Finite Group Databasebeta

← C11×#24027 #14601220

Subgroups — C11×#24027 #14601220

Order 2816.

1348 conjugacy classes of subgroups.

The subgroup lattice has 816 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×#2504C211yesmaximal, characteristic, complemented
5C11×#2040C212yesmaximal, complemented
6C11×#2037C212yesmaximal, complemented
7C11×#1900C211yesmaximal, characteristic, complemented
8C11×#1871C211yesmaximal, characteristic, complemented
9C11×#1860C212yesmaximal, 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×#121—21no—
28C2×C11×#121C2211yescharacteristic
29C11×#520C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic, complemented
31C11×#484—21no—
32C11×#483—21no—
33C11×#481—21no—
34C11×#480—21no—
35C11×#428C2212yescomplemented
36C2×C11×#104C2212yes—
37C2×C11×#104C2212yescomplemented
38C2×C11×#104C2212yescomplemented
39C11×#417—21no—
40C11×#417—21no—
41C11×#417C2212yes—
42C11×#417C2212yescomplemented
43C11×#417C2212yescomplemented
44C2×C11×#103—21no—
45C2×C11×#102—21no—
46C2×C11×#100C2212yescomplemented
47C11×#407C2211yescharacteristic, complemented
48C11×#397—22no—
49C11×#390C2212yescomplemented
50C11×#386—22no—
51C11×#382C2212yescomplemented
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×C22⋊Q8—22no—
92C11×C22⋊Q8—21no—
93C11×C22⋊Q8—21no—
94C11×C22⋊Q8D411yescharacteristic
95C11×C22⋊Q8D411yescharacteristic
96C11×#121—22no—
97C11×#121—22no—
98C11×#121—22no—
99C11×#121—22no—
100C11×#121—22no—
101C11×#121—21no—
102C11×#121—21no—
103C11×#121—21no—
104C11×#121—21no—
105C11×#121—21no—
106C11×#121—21no—
107C11×#121—22no—
108C11×#121—21no—
109C11×#121—21no—
110C11×#121D411yescharacteristic
111C11×#121D411yescharacteristic
112C11×#120—22no—
113C11×#120—22no—
114C11×#120—22no—
115C11×#120—21no—
116C11×#120—22no—
117C4×Q8×C11—21no—
118C4×D4×C11—22no—
119C4×D4×C11—22no—
120C4×D4×C11—21no—
121C4×D4×C11—22no—
122C4×D4×C11—21no—
123C4×D4×C11—21no—
124C11×#117—21no—
125C11×#117C2311yescharacteristic
126C2×C11×C4⋊C4—21no—
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⋊C4C2312yes—
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C22⋊C4—22no—
135C2×C11×C22⋊C4—21no—
136C2×C11×C22⋊C4—24no—
137C2×C11×C22⋊C4D412yes—
138C2×C42×C11C2312yes—
139C11×#107—22no—
140C11×#106—22no—
141C11×#104—24no—
142C11×#104—42no—
143C11×#104—42no—
144C11×#103—22no—
145C11×#103—22no—
146C11×#103—22no—
147C11×#102—22no—
148C11×#102—22no—
149C11×#102—22no—
150C11×#100—42no—
151C11×C22⋊C8—21no—
152C11×C22⋊C8—21no—
153C11×#95—21no—
154C11×#95—24no—
155#24027C1111yesmaximal, characteristic, direct product factor, Sylow
156C24×C11—22no—
157C24×C11—21no—
158C24×C11C2×D411yescharacteristic
159C24×C11C2×D412yes—
160C11×#41—22no—
161C11×#41—22no—
162C11×#41—22no—
163C11×#41—22no—
164C11×#41—22no—
165C11×#41—22no—
166C11×#41—22no—
167C11×#41—44no—
168C11×#41—41no—
169C11×#41—41no—
170C11×#41—44no—
171C11×#41—44no—
172C11×#41—42no—
173C11×#41—42no—
174C11×#41#4114yes—
175C2×Q8×C11—21no—
176C2×Q8×C11—22no—
177C2×Q8×C11—41no—
178C2×Q8×C11C2×D411yescharacteristic
179C2×Q8×C11C2×D411yescharacteristic
180C2×Q8×C11C2×D411yescharacteristic
181C2×D4×C11—21no—
182C2×D4×C11—22no—
183C2×D4×C11—22no—
184C2×D4×C11—22no—
185C2×D4×C11—22no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—21no—
195C2×D4×C11—22no—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11—41no—
202C2×D4×C11—44no—
203C2×D4×C11—44no—
204C2×D4×C11—48no—
205C2×D4×C11—42no—
206C2×D4×C11—42no—
207C2×D4×C11—44no—
208C2×D4×C11—84no—
209C2×D4×C11C2×D411yescharacteristic
210C2×D4×C11C2×D411yescharacteristic
211C2×D4×C11C2×D411yescharacteristic
212C22×C4×C11—21no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—21no—
217C22×C4×C11—22no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—44no—
225C22×C4×C11—41no—
226C22×C4×C11—41no—
227C22×C4×C11—82no—
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2411yescharacteristic
235C11×M16—22no—
236C11×M16—22no—
237C11×M16—22no—
238C11×M16—22no—
239C11×M16—42no—
240C2×C8×C11—22no—
241C2×C8×C11—22no—
242C2×C8×C11—42no—
243C11×C4⋊C4—22no—
244C11×C4⋊C4—22no—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—22no—
250C11×C4⋊C4—22no—
251C11×C4⋊C4—41no—
252C11×C4⋊C4—41no—
253C11×C4⋊C4C2×D411yescharacteristic
254C11×C4⋊C4C2×D411yescharacteristic
255C11×C22⋊C4—22no—
256C11×C22⋊C4—22no—
257C11×C22⋊C4—22no—
258C11×C22⋊C4—22no—
259C11×C22⋊C4—22no—
260C11×C22⋊C4—21no—
261C11×C22⋊C4—21no—
262C11×C22⋊C4—21no—
263C11×C22⋊C4—21no—
264C11×C22⋊C4—22no—
265C11×C22⋊C4—22no—
266C11×C22⋊C4—21no—
267C11×C22⋊C4—42no—
268C11×C22⋊C4—84no—
269C42×C11—22no—
270C42×C11—21no—
271C42×C11—22no—
272C42×C11—22no—
273#3488C2×C1111yescharacteristic
274#3092C2×C1111yescharacteristic, complemented
275C2×#417C2×C1111yescharacteristic, complemented
276#2504C2×C1111yescharacteristic, complemented
277#2040C2×C1112yescomplemented
278#2037C2×C1112yescomplemented
279#1900C2×C1111yescharacteristic, complemented
280#1871C2×C1111yescharacteristic, complemented
281#1860C2×C1112yescomplemented
282#1792C2×C1112yescomplemented
283#1789C2×C1111yescharacteristic, complemented
284C23×C11—21no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—24no—
291C23×C11—41no—
292C23×C11—42no—
293C23×C11—44no—
294C23×C11—42no—
295C23×C11—42no—
296C23×C11—42no—
297C23×C11—81no—
298C23×C11—82no—
299C23×C11—82no—
300C23×C11#12011yescharacteristic
301C23×C11#12011yescharacteristic
302C23×C11C22×D411yescharacteristic
303Q8×C11—21no—
304Q8×C11—21no—
305Q8×C11—21no—
306Q8×C11—22no—
307Q8×C11—42no—
308Q8×C11#12312yes—
309D4×C11—24no—
310D4×C11—21no—
311D4×C11—21no—
312D4×C11—21no—
313D4×C11—22no—
314D4×C11—42no—
315D4×C11—42no—
316D4×C11—44no—
317D4×C11—42no—
318D4×C11—44no—
319D4×C11—42no—
320D4×C11—42no—
321D4×C11—44no—
322D4×C11—42no—
323D4×C11—41no—
324D4×C11—41no—
325D4×C11—42no—
326D4×C11—81no—
327D4×C11—82no—
328D4×C11—82no—
329D4×C11—82no—
330D4×C11—82no—
331D4×C11#12312yes—
332C2×C4×C11—21no—
333C2×C4×C11—22no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—24no—
341C2×C4×C11—21no—
342C2×C4×C11—22no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—42no—
347C2×C4×C11—42no—
348C2×C4×C11—42no—
349C2×C4×C11—44no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—42no—
353C2×C4×C11—42no—
354C2×C4×C11—42no—
355C2×C4×C11—42no—
356C2×C4×C11—44no—
357C2×C4×C11—42no—
358C2×C4×C11—42no—
359C2×C4×C11—82no—
360C2×C4×C11—82no—
361C2×C4×C11—82no—
362C2×C4×C11#12011yescharacteristic
363C2×C4×C11#12011yescharacteristic
364C2×C4×C11C22×D411yescharacteristic
365C2×C4×C11C22×D411yescharacteristic
366C2×C4×C11C2×#4112yes—
367C2×C4×C11H(5,𝔽2)12yes—
368C8×C11—42no—
369C8×C11—42no—
370C2×H(5,𝔽2)C22×C1111yescharacteristic
371C22×#41C22×C1111yescharacteristic
372C22×M16C22×C1111yescharacteristic, complemented
373#550—21no—
374#548—21no—
375#546—21no—
376#546—22no—
377D42—22no—
378D42—21no—
379#537—21no—
380#537C22×C1111yescharacteristic
381#535—21no—
382#535C22×C1111yescharacteristic
383#525—21no—
384#525C22×C1111yescharacteristic
385C2×#121—21no—
386C2×#121C22×C1111yescharacteristic
387#520C22×C1111yescharacteristic
388C22×C4⋊C4C22×C1111yescharacteristic, complemented
389#484—21no—
390#483—21no—
391#481—21no—
392#480—21no—
393#428C22×C1112yescomplemented
394C2×#104C22×C1112yes—
395C2×#104C22×C1112yescomplemented
396C2×#104C22×C1112yescomplemented
397#417—21no—
398#417—21no—
399#417C22×C1112yes—
400#417C22×C1112yescomplemented
401#417C22×C1112yescomplemented
402C2×#103—21no—
403C2×#102—21no—
404C2×#100C22×C1112yescomplemented
405#407C22×C1111yescharacteristic, complemented
406#397—22no—
407#390C22×C1112yescomplemented
408#386—22no—
409#382C22×C1112yescomplemented
410C4×C22⋊C4C22×C1111yescharacteristic, complemented
411#343C22×C1112yescomplemented
412#339C22×C1112yescomplemented
413C22×C11—21no—
414C22×C11—21no—
415C22×C11—21no—
416C22×C11—21no—
417C22×C11—21no—
418C22×C11—22no—
419C22×C11—21no—
420C22×C11—21no—
421C22×C11—44no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—41no—
431C22×C11—42no—
432C22×C11—41no—
433C22×C11—84no—
434C22×C11—84no—
435C22×C11—164no—
436C22×C11#45512yes—
437C22×C11C2×#12011yescharacteristic
438C22×C11#54612yes—
439C4×C11—21no—
440C4×C11—21no—
441C4×C11—22no—
442C4×C11—41no—
443C4×C11—41no—
444C4×C11—42no—
445C4×C11—41no—
446C4×C11—41no—
447C4×C11—82no—
448C4×C11—82no—
449C4×C11C2×#12311yescharacteristic
450C4×C11#53411yescharacteristic
451C4×C11#54612yes—
452H(5,𝔽2)—24no—
453H(5,𝔽2)—42no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—24no—
459C2×#41—42no—
460C2×#41D4×C1111yescharacteristic
461C2×#41D4×C1111yescharacteristic
462C2×#41C23×C1111yescharacteristic
463C2×#41C23×C1111yescharacteristic
464C2×#41C23×C1111yescharacteristic
465C22×Q8D4×C1111yescharacteristic
466C22×D4—21no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4D4×C1111yescharacteristic
472C22×D4D4×C1112yes—
473C22×D4C23×C1111yescharacteristic
474C23×C4—21no—
475C23×C4—21no—
476C23×C4C23×C1111yescharacteristic
477C2×M16—21no—
478C2×M16—42no—
479C2×M16C23×C1112yes—
480C2×M16C23×C1112yes—
481C22×C8—21no—
482#127—22no—
483#127—21no—
484#124—22no—
485#124—21no—
486#123—22no—
487#123—21no—
488C22⋊Q8—22no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8D4×C1111yescharacteristic
492C22⋊Q8D4×C1111yescharacteristic
493#121—22no—
494#121—22no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—21no—
499#121—21no—
500#121—21no—
501#121—21no—
502#121—21no—
503#121—21no—
504#121—22no—
505#121—21no—
506#121—21no—
507#121D4×C1111yescharacteristic
508#121D4×C1111yescharacteristic
509#120—22no—
510#120—22no—
511#120—22no—
512#120—21no—
513#120—22no—
514C4×Q8—21no—
515C4×D4—22no—
516C4×D4—22no—
517C4×D4—21no—
518C4×D4—22no—
519C4×D4—21no—
520C4×D4—21no—
521#117—21no—
522#117C23×C1111yescharacteristic
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4C23×C1112yes—
530C2×C4⋊C4C23×C1111yescharacteristic
531C2×C22⋊C4—22no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4D4×C1112yes—
535C2×C42C23×C1112yes—
536#107—22no—
537#106—22no—
538#104—24no—
539#104—42no—
540#104—42no—
541#103—22no—
542#103—22no—
543#103—22no—
544#102—22no—
545#102—22no—
546#102—22no—
547#100—42no—
548C22⋊C8—21no—
549C22⋊C8—21no—
550#95—21no—
551#95—24no—
552C2×C11—22no—
553C2×C11—22no—
554C2×C11—41no—
555C2×C11—42no—
556C2×C11—81no—
557C2×C11—82no—
558C2×C11—81no—
559C2×C11#240511yescharacteristic
560C2×C11C2×#45511yescharacteristic
561C2×C11#302111yescharacteristic
562C24—22no—
563C24—21no—
564C24C2×D4×C1111yescharacteristic
565C24C2×D4×C1112yes—
566#41—22no—
567#41—22no—
568#41—22no—
569#41—22no—
570#41—22no—
571#41—22no—
572#41—22no—
573#41—44no—
574#41—41no—
575#41—41no—
576#41—44no—
577#41—44no—
578#41—42no—
579#41—42no—
580#41C11×#4114yes—
581C2×Q8—21no—
582C2×Q8—22no—
583C2×Q8—41no—
584C2×Q8C2×D4×C1111yescharacteristic
585C2×Q8C2×D4×C1111yescharacteristic
586C2×Q8C2×D4×C1111yescharacteristic
587C2×D4—21no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—41no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—48no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—84no—
615C2×D4C2×D4×C1111yescharacteristic
616C2×D4C2×D4×C1111yescharacteristic
617C2×D4C2×D4×C1111yescharacteristic
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—44no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—82no—
634C22×C4C2×D4×C1111yescharacteristic
635C22×C4C2×D4×C1111yescharacteristic
636C22×C4C2×D4×C1111yescharacteristic
637C22×C4C2×D4×C1111yescharacteristic
638C22×C4C2×D4×C1111yescharacteristic
639C22×C4C2×D4×C1112yes—
640C22×C4C24×C1111yescharacteristic
641M16—22no—
642M16—22no—
643M16—22no—
644M16—22no—
645M16—42no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—42no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4C2×D4×C1111yescharacteristic
660C4⋊C4C2×D4×C1111yescharacteristic
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—42no—
674C22⋊C4—84no—
675C42—22no—
676C42—21no—
677C42—22no—
678C42—22no—
679C11#2402711yescharacteristic, direct product factor, Sylow
680C23—21no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—21no—
685C23—21no—
686C23—24no—
687C23—41no—
688C23—42no—
689C23—44no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—81no—
694C23—82no—
695C23—82no—
696C23C11×#12011yescharacteristic
697C23C11×#12011yescharacteristic
698C23C22×D4×C1111yescharacteristic
699Q8—21no—
700Q8—21no—
701Q8—21no—
702Q8—22no—
703Q8—42no—
704Q8C11×#12312yes—
705D4—24no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—22no—
710D4—42no—
711D4—42no—
712D4—44no—
713D4—42no—
714D4—44no—
715D4—42no—
716D4—42no—
717D4—44no—
718D4—42no—
719D4—41no—
720D4—41no—
721D4—42no—
722D4—81no—
723D4—82no—
724D4—82no—
725D4—82no—
726D4—82no—
727D4C11×#12312yes—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—44no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4—82no—
758C2×C4C11×#12011yescharacteristic
759C2×C4C11×#12011yescharacteristic
760C2×C4C22×D4×C1111yescharacteristic
761C2×C4C22×D4×C1111yescharacteristic
762C2×C4C2×C11×#4112yes—
763C2×C4C11×H(5,𝔽2)12yes—
764C8—42no—
765C8—42no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—22no—
772C22—21no—
773C22—21no—
774C22—44no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—42no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—42no—
785C22—41no—
786C22—84no—
787C22—84no—
788C22—164no—
789C22C11×#45512yes—
790C22C2×C11×#12011yescharacteristic
791C22C11×#54612yes—
792C4—21no—
793C4—21no—
794C4—22no—
795C4—41no—
796C4—41no—
797C4—42no—
798C4—41no—
799C4—41no—
800C4—82no—
801C4—82no—
802C4C2×C11×#12311yescharacteristic
803C4C11×#53411yescharacteristic
804C4C11×#54612yes—
805C2—22no—
806C2—22no—
807C2—41no—
808C2—42no—
809C2—81no—
810C2—82no—
811C2—81no—
812C2C11×#240511yescharacteristic
813C2C2×C11×#45511yescharacteristic
814C2C11×#302111yescharacteristic
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×#2504C2semidirect
5. C11×#2040C2semidirect
6. C11×#2037C2semidirect
7. C11×#1900C2semidirect
8. C11×#1871C2semidirect
9. C11×#1860C2semidirect
10. C11×#1792C2semidirect
11. C11×#1789C2semidirect
14. C22×C11×M16C22semidirect
30. C22×C11×C4⋊C4C22semidirect
35. C11×#428C22semidirect
37. C2×C11×#104C22semidirect
38. C2×C11×#104C22semidirect
42. C11×#417C22semidirect
43. C11×#417C22semidirect
46. C2×C11×#100C22semidirect
47. C11×#407C22semidirect
49. C11×#390C22semidirect
51. C11×#382C22semidirect
52. C4×C11×C22⋊C4C22semidirect
53. C11×#343C22semidirect
54. C11×#339C22semidirect
155. #24027C11direct (N × H)
274. #3092C2×C11semidirect
275. C2×#417C2×C11semidirect
276. #2504C2×C11semidirect
277. #2040C2×C11semidirect
278. #2037C2×C11semidirect
279. #1900C2×C11semidirect
280. #1871C2×C11semidirect
281. #1860C2×C11semidirect
282. #1792C2×C11semidirect
283. #1789C2×C11semidirect
372. C22×M16C22×C11semidirect
388. C22×C4⋊C4C22×C11semidirect
393. #428C22×C11semidirect
395. C2×#104C22×C11semidirect
396. C2×#104C22×C11semidirect
400. #417C22×C11semidirect
401. #417C22×C11semidirect
404. C2×#100C22×C11semidirect
405. #407C22×C11semidirect
407. #390C22×C11semidirect
409. #382C22×C11semidirect
410. C4×C22⋊C4C22×C11semidirect
411. #343C22×C11semidirect
412. #339C22×C11semidirect
679. C11#24027direct (N × H)

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×#25042
C11×#20402
C11×#20372
C11×#19002
C11×#18712
C11×#18602
C11×#17922
C11×#17892
#2402711