Finite Group Databasebeta

← C11×#24776 #14601969

Subgroups — C11×#24776 #14601969

Order 2816.

1080 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#465C211yesmaximal, characteristic, complemented
2C2×C11×#465C211yesmaximal, characteristic, complemented
3C2×C8×D4×C11C211yesmaximal, characteristic, complemented
4C22×C11×#106C211yesmaximal, characteristic, complemented
5C11×#2417C211yesmaximal, characteristic, complemented
6C11×#2416C211yesmaximal, characteristic
7C11×#2066C211yesmaximal, characteristic, complemented
8C11×#2065C211yesmaximal, characteristic, complemented
9C11×#2035C211yesmaximal, characteristic, complemented
10C11×#2034C211yesmaximal, characteristic, complemented
11C11×#1968C211yesmaximal, characteristic, complemented
12C11×#1941C211yesmaximal, characteristic, complemented
13C11×#1874C211yesmaximal, characteristic, complemented
14C11×#1872C211yesmaximal, characteristic, complemented
15C11×#1807C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121—21no—
22C2×C11×#121C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C11×#465—24no—
28C11×#465—24no—
29C8×D4×C11—24no—
30C2×C11×#106—24no—
31C2×C11×#106C2211yescharacteristic
32C2×C11×#106C2211yescharacteristic
33C2×C11×#106C2211yescharacteristic
34C2×C11×#106C2211yescharacteristic
35C2×C11×#106C2211yescharacteristic
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×C22⋊C8C2211yescharacteristic
44C2×C11×C22⋊C8C2211yescharacteristic
45C2×C4×C8×C11C2211yescharacteristic
46C11×#398—21no—
47C11×#396—21no—
48C11×#396—21no—
49C11×#394—21no—
50C11×#391C2211yescharacteristic
51C11×#390C2211yescharacteristic
52C11×#389C2211yescharacteristic
53C11×#389C2211yescharacteristic
54C11×#386—21no—
55C11×#386—21no—
56C11×#380—21no—
57C11×#380C2211yescharacteristic
58C11×#380C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11D411yescharacteristic
67C22×D4×C11C2311yescharacteristic
68C23×C4×C11—21no—
69C23×C4×C11—21no—
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C2×C11×SD16—22no—
73C2×C11×SD16—22no—
74C2×C11×SD16—22no—
75C22×C8×C11—22no—
76C22×C8×C11—22no—
77C22×C8×C11—22no—
78C22×C8×C11—22no—
79C22×C8×C11—22no—
80C22×C8×C11D414yescomplemented
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—41no—
89C11×#121—22no—
90C11×#121—22no—
91C11×#121—22no—
92C11×#121—41no—
93C11×#121—44no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—41no—
105C2×C11×C4⋊C4—41no—
106C2×C11×C4⋊C4D411yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4D411yescharacteristic
122C2×C11×C22⋊C4D411yescharacteristic
123C2×C42×C11C2311yescharacteristic
124C11×#106—22no—
125C11×#106—22no—
126C11×#106—22no—
127C11×#106—22no—
128C11×#106D414yescomplemented
129C11×C4⋊C8—22no—
130C11×#103—22no—
131C11×#103—22no—
132C11×#103—41no—
133C11×#102—22no—
134C11×#102—22no—
135C11×#102—41no—
136C11×C22⋊C8—22no—
137C11×C22⋊C8—22no—
138C4×C8×C11—22no—
139C11×#95—21no—
140C11×#95—21no—
141C11×#95—21no—
142C11×#95—21no—
143C11×#95—21no—
144C11×#95—21no—
145#24776C1111yesmaximal, characteristic, direct product factor, Sylow
146C24×C11—21no—
147C24×C11C2×D411yescharacteristic
148C24×C11C2×D411yescharacteristic
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11—42no—
168C2×D4×C11—81no—
169C2×D4×C11SD1614yescomplemented
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—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—42no—
188C22×C4×C11—42no—
189C22×C4×C11—42no—
190C22×C4×C11—42no—
191C22×C4×C11—81no—
192C22×C4×C11—81no—
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11#4112yes—
199C22×C4×C11C2411yescharacteristic
200C11×SD16—44no—
201C2×C8×C11—28no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—44no—
211C2×C8×C11C2×D412yes—
212C2×C8×C11C2×D412yes—
213C2×C8×C11C2×D412yes—
214C2×C8×C11#4112yes—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—42no—
227C11×C4⋊C4—42no—
228C11×C4⋊C4—42no—
229C11×C4⋊C4—42no—
230C11×C4⋊C4—42no—
231C11×C4⋊C4—81no—
232C11×C4⋊C4C2×D412yes—
233C11×C4⋊C4C2×D412yes—
234C11×C22⋊C4—22no—
235C11×C22⋊C4—22no—
236C11×C22⋊C4—42no—
237C11×C22⋊C4—42no—
238C11×C22⋊C4—42no—
239C11×C22⋊C4—42no—
240C11×C22⋊C4—42no—
241C11×C22⋊C4—42no—
242C11×C22⋊C4—81no—
243C11×C22⋊C4—81no—
244C42×C11—21no—
245C42×C11—21no—
246C2×#465C2×C1111yescharacteristic, complemented
247C2×#465C2×C1111yescharacteristic, complemented
248C2×C8×D4C2×C1111yescharacteristic, complemented
249C22×#106C2×C1111yescharacteristic, complemented
250#2417C2×C1111yescharacteristic, complemented
251#2416C2×C1111yescharacteristic
252#2066C2×C1111yescharacteristic, complemented
253#2065C2×C1111yescharacteristic, complemented
254#2035C2×C1111yescharacteristic, complemented
255#2034C2×C1111yescharacteristic, complemented
256#1968C2×C1111yescharacteristic, complemented
257#1941C2×C1111yescharacteristic, complemented
258#1874C2×C1111yescharacteristic, complemented
259#1872C2×C1111yescharacteristic, complemented
260#1807C2×C1111yescharacteristic, complemented
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11#12112yes—
279C23×C11C2×SD1612yes—
280C23×C11C2×SD1612yes—
281C23×C11#13512yes—
282C23×C11C22×D411yescharacteristic
283Q8×C11—41no—
284Q8×C11—41no—
285Q8×C11—41no—
286Q8×C11—41no—
287D4×C11—28no—
288D4×C11—41no—
289D4×C11—41no—
290D4×C11—41no—
291D4×C11—41no—
292D4×C11—84no—
293D4×C11—84no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—84no—
334C2×C4×C11—84no—
335C2×C4×C11#12112yes—
336C2×C4×C11C2×SD1612yes—
337C2×C4×C11C22×D411yescharacteristic
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C2×#4111yescharacteristic
340C2×C4×C11C2×#4111yescharacteristic
341C2×C4×C11H(5,𝔽2)11yescharacteristic
342C2×C4×C112−1+411yescharacteristic
343C8×C11—22no—
344C8×C11—41no—
345C8×C11—41no—
346C8×C11#12114yescomplemented
347C22×SD16C22×C1111yescharacteristic
348C23×C8C22×C1111yescharacteristic
349C23×C8C22×C1111yescharacteristic
350C2×C22⋊Q8C22×C1111yescharacteristic
351C2×C22⋊Q8C22×C1111yescharacteristic
352C2×#121—21no—
353C2×#121C22×C1111yescharacteristic
354C2×#121C22×C1111yescharacteristic
355C2×C4×D4C22×C1111yescharacteristic
356C22×C4⋊C4C22×C1111yescharacteristic
357C22×C4⋊C4C22×C1111yescharacteristic
358#465—24no—
359#465—24no—
360C8×D4—24no—
361C2×#106—24no—
362C2×#106C22×C1111yescharacteristic
363C2×#106C22×C1111yescharacteristic
364C2×#106C22×C1111yescharacteristic
365C2×#106C22×C1111yescharacteristic
366C2×#106C22×C1111yescharacteristic
367C2×C4⋊C8C22×C1111yescharacteristic
368C2×#103C22×C1111yescharacteristic
369C2×#103C22×C1111yescharacteristic
370C2×#103C22×C1111yescharacteristic
371C2×#102C22×C1111yescharacteristic
372C2×#102C22×C1111yescharacteristic
373C2×#102C22×C1111yescharacteristic
374C2×C22⋊C8C22×C1111yescharacteristic
375C2×C22⋊C8C22×C1111yescharacteristic
376C2×C4×C8C22×C1111yescharacteristic
377#398—21no—
378#396—21no—
379#396—21no—
380#394—21no—
381#391C22×C1111yescharacteristic
382#390C22×C1111yescharacteristic
383#389C22×C1111yescharacteristic
384#389C22×C1111yescharacteristic
385#386—21no—
386#386—21no—
387#380—21no—
388#380C22×C1111yescharacteristic
389#380C22×C1111yescharacteristic
390#340C22×C1111yescharacteristic
391#340C22×C1111yescharacteristic
392#340C22×C1111yescharacteristic
393#340C22×C1111yescharacteristic
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—22no—
401C22×C11—22no—
402C22×C11—22no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—81no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11—81no—
411C22×C11—81no—
412C22×C11—81no—
413C22×C11—81no—
414C22×C11#46514yescomplemented
415C22×C11C2×#12111yescharacteristic
416C22×C11D4211yescharacteristic
417C22×C11#54711yescharacteristic
418C22×C11C22×SD1611yescharacteristic
419C22×C11C2×#13511yescharacteristic
420C22×C11#57711yescharacteristic
421C22×C11#57711yescharacteristic
422C4×C11—22no—
423C4×C11—22no—
424C4×C11—41no—
425C4×C11—42no—
426C4×C11—42no—
427C4×C11—41no—
428C4×C11—81no—
429C4×C11—81no—
430C4×C11—81no—
431C4×C11—81no—
432C4×C11—81no—
433C4×C11C2×#12111yescharacteristic
434C4×C11#53711yescharacteristic
435C4×C11#54811yescharacteristic
436C4×C11#55311yescharacteristic
437C22×Q8C23×C1111yescharacteristic
438C22×D4—21no—
439C22×D4—21no—
440C22×D4D4×C1111yescharacteristic
441C22×D4C23×C1111yescharacteristic
442C23×C4—21no—
443C23×C4—21no—
444C23×C4C23×C1111yescharacteristic
445C23×C4C23×C1111yescharacteristic
446C2×SD16—22no—
447C2×SD16—22no—
448C2×SD16—22no—
449C22×C8—22no—
450C22×C8—22no—
451C22×C8—22no—
452C22×C8—22no—
453C22×C8—22no—
454C22×C8D4×C1114yescomplemented
455C22×C8C23×C1111yescharacteristic
456C22×C8C23×C1111yescharacteristic
457C22×C8C23×C1111yescharacteristic
458C22×C8C23×C1111yescharacteristic
459C22⋊Q8—22no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—41no—
463#121—22no—
464#121—22no—
465#121—22no—
466#121—41no—
467#121—44no—
468C4×D4—22no—
469C4×D4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—41no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4D4×C1111yescharacteristic
481C2×C4⋊C4C23×C1111yescharacteristic
482C2×C4⋊C4C23×C1111yescharacteristic
483C2×C4⋊C4C23×C1111yescharacteristic
484C2×C4⋊C4C23×C1111yescharacteristic
485C2×C4⋊C4C23×C1111yescharacteristic
486C2×C4⋊C4C23×C1111yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4D4×C1111yescharacteristic
496C2×C22⋊C4D4×C1111yescharacteristic
497C2×C42C23×C1111yescharacteristic
498#106—22no—
499#106—22no—
500#106—22no—
501#106—22no—
502#106D4×C1114yescomplemented
503C4⋊C8—22no—
504#103—22no—
505#103—22no—
506#103—41no—
507#102—22no—
508#102—22no—
509#102—41no—
510C22⋊C8—22no—
511C22⋊C8—22no—
512C4×C8—22no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519C2×C11—24no—
520C2×C11—42no—
521C2×C11—161no—
522C2×C11#241611yescharacteristic
523C2×C11C2×#46511yescharacteristic
524C2×C11#306011yescharacteristic
525C2×C11D4×SD1611yescharacteristic
526C2×C11#328211yescharacteristic
527C2×C11#333511yescharacteristic
528C2×C11#333711yescharacteristic
529C24—21no—
530C24C2×D4×C1111yescharacteristic
531C24C2×D4×C1111yescharacteristic
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—81no—
552C2×D4C11×SD1614yescomplemented
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—81no—
575C22×C4—81no—
576C22×C4C2×D4×C1111yescharacteristic
577C22×C4C2×D4×C1111yescharacteristic
578C22×C4C2×D4×C1111yescharacteristic
579C22×C4C2×D4×C1112yes—
580C22×C4C2×D4×C1111yescharacteristic
581C22×C4C11×#4112yes—
582C22×C4C24×C1111yescharacteristic
583SD16—44no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—28no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—44no—
594C2×C8C2×D4×C1112yes—
595C2×C8C2×D4×C1112yes—
596C2×C8C2×D4×C1112yes—
597C2×C8C11×#4112yes—
598C4⋊C4—22no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—81no—
615C4⋊C4C2×D4×C1112yes—
616C4⋊C4C2×D4×C1112yes—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C42—21no—
628C42—21no—
629C11#2477611yescharacteristic, direct product factor, Sylow
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23C11×#12112yes—
648C23C2×C11×SD1612yes—
649C23C2×C11×SD1612yes—
650C23C11×#13512yes—
651C23C22×D4×C1111yescharacteristic
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—41no—
656D4—28no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—84no—
662D4—84no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—84no—
703C2×C4—84no—
704C2×C4C11×#12112yes—
705C2×C4C2×C11×SD1612yes—
706C2×C4C22×D4×C1111yescharacteristic
707C2×C4C22×D4×C1111yescharacteristic
708C2×C4C2×C11×#4111yescharacteristic
709C2×C4C2×C11×#4111yescharacteristic
710C2×C4C11×H(5,𝔽2)11yescharacteristic
711C2×C4C11×2−1+411yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8C11×#12114yescomplemented
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22C11×#46514yescomplemented
737C22C2×C11×#12111yescharacteristic
738C22D42×C1111yescharacteristic
739C22C11×#54711yescharacteristic
740C22C22×C11×SD1611yescharacteristic
741C22C2×C11×#13511yescharacteristic
742C22C11×#57711yescharacteristic
743C22C11×#57711yescharacteristic
744C4—22no—
745C4—22no—
746C4—41no—
747C4—42no—
748C4—42no—
749C4—41no—
750C4—81no—
751C4—81no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4C2×C11×#12111yescharacteristic
756C4C11×#53711yescharacteristic
757C4C11×#54811yescharacteristic
758C4C11×#55311yescharacteristic
759C2—24no—
760C2—42no—
761C2—161no—
762C2C11×#241611yescharacteristic
763C2C2×C11×#46511yescharacteristic
764C2C11×#306011yescharacteristic
765C2D4×C11×SD1611yescharacteristic
766C2C11×#328211yescharacteristic
767C2C11×#333511yescharacteristic
768C2C11×#333711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2416C2
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×#465C2semidirect
2. C2×C11×#465C2semidirect
3. C2×C8×D4×C11C2semidirect
4. C22×C11×#106C2semidirect
5. C11×#2417C2semidirect
7. C11×#2066C2semidirect
8. C11×#2065C2semidirect
9. C11×#2035C2semidirect
10. C11×#2034C2semidirect
11. C11×#1968C2semidirect
12. C11×#1941C2semidirect
13. C11×#1874C2semidirect
14. C11×#1872C2semidirect
15. C11×#1807C2semidirect
80. C22×C8×C11D4semidirect
128. C11×#106D4semidirect
145. #24776C11direct (N × H)
169. C2×D4×C11SD16semidirect
246. C2×#465C2×C11semidirect
247. C2×#465C2×C11semidirect
248. C2×C8×D4C2×C11semidirect
249. C22×#106C2×C11semidirect
250. #2417C2×C11semidirect
252. #2066C2×C11semidirect
253. #2065C2×C11semidirect
254. #2035C2×C11semidirect
255. #2034C2×C11semidirect
256. #1968C2×C11semidirect
257. #1941C2×C11semidirect
258. #1874C2×C11semidirect
259. #1872C2×C11semidirect
260. #1807C2×C11semidirect
346. C8×C11#121semidirect
414. C22×C11#465semidirect
454. C22×C8D4×C11semidirect
502. #106D4×C11semidirect
552. C2×D4C11×SD16semidirect
629. C11#24776direct (N × H)
715. C8C11×#121semidirect
736. C22C11×#465semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4652
C2×C8×D4×C112
C22×C11×#1062
C11×#24172
C11×#24162
C11×#20662
C11×#20652
C11×#20352
C11×#20342
C11×#19682
C11×#19412
C11×#18742
C11×#18722
C11×#18072
#2477611