Finite Group Databasebeta

← C11×#11068 #14588261

Subgroups — C11×#11068 #14588261

Order 2816.

934 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#424C211yesmaximal, characteristic, complemented
2C22×C11×#104C211yesmaximal, characteristic
3C2×C11×#416C211yesmaximal, characteristic
4C2×C11×#408C211yesmaximal, characteristic
5C2×C11×#341C211yesmaximal, characteristic, complemented
6C2×C11×#339C211yesmaximal, characteristic, complemented
7C2×C11×#336C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C11×#424—22no—
16C11×#424—22no—
17C2×C11×C4⋊C8—22no—
18C2×C11×#104—22no—
19C2×C11×#104—22no—
20C2×C11×#104—22no—
21C11×#416—22no—
22C11×#416—22no—
23C2×C11×#103C412yescomplemented
24C2×C11×#102C412yescomplemented
25C11×#408—22no—
26C11×#408—22no—
27C2×C11×C22⋊C8—22no—
28C11×#341—22no—
29C11×#339—22no—
30C11×#336—22no—
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×#41—21no—
41C2×C11×#41D412yes—
42C2×C11×#41Q812yes—
43C22×Q8×C11C2×C411yescharacteristic
44C22×D4×C11—21no—
45C22×D4×C11C2×C411yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
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×M16D412yes—
60C2×C11×M16D412yes—
61C22×C8×C11—21no—
62C22×C8×C11—21no—
63C22×C8×C11—21no—
64C22×C8×C11—21no—
65C22×C8×C11—21no—
66C22×C8×C11—21no—
67C22×C8×C11—21no—
68C22×C8×C11—21no—
69C22×C8×C11—21no—
70C22×C8×C11—21no—
71C22×C8×C11—21no—
72C22×C8×C11—21no—
73C22×C8×C11—21no—
74C22×C8×C11—21no—
75C22×C8×C11C2×C412yes—
76C22×C8×C11D412yes—
77C11×#117—21no—
78C11×#117—21no—
79C11×#117D412yes—
80C11×#117D412yes—
81C2×C11×C4⋊C4C2×C412yes—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11D412yes—
90C11×C4⋊C8—28no—
91C11×#104—28no—
92C11×#103—24no—
93C11×#102—24no—
94C11×C22⋊C8—28no—
95#11068C1111yesmaximal, characteristic, direct product factor, Sylow
96C24×C11—21no—
97C24×C11#4111yescharacteristic
98C11×#41—22no—
99C11×#41—22no—
100C11×#41—22no—
101C11×#41—22no—
102C11×#41—22no—
103C11×#41—22no—
104C11×#41—22no—
105C11×#41—22no—
106C11×#41—41no—
107C11×#41—41no—
108C11×#41—41no—
109C11×#41—41no—
110C11×#41—41no—
111C11×#41—41no—
112C11×#41—41no—
113C11×#41—41no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11C4⋊C412yes—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11—41no—
131C2×D4×C11C4⋊C412yes—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
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×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
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
159C11×M16—22no—
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—41no—
164C11×M16—41no—
165C11×M16—41no—
166C11×M16—41no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—41no—
176C2×C8×C11—41no—
177C2×C8×C11—41no—
178C2×C8×C11—41no—
179C2×C8×C11—41no—
180C2×C8×C11—41no—
181C2×C8×C11—41no—
182C2×C8×C11—41no—
183C2×C8×C11—41no—
184C2×C8×C11—41no—
185C2×C8×C11—41no—
186C2×C8×C11—41no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4C22⋊C414yes—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C42×C11—22no—
192C42×C11—22no—
193C42×C11—22no—
194C42×C11—22no—
195C42×C11—41no—
196C42×C11—41no—
197C2×#424C2×C1111yescharacteristic, complemented
198C22×#104C2×C1111yescharacteristic
199C2×#416C2×C1111yescharacteristic
200C2×#408C2×C1111yescharacteristic
201C2×#341C2×C1111yescharacteristic, complemented
202C2×#339C2×C1111yescharacteristic, complemented
203C2×#336C2×C1111yescharacteristic, complemented
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11C4×D411yescharacteristic
212C23×C11#12111yescharacteristic
213C23×C11C22⋊Q811yescharacteristic
214C23×C11#12311yescharacteristic
215C23×C11#12311yescharacteristic
216C23×C11#12311yescharacteristic
217C23×C11#12611yescharacteristic
218Q8×C11—22no—
219Q8×C11—22no—
220Q8×C11—41no—
221Q8×C11—41no—
222D4×C11—22no—
223D4×C11—22no—
224D4×C11—42no—
225D4×C11—42no—
226D4×C11—42no—
227D4×C11—42no—
228D4×C11—41no—
229D4×C11—41no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—44no—
234C2×C4×C11—44no—
235C2×C4×C11—42no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11C2×C22⋊C411yescharacteristic
246C2×C4×C11C2×C4⋊C411yescharacteristic
247C2×C4×C11#11711yescharacteristic
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11#12111yescharacteristic
261C2×C4×C11C22⋊Q811yescharacteristic
262C2×C4×C11C22⋊Q811yescharacteristic
263C2×C4×C11C22⋊Q811yescharacteristic
264C2×C4×C11C22⋊Q811yescharacteristic
265C2×C4×C11C22⋊Q811yescharacteristic
266C2×C4×C11#12311yescharacteristic
267C2×C4×C11#12311yescharacteristic
268C2×C4×C11#12411yescharacteristic
269C2×C4×C11#12411yescharacteristic
270C2×C4×C11#12411yescharacteristic
271C2×C4×C11#12611yescharacteristic
272C2×C4×C11#12711yescharacteristic
273C8×C11—42no—
274C8×C11—42no—
275C8×C11—42no—
276C8×C11—42no—
277C22×#41C22×C1111yescharacteristic
278C22×M16C22×C1111yescharacteristic
279C22×M16C22×C1111yescharacteristic
280C23×C8C22×C1111yescharacteristic
281C23×C8C22×C1111yescharacteristic
282C2×#117C22×C1111yescharacteristic
283C22×C42C22×C1111yescharacteristic
284#424—22no—
285#424—22no—
286C2×C4⋊C8—22no—
287C2×#104—22no—
288C2×#104—22no—
289C2×#104—22no—
290#416—22no—
291#416—22no—
292C2×#103C4×C1112yescomplemented
293C2×#102C4×C1112yescomplemented
294#408—22no—
295#408—22no—
296C2×C22⋊C8—22no—
297#341—22no—
298#339—22no—
299#336—22no—
300C22×C11—22no—
301C22×C11—22no—
302C22×C11—22no—
303C22×C11—22no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—44no—
309C22×C11—42no—
310C22×C11—82no—
311C22×C11—81no—
312C22×C11—81no—
313C22×C11#38511yescharacteristic
314C22×C11#38611yescharacteristic
315C22×C11#38811yescharacteristic
316C22×C11#39411yescharacteristic
317C22×C11#39611yescharacteristic
318C22×C11#39711yescharacteristic
319C22×C11#39911yescharacteristic
320C22×C11#44312yes—
321C22×C11#44412yes—
322C4×C11—44no—
323C4×C11—44no—
324C4×C11—42no—
325C4×C11#38011yescharacteristic
326C4×C11#38511yescharacteristic
327C4×C11#38811yescharacteristic
328C4×C11#39011yescharacteristic
329C4×C11#39211yescharacteristic
330C4×C11#39311yescharacteristic
331C4×C11#39411yescharacteristic
332C4×C11#39611yescharacteristic
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41D4×C1112yes—
344C2×#41Q8×C1112yes—
345C22×Q8C2×C4×C1111yescharacteristic
346C22×D4—21no—
347C22×D4C2×C4×C1111yescharacteristic
348C23×C4—21no—
349C23×C4—21no—
350C23×C4C23×C1111yescharacteristic
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×M16—21no—
360C2×M16—21no—
361C2×M16D4×C1112yes—
362C2×M16D4×C1112yes—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8C2×C4×C1112yes—
378C22×C8D4×C1112yes—
379#117—21no—
380#117—21no—
381#117D4×C1112yes—
382#117D4×C1112yes—
383C2×C4⋊C4C2×C4×C1112yes—
384C2×C22⋊C4—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42D4×C1112yes—
392C4⋊C8—28no—
393#104—28no—
394#103—24no—
395#102—24no—
396C22⋊C8—28no—
397C2×C11—21no—
398C2×C11—21no—
399C2×C11—21no—
400C2×C11—21no—
401C2×C11—82no—
402C2×C11#143911yescharacteristic
403C2×C11#186612yes—
404C2×C11#187612yes—
405C2×C11#193711yescharacteristic
406C2×C11#193811yescharacteristic
407C24—21no—
408C24C11×#4111yescharacteristic
409#41—22no—
410#41—22no—
411#41—22no—
412#41—22no—
413#41—22no—
414#41—22no—
415#41—22no—
416#41—22no—
417#41—41no—
418#41—41no—
419#41—41no—
420#41—41no—
421#41—41no—
422#41—41no—
423#41—41no—
424#41—41no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8C11×C4⋊C412yes—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4C11×C4⋊C412yes—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—42no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4C22×C4×C1111yescharacteristic
457C22×C4C2×D4×C1111yescharacteristic
458C22×C4C2×D4×C1111yescharacteristic
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C2×D4×C1111yescharacteristic
461C22×C4C2×D4×C1111yescharacteristic
462C22×C4C2×D4×C1111yescharacteristic
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C2×Q8×C1111yescharacteristic
465C22×C4C11×#4111yescharacteristic
466C22×C4C11×#4111yescharacteristic
467C22×C4C11×#4111yescharacteristic
468C22×C4C11×#4111yescharacteristic
469C22×C4C11×#4111yescharacteristic
470M16—22no—
471M16—22no—
472M16—22no—
473M16—22no—
474M16—41no—
475M16—41no—
476M16—41no—
477M16—41no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C4⋊C4—22no—
499C4⋊C4C11×C22⋊C414yes—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C42—22no—
503C42—22no—
504C42—22no—
505C42—22no—
506C42—41no—
507C42—41no—
508C11#1106811yescharacteristic, direct product factor, Sylow
509C23—22no—
510C23—22no—
511C23—22no—
512C23—41no—
513C23—41no—
514C23—42no—
515C23—42no—
516C23C4×D4×C1111yescharacteristic
517C23C11×#12111yescharacteristic
518C23C11×C22⋊Q811yescharacteristic
519C23C11×#12311yescharacteristic
520C23C11×#12311yescharacteristic
521C23C11×#12311yescharacteristic
522C23C11×#12611yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—41no—
526Q8—41no—
527D4—22no—
528D4—22no—
529D4—42no—
530D4—42no—
531D4—42no—
532D4—42no—
533D4—41no—
534D4—41no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—44no—
539C2×C4—44no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4C2×C11×C22⋊C411yescharacteristic
551C2×C4C2×C11×C4⋊C411yescharacteristic
552C2×C4C11×#11711yescharacteristic
553C2×C4C4×D4×C1111yescharacteristic
554C2×C4C4×D4×C1111yescharacteristic
555C2×C4C4×D4×C1111yescharacteristic
556C2×C4C11×#12011yescharacteristic
557C2×C4C11×#12011yescharacteristic
558C2×C4C11×#12011yescharacteristic
559C2×C4C11×#12111yescharacteristic
560C2×C4C11×#12111yescharacteristic
561C2×C4C11×#12111yescharacteristic
562C2×C4C11×#12111yescharacteristic
563C2×C4C11×#12111yescharacteristic
564C2×C4C11×#12111yescharacteristic
565C2×C4C11×#12111yescharacteristic
566C2×C4C11×C22⋊Q811yescharacteristic
567C2×C4C11×C22⋊Q811yescharacteristic
568C2×C4C11×C22⋊Q811yescharacteristic
569C2×C4C11×C22⋊Q811yescharacteristic
570C2×C4C11×C22⋊Q811yescharacteristic
571C2×C4C11×#12311yescharacteristic
572C2×C4C11×#12311yescharacteristic
573C2×C4C11×#12411yescharacteristic
574C2×C4C11×#12411yescharacteristic
575C2×C4C11×#12411yescharacteristic
576C2×C4C11×#12611yescharacteristic
577C2×C4C11×#12711yescharacteristic
578C8—42no—
579C8—42no—
580C8—42no—
581C8—42no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—44no—
591C22—42no—
592C22—82no—
593C22—81no—
594C22—81no—
595C22C11×#38511yescharacteristic
596C22C11×#38611yescharacteristic
597C22C11×#38811yescharacteristic
598C22C11×#39411yescharacteristic
599C22C11×#39611yescharacteristic
600C22C11×#39711yescharacteristic
601C22C11×#39911yescharacteristic
602C22C11×#44312yes—
603C22C11×#44412yes—
604C4—44no—
605C4—44no—
606C4—42no—
607C4C11×#38011yescharacteristic
608C4C11×#38511yescharacteristic
609C4C11×#38811yescharacteristic
610C4C11×#39011yescharacteristic
611C4C11×#39211yescharacteristic
612C4C11×#39311yescharacteristic
613C4C11×#39411yescharacteristic
614C4C11×#39611yescharacteristic
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—82no—
620C2C11×#143911yescharacteristic
621C2C11×#186612yes—
622C2C11×#187612yes—
623C2C11×#193711yescharacteristic
624C2C11×#193811yescharacteristic
subgroupG/H
centerC22×C4×C11C2×D4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC23×C11C4×D4
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ C23×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#424C2semidirect
5. C2×C11×#341C2semidirect
6. C2×C11×#339C2semidirect
7. C2×C11×#336C2semidirect
23. C2×C11×#103C4semidirect
24. C2×C11×#102C4semidirect
95. #11068C11direct (N × H)
197. C2×#424C2×C11semidirect
201. C2×#341C2×C11semidirect
202. C2×#339C2×C11semidirect
203. C2×#336C2×C11semidirect
292. C2×#103C4×C11semidirect
293. C2×#102C4×C11semidirect
508. C11#11068direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4242
C22×C11×#1042
C2×C11×#4162
C2×C11×#4082
C2×C11×#3412
C2×C11×#3392
C2×C11×#3362
#1106811