescharacteristic
297C22×C42C22×C1111yescharacteristic
298C2×#104—22no—
299C2×#104—22no—
300C2×#104C4×C1114yescomplemented
301#417—22no—
302#417—22no—
303C2×#103—21no—
304C2×#102—21no—
305#391—21no—
306#390—21no—
307#386—22no—
308#384—22no—
309#384—22no—
310#380—22no—
311#343—22no—
312#340—22no—
313#339—22no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—44no—
323C22×C11—42no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11—82no—
327C22×C11#38511yescharacteristic
328C22×C11#38611yescharacteristic
329C22×C11#38811yescharacteristic
330C22×C11#39211yescharacteristic
331C22×C11#39311yescharacteristic
332C22×C11#39411yescharacteristic
333C22×C11#39611yescharacteristic
334C22×C11#45312yes—
335C22×C11#45612yes—
336C4×C11—28no—
337C4×C11—42no—
338C4×C11—82no—
339C4×C11—82no—
340C4×C11—82no—
341C4×C11#38011yescharacteristic
342C4×C11#38511yescharacteristic
343C4×C11#38811yescharacteristic
344C4×C11#39011yescharacteristic
345C4×C11#39411yescharacteristic
346C4×C11#39611yescharacteristic
347C4×C11#39711yescharacteristic
348C4×C11#39911yescharacteristic
349C2×#41—21no—
350C2×#41—21no—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41—21no—
354C2×#41—21no—
355C2×#41—21no—
356C2×#41—21no—
357C2×#41—21no—
358C2×#41—21no—
359C2×#41C2×C4×C1112yes—
360C2×#41Q8×C1112yes—
361C22×Q8D4×C1111yescharacteristic
362C22×D4—21no—
363C22×D4D4×C1111yescharacteristic
364C23×C4—21no—
365C23×C4—21no—
366C23×C4—21no—
367C23×C4D4×C1112yes—
368C23×C4C23×C1111yescharacteristic
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16C2×C4×C1112yes—
380C2×M16D4×C1112yes—
381C22×C8—21no—
382C22×C8—21no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—28no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—48no—
400C2×C4⋊C4D4×C1112yes—
401C2×C4⋊C4D4×C1112yes—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—24no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42C2×C4×C1112yes—
409C2×C42D4×C1112yes—
410C2×C42D4×C1112yes—
411#104—28no—
412#103—24no—
413#102—24no—
414#95—24no—
415C2×C11—21no—
416C2×C11—21no—
417C2×C11—21no—
418C2×C11—21no—
419C2×C11—82no—
420C2×C11#143911yescharacteristic
421C2×C11#185912yes—
422C2×C11#200211yescharacteristic
423C2×C11#200511yescharacteristic
424C2×C11#203912yes—
425C24—21no—
426C24C2×D4×C1111yescharacteristic
427#41—22no—
428#41—22no—
429#41—22no—
430#41—22no—
431#41—22no—
432#41—22no—
433#41—22no—
434#41—22no—
435#41—41no—
436#41—41no—
437#41—41no—
438#41—41no—
439#41—41no—
440#41—41no—
441#41—41no—
442#41—41no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8C11×C4⋊C412yescomplemented
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4C11×C4⋊C412yescomplemented
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—44no—
479C22×C4—44no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4C22×C4×C1111yescharacteristic
483C22×C4C2×D4×C1111yescharacteristic
484C22×C4C2×D4×C1111yescharacteristic
485C22×C4C2×D4×C1111yescharacteristic
486C22×C4C2×D4×C1111yescharacteristic
487C22×C4C2×D4×C1111yescharacteristic
488C22×C4C2×D4×C1111yescharacteristic
489C22×C4C2×Q8×C1111yescharacteristic
490C22×C4C11×#4111yescharacteristic
491C22×C4C11×#4111yescharacteristic
492C22×C4C11×#4111yescharacteristic
493C22×C4C11×#4111yescharacteristic
494C22×C4C11×#4111yescharacteristic
495C22×C4C11×#4111yescharacteristic
496M16—22no—
497M16—22no—
498M16—22no—
499M16—22no—
500M16—41no—
501M16—41no—
502M16—41no—
503M16—41no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—416no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—84no—
524C42—22no—
525C42—22no—
526C42—22no—
527C42—41no—
528C42—41no—
529C42C11×C22⋊C414yescomplemented
530C11#1107811yescharacteristic, direct product factor, Sylow
531C23—22no—
532C23—22no—
533C23—22no—
534C23—41no—
535C23—41no—
536C23—42no—
537C23—42no—
538C23C4×D4×C1111yescharacteristic
539C23C11×#12011yescharacteristic
540C23C11×#12011yescharacteristic
541C23C11×#12111yescharacteristic
542C23C11×#12111yescharacteristic
543C23C11×C22⋊Q811yescharacteristic
544C23C11×#12411yescharacteristic
545Q8—22no—
546Q8—22no—
547Q8—41no—
548Q8—41no—
549D4—22no—
550D4—22no—
551D4—42no—
552D4—42no—
553D4—42no—
554D4—42no—
555D4—41no—
556D4—41no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—28no—
560C2×C4—28no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—44no—
570C2×C4—44no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—44no—
576C2×C4—42no—
577C2×C4—82no—
578C2×C4—82no—
579C2×C4—82no—
580C2×C4C2×C11×C22⋊C411yescharacteristic
581C2×C4C2×C11×C4⋊C411yescharacteristic
582C2×C4C11×#11711yescharacteristic
583C2×C4C4×D4×C1111yescharacteristic
584C2×C4C4×D4×C1111yescharacteristic
585C2×C4C4×D4×C1111yescharacteristic
586C2×C4C11×#12011yescharacteristic
587C2×C4C11×#12111yescharacteristic
588C2×C4C11×#12111yescharacteristic
589C2×C4C11×#12111yescharacteristic
590C2×C4C11×#12111yescharacteristic
591C2×C4C11×#12111yescharacteristic
592C2×C4C11×#12111yescharacteristic
593C2×C4C11×C22⋊Q811yescharacteristic
594C2×C4C11×C22⋊Q811yescharacteristic
595C2×C4C11×C22⋊Q811yescharacteristic
596C2×C4C11×C22⋊Q811yescharacteristic
597C2×C4C11×C22⋊Q811yescharacteristic
598C2×C4C11×#12311yescharacteristic
599C2×C4C11×#12311yescharacteristic
600C2×C4C11×#12311yescharacteristic
601C2×C4C11×#12311yescharacteristic
602C2×C4C11×#12311yescharacteristic
603C2×C4C11×#12411yescharacteristic
604C2×C4C11×#12411yescharacteristic
605C2×C4C11×#12611yescharacteristic
606C2×C4C11×#12611yescharacteristic
607C2×C4C11×#12711yescharacteristic
608C8—42no—
609C8—42no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—42no—
619C22—44no—
620C22—81no—
621C22—81no—
622C22—82no—
623C22C11×#38511yescharacteristic
624C22C11×#38611yescharacteristic
625C22C11×#38811yescharacteristic
626C22C11×#39211yescharacteristic
627C22C11×#39311yescharacteristic
628C22C11×#39411yescharacteristic
629C22C11×#39611yescharacteristic
630C22C11×#45312yes—
631C22C11×#45612yes—
632C4—28no—
633C4—42no—
634C4—82no—
635C4—82no—
636C4—82no—
637C4C11×#38011yescharacteristic
638C4C11×#38511yescharacteristic
639C4C11×#38811yescharacteristic
640C4C11×#39011yescharacteristic
641C4C11×#39411yescharacteristic
642C4C11×#39611yescharacteristic
643C4C11×#39711yescharacteristic
644C4C11×#39911yescharacteristic
645C2—21no—
646C2—21no—
647C2—21no—
648C2—21no—
649C2—82no—
650C2C11×#143911yescharacteristic
651C2C11×#185912yes—
652C2C11×#200211yescharacteristic
653C2C11×#200511yescharacteristic
654C2C11×#203912yes—
subgroupG/H
center, socleC23×C11#120
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC22×C11×#41C22
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
4. C2×C11×#384C2semidirect
5. C2×C11×#343C2semidirect
6. C11×#1736C2semidirect
7. C2×C11×#339C2semidirect
18. C2×C11×#104C4semidirect
98. #11078C11direct (N × H)
122. C2×Q8×C11C4⋊C4semidirect
134. C2×D4×C11C4⋊C4semidirect
203. C42×C11C22⋊C4semidirect
207. C2×#384C2×C11semidirect
208. C2×#343C2×C11semidirect
209. #1736C2×C11semidirect
210. C2×#339C2×C11semidirect
300. C2×#104C4×C11semidirect
448. C2×Q8C11×C4⋊C4semidirect
460. C2×D4C11×C4⋊C4semidirect
529. C42C11×C22⋊C4semidirect
530. C11#11078direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1042
C2×C11×#4172
C11×#23112
C2×C11×#3842
C2×C11×#3432
C11×#17362
C2×C11×#3392
#1107811