Finite Group Databasebeta

← C11×#11114 #14588307

Subgroups — C11×#11114 #14588307

Order 2816.

898 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#430C211yesmaximal, characteristic, complemented
2C2×C11×#421C211yesmaximal, characteristic
3C22×C11×#104C211yesmaximal, characteristic
4C11×#2879C211yesmaximal, characteristic
5C2×C11×#344C211yesmaximal, characteristic, complemented
6C2×C11×#339C211yesmaximal, characteristic, complemented
7C11×#1728C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C11×#430—22no—
16C11×#430—22no—
17C2×C11×#108—22no—
18C11×#421—22no—
19C11×#421—22no—
20C2×C11×#104—22no—
21C2×C11×#104—22no—
22C2×C11×#104—22no—
23C2×C11×#104C414yescomplemented
24C11×#408—22no—
25C11×#408—22no—
26C11×#407—22no—
27C11×#344—22no—
28C11×#339—22no—
29C11×#336—22no—
30C2×C11×#41—21no—
31C2×C11×#41—21no—
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×#41C2×C412yes—
41C2×C11×#41D412yes—
42C22×Q8×C11Q811yescharacteristic
43C22×D4×C11—21no—
44C22×D4×C11Q811yescharacteristic
45C23×C4×C11—21no—
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C2×C11×M16—21no—
49C2×C11×M16—21no—
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×M16—21no—
61C2×C11×M16—21no—
62C2×C11×M16—21no—
63C2×C11×M16—21no—
64C2×C11×M16—21no—
65C2×C11×M16—21no—
66C2×C11×M16—21no—
67C2×C11×M16C2×C412yes—
68C2×C11×M16D412yes—
69C2×C11×M16D412yes—
70C2×C11×M16D412yes—
71C2×C11×M16D412yes—
72C22×C8×C11—21no—
73C22×C8×C11—21no—
74C22×C8×C11—21no—
75C22×C8×C11D412yes—
76C11×#117—21no—
77C11×#117—21no—
78C11×#117—21no—
79C11×#117D412yes—
80C2×C11×C4⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11C2×C412yes—
89C11×#108—28no—
90C11×#104—28no—
91C11×#104—28no—
92C11×C22⋊C8—28no—
93#11114C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11—21no—
95C24×C11#4111yescharacteristic
96C11×#41—22no—
97C11×#41—22no—
98C11×#41—22no—
99C11×#41—22no—
100C11×#41—22no—
101C11×#41—22no—
102C11×#41—22no—
103C11×#41—22no—
104C11×#41—41no—
105C11×#41—41no—
106C11×#41—41no—
107C11×#41—41no—
108C11×#41—41no—
109C11×#41—41no—
110C11×#41—41no—
111C11×#41—41no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11C4⋊C412yes—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11C4⋊C412yes—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—44no—
135C22×C4×C11—41no—
136C22×C4×C11—41no—
137C22×C4×C11—41no—
138C22×C4×C11—41no—
139C22×C4×C11—41no—
140C22×C4×C11—41no—
141C22×C4×C11—41no—
142C22×C4×C11C22×C411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×Q811yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C11×M16—22no—
157C11×M16—22no—
158C11×M16—22no—
159C11×M16—22no—
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—41no—
164C11×M16—41no—
165C11×M16—41no—
166C11×M16—41no—
167C11×M16—41no—
168C11×M16—41no—
169C11×M16—41no—
170C11×M16—41no—
171C11×M16C22⋊C414yes—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
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—41no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—41no—
188C42×C11—22no—
189C42×C11—22no—
190C42×C11—22no—
191C42×C11—41no—
192C42×C11—41no—
193C42×C11—41no—
194C2×#430C2×C1111yescharacteristic, complemented
195C2×#421C2×C1111yescharacteristic
196C22×#104C2×C1111yescharacteristic
197#2879C2×C1111yescharacteristic
198C2×#344C2×C1111yescharacteristic, complemented
199C2×#339C2×C1111yescharacteristic, complemented
200#1728C2×C1111yescharacteristic, complemented
201C23×C11—22no—
202C23×C11—42no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—82no—
206C23×C11C4×D411yescharacteristic
207C23×C11#12111yescharacteristic
208C23×C11C22⋊Q811yescharacteristic
209C23×C11#12311yescharacteristic
210C23×C11#12411yescharacteristic
211C23×C11#12411yescharacteristic
212C23×C11#12611yescharacteristic
213Q8×C11—22no—
214Q8×C11—22no—
215Q8×C11—41no—
216Q8×C11—41no—
217D4×C11—22no—
218D4×C11—22no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—41no—
224D4×C11—41no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—42no—
228C2×C4×C11—44no—
229C2×C4×C11—44no—
230C2×C4×C11—42no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—82no—
239C2×C4×C11C2×C22⋊C411yescharacteristic
240C2×C4×C11C2×C4⋊C411yescharacteristic
241C2×C4×C11#11711yescharacteristic
242C2×C4×C11C4×D411yescharacteristic
243C2×C4×C11C4×D411yescharacteristic
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11#12011yescharacteristic
246C2×C4×C11#12011yescharacteristic
247C2×C4×C11#12011yescharacteristic
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11C22⋊Q811yescharacteristic
256C2×C4×C11C22⋊Q811yescharacteristic
257C2×C4×C11C22⋊Q811yescharacteristic
258C2×C4×C11C22⋊Q811yescharacteristic
259C2×C4×C11C22⋊Q811yescharacteristic
260C2×C4×C11#12311yescharacteristic
261C2×C4×C11#12311yescharacteristic
262C2×C4×C11#12311yescharacteristic
263C2×C4×C11#12311yescharacteristic
264C2×C4×C11#12411yescharacteristic
265C2×C4×C11#12611yescharacteristic
266C2×C4×C11#12711yescharacteristic
267C8×C11—24no—
268C8×C11—42no—
269C8×C11—42no—
270C8×C11—42no—
271C22×#41C22×C1111yescharacteristic
272C22×M16C22×C1111yescharacteristic
273C22×M16C22×C1111yescharacteristic
274C22×M16C22×C1111yescharacteristic
275C22×M16C22×C1111yescharacteristic
276C2×#117C22×C1111yescharacteristic
277C22×C42C22×C1111yescharacteristic
278#430—22no—
279#430—22no—
280C2×#108—22no—
281#421—22no—
282#421—22no—
283C2×#104—22no—
284C2×#104—22no—
285C2×#104—22no—
286C2×#104C4×C1114yescomplemented
287#408—22no—
288#408—22no—
289#407—22no—
290#344—22no—
291#339—22no—
292#336—22no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—41no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—44no—
301C22×C11—42no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11#38511yescharacteristic
305C22×C11#38811yescharacteristic
306C22×C11#39011yescharacteristic
307C22×C11#39311yescharacteristic
308C22×C11#39411yescharacteristic
309C22×C11#39611yescharacteristic
310C22×C11#39711yescharacteristic
311C4×C11—44no—
312C4×C11—42no—
313C4×C11—82no—
314C4×C11#38011yescharacteristic
315C4×C11#38511yescharacteristic
316C4×C11#38611yescharacteristic
317C4×C11#38811yescharacteristic
318C4×C11#39211yescharacteristic
319C4×C11#39411yescharacteristic
320C4×C11#39611yescharacteristic
321C4×C11#39911yescharacteristic
322C2×#41—21no—
323C2×#41—21no—
324C2×#41—21no—
325C2×#41—21no—
326C2×#41—21no—
327C2×#41—21no—
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41—21no—
332C2×#41C2×C4×C1112yes—
333C2×#41D4×C1112yes—
334C22×Q8Q8×C1111yescharacteristic
335C22×D4—21no—
336C22×D4Q8×C1111yescharacteristic
337C23×C4—21no—
338C23×C4—21no—
339C23×C4C23×C1111yescharacteristic
340C2×M16—21no—
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
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×M16—21no—
358C2×M16—21no—
359C2×M16C2×C4×C1112yes—
360C2×M16D4×C1112yes—
361C2×M16D4×C1112yes—
362C2×M16D4×C1112yes—
363C2×M16D4×C1112yes—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8D4×C1112yes—
368#117—21no—
369#117—21no—
370#117—21no—
371#117D4×C1112yes—
372C2×C4⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42C2×C4×C1112yes—
381#108—28no—
382#104—28no—
383#104—28no—
384C22⋊C8—28no—
385C2×C11—21no—
386C2×C11—21no—
387C2×C11—21no—
388C2×C11—21no—
389C2×C11—21no—
390C2×C11—21no—
391C2×C11—82no—
392C2×C11#143911yescharacteristic
393C2×C11#186112yes—
394C24—21no—
395C24C11×#4111yescharacteristic
396#41—22no—
397#41—22no—
398#41—22no—
399#41—22no—
400#41—22no—
401#41—22no—
402#41—22no—
403#41—22no—
404#41—41no—
405#41—41no—
406#41—41no—
407#41—41no—
408#41—41no—
409#41—41no—
410#41—41no—
411#41—41no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8C11×C4⋊C412yes—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4C11×C4⋊C412yes—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—44no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4C22×C4×C1111yescharacteristic
443C22×C4C2×D4×C1111yescharacteristic
444C22×C4C2×D4×C1111yescharacteristic
445C22×C4C2×D4×C1111yescharacteristic
446C22×C4C2×D4×C1111yescharacteristic
447C22×C4C2×D4×C1111yescharacteristic
448C22×C4C2×D4×C1111yescharacteristic
449C22×C4C2×D4×C1111yescharacteristic
450C22×C4C2×Q8×C1111yescharacteristic
451C22×C4C11×#4111yescharacteristic
452C22×C4C11×#4111yescharacteristic
453C22×C4C11×#4111yescharacteristic
454C22×C4C11×#4111yescharacteristic
455C22×C4C11×#4111yescharacteristic
456M16—22no—
457M16—22no—
458M16—22no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—22no—
463M16—41no—
464M16—41no—
465M16—41no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—41no—
470M16—41no—
471M16C11×C22⋊C414yes—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C4⋊C4—22no—
485C4⋊C4—41no—
486C22⋊C4—22no—
487C22⋊C4—41no—
488C42—22no—
489C42—22no—
490C42—22no—
491C42—41no—
492C42—41no—
493C42—41no—
494C11#1111411yescharacteristic, direct product factor, Sylow
495C23—22no—
496C23—42no—
497C23—41no—
498C23—41no—
499C23—82no—
500C23C4×D4×C1111yescharacteristic
501C23C11×#12111yescharacteristic
502C23C11×C22⋊Q811yescharacteristic
503C23C11×#12311yescharacteristic
504C23C11×#12411yescharacteristic
505C23C11×#12411yescharacteristic
506C23C11×#12611yescharacteristic
507Q8—22no—
508Q8—22no—
509Q8—41no—
510Q8—41no—
511D4—22no—
512D4—22no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—41no—
518D4—41no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—42no—
522C2×C4—44no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—82no—
533C2×C4C2×C11×C22⋊C411yescharacteristic
534C2×C4C2×C11×C4⋊C411yescharacteristic
535C2×C4C11×#11711yescharacteristic
536C2×C4C4×D4×C1111yescharacteristic
537C2×C4C4×D4×C1111yescharacteristic
538C2×C4C4×D4×C1111yescharacteristic
539C2×C4C11×#12011yescharacteristic
540C2×C4C11×#12011yescharacteristic
541C2×C4C11×#12011yescharacteristic
542C2×C4C11×#12111yescharacteristic
543C2×C4C11×#12111yescharacteristic
544C2×C4C11×#12111yescharacteristic
545C2×C4C11×#12111yescharacteristic
546C2×C4C11×#12111yescharacteristic
547C2×C4C11×#12111yescharacteristic
548C2×C4C11×#12111yescharacteristic
549C2×C4C11×C22⋊Q811yescharacteristic
550C2×C4C11×C22⋊Q811yescharacteristic
551C2×C4C11×C22⋊Q811yescharacteristic
552C2×C4C11×C22⋊Q811yescharacteristic
553C2×C4C11×C22⋊Q811yescharacteristic
554C2×C4C11×#12311yescharacteristic
555C2×C4C11×#12311yescharacteristic
556C2×C4C11×#12311yescharacteristic
557C2×C4C11×#12311yescharacteristic
558C2×C4C11×#12411yescharacteristic
559C2×C4C11×#12611yescharacteristic
560C2×C4C11×#12711yescharacteristic
561C8—24no—
562C8—42no—
563C8—42no—
564C8—42no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—42no—
573C22—44no—
574C22—82no—
575C22—82no—
576C22C11×#38511yescharacteristic
577C22C11×#38811yescharacteristic
578C22C11×#39011yescharacteristic
579C22C11×#39311yescharacteristic
580C22C11×#39411yescharacteristic
581C22C11×#39611yescharacteristic
582C22C11×#39711yescharacteristic
583C4—44no—
584C4—42no—
585C4—82no—
586C4C11×#38011yescharacteristic
587C4C11×#38511yescharacteristic
588C4C11×#38611yescharacteristic
589C4C11×#38811yescharacteristic
590C4C11×#39211yescharacteristic
591C4C11×#39411yescharacteristic
592C4C11×#39611yescharacteristic
593C4C11×#39911yescharacteristic
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—82no—
601C2C11×#143911yescharacteristic
602C2C11×#186112yes—
subgroupG/H
centerC2×C4×C11#120
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC22×C11#385
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#430C2semidirect
5. C2×C11×#344C2semidirect
6. C2×C11×#339C2semidirect
7. C11×#1728C2semidirect
23. C2×C11×#104C4semidirect
93. #11114C11direct (N × H)
194. C2×#430C2×C11semidirect
198. C2×#344C2×C11semidirect
199. C2×#339C2×C11semidirect
200. #1728C2×C11semidirect
286. C2×#104C4×C11semidirect
494. C11#11114direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4302
C2×C11×#4212
C22×C11×#1042
C11×#28792
C2×C11×#3442
C2×C11×#3392
C11×#17282
#1111411