Finite Group Databasebeta

← C11×#25023 #14602216

Subgroups — C11×#25023 #14602216

Order 2816.

876 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#482C211yesmaximal, characteristic, complemented
2C2×C11×#482C211yesmaximal, characteristic, complemented
3C11×#2535C211yesmaximal, characteristic
4C11×#2354C211yesmaximal, characteristic, complemented
5C11×#2077C211yesmaximal, characteristic, complemented
6C11×#2075C211yesmaximal, characteristic, complemented
7C11×#2034C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#1955C211yesmaximal, characteristic, complemented
10C11×#1949C211yesmaximal, characteristic, complemented
11C11×#1854C211yesmaximal, characteristic, complemented
12C11×#1854C211yesmaximal, characteristic, complemented
13C11×#1847C211yesmaximal, characteristic, complemented
14C11×#1802C211yesmaximal, characteristic, complemented
15C11×#1762C211yesmaximal, characteristic, complemented
16C2×C11×#121C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C11×#482—24no—
23C11×#482—24no—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#107C2211yescharacteristic
26C2×C11×#107C2211yescharacteristic
27C2×C11×#106C2211yescharacteristic
28C2×C11×#106C2211yescharacteristic
29C2×C11×#106C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×#97C2211yescharacteristic
40C11×#397—21no—
41C11×#392—21no—
42C11×#390—21no—
43C11×#388—21no—
44C11×#388—21no—
45C11×#386—21no—
46C11×#386—21no—
47C11×#384C2211yescharacteristic
48C11×#382C2211yescharacteristic
49C11×#380C2211yescharacteristic
50C11×#380C2211yescharacteristic
51C11×#380C2211yescharacteristic
52C11×#380C2211yescharacteristic
53C4×C11×C4⋊C4—21no—
54C4×C11×C4⋊C4C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×D4×C11D411yescharacteristic
64C22×D4×C11C2311yescharacteristic
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—
80C11×#117—22no—
81C11×#117—22no—
82C11×#117—41no—
83C11×#117—41no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4D411yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
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⋊C4D411yescharacteristic
104C2×C11×C22⋊C4D411yescharacteristic
105C2×C42×C11—21no—
106C2×C42×C11—21no—
107C2×C42×C11—21no—
108C2×C42×C11C2311yescharacteristic
109C11×#107—22no—
110C11×#107—22no—
111C11×#107—41no—
112C11×#106—22no—
113C11×#106—22no—
114C11×#106—41no—
115C11×C4⋊C8—22no—
116C11×#102—22no—
117C11×#102—22no—
118C11×#102—22no—
119C11×#102D414yescomplemented
120C11×C22⋊C8—22no—
121C11×C22⋊C8—22no—
122C11×C22⋊C8—22no—
123C11×C22⋊C8—22no—
124C11×#97—22no—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132#25023C1111yesmaximal, characteristic, direct product factor, Sylow
133C24×C11—21no—
134C24×C11C2×D411yescharacteristic
135C24×C11C2×D411yescharacteristic
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—41no—
143C2×D4×C11—41no—
144C2×D4×C11—42no—
145C2×D4×C11—42no—
146C2×D4×C11—42no—
147C2×D4×C11—42no—
148C2×D4×C11—81no—
149C2×D4×C11—81no—
150C2×D4×C11C2×D412yes—
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—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—42no—
171C22×C4×C11—81no—
172C22×C4×C11—81no—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2411yescharacteristic
178C2×C8×C11—21no—
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×C11C2×D412yes—
189C2×C8×C11#4112yes—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—21no—
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—42no—
205C11×C4⋊C4—81no—
206C11×C4⋊C4C2×D412yes—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—42no—
210C11×C22⋊C4—42no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—42no—
213C11×C22⋊C4—42no—
214C11×C22⋊C4—81no—
215C11×C22⋊C4—81no—
216C11×C22⋊C4—81no—
217C11×C22⋊C4—81no—
218C42×C11—42no—
219C42×C11—42no—
220C42×C11—42no—
221C42×C11#4112yes—
222C42×C11#4112yes—
223C2×#482C2×C1111yescharacteristic, complemented
224C2×#482C2×C1111yescharacteristic, complemented
225#2535C2×C1111yescharacteristic
226#2354C2×C1111yescharacteristic, complemented
227#2077C2×C1111yescharacteristic, complemented
228#2075C2×C1111yescharacteristic, complemented
229#2034C2×C1111yescharacteristic, complemented
230#2033C2×C1111yescharacteristic, complemented
231#1955C2×C1111yescharacteristic, complemented
232#1949C2×C1111yescharacteristic, complemented
233#1854C2×C1111yescharacteristic, complemented
234#1854C2×C1111yescharacteristic, complemented
235#1847C2×C1111yescharacteristic, complemented
236#1802C2×C1111yescharacteristic, complemented
237#1762C2×C1111yescharacteristic, complemented
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—22no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11C22×D411yescharacteristic
260D4×C11—22no—
261D4×C11—22no—
262D4×C11—44no—
263D4×C11—41no—
264D4×C11—41no—
265D4×C11—84no—
266D4×C11—84no—
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—22no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
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—41no—
306C2×C4×C11—84no—
307C2×C4×C11#12312yes—
308C2×C4×C11#12312yes—
309C2×C4×C11C22×D411yescharacteristic
310C2×C4×C11C2×#4111yescharacteristic
311C2×C4×C11C2×#4111yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11H(5,𝔽2)11yescharacteristic
314C2×C4×C112−1+411yescharacteristic
315C8×C11—22no—
316C8×C11—22no—
317C8×C11—41no—
318C8×C11—41no—
319C2×#121C22×C1111yescharacteristic
320C2×#121C22×C1111yescharacteristic
321C2×C4×D4C22×C1111yescharacteristic
322C2×C4×D4C22×C1111yescharacteristic
323C2×#117C22×C1111yescharacteristic
324C2×#117C22×C1111yescharacteristic
325#482—24no—
326#482—24no—
327C2×#107C22×C1111yescharacteristic
328C2×#107C22×C1111yescharacteristic
329C2×#107C22×C1111yescharacteristic
330C2×#106C22×C1111yescharacteristic
331C2×#106C22×C1111yescharacteristic
332C2×#106C22×C1111yescharacteristic
333C2×C4⋊C8C22×C1111yescharacteristic
334C2×#102C22×C1111yescharacteristic
335C2×#102C22×C1111yescharacteristic
336C2×#102C22×C1111yescharacteristic
337C2×#102C22×C1111yescharacteristic
338C2×C22⋊C8C22×C1111yescharacteristic
339C2×C22⋊C8C22×C1111yescharacteristic
340C2×C22⋊C8C22×C1111yescharacteristic
341C2×C22⋊C8C22×C1111yescharacteristic
342C2×#97C22×C1111yescharacteristic
343#397—21no—
344#392—21no—
345#390—21no—
346#388—21no—
347#388—21no—
348#386—21no—
349#386—21no—
350#384C22×C1111yescharacteristic
351#382C22×C1111yescharacteristic
352#380C22×C1111yescharacteristic
353#380C22×C1111yescharacteristic
354#380C22×C1111yescharacteristic
355#380C22×C1111yescharacteristic
356C4×C4⋊C4—21no—
357C4×C4⋊C4C22×C1111yescharacteristic
358#340C22×C1111yescharacteristic
359#340C22×C1111yescharacteristic
360#340C22×C1111yescharacteristic
361#340C22×C1111yescharacteristic
362#340C22×C1111yescharacteristic
363#340C22×C1111yescharacteristic
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11—41no—
373C22×C11—41no—
374C22×C11—42no—
375C22×C11—41no—
376C22×C11—42no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—42no—
380C22×C11—41no—
381C22×C11—81no—
382C22×C11—81no—
383C22×C11—81no—
384C22×C11—81no—
385C22×C11C2×#12311yescharacteristic
386C22×C11D4211yescharacteristic
387C22×C11#54711yescharacteristic
388C22×C11#57511yescharacteristic
389C22×C11#57511yescharacteristic
390C22×C11#57611yescharacteristic
391C22×C11#57711yescharacteristic
392C4×C11—22no—
393C4×C11—22no—
394C4×C11—41no—
395C4×C11—41no—
396C4×C11—42no—
397C4×C11—81no—
398C4×C11—81no—
399C4×C11—81no—
400C4×C11—81no—
401C4×C11—81no—
402C4×C11—81no—
403C4×C11#53211yescharacteristic
404C4×C11#54211yescharacteristic
405C4×C11#54711yescharacteristic
406C4×C11#55311yescharacteristic
407C22×D4—21no—
408C22×D4—21no—
409C22×D4D4×C1111yescharacteristic
410C22×D4C23×C1111yescharacteristic
411C23×C4—21no—
412C23×C4C23×C1111yescharacteristic
413C23×C4C23×C1111yescharacteristic
414C22×C8C23×C1111yescharacteristic
415C22×C8C23×C1111yescharacteristic
416C22×C8C23×C1111yescharacteristic
417C22×C8C23×C1111yescharacteristic
418#121—22no—
419#121—22no—
420#121—41no—
421#121—41no—
422C4×D4—22no—
423C4×D4—22no—
424C4×D4—22no—
425C4×D4—22no—
426#117—22no—
427#117—22no—
428#117—41no—
429#117—41no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4D4×C1111yescharacteristic
433C2×C4⋊C4C23×C1111yescharacteristic
434C2×C4⋊C4C23×C1111yescharacteristic
435C2×C4⋊C4C23×C1111yescharacteristic
436C2×C4⋊C4C23×C1111yescharacteristic
437C2×C4⋊C4C23×C1111yescharacteristic
438C2×C4⋊C4C23×C1111yescharacteristic
439C2×C4⋊C4C23×C1111yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
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⋊C4D4×C1111yescharacteristic
450C2×C22⋊C4D4×C1111yescharacteristic
451C2×C42—21no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42C23×C1111yescharacteristic
455#107—22no—
456#107—22no—
457#107—41no—
458#106—22no—
459#106—22no—
460#106—41no—
461C4⋊C8—22no—
462#102—22no—
463#102—22no—
464#102—22no—
465#102D4×C1114yescomplemented
466C22⋊C8—22no—
467C22⋊C8—22no—
468C22⋊C8—22no—
469C22⋊C8—22no—
470#97—22no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478C2×C11—81no—
479C2×C11—81no—
480C2×C11—82no—
481C2×C11#242211yescharacteristic
482C2×C11#309311yescharacteristic
483C2×C11#309611yescharacteristic
484C2×C11#326711yescharacteristic
485C2×C11#326811yescharacteristic
486C2×C11#334711yescharacteristic
487C2×C11#335011yescharacteristic
488C24—21no—
489C24C2×D4×C1111yescharacteristic
490C24C2×D4×C1111yescharacteristic
491C2×D4—22no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—41no—
498C2×D4—41no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—81no—
504C2×D4—81no—
505C2×D4C2×D4×C1112yes—
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—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—42no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4C2×D4×C1111yescharacteristic
529C22×C4C2×D4×C1111yescharacteristic
530C22×C4C2×D4×C1111yescharacteristic
531C22×C4C2×D4×C1111yescharacteristic
532C22×C4C24×C1111yescharacteristic
533C2×C8—21no—
534C2×C8—21no—
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×C8C2×D4×C1112yes—
544C2×C8C11×#4112yes—
545C4⋊C4—22no—
546C4⋊C4—21no—
547C4⋊C4—21no—
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—42no—
560C4⋊C4—81no—
561C4⋊C4C2×D4×C1112yes—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—81no—
570C22⋊C4—81no—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C42—42no—
574C42—42no—
575C42—42no—
576C42C11×#4112yes—
577C42C11×#4112yes—
578C11#2502311yescharacteristic, direct product factor, Sylow
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—22no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C22×D4×C1111yescharacteristic
601D4—22no—
602D4—22no—
603D4—44no—
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—22no—
615C2×C4—21no—
616C2×C4—21no—
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×C4C11×#12312yes—
649C2×C4C11×#12312yes—
650C2×C4C22×D4×C1111yescharacteristic
651C2×C4C2×C11×#4111yescharacteristic
652C2×C4C2×C11×#4111yescharacteristic
653C2×C4C2×C11×#4111yescharacteristic
654C2×C4C11×H(5,𝔽2)11yescharacteristic
655C2×C4C11×2−1+411yescharacteristic
656C8—22no—
657C8—22no—
658C8—41no—
659C8—41no—
660C22—41no—
661C22—41no—
662C22—42no—
663C22—41no—
664C22—42no—
665C22—41no—
666C22—41no—
667C22—42no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C2×C11×#12311yescharacteristic
682C22D42×C1111yescharacteristic
683C22C11×#54711yescharacteristic
684C22C11×#57511yescharacteristic
685C22C11×#57511yescharacteristic
686C22C11×#57611yescharacteristic
687C22C11×#57711yescharacteristic
688C4—22no—
689C4—22no—
690C4—41no—
691C4—41no—
692C4—42no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4C11×#53211yescharacteristic
700C4C11×#54211yescharacteristic
701C4C11×#54711yescharacteristic
702C4C11×#55311yescharacteristic
703C2—81no—
704C2—81no—
705C2—82no—
706C2C11×#242211yescharacteristic
707C2C11×#309311yescharacteristic
708C2C11×#309611yescharacteristic
709C2C11×#326711yescharacteristic
710C2C11×#326811yescharacteristic
711C2C11×#334711yescharacteristic
712C2C11×#335011yescharacteristic
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
1. C2×C11×#482C2semidirect
2. C2×C11×#482C2semidirect
4. C11×#2354C2semidirect
5. C11×#2077C2semidirect
6. C11×#2075C2semidirect
7. C11×#2034C2semidirect
8. C11×#2033C2semidirect
9. C11×#1955C2semidirect
10. C11×#1949C2semidirect
11. C11×#1854C2semidirect
12. C11×#1854C2semidirect
13. C11×#1847C2semidirect
14. C11×#1802C2semidirect
15. C11×#1762C2semidirect
119. C11×#102D4semidirect
132. #25023C11direct (N × H)
223. C2×#482C2×C11semidirect
224. C2×#482C2×C11semidirect
226. #2354C2×C11semidirect
227. #2077C2×C11semidirect
228. #2075C2×C11semidirect
229. #2034C2×C11semidirect
230. #2033C2×C11semidirect
231. #1955C2×C11semidirect
232. #1949C2×C11semidirect
233. #1854C2×C11semidirect
234. #1854C2×C11semidirect
235. #1847C2×C11semidirect
236. #1802C2×C11semidirect
237. #1762C2×C11semidirect
465. #102D4×C11semidirect
578. C11#25023direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4822
C11×#25352
C11×#23542
C11×#20772
C11×#20752
C11×#20342
C11×#20332
C11×#19552
C11×#19492
C11×#18542
C11×#18472
C11×#18022
C11×#17622
#2502311