Finite Group Databasebeta

← C11×#24666 #14601859

Subgroups — C11×#24666 #14601859

Order 2816.

870 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#461C211yesmaximal, characteristic, complemented
2C2×C11×#433C211yesmaximal, characteristic, complemented
3C11×#2621C211yesmaximal, characteristic, complemented
4C11×#2324C211yesmaximal, characteristic
5C11×#2036C211yesmaximal, characteristic, complemented
6C11×#2035C211yesmaximal, characteristic, complemented
7C11×#2000C211yesmaximal, characteristic
8C11×#2000C211yesmaximal, characteristic
9C11×#1981C211yesmaximal, characteristic, complemented
10C11×#1973C211yesmaximal, characteristic, complemented
11C11×#1968C211yesmaximal, characteristic, complemented
12C11×#1949C211yesmaximal, characteristic, complemented
13C11×#1935C211yesmaximal, characteristic, complemented
14C11×#1933C211yesmaximal, characteristic, complemented
15C11×#1804C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C11×#461—24no—
25C11×#433—24no—
26C2×C11×#107C2211yescharacteristic
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×#103C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×#97C2211yescharacteristic
41C2×C4×C8×C11C2211yescharacteristic
42C11×#398—21no—
43C11×#398—21no—
44C11×#397—21no—
45C11×#397—21no—
46C11×#391C2211yescharacteristic
47C11×#391C2211yescharacteristic
48C11×#390—21no—
49C11×#390C2211yescharacteristic
50C11×#389C2211yescharacteristic
51C11×#388—21no—
52C11×#386—21no—
53C11×#385—21no—
54C11×#382C2211yescharacteristic
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×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C2×C11×SD16—22no—
68C2×C11×SD16—22no—
69C2×C11×SD16—22no—
70C2×C11×SD16—22no—
71C2×C11×SD16—41no—
72C2×C11×SD16—41no—
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×C4⋊Q8—22no—
78C11×C4⋊Q8—22no—
79C11×C22⋊Q8—41no—
80C11×C22⋊Q8—41no—
81C11×C22⋊Q8—41no—
82C11×C22⋊Q8—41no—
83C11×#121—22no—
84C11×#121—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C11×#117—22no—
88C11×#117—22no—
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⋊C4D411yescharacteristic
109C2×C11×C22⋊C4D411yescharacteristic
110C2×C42×C11—21no—
111C2×C42×C11C2311yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C11×#107—41no—
114C11×#106—41no—
115C11×C4⋊C8—22no—
116C11×C4⋊C8D414yescomplemented
117C11×#103—22no—
118C11×#103—22no—
119C11×#103—22no—
120C11×#103—22no—
121C11×#103—41no—
122C11×#103—41no—
123C11×#102—41no—
124C11×#102—41no—
125C11×C22⋊C8—22no—
126C11×C22⋊C8—22no—
127C11×#97—22no—
128C4×C8×C11—22no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138#24666C1111yesmaximal, 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—21no—
153C2×D4×C11—24no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—81no—
160C2×D4×C11—81no—
161C2×D4×C11#4112yes—
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×C11—42no—
176C22×C4×C11—81no—
177C22×C4×C11—81no—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2411yescharacteristic
184C11×SD16—44no—
185C11×SD16—44no—
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×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11C2×D412yes—
197C2×C8×C11C2×D412yes—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—22no—
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—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—42no—
210C11×C4⋊C4—42no—
211C11×C4⋊C4—42no—
212C11×C4⋊C4—42no—
213C11×C4⋊C4—81no—
214C11×C4⋊C4#4112yes—
215C11×C22⋊C4—24no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—42no—
219C11×C22⋊C4—42no—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—81no—
222C11×C22⋊C4—81no—
223C11×C22⋊C4—81no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11—81no—
227C42×C11C2×D412yes—
228C42×C11#4112yes—
229C2×#461C2×C1111yescharacteristic, complemented
230C2×#433C2×C1111yescharacteristic, complemented
231#2621C2×C1111yescharacteristic, complemented
232#2324C2×C1111yescharacteristic
233#2036C2×C1111yescharacteristic, complemented
234#2035C2×C1111yescharacteristic, complemented
235#2000C2×C1111yescharacteristic
236#2000C2×C1111yescharacteristic
237#1981C2×C1111yescharacteristic, complemented
238#1973C2×C1111yescharacteristic, complemented
239#1968C2×C1111yescharacteristic, complemented
240#1949C2×C1111yescharacteristic, complemented
241#1935C2×C1111yescharacteristic, complemented
242#1933C2×C1111yescharacteristic, complemented
243#1804C2×C1111yescharacteristic, complemented
244C23×C11—21no—
245C23×C11—22no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11C22×D411yescharacteristic
259Q8×C11—41no—
260Q8×C11—41no—
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—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—21no—
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—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—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×C11C22×D411yescharacteristic
314C2×C4×C11C2×#4111yescharacteristic
315C2×C4×C11C2×#4111yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11H(5,𝔽2)11yescharacteristic
318C2×C4×C11H(5,𝔽2)11yescharacteristic
319C8×C11—22no—
320C8×C11—22no—
321C8×C11—41no—
322C8×C11—41no—
323C22×SD16C22×C1111yescharacteristic
324C22×SD16C22×C1111yescharacteristic
325C2×C4⋊Q8C22×C1111yescharacteristic
326C2×C22⋊Q8C22×C1111yescharacteristic
327C2×C22⋊Q8C22×C1111yescharacteristic
328C2×#121C22×C1111yescharacteristic
329C2×C4×D4C22×C1111yescharacteristic
330C2×#117C22×C1111yescharacteristic
331#461—24no—
332#433—24no—
333C2×#107C22×C1111yescharacteristic
334C2×#106C22×C1111yescharacteristic
335C2×C4⋊C8C22×C1111yescharacteristic
336C2×C4⋊C8C22×C1111yescharacteristic
337C2×#103C22×C1111yescharacteristic
338C2×#103C22×C1111yescharacteristic
339C2×#103C22×C1111yescharacteristic
340C2×#103C22×C1111yescharacteristic
341C2×#103C22×C1111yescharacteristic
342C2×#103C22×C1111yescharacteristic
343C2×#102C22×C1111yescharacteristic
344C2×#102C22×C1111yescharacteristic
345C2×C22⋊C8C22×C1111yescharacteristic
346C2×C22⋊C8C22×C1111yescharacteristic
347C2×#97C22×C1111yescharacteristic
348C2×C4×C8C22×C1111yescharacteristic
349#398—21no—
350#398—21no—
351#397—21no—
352#397—21no—
353#391C22×C1111yescharacteristic
354#391C22×C1111yescharacteristic
355#390—21no—
356#390C22×C1111yescharacteristic
357#389C22×C1111yescharacteristic
358#388—21no—
359#386—21no—
360#385—21no—
361#382C22×C1111yescharacteristic
362#380C22×C1111yescharacteristic
363C4×C4⋊C4C22×C1111yescharacteristic
364#340C22×C1111yescharacteristic
365#340C22×C1111yescharacteristic
366#340C22×C1111yescharacteristic
367#340C22×C1111yescharacteristic
368C22×C11—41no—
369C22×C11—42no—
370C22×C11—41no—
371C22×C11—42no—
372C22×C11—41no—
373C22×C11—42no—
374C22×C11—41no—
375C22×C11—41no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11—81no—
379C22×C11—81no—
380C22×C11—81no—
381C22×C11—81no—
382C22×C11C2×#12111yescharacteristic
383C22×C11#52511yescharacteristic
384C22×C11#53511yescharacteristic
385C22×C11#57711yescharacteristic
386C22×C11#57711yescharacteristic
387C22×C11#57711yescharacteristic
388C22×C11#57811yescharacteristic
389C4×C11—22no—
390C4×C11—22no—
391C4×C11—42no—
392C4×C11—41no—
393C4×C11—41no—
394C4×C11—41no—
395C4×C11—81no—
396C4×C11—81no—
397C4×C11—81no—
398C4×C11—81no—
399C4×C11—81no—
400C4×C11—81no—
401C4×C11#54611yescharacteristic
402C4×C11#55011yescharacteristic
403C4×C11#55311yescharacteristic
404C4×C11#55511yescharacteristic
405C22×Q8C23×C1111yescharacteristic
406C22×Q8C23×C1111yescharacteristic
407C22×D4—21no—
408C22×D4C23×C1111yescharacteristic
409C23×C4—21no—
410C23×C4C23×C1111yescharacteristic
411C2×SD16—22no—
412C2×SD16—22no—
413C2×SD16—22no—
414C2×SD16—22no—
415C2×SD16—41no—
416C2×SD16—41no—
417C22×C8C23×C1111yescharacteristic
418C22×C8C23×C1111yescharacteristic
419C22×C8C23×C1111yescharacteristic
420C22×C8C23×C1111yescharacteristic
421C4⋊Q8—22no—
422C4⋊Q8—22no—
423C22⋊Q8—41no—
424C22⋊Q8—41no—
425C22⋊Q8—41no—
426C22⋊Q8—41no—
427#121—22no—
428#121—22no—
429C4×D4—22no—
430C4×D4—22no—
431#117—22no—
432#117—22no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4D4×C1111yescharacteristic
439C2×C4⋊C4D4×C1111yescharacteristic
440C2×C4⋊C4C23×C1111yescharacteristic
441C2×C4⋊C4C23×C1111yescharacteristic
442C2×C4⋊C4C23×C1111yescharacteristic
443C2×C4⋊C4C23×C1111yescharacteristic
444C2×C4⋊C4C23×C1111yescharacteristic
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×C42C23×C1111yescharacteristic
456C2×C42C23×C1111yescharacteristic
457#107—41no—
458#106—41no—
459C4⋊C8—22no—
460C4⋊C8D4×C1114yescomplemented
461#103—22no—
462#103—22no—
463#103—22no—
464#103—22no—
465#103—41no—
466#103—41no—
467#102—41no—
468#102—41no—
469C22⋊C8—22no—
470C22⋊C8—22no—
471#97—22no—
472C4×C8—22no—
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#95—21no—
482C2×C11—81no—
483C2×C11—82no—
484C2×C11#241411yescharacteristic
485C2×C11#305711yescharacteristic
486C2×C11#306311yescharacteristic
487C2×C11#312011yescharacteristic
488C2×C11#312311yescharacteristic
489C2×C11#322111yescharacteristic
490C2×C11#322511yescharacteristic
491C24—21no—
492C24C2×D4×C1111yescharacteristic
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×Q8—21no—
504C2×Q8—21no—
505C2×D4—24no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—81no—
512C2×D4—81no—
513C2×D4C11×#4112yes—
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×C4—21no—
527C22×C4—42no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4C2×D4×C1111yescharacteristic
531C22×C4C2×D4×C1111yescharacteristic
532C22×C4C2×D4×C1111yescharacteristic
533C22×C4C2×D4×C1111yescharacteristic
534C22×C4C2×D4×C1111yescharacteristic
535C22×C4C24×C1111yescharacteristic
536SD16—44no—
537SD16—44no—
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—
547C2×C8—21no—
548C2×C8C2×D4×C1112yes—
549C2×C8C2×D4×C1112yes—
550C4⋊C4—22no—
551C4⋊C4—22no—
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—42no—
565C4⋊C4—81no—
566C4⋊C4C11×#4112yes—
567C22⋊C4—24no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—81no—
574C22⋊C4—81no—
575C22⋊C4—81no—
576C42—21no—
577C42—21no—
578C42—81no—
579C42C2×D4×C1112yes—
580C42C11×#4112yes—
581C11#2466611yescharacteristic, direct product factor, Sylow
582C23—21no—
583C23—22no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23C22×D4×C1111yescharacteristic
597Q8—41no—
598Q8—41no—
599Q8—41no—
600Q8—41no—
601Q8—41no—
602Q8—41no—
603Q8—41no—
604Q8—41no—
605D4—22no—
606D4—22no—
607D4—41no—
608D4—41no—
609D4—84no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
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×C4—41no—
648C2×C4—84no—
649C2×C4C11×#12112yes—
650C2×C4C11×#12112yes—
651C2×C4C22×D4×C1111yescharacteristic
652C2×C4C2×C11×#4111yescharacteristic
653C2×C4C2×C11×#4111yescharacteristic
654C2×C4C2×C11×#4111yescharacteristic
655C2×C4C11×H(5,𝔽2)11yescharacteristic
656C2×C4C11×H(5,𝔽2)11yescharacteristic
657C8—22no—
658C8—22no—
659C8—41no—
660C8—41no—
661C22—41no—
662C22—42no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—42no—
669C22—41no—
670C22—42no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22C2×C11×#12111yescharacteristic
676C22C11×#52511yescharacteristic
677C22C11×#53511yescharacteristic
678C22C11×#57711yescharacteristic
679C22C11×#57711yescharacteristic
680C22C11×#57711yescharacteristic
681C22C11×#57811yescharacteristic
682C4—22no—
683C4—22no—
684C4—41no—
685C4—41no—
686C4—41no—
687C4—42no—
688C4—81no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4C11×#54611yescharacteristic
695C4C11×#55011yescharacteristic
696C4C11×#55311yescharacteristic
697C4C11×#55511yescharacteristic
698C2—81no—
699C2—82no—
700C2C11×#241411yescharacteristic
701C2C11×#305711yescharacteristic
702C2C11×#306311yescharacteristic
703C2C11×#312011yescharacteristic
704C2C11×#312311yescharacteristic
705C2C11×#322111yescharacteristic
706C2C11×#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×#461C2semidirect
2. C2×C11×#433C2semidirect
3. C11×#2621C2semidirect
5. C11×#2036C2semidirect
6. C11×#2035C2semidirect
9. C11×#1981C2semidirect
10. C11×#1973C2semidirect
11. C11×#1968C2semidirect
12. C11×#1949C2semidirect
13. C11×#1935C2semidirect
14. C11×#1933C2semidirect
15. C11×#1804C2semidirect
116. C11×C4⋊C8D4semidirect
138. #24666C11direct (N × H)
229. C2×#461C2×C11semidirect
230. C2×#433C2×C11semidirect
231. #2621C2×C11semidirect
233. #2036C2×C11semidirect
234. #2035C2×C11semidirect
237. #1981C2×C11semidirect
238. #1973C2×C11semidirect
239. #1968C2×C11semidirect
240. #1949C2×C11semidirect
241. #1935C2×C11semidirect
242. #1933C2×C11semidirect
243. #1804C2×C11semidirect
460. C4⋊C8D4×C11semidirect
581. C11#24666direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4612
C2×C11×#4332
C11×#26212
C11×#23242
C11×#20362
C11×#20352
C11×#20002
C11×#19812
C11×#19732
C11×#19682
C11×#19492
C11×#19352
C11×#19332
C11×#18042
#2466611