Finite Group Databasebeta

← C11×#23954 #14601147

Subgroups — C11×#23954 #14601147

Order 2816.

1482 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3494C211yesmaximal, characteristic, complemented
2C11×#3003C211yesmaximal, characteristic, complemented
3C2×C11×#418C211yesmaximal, characteristic, complemented
4C11×#2433C211yesmaximal, characteristic, complemented
5C11×#2027C212yesmaximal, complemented
6C11×#2002C212yesmaximal, complemented
7C11×#1900C211yesmaximal, characteristic, complemented
8C11×#1887C212yesmaximal, complemented
9C11×#1883C212yesmaximal, complemented
10C11×#1871C211yesmaximal, characteristic, complemented
11C11×#1826C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C2×C11×AGL(1,ℤ/8)C2212yes—
14C22×C11×M16C2211yescharacteristic
15C11×#555—21no—
16C11×#553—21no—
17C11×#553—21no—
18C11×#551—22no—
19C11×#547—21no—
20C11×#546—22no—
21C11×#544C2211yescharacteristic, complemented
22C11×#542—21no—
23C11×#540—21no—
24C11×#535C2211yescharacteristic, complemented
25C11×#532—21no—
26C2×C11×#127C2212yes—
27C11×#529—21no—
28C11×#525C2211yescharacteristic
29C2×C11×#121C2211yescharacteristic
30C2×C11×#120—22no—
31C11×#520C2211yescharacteristic, complemented
32C11×#518C2211yescharacteristic, complemented
33C2×C11×#117C2211yescharacteristic
34C11×#450—21no—
35C11×#450—21no—
36C11×#447—21no—
37C11×#447—21no—
38C2×C11×#104C2212yescomplemented
39C11×#418—21no—
40C11×#418—21no—
41C11×#418C2212yes—
42C11×#418C2212yes—
43C11×#418C2212yes—
44C2×C11×#102—21no—
45C2×C11×#102—21no—
46C2×C11×#100C2212yescomplemented
47C11×#407C2211yescharacteristic
48C11×#392—22no—
49C11×#390C2212yes—
50C4×C11×C22⋊C4C2211yescharacteristic
51C11×#343C2212yescomplemented
52C11×#339C2212yescomplemented
53C11×#339C2212yescomplemented
54C11×#339C2212yescomplemented
55C25×C11—21no—
56C2×C11×#41—22no—
57C2×C11×#41C2311yescharacteristic
58C22×D4×C11—24no—
59C22×D4×C11—24no—
60C22×D4×C11—21no—
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11—42no—
66C22×D4×C11D412yes—
67C22×D4×C11C2311yescharacteristic
68C22×D4×C11C2312yes—
69C23×C4×C11C2311yescharacteristic
70C11×AGL(1,ℤ/8)—24no—
71C11×AGL(1,ℤ/8)—42no—
72C2×C11×SD16—22no—
73C2×C11×D8—22no—
74C2×C11×M16—21no—
75C2×C11×M16—42no—
76C2×C11×M16C2312yes—
77C2×C11×M16C2312yes—
78C22×C8×C11—21no—
79C11×C4⋊Q8—21no—
80C11×C4⋊Q8—21no—
81C11×#127—21no—
82C11×#127—24no—
83C11×#127—42no—
84C11×#126—22no—
85C11×#126—22no—
86C11×#125—21no—
87C11×#125—21no—
88C11×#124—22no—
89C11×#124—22no—
90C11×#124—21no—
91C11×#123—22no—
92C11×#123—22no—
93C11×#123—22no—
94C11×#123—22no—
95C11×#123—21no—
96C11×C22⋊Q8—22no—
97C11×C22⋊Q8—22no—
98C11×C22⋊Q8D411yescharacteristic, complemented
99C11×C22⋊Q8D411yescharacteristic, complemented
100C11×#121—22no—
101C11×#121—22no—
102C11×#121—22no—
103C11×#121—21no—
104C11×#121—21no—
105C11×#121—21no—
106C11×#121—21no—
107C11×#121—21no—
108C11×#121—21no—
109C11×#121D411yescharacteristic, complemented
110C11×#121D411yescharacteristic, complemented
111C11×#120—21no—
112C11×#120—22no—
113C11×#120—48no—
114C4×Q8×C11—21no—
115C4×D4×C11—22no—
116C4×D4×C11—22no—
117C4×D4×C11—21no—
118C4×D4×C11—22no—
119C4×D4×C11—21no—
120C4×D4×C11—21no—
121C4×D4×C11—21no—
122C4×D4×C11—21no—
123C4×D4×C11—21no—
124C4×D4×C11—21no—
125C11×#117—22no—
126C11×#117—21no—
127C11×#117—21no—
128C11×#117—21no—
129C11×#117D411yescharacteristic, complemented
130C11×#117D411yescharacteristic, complemented
131C11×#117C2311yescharacteristic
132C11×#117C2311yescharacteristic
133C11×#117C2311yescharacteristic
134C2×C11×C4⋊C4—21no—
135C2×C11×C4⋊C4D411yescharacteristic, complemented
136C2×C11×C4⋊C4D411yescharacteristic, complemented
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4—21no—
140C2×C11×C22⋊C4—22no—
141C2×C11×C22⋊C4—24no—
142C2×C11×C22⋊C4D412yes—
143C2×C42×C11—21no—
144C2×C42×C11C2312yes—
145C11×#104—42no—
146C11×#102—22no—
147C11×#102—22no—
148C11×#102—22no—
149C11×#102—22no—
150C11×#102—22no—
151C11×#102—22no—
152C11×#100—42no—
153C11×C22⋊C8—21no—
154C11×C22⋊C8—21no—
155C11×#95—21no—
156#23954C1111yesmaximal, characteristic, direct product factor, Sylow
157C24×C11—22no—
158C24×C11—44no—
159C24×C11—44no—
160C24×C11—41no—
161C24×C11—41no—
162C24×C11—82no—
163C24×C11C2×D411yescharacteristic
164C24×C11C2×D412yes—
165C11×#41—22no—
166C11×#41—22no—
167C11×#41—84no—
168C2×Q8×C11—22no—
169C2×Q8×C11C2×D411yescharacteristic
170C2×D4×C11—24no—
171C2×D4×C11—24no—
172C2×D4×C11—21no—
173C2×D4×C11—22no—
174C2×D4×C11—21no—
175C2×D4×C11—22no—
176C2×D4×C11—22no—
177C2×D4×C11—21no—
178C2×D4×C11—22no—
179C2×D4×C11—22no—
180C2×D4×C11—22no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11—22no—
184C2×D4×C11—22no—
185C2×D4×C11—22no—
186C2×D4×C11—22no—
187C2×D4×C11—22no—
188C2×D4×C11—44no—
189C2×D4×C11—44no—
190C2×D4×C11—44no—
191C2×D4×C11—42no—
192C2×D4×C11—42no—
193C2×D4×C11—48no—
194C2×D4×C11—44no—
195C2×D4×C11—48no—
196C2×D4×C11—41no—
197C2×D4×C11—41no—
198C2×D4×C11—84no—
199C2×D4×C11C2×D411yescharacteristic
200C2×D4×C11#4114yescomplemented
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—21no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D412yes—
216C22×C4×C11C2411yescharacteristic
217C11×SD16—44no—
218C11×D8—44no—
219C11×M16—22no—
220C11×M16—22no—
221C11×M16—22no—
222C11×M16—22no—
223C11×M16—42no—
224C2×C8×C11—22no—
225C2×C8×C11—22no—
226C2×C8×C11—42no—
227C11×C4⋊C4—22no—
228C11×C4⋊C4—22no—
229C11×C4⋊C4—22no—
230C11×C4⋊C4—22no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4C2×D411yescharacteristic
238C11×C4⋊C4C2×D411yescharacteristic
239C11×C4⋊C4C2×D411yescharacteristic
240C11×C4⋊C4C2×D411yescharacteristic
241C11×C4⋊C4C2×D411yescharacteristic
242C11×C4⋊C4C2×D411yescharacteristic
243C11×C22⋊C4—22no—
244C11×C22⋊C4—22no—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—22no—
247C11×C22⋊C4—22no—
248C11×C22⋊C4—22no—
249C11×C22⋊C4—21no—
250C11×C22⋊C4—21no—
251C11×C22⋊C4—21no—
252C11×C22⋊C4—21no—
253C11×C22⋊C4—21no—
254C11×C22⋊C4—21no—
255C11×C22⋊C4—21no—
256C11×C22⋊C4—22no—
257C11×C22⋊C4—22no—
258C11×C22⋊C4—21no—
259C11×C22⋊C4—21no—
260C11×C22⋊C4—48no—
261C42×C11—22no—
262C42×C11—21no—
263C42×C11—21no—
264C42×C11—21no—
265C42×C11—21no—
266C42×C11—21no—
267C42×C11—22no—
268C42×C11—22no—
269#3494C2×C1111yescharacteristic, complemented
270#3003C2×C1111yescharacteristic, complemented
271C2×#418C2×C1111yescharacteristic, complemented
272#2433C2×C1111yescharacteristic, complemented
273#2027C2×C1112yescomplemented
274#2002C2×C1112yescomplemented
275#1900C2×C1111yescharacteristic, complemented
276#1887C2×C1112yescomplemented
277#1883C2×C1112yescomplemented
278#1871C2×C1111yescharacteristic, complemented
279#1826C2×C1111yescharacteristic, complemented
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—21no—
284C23×C11—24no—
285C23×C11—24no—
286C23×C11—41no—
287C23×C11—44no—
288C23×C11—44no—
289C23×C11—44no—
290C23×C11—44no—
291C23×C11—42no—
292C23×C11—42no—
293C23×C11—42no—
294C23×C11—42no—
295C23×C11—82no—
296C23×C11—82no—
297C23×C11—82no—
298C23×C11—816no—
299C23×C11—82no—
300C23×C11#12011yescharacteristic
301C23×C11#12011yescharacteristic
302C23×C11C22×D411yescharacteristic
303Q8×C11—22no—
304Q8×C11—82no—
305D4×C11—24no—
306D4×C11—22no—
307D4×C11—24no—
308D4×C11—44no—
309D4×C11—44no—
310D4×C11—42no—
311D4×C11—44no—
312D4×C11—42no—
313D4×C11—41no—
314D4×C11—41no—
315D4×C11—42no—
316D4×C11—42no—
317D4×C11—42no—
318D4×C11—81no—
319D4×C11—82no—
320D4×C11—82no—
321D4×C11—82no—
322D4×C11—816no—
323C2×C4×C11—22no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—24no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—22no—
339C2×C4×C11—42no—
340C2×C4×C11—42no—
341C2×C4×C11—42no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—42no—
345C2×C4×C11—81no—
346C2×C4×C11—82no—
347C2×C4×C11—82no—
348C2×C4×C11—82no—
349C2×C4×C11#12011yescharacteristic
350C2×C4×C11#12011yescharacteristic
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11C22×D411yescharacteristic
353C2×C4×C11C2×#4112yes—
354C2×C4×C11H(5,𝔽2)12yes—
355C8×C11—42no—
356C8×C11—42no—
357C23×D4C22×C1111yescharacteristic
358C2×AGL(1,ℤ/8)C22×C1112yes—
359C22×M16C22×C1111yescharacteristic
360#555—21no—
361#553—21no—
362#553—21no—
363#551—22no—
364#547—21no—
365#546—22no—
366#544C22×C1111yescharacteristic, complemented
367#542—21no—
368#540—21no—
369#535C22×C1111yescharacteristic, complemented
370#532—21no—
371C2×#127C22×C1112yes—
372#529—21no—
373#525C22×C1111yescharacteristic
374C2×#121C22×C1111yescharacteristic
375C2×#120—22no—
376#520C22×C1111yescharacteristic, complemented
377#518C22×C1111yescharacteristic, complemented
378C2×#117C22×C1111yescharacteristic
379#450—21no—
380#450—21no—
381#447—21no—
382#447—21no—
383C2×#104C22×C1112yescomplemented
384#418—21no—
385#418—21no—
386#418C22×C1112yes—
387#418C22×C1112yes—
388#418C22×C1112yes—
389C2×#102—21no—
390C2×#102—21no—
391C2×#100C22×C1112yescomplemented
392#407C22×C1111yescharacteristic
393#392—22no—
394#390C22×C1112yes—
395C4×C22⋊C4C22×C1111yescharacteristic
396#343C22×C1112yescomplemented
397#339C22×C1112yescomplemented
398#339C22×C1112yescomplemented
399#339C22×C1112yescomplemented
400C22×C11—21no—
401C22×C11—21no—
402C22×C11—21no—
403C22×C11—21no—
404C22×C11—21no—
405C22×C11—21no—
406C22×C11—21no—
407C22×C11—44no—
408C22×C11—48no—
409C22×C11—41no—
410C22×C11—44no—
411C22×C11—42no—
412C22×C11—41no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—41no—
416C22×C11—84no—
417C22×C11—84no—
418C22×C11—88no—
419C22×C11—88no—
420C22×C11—82no—
421C22×C11—82no—
422C22×C11#45312yes—
423C22×C11C2×#12011yescharacteristic
424C22×C11#54612yes—
425C4×C11—21no—
426C4×C11—21no—
427C4×C11—44no—
428C4×C11—41no—
429C4×C11—41no—
430C4×C11—41no—
431C4×C11—42no—
432C4×C11—41no—
433C4×C11—41no—
434C4×C11—41no—
435C4×C11—41no—
436C4×C11#52511yescharacteristic
437C4×C11#53511yescharacteristic
438C4×C11#54612yes—
439C25—21no—
440C2×#41—22no—
441C2×#41C23×C1111yescharacteristic
442C22×D4—24no—
443C22×D4—24no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—42no—
450C22×D4D4×C1112yes—
451C22×D4C23×C1111yescharacteristic
452C22×D4C23×C1112yes—
453C23×C4C23×C1111yescharacteristic
454AGL(1,ℤ/8)—24no—
455AGL(1,ℤ/8)—42no—
456C2×SD16—22no—
457C2×D8—22no—
458C2×M16—21no—
459C2×M16—42no—
460C2×M16C23×C1112yes—
461C2×M16C23×C1112yes—
462C22×C8—21no—
463C4⋊Q8—21no—
464C4⋊Q8—21no—
465#127—21no—
466#127—24no—
467#127—42no—
468#126—22no—
469#126—22no—
470#125—21no—
471#125—21no—
472#124—22no—
473#124—22no—
474#124—21no—
475#123—22no—
476#123—22no—
477#123—22no—
478#123—22no—
479#123—21no—
480C22⋊Q8—22no—
481C22⋊Q8—22no—
482C22⋊Q8D4×C1111yescharacteristic, complemented
483C22⋊Q8D4×C1111yescharacteristic, complemented
484#121—22no—
485#121—22no—
486#121—22no—
487#121—21no—
488#121—21no—
489#121—21no—
490#121—21no—
491#121—21no—
492#121—21no—
493#121D4×C1111yescharacteristic, complemented
494#121D4×C1111yescharacteristic, complemented
495#120—21no—
496#120—22no—
497#120—48no—
498C4×Q8—21no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—21no—
502C4×D4—22no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509#117—22no—
510#117—21no—
511#117—21no—
512#117—21no—
513#117D4×C1111yescharacteristic, complemented
514#117D4×C1111yescharacteristic, complemented
515#117C23×C1111yescharacteristic
516#117C23×C1111yescharacteristic
517#117C23×C1111yescharacteristic
518C2×C4⋊C4—21no—
519C2×C4⋊C4D4×C1111yescharacteristic, complemented
520C2×C4⋊C4D4×C1111yescharacteristic, complemented
521C2×C4⋊C4C23×C1111yescharacteristic
522C2×C22⋊C4—21no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4D4×C1112yes—
527C2×C42—21no—
528C2×C42C23×C1112yes—
529#104—42no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—22no—
534#102—22no—
535#102—22no—
536#100—42no—
537C22⋊C8—21no—
538C22⋊C8—21no—
539#95—21no—
540C2×C11—22no—
541C2×C11—22no—
542C2×C11—41no—
543C2×C11—81no—
544C2×C11—82no—
545C2×C11—84no—
546C2×C11#240411yescharacteristic
547C2×C11C2×#45311yescharacteristic
548C2×C11#302111yescharacteristic
549C24—22no—
550C24—44no—
551C24—44no—
552C24—41no—
553C24—41no—
554C24—82no—
555C24C2×D4×C1111yescharacteristic
556C24C2×D4×C1112yes—
557#41—22no—
558#41—22no—
559#41—84no—
560C2×Q8—22no—
561C2×Q8C2×D4×C1111yescharacteristic
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—44no—
581C2×D4—44no—
582C2×D4—44no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—48no—
586C2×D4—44no—
587C2×D4—48no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—84no—
591C2×D4C2×D4×C1111yescharacteristic
592C2×D4C11×#4114yescomplemented
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4C2×D4×C1111yescharacteristic
603C22×C4C2×D4×C1111yescharacteristic
604C22×C4C2×D4×C1111yescharacteristic
605C22×C4C2×D4×C1111yescharacteristic
606C22×C4C2×D4×C1111yescharacteristic
607C22×C4C2×D4×C1112yes—
608C22×C4C24×C1111yescharacteristic
609SD16—44no—
610D8—44no—
611M16—22no—
612M16—22no—
613M16—22no—
614M16—22no—
615M16—42no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—42no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4C2×D4×C1111yescharacteristic
630C4⋊C4C2×D4×C1111yescharacteristic
631C4⋊C4C2×D4×C1111yescharacteristic
632C4⋊C4C2×D4×C1111yescharacteristic
633C4⋊C4C2×D4×C1111yescharacteristic
634C4⋊C4C2×D4×C1111yescharacteristic
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—24no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—48no—
653C42—22no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—22no—
660C42—22no—
661C11#2395411yescharacteristic, direct product factor, Sylow
662C23—22no—
663C23—22no—
664C23—22no—
665C23—21no—
666C23—24no—
667C23—24no—
668C23—41no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—82no—
678C23—82no—
679C23—82no—
680C23—816no—
681C23—82no—
682C23C11×#12011yescharacteristic
683C23C11×#12011yescharacteristic
684C23C22×D4×C1111yescharacteristic
685Q8—22no—
686Q8—82no—
687D4—24no—
688D4—22no—
689D4—24no—
690D4—44no—
691D4—44no—
692D4—42no—
693D4—44no—
694D4—42no—
695D4—41no—
696D4—41no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—81no—
701D4—82no—
702D4—82no—
703D4—82no—
704D4—816no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—81no—
728C2×C4—82no—
729C2×C4—82no—
730C2×C4—82no—
731C2×C4C11×#12011yescharacteristic
732C2×C4C11×#12011yescharacteristic
733C2×C4C22×D4×C1111yescharacteristic
734C2×C4C22×D4×C1111yescharacteristic
735C2×C4C2×C11×#4112yes—
736C2×C4C11×H(5,𝔽2)12yes—
737C8—42no—
738C8—42no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—44no—
747C22—48no—
748C22—41no—
749C22—44no—
750C22—42no—
751C22—41no—
752C22—42no—
753C22—42no—
754C22—41no—
755C22—84no—
756C22—84no—
757C22—88no—
758C22—88no—
759C22—82no—
760C22—82no—
761C22C11×#45312yes—
762C22C2×C11×#12011yescharacteristic
763C22C11×#54612yes—
764C4—21no—
765C4—21no—
766C4—44no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4C11×#52511yescharacteristic
776C4C11×#53511yescharacteristic
777C4C11×#54612yes—
778C2—22no—
779C2—22no—
780C2—41no—
781C2—84no—
782C2—82no—
783C2—81no—
784C2C11×#240411yescharacteristic
785C2C2×C11×#45311yescharacteristic
786C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3494C2semidirect
2. C11×#3003C2semidirect
3. C2×C11×#418C2semidirect
4. C11×#2433C2semidirect
5. C11×#2027C2semidirect
6. C11×#2002C2semidirect
7. C11×#1900C2semidirect
8. C11×#1887C2semidirect
9. C11×#1883C2semidirect
10. C11×#1871C2semidirect
11. C11×#1826C2semidirect
21. C11×#544C22semidirect
24. C11×#535C22semidirect
31. C11×#520C22semidirect
32. C11×#518C22semidirect
38. C2×C11×#104C22semidirect
46. C2×C11×#100C22semidirect
51. C11×#343C22semidirect
52. C11×#339C22semidirect
53. C11×#339C22semidirect
54. C11×#339C22semidirect
98. C11×C22⋊Q8D4semidirect
99. C11×C22⋊Q8D4semidirect
109. C11×#121D4semidirect
110. C11×#121D4semidirect
129. C11×#117D4semidirect
130. C11×#117D4semidirect
135. C2×C11×C4⋊C4D4semidirect
136. C2×C11×C4⋊C4D4semidirect
156. #23954C11direct (N × H)
200. C2×D4×C11#41semidirect
269. #3494C2×C11semidirect
270. #3003C2×C11semidirect
271. C2×#418C2×C11semidirect
272. #2433C2×C11semidirect
273. #2027C2×C11semidirect
274. #2002C2×C11semidirect
275. #1900C2×C11semidirect
276. #1887C2×C11semidirect
277. #1883C2×C11semidirect
278. #1871C2×C11semidirect
279. #1826C2×C11semidirect
366. #544C22×C11semidirect
369. #535C22×C11semidirect
376. #520C22×C11semidirect
377. #518C22×C11semidirect
383. C2×#104C22×C11semidirect
391. C2×#100C22×C11semidirect
396. #343C22×C11semidirect
397. #339C22×C11semidirect
398. #339C22×C11semidirect
399. #339C22×C11semidirect
482. C22⋊Q8D4×C11semidirect
483. C22⋊Q8D4×C11semidirect
493. #121D4×C11semidirect
494. #121D4×C11semidirect
513. #117D4×C11semidirect
514. #117D4×C11semidirect
519. C2×C4⋊C4D4×C11semidirect
520. C2×C4⋊C4D4×C11semidirect
592. C2×D4C11×#41semidirect
661. C11#23954direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34942
C11×#30032
C2×C11×#4182
C11×#24332
C11×#20272
C11×#20022
C11×#19002
C11×#18872
C11×#18832
C11×#18712
C11×#18262
#2395411