Finite Group Databasebeta

← C11×#24241 #14601434

Subgroups — C11×#24241 #14601434

Order 2816.

1438 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#547C211yesmaximal, characteristic
2C2×C11×#462C211yesmaximal, characteristic, complemented
3C2×C11×#452C212yesmaximal, complemented
4C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
5C11×#2538C211yesmaximal, characteristic, complemented
6C11×#2035C212yesmaximal, complemented
7C11×#2001C212yesmaximal, complemented
8C11×#1956C211yesmaximal, characteristic, complemented
9C11×#1954C211yesmaximal, characteristic, complemented
10C11×#1802C211yesmaximal, characteristic, complemented
11C11×#1788C212yesmaximal, complemented
12C22×C11×#41C2212yes—
13C22×C11×Q16C2212yes—
14C22×C11×SD16C2211yescharacteristic
15C11×#547—24no—
16C11×#547—24no—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#123—22no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×C22⋊Q8C2212yes—
21C2×C11×#121—21no—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C22×C11×C4⋊C4—21no—
26C11×#462—24no—
27C11×#452—28no—
28C4×C11×SD16—24no—
29C2×C11×#106C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#103C2212yes—
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2212yes—
37C2×C11×C22⋊C8C2212yes—
38C2×C11×C22⋊C8C2212yes—
39C2×C4×C8×C11C2211yescharacteristic
40C11×#396—22no—
41C11×#390—21no—
42C11×#389—21no—
43C11×#384C2211yescharacteristic
44C11×#380C2212yes—
45C11×#340C2212yes—
46C2×C11×#41—24no—
47C2×C11×#41—24no—
48C2×C11×#41—24no—
49C2×C11×#41—24no—
50C2×C11×#41—42no—
51C2×C11×#41—42no—
52C22×Q8×C11C2311yescharacteristic
53C22×Q8×C11C2312yes—
54C22×D4×C11—22no—
55C22×D4×C11D411yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×C4×C11—22no—
59C23×C4×C11C2312yes—
60C2×C11×Q16—24no—
61C2×C11×Q16—24no—
62C2×C11×Q16—42no—
63C2×C11×SD16—22no—
64C2×C11×SD16—22no—
65C2×C11×SD16D414yescomplemented
66C22×C8×C11C2312yes—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8D414yes—
71C11×#123—216no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—42no—
76C11×#121—28no—
77C4×Q8×C11—22no—
78C4×Q8×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C4×D4×C11D414yes—
83C2×C11×C4⋊C4—28no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4D411yescharacteristic
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4D412yes—
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102C11×#106—22no—
103C11×C4⋊C8—22no—
104C11×#103—24no—
105C11×#103—24no—
106C11×#103—22no—
107C11×#103—42no—
108C11×#102—22no—
109C11×#102—24no—
110C11×C22⋊C8—24no—
111C11×C22⋊C8—42no—
112C4×C8×C11—22no—
113C11×#95—22no—
114#24241C1111yesmaximal, characteristic, direct product factor, Sylow
115C24×C11—21no—
116C24×C11C2×D412yes—
117C11×#41—48no—
118C11×#41—48no—
119C11×#41—48no—
120C11×#41—48no—
121C2×Q8×C11—22no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—22no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—21no—
130C2×Q8×C11—22no—
131C2×Q8×C11C2×D414yes—
132C2×Q8×C11C2×D412yes—
133C2×D4×C11—28no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—44no—
141C2×D4×C11—44no—
142C2×D4×C11C2×D412yes—
143C2×D4×C11C2×D412yes—
144C2×D4×C11#4112yes—
145C22×C4×C11—28no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—24no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—44no—
159C22×C4×C11—44no—
160C22×C4×C11—42no—
161C22×C4×C11—42no—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2411yescharacteristic
166C11×Q16—48no—
167C11×SD16—28no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—22no—
175C2×C8×C11—21no—
176C2×C8×C11C2×D412yes—
177C11×C4⋊C4—28no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—44no—
187C11×C4⋊C4—42no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4—81no—
190C11×C4⋊C4C2×D412yes—
191C11×C22⋊C4—28no—
192C11×C22⋊C4—24no—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—44no—
195C11×C22⋊C4—82no—
196C42×C11—42no—
197C42×C11C2×D412yes—
198C42×C11C2×D412yes—
199C2×#547C2×C1111yescharacteristic
200C2×#462C2×C1111yescharacteristic, complemented
201C2×#452C2×C1112yescomplemented
202C2×C4×SD16C2×C1111yescharacteristic, complemented
203#2538C2×C1111yescharacteristic, complemented
204#2035C2×C1112yescomplemented
205#2001C2×C1112yescomplemented
206#1956C2×C1111yescharacteristic, complemented
207#1954C2×C1111yescharacteristic, complemented
208#1802C2×C1111yescharacteristic, complemented
209#1788C2×C1112yescomplemented
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11C22×D411yescharacteristic
225Q8×C11—22no—
226Q8×C11—22no—
227Q8×C11—24no—
228Q8×C11—24no—
229Q8×C11—42no—
230Q8×C11—41no—
231Q8×C11—42no—
232Q8×C11—41no—
233D4×C11—22no—
234D4×C11—22no—
235D4×C11—22no—
236D4×C11—416no—
237D4×C11—44no—
238D4×C11#12114yes—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—416no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—48no—
259C2×C4×C11—41no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—41no—
265C2×C4×C11#12012yes—
266C2×C4×C11#12012yes—
267C2×C4×C11#13512yes—
268C2×C4×C11#13712yes—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C8×C11—22no—
276C8×C11—41no—
277C8×C11—42no—
278C22×#41C22×C1112yes—
279C22×Q16C22×C1112yes—
280C22×SD16C22×C1111yescharacteristic
281#547—24no—
282#547—24no—
283C2×C4⋊Q8C22×C1111yescharacteristic
284C2×#123—22no—
285C2×C22⋊Q8C22×C1112yes—
286C2×C22⋊Q8C22×C1112yes—
287C2×#121—21no—
288C2×C4×Q8C22×C1111yescharacteristic
289C2×C4×D4C22×C1111yescharacteristic
290C2×C4×D4C22×C1111yescharacteristic
291C22×C4⋊C4—21no—
292#462—24no—
293#452—28no—
294C4×SD16—24no—
295C2×#106C22×C1111yescharacteristic
296C2×C4⋊C8C22×C1111yescharacteristic
297C2×#103C22×C1111yescharacteristic
298C2×#103C22×C1112yes—
299C2×#103C22×C1112yes—
300C2×#103C22×C1112yes—
301C2×#102C22×C1112yes—
302C2×#102C22×C1111yescharacteristic
303C2×C22⋊C8C22×C1112yes—
304C2×C22⋊C8C22×C1112yes—
305C2×C4×C8C22×C1111yescharacteristic
306#396—22no—
307#390—21no—
308#389—21no—
309#384C22×C1111yescharacteristic
310#380C22×C1112yes—
311#340C22×C1112yes—
312C22×C11—24no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11C2×#12011yescharacteristic
327C22×C11D4211yescharacteristic
328C22×C11#54611yescharacteristic
329C22×C11C2×#13511yescharacteristic
330C22×C11C2×#13711yescharacteristic
331C22×C11#57711yescharacteristic
332C22×C11#57811yescharacteristic
333C4×C11—22no—
334C4×C11—42no—
335C4×C11—44no—
336C4×C11—42no—
337C4×C11—42no—
338C4×C11—81no—
339C4×C11—82no—
340C4×C11#45214yescomplemented
341C4×C11C2×#12111yescharacteristic
342C4×C11#53511yescharacteristic
343C4×C11D4211yescharacteristic
344C4×C11#54611yescharacteristic
345C2×#41—24no—
346C2×#41—24no—
347C2×#41—24no—
348C2×#41—24no—
349C2×#41—42no—
350C2×#41—42no—
351C22×Q8C23×C1111yescharacteristic
352C22×Q8C23×C1112yes—
353C22×D4—22no—
354C22×D4D4×C1111yescharacteristic
355C22×D4C23×C1111yescharacteristic
356C23×C4—21no—
357C23×C4—22no—
358C23×C4C23×C1112yes—
359C2×Q16—24no—
360C2×Q16—24no—
361C2×Q16—42no—
362C2×SD16—22no—
363C2×SD16—22no—
364C2×SD16D4×C1114yescomplemented
365C22×C8C23×C1112yes—
366C22×C8C23×C1111yescharacteristic
367C22×C8C23×C1111yescharacteristic
368C4⋊Q8—22no—
369C4⋊Q8D4×C1114yes—
370#123—216no—
371C22⋊Q8—24no—
372C22⋊Q8—24no—
373C22⋊Q8—24no—
374C22⋊Q8—42no—
375#121—28no—
376C4×Q8—22no—
377C4×Q8—22no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4D4×C1114yes—
382C2×C4⋊C4—28no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4D4×C1111yescharacteristic
391C2×C4⋊C4C23×C1111yescharacteristic
392C2×C4⋊C4C23×C1112yes—
393C2×C4⋊C4C23×C1111yescharacteristic
394C2×C22⋊C4—22no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4D4×C1112yes—
399C2×C42—21no—
400C2×C42C23×C1111yescharacteristic
401#106—22no—
402C4⋊C8—22no—
403#103—24no—
404#103—24no—
405#103—22no—
406#103—42no—
407#102—22no—
408#102—24no—
409C22⋊C8—24no—
410C22⋊C8—42no—
411C4×C8—22no—
412#95—22no—
413C2×C11—44no—
414C2×C11—82no—
415C2×C11#240811yescharacteristic
416C2×C11C2×#45211yescharacteristic
417C2×C11#301311yescharacteristic
418C2×C11#327611yescharacteristic
419C2×C11#328411yescharacteristic
420C2×C11#330211yescharacteristic
421C2×C11#333111yescharacteristic
422C24—21no—
423C24C2×D4×C1112yes—
424#41—48no—
425#41—48no—
426#41—48no—
427#41—48no—
428C2×Q8—22no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—22no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—21no—
437C2×Q8—22no—
438C2×Q8C2×D4×C1114yes—
439C2×Q8C2×D4×C1112yes—
440C2×D4—28no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—44no—
448C2×D4—44no—
449C2×D4C2×D4×C1112yes—
450C2×D4C2×D4×C1112yes—
451C2×D4C11×#4112yes—
452C22×C4—28no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4C2×D4×C1112yes—
470C22×C4C2×D4×C1111yescharacteristic
471C22×C4C2×D4×C1111yescharacteristic
472C22×C4C24×C1111yescharacteristic
473Q16—48no—
474SD16—28no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—21no—
481C2×C8—22no—
482C2×C8—21no—
483C2×C8C2×D4×C1112yes—
484C4⋊C4—28no—
485C4⋊C4—22no—
486C4⋊C4—24no—
487C4⋊C4—24no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—44no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—81no—
497C4⋊C4C2×D4×C1112yes—
498C22⋊C4—28no—
499C22⋊C4—24no—
500C22⋊C4—24no—
501C22⋊C4—44no—
502C22⋊C4—82no—
503C42—42no—
504C42C2×D4×C1112yes—
505C42C2×D4×C1112yes—
506C11#2424111yescharacteristic, direct product factor, Sylow
507C23—22no—
508C23—22no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23C22×D4×C1111yescharacteristic
522Q8—22no—
523Q8—22no—
524Q8—24no—
525Q8—24no—
526Q8—42no—
527Q8—41no—
528Q8—42no—
529Q8—41no—
530D4—22no—
531D4—22no—
532D4—22no—
533D4—416no—
534D4—44no—
535D4C11×#12114yes—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—416no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—48no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4C11×#12012yes—
563C2×C4C11×#12012yes—
564C2×C4C11×#13512yes—
565C2×C4C11×#13712yes—
566C2×C4C22×D4×C1111yescharacteristic
567C2×C4C22×D4×C1111yescharacteristic
568C2×C4C22×D4×C1111yescharacteristic
569C2×C4C2×C11×#4111yescharacteristic
570C2×C4C11×H(5,𝔽2)11yescharacteristic
571C2×C4C11×H(5,𝔽2)11yescharacteristic
572C8—22no—
573C8—41no—
574C8—42no—
575C22—24no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22C2×C11×#12011yescharacteristic
590C22D42×C1111yescharacteristic
591C22C11×#54611yescharacteristic
592C22C2×C11×#13511yescharacteristic
593C22C2×C11×#13711yescharacteristic
594C22C11×#57711yescharacteristic
595C22C11×#57811yescharacteristic
596C4—22no—
597C4—42no—
598C4—44no—
599C4—42no—
600C4—42no—
601C4—81no—
602C4—82no—
603C4C11×#45214yescomplemented
604C4C2×C11×#12111yescharacteristic
605C4C11×#53511yescharacteristic
606C4D42×C1111yescharacteristic
607C4C11×#54611yescharacteristic
608C2—44no—
609C2—82no—
610C2C11×#240811yescharacteristic
611C2C2×C11×#45211yescharacteristic
612C2C11×#301311yescharacteristic
613C2C11×#327611yescharacteristic
614C2C11×#328411yescharacteristic
615C2C11×#330211yescharacteristic
616C2C11×#333111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#547C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#462C2semidirect
3. C2×C11×#452C2semidirect
4. C2×C4×C11×SD16C2semidirect
5. C11×#2538C2semidirect
6. C11×#2035C2semidirect
7. C11×#2001C2semidirect
8. C11×#1956C2semidirect
9. C11×#1954C2semidirect
10. C11×#1802C2semidirect
11. C11×#1788C2semidirect
65. C2×C11×SD16D4semidirect
114. #24241C11direct (N × H)
200. C2×#462C2×C11semidirect
201. C2×#452C2×C11semidirect
202. C2×C4×SD16C2×C11semidirect
203. #2538C2×C11semidirect
204. #2035C2×C11semidirect
205. #2001C2×C11semidirect
206. #1956C2×C11semidirect
207. #1954C2×C11semidirect
208. #1802C2×C11semidirect
209. #1788C2×C11semidirect
340. C4×C11#452semidirect
364. C2×SD16D4×C11semidirect
506. C11#24241direct (N × H)
603. C4C11×#452semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5472
C2×C11×#4622
C2×C11×#4522
C2×C4×C11×SD162
C11×#25382
C11×#20352
C11×#20012
C11×#19562
C11×#19542
C11×#18022
C11×#17882
#2424111