Finite Group Databasebeta

← C11×#11088 #14588281

Subgroups — C11×#11088 #14588281

Order 2816.

882 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#424C211yesmaximal, characteristic, complemented
2C2×C11×#410C211yesmaximal, characteristic
3C11×#2879C211yesmaximal, characteristic
4C2×C11×#408C211yesmaximal, characteristic
5C2×C11×#344C211yesmaximal, characteristic, complemented
6C2×C11×#344C211yesmaximal, characteristic, complemented
7C11×#1729C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C11×#424—22no—
16C11×#424—22no—
17C2×C11×C4⋊C8—22no—
18C11×#410—22no—
19C11×#410—22no—
20C2×C11×#99C414yes—
21C11×#408—22no—
22C11×#408—22no—
23C11×#408—22no—
24C11×#408—22no—
25C11×#407—22no—
26C2×C11×C22⋊C8—22no—
27C11×#344—22no—
28C11×#344—22no—
29C11×#336—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×#41—21no—
41C2×C11×#41—21no—
42C22×Q8×C11Q811yescharacteristic
43C22×D4×C11C2×C412yes—
44C22×D4×C11Q811yescharacteristic
45C23×C4×C11D412yes—
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×M16—21no—
63C2×C11×M16—21no—
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×C11D412yes—
73C22×C8×C11D412yes—
74C22×C8×C11D412yes—
75C11×#117—21no—
76C11×#117—21no—
77C11×#117—21no—
78C11×#117—21no—
79C11×#117—21no—
80C11×#117—21no—
81C11×#117D412yes—
82C11×#117D412yes—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C22⋊C4C2×C412yes—
86C2×C11×C22⋊C4C2×C412yes—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C11×C4⋊C8—28no—
90C11×#99—28no—
91C11×C22⋊C8—28no—
92C11×C22⋊C8—28no—
93#11088C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11C4⋊C412yes—
95C24×C11C22×C411yescharacteristic
96C11×#41—41no—
97C11×#41—41no—
98C11×#41—41no—
99C11×#41—41no—
100C11×#41—41no—
101C11×#41—41no—
102C11×#41—41no—
103C11×#41—41no—
104C11×#41—41no—
105C11×#41—41no—
106C11×#41—41no—
107C11×#41—41no—
108C11×#41—41no—
109C11×#41—41no—
110C11×#41—41no—
111C11×#41—41no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11C4⋊C412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×Q811yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C22×C4×C11#4111yescharacteristic
150C22×C4×C11#4111yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C11×M16—22no—
154C11×M16—22no—
155C11×M16—41no—
156C11×M16—41no—
157C11×M16—41no—
158C11×M16—41no—
159C11×M16—41no—
160C11×M16—41no—
161C11×M16—41no—
162C11×M16—41no—
163C11×M16—41no—
164C11×M16—41no—
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—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—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—41no—
184C11×C4⋊C4—41no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4C22⋊C414yes—
189C42×C11—22no—
190C42×C11—22no—
191C42×C11—41no—
192C42×C11—41no—
193C2×#424C2×C1111yescharacteristic, complemented
194C2×#410C2×C1111yescharacteristic
195#2879C2×C1111yescharacteristic
196C2×#408C2×C1111yescharacteristic
197C2×#344C2×C1111yescharacteristic, complemented
198C2×#344C2×C1111yescharacteristic, complemented
199#1729C2×C1111yescharacteristic, complemented
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—42no—
204C23×C11—44no—
205C23×C11C2×C22⋊C411yescharacteristic
206C23×C11C2×C4⋊C411yescharacteristic
207C23×C11#11711yescharacteristic
208C23×C11C4×D411yescharacteristic
209C23×C11C4×D411yescharacteristic
210C23×C11C4×D411yescharacteristic
211C23×C11C4×D411yescharacteristic
212Q8×C11—41no—
213Q8×C11—41no—
214Q8×C11—41no—
215Q8×C11—41no—
216D4×C11—42no—
217D4×C11—42no—
218D4×C11—42no—
219D4×C11—42no—
220D4×C11—41no—
221D4×C11—41no—
222D4×C11—41no—
223D4×C11—41no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—44no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—44no—
234C2×C4×C11—42no—
235C2×C4×C11#12011yescharacteristic
236C2×C4×C11#12011yescharacteristic
237C2×C4×C11#12011yescharacteristic
238C2×C4×C11#12111yescharacteristic
239C2×C4×C11#12111yescharacteristic
240C2×C4×C11#12111yescharacteristic
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11C22⋊Q811yescharacteristic
247C2×C4×C11C22⋊Q811yescharacteristic
248C2×C4×C11C22⋊Q811yescharacteristic
249C2×C4×C11C22⋊Q811yescharacteristic
250C2×C4×C11C22⋊Q811yescharacteristic
251C2×C4×C11C22⋊Q811yescharacteristic
252C2×C4×C11#12311yescharacteristic
253C2×C4×C11#12311yescharacteristic
254C2×C4×C11#12311yescharacteristic
255C2×C4×C11#12311yescharacteristic
256C2×C4×C11#12311yescharacteristic
257C2×C4×C11#12411yescharacteristic
258C2×C4×C11#12411yescharacteristic
259C2×C4×C11#12411yescharacteristic
260C2×C4×C11#12611yescharacteristic
261C2×C4×C11#12611yescharacteristic
262C2×C4×C11#12711yescharacteristic
263C8×C11—42no—
264C8×C11—42no—
265C8×C11—42no—
266C8×C11—42no—
267C22×#41C22×C1111yescharacteristic
268C22×M16C22×C1111yescharacteristic
269C22×M16C22×C1111yescharacteristic
270C22×M16C22×C1111yescharacteristic
271C23×C8C22×C1111yescharacteristic
272C2×#117C22×C1111yescharacteristic
273C2×#117C22×C1111yescharacteristic
274#424—22no—
275#424—22no—
276C2×C4⋊C8—22no—
277#410—22no—
278#410—22no—
279C2×#99C4×C1114yes—
280#408—22no—
281#408—22no—
282#408—22no—
283#408—22no—
284#407—22no—
285C2×C22⋊C8—22no—
286#344—22no—
287#344—22no—
288#336—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—41no—
293C22×C11—41no—
294C22×C11—41no—
295C22×C11—41no—
296C22×C11—44no—
297C22×C11—44no—
298C22×C11—42no—
299C22×C11—82no—
300C22×C11#38011yescharacteristic
301C22×C11#38511yescharacteristic
302C22×C11#38511yescharacteristic
303C22×C11#38611yescharacteristic
304C22×C11#38811yescharacteristic
305C22×C11#38811yescharacteristic
306C22×C11#39011yescharacteristic
307C4×C11—44no—
308C4×C11—42no—
309C4×C11—82no—
310C4×C11#39211yescharacteristic
311C4×C11#39311yescharacteristic
312C4×C11#39411yescharacteristic
313C4×C11#39411yescharacteristic
314C4×C11#39611yescharacteristic
315C4×C11#39611yescharacteristic
316C4×C11#39711yescharacteristic
317C4×C11#39911yescharacteristic
318C2×#41—21no—
319C2×#41—21no—
320C2×#41—21no—
321C2×#41—21no—
322C2×#41—21no—
323C2×#41—21no—
324C2×#41—21no—
325C2×#41—21no—
326C2×#41—21no—
327C2×#41—21no—
328C2×#41—21no—
329C2×#41—21no—
330C22×Q8Q8×C1111yescharacteristic
331C22×D4C2×C4×C1112yes—
332C22×D4Q8×C1111yescharacteristic
333C23×C4D4×C1112yes—
334C23×C4C23×C1111yescharacteristic
335C2×M16—21no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—21no—
339C2×M16—21no—
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×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16D4×C1112yes—
353C22×C8—21no—
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—21no—
360C22×C8D4×C1112yes—
361C22×C8D4×C1112yes—
362C22×C8D4×C1112yes—
363#117—21no—
364#117—21no—
365#117—21no—
366#117—21no—
367#117—21no—
368#117—21no—
369#117D4×C1112yes—
370#117D4×C1112yes—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C22⋊C4C2×C4×C1112yes—
374C2×C22⋊C4C2×C4×C1112yes—
375C2×C42—21no—
376C2×C42—21no—
377C4⋊C8—28no—
378#99—28no—
379C22⋊C8—28no—
380C22⋊C8—28no—
381C2×C11—21no—
382C2×C11—21no—
383C2×C11—21no—
384C2×C11—21no—
385C2×C11—21no—
386C2×C11—21no—
387C2×C11—82no—
388C2×C11#143911yescharacteristic
389C2×C11#186812yes—
390C24C11×C4⋊C412yes—
391C24C22×C4×C1111yescharacteristic
392#41—41no—
393#41—41no—
394#41—41no—
395#41—41no—
396#41—41no—
397#41—41no—
398#41—41no—
399#41—41no—
400#41—41no—
401#41—41no—
402#41—41no—
403#41—41no—
404#41—41no—
405#41—41no—
406#41—41no—
407#41—41no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4C11×C4⋊C412yes—
435C22×C4C2×D4×C1111yescharacteristic
436C22×C4C2×D4×C1111yescharacteristic
437C22×C4C2×D4×C1111yescharacteristic
438C22×C4C2×D4×C1111yescharacteristic
439C22×C4C2×D4×C1111yescharacteristic
440C22×C4C2×D4×C1111yescharacteristic
441C22×C4C2×D4×C1111yescharacteristic
442C22×C4C2×Q8×C1111yescharacteristic
443C22×C4C11×#4111yescharacteristic
444C22×C4C11×#4111yescharacteristic
445C22×C4C11×#4111yescharacteristic
446C22×C4C11×#4111yescharacteristic
447C22×C4C11×#4111yescharacteristic
448C22×C4C11×#4111yescharacteristic
449M16—22no—
450M16—22no—
451M16—41no—
452M16—41no—
453M16—41no—
454M16—41no—
455M16—41no—
456M16—41no—
457M16—41no—
458M16—41no—
459M16—41no—
460M16—41no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4C11×C22⋊C414yes—
485C42—22no—
486C42—22no—
487C42—41no—
488C42—41no—
489C11#1108811yescharacteristic, direct product factor, Sylow
490C23—22no—
491C23—22no—
492C23—22no—
493C23—42no—
494C23—44no—
495C23C2×C11×C22⋊C411yescharacteristic
496C23C2×C11×C4⋊C411yescharacteristic
497C23C11×#11711yescharacteristic
498C23C4×D4×C1111yescharacteristic
499C23C4×D4×C1111yescharacteristic
500C23C4×D4×C1111yescharacteristic
501C23C4×D4×C1111yescharacteristic
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506D4—42no—
507D4—42no—
508D4—42no—
509D4—42no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—44no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4C11×#12011yescharacteristic
526C2×C4C11×#12011yescharacteristic
527C2×C4C11×#12011yescharacteristic
528C2×C4C11×#12111yescharacteristic
529C2×C4C11×#12111yescharacteristic
530C2×C4C11×#12111yescharacteristic
531C2×C4C11×#12111yescharacteristic
532C2×C4C11×#12111yescharacteristic
533C2×C4C11×#12111yescharacteristic
534C2×C4C11×#12111yescharacteristic
535C2×C4C11×#12111yescharacteristic
536C2×C4C11×C22⋊Q811yescharacteristic
537C2×C4C11×C22⋊Q811yescharacteristic
538C2×C4C11×C22⋊Q811yescharacteristic
539C2×C4C11×C22⋊Q811yescharacteristic
540C2×C4C11×C22⋊Q811yescharacteristic
541C2×C4C11×C22⋊Q811yescharacteristic
542C2×C4C11×#12311yescharacteristic
543C2×C4C11×#12311yescharacteristic
544C2×C4C11×#12311yescharacteristic
545C2×C4C11×#12311yescharacteristic
546C2×C4C11×#12311yescharacteristic
547C2×C4C11×#12411yescharacteristic
548C2×C4C11×#12411yescharacteristic
549C2×C4C11×#12411yescharacteristic
550C2×C4C11×#12611yescharacteristic
551C2×C4C11×#12611yescharacteristic
552C2×C4C11×#12711yescharacteristic
553C8—42no—
554C8—42no—
555C8—42no—
556C8—42no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—44no—
565C22—44no—
566C22—42no—
567C22—82no—
568C22C11×#38011yescharacteristic
569C22C11×#38511yescharacteristic
570C22C11×#38511yescharacteristic
571C22C11×#38611yescharacteristic
572C22C11×#38811yescharacteristic
573C22C11×#38811yescharacteristic
574C22C11×#39011yescharacteristic
575C4—44no—
576C4—42no—
577C4—82no—
578C4C11×#39211yescharacteristic
579C4C11×#39311yescharacteristic
580C4C11×#39411yescharacteristic
581C4C11×#39411yescharacteristic
582C4C11×#39611yescharacteristic
583C4C11×#39611yescharacteristic
584C4C11×#39711yescharacteristic
585C4C11×#39911yescharacteristic
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—82no—
593C2C11×#143911yescharacteristic
594C2C11×#186812yes—
subgroupG/H
centerC2×C4×C11#120
commutatorC24C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC22×C11#385
prime radicalC22×C11×#41C22
LCSG ▷ C24 ▷ 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×#424C2semidirect
5. C2×C11×#344C2semidirect
6. C2×C11×#344C2semidirect
7. C11×#1729C2semidirect
93. #11088C11direct (N × H)
193. C2×#424C2×C11semidirect
197. C2×#344C2×C11semidirect
198. C2×#344C2×C11semidirect
199. #1729C2×C11semidirect
489. C11#11088direct (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
C2×C11×#4102
C11×#28792
C2×C11×#4082
C2×C11×#3442
C11×#17292
#1108811