Finite Group Databasebeta

← C11×#24524 #14601717

Subgroups — C11×#24524 #14601717

Order 2816.

884 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3094C211yesmaximal, characteristic, complemented
2C2×C11×#449C211yesmaximal, characteristic
3C11×#2924C211yesmaximal, characteristic, complemented
4C11×#2896C211yesmaximal, characteristic, complemented
5C11×#2064C211yesmaximal, characteristic, complemented
6C11×#2063C211yesmaximal, characteristic, complemented
7C11×#2046C211yesmaximal, characteristic, complemented
8C11×#2045C211yesmaximal, characteristic, complemented
9C11×#1978C211yesmaximal, characteristic, complemented
10C11×#1977C211yesmaximal, characteristic, complemented
11C11×#1931C211yesmaximal, characteristic, complemented
12C11×#1930C211yesmaximal, characteristic, complemented
13C11×#1900C211yesmaximal, characteristic, complemented
14C11×#1855C211yesmaximal, characteristic, complemented
15C11×#1785C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C11×#482—21no—
23C11×#482—21no—
24C11×#481—21no—
25C11×#480—21no—
26C11×#449—21no—
27C11×#449—21no—
28C11×#449—21no—
29C11×#449—21no—
30C11×#433—21no—
31C11×#433—21no—
32C11×#432—21no—
33C11×#431—21no—
34C2×C11×#108C2211yescharacteristic
35C2×C11×#108C2211yescharacteristic
36C11×#428C2211yescharacteristic
37C11×#428C2211yescharacteristic
38C11×#424C2211yescharacteristic
39C11×#424C2211yescharacteristic
40C11×#419C2211yescharacteristic
41C11×#419C2211yescharacteristic
42C11×#418C2211yescharacteristic
43C11×#418C2211yescharacteristic
44C11×#418C2211yescharacteristic
45C11×#418C2211yescharacteristic
46C11×#417—21no—
47C11×#417—21no—
48C11×#416—21no—
49C11×#416—21no—
50C2×C11×#103C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×C11×#101C2211yescharacteristic
53C2×C11×#101C2211yescharacteristic
54C2×C11×#100C2211yescharacteristic
55C2×C11×#100C2211yescharacteristic
56C2×C11×#100C2211yescharacteristic
57C2×C11×#100C2211yescharacteristic
58C11×#407C2211yescharacteristic
59C11×#407C2211yescharacteristic
60C2×C11×C22⋊C8C2211yescharacteristic
61C11×#405C2211yescharacteristic
62C11×#405C2211yescharacteristic
63C11×#343C2211yescharacteristic
64C11×#343C2211yescharacteristic
65C11×#341C2211yescharacteristic
66C11×#341C2211yescharacteristic
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—21no—
70C2×C11×#41—21no—
71C2×C11×#41—21no—
72C2×C11×#41—21no—
73C2×C11×#41—41no—
74C2×C11×#41—41no—
75C22×Q8×C11C2311yescharacteristic
76C22×D4×C11—21no—
77C22×D4×C11—21no—
78C22×D4×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11—21no—
81C23×C4×C11C2311yescharacteristic
82C2×C11×SD16—22no—
83C2×C11×SD16—21no—
84C2×C11×SD16—21no—
85C2×C11×SD16—41no—
86C2×C11×D8—22no—
87C2×C11×D8—21no—
88C2×C11×D8—21no—
89C2×C11×D8—41no—
90C2×C11×M16—21no—
91C2×C11×M16—41no—
92C2×C11×M16—41no—
93C2×C11×M16C2311yescharacteristic
94C2×C11×M16C2311yescharacteristic
95C2×C11×M16C2311yescharacteristic
96C2×C11×M16C2311yescharacteristic
97C2×C11×M16C2311yescharacteristic
98C2×C11×M16C2311yescharacteristic
99C22×C8×C11—21no—
100C22×C8×C11C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C11×#121—21no—
103C11×#121—21no—
104C11×#121—21no—
105C11×#121—21no—
106C11×#117—21no—
107C11×#117—21no—
108C11×#117D411yescharacteristic
109C11×#117D411yescharacteristic
110C11×#117C2311yescharacteristic
111C11×#117C2311yescharacteristic
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C4⋊C4D411yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C42×C11—21no—
118C11×#108—41no—
119C11×#108—41no—
120C11×#107—21no—
121C11×#107—21no—
122C11×#106—21no—
123C11×#106—21no—
124C11×C4⋊C8—21no—
125C11×C4⋊C8—21no—
126C11×C4⋊C8—21no—
127C11×C4⋊C8—21no—
128C11×#103—21no—
129C11×#103—21no—
130C11×#103—21no—
131C11×#103—21no—
132C11×#103—21no—
133C11×#103—21no—
134C11×#102—21no—
135C11×#102—21no—
136C11×#102—21no—
137C11×#102—21no—
138C11×#102—21no—
139C11×#102—21no—
140C11×#102—21no—
141C11×#102—21no—
142C11×#102—21no—
143C11×#102—21no—
144C11×#101—22no—
145C11×#101—41no—
146C11×#100—22no—
147C11×#100—41no—
148C11×#100—41no—
149C11×#100—41no—
150C11×C22⋊C8—21no—
151C11×C22⋊C8—21no—
152C11×C22⋊C8—21no—
153C11×C22⋊C8—21no—
154C11×C22⋊C8D411yescharacteristic
155C11×C22⋊C8D411yescharacteristic
156C11×C22⋊C8D411yescharacteristic
157C11×C22⋊C8D411yescharacteristic
158C11×#97—21no—
159C11×#97—21no—
160C4×C8×C11—21no—
161C4×C8×C11—21no—
162#24524C1111yesmaximal, characteristic, direct product factor, Sylow
163C24×C11—21no—
164C24×C11—21no—
165C24×C11#4111yescharacteristic
166C11×#41—24no—
167C11×#41—24no—
168C11×#41—42no—
169C11×#41—42no—
170C11×#41—42no—
171C11×#41—42no—
172C11×#41—42no—
173C11×#41—42no—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11#4112yes—
180C2×D4×C11—21no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—42no—
192C2×D4×C11—42no—
193C2×D4×C11—41no—
194C2×D4×C11—41no—
195C2×D4×C11—41no—
196C2×D4×C11—41no—
197C2×D4×C11—82no—
198C2×D4×C11#4112yes—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—42no—
208C22×C4×C11—42no—
209C22×C4×C11—41no—
210C22×C4×C11—41no—
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11#4111yescharacteristic
216C22×C4×C11C2411yescharacteristic
217C11×SD16—42no—
218C11×SD16—42no—
219C11×D8—42no—
220C11×D8—42no—
221C11×M16—21no—
222C11×M16—21no—
223C11×M16—21no—
224C11×M16—21no—
225C11×M16—21no—
226C11×M16—21no—
227C11×M16—21no—
228C11×M16—21no—
229C11×M16—21no—
230C11×M16—21no—
231C11×M16—21no—
232C11×M16—21no—
233C11×M16—42no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—42no—
245C2×C8×C11C2×D411yescharacteristic
246C2×C8×C11C2×D411yescharacteristic
247C2×C8×C11C2×D411yescharacteristic
248C2×C8×C11C2×D411yescharacteristic
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4C2×D411yescharacteristic
254C11×C4⋊C4C2×D411yescharacteristic
255C11×C4⋊C4C2×D411yescharacteristic
256C11×C4⋊C4C2×D411yescharacteristic
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—21no—
264C42×C11—21no—
265C42×C11—21no—
266C42×C11—21no—
267#3094C2×C1111yescharacteristic, complemented
268C2×#449C2×C1111yescharacteristic
269#2924C2×C1111yescharacteristic, complemented
270#2896C2×C1111yescharacteristic, complemented
271#2064C2×C1111yescharacteristic, complemented
272#2063C2×C1111yescharacteristic, complemented
273#2046C2×C1111yescharacteristic, complemented
274#2045C2×C1111yescharacteristic, complemented
275#1978C2×C1111yescharacteristic, complemented
276#1977C2×C1111yescharacteristic, complemented
277#1931C2×C1111yescharacteristic, complemented
278#1930C2×C1111yescharacteristic, complemented
279#1900C2×C1111yescharacteristic, complemented
280#1855C2×C1111yescharacteristic, complemented
281#1785C2×C1111yescharacteristic, complemented
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—22no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—81no—
293C23×C11—81no—
294C23×C11—81no—
295C23×C11—81no—
296C23×C11#12111yescharacteristic
297C23×C11#12111yescharacteristic
298C23×C11C2×#4111yescharacteristic
299Q8×C11—22no—
300Q8×C11—22no—
301Q8×C11—41no—
302Q8×C11—41no—
303D4×C11—22no—
304D4×C11—22no—
305D4×C11—44no—
306D4×C11—44no—
307D4×C11—41no—
308D4×C11—41no—
309D4×C11—41no—
310D4×C11—41no—
311D4×C11—41no—
312D4×C11—41no—
313D4×C11—82no—
314D4×C11—82no—
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—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—44no—
331C2×C4×C11—44no—
332C2×C4×C11—42no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—81no—
337C2×C4×C11—81no—
338C2×C4×C11#12111yescharacteristic
339C2×C4×C11#12111yescharacteristic
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C2×#4111yescharacteristic
343C2×C4×C11C2×#4111yescharacteristic
344C2×C4×C11H(5,𝔽2)11yescharacteristic
345C2×C4×C11H(5,𝔽2)11yescharacteristic
346C8×C11—21no—
347C8×C11—21no—
348C8×C11—21no—
349C8×C11—21no—
350C8×C11—41no—
351C8×C11—41no—
352C8×C11—41no—
353C8×C11—41no—
354C8×C11—41no—
355C8×C11—41no—
356C22×#41C22×C1111yescharacteristic
357C22×SD16C22×C1111yescharacteristic
358C22×D8C22×C1111yescharacteristic
359C22×M16C22×C1111yescharacteristic
360C2×#121C22×C1111yescharacteristic
361C2×#117C22×C1111yescharacteristic
362#482—21no—
363#482—21no—
364#481—21no—
365#480—21no—
366#449—21no—
367#449—21no—
368#449—21no—
369#449—21no—
370#433—21no—
371#433—21no—
372#432—21no—
373#431—21no—
374C2×#108C22×C1111yescharacteristic
375C2×#108C22×C1111yescharacteristic
376#428C22×C1111yescharacteristic
377#428C22×C1111yescharacteristic
378#424C22×C1111yescharacteristic
379#424C22×C1111yescharacteristic
380#419C22×C1111yescharacteristic
381#419C22×C1111yescharacteristic
382#418C22×C1111yescharacteristic
383#418C22×C1111yescharacteristic
384#418C22×C1111yescharacteristic
385#418C22×C1111yescharacteristic
386#417—21no—
387#417—21no—
388#416—21no—
389#416—21no—
390C2×#103C22×C1111yescharacteristic
391C2×#102C22×C1111yescharacteristic
392C2×#101C22×C1111yescharacteristic
393C2×#101C22×C1111yescharacteristic
394C2×#100C22×C1111yescharacteristic
395C2×#100C22×C1111yescharacteristic
396C2×#100C22×C1111yescharacteristic
397C2×#100C22×C1111yescharacteristic
398#407C22×C1111yescharacteristic
399#407C22×C1111yescharacteristic
400C2×C22⋊C8C22×C1111yescharacteristic
401#405C22×C1111yescharacteristic
402#405C22×C1111yescharacteristic
403#343C22×C1111yescharacteristic
404#343C22×C1111yescharacteristic
405#341C22×C1111yescharacteristic
406#341C22×C1111yescharacteristic
407C22×C11—21no—
408C22×C11—21no—
409C22×C11—21no—
410C22×C11—21no—
411C22×C11—21no—
412C22×C11—21no—
413C22×C11—21no—
414C22×C11—21no—
415C22×C11—42no—
416C22×C11—81no—
417C22×C11—81no—
418C22×C11—82no—
419C22×C11—82no—
420C22×C11—81no—
421C22×C11—81no—
422C22×C11—81no—
423C22×C11—81no—
424C22×C11—81no—
425C22×C11—161no—
426C22×C11—161no—
427C22×C11C2×#12111yescharacteristic
428C22×C11#55111yescharacteristic
429C22×C11#55111yescharacteristic
430C4×C11—21no—
431C4×C11—21no—
432C4×C11—42no—
433C4×C11—41no—
434C4×C11—41no—
435C4×C11—41no—
436C4×C11—41no—
437C4×C11—81no—
438C4×C11#52511yescharacteristic
439C4×C11#53511yescharacteristic
440C4×C11#54611yescharacteristic
441C4×C11#54611yescharacteristic
442C2×#41—22no—
443C2×#41—22no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—41no—
449C2×#41—41no—
450C22×Q8C23×C1111yescharacteristic
451C22×D4—21no—
452C22×D4—21no—
453C22×D4C23×C1111yescharacteristic
454C22×D4C23×C1111yescharacteristic
455C23×C4—21no—
456C23×C4C23×C1111yescharacteristic
457C2×SD16—22no—
458C2×SD16—21no—
459C2×SD16—21no—
460C2×SD16—41no—
461C2×D8—22no—
462C2×D8—21no—
463C2×D8—21no—
464C2×D8—41no—
465C2×M16—21no—
466C2×M16—41no—
467C2×M16—41no—
468C2×M16C23×C1111yescharacteristic
469C2×M16C23×C1111yescharacteristic
470C2×M16C23×C1111yescharacteristic
471C2×M16C23×C1111yescharacteristic
472C2×M16C23×C1111yescharacteristic
473C2×M16C23×C1111yescharacteristic
474C22×C8—21no—
475C22×C8C23×C1111yescharacteristic
476C22×C8C23×C1111yescharacteristic
477#121—21no—
478#121—21no—
479#121—21no—
480#121—21no—
481#117—21no—
482#117—21no—
483#117D4×C1111yescharacteristic
484#117D4×C1111yescharacteristic
485#117C23×C1111yescharacteristic
486#117C23×C1111yescharacteristic
487C2×C4⋊C4D4×C1111yescharacteristic
488C2×C4⋊C4D4×C1111yescharacteristic
489C2×C4⋊C4C23×C1111yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C42—21no—
493#108—41no—
494#108—41no—
495#107—21no—
496#107—21no—
497#106—21no—
498#106—21no—
499C4⋊C8—21no—
500C4⋊C8—21no—
501C4⋊C8—21no—
502C4⋊C8—21no—
503#103—21no—
504#103—21no—
505#103—21no—
506#103—21no—
507#103—21no—
508#103—21no—
509#102—21no—
510#102—21no—
511#102—21no—
512#102—21no—
513#102—21no—
514#102—21no—
515#102—21no—
516#102—21no—
517#102—21no—
518#102—21no—
519#101—22no—
520#101—41no—
521#100—22no—
522#100—41no—
523#100—41no—
524#100—41no—
525C22⋊C8—21no—
526C22⋊C8—21no—
527C22⋊C8—21no—
528C22⋊C8—21no—
529C22⋊C8D4×C1111yescharacteristic
530C22⋊C8D4×C1111yescharacteristic
531C22⋊C8D4×C1111yescharacteristic
532C22⋊C8D4×C1111yescharacteristic
533#97—21no—
534#97—21no—
535C4×C8—21no—
536C4×C8—21no—
537C2×C11—21no—
538C2×C11—21no—
539C2×C11—41no—
540C2×C11—41no—
541C2×C11—82no—
542C2×C11—161no—
543C2×C11#241111yescharacteristic
544C2×C11#306711yescharacteristic
545C2×C11#306811yescharacteristic
546C24—21no—
547C24—21no—
548C24C11×#4111yescharacteristic
549#41—24no—
550#41—24no—
551#41—42no—
552#41—42no—
553#41—42no—
554#41—42no—
555#41—42no—
556#41—42no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8C11×#4112yes—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—82no—
581C2×D4C11×#4112yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4C2×D4×C1111yescharacteristic
595C22×C4C2×D4×C1111yescharacteristic
596C22×C4C2×D4×C1111yescharacteristic
597C22×C4C2×D4×C1111yescharacteristic
598C22×C4C11×#4111yescharacteristic
599C22×C4C24×C1111yescharacteristic
600SD16—42no—
601SD16—42no—
602D8—42no—
603D8—42no—
604M16—21no—
605M16—21no—
606M16—21no—
607M16—21no—
608M16—21no—
609M16—21no—
610M16—21no—
611M16—21no—
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—42no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—42no—
628C2×C8C2×D4×C1111yescharacteristic
629C2×C8C2×D4×C1111yescharacteristic
630C2×C8C2×D4×C1111yescharacteristic
631C2×C8C2×D4×C1111yescharacteristic
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4C2×D4×C1111yescharacteristic
637C4⋊C4C2×D4×C1111yescharacteristic
638C4⋊C4C2×D4×C1111yescharacteristic
639C4⋊C4C2×D4×C1111yescharacteristic
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—41no—
645C22⋊C4—41no—
646C42—21no—
647C42—21no—
648C42—21no—
649C42—21no—
650C11#2452411yescharacteristic, direct product factor, Sylow
651C23—21no—
652C23—21no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—81no—
662C23—81no—
663C23—81no—
664C23—81no—
665C23C11×#12111yescharacteristic
666C23C11×#12111yescharacteristic
667C23C2×C11×#4111yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672D4—22no—
673D4—22no—
674D4—44no—
675D4—44no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—82no—
683D4—82no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4C11×#12111yescharacteristic
708C2×C4C11×#12111yescharacteristic
709C2×C4C22×D4×C1111yescharacteristic
710C2×C4C22×D4×C1111yescharacteristic
711C2×C4C2×C11×#4111yescharacteristic
712C2×C4C2×C11×#4111yescharacteristic
713C2×C4C11×H(5,𝔽2)11yescharacteristic
714C2×C4C11×H(5,𝔽2)11yescharacteristic
715C8—21no—
716C8—21no—
717C8—21no—
718C8—21no—
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8—41no—
724C8—41no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—42no—
734C22—81no—
735C22—81no—
736C22—82no—
737C22—82no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—161no—
744C22—161no—
745C22C2×C11×#12111yescharacteristic
746C22C11×#55111yescharacteristic
747C22C11×#55111yescharacteristic
748C4—21no—
749C4—21no—
750C4—42no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—81no—
756C4C11×#52511yescharacteristic
757C4C11×#53511yescharacteristic
758C4C11×#54611yescharacteristic
759C4C11×#54611yescharacteristic
760C2—21no—
761C2—21no—
762C2—41no—
763C2—41no—
764C2—82no—
765C2—161no—
766C2C11×#241111yescharacteristic
767C2C11×#306711yescharacteristic
768C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3094C2semidirect
3. C11×#2924C2semidirect
4. C11×#2896C2semidirect
5. C11×#2064C2semidirect
6. C11×#2063C2semidirect
7. C11×#2046C2semidirect
8. C11×#2045C2semidirect
9. C11×#1978C2semidirect
10. C11×#1977C2semidirect
11. C11×#1931C2semidirect
12. C11×#1930C2semidirect
13. C11×#1900C2semidirect
14. C11×#1855C2semidirect
15. C11×#1785C2semidirect
162. #24524C11direct (N × H)
267. #3094C2×C11semidirect
269. #2924C2×C11semidirect
270. #2896C2×C11semidirect
271. #2064C2×C11semidirect
272. #2063C2×C11semidirect
273. #2046C2×C11semidirect
274. #2045C2×C11semidirect
275. #1978C2×C11semidirect
276. #1977C2×C11semidirect
277. #1931C2×C11semidirect
278. #1930C2×C11semidirect
279. #1900C2×C11semidirect
280. #1855C2×C11semidirect
281. #1785C2×C11semidirect
650. C11#24524direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30942
C2×C11×#4492
C11×#29242
C11×#28962
C11×#20642
C11×#20632
C11×#20462
C11×#20452
C11×#19782
C11×#19772
C11×#19312
C11×#19302
C11×#19002
C11×#18552
C11×#17852
#2452411