Finite Group Databasebeta

← C11×#24624 #14601817

Subgroups — C11×#24624 #14601817

Order 2816.

670 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×#3095C211yesmaximal, characteristic
2C2×C11×#485C211yesmaximal, characteristic
3C11×#2924C211yesmaximal, characteristic
4C11×#2911C211yesmaximal, characteristic
5C11×#2090C211yesmaximal, characteristic, complemented
6C11×#2089C211yesmaximal, characteristic, complemented
7C11×#2064C211yesmaximal, characteristic, complemented
8C11×#2064C211yesmaximal, characteristic, complemented
9C11×#1952C211yesmaximal, characteristic, complemented
10C11×#1951C211yesmaximal, characteristic, complemented
11C11×#1930C211yesmaximal, characteristic, complemented
12C11×#1930C211yesmaximal, characteristic, complemented
13C11×#1901C211yesmaximal, characteristic
14C11×#1855C211yesmaximal, characteristic
15C11×#1822C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C11×#485—21no—
21C11×#485—21no—
22C11×#485—21no—
23C11×#485—21no—
24C11×#485—21no—
25C11×#485—21no—
26C11×#484—21no—
27C11×#483—21no—
28C11×#433—21no—
29C11×#433—21no—
30C11×#432—21no—
31C11×#431—21no—
32C2×C11×#108C2211yescharacteristic
33C2×C11×#108C2211yescharacteristic
34C11×#428—21no—
35C11×#428—21no—
36C11×#428C2211yescharacteristic
37C11×#428C2211yescharacteristic
38C11×#428C2211yescharacteristic
39C11×#428C2211yescharacteristic
40C11×#428C2211yescharacteristic
41C11×#428C2211yescharacteristic
42C11×#427—21no—
43C11×#427—21no—
44C2×C11×#107C2211yescharacteristic
45C2×C11×#106C2211yescharacteristic
46C11×#424C2211yescharacteristic
47C11×#424C2211yescharacteristic
48C11×#419C2211yescharacteristic
49C11×#419C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#103C2211yescharacteristic
52C2×C11×#101C2211yescharacteristic
53C2×C11×#101C2211yescharacteristic
54C11×#407C2211yescharacteristic
55C11×#407C2211yescharacteristic
56C2×C11×C22⋊C8C2211yescharacteristic
57C11×#405C2211yescharacteristic
58C11×#405C2211yescharacteristic
59C11×#343C2211yescharacteristic
60C11×#343C2211yescharacteristic
61C11×#343C2211yescharacteristic
62C11×#343C2211yescharacteristic
63C11×#343C2211yescharacteristic
64C11×#343C2211yescharacteristic
65C11×#341C2211yescharacteristic
66C11×#341C2211yescharacteristic
67C22×Q8×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C2×C11×M16—21no—
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C2×C11×M16C2311yescharacteristic
73C2×C11×M16C2311yescharacteristic
74C2×C11×M16C2311yescharacteristic
75C2×C11×M16C2311yescharacteristic
76C2×C11×M16C2311yescharacteristic
77C2×C11×M16C2311yescharacteristic
78C22×C8×C11—21no—
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—21no—
85C11×#117—21no—
86C11×#117—21no—
87C11×#117—21no—
88C11×#117—21no—
89C11×#117—21no—
90C11×#117—21no—
91C11×#117D411yescharacteristic
92C11×#117D411yescharacteristic
93C11×#117C2311yescharacteristic
94C11×#117C2311yescharacteristic
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4D411yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C42×C11—21no—
105C2×C42×C11—21no—
106C11×#108—22no—
107C11×#108—22no—
108C11×#107—21no—
109C11×#107—21no—
110C11×#107—21no—
111C11×#107—21no—
112C11×#107—21no—
113C11×#107—21no—
114C11×#107—21no—
115C11×#107—21no—
116C11×#106—21no—
117C11×#106—21no—
118C11×#106—21no—
119C11×#106—21no—
120C11×#106—21no—
121C11×#106—21no—
122C11×#106—21no—
123C11×#106—21no—
124C11×C4⋊C8—21no—
125C11×C4⋊C8—21no—
126C11×C4⋊C8—21no—
127C11×C4⋊C8—21no—
128C11×#103—21no—
129C11×#103—21no—
130C11×#103—21no—
131C11×#103—21no—
132C11×#103—21no—
133C11×#103—21no—
134C11×#103—21no—
135C11×#103—21no—
136C11×#101—22no—
137C11×#101—22no—
138C11×C22⋊C8—21no—
139C11×C22⋊C8—21no—
140C11×C22⋊C8—21no—
141C11×C22⋊C8—21no—
142C11×C22⋊C8D411yescharacteristic
143C11×C22⋊C8D411yescharacteristic
144C11×C22⋊C8D411yescharacteristic
145C11×C22⋊C8D411yescharacteristic
146C11×#97—21no—
147C11×#97—21no—
148C4×C8×C11—21no—
149C4×C8×C11—21no—
150#24624C1111yesmaximal, characteristic, direct product factor, Sylow
151C24×C11#4111yescharacteristic
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×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—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11#4111yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C11×M16—24no—
175C11×M16—21no—
176C11×M16—21no—
177C11×M16—21no—
178C11×M16—21no—
179C11×M16—21no—
180C11×M16—21no—
181C11×M16—21no—
182C11×M16—21no—
183C11×M16—21no—
184C11×M16—21no—
185C11×M16#4112yes—
186C11×M16#4112yes—
187C2×C8×C11—24no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11C2×D411yescharacteristic
199C2×C8×C11C2×D411yescharacteristic
200C2×C8×C11C2×D411yescharacteristic
201C2×C8×C11C2×D411yescharacteristic
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—41no—
211C11×C4⋊C4—41no—
212C11×C4⋊C4C2×D411yescharacteristic
213C11×C4⋊C4C2×D411yescharacteristic
214C11×C4⋊C4C2×D411yescharacteristic
215C11×C4⋊C4C2×D411yescharacteristic
216C11×C22⋊C4—21no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—21no—
219C11×C22⋊C4—21no—
220C11×C22⋊C4—41no—
221C11×C22⋊C4—41no—
222C11×C22⋊C4—41no—
223C11×C22⋊C4—41no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11—21no—
227C42×C11—21no—
228C42×C11—41no—
229C42×C11—41no—
230#3095C2×C1111yescharacteristic
231C2×#485C2×C1111yescharacteristic
232#2924C2×C1111yescharacteristic
233#2911C2×C1111yescharacteristic
234#2090C2×C1111yescharacteristic, complemented
235#2089C2×C1111yescharacteristic, complemented
236#2064C2×C1111yescharacteristic, complemented
237#2064C2×C1111yescharacteristic, complemented
238#1952C2×C1111yescharacteristic, complemented
239#1951C2×C1111yescharacteristic, complemented
240#1930C2×C1111yescharacteristic, complemented
241#1930C2×C1111yescharacteristic, complemented
242#1901C2×C1111yescharacteristic
243#1855C2×C1111yescharacteristic
244#1822C2×C1111yescharacteristic
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11#12111yescharacteristic
250C23×C11#12111yescharacteristic
251C23×C11C2×#4111yescharacteristic
252Q8×C11—41no—
253Q8×C11—41no—
254Q8×C11—41no—
255Q8×C11—41no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—42no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—81no—
278C2×C4×C11—81no—
279C2×C4×C11—81no—
280C2×C4×C11—81no—
281C2×C4×C11#12111yescharacteristic
282C2×C4×C11#12111yescharacteristic
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C2×C4×C112−1+411yescharacteristic
288C2×C4×C112−1+411yescharacteristic
289C8×C11—22no—
290C8×C11—22no—
291C8×C11—21no—
292C8×C11—21no—
293C8×C11—21no—
294C8×C11—21no—
295C8×C11—41no—
296C8×C11—41no—
297C8×C11—41no—
298C8×C11—41no—
299C22×M16C22×C1111yescharacteristic
300C2×C22⋊Q8C22×C1111yescharacteristic
301C2×#117C22×C1111yescharacteristic
302C2×#117C22×C1111yescharacteristic
303#485—21no—
304#485—21no—
305#485—21no—
306#485—21no—
307#485—21no—
308#485—21no—
309#484—21no—
310#483—21no—
311#433—21no—
312#433—21no—
313#432—21no—
314#431—21no—
315C2×#108C22×C1111yescharacteristic
316C2×#108C22×C1111yescharacteristic
317#428—21no—
318#428—21no—
319#428C22×C1111yescharacteristic
320#428C22×C1111yescharacteristic
321#428C22×C1111yescharacteristic
322#428C22×C1111yescharacteristic
323#428C22×C1111yescharacteristic
324#428C22×C1111yescharacteristic
325#427—21no—
326#427—21no—
327C2×#107C22×C1111yescharacteristic
328C2×#106C22×C1111yescharacteristic
329#424C22×C1111yescharacteristic
330#424C22×C1111yescharacteristic
331#419C22×C1111yescharacteristic
332#419C22×C1111yescharacteristic
333C2×#103C22×C1111yescharacteristic
334C2×#103C22×C1111yescharacteristic
335C2×#101C22×C1111yescharacteristic
336C2×#101C22×C1111yescharacteristic
337#407C22×C1111yescharacteristic
338#407C22×C1111yescharacteristic
339C2×C22⋊C8C22×C1111yescharacteristic
340#405C22×C1111yescharacteristic
341#405C22×C1111yescharacteristic
342#343C22×C1111yescharacteristic
343#343C22×C1111yescharacteristic
344#343C22×C1111yescharacteristic
345#343C22×C1111yescharacteristic
346#343C22×C1111yescharacteristic
347#343C22×C1111yescharacteristic
348#341C22×C1111yescharacteristic
349#341C22×C1111yescharacteristic
350C22×C11—21no—
351C22×C11—21no—
352C22×C11—21no—
353C22×C11—21no—
354C22×C11—21no—
355C22×C11—21no—
356C22×C11—21no—
357C22×C11—21no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11C2×#12111yescharacteristic
361C22×C11#55211yescharacteristic
362C22×C11#55211yescharacteristic
363C4×C11—21no—
364C4×C11—21no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—81no—
370C4×C11—81no—
371C4×C11—81no—
372C4×C11—81no—
373C4×C11#52511yescharacteristic
374C4×C11#53611yescharacteristic
375C4×C11#54711yescharacteristic
376C4×C11#54711yescharacteristic
377C22×Q8C23×C1111yescharacteristic
378C23×C4C23×C1111yescharacteristic
379C2×M16—21no—
380C2×M16—22no—
381C2×M16—22no—
382C2×M16C23×C1111yescharacteristic
383C2×M16C23×C1111yescharacteristic
384C2×M16C23×C1111yescharacteristic
385C2×M16C23×C1111yescharacteristic
386C2×M16C23×C1111yescharacteristic
387C2×M16C23×C1111yescharacteristic
388C22×C8—21no—
389C22×C8C23×C1111yescharacteristic
390C22×C8C23×C1111yescharacteristic
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395#117—21no—
396#117—21no—
397#117—21no—
398#117—21no—
399#117—21no—
400#117—21no—
401#117D4×C1111yescharacteristic
402#117D4×C1111yescharacteristic
403#117C23×C1111yescharacteristic
404#117C23×C1111yescharacteristic
405C2×C4⋊C4—21no—
406C2×C4⋊C4D4×C1111yescharacteristic
407C2×C4⋊C4D4×C1111yescharacteristic
408C2×C4⋊C4C23×C1111yescharacteristic
409C2×C4⋊C4C23×C1111yescharacteristic
410C2×C4⋊C4C23×C1111yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C42—21no—
415C2×C42—21no—
416#108—22no—
417#108—22no—
418#107—21no—
419#107—21no—
420#107—21no—
421#107—21no—
422#107—21no—
423#107—21no—
424#107—21no—
425#107—21no—
426#106—21no—
427#106—21no—
428#106—21no—
429#106—21no—
430#106—21no—
431#106—21no—
432#106—21no—
433#106—21no—
434C4⋊C8—21no—
435C4⋊C8—21no—
436C4⋊C8—21no—
437C4⋊C8—21no—
438#103—21no—
439#103—21no—
440#103—21no—
441#103—21no—
442#103—21no—
443#103—21no—
444#103—21no—
445#103—21no—
446#101—22no—
447#101—22no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452C22⋊C8D4×C1111yescharacteristic
453C22⋊C8D4×C1111yescharacteristic
454C22⋊C8D4×C1111yescharacteristic
455C22⋊C8D4×C1111yescharacteristic
456#97—21no—
457#97—21no—
458C4×C8—21no—
459C4×C8—21no—
460C2×C11—21no—
461C2×C11—21no—
462C2×C11—41no—
463C2×C11—41no—
464C2×C11#241311yescharacteristic
465C2×C11#306711yescharacteristic
466C2×C11#306911yescharacteristic
467C24C11×#4111yescharacteristic
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4C2×D4×C1111yescharacteristic
485C22×C4C2×D4×C1111yescharacteristic
486C22×C4C2×D4×C1111yescharacteristic
487C22×C4C2×D4×C1111yescharacteristic
488C22×C4C11×#4111yescharacteristic
489C22×C4C24×C1111yescharacteristic
490M16—24no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16—21no—
496M16—21no—
497M16—21no—
498M16—21no—
499M16—21no—
500M16—21no—
501M16C11×#4112yes—
502M16C11×#4112yes—
503C2×C8—24no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8C2×D4×C1111yescharacteristic
515C2×C8C2×D4×C1111yescharacteristic
516C2×C8C2×D4×C1111yescharacteristic
517C2×C8C2×D4×C1111yescharacteristic
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4C2×D4×C1111yescharacteristic
529C4⋊C4C2×D4×C1111yescharacteristic
530C4⋊C4C2×D4×C1111yescharacteristic
531C4⋊C4C2×D4×C1111yescharacteristic
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—41no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—41no—
545C42—41no—
546C11#2462411yescharacteristic, direct product factor, Sylow
547C23—21no—
548C23—21no—
549C23—41no—
550C23—41no—
551C23C11×#12111yescharacteristic
552C23C11×#12111yescharacteristic
553C23C2×C11×#4111yescharacteristic
554Q8—41no—
555Q8—41no—
556Q8—41no—
557Q8—41no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—81no—
580C2×C4—81no—
581C2×C4—81no—
582C2×C4—81no—
583C2×C4C11×#12111yescharacteristic
584C2×C4C11×#12111yescharacteristic
585C2×C4C22×D4×C1111yescharacteristic
586C2×C4C22×D4×C1111yescharacteristic
587C2×C4C2×C11×#4111yescharacteristic
588C2×C4C2×C11×#4111yescharacteristic
589C2×C4C11×2−1+411yescharacteristic
590C2×C4C11×2−1+411yescharacteristic
591C8—22no—
592C8—22no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—41no—
598C8—41no—
599C8—41no—
600C8—41no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—81no—
610C22—81no—
611C22C2×C11×#12111yescharacteristic
612C22C11×#55211yescharacteristic
613C22C11×#55211yescharacteristic
614C4—21no—
615C4—21no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—81no—
621C4—81no—
622C4—81no—
623C4—81no—
624C4C11×#52511yescharacteristic
625C4C11×#53611yescharacteristic
626C4C11×#54711yescharacteristic
627C4C11×#54711yescharacteristic
628C2—21no—
629C2—21no—
630C2—41no—
631C2—41no—
632C2C11×#241311yescharacteristic
633C2C11×#306711yescharacteristic
634C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11#41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
5. C11×#2090C2semidirect
6. C11×#2089C2semidirect
7. C11×#2064C2semidirect
8. C11×#2064C2semidirect
9. C11×#1952C2semidirect
10. C11×#1951C2semidirect
11. C11×#1930C2semidirect
12. C11×#1930C2semidirect
150. #24624C11direct (N × H)
234. #2090C2×C11semidirect
235. #2089C2×C11semidirect
236. #2064C2×C11semidirect
237. #2064C2×C11semidirect
238. #1952C2×C11semidirect
239. #1951C2×C11semidirect
240. #1930C2×C11semidirect
241. #1930C2×C11semidirect
546. C11#24624direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30952
C2×C11×#4852
C11×#29242
C11×#29112
C11×#20902
C11×#20892
C11×#20642
C11×#19522
C11×#19512
C11×#19302
C11×#19012
C11×#18552
C11×#18222
#2462411