Finite Group Databasebeta

← C11×#11127 #14588320

Subgroups — C11×#11127 #14588320

Order 2816.

1002 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#108C211yesmaximal, characteristic, complemented
2C2×C11×#418C211yesmaximal, characteristic
3C22×C11×#102C211yesmaximal, characteristic
4C22×C11×#100C211yesmaximal, characteristic
5C2×C11×#343C211yesmaximal, characteristic, complemented
6C11×#1736C211yesmaximal, characteristic, complemented
7C11×#1729C211yesmaximal, characteristic, complemented
8C23×D4×C11C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×C11×#108—22no—
16C2×C11×#108—22no—
17C2×C11×#108—22no—
18C11×#418—22no—
19C11×#418—22no—
20C2×C11×#102—22no—
21C2×C11×#102—22no—
22C2×C11×#102—22no—
23C2×C11×#102C414yescomplemented
24C2×C11×#100—22no—
25C2×C11×#100—22no—
26C2×C11×#100—22no—
27C11×#343—22no—
28C11×#340—22no—
29C11×#336—22no—
30C25×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11C2×C412yes—
43C22×D4×C11D412yes—
44C22×D4×C11Q812yes—
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×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×M16D412yes—
63C2×C11×M16D412yes—
64C2×C11×M16D412yes—
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×C11C2×C412yes—
73C22×C8×C11D412yes—
74C22×C8×C11D412yes—
75C11×#117—21no—
76C11×#117—21no—
77C11×#117—21no—
78C11×#117—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2×C412yes—
85C2×C11×C4⋊C4D412yes—
86C2×C11×C22⋊C4—21no—
87C2×C42×C11—21no—
88C11×#108—28no—
89C11×#102—28no—
90C11×#102—28no—
91C11×#100—28no—
92#11127C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—22no—
96C24×C11—41no—
97C24×C11—41no—
98C24×C11—41no—
99C24×C11—41no—
100C24×C11—82no—
101C24×C11—82no—
102C24×C11#4111yescharacteristic
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—41no—
119C2×D4×C11—41no—
120C2×D4×C11—41no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11C4⋊C414yes—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—41no—
134C22×C4×C11—41no—
135C22×C4×C11—82no—
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×Q811yescharacteristic
145C22×C4×C11#4111yescharacteristic
146C22×C4×C11#4111yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C22×C4×C11#4111yescharacteristic
150C11×M16—22no—
151C11×M16—22no—
152C11×M16—22no—
153C11×M16—22no—
154C11×M16—22no—
155C11×M16—22no—
156C11×M16—41no—
157C11×M16—41no—
158C11×M16—41no—
159C11×M16—41no—
160C11×M16—41no—
161C11×M16—41no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—41no—
172C2×C8×C11—41no—
173C2×C8×C11—41no—
174C2×C8×C11—41no—
175C2×C8×C11—41no—
176C2×C8×C11—41no—
177C2×C8×C11C22⋊C414yes—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—41no—
183C11×C4⋊C4—41no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—41no—
186C42×C11—41no—
187C42×C11—41no—
188C22×#108C2×C1111yescharacteristic, complemented
189C2×#418C2×C1111yescharacteristic
190C22×#102C2×C1111yescharacteristic
191C22×#100C2×C1111yescharacteristic
192C2×#343C2×C1111yescharacteristic, complemented
193#1736C2×C1111yescharacteristic, complemented
194#1729C2×C1111yescharacteristic, complemented
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—24no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—84no—
205C23×C11—84no—
206C23×C11—82no—
207C23×C11—82no—
208C23×C11—84no—
209C23×C11—84no—
210C23×C11—82no—
211C23×C11—82no—
212C23×C11—82no—
213C23×C11—82no—
214C23×C11C4×D411yescharacteristic
215C23×C11#12111yescharacteristic
216C23×C11C22⋊Q811yescharacteristic
217C23×C11#12311yescharacteristic
218C23×C11#12411yescharacteristic
219C23×C11#12411yescharacteristic
220C23×C11#12611yescharacteristic
221D4×C11—24no—
222D4×C11—24no—
223D4×C11—42no—
224D4×C11—42no—
225D4×C11—42no—
226D4×C11—42no—
227D4×C11—42no—
228D4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—82no—
234C2×C4×C11—82no—
235C2×C4×C11—82no—
236C2×C4×C11C2×C22⋊C411yescharacteristic
237C2×C4×C11C2×C4⋊C411yescharacteristic
238C2×C4×C11#11711yescharacteristic
239C2×C4×C11C4×D411yescharacteristic
240C2×C4×C11C4×D411yescharacteristic
241C2×C4×C11C4×D411yescharacteristic
242C2×C4×C11#12011yescharacteristic
243C2×C4×C11#12011yescharacteristic
244C2×C4×C11#12011yescharacteristic
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11C22⋊Q811yescharacteristic
253C2×C4×C11C22⋊Q811yescharacteristic
254C2×C4×C11C22⋊Q811yescharacteristic
255C2×C4×C11C22⋊Q811yescharacteristic
256C2×C4×C11C22⋊Q811yescharacteristic
257C2×C4×C11#12311yescharacteristic
258C2×C4×C11#12311yescharacteristic
259C2×C4×C11#12311yescharacteristic
260C2×C4×C11#12311yescharacteristic
261C2×C4×C11#12411yescharacteristic
262C2×C4×C11#12611yescharacteristic
263C2×C4×C11#12711yescharacteristic
264C8×C11—24no—
265C8×C11—42no—
266C8×C11—42no—
267C8×C11—42no—
268C23×D4C22×C1111yescharacteristic
269C22×M16C22×C1111yescharacteristic
270C22×M16C22×C1111yescharacteristic
271C22×M16C22×C1111yescharacteristic
272C23×C8C22×C1111yescharacteristic
273C2×#117C22×C1111yescharacteristic
274C22×C4⋊C4C22×C1111yescharacteristic
275C2×#108—22no—
276C2×#108—22no—
277C2×#108—22no—
278#418—22no—
279#418—22no—
280C2×#102—22no—
281C2×#102—22no—
282C2×#102—22no—
283C2×#102C4×C1114yescomplemented
284C2×#100—22no—
285C2×#100—22no—
286C2×#100—22no—
287#343—22no—
288#340—22no—
289#336—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—44no—
299C22×C11—84no—
300C22×C11—84no—
301C22×C11—84no—
302C22×C11—84no—
303C22×C11—84no—
304C22×C11—84no—
305C22×C11—82no—
306C22×C11—82no—
307C22×C11#38511yescharacteristic
308C22×C11#38811yescharacteristic
309C22×C11#39011yescharacteristic
310C22×C11#39311yescharacteristic
311C22×C11#39411yescharacteristic
312C22×C11#39611yescharacteristic
313C22×C11#39711yescharacteristic
314C22×C11#47112yes—
315C22×C11#47212yes—
316C4×C11—82no—
317C4×C11—82no—
318C4×C11#38011yescharacteristic
319C4×C11#38511yescharacteristic
320C4×C11#38611yescharacteristic
321C4×C11#38811yescharacteristic
322C4×C11#39211yescharacteristic
323C4×C11#39411yescharacteristic
324C4×C11#39611yescharacteristic
325C4×C11#39911yescharacteristic
326C25—21no—
327C22×D4—21no—
328C22×D4—21no—
329C22×D4—21no—
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—21no—
337C22×D4—21no—
338C22×D4C2×C4×C1112yes—
339C22×D4D4×C1112yes—
340C22×D4Q8×C1112yes—
341C23×C4—21no—
342C23×C4C23×C1111yescharacteristic
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×M16D4×C1112yes—
359C2×M16D4×C1112yes—
360C2×M16D4×C1112yes—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8C2×C4×C1112yes—
369C22×C8D4×C1112yes—
370C22×C8D4×C1112yes—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4C2×C4×C1112yes—
381C2×C4⋊C4D4×C1112yes—
382C2×C22⋊C4—21no—
383C2×C42—21no—
384#108—28no—
385#102—28no—
386#102—28no—
387#100—28no—
388C2×C11—21no—
389C2×C11—21no—
390C2×C11—21no—
391C2×C11—21no—
392C2×C11—84no—
393C2×C11#143911yescharacteristic
394C2×C11#197711yescharacteristic
395C2×C11#197811yescharacteristic
396C2×C11#205112yes—
397C2×C11#206312yes—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—41no—
402C24—41no—
403C24—41no—
404C24—41no—
405C24—82no—
406C24—82no—
407C24C11×#4111yescharacteristic
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4C11×C4⋊C414yes—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—82no—
441C22×C4C22×C4×C1111yescharacteristic
442C22×C4C2×D4×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×Q8×C1111yescharacteristic
450C22×C4C11×#4111yescharacteristic
451C22×C4C11×#4111yescharacteristic
452C22×C4C11×#4111yescharacteristic
453C22×C4C11×#4111yescharacteristic
454C22×C4C11×#4111yescharacteristic
455M16—22no—
456M16—22no—
457M16—22no—
458M16—22no—
459M16—22no—
460M16—22no—
461M16—41no—
462M16—41no—
463M16—41no—
464M16—41no—
465M16—41no—
466M16—41no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8C11×C22⋊C414yes—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C42—41no—
492C42—41no—
493C11#1112711yescharacteristic, direct product factor, Sylow
494C23—22no—
495C23—22no—
496C23—24no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—82no—
504C23—82no—
505C23—84no—
506C23—84no—
507C23—82no—
508C23—82no—
509C23—84no—
510C23—84no—
511C23—82no—
512C23—82no—
513C23C4×D4×C1111yescharacteristic
514C23C11×#12111yescharacteristic
515C23C11×C22⋊Q811yescharacteristic
516C23C11×#12311yescharacteristic
517C23C11×#12411yescharacteristic
518C23C11×#12411yescharacteristic
519C23C11×#12611yescharacteristic
520D4—24no—
521D4—24no—
522D4—42no—
523D4—42no—
524D4—42no—
525D4—42no—
526D4—42no—
527D4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
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×#12011yescharacteristic
544C2×C4C11×#12111yescharacteristic
545C2×C4C11×#12111yescharacteristic
546C2×C4C11×#12111yescharacteristic
547C2×C4C11×#12111yescharacteristic
548C2×C4C11×#12111yescharacteristic
549C2×C4C11×#12111yescharacteristic
550C2×C4C11×#12111yescharacteristic
551C2×C4C11×C22⋊Q811yescharacteristic
552C2×C4C11×C22⋊Q811yescharacteristic
553C2×C4C11×C22⋊Q811yescharacteristic
554C2×C4C11×C22⋊Q811yescharacteristic
555C2×C4C11×C22⋊Q811yescharacteristic
556C2×C4C11×#12311yescharacteristic
557C2×C4C11×#12311yescharacteristic
558C2×C4C11×#12311yescharacteristic
559C2×C4C11×#12311yescharacteristic
560C2×C4C11×#12411yescharacteristic
561C2×C4C11×#12611yescharacteristic
562C2×C4C11×#12711yescharacteristic
563C8—24no—
564C8—42no—
565C8—42no—
566C8—42no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—22no—
575C22—44no—
576C22—84no—
577C22—84no—
578C22—84no—
579C22—84no—
580C22—82no—
581C22—82no—
582C22—84no—
583C22—84no—
584C22C11×#38511yescharacteristic
585C22C11×#38811yescharacteristic
586C22C11×#39011yescharacteristic
587C22C11×#39311yescharacteristic
588C22C11×#39411yescharacteristic
589C22C11×#39611yescharacteristic
590C22C11×#39711yescharacteristic
591C22C11×#47112yes—
592C22C11×#47212yes—
593C4—82no—
594C4—82no—
595C4C11×#38011yescharacteristic
596C4C11×#38511yescharacteristic
597C4C11×#38611yescharacteristic
598C4C11×#38811yescharacteristic
599C4C11×#39211yescharacteristic
600C4C11×#39411yescharacteristic
601C4C11×#39611yescharacteristic
602C4C11×#39911yescharacteristic
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—84no—
608C2C11×#143911yescharacteristic
609C2C11×#197711yescharacteristic
610C2C11×#197811yescharacteristic
611C2C11×#205112yes—
612C2C11×#206312yes—
subgroupG/H
center, socleC23×C11#121
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#108C2semidirect
5. C2×C11×#343C2semidirect
6. C11×#1736C2semidirect
7. C11×#1729C2semidirect
23. C2×C11×#102C4semidirect
92. #11127C11direct (N × H)
188. C22×#108C2×C11semidirect
192. C2×#343C2×C11semidirect
193. #1736C2×C11semidirect
194. #1729C2×C11semidirect
283. C2×#102C4×C11semidirect
493. C11#11127direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1082
C2×C11×#4182
C22×C11×#1022
C22×C11×#1002
C2×C11×#3432
C11×#17362
C11×#17292
#1112711