Finite Group Databasebeta

← C11×#11083 #14588276

Subgroups — C11×#11083 #14588276

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#421C211yesmaximal, characteristic
2C11×#2896C211yesmaximal, characteristic
3C11×#2297C211yesmaximal, characteristic
4C11×#2296C211yesmaximal, characteristic, complemented
5C11×#1733C211yesmaximal, characteristic, complemented
6C2×C11×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
7C11×#1728C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C11×#421—22no—
16C11×#421C414yescomplemented
17C2×C11×#104—22no—
18C11×#419—21no—
19C11×#418—21no—
20C11×#417—22no—
21C11×#416—22no—
22C11×#391—21no—
23C11×#390—21no—
24C11×#389—22no—
25C11×#386—22no—
26C11×#385—22no—
27C4×C11×C4⋊C4—22no—
28C4×C11×C22⋊C4—22no—
29C11×#339—22no—
30C11×H(3,ℤ/4)—22no—
31C11×#336—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×C11D412yes—
49C23×C4×C11C2311yescharacteristic
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×M16C2×C412yes—
62C22×C8×C11—21no—
63C22×C8×C11D412yes—
64C11×#117—21no—
65C11×#117—21no—
66C11×#117—21no—
67C11×#117—21no—
68C11×#117—21no—
69C11×#117—21no—
70C11×#117—21no—
71C11×#117—21no—
72C11×#117—21no—
73C11×#117—21no—
74C11×#117C2×C412yes—
75C11×#117D412yes—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4D412yes—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11D412yes—
92C2×C42×C11D412yes—
93C11×#104—28no—
94C11×#103—24no—
95C11×#102—24no—
96C11×#95—24no—
97C11×#95—24no—
98#11083C1111yesmaximal, 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—21no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—44no—
145C22×C4×C11—41no—
146C22×C4×C11—41no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×Q811yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C22×C4×C11#4111yescharacteristic
161C22×C4×C11#4111yescharacteristic
162C22×C4×C11#4111yescharacteristic
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—41no—
166C11×M16—41no—
167C11×M16—41no—
168C11×M16—41no—
169C11×M16—41no—
170C11×M16—41no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—41no—
176C2×C8×C11—41no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—48no—
182C11×C4⋊C4—41no—
183C11×C4⋊C4—41no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—48no—
187C11×C22⋊C4—41no—
188C11×C22⋊C4—41no—
189C11×C22⋊C4—41no—
190C11×C22⋊C4—41no—
191C42×C11—22no—
192C42×C11—22no—
193C42×C11—22no—
194C42×C11—41no—
195C42×C11—41no—
196C42×C11—41no—
197C42×C11—41no—
198C42×C11—41no—
199C42×C11—41no—
200C42×C11C22⋊C414yescomplemented
201C2×#421C2×C1111yescharacteristic
202#2896C2×C1111yescharacteristic
203#2297C2×C1111yescharacteristic
204#2296C2×C1111yescharacteristic, complemented
205#1733C2×C1111yescharacteristic, complemented
206C2×H(3,ℤ/4)C2×C1111yescharacteristic, complemented
207#1728C2×C1111yescharacteristic, complemented
208C23×C11—22no—
209C23×C11—42no—
210C23×C11—44no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11C4×D411yescharacteristic
214C23×C11#12011yescharacteristic
215C23×C11#12011yescharacteristic
216C23×C11#12111yescharacteristic
217C23×C11#12111yescharacteristic
218C23×C11C22⋊Q811yescharacteristic
219C23×C11#12411yescharacteristic
220Q8×C11—22no—
221Q8×C11—22no—
222Q8×C11—41no—
223Q8×C11—41no—
224D4×C11—22no—
225D4×C11—22no—
226D4×C11—42no—
227D4×C11—42no—
228D4×C11—42no—
229D4×C11—42no—
230D4×C11—41no—
231D4×C11—41no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—44no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—44no—
249C2×C4×C11—44no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11C2×C22⋊C411yescharacteristic
253C2×C4×C11C2×C4⋊C411yescharacteristic
254C2×C4×C11#11711yescharacteristic
255C2×C4×C11C4×D411yescharacteristic
256C2×C4×C11C4×D411yescharacteristic
257C2×C4×C11C4×D411yescharacteristic
258C2×C4×C11#12011yescharacteristic
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11#12111yescharacteristic
261C2×C4×C11#12111yescharacteristic
262C2×C4×C11#12111yescharacteristic
263C2×C4×C11#12111yescharacteristic
264C2×C4×C11#12111yescharacteristic
265C2×C4×C11C22⋊Q811yescharacteristic
266C2×C4×C11C22⋊Q811yescharacteristic
267C2×C4×C11C22⋊Q811yescharacteristic
268C2×C4×C11C22⋊Q811yescharacteristic
269C2×C4×C11C22⋊Q811yescharacteristic
270C2×C4×C11#12311yescharacteristic
271C2×C4×C11#12311yescharacteristic
272C2×C4×C11#12311yescharacteristic
273C2×C4×C11#12311yescharacteristic
274C2×C4×C11#12311yescharacteristic
275C2×C4×C11#12411yescharacteristic
276C2×C4×C11#12411yescharacteristic
277C2×C4×C11#12611yescharacteristic
278C2×C4×C11#12611yescharacteristic
279C2×C4×C11#12711yescharacteristic
280C8×C11—42no—
281C8×C11—42no—
282C22×#41C22×C1111yescharacteristic
283C22×M16C22×C1111yescharacteristic
284C22×M16C22×C1111yescharacteristic
285C2×#117C22×C1111yescharacteristic
286C2×#117C22×C1111yescharacteristic
287C2×#117C22×C1111yescharacteristic
288C22×C42C22×C1111yescharacteristic
289#421—22no—
290#421C4×C1114yescomplemented
291C2×#104—22no—
292#419—21no—
293#418—21no—
294#417—22no—
295#416—22no—
296#391—21no—
297#390—21no—
298#389—22no—
299#386—22no—
300#385—22no—
301C4×C4⋊C4—22no—
302C4×C22⋊C4—22no—
303#339—22no—
304H(3,ℤ/4)—22no—
305#336—22no—
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—22no—
309C22×C11—41no—
310C22×C11—41no—
311C22×C11—41no—
312C22×C11—41no—
313C22×C11—44no—
314C22×C11—42no—
315C22×C11—82no—
316C22×C11—82no—
317C22×C11#38511yescharacteristic
318C22×C11#38611yescharacteristic
319C22×C11#38811yescharacteristic
320C22×C11#39211yescharacteristic
321C22×C11#39311yescharacteristic
322C22×C11#39411yescharacteristic
323C22×C11#39611yescharacteristic
324C4×C11—44no—
325C4×C11—42no—
326C4×C11—44no—
327C4×C11—82no—
328C4×C11—82no—
329C4×C11#38011yescharacteristic
330C4×C11#38511yescharacteristic
331C4×C11#38811yescharacteristic
332C4×C11#39011yescharacteristic
333C4×C11#39411yescharacteristic
334C4×C11#39611yescharacteristic
335C4×C11#39711yescharacteristic
336C4×C11#39911yescharacteristic
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—21no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41—21no—
347C2×#41C2×C4×C1112yes—
348C2×#41Q8×C1112yes—
349C22×Q8D4×C1111yescharacteristic
350C22×D4—21no—
351C22×D4D4×C1111yescharacteristic
352C23×C4—21no—
353C23×C4D4×C1112yes—
354C23×C4C23×C1111yescharacteristic
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×M16C2×C4×C1112yes—
367C22×C8—21no—
368C22×C8D4×C1112yes—
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117C2×C4×C1112yes—
380#117D4×C1112yes—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4D4×C1112yes—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42D4×C1112yes—
397C2×C42D4×C1112yes—
398#104—28no—
399#103—24no—
400#102—24no—
401#95—24no—
402#95—24no—
403C2×C11—21no—
404C2×C11—21no—
405C2×C11—21no—
406C2×C11—21no—
407C2×C11—21no—
408C2×C11—21no—
409C2×C11—82no—
410C2×C11#143911yescharacteristic
411C2×C11#201012yes—
412C24—21no—
413C24C2×D4×C1111yescharacteristic
414#41—22no—
415#41—22no—
416#41—22no—
417#41—22no—
418#41—22no—
419#41—22no—
420#41—22no—
421#41—22no—
422#41—41no—
423#41—41no—
424#41—41no—
425#41—41no—
426#41—41no—
427#41—41no—
428#41—41no—
429#41—41no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8C11×C4⋊C412yescomplemented
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4C11×C4⋊C412yescomplemented
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—44no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4C22×C4×C1111yescharacteristic
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C2×D4×C1111yescharacteristic
465C22×C4C2×D4×C1111yescharacteristic
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C2×D4×C1111yescharacteristic
468C22×C4C2×D4×C1111yescharacteristic
469C22×C4C2×Q8×C1111yescharacteristic
470C22×C4C11×#4111yescharacteristic
471C22×C4C11×#4111yescharacteristic
472C22×C4C11×#4111yescharacteristic
473C22×C4C11×#4111yescharacteristic
474C22×C4C11×#4111yescharacteristic
475C22×C4C11×#4111yescharacteristic
476M16—22no—
477M16—22no—
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—41no—
489C2×C8—41no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—48no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—48no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C42—22no—
505C42—22no—
506C42—22no—
507C42—41no—
508C42—41no—
509C42—41no—
510C42—41no—
511C42—41no—
512C42—41no—
513C42C11×C22⋊C414yescomplemented
514C11#1108311yescharacteristic, direct product factor, Sylow
515C23—22no—
516C23—42no—
517C23—44no—
518C23—41no—
519C23—41no—
520C23C4×D4×C1111yescharacteristic
521C23C11×#12011yescharacteristic
522C23C11×#12011yescharacteristic
523C23C11×#12111yescharacteristic
524C23C11×#12111yescharacteristic
525C23C11×C22⋊Q811yescharacteristic
526C23C11×#12411yescharacteristic
527Q8—22no—
528Q8—22no—
529Q8—41no—
530Q8—41no—
531D4—22no—
532D4—22no—
533D4—42no—
534D4—42no—
535D4—42no—
536D4—42no—
537D4—41no—
538D4—41no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—44no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4C2×C11×C22⋊C411yescharacteristic
560C2×C4C2×C11×C4⋊C411yescharacteristic
561C2×C4C11×#11711yescharacteristic
562C2×C4C4×D4×C1111yescharacteristic
563C2×C4C4×D4×C1111yescharacteristic
564C2×C4C4×D4×C1111yescharacteristic
565C2×C4C11×#12011yescharacteristic
566C2×C4C11×#12111yescharacteristic
567C2×C4C11×#12111yescharacteristic
568C2×C4C11×#12111yescharacteristic
569C2×C4C11×#12111yescharacteristic
570C2×C4C11×#12111yescharacteristic
571C2×C4C11×#12111yescharacteristic
572C2×C4C11×C22⋊Q811yescharacteristic
573C2×C4C11×C22⋊Q811yescharacteristic
574C2×C4C11×C22⋊Q811yescharacteristic
575C2×C4C11×C22⋊Q811yescharacteristic
576C2×C4C11×C22⋊Q811yescharacteristic
577C2×C4C11×#12311yescharacteristic
578C2×C4C11×#12311yescharacteristic
579C2×C4C11×#12311yescharacteristic
580C2×C4C11×#12311yescharacteristic
581C2×C4C11×#12311yescharacteristic
582C2×C4C11×#12411yescharacteristic
583C2×C4C11×#12411yescharacteristic
584C2×C4C11×#12611yescharacteristic
585C2×C4C11×#12611yescharacteristic
586C2×C4C11×#12711yescharacteristic
587C8—42no—
588C8—42no—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—44no—
597C22—42no—
598C22—82no—
599C22—82no—
600C22C11×#38511yescharacteristic
601C22C11×#38611yescharacteristic
602C22C11×#38811yescharacteristic
603C22C11×#39211yescharacteristic
604C22C11×#39311yescharacteristic
605C22C11×#39411yescharacteristic
606C22C11×#39611yescharacteristic
607C4—44no—
608C4—42no—
609C4—44no—
610C4—82no—
611C4—82no—
612C4C11×#38011yescharacteristic
613C4C11×#38511yescharacteristic
614C4C11×#38811yescharacteristic
615C4C11×#39011yescharacteristic
616C4C11×#39411yescharacteristic
617C4C11×#39611yescharacteristic
618C4C11×#39711yescharacteristic
619C4C11×#39911yescharacteristic
620C2—21no—
621C2—21no—
622C2—21no—
623C2—21no—
624C2—21no—
625C2—21no—
626C2—82no—
627C2C11×#143911yescharacteristic
628C2C11×#201012yes—
subgroupG/H
centerC2×C4×C11#127
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC22×C11#392
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
4. C11×#2296C2semidirect
5. C11×#1733C2semidirect
6. C2×C11×H(3,ℤ/4)C2semidirect
7. C11×#1728C2semidirect
16. C11×#421C4semidirect
98. #11083C11direct (N × H)
122. C2×Q8×C11C4⋊C4semidirect
134. C2×D4×C11C4⋊C4semidirect
200. C42×C11C22⋊C4semidirect
204. #2296C2×C11semidirect
205. #1733C2×C11semidirect
206. C2×H(3,ℤ/4)C2×C11semidirect
207. #1728C2×C11semidirect
290. #421C4×C11semidirect
435. C2×Q8C11×C4⋊C4semidirect
447. C2×D4C11×C4⋊C4semidirect
513. C42C11×C22⋊C4semidirect
514. C11#11083direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4212
C11×#28962
C11×#22972
C11×#22962
C11×#17332
C2×C11×H(3,ℤ/4)2
C11×#17282
#1108311