Finite Group Databasebeta

← C11×#22043 #14599236

Subgroups — C11×#22043 #14599236

Order 2816.

1224 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#450C211yesmaximal, characteristic
2C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C11×#390C211yesmaximal, characteristic
4C11×#1968C212yesmaximal, complemented
5C11×#1934C212yesmaximal, complemented
6C11×#1926C212yesmaximal, complemented
7C11×#1880C212yesmaximal, complemented
8C11×#1872C211yesmaximal, characteristic, complemented
9C11×#1853C211yesmaximal, characteristic, complemented
10C11×#1786C211yesmaximal, characteristic
11C4×C11×C22⋊C8C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C2×C11×C22⋊Q8C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic, complemented
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4—21no—
18C22×C11×C22⋊C4—21no—
19C22×C42×C11C2211yescharacteristic
20C11×#450C418yescomplemented
21C2×C11×#106C2212yescomplemented
22C2×C11×#103C2212yescomplemented
23C2×C11×#102C2212yes—
24C2×C11×#102C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C4×C8×C11C2212yescomplemented
29C11×#391C2211yescharacteristic, complemented
30C11×#390—21no—
31C11×#390—21no—
32C11×#390C2212yes—
33C11×#390C2212yes—
34C11×#389C2211yescharacteristic, complemented
35C11×#387—21no—
36C11×#385—21no—
37C11×#380C2211yescharacteristic
38C4×C11×C4⋊C4—21no—
39C4×C11×C4⋊C4C2211yescharacteristic, complemented
40C4×C11×C22⋊C4—21no—
41C11×#340C2212yescomplemented
42C11×#340C2212yescomplemented
43C11×#336C2212yescomplemented
44C25×C11—21no—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11—22no—
48C22×D4×C11—42no—
49C22×D4×C11—42no—
50C22×D4×C11C2×C414yes—
51C22×D4×C11C2312yes—
52C23×C4×C11—21no—
53C23×C4×C11D411yescharacteristic
54C23×C4×C11D411yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C2×C11×SD16—42no—
57C2×C11×SD16—42no—
58C2×C11×SD16C2×C418yescomplemented
59C22×C8×C11C2312yes—
60C22×C8×C11C2312yes—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8C2×C414yes—
63C4×Q8×C11—42no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—42no—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—44no—
80C2×C11×C22⋊C4—44no—
81C2×C42×C11—21no—
82C2×C42×C11—21no—
83C2×C42×C11—42no—
84C2×C42×C11D411yescharacteristic
85C2×C42×C11D411yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C11×#106—42no—
89C11×#103—42no—
90C11×#102—42no—
91C11×#102—42no—
92C11×#102C2×C418yescomplemented
93C11×C22⋊C8—22no—
94C11×C22⋊C8C2×C414yes—
95C4×C8×C11—42no—
96C11×#95—21no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101#22043C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—24no—
103C24×C11—22no—
104C24×C11—42no—
105C24×C11—42no—
106C24×C11—42no—
107C24×C11—42no—
108C24×C11—42no—
109C24×C11—42no—
110C24×C11C2×D411yescharacteristic
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11C22×C412yes—
115C2×D4×C11—24no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—48no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—48no—
125C2×D4×C11C22×C414yes—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—41no—
136C22×C4×C11—41no—
137C22×C4×C11—41no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11SD1614yescomplemented
142C22×C4×C11C22×C412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4112yes—
149C22×C4×C11C2411yescharacteristic
150C11×SD16—48no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11C22×C414yes—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4C22×C412yes—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—44no—
169C11×C22⋊C4—42no—
170C11×C22⋊C4—44no—
171C11×C22⋊C4—44no—
172C11×C22⋊C4—44no—
173C42×C11—22no—
174C42×C11—22no—
175C42×C11—41no—
176C42×C11—41no—
177C42×C11—42no—
178C42×C11—42no—
179C2×#450C2×C1111yescharacteristic
180C4×C22⋊Q8C2×C1111yescharacteristic, complemented
181C2×#390C2×C1111yescharacteristic
182#1968C2×C1112yescomplemented
183#1934C2×C1112yescomplemented
184#1926C2×C1112yescomplemented
185#1880C2×C1112yescomplemented
186#1872C2×C1111yescharacteristic, complemented
187#1853C2×C1111yescharacteristic, complemented
188#1786C2×C1111yescharacteristic
189C4×C22⋊C8C2×C1111yescharacteristic, complemented
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—24no—
195C23×C11—48no—
196C23×C11—48no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—48no—
204C23×C11—84no—
205C23×C11—84no—
206C23×C11—84no—
207C23×C11—84no—
208C23×C11C4×D412yes—
209C23×C11C2×SD1612yes—
210C23×C11#13512yes—
211C23×C11C22×D411yescharacteristic
212Q8×C11—24no—
213Q8×C11—42no—
214D4×C11—24no—
215D4×C11—24no—
216D4×C11—48no—
217D4×C11—42no—
218D4×C11—42no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—44no—
235C2×C4×C11—44no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—42no—
242C2×C4×C11—41no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—84no—
250C2×C4×C11C4×D412yes—
251C2×C4×C11C2×SD1612yes—
252C2×C4×C11C2×SD1612yes—
253C2×C4×C11AGL(1,ℤ/8)12yes—
254C2×C4×C11C23×C411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11H(5,𝔽2)12yes—
257C2×C4×C11H(5,𝔽2)12yes—
258C8×C11—24no—
259C8×C11—42no—
260C23×D4C22×C1111yescharacteristic
261C22×SD16C22×C1112yes—
262C2×C22⋊Q8C22×C1111yescharacteristic
263C2×C4×Q8C22×C1111yescharacteristic, complemented
264C22×C4⋊C4C22×C1111yescharacteristic
265C22×C22⋊C4—21no—
266C22×C22⋊C4—21no—
267C22×C42C22×C1111yescharacteristic
268#450C4×C1118yescomplemented
269C2×#106C22×C1112yescomplemented
270C2×#103C22×C1112yescomplemented
271C2×#102C22×C1112yes—
272C2×#102C22×C1112yes—
273C2×#102C22×C1112yes—
274C2×C22⋊C8C22×C1111yescharacteristic
275C2×C22⋊C8C22×C1111yescharacteristic
276C2×C4×C8C22×C1112yescomplemented
277#391C22×C1111yescharacteristic, complemented
278#390—21no—
279#390—21no—
280#390C22×C1112yes—
281#390C22×C1112yes—
282#389C22×C1111yescharacteristic, complemented
283#387—21no—
284#385—21no—
285#380C22×C1111yescharacteristic
286C4×C4⋊C4—21no—
287C4×C4⋊C4C22×C1111yescharacteristic, complemented
288C4×C22⋊C4—21no—
289#340C22×C1112yescomplemented
290#340C22×C1112yescomplemented
291#336C22×C1112yescomplemented
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—22no—
298C22×C11—44no—
299C22×C11—44no—
300C22×C11—44no—
301C22×C11—816no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11—82no—
305C22×C11—82no—
306C22×C11C4×SD1614yes—
307C22×C11C2×C4×D411yescharacteristic
308C22×C11#53411yescharacteristic
309C22×C11#53511yescharacteristic
310C22×C11C22×SD1611yescharacteristic
311C22×C11C2×#13511yescharacteristic
312C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
313C22×C11#57511yescharacteristic
314C4×C11—22no—
315C4×C11—22no—
316C4×C11—22no—
317C4×C11—22no—
318C4×C11—42no—
319C4×C11—41no—
320C4×C11—42no—
321C4×C11—81no—
322C4×C11—82no—
323C4×C11—81no—
324C4×C11#51812yes—
325C4×C11#53812yes—
326C25—21no—
327C22×Q8C23×C1111yescharacteristic
328C22×D4—21no—
329C22×D4—22no—
330C22×D4—42no—
331C22×D4—42no—
332C22×D4C2×C4×C1114yes—
333C22×D4C23×C1112yes—
334C23×C4—21no—
335C23×C4D4×C1111yescharacteristic
336C23×C4D4×C1111yescharacteristic
337C23×C4C23×C1111yescharacteristic
338C2×SD16—42no—
339C2×SD16—42no—
340C2×SD16C2×C4×C1118yescomplemented
341C22×C8C23×C1112yes—
342C22×C8C23×C1112yes—
343C22⋊Q8—22no—
344C22⋊Q8C2×C4×C1114yes—
345C4×Q8—42no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4C23×C1112yes—
352C2×C4⋊C4C23×C1111yescharacteristic
353C2×C4⋊C4C23×C1111yescharacteristic
354C2×C4⋊C4C23×C1111yescharacteristic
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—42no—
366C2×C42D4×C1111yescharacteristic
367C2×C42D4×C1111yescharacteristic
368C2×C42C23×C1111yescharacteristic
369C2×C42C23×C1111yescharacteristic
370#106—42no—
371#103—42no—
372#102—42no—
373#102—42no—
374#102C2×C4×C1118yescomplemented
375C22⋊C8—22no—
376C22⋊C8C2×C4×C1114yes—
377C4×C8—42no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—21no—
383C2×C11—24no—
384C2×C11—84no—
385C2×C11#232111yescharacteristic
386C2×C11C2×C4×SD1611yescharacteristic
387C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
388C2×C11#318711yescharacteristic
389C2×C11#318811yescharacteristic
390C2×C11#320811yescharacteristic
391C2×C11#321111yescharacteristic
392C24—24no—
393C24—22no—
394C24—42no—
395C24—42no—
396C24—42no—
397C24—42no—
398C24—42no—
399C24—42no—
400C24C2×D4×C1111yescharacteristic
401C2×Q8—21no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8C22×C4×C1112yes—
405C2×D4—24no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—48no—
412C2×D4—42no—
413C2×D4—42no—
414C2×D4—48no—
415C2×D4C22×C4×C1114yes—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4C11×SD1614yescomplemented
432C22×C4C22×C4×C1112yes—
433C22×C4C2×D4×C1111yescharacteristic
434C22×C4C2×D4×C1111yescharacteristic
435C22×C4C2×D4×C1111yescharacteristic
436C22×C4C2×D4×C1111yescharacteristic
437C22×C4C2×D4×C1111yescharacteristic
438C22×C4C11×#4112yes—
439C22×C4C24×C1111yescharacteristic
440SD16—48no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8C22×C4×C1114yes—
447C4⋊C4—24no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—42no—
454C4⋊C4—42no—
455C4⋊C4—42no—
456C4⋊C4C22×C4×C1112yes—
457C22⋊C4—24no—
458C22⋊C4—44no—
459C22⋊C4—42no—
460C22⋊C4—44no—
461C22⋊C4—44no—
462C22⋊C4—44no—
463C42—22no—
464C42—22no—
465C42—41no—
466C42—41no—
467C42—42no—
468C42—42no—
469C11#2204311yescharacteristic, direct product factor, Sylow
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—24no—
475C23—48no—
476C23—48no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—48no—
484C23—84no—
485C23—84no—
486C23—84no—
487C23—84no—
488C23C4×D4×C1112yes—
489C23C2×C11×SD1612yes—
490C23C11×#13512yes—
491C23C22×D4×C1111yescharacteristic
492Q8—24no—
493Q8—42no—
494D4—24no—
495D4—24no—
496D4—48no—
497D4—42no—
498D4—42no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—44no—
515C2×C4—44no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—84no—
530C2×C4C4×D4×C1112yes—
531C2×C4C2×C11×SD1612yes—
532C2×C4C2×C11×SD1612yes—
533C2×C4C11×AGL(1,ℤ/8)12yes—
534C2×C4C23×C4×C1111yescharacteristic
535C2×C4C2×C11×#4111yescharacteristic
536C2×C4C11×H(5,𝔽2)12yes—
537C2×C4C11×H(5,𝔽2)12yes—
538C8—24no—
539C8—42no—
540C22—22no—
541C22—22no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—816no—
550C22—82no—
551C22—82no—
552C22—82no—
553C22—82no—
554C22C4×C11×SD1614yes—
555C22C2×C4×D4×C1111yescharacteristic
556C22C11×#53411yescharacteristic
557C22C11×#53511yescharacteristic
558C22C22×C11×SD1611yescharacteristic
559C22C2×C11×#13511yescharacteristic
560C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
561C22C11×#57511yescharacteristic
562C4—22no—
563C4—22no—
564C4—22no—
565C4—22no—
566C4—41no—
567C4—42no—
568C4—42no—
569C4—81no—
570C4—82no—
571C4—81no—
572C4C11×#51812yes—
573C4C11×#53812yes—
574C2—24no—
575C2—84no—
576C2C11×#232111yescharacteristic
577C2C2×C4×C11×SD1611yescharacteristic
578C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
579C2C11×#318711yescharacteristic
580C2C11×#318811yescharacteristic
581C2C11×#320811yescharacteristic
582C2C11×#321111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×C22⋊Q8C2semidirect
4. C11×#1968C2semidirect
5. C11×#1934C2semidirect
6. C11×#1926C2semidirect
7. C11×#1880C2semidirect
8. C11×#1872C2semidirect
9. C11×#1853C2semidirect
11. C4×C11×C22⋊C8C2semidirect
15. C2×C4×Q8×C11C22semidirect
20. C11×#450C4semidirect
21. C2×C11×#106C22semidirect
22. C2×C11×#103C22semidirect
28. C2×C4×C8×C11C22semidirect
29. C11×#391C22semidirect
34. C11×#389C22semidirect
39. C4×C11×C4⋊C4C22semidirect
41. C11×#340C22semidirect
42. C11×#340C22semidirect
43. C11×#336C22semidirect
58. C2×C11×SD16C2×C4semidirect
92. C11×#102C2×C4semidirect
101. #22043C11direct (N × H)
141. C22×C4×C11SD16semidirect
180. C4×C22⋊Q8C2×C11semidirect
182. #1968C2×C11semidirect
183. #1934C2×C11semidirect
184. #1926C2×C11semidirect
185. #1880C2×C11semidirect
186. #1872C2×C11semidirect
187. #1853C2×C11semidirect
189. C4×C22⋊C8C2×C11semidirect
263. C2×C4×Q8C22×C11semidirect
268. #450C4×C11semidirect
269. C2×#106C22×C11semidirect
270. C2×#103C22×C11semidirect
276. C2×C4×C8C22×C11semidirect
277. #391C22×C11semidirect
282. #389C22×C11semidirect
287. C4×C4⋊C4C22×C11semidirect
289. #340C22×C11semidirect
290. #340C22×C11semidirect
291. #336C22×C11semidirect
340. C2×SD16C2×C4×C11semidirect
374. #102C2×C4×C11semidirect
431. C22×C4C11×SD16semidirect
469. C11#22043direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4502
C4×C11×C22⋊Q82
C2×C11×#3902
C11×#19682
C11×#19342
C11×#19262
C11×#18802
C11×#18722
C11×#18532
C11×#17862
C4×C11×C22⋊C82
#2204311