Finite Group Databasebeta

← C11×#23832 #14601025

Subgroups — C11×#23832 #14601025

Order 2816.

730 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2330C211yesmaximal, characteristic, complemented
2C11×#2326C211yesmaximal, characteristic
3C11×#2100C211yesmaximal, characteristic, complemented
4C11×#2099C211yesmaximal, characteristic, complemented
5C11×#2072C211yesmaximal, characteristic, complemented
6C11×#2071C211yesmaximal, characteristic
7C11×#2042C211yesmaximal, characteristic
8C11×#2042C211yesmaximal, characteristic
9C11×#2026C211yesmaximal, characteristic, complemented
10C11×#2025C211yesmaximal, characteristic
11C11×#1763C211yesmaximal, characteristic, complemented
12C11×#1762C211yesmaximal, characteristic
13C4×C11×#103C211yesmaximal, characteristic, complemented
14C4×C11×#102C211yesmaximal, characteristic
15C11×#1746C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×C11×#124C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C11×#103C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#97C2211yescharacteristic
29C2×C4×C8×C11C2211yescharacteristic
30C11×#391C2211yescharacteristic
31C11×#390C2211yescharacteristic
32C11×#389—21no—
33C11×#389—21no—
34C11×#389C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#388—21no—
37C11×#388—21no—
38C11×#387—21no—
39C11×#387—21no—
40C11×#385—21no—
41C11×#385—21no—
42C11×#384C2211yescharacteristic
43C11×#384C2211yescharacteristic
44C4×C11×C4⋊C4C2211yescharacteristic
45C4×C11×C4⋊C4C2211yescharacteristic
46C11×#376C2211yescharacteristic
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×#125—22no—
67C11×#125—22no—
68C11×#124—22no—
69C11×#124—22no—
70C4×Q8×C11—22no—
71C4×Q8×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
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⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C42×C11—21no—
95C2×C42×C11—21no—
96C2×C42×C11—21no—
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C11×#103—22no—
101C11×#103—22no—
102C11×#103—22no—
103C11×#103—22no—
104C11×#102—22no—
105C11×#102—22no—
106C11×#102—22no—
107C11×#102—22no—
108C11×#97—22no—
109C4×C8×C11—22no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95D411yescharacteristic
117C11×#95D411yescharacteristic
118C11×#95D411yescharacteristic
119C11×#95D411yescharacteristic
120#23832C1111yesmaximal, characteristic, direct product factor, Sylow
121C24×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11#4112yes—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11#4112yes—
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—42no—
142C22×C4×C11—81no—
143C22×C4×C11—81no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
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—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
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—42no—
176C11×C4⋊C4—81no—
177C11×C4⋊C4—81no—
178C11×C4⋊C4—81no—
179C11×C4⋊C4—81no—
180C11×C4⋊C4—81no—
181C11×C4⋊C4—81no—
182C11×C4⋊C4#4112yes—
183C11×C4⋊C4#4112yes—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—81no—
188C11×C22⋊C4—81no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—42no—
194C42×C11—81no—
195C42×C11—81no—
196C42×C11#4112yes—
197C42×C11#4112yes—
198#2330C2×C1111yescharacteristic, complemented
199#2326C2×C1111yescharacteristic
200#2100C2×C1111yescharacteristic, complemented
201#2099C2×C1111yescharacteristic, complemented
202#2072C2×C1111yescharacteristic, complemented
203#2071C2×C1111yescharacteristic
204#2042C2×C1111yescharacteristic
205#2042C2×C1111yescharacteristic
206#2026C2×C1111yescharacteristic, complemented
207#2025C2×C1111yescharacteristic
208#1763C2×C1111yescharacteristic, complemented
209#1762C2×C1111yescharacteristic
210C4×#103C2×C1111yescharacteristic, complemented
211C4×#102C2×C1111yescharacteristic
212#1746C2×C1111yescharacteristic, complemented
213C23×C11—22no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11C22×D411yescharacteristic
221Q8×C11—22no—
222Q8×C11—22no—
223Q8×C11—41no—
224Q8×C11—41no—
225D4×C11—22no—
226D4×C11—22no—
227D4×C11—41no—
228D4×C11—41no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
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—84no—
267C2×C4×C11#12412yes—
268C2×C4×C11#12412yes—
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C8×C11—41no—
276C8×C11—41no—
277C8×C11—41no—
278C8×C11—41no—
279C2×#125C22×C1111yescharacteristic
280C2×#124C22×C1111yescharacteristic
281C2×C4×Q8C22×C1111yescharacteristic
282C2×C4×D4C22×C1111yescharacteristic
283C2×#103C22×C1111yescharacteristic
284C2×#103C22×C1111yescharacteristic
285C2×#103C22×C1111yescharacteristic
286C2×#103C22×C1111yescharacteristic
287C2×#102C22×C1111yescharacteristic
288C2×#102C22×C1111yescharacteristic
289C2×#102C22×C1111yescharacteristic
290C2×#102C22×C1111yescharacteristic
291C2×#97C22×C1111yescharacteristic
292C2×C4×C8C22×C1111yescharacteristic
293#391C22×C1111yescharacteristic
294#390C22×C1111yescharacteristic
295#389—21no—
296#389—21no—
297#389C22×C1111yescharacteristic
298#389C22×C1111yescharacteristic
299#388—21no—
300#388—21no—
301#387—21no—
302#387—21no—
303#385—21no—
304#385—21no—
305#384C22×C1111yescharacteristic
306#384C22×C1111yescharacteristic
307C4×C4⋊C4C22×C1111yescharacteristic
308C4×C4⋊C4C22×C1111yescharacteristic
309#376C22×C1111yescharacteristic
310#340C22×C1111yescharacteristic
311#340C22×C1111yescharacteristic
312#340C22×C1111yescharacteristic
313#340C22×C1111yescharacteristic
314#340C22×C1111yescharacteristic
315#340C22×C1111yescharacteristic
316#340C22×C1111yescharacteristic
317#340C22×C1111yescharacteristic
318#336C22×C1111yescharacteristic
319#336C22×C1111yescharacteristic
320#336C22×C1111yescharacteristic
321#336C22×C1111yescharacteristic
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11#52511yescharacteristic
330C22×C11#52511yescharacteristic
331C22×C11C2×#12411yescharacteristic
332C22×C11#57611yescharacteristic
333C22×C11#57711yescharacteristic
334C22×C11#57711yescharacteristic
335C22×C11#57811yescharacteristic
336C4×C11—22no—
337C4×C11—22no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—42no—
342C4×C11—41no—
343C4×C11—42no—
344C4×C11—42no—
345C4×C11—81no—
346C4×C11—81no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11#52911yescharacteristic
350C4×C11#52911yescharacteristic
351C4×C11#52911yescharacteristic
352C4×C11#52911yescharacteristic
353C22×Q8C23×C1111yescharacteristic
354C22×D4C23×C1111yescharacteristic
355C23×C4—21no—
356C22×C8C23×C1111yescharacteristic
357C22×C8C23×C1111yescharacteristic
358C22×C8C23×C1111yescharacteristic
359C22×C8C23×C1111yescharacteristic
360#125—22no—
361#125—22no—
362#124—22no—
363#124—22no—
364C4×Q8—22no—
365C4×Q8—22no—
366C4×D4—22no—
367C4×D4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4C23×C1111yescharacteristic
378C2×C4⋊C4C23×C1111yescharacteristic
379C2×C4⋊C4C23×C1111yescharacteristic
380C2×C4⋊C4C23×C1111yescharacteristic
381C2×C4⋊C4C23×C1111yescharacteristic
382C2×C4⋊C4C23×C1111yescharacteristic
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42C23×C1111yescharacteristic
392C2×C42C23×C1111yescharacteristic
393C2×C42C23×C1111yescharacteristic
394#103—22no—
395#103—22no—
396#103—22no—
397#103—22no—
398#102—22no—
399#102—22no—
400#102—22no—
401#102—22no—
402#97—22no—
403C4×C8—22no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95D4×C1111yescharacteristic
411#95D4×C1111yescharacteristic
412#95D4×C1111yescharacteristic
413#95D4×C1111yescharacteristic
414C2×C11—82no—
415C2×C11#239811yescharacteristic
416C2×C11#311911yescharacteristic
417C2×C11#312011yescharacteristic
418C2×C11#312411yescharacteristic
419C2×C11#312511yescharacteristic
420C2×C11#313611yescharacteristic
421C2×C11#313711yescharacteristic
422C24—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8C11×#4112yes—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4C11×#4112yes—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—42no—
443C22×C4—81no—
444C22×C4—81no—
445C22×C4C2×D4×C1111yescharacteristic
446C22×C4C2×D4×C1111yescharacteristic
447C22×C4C2×D4×C1111yescharacteristic
448C22×C4C2×D4×C1111yescharacteristic
449C22×C4C2×D4×C1111yescharacteristic
450C22×C4C2×D4×C1111yescharacteristic
451C22×C4C24×C1111yescharacteristic
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C4⋊C4—24no—
465C4⋊C4—24no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—42no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4—81no—
481C4⋊C4—81no—
482C4⋊C4—81no—
483C4⋊C4C11×#4112yes—
484C4⋊C4C11×#4112yes—
485C22⋊C4—24no—
486C22⋊C4—24no—
487C22⋊C4—42no—
488C22⋊C4—81no—
489C22⋊C4—81no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—42no—
495C42—81no—
496C42—81no—
497C42C11×#4112yes—
498C42C11×#4112yes—
499C11#2383211yescharacteristic, direct product factor, Sylow
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23C22×D4×C1111yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—41no—
511Q8—41no—
512D4—22no—
513D4—22no—
514D4—41no—
515D4—41no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—84no—
554C2×C4C11×#12412yes—
555C2×C4C11×#12412yes—
556C2×C4C2×C11×#4111yescharacteristic
557C2×C4C2×C11×#4111yescharacteristic
558C2×C4C2×C11×#4111yescharacteristic
559C2×C4C2×C11×#4111yescharacteristic
560C2×C4C2×C11×#4111yescharacteristic
561C2×C4C2×C11×#4111yescharacteristic
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22C11×#52511yescharacteristic
574C22C11×#52511yescharacteristic
575C22C2×C11×#12411yescharacteristic
576C22C11×#57611yescharacteristic
577C22C11×#57711yescharacteristic
578C22C11×#57711yescharacteristic
579C22C11×#57811yescharacteristic
580C4—22no—
581C4—22no—
582C4—42no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—42no—
587C4—41no—
588C4—42no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4C11×#52911yescharacteristic
594C4C11×#52911yescharacteristic
595C4C11×#52911yescharacteristic
596C4C11×#52911yescharacteristic
597C2—82no—
598C2C11×#239811yescharacteristic
599C2C11×#311911yescharacteristic
600C2C11×#312011yescharacteristic
601C2C11×#312411yescharacteristic
602C2C11×#312511yescharacteristic
603C2C11×#313611yescharacteristic
604C2C11×#313711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C11×#376 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2330C2semidirect
3. C11×#2100C2semidirect
4. C11×#2099C2semidirect
5. C11×#2072C2semidirect
9. C11×#2026C2semidirect
11. C11×#1763C2semidirect
13. C4×C11×#103C2semidirect
15. C11×#1746C2semidirect
120. #23832C11direct (N × H)
198. #2330C2×C11semidirect
200. #2100C2×C11semidirect
201. #2099C2×C11semidirect
202. #2072C2×C11semidirect
206. #2026C2×C11semidirect
208. #1763C2×C11semidirect
210. C4×#103C2×C11semidirect
212. #1746C2×C11semidirect
499. C11#23832direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23302
C11×#23262
C11×#21002
C11×#20992
C11×#20722
C11×#20712
C11×#20422
C11×#20262
C11×#20252
C11×#17632
C11×#17622
C4×C11×#1032
C4×C11×#1022
C11×#17462
#2383211