Finite Group Databasebeta

← C11×#18965 #14596158

Subgroups — C11×#18965 #14596158

Order 2816.

900 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3547C211yesmaximal, characteristic, complemented
2C11×#3253C211yesmaximal, characteristic, complemented
3C11×#3247C211yesmaximal, characteristic, complemented
4C11×#3210C211yesmaximal, characteristic, complemented
5C11×#1637C211yesmaximal, characteristic, complemented
6C11×#1635C211yesmaximal, characteristic, complemented
7C11×#1634C211yesmaximal, characteristic, complemented
8C11×#1632C211yesmaximal, characteristic, complemented
9C11×#1627C211yesmaximal, characteristic, complemented
10C11×#1625C211yesmaximal, characteristic, complemented
11C11×#1624C211yesmaximal, characteristic, complemented
12C11×#1622C211yesmaximal, characteristic, complemented
13C11×#1550C211yesmaximal, characteristic, complemented
14C11×#1495C211yesmaximal, characteristic, complemented
15C11×#1480C211yesmaximal, characteristic, complemented
16C11×#562—22no—
17C11×#555—21no—
18C11×#555C2211yescharacteristic
19C11×#554C2211yescharacteristic
20C11×#553—21no—
21C11×#552—21no—
22D4×Q8×C11C2211yescharacteristic
23C11×#548—21no—
24C11×#547C2211yescharacteristic
25C11×#544—21no—
26C11×#542—22no—
27C11×#540—21no—
28C11×#537—21no—
29C11×#536—21no—
30C11×#533C2211yescharacteristic
31C11×#532C2211yescharacteristic
32C11×#532C2211yescharacteristic
33C11×#529C2211yescharacteristic
34C11×#494C2211yescharacteristic
35C11×#492C2211yescharacteristic
36C11×#487C2211yescharacteristic
37C11×#486C2211yescharacteristic
38C11×#478—21no—
39C11×#477C2211yescharacteristic
40C11×#476—21no—
41C11×#476C2211yescharacteristic
42C11×#476C2211yescharacteristic
43C11×#476C2211yescharacteristic
44C11×#469—21no—
45C11×#469—21no—
46C11×#466—21no—
47C11×#465—21no—
48C11×#464—22no—
49C11×#463—21no—
50C11×#460C2211yescharacteristic
51C11×#459—21no—
52C11×#459C2211yescharacteristic
53C11×#459C2211yescharacteristic
54C11×#459C2211yescharacteristic
55C11×#452—22no—
56C11×#431C2211yescharacteristic
57C11×#423C2211yescharacteristic
58C2×C11×C4⋊C8C2211yescharacteristic
59C11×#333C2211yescharacteristic
60C11×#333C2211yescharacteristic
61C11×#332C2211yescharacteristic
62C11×#332C2211yescharacteristic
63C11×Q8⋊C8C2211yescharacteristic
64C11×Q8⋊C8C2211yescharacteristic
65C11×D4⋊C8C2211yescharacteristic
66C11×D4⋊C8C2211yescharacteristic
67C11×D4⋊C8C2211yescharacteristic
68C11×D4⋊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×Q16—22no—
76C2×C11×SD16—22no—
77C2×C11×SD16—21no—
78C2×C11×D8—21no—
79C2×C11×D8—21no—
80C2×C11×D8—21no—
81C2×C11×M16—21no—
82C22×C8×C11—21no—
83C11×C4⋊Q8—22no—
84C11×C4⋊Q8—21no—
85C11×C4⋊Q8D411yescharacteristic
86C11×C4⋊Q8C2311yescharacteristic
87C11×C4⋊Q8C2311yescharacteristic
88C11×C4⋊Q8C2311yescharacteristic
89C11×#127D411yescharacteristic
90C11×#127C2311yescharacteristic
91C11×#126—22no—
92C11×#126—21no—
93C11×#125—22no—
94C11×#125—21no—
95C11×#125—21no—
96C11×#125D411yescharacteristic
97C11×#124—22no—
98C11×#124—22no—
99C11×#124—22no—
100C11×#124—21no—
101C11×#124—21no—
102C11×#124D411yescharacteristic
103C11×#123—22no—
104C11×#123—22no—
105C11×#123—22no—
106C11×#123—21no—
107C11×#123—22no—
108C11×C22⋊Q8—22no—
109C11×C22⋊Q8—22no—
110C11×C22⋊Q8—21no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—21no—
113C11×C22⋊Q8—21no—
114C11×C22⋊Q8—21no—
115C11×C22⋊Q8—22no—
116C11×C22⋊Q8D411yescharacteristic
117C11×C22⋊Q8D412yes—
118C11×#121—22no—
119C11×#121—22no—
120C11×#121—22no—
121C11×#121—22no—
122C11×#121—21no—
123C11×#121—21no—
124C11×#121—21no—
125C11×#121—21no—
126C11×#121—21no—
127C11×#121—21no—
128C11×#121D411yescharacteristic
129C11×#121D411yescharacteristic
130C11×#121D411yescharacteristic
131C4×Q8×C11—21no—
132C4×Q8×C11D412yes—
133C4×Q8×C11C2311yescharacteristic
134C4×D4×C11—22no—
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
143C4×D4×C11C2311yescharacteristic
144C11×#117—22no—
145C11×#117—21no—
146C11×#117—21no—
147C11×#117—21no—
148C11×#117—21no—
149C2×C11×C4⋊C4—21no—
150C2×C11×C4⋊C4—21no—
151C2×C42×C11C2311yescharacteristic
152C11×#107—21no—
153C11×#106—21no—
154C11×#106—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—22no—
165C11×#102—21no—
166C11×#102—21no—
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#18965C1111yesmaximal, 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×D412yes—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—21no—
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×D411yescharacteristic
203C2×D4×C11C2×D411yescharacteristic
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—41no—
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C11×Q16—82no—
215C11×SD16—81no—
216C11×SD16—82no—
217C11×D8—81no—
218C11×D8—81no—
219C11×D8—81no—
220C11×M16—81no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C2×C8×C11—81no—
228C11×C4⋊C4—22no—
229C11×C4⋊C4—22no—
230C11×C4⋊C4—22no—
231C11×C4⋊C4—22no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—22no—
237C11×C4⋊C4—22no—
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—22no—
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—21no—
264C11×C22⋊C4—41no—
265C11×C22⋊C4—41no—
266C42×C11—22no—
267C42×C11—22no—
268C42×C11—21no—
269C42×C11C2×D411yescharacteristic
270C42×C11C2×D411yescharacteristic
271C42×C11C2×D411yescharacteristic
272C42×C11C2411yescharacteristic
273#3547C2×C1111yescharacteristic, complemented
274#3253C2×C1111yescharacteristic, complemented
275#3247C2×C1111yescharacteristic, complemented
276#3210C2×C1111yescharacteristic, complemented
277#1637C2×C1111yescharacteristic, complemented
278#1635C2×C1111yescharacteristic, complemented
279#1634C2×C1111yescharacteristic, complemented
280#1632C2×C1111yescharacteristic, complemented
281#1627C2×C1111yescharacteristic, complemented
282#1625C2×C1111yescharacteristic, complemented
283#1624C2×C1111yescharacteristic, complemented
284#1622C2×C1111yescharacteristic, complemented
285#1550C2×C1111yescharacteristic, complemented
286#1495C2×C1111yescharacteristic, complemented
287#1480C2×C1111yescharacteristic, complemented
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—41no—
292C23×C11#12011yescharacteristic
293Q8×C11—21no—
294Q8×C11—21no—
295Q8×C11—42no—
296Q8×C11—42no—
297Q8×C11—41no—
298Q8×C11—41no—
299Q8×C11—81no—
300Q8×C11—82no—
301D4×C11—21no—
302D4×C11—21no—
303D4×C11—21no—
304D4×C11—21no—
305D4×C11—21no—
306D4×C11—21no—
307D4×C11—42no—
308D4×C11—41no—
309D4×C11—41no—
310D4×C11—41no—
311D4×C11—41no—
312D4×C11—81no—
313D4×C11—81no—
314D4×C11—81no—
315D4×C11—81no—
316D4×C11—81no—
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—22no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—22no—
330C2×C4×C11—21no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—82no—
340C2×C4×C11—82no—
341C2×C4×C11—82no—
342C2×C4×C11—82no—
343C2×C4×C11#12011yescharacteristic
344C2×C4×C11#12011yescharacteristic
345C2×C4×C11#12011yescharacteristic
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C22×D411yescharacteristic
348C2×C4×C11C22×D411yescharacteristic
349C8×C11—41no—
350C8×C11—41no—
351C8×C11—41no—
352C8×C11—41no—
353C8×C11—41no—
354C8×C11—41no—
355#562—22no—
356#555—21no—
357#555C22×C1111yescharacteristic
358#554C22×C1111yescharacteristic
359#553—21no—
360#552—21no—
361D4×Q8C22×C1111yescharacteristic
362#548—21no—
363#547C22×C1111yescharacteristic
364#544—21no—
365#542—22no—
366#540—21no—
367#537—21no—
368#536—21no—
369#533C22×C1111yescharacteristic
370#532C22×C1111yescharacteristic
371#532C22×C1111yescharacteristic
372#529C22×C1111yescharacteristic
373#494C22×C1111yescharacteristic
374#492C22×C1111yescharacteristic
375#487C22×C1111yescharacteristic
376#486C22×C1111yescharacteristic
377#478—21no—
378#477C22×C1111yescharacteristic
379#476—21no—
380#476C22×C1111yescharacteristic
381#476C22×C1111yescharacteristic
382#476C22×C1111yescharacteristic
383#469—21no—
384#469—21no—
385#466—21no—
386#465—21no—
387#464—22no—
388#463—21no—
389#460C22×C1111yescharacteristic
390#459—21no—
391#459C22×C1111yescharacteristic
392#459C22×C1111yescharacteristic
393#459C22×C1111yescharacteristic
394#452—22no—
395#431C22×C1111yescharacteristic
396#423C22×C1111yescharacteristic
397C2×C4⋊C8C22×C1111yescharacteristic
398#333C22×C1111yescharacteristic
399#333C22×C1111yescharacteristic
400#332C22×C1111yescharacteristic
401#332C22×C1111yescharacteristic
402Q8⋊C8C22×C1111yescharacteristic
403Q8⋊C8C22×C1111yescharacteristic
404D4⋊C8C22×C1111yescharacteristic
405D4⋊C8C22×C1111yescharacteristic
406D4⋊C8C22×C1111yescharacteristic
407D4⋊C8C22×C1111yescharacteristic
408D4⋊C8C22×C1111yescharacteristic
409D4⋊C8C22×C1111yescharacteristic
410C22×C11—21no—
411C22×C11—21no—
412C22×C11—21no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—81no—
423C22×C11—81no—
424C22×C11—81no—
425C22×C11C2×#12011yescharacteristic
426C4×C11—21no—
427C4×C11—21no—
428C4×C11—21no—
429C4×C11—21no—
430C4×C11—41no—
431C4×C11—41no—
432C4×C11—42no—
433C4×C11—41no—
434C4×C11—41no—
435C4×C11—41no—
436C4×C11—42no—
437C4×C11—81no—
438C4×C11#57611yescharacteristic
439C4×C11#57711yescharacteristic
440C4×C11#57711yescharacteristic
441C4×C11#57811yescharacteristic
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C22×Q8—21no—
446C2×Q16—22no—
447C2×SD16—22no—
448C2×SD16—21no—
449C2×D8—21no—
450C2×D8—21no—
451C2×D8—21no—
452C2×M16—21no—
453C22×C8—21no—
454C4⋊Q8—22no—
455C4⋊Q8—21no—
456C4⋊Q8D4×C1111yescharacteristic
457C4⋊Q8C23×C1111yescharacteristic
458C4⋊Q8C23×C1111yescharacteristic
459C4⋊Q8C23×C1111yescharacteristic
460#127D4×C1111yescharacteristic
461#127C23×C1111yescharacteristic
462#126—22no—
463#126—21no—
464#125—22no—
465#125—21no—
466#125—21no—
467#125D4×C1111yescharacteristic
468#124—22no—
469#124—22no—
470#124—22no—
471#124—21no—
472#124—21no—
473#124D4×C1111yescharacteristic
474#123—22no—
475#123—22no—
476#123—22no—
477#123—21no—
478#123—22no—
479C22⋊Q8—22no—
480C22⋊Q8—22no—
481C22⋊Q8—21no—
482C22⋊Q8—22no—
483C22⋊Q8—21no—
484C22⋊Q8—21no—
485C22⋊Q8—21no—
486C22⋊Q8—22no—
487C22⋊Q8D4×C1111yescharacteristic
488C22⋊Q8D4×C1112yes—
489#121—22no—
490#121—22no—
491#121—22no—
492#121—22no—
493#121—21no—
494#121—21no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121—21no—
499#121D4×C1111yescharacteristic
500#121D4×C1111yescharacteristic
501#121D4×C1111yescharacteristic
502C4×Q8—21no—
503C4×Q8D4×C1112yes—
504C4×Q8C23×C1111yescharacteristic
505C4×D4—22no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4C23×C1111yescharacteristic
513C4×D4C23×C1111yescharacteristic
514C4×D4C23×C1111yescharacteristic
515#117—22no—
516#117—21no—
517#117—21no—
518#117—21no—
519#117—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C42C23×C1111yescharacteristic
523#107—21no—
524#106—21no—
525#106—21no—
526#106—21no—
527C4⋊C8—21no—
528C4⋊C8—21no—
529C4⋊C8—21no—
530C4⋊C8C23×C1111yescharacteristic
531C4⋊C8C23×C1111yescharacteristic
532C4⋊C8C23×C1111yescharacteristic
533C4⋊C8C23×C1111yescharacteristic
534#103—21no—
535#103—22no—
536#102—21no—
537#102—21no—
538#102—21no—
539#102—22no—
540#102—21no—
541#102—21no—
542#102—21no—
543#102—21no—
544C22⋊C8—21no—
545C4×C8C23×C1111yescharacteristic
546C4×C8C23×C1111yescharacteristic
547C2×C11—41no—
548C2×C11—81no—
549C2×C11—81no—
550C2×C11—81no—
551C2×C11—161no—
552C2×C11#301211yescharacteristic
553C2×C11#301311yescharacteristic
554C2×C11#302111yescharacteristic
555#41—81no—
556#41—81no—
557#41—81no—
558#41—81no—
559#41—82no—
560C2×Q8—22no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—81no—
565C2×Q8—81no—
566C2×Q8C2×D4×C1111yescharacteristic
567C2×Q8C2×D4×C1112yes—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4C2×D4×C1111yescharacteristic
580C2×D4C2×D4×C1111yescharacteristic
581C2×D4C2×D4×C1111yescharacteristic
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—41no—
589C22×C4C2×D4×C1111yescharacteristic
590C22×C4C2×D4×C1111yescharacteristic
591C22×C4C2×D4×C1111yescharacteristic
592Q16—82no—
593SD16—81no—
594SD16—82no—
595D8—81no—
596D8—81no—
597D8—81no—
598M16—81no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—81no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4C2×D4×C1112yes—
623C4⋊C4C2×D4×C1111yescharacteristic
624C4⋊C4C2×D4×C1111yescharacteristic
625C4⋊C4C2×D4×C1111yescharacteristic
626C4⋊C4C2×D4×C1111yescharacteristic
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—41no—
643C22⋊C4—41no—
644C42—22no—
645C42—22no—
646C42—21no—
647C42C2×D4×C1111yescharacteristic
648C42C2×D4×C1111yescharacteristic
649C42C2×D4×C1111yescharacteristic
650C42C24×C1111yescharacteristic
651C11#1896511yescharacteristic, direct product factor, Sylow
652C23—21no—
653C23—21no—
654C23—21no—
655C23—41no—
656C23C11×#12011yescharacteristic
657Q8—21no—
658Q8—21no—
659Q8—42no—
660Q8—42no—
661Q8—41no—
662Q8—41no—
663Q8—81no—
664Q8—82no—
665D4—21no—
666D4—21no—
667D4—21no—
668D4—21no—
669D4—21no—
670D4—21no—
671D4—42no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—81no—
677D4—81no—
678D4—81no—
679D4—81no—
680D4—81no—
681D4—82no—
682D4—82no—
683D4—82no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4—82no—
707C2×C4C11×#12011yescharacteristic
708C2×C4C11×#12011yescharacteristic
709C2×C4C11×#12011yescharacteristic
710C2×C4C22×D4×C1111yescharacteristic
711C2×C4C22×D4×C1111yescharacteristic
712C2×C4C22×D4×C1111yescharacteristic
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C8—41no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22C2×C11×#12011yescharacteristic
735C4—21no—
736C4—21no—
737C4—21no—
738C4—21no—
739C4—41no—
740C4—41no—
741C4—42no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—42no—
746C4—81no—
747C4C11×#57611yescharacteristic
748C4C11×#57711yescharacteristic
749C4C11×#57711yescharacteristic
750C4C11×#57811yescharacteristic
751C2—41no—
752C2—81no—
753C2—81no—
754C2—81no—
755C2—161no—
756C2C11×#301211yescharacteristic
757C2C11×#301311yescharacteristic
758C2C11×#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×#3547C2semidirect
2. C11×#3253C2semidirect
3. C11×#3247C2semidirect
4. C11×#3210C2semidirect
5. C11×#1637C2semidirect
6. C11×#1635C2semidirect
7. C11×#1634C2semidirect
8. C11×#1632C2semidirect
9. C11×#1627C2semidirect
10. C11×#1625C2semidirect
11. C11×#1624C2semidirect
12. C11×#1622C2semidirect
13. C11×#1550C2semidirect
14. C11×#1495C2semidirect
15. C11×#1480C2semidirect
176. #18965C11direct (N × H)
273. #3547C2×C11semidirect
274. #3253C2×C11semidirect
275. #3247C2×C11semidirect
276. #3210C2×C11semidirect
277. #1637C2×C11semidirect
278. #1635C2×C11semidirect
279. #1634C2×C11semidirect
280. #1632C2×C11semidirect
281. #1627C2×C11semidirect
282. #1625C2×C11semidirect
283. #1624C2×C11semidirect
284. #1622C2×C11semidirect
285. #1550C2×C11semidirect
286. #1495C2×C11semidirect
287. #1480C2×C11semidirect
651. C11#18965direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35472
C11×#32532
C11×#32472
C11×#32102
C11×#16372
C11×#16352
C11×#16342
C11×#16322
C11×#16272
C11×#16252
C11×#16242
C11×#16222
C11×#15502
C11×#14952
C11×#14802
#1896511