Finite Group Databasebeta

← C11×#11092 #14588285

Subgroups — C11×#11092 #14588285

Order 2816.

882 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#424C211yesmaximal, characteristic, complemented
2C11×#2896C211yesmaximal, characteristic
3C2×C11×#416C211yesmaximal, characteristic
4C2×C11×#410C211yesmaximal, characteristic
5C11×#1740C211yesmaximal, characteristic, complemented
6C11×#1735C211yesmaximal, characteristic, complemented
7C2×C11×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C11×#424—22no—
16C11×#424—22no—
17C2×C11×C4⋊C8—22no—
18C11×#419—21no—
19C11×#418—21no—
20C11×#417—22no—
21C11×#416—22no—
22C11×#416—22no—
23C11×#416—22no—
24C2×C11×#103—21no—
25C2×C11×#102—21no—
26C11×#410—22no—
27C11×#410C414yescomplemented
28C2×C11×#99—22no—
29C11×#342—22no—
30C11×#340—22no—
31C11×H(3,ℤ/4)—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×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—
55C22×C8×C11—21no—
56C22×C8×C11—21no—
57C22×C8×C11—21no—
58C22×C8×C11—21no—
59C22×C8×C11—21no—
60C22×C8×C11—21no—
61C22×C8×C11D412yes—
62C22×C8×C11D412yes—
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×#117C2×C412yes—
76C11×#117C2×C412yes—
77C11×#117D412yes—
78C11×#117D412yes—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D412yes—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4D412yes—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C11×C4⋊C8—28no—
92C11×#103—24no—
93C11×#103—24no—
94C11×#102—24no—
95C11×#102—24no—
96C11×#99—28no—
97#11092C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—21no—
99C24×C11C2×D411yescharacteristic
100C11×#41—22no—
101C11×#41—22no—
102C11×#41—22no—
103C11×#41—22no—
104C11×#41—22no—
105C11×#41—22no—
106C11×#41—22no—
107C11×#41—22no—
108C11×#41—41no—
109C11×#41—41no—
110C11×#41—41no—
111C11×#41—41no—
112C11×#41—41no—
113C11×#41—41no—
114C11×#41—41no—
115C11×#41—41no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11C4⋊C412yes—
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—41no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C2×D4×C11—41no—
133C2×D4×C11C4⋊C412yes—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—41no—
140C22×C4×C11—41no—
141C22×C4×C11—41no—
142C22×C4×C11—41no—
143C22×C4×C11—41no—
144C22×C4×C11—41no—
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×Q811yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C11×M16—41no—
160C11×M16—41no—
161C11×M16—41no—
162C11×M16—41no—
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—41no—
170C2×C8×C11—41no—
171C2×C8×C11—41no—
172C2×C8×C11—41no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4—41no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—41no—
186C11×C22⋊C4—41no—
187C11×C22⋊C4—41no—
188C11×C22⋊C4C22⋊C414yes—
189C42×C11—22no—
190C42×C11—22no—
191C42×C11—22no—
192C42×C11—22no—
193C42×C11—41no—
194C42×C11—41no—
195C42×C11—41no—
196C42×C11—41no—
197C2×#424C2×C1111yescharacteristic, complemented
198#2896C2×C1111yescharacteristic
199C2×#416C2×C1111yescharacteristic
200C2×#410C2×C1111yescharacteristic
201#1740C2×C1111yescharacteristic, complemented
202#1735C2×C1111yescharacteristic, complemented
203C2×H(3,ℤ/4)C2×C1111yescharacteristic, complemented
204C23×C11—22no—
205C23×C11—42no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—82no—
209C23×C11C2×C22⋊C411yescharacteristic
210C23×C11#12111yescharacteristic
211C23×C11#12111yescharacteristic
212C23×C11#12111yescharacteristic
213C23×C11#12111yescharacteristic
214C23×C11#12111yescharacteristic
215C23×C11C22⋊Q811yescharacteristic
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—41no—
219Q8×C11—41no—
220D4×C11—22no—
221D4×C11—22no—
222D4×C11—42no—
223D4×C11—42no—
224D4×C11—42no—
225D4×C11—42no—
226D4×C11—41no—
227D4×C11—41no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—44no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—82no—
241C2×C4×C11—82no—
242C2×C4×C11—82no—
243C2×C4×C11C2×C4⋊C411yescharacteristic
244C2×C4×C11#11711yescharacteristic
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C4×D411yescharacteristic
247C2×C4×C11C4×D411yescharacteristic
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11#12011yescharacteristic
250C2×C4×C11#12011yescharacteristic
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11C22⋊Q811yescharacteristic
256C2×C4×C11C22⋊Q811yescharacteristic
257C2×C4×C11C22⋊Q811yescharacteristic
258C2×C4×C11C22⋊Q811yescharacteristic
259C2×C4×C11C22⋊Q811yescharacteristic
260C2×C4×C11#12311yescharacteristic
261C2×C4×C11#12311yescharacteristic
262C2×C4×C11#12311yescharacteristic
263C2×C4×C11#12311yescharacteristic
264C2×C4×C11#12311yescharacteristic
265C2×C4×C11#12411yescharacteristic
266C2×C4×C11#12411yescharacteristic
267C2×C4×C11#12411yescharacteristic
268C2×C4×C11#12611yescharacteristic
269C2×C4×C11#12611yescharacteristic
270C2×C4×C11#12711yescharacteristic
271C8×C11—42no—
272C8×C11—42no—
273C22×#41C22×C1111yescharacteristic
274C22×M16C22×C1111yescharacteristic
275C23×C8C22×C1111yescharacteristic
276C2×#117C22×C1111yescharacteristic
277C2×#117C22×C1111yescharacteristic
278C2×#117C22×C1111yescharacteristic
279C2×#117C22×C1111yescharacteristic
280#424—22no—
281#424—22no—
282C2×C4⋊C8—22no—
283#419—21no—
284#418—21no—
285#417—22no—
286#416—22no—
287#416—22no—
288#416—22no—
289C2×#103—21no—
290C2×#102—21no—
291#410—22no—
292#410C4×C1114yescomplemented
293C2×#99—22no—
294#342—22no—
295#340—22no—
296H(3,ℤ/4)—22no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11—42no—
305C22×C11—82no—
306C22×C11—82no—
307C22×C11—82no—
308C22×C11#38011yescharacteristic
309C22×C11#38611yescharacteristic
310C22×C11#39011yescharacteristic
311C22×C11#39411yescharacteristic
312C22×C11#39411yescharacteristic
313C22×C11#39611yescharacteristic
314C22×C11#39611yescharacteristic
315C4×C11—44no—
316C4×C11—42no—
317C4×C11—82no—
318C4×C11—82no—
319C4×C11—82no—
320C4×C11#38511yescharacteristic
321C4×C11#38511yescharacteristic
322C4×C11#38811yescharacteristic
323C4×C11#38811yescharacteristic
324C4×C11#39211yescharacteristic
325C4×C11#39311yescharacteristic
326C4×C11#39711yescharacteristic
327C4×C11#39911yescharacteristic
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41—21no—
332C2×#41—21no—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41C2×C4×C1112yes—
339C2×#41Q8×C1112yes—
340C22×Q8D4×C1111yescharacteristic
341C22×D4—21no—
342C22×D4D4×C1111yescharacteristic
343C23×C4—21no—
344C23×C4C23×C1111yescharacteristic
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C22×C8—21no—
352C22×C8—21no—
353C22×C8—21no—
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—21no—
357C22×C8D4×C1112yes—
358C22×C8D4×C1112yes—
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#117—21no—
369#117—21no—
370#117—21no—
371#117C2×C4×C1112yes—
372#117C2×C4×C1112yes—
373#117D4×C1112yes—
374#117D4×C1112yes—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4D4×C1112yes—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4D4×C1112yes—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C4⋊C8—28no—
388#103—24no—
389#103—24no—
390#102—24no—
391#102—24no—
392#99—28no—
393C2×C11—21no—
394C2×C11—21no—
395C2×C11—21no—
396C2×C11—21no—
397C2×C11—21no—
398C2×C11—21no—
399C2×C11—82no—
400C2×C11#143911yescharacteristic
401C2×C11#205312yes—
402C24—21no—
403C24C2×D4×C1111yescharacteristic
404#41—22no—
405#41—22no—
406#41—22no—
407#41—22no—
408#41—22no—
409#41—22no—
410#41—22no—
411#41—22no—
412#41—41no—
413#41—41no—
414#41—41no—
415#41—41no—
416#41—41no—
417#41—41no—
418#41—41no—
419#41—41no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8C11×C4⋊C412yes—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4C11×C4⋊C412yes—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4C22×C4×C1111yescharacteristic
450C22×C4C2×D4×C1111yescharacteristic
451C22×C4C2×D4×C1111yescharacteristic
452C22×C4C2×D4×C1111yescharacteristic
453C22×C4C2×D4×C1111yescharacteristic
454C22×C4C2×D4×C1111yescharacteristic
455C22×C4C2×D4×C1111yescharacteristic
456C22×C4C2×Q8×C1111yescharacteristic
457C22×C4C11×#4111yescharacteristic
458C22×C4C11×#4111yescharacteristic
459C22×C4C11×#4111yescharacteristic
460C22×C4C11×#4111yescharacteristic
461C22×C4C11×#4111yescharacteristic
462C22×C4C11×#4111yescharacteristic
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—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4C11×C22⋊C414yes—
493C42—22no—
494C42—22no—
495C42—22no—
496C42—22no—
497C42—41no—
498C42—41no—
499C42—41no—
500C42—41no—
501C11#1109211yescharacteristic, direct product factor, Sylow
502C23—22no—
503C23—42no—
504C23—41no—
505C23—41no—
506C23—82no—
507C23C2×C11×C22⋊C411yescharacteristic
508C23C11×#12111yescharacteristic
509C23C11×#12111yescharacteristic
510C23C11×#12111yescharacteristic
511C23C11×#12111yescharacteristic
512C23C11×#12111yescharacteristic
513C23C11×C22⋊Q811yescharacteristic
514Q8—22no—
515Q8—22no—
516Q8—41no—
517Q8—41no—
518D4—22no—
519D4—22no—
520D4—42no—
521D4—42no—
522D4—42no—
523D4—42no—
524D4—41no—
525D4—41no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—44no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4C2×C11×C4⋊C411yescharacteristic
542C2×C4C11×#11711yescharacteristic
543C2×C4C4×D4×C1111yescharacteristic
544C2×C4C4×D4×C1111yescharacteristic
545C2×C4C4×D4×C1111yescharacteristic
546C2×C4C4×D4×C1111yescharacteristic
547C2×C4C11×#12011yescharacteristic
548C2×C4C11×#12011yescharacteristic
549C2×C4C11×#12011yescharacteristic
550C2×C4C11×#12111yescharacteristic
551C2×C4C11×#12111yescharacteristic
552C2×C4C11×#12111yescharacteristic
553C2×C4C11×C22⋊Q811yescharacteristic
554C2×C4C11×C22⋊Q811yescharacteristic
555C2×C4C11×C22⋊Q811yescharacteristic
556C2×C4C11×C22⋊Q811yescharacteristic
557C2×C4C11×C22⋊Q811yescharacteristic
558C2×C4C11×#12311yescharacteristic
559C2×C4C11×#12311yescharacteristic
560C2×C4C11×#12311yescharacteristic
561C2×C4C11×#12311yescharacteristic
562C2×C4C11×#12311yescharacteristic
563C2×C4C11×#12411yescharacteristic
564C2×C4C11×#12411yescharacteristic
565C2×C4C11×#12411yescharacteristic
566C2×C4C11×#12611yescharacteristic
567C2×C4C11×#12611yescharacteristic
568C2×C4C11×#12711yescharacteristic
569C8—42no—
570C8—42no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—42no—
579C22—82no—
580C22—82no—
581C22—82no—
582C22C11×#38011yescharacteristic
583C22C11×#38611yescharacteristic
584C22C11×#39011yescharacteristic
585C22C11×#39411yescharacteristic
586C22C11×#39411yescharacteristic
587C22C11×#39611yescharacteristic
588C22C11×#39611yescharacteristic
589C4—44no—
590C4—42no—
591C4—82no—
592C4—82no—
593C4—82no—
594C4C11×#38511yescharacteristic
595C4C11×#38511yescharacteristic
596C4C11×#38811yescharacteristic
597C4C11×#38811yescharacteristic
598C4C11×#39211yescharacteristic
599C4C11×#39311yescharacteristic
600C4C11×#39711yescharacteristic
601C4C11×#39911yescharacteristic
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—21no—
608C2—82no—
609C2C11×#143911yescharacteristic
610C2C11×#205312yes—
subgroupG/H
centerC2×C4×C11#124
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC22×C11#394
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×#424C2semidirect
5. C11×#1740C2semidirect
6. C11×#1735C2semidirect
7. C2×C11×H(3,ℤ/4)C2semidirect
27. C11×#410C4semidirect
97. #11092C11direct (N × H)
197. C2×#424C2×C11semidirect
201. #1740C2×C11semidirect
202. #1735C2×C11semidirect
203. C2×H(3,ℤ/4)C2×C11semidirect
292. #410C4×C11semidirect
501. C11#11092direct (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
C11×#28962
C2×C11×#4162
C2×C11×#4102
C11×#17402
C11×#17352
C2×C11×H(3,ℤ/4)2
#1109211