Finite Group Databasebeta

← C11×#11115 #14588308

Subgroups — C11×#11115 #14588308

Order 2816.

864 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2911C211yesmaximal, characteristic, complemented
2C2×C11×#421C211yesmaximal, characteristic
3C2×C11×#421C211yesmaximal, characteristic
4C2×C11×#410C211yesmaximal, characteristic
5C11×#1742C211yesmaximal, characteristic, complemented
6C11×#1740C211yesmaximal, characteristic, complemented
7C2×C11×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C11×#428—22no—
16C11×#428—22no—
17C11×#427—22no—
18C11×#421—22no—
19C11×#421—22no—
20C11×#421—22no—
21C11×#421—22no—
22C2×C11×#104—22no—
23C2×C11×#104C414yescomplemented
24C11×#410—22no—
25C11×#410—22no—
26C2×C11×#99—22no—
27C11×#343—22no—
28C11×#342—22no—
29C11×H(3,ℤ/4)—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×C11C2311yescharacteristic
47C2×C11×M16—21no—
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×M16C2×C412yes—
56C2×C11×M16D412yes—
57C2×C11×M16D412yes—
58C2×C11×M16D412yes—
59C22×C8×C11—21no—
60C22×C8×C11—21no—
61C11×#117—21no—
62C11×#117—21no—
63C11×#117—21no—
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×#117—21no—
75C11×#117D412yes—
76C11×#117D412yes—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4D412yes—
85C2×C42×C11—21no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11C2×C412yes—
89C11×#107—24no—
90C11×#106—24no—
91C11×#104—28no—
92C11×#104—28no—
93C11×#99—28no—
94#11115C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—21no—
96C24×C11C2×D411yescharacteristic
97C11×#41—22no—
98C11×#41—22no—
99C11×#41—22no—
100C11×#41—22no—
101C11×#41—22no—
102C11×#41—22no—
103C11×#41—22no—
104C11×#41—22no—
105C11×#41—41no—
106C11×#41—41no—
107C11×#41—41no—
108C11×#41—41no—
109C11×#41—41no—
110C11×#41—41no—
111C11×#41—41no—
112C11×#41—41no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11C4⋊C412yes—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—41no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11C4⋊C412yes—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
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×Q811yescharacteristic
150C22×C4×C11#4111yescharacteristic
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—41no—
162C11×M16—41no—
163C11×M16C22⋊C414yes—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—41no—
169C2×C8×C11—41no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—41no—
173C11×C4⋊C4—41no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4—41no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—41no—
183C11×C22⋊C4—41no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—41no—
186C42×C11—22no—
187C42×C11—22no—
188C42×C11—22no—
189C42×C11—22no—
190C42×C11—41no—
191C42×C11—41no—
192C42×C11—41no—
193C42×C11—41no—
194#2911C2×C1111yescharacteristic, complemented
195C2×#421C2×C1111yescharacteristic
196C2×#421C2×C1111yescharacteristic
197C2×#410C2×C1111yescharacteristic
198#1742C2×C1111yescharacteristic, complemented
199#1740C2×C1111yescharacteristic, complemented
200C2×H(3,ℤ/4)C2×C1111yescharacteristic, complemented
201C23×C11—22no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—81no—
205C23×C11—82no—
206C23×C11C4×D411yescharacteristic
207C23×C11#12011yescharacteristic
208C23×C11#12111yescharacteristic
209C23×C11#12111yescharacteristic
210C23×C11C22⋊Q811yescharacteristic
211C23×C11#12311yescharacteristic
212C23×C11#12711yescharacteristic
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—22no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—82no—
237C2×C4×C11—82no—
238C2×C4×C11—82no—
239C2×C4×C11—82no—
240C2×C4×C11C2×C22⋊C411yescharacteristic
241C2×C4×C11C2×C4⋊C411yescharacteristic
242C2×C4×C11#11711yescharacteristic
243C2×C4×C11C4×D411yescharacteristic
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11C4×D411yescharacteristic
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×C11C22⋊Q811yescharacteristic
255C2×C4×C11C22⋊Q811yescharacteristic
256C2×C4×C11C22⋊Q811yescharacteristic
257C2×C4×C11C22⋊Q811yescharacteristic
258C2×C4×C11C22⋊Q811yescharacteristic
259C2×C4×C11#12311yescharacteristic
260C2×C4×C11#12311yescharacteristic
261C2×C4×C11#12311yescharacteristic
262C2×C4×C11#12311yescharacteristic
263C2×C4×C11#12411yescharacteristic
264C2×C4×C11#12411yescharacteristic
265C2×C4×C11#12411yescharacteristic
266C2×C4×C11#12611yescharacteristic
267C2×C4×C11#12611yescharacteristic
268C8×C11—24no—
269C8×C11—42no—
270C22×#41C22×C1111yescharacteristic
271C22×M16C22×C1111yescharacteristic
272C22×M16C22×C1111yescharacteristic
273C2×#117C22×C1111yescharacteristic
274C2×#117C22×C1111yescharacteristic
275C2×#117C22×C1111yescharacteristic
276C2×#117C22×C1111yescharacteristic
277#428—22no—
278#428—22no—
279#427—22no—
280#421—22no—
281#421—22no—
282#421—22no—
283#421—22no—
284C2×#104—22no—
285C2×#104C4×C1114yescomplemented
286#410—22no—
287#410—22no—
288C2×#99—22no—
289#343—22no—
290#342—22no—
291H(3,ℤ/4)—22no—
292C22×C11—41no—
293C22×C11—41no—
294C22×C11—41no—
295C22×C11—41no—
296C22×C11—41no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—42no—
300C22×C11—82no—
301C22×C11—82no—
302C22×C11—82no—
303C22×C11#38511yescharacteristic
304C22×C11#38811yescharacteristic
305C22×C11#39011yescharacteristic
306C22×C11#39211yescharacteristic
307C22×C11#39411yescharacteristic
308C22×C11#39611yescharacteristic
309C22×C11#39911yescharacteristic
310C4×C11—42no—
311C4×C11—82no—
312C4×C11—82no—
313C4×C11—82no—
314C4×C11—82no—
315C4×C11#38011yescharacteristic
316C4×C11#38511yescharacteristic
317C4×C11#38611yescharacteristic
318C4×C11#38811yescharacteristic
319C4×C11#39311yescharacteristic
320C4×C11#39411yescharacteristic
321C4×C11#39611yescharacteristic
322C4×C11#39711yescharacteristic
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×#41—21no—
333C2×#41C2×C4×C1112yes—
334C2×#41D4×C1112yes—
335C22×Q8Q8×C1111yescharacteristic
336C22×D4—21no—
337C22×D4Q8×C1111yescharacteristic
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×M16C2×C4×C1112yes—
349C2×M16D4×C1112yes—
350C2×M16D4×C1112yes—
351C2×M16D4×C1112yes—
352C22×C8—21no—
353C22×C8—21no—
354#117—21no—
355#117—21no—
356#117—21no—
357#117—21no—
358#117—21no—
359#117—21no—
360#117—21no—
361#117—21no—
362#117—21no—
363#117—21no—
364#117—21no—
365#117—21no—
366#117—21no—
367#117—21no—
368#117D4×C1112yes—
369#117D4×C1112yes—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4D4×C1112yes—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42C2×C4×C1112yes—
382#107—24no—
383#106—24no—
384#104—28no—
385#104—28no—
386#99—28no—
387C2×C11—21no—
388C2×C11—21no—
389C2×C11—21no—
390C2×C11—21no—
391C2×C11—21no—
392C2×C11—21no—
393C2×C11—21no—
394C2×C11—82no—
395C2×C11#143911yescharacteristic
396C24—21no—
397C24C2×D4×C1111yescharacteristic
398#41—22no—
399#41—22no—
400#41—22no—
401#41—22no—
402#41—22no—
403#41—22no—
404#41—22no—
405#41—22no—
406#41—41no—
407#41—41no—
408#41—41no—
409#41—41no—
410#41—41no—
411#41—41no—
412#41—41no—
413#41—41no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8C11×C4⋊C412yes—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4C11×C4⋊C412yes—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4C22×C4×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
456C22×C4C11×#4111yescharacteristic
457M16—22no—
458M16—22no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—41no—
463M16—41no—
464M16C11×C22⋊C414yes—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—41no—
470C2×C8—41no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C42—22no—
488C42—22no—
489C42—22no—
490C42—22no—
491C42—41no—
492C42—41no—
493C42—41no—
494C42—41no—
495C11#1111511yescharacteristic, direct product factor, Sylow
496C23—22no—
497C23—41no—
498C23—41no—
499C23—81no—
500C23—82no—
501C23C4×D4×C1111yescharacteristic
502C23C11×#12011yescharacteristic
503C23C11×#12111yescharacteristic
504C23C11×#12111yescharacteristic
505C23C11×C22⋊Q811yescharacteristic
506C23C11×#12311yescharacteristic
507C23C11×#12711yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—41no—
511Q8—41no—
512D4—22no—
513D4—22no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—42no—
518D4—41no—
519D4—41no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—82no—
532C2×C4—82no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4C2×C11×C22⋊C411yescharacteristic
536C2×C4C2×C11×C4⋊C411yescharacteristic
537C2×C4C11×#11711yescharacteristic
538C2×C4C4×D4×C1111yescharacteristic
539C2×C4C4×D4×C1111yescharacteristic
540C2×C4C4×D4×C1111yescharacteristic
541C2×C4C11×#12011yescharacteristic
542C2×C4C11×#12011yescharacteristic
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×#12411yescharacteristic
560C2×C4C11×#12411yescharacteristic
561C2×C4C11×#12611yescharacteristic
562C2×C4C11×#12611yescharacteristic
563C8—24no—
564C8—42no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—42no—
573C22—82no—
574C22—82no—
575C22—82no—
576C22C11×#38511yescharacteristic
577C22C11×#38811yescharacteristic
578C22C11×#39011yescharacteristic
579C22C11×#39211yescharacteristic
580C22C11×#39411yescharacteristic
581C22C11×#39611yescharacteristic
582C22C11×#39911yescharacteristic
583C4—42no—
584C4—82no—
585C4—82no—
586C4—82no—
587C4—82no—
588C4C11×#38011yescharacteristic
589C4C11×#38511yescharacteristic
590C4C11×#38611yescharacteristic
591C4C11×#38811yescharacteristic
592C4C11×#39311yescharacteristic
593C4C11×#39411yescharacteristic
594C4C11×#39611yescharacteristic
595C4C11×#39711yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—21no—
603C2—82no—
604C2C11×#143911yescharacteristic
subgroupG/H
centerC4×C11#388
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC2×C11#1439
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2911C2semidirect
5. C11×#1742C2semidirect
6. C11×#1740C2semidirect
7. C2×C11×H(3,ℤ/4)C2semidirect
23. C2×C11×#104C4semidirect
94. #11115C11direct (N × H)
194. #2911C2×C11semidirect
198. #1742C2×C11semidirect
199. #1740C2×C11semidirect
200. C2×H(3,ℤ/4)C2×C11semidirect
285. C2×#104C4×C11semidirect
495. C11#11115direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29112
C2×C11×#4212
C2×C11×#4102
C11×#17422
C11×#17402
C2×C11×H(3,ℤ/4)2
#1111511