Finite Group Databasebeta

← C11×#10934 #14588127

Subgroups — C11×#10934 #14588127

Order 2816.

982 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#104C211yesmaximal, characteristic
2C2×C11×#416C211yesmaximal, characteristic
3C2×C11×#408C211yesmaximal, characteristic
4C2×C11×#405C211yesmaximal, characteristic, complemented
5C2×C11×#341C211yesmaximal, characteristic, complemented
6C2×C11×#339C211yesmaximal, characteristic, complemented
7C2×C11×#336C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C2×C11×#104—22no—
16C2×C11×#104—22no—
17C2×C11×#104C414yescomplemented
18C11×#416—22no—
19C11×#416—22no—
20C2×C11×#103C412yescomplemented
21C2×C11×#102C412yescomplemented
22C11×#408—22no—
23C11×#408C414yescomplemented
24C2×C11×C22⋊C8—21no—
25C2×C11×C22⋊C8—21no—
26C11×#405—22no—
27C11×#405—22no—
28C2×C11×#97—21no—
29C2×C4×C8×C11—21no—
30C11×#341—22no—
31C11×#339—22no—
32C11×#336—22no—
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×#41—21no—
43C2×C11×#41C2×C412yes—
44C2×C11×#41C2×C412yes—
45C22×Q8×C11C2×C411yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11C2×C411yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
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×M16C2×C412yes—
60C2×C11×M16C2×C412yes—
61C2×C11×M16D412yes—
62C2×C11×M16D412yes—
63C22×C8×C11—21no—
64C22×C8×C11—21no—
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×C11—21no—
73C22×C8×C11—21no—
74C22×C8×C11—21no—
75C22×C8×C11C2×C412yes—
76C22×C8×C11C2×C412yes—
77C22×C8×C11D412yes—
78C22×C8×C11D411yescharacteristic
79C22×C8×C11D411yescharacteristic
80C11×#117—21no—
81C11×#117—21no—
82C11×#117D412yes—
83C11×#117D412yes—
84C2×C11×C4⋊C4C2×C412yes—
85C2×C11×C22⋊C4—21no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11—21no—
92C2×C42×C11C2×C412yes—
93C11×#104—28no—
94C11×#103—24no—
95C11×#102—24no—
96C11×C22⋊C8—24no—
97C11×C22⋊C8—24no—
98C11×#97—24no—
99C4×C8×C11—24no—
100#10934C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11—21no—
102C24×C11#4111yescharacteristic
103C11×#41—22no—
104C11×#41—22no—
105C11×#41—22no—
106C11×#41—22no—
107C11×#41—22no—
108C11×#41—22no—
109C11×#41—22no—
110C11×#41—22no—
111C11×#41—41no—
112C11×#41—41no—
113C11×#41—41no—
114C11×#41—41no—
115C11×#41—41no—
116C11×#41—41no—
117C11×#41—41no—
118C11×#41—41no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11C4212yes—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—41no—
133C2×D4×C11—41no—
134C2×D4×C11—41no—
135C2×D4×C11—41no—
136C2×D4×C11C4212yes—
137C22×C4×C11—24no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—42no—
144C22×C4×C11—41no—
145C22×C4×C11—41no—
146C22×C4×C11—41no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C22×C4×C11#4111yescharacteristic
161C22×C4×C11#4111yescharacteristic
162C22×C4×C11#4111yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C11×M16—22no—
165C11×M16—22no—
166C11×M16—22no—
167C11×M16—22no—
168C11×M16—22no—
169C11×M16—41no—
170C11×M16—41no—
171C11×M16C22⋊C414yes—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—21no—
180C2×C8×C11—22no—
181C2×C8×C11—21no—
182C2×C8×C11—22no—
183C2×C8×C11—22no—
184C2×C8×C11—22no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—41no—
188C2×C8×C11—41no—
189C2×C8×C11—41no—
190C2×C8×C11—41no—
191C2×C8×C11—41no—
192C2×C8×C11—41no—
193C2×C8×C11C22⋊C412yes—
194C2×C8×C11C22⋊C412yes—
195C11×C4⋊C4—22no—
196C11×C4⋊C4C22⋊C414yes—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C42×C11—22no—
200C42×C11—22no—
201C42×C11—22no—
202C42×C11—22no—
203C42×C11—41no—
204C42×C11—41no—
205C22×#104C2×C1111yescharacteristic
206C2×#416C2×C1111yescharacteristic
207C2×#408C2×C1111yescharacteristic
208C2×#405C2×C1111yescharacteristic, complemented
209C2×#341C2×C1111yescharacteristic, complemented
210C2×#339C2×C1111yescharacteristic, complemented
211C2×#336C2×C1111yescharacteristic, complemented
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11#11711yescharacteristic
220C23×C11C4×D411yescharacteristic
221C23×C11C4×D411yescharacteristic
222C23×C11#12111yescharacteristic
223C23×C11#12311yescharacteristic
224C23×C11#12411yescharacteristic
225C23×C11#12611yescharacteristic
226Q8×C11—22no—
227Q8×C11—22no—
228Q8×C11—41no—
229Q8×C11—41no—
230D4×C11—22no—
231D4×C11—22no—
232D4×C11—42no—
233D4×C11—42no—
234D4×C11—42no—
235D4×C11—42no—
236D4×C11—41no—
237D4×C11—41no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—44no—
242C2×C4×C11—44no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11C2×C4211yescharacteristic
254C2×C4×C11C2×C22⋊C411yescharacteristic
255C2×C4×C11C2×C22⋊C411yescharacteristic
256C2×C4×C11C2×C22⋊C411yescharacteristic
257C2×C4×C11#11711yescharacteristic
258C2×C4×C11#11711yescharacteristic
259C2×C4×C11C4×D411yescharacteristic
260C2×C4×C11C4×D411yescharacteristic
261C2×C4×C11C4×D411yescharacteristic
262C2×C4×C11C4×D411yescharacteristic
263C2×C4×C11C4×D411yescharacteristic
264C2×C4×C11C4×D411yescharacteristic
265C2×C4×C11C4×D411yescharacteristic
266C2×C4×C11C4×D411yescharacteristic
267C2×C4×C11C4×D411yescharacteristic
268C2×C4×C11C4×D411yescharacteristic
269C2×C4×C11#12011yescharacteristic
270C2×C4×C11#12111yescharacteristic
271C2×C4×C11#12111yescharacteristic
272C2×C4×C11#12111yescharacteristic
273C2×C4×C11#12111yescharacteristic
274C2×C4×C11#12111yescharacteristic
275C2×C4×C11#12311yescharacteristic
276C2×C4×C11#12311yescharacteristic
277C2×C4×C11#12411yescharacteristic
278C2×C4×C11#12411yescharacteristic
279C2×C4×C11#12611yescharacteristic
280C2×C4×C11#12711yescharacteristic
281C8×C11—22no—
282C8×C11—22no—
283C8×C11—24no—
284C8×C11—42no—
285C8×C11—42no—
286C22×#41C22×C1111yescharacteristic
287C22×M16C22×C1111yescharacteristic
288C22×M16C22×C1111yescharacteristic
289C23×C8C22×C1111yescharacteristic
290C23×C8C22×C1111yescharacteristic
291C2×#117C22×C1111yescharacteristic
292C22×C42C22×C1111yescharacteristic
293C2×#104—22no—
294C2×#104—22no—
295C2×#104C4×C1114yescomplemented
296#416—22no—
297#416—22no—
298C2×#103C4×C1112yescomplemented
299C2×#102C4×C1112yescomplemented
300#408—22no—
301#408C4×C1114yescomplemented
302C2×C22⋊C8—21no—
303C2×C22⋊C8—21no—
304#405—22no—
305#405—22no—
306C2×#97—21no—
307C2×C4×C8—21no—
308#341—22no—
309#339—22no—
310#336—22no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—21no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—82no—
323C22×C11—82no—
324C22×C11C4×C22⋊C411yescharacteristic
325C22×C11#38611yescharacteristic
326C22×C11#38811yescharacteristic
327C22×C11#38811yescharacteristic
328C22×C11#38811yescharacteristic
329C22×C11#38811yescharacteristic
330C22×C11#39011yescharacteristic
331C22×C11#44312yes—
332C22×C11#44412yes—
333C4×C11—44no—
334C4×C11—44no—
335C4×C11—42no—
336C4×C11C4×C22⋊C411yescharacteristic
337C4×C11C4×C22⋊C411yescharacteristic
338C4×C11#38611yescharacteristic
339C4×C11#38611yescharacteristic
340C4×C11#38811yescharacteristic
341C4×C11#38811yescharacteristic
342C4×C11#39011yescharacteristic
343C4×C11#39011yescharacteristic
344C2×#41—21no—
345C2×#41—21no—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41—21no—
350C2×#41—21no—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41—21no—
354C2×#41C2×C4×C1112yes—
355C2×#41C2×C4×C1112yes—
356C22×Q8C2×C4×C1111yescharacteristic
357C22×D4—21no—
358C22×D4C2×C4×C1111yescharacteristic
359C23×C4—21no—
360C23×C4—21no—
361C23×C4C23×C1111yescharacteristic
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16C2×C4×C1112yes—
371C2×M16C2×C4×C1112yes—
372C2×M16D4×C1112yes—
373C2×M16D4×C1112yes—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—21no—
382C22×C8—21no—
383C22×C8—21no—
384C22×C8—21no—
385C22×C8—21no—
386C22×C8C2×C4×C1112yes—
387C22×C8C2×C4×C1112yes—
388C22×C8D4×C1112yes—
389C22×C8D4×C1111yescharacteristic
390C22×C8D4×C1111yescharacteristic
391#117—21no—
392#117—21no—
393#117D4×C1112yes—
394#117D4×C1112yes—
395C2×C4⋊C4C2×C4×C1112yes—
396C2×C22⋊C4—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42C2×C4×C1112yes—
404#104—28no—
405#103—24no—
406#102—24no—
407C22⋊C8—24no—
408C22⋊C8—24no—
409#97—24no—
410C4×C8—24no—
411C2×C11—21no—
412C2×C11—21no—
413C2×C11—21no—
414C2×C11—21no—
415C2×C11—82no—
416C2×C11#143711yescharacteristic
417C2×C11#176411yescharacteristic
418C2×C11#176511yescharacteristic
419C2×C11#187612yes—
420C2×C11#192912yes—
421C24—21no—
422C24C11×#4111yescharacteristic
423#41—22no—
424#41—22no—
425#41—22no—
426#41—22no—
427#41—22no—
428#41—22no—
429#41—22no—
430#41—22no—
431#41—41no—
432#41—41no—
433#41—41no—
434#41—41no—
435#41—41no—
436#41—41no—
437#41—41no—
438#41—41no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8C42×C1112yes—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4C42×C1112yes—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—42no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4C22×C4×C1111yescharacteristic
471C22×C4C22×C4×C1111yescharacteristic
472C22×C4C22×C4×C1111yescharacteristic
473C22×C4C2×D4×C1111yescharacteristic
474C22×C4C2×D4×C1111yescharacteristic
475C22×C4C2×D4×C1111yescharacteristic
476C22×C4C2×D4×C1111yescharacteristic
477C22×C4C2×D4×C1111yescharacteristic
478C22×C4C2×D4×C1111yescharacteristic
479C22×C4C11×#4111yescharacteristic
480C22×C4C11×#4111yescharacteristic
481C22×C4C11×#4111yescharacteristic
482C22×C4C11×#4111yescharacteristic
483C22×C4C11×#4111yescharacteristic
484M16—22no—
485M16—22no—
486M16—22no—
487M16—22no—
488M16—22no—
489M16—41no—
490M16—41no—
491M16C11×C22⋊C414yes—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—21no—
496C2×C8—22no—
497C2×C8—21no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8C11×C22⋊C412yes—
514C2×C8C11×C22⋊C412yes—
515C4⋊C4—22no—
516C4⋊C4C11×C22⋊C414yes—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C42—22no—
520C42—22no—
521C42—22no—
522C42—22no—
523C42—41no—
524C42—41no—
525C11#1093411yescharacteristic, direct product factor, Sylow
526C23—22no—
527C23—22no—
528C23—22no—
529C23—41no—
530C23—41no—
531C23—42no—
532C23—42no—
533C23C11×#11711yescharacteristic
534C23C4×D4×C1111yescharacteristic
535C23C4×D4×C1111yescharacteristic
536C23C11×#12111yescharacteristic
537C23C11×#12311yescharacteristic
538C23C11×#12411yescharacteristic
539C23C11×#12611yescharacteristic
540Q8—22no—
541Q8—22no—
542Q8—41no—
543Q8—41no—
544D4—22no—
545D4—22no—
546D4—42no—
547D4—42no—
548D4—42no—
549D4—42no—
550D4—41no—
551D4—41no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4C2×C42×C1111yescharacteristic
568C2×C4C2×C11×C22⋊C411yescharacteristic
569C2×C4C2×C11×C22⋊C411yescharacteristic
570C2×C4C2×C11×C22⋊C411yescharacteristic
571C2×C4C11×#11711yescharacteristic
572C2×C4C11×#11711yescharacteristic
573C2×C4C4×D4×C1111yescharacteristic
574C2×C4C4×D4×C1111yescharacteristic
575C2×C4C4×D4×C1111yescharacteristic
576C2×C4C4×D4×C1111yescharacteristic
577C2×C4C4×D4×C1111yescharacteristic
578C2×C4C4×D4×C1111yescharacteristic
579C2×C4C4×D4×C1111yescharacteristic
580C2×C4C4×D4×C1111yescharacteristic
581C2×C4C4×D4×C1111yescharacteristic
582C2×C4C4×D4×C1111yescharacteristic
583C2×C4C11×#12011yescharacteristic
584C2×C4C11×#12111yescharacteristic
585C2×C4C11×#12111yescharacteristic
586C2×C4C11×#12111yescharacteristic
587C2×C4C11×#12111yescharacteristic
588C2×C4C11×#12111yescharacteristic
589C2×C4C11×#12311yescharacteristic
590C2×C4C11×#12311yescharacteristic
591C2×C4C11×#12411yescharacteristic
592C2×C4C11×#12411yescharacteristic
593C2×C4C11×#12611yescharacteristic
594C2×C4C11×#12711yescharacteristic
595C8—22no—
596C8—22no—
597C8—24no—
598C8—42no—
599C8—42no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—82no—
612C22—82no—
613C22C4×C11×C22⋊C411yescharacteristic
614C22C11×#38611yescharacteristic
615C22C11×#38811yescharacteristic
616C22C11×#38811yescharacteristic
617C22C11×#38811yescharacteristic
618C22C11×#38811yescharacteristic
619C22C11×#39011yescharacteristic
620C22C11×#44312yes—
621C22C11×#44412yes—
622C4—44no—
623C4—44no—
624C4—42no—
625C4C4×C11×C22⋊C411yescharacteristic
626C4C4×C11×C22⋊C411yescharacteristic
627C4C11×#38611yescharacteristic
628C4C11×#38611yescharacteristic
629C4C11×#38811yescharacteristic
630C4C11×#38811yescharacteristic
631C4C11×#39011yescharacteristic
632C4C11×#39011yescharacteristic
633C2—21no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—82no—
638C2C11×#143711yescharacteristic
639C2C11×#176411yescharacteristic
640C2C11×#176511yescharacteristic
641C2C11×#187612yes—
642C2C11×#192912yes—
subgroupG/H
centerC22×C4×C11C2×D4
commutatorC2×C4C2×C42×C11
Frattini, cosocleC23×C4C23×C11
socleC23×C11C4×D4
prime radicalC22×C11×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ C23×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C11×#405C2semidirect
5. C2×C11×#341C2semidirect
6. C2×C11×#339C2semidirect
7. C2×C11×#336C2semidirect
17. C2×C11×#104C4semidirect
20. C2×C11×#103C4semidirect
21. C2×C11×#102C4semidirect
23. C11×#408C4semidirect
100. #10934C11direct (N × H)
208. C2×#405C2×C11semidirect
209. C2×#341C2×C11semidirect
210. C2×#339C2×C11semidirect
211. C2×#336C2×C11semidirect
295. C2×#104C4×C11semidirect
298. C2×#103C4×C11semidirect
299. C2×#102C4×C11semidirect
301. #408C4×C11semidirect
525. C11#10934direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1042
C2×C11×#4162
C2×C11×#4082
C2×C11×#4052
C2×C11×#3412
C2×C11×#3392
C2×C11×#3362
#1093411