Finite Group Databasebeta

← C11×#23964 #14601157

Subgroups — C11×#23964 #14601157

Order 2816.

1304 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#553C211yesmaximal, characteristic
2C2×C11×#448C211yesmaximal, characteristic, complemented
3C22×C11×#103C211yesmaximal, characteristic, complemented
4C11×#2409C211yesmaximal, characteristic, complemented
5C11×#2026C212yesmaximal, complemented
6C11×#2000C212yesmaximal, complemented
7C11×#1893C211yesmaximal, characteristic, complemented
8C11×#1877C212yesmaximal, complemented
9C11×#1873C212yesmaximal, complemented
10C11×#1869C211yesmaximal, characteristic, complemented
11C11×#1824C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C23×C8×C11C2211yescharacteristic
15C11×#553—24no—
16C11×#553—24no—
17C2×C11×#126—21no—
18C2×C11×#125C2211yescharacteristic
19C2×C11×#123—21no—
20C2×C11×C22⋊Q8C2212yes—
21C2×C11×#121—21no—
22C2×C11×#121C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×C4×D4×C11—21no—
25C2×C4×D4×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C11×#117C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C11×#448—24no—
30C2×C11×#103—24no—
31C2×C11×#103C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2212yes—
37C11×#395—21no—
38C11×#393—21no—
39C11×#391C2212yes—
40C11×#386—21no—
41C11×#385—21no—
42C11×#380C2211yescharacteristic
43C11×#340C2212yes—
44C11×#340C2212yes—
45C11×#340C2212yes—
46C11×#336C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11—24no—
49C22×Q8×C11—22no—
50C22×Q8×C11—22no—
51C22×Q8×C11—42no—
52C22×Q8×C11C2312yes—
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11D411yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C2×C11×SD16—24no—
63C2×C11×SD16—24no—
64C2×C11×SD16—42no—
65C22×C8×C11—22no—
66C22×C8×C11—42no—
67C22×C8×C11C2312yes—
68C22×C8×C11C2312yes—
69C11×#126—28no—
70C11×#125—22no—
71C11×#125—22no—
72C11×#123—28no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8—42no—
75C11×#121—28no—
76C11×#121—22no—
77C11×#121—22no—
78C11×#121—22no—
79C11×#121D414yes—
80C4×D4×C11—28no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C11×#117—22no—
86C11×#117—22no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4D414yes—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4D411yescharacteristic
105C2×C11×C22⋊C4D411yescharacteristic
106C2×C42×C11—21no—
107C2×C42×C11C2311yescharacteristic
108C11×#103—24no—
109C11×#103—24no—
110C11×#103—24no—
111C11×#102—42no—
112C11×C22⋊C8—22no—
113C11×C22⋊C8—42no—
114C11×#95—21no—
115C11×#95—22no—
116C11×#95—22no—
117#23964C1111yesmaximal, characteristic, direct product factor, Sylow
118C24×C11—21no—
119C24×C11C2×D411yescharacteristic
120C24×C11C2×D411yescharacteristic
121C2×Q8×C11—22no—
122C2×Q8×C11—28no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—44no—
128C2×Q8×C11—48no—
129C2×Q8×C11—44no—
130C2×Q8×C11—42no—
131C2×Q8×C11#4114yes—
132C2×D4×C11—22no—
133C2×D4×C11—24no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—24no—
137C2×D4×C11—21no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—42no—
141C2×D4×C11—42no—
142C2×D4×C11—82no—
143C2×D4×C11C2×D412yes—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—44no—
158C22×C4×C11—42no—
159C22×C4×C11—82no—
160C22×C4×C11—82no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2411yescharacteristic
168C11×SD16—48no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—44no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—44no—
186C11×C4⋊C4C2×D412yes—
187C11×C4⋊C4C2×D412yes—
188C11×C4⋊C4C2×D412yes—
189C11×C22⋊C4—24no—
190C11×C22⋊C4—24no—
191C11×C22⋊C4—24no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—44no—
196C11×C22⋊C4—42no—
197C42×C11—24no—
198C42×C11—21no—
199C42×C11—21no—
200C2×#553C2×C1111yescharacteristic
201C2×#448C2×C1111yescharacteristic, complemented
202C22×#103C2×C1111yescharacteristic, complemented
203#2409C2×C1111yescharacteristic, complemented
204#2026C2×C1112yescomplemented
205#2000C2×C1112yescomplemented
206#1893C2×C1111yescharacteristic, complemented
207#1877C2×C1112yescomplemented
208#1873C2×C1112yescomplemented
209#1869C2×C1111yescharacteristic, complemented
210#1824C2×C1111yescharacteristic, complemented
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—21no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—22no—
219C23×C11—42no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—42no—
223C23×C11#12012yes—
224C23×C11#13512yes—
225C23×C11#13712yes—
226C23×C11C22×D411yescharacteristic
227Q8×C11—24no—
228Q8×C11—24no—
229Q8×C11—48no—
230Q8×C11—42no—
231Q8×C11—42no—
232D4×C11—24no—
233D4×C11—44no—
234D4×C11—48no—
235D4×C11—41no—
236D4×C11—41no—
237D4×C11—84no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—48no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—84no—
267C2×C4×C11—84no—
268C2×C4×C11#12012yes—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C2×#4112yes—
272C2×C4×C11H(5,𝔽2)12yes—
273C8×C11—42no—
274C8×C11—42no—
275C23×Q8C22×C1111yescharacteristic
276C22×SD16C22×C1112yes—
277C23×C8C22×C1111yescharacteristic
278#553—24no—
279#553—24no—
280C2×#126—21no—
281C2×#125C22×C1111yescharacteristic
282C2×#123—21no—
283C2×C22⋊Q8C22×C1112yes—
284C2×#121—21no—
285C2×#121C22×C1111yescharacteristic
286C2×#121C22×C1111yescharacteristic
287C2×C4×D4—21no—
288C2×C4×D4C22×C1111yescharacteristic
289C2×C4×D4C22×C1111yescharacteristic
290C2×#117C22×C1111yescharacteristic
291C22×C4⋊C4C22×C1111yescharacteristic
292#448—24no—
293C2×#103—24no—
294C2×#103C22×C1112yes—
295C2×#103C22×C1112yes—
296C2×#103C22×C1112yes—
297C2×#102C22×C1112yes—
298C2×C22⋊C8C22×C1111yescharacteristic
299C2×C22⋊C8C22×C1112yes—
300#395—21no—
301#393—21no—
302#391C22×C1112yes—
303#386—21no—
304#385—21no—
305#380C22×C1111yescharacteristic
306#340C22×C1112yes—
307#340C22×C1112yes—
308#340C22×C1112yes—
309#336C22×C1112yes—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—24no—
313C22×C11—24no—
314C22×C11—41no—
315C22×C11—42no—
316C22×C11—41no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—41no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—82no—
323C22×C11—82no—
324C22×C11#45214yes—
325C22×C11C2×#12011yescharacteristic
326C22×C11#54612yes—
327C22×C11C2×#13511yescharacteristic
328C22×C11C2×#13711yescharacteristic
329C22×C11#57712yes—
330C4×C11—22no—
331C4×C11—41no—
332C4×C11—44no—
333C4×C11—41no—
334C4×C11—42no—
335C4×C11—41no—
336C4×C11—42no—
337C4×C11—42no—
338C4×C11—82no—
339C4×C11#52511yescharacteristic
340C4×C11#53511yescharacteristic
341C4×C11#54612yes—
342C22×Q8—21no—
343C22×Q8—24no—
344C22×Q8—22no—
345C22×Q8—22no—
346C22×Q8—42no—
347C22×Q8C23×C1112yes—
348C22×D4—21no—
349C22×D4—21no—
350C22×D4D4×C1111yescharacteristic
351C22×D4C23×C1111yescharacteristic
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4C23×C1111yescharacteristic
356C23×C4C23×C1111yescharacteristic
357C2×SD16—24no—
358C2×SD16—24no—
359C2×SD16—42no—
360C22×C8—22no—
361C22×C8—42no—
362C22×C8C23×C1112yes—
363C22×C8C23×C1112yes—
364#126—28no—
365#125—22no—
366#125—22no—
367#123—28no—
368C22⋊Q8—24no—
369C22⋊Q8—42no—
370#121—28no—
371#121—22no—
372#121—22no—
373#121—22no—
374#121D4×C1114yes—
375C4×D4—28no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4—22no—
380#117—22no—
381#117—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4D4×C1111yescharacteristic
388C2×C4⋊C4D4×C1114yes—
389C2×C4⋊C4C23×C1112yes—
390C2×C4⋊C4C23×C1111yescharacteristic
391C2×C4⋊C4C23×C1111yescharacteristic
392C2×C4⋊C4C23×C1111yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4D4×C1111yescharacteristic
400C2×C22⋊C4D4×C1111yescharacteristic
401C2×C42—21no—
402C2×C42C23×C1111yescharacteristic
403#103—24no—
404#103—24no—
405#103—24no—
406#102—42no—
407C22⋊C8—22no—
408C22⋊C8—42no—
409#95—21no—
410#95—22no—
411#95—22no—
412C2×C11—24no—
413C2×C11—81no—
414C2×C11—82no—
415C2×C11#240411yescharacteristic
416C2×C11C2×#45211yescharacteristic
417C2×C11#300911yescharacteristic
418C2×C11#330112yes—
419C2×C11#332012yes—
420C24—21no—
421C24C2×D4×C1111yescharacteristic
422C24C2×D4×C1111yescharacteristic
423C2×Q8—22no—
424C2×Q8—28no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—44no—
430C2×Q8—48no—
431C2×Q8—44no—
432C2×Q8—42no—
433C2×Q8C11×#4114yes—
434C2×D4—22no—
435C2×D4—24no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—24no—
439C2×D4—21no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4—82no—
445C2×D4C2×D4×C1112yes—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—44no—
460C22×C4—42no—
461C22×C4—82no—
462C22×C4—82no—
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C2×D4×C1111yescharacteristic
465C22×C4C2×D4×C1111yescharacteristic
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C2×D4×C1112yes—
468C22×C4C2×D4×C1112yes—
469C22×C4C24×C1111yescharacteristic
470SD16—48no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—44no—
478C4⋊C4—24no—
479C4⋊C4—24no—
480C4⋊C4—24no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—44no—
488C4⋊C4C2×D4×C1112yes—
489C4⋊C4C2×D4×C1112yes—
490C4⋊C4C2×D4×C1112yes—
491C22⋊C4—24no—
492C22⋊C4—24no—
493C22⋊C4—24no—
494C22⋊C4—22no—
495C22⋊C4—24no—
496C22⋊C4—22no—
497C22⋊C4—44no—
498C22⋊C4—42no—
499C42—24no—
500C42—21no—
501C42—21no—
502C11#2396411yescharacteristic, direct product factor, Sylow
503C23—22no—
504C23—22no—
505C23—21no—
506C23—22no—
507C23—22no—
508C23—21no—
509C23—21no—
510C23—22no—
511C23—42no—
512C23—41no—
513C23—41no—
514C23—42no—
515C23C11×#12012yes—
516C23C11×#13512yes—
517C23C11×#13712yes—
518C23C22×D4×C1111yescharacteristic
519Q8—24no—
520Q8—24no—
521Q8—48no—
522Q8—42no—
523Q8—42no—
524D4—24no—
525D4—44no—
526D4—48no—
527D4—41no—
528D4—41no—
529D4—84no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—48no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—84no—
559C2×C4—84no—
560C2×C4C11×#12012yes—
561C2×C4C22×D4×C1111yescharacteristic
562C2×C4C22×D4×C1111yescharacteristic
563C2×C4C2×C11×#4112yes—
564C2×C4C11×H(5,𝔽2)12yes—
565C8—42no—
566C8—42no—
567C22—22no—
568C22—22no—
569C22—24no—
570C22—24no—
571C22—41no—
572C22—42no—
573C22—41no—
574C22—42no—
575C22—42no—
576C22—41no—
577C22—42no—
578C22—42no—
579C22—82no—
580C22—82no—
581C22C11×#45214yes—
582C22C2×C11×#12011yescharacteristic
583C22C11×#54612yes—
584C22C2×C11×#13511yescharacteristic
585C22C2×C11×#13711yescharacteristic
586C22C11×#57712yes—
587C4—22no—
588C4—41no—
589C4—44no—
590C4—41no—
591C4—42no—
592C4—41no—
593C4—42no—
594C4—42no—
595C4—82no—
596C4C11×#52511yescharacteristic
597C4C11×#53511yescharacteristic
598C4C11×#54612yes—
599C2—24no—
600C2—81no—
601C2—82no—
602C2C11×#240411yescharacteristic
603C2C2×C11×#45211yescharacteristic
604C2C11×#300911yescharacteristic
605C2C11×#330112yes—
606C2C11×#332012yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#553C2
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×#448C2semidirect
3. C22×C11×#103C2semidirect
4. C11×#2409C2semidirect
5. C11×#2026C2semidirect
6. C11×#2000C2semidirect
7. C11×#1893C2semidirect
8. C11×#1877C2semidirect
9. C11×#1873C2semidirect
10. C11×#1869C2semidirect
11. C11×#1824C2semidirect
117. #23964C11direct (N × H)
201. C2×#448C2×C11semidirect
202. C22×#103C2×C11semidirect
203. #2409C2×C11semidirect
204. #2026C2×C11semidirect
205. #2000C2×C11semidirect
206. #1893C2×C11semidirect
207. #1877C2×C11semidirect
208. #1873C2×C11semidirect
209. #1869C2×C11semidirect
210. #1824C2×C11semidirect
502. C11#23964direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5532
C2×C11×#4482
C22×C11×#1032
C11×#24092
C11×#20262
C11×#20002
C11×#18932
C11×#18772
C11×#18732
C11×#18692
C11×#18242
#2396411