Finite Group Databasebeta

← C11×#24718 #14601911

Subgroups — C11×#24718 #14601911

Order 2816.

746 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×#475C211yesmaximal, characteristic, complemented
2C2×C11×#433C211yesmaximal, characteristic
3C11×#2628C211yesmaximal, characteristic
4C11×#2323C211yesmaximal, characteristic
5C11×#2077C211yesmaximal, characteristic
6C11×#2077C211yesmaximal, characteristic
7C11×#2036C211yesmaximal, characteristic
8C11×#2035C211yesmaximal, characteristic
9C11×#1987C211yesmaximal, characteristic, complemented
10C11×#1949C211yesmaximal, characteristic, complemented
11C11×#1943C211yesmaximal, characteristic, complemented
12C11×#1941C211yesmaximal, characteristic, complemented
13C11×#1935C211yesmaximal, characteristic, complemented
14C11×#1933C211yesmaximal, characteristic, complemented
15C11×#1805C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C11×#475—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×#399—21no—
38C11×#395—21no—
39C11×#393—21no—
40C11×#391C2211yescharacteristic
41C11×#389—21no—
42C11×#389C2211yescharacteristic
43C11×#389C2211yescharacteristic
44C11×#389C2211yescharacteristic
45C11×#388—21no—
46C11×#388—21no—
47C11×#387—21no—
48C11×#382C2211yescharacteristic
49C11×#380C2211yescharacteristic
50C11×#380C2211yescharacteristic
51C11×#380C2211yescharacteristic
52C4×C11×C4⋊C4C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8—22no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—22no—
72C4×Q8×C11—22no—
73C4×Q8×C11—22no—
74C11×#117—22no—
75C11×#117—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⋊C4D411yescharacteristic
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4D411yescharacteristic
96C2×C11×C22⋊C4D411yescharacteristic
97C2×C42×C11—21no—
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⋊C8D414yes—
107C11×#103—22no—
108C11×#103—22no—
109C11×#103—22no—
110C11×#103—22no—
111C11×C22⋊C8—22no—
112C11×C22⋊C8—22no—
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#24718C1111yesmaximal, 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—42no—
134C2×Q8×C11—81no—
135C2×Q8×C11—81no—
136C2×Q8×C11#4112yes—
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—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
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—24no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
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—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—42no—
186C11×C4⋊C4—42no—
187C11×C4⋊C4—81no—
188C11×C4⋊C4—81no—
189C11×C4⋊C4—81no—
190C11×C4⋊C4#4112yes—
191C11×C22⋊C4—24no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—81no—
195C11×C22⋊C4—81no—
196C11×C22⋊C4—81no—
197C42×C11—21no—
198C42×C11—21no—
199C42×C11—42no—
200C42×C11—81no—
201C42×C11C2×D412yes—
202C42×C11#4112yes—
203C2×#475C2×C1111yescharacteristic, complemented
204C2×#433C2×C1111yescharacteristic
205#2628C2×C1111yescharacteristic
206#2323C2×C1111yescharacteristic
207#2077C2×C1111yescharacteristic
208#2077C2×C1111yescharacteristic
209#2036C2×C1111yescharacteristic
210#2035C2×C1111yescharacteristic
211#1987C2×C1111yescharacteristic, complemented
212#1949C2×C1111yescharacteristic, complemented
213#1943C2×C1111yescharacteristic, complemented
214#1941C2×C1111yescharacteristic, complemented
215#1935C2×C1111yescharacteristic, complemented
216#1933C2×C1111yescharacteristic, complemented
217#1805C2×C1111yescharacteristic, complemented
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11C22×D411yescharacteristic
226Q8×C11—22no—
227Q8×C11—22no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—84no—
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—21no—
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—41no—
247C2×C4×C11—41no—
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—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11#12112yes—
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×C4⋊Q8C22×C1111yescharacteristic
285C2×C22⋊Q8C22×C1111yescharacteristic
286C2×C4×Q8C22×C1111yescharacteristic
287C2×#117C22×C1111yescharacteristic
288#475—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#399—21no—
306#395—21no—
307#393—21no—
308#391C22×C1111yescharacteristic
309#389—21no—
310#389C22×C1111yescharacteristic
311#389C22×C1111yescharacteristic
312#389C22×C1111yescharacteristic
313#388—21no—
314#388—21no—
315#387—21no—
316#382C22×C1111yescharacteristic
317#380C22×C1111yescharacteristic
318#380C22×C1111yescharacteristic
319#380C22×C1111yescharacteristic
320C4×C4⋊C4C22×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—41no—
330C22×C11—41no—
331C22×C11—41no—
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—22no—
345C4×C11—42no—
346C4×C11—41no—
347C4×C11—42no—
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#54811yescharacteristic
358C4×C11#55211yescharacteristic
359C4×C11#55611yescharacteristic
360C22×Q8—21no—
361C22×Q8C23×C1111yescharacteristic
362C23×C4C23×C1111yescharacteristic
363C22×C8C23×C1111yescharacteristic
364C22×C8C23×C1111yescharacteristic
365C22×C8C23×C1111yescharacteristic
366C22×C8C23×C1111yescharacteristic
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C4×Q8—22no—
372C4×Q8—22no—
373#117—22no—
374#117—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⋊C4D4×C1111yescharacteristic
382C2×C4⋊C4D4×C1111yescharacteristic
383C2×C4⋊C4C23×C1111yescharacteristic
384C2×C4⋊C4C23×C1111yescharacteristic
385C2×C4⋊C4C23×C1111yescharacteristic
386C2×C4⋊C4C23×C1111yescharacteristic
387C2×C4⋊C4C23×C1111yescharacteristic
388C2×C4⋊C4C23×C1111yescharacteristic
389C2×C4⋊C4C23×C1111yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4D4×C1111yescharacteristic
395C2×C22⋊C4D4×C1111yescharacteristic
396C2×C42—21no—
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⋊C8D4×C1114yes—
406#103—22no—
407#103—22no—
408#103—22no—
409#103—22no—
410C22⋊C8—22no—
411C22⋊C8—22no—
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—81no—
426C2×C11#241511yescharacteristic
427C2×C11#305711yescharacteristic
428C2×C11#306311yescharacteristic
429C2×C11#312111yescharacteristic
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—42no—
440C2×Q8—81no—
441C2×Q8—81no—
442C2×Q8C11×#4112yes—
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—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4C2×D4×C1111yescharacteristic
458C22×C4C2×D4×C1111yescharacteristic
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C2×D4×C1111yescharacteristic
461C22×C4C2×D4×C1111yescharacteristic
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—24no—
476C4⋊C4—22no—
477C4⋊C4—22no—
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—21no—
490C4⋊C4—21no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4—81no—
494C4⋊C4—81no—
495C4⋊C4—81no—
496C4⋊C4C11×#4112yes—
497C22⋊C4—24no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—81no—
501C22⋊C4—81no—
502C22⋊C4—81no—
503C42—21no—
504C42—21no—
505C42—42no—
506C42—81no—
507C42C2×D4×C1112yes—
508C42C11×#4112yes—
509C11#2471811yescharacteristic, direct product factor, Sylow
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23C22×D4×C1111yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522Q8—84no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
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—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×C4C11×#12112yes—
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—41no—
577C22—41no—
578C22—41no—
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—22no—
592C4—41no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4C11×#54711yescharacteristic
604C4C11×#54811yescharacteristic
605C4C11×#55211yescharacteristic
606C4C11×#55611yescharacteristic
607C2—81no—
608C2C11×#241511yescharacteristic
609C2C11×#305711yescharacteristic
610C2C11×#306311yescharacteristic
611C2C11×#312111yescharacteristic
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
1. C2×C11×#475C2semidirect
9. C11×#1987C2semidirect
10. C11×#1949C2semidirect
11. C11×#1943C2semidirect
12. C11×#1941C2semidirect
13. C11×#1935C2semidirect
14. C11×#1933C2semidirect
15. C11×#1805C2semidirect
126. #24718C11direct (N × H)
203. C2×#475C2×C11semidirect
211. #1987C2×C11semidirect
212. #1949C2×C11semidirect
213. #1943C2×C11semidirect
214. #1941C2×C11semidirect
215. #1935C2×C11semidirect
216. #1933C2×C11semidirect
217. #1805C2×C11semidirect
509. C11#24718direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4752
C2×C11×#4332
C11×#26282
C11×#23232
C11×#20772
C11×#20362
C11×#20352
C11×#19872
C11×#19492
C11×#19432
C11×#19412
C11×#19352
C11×#19332
C11×#18052
#2471811