Finite Group Databasebeta

← C11×#18932 #14596125

Subgroups — C11×#18932 #14596125

Order 2816.

892 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3544C211yesmaximal, characteristic, complemented
2C11×#3251C211yesmaximal, characteristic, complemented
3C11×#3212C211yesmaximal, characteristic, complemented
4C11×#3206C211yesmaximal, characteristic, complemented
5C11×#1646C211yesmaximal, characteristic, complemented
6C11×#1645C211yesmaximal, characteristic, complemented
7C11×#1644C211yesmaximal, characteristic, complemented
8C11×#1643C211yesmaximal, characteristic, complemented
9C11×#1624C211yesmaximal, characteristic, complemented
10C11×#1623C211yesmaximal, characteristic, complemented
11C11×#1622C211yesmaximal, characteristic, complemented
12C11×#1622C211yesmaximal, characteristic, complemented
13C11×#1548C211yesmaximal, characteristic, complemented
14C11×#1495C211yesmaximal, characteristic, complemented
15C11×#1482C211yesmaximal, characteristic, complemented
16C11×#563—22no—
17Q82×C11C2211yescharacteristic
18C11×#555C2211yescharacteristic
19C11×#554C2211yescharacteristic
20C11×#554C2211yescharacteristic
21C11×#552—21no—
22C11×#552—21no—
23C11×#547—21no—
24C11×#547—21no—
25C11×#544—21no—
26C11×#544—21no—
27C11×#542—21no—
28C11×#542—21no—
29C11×#536—22no—
30C11×#532C2211yescharacteristic
31C2×C11×C4⋊Q8C2211yescharacteristic
32C11×#529C2211yescharacteristic
33C11×#529C2211yescharacteristic
34C11×#495—21no—
35C11×#492C2211yescharacteristic
36C11×#492C2211yescharacteristic
37C11×#488—21no—
38C11×#487C2211yescharacteristic
39C11×#487C2211yescharacteristic
40C11×#478—21no—
41C11×#475C2211yescharacteristic
42C11×#474C2211yescharacteristic
43C11×#469—21no—
44C11×#468—21no—
45C11×#463—21no—
46C11×#462C2211yescharacteristic
47C11×#461—22no—
48C11×#461C2211yescharacteristic
49C11×#460C2211yescharacteristic
50C11×#460C2211yescharacteristic
51C11×#459C2211yescharacteristic
52C11×#459C2211yescharacteristic
53C11×#452—21no—
54C11×#449—21no—
55C11×#448—22no—
56C11×#431C2211yescharacteristic
57C11×#431C2211yescharacteristic
58C11×#423C2211yescharacteristic
59C11×#333C2211yescharacteristic
60C11×#333C2211yescharacteristic
61C11×#333C2211yescharacteristic
62C11×#333C2211yescharacteristic
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—22no—
72C2×C11×#41—21no—
73C22×Q8×C11D412yes—
74C2×C11×Q16—21no—
75C2×C11×SD16—22no—
76C2×C11×SD16—22no—
77C2×C11×SD16—21no—
78C2×C11×SD16—21no—
79C2×C11×SD16—21no—
80C2×C11×D8—21no—
81C2×C11×D8—21no—
82C2×C11×M16—21no—
83C11×C4⋊Q8—22no—
84C11×C4⋊Q8—22no—
85C11×C4⋊Q8—21no—
86C11×C4⋊Q8—21no—
87C11×C4⋊Q8—21no—
88C11×C4⋊Q8—21no—
89C11×C4⋊Q8D412yes—
90C11×C4⋊Q8C2311yescharacteristic
91C11×C4⋊Q8C2311yescharacteristic
92C11×C4⋊Q8C2311yescharacteristic
93C11×#127C2311yescharacteristic
94C11×#126—22no—
95C11×#126—22no—
96C11×#126—21no—
97C11×#126—21no—
98C11×#125—22no—
99C11×#125—22no—
100C11×#125—21no—
101C11×#125—21no—
102C11×#125D411yescharacteristic
103C11×#125D411yescharacteristic
104C11×#124—22no—
105C11×#124—22no—
106C11×#124—21no—
107C11×#124D411yescharacteristic
108C11×#124D411yescharacteristic
109C11×#123—22no—
110C11×#123—22no—
111C11×#123—22no—
112C11×#123—22no—
113C11×#123—21no—
114C11×#123—21no—
115C11×C22⋊Q8—22no—
116C11×C22⋊Q8—22no—
117C11×C22⋊Q8—22no—
118C11×C22⋊Q8—22no—
119C11×C22⋊Q8—22no—
120C11×C22⋊Q8—22no—
121C11×C22⋊Q8—21no—
122C11×C22⋊Q8—21no—
123C11×C22⋊Q8D411yescharacteristic
124C11×C22⋊Q8D411yescharacteristic
125C11×#121—21no—
126C11×#121—21no—
127C11×#121—21no—
128C11×#121—21no—
129C11×#121D411yescharacteristic
130C11×#121D411yescharacteristic
131C4×Q8×C11—21no—
132C4×Q8×C11—21no—
133C4×Q8×C11C2311yescharacteristic
134C4×Q8×C11C2311yescharacteristic
135C4×D4×C11—21no—
136C4×D4×C11—21no—
137C4×D4×C11—21no—
138C4×D4×C11—21no—
139C4×D4×C11—21no—
140C4×D4×C11—21no—
141C4×D4×C11C2311yescharacteristic
142C4×D4×C11C2311yescharacteristic
143C11×#117—22no—
144C11×#117—21no—
145C11×#117—21no—
146C11×#117—21no—
147C11×#117—21no—
148C2×C11×C4⋊C4—21no—
149C2×C11×C4⋊C4—21no—
150C2×C11×C4⋊C4—21no—
151C2×C11×C4⋊C4—21no—
152C2×C42×C11C2311yescharacteristic
153C11×#107—21no—
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—22no—
162C11×#103—22no—
163C11×#103—21no—
164C11×#103—21no—
165C11×#103—21no—
166C11×#102—21no—
167C11×#102—21no—
168C11×#102—21no—
169C11×#102—21no—
170C11×#102—21no—
171C11×C22⋊C8—21no—
172C11×C22⋊C8—21no—
173C4×C8×C11—21no—
174C4×C8×C11C2311yescharacteristic
175C4×C8×C11C2311yescharacteristic
176#18932C1111yesmaximal, characteristic, direct product factor, Sylow
177C11×#41—81no—
178C11×#41—81no—
179C11×#41—84no—
180C2×Q8×C11—22no—
181C2×Q8×C11—22no—
182C2×Q8×C11—21no—
183C2×Q8×C11—82no—
184C2×Q8×C11C2×D411yescharacteristic
185C2×Q8×C11C2×D411yescharacteristic
186C2×Q8×C11C2×D412yes—
187C2×Q8×C11C2×D412yes—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—22no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—41no—
195C2×D4×C11C2×D411yescharacteristic
196C2×D4×C11C2×D411yescharacteristic
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—41no—
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C11×Q16—81no—
207C11×SD16—81no—
208C11×SD16—81no—
209C11×SD16—81no—
210C11×SD16—82no—
211C11×SD16—82no—
212C11×D8—81no—
213C11×D8—81no—
214C11×M16—81no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11—21no—
218C2×C8×C11—21no—
219C2×C8×C11—21no—
220C2×C8×C11—21no—
221C11×C4⋊C4—22no—
222C11×C4⋊C4—22no—
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—21no—
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⋊C4C2×D411yescharacteristic
244C11×C4⋊C4C2×D411yescharacteristic
245C11×C4⋊C4C2×D411yescharacteristic
246C11×C4⋊C4C2×D411yescharacteristic
247C11×C22⋊C4—22no—
248C11×C22⋊C4—22no—
249C11×C22⋊C4—22no—
250C11×C22⋊C4—22no—
251C11×C22⋊C4—21no—
252C11×C22⋊C4—21no—
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—41no—
262C11×C22⋊C4—41no—
263C42×C11—22no—
264C42×C11—22no—
265C42×C11—21no—
266C42×C11—21no—
267C42×C11C2×D411yescharacteristic
268C42×C11C2×D411yescharacteristic
269C42×C11C2×D411yescharacteristic
270C42×C11C2411yescharacteristic
271#3544C2×C1111yescharacteristic, complemented
272#3251C2×C1111yescharacteristic, complemented
273#3212C2×C1111yescharacteristic, complemented
274#3206C2×C1111yescharacteristic, complemented
275#1646C2×C1111yescharacteristic, complemented
276#1645C2×C1111yescharacteristic, complemented
277#1644C2×C1111yescharacteristic, complemented
278#1643C2×C1111yescharacteristic, complemented
279#1624C2×C1111yescharacteristic, complemented
280#1623C2×C1111yescharacteristic, complemented
281#1622C2×C1111yescharacteristic, complemented
282#1622C2×C1111yescharacteristic, complemented
283#1548C2×C1111yescharacteristic, complemented
284#1495C2×C1111yescharacteristic, complemented
285#1482C2×C1111yescharacteristic, complemented
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—41no—
289C23×C11#12011yescharacteristic
290Q8×C11—21no—
291Q8×C11—21no—
292Q8×C11—21no—
293Q8×C11—21no—
294Q8×C11—42no—
295Q8×C11—42no—
296Q8×C11—41no—
297Q8×C11—41no—
298Q8×C11—82no—
299Q8×C11—82no—
300D4×C11—21no—
301D4×C11—21no—
302D4×C11—21no—
303D4×C11—21no—
304D4×C11—42no—
305D4×C11—42no—
306D4×C11—42no—
307D4×C11—41no—
308D4×C11—41no—
309D4×C11—41no—
310D4×C11—41no—
311D4×C11—82no—
312D4×C11—82no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—22no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—22no—
325C2×C4×C11—41no—
326C2×C4×C11—44no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—82no—
333C2×C4×C11—82no—
334C2×C4×C11—82no—
335C2×C4×C11#12011yescharacteristic
336C2×C4×C11#12011yescharacteristic
337C2×C4×C11#12011yescharacteristic
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C22×D411yescharacteristic
341C8×C11—41no—
342C8×C11—41no—
343C8×C11—41no—
344C8×C11—41no—
345C8×C11—41no—
346C8×C11—41no—
347#563—22no—
348Q82C22×C1111yescharacteristic
349#555C22×C1111yescharacteristic
350#554C22×C1111yescharacteristic
351#554C22×C1111yescharacteristic
352#552—21no—
353#552—21no—
354#547—21no—
355#547—21no—
356#544—21no—
357#544—21no—
358#542—21no—
359#542—21no—
360#536—22no—
361#532C22×C1111yescharacteristic
362C2×C4⋊Q8C22×C1111yescharacteristic
363#529C22×C1111yescharacteristic
364#529C22×C1111yescharacteristic
365#495—21no—
366#492C22×C1111yescharacteristic
367#492C22×C1111yescharacteristic
368#488—21no—
369#487C22×C1111yescharacteristic
370#487C22×C1111yescharacteristic
371#478—21no—
372#475C22×C1111yescharacteristic
373#474C22×C1111yescharacteristic
374#469—21no—
375#468—21no—
376#463—21no—
377#462C22×C1111yescharacteristic
378#461—22no—
379#461C22×C1111yescharacteristic
380#460C22×C1111yescharacteristic
381#460C22×C1111yescharacteristic
382#459C22×C1111yescharacteristic
383#459C22×C1111yescharacteristic
384#452—21no—
385#449—21no—
386#448—22no—
387#431C22×C1111yescharacteristic
388#431C22×C1111yescharacteristic
389#423C22×C1111yescharacteristic
390#333C22×C1111yescharacteristic
391#333C22×C1111yescharacteristic
392#333C22×C1111yescharacteristic
393#333C22×C1111yescharacteristic
394Q8⋊C8C22×C1111yescharacteristic
395Q8⋊C8C22×C1111yescharacteristic
396Q8⋊C8C22×C1111yescharacteristic
397Q8⋊C8C22×C1111yescharacteristic
398D4⋊C8C22×C1111yescharacteristic
399D4⋊C8C22×C1111yescharacteristic
400D4⋊C8C22×C1111yescharacteristic
401D4⋊C8C22×C1111yescharacteristic
402C22×C11—21no—
403C22×C11—21no—
404C22×C11—21no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—81no—
412C22×C11—81no—
413C22×C11—81no—
414C22×C11C2×#12011yescharacteristic
415C4×C11—21no—
416C4×C11—21no—
417C4×C11—21no—
418C4×C11—21no—
419C4×C11—41no—
420C4×C11—41no—
421C4×C11—41no—
422C4×C11—41no—
423C4×C11—42no—
424C4×C11—42no—
425C4×C11—41no—
426C4×C11—41no—
427C4×C11—81no—
428C4×C11#57711yescharacteristic
429C4×C11#57711yescharacteristic
430C4×C11#57711yescharacteristic
431C4×C11#57811yescharacteristic
432C2×#41—22no—
433C2×#41—21no—
434C22×Q8D4×C1112yes—
435C2×Q16—21no—
436C2×SD16—22no—
437C2×SD16—22no—
438C2×SD16—21no—
439C2×SD16—21no—
440C2×SD16—21no—
441C2×D8—21no—
442C2×D8—21no—
443C2×M16—21no—
444C4⋊Q8—22no—
445C4⋊Q8—22no—
446C4⋊Q8—21no—
447C4⋊Q8—21no—
448C4⋊Q8—21no—
449C4⋊Q8—21no—
450C4⋊Q8D4×C1112yes—
451C4⋊Q8C23×C1111yescharacteristic
452C4⋊Q8C23×C1111yescharacteristic
453C4⋊Q8C23×C1111yescharacteristic
454#127C23×C1111yescharacteristic
455#126—22no—
456#126—22no—
457#126—21no—
458#126—21no—
459#125—22no—
460#125—22no—
461#125—21no—
462#125—21no—
463#125D4×C1111yescharacteristic
464#125D4×C1111yescharacteristic
465#124—22no—
466#124—22no—
467#124—21no—
468#124D4×C1111yescharacteristic
469#124D4×C1111yescharacteristic
470#123—22no—
471#123—22no—
472#123—22no—
473#123—22no—
474#123—21no—
475#123—21no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—22no—
479C22⋊Q8—22no—
480C22⋊Q8—22no—
481C22⋊Q8—22no—
482C22⋊Q8—21no—
483C22⋊Q8—21no—
484C22⋊Q8D4×C1111yescharacteristic
485C22⋊Q8D4×C1111yescharacteristic
486#121—21no—
487#121—21no—
488#121—21no—
489#121—21no—
490#121D4×C1111yescharacteristic
491#121D4×C1111yescharacteristic
492C4×Q8—21no—
493C4×Q8—21no—
494C4×Q8C23×C1111yescharacteristic
495C4×Q8C23×C1111yescharacteristic
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—21no—
499C4×D4—21no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4C23×C1111yescharacteristic
503C4×D4C23×C1111yescharacteristic
504#117—22no—
505#117—21no—
506#117—21no—
507#117—21no—
508#117—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C42C23×C1111yescharacteristic
514#107—21no—
515#106—21no—
516C4⋊C8—21no—
517C4⋊C8—21no—
518C4⋊C8C23×C1111yescharacteristic
519C4⋊C8C23×C1111yescharacteristic
520C4⋊C8C23×C1111yescharacteristic
521C4⋊C8C23×C1111yescharacteristic
522#103—22no—
523#103—22no—
524#103—21no—
525#103—21no—
526#103—21no—
527#102—21no—
528#102—21no—
529#102—21no—
530#102—21no—
531#102—21no—
532C22⋊C8—21no—
533C22⋊C8—21no—
534C4×C8—21no—
535C4×C8C23×C1111yescharacteristic
536C4×C8C23×C1111yescharacteristic
537C2×C11—41no—
538C2×C11—81no—
539C2×C11—81no—
540C2×C11—161no—
541C2×C11#301011yescharacteristic
542C2×C11#301311yescharacteristic
543C2×C11#301911yescharacteristic
544#41—81no—
545#41—81no—
546#41—84no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—21no—
550C2×Q8—82no—
551C2×Q8C2×D4×C1111yescharacteristic
552C2×Q8C2×D4×C1111yescharacteristic
553C2×Q8C2×D4×C1112yes—
554C2×Q8C2×D4×C1112yes—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—41no—
562C2×D4C2×D4×C1111yescharacteristic
563C2×D4C2×D4×C1111yescharacteristic
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—41no—
570C22×C4C2×D4×C1111yescharacteristic
571C22×C4C2×D4×C1111yescharacteristic
572C22×C4C2×D4×C1111yescharacteristic
573Q16—81no—
574SD16—81no—
575SD16—81no—
576SD16—81no—
577SD16—82no—
578SD16—82no—
579D8—81no—
580D8—81no—
581M16—81no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
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⋊C4C2×D4×C1111yescharacteristic
611C4⋊C4C2×D4×C1111yescharacteristic
612C4⋊C4C2×D4×C1111yescharacteristic
613C4⋊C4C2×D4×C1111yescharacteristic
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—41no—
629C22⋊C4—41no—
630C42—22no—
631C42—22no—
632C42—21no—
633C42—21no—
634C42C2×D4×C1111yescharacteristic
635C42C2×D4×C1111yescharacteristic
636C42C2×D4×C1111yescharacteristic
637C42C24×C1111yescharacteristic
638C11#1893211yescharacteristic, direct product factor, Sylow
639C23—21no—
640C23—21no—
641C23—41no—
642C23C11×#12011yescharacteristic
643Q8—21no—
644Q8—21no—
645Q8—21no—
646Q8—21no—
647Q8—42no—
648Q8—42no—
649Q8—41no—
650Q8—41no—
651Q8—82no—
652Q8—82no—
653D4—21no—
654D4—21no—
655D4—21no—
656D4—21no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—82no—
665D4—82no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—44no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—82no—
686C2×C4—82no—
687C2×C4—82no—
688C2×C4C11×#12011yescharacteristic
689C2×C4C11×#12011yescharacteristic
690C2×C4C11×#12011yescharacteristic
691C2×C4C22×D4×C1111yescharacteristic
692C2×C4C22×D4×C1111yescharacteristic
693C2×C4C22×D4×C1111yescharacteristic
694C8—41no—
695C8—41no—
696C8—41no—
697C8—41no—
698C8—41no—
699C8—41no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22C2×C11×#12011yescharacteristic
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—41no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—42no—
722C4—42no—
723C4—41no—
724C4—41no—
725C4—81no—
726C4C11×#57711yescharacteristic
727C4C11×#57711yescharacteristic
728C4C11×#57711yescharacteristic
729C4C11×#57811yescharacteristic
730C2—41no—
731C2—81no—
732C2—81no—
733C2—161no—
734C2C11×#301011yescharacteristic
735C2C11×#301311yescharacteristic
736C2C11×#301911yescharacteristic
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×#3544C2semidirect
2. C11×#3251C2semidirect
3. C11×#3212C2semidirect
4. C11×#3206C2semidirect
5. C11×#1646C2semidirect
6. C11×#1645C2semidirect
7. C11×#1644C2semidirect
8. C11×#1643C2semidirect
9. C11×#1624C2semidirect
10. C11×#1623C2semidirect
11. C11×#1622C2semidirect
12. C11×#1622C2semidirect
13. C11×#1548C2semidirect
14. C11×#1495C2semidirect
15. C11×#1482C2semidirect
176. #18932C11direct (N × H)
271. #3544C2×C11semidirect
272. #3251C2×C11semidirect
273. #3212C2×C11semidirect
274. #3206C2×C11semidirect
275. #1646C2×C11semidirect
276. #1645C2×C11semidirect
277. #1644C2×C11semidirect
278. #1643C2×C11semidirect
279. #1624C2×C11semidirect
280. #1623C2×C11semidirect
281. #1622C2×C11semidirect
282. #1622C2×C11semidirect
283. #1548C2×C11semidirect
284. #1495C2×C11semidirect
285. #1482C2×C11semidirect
638. C11#18932direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35442
C11×#32512
C11×#32122
C11×#32062
C11×#16462
C11×#16452
C11×#16442
C11×#16432
C11×#16242
C11×#16232
C11×#16222
C11×#15482
C11×#14952
C11×#14822
#1893211