Finite Group Databasebeta

← C11×#23771 #14600964

Subgroups — C11×#23771 #14600964

Order 2816.

750 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2324C211yesmaximal, characteristic
2C11×#2314C211yesmaximal, characteristic, complemented
3C11×#2101C211yesmaximal, characteristic, complemented
4C11×#2092C211yesmaximal, characteristic, complemented
5C11×#2084C211yesmaximal, characteristic, complemented
6C11×#2077C211yesmaximal, characteristic, complemented
7C11×#2075C211yesmaximal, characteristic, complemented
8C11×#2071C211yesmaximal, characteristic, complemented
9C11×#2034C211yesmaximal, characteristic
10C11×#2034C211yesmaximal, characteristic
11C11×#1776C211yesmaximal, characteristic, complemented
12C4×C11×#106C211yesmaximal, characteristic, complemented
13C11×#1762C211yesmaximal, characteristic, complemented
14C4×C11×#102C211yesmaximal, characteristic, complemented
15C11×#1750C211yesmaximal, characteristic, complemented
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C11×#97C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31C11×#390—21no—
32C11×#390C2211yescharacteristic
33C11×#389C2211yescharacteristic
34C11×#388—21no—
35C11×#388—21no—
36C11×#388—21no—
37C11×#387—21no—
38C11×#387—21no—
39C11×#386—21no—
40C11×#385—21no—
41C11×#384C2211yescharacteristic
42C11×#382C2211yescharacteristic
43C11×#380C2211yescharacteristic
44C11×#380C2211yescharacteristic
45C11×#380C2211yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#121—22no—
68C11×#121—22no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C11×#117—22no—
72C11×#117—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C42×C11—21no—
95C2×C42×C11—21no—
96C2×C42×C11—21no—
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C11×#107—22no—
100C11×#106—22no—
101C11×#106—22no—
102C11×#106—22no—
103C11×#102—22no—
104C11×#102—22no—
105C11×#102—22no—
106C11×#102—22no—
107C11×C22⋊C8—22no—
108C11×C22⋊C8—22no—
109C11×#97—22no—
110C4×C8×C11—22no—
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—
120#23771C1111yesmaximal, characteristic, direct product factor, Sylow
121C24×C11—21no—
122C24×C11C2×D411yescharacteristic
123C2×D4×C11—24no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—81no—
130C2×D4×C11—81no—
131C2×D4×C11#4112yes—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—42no—
146C22×C4×C11—81no—
147C22×C4×C11—81no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11#4112yes—
165C2×C8×C11#4112yes—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—81no—
182C11×C4⋊C4—81no—
183C11×C4⋊C4—81no—
184C11×C4⋊C4#4112yes—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—42no—
189C11×C22⋊C4—81no—
190C11×C22⋊C4—81no—
191C11×C22⋊C4—81no—
192C11×C22⋊C4—81no—
193C11×C22⋊C4—81no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—81no—
197C42×C11—81no—
198C42×C11—81no—
199C42×C11#4112yes—
200C42×C11#4112yes—
201#2324C2×C1111yescharacteristic
202#2314C2×C1111yescharacteristic, complemented
203#2101C2×C1111yescharacteristic, complemented
204#2092C2×C1111yescharacteristic, complemented
205#2084C2×C1111yescharacteristic, complemented
206#2077C2×C1111yescharacteristic, complemented
207#2075C2×C1111yescharacteristic, complemented
208#2071C2×C1111yescharacteristic, complemented
209#2034C2×C1111yescharacteristic
210#2034C2×C1111yescharacteristic
211#1776C2×C1111yescharacteristic, complemented
212C4×#106C2×C1111yescharacteristic, complemented
213#1762C2×C1111yescharacteristic, complemented
214C4×#102C2×C1111yescharacteristic, complemented
215#1750C2×C1111yescharacteristic, complemented
216C23×C11—21no—
217C23×C11—22no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11C22×D411yescharacteristic
231D4×C11—22no—
232D4×C11—22no—
233D4×C11—41no—
234D4×C11—41no—
235D4×C11—84no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
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—21no—
249C2×C4×C11—21no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
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—84no—
275C2×C4×C11#12312yes—
276C2×C4×C11#12312yes—
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C8×C11—22no—
284C8×C11—22no—
285C8×C11—41no—
286C8×C11—41no—
287C2×#121C22×C1111yescharacteristic
288C2×C4×D4C22×C1111yescharacteristic
289C2×#117C22×C1111yescharacteristic
290C2×#107C22×C1111yescharacteristic
291C2×#106C22×C1111yescharacteristic
292C2×#106C22×C1111yescharacteristic
293C2×#106C22×C1111yescharacteristic
294C2×#102C22×C1111yescharacteristic
295C2×#102C22×C1111yescharacteristic
296C2×#102C22×C1111yescharacteristic
297C2×#102C22×C1111yescharacteristic
298C2×C22⋊C8C22×C1111yescharacteristic
299C2×C22⋊C8C22×C1111yescharacteristic
300C2×#97C22×C1111yescharacteristic
301C2×C4×C8C22×C1111yescharacteristic
302#390—21no—
303#390C22×C1111yescharacteristic
304#389C22×C1111yescharacteristic
305#388—21no—
306#388—21no—
307#388—21no—
308#387—21no—
309#387—21no—
310#386—21no—
311#385—21no—
312#384C22×C1111yescharacteristic
313#382C22×C1111yescharacteristic
314#380C22×C1111yescharacteristic
315#380C22×C1111yescharacteristic
316#380C22×C1111yescharacteristic
317C4×C4⋊C4C22×C1111yescharacteristic
318C4×C4⋊C4C22×C1111yescharacteristic
319C4×C4⋊C4C22×C1111yescharacteristic
320#340C22×C1111yescharacteristic
321#340C22×C1111yescharacteristic
322#340C22×C1111yescharacteristic
323#340C22×C1111yescharacteristic
324#340C22×C1111yescharacteristic
325#340C22×C1111yescharacteristic
326#340C22×C1111yescharacteristic
327#340C22×C1111yescharacteristic
328#336C22×C1111yescharacteristic
329#336C22×C1111yescharacteristic
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—42no—
334C22×C11—41no—
335C22×C11—42no—
336C22×C11—41no—
337C22×C11—42no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11C2×#12311yescharacteristic
345C22×C11#52511yescharacteristic
346C22×C11#53211yescharacteristic
347C22×C11#57611yescharacteristic
348C22×C11#57711yescharacteristic
349C22×C11#57711yescharacteristic
350C22×C11#57711yescharacteristic
351C4×C11—22no—
352C4×C11—22no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—42no—
356C4×C11—41no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11—81no—
360C4×C11—81no—
361C4×C11—81no—
362C4×C11—81no—
363C4×C11#52911yescharacteristic
364C4×C11#52911yescharacteristic
365C4×C11#52911yescharacteristic
366C4×C11#52911yescharacteristic
367C22×D4—21no—
368C22×D4C23×C1111yescharacteristic
369C23×C4—21no—
370C23×C4C23×C1111yescharacteristic
371C22×C8C23×C1111yescharacteristic
372C22×C8C23×C1111yescharacteristic
373C22×C8C23×C1111yescharacteristic
374C22×C8C23×C1111yescharacteristic
375#121—22no—
376#121—22no—
377C4×D4—22no—
378C4×D4—22no—
379#117—22no—
380#117—22no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4D4×C1111yescharacteristic
385C2×C4⋊C4D4×C1111yescharacteristic
386C2×C4⋊C4C23×C1111yescharacteristic
387C2×C4⋊C4C23×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×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4D4×C1111yescharacteristic
401C2×C22⋊C4D4×C1111yescharacteristic
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42C23×C1111yescharacteristic
406C2×C42C23×C1111yescharacteristic
407#107—22no—
408#106—22no—
409#106—22no—
410#106—22no—
411#102—22no—
412#102—22no—
413#102—22no—
414#102—22no—
415C22⋊C8—22no—
416C22⋊C8—22no—
417#97—22no—
418C4×C8—22no—
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—
428C2×C11—81no—
429C2×C11—82no—
430C2×C11#239511yescharacteristic
431C2×C11#309611yescharacteristic
432C2×C11#309911yescharacteristic
433C2×C11#311911yescharacteristic
434C2×C11#312311yescharacteristic
435C2×C11#317311yescharacteristic
436C2×C11#317911yescharacteristic
437C24—21no—
438C24C2×D4×C1111yescharacteristic
439C2×D4—24no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—81no—
446C2×D4—81no—
447C2×D4C11×#4112yes—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—42no—
462C22×C4—81no—
463C22×C4—81no—
464C22×C4C2×D4×C1111yescharacteristic
465C22×C4C2×D4×C1111yescharacteristic
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C2×D4×C1111yescharacteristic
468C22×C4C2×D4×C1111yescharacteristic
469C22×C4C24×C1111yescharacteristic
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8C11×#4112yes—
481C2×C8C11×#4112yes—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—81no—
498C4⋊C4—81no—
499C4⋊C4—81no—
500C4⋊C4C11×#4112yes—
501C22⋊C4—24no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—42no—
505C22⋊C4—81no—
506C22⋊C4—81no—
507C22⋊C4—81no—
508C22⋊C4—81no—
509C22⋊C4—81no—
510C42—21no—
511C42—21no—
512C42—81no—
513C42—81no—
514C42—81no—
515C42C11×#4112yes—
516C42C11×#4112yes—
517C11#2377111yescharacteristic, direct product factor, Sylow
518C23—21no—
519C23—22no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23C22×D4×C1111yescharacteristic
533D4—22no—
534D4—22no—
535D4—41no—
536D4—41no—
537D4—84no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
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—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
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×#12312yes—
578C2×C4C11×#12312yes—
579C2×C4C2×C11×#4111yescharacteristic
580C2×C4C2×C11×#4111yescharacteristic
581C2×C4C2×C11×#4111yescharacteristic
582C2×C4C2×C11×#4111yescharacteristic
583C2×C4C2×C11×#4111yescharacteristic
584C2×C4C2×C11×#4111yescharacteristic
585C8—22no—
586C8—22no—
587C8—41no—
588C8—41no—
589C22—41no—
590C22—42no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—42no—
597C22—41no—
598C22—42no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22C2×C11×#12311yescharacteristic
604C22C11×#52511yescharacteristic
605C22C11×#53211yescharacteristic
606C22C11×#57611yescharacteristic
607C22C11×#57711yescharacteristic
608C22C11×#57711yescharacteristic
609C22C11×#57711yescharacteristic
610C4—22no—
611C4—22no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—42no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4—81no—
620C4—81no—
621C4—81no—
622C4C11×#52911yescharacteristic
623C4C11×#52911yescharacteristic
624C4C11×#52911yescharacteristic
625C4C11×#52911yescharacteristic
626C2—81no—
627C2—82no—
628C2C11×#239511yescharacteristic
629C2C11×#309611yescharacteristic
630C2C11×#309911yescharacteristic
631C2C11×#311911yescharacteristic
632C2C11×#312311yescharacteristic
633C2C11×#317311yescharacteristic
634C2C11×#317911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2314C2semidirect
3. C11×#2101C2semidirect
4. C11×#2092C2semidirect
5. C11×#2084C2semidirect
6. C11×#2077C2semidirect
7. C11×#2075C2semidirect
8. C11×#2071C2semidirect
11. C11×#1776C2semidirect
12. C4×C11×#106C2semidirect
13. C11×#1762C2semidirect
14. C4×C11×#102C2semidirect
15. C11×#1750C2semidirect
120. #23771C11direct (N × H)
202. #2314C2×C11semidirect
203. #2101C2×C11semidirect
204. #2092C2×C11semidirect
205. #2084C2×C11semidirect
206. #2077C2×C11semidirect
207. #2075C2×C11semidirect
208. #2071C2×C11semidirect
211. #1776C2×C11semidirect
212. C4×#106C2×C11semidirect
213. #1762C2×C11semidirect
214. C4×#102C2×C11semidirect
215. #1750C2×C11semidirect
517. C11#23771direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23242
C11×#23142
C11×#21012
C11×#20922
C11×#20842
C11×#20772
C11×#20752
C11×#20712
C11×#20342
C11×#17762
C4×C11×#1062
C11×#17622
C4×C11×#1022
C11×#17502
#2377111