Finite Group Databasebeta

← C11×#23987 #14601180

Subgroups — C11×#23987 #14601180

Order 2816.

1514 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×#3490C211yesmaximal, characteristic, complemented
2C11×#2613C212yesmaximal, complemented
3C11×#2308C211yesmaximal, characteristic, complemented
4C11×#2030C211yesmaximal, characteristic, complemented
5C11×#2029C211yesmaximal, characteristic, complemented
6C11×#2022C211yesmaximal, characteristic, complemented
7C11×#2021C211yesmaximal, characteristic, complemented
8C11×#1898C212yesmaximal, complemented
9C11×#1890C212yesmaximal, complemented
10C11×#1889C212yesmaximal, complemented
11C11×#1819C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C11×#551—24no—
14C11×#546—24no—
15C11×#543C2211yescharacteristic
16C11×#538—22no—
17C11×#534C2211yescharacteristic
18C11×#525—22no—
19C2×C11×#123C2212yes—
20C2×C11×#120C2212yes—
21C2×C11×#120C2212yes—
22C11×#518C2212yes—
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C2×C11×#99C2212yes—
26C2×C11×#99C2212yes—
27C11×#394—24no—
28C11×#392—24no—
29C11×#386—22no—
30C11×#386—22no—
31C11×#381C2211yescharacteristic
32C11×#381C2212yes—
33C11×#381C2211yescharacteristic
34C11×#379C2211yescharacteristic
35C11×#379C2212yes—
36C11×#379C2211yescharacteristic
37C11×#379C2212yes—
38C11×#342C2212yes—
39C11×#342C2212yes—
40C11×#342C2212yes—
41C11×#342C2211yescharacteristic
42C11×#342C2211yescharacteristic
43C25×C11C2311yescharacteristic
44C25×C11C2311yescharacteristic
45C2×C11×#41—22no—
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11—22no—
49C22×D4×C11—24no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—42no—
53C22×D4×C11D414yescomplemented
54C22×D4×C11C2312yes—
55C23×C4×C11—21no—
56C23×C4×C11D412yescomplemented
57C23×C4×C11C2311yescharacteristic
58C11×#126—24no—
59C11×#124—24no—
60C11×#123—24no—
61C11×#123—24no—
62C11×#123—22no—
63C11×#123—24no—
64C11×#123—42no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—24no—
68C11×#121—22no—
69C11×#121—24no—
70C11×#121—22no—
71C11×#120—22no—
72C11×#120—22no—
73C11×#120—24no—
74C11×#120—22no—
75C11×#120—24no—
76C11×#120—42no—
77C4×D4×C11—24no—
78C4×D4×C11—24no—
79C4×D4×C11—24no—
80C11×#117—22no—
81C11×#117—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C22⋊C4—24no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—24no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—24no—
92C2×C11×C22⋊C4—42no—
93C2×C11×C22⋊C4D412yescomplemented
94C2×C11×C22⋊C4D414yescomplemented
95C2×C11×C22⋊C4C2312yes—
96C2×C11×C22⋊C4C2312yes—
97C2×C11×C22⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4C2312yes—
102C11×#99—42no—
103C11×#99—42no—
104C11×#95—22no—
105C11×#95—22no—
106C11×#95—24no—
107#23987C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11—21no—
109C24×C11—21no—
110C24×C11—22no—
111C24×C11—21no—
112C24×C11—22no—
113C24×C11—21no—
114C24×C11—22no—
115C24×C11—82no—
116C24×C11—82no—
117C24×C11C2×D412yes—
118C24×C11C2×D414yes—
119C24×C11C2×D411yescharacteristic
120C24×C11C2×D411yescharacteristic
121C24×C11#4112yescomplemented
122C24×C11C2411yescharacteristic
123C11×#41—84no—
124C2×Q8×C11—22no—
125C2×D4×C11—24no—
126C2×D4×C11—24no—
127C2×D4×C11—24no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—24no—
136C2×D4×C11—48no—
137C2×D4×C11—48no—
138C2×D4×C11—42no—
139C2×D4×C11—42no—
140C2×D4×C11—42no—
141C2×D4×C11—42no—
142C2×D4×C11—44no—
143C2×D4×C11—84no—
144C2×D4×C11—84no—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—24no—
151C22×C4×C11—22no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—42no—
157C22×C4×C11—82no—
158C22×C4×C11—82no—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D414yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11#4112yescomplemented
164C11×C4⋊C4—24no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—44no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—44no—
185C11×C22⋊C4—44no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—82no—
188C11×C22⋊C4—82no—
189C11×C22⋊C4—84no—
190C11×C22⋊C4—84no—
191C42×C11—24no—
192#3490C2×C1111yescharacteristic, complemented
193#2613C2×C1112yescomplemented
194#2308C2×C1111yescharacteristic, complemented
195#2030C2×C1111yescharacteristic, complemented
196#2029C2×C1111yescharacteristic, complemented
197#2022C2×C1111yescharacteristic, complemented
198#2021C2×C1111yescharacteristic, complemented
199#1898C2×C1112yescomplemented
200#1890C2×C1112yescomplemented
201#1889C2×C1112yescomplemented
202#1819C2×C1111yescharacteristic, complemented
203C23×C11—21no—
204C23×C11—21no—
205C23×C11—21no—
206C23×C11—21no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—24no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—44no—
218C23×C11—44no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—44no—
222C23×C11—44no—
223C23×C11—44no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—42no—
227C23×C11—82no—
228C23×C11—82no—
229C23×C11—82no—
230C23×C11—82no—
231C23×C11—84no—
232C23×C11—84no—
233C23×C11#12012yes—
234C23×C11#12012yes—
235C23×C11C22×D411yescharacteristic
236C23×C11C22×D412yes—
237C23×C11C2×#4111yescharacteristic
238C23×C11C2×#4111yescharacteristic
239C23×C11H(5,𝔽2)12yes—
240Q8×C11—82no—
241D4×C11—48no—
242D4×C11—48no—
243D4×C11—48no—
244D4×C11—42no—
245D4×C11—42no—
246D4×C11—42no—
247D4×C11—42no—
248D4×C11—84no—
249D4×C11—82no—
250D4×C11—88no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—24no—
258C2×C4×C11—22no—
259C2×C4×C11—44no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—44no—
266C2×C4×C11—44no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—44no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—82no—
275C2×C4×C11—84no—
276C2×C4×C11—84no—
277C23×D4C22×C1111yescharacteristic
278#551—24no—
279#546—24no—
280#543C22×C1111yescharacteristic
281#538—22no—
282#534C22×C1111yescharacteristic
283#525—22no—
284C2×#123C22×C1112yes—
285C2×#120C22×C1112yes—
286C2×#120C22×C1112yes—
287#518C22×C1112yes—
288C22×C22⋊C4C22×C1111yescharacteristic
289C22×C22⋊C4C22×C1111yescharacteristic
290C2×#99C22×C1112yes—
291C2×#99C22×C1112yes—
292#394—24no—
293#392—24no—
294#386—22no—
295#386—22no—
296#381C22×C1111yescharacteristic
297#381C22×C1111yescharacteristic
298#381C22×C1112yes—
299#379C22×C1111yescharacteristic
300#379C22×C1111yescharacteristic
301#379C22×C1112yes—
302#379C22×C1112yes—
303#342C22×C1112yes—
304#342C22×C1111yescharacteristic
305#342C22×C1111yescharacteristic
306#342C22×C1112yes—
307#342C22×C1112yes—
308C22×C11—22no—
309C22×C11—24no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—24no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—44no—
329C22×C11—84no—
330C22×C11—84no—
331C22×C11—82no—
332C22×C11—82no—
333C22×C11—82no—
334C22×C11—84no—
335C22×C11—82no—
336C22×C11C2×#12011yescharacteristic
337C22×C11#52511yescharacteristic
338C22×C11#53511yescharacteristic
339C22×C11#54612yes—
340C22×C11#54612yes—
341C4×C11—42no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11—42no—
345C4×C11—44no—
346C4×C11—82no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11—82no—
350C25C23×C1111yescharacteristic
351C25C23×C1111yescharacteristic
352C2×#41—22no—
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—22no—
356C22×D4—24no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—42no—
360C22×D4D4×C1114yescomplemented
361C22×D4C23×C1112yes—
362C23×C4—21no—
363C23×C4D4×C1112yescomplemented
364C23×C4C23×C1111yescharacteristic
365#126—24no—
366#124—24no—
367#123—24no—
368#123—24no—
369#123—22no—
370#123—24no—
371#123—42no—
372C22⋊Q8—22no—
373C22⋊Q8—22no—
374C22⋊Q8—24no—
375#121—22no—
376#121—24no—
377#121—22no—
378#120—22no—
379#120—22no—
380#120—24no—
381#120—22no—
382#120—24no—
383#120—42no—
384C4×D4—24no—
385C4×D4—24no—
386C4×D4—24no—
387#117—22no—
388#117—22no—
389C2×C4⋊C4—22no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4D4×C1112yescomplemented
401C2×C22⋊C4D4×C1114yescomplemented
402C2×C22⋊C4C23×C1111yescharacteristic
403C2×C22⋊C4C23×C1111yescharacteristic
404C2×C22⋊C4C23×C1112yes—
405C2×C22⋊C4C23×C1112yes—
406C2×C22⋊C4C23×C1111yescharacteristic
407C2×C22⋊C4C23×C1111yescharacteristic
408C2×C22⋊C4C23×C1112yes—
409#99—42no—
410#99—42no—
411#95—22no—
412#95—22no—
413#95—24no—
414C2×C11—21no—
415C2×C11—22no—
416C2×C11—22no—
417C2×C11—21no—
418C2×C11—42no—
419C2×C11—42no—
420C2×C11—82no—
421C2×C11—82no—
422C2×C11#240411yescharacteristic
423C2×C11#302612yes—
424C24—21no—
425C24—21no—
426C24—22no—
427C24—21no—
428C24—22no—
429C24—21no—
430C24—22no—
431C24—82no—
432C24—82no—
433C24C2×D4×C1112yes—
434C24C2×D4×C1114yes—
435C24C2×D4×C1111yescharacteristic
436C24C2×D4×C1111yescharacteristic
437C24C11×#4112yescomplemented
438C24C24×C1111yescharacteristic
439#41—84no—
440C2×Q8—22no—
441C2×D4—24no—
442C2×D4—24no—
443C2×D4—24no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—24no—
452C2×D4—48no—
453C2×D4—48no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4—42no—
457C2×D4—42no—
458C2×D4—44no—
459C2×D4—84no—
460C2×D4—84no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—42no—
473C22×C4—82no—
474C22×C4—82no—
475C22×C4C2×D4×C1112yes—
476C22×C4C2×D4×C1112yes—
477C22×C4C2×D4×C1114yes—
478C22×C4C2×D4×C1112yes—
479C22×C4C11×#4112yescomplemented
480C4⋊C4—24no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—24no—
484C4⋊C4—44no—
485C22⋊C4—24no—
486C22⋊C4—24no—
487C22⋊C4—24no—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—44no—
501C22⋊C4—44no—
502C22⋊C4—42no—
503C22⋊C4—82no—
504C22⋊C4—82no—
505C22⋊C4—84no—
506C22⋊C4—84no—
507C42—24no—
508C11#2398711yescharacteristic, direct product factor, Sylow
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—24no—
514C23—24no—
515C23—22no—
516C23—22no—
517C23—24no—
518C23—22no—
519C23—22no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—44no—
524C23—44no—
525C23—42no—
526C23—42no—
527C23—44no—
528C23—44no—
529C23—44no—
530C23—41no—
531C23—41no—
532C23—42no—
533C23—82no—
534C23—82no—
535C23—82no—
536C23—82no—
537C23—84no—
538C23—84no—
539C23C11×#12012yes—
540C23C11×#12012yes—
541C23C22×D4×C1111yescharacteristic
542C23C22×D4×C1112yes—
543C23C2×C11×#4111yescharacteristic
544C23C2×C11×#4111yescharacteristic
545C23C11×H(5,𝔽2)12yes—
546Q8—82no—
547D4—48no—
548D4—48no—
549D4—48no—
550D4—42no—
551D4—42no—
552D4—42no—
553D4—42no—
554D4—84no—
555D4—82no—
556D4—88no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—44no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—44no—
572C2×C4—44no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—44no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—82no—
581C2×C4—84no—
582C2×C4—84no—
583C22—22no—
584C22—24no—
585C22—22no—
586C22—22no—
587C22—22no—
588C22—22no—
589C22—24no—
590C22—41no—
591C22—41no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22—44no—
598C22—44no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—44no—
604C22—84no—
605C22—84no—
606C22—82no—
607C22—82no—
608C22—82no—
609C22—84no—
610C22—82no—
611C22C2×C11×#12011yescharacteristic
612C22C11×#52511yescharacteristic
613C22C11×#53511yescharacteristic
614C22C11×#54612yes—
615C22C11×#54612yes—
616C4—42no—
617C4—42no—
618C4—42no—
619C4—42no—
620C4—44no—
621C4—81no—
622C4—81no—
623C4—82no—
624C4—82no—
625C2—21no—
626C2—22no—
627C2—22no—
628C2—21no—
629C2—42no—
630C2—42no—
631C2—82no—
632C2—82no—
633C2C11×#240411yescharacteristic
634C2C11×#302612yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC24C24×C11
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3490C2semidirect
2. C11×#2613C2semidirect
3. C11×#2308C2semidirect
4. C11×#2030C2semidirect
5. C11×#2029C2semidirect
6. C11×#2022C2semidirect
7. C11×#2021C2semidirect
8. C11×#1898C2semidirect
9. C11×#1890C2semidirect
10. C11×#1889C2semidirect
11. C11×#1819C2semidirect
53. C22×D4×C11D4semidirect
56. C23×C4×C11D4semidirect
93. C2×C11×C22⋊C4D4semidirect
94. C2×C11×C22⋊C4D4semidirect
107. #23987C11direct (N × H)
121. C24×C11#41semidirect
163. C22×C4×C11#41semidirect
192. #3490C2×C11semidirect
193. #2613C2×C11semidirect
194. #2308C2×C11semidirect
195. #2030C2×C11semidirect
196. #2029C2×C11semidirect
197. #2022C2×C11semidirect
198. #2021C2×C11semidirect
199. #1898C2×C11semidirect
200. #1890C2×C11semidirect
201. #1889C2×C11semidirect
202. #1819C2×C11semidirect
360. C22×D4D4×C11semidirect
363. C23×C4D4×C11semidirect
400. C2×C22⋊C4D4×C11semidirect
401. C2×C22⋊C4D4×C11semidirect
437. C24C11×#41semidirect
479. C22×C4C11×#41semidirect
508. C11#23987direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34902
C11×#26132
C11×#23082
C11×#20302
C11×#20292
C11×#20222
C11×#20212
C11×#18982
C11×#18902
C11×#18892
C11×#18192
#2398711