Finite Group Databasebeta

← C11×#24977 #14602170

Subgroups — C11×#24977 #14602170

Order 2816.

892 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2535C211yesmaximal, characteristic
2D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
3C11×#2077C211yesmaximal, characteristic, complemented
4C11×#2076C211yesmaximal, characteristic, complemented
5C11×#2034C211yesmaximal, characteristic, complemented
6C11×#2033C211yesmaximal, characteristic, complemented
7C11×#1955C211yesmaximal, characteristic, complemented
8C11×#1949C211yesmaximal, characteristic, complemented
9C11×#1874C211yesmaximal, characteristic, complemented
10C11×#1874C211yesmaximal, characteristic, complemented
11C11×#1836C211yesmaximal, characteristic, complemented
12C11×#1824C211yesmaximal, characteristic, complemented
13C11×#1823C211yesmaximal, characteristic, complemented
14C11×#1802C211yesmaximal, characteristic, complemented
15C11×#1762C211yesmaximal, characteristic, complemented
16C2×C11×#121C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C4×D4×C11—21no—
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×C22⋊C8C2211yescharacteristic
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×#97C2211yescharacteristic
35C11×#397—21no—
36C11×#392—21no—
37C11×#389—21no—
38C11×#386—21no—
39C11×#386—21no—
40C11×#385—21no—
41C11×#385—21no—
42C11×#384C2211yescharacteristic
43C11×#382C2211yescharacteristic
44C11×#380C2211yescharacteristic
45C11×#380C2211yescharacteristic
46C11×#380C2211yescharacteristic
47C11×#380C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11D411yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×#121—22no—
73C11×#121—22no—
74C11×#121—41no—
75C11×#121—41no—
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—44no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—41no—
88C2×C11×C4⋊C4—41no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—21no—
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⋊C4D411yescharacteristic
105C2×C11×C22⋊C4D411yescharacteristic
106C2×C42×C11—21no—
107C2×C42×C11C2311yescharacteristic
108C11×#107—41no—
109C11×#106—41no—
110C11×C4⋊C8—22no—
111C11×#102—22no—
112C11×#102—22no—
113C11×#102—41no—
114C11×#102—41no—
115C11×C22⋊C8—41no—
116C11×C22⋊C8—41no—
117C11×C22⋊C8—41no—
118C11×C22⋊C8—41no—
119C11×#97—22no—
120C11×#95—21no—
121C11×#95—21no—
122C11×#95—21no—
123C11×#95—21no—
124C11×#95—21no—
125C11×#95—21no—
126C11×#95—21no—
127#24977C1111yesmaximal, characteristic, direct product factor, Sylow
128C24×C11—21no—
129C24×C11C2×D411yescharacteristic
130C24×C11C2×D411yescharacteristic
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—42no—
140C2×D4×C11—42no—
141C2×D4×C11—42no—
142C2×D4×C11—42no—
143C2×D4×C11—81no—
144C2×D4×C11—81no—
145C2×D4×C11#4112yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—42no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11—42no—
169C22×C4×C11—42no—
170C22×C4×C11—81no—
171C22×C4×C11—81no—
172C22×C4×C11—81no—
173C22×C4×C11—81no—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2411yescharacteristic
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—42no—
206C11×C4⋊C4—42no—
207C11×C4⋊C4—42no—
208C11×C4⋊C4—81no—
209C11×C4⋊C4#4112yes—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—42no—
213C11×C22⋊C4—42no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—42no—
217C11×C22⋊C4—81no—
218C11×C22⋊C4—81no—
219C42×C11—42no—
220C42×C11#4112yes—
221C42×C11#4112yes—
222#2535C2×C1111yescharacteristic
223D4×C4⋊C4C2×C1111yescharacteristic, complemented
224#2077C2×C1111yescharacteristic, complemented
225#2076C2×C1111yescharacteristic, complemented
226#2034C2×C1111yescharacteristic, complemented
227#2033C2×C1111yescharacteristic, complemented
228#1955C2×C1111yescharacteristic, complemented
229#1949C2×C1111yescharacteristic, complemented
230#1874C2×C1111yescharacteristic, complemented
231#1874C2×C1111yescharacteristic, complemented
232#1836C2×C1111yescharacteristic, complemented
233#1824C2×C1111yescharacteristic, complemented
234#1823C2×C1111yescharacteristic, complemented
235#1802C2×C1111yescharacteristic, complemented
236#1762C2×C1111yescharacteristic, complemented
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—22no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11AGL(1,ℤ/8)12yes—
257C23×C11#13712yes—
258C23×C11C22×D411yescharacteristic
259D4×C11—28no—
260D4×C11—22no—
261D4×C11—22no—
262D4×C11—41no—
263D4×C11—41no—
264D4×C11—84no—
265D4×C11—84no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—22no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
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—84no—
306C2×C4×C11—84no—
307C2×C4×C11—84no—
308C2×C4×C11#12312yes—
309C2×C4×C11#12312yes—
310C2×C4×C11C2×#4111yescharacteristic
311C2×C4×C11C2×#4111yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11C2×#4111yescharacteristic
314C2×C4×C11H(5,𝔽2)11yescharacteristic
315C2×C4×C11H(5,𝔽2)11yescharacteristic
316C8×C11—41no—
317C8×C11—41no—
318C8×C11—41no—
319C8×C11—41no—
320C2×#121C22×C1111yescharacteristic
321C2×#121C22×C1111yescharacteristic
322C2×C4×D4—21no—
323C2×C4×D4C22×C1111yescharacteristic
324C2×C4×D4C22×C1111yescharacteristic
325C22×C4⋊C4C22×C1111yescharacteristic
326C22×C4⋊C4C22×C1111yescharacteristic
327C2×#107C22×C1111yescharacteristic
328C2×#106C22×C1111yescharacteristic
329C2×C4⋊C8C22×C1111yescharacteristic
330C2×#102C22×C1111yescharacteristic
331C2×#102C22×C1111yescharacteristic
332C2×#102C22×C1111yescharacteristic
333C2×#102C22×C1111yescharacteristic
334C2×C22⋊C8C22×C1111yescharacteristic
335C2×C22⋊C8C22×C1111yescharacteristic
336C2×C22⋊C8C22×C1111yescharacteristic
337C2×C22⋊C8C22×C1111yescharacteristic
338C2×#97C22×C1111yescharacteristic
339#397—21no—
340#392—21no—
341#389—21no—
342#386—21no—
343#386—21no—
344#385—21no—
345#385—21no—
346#384C22×C1111yescharacteristic
347#382C22×C1111yescharacteristic
348#380C22×C1111yescharacteristic
349#380C22×C1111yescharacteristic
350#380C22×C1111yescharacteristic
351#380C22×C1111yescharacteristic
352C4×C4⋊C4C22×C1111yescharacteristic
353#340C22×C1111yescharacteristic
354#340C22×C1111yescharacteristic
355#340C22×C1111yescharacteristic
356#340C22×C1111yescharacteristic
357#340C22×C1111yescharacteristic
358#340C22×C1111yescharacteristic
359#340C22×C1111yescharacteristic
360#340C22×C1111yescharacteristic
361#340C22×C1111yescharacteristic
362#340C22×C1111yescharacteristic
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—22no—
368C22×C11—22no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11—41no—
373C22×C11—41no—
374C22×C11—41no—
375C22×C11—41no—
376C22×C11—41no—
377C22×C11—42no—
378C22×C11—42no—
379C22×C11—42no—
380C22×C11—81no—
381C22×C11—81no—
382C22×C11—81no—
383C22×C11—81no—
384C22×C11C2×#12311yescharacteristic
385C22×C11#54611yescharacteristic
386C22×C11#54611yescharacteristic
387C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
388C22×C11C2×#13711yescharacteristic
389C22×C11#57611yescharacteristic
390C22×C11#57711yescharacteristic
391C4×C11—22no—
392C4×C11—22no—
393C4×C11—41no—
394C4×C11—41no—
395C4×C11—42no—
396C4×C11—81no—
397C4×C11—81no—
398C4×C11—81no—
399C4×C11—81no—
400C4×C11—81no—
401C4×C11—81no—
402C4×C11#52911yescharacteristic
403C4×C11#54011yescharacteristic
404C4×C11#55311yescharacteristic
405C4×C11#55511yescharacteristic
406C22×D4—21no—
407C22×D4—21no—
408C22×D4D4×C1111yescharacteristic
409C22×D4C23×C1111yescharacteristic
410C23×C4—21no—
411C23×C4—21no—
412C23×C4—21no—
413C23×C4C23×C1111yescharacteristic
414C23×C4C23×C1111yescharacteristic
415C22×C8C23×C1111yescharacteristic
416C22×C8C23×C1111yescharacteristic
417C22×C8C23×C1111yescharacteristic
418C22×C8C23×C1111yescharacteristic
419#121—22no—
420#121—22no—
421#121—41no—
422#121—41no—
423C4×D4—22no—
424C4×D4—22no—
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—44no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—41no—
435C2×C4⋊C4—41no—
436C2×C4⋊C4D4×C1111yescharacteristic
437C2×C4⋊C4C23×C1111yescharacteristic
438C2×C4⋊C4C23×C1111yescharacteristic
439C2×C4⋊C4C23×C1111yescharacteristic
440C2×C4⋊C4C23×C1111yescharacteristic
441C2×C4⋊C4C23×C1111yescharacteristic
442C2×C4⋊C4C23×C1111yescharacteristic
443C2×C4⋊C4C23×C1111yescharacteristic
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×C22⋊C4—21no—
451C2×C22⋊C4D4×C1111yescharacteristic
452C2×C22⋊C4D4×C1111yescharacteristic
453C2×C42—21no—
454C2×C42C23×C1111yescharacteristic
455#107—41no—
456#106—41no—
457C4⋊C8—22no—
458#102—22no—
459#102—22no—
460#102—41no—
461#102—41no—
462C22⋊C8—41no—
463C22⋊C8—41no—
464C22⋊C8—41no—
465C22⋊C8—41no—
466#97—22no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474C2×C11—42no—
475C2×C11—42no—
476C2×C11—82no—
477C2×C11#242011yescharacteristic
478C2×C11#309211yescharacteristic
479C2×C11#309611yescharacteristic
480C2×C11#330611yescharacteristic
481C2×C11#331411yescharacteristic
482C2×C11#331811yescharacteristic
483C2×C11#332011yescharacteristic
484C24—21no—
485C24C2×D4×C1111yescharacteristic
486C24C2×D4×C1111yescharacteristic
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—81no—
500C2×D4—81no—
501C2×D4C11×#4112yes—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4C2×D4×C1111yescharacteristic
531C22×C4C2×D4×C1111yescharacteristic
532C22×C4C2×D4×C1111yescharacteristic
533C22×C4C2×D4×C1111yescharacteristic
534C22×C4C24×C1111yescharacteristic
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C4⋊C4—22no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—81no—
565C4⋊C4C11×#4112yes—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—81no—
574C22⋊C4—81no—
575C42—42no—
576C42C11×#4112yes—
577C42C11×#4112yes—
578C11#2497711yescharacteristic, direct product factor, Sylow
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—22no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23C11×AGL(1,ℤ/8)12yes—
599C23C11×#13712yes—
600C23C22×D4×C1111yescharacteristic
601D4—28no—
602D4—22no—
603D4—22no—
604D4—41no—
605D4—41no—
606D4—84no—
607D4—84no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
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—84no—
648C2×C4—84no—
649C2×C4—84no—
650C2×C4C11×#12312yes—
651C2×C4C11×#12312yes—
652C2×C4C2×C11×#4111yescharacteristic
653C2×C4C2×C11×#4111yescharacteristic
654C2×C4C2×C11×#4111yescharacteristic
655C2×C4C2×C11×#4111yescharacteristic
656C2×C4C11×H(5,𝔽2)11yescharacteristic
657C2×C4C11×H(5,𝔽2)11yescharacteristic
658C8—41no—
659C8—41no—
660C8—41no—
661C8—41no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C2×C11×#12311yescharacteristic
684C22C11×#54611yescharacteristic
685C22C11×#54611yescharacteristic
686C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
687C22C2×C11×#13711yescharacteristic
688C22C11×#57611yescharacteristic
689C22C11×#57711yescharacteristic
690C4—22no—
691C4—22no—
692C4—41no—
693C4—41no—
694C4—42no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4C11×#52911yescharacteristic
702C4C11×#54011yescharacteristic
703C4C11×#55311yescharacteristic
704C4C11×#55511yescharacteristic
705C2—42no—
706C2—42no—
707C2—82no—
708C2C11×#242011yescharacteristic
709C2C11×#309211yescharacteristic
710C2C11×#309611yescharacteristic
711C2C11×#330611yescharacteristic
712C2C11×#331411yescharacteristic
713C2C11×#331811yescharacteristic
714C2C11×#332011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. D4×C11×C4⋊C4C2semidirect
3. C11×#2077C2semidirect
4. C11×#2076C2semidirect
5. C11×#2034C2semidirect
6. C11×#2033C2semidirect
7. C11×#1955C2semidirect
8. C11×#1949C2semidirect
9. C11×#1874C2semidirect
10. C11×#1874C2semidirect
11. C11×#1836C2semidirect
12. C11×#1824C2semidirect
13. C11×#1823C2semidirect
14. C11×#1802C2semidirect
15. C11×#1762C2semidirect
127. #24977C11direct (N × H)
223. D4×C4⋊C4C2×C11semidirect
224. #2077C2×C11semidirect
225. #2076C2×C11semidirect
226. #2034C2×C11semidirect
227. #2033C2×C11semidirect
228. #1955C2×C11semidirect
229. #1949C2×C11semidirect
230. #1874C2×C11semidirect
231. #1874C2×C11semidirect
232. #1836C2×C11semidirect
233. #1824C2×C11semidirect
234. #1823C2×C11semidirect
235. #1802C2×C11semidirect
236. #1762C2×C11semidirect
578. C11#24977direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25352
D4×C11×C4⋊C42
C11×#20772
C11×#20762
C11×#20342
C11×#20332
C11×#19552
C11×#19492
C11×#18742
C11×#18362
C11×#18242
C11×#18232
C11×#18022
C11×#17622
#2497711