Finite Group Databasebeta

← C11×#24669 #14601862

Subgroups — C11×#24669 #14601862

Order 2816.

856 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#464C211yesmaximal, characteristic, complemented
2C2×C11×#433C211yesmaximal, characteristic, complemented
3C11×#2620C211yesmaximal, characteristic
4C11×#2323C211yesmaximal, characteristic, complemented
5C11×#2035C211yesmaximal, characteristic, complemented
6C11×#2034C211yesmaximal, characteristic
7C11×#2001C211yesmaximal, characteristic, complemented
8C11×#2000C211yesmaximal, characteristic
9C11×#1983C211yesmaximal, characteristic, complemented
10C11×#1971C211yesmaximal, characteristic, complemented
11C11×#1968C211yesmaximal, characteristic, complemented
12C11×#1948C211yesmaximal, characteristic, complemented
13C11×#1936C211yesmaximal, characteristic, complemented
14C11×#1933C211yesmaximal, characteristic, complemented
15C11×#1803C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C11×#464—24no—
25C11×#433—24no—
26C2×C11×#106C2211yescharacteristic
27C2×C11×#106C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×#97C2211yescharacteristic
41C2×C4×C8×C11C2211yescharacteristic
42C11×#396—21no—
43C11×#396—21no—
44C11×#394—21no—
45C11×#394—21no—
46C11×#391C2211yescharacteristic
47C11×#391C2211yescharacteristic
48C11×#390C2211yescharacteristic
49C11×#389—21no—
50C11×#389C2211yescharacteristic
51C11×#388—21no—
52C11×#388—21no—
53C11×#387—21no—
54C11×#384C2211yescharacteristic
55C11×#380C2211yescharacteristic
56C4×C11×C4⋊C4C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C2×C11×Q16—22no—
67C2×C11×Q16—22no—
68C2×C11×Q16—41no—
69C2×C11×SD16—22no—
70C2×C11×SD16—22no—
71C2×C11×SD16—41no—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×#124—22no—
77C11×#124—22no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—41no—
81C11×C22⋊Q8—41no—
82C11×#121—41no—
83C11×#121—41no—
84C4×Q8×C11—22no—
85C4×Q8×C11—22no—
86C11×#117—22no—
87C11×#117—22no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4D411yescharacteristic
110C2×C11×C22⋊C4D411yescharacteristic
111C2×C42×C11—21no—
112C2×C42×C11—21no—
113C2×C42×C11C2311yescharacteristic
114C2×C42×C11C2311yescharacteristic
115C11×#106—41no—
116C11×#106—41no—
117C11×C4⋊C8—22no—
118C11×C4⋊C8D414yescomplemented
119C11×#103—22no—
120C11×#103—22no—
121C11×#103—41no—
122C11×#103—41no—
123C11×#103—41no—
124C11×#102—22no—
125C11×#102—22no—
126C11×#102—41no—
127C11×C22⋊C8—22no—
128C11×C22⋊C8—22no—
129C11×#97—22no—
130C4×C8×C11—22no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138#24669C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
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×C11#4112yes—
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—42no—
160C2×D4×C11—81no—
161C2×D4×C11—81no—
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—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2411yescharacteristic
181C11×Q16—44no—
182C11×SD16—44no—
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—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11C2×D412yes—
194C2×C8×C11C2×D412yes—
195C11×C4⋊C4—24no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—22no—
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—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—42no—
208C11×C4⋊C4—42no—
209C11×C4⋊C4—81no—
210C11×C4⋊C4—81no—
211C11×C4⋊C4—81no—
212C11×C4⋊C4#4112yes—
213C11×C22⋊C4—24no—
214C11×C22⋊C4—22no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—42no—
217C11×C22⋊C4—42no—
218C11×C22⋊C4—42no—
219C11×C22⋊C4—42no—
220C11×C22⋊C4—81no—
221C11×C22⋊C4—81no—
222C11×C22⋊C4—81no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—42no—
226C42×C11—81no—
227C42×C11C2×D412yes—
228C42×C11#4112yes—
229C2×#464C2×C1111yescharacteristic, complemented
230C2×#433C2×C1111yescharacteristic, complemented
231#2620C2×C1111yescharacteristic
232#2323C2×C1111yescharacteristic, complemented
233#2035C2×C1111yescharacteristic, complemented
234#2034C2×C1111yescharacteristic
235#2001C2×C1111yescharacteristic, complemented
236#2000C2×C1111yescharacteristic
237#1983C2×C1111yescharacteristic, complemented
238#1971C2×C1111yescharacteristic, complemented
239#1968C2×C1111yescharacteristic, complemented
240#1948C2×C1111yescharacteristic, complemented
241#1936C2×C1111yescharacteristic, complemented
242#1933C2×C1111yescharacteristic, complemented
243#1803C2×C1111yescharacteristic, complemented
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
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—41no—
268D4×C11—41no—
269D4×C11—41no—
270D4×C11—41no—
271D4×C11—84no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
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—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11#12112yes—
311C2×C4×C11#12112yes—
312C2×C4×C11C22×D411yescharacteristic
313C2×C4×C11C2×#4111yescharacteristic
314C2×C4×C11C2×#4111yescharacteristic
315C2×C4×C11C2×#4111yescharacteristic
316C2×C4×C11H(5,𝔽2)11yescharacteristic
317C2×C4×C11H(5,𝔽2)11yescharacteristic
318C8×C11—22no—
319C8×C11—22no—
320C8×C11—41no—
321C8×C11—41no—
322C22×Q16C22×C1111yescharacteristic
323C22×SD16C22×C1111yescharacteristic
324C2×#124C22×C1111yescharacteristic
325C2×C22⋊Q8C22×C1111yescharacteristic
326C2×C22⋊Q8C22×C1111yescharacteristic
327C2×#121C22×C1111yescharacteristic
328C2×C4×Q8C22×C1111yescharacteristic
329C2×#117C22×C1111yescharacteristic
330#464—24no—
331#433—24no—
332C2×#106C22×C1111yescharacteristic
333C2×#106C22×C1111yescharacteristic
334C2×C4⋊C8C22×C1111yescharacteristic
335C2×C4⋊C8C22×C1111yescharacteristic
336C2×#103C22×C1111yescharacteristic
337C2×#103C22×C1111yescharacteristic
338C2×#103C22×C1111yescharacteristic
339C2×#103C22×C1111yescharacteristic
340C2×#103C22×C1111yescharacteristic
341C2×#102C22×C1111yescharacteristic
342C2×#102C22×C1111yescharacteristic
343C2×#102C22×C1111yescharacteristic
344C2×C22⋊C8C22×C1111yescharacteristic
345C2×C22⋊C8C22×C1111yescharacteristic
346C2×#97C22×C1111yescharacteristic
347C2×C4×C8C22×C1111yescharacteristic
348#396—21no—
349#396—21no—
350#394—21no—
351#394—21no—
352#391C22×C1111yescharacteristic
353#391C22×C1111yescharacteristic
354#390C22×C1111yescharacteristic
355#389—21no—
356#389C22×C1111yescharacteristic
357#388—21no—
358#388—21no—
359#387—21no—
360#384C22×C1111yescharacteristic
361#380C22×C1111yescharacteristic
362C4×C4⋊C4C22×C1111yescharacteristic
363#340C22×C1111yescharacteristic
364#340C22×C1111yescharacteristic
365#340C22×C1111yescharacteristic
366#340C22×C1111yescharacteristic
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11—41no—
373C22×C11—41no—
374C22×C11—81no—
375C22×C11—81no—
376C22×C11—81no—
377C22×C11—81no—
378C22×C11—81no—
379C22×C11—81no—
380C22×C11—81no—
381C22×C11C2×#12111yescharacteristic
382C22×C11#52511yescharacteristic
383C22×C11#53511yescharacteristic
384C22×C11#57711yescharacteristic
385C22×C11#57711yescharacteristic
386C22×C11#57711yescharacteristic
387C22×C11#57811yescharacteristic
388C4×C11—22no—
389C4×C11—22no—
390C4×C11—42no—
391C4×C11—41no—
392C4×C11—42no—
393C4×C11—41no—
394C4×C11—41no—
395C4×C11—81no—
396C4×C11—81no—
397C4×C11—81no—
398C4×C11—81no—
399C4×C11—81no—
400C4×C11#54611yescharacteristic
401C4×C11#55011yescharacteristic
402C4×C11#55311yescharacteristic
403C4×C11#55511yescharacteristic
404C22×Q8C23×C1111yescharacteristic
405C22×Q8C23×C1111yescharacteristic
406C22×D4—21no—
407C22×D4C23×C1111yescharacteristic
408C23×C4C23×C1111yescharacteristic
409C2×Q16—22no—
410C2×Q16—22no—
411C2×Q16—41no—
412C2×SD16—22no—
413C2×SD16—22no—
414C2×SD16—41no—
415C22×C8C23×C1111yescharacteristic
416C22×C8C23×C1111yescharacteristic
417C22×C8C23×C1111yescharacteristic
418C22×C8C23×C1111yescharacteristic
419#124—22no—
420#124—22no—
421C22⋊Q8—22no—
422C22⋊Q8—22no—
423C22⋊Q8—41no—
424C22⋊Q8—41no—
425#121—41no—
426#121—41no—
427C4×Q8—22no—
428C4×Q8—22no—
429#117—22no—
430#117—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
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×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⋊C4—21no—
452C2×C22⋊C4D4×C1111yescharacteristic
453C2×C22⋊C4D4×C1111yescharacteristic
454C2×C42—21no—
455C2×C42—21no—
456C2×C42C23×C1111yescharacteristic
457C2×C42C23×C1111yescharacteristic
458#106—41no—
459#106—41no—
460C4⋊C8—22no—
461C4⋊C8D4×C1114yescomplemented
462#103—22no—
463#103—22no—
464#103—41no—
465#103—41no—
466#103—41no—
467#102—22no—
468#102—22no—
469#102—41no—
470C22⋊C8—22no—
471C22⋊C8—22no—
472#97—22no—
473C4×C8—22no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481C2×C11—81no—
482C2×C11—161no—
483C2×C11#241411yescharacteristic
484C2×C11#306011yescharacteristic
485C2×C11#306311yescharacteristic
486C2×C11#312111yescharacteristic
487C2×C11#312511yescharacteristic
488C2×C11#322211yescharacteristic
489C2×C11#322511yescharacteristic
490C24—21no—
491C24C2×D4×C1111yescharacteristic
492C2×Q8—21no—
493C2×Q8—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×Q8C11×#4112yes—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—42no—
511C2×D4—81no—
512C2×D4—81no—
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—21no—
526C22×C4C2×D4×C1111yescharacteristic
527C22×C4C2×D4×C1111yescharacteristic
528C22×C4C2×D4×C1111yescharacteristic
529C22×C4C2×D4×C1111yescharacteristic
530C22×C4C2×D4×C1111yescharacteristic
531C22×C4C24×C1111yescharacteristic
532Q16—44no—
533SD16—44no—
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×C8—21no—
544C2×C8C2×D4×C1112yes—
545C2×C8C2×D4×C1112yes—
546C4⋊C4—24no—
547C4⋊C4—22no—
548C4⋊C4—22no—
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—42no—
559C4⋊C4—42no—
560C4⋊C4—81no—
561C4⋊C4—81no—
562C4⋊C4—81no—
563C4⋊C4C11×#4112yes—
564C22⋊C4—24no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C22⋊C4—81no—
574C42—21no—
575C42—21no—
576C42—42no—
577C42—81no—
578C42C2×D4×C1112yes—
579C42C11×#4112yes—
580C11#2466911yescharacteristic, direct product factor, Sylow
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23C22×D4×C1111yescharacteristic
596Q8—22no—
597Q8—22no—
598Q8—41no—
599Q8—41no—
600Q8—41no—
601Q8—41no—
602Q8—41no—
603Q8—41no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—84no—
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—22no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
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×C4C11×#12112yes—
648C2×C4C11×#12112yes—
649C2×C4C22×D4×C1111yescharacteristic
650C2×C4C2×C11×#4111yescharacteristic
651C2×C4C2×C11×#4111yescharacteristic
652C2×C4C2×C11×#4111yescharacteristic
653C2×C4C11×H(5,𝔽2)11yescharacteristic
654C2×C4C11×H(5,𝔽2)11yescharacteristic
655C8—22no—
656C8—22no—
657C8—41no—
658C8—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22C2×C11×#12111yescharacteristic
674C22C11×#52511yescharacteristic
675C22C11×#53511yescharacteristic
676C22C11×#57711yescharacteristic
677C22C11×#57711yescharacteristic
678C22C11×#57711yescharacteristic
679C22C11×#57811yescharacteristic
680C4—22no—
681C4—22no—
682C4—41no—
683C4—42no—
684C4—41no—
685C4—41no—
686C4—42no—
687C4—81no—
688C4—81no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4C11×#54611yescharacteristic
693C4C11×#55011yescharacteristic
694C4C11×#55311yescharacteristic
695C4C11×#55511yescharacteristic
696C2—81no—
697C2—161no—
698C2C11×#241411yescharacteristic
699C2C11×#306011yescharacteristic
700C2C11×#306311yescharacteristic
701C2C11×#312111yescharacteristic
702C2C11×#312511yescharacteristic
703C2C11×#322211yescharacteristic
704C2C11×#322511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#464C2semidirect
2. C2×C11×#433C2semidirect
4. C11×#2323C2semidirect
5. C11×#2035C2semidirect
7. C11×#2001C2semidirect
9. C11×#1983C2semidirect
10. C11×#1971C2semidirect
11. C11×#1968C2semidirect
12. C11×#1948C2semidirect
13. C11×#1936C2semidirect
14. C11×#1933C2semidirect
15. C11×#1803C2semidirect
118. C11×C4⋊C8D4semidirect
138. #24669C11direct (N × H)
229. C2×#464C2×C11semidirect
230. C2×#433C2×C11semidirect
232. #2323C2×C11semidirect
233. #2035C2×C11semidirect
235. #2001C2×C11semidirect
237. #1983C2×C11semidirect
238. #1971C2×C11semidirect
239. #1968C2×C11semidirect
240. #1948C2×C11semidirect
241. #1936C2×C11semidirect
242. #1933C2×C11semidirect
243. #1803C2×C11semidirect
461. C4⋊C8D4×C11semidirect
580. C11#24669direct (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×C11×#4332
C11×#26202
C11×#23232
C11×#20352
C11×#20342
C11×#20012
C11×#20002
C11×#19832
C11×#19712
C11×#19682
C11×#19482
C11×#19362
C11×#19332
C11×#18032
#2466911