Finite Group Databasebeta

← C11×#24005 #14601198

Subgroups — C11×#24005 #14601198

Order 2816.

1844 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#121C211yesmaximal, characteristic
2C2×C11×#481C212yesmaximal, complemented
3C2×C11×#380C211yesmaximal, characteristic, complemented
4C11×#2034C214yesmaximal, complemented
5C11×#1874C212yesmaximal, complemented
6C11×#1853C212yesmaximal, complemented
7C11×#1786C212yesmaximal, complemented
8C11×#1779C211yesmaximal, characteristic, complemented
9C23×D4×C11—21no—
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C2×C11×#121—21no—
13C2×C11×#121—21no—
14C2×C11×#121—28no—
15C2×C11×#121C2212yes—
16C2×C11×#121C2212yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic, complemented
19C22×C11×C4⋊C4C2211yescharacteristic, complemented
20C22×C11×C22⋊C4—21no—
21C22×C11×C22⋊C4—21no—
22C11×#481—28no—
23C2×C11×#106C2214yescomplemented
24C2×C11×#102C2214yescomplemented
25C2×C11×#102C2214yescomplemented
26C2×C11×C22⋊C8C2212yes—
27C2×C11×C22⋊C8C2212yescomplemented
28C2×C11×C22⋊C8C2212yescomplemented
29C11×#380—21no—
30C11×#380—21no—
31C11×#380C2212yes—
32C11×#380C2212yescomplemented
33C2×C11×#95—21no—
34C11×#340C2214yescomplemented
35C25×C11—21no—
36C25×C11D411yescharacteristic
37C22×D4×C11—28no—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11—24no—
41C22×D4×C11—21no—
42C22×D4×C11—24no—
43C22×D4×C11—42no—
44C22×D4×C11—44no—
45C22×D4×C11—44no—
46C22×D4×C11C2312yes—
47C23×C4×C11—21no—
48C23×C4×C11—24no—
49C23×C4×C11—24no—
50C23×C4×C11—21no—
51C23×C4×C11—21no—
52C23×C4×C11—42no—
53C23×C4×C11D411yescharacteristic
54C23×C4×C11D411yescharacteristic
55C23×C4×C11D411yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C22×C8×C11C2314yes—
60C11×#121—28no—
61C11×#121—28no—
62C11×#121—24no—
63C11×#121—24no—
64C11×#121—24no—
65C11×#121D418yes—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—24no—
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—42no—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C22⋊C4—28no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—44no—
81C11×#106—28no—
82C11×#102—28no—
83C11×#102—44no—
84C11×C22⋊C8—24no—
85C11×C22⋊C8—24no—
86C11×C22⋊C8—42no—
87C11×#95—22no—
88C11×#95—22no—
89#24005C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—24no—
95C24×C11—22no—
96C24×C11—41no—
97C24×C11—41no—
98C24×C11—42no—
99C24×C11—42no—
100C24×C11—42no—
101C24×C11—42no—
102C24×C11—42no—
103C24×C11—42no—
104C24×C11SD1614yes—
105C24×C11C2×D411yescharacteristic
106C24×C11C2×D411yescharacteristic
107C24×C11C2×D411yescharacteristic
108C2×D4×C11—24no—
109C2×D4×C11—28no—
110C2×D4×C11—28no—
111C2×D4×C11—22no—
112C2×D4×C11—24no—
113C2×D4×C11—24no—
114C2×D4×C11—416no—
115C2×D4×C11—42no—
116C2×D4×C11—432no—
117C2×D4×C11—44no—
118C2×D4×C11—44no—
119C2×D4×C11—44no—
120C2×D4×C11—44no—
121C2×D4×C11—42no—
122C2×D4×C11C2×D414yes—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—41no—
141C22×C4×C11—41no—
142C22×C4×C11—41no—
143C22×C4×C11—416no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D414yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11#4114yes—
157C22×C4×C11C2411yescharacteristic
158C2×C8×C11—24no—
159C2×C8×C11—24no—
160C2×C8×C11—24no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4C2×D414yes—
168C11×C22⋊C4—28no—
169C11×C22⋊C4—28no—
170C11×C22⋊C4—44no—
171C11×C22⋊C4—44no—
172C22×#121C2×C1111yescharacteristic
173C2×#481C2×C1112yescomplemented
174C2×#380C2×C1111yescharacteristic, complemented
175#2034C2×C1114yescomplemented
176#1874C2×C1112yescomplemented
177#1853C2×C1112yescomplemented
178#1786C2×C1112yescomplemented
179#1779C2×C1111yescharacteristic, complemented
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—28no—
195C23×C11—28no—
196C23×C11—24no—
197C23×C11—44no—
198C23×C11—44no—
199C23×C11—44no—
200C23×C11—44no—
201C23×C11—44no—
202C23×C11—48no—
203C23×C11—48no—
204C23×C11—48no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—84no—
212C23×C11—84no—
213C23×C11—84no—
214C23×C11—84no—
215C23×C11#12012yes—
216C23×C11#12312yes—
217C23×C11C2×SD1612yes—
218C23×C11C2×SD1612yes—
219C23×C11C2×SD1612yes—
220C23×C11AGL(1,ℤ/8)12yes—
221C23×C11AGL(1,ℤ/8)12yes—
222C23×C11C22×D411yescharacteristic
223D4×C11—28no—
224D4×C11—48no—
225D4×C11—416no—
226D4×C11—416no—
227D4×C11—44no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—28no—
233C2×C4×C11—28no—
234C2×C4×C11—21no—
235C2×C4×C11—24no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—44no—
239C2×C4×C11—44no—
240C2×C4×C11—44no—
241C2×C4×C11—48no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—44no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—84no—
252C2×C4×C11—84no—
253C2×C4×C11#12012yes—
254C2×C4×C11#12312yes—
255C2×C4×C11C22×D412yes—
256C2×C4×C11C2×#4112yes—
257C2×C4×C11H(5,𝔽2)12yes—
258C8×C11—44no—
259C23×D4—21no—
260C23×D4C22×C1111yescharacteristic
261C24×C4C22×C1111yescharacteristic
262C2×#121—21no—
263C2×#121—21no—
264C2×#121—28no—
265C2×#121C22×C1112yes—
266C2×#121C22×C1112yes—
267C22×C4⋊C4C22×C1111yescharacteristic
268C22×C4⋊C4C22×C1111yescharacteristic, complemented
269C22×C4⋊C4C22×C1111yescharacteristic, complemented
270C22×C22⋊C4—21no—
271C22×C22⋊C4—21no—
272#481—28no—
273C2×#106C22×C1114yescomplemented
274C2×#102C22×C1114yescomplemented
275C2×#102C22×C1114yescomplemented
276C2×C22⋊C8C22×C1112yes—
277C2×C22⋊C8C22×C1112yescomplemented
278C2×C22⋊C8C22×C1112yescomplemented
279#380—21no—
280#380—21no—
281#380C22×C1112yes—
282#380C22×C1112yescomplemented
283C2×#95—21no—
284#340C22×C1114yescomplemented
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—416no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11—41no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—816no—
309C22×C11—82no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11—82no—
313C22×C11#45014yes—
314C22×C11#48114yescomplemented
315C22×C11C2×#12011yescharacteristic
316C22×C11C2×#12311yescharacteristic
317C22×C11#53411yescharacteristic
318C22×C11C22×SD1611yescharacteristic
319C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
320C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
321C22×C11#57511yescharacteristic
322C4×C11—22no—
323C4×C11—22no—
324C4×C11—41no—
325C4×C11—44no—
326C4×C11—82no—
327C4×C11—82no—
328C4×C11#54614yes—
329C25—21no—
330C25D4×C1111yescharacteristic
331C22×D4—28no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—24no—
335C22×D4—21no—
336C22×D4—24no—
337C22×D4—42no—
338C22×D4—44no—
339C22×D4—44no—
340C22×D4C23×C1112yes—
341C23×C4—21no—
342C23×C4—24no—
343C23×C4—24no—
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—42no—
347C23×C4D4×C1111yescharacteristic
348C23×C4D4×C1111yescharacteristic
349C23×C4D4×C1111yescharacteristic
350C23×C4C23×C1111yescharacteristic
351C23×C4C23×C1111yescharacteristic
352C23×C4C23×C1111yescharacteristic
353C22×C8C23×C1114yes—
354#121—28no—
355#121—28no—
356#121—24no—
357#121—24no—
358#121—24no—
359#121D4×C1118yes—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4C23×C1112yes—
367C2×C4⋊C4C23×C1112yes—
368C2×C4⋊C4C23×C1112yes—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—44no—
375#106—28no—
376#102—28no—
377#102—44no—
378C22⋊C8—24no—
379C22⋊C8—24no—
380C22⋊C8—42no—
381#95—22no—
382#95—22no—
383C2×C11—24no—
384C2×C11—24no—
385C2×C11—42no—
386C2×C11—84no—
387C2×C11#240511yescharacteristic
388C2×C11C2×#45011yescharacteristic
389C2×C11#300611yescharacteristic
390C2×C11C2×#48111yescharacteristic
391C2×C11#309411yescharacteristic
392C2×C11#318711yescharacteristic
393C2×C11#319211yescharacteristic
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—24no—
399C24—22no—
400C24—41no—
401C24—41no—
402C24—42no—
403C24—42no—
404C24—42no—
405C24—42no—
406C24—42no—
407C24—42no—
408C24C11×SD1614yes—
409C24C2×D4×C1111yescharacteristic
410C24C2×D4×C1111yescharacteristic
411C24C2×D4×C1111yescharacteristic
412C2×D4—24no—
413C2×D4—28no—
414C2×D4—28no—
415C2×D4—22no—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—416no—
419C2×D4—42no—
420C2×D4—432no—
421C2×D4—44no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—42no—
426C2×D4C2×D4×C1114yes—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—416no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4C2×D4×C1111yescharacteristic
457C22×C4C2×D4×C1111yescharacteristic
458C22×C4C2×D4×C1114yes—
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C11×#4114yes—
461C22×C4C24×C1111yescharacteristic
462C2×C8—24no—
463C2×C8—24no—
464C2×C8—24no—
465C4⋊C4—24no—
466C4⋊C4—22no—
467C4⋊C4—24no—
468C4⋊C4—24no—
469C4⋊C4—42no—
470C4⋊C4—42no—
471C4⋊C4C2×D4×C1114yes—
472C22⋊C4—28no—
473C22⋊C4—28no—
474C22⋊C4—44no—
475C22⋊C4—44no—
476C11#2400511yescharacteristic, direct product factor, Sylow
477C23—21no—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—28no—
492C23—28no—
493C23—24no—
494C23—44no—
495C23—44no—
496C23—44no—
497C23—44no—
498C23—44no—
499C23—48no—
500C23—48no—
501C23—48no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—84no—
509C23—84no—
510C23—84no—
511C23—84no—
512C23C11×#12012yes—
513C23C11×#12312yes—
514C23C2×C11×SD1612yes—
515C23C2×C11×SD1612yes—
516C23C2×C11×SD1612yes—
517C23C11×AGL(1,ℤ/8)12yes—
518C23C11×AGL(1,ℤ/8)12yes—
519C23C22×D4×C1111yescharacteristic
520D4—28no—
521D4—48no—
522D4—416no—
523D4—416no—
524D4—44no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—28no—
530C2×C4—28no—
531C2×C4—21no—
532C2×C4—24no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—48no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—84no—
549C2×C4—84no—
550C2×C4C11×#12012yes—
551C2×C4C11×#12312yes—
552C2×C4C22×D4×C1112yes—
553C2×C4C2×C11×#4112yes—
554C2×C4C11×H(5,𝔽2)12yes—
555C8—44no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—416no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—44no—
577C22—44no—
578C22—44no—
579C22—816no—
580C22—82no—
581C22—82no—
582C22—82no—
583C22—82no—
584C22C11×#45014yes—
585C22C11×#48114yescomplemented
586C22C2×C11×#12011yescharacteristic
587C22C2×C11×#12311yescharacteristic
588C22C11×#53411yescharacteristic
589C22C22×C11×SD1611yescharacteristic
590C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
591C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
592C22C11×#57511yescharacteristic
593C4—22no—
594C4—22no—
595C4—41no—
596C4—44no—
597C4—82no—
598C4—82no—
599C4C11×#54614yes—
600C2—24no—
601C2—24no—
602C2—42no—
603C2—84no—
604C2C11×#240511yescharacteristic
605C2C2×C11×#45011yescharacteristic
606C2C11×#300611yescharacteristic
607C2C2×C11×#48111yescharacteristic
608C2C11×#309411yescharacteristic
609C2C11×#318711yescharacteristic
610C2C11×#319211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#121C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#481C2semidirect
3. C2×C11×#380C2semidirect
4. C11×#2034C2semidirect
5. C11×#1874C2semidirect
6. C11×#1853C2semidirect
7. C11×#1786C2semidirect
8. C11×#1779C2semidirect
18. C22×C11×C4⋊C4C22semidirect
19. C22×C11×C4⋊C4C22semidirect
23. C2×C11×#106C22semidirect
24. C2×C11×#102C22semidirect
25. C2×C11×#102C22semidirect
27. C2×C11×C22⋊C8C22semidirect
28. C2×C11×C22⋊C8C22semidirect
32. C11×#380C22semidirect
34. C11×#340C22semidirect
89. #24005C11direct (N × H)
173. C2×#481C2×C11semidirect
174. C2×#380C2×C11semidirect
175. #2034C2×C11semidirect
176. #1874C2×C11semidirect
177. #1853C2×C11semidirect
178. #1786C2×C11semidirect
179. #1779C2×C11semidirect
268. C22×C4⋊C4C22×C11semidirect
269. C22×C4⋊C4C22×C11semidirect
273. C2×#106C22×C11semidirect
274. C2×#102C22×C11semidirect
275. C2×#102C22×C11semidirect
277. C2×C22⋊C8C22×C11semidirect
278. C2×C22⋊C8C22×C11semidirect
282. #380C22×C11semidirect
284. #340C22×C11semidirect
314. C22×C11#481semidirect
476. C11#24005direct (N × H)
585. C22C11×#481semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1212
C2×C11×#4812
C2×C11×#3802
C11×#20342
C11×#18742
C11×#18532
C11×#17862
C11×#17792
#2400511