Finite Group Databasebeta

← C11×#27070 #14604263

Subgroups — C11×#27070 #14604263

Order 2816.

740 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2514C211yesmaximal, characteristic, complemented
2C11×#2367C211yesmaximal, characteristic
3C11×#2092C211yesmaximal, characteristic
4C11×#2055C211yesmaximal, characteristic
5C11×#2042C211yesmaximal, characteristic
6C11×#2015C211yesmaximal, characteristic
7C11×#1969C211yesmaximal, characteristic, complemented
8C11×#1927C211yesmaximal, characteristic, complemented
9C11×#1927C211yesmaximal, characteristic, complemented
10C11×#1921C211yesmaximal, characteristic, complemented
11C11×#1916C211yesmaximal, characteristic, complemented
12C11×#1878C211yesmaximal, characteristic, complemented
13C11×#1877C211yesmaximal, characteristic
14C11×#1805C211yesmaximal, characteristic, complemented
15C4×C11×#102C211yesmaximal, characteristic
16C22×C11×Q16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C4×C8×C11C2211yescharacteristic
33C11×#401—21no—
34C11×#400—21no—
35C11×#391C2211yescharacteristic
36C11×#391C2211yescharacteristic
37C11×#391C2211yescharacteristic
38C11×#391C2211yescharacteristic
39C11×#390C2211yescharacteristic
40C11×#389C2211yescharacteristic
41C11×#388—21no—
42C11×#388—21no—
43C11×#387—21no—
44C11×#385—21no—
45C11×#383—21no—
46C11×#382C2211yescharacteristic
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C4×C11×C4⋊C4C2211yescharacteristic
50C4×C11×C22⋊C4—21no—
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C2×C11×Q16—22no—
64C2×C11×Q16—22no—
65C2×C11×Q16—41no—
66C2×C11×SD16—22no—
67C2×C11×SD16—41no—
68C2×C11×SD16—41no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#124—22no—
74C11×#124—22no—
75C4×Q8×C11—22no—
76C4×Q8×C11—41no—
77C4×D4×C11—22no—
78C4×D4×C11—41no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C42×C11—21no—
94C2×C42×C11—21no—
95C2×C42×C11—21no—
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C11×#107—22no—
100C11×#106—41no—
101C11×C4⋊C8—41no—
102C11×#103—22no—
103C11×#103—22no—
104C11×#103—41no—
105C11×#103—41no—
106C11×#103—41no—
107C11×#102—22no—
108C11×#102—22no—
109C11×#102—41no—
110C4×C8×C11—41no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119C11×#95—21no—
120C11×#95—21no—
121C11×#95—21no—
122C11×#95—21no—
123C11×#95—21no—
124C11×#95D411yescharacteristic
125C11×#95D411yescharacteristic
126#27070C1111yesmaximal, characteristic, direct product factor, Sylow
127C24×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11#4112yes—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11#4112yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—81no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2411yescharacteristic
163C11×Q16—44no—
164C11×SD16—44no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11#4112yes—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—41no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4—42no—
190C11×C4⋊C4#4112yes—
191C11×C22⋊C4—24no—
192C11×C22⋊C4—24no—
193C11×C22⋊C4—42no—
194C11×C22⋊C4—42no—
195C11×C22⋊C4—81no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11—21no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—42no—
203C42×C11—42no—
204C42×C11—81no—
205#2514C2×C1111yescharacteristic, complemented
206#2367C2×C1111yescharacteristic
207#2092C2×C1111yescharacteristic
208#2055C2×C1111yescharacteristic
209#2042C2×C1111yescharacteristic
210#2015C2×C1111yescharacteristic
211#1969C2×C1111yescharacteristic, complemented
212#1927C2×C1111yescharacteristic, complemented
213#1927C2×C1111yescharacteristic, complemented
214#1921C2×C1111yescharacteristic, complemented
215#1916C2×C1111yescharacteristic, complemented
216#1878C2×C1111yescharacteristic, complemented
217#1877C2×C1111yescharacteristic
218#1805C2×C1111yescharacteristic, complemented
219C4×#102C2×C1111yescharacteristic
220C23×C11—22no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11C22×D411yescharacteristic
228Q8×C11—22no—
229Q8×C11—22no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—41no—
236D4×C11—22no—
237D4×C11—22no—
238D4×C11—41no—
239D4×C11—41no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—84no—
279C2×C4×C11#13512yes—
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11H(5,𝔽2)11yescharacteristic
285C2×C4×C11H(5,𝔽2)11yescharacteristic
286C8×C11—22no—
287C8×C11—41no—
288C8×C11—41no—
289C8×C11—41no—
290C22×Q16C22×C1111yescharacteristic
291C22×SD16C22×C1111yescharacteristic
292C2×#124C22×C1111yescharacteristic
293C2×C4×Q8C22×C1111yescharacteristic
294C2×C4×D4C22×C1111yescharacteristic
295C2×#107C22×C1111yescharacteristic
296C2×#106C22×C1111yescharacteristic
297C2×C4⋊C8C22×C1111yescharacteristic
298C2×#103C22×C1111yescharacteristic
299C2×#103C22×C1111yescharacteristic
300C2×#103C22×C1111yescharacteristic
301C2×#103C22×C1111yescharacteristic
302C2×#103C22×C1111yescharacteristic
303C2×#102C22×C1111yescharacteristic
304C2×#102C22×C1111yescharacteristic
305C2×#102C22×C1111yescharacteristic
306C2×C4×C8C22×C1111yescharacteristic
307#401—21no—
308#400—21no—
309#391C22×C1111yescharacteristic
310#391C22×C1111yescharacteristic
311#391C22×C1111yescharacteristic
312#391C22×C1111yescharacteristic
313#390C22×C1111yescharacteristic
314#389C22×C1111yescharacteristic
315#388—21no—
316#388—21no—
317#387—21no—
318#385—21no—
319#383—21no—
320#382C22×C1111yescharacteristic
321C4×C4⋊C4C22×C1111yescharacteristic
322C4×C4⋊C4C22×C1111yescharacteristic
323C4×C4⋊C4C22×C1111yescharacteristic
324C4×C22⋊C4—21no—
325#340C22×C1111yescharacteristic
326#340C22×C1111yescharacteristic
327#340C22×C1111yescharacteristic
328#340C22×C1111yescharacteristic
329#336C22×C1111yescharacteristic
330#336C22×C1111yescharacteristic
331#336C22×C1111yescharacteristic
332#336C22×C1111yescharacteristic
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11#52511yescharacteristic
341C22×C11#54611yescharacteristic
342C22×C11#55011yescharacteristic
343C22×C11C2×#13511yescharacteristic
344C22×C11#57511yescharacteristic
345C22×C11#57711yescharacteristic
346C22×C11#57811yescharacteristic
347C4×C11—22no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—42no—
351C4×C11—41no—
352C4×C11—42no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11—81no—
360C4×C11#52911yescharacteristic
361C4×C11#53811yescharacteristic
362C4×C11#55111yescharacteristic
363C4×C11#55311yescharacteristic
364C22×Q8C23×C1111yescharacteristic
365C22×Q8C23×C1111yescharacteristic
366C22×D4C23×C1111yescharacteristic
367C23×C4—21no—
368C2×Q16—22no—
369C2×Q16—22no—
370C2×Q16—41no—
371C2×SD16—22no—
372C2×SD16—41no—
373C2×SD16—41no—
374C22×C8C23×C1111yescharacteristic
375C22×C8C23×C1111yescharacteristic
376C22×C8C23×C1111yescharacteristic
377C22×C8C23×C1111yescharacteristic
378#124—22no—
379#124—22no—
380C4×Q8—22no—
381C4×Q8—41no—
382C4×D4—22no—
383C4×D4—41no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4D4×C1111yescharacteristic
387C2×C4⋊C4D4×C1111yescharacteristic
388C2×C4⋊C4C23×C1111yescharacteristic
389C2×C4⋊C4C23×C1111yescharacteristic
390C2×C4⋊C4C23×C1111yescharacteristic
391C2×C4⋊C4C23×C1111yescharacteristic
392C2×C4⋊C4C23×C1111yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42C23×C1111yescharacteristic
402C2×C42C23×C1111yescharacteristic
403C2×C42C23×C1111yescharacteristic
404#107—22no—
405#106—41no—
406C4⋊C8—41no—
407#103—22no—
408#103—22no—
409#103—41no—
410#103—41no—
411#103—41no—
412#102—22no—
413#102—22no—
414#102—41no—
415C4×C8—41no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95D4×C1111yescharacteristic
430#95D4×C1111yescharacteristic
431C2×C11—82no—
432C2×C11#246711yescharacteristic
433C2×C11#310211yescharacteristic
434C2×C11#312011yescharacteristic
435C2×C11#329611yescharacteristic
436C2×C11#331311yescharacteristic
437C2×C11#339311yescharacteristic
438C2×C11#340111yescharacteristic
439C24—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8C11×#4112yes—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4C11×#4112yes—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—81no—
468C22×C4C2×D4×C1111yescharacteristic
469C22×C4C2×D4×C1111yescharacteristic
470C22×C4C2×D4×C1111yescharacteristic
471C22×C4C2×D4×C1111yescharacteristic
472C22×C4C2×D4×C1111yescharacteristic
473C22×C4C2×D4×C1111yescharacteristic
474C22×C4C24×C1111yescharacteristic
475Q16—44no—
476SD16—44no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8C11×#4112yes—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—41no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4C11×#4112yes—
503C22⋊C4—24no—
504C22⋊C4—24no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—81no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—42no—
515C42—42no—
516C42—81no—
517C11#2707011yescharacteristic, direct product factor, Sylow
518C23—22no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23C22×D4×C1111yescharacteristic
526Q8—22no—
527Q8—22no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533Q8—41no—
534D4—22no—
535D4—22no—
536D4—41no—
537D4—41no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—84no—
577C2×C4C11×#13512yes—
578C2×C4C2×C11×#4111yescharacteristic
579C2×C4C2×C11×#4111yescharacteristic
580C2×C4C2×C11×#4111yescharacteristic
581C2×C4C2×C11×#4111yescharacteristic
582C2×C4C11×H(5,𝔽2)11yescharacteristic
583C2×C4C11×H(5,𝔽2)11yescharacteristic
584C8—22no—
585C8—41no—
586C8—41no—
587C8—41no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22C11×#52511yescharacteristic
596C22C11×#54611yescharacteristic
597C22C11×#55011yescharacteristic
598C22C2×C11×#13511yescharacteristic
599C22C11×#57511yescharacteristic
600C22C11×#57711yescharacteristic
601C22C11×#57811yescharacteristic
602C4—22no—
603C4—42no—
604C4—41no—
605C4—42no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4—81no—
614C4—81no—
615C4C11×#52911yescharacteristic
616C4C11×#53811yescharacteristic
617C4C11×#55111yescharacteristic
618C4C11×#55311yescharacteristic
619C2—82no—
620C2C11×#246711yescharacteristic
621C2C11×#310211yescharacteristic
622C2C11×#312011yescharacteristic
623C2C11×#329611yescharacteristic
624C2C11×#331311yescharacteristic
625C2C11×#339311yescharacteristic
626C2C11×#340111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2514C2semidirect
7. C11×#1969C2semidirect
8. C11×#1927C2semidirect
9. C11×#1927C2semidirect
10. C11×#1921C2semidirect
11. C11×#1916C2semidirect
12. C11×#1878C2semidirect
14. C11×#1805C2semidirect
126. #27070C11direct (N × H)
205. #2514C2×C11semidirect
211. #1969C2×C11semidirect
212. #1927C2×C11semidirect
213. #1927C2×C11semidirect
214. #1921C2×C11semidirect
215. #1916C2×C11semidirect
216. #1878C2×C11semidirect
218. #1805C2×C11semidirect
517. C11#27070direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25142
C11×#23672
C11×#20922
C11×#20552
C11×#20422
C11×#20152
C11×#19692
C11×#19272
C11×#19212
C11×#19162
C11×#18782
C11×#18772
C11×#18052
C4×C11×#1022
#2707011