Finite Group Databasebeta

← C11×#18964 #14596157

Subgroups — C11×#18964 #14596157

Order 2816.

900 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3554C211yesmaximal, characteristic, complemented
2C11×#3254C211yesmaximal, characteristic, complemented
3C11×#3247C211yesmaximal, characteristic, complemented
4C11×#3207C211yesmaximal, characteristic, complemented
5C11×#1637C211yesmaximal, characteristic, complemented
6C11×#1636C211yesmaximal, characteristic, complemented
7C11×#1631C211yesmaximal, characteristic, complemented
8C11×#1630C211yesmaximal, characteristic, complemented
9C11×#1627C211yesmaximal, characteristic, complemented
10C11×#1626C211yesmaximal, characteristic, complemented
11C11×#1621C211yesmaximal, characteristic, complemented
12C11×#1620C211yesmaximal, characteristic, complemented
13C11×#1547C211yesmaximal, characteristic, complemented
14C11×#1495C211yesmaximal, characteristic, complemented
15C11×#1481C211yesmaximal, characteristic, complemented
16C11×#562—22no—
17C11×#559—21no—
18C11×#559C2211yescharacteristic
19C11×#557C2211yescharacteristic
20C11×#554—21no—
21C11×#550C2211yescharacteristic
22D4×Q8×C11C2211yescharacteristic
23C11×#548—21no—
24C11×#547—21no—
25C11×#542—21no—
26C11×#542—21no—
27C11×#540—21no—
28C11×#539—22no—
29C11×#536—21no—
30C11×#533C2211yescharacteristic
31C11×#532C2211yescharacteristic
32C11×#532C2211yescharacteristic
33C11×#529C2211yescharacteristic
34C11×#493C2211yescharacteristic
35C11×#492C2211yescharacteristic
36C11×#487C2211yescharacteristic
37C11×#486C2211yescharacteristic
38C11×#478—21no—
39C11×#477C2211yescharacteristic
40C11×#477C2211yescharacteristic
41C11×#477C2211yescharacteristic
42C11×#476C2211yescharacteristic
43C11×#474—21no—
44C11×#468—21no—
45C11×#468—21no—
46C11×#466—21no—
47C11×#465—21no—
48C11×#463—21no—
49C11×#463—22no—
50C11×#461—21no—
51C11×#460C2211yescharacteristic
52C11×#460C2211yescharacteristic
53C11×#460C2211yescharacteristic
54C11×#459C2211yescharacteristic
55C11×#449—22no—
56C11×#431C2211yescharacteristic
57C11×#423C2211yescharacteristic
58C2×C11×C4⋊C8C2211yescharacteristic
59C11×#332C2211yescharacteristic
60C11×#332C2211yescharacteristic
61C11×#331C2211yescharacteristic
62C11×#331C2211yescharacteristic
63C11×Q8⋊C8C2211yescharacteristic
64C11×Q8⋊C8C2211yescharacteristic
65C11×Q8⋊C8C2211yescharacteristic
66C11×Q8⋊C8C2211yescharacteristic
67C11×Q8⋊C8C2211yescharacteristic
68C11×Q8⋊C8C2211yescharacteristic
69C11×D4⋊C8C2211yescharacteristic
70C11×D4⋊C8C2211yescharacteristic
71C2×C11×#41—21no—
72C2×C11×#41—21no—
73C2×C11×#41—21no—
74C22×Q8×C11—21no—
75C2×C11×SD16—21no—
76C2×C11×SD16—21no—
77C2×C11×SD16—21no—
78C2×C11×SD16—22no—
79C2×C11×D8—22no—
80C2×C11×D8—21no—
81C2×C11×M16—21no—
82C22×C8×C11—21no—
83C11×C4⋊Q8—21no—
84C11×C4⋊Q8—21no—
85C11×C4⋊Q8D411yescharacteristic
86C11×C4⋊Q8D411yescharacteristic
87C11×C4⋊Q8C2311yescharacteristic
88C11×C4⋊Q8C2311yescharacteristic
89C11×#127—21no—
90C11×#127C2311yescharacteristic
91C11×#127C2311yescharacteristic
92C11×#126—22no—
93C11×#126—21no—
94C11×#125—22no—
95C11×#125—21no—
96C11×#125—21no—
97C11×#125D411yescharacteristic
98C11×#124—22no—
99C11×#124—22no—
100C11×#124—21no—
101C11×#124—21no—
102C11×#124—21no—
103C11×#124—21no—
104C11×#124D411yescharacteristic
105C11×#123—22no—
106C11×#123—22no—
107C11×#123—22no—
108C11×#123—22no—
109C11×#123—22no—
110C11×#123—22no—
111C11×#123—21no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8—22no—
116C11×C22⋊Q8—21no—
117C11×C22⋊Q8—22no—
118C11×C22⋊Q8—21no—
119C11×C22⋊Q8D411yescharacteristic
120C11×C22⋊Q8D411yescharacteristic
121C11×C22⋊Q8D411yescharacteristic
122C11×#121—22no—
123C11×#121—22no—
124C11×#121—22no—
125C11×#121—21no—
126C11×#121—21no—
127C11×#121—21no—
128C11×#121—21no—
129C11×#121D411yescharacteristic
130C11×#121D412yes—
131C4×Q8×C11—21no—
132C4×Q8×C11—21no—
133C4×Q8×C11—21no—
134C4×Q8×C11C2311yescharacteristic
135C4×Q8×C11C2311yescharacteristic
136C4×Q8×C11C2311yescharacteristic
137C4×D4×C11—22no—
138C4×D4×C11—21no—
139C4×D4×C11—21no—
140C4×D4×C11—21no—
141C4×D4×C11—21no—
142C4×D4×C11—21no—
143C4×D4×C11—21no—
144C4×D4×C11—21no—
145C4×D4×C11—21no—
146C4×D4×C11D412yes—
147C4×D4×C11C2311yescharacteristic
148C11×#117—21no—
149C11×#117—21no—
150C2×C11×C4⋊C4—22no—
151C2×C42×C11C2311yescharacteristic
152C11×#107—21no—
153C11×#107—21no—
154C11×#107—21no—
155C11×#106—21no—
156C11×C4⋊C8—21no—
157C11×C4⋊C8—21no—
158C11×C4⋊C8—21no—
159C11×C4⋊C8C2311yescharacteristic
160C11×C4⋊C8C2311yescharacteristic
161C11×C4⋊C8C2311yescharacteristic
162C11×C4⋊C8C2311yescharacteristic
163C11×#103—21no—
164C11×#103—21no—
165C11×#103—21no—
166C11×#103—22no—
167C11×#102—21no—
168C11×#102—22no—
169C11×#102—21no—
170C11×#102—21no—
171C11×#102—21no—
172C11×#102—21no—
173C11×C22⋊C8—21no—
174C4×C8×C11C2311yescharacteristic
175C4×C8×C11C2311yescharacteristic
176#18964C1111yesmaximal, characteristic, direct product factor, Sylow
177C11×#41—81no—
178C11×#41—81no—
179C11×#41—81no—
180C11×#41—81no—
181C11×#41—82no—
182C2×Q8×C11—22no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—81no—
187C2×Q8×C11—81no—
188C2×Q8×C11C2×D411yescharacteristic
189C2×Q8×C11C2×D411yescharacteristic
190C2×Q8×C11C2×D411yescharacteristic
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11—21no—
194C2×D4×C11—22no—
195C2×D4×C11—21no—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—41no—
201C2×D4×C11C2×D411yescharacteristic
202C2×D4×C11C2×D412yes—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—21no—
207C22×C4×C11—22no—
208C22×C4×C11—41no—
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C11×SD16—81no—
213C11×SD16—81no—
214C11×SD16—81no—
215C11×SD16—82no—
216C11×D8—81no—
217C11×D8—82no—
218C11×M16—81no—
219C2×C8×C11—21no—
220C2×C8×C11—21no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—81no—
226C11×C4⋊C4—22no—
227C11×C4⋊C4—22no—
228C11×C4⋊C4—22no—
229C11×C4⋊C4—22no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4C2×D412yes—
245C11×C4⋊C4C2×D411yescharacteristic
246C11×C4⋊C4C2×D411yescharacteristic
247C11×C4⋊C4C2×D411yescharacteristic
248C11×C4⋊C4C2×D411yescharacteristic
249C11×C22⋊C4—22no—
250C11×C22⋊C4—22no—
251C11×C22⋊C4—22no—
252C11×C22⋊C4—22no—
253C11×C22⋊C4—22no—
254C11×C22⋊C4—21no—
255C11×C22⋊C4—21no—
256C11×C22⋊C4—21no—
257C11×C22⋊C4—21no—
258C11×C22⋊C4—21no—
259C11×C22⋊C4—21no—
260C11×C22⋊C4—22no—
261C11×C22⋊C4—22no—
262C11×C22⋊C4—21no—
263C11×C22⋊C4—41no—
264C11×C22⋊C4—41no—
265C42×C11—22no—
266C42×C11—21no—
267C42×C11—21no—
268C42×C11—21no—
269C42×C11C2×D411yescharacteristic
270C42×C11C2×D411yescharacteristic
271C42×C11C2×D411yescharacteristic
272C42×C11C2411yescharacteristic
273#3554C2×C1111yescharacteristic, complemented
274#3254C2×C1111yescharacteristic, complemented
275#3247C2×C1111yescharacteristic, complemented
276#3207C2×C1111yescharacteristic, complemented
277#1637C2×C1111yescharacteristic, complemented
278#1636C2×C1111yescharacteristic, complemented
279#1631C2×C1111yescharacteristic, complemented
280#1630C2×C1111yescharacteristic, complemented
281#1627C2×C1111yescharacteristic, complemented
282#1626C2×C1111yescharacteristic, complemented
283#1621C2×C1111yescharacteristic, complemented
284#1620C2×C1111yescharacteristic, complemented
285#1547C2×C1111yescharacteristic, complemented
286#1495C2×C1111yescharacteristic, complemented
287#1481C2×C1111yescharacteristic, complemented
288C23×C11—21no—
289C23×C11—22no—
290C23×C11—41no—
291C23×C11#12011yescharacteristic
292Q8×C11—21no—
293Q8×C11—21no—
294Q8×C11—21no—
295Q8×C11—21no—
296Q8×C11—21no—
297Q8×C11—21no—
298Q8×C11—42no—
299Q8×C11—41no—
300Q8×C11—41no—
301Q8×C11—81no—
302Q8×C11—82no—
303D4×C11—21no—
304D4×C11—21no—
305D4×C11—42no—
306D4×C11—42no—
307D4×C11—41no—
308D4×C11—41no—
309D4×C11—41no—
310D4×C11—41no—
311D4×C11—41no—
312D4×C11—41no—
313D4×C11—41no—
314D4×C11—41no—
315D4×C11—81no—
316D4×C11—82no—
317D4×C11—82no—
318D4×C11—82no—
319D4×C11—82no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—22no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—82no—
337C2×C4×C11—82no—
338C2×C4×C11—82no—
339C2×C4×C11—82no—
340C2×C4×C11—82no—
341C2×C4×C11#12011yescharacteristic
342C2×C4×C11#12011yescharacteristic
343C2×C4×C11#12011yescharacteristic
344C2×C4×C11C22×D411yescharacteristic
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C22×D411yescharacteristic
347C8×C11—41no—
348C8×C11—41no—
349C8×C11—41no—
350C8×C11—41no—
351C8×C11—41no—
352C8×C11—41no—
353#562—22no—
354#559—21no—
355#559C22×C1111yescharacteristic
356#557C22×C1111yescharacteristic
357#554—21no—
358#550C22×C1111yescharacteristic
359D4×Q8C22×C1111yescharacteristic
360#548—21no—
361#547—21no—
362#542—21no—
363#542—21no—
364#540—21no—
365#539—22no—
366#536—21no—
367#533C22×C1111yescharacteristic
368#532C22×C1111yescharacteristic
369#532C22×C1111yescharacteristic
370#529C22×C1111yescharacteristic
371#493C22×C1111yescharacteristic
372#492C22×C1111yescharacteristic
373#487C22×C1111yescharacteristic
374#486C22×C1111yescharacteristic
375#478—21no—
376#477C22×C1111yescharacteristic
377#477C22×C1111yescharacteristic
378#477C22×C1111yescharacteristic
379#476C22×C1111yescharacteristic
380#474—21no—
381#468—21no—
382#468—21no—
383#466—21no—
384#465—21no—
385#463—21no—
386#463—22no—
387#461—21no—
388#460C22×C1111yescharacteristic
389#460C22×C1111yescharacteristic
390#460C22×C1111yescharacteristic
391#459C22×C1111yescharacteristic
392#449—22no—
393#431C22×C1111yescharacteristic
394#423C22×C1111yescharacteristic
395C2×C4⋊C8C22×C1111yescharacteristic
396#332C22×C1111yescharacteristic
397#332C22×C1111yescharacteristic
398#331C22×C1111yescharacteristic
399#331C22×C1111yescharacteristic
400Q8⋊C8C22×C1111yescharacteristic
401Q8⋊C8C22×C1111yescharacteristic
402Q8⋊C8C22×C1111yescharacteristic
403Q8⋊C8C22×C1111yescharacteristic
404Q8⋊C8C22×C1111yescharacteristic
405Q8⋊C8C22×C1111yescharacteristic
406D4⋊C8C22×C1111yescharacteristic
407D4⋊C8C22×C1111yescharacteristic
408C22×C11—21no—
409C22×C11—21no—
410C22×C11—21no—
411C22×C11—41no—
412C22×C11—42no—
413C22×C11—41no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—41no—
417C22×C11—81no—
418C22×C11—81no—
419C22×C11—81no—
420C22×C11C2×#12011yescharacteristic
421C4×C11—21no—
422C4×C11—21no—
423C4×C11—21no—
424C4×C11—21no—
425C4×C11—41no—
426C4×C11—41no—
427C4×C11—42no—
428C4×C11—41no—
429C4×C11—41no—
430C4×C11—41no—
431C4×C11—41no—
432C4×C11—41no—
433C4×C11—81no—
434C4×C11#57611yescharacteristic
435C4×C11#57711yescharacteristic
436C4×C11#57711yescharacteristic
437C4×C11#57811yescharacteristic
438C2×#41—21no—
439C2×#41—21no—
440C2×#41—21no—
441C22×Q8—21no—
442C2×SD16—21no—
443C2×SD16—21no—
444C2×SD16—21no—
445C2×SD16—22no—
446C2×D8—22no—
447C2×D8—21no—
448C2×M16—21no—
449C22×C8—21no—
450C4⋊Q8—21no—
451C4⋊Q8—21no—
452C4⋊Q8D4×C1111yescharacteristic
453C4⋊Q8D4×C1111yescharacteristic
454C4⋊Q8C23×C1111yescharacteristic
455C4⋊Q8C23×C1111yescharacteristic
456#127—21no—
457#127C23×C1111yescharacteristic
458#127C23×C1111yescharacteristic
459#126—22no—
460#126—21no—
461#125—22no—
462#125—21no—
463#125—21no—
464#125D4×C1111yescharacteristic
465#124—22no—
466#124—22no—
467#124—21no—
468#124—21no—
469#124—21no—
470#124—21no—
471#124D4×C1111yescharacteristic
472#123—22no—
473#123—22no—
474#123—22no—
475#123—22no—
476#123—22no—
477#123—22no—
478#123—21no—
479C22⋊Q8—22no—
480C22⋊Q8—22no—
481C22⋊Q8—22no—
482C22⋊Q8—22no—
483C22⋊Q8—21no—
484C22⋊Q8—22no—
485C22⋊Q8—21no—
486C22⋊Q8D4×C1111yescharacteristic
487C22⋊Q8D4×C1111yescharacteristic
488C22⋊Q8D4×C1111yescharacteristic
489#121—22no—
490#121—22no—
491#121—22no—
492#121—21no—
493#121—21no—
494#121—21no—
495#121—21no—
496#121D4×C1111yescharacteristic
497#121D4×C1112yes—
498C4×Q8—21no—
499C4×Q8—21no—
500C4×Q8—21no—
501C4×Q8C23×C1111yescharacteristic
502C4×Q8C23×C1111yescharacteristic
503C4×Q8C23×C1111yescharacteristic
504C4×D4—22no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—21no—
513C4×D4D4×C1112yes—
514C4×D4C23×C1111yescharacteristic
515#117—21no—
516#117—21no—
517C2×C4⋊C4—22no—
518C2×C42C23×C1111yescharacteristic
519#107—21no—
520#107—21no—
521#107—21no—
522#106—21no—
523C4⋊C8—21no—
524C4⋊C8—21no—
525C4⋊C8—21no—
526C4⋊C8C23×C1111yescharacteristic
527C4⋊C8C23×C1111yescharacteristic
528C4⋊C8C23×C1111yescharacteristic
529C4⋊C8C23×C1111yescharacteristic
530#103—21no—
531#103—21no—
532#103—21no—
533#103—22no—
534#102—21no—
535#102—22no—
536#102—21no—
537#102—21no—
538#102—21no—
539#102—21no—
540C22⋊C8—21no—
541C4×C8C23×C1111yescharacteristic
542C4×C8C23×C1111yescharacteristic
543C2×C11—41no—
544C2×C11—81no—
545C2×C11—82no—
546C2×C11—161no—
547C2×C11#301211yescharacteristic
548C2×C11#301311yescharacteristic
549C2×C11#302111yescharacteristic
550#41—81no—
551#41—81no—
552#41—81no—
553#41—81no—
554#41—82no—
555C2×Q8—22no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—81no—
560C2×Q8—81no—
561C2×Q8C2×D4×C1111yescharacteristic
562C2×Q8C2×D4×C1111yescharacteristic
563C2×Q8C2×D4×C1111yescharacteristic
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—41no—
574C2×D4C2×D4×C1111yescharacteristic
575C2×D4C2×D4×C1112yes—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—41no—
582C22×C4C2×D4×C1111yescharacteristic
583C22×C4C2×D4×C1111yescharacteristic
584C22×C4C2×D4×C1111yescharacteristic
585SD16—81no—
586SD16—81no—
587SD16—81no—
588SD16—82no—
589D8—81no—
590D8—82no—
591M16—81no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—81no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4C2×D4×C1112yes—
618C4⋊C4C2×D4×C1111yescharacteristic
619C4⋊C4C2×D4×C1111yescharacteristic
620C4⋊C4C2×D4×C1111yescharacteristic
621C4⋊C4C2×D4×C1111yescharacteristic
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—21no—
636C22⋊C4—41no—
637C22⋊C4—41no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42C2×D4×C1111yescharacteristic
643C42C2×D4×C1111yescharacteristic
644C42C2×D4×C1111yescharacteristic
645C42C24×C1111yescharacteristic
646C11#1896411yescharacteristic, direct product factor, Sylow
647C23—21no—
648C23—22no—
649C23—41no—
650C23C11×#12011yescharacteristic
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8—21no—
655Q8—21no—
656Q8—21no—
657Q8—42no—
658Q8—41no—
659Q8—41no—
660Q8—81no—
661Q8—82no—
662D4—21no—
663D4—21no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—81no—
675D4—82no—
676D4—82no—
677D4—82no—
678D4—82no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—82no—
696C2×C4—82no—
697C2×C4—82no—
698C2×C4—82no—
699C2×C4—82no—
700C2×C4C11×#12011yescharacteristic
701C2×C4C11×#12011yescharacteristic
702C2×C4C11×#12011yescharacteristic
703C2×C4C22×D4×C1111yescharacteristic
704C2×C4C22×D4×C1111yescharacteristic
705C2×C4C22×D4×C1111yescharacteristic
706C8—41no—
707C8—41no—
708C8—41no—
709C8—41no—
710C8—41no—
711C8—41no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—41no—
716C22—42no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—41no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22C2×C11×#12011yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—21no—
729C4—41no—
730C4—41no—
731C4—42no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—81no—
738C4C11×#57611yescharacteristic
739C4C11×#57711yescharacteristic
740C4C11×#57711yescharacteristic
741C4C11×#57811yescharacteristic
742C2—41no—
743C2—81no—
744C2—82no—
745C2—161no—
746C2C11×#301211yescharacteristic
747C2C11×#301311yescharacteristic
748C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3554C2semidirect
2. C11×#3254C2semidirect
3. C11×#3247C2semidirect
4. C11×#3207C2semidirect
5. C11×#1637C2semidirect
6. C11×#1636C2semidirect
7. C11×#1631C2semidirect
8. C11×#1630C2semidirect
9. C11×#1627C2semidirect
10. C11×#1626C2semidirect
11. C11×#1621C2semidirect
12. C11×#1620C2semidirect
13. C11×#1547C2semidirect
14. C11×#1495C2semidirect
15. C11×#1481C2semidirect
176. #18964C11direct (N × H)
273. #3554C2×C11semidirect
274. #3254C2×C11semidirect
275. #3247C2×C11semidirect
276. #3207C2×C11semidirect
277. #1637C2×C11semidirect
278. #1636C2×C11semidirect
279. #1631C2×C11semidirect
280. #1630C2×C11semidirect
281. #1627C2×C11semidirect
282. #1626C2×C11semidirect
283. #1621C2×C11semidirect
284. #1620C2×C11semidirect
285. #1547C2×C11semidirect
286. #1495C2×C11semidirect
287. #1481C2×C11semidirect
646. C11#18964direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35542
C11×#32542
C11×#32472
C11×#32072
C11×#16372
C11×#16362
C11×#16312
C11×#16302
C11×#16272
C11×#16262
C11×#16212
C11×#16202
C11×#15472
C11×#14952
C11×#14812
#1896411