Finite Group Databasebeta

← C11×#11080 #14588273

Subgroups — C11×#11080 #14588273

Order 2816.

902 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#423C211yesmaximal, characteristic, complemented
2C2×C11×#421C211yesmaximal, characteristic
3C22×C11×#104C211yesmaximal, characteristic
4C11×#2879C211yesmaximal, characteristic
5C2×C11×#344C211yesmaximal, characteristic, complemented
6C11×#1738C211yesmaximal, characteristic, complemented
7C2×C11×#339C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C11×#423—22no—
16C11×#423—22no—
17C2×C11×C4⋊C8—22no—
18C11×#421—22no—
19C11×#421—22no—
20C2×C11×#104—22no—
21C2×C11×#104—22no—
22C2×C11×#104—22no—
23C2×C11×#104C412yescomplemented
24C2×C11×#104C412yescomplemented
25C11×#408—22no—
26C11×#408—22no—
27C11×#407—22no—
28C11×#344—22no—
29C11×#341—22no—
30C11×#339—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×#41C2×C412yes—
42C2×C11×#41D412yes—
43C22×Q8×C11Q811yescharacteristic
44C22×D4×C11—21no—
45C22×D4×C11Q811yescharacteristic
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×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×M16—21no—
68C2×C11×M16—21no—
69C2×C11×M16—21no—
70C2×C11×M16C2×C412yes—
71C2×C11×M16D412yes—
72C2×C11×M16D412yes—
73C22×C8×C11—21no—
74C22×C8×C11—21no—
75C22×C8×C11—21no—
76C22×C8×C11D412yes—
77C11×#117—21no—
78C11×#117—21no—
79C11×#117—21no—
80C11×#117D412yes—
81C2×C11×C4⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11—21no—
87C2×C42×C11C2×C411yescharacteristic
88C2×C42×C11C2×C411yescharacteristic
89C2×C42×C11D412yes—
90C2×C42×C11D412yes—
91C11×C4⋊C8—28no—
92C11×#104—28no—
93C11×#104—24no—
94C11×#104—24no—
95C11×C22⋊C8—28no—
96#11080C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11—21no—
98C24×C11#4111yescharacteristic
99C11×#41—22no—
100C11×#41—22no—
101C11×#41—22no—
102C11×#41—22no—
103C11×#41—22no—
104C11×#41—22no—
105C11×#41—22no—
106C11×#41—22no—
107C11×#41—41no—
108C11×#41—41no—
109C11×#41—41no—
110C11×#41—41no—
111C11×#41—41no—
112C11×#41—41no—
113C11×#41—41no—
114C11×#41—41no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11C4⋊C412yes—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C2×D4×C11C4⋊C412yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—44no—
141C22×C4×C11—41no—
142C22×C4×C11—41no—
143C22×C4×C11—41no—
144C22×C4×C11—41no—
145C22×C4×C11—41no—
146C22×C4×C11C22×C411yescharacteristic
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×D411yescharacteristic
154C22×C4×C11C2×Q811yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—22no—
166C11×M16—41no—
167C11×M16—41no—
168C11×M16—41no—
169C11×M16—41no—
170C11×M16—41no—
171C11×M16—41no—
172C11×M16—41no—
173C11×M16—41no—
174C11×M16—41no—
175C11×M16—41no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—41no—
183C2×C8×C11—41no—
184C2×C8×C11—41no—
185C2×C8×C11—41no—
186C2×C8×C11—41no—
187C2×C8×C11—41no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—41no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—41no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—22no—
195C42×C11—22no—
196C42×C11—22no—
197C42×C11—41no—
198C42×C11C22⋊C412yes—
199C42×C11C22⋊C412yes—
200C2×#423C2×C1111yescharacteristic, complemented
201C2×#421C2×C1111yescharacteristic
202C22×#104C2×C1111yescharacteristic
203#2879C2×C1111yescharacteristic
204C2×#344C2×C1111yescharacteristic, complemented
205#1738C2×C1111yescharacteristic, complemented
206C2×#339C2×C1111yescharacteristic, complemented
207C23×C11—22no—
208C23×C11—42no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—82no—
212C23×C11C4×D411yescharacteristic
213C23×C11#12111yescharacteristic
214C23×C11C22⋊Q811yescharacteristic
215C23×C11#12311yescharacteristic
216C23×C11#12311yescharacteristic
217C23×C11#12311yescharacteristic
218C23×C11#12611yescharacteristic
219Q8×C11—22no—
220Q8×C11—22no—
221Q8×C11—41no—
222Q8×C11—41no—
223D4×C11—22no—
224D4×C11—22no—
225D4×C11—42no—
226D4×C11—42no—
227D4×C11—42no—
228D4×C11—42no—
229D4×C11—41no—
230D4×C11—41no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—44no—
236C2×C4×C11—44no—
237C2×C4×C11—42no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—82no—
246C2×C4×C11C2×C22⋊C411yescharacteristic
247C2×C4×C11C2×C4⋊C411yescharacteristic
248C2×C4×C11#11711yescharacteristic
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C4×D411yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11#12011yescharacteristic
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×C11#12111yescharacteristic
262C2×C4×C11C22⋊Q811yescharacteristic
263C2×C4×C11C22⋊Q811yescharacteristic
264C2×C4×C11C22⋊Q811yescharacteristic
265C2×C4×C11C22⋊Q811yescharacteristic
266C2×C4×C11C22⋊Q811yescharacteristic
267C2×C4×C11#12311yescharacteristic
268C2×C4×C11#12311yescharacteristic
269C2×C4×C11#12411yescharacteristic
270C2×C4×C11#12411yescharacteristic
271C2×C4×C11#12411yescharacteristic
272C2×C4×C11#12611yescharacteristic
273C2×C4×C11#12711yescharacteristic
274C8×C11—42no—
275C8×C11—42no—
276C8×C11—42no—
277C8×C11—42no—
278C22×#41C22×C1111yescharacteristic
279C22×M16C22×C1111yescharacteristic
280C22×M16C22×C1111yescharacteristic
281C22×M16C22×C1111yescharacteristic
282C22×M16C22×C1111yescharacteristic
283C2×#117C22×C1111yescharacteristic
284C22×C42C22×C1111yescharacteristic
285#423—22no—
286#423—22no—
287C2×C4⋊C8—22no—
288#421—22no—
289#421—22no—
290C2×#104—22no—
291C2×#104—22no—
292C2×#104—22no—
293C2×#104C4×C1112yescomplemented
294C2×#104C4×C1112yescomplemented
295#408—22no—
296#408—22no—
297#407—22no—
298#344—22no—
299#341—22no—
300#339—22no—
301C22×C11—22no—
302C22×C11—22no—
303C22×C11—22no—
304C22×C11—41no—
305C22×C11—41no—
306C22×C11—41no—
307C22×C11—41no—
308C22×C11—44no—
309C22×C11—42no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11#38511yescharacteristic
313C22×C11#38611yescharacteristic
314C22×C11#38811yescharacteristic
315C22×C11#39411yescharacteristic
316C22×C11#39611yescharacteristic
317C22×C11#39711yescharacteristic
318C22×C11#39911yescharacteristic
319C4×C11—24no—
320C4×C11—42no—
321C4×C11—42no—
322C4×C11—82no—
323C4×C11#38011yescharacteristic
324C4×C11#38511yescharacteristic
325C4×C11#38811yescharacteristic
326C4×C11#39011yescharacteristic
327C4×C11#39211yescharacteristic
328C4×C11#39311yescharacteristic
329C4×C11#39411yescharacteristic
330C4×C11#39611yescharacteristic
331C2×#41—21no—
332C2×#41—21no—
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×#41C2×C4×C1112yes—
342C2×#41D4×C1112yes—
343C22×Q8Q8×C1111yescharacteristic
344C22×D4—21no—
345C22×D4Q8×C1111yescharacteristic
346C23×C4—21no—
347C23×C4—21no—
348C23×C4C23×C1111yescharacteristic
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×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16C2×C4×C1112yes—
371C2×M16D4×C1112yes—
372C2×M16D4×C1112yes—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8D4×C1112yes—
377#117—21no—
378#117—21no—
379#117—21no—
380#117D4×C1112yes—
381C2×C4⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42C2×C4×C1111yescharacteristic
388C2×C42C2×C4×C1111yescharacteristic
389C2×C42D4×C1112yes—
390C2×C42D4×C1112yes—
391C4⋊C8—28no—
392#104—28no—
393#104—24no—
394#104—24no—
395C22⋊C8—28no—
396C2×C11—21no—
397C2×C11—21no—
398C2×C11—21no—
399C2×C11—21no—
400C2×C11—21no—
401C2×C11—21no—
402C2×C11—82no—
403C2×C11#143911yescharacteristic
404C2×C11#186112yes—
405C24—21no—
406C24C11×#4111yescharacteristic
407#41—22no—
408#41—22no—
409#41—22no—
410#41—22no—
411#41—22no—
412#41—22no—
413#41—22no—
414#41—22no—
415#41—41no—
416#41—41no—
417#41—41no—
418#41—41no—
419#41—41no—
420#41—41no—
421#41—41no—
422#41—41no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8C11×C4⋊C412yes—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4C11×C4⋊C412yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—44no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4C22×C4×C1111yescharacteristic
455C22×C4C2×D4×C1111yescharacteristic
456C22×C4C2×D4×C1111yescharacteristic
457C22×C4C2×D4×C1111yescharacteristic
458C22×C4C2×D4×C1111yescharacteristic
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C2×D4×C1111yescharacteristic
461C22×C4C2×D4×C1111yescharacteristic
462C22×C4C2×Q8×C1111yescharacteristic
463C22×C4C11×#4111yescharacteristic
464C22×C4C11×#4111yescharacteristic
465C22×C4C11×#4111yescharacteristic
466C22×C4C11×#4111yescharacteristic
467C22×C4C11×#4111yescharacteristic
468M16—22no—
469M16—22no—
470M16—22no—
471M16—22no—
472M16—22no—
473M16—22no—
474M16—41no—
475M16—41no—
476M16—41no—
477M16—41no—
478M16—41no—
479M16—41no—
480M16—41no—
481M16—41no—
482M16—41no—
483M16—41no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C4⋊C4—22no—
497C4⋊C4—41no—
498C22⋊C4—22no—
499C22⋊C4—41no—
500C42—21no—
501C42—21no—
502C42—22no—
503C42—22no—
504C42—22no—
505C42—41no—
506C42C11×C22⋊C412yes—
507C42C11×C22⋊C412yes—
508C11#1108011yescharacteristic, direct product factor, Sylow
509C23—22no—
510C23—42no—
511C23—41no—
512C23—41no—
513C23—82no—
514C23C4×D4×C1111yescharacteristic
515C23C11×#12111yescharacteristic
516C23C11×C22⋊Q811yescharacteristic
517C23C11×#12311yescharacteristic
518C23C11×#12311yescharacteristic
519C23C11×#12311yescharacteristic
520C23C11×#12611yescharacteristic
521Q8—22no—
522Q8—22no—
523Q8—41no—
524Q8—41no—
525D4—22no—
526D4—22no—
527D4—42no—
528D4—42no—
529D4—42no—
530D4—42no—
531D4—41no—
532D4—41no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—44no—
538C2×C4—44no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—82no—
548C2×C4C2×C11×C22⋊C411yescharacteristic
549C2×C4C2×C11×C4⋊C411yescharacteristic
550C2×C4C11×#11711yescharacteristic
551C2×C4C4×D4×C1111yescharacteristic
552C2×C4C4×D4×C1111yescharacteristic
553C2×C4C4×D4×C1111yescharacteristic
554C2×C4C11×#12011yescharacteristic
555C2×C4C11×#12011yescharacteristic
556C2×C4C11×#12011yescharacteristic
557C2×C4C11×#12111yescharacteristic
558C2×C4C11×#12111yescharacteristic
559C2×C4C11×#12111yescharacteristic
560C2×C4C11×#12111yescharacteristic
561C2×C4C11×#12111yescharacteristic
562C2×C4C11×#12111yescharacteristic
563C2×C4C11×#12111yescharacteristic
564C2×C4C11×C22⋊Q811yescharacteristic
565C2×C4C11×C22⋊Q811yescharacteristic
566C2×C4C11×C22⋊Q811yescharacteristic
567C2×C4C11×C22⋊Q811yescharacteristic
568C2×C4C11×C22⋊Q811yescharacteristic
569C2×C4C11×#12311yescharacteristic
570C2×C4C11×#12311yescharacteristic
571C2×C4C11×#12411yescharacteristic
572C2×C4C11×#12411yescharacteristic
573C2×C4C11×#12411yescharacteristic
574C2×C4C11×#12611yescharacteristic
575C2×C4C11×#12711yescharacteristic
576C8—42no—
577C8—42no—
578C8—42no—
579C8—42no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—42no—
588C22—44no—
589C22—82no—
590C22—82no—
591C22C11×#38511yescharacteristic
592C22C11×#38611yescharacteristic
593C22C11×#38811yescharacteristic
594C22C11×#39411yescharacteristic
595C22C11×#39611yescharacteristic
596C22C11×#39711yescharacteristic
597C22C11×#39911yescharacteristic
598C4—24no—
599C4—42no—
600C4—42no—
601C4—82no—
602C4C11×#38011yescharacteristic
603C4C11×#38511yescharacteristic
604C4C11×#38811yescharacteristic
605C4C11×#39011yescharacteristic
606C4C11×#39211yescharacteristic
607C4C11×#39311yescharacteristic
608C4C11×#39411yescharacteristic
609C4C11×#39611yescharacteristic
610C2—21no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—82no—
617C2C11×#143911yescharacteristic
618C2C11×#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×#423C2semidirect
5. C2×C11×#344C2semidirect
6. C11×#1738C2semidirect
7. C2×C11×#339C2semidirect
23. C2×C11×#104C4semidirect
24. C2×C11×#104C4semidirect
96. #11080C11direct (N × H)
200. C2×#423C2×C11semidirect
204. C2×#344C2×C11semidirect
205. #1738C2×C11semidirect
206. C2×#339C2×C11semidirect
293. C2×#104C4×C11semidirect
294. C2×#104C4×C11semidirect
508. C11#11080direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4232
C2×C11×#4212
C22×C11×#1042
C11×#28792
C2×C11×#3442
C11×#17382
C2×C11×#3392
#1108011