Finite Group Databasebeta

← C11×#24026 #14601219

Subgroups — C11×#24026 #14601219

Order 2816.

1404 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3488C211yesmaximal, characteristic
2C11×#3092C211yesmaximal, characteristic, complemented
3C2×C11×#417C211yesmaximal, characteristic, complemented
4C11×#2501C211yesmaximal, characteristic, complemented
5C11×#2039C212yesmaximal, complemented
6C11×#2037C212yesmaximal, complemented
7C11×#1900C211yesmaximal, characteristic, complemented
8C11×#1871C211yesmaximal, characteristic, complemented
9C11×#1859C212yesmaximal, complemented
10C11×#1792C212yesmaximal, complemented
11C11×#1789C211yesmaximal, characteristic, complemented
12C2×C11×H(5,𝔽2)C2211yescharacteristic
13C22×C11×#41C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic, complemented
15C11×#550—21no—
16C11×#548—21no—
17C11×#546—21no—
18C11×#546—22no—
19D42×C11—22no—
20D42×C11—21no—
21C11×#537—21no—
22C11×#537C2211yescharacteristic
23C11×#535—21no—
24C11×#535C2211yescharacteristic
25C11×#525—21no—
26C11×#525C2211yescharacteristic
27C2×C11×#123—22no—
28C2×C11×#121—21no—
29C2×C11×#121C2211yescharacteristic
30C11×#520C2211yescharacteristic
31C22×C11×C4⋊C4C2211yescharacteristic, complemented
32C11×#484—21no—
33C11×#483—21no—
34C11×#481—21no—
35C11×#480—21no—
36C11×#428C2212yescomplemented
37C2×C11×#104C2212yes—
38C2×C11×#104C2212yescomplemented
39C2×C11×#104C2212yescomplemented
40C11×#417—21no—
41C11×#417—21no—
42C11×#417C2212yes—
43C11×#417C2212yescomplemented
44C11×#417C2212yescomplemented
45C2×C11×#103—21no—
46C2×C11×#102—21no—
47C2×C11×#100C2212yescomplemented
48C11×#407C2211yescharacteristic, complemented
49C11×#399—22no—
50C11×#390C2212yescomplemented
51C11×#384C2212yescomplemented
52C4×C11×C22⋊C4C2211yescharacteristic, complemented
53C11×#343C2212yescomplemented
54C11×#339C2212yescomplemented
55C11×H(5,𝔽2)—24no—
56C11×H(5,𝔽2)—42no—
57C2×C11×#41—21no—
58C2×C11×#41—21no—
59C2×C11×#41—21no—
60C2×C11×#41—21no—
61C2×C11×#41—24no—
62C2×C11×#41—42no—
63C2×C11×#41D411yescharacteristic
64C2×C11×#41D411yescharacteristic
65C2×C11×#41C2311yescharacteristic
66C2×C11×#41C2311yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C22×Q8×C11D411yescharacteristic
69C22×D4×C11—21no—
70C22×D4×C11—22no—
71C22×D4×C11—22no—
72C22×D4×C11—21no—
73C22×D4×C11—21no—
74C22×D4×C11D411yescharacteristic
75C22×D4×C11D412yes—
76C22×D4×C11C2311yescharacteristic
77C23×C4×C11—21no—
78C23×C4×C11—21no—
79C23×C4×C11C2311yescharacteristic
80C2×C11×M16—21no—
81C2×C11×M16—42no—
82C2×C11×M16C2312yes—
83C2×C11×M16C2312yes—
84C22×C8×C11—21no—
85C11×#127—22no—
86C11×#127—21no—
87C11×#124—22no—
88C11×#124—21no—
89C11×#123—22no—
90C11×#123—21no—
91C11×#123—48no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—21no—
94C11×C22⋊Q8—21no—
95C11×C22⋊Q8D411yescharacteristic
96C11×C22⋊Q8D411yescharacteristic
97C11×#121—22no—
98C11×#121—22no—
99C11×#121—22no—
100C11×#121—22no—
101C11×#121—22no—
102C11×#121—21no—
103C11×#121—21no—
104C11×#121—21no—
105C11×#121—21no—
106C11×#121—21no—
107C11×#121—21no—
108C11×#121—22no—
109C11×#121—21no—
110C11×#121—21no—
111C11×#121D411yescharacteristic
112C11×#121D411yescharacteristic
113C11×#120—22no—
114C11×#120—22no—
115C11×#120—22no—
116C11×#120—21no—
117C11×#120—22no—
118C4×Q8×C11—21no—
119C4×D4×C11—22no—
120C4×D4×C11—22no—
121C4×D4×C11—21no—
122C4×D4×C11—22no—
123C4×D4×C11—21no—
124C4×D4×C11—21no—
125C11×#117—21no—
126C11×#117C2311yescharacteristic
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4—21no—
132C2×C11×C4⋊C4—21no—
133C2×C11×C4⋊C4—24no—
134C2×C11×C4⋊C4C2312yes—
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C22⋊C4—22no—
137C2×C11×C22⋊C4—21no—
138C2×C11×C22⋊C4—24no—
139C2×C11×C22⋊C4D412yes—
140C2×C42×C11C2312yes—
141C11×#107—22no—
142C11×#106—22no—
143C11×#104—24no—
144C11×#104—42no—
145C11×#104—42no—
146C11×#103—22no—
147C11×#103—22no—
148C11×#103—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#24026C1111yesmaximal, characteristic, direct product factor, Sylow
157C24×C11—22no—
158C24×C11—21no—
159C24×C11C2×D411yescharacteristic
160C24×C11C2×D412yes—
161C11×#41—22no—
162C11×#41—22no—
163C11×#41—22no—
164C11×#41—22no—
165C11×#41—22no—
166C11×#41—22no—
167C11×#41—22no—
168C11×#41—44no—
169C11×#41—41no—
170C11×#41—41no—
171C11×#41—44no—
172C11×#41—44no—
173C11×#41—42no—
174C11×#41—42no—
175C11×#41#4114yes—
176C2×Q8×C11—21no—
177C2×Q8×C11—22no—
178C2×Q8×C11—41no—
179C2×Q8×C11C2×D411yescharacteristic
180C2×Q8×C11C2×D411yescharacteristic
181C2×Q8×C11C2×D411yescharacteristic
182C2×D4×C11—21no—
183C2×D4×C11—22no—
184C2×D4×C11—22no—
185C2×D4×C11—22no—
186C2×D4×C11—22no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11—21no—
196C2×D4×C11—22no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11—41no—
203C2×D4×C11—44no—
204C2×D4×C11—44no—
205C2×D4×C11—48no—
206C2×D4×C11—42no—
207C2×D4×C11—42no—
208C2×D4×C11—44no—
209C2×D4×C11—84no—
210C2×D4×C11C2×D411yescharacteristic
211C2×D4×C11C2×D411yescharacteristic
212C2×D4×C11C2×D411yescharacteristic
213C22×C4×C11—21no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—21no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—22no—
225C22×C4×C11—44no—
226C22×C4×C11—44no—
227C22×C4×C11—41no—
228C22×C4×C11—41no—
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2411yescharacteristic
236C11×M16—22no—
237C11×M16—22no—
238C11×M16—22no—
239C11×M16—22no—
240C11×M16—42no—
241C2×C8×C11—22no—
242C2×C8×C11—22no—
243C2×C8×C11—42no—
244C11×C4⋊C4—22no—
245C11×C4⋊C4—22no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—22no—
251C11×C4⋊C4—22no—
252C11×C4⋊C4—48no—
253C11×C4⋊C4—41no—
254C11×C4⋊C4—41no—
255C11×C4⋊C4C2×D411yescharacteristic
256C11×C4⋊C4C2×D411yescharacteristic
257C11×C22⋊C4—22no—
258C11×C22⋊C4—22no—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—22no—
261C11×C22⋊C4—22no—
262C11×C22⋊C4—22no—
263C11×C22⋊C4—21no—
264C11×C22⋊C4—21no—
265C11×C22⋊C4—21no—
266C11×C22⋊C4—21no—
267C11×C22⋊C4—22no—
268C11×C22⋊C4—22no—
269C11×C22⋊C4—21no—
270C11×C22⋊C4—48no—
271C42×C11—22no—
272C42×C11—21no—
273C42×C11—22no—
274C42×C11—22no—
275#3488C2×C1111yescharacteristic
276#3092C2×C1111yescharacteristic, complemented
277C2×#417C2×C1111yescharacteristic, complemented
278#2501C2×C1111yescharacteristic, complemented
279#2039C2×C1112yescomplemented
280#2037C2×C1112yescomplemented
281#1900C2×C1111yescharacteristic, complemented
282#1871C2×C1111yescharacteristic, complemented
283#1859C2×C1112yescomplemented
284#1792C2×C1112yescomplemented
285#1789C2×C1111yescharacteristic, complemented
286C23×C11—21no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—24no—
293C23×C11—41no—
294C23×C11—42no—
295C23×C11—44no—
296C23×C11—42no—
297C23×C11—42no—
298C23×C11—42no—
299C23×C11—81no—
300C23×C11—82no—
301C23×C11—82no—
302C23×C11#12011yescharacteristic
303C23×C11#12011yescharacteristic
304C23×C11C22×D411yescharacteristic
305Q8×C11—21no—
306Q8×C11—21no—
307Q8×C11—21no—
308Q8×C11—22no—
309Q8×C11—42no—
310Q8×C11#12312yescomplemented
311D4×C11—24no—
312D4×C11—21no—
313D4×C11—21no—
314D4×C11—21no—
315D4×C11—22no—
316D4×C11—42no—
317D4×C11—42no—
318D4×C11—44no—
319D4×C11—42no—
320D4×C11—44no—
321D4×C11—42no—
322D4×C11—42no—
323D4×C11—44no—
324D4×C11—42no—
325D4×C11—41no—
326D4×C11—41no—
327D4×C11—42no—
328D4×C11—81no—
329D4×C11—82no—
330D4×C11—82no—
331D4×C11—82no—
332D4×C11—82no—
333D4×C11#12312yescomplemented
334C2×C4×C11—21no—
335C2×C4×C11—22no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—24no—
343C2×C4×C11—24no—
344C2×C4×C11—21no—
345C2×C4×C11—22no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11—21no—
349C2×C4×C11—42no—
350C2×C4×C11—42no—
351C2×C4×C11—42no—
352C2×C4×C11—44no—
353C2×C4×C11—42no—
354C2×C4×C11—42no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—42no—
358C2×C4×C11—42no—
359C2×C4×C11—44no—
360C2×C4×C11—42no—
361C2×C4×C11—82no—
362C2×C4×C11—82no—
363C2×C4×C11—82no—
364C2×C4×C11#12011yescharacteristic
365C2×C4×C11#12011yescharacteristic
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11C22×D411yescharacteristic
368C2×C4×C11C2×#4112yes—
369C2×C4×C11H(5,𝔽2)12yes—
370C8×C11—42no—
371C8×C11—42no—
372C2×H(5,𝔽2)C22×C1111yescharacteristic
373C22×#41C22×C1111yescharacteristic
374C22×M16C22×C1111yescharacteristic, complemented
375#550—21no—
376#548—21no—
377#546—21no—
378#546—22no—
379D42—22no—
380D42—21no—
381#537—21no—
382#537C22×C1111yescharacteristic
383#535—21no—
384#535C22×C1111yescharacteristic
385#525—21no—
386#525C22×C1111yescharacteristic
387C2×#123—22no—
388C2×#121—21no—
389C2×#121C22×C1111yescharacteristic
390#520C22×C1111yescharacteristic
391C22×C4⋊C4C22×C1111yescharacteristic, complemented
392#484—21no—
393#483—21no—
394#481—21no—
395#480—21no—
396#428C22×C1112yescomplemented
397C2×#104C22×C1112yes—
398C2×#104C22×C1112yescomplemented
399C2×#104C22×C1112yescomplemented
400#417—21no—
401#417—21no—
402#417C22×C1112yes—
403#417C22×C1112yescomplemented
404#417C22×C1112yescomplemented
405C2×#103—21no—
406C2×#102—21no—
407C2×#100C22×C1112yescomplemented
408#407C22×C1111yescharacteristic, complemented
409#399—22no—
410#390C22×C1112yescomplemented
411#384C22×C1112yescomplemented
412C4×C22⋊C4C22×C1111yescharacteristic, complemented
413#343C22×C1112yescomplemented
414#339C22×C1112yescomplemented
415C22×C11—21no—
416C22×C11—21no—
417C22×C11—21no—
418C22×C11—21no—
419C22×C11—21no—
420C22×C11—22no—
421C22×C11—21no—
422C22×C11—21no—
423C22×C11—44no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11—41no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—41no—
431C22×C11—41no—
432C22×C11—41no—
433C22×C11—42no—
434C22×C11—41no—
435C22×C11—84no—
436C22×C11—84no—
437C22×C11—164no—
438C22×C11#45312yes—
439C22×C11C2×#12011yescharacteristic
440C22×C11#54612yes—
441C4×C11—21no—
442C4×C11—21no—
443C4×C11—22no—
444C4×C11—44no—
445C4×C11—41no—
446C4×C11—41no—
447C4×C11—42no—
448C4×C11—41no—
449C4×C11—41no—
450C4×C11—82no—
451C4×C11C2×#12311yescharacteristic
452C4×C11#53411yescharacteristic
453C4×C11#54612yes—
454H(5,𝔽2)—24no—
455H(5,𝔽2)—42no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—24no—
461C2×#41—42no—
462C2×#41D4×C1111yescharacteristic
463C2×#41D4×C1111yescharacteristic
464C2×#41C23×C1111yescharacteristic
465C2×#41C23×C1111yescharacteristic
466C2×#41C23×C1111yescharacteristic
467C22×Q8D4×C1111yescharacteristic
468C22×D4—21no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4D4×C1111yescharacteristic
474C22×D4D4×C1112yes—
475C22×D4C23×C1111yescharacteristic
476C23×C4—21no—
477C23×C4—21no—
478C23×C4C23×C1111yescharacteristic
479C2×M16—21no—
480C2×M16—42no—
481C2×M16C23×C1112yes—
482C2×M16C23×C1112yes—
483C22×C8—21no—
484#127—22no—
485#127—21no—
486#124—22no—
487#124—21no—
488#123—22no—
489#123—21no—
490#123—48no—
491C22⋊Q8—22no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8D4×C1111yescharacteristic
495C22⋊Q8D4×C1111yescharacteristic
496#121—22no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—21no—
502#121—21no—
503#121—21no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—22no—
508#121—21no—
509#121—21no—
510#121D4×C1111yescharacteristic
511#121D4×C1111yescharacteristic
512#120—22no—
513#120—22no—
514#120—22no—
515#120—21no—
516#120—22no—
517C4×Q8—21no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—21no—
521C4×D4—22no—
522C4×D4—21no—
523C4×D4—21no—
524#117—21no—
525#117C23×C1111yescharacteristic
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—24no—
533C2×C4⋊C4C23×C1112yes—
534C2×C4⋊C4C23×C1111yescharacteristic
535C2×C22⋊C4—22no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4D4×C1112yes—
539C2×C42C23×C1112yes—
540#107—22no—
541#106—22no—
542#104—24no—
543#104—42no—
544#104—42no—
545#103—22no—
546#103—22no—
547#103—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551#100—42no—
552C22⋊C8—21no—
553C22⋊C8—21no—
554#95—21no—
555C2×C11—22no—
556C2×C11—22no—
557C2×C11—41no—
558C2×C11—42no—
559C2×C11—81no—
560C2×C11—82no—
561C2×C11—81no—
562C2×C11#240511yescharacteristic
563C2×C11C2×#45311yescharacteristic
564C2×C11#302211yescharacteristic
565C24—22no—
566C24—21no—
567C24C2×D4×C1111yescharacteristic
568C24C2×D4×C1112yes—
569#41—22no—
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—44no—
577#41—41no—
578#41—41no—
579#41—44no—
580#41—44no—
581#41—42no—
582#41—42no—
583#41C11×#4114yes—
584C2×Q8—21no—
585C2×Q8—22no—
586C2×Q8—41no—
587C2×Q8C2×D4×C1111yescharacteristic
588C2×Q8C2×D4×C1111yescharacteristic
589C2×Q8C2×D4×C1111yescharacteristic
590C2×D4—21no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—21no—
604C2×D4—22no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—41no—
611C2×D4—44no—
612C2×D4—44no—
613C2×D4—48no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—44no—
617C2×D4—84no—
618C2×D4C2×D4×C1111yescharacteristic
619C2×D4C2×D4×C1111yescharacteristic
620C2×D4C2×D4×C1111yescharacteristic
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4C2×D4×C1111yescharacteristic
638C22×C4C2×D4×C1111yescharacteristic
639C22×C4C2×D4×C1111yescharacteristic
640C22×C4C2×D4×C1111yescharacteristic
641C22×C4C2×D4×C1111yescharacteristic
642C22×C4C2×D4×C1112yes—
643C22×C4C24×C1111yescharacteristic
644M16—22no—
645M16—22no—
646M16—22no—
647M16—22no—
648M16—42no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—42no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—48no—
661C4⋊C4—41no—
662C4⋊C4—41no—
663C4⋊C4C2×D4×C1111yescharacteristic
664C4⋊C4C2×D4×C1111yescharacteristic
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—24no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—21no—
678C22⋊C4—48no—
679C42—22no—
680C42—21no—
681C42—22no—
682C42—22no—
683C11#2402611yescharacteristic, direct product factor, Sylow
684C23—21no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—21no—
689C23—21no—
690C23—24no—
691C23—41no—
692C23—42no—
693C23—44no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—81no—
698C23—82no—
699C23—82no—
700C23C11×#12011yescharacteristic
701C23C11×#12011yescharacteristic
702C23C22×D4×C1111yescharacteristic
703Q8—21no—
704Q8—21no—
705Q8—21no—
706Q8—22no—
707Q8—42no—
708Q8C11×#12312yescomplemented
709D4—24no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—22no—
714D4—42no—
715D4—42no—
716D4—44no—
717D4—42no—
718D4—44no—
719D4—42no—
720D4—42no—
721D4—44no—
722D4—42no—
723D4—41no—
724D4—41no—
725D4—42no—
726D4—81no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4—82no—
731D4C11×#12312yescomplemented
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—82no—
760C2×C4—82no—
761C2×C4—82no—
762C2×C4C11×#12011yescharacteristic
763C2×C4C11×#12011yescharacteristic
764C2×C4C22×D4×C1111yescharacteristic
765C2×C4C22×D4×C1111yescharacteristic
766C2×C4C2×C11×#4112yes—
767C2×C4C11×H(5,𝔽2)12yes—
768C8—42no—
769C8—42no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—22no—
776C22—21no—
777C22—21no—
778C22—44no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—42no—
784C22—42no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—42no—
789C22—41no—
790C22—84no—
791C22—84no—
792C22—164no—
793C22C11×#45312yes—
794C22C2×C11×#12011yescharacteristic
795C22C11×#54612yes—
796C4—21no—
797C4—21no—
798C4—22no—
799C4—44no—
800C4—41no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—41no—
805C4—82no—
806C4C2×C11×#12311yescharacteristic
807C4C11×#53411yescharacteristic
808C4C11×#54612yes—
809C2—22no—
810C2—22no—
811C2—41no—
812C2—42no—
813C2—81no—
814C2—82no—
815C2—81no—
816C2C11×#240511yescharacteristic
817C2C2×C11×#45311yescharacteristic
818C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3488C2
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
2. C11×#3092C2semidirect
3. C2×C11×#417C2semidirect
4. C11×#2501C2semidirect
5. C11×#2039C2semidirect
6. C11×#2037C2semidirect
7. C11×#1900C2semidirect
8. C11×#1871C2semidirect
9. C11×#1859C2semidirect
10. C11×#1792C2semidirect
11. C11×#1789C2semidirect
14. C22×C11×M16C22semidirect
31. C22×C11×C4⋊C4C22semidirect
36. C11×#428C22semidirect
38. C2×C11×#104C22semidirect
39. C2×C11×#104C22semidirect
43. C11×#417C22semidirect
44. C11×#417C22semidirect
47. C2×C11×#100C22semidirect
48. C11×#407C22semidirect
50. C11×#390C22semidirect
51. C11×#384C22semidirect
52. C4×C11×C22⋊C4C22semidirect
53. C11×#343C22semidirect
54. C11×#339C22semidirect
156. #24026C11direct (N × H)
276. #3092C2×C11semidirect
277. C2×#417C2×C11semidirect
278. #2501C2×C11semidirect
279. #2039C2×C11semidirect
280. #2037C2×C11semidirect
281. #1900C2×C11semidirect
282. #1871C2×C11semidirect
283. #1859C2×C11semidirect
284. #1792C2×C11semidirect
285. #1789C2×C11semidirect
310. Q8×C11#123semidirect
333. D4×C11#123semidirect
374. C22×M16C22×C11semidirect
391. C22×C4⋊C4C22×C11semidirect
396. #428C22×C11semidirect
398. C2×#104C22×C11semidirect
399. C2×#104C22×C11semidirect
403. #417C22×C11semidirect
404. #417C22×C11semidirect
407. C2×#100C22×C11semidirect
408. #407C22×C11semidirect
410. #390C22×C11semidirect
411. #384C22×C11semidirect
412. C4×C22⋊C4C22×C11semidirect
413. #343C22×C11semidirect
414. #339C22×C11semidirect
683. C11#24026direct (N × H)
708. Q8C11×#123semidirect
731. D4C11×#123semidirect

Maximal subgroups

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

subgroupindex
C11×#34882
C11×#30922
C2×C11×#4172
C11×#25012
C11×#20392
C11×#20372
C11×#19002
C11×#18712
C11×#18592
C11×#17922
C11×#17892
#2402611