Finite Group Databasebeta

← C11×#24655 #14601848

Subgroups — C11×#24655 #14601848

Order 2816.

922 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×#464C211yesmaximal, characteristic, complemented
2C2×C11×#431C211yesmaximal, characteristic, complemented
3C11×#2850C211yesmaximal, characteristic
4C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
5C11×#2035C211yesmaximal, characteristic, complemented
6C11×#2033C211yesmaximal, characteristic
7C11×#2001C211yesmaximal, characteristic, complemented
8C11×#2000C211yesmaximal, characteristic
9C11×#1983C211yesmaximal, characteristic, complemented
10C11×#1969C211yesmaximal, characteristic, complemented
11C11×#1968C211yesmaximal, characteristic, complemented
12C11×#1949C211yesmaximal, characteristic, complemented
13C11×#1934C211yesmaximal, characteristic, complemented
14C11×#1933C211yesmaximal, characteristic, complemented
15C11×#1805C211yesmaximal, 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
23C22×C42×C11C2211yescharacteristic
24C11×#464—24no—
25C11×#431—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×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C4×C8×C11C2211yescharacteristic
41C2×C4×C8×C11C2211yescharacteristic
42C11×#391C2211yescharacteristic
43C11×#391C2211yescharacteristic
44C11×#390C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#388—21no—
47C11×#388—21no—
48C11×#387—21no—
49C11×#386—21no—
50C11×#386—21no—
51C11×#385—21no—
52C11×#382C2211yescharacteristic
53C11×#380C2211yescharacteristic
54C4×C11×C4⋊C4—21no—
55C4×C11×C4⋊C4C2211yescharacteristic
56C4×C11×C22⋊C4—21no—
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11D411yescharacteristic
66C23×C4×C11D411yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C2×C11×Q16—22no—
69C2×C11×Q16—22no—
70C2×C11×Q16—41no—
71C2×C11×SD16—22no—
72C2×C11×SD16—22no—
73C2×C11×SD16—41no—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C11×#124—22no—
79C11×#124—22no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—41no—
83C11×C22⋊Q8—41no—
84C11×#121—41no—
85C11×#121—41no—
86C4×Q8×C11—22no—
87C4×Q8×C11—22no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
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⋊C4—21no—
105C2×C42×C11—22no—
106C2×C42×C11—22no—
107C2×C42×C11—21no—
108C2×C42×C11—21no—
109C2×C42×C11D411yescharacteristic
110C2×C42×C11D411yescharacteristic
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—41no—
120C11×#103—41no—
121C11×#103—41no—
122C11×#102—22no—
123C11×#102—22no—
124C11×#102—41no—
125C11×C22⋊C8—22no—
126C11×C22⋊C8—22no—
127C4×C8×C11—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#24655C1111yesmaximal, 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—42no—
161C2×D4×C11—42no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
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—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—41no—
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—44no—
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×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11C2×D412yes—
200C2×C8×C11C2×D412yes—
201C11×C4⋊C4—24no—
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—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—42no—
212C11×C4⋊C4—42no—
213C11×C4⋊C4—42no—
214C11×C4⋊C4#4112yes—
215C11×C22⋊C4—24no—
216C11×C22⋊C4—42no—
217C11×C22⋊C4—42no—
218C11×C22⋊C4—42no—
219C11×C22⋊C4—42no—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—42no—
222C11×C22⋊C4—42no—
223C42×C11—22no—
224C42×C11—22no—
225C42×C11—21no—
226C42×C11—21no—
227C42×C11—42no—
228C42×C11—42no—
229C42×C11C2×D412yes—
230C42×C11#4112yes—
231C2×#464C2×C1111yescharacteristic, complemented
232C2×#431C2×C1111yescharacteristic, complemented
233#2850C2×C1111yescharacteristic
234C4×C22⋊Q8C2×C1111yescharacteristic, complemented
235#2035C2×C1111yescharacteristic, complemented
236#2033C2×C1111yescharacteristic
237#2001C2×C1111yescharacteristic, complemented
238#2000C2×C1111yescharacteristic
239#1983C2×C1111yescharacteristic, complemented
240#1969C2×C1111yescharacteristic, complemented
241#1968C2×C1111yescharacteristic, complemented
242#1949C2×C1111yescharacteristic, complemented
243#1934C2×C1111yescharacteristic, complemented
244#1933C2×C1111yescharacteristic, complemented
245#1805C2×C1111yescharacteristic, complemented
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×C11—41no—
259C23×C11#13512yes—
260C23×C11C22×D411yescharacteristic
261Q8×C11—22no—
262Q8×C11—22no—
263Q8×C11—41no—
264Q8×C11—41no—
265Q8×C11—41no—
266Q8×C11—41no—
267Q8×C11—41no—
268Q8×C11—41no—
269D4×C11—41no—
270D4×C11—41no—
271D4×C11—41no—
272D4×C11—41no—
273D4×C11—84no—
274C2×C4×C11—28no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
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—21no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—44no—
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—41no—
311C2×C4×C11—41no—
312C2×C4×C11#12112yes—
313C2×C4×C11#12112yes—
314C2×C4×C11#13512yes—
315C2×C4×C11#13712yes—
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C2×C4×C11C2×#4111yescharacteristic
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C8×C11—22no—
323C8×C11—22no—
324C8×C11—41no—
325C8×C11—41no—
326C22×Q16C22×C1111yescharacteristic
327C22×SD16C22×C1111yescharacteristic
328C2×#124C22×C1111yescharacteristic
329C2×C22⋊Q8C22×C1111yescharacteristic
330C2×C22⋊Q8C22×C1111yescharacteristic
331C2×#121C22×C1111yescharacteristic
332C2×C4×Q8C22×C1111yescharacteristic
333C22×C42C22×C1111yescharacteristic
334#464—24no—
335#431—24no—
336C2×#107C22×C1111yescharacteristic
337C2×#106C22×C1111yescharacteristic
338C2×C4⋊C8C22×C1111yescharacteristic
339C2×C4⋊C8C22×C1111yescharacteristic
340C2×#103C22×C1111yescharacteristic
341C2×#103C22×C1111yescharacteristic
342C2×#103C22×C1111yescharacteristic
343C2×#103C22×C1111yescharacteristic
344C2×#103C22×C1111yescharacteristic
345C2×#102C22×C1111yescharacteristic
346C2×#102C22×C1111yescharacteristic
347C2×#102C22×C1111yescharacteristic
348C2×C22⋊C8C22×C1111yescharacteristic
349C2×C22⋊C8C22×C1111yescharacteristic
350C2×C4×C8C22×C1111yescharacteristic
351C2×C4×C8C22×C1111yescharacteristic
352#391C22×C1111yescharacteristic
353#391C22×C1111yescharacteristic
354#390C22×C1111yescharacteristic
355#389C22×C1111yescharacteristic
356#388—21no—
357#388—21no—
358#387—21no—
359#386—21no—
360#386—21no—
361#385—21no—
362#382C22×C1111yescharacteristic
363#380C22×C1111yescharacteristic
364C4×C4⋊C4—21no—
365C4×C4⋊C4C22×C1111yescharacteristic
366C4×C22⋊C4—21no—
367#340C22×C1111yescharacteristic
368#340C22×C1111yescharacteristic
369#340C22×C1111yescharacteristic
370#340C22×C1111yescharacteristic
371C22×C11—22no—
372C22×C11—22no—
373C22×C11—22no—
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×C11—81no—
383C22×C11—81no—
384C22×C11—81no—
385C22×C11C2×#12111yescharacteristic
386C22×C11#52511yescharacteristic
387C22×C11#53511yescharacteristic
388C22×C11C2×#13511yescharacteristic
389C22×C11C2×#13511yescharacteristic
390C22×C11C2×#13711yescharacteristic
391C22×C11#57511yescharacteristic
392C4×C11—22no—
393C4×C11—22no—
394C4×C11—22no—
395C4×C11—22no—
396C4×C11—42no—
397C4×C11—41no—
398C4×C11—42no—
399C4×C11—81no—
400C4×C11—81no—
401C4×C11—81no—
402C4×C11—81no—
403C4×C11—81no—
404C4×C11#54611yescharacteristic
405C4×C11#55011yescharacteristic
406C4×C11#55311yescharacteristic
407C4×C11#55511yescharacteristic
408C22×Q8C23×C1111yescharacteristic
409C22×Q8C23×C1111yescharacteristic
410C22×D4—21no—
411C22×D4C23×C1111yescharacteristic
412C23×C4D4×C1111yescharacteristic
413C23×C4D4×C1111yescharacteristic
414C23×C4C23×C1111yescharacteristic
415C2×Q16—22no—
416C2×Q16—22no—
417C2×Q16—41no—
418C2×SD16—22no—
419C2×SD16—22no—
420C2×SD16—41no—
421C22×C8C23×C1111yescharacteristic
422C22×C8C23×C1111yescharacteristic
423C22×C8C23×C1111yescharacteristic
424C22×C8C23×C1111yescharacteristic
425#124—22no—
426#124—22no—
427C22⋊Q8—22no—
428C22⋊Q8—22no—
429C22⋊Q8—41no—
430C22⋊Q8—41no—
431#121—41no—
432#121—41no—
433C4×Q8—22no—
434C4×Q8—22no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
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×C42—22no—
453C2×C42—22no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42D4×C1111yescharacteristic
457C2×C42D4×C1111yescharacteristic
458C2×C42C23×C1111yescharacteristic
459C2×C42C23×C1111yescharacteristic
460#107—41no—
461#106—41no—
462C4⋊C8—22no—
463C4⋊C8D4×C1114yescomplemented
464#103—22no—
465#103—22no—
466#103—41no—
467#103—41no—
468#103—41no—
469#102—22no—
470#102—22no—
471#102—41no—
472C22⋊C8—22no—
473C22⋊C8—22no—
474C4×C8—22no—
475C4×C8—22no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485C2×C11—42no—
486C2×C11—161no—
487C2×C11#241411yescharacteristic
488C2×C11#305011yescharacteristic
489C2×C11#305611yescharacteristic
490C2×C11#310211yescharacteristic
491C2×C11#310811yescharacteristic
492C2×C11#321011yescharacteristic
493C2×C11#321111yescharacteristic
494C24—21no—
495C24C2×D4×C1111yescharacteristic
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×Q8—21no—
506C2×Q8—21no—
507C2×Q8C11×#4112yes—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—42no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—41no—
536C22×C4C2×D4×C1111yescharacteristic
537C22×C4C2×D4×C1111yescharacteristic
538C22×C4C2×D4×C1111yescharacteristic
539C22×C4C2×D4×C1111yescharacteristic
540C22×C4C2×D4×C1111yescharacteristic
541C22×C4C24×C1111yescharacteristic
542Q16—44no—
543SD16—44no—
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×C8C2×D4×C1112yes—
555C2×C8C2×D4×C1112yes—
556C4⋊C4—24no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4C11×#4112yes—
570C22⋊C4—24no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C42—22no—
579C42—22no—
580C42—21no—
581C42—21no—
582C42—42no—
583C42—42no—
584C42C2×D4×C1112yes—
585C42C11×#4112yes—
586C11#2465511yescharacteristic, direct product factor, Sylow
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C11×#13512yes—
601C23C22×D4×C1111yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—41no—
605Q8—41no—
606Q8—41no—
607Q8—41no—
608Q8—41no—
609Q8—41no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—41no—
614D4—84no—
615C2×C4—28no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—44no—
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—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4C11×#12112yes—
654C2×C4C11×#12112yes—
655C2×C4C11×#13512yes—
656C2×C4C11×#13712yes—
657C2×C4C22×D4×C1111yescharacteristic
658C2×C4C2×C11×#4111yescharacteristic
659C2×C4C2×C11×#4111yescharacteristic
660C2×C4C2×C11×#4111yescharacteristic
661C2×C4C11×H(5,𝔽2)11yescharacteristic
662C2×C4C11×H(5,𝔽2)11yescharacteristic
663C8—22no—
664C8—22no—
665C8—41no—
666C8—41no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C2×C11×#12111yescharacteristic
682C22C11×#52511yescharacteristic
683C22C11×#53511yescharacteristic
684C22C2×C11×#13511yescharacteristic
685C22C2×C11×#13511yescharacteristic
686C22C2×C11×#13711yescharacteristic
687C22C11×#57511yescharacteristic
688C4—22no—
689C4—22no—
690C4—22no—
691C4—22no—
692C4—41no—
693C4—42no—
694C4—42no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4C11×#54611yescharacteristic
701C4C11×#55011yescharacteristic
702C4C11×#55311yescharacteristic
703C4C11×#55511yescharacteristic
704C2—42no—
705C2—161no—
706C2C11×#241411yescharacteristic
707C2C11×#305011yescharacteristic
708C2C11×#305611yescharacteristic
709C2C11×#310211yescharacteristic
710C2C11×#310811yescharacteristic
711C2C11×#321011yescharacteristic
712C2C11×#321111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#464C2semidirect
2. C2×C11×#431C2semidirect
4. C4×C11×C22⋊Q8C2semidirect
5. C11×#2035C2semidirect
7. C11×#2001C2semidirect
9. C11×#1983C2semidirect
10. C11×#1969C2semidirect
11. C11×#1968C2semidirect
12. C11×#1949C2semidirect
13. C11×#1934C2semidirect
14. C11×#1933C2semidirect
15. C11×#1805C2semidirect
116. C11×C4⋊C8D4semidirect
138. #24655C11direct (N × H)
231. C2×#464C2×C11semidirect
232. C2×#431C2×C11semidirect
234. C4×C22⋊Q8C2×C11semidirect
235. #2035C2×C11semidirect
237. #2001C2×C11semidirect
239. #1983C2×C11semidirect
240. #1969C2×C11semidirect
241. #1968C2×C11semidirect
242. #1949C2×C11semidirect
243. #1934C2×C11semidirect
244. #1933C2×C11semidirect
245. #1805C2×C11semidirect
463. C4⋊C8D4×C11semidirect
586. C11#24655direct (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×#4312
C11×#28502
C4×C11×C22⋊Q82
C11×#20352
C11×#20332
C11×#20012
C11×#20002
C11×#19832
C11×#19692
C11×#19682
C11×#19492
C11×#19342
C11×#19332
C11×#18052
#2465511