Finite Group Databasebeta

← C11×#10956 #14588149

Subgroups — C11×#10956 #14588149

Order 2816.

918 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#421C211yesmaximal, characteristic
2C11×#2896C211yesmaximal, characteristic
3C2×C11×#408C211yesmaximal, characteristic
4C11×#2873C211yesmaximal, characteristic, complemented
5C2×C11×#344C211yesmaximal, characteristic, complemented
6C2×C11×#341C211yesmaximal, characteristic, complemented
7C11×#1735C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C11×#421—22no—
16C11×#421C414yescomplemented
17C2×C11×#104—22no—
18C11×#419C412yescomplemented
19C11×#418C412yescomplemented
20C11×#417—22no—
21C11×#416—22no—
22C11×#408—22no—
23C11×#408C414yescomplemented
24C2×C11×C22⋊C8—22no—
25C11×#405—22no—
26C11×#405—22no—
27C4×C11×M16—22no—
28C11×#344—22no—
29C11×#341—22no—
30C11×#340—22no—
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×#41C2×C412yes—
42C2×C11×#41C2×C412yes—
43C22×Q8×C11C2×C411yescharacteristic
44C22×D4×C11—21no—
45C22×D4×C11C2×C411yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
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×M16C2×C412yes—
61C2×C11×M16C2×C412yes—
62C2×C11×M16C2×C412yes—
63C2×C11×M16D412yes—
64C2×C11×M16D412yes—
65C2×C11×M16D412yes—
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×C11—21no—
73C22×C8×C11—21no—
74C22×C8×C11C2×C412yes—
75C22×C8×C11D412yes—
76C11×#117—21no—
77C11×#117—21no—
78C11×#117—21no—
79C11×#117—21no—
80C11×#117—21no—
81C11×#117C2×C412yes—
82C11×#117C2×C412yes—
83C11×#117D412yes—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4D412yes—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C11×#104—28no—
91C11×#103—24no—
92C11×#102—24no—
93C11×C22⋊C8—28no—
94C11×#97—24no—
95C4×C8×C11—24no—
96#10956C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11—21no—
98C24×C11#4111yescharacteristic
99C11×#41—22no—
100C11×#41—22no—
101C11×#41—22no—
102C11×#41—22no—
103C11×#41—22no—
104C11×#41—22no—
105C11×#41—22no—
106C11×#41—22no—
107C11×#41—41no—
108C11×#41—41no—
109C11×#41—41no—
110C11×#41—41no—
111C11×#41—41no—
112C11×#41—41no—
113C11×#41—41no—
114C11×#41—41no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11C4212yes—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C2×D4×C11C4212yes—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
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×C11C22×C411yescharacteristic
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
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—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—41no—
166C11×M16—41no—
167C11×M16C22⋊C414yes—
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—22no—
176C2×C8×C11—22no—
177C2×C8×C11—41no—
178C2×C8×C11—41no—
179C2×C8×C11—41no—
180C2×C8×C11—41no—
181C2×C8×C11—41no—
182C2×C8×C11—41no—
183C2×C8×C11C22⋊C414yes—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—41no—
187C11×C4⋊C4C22⋊C414yes—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—41no—
192C42×C11—22no—
193C42×C11—22no—
194C42×C11—22no—
195C42×C11—41no—
196C2×#421C2×C1111yescharacteristic
197#2896C2×C1111yescharacteristic
198C2×#408C2×C1111yescharacteristic
199#2873C2×C1111yescharacteristic, complemented
200C2×#344C2×C1111yescharacteristic, complemented
201C2×#341C2×C1111yescharacteristic, complemented
202#1735C2×C1111yescharacteristic, complemented
203C23×C11—22no—
204C23×C11—42no—
205C23×C11—44no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11#11711yescharacteristic
209C23×C11C4×D411yescharacteristic
210C23×C11C4×D411yescharacteristic
211C23×C11#12111yescharacteristic
212C23×C11#12311yescharacteristic
213C23×C11#12411yescharacteristic
214C23×C11#12611yescharacteristic
215Q8×C11—22no—
216Q8×C11—22no—
217Q8×C11—41no—
218Q8×C11—41no—
219D4×C11—22no—
220D4×C11—22no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—42no—
224D4×C11—42no—
225D4×C11—41no—
226D4×C11—41no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
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×C11C2×C4211yescharacteristic
239C2×C4×C11C2×C22⋊C411yescharacteristic
240C2×C4×C11C2×C22⋊C411yescharacteristic
241C2×C4×C11C2×C22⋊C411yescharacteristic
242C2×C4×C11#11711yescharacteristic
243C2×C4×C11#11711yescharacteristic
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C4×D411yescharacteristic
247C2×C4×C11C4×D411yescharacteristic
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C4×D411yescharacteristic
252C2×C4×C11C4×D411yescharacteristic
253C2×C4×C11C4×D411yescharacteristic
254C2×C4×C11#12011yescharacteristic
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11#12311yescharacteristic
261C2×C4×C11#12311yescharacteristic
262C2×C4×C11#12411yescharacteristic
263C2×C4×C11#12411yescharacteristic
264C2×C4×C11#12611yescharacteristic
265C2×C4×C11#12711yescharacteristic
266C8×C11—24no—
267C8×C11—24no—
268C8×C11—42no—
269C8×C11—42no—
270C22×#41C22×C1111yescharacteristic
271C22×M16C22×C1111yescharacteristic
272C22×M16C22×C1111yescharacteristic
273C22×M16C22×C1111yescharacteristic
274C23×C8C22×C1111yescharacteristic
275C2×#117C22×C1111yescharacteristic
276C2×#117C22×C1111yescharacteristic
277#421—22no—
278#421C4×C1114yescomplemented
279C2×#104—22no—
280#419C4×C1112yescomplemented
281#418C4×C1112yescomplemented
282#417—22no—
283#416—22no—
284#408—22no—
285#408C4×C1114yescomplemented
286C2×C22⋊C8—22no—
287#405—22no—
288#405—22no—
289C4×M16—22no—
290#344—22no—
291#341—22no—
292#340—22no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—41no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—44no—
301C22×C11—42no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11C4×C22⋊C411yescharacteristic
305C22×C11#38611yescharacteristic
306C22×C11#38811yescharacteristic
307C22×C11#38811yescharacteristic
308C22×C11#38811yescharacteristic
309C22×C11#38811yescharacteristic
310C22×C11#39011yescharacteristic
311C4×C11—44no—
312C4×C11—42no—
313C4×C11—82no—
314C4×C11C4×C22⋊C411yescharacteristic
315C4×C11C4×C22⋊C411yescharacteristic
316C4×C11#38611yescharacteristic
317C4×C11#38611yescharacteristic
318C4×C11#38811yescharacteristic
319C4×C11#38811yescharacteristic
320C4×C11#39011yescharacteristic
321C4×C11#39011yescharacteristic
322C2×#41—21no—
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×#41C2×C4×C1112yes—
333C2×#41C2×C4×C1112yes—
334C22×Q8C2×C4×C1111yescharacteristic
335C22×D4—21no—
336C22×D4C2×C4×C1111yescharacteristic
337C23×C4—21no—
338C23×C4C23×C1111yescharacteristic
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×M16C2×C4×C1112yes—
352C2×M16C2×C4×C1112yes—
353C2×M16C2×C4×C1112yes—
354C2×M16D4×C1112yes—
355C2×M16D4×C1112yes—
356C2×M16D4×C1112yes—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8C2×C4×C1112yes—
366C22×C8D4×C1112yes—
367#117—21no—
368#117—21no—
369#117—21no—
370#117—21no—
371#117—21no—
372#117C2×C4×C1112yes—
373#117C2×C4×C1112yes—
374#117D4×C1112yes—
375C2×C4⋊C4—21no—
376C2×C4⋊C4D4×C1112yes—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C42—21no—
380C2×C42—21no—
381#104—28no—
382#103—24no—
383#102—24no—
384C22⋊C8—28no—
385#97—24no—
386C4×C8—24no—
387C2×C11—21no—
388C2×C11—21no—
389C2×C11—21no—
390C2×C11—21no—
391C2×C11—21no—
392C2×C11—21no—
393C2×C11—82no—
394C2×C11#143711yescharacteristic
395C2×C11#188112yes—
396C24—21no—
397C24C11×#4111yescharacteristic
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×Q8C42×C1112yes—
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×D4C42×C1112yes—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4C22×C4×C1111yescharacteristic
442C22×C4C22×C4×C1111yescharacteristic
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×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—22no—
462M16—22no—
463M16—22no—
464M16—41no—
465M16—41no—
466M16C11×C22⋊C414yes—
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—41no—
486C4⋊C4C11×C22⋊C414yes—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—41no—
491C42—22no—
492C42—22no—
493C42—22no—
494C42—41no—
495C11#1095611yescharacteristic, direct product factor, Sylow
496C23—22no—
497C23—42no—
498C23—44no—
499C23—41no—
500C23—41no—
501C23C11×#11711yescharacteristic
502C23C4×D4×C1111yescharacteristic
503C23C4×D4×C1111yescharacteristic
504C23C11×#12111yescharacteristic
505C23C11×#12311yescharacteristic
506C23C11×#12411yescharacteristic
507C23C11×#12611yescharacteristic
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—24no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—82no—
530C2×C4—82no—
531C2×C4C2×C42×C1111yescharacteristic
532C2×C4C2×C11×C22⋊C411yescharacteristic
533C2×C4C2×C11×C22⋊C411yescharacteristic
534C2×C4C2×C11×C22⋊C411yescharacteristic
535C2×C4C11×#11711yescharacteristic
536C2×C4C11×#11711yescharacteristic
537C2×C4C4×D4×C1111yescharacteristic
538C2×C4C4×D4×C1111yescharacteristic
539C2×C4C4×D4×C1111yescharacteristic
540C2×C4C4×D4×C1111yescharacteristic
541C2×C4C4×D4×C1111yescharacteristic
542C2×C4C4×D4×C1111yescharacteristic
543C2×C4C4×D4×C1111yescharacteristic
544C2×C4C4×D4×C1111yescharacteristic
545C2×C4C4×D4×C1111yescharacteristic
546C2×C4C4×D4×C1111yescharacteristic
547C2×C4C11×#12011yescharacteristic
548C2×C4C11×#12111yescharacteristic
549C2×C4C11×#12111yescharacteristic
550C2×C4C11×#12111yescharacteristic
551C2×C4C11×#12111yescharacteristic
552C2×C4C11×#12111yescharacteristic
553C2×C4C11×#12311yescharacteristic
554C2×C4C11×#12311yescharacteristic
555C2×C4C11×#12411yescharacteristic
556C2×C4C11×#12411yescharacteristic
557C2×C4C11×#12611yescharacteristic
558C2×C4C11×#12711yescharacteristic
559C8—24no—
560C8—24no—
561C8—42no—
562C8—42no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—44no—
571C22—42no—
572C22—82no—
573C22—82no—
574C22C4×C11×C22⋊C411yescharacteristic
575C22C11×#38611yescharacteristic
576C22C11×#38811yescharacteristic
577C22C11×#38811yescharacteristic
578C22C11×#38811yescharacteristic
579C22C11×#38811yescharacteristic
580C22C11×#39011yescharacteristic
581C4—44no—
582C4—42no—
583C4—82no—
584C4C4×C11×C22⋊C411yescharacteristic
585C4C4×C11×C22⋊C411yescharacteristic
586C4C11×#38611yescharacteristic
587C4C11×#38611yescharacteristic
588C4C11×#38811yescharacteristic
589C4C11×#38811yescharacteristic
590C4C11×#39011yescharacteristic
591C4C11×#39011yescharacteristic
592C2—21no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—82no—
599C2C11×#143711yescharacteristic
600C2C11×#188112yes—
subgroupG/H
centerC2×C4×C11#120
commutatorC2×C4C2×C42×C11
Frattini, cosocleC23×C4C23×C11
socleC22×C11#386
prime radicalC22×C11×#41C22
LCSG ▷ C2×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×#2873C2semidirect
5. C2×C11×#344C2semidirect
6. C2×C11×#341C2semidirect
7. C11×#1735C2semidirect
16. C11×#421C4semidirect
18. C11×#419C4semidirect
19. C11×#418C4semidirect
23. C11×#408C4semidirect
96. #10956C11direct (N × H)
199. #2873C2×C11semidirect
200. C2×#344C2×C11semidirect
201. C2×#341C2×C11semidirect
202. #1735C2×C11semidirect
278. #421C4×C11semidirect
280. #419C4×C11semidirect
281. #418C4×C11semidirect
285. #408C4×C11semidirect
495. C11#10956direct (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
C2×C11×#4082
C11×#28732
C2×C11×#3442
C2×C11×#3412
C11×#17352
#1095611