Finite Group Databasebeta

← C11×#27084 #14604277

Subgroups — C11×#27084 #14604277

Order 2816.

728 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2513C211yesmaximal, characteristic
2C11×#2365C211yesmaximal, characteristic, complemented
3C11×#2097C211yesmaximal, characteristic, complemented
4C11×#2055C211yesmaximal, characteristic
5C11×#2043C211yesmaximal, characteristic, complemented
6C11×#2013C211yesmaximal, characteristic
7C11×#1973C211yesmaximal, characteristic
8C11×#1927C211yesmaximal, characteristic, complemented
9C11×#1926C211yesmaximal, characteristic
10C11×#1921C211yesmaximal, characteristic, complemented
11C11×#1917C211yesmaximal, characteristic, complemented
12C11×#1880C211yesmaximal, characteristic
13C11×#1880C211yesmaximal, characteristic
14C11×#1805C211yesmaximal, characteristic, complemented
15C11×#1763C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×Q8×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×#103C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#97C2211yescharacteristic
33C11×#397—21no—
34C11×#397—21no—
35C11×#391C2211yescharacteristic
36C11×#391C2211yescharacteristic
37C11×#390C2211yescharacteristic
38C11×#390C2211yescharacteristic
39C11×#390C2211yescharacteristic
40C11×#389—21no—
41C11×#389C2211yescharacteristic
42C11×#388—21no—
43C11×#388—21no—
44C11×#387—21no—
45C11×#387—21no—
46C11×#382C2211yescharacteristic
47C4×C11×C4⋊C4—21no—
48C4×C11×C4⋊C4C2211yescharacteristic
49C4×C11×C4⋊C4C2211yescharacteristic
50C4×C11×C4⋊C4C2211yescharacteristic
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
62C2×C11×SD16—22no—
63C2×C11×SD16—22no—
64C2×C11×SD16—22no—
65C2×C11×SD16—41no—
66C2×C11×SD16—41no—
67C2×C11×SD16—41no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×C4⋊Q8—22no—
73C11×C4⋊Q8—22no—
74C4×Q8×C11—22no—
75C4×Q8×C11—22no—
76C4×Q8×C11—41no—
77C4×Q8×C11—41no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C42×C11—21no—
97C2×C42×C11—21no—
98C2×C42×C11—21no—
99C2×C42×C11—21no—
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2311yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C11×#107—22no—
104C11×#106—41no—
105C11×C4⋊C8—41no—
106C11×#103—22no—
107C11×#103—22no—
108C11×#103—22no—
109C11×#103—41no—
110C11×#103—41no—
111C11×#103—41no—
112C11×#102—22no—
113C11×#102—41no—
114C11×#97—41no—
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#27084C1111yesmaximal, 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#4112yes—
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—21no—
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×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C11×SD16—44no—
161C11×SD16—44no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
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#4112yes—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—21no—
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—41no—
187C11×C4⋊C4—42no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4—81no—
190C11×C4⋊C4#4112yes—
191C11×C22⋊C4—42no—
192C11×C22⋊C4—42no—
193C11×C22⋊C4—81no—
194C11×C22⋊C4—81no—
195C11×C22⋊C4—81no—
196C11×C22⋊C4—81no—
197C42×C11—21no—
198C42×C11—21no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11—42no—
204C42×C11—42no—
205C42×C11—42no—
206C42×C11—81no—
207#2513C2×C1111yescharacteristic
208#2365C2×C1111yescharacteristic, complemented
209#2097C2×C1111yescharacteristic, complemented
210#2055C2×C1111yescharacteristic
211#2043C2×C1111yescharacteristic, complemented
212#2013C2×C1111yescharacteristic
213#1973C2×C1111yescharacteristic
214#1927C2×C1111yescharacteristic, complemented
215#1926C2×C1111yescharacteristic
216#1921C2×C1111yescharacteristic, complemented
217#1917C2×C1111yescharacteristic, complemented
218#1880C2×C1111yescharacteristic
219#1880C2×C1111yescharacteristic
220#1805C2×C1111yescharacteristic, complemented
221#1763C2×C1111yescharacteristic, complemented
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11C22×D411yescharacteristic
230Q8×C11—22no—
231Q8×C11—22no—
232Q8×C11—22no—
233Q8×C11—22no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—41no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
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—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
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—41no—
279C2×C4×C11—41no—
280C2×C4×C11#13712yes—
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11H(5,𝔽2)11yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C8×C11—22no—
288C8×C11—41no—
289C8×C11—41no—
290C8×C11—41no—
291C22×SD16C22×C1111yescharacteristic
292C22×SD16C22×C1111yescharacteristic
293C2×C4⋊Q8C22×C1111yescharacteristic
294C2×C4×Q8C22×C1111yescharacteristic
295C2×C4×Q8C22×C1111yescharacteristic
296C2×#107C22×C1111yescharacteristic
297C2×#106C22×C1111yescharacteristic
298C2×C4⋊C8C22×C1111yescharacteristic
299C2×#103C22×C1111yescharacteristic
300C2×#103C22×C1111yescharacteristic
301C2×#103C22×C1111yescharacteristic
302C2×#103C22×C1111yescharacteristic
303C2×#103C22×C1111yescharacteristic
304C2×#103C22×C1111yescharacteristic
305C2×#102C22×C1111yescharacteristic
306C2×#102C22×C1111yescharacteristic
307C2×#97C22×C1111yescharacteristic
308#397—21no—
309#397—21no—
310#391C22×C1111yescharacteristic
311#391C22×C1111yescharacteristic
312#390C22×C1111yescharacteristic
313#390C22×C1111yescharacteristic
314#390C22×C1111yescharacteristic
315#389—21no—
316#389C22×C1111yescharacteristic
317#388—21no—
318#388—21no—
319#387—21no—
320#387—21no—
321#382C22×C1111yescharacteristic
322C4×C4⋊C4—21no—
323C4×C4⋊C4C22×C1111yescharacteristic
324C4×C4⋊C4C22×C1111yescharacteristic
325C4×C4⋊C4C22×C1111yescharacteristic
326#340C22×C1111yescharacteristic
327#340C22×C1111yescharacteristic
328#340C22×C1111yescharacteristic
329#340C22×C1111yescharacteristic
330#336C22×C1111yescharacteristic
331#336C22×C1111yescharacteristic
332#336C22×C1111yescharacteristic
333#336C22×C1111yescharacteristic
334C22×C11—81no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11#52511yescharacteristic
342C22×C11#54611yescharacteristic
343C22×C11#55011yescharacteristic
344C22×C11C2×#13711yescharacteristic
345C22×C11#57511yescharacteristic
346C22×C11#57711yescharacteristic
347C22×C11#57711yescharacteristic
348C4×C11—22no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—42no—
353C4×C11—42no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—42no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11—81no—
360C4×C11—81no—
361C4×C11#52911yescharacteristic
362C4×C11#53811yescharacteristic
363C4×C11#55111yescharacteristic
364C4×C11#55311yescharacteristic
365C22×Q8C23×C1111yescharacteristic
366C22×Q8C23×C1111yescharacteristic
367C22×D4C23×C1111yescharacteristic
368C2×SD16—22no—
369C2×SD16—22no—
370C2×SD16—22no—
371C2×SD16—41no—
372C2×SD16—41no—
373C2×SD16—41no—
374C22×C8C23×C1111yescharacteristic
375C22×C8C23×C1111yescharacteristic
376C22×C8C23×C1111yescharacteristic
377C22×C8C23×C1111yescharacteristic
378C4⋊Q8—22no—
379C4⋊Q8—22no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—41no—
383C4×Q8—41no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4D4×C1111yescharacteristic
390C2×C4⋊C4D4×C1111yescharacteristic
391C2×C4⋊C4C23×C1111yescharacteristic
392C2×C4⋊C4C23×C1111yescharacteristic
393C2×C4⋊C4C23×C1111yescharacteristic
394C2×C4⋊C4C23×C1111yescharacteristic
395C2×C4⋊C4C23×C1111yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42C23×C1111yescharacteristic
407C2×C42C23×C1111yescharacteristic
408C2×C42C23×C1111yescharacteristic
409#107—22no—
410#106—41no—
411C4⋊C8—41no—
412#103—22no—
413#103—22no—
414#103—22no—
415#103—41no—
416#103—41no—
417#103—41no—
418#102—22no—
419#102—41no—
420#97—41no—
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#95—21no—
430#95D4×C1111yescharacteristic
431#95D4×C1111yescharacteristic
432C2×C11—161no—
433C2×C11#246711yescharacteristic
434C2×C11#311711yescharacteristic
435C2×C11#312611yescharacteristic
436C2×C11#330711yescharacteristic
437C2×C11#332911yescharacteristic
438C2×C11#340011yescharacteristic
439C2×C11#340111yescharacteristic
440C24—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×Q8C11×#4112yes—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C2×D4×C1111yescharacteristic
468C22×C4C2×D4×C1111yescharacteristic
469C22×C4C2×D4×C1111yescharacteristic
470C22×C4C2×D4×C1111yescharacteristic
471C22×C4C2×D4×C1111yescharacteristic
472C22×C4C24×C1111yescharacteristic
473SD16—44no—
474SD16—44no—
475C2×C8—21no—
476C2×C8—21no—
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×C8C11×#4112yes—
487C4⋊C4—24no—
488C4⋊C4—24no—
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⋊C4—81no—
503C4⋊C4C11×#4112yes—
504C22⋊C4—42no—
505C22⋊C4—42no—
506C22⋊C4—81no—
507C22⋊C4—81no—
508C22⋊C4—81no—
509C22⋊C4—81no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—42no—
517C42—42no—
518C42—42no—
519C42—81no—
520C11#2708411yescharacteristic, direct product factor, Sylow
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23C22×D4×C1111yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—22no—
532Q8—22no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
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—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4C11×#13712yes—
580C2×C4C2×C11×#4111yescharacteristic
581C2×C4C2×C11×#4111yescharacteristic
582C2×C4C2×C11×#4111yescharacteristic
583C2×C4C2×C11×#4111yescharacteristic
584C2×C4C11×H(5,𝔽2)11yescharacteristic
585C2×C4C11×H(5,𝔽2)11yescharacteristic
586C8—22no—
587C8—41no—
588C8—41no—
589C8—41no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22C11×#52511yescharacteristic
598C22C11×#54611yescharacteristic
599C22C11×#55011yescharacteristic
600C22C2×C11×#13711yescharacteristic
601C22C11×#57511yescharacteristic
602C22C11×#57711yescharacteristic
603C22C11×#57711yescharacteristic
604C4—22no—
605C4—42no—
606C4—42no—
607C4—41no—
608C4—41no—
609C4—42no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—81no—
614C4—81no—
615C4—81no—
616C4—81no—
617C4C11×#52911yescharacteristic
618C4C11×#53811yescharacteristic
619C4C11×#55111yescharacteristic
620C4C11×#55311yescharacteristic
621C2—161no—
622C2C11×#246711yescharacteristic
623C2C11×#311711yescharacteristic
624C2C11×#312611yescharacteristic
625C2C11×#330711yescharacteristic
626C2C11×#332911yescharacteristic
627C2C11×#340011yescharacteristic
628C2C11×#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
2. C11×#2365C2semidirect
3. C11×#2097C2semidirect
5. C11×#2043C2semidirect
8. C11×#1927C2semidirect
10. C11×#1921C2semidirect
11. C11×#1917C2semidirect
14. C11×#1805C2semidirect
15. C11×#1763C2semidirect
126. #27084C11direct (N × H)
208. #2365C2×C11semidirect
209. #2097C2×C11semidirect
211. #2043C2×C11semidirect
214. #1927C2×C11semidirect
216. #1921C2×C11semidirect
217. #1917C2×C11semidirect
220. #1805C2×C11semidirect
221. #1763C2×C11semidirect
520. C11#27084direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25132
C11×#23652
C11×#20972
C11×#20552
C11×#20432
C11×#20132
C11×#19732
C11×#19272
C11×#19262
C11×#19212
C11×#19172
C11×#18802
C11×#18052
C11×#17632
#2708411