Finite Group Databasebeta

← C11×#23809 #14601002

Subgroups — C11×#23809 #14601002

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#441C211yesmaximal, characteristic, complemented
2C2×C11×#440C211yesmaximal, characteristic
3C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
4C2×C4×C11×SD16C211yesmaximal, characteristic
5C11×#2327C211yesmaximal, characteristic, complemented
6C11×#2326C211yesmaximal, characteristic
7C11×#2097C211yesmaximal, characteristic, complemented
8C11×#2096C211yesmaximal, characteristic, complemented
9C11×#2095C211yesmaximal, characteristic, complemented
10C11×#2092C211yesmaximal, characteristic
11C11×#2016C211yesmaximal, characteristic, complemented
12C11×#2015C211yesmaximal, characteristic
13C11×#2015C211yesmaximal, characteristic
14C11×#2013C211yesmaximal, characteristic
15C11×#1746C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C11×#441—24no—
27C11×#440—24no—
28C4×C11×Q16—24no—
29C4×C11×SD16—24no—
30C2×C11×#107C2211yescharacteristic
31C2×C11×#107C2211yescharacteristic
32C2×C11×#106C2211yescharacteristic
33C2×C11×#106C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#97C2211yescharacteristic
43C2×C4×C8×C11C2211yescharacteristic
44C11×#391C2211yescharacteristic
45C11×#391C2211yescharacteristic
46C11×#391C2211yescharacteristic
47C11×#390C2211yescharacteristic
48C11×#388—22no—
49C11×#387—22no—
50C11×#387—22no—
51C11×#385—22no—
52C11×#384C2211yescharacteristic
53C11×#382C2211yescharacteristic
54C11×#376C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C2×C11×Q16—22no—
65C2×C11×Q16—22no—
66C2×C11×Q16—22no—
67C2×C11×Q16—22no—
68C2×C11×Q16—22no—
69C2×C11×Q16—22no—
70C2×C11×SD16—22no—
71C2×C11×SD16—22no—
72C2×C11×SD16—22no—
73C2×C11×SD16—22no—
74C2×C11×SD16—22no—
75C2×C11×SD16—22no—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C11×C4⋊Q8—22no—
81C11×C4⋊Q8—22no—
82C11×#124—22no—
83C11×#124—22no—
84C4×Q8×C11—22no—
85C4×Q8×C11—22no—
86C4×Q8×C11—22no—
87C4×Q8×C11—22no—
88C4×Q8×C11—22no—
89C4×Q8×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—22no—
104C2×C42×C11—21no—
105C2×C42×C11—21no—
106C2×C42×C11—21no—
107C2×C42×C11C2311yescharacteristic
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C11×#107—22no—
111C11×#107—22no—
112C11×#106—22no—
113C11×#106—22no—
114C11×#103—22no—
115C11×#103—22no—
116C11×#103—22no—
117C11×#103—22no—
118C11×#103—22no—
119C11×#103—22no—
120C11×#102—22no—
121C11×#102—22no—
122C11×#97D414yes—
123C4×C8×C11D414yes—
124C11×#95—22no—
125C11×#95—22no—
126C11×#95—22no—
127C11×#95—22no—
128C11×#95D412yes—
129C11×#95D412yes—
130#23809C1111yesmaximal, characteristic, direct product factor, Sylow
131C24×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—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11#4112yes—
148C2×Q8×C11#4112yes—
149C2×Q8×C11#4112yes—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11#4112yes—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—42no—
164C22×C4×C11—82no—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2411yescharacteristic
170C11×Q16—28no—
171C11×Q16—28no—
172C11×SD16—28no—
173C11×SD16—28no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11C2×D412yes—
183C2×C8×C11C2×D412yes—
184C2×C8×C11C2×D412yes—
185C2×C8×C11C2×D412yes—
186C11×C4⋊C4—28no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—42no—
196C11×C4⋊C4—42no—
197C11×C4⋊C4—42no—
198C11×C4⋊C4—82no—
199C11×C22⋊C4—28no—
200C11×C22⋊C4—42no—
201C11×C22⋊C4—82no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—42no—
207C42×C11—42no—
208C42×C11—42no—
209C42×C11C2×D412yes—
210C42×C11C2×D412yes—
211C2×#441C2×C1111yescharacteristic, complemented
212C2×#440C2×C1111yescharacteristic
213C2×C4×Q16C2×C1111yescharacteristic, complemented
214C2×C4×SD16C2×C1111yescharacteristic
215#2327C2×C1111yescharacteristic, complemented
216#2326C2×C1111yescharacteristic
217#2097C2×C1111yescharacteristic, complemented
218#2096C2×C1111yescharacteristic, complemented
219#2095C2×C1111yescharacteristic, complemented
220#2092C2×C1111yescharacteristic
221#2016C2×C1111yescharacteristic, complemented
222#2015C2×C1111yescharacteristic
223#2015C2×C1111yescharacteristic
224#2013C2×C1111yescharacteristic
225#1746C2×C1111yescharacteristic, complemented
226C23×C11—22no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11C22×D411yescharacteristic
232Q8×C11—22no—
233Q8×C11—22no—
234Q8×C11—22no—
235Q8×C11—22no—
236Q8×C11—22no—
237Q8×C11—22no—
238Q8×C11—41no—
239Q8×C11—41no—
240Q8×C11—41no—
241Q8×C11—41no—
242Q8×C11—41no—
243Q8×C11—41no—
244D4×C11—22no—
245D4×C11—22no—
246D4×C11—41no—
247D4×C11—41no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
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—42no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—84no—
274C2×C4×C11#12712yes—
275C2×C4×C11#12712yes—
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C8×C11—22no—
283C8×C11—22no—
284C8×C11—22no—
285C8×C11—22no—
286C22×Q16C22×C1111yescharacteristic
287C22×Q16C22×C1111yescharacteristic
288C22×SD16C22×C1111yescharacteristic
289C22×SD16C22×C1111yescharacteristic
290C2×C4⋊Q8C22×C1111yescharacteristic
291C2×#124C22×C1111yescharacteristic
292C2×C4×Q8C22×C1111yescharacteristic
293C2×C4×Q8C22×C1111yescharacteristic
294C2×C4×Q8C22×C1111yescharacteristic
295C2×C4×D4C22×C1111yescharacteristic
296#441—24no—
297#440—24no—
298C4×Q16—24no—
299C4×SD16—24no—
300C2×#107C22×C1111yescharacteristic
301C2×#107C22×C1111yescharacteristic
302C2×#106C22×C1111yescharacteristic
303C2×#106C22×C1111yescharacteristic
304C2×#103C22×C1111yescharacteristic
305C2×#103C22×C1111yescharacteristic
306C2×#103C22×C1111yescharacteristic
307C2×#103C22×C1111yescharacteristic
308C2×#103C22×C1111yescharacteristic
309C2×#103C22×C1111yescharacteristic
310C2×#102C22×C1111yescharacteristic
311C2×#102C22×C1111yescharacteristic
312C2×#97C22×C1111yescharacteristic
313C2×C4×C8C22×C1111yescharacteristic
314#391C22×C1111yescharacteristic
315#391C22×C1111yescharacteristic
316#391C22×C1111yescharacteristic
317#390C22×C1111yescharacteristic
318#388—22no—
319#387—22no—
320#387—22no—
321#385—22no—
322#384C22×C1111yescharacteristic
323#382C22×C1111yescharacteristic
324#376C22×C1111yescharacteristic
325#336C22×C1111yescharacteristic
326#336C22×C1111yescharacteristic
327#336C22×C1111yescharacteristic
328#336C22×C1111yescharacteristic
329C22×C11—44no—
330C22×C11—42no—
331C22×C11—82no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11#52511yescharacteristic
335C22×C11#52511yescharacteristic
336C22×C11C2×#12711yescharacteristic
337C22×C11#57712yes—
338C22×C11#57812yes—
339C4×C11—22no—
340C4×C11—22no—
341C4×C11—42no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11—42no—
345C4×C11—42no—
346C4×C11—81no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11—81no—
350C4×C11#52511yescharacteristic
351C4×C11#52511yescharacteristic
352C4×C11#52511yescharacteristic
353C4×C11#52511yescharacteristic
354C22×Q8C23×C1111yescharacteristic
355C22×Q8C23×C1111yescharacteristic
356C22×Q8C23×C1111yescharacteristic
357C22×D4C23×C1111yescharacteristic
358C23×C4—21no—
359C2×Q16—22no—
360C2×Q16—22no—
361C2×Q16—22no—
362C2×Q16—22no—
363C2×Q16—22no—
364C2×Q16—22no—
365C2×SD16—22no—
366C2×SD16—22no—
367C2×SD16—22no—
368C2×SD16—22no—
369C2×SD16—22no—
370C2×SD16—22no—
371C22×C8C23×C1111yescharacteristic
372C22×C8C23×C1111yescharacteristic
373C22×C8C23×C1111yescharacteristic
374C22×C8C23×C1111yescharacteristic
375C4⋊Q8—22no—
376C4⋊Q8—22no—
377#124—22no—
378#124—22no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—22no—
385C4×D4—22no—
386C4×D4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4C23×C1111yescharacteristic
393C2×C4⋊C4C23×C1111yescharacteristic
394C2×C4⋊C4C23×C1111yescharacteristic
395C2×C4⋊C4C23×C1111yescharacteristic
396C2×C22⋊C4—22no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—22no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42C23×C1111yescharacteristic
403C2×C42C23×C1111yescharacteristic
404C2×C42C23×C1111yescharacteristic
405#107—22no—
406#107—22no—
407#106—22no—
408#106—22no—
409#103—22no—
410#103—22no—
411#103—22no—
412#103—22no—
413#103—22no—
414#103—22no—
415#102—22no—
416#102—22no—
417#97D4×C1114yes—
418C4×C8D4×C1114yes—
419#95—22no—
420#95—22no—
421#95—22no—
422#95—22no—
423#95D4×C1112yes—
424#95D4×C1112yes—
425C2×C11—82no—
426C2×C11#239711yescharacteristic
427C2×C11#312012yes—
428C2×C11#312112yes—
429C2×C11#315411yescharacteristic
430C2×C11#315611yescharacteristic
431C24—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8C11×#4112yes—
448C2×Q8C11×#4112yes—
449C2×Q8C11×#4112yes—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4C11×#4112yes—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—42no—
464C22×C4—82no—
465C22×C4C2×D4×C1112yes—
466C22×C4C2×D4×C1112yes—
467C22×C4C2×D4×C1111yescharacteristic
468C22×C4C2×D4×C1111yescharacteristic
469C22×C4C24×C1111yescharacteristic
470Q16—28no—
471Q16—28no—
472SD16—28no—
473SD16—28no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8C2×D4×C1112yes—
483C2×C8C2×D4×C1112yes—
484C2×C8C2×D4×C1112yes—
485C2×C8C2×D4×C1112yes—
486C4⋊C4—28no—
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—42no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—82no—
499C22⋊C4—28no—
500C22⋊C4—42no—
501C22⋊C4—82no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—42no—
507C42—42no—
508C42—42no—
509C42C2×D4×C1112yes—
510C42C2×D4×C1112yes—
511C11#2380911yescharacteristic, direct product factor, Sylow
512C23—22no—
513C23—41no—
514C23—41no—
515C23—42no—
516C23—42no—
517C23C22×D4×C1111yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—22no—
521Q8—22no—
522Q8—22no—
523Q8—22no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530D4—22no—
531D4—22no—
532D4—41no—
533D4—41no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
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—41no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—84no—
560C2×C4C11×#12712yes—
561C2×C4C11×#12712yes—
562C2×C4C22×D4×C1111yescharacteristic
563C2×C4C22×D4×C1111yescharacteristic
564C2×C4C2×C11×#4111yescharacteristic
565C2×C4C2×C11×#4111yescharacteristic
566C2×C4C2×C11×#4111yescharacteristic
567C2×C4C2×C11×#4111yescharacteristic
568C8—22no—
569C8—22no—
570C8—22no—
571C8—22no—
572C22—42no—
573C22—44no—
574C22—81no—
575C22—81no—
576C22—82no—
577C22C11×#52511yescharacteristic
578C22C11×#52511yescharacteristic
579C22C2×C11×#12711yescharacteristic
580C22C11×#57712yes—
581C22C11×#57812yes—
582C4—22no—
583C4—22no—
584C4—42no—
585C4—42no—
586C4—42no—
587C4—42no—
588C4—42no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4C11×#52511yescharacteristic
594C4C11×#52511yescharacteristic
595C4C11×#52511yescharacteristic
596C4C11×#52511yescharacteristic
597C2—82no—
598C2C11×#239711yescharacteristic
599C2C11×#312012yes—
600C2C11×#312112yes—
601C2C11×#315411yescharacteristic
602C2C11×#315611yescharacteristic
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. C2×C11×#441C2semidirect
3. C2×C4×C11×Q16C2semidirect
5. C11×#2327C2semidirect
7. C11×#2097C2semidirect
8. C11×#2096C2semidirect
9. C11×#2095C2semidirect
11. C11×#2016C2semidirect
15. C11×#1746C2semidirect
130. #23809C11direct (N × H)
211. C2×#441C2×C11semidirect
213. C2×C4×Q16C2×C11semidirect
215. #2327C2×C11semidirect
217. #2097C2×C11semidirect
218. #2096C2×C11semidirect
219. #2095C2×C11semidirect
221. #2016C2×C11semidirect
225. #1746C2×C11semidirect
511. C11#23809direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4412
C2×C11×#4402
C2×C4×C11×Q162
C2×C4×C11×SD162
C11×#23272
C11×#23262
C11×#20972
C11×#20962
C11×#20952
C11×#20922
C11×#20162
C11×#20152
C11×#20132
C11×#17462
#2380911