Finite Group Databasebeta

← C11×#18944 #14596137

Subgroups — C11×#18944 #14596137

Order 2816.

880 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3552C211yesmaximal, characteristic, complemented
2C11×#3251C211yesmaximal, characteristic, complemented
3C11×#3227C211yesmaximal, characteristic, complemented
4C11×#3212C211yesmaximal, characteristic, complemented
5C11×#1654C211yesmaximal, characteristic, complemented
6C11×#1653C211yesmaximal, characteristic, complemented
7C11×#1652C211yesmaximal, characteristic, complemented
8C11×#1651C211yesmaximal, characteristic, complemented
9C11×#1628C211yesmaximal, characteristic, complemented
10C11×#1627C211yesmaximal, characteristic, complemented
11C11×#1626C211yesmaximal, characteristic, complemented
12C11×#1625C211yesmaximal, characteristic, complemented
13C11×#1546C211yesmaximal, characteristic, complemented
14C11×#1495C211yesmaximal, characteristic, complemented
15C11×#1482C211yesmaximal, characteristic, complemented
16C11×#563—22no—
17C11×#557C2211yescharacteristic
18C11×#556C2211yescharacteristic
19C11×#554—21no—
20C11×#553—21no—
21D4×Q8×C11—21no—
22D4×Q8×C11C2211yescharacteristic
23C11×#548—21no—
24C11×#547C2211yescharacteristic
25C11×#544—21no—
26C11×#542—21no—
27C11×#541—21no—
28C11×#539—22no—
29C11×#536—21no—
30C11×#532C2211yescharacteristic
31C2×C11×C4⋊Q8C2211yescharacteristic
32C11×#529C2211yescharacteristic
33C11×#529C2211yescharacteristic
34C11×#498C2211yescharacteristic
35C11×#498C2211yescharacteristic
36C11×#495—21no—
37C11×#488—21no—
38C11×#486C2211yescharacteristic
39C11×#486C2211yescharacteristic
40C11×#481—22no—
41C11×#478—21no—
42C11×#476—22no—
43C11×#475C2211yescharacteristic
44C11×#474C2211yescharacteristic
45C11×#469—21no—
46C11×#468—21no—
47C11×#463—21no—
48C11×#462C2211yescharacteristic
49C11×#461C2211yescharacteristic
50C11×#460C2211yescharacteristic
51C11×#460C2211yescharacteristic
52C11×#459C2211yescharacteristic
53C11×#459C2211yescharacteristic
54C11×#452—21no—
55C11×#449—21no—
56C11×#431C2211yescharacteristic
57C11×#431C2211yescharacteristic
58C11×#423C2211yescharacteristic
59C11×#332C2211yescharacteristic
60C11×#332C2211yescharacteristic
61C11×#332C2211yescharacteristic
62C11×#332C2211yescharacteristic
63C11×Q8⋊C8C2211yescharacteristic
64C11×Q8⋊C8C2211yescharacteristic
65C11×Q8⋊C8C2211yescharacteristic
66C11×Q8⋊C8C2211yescharacteristic
67C11×D4⋊C8C2211yescharacteristic
68C11×D4⋊C8C2211yescharacteristic
69C11×D4⋊C8C2211yescharacteristic
70C11×D4⋊C8C2211yescharacteristic
71C2×C11×#41—21no—
72C2×C11×#41—21no—
73C22×Q8×C11—21no—
74C22×Q8×C11—21no—
75C2×C11×Q16—21no—
76C2×C11×SD16—21no—
77C2×C11×SD16—21no—
78C2×C11×SD16—21no—
79C2×C11×D8—21no—
80C2×C11×D8—21no—
81C2×C11×M16—21no—
82C11×C4⋊Q8—22no—
83C11×C4⋊Q8—21no—
84C11×C4⋊Q8—21no—
85C11×C4⋊Q8—21no—
86C11×C4⋊Q8—21no—
87C11×C4⋊Q8D412yes—
88C11×C4⋊Q8C2311yescharacteristic
89C11×C4⋊Q8C2311yescharacteristic
90C11×C4⋊Q8C2311yescharacteristic
91C11×#127C2311yescharacteristic
92C11×#126—22no—
93C11×#126—22no—
94C11×#126—22no—
95C11×#126—21no—
96C11×#126—21no—
97C11×#125—22no—
98C11×#125—22no—
99C11×#125—22no—
100C11×#125—21no—
101C11×#125D411yescharacteristic
102C11×#125D411yescharacteristic
103C11×#124—22no—
104C11×#124—21no—
105C11×#124—21no—
106C11×#124D411yescharacteristic
107C11×#124D411yescharacteristic
108C11×#123—22no—
109C11×#123—22no—
110C11×#123—21no—
111C11×#123—21no—
112C11×#123—22no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8—22no—
116C11×C22⋊Q8—22no—
117C11×C22⋊Q8—22no—
118C11×C22⋊Q8—21no—
119C11×C22⋊Q8—22no—
120C11×C22⋊Q8—21no—
121C11×C22⋊Q8—21no—
122C11×C22⋊Q8D411yescharacteristic
123C11×C22⋊Q8D411yescharacteristic
124C11×#121—22no—
125C11×#121—21no—
126C11×#121—21no—
127C11×#121—21no—
128C11×#121D411yescharacteristic
129C11×#121D411yescharacteristic
130C4×Q8×C11—21no—
131C4×Q8×C11—21no—
132C4×Q8×C11—21no—
133C4×Q8×C11C2311yescharacteristic
134C4×Q8×C11C2311yescharacteristic
135C4×D4×C11—22no—
136C4×D4×C11—22no—
137C4×D4×C11—21no—
138C4×D4×C11—21no—
139C4×D4×C11—21no—
140C4×D4×C11—21no—
141C4×D4×C11—21no—
142C4×D4×C11C2311yescharacteristic
143C4×D4×C11C2311yescharacteristic
144C11×#117—21no—
145C11×#117—21no—
146C11×#117—21no—
147C2×C11×C4⋊C4—21no—
148C2×C11×C4⋊C4—21no—
149C2×C11×C4⋊C4D412yes—
150C2×C42×C11C2311yescharacteristic
151C11×#107—21no—
152C11×#106—22no—
153C11×#106—22no—
154C11×#106—21no—
155C11×C4⋊C8—21no—
156C11×C4⋊C8—21no—
157C11×C4⋊C8C2311yescharacteristic
158C11×C4⋊C8C2311yescharacteristic
159C11×C4⋊C8C2311yescharacteristic
160C11×C4⋊C8C2311yescharacteristic
161C11×#103—21no—
162C11×#103—21no—
163C11×#103—21no—
164C11×#102—21no—
165C11×#102—21no—
166C11×#102—21no—
167C11×#102—21no—
168C11×#102—21no—
169C11×#102—22no—
170C11×#102—22no—
171C11×C22⋊C8—21no—
172C11×C22⋊C8—21no—
173C4×C8×C11—21no—
174C4×C8×C11C2311yescharacteristic
175C4×C8×C11C2311yescharacteristic
176#18944C1111yesmaximal, characteristic, direct product factor, Sylow
177C11×#41—81no—
178C11×#41—81no—
179C11×#41—81no—
180C11×#41—81no—
181C2×Q8×C11—22no—
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×C11—81no—
189C2×Q8×C11—81no—
190C2×Q8×C11C2×D411yescharacteristic
191C2×Q8×C11C2×D411yescharacteristic
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—22no—
195C2×D4×C11—21no—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—41no—
199C2×D4×C11C2×D411yescharacteristic
200C2×D4×C11C2×D411yescharacteristic
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—41no—
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C11×Q16—81no—
211C11×SD16—81no—
212C11×SD16—81no—
213C11×SD16—81no—
214C11×D8—81no—
215C11×D8—81no—
216C11×M16—81no—
217C2×C8×C11—21no—
218C2×C8×C11—21no—
219C2×C8×C11—21no—
220C2×C8×C11—21no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C11×C4⋊C4—22no—
224C11×C4⋊C4—22no—
225C11×C4⋊C4—22no—
226C11×C4⋊C4—22no—
227C11×C4⋊C4—22no—
228C11×C4⋊C4—22no—
229C11×C4⋊C4—22no—
230C11×C4⋊C4—22no—
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⋊C4C2×D411yescharacteristic
244C11×C4⋊C4C2×D411yescharacteristic
245C11×C4⋊C4C2×D412yes—
246C11×C4⋊C4C2×D412yes—
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—21no—
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—21no—
261C11×C22⋊C4—21no—
262C11×C22⋊C4—21no—
263C11×C22⋊C4—41no—
264C11×C22⋊C4—41no—
265C42×C11—22no—
266C42×C11—22no—
267C42×C11—21no—
268C42×C11—21no—
269C42×C11C2×D411yescharacteristic
270C42×C11C2×D411yescharacteristic
271C42×C11C2×D411yescharacteristic
272C42×C11C2411yescharacteristic
273#3552C2×C1111yescharacteristic, complemented
274#3251C2×C1111yescharacteristic, complemented
275#3227C2×C1111yescharacteristic, complemented
276#3212C2×C1111yescharacteristic, complemented
277#1654C2×C1111yescharacteristic, complemented
278#1653C2×C1111yescharacteristic, complemented
279#1652C2×C1111yescharacteristic, complemented
280#1651C2×C1111yescharacteristic, complemented
281#1628C2×C1111yescharacteristic, complemented
282#1627C2×C1111yescharacteristic, complemented
283#1626C2×C1111yescharacteristic, complemented
284#1625C2×C1111yescharacteristic, complemented
285#1546C2×C1111yescharacteristic, complemented
286#1495C2×C1111yescharacteristic, complemented
287#1482C2×C1111yescharacteristic, complemented
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—41no—
291C23×C11#12011yescharacteristic
292Q8×C11—21no—
293Q8×C11—21no—
294Q8×C11—21no—
295Q8×C11—21no—
296Q8×C11—41no—
297Q8×C11—41no—
298Q8×C11—41no—
299Q8×C11—41no—
300Q8×C11—41no—
301Q8×C11—41no—
302Q8×C11—82no—
303Q8×C11—82no—
304D4×C11—21no—
305D4×C11—21no—
306D4×C11—21no—
307D4×C11—21no—
308D4×C11—42no—
309D4×C11—42no—
310D4×C11—42no—
311D4×C11—41no—
312D4×C11—41no—
313D4×C11—41no—
314D4×C11—41no—
315D4×C11—82no—
316D4×C11—82no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
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—22no—
327C2×C4×C11—22no—
328C2×C4×C11—21no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—82no—
336C2×C4×C11—82no—
337C2×C4×C11—82no—
338C2×C4×C11—82no—
339C2×C4×C11#12011yescharacteristic
340C2×C4×C11#12011yescharacteristic
341C2×C4×C11#12011yescharacteristic
342C2×C4×C11C22×D411yescharacteristic
343C2×C4×C11C22×D411yescharacteristic
344C2×C4×C11C22×D411yescharacteristic
345C8×C11—41no—
346C8×C11—41no—
347C8×C11—41no—
348C8×C11—41no—
349C8×C11—41no—
350C8×C11—41no—
351#563—22no—
352#557C22×C1111yescharacteristic
353#556C22×C1111yescharacteristic
354#554—21no—
355#553—21no—
356D4×Q8—21no—
357D4×Q8C22×C1111yescharacteristic
358#548—21no—
359#547C22×C1111yescharacteristic
360#544—21no—
361#542—21no—
362#541—21no—
363#539—22no—
364#536—21no—
365#532C22×C1111yescharacteristic
366C2×C4⋊Q8C22×C1111yescharacteristic
367#529C22×C1111yescharacteristic
368#529C22×C1111yescharacteristic
369#498C22×C1111yescharacteristic
370#498C22×C1111yescharacteristic
371#495—21no—
372#488—21no—
373#486C22×C1111yescharacteristic
374#486C22×C1111yescharacteristic
375#481—22no—
376#478—21no—
377#476—22no—
378#475C22×C1111yescharacteristic
379#474C22×C1111yescharacteristic
380#469—21no—
381#468—21no—
382#463—21no—
383#462C22×C1111yescharacteristic
384#461C22×C1111yescharacteristic
385#460C22×C1111yescharacteristic
386#460C22×C1111yescharacteristic
387#459C22×C1111yescharacteristic
388#459C22×C1111yescharacteristic
389#452—21no—
390#449—21no—
391#431C22×C1111yescharacteristic
392#431C22×C1111yescharacteristic
393#423C22×C1111yescharacteristic
394#332C22×C1111yescharacteristic
395#332C22×C1111yescharacteristic
396#332C22×C1111yescharacteristic
397#332C22×C1111yescharacteristic
398Q8⋊C8C22×C1111yescharacteristic
399Q8⋊C8C22×C1111yescharacteristic
400Q8⋊C8C22×C1111yescharacteristic
401Q8⋊C8C22×C1111yescharacteristic
402D4⋊C8C22×C1111yescharacteristic
403D4⋊C8C22×C1111yescharacteristic
404D4⋊C8C22×C1111yescharacteristic
405D4⋊C8C22×C1111yescharacteristic
406C22×C11—21no—
407C22×C11—21no—
408C22×C11—21no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—81no—
416C22×C11—81no—
417C22×C11—81no—
418C22×C11C2×#12011yescharacteristic
419C4×C11—21no—
420C4×C11—21no—
421C4×C11—21no—
422C4×C11—21no—
423C4×C11—41no—
424C4×C11—41no—
425C4×C11—41no—
426C4×C11—42no—
427C4×C11—41no—
428C4×C11—42no—
429C4×C11—41no—
430C4×C11—41no—
431C4×C11—81no—
432C4×C11#57611yescharacteristic
433C4×C11#57711yescharacteristic
434C4×C11#57711yescharacteristic
435C4×C11#57711yescharacteristic
436C2×#41—21no—
437C2×#41—21no—
438C22×Q8—21no—
439C22×Q8—21no—
440C2×Q16—21no—
441C2×SD16—21no—
442C2×SD16—21no—
443C2×SD16—21no—
444C2×D8—21no—
445C2×D8—21no—
446C2×M16—21no—
447C4⋊Q8—22no—
448C4⋊Q8—21no—
449C4⋊Q8—21no—
450C4⋊Q8—21no—
451C4⋊Q8—21no—
452C4⋊Q8D4×C1112yes—
453C4⋊Q8C23×C1111yescharacteristic
454C4⋊Q8C23×C1111yescharacteristic
455C4⋊Q8C23×C1111yescharacteristic
456#127C23×C1111yescharacteristic
457#126—22no—
458#126—22no—
459#126—22no—
460#126—21no—
461#126—21no—
462#125—22no—
463#125—22no—
464#125—22no—
465#125—21no—
466#125D4×C1111yescharacteristic
467#125D4×C1111yescharacteristic
468#124—22no—
469#124—21no—
470#124—21no—
471#124D4×C1111yescharacteristic
472#124D4×C1111yescharacteristic
473#123—22no—
474#123—22no—
475#123—21no—
476#123—21no—
477#123—22no—
478C22⋊Q8—22no—
479C22⋊Q8—22no—
480C22⋊Q8—22no—
481C22⋊Q8—22no—
482C22⋊Q8—22no—
483C22⋊Q8—21no—
484C22⋊Q8—22no—
485C22⋊Q8—21no—
486C22⋊Q8—21no—
487C22⋊Q8D4×C1111yescharacteristic
488C22⋊Q8D4×C1111yescharacteristic
489#121—22no—
490#121—21no—
491#121—21no—
492#121—21no—
493#121D4×C1111yescharacteristic
494#121D4×C1111yescharacteristic
495C4×Q8—21no—
496C4×Q8—21no—
497C4×Q8—21no—
498C4×Q8C23×C1111yescharacteristic
499C4×Q8C23×C1111yescharacteristic
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4C23×C1111yescharacteristic
508C4×D4C23×C1111yescharacteristic
509#117—21no—
510#117—21no—
511#117—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4D4×C1112yes—
515C2×C42C23×C1111yescharacteristic
516#107—21no—
517#106—21no—
518#106—22no—
519#106—22no—
520C4⋊C8—21no—
521C4⋊C8—21no—
522C4⋊C8C23×C1111yescharacteristic
523C4⋊C8C23×C1111yescharacteristic
524C4⋊C8C23×C1111yescharacteristic
525C4⋊C8C23×C1111yescharacteristic
526#103—21no—
527#103—21no—
528#103—21no—
529#102—21no—
530#102—21no—
531#102—21no—
532#102—21no—
533#102—21no—
534#102—22no—
535#102—22no—
536C22⋊C8—21no—
537C22⋊C8—21no—
538C4×C8—21no—
539C4×C8C23×C1111yescharacteristic
540C4×C8C23×C1111yescharacteristic
541C2×C11—41no—
542C2×C11—81no—
543C2×C11—81no—
544C2×C11—161no—
545C2×C11#301011yescharacteristic
546C2×C11#301211yescharacteristic
547C2×C11#302011yescharacteristic
548#41—81no—
549#41—81no—
550#41—81no—
551#41—81no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—81no—
558C2×Q8—81no—
559C2×Q8—81no—
560C2×Q8—81no—
561C2×Q8C2×D4×C1111yescharacteristic
562C2×Q8C2×D4×C1111yescharacteristic
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—41no—
570C2×D4C2×D4×C1111yescharacteristic
571C2×D4C2×D4×C1111yescharacteristic
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—41no—
578C22×C4C2×D4×C1111yescharacteristic
579C22×C4C2×D4×C1111yescharacteristic
580C22×C4C2×D4×C1111yescharacteristic
581Q16—81no—
582SD16—81no—
583SD16—81no—
584SD16—81no—
585D8—81no—
586D8—81no—
587M16—81no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—21no—
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⋊C4C2×D4×C1111yescharacteristic
615C4⋊C4C2×D4×C1111yescharacteristic
616C4⋊C4C2×D4×C1112yes—
617C4⋊C4C2×D4×C1112yes—
618C4⋊C4C2×D4×C1111yescharacteristic
619C4⋊C4C2×D4×C1111yescharacteristic
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—41no—
635C22⋊C4—41no—
636C42—22no—
637C42—22no—
638C42—21no—
639C42—21no—
640C42C2×D4×C1111yescharacteristic
641C42C2×D4×C1111yescharacteristic
642C42C2×D4×C1111yescharacteristic
643C42C24×C1111yescharacteristic
644C11#1894411yescharacteristic, direct product factor, Sylow
645C23—21no—
646C23—21no—
647C23—41no—
648C23C11×#12011yescharacteristic
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—41no—
654Q8—41no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—82no—
660Q8—82no—
661D4—21no—
662D4—21no—
663D4—21no—
664D4—21no—
665D4—42no—
666D4—42no—
667D4—42no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—82no—
673D4—82no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—82no—
693C2×C4—82no—
694C2×C4—82no—
695C2×C4—82no—
696C2×C4C11×#12011yescharacteristic
697C2×C4C11×#12011yescharacteristic
698C2×C4C11×#12011yescharacteristic
699C2×C4C22×D4×C1111yescharacteristic
700C2×C4C22×D4×C1111yescharacteristic
701C2×C4C22×D4×C1111yescharacteristic
702C8—41no—
703C8—41no—
704C8—41no—
705C8—41no—
706C8—41no—
707C8—41no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22C2×C11×#12011yescharacteristic
721C4—21no—
722C4—21no—
723C4—21no—
724C4—21no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—42no—
729C4—41no—
730C4—42no—
731C4—41no—
732C4—41no—
733C4—81no—
734C4C11×#57611yescharacteristic
735C4C11×#57711yescharacteristic
736C4C11×#57711yescharacteristic
737C4C11×#57711yescharacteristic
738C2—41no—
739C2—81no—
740C2—81no—
741C2—161no—
742C2C11×#301011yescharacteristic
743C2C11×#301211yescharacteristic
744C2C11×#302011yescharacteristic
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×#3552C2semidirect
2. C11×#3251C2semidirect
3. C11×#3227C2semidirect
4. C11×#3212C2semidirect
5. C11×#1654C2semidirect
6. C11×#1653C2semidirect
7. C11×#1652C2semidirect
8. C11×#1651C2semidirect
9. C11×#1628C2semidirect
10. C11×#1627C2semidirect
11. C11×#1626C2semidirect
12. C11×#1625C2semidirect
13. C11×#1546C2semidirect
14. C11×#1495C2semidirect
15. C11×#1482C2semidirect
176. #18944C11direct (N × H)
273. #3552C2×C11semidirect
274. #3251C2×C11semidirect
275. #3227C2×C11semidirect
276. #3212C2×C11semidirect
277. #1654C2×C11semidirect
278. #1653C2×C11semidirect
279. #1652C2×C11semidirect
280. #1651C2×C11semidirect
281. #1628C2×C11semidirect
282. #1627C2×C11semidirect
283. #1626C2×C11semidirect
284. #1625C2×C11semidirect
285. #1546C2×C11semidirect
286. #1495C2×C11semidirect
287. #1482C2×C11semidirect
644. C11#18944direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35522
C11×#32512
C11×#32272
C11×#32122
C11×#16542
C11×#16532
C11×#16522
C11×#16512
C11×#16282
C11×#16272
C11×#16262
C11×#16252
C11×#15462
C11×#14952
C11×#14822
#1894411