Finite Group Databasebeta

← C11×#24635 #14601828

Subgroups — C11×#24635 #14601828

Order 2816.

904 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#464C211yesmaximal, characteristic, complemented
2C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
3C11×#2544C211yesmaximal, characteristic
4C11×#2356C211yesmaximal, characteristic, complemented
5C11×#2056C211yesmaximal, characteristic, complemented
6C11×#2055C211yesmaximal, characteristic, complemented
7C11×#2015C211yesmaximal, characteristic, complemented
8C11×#2014C211yesmaximal, characteristic
9C11×#1983C211yesmaximal, characteristic, complemented
10C11×#1982C211yesmaximal, characteristic
11C11×#1958C211yesmaximal, characteristic, complemented
12C11×#1939C211yesmaximal, characteristic, complemented
13C11×#1927C211yesmaximal, characteristic, complemented
14C11×#1926C211yesmaximal, characteristic, complemented
15C11×#1804C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C11×#127C2211yescharacteristic
20C2×C11×#124C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C11×#464—24no—
25C4×C11×SD16—24no—
26C2×C11×#106C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#102C2211yescharacteristic
40C2×C4×C8×C11C2211yescharacteristic
41C11×#394—21no—
42C11×#394—21no—
43C11×#391C2211yescharacteristic
44C11×#391C2211yescharacteristic
45C11×#391C2211yescharacteristic
46C11×#390C2211yescharacteristic
47C11×#387—21no—
48C11×#387—21no—
49C11×#386—21no—
50C11×#386—21no—
51C11×#383—21no—
52C11×#382C2211yescharacteristic
53C4×C11×C4⋊C4C2211yescharacteristic
54C4×C11×C4⋊C4C2211yescharacteristic
55C4×C11×C4⋊C4C2211yescharacteristic
56C11×#376—21no—
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11C2311yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C2×C11×Q16—22no—
69C2×C11×Q16—41no—
70C2×C11×Q16—41no—
71C2×C11×SD16—22no—
72C2×C11×SD16—22no—
73C2×C11×SD16—22no—
74C2×C11×SD16—22no—
75C2×C11×SD16—41no—
76C2×C11×SD16—41no—
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C11×#127—22no—
82C11×#127—41no—
83C11×#124—22no—
84C11×#124—22no—
85C11×#124—22no—
86C11×#124—41no—
87C4×Q8×C11—22no—
88C4×Q8×C11D414yescomplemented
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C42×C11—21no—
106C2×C42×C11—21no—
107C2×C42×C11—21no—
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C11×#106—22no—
112C11×C4⋊C8—22no—
113C11×C4⋊C8—41no—
114C11×C4⋊C8—41no—
115C11×#103—22no—
116C11×#103—22no—
117C11×#103—22no—
118C11×#103—41no—
119C11×#102—22no—
120C11×#102—22no—
121C11×#102—22no—
122C11×#102—41no—
123C11×#102—41no—
124C11×#102—41no—
125C4×C8×C11—22no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95D411yescharacteristic
137C11×#95D411yescharacteristic
138#24635C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—21no—
140C24×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11C2×D412yes—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—42no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11—42no—
168C2×D4×C11—81no—
169C2×D4×C11—81no—
170C2×D4×C11#4112yes—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—42no—
178C22×C4×C11—81no—
179C22×C4×C11—81no—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2411yescharacteristic
187C11×Q16—44no—
188C11×SD16—28no—
189C11×SD16—44no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11#4112yes—
202C11×C4⋊C4—24no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—41no—
212C11×C4⋊C4C2×D412yes—
213C11×C22⋊C4—42no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—42no—
217C11×C22⋊C4—42no—
218C11×C22⋊C4—81no—
219C11×C22⋊C4—81no—
220C42×C11—24no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—42no—
226C42×C11—42no—
227C42×C11C2×D412yes—
228C42×C11#4112yes—
229C2×#464C2×C1111yescharacteristic, complemented
230C2×C4×SD16C2×C1111yescharacteristic, complemented
231#2544C2×C1111yescharacteristic
232#2356C2×C1111yescharacteristic, complemented
233#2056C2×C1111yescharacteristic, complemented
234#2055C2×C1111yescharacteristic, complemented
235#2015C2×C1111yescharacteristic, complemented
236#2014C2×C1111yescharacteristic
237#1983C2×C1111yescharacteristic, complemented
238#1982C2×C1111yescharacteristic
239#1958C2×C1111yescharacteristic, complemented
240#1939C2×C1111yescharacteristic, complemented
241#1927C2×C1111yescharacteristic, complemented
242#1926C2×C1111yescharacteristic, complemented
243#1804C2×C1111yescharacteristic, complemented
244C23×C11—22no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11C22×D411yescharacteristic
259Q8×C11—22no—
260Q8×C11—22no—
261Q8×C11—41no—
262Q8×C11—41no—
263Q8×C11—41no—
264Q8×C11—41no—
265Q8×C11—41no—
266Q8×C11—41no—
267D4×C11—22no—
268D4×C11—22no—
269D4×C11—41no—
270D4×C11—41no—
271D4×C11—41no—
272D4×C11—41no—
273D4×C11—41no—
274D4×C11—41no—
275D4×C11—84no—
276D4×C11—84no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—84no—
311C2×C4×C11#12112yes—
312C2×C4×C11#12112yes—
313C2×C4×C11#13512yes—
314C2×C4×C11C22×D411yescharacteristic
315C2×C4×C11C2×#4111yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11H(5,𝔽2)11yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C8×C11—22no—
321C8×C11—41no—
322C8×C11—41no—
323C8×C11—41no—
324C22×Q16C22×C1111yescharacteristic
325C22×SD16C22×C1111yescharacteristic
326C22×SD16C22×C1111yescharacteristic
327C2×#127C22×C1111yescharacteristic
328C2×#124C22×C1111yescharacteristic
329C2×#124C22×C1111yescharacteristic
330C2×C4×Q8C22×C1111yescharacteristic
331C2×C4×D4C22×C1111yescharacteristic
332#464—24no—
333C4×SD16—24no—
334C2×#106C22×C1111yescharacteristic
335C2×C4⋊C8C22×C1111yescharacteristic
336C2×C4⋊C8C22×C1111yescharacteristic
337C2×C4⋊C8C22×C1111yescharacteristic
338C2×#103C22×C1111yescharacteristic
339C2×#103C22×C1111yescharacteristic
340C2×#103C22×C1111yescharacteristic
341C2×#103C22×C1111yescharacteristic
342C2×#102C22×C1111yescharacteristic
343C2×#102C22×C1111yescharacteristic
344C2×#102C22×C1111yescharacteristic
345C2×#102C22×C1111yescharacteristic
346C2×#102C22×C1111yescharacteristic
347C2×#102C22×C1111yescharacteristic
348C2×C4×C8C22×C1111yescharacteristic
349#394—21no—
350#394—21no—
351#391C22×C1111yescharacteristic
352#391C22×C1111yescharacteristic
353#391C22×C1111yescharacteristic
354#390C22×C1111yescharacteristic
355#387—21no—
356#387—21no—
357#386—21no—
358#386—21no—
359#383—21no—
360#382C22×C1111yescharacteristic
361C4×C4⋊C4C22×C1111yescharacteristic
362C4×C4⋊C4C22×C1111yescharacteristic
363C4×C4⋊C4C22×C1111yescharacteristic
364#376—21no—
365#340C22×C1111yescharacteristic
366#340C22×C1111yescharacteristic
367#336C22×C1111yescharacteristic
368#336C22×C1111yescharacteristic
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—81no—
373C22×C11—81no—
374C22×C11—81no—
375C22×C11—81no—
376C22×C11—81no—
377C22×C11—81no—
378C22×C11—81no—
379C22×C11—81no—
380C22×C11—81no—
381C22×C11—81no—
382C22×C11—81no—
383C22×C11C2×#12111yescharacteristic
384C22×C11#54611yescharacteristic
385C22×C11#55011yescharacteristic
386C22×C11C2×#13511yescharacteristic
387C22×C11#57511yescharacteristic
388C22×C11#57711yescharacteristic
389C22×C11#57711yescharacteristic
390C4×C11—22no—
391C4×C11—22no—
392C4×C11—22no—
393C4×C11—42no—
394C4×C11—42no—
395C4×C11—41no—
396C4×C11—41no—
397C4×C11—41no—
398C4×C11—81no—
399C4×C11—81no—
400C4×C11—81no—
401C4×C11—81no—
402C4×C11#52511yescharacteristic
403C4×C11#53511yescharacteristic
404C4×C11#55311yescharacteristic
405C4×C11#55511yescharacteristic
406C22×Q8C23×C1111yescharacteristic
407C22×Q8C23×C1111yescharacteristic
408C22×D4—21no—
409C22×D4—21no—
410C22×D4C23×C1111yescharacteristic
411C22×D4C23×C1111yescharacteristic
412C23×C4—21no—
413C2×Q16—22no—
414C2×Q16—41no—
415C2×Q16—41no—
416C2×SD16—22no—
417C2×SD16—22no—
418C2×SD16—22no—
419C2×SD16—22no—
420C2×SD16—41no—
421C2×SD16—41no—
422C22×C8C23×C1111yescharacteristic
423C22×C8C23×C1111yescharacteristic
424C22×C8C23×C1111yescharacteristic
425C22×C8C23×C1111yescharacteristic
426#127—22no—
427#127—41no—
428#124—22no—
429#124—22no—
430#124—22no—
431#124—41no—
432C4×Q8—22no—
433C4×Q8D4×C1114yescomplemented
434C4×D4—22no—
435C4×D4—22no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4D4×C1111yescharacteristic
438C2×C4⋊C4D4×C1111yescharacteristic
439C2×C4⋊C4C23×C1111yescharacteristic
440C2×C4⋊C4C23×C1111yescharacteristic
441C2×C4⋊C4C23×C1111yescharacteristic
442C2×C4⋊C4C23×C1111yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—21no—
453C2×C42C23×C1111yescharacteristic
454C2×C42C23×C1111yescharacteristic
455C2×C42C23×C1111yescharacteristic
456#106—22no—
457C4⋊C8—22no—
458C4⋊C8—41no—
459C4⋊C8—41no—
460#103—22no—
461#103—22no—
462#103—22no—
463#103—41no—
464#102—22no—
465#102—22no—
466#102—22no—
467#102—41no—
468#102—41no—
469#102—41no—
470C4×C8—22no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95D4×C1111yescharacteristic
482#95D4×C1111yescharacteristic
483C2×C11—82no—
484C2×C11—161no—
485C2×C11#241411yescharacteristic
486C2×C11#303511yescharacteristic
487C2×C11#304311yescharacteristic
488C2×C11#329611yescharacteristic
489C2×C11#332311yescharacteristic
490C2×C11#339411yescharacteristic
491C2×C11#340111yescharacteristic
492C24—21no—
493C24—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8C2×D4×C1112yes—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—81no—
522C2×D4—81no—
523C2×D4C11×#4112yes—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—42no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4C2×D4×C1111yescharacteristic
534C22×C4C2×D4×C1111yescharacteristic
535C22×C4C2×D4×C1111yescharacteristic
536C22×C4C2×D4×C1111yescharacteristic
537C22×C4C2×D4×C1111yescharacteristic
538C22×C4C2×D4×C1111yescharacteristic
539C22×C4C24×C1111yescharacteristic
540Q16—44no—
541SD16—28no—
542SD16—44no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8C11×#4112yes—
555C4⋊C4—24no—
556C4⋊C4—22no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—41no—
565C4⋊C4C2×D4×C1112yes—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C42—24no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—42no—
579C42—42no—
580C42C2×D4×C1112yes—
581C42C11×#4112yes—
582C11#2463511yescharacteristic, direct product factor, Sylow
583C23—22no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23C22×D4×C1111yescharacteristic
598Q8—22no—
599Q8—22no—
600Q8—41no—
601Q8—41no—
602Q8—41no—
603Q8—41no—
604Q8—41no—
605Q8—41no—
606D4—22no—
607D4—22no—
608D4—41no—
609D4—41no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—41no—
614D4—84no—
615D4—84no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—84no—
650C2×C4C11×#12112yes—
651C2×C4C11×#12112yes—
652C2×C4C11×#13512yes—
653C2×C4C22×D4×C1111yescharacteristic
654C2×C4C2×C11×#4111yescharacteristic
655C2×C4C2×C11×#4111yescharacteristic
656C2×C4C2×C11×#4111yescharacteristic
657C2×C4C11×H(5,𝔽2)11yescharacteristic
658C2×C4C11×H(5,𝔽2)11yescharacteristic
659C8—22no—
660C8—41no—
661C8—41no—
662C8—41no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22C2×C11×#12111yescharacteristic
678C22C11×#54611yescharacteristic
679C22C11×#55011yescharacteristic
680C22C2×C11×#13511yescharacteristic
681C22C11×#57511yescharacteristic
682C22C11×#57711yescharacteristic
683C22C11×#57711yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—42no—
688C4—42no—
689C4—41no—
690C4—41no—
691C4—41no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4C11×#52511yescharacteristic
697C4C11×#53511yescharacteristic
698C4C11×#55311yescharacteristic
699C4C11×#55511yescharacteristic
700C2—82no—
701C2—161no—
702C2C11×#241411yescharacteristic
703C2C11×#303511yescharacteristic
704C2C11×#304311yescharacteristic
705C2C11×#329611yescharacteristic
706C2C11×#332311yescharacteristic
707C2C11×#339411yescharacteristic
708C2C11×#340111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#464C2semidirect
2. C2×C4×C11×SD16C2semidirect
4. C11×#2356C2semidirect
5. C11×#2056C2semidirect
6. C11×#2055C2semidirect
7. C11×#2015C2semidirect
9. C11×#1983C2semidirect
11. C11×#1958C2semidirect
12. C11×#1939C2semidirect
13. C11×#1927C2semidirect
14. C11×#1926C2semidirect
15. C11×#1804C2semidirect
88. C4×Q8×C11D4semidirect
138. #24635C11direct (N × H)
229. C2×#464C2×C11semidirect
230. C2×C4×SD16C2×C11semidirect
232. #2356C2×C11semidirect
233. #2056C2×C11semidirect
234. #2055C2×C11semidirect
235. #2015C2×C11semidirect
237. #1983C2×C11semidirect
239. #1958C2×C11semidirect
240. #1939C2×C11semidirect
241. #1927C2×C11semidirect
242. #1926C2×C11semidirect
243. #1804C2×C11semidirect
433. C4×Q8D4×C11semidirect
582. C11#24635direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4642
C2×C4×C11×SD162
C11×#25442
C11×#23562
C11×#20562
C11×#20552
C11×#20152
C11×#20142
C11×#19832
C11×#19822
C11×#19582
C11×#19392
C11×#19272
C11×#19262
C11×#18042
#2463511