Finite Group Databasebeta

← C11×#24015 #14601208

Subgroups — C11×#24015 #14601208

Order 2816.

1468 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#535C211yesmaximal, characteristic
2C2×C11×#482C212yesmaximal, complemented
3C11×#2311C211yesmaximal, characteristic, complemented
4C11×#2034C212yesmaximal, complemented
5C11×#2033C212yesmaximal, complemented
6C11×#1874C212yesmaximal, complemented
7C11×#1854C212yesmaximal, complemented
8C11×#1786C212yesmaximal, complemented
9C11×#1780C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C11×#535—28no—
13C2×C11×#127—21no—
14C2×C11×#124—21no—
15C2×C11×#121C2212yes—
16C2×C11×#121C2212yes—
17C2×C11×#120—21no—
18C2×C11×#120—21no—
19C2×C11×#117C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic, complemented
21C22×C11×C4⋊C4C2211yescharacteristic, complemented
22C11×#482—28no—
23C2×C11×#107C2212yescomplemented
24C2×C11×#106C2212yescomplemented
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#102C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×C22⋊C8C2212yes—
30C2×C11×C22⋊C8C2212yescomplemented
31C2×C11×C22⋊C8C2211yescharacteristic, complemented
32C2×C11×C22⋊C8C2211yescharacteristic, complemented
33C11×#391—21no—
34C11×#390—21no—
35C11×#386—21no—
36C11×#386—21no—
37C11×#380C2212yes—
38C11×#380C2212yescomplemented
39C11×#340C2212yescomplemented
40C11×#340C2212yescomplemented
41C25×C11—21no—
42C2×C11×#41—24no—
43C2×C11×#41—24no—
44C2×C11×#41—41no—
45C2×C11×#41—41no—
46C22×Q8×C11D411yescharacteristic
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—24no—
50C22×D4×C11—21no—
51C22×D4×C11—24no—
52C22×D4×C11—41no—
53C22×D4×C11—41no—
54C22×D4×C11D411yescharacteristic
55C22×D4×C11D411yescharacteristic
56C22×D4×C11D411yescharacteristic
57C22×D4×C11C2312yes—
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C8×C11C2312yes—
63C22×C8×C11C2312yes—
64C11×#127—28no—
65C11×#124—28no—
66C11×#121—24no—
67C11×#121—24no—
68C11×#121—24no—
69C11×#121D418yes—
70C11×#120—28no—
71C11×#120—28no—
72C11×#117—24no—
73C11×#117—24no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—41no—
76C2×C11×C4⋊C4—41no—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C11×#107—24no—
89C11×#106—24no—
90C11×#102—24no—
91C11×#102—24no—
92C11×#102—42no—
93C11×#102—42no—
94C11×C22⋊C8—24no—
95C11×C22⋊C8—24no—
96C11×C22⋊C8—41no—
97C11×C22⋊C8—41no—
98C11×#95—22no—
99C11×#95—22no—
100#24015C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11—24no—
102C24×C11—22no—
103C24×C11—42no—
104C24×C11—42no—
105C24×C11—82no—
106C24×C11—82no—
107C24×C11C2×D411yescharacteristic
108C24×C11C2×D411yescharacteristic
109C24×C11C2×D411yescharacteristic
110C11×#41—48no—
111C11×#41—48no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—41no—
115C2×D4×C11—24no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—28no—
121C2×D4×C11—28no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—48no—
130C2×D4×C11—48no—
131C2×D4×C11—41no—
132C2×D4×C11—41no—
133C2×D4×C11—41no—
134C2×D4×C11—42no—
135C2×D4×C11—42no—
136C2×D4×C11—82no—
137C2×D4×C11—82no—
138C2×D4×C11—82no—
139C2×D4×C11—82no—
140C2×D4×C11C2×D414yes—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—42no—
155C22×C4×C11—82no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D414yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11#4114yes—
161C22×C4×C11C2411yescharacteristic
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4C2×D414yes—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—28no—
177C11×C22⋊C4—28no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—82no—
180C11×C22⋊C4—82no—
181C42×C11—24no—
182C42×C11—42no—
183C2×#535C2×C1111yescharacteristic
184C2×#482C2×C1112yescomplemented
185#2311C2×C1111yescharacteristic, complemented
186#2034C2×C1112yescomplemented
187#2033C2×C1112yescomplemented
188#1874C2×C1112yescomplemented
189#1854C2×C1112yescomplemented
190#1786C2×C1112yescomplemented
191#1780C2×C1111yescharacteristic, complemented
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—24no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—21no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—48no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—88no—
214C23×C11—88no—
215C23×C11—84no—
216C23×C11—84no—
217C23×C11#12012yes—
218C23×C11#12312yes—
219C23×C11C22×D411yescharacteristic
220Q8×C11—44no—
221D4×C11—24no—
222D4×C11—24no—
223D4×C11—44no—
224D4×C11—44no—
225D4×C11—48no—
226D4×C11—44no—
227D4×C11—42no—
228D4×C11—42no—
229D4×C11—88no—
230D4×C11—88no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
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—42no—
252C2×C4×C11—42no—
253C2×C4×C11—84no—
254C2×C4×C11#12012yes—
255C2×C4×C11#12312yes—
256C2×C4×C11C22×D412yes—
257C2×C4×C11C2×#4112yes—
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C8×C11—42no—
261C8×C11—42no—
262C22×#41C22×C1111yescharacteristic
263C23×D4C22×C1111yescharacteristic
264#535—28no—
265C2×#127—21no—
266C2×#124—21no—
267C2×#121C22×C1112yes—
268C2×#121C22×C1112yes—
269C2×#120—21no—
270C2×#120—21no—
271C2×#117C22×C1111yescharacteristic
272C2×#117C22×C1111yescharacteristic, complemented
273C22×C4⋊C4C22×C1111yescharacteristic, complemented
274#482—28no—
275C2×#107C22×C1112yescomplemented
276C2×#106C22×C1112yescomplemented
277C2×#102C22×C1112yes—
278C2×#102C22×C1112yes—
279C2×#102C22×C1112yes—
280C2×#102C22×C1112yes—
281C2×C22⋊C8C22×C1112yes—
282C2×C22⋊C8C22×C1112yescomplemented
283C2×C22⋊C8C22×C1111yescharacteristic, complemented
284C2×C22⋊C8C22×C1111yescharacteristic, complemented
285#391—21no—
286#390—21no—
287#386—21no—
288#386—21no—
289#380C22×C1112yes—
290#380C22×C1112yescomplemented
291#340C22×C1112yescomplemented
292#340C22×C1112yescomplemented
293C22×C11—24no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—24no—
297C22×C11—42no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—41no—
305C22×C11—44no—
306C22×C11—41no—
307C22×C11—41no—
308C22×C11—42no—
309C22×C11—44no—
310C22×C11—44no—
311C22×C11—816no—
312C22×C11—82no—
313C22×C11—82no—
314C22×C11—82no—
315C22×C11—82no—
316C22×C11C2×#12011yescharacteristic
317C22×C11C2×#12311yescharacteristic
318C22×C11#53411yescharacteristic
319C22×C11#57612yes—
320C22×C11#57712yes—
321C4×C11—22no—
322C4×C11—22no—
323C4×C11—41no—
324C4×C11—44no—
325C4×C11—82no—
326C4×C11—82no—
327C4×C11#54612yes—
328C4×C11#54612yes—
329C25—21no—
330C2×#41—24no—
331C2×#41—24no—
332C2×#41—41no—
333C2×#41—41no—
334C22×Q8D4×C1111yescharacteristic
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—24no—
338C22×D4—21no—
339C22×D4—24no—
340C22×D4—41no—
341C22×D4—41no—
342C22×D4D4×C1111yescharacteristic
343C22×D4D4×C1111yescharacteristic
344C22×D4D4×C1111yescharacteristic
345C22×D4C23×C1112yes—
346C23×C4—21no—
347C23×C4C23×C1111yescharacteristic
348C23×C4C23×C1111yescharacteristic
349C23×C4C23×C1111yescharacteristic
350C22×C8C23×C1112yes—
351C22×C8C23×C1112yes—
352#127—28no—
353#124—28no—
354#121—24no—
355#121—24no—
356#121—24no—
357#121D4×C1118yes—
358#120—28no—
359#120—28no—
360#117—24no—
361#117—24no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—41no—
364C2×C4⋊C4—41no—
365C2×C4⋊C4C23×C1112yes—
366C2×C4⋊C4C23×C1112yes—
367C2×C4⋊C4C23×C1112yes—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C42—21no—
375C2×C42—21no—
376#107—24no—
377#106—24no—
378#102—24no—
379#102—24no—
380#102—42no—
381#102—42no—
382C22⋊C8—24no—
383C22⋊C8—24no—
384C22⋊C8—41no—
385C22⋊C8—41no—
386#95—22no—
387#95—22no—
388C2×C11—42no—
389C2×C11—42no—
390C2×C11—81no—
391C2×C11—84no—
392C2×C11#240511yescharacteristic
393C2×C11#301212yes—
394C2×C11#309612yes—
395C2×C11#319911yescharacteristic
396C2×C11#320011yescharacteristic
397C24—24no—
398C24—22no—
399C24—42no—
400C24—42no—
401C24—82no—
402C24—82no—
403C24C2×D4×C1111yescharacteristic
404C24C2×D4×C1111yescharacteristic
405C24C2×D4×C1111yescharacteristic
406#41—48no—
407#41—48no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—41no—
411C2×D4—24no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—28no—
417C2×D4—28no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—48no—
426C2×D4—48no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—42no—
431C2×D4—42no—
432C2×D4—82no—
433C2×D4—82no—
434C2×D4—82no—
435C2×D4—82no—
436C2×D4C2×D4×C1114yes—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—42no—
451C22×C4—82no—
452C22×C4C2×D4×C1111yescharacteristic
453C22×C4C2×D4×C1111yescharacteristic
454C22×C4C2×D4×C1114yes—
455C22×C4C2×D4×C1111yescharacteristic
456C22×C4C11×#4114yes—
457C22×C4C24×C1111yescharacteristic
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—42no—
470C4⋊C4C2×D4×C1114yes—
471C22⋊C4—24no—
472C22⋊C4—28no—
473C22⋊C4—28no—
474C22⋊C4—42no—
475C22⋊C4—82no—
476C22⋊C4—82no—
477C42—24no—
478C42—42no—
479C11#2401511yescharacteristic, direct product factor, Sylow
480C23—21no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—24no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—22no—
493C23—22no—
494C23—48no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—88no—
502C23—88no—
503C23—84no—
504C23—84no—
505C23C11×#12012yes—
506C23C11×#12312yes—
507C23C22×D4×C1111yescharacteristic
508Q8—44no—
509D4—24no—
510D4—24no—
511D4—44no—
512D4—44no—
513D4—48no—
514D4—44no—
515D4—42no—
516D4—42no—
517D4—88no—
518D4—88no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—84no—
542C2×C4C11×#12012yes—
543C2×C4C11×#12312yes—
544C2×C4C22×D4×C1112yes—
545C2×C4C2×C11×#4112yes—
546C2×C4C11×H(5,𝔽2)11yescharacteristic
547C2×C4C11×H(5,𝔽2)11yescharacteristic
548C8—42no—
549C8—42no—
550C22—22no—
551C22—22no—
552C22—24no—
553C22—24no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—42no—
559C22—42no—
560C22—41no—
561C22—44no—
562C22—41no—
563C22—41no—
564C22—42no—
565C22—44no—
566C22—44no—
567C22—42no—
568C22—816no—
569C22—82no—
570C22—82no—
571C22—82no—
572C22—82no—
573C22C2×C11×#12011yescharacteristic
574C22C2×C11×#12311yescharacteristic
575C22C11×#53411yescharacteristic
576C22C11×#57612yes—
577C22C11×#57712yes—
578C4—22no—
579C4—22no—
580C4—41no—
581C4—44no—
582C4—82no—
583C4—82no—
584C4C11×#54612yes—
585C4C11×#54612yes—
586C2—42no—
587C2—42no—
588C2—81no—
589C2—84no—
590C2C11×#240511yescharacteristic
591C2C11×#301212yes—
592C2C11×#309612yes—
593C2C11×#319911yescharacteristic
594C2C11×#320011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#482C2semidirect
3. C11×#2311C2semidirect
4. C11×#2034C2semidirect
5. C11×#2033C2semidirect
6. C11×#1874C2semidirect
7. C11×#1854C2semidirect
8. C11×#1786C2semidirect
9. C11×#1780C2semidirect
20. C2×C11×#117C22semidirect
21. C22×C11×C4⋊C4C22semidirect
23. C2×C11×#107C22semidirect
24. C2×C11×#106C22semidirect
30. C2×C11×C22⋊C8C22semidirect
31. C2×C11×C22⋊C8C22semidirect
32. C2×C11×C22⋊C8C22semidirect
38. C11×#380C22semidirect
39. C11×#340C22semidirect
40. C11×#340C22semidirect
100. #24015C11direct (N × H)
184. C2×#482C2×C11semidirect
185. #2311C2×C11semidirect
186. #2034C2×C11semidirect
187. #2033C2×C11semidirect
188. #1874C2×C11semidirect
189. #1854C2×C11semidirect
190. #1786C2×C11semidirect
191. #1780C2×C11semidirect
272. C2×#117C22×C11semidirect
273. C22×C4⋊C4C22×C11semidirect
275. C2×#107C22×C11semidirect
276. C2×#106C22×C11semidirect
282. C2×C22⋊C8C22×C11semidirect
283. C2×C22⋊C8C22×C11semidirect
284. C2×C22⋊C8C22×C11semidirect
290. #380C22×C11semidirect
291. #340C22×C11semidirect
292. #340C22×C11semidirect
479. C11#24015direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5352
C2×C11×#4822
C11×#23112
C11×#20342
C11×#20332
C11×#18742
C11×#18542
C11×#17862
C11×#17802
#2401511