Finite Group Databasebeta

← C11×#23937 #14601130

Subgroups — C11×#23937 #14601130

Order 2816.

1304 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#529C211yesmaximal, characteristic
2C2×C11×#451C211yesmaximal, characteristic, complemented
3C2×C11×#448C211yesmaximal, characteristic
4C2×C11×#391C211yesmaximal, characteristic, complemented
5C11×#2026C212yesmaximal, complemented
6C11×#2015C212yesmaximal, complemented
7C11×#1878C212yesmaximal, complemented
8C11×#1877C212yesmaximal, complemented
9C11×#1874C211yesmaximal, characteristic
10C11×#1872C211yesmaximal, characteristic, complemented
11C11×#1817C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C22×C11×Q16C2212yes—
14C22×C11×SD16C2212yes—
15C11×#529—24no—
16C11×#529—24no—
17C2×C11×#126—21no—
18C2×C11×#125C2211yescharacteristic
19C2×C11×#124C2211yescharacteristic
20C2×C11×#123—21no—
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×D4×C11—21no—
25C2×C4×D4×C11C2211yescharacteristic
26C2×C11×#117—21no—
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic
29C11×#451—24no—
30C11×#448—24no—
31C2×C11×#103C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C11×#391—21no—
38C11×#391—21no—
39C11×#391C2212yes—
40C11×#391C2212yes—
41C2×C11×#95—21no—
42C2×C11×#95—21no—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C11×#336C2212yes—
46C11×#336C2212yes—
47C22×Q8×C11—24no—
48C22×Q8×C11—21no—
49C22×Q8×C11—22no—
50C22×Q8×C11—22no—
51C22×Q8×C11—42no—
52C22×Q8×C11C2311yescharacteristic
53C22×Q8×C11C2312yes—
54C22×D4×C11—21no—
55C22×D4×C11C2311yescharacteristic
56C23×C4×C11—21no—
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C23×C4×C11D411yescharacteristic
60C23×C4×C11D411yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C2×C11×Q16—24no—
63C2×C11×Q16—24no—
64C2×C11×Q16—42no—
65C2×C11×SD16—24no—
66C2×C11×SD16—24no—
67C2×C11×SD16—42no—
68C22×C8×C11C2312yes—
69C22×C8×C11C2312yes—
70C11×#126—28no—
71C11×#125—22no—
72C11×#125—22no—
73C11×#124—22no—
74C11×#124—22no—
75C11×#123—28no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8D414yes—
78C11×#121—22no—
79C11×#121D414yes—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×D4×C11—28no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C11×#117—28no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—42no—
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C42×C11—22no—
101C2×C42×C11—22no—
102C2×C42×C11—21no—
103C2×C42×C11D411yescharacteristic
104C2×C42×C11D411yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C11×#103—24no—
108C11×#103—24no—
109C11×#103—42no—
110C11×#102—42no—
111C11×C22⋊C8—22no—
112C11×C22⋊C8—22no—
113C11×#95—22no—
114C11×#95—22no—
115C11×#95—22no—
116C11×#95—22no—
117#23937C1111yesmaximal, characteristic, direct product factor, Sylow
118C24×C11—21no—
119C24×C11C2×D411yescharacteristic
120C2×Q8×C11—24no—
121C2×Q8×C11—21no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—48no—
130C2×Q8×C11—48no—
131C2×Q8×C11—42no—
132C2×Q8×C11—42no—
133C2×Q8×C11C2×D412yes—
134C2×Q8×C11#4114yes—
135C2×D4×C11—24no—
136C2×D4×C11—21no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—42no—
140C2×D4×C11—42no—
141C2×D4×C11C2×D412yes—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—41no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11—42no—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2×D412yes—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C11×Q16—48no—
173C11×SD16—48no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4C2×D412yes—
190C11×C4⋊C4C2×D412yes—
191C11×C22⋊C4—24no—
192C11×C22⋊C4—24no—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—24no—
195C11×C22⋊C4—24no—
196C42×C11—24no—
197C42×C11—22no—
198C42×C11—22no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—21no—
203C2×#529C2×C1111yescharacteristic
204C2×#451C2×C1111yescharacteristic, complemented
205C2×#448C2×C1111yescharacteristic
206C2×#391C2×C1111yescharacteristic, complemented
207#2026C2×C1112yescomplemented
208#2015C2×C1112yescomplemented
209#1878C2×C1112yescomplemented
210#1877C2×C1112yescomplemented
211#1874C2×C1111yescharacteristic
212#1872C2×C1111yescharacteristic, complemented
213#1817C2×C1111yescharacteristic, complemented
214C23×C11—21no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—22no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11#12012yes—
226C23×C11#13512yes—
227C23×C11#13712yes—
228C23×C11C22×D411yescharacteristic
229Q8×C11—24no—
230Q8×C11—24no—
231Q8×C11—24no—
232Q8×C11—48no—
233Q8×C11—42no—
234Q8×C11—42no—
235Q8×C11—42no—
236D4×C11—24no—
237D4×C11—48no—
238D4×C11—42no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—24no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—44no—
259C2×C4×C11—48no—
260C2×C4×C11—48no—
261C2×C4×C11—42no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—44no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—84no—
274C2×C4×C11#12012yes—
275C2×C4×C11#13712yes—
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C2×#4112yes—
279C2×C4×C11H(5,𝔽2)12yes—
280C8×C11—42no—
281C8×C11—42no—
282C23×Q8C22×C1111yescharacteristic
283C22×Q16C22×C1112yes—
284C22×SD16C22×C1112yes—
285#529—24no—
286#529—24no—
287C2×#126—21no—
288C2×#125C22×C1111yescharacteristic
289C2×#124C22×C1111yescharacteristic
290C2×#123—21no—
291C2×C22⋊Q8C22×C1111yescharacteristic
292C2×#121C22×C1111yescharacteristic
293C2×C4×Q8C22×C1111yescharacteristic
294C2×C4×D4—21no—
295C2×C4×D4C22×C1111yescharacteristic
296C2×#117—21no—
297C22×C4⋊C4C22×C1111yescharacteristic
298C22×C42C22×C1111yescharacteristic
299#451—24no—
300#448—24no—
301C2×#103C22×C1112yes—
302C2×#103C22×C1112yes—
303C2×#103C22×C1112yes—
304C2×#102C22×C1112yes—
305C2×C22⋊C8C22×C1111yescharacteristic
306C2×C22⋊C8C22×C1111yescharacteristic
307#391—21no—
308#391—21no—
309#391C22×C1112yes—
310#391C22×C1112yes—
311C2×#95—21no—
312C2×#95—21no—
313#340C22×C1112yes—
314#340C22×C1112yes—
315#336C22×C1112yes—
316#336C22×C1112yes—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—22no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11#45214yes—
331C22×C11C2×#12011yescharacteristic
332C22×C11#52511yescharacteristic
333C22×C11#53511yescharacteristic
334C22×C11C2×#13511yescharacteristic
335C22×C11C2×#13711yescharacteristic
336C22×C11C2×#13711yescharacteristic
337C22×C11#57511yescharacteristic
338C4×C11—22no—
339C4×C11—22no—
340C4×C11—44no—
341C4×C11—42no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—42no—
345C4×C11—41no—
346C4×C11—42no—
347C4×C11—82no—
348C4×C11#54612yes—
349C4×C11#54612yes—
350C22×Q8—24no—
351C22×Q8—21no—
352C22×Q8—22no—
353C22×Q8—22no—
354C22×Q8—42no—
355C22×Q8C23×C1111yescharacteristic
356C22×Q8C23×C1112yes—
357C22×D4—21no—
358C22×D4C23×C1111yescharacteristic
359C23×C4—21no—
360C23×C4—21no—
361C23×C4—21no—
362C23×C4D4×C1111yescharacteristic
363C23×C4D4×C1111yescharacteristic
364C23×C4C23×C1111yescharacteristic
365C2×Q16—24no—
366C2×Q16—24no—
367C2×Q16—42no—
368C2×SD16—24no—
369C2×SD16—24no—
370C2×SD16—42no—
371C22×C8C23×C1112yes—
372C22×C8C23×C1112yes—
373#126—28no—
374#125—22no—
375#125—22no—
376#124—22no—
377#124—22no—
378#123—28no—
379C22⋊Q8—22no—
380C22⋊Q8D4×C1114yes—
381#121—22no—
382#121D4×C1114yes—
383C4×Q8—22no—
384C4×Q8—22no—
385C4×D4—28no—
386C4×D4—22no—
387C4×D4—22no—
388#117—28no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4C23×C1112yes—
396C2×C4⋊C4C23×C1111yescharacteristic
397C2×C4⋊C4C23×C1111yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C42—21no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42D4×C1111yescharacteristic
407C2×C42D4×C1111yescharacteristic
408C2×C42C23×C1111yescharacteristic
409C2×C42C23×C1111yescharacteristic
410#103—24no—
411#103—24no—
412#103—42no—
413#102—42no—
414C22⋊C8—22no—
415C22⋊C8—22no—
416#95—22no—
417#95—22no—
418#95—22no—
419#95—22no—
420C2×C11—24no—
421C2×C11—82no—
422C2×C11#240411yescharacteristic
423C2×C11C2×#45211yescharacteristic
424C2×C11#300711yescharacteristic
425C2×C11#310811yescharacteristic
426C2×C11#311711yescharacteristic
427C2×C11#321111yescharacteristic
428C2×C11#321811yescharacteristic
429C24—21no—
430C24C2×D4×C1111yescharacteristic
431C2×Q8—24no—
432C2×Q8—21no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—48no—
441C2×Q8—48no—
442C2×Q8—42no—
443C2×Q8—42no—
444C2×Q8C2×D4×C1112yes—
445C2×Q8C11×#4114yes—
446C2×D4—24no—
447C2×D4—21no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—42no—
451C2×D4—42no—
452C2×D4C2×D4×C1112yes—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—41no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4C2×D4×C1111yescharacteristic
476C22×C4C2×D4×C1111yescharacteristic
477C22×C4C2×D4×C1111yescharacteristic
478C22×C4C2×D4×C1111yescharacteristic
479C22×C4C2×D4×C1112yes—
480C22×C4C2×D4×C1112yes—
481C22×C4C2×D4×C1111yescharacteristic
482C22×C4C24×C1111yescharacteristic
483Q16—48no—
484SD16—48no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C4⋊C4—24no—
492C4⋊C4—24no—
493C4⋊C4—24no—
494C4⋊C4—24no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—42no—
500C4⋊C4C2×D4×C1112yes—
501C4⋊C4C2×D4×C1112yes—
502C22⋊C4—24no—
503C22⋊C4—24no—
504C22⋊C4—24no—
505C22⋊C4—24no—
506C22⋊C4—24no—
507C42—24no—
508C42—22no—
509C42—22no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C11#2393711yescharacteristic, direct product factor, Sylow
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—22no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23C11×#12012yes—
527C23C11×#13512yes—
528C23C11×#13712yes—
529C23C22×D4×C1111yescharacteristic
530Q8—24no—
531Q8—24no—
532Q8—24no—
533Q8—48no—
534Q8—42no—
535Q8—42no—
536Q8—42no—
537D4—24no—
538D4—48no—
539D4—42no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—44no—
560C2×C4—48no—
561C2×C4—48no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—44no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—84no—
575C2×C4C11×#12012yes—
576C2×C4C11×#13712yes—
577C2×C4C22×D4×C1111yescharacteristic
578C2×C4C22×D4×C1111yescharacteristic
579C2×C4C2×C11×#4112yes—
580C2×C4C11×H(5,𝔽2)12yes—
581C8—42no—
582C8—42no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—22no—
588C22—22no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22C11×#45214yes—
597C22C2×C11×#12011yescharacteristic
598C22C11×#52511yescharacteristic
599C22C11×#53511yescharacteristic
600C22C2×C11×#13511yescharacteristic
601C22C2×C11×#13711yescharacteristic
602C22C2×C11×#13711yescharacteristic
603C22C11×#57511yescharacteristic
604C4—22no—
605C4—22no—
606C4—44no—
607C4—42no—
608C4—41no—
609C4—41no—
610C4—42no—
611C4—41no—
612C4—42no—
613C4—82no—
614C4C11×#54612yes—
615C4C11×#54612yes—
616C2—24no—
617C2—82no—
618C2C11×#240411yescharacteristic
619C2C2×C11×#45211yescharacteristic
620C2C11×#300711yescharacteristic
621C2C11×#310811yescharacteristic
622C2C11×#311711yescharacteristic
623C2C11×#321111yescharacteristic
624C2C11×#321811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#451C2semidirect
4. C2×C11×#391C2semidirect
5. C11×#2026C2semidirect
6. C11×#2015C2semidirect
7. C11×#1878C2semidirect
8. C11×#1877C2semidirect
10. C11×#1872C2semidirect
11. C11×#1817C2semidirect
117. #23937C11direct (N × H)
204. C2×#451C2×C11semidirect
206. C2×#391C2×C11semidirect
207. #2026C2×C11semidirect
208. #2015C2×C11semidirect
209. #1878C2×C11semidirect
210. #1877C2×C11semidirect
212. #1872C2×C11semidirect
213. #1817C2×C11semidirect
514. C11#23937direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5292
C2×C11×#4512
C2×C11×#4482
C2×C11×#3912
C11×#20262
C11×#20152
C11×#18782
C11×#18772
C11×#18742
C11×#18722
C11×#18172
#2393711