Finite Group Databasebeta

← C11×#24230 #14601423

Subgroups — C11×#24230 #14601423

Order 2816.

1624 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3498C211yesmaximal, characteristic, complemented
2C11×#3036C211yesmaximal, characteristic, complemented
3C2×C11×#453C212yesmaximal, complemented
4C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
5C11×#2541C211yesmaximal, characteristic, complemented
6C11×#2037C212yesmaximal, complemented
7C11×#2002C212yesmaximal, complemented
8C11×#1980C211yesmaximal, characteristic, complemented
9C11×#1965C211yesmaximal, characteristic, complemented
10C11×#1806C211yesmaximal, characteristic, complemented
11C11×#1792C212yesmaximal, complemented
12C2×C11×H(5,𝔽2)C2212yes—
13C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
14C2×C11×AGL(1,ℤ/8)C2212yescomplemented
15C11×#550—21no—
16C11×#550—21no—
17D42×C11—22no—
18D42×C11—22no—
19D42×C11—21no—
20D42×C11—21no—
21C11×#535—22no—
22C11×#535C2212yes—
23C11×#532—21no—
24C11×#532C2211yescharacteristic
25C2×C11×#127—21no—
26C2×C11×#127C2211yescharacteristic
27C2×C11×#127C2212yescomplemented
28C2×C11×#121—22no—
29C4×C11×#41C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic, complemented
31C11×#463—22no—
32C11×#461—21no—
33C11×#459—21no—
34C11×#453—28no—
35C11×#442—21no—
36C11×#440—21no—
37C4×C11×SD16—21no—
38C4×C11×D8—21no—
39C11×#428C2211yescharacteristic, complemented
40C11×#423C2211yescharacteristic, complemented
41C2×C11×#104C2212yes—
42C2×C11×#104C2212yescomplemented
43C2×C11×#104C2212yescomplemented
44C11×#418C2211yescharacteristic, complemented
45C11×#417C2211yescharacteristic
46C11×#417C2212yescomplemented
47C2×C11×#100C2212yescomplemented
48C2×C11×#100C2212yescomplemented
49C4×C11×M16C2211yescharacteristic, complemented
50C11×#392—22no—
51C11×#390C2212yescomplemented
52C4×C11×C4⋊C4C2211yescharacteristic, complemented
53C11×#339C2212yescomplemented
54C11×H(5,𝔽2)—24no—
55C11×H(5,𝔽2)—24no—
56C11×H(5,𝔽2)—42no—
57C11×H(5,𝔽2)—42no—
58C2×C11×#41—22no—
59C2×C11×#41—22no—
60C2×C11×#41C2312yes—
61C2×C11×#41C2311yescharacteristic
62C22×D4×C11—24no—
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—24no—
68C22×D4×C11D412yes—
69C22×D4×C11D412yes—
70C22×D4×C11C2312yes—
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C11×AGL(1,ℤ/8)—22no—
74C11×AGL(1,ℤ/8)—24no—
75C11×AGL(1,ℤ/8)—42no—
76C11×AGL(1,ℤ/8)D414yescomplemented
77C2×C11×SD16—21no—
78C2×C11×SD16—22no—
79C2×C11×D8—21no—
80C2×C11×D8—22no—
81C2×C11×M16C2312yes—
82C2×C11×M16C2311yescharacteristic
83C2×C11×M16C2311yescharacteristic
84C11×C4⋊Q8D411yescharacteristic, complemented
85C11×#127—22no—
86C11×#127—22no—
87C11×#127—22no—
88C11×#127—24no—
89C11×#127—21no—
90C11×#127—21no—
91C11×#127—21no—
92C11×#127—21no—
93C11×#127—42no—
94C11×#127D411yescharacteristic, complemented
95C11×#124—22no—
96C11×#124D412yescomplemented
97C11×#121—22no—
98C11×#121—22no—
99C11×#121—24no—
100C11×#121—24no—
101C11×#121—21no—
102C11×#121—21no—
103C11×#121—22no—
104C11×#121—22no—
105C11×#121—48no—
106C11×#120—24no—
107C11×#120—24no—
108C11×#120—24no—
109C4×Q8×C11D411yescharacteristic, complemented
110C4×Q8×C11D411yescharacteristic, complemented
111C4×D4×C11—22no—
112C4×D4×C11—22no—
113C4×D4×C11—21no—
114C4×D4×C11—21no—
115C4×D4×C11—21no—
116C4×D4×C11—21no—
117C4×D4×C11—21no—
118C4×D4×C11—21no—
119C4×D4×C11—21no—
120C4×D4×C11—21no—
121C4×D4×C11D411yescharacteristic, complemented
122C4×D4×C11D411yescharacteristic, complemented
123C11×#117—21no—
124C11×#117C2311yescharacteristic
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4C2311yescharacteristic
127C2×C11×C22⋊C4—24no—
128C2×C11×C22⋊C4—21no—
129C2×C42×C11—21no—
130C2×C42×C11C2312yes—
131C2×C42×C11C2311yescharacteristic
132C11×#107—21no—
133C11×#106—21no—
134C11×C4⋊C8—21no—
135C11×C4⋊C8—21no—
136C11×#104—24no—
137C11×#104—24no—
138C11×#104—42no—
139C11×#103—21no—
140C11×#103—22no—
141C11×#102—21no—
142C11×#102—22no—
143C11×#102—21no—
144C11×#102—21no—
145C11×#100—24no—
146C11×#100—42no—
147C11×#97—21no—
148C4×C8×C11—21no—
149C11×#95—21no—
150#24230C1111yesmaximal, characteristic, direct product factor, Sylow
151C24×C11—24no—
152C24×C11—21no—
153C24×C11C2×D414yes—
154C11×#41—21no—
155C11×#41—21no—
156C11×#41—22no—
157C11×#41—22no—
158C11×#41—22no—
159C11×#41—22no—
160C11×#41—44no—
161C11×#41—44no—
162C11×#41—44no—
163C11×#41—44no—
164C11×#41C2×D412yes—
165C11×#41#4112yes—
166C2×Q8×C11C2×D412yes—
167C2×Q8×C11C2×D411yescharacteristic
168C2×D4×C11—21no—
169C2×D4×C11—24no—
170C2×D4×C11—24no—
171C2×D4×C11—22no—
172C2×D4×C11—24no—
173C2×D4×C11—24no—
174C2×D4×C11—22no—
175C2×D4×C11—22no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—22no—
179C2×D4×C11—22no—
180C2×D4×C11—21no—
181C2×D4×C11—21no—
182C2×D4×C11—22no—
183C2×D4×C11—22no—
184C2×D4×C11—22no—
185C2×D4×C11—21no—
186C2×D4×C11—22no—
187C2×D4×C11—21no—
188C2×D4×C11—22no—
189C2×D4×C11—21no—
190C2×D4×C11—22no—
191C2×D4×C11—44no—
192C2×D4×C11—44no—
193C2×D4×C11—44no—
194C2×D4×C11—48no—
195C2×D4×C11—48no—
196C2×D4×C11—48no—
197C2×D4×C11—44no—
198C2×D4×C11—44no—
199C2×D4×C11—48no—
200C2×D4×C11—84no—
201C2×D4×C11—84no—
202C2×D4×C11—82no—
203C2×D4×C11—84no—
204C2×D4×C11C2×D412yes—
205C2×D4×C11C2×D411yescharacteristic
206C2×D4×C11C2×D412yescomplemented
207C22×C4×C11—21no—
208C22×C4×C11—24no—
209C22×C4×C11—22no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—22no—
213C22×C4×C11—21no—
214C22×C4×C11—44no—
215C22×C4×C11—41no—
216C22×C4×C11—41no—
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2411yescharacteristic
220C11×SD16—24no—
221C11×SD16—44no—
222C11×D8—24no—
223C11×D8—44no—
224C11×M16—22no—
225C11×M16—21no—
226C11×M16—21no—
227C11×M16—22no—
228C11×M16—21no—
229C11×M16C2×D412yescomplemented
230C2×C8×C11—21no—
231C2×C8×C11—21no—
232C2×C8×C11—22no—
233C11×C4⋊C4—24no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4C2×D411yescharacteristic
241C11×C4⋊C4C2×D411yescharacteristic
242C11×C22⋊C4—24no—
243C11×C22⋊C4—24no—
244C11×C22⋊C4—21no—
245C11×C22⋊C4—21no—
246C11×C22⋊C4—21no—
247C11×C22⋊C4—22no—
248C11×C22⋊C4—22no—
249C11×C22⋊C4—48no—
250C11×C22⋊C4—41no—
251C11×C22⋊C4—41no—
252C42×C11—21no—
253C42×C11—21no—
254C42×C11—21no—
255C42×C11—22no—
256C42×C11—22no—
257C42×C11C2×D411yescharacteristic
258C42×C11C2×D411yescharacteristic
259C42×C11C2×D411yescharacteristic
260C42×C11C2×D411yescharacteristic
261#3498C2×C1111yescharacteristic, complemented
262#3036C2×C1111yescharacteristic, complemented
263C2×#453C2×C1112yescomplemented
264C4×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
265#2541C2×C1111yescharacteristic, complemented
266#2037C2×C1112yescomplemented
267#2002C2×C1112yescomplemented
268#1980C2×C1111yescharacteristic, complemented
269#1965C2×C1111yescharacteristic, complemented
270#1806C2×C1111yescharacteristic, complemented
271#1792C2×C1112yescomplemented
272C23×C11—21no—
273C23×C11—24no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—24no—
277C23×C11—24no—
278C23×C11—42no—
279C23×C11—42no—
280C23×C11—48no—
281C23×C11—44no—
282C23×C11—44no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—84no—
286C23×C11—84no—
287C23×C11C22×D411yescharacteristic
288Q8×C11—21no—
289Q8×C11—22no—
290Q8×C11—22no—
291Q8×C11#12112yescomplemented
292D4×C11—22no—
293D4×C11—22no—
294D4×C11—22no—
295D4×C11—21no—
296D4×C11—22no—
297D4×C11—22no—
298D4×C11—22no—
299D4×C11—48no—
300D4×C11—44no—
301D4×C11—42no—
302D4×C11—48no—
303D4×C11—42no—
304D4×C11—42no—
305D4×C11—42no—
306D4×C11—41no—
307D4×C11—42no—
308D4×C11—42no—
309D4×C11—41no—
310D4×C11—42no—
311D4×C11—44no—
312D4×C11—42no—
313D4×C11—82no—
314D4×C11—82no—
315D4×C11—84no—
316D4×C11—84no—
317D4×C11—816no—
318D4×C11#12112yescomplemented
319C2×C4×C11—21no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—24no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—22no—
327C2×C4×C11—41no—
328C2×C4×C11—48no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11—41no—
337C2×C4×C11—82no—
338C2×C4×C11—82no—
339C2×C4×C11#12011yescharacteristic
340C2×C4×C11#12011yescharacteristic
341C2×C4×C11#12011yescharacteristic
342C2×C4×C11#12011yescharacteristic
343C2×C4×C11C22×D411yescharacteristic
344C2×C4×C11C22×D411yescharacteristic
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C2×#4111yescharacteristic
347C2×C4×C11H(5,𝔽2)11yescharacteristic
348C2×C4×C11H(5,𝔽2)11yescharacteristic
349C8×C11—22no—
350C8×C11—41no—
351C8×C11—42no—
352C2×H(5,𝔽2)C22×C1112yes—
353C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
354C2×AGL(1,ℤ/8)C22×C1112yescomplemented
355#550—21no—
356#550—21no—
357D42—22no—
358D42—22no—
359D42—21no—
360D42—21no—
361#535—22no—
362#535C22×C1112yes—
363#532—21no—
364#532C22×C1111yescharacteristic
365C2×#127—21no—
366C2×#127C22×C1111yescharacteristic
367C2×#127C22×C1112yescomplemented
368C2×#121—22no—
369C4×#41C22×C1111yescharacteristic
370C2×C4×D4C22×C1111yescharacteristic, complemented
371#463—22no—
372#461—21no—
373#459—21no—
374#453—28no—
375#442—21no—
376#440—21no—
377C4×SD16—21no—
378C4×D8—21no—
379#428C22×C1111yescharacteristic, complemented
380#423C22×C1111yescharacteristic, complemented
381C2×#104C22×C1112yes—
382C2×#104C22×C1112yescomplemented
383C2×#104C22×C1112yescomplemented
384#418C22×C1111yescharacteristic, complemented
385#417C22×C1111yescharacteristic
386#417C22×C1112yescomplemented
387C2×#100C22×C1112yescomplemented
388C2×#100C22×C1112yescomplemented
389C4×M16C22×C1111yescharacteristic, complemented
390#392—22no—
391#390C22×C1112yescomplemented
392C4×C4⋊C4C22×C1111yescharacteristic, complemented
393#339C22×C1112yescomplemented
394C22×C11—21no—
395C22×C11—21no—
396C22×C11—22no—
397C22×C11—44no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—42no—
401C22×C11—44no—
402C22×C11—42no—
403C22×C11—44no—
404C22×C11—42no—
405C22×C11—44no—
406C22×C11—42no—
407C22×C11—84no—
408C22×C11—84no—
409C22×C11—82no—
410C22×C11—81no—
411C22×C11—81no—
412C22×C11—168no—
413C22×C11C2×#12011yescharacteristic
414C22×C11D4211yescharacteristic
415C22×C11#54611yescharacteristic
416C4×C11—22no—
417C4×C11—21no—
418C4×C11—21no—
419C4×C11—21no—
420C4×C11—44no—
421C4×C11—42no—
422C4×C11—41no—
423C4×C11—41no—
424C4×C11—81no—
425C4×C11#45312yescomplemented
426C4×C11C2×#12111yescharacteristic
427C4×C11#53511yescharacteristic
428C4×C11D4211yescharacteristic
429C4×C11#54611yescharacteristic
430H(5,𝔽2)—24no—
431H(5,𝔽2)—24no—
432H(5,𝔽2)—42no—
433H(5,𝔽2)—42no—
434C2×#41—22no—
435C2×#41—22no—
436C2×#41C23×C1112yes—
437C2×#41C23×C1111yescharacteristic
438C22×D4—24no—
439C22×D4—22no—
440C22×D4—22no—
441C22×D4—22no—
442C22×D4—22no—
443C22×D4—24no—
444C22×D4D4×C1112yes—
445C22×D4D4×C1112yes—
446C22×D4C23×C1112yes—
447C22×D4C23×C1111yescharacteristic
448C23×C4—21no—
449AGL(1,ℤ/8)—22no—
450AGL(1,ℤ/8)—24no—
451AGL(1,ℤ/8)—42no—
452AGL(1,ℤ/8)D4×C1114yescomplemented
453C2×SD16—21no—
454C2×SD16—22no—
455C2×D8—21no—
456C2×D8—22no—
457C2×M16C23×C1112yes—
458C2×M16C23×C1111yescharacteristic
459C2×M16C23×C1111yescharacteristic
460C4⋊Q8D4×C1111yescharacteristic, complemented
461#127—22no—
462#127—22no—
463#127—22no—
464#127—24no—
465#127—21no—
466#127—21no—
467#127—21no—
468#127—21no—
469#127—42no—
470#127D4×C1111yescharacteristic, complemented
471#124—22no—
472#124D4×C1112yescomplemented
473#121—22no—
474#121—22no—
475#121—24no—
476#121—24no—
477#121—21no—
478#121—21no—
479#121—22no—
480#121—22no—
481#121—48no—
482#120—24no—
483#120—24no—
484#120—24no—
485C4×Q8D4×C1111yescharacteristic, complemented
486C4×Q8D4×C1111yescharacteristic, complemented
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—21no—
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4D4×C1111yescharacteristic, complemented
498C4×D4D4×C1111yescharacteristic, complemented
499#117—21no—
500#117C23×C1111yescharacteristic
501C2×C4⋊C4—21no—
502C2×C4⋊C4C23×C1111yescharacteristic
503C2×C22⋊C4—24no—
504C2×C22⋊C4—21no—
505C2×C42—21no—
506C2×C42C23×C1112yes—
507C2×C42C23×C1111yescharacteristic
508#107—21no—
509#106—21no—
510C4⋊C8—21no—
511C4⋊C8—21no—
512#104—24no—
513#104—24no—
514#104—42no—
515#103—21no—
516#103—22no—
517#102—21no—
518#102—22no—
519#102—21no—
520#102—21no—
521#100—24no—
522#100—42no—
523#97—21no—
524C4×C8—21no—
525#95—21no—
526C2×C11—21no—
527C2×C11—21no—
528C2×C11—42no—
529C2×C11—82no—
530C2×C11—84no—
531C2×C11—82no—
532C2×C11#240811yescharacteristic
533C2×C11C2×#45311yescharacteristic
534C2×C11#301911yescharacteristic
535C24—24no—
536C24—21no—
537C24C2×D4×C1114yes—
538#41—21no—
539#41—21no—
540#41—22no—
541#41—22no—
542#41—22no—
543#41—22no—
544#41—44no—
545#41—44no—
546#41—44no—
547#41—44no—
548#41C2×D4×C1112yes—
549#41C11×#4112yes—
550C2×Q8C2×D4×C1112yes—
551C2×Q8C2×D4×C1111yescharacteristic
552C2×D4—21no—
553C2×D4—24no—
554C2×D4—24no—
555C2×D4—22no—
556C2×D4—24no—
557C2×D4—24no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4—44no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—48no—
579C2×D4—48no—
580C2×D4—48no—
581C2×D4—44no—
582C2×D4—44no—
583C2×D4—48no—
584C2×D4—84no—
585C2×D4—84no—
586C2×D4—82no—
587C2×D4—84no—
588C2×D4C2×D4×C1112yes—
589C2×D4C2×D4×C1111yescharacteristic
590C2×D4C2×D4×C1112yescomplemented
591C22×C4—21no—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—44no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4C2×D4×C1111yescharacteristic
602C22×C4C2×D4×C1111yescharacteristic
603C22×C4C24×C1111yescharacteristic
604SD16—24no—
605SD16—44no—
606D8—24no—
607D8—44no—
608M16—21no—
609M16—22no—
610M16—21no—
611M16—22no—
612M16—21no—
613M16C2×D4×C1112yescomplemented
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—22no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4C2×D4×C1111yescharacteristic
625C4⋊C4C2×D4×C1111yescharacteristic
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—48no—
634C22⋊C4—41no—
635C22⋊C4—41no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—22no—
640C42—22no—
641C42C2×D4×C1111yescharacteristic
642C42C2×D4×C1111yescharacteristic
643C42C2×D4×C1111yescharacteristic
644C42C2×D4×C1111yescharacteristic
645C11#2423011yescharacteristic, direct product factor, Sylow
646C23—21no—
647C23—24no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—24no—
652C23—42no—
653C23—42no—
654C23—48no—
655C23—44no—
656C23—44no—
657C23—41no—
658C23—41no—
659C23—84no—
660C23—84no—
661C23C22×D4×C1111yescharacteristic
662Q8—21no—
663Q8—22no—
664Q8—22no—
665Q8C11×#12112yescomplemented
666D4—22no—
667D4—22no—
668D4—22no—
669D4—21no—
670D4—22no—
671D4—22no—
672D4—22no—
673D4—48no—
674D4—44no—
675D4—42no—
676D4—48no—
677D4—42no—
678D4—42no—
679D4—42no—
680D4—41no—
681D4—42no—
682D4—42no—
683D4—41no—
684D4—42no—
685D4—44no—
686D4—42no—
687D4—82no—
688D4—82no—
689D4—84no—
690D4—84no—
691D4—816no—
692D4C11×#12112yescomplemented
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—41no—
702C2×C4—48no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—82no—
712C2×C4—82no—
713C2×C4C11×#12011yescharacteristic
714C2×C4C11×#12011yescharacteristic
715C2×C4C11×#12011yescharacteristic
716C2×C4C11×#12011yescharacteristic
717C2×C4C22×D4×C1111yescharacteristic
718C2×C4C22×D4×C1111yescharacteristic
719C2×C4C22×D4×C1111yescharacteristic
720C2×C4C2×C11×#4111yescharacteristic
721C2×C4C11×H(5,𝔽2)11yescharacteristic
722C2×C4C11×H(5,𝔽2)11yescharacteristic
723C8—22no—
724C8—41no—
725C8—42no—
726C22—21no—
727C22—21no—
728C22—22no—
729C22—44no—
730C22—41no—
731C22—41no—
732C22—42no—
733C22—44no—
734C22—42no—
735C22—44no—
736C22—42no—
737C22—44no—
738C22—42no—
739C22—84no—
740C22—84no—
741C22—82no—
742C22—81no—
743C22—81no—
744C22—168no—
745C22C2×C11×#12011yescharacteristic
746C22D42×C1111yescharacteristic
747C22C11×#54611yescharacteristic
748C4—22no—
749C4—21no—
750C4—21no—
751C4—21no—
752C4—44no—
753C4—42no—
754C4—41no—
755C4—41no—
756C4—81no—
757C4C11×#45312yescomplemented
758C4C2×C11×#12111yescharacteristic
759C4C11×#53511yescharacteristic
760C4D42×C1111yescharacteristic
761C4C11×#54611yescharacteristic
762C2—21no—
763C2—21no—
764C2—42no—
765C2—82no—
766C2—84no—
767C2—82no—
768C2C11×#240811yescharacteristic
769C2C2×C11×#45311yescharacteristic
770C2C11×#301911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3498C2semidirect
2. C11×#3036C2semidirect
3. C2×C11×#453C2semidirect
4. C4×C11×AGL(1,ℤ/8)C2semidirect
5. C11×#2541C2semidirect
6. C11×#2037C2semidirect
7. C11×#2002C2semidirect
8. C11×#1980C2semidirect
9. C11×#1965C2semidirect
10. C11×#1806C2semidirect
11. C11×#1792C2semidirect
14. C2×C11×AGL(1,ℤ/8)C22semidirect
27. C2×C11×#127C22semidirect
30. C2×C4×D4×C11C22semidirect
39. C11×#428C22semidirect
40. C11×#423C22semidirect
42. C2×C11×#104C22semidirect
43. C2×C11×#104C22semidirect
44. C11×#418C22semidirect
46. C11×#417C22semidirect
47. C2×C11×#100C22semidirect
48. C2×C11×#100C22semidirect
49. C4×C11×M16C22semidirect
51. C11×#390C22semidirect
52. C4×C11×C4⋊C4C22semidirect
53. C11×#339C22semidirect
76. C11×AGL(1,ℤ/8)D4semidirect
84. C11×C4⋊Q8D4semidirect
94. C11×#127D4semidirect
96. C11×#124D4semidirect
109. C4×Q8×C11D4semidirect
110. C4×Q8×C11D4semidirect
121. C4×D4×C11D4semidirect
122. C4×D4×C11D4semidirect
150. #24230C11direct (N × H)
206. C2×D4×C11C2×D4semidirect
229. C11×M16C2×D4semidirect
261. #3498C2×C11semidirect
262. #3036C2×C11semidirect
263. C2×#453C2×C11semidirect
264. C4×AGL(1,ℤ/8)C2×C11semidirect
265. #2541C2×C11semidirect
266. #2037C2×C11semidirect
267. #2002C2×C11semidirect
268. #1980C2×C11semidirect
269. #1965C2×C11semidirect
270. #1806C2×C11semidirect
271. #1792C2×C11semidirect
291. Q8×C11#121semidirect
318. D4×C11#121semidirect
354. C2×AGL(1,ℤ/8)C22×C11semidirect
367. C2×#127C22×C11semidirect
370. C2×C4×D4C22×C11semidirect
379. #428C22×C11semidirect
380. #423C22×C11semidirect
382. C2×#104C22×C11semidirect
383. C2×#104C22×C11semidirect
384. #418C22×C11semidirect
386. #417C22×C11semidirect
387. C2×#100C22×C11semidirect
388. C2×#100C22×C11semidirect
389. C4×M16C22×C11semidirect
391. #390C22×C11semidirect
392. C4×C4⋊C4C22×C11semidirect
393. #339C22×C11semidirect
425. C4×C11#453semidirect
452. AGL(1,ℤ/8)D4×C11semidirect
460. C4⋊Q8D4×C11semidirect
470. #127D4×C11semidirect
472. #124D4×C11semidirect
485. C4×Q8D4×C11semidirect
486. C4×Q8D4×C11semidirect
497. C4×D4D4×C11semidirect
498. C4×D4D4×C11semidirect
590. C2×D4C2×D4×C11semidirect
613. M16C2×D4×C11semidirect
645. C11#24230direct (N × H)
665. Q8C11×#121semidirect
692. D4C11×#121semidirect
757. C4C11×#453semidirect

Maximal subgroups

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

subgroupindex
C11×#34982
C11×#30362
C2×C11×#4532
C4×C11×AGL(1,ℤ/8)2
C11×#25412
C11×#20372
C11×#20022
C11×#19802
C11×#19652
C11×#18062
C11×#17922
#2423011