Finite Group Databasebeta

← C11×#24616 #14601809

Subgroups — C11×#24616 #14601809

Order 2816.

756 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#483C211yesmaximal, characteristic
2C2×C11×#433C211yesmaximal, characteristic
3C11×#2625C211yesmaximal, characteristic
4C11×#2317C211yesmaximal, characteristic
5C11×#2088C211yesmaximal, characteristic, complemented
6C11×#2088C211yesmaximal, characteristic, complemented
7C11×#2068C211yesmaximal, characteristic, complemented
8C11×#2066C211yesmaximal, characteristic, complemented
9C11×#1943C211yesmaximal, characteristic, complemented
10C11×#1941C211yesmaximal, characteristic, complemented
11C11×#1935C211yesmaximal, characteristic, complemented
12C11×#1933C211yesmaximal, characteristic, complemented
13C11×#1873C211yesmaximal, characteristic
14C11×#1854C211yesmaximal, characteristic
15C11×#1824C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C11×#483—24no—
21C11×#433—24no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×#97C2211yescharacteristic
35C2×C4×C8×C11C2211yescharacteristic
36C11×#400—21no—
37C11×#398—21no—
38C11×#397—21no—
39C11×#397—21no—
40C11×#391C2211yescharacteristic
41C11×#391C2211yescharacteristic
42C11×#389C2211yescharacteristic
43C11×#389C2211yescharacteristic
44C11×#389C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#389C2211yescharacteristic
47C11×#389C2211yescharacteristic
48C11×#385—21no—
49C11×#385—21no—
50C11×#384—21no—
51C11×#382—21no—
52C11×#380C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—22no—
70C11×#117—22no—
71C11×#117—22no—
72C11×#117—22no—
73C11×#117—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—22no—
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⋊C4—21no—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4D411yescharacteristic
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C42×C11—21no—
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C11×#107—22no—
102C11×#106—22no—
103C11×#106—22no—
104C11×#106—22no—
105C11×C4⋊C8—22no—
106C11×C4⋊C8—22no—
107C11×#103—22no—
108C11×#103—22no—
109C11×#103—22no—
110C11×#103—22no—
111C11×C22⋊C8—22no—
112C11×C22⋊C8D414yes—
113C11×#97—22no—
114C4×C8×C11—22no—
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×#95—21no—
125C11×#95—21no—
126#24616C1111yesmaximal, characteristic, direct product factor, Sylow
127C24×C11C2×D411yescharacteristic
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×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—21no—
146C22×C4×C11—42no—
147C22×C4×C11—81no—
148C22×C4×C11—81no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D412yes—
155C22×C4×C11#4112yes—
156C22×C4×C11C2411yescharacteristic
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—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11C2×D412yes—
168C2×C8×C11C2×D412yes—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
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—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4—81no—
186C11×C4⋊C4—81no—
187C11×C4⋊C4—81no—
188C11×C4⋊C4—81no—
189C11×C4⋊C4—81no—
190C11×C4⋊C4—81no—
191C11×C4⋊C4#4112yes—
192C11×C4⋊C4#4112yes—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—42no—
197C11×C22⋊C4—81no—
198C42×C11—24no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—21no—
203C2×#483C2×C1111yescharacteristic
204C2×#433C2×C1111yescharacteristic
205#2625C2×C1111yescharacteristic
206#2317C2×C1111yescharacteristic
207#2088C2×C1111yescharacteristic, complemented
208#2088C2×C1111yescharacteristic, complemented
209#2068C2×C1111yescharacteristic, complemented
210#2066C2×C1111yescharacteristic, complemented
211#1943C2×C1111yescharacteristic, complemented
212#1941C2×C1111yescharacteristic, complemented
213#1935C2×C1111yescharacteristic, complemented
214#1933C2×C1111yescharacteristic, complemented
215#1873C2×C1111yescharacteristic
216#1854C2×C1111yescharacteristic
217#1824C2×C1111yescharacteristic
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11#12112yes—
225C23×C11C22×D411yescharacteristic
226Q8×C11—41no—
227Q8×C11—41no—
228Q8×C11—41no—
229Q8×C11—41no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
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—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—84no—
273C2×C4×C11#12112yes—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C112−1+411yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C8×C11—22no—
281C8×C11—22no—
282C8×C11—41no—
283C8×C11—41no—
284C2×C22⋊Q8C22×C1111yescharacteristic
285C2×#117C22×C1111yescharacteristic
286C2×#117C22×C1111yescharacteristic
287C22×C4⋊C4C22×C1111yescharacteristic
288#483—24no—
289#433—24no—
290C2×#107C22×C1111yescharacteristic
291C2×#106C22×C1111yescharacteristic
292C2×#106C22×C1111yescharacteristic
293C2×#106C22×C1111yescharacteristic
294C2×C4⋊C8C22×C1111yescharacteristic
295C2×C4⋊C8C22×C1111yescharacteristic
296C2×#103C22×C1111yescharacteristic
297C2×#103C22×C1111yescharacteristic
298C2×#103C22×C1111yescharacteristic
299C2×#103C22×C1111yescharacteristic
300C2×C22⋊C8C22×C1111yescharacteristic
301C2×C22⋊C8C22×C1111yescharacteristic
302C2×#97C22×C1111yescharacteristic
303C2×C4×C8C22×C1111yescharacteristic
304#400—21no—
305#398—21no—
306#397—21no—
307#397—21no—
308#391C22×C1111yescharacteristic
309#391C22×C1111yescharacteristic
310#389C22×C1111yescharacteristic
311#389C22×C1111yescharacteristic
312#389C22×C1111yescharacteristic
313#389C22×C1111yescharacteristic
314#389C22×C1111yescharacteristic
315#389C22×C1111yescharacteristic
316#385—21no—
317#385—21no—
318#384—21no—
319#382—21no—
320#380C22×C1111yescharacteristic
321#340C22×C1111yescharacteristic
322#340C22×C1111yescharacteristic
323#340C22×C1111yescharacteristic
324#340C22×C1111yescharacteristic
325#340C22×C1111yescharacteristic
326#340C22×C1111yescharacteristic
327#340C22×C1111yescharacteristic
328#340C22×C1111yescharacteristic
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—22no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11C2×#12111yescharacteristic
337C22×C11#52511yescharacteristic
338C22×C11#53611yescharacteristic
339C22×C11#57711yescharacteristic
340C22×C11#57711yescharacteristic
341C22×C11#57711yescharacteristic
342C22×C11#57811yescharacteristic
343C4×C11—22no—
344C4×C11—42no—
345C4×C11—42no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—81no—
351C4×C11—81no—
352C4×C11—81no—
353C4×C11—81no—
354C4×C11—81no—
355C4×C11—81no—
356C4×C11#54711yescharacteristic
357C4×C11#54711yescharacteristic
358C4×C11#55211yescharacteristic
359C4×C11#55211yescharacteristic
360C22×Q8C23×C1111yescharacteristic
361C23×C4—21no—
362C23×C4C23×C1111yescharacteristic
363C22×C8C23×C1111yescharacteristic
364C22×C8C23×C1111yescharacteristic
365C22×C8C23×C1111yescharacteristic
366C22×C8C23×C1111yescharacteristic
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369#117—22no—
370#117—22no—
371#117—22no—
372#117—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4D4×C1111yescharacteristic
384C2×C4⋊C4D4×C1111yescharacteristic
385C2×C4⋊C4C23×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×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4D4×C1111yescharacteristic
396C2×C22⋊C4D4×C1111yescharacteristic
397C2×C42—21no—
398C2×C42C23×C1111yescharacteristic
399C2×C42C23×C1111yescharacteristic
400#107—22no—
401#106—22no—
402#106—22no—
403#106—22no—
404C4⋊C8—22no—
405C4⋊C8—22no—
406#103—22no—
407#103—22no—
408#103—22no—
409#103—22no—
410C22⋊C8—22no—
411C22⋊C8D4×C1114yes—
412#97—22no—
413C4×C8—22no—
414#95—21no—
415#95—21no—
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—
425C2×C11—42no—
426C2×C11#241311yescharacteristic
427C2×C11#305711yescharacteristic
428C2×C11#306311yescharacteristic
429C2×C11#312011yescharacteristic
430C2×C11#312511yescharacteristic
431C2×C11#324211yescharacteristic
432C2×C11#324411yescharacteristic
433C24C2×D4×C1111yescharacteristic
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—42no—
453C22×C4—81no—
454C22×C4—81no—
455C22×C4C2×D4×C1111yescharacteristic
456C22×C4C2×D4×C1111yescharacteristic
457C22×C4C2×D4×C1111yescharacteristic
458C22×C4C2×D4×C1111yescharacteristic
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C2×D4×C1112yes—
461C22×C4C11×#4112yes—
462C22×C4C24×C1111yescharacteristic
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8C2×D4×C1112yes—
474C2×C8C2×D4×C1112yes—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—81no—
492C4⋊C4—81no—
493C4⋊C4—81no—
494C4⋊C4—81no—
495C4⋊C4—81no—
496C4⋊C4—81no—
497C4⋊C4C11×#4112yes—
498C4⋊C4C11×#4112yes—
499C22⋊C4—24no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—42no—
503C22⋊C4—81no—
504C42—24no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C11#2461611yescharacteristic, direct product factor, Sylow
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23C11×#12112yes—
517C23C22×D4×C1111yescharacteristic
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
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—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—84no—
565C2×C4C11×#12112yes—
566C2×C4C22×D4×C1111yescharacteristic
567C2×C4C2×C11×#4111yescharacteristic
568C2×C4C2×C11×#4111yescharacteristic
569C2×C4C2×C11×#4111yescharacteristic
570C2×C4C11×2−1+411yescharacteristic
571C2×C4C11×2−1+411yescharacteristic
572C8—22no—
573C8—22no—
574C8—41no—
575C8—41no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22C2×C11×#12111yescharacteristic
584C22C11×#52511yescharacteristic
585C22C11×#53611yescharacteristic
586C22C11×#57711yescharacteristic
587C22C11×#57711yescharacteristic
588C22C11×#57711yescharacteristic
589C22C11×#57811yescharacteristic
590C4—22no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—42no—
596C4—42no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4C11×#54711yescharacteristic
604C4C11×#54711yescharacteristic
605C4C11×#55211yescharacteristic
606C4C11×#55211yescharacteristic
607C2—42no—
608C2C11×#241311yescharacteristic
609C2C11×#305711yescharacteristic
610C2C11×#306311yescharacteristic
611C2C11×#312011yescharacteristic
612C2C11×#312511yescharacteristic
613C2C11×#324211yescharacteristic
614C2C11×#324411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
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
5. C11×#2088C2semidirect
6. C11×#2088C2semidirect
7. C11×#2068C2semidirect
8. C11×#2066C2semidirect
9. C11×#1943C2semidirect
10. C11×#1941C2semidirect
11. C11×#1935C2semidirect
12. C11×#1933C2semidirect
126. #24616C11direct (N × H)
207. #2088C2×C11semidirect
208. #2088C2×C11semidirect
209. #2068C2×C11semidirect
210. #2066C2×C11semidirect
211. #1943C2×C11semidirect
212. #1941C2×C11semidirect
213. #1935C2×C11semidirect
214. #1933C2×C11semidirect
509. C11#24616direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4832
C2×C11×#4332
C11×#26252
C11×#23172
C11×#20882
C11×#20682
C11×#20662
C11×#19432
C11×#19412
C11×#19352
C11×#19332
C11×#18732
C11×#18542
C11×#18242
#2461611