Finite Group Databasebeta

← #14657041

Subgroups — #14657041

Order 2816.

772 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074350C211yesmaximal, characteristic
2#13068933C211yesmaximal, characteristic, complemented
3#13068804C211yesmaximal, characteristic, complemented
4C2×#10622089C211yesmaximal, characteristic, complemented
5C2×#10622163C211yesmaximal, characteristic, complemented
6#13066495C211yesmaximal, characteristic, complemented
7C11×#1439C211yesmaximal, characteristic, complemented
8C22×C11×C4⋊C4C2211yescharacteristic
9C22×C11×C22⋊C4—21no—
10C22×C11×C22⋊C4C2211yescharacteristic
11C2×#67006—21no—
12C2×#66983C2211yescharacteristic
13C2×C11×#95—21no—
14C2×C11×#95C2211yescharacteristic
15#10622826—21no—
16#10622825C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×#66873—21no—
20C2×#66871—21no—
21#10622574—21no—
22#10622574—21no—
23#10622573—21no—
24#10622566—21no—
25#10622167—21no—
26#10622167—21no—
27#10622163—22no—
28#10622089—22no—
29C25×C11D411yescharacteristic
30C23×C4×C11—21no—
31C23×C4×C11—21no—
32C23×C4×C11D411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C22×C22⋊D11—21no—
35C22×C22⋊D11—21no—
36C22×C22⋊D11—21no—
37C22×D44D411yescharacteristic
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—42no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—42no—
48C2×C11×C22⋊C4—42no—
49C2×C11×C22⋊C4—42no—
50#67006—42no—
51#67006—42no—
52C2×C22⋊Dic11—21no—
53C2×C22⋊Dic11—21no—
54C2×C22⋊Dic11—21no—
55#66983—21no—
56#66983—21no—
57#66983—21no—
58#66983—21no—
59C2×(C2×D11)⋊C4—21no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—21no—
62C2×C4⋊Dic11D411yescharacteristic
63C2×C4⋊Dic11D411yescharacteristic
64C2×C4⋊Dic11D411yescharacteristic
65C22×C11⋊C8—21no—
66C22×C11⋊C8—21no—
67C11×#95—21no—
68C11×#95—21no—
69C11×#95—42no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)D412yescomplemented
77#66873—42no—
78#66871—42no—
79#10394—111nomaximal, Sylow
80C24×C11—21no—
81C24×C11—21no—
82C24×C11—21no—
83C24×C11—21no—
84C24×C11—21no—
85C24×C11—21no—
86C24×C11—41no—
87C24×C11—41no—
88C24×C11—41no—
89C24×C11—41no—
90C24×C11D812yes—
91C24×C11C2×D411yescharacteristic
92C23×D11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11—41no—
111C22×C4×C11—41no—
112C22×C4×C11—41no—
113C22×C4×C11—41no—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C22×C4×C11#4111yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C2×C22⋊D11—42no—
121C2×C22⋊D11—42no—
122C2×C22⋊D11—41no—
123C2×C22⋊D11—41no—
124C2×C22⋊D11—41no—
125C2×C22⋊D11—41no—
126C2×C22⋊D11—41no—
127C2×C22⋊D11—41no—
128C2×C22⋊D11—81no—
129C2×C22⋊D11—81no—
130C2×C22⋊D11—81no—
131C2×C22⋊D11—81no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—41no—
138C2×D44—41no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—41no—
142C11×C4⋊C4—41no—
143C11×C22⋊C4—48no—
144C11×C22⋊C4—41no—
145C11×C22⋊C4—41no—
146C11×C22⋊C4—41no—
147C11×C22⋊C4—41no—
148C22⋊Dic11—42no—
149C22⋊Dic11—42no—
150C22⋊Dic11—41no—
151C22⋊Dic11—41no—
152(C2×D11)⋊C4—41no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—81no—
155(C2×D11)⋊C4—81no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—41no—
159C4⋊Dic11—41no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—41no—
162C2×C11⋊C8—41no—
163C2×C11⋊C8—41no—
164C2×C11⋊C8—41no—
165C2×C11⋊C8—41no—
166#2617—111no—
167#1874—111no—
168#1852—111no—
169C2×#327—111no—
170C2×#323—111no—
171#1439D1111yescharacteristic, complemented
172#1294—111no—
173C23×C11—21no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—81no—
195C23×C11—81no—
196C23×C11—81no—
197C23×C11—81no—
198C23×C11—81no—
199C23×C11—81no—
200C23×C11#12011yescharacteristic
201C23×C11#12111yescharacteristic
202C23×C11#12311yescharacteristic
203C23×C11C2×D811yescharacteristic
204C23×C11#13511yescharacteristic
205C23×C11AGL(1,ℤ/8)11yescharacteristic
206C23×C11#13711yescharacteristic
207C22×D11—41no—
208C22×D11—41no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—41no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—81no—
233C2×C4×C11—81no—
234C2×C4×C11—81no—
235C2×C4×C11—81no—
236C2×C4×C11—81no—
237C2×C4×C11—81no—
238C2×C4×C11—81no—
239C2×C4×C11—81no—
240C2×C4×C11—81no—
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11#12311yescharacteristic
244C2×C4×C11#12411yescharacteristic
245C22⋊D11—84no—
246C22⋊D11—84no—
247C22⋊D11—81no—
248C22⋊D11—81no—
249C22⋊D11—81no—
250C22⋊D11—81no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260D44—42no—
261D44—81no—
262C11⋊C8—42no—
263C11⋊C8—81no—
264C2×#121—111no—
265C2×#120—221no—
266C22×C4⋊C4C2×D1111yescharacteristic
267C22×C22⋊C4—21no—
268C22×C22⋊C4C2×D1111yescharacteristic
269C2×#107—221no—
270C2×#102—221no—
271C2×C22⋊C8—111no—
272C2×C22⋊C8—111no—
273#397—221no—
274#394—221no—
275#394—221no—
276#392—221no—
277#386—221no—
278#380—111no—
279C2×#95—21no—
280C2×#95C2×D1111yescharacteristic
281#340—221no—
282#340—221no—
283#327—222no—
284#323—222no—
285C22×C11—21no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—44no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—82no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11—81no—
305C22×C11—81no—
306C22×C11—81no—
307C22×C11—81no—
308C22×C11#39411yescharacteristic
309C22×C11#44711yescharacteristic
310C22×C11#45211yescharacteristic
311C22×C11#45311yescharacteristic
312C22×C11#45511yescharacteristic
313C22×C11B(4,𝔽2)11yescharacteristic
314C22×C11#45811yescharacteristic
315C22×C11#46611yescharacteristic
316C22×C11#46811yescharacteristic
317C22×C11#48011yescharacteristic
318C22×C11#48211yescharacteristic
319C2×D11—81no—
320C2×D11—81no—
321C2×D11—81no—
322C2×D11—81no—
323C2×D11—81no—
324C2×D11—81no—
325C2×D11—81no—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—82no—
331C4×C11—82no—
332C4×C11—81no—
333Dic11—81no—
334Dic11—81no—
335Dic11—81no—
336C25C22⋊D1111yescharacteristic
337C22×D4—111no—
338C22×D4—221no—
339C22×D4—221no—
340C22×D4—221no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4C22⋊D1111yescharacteristic
344C23×C4C22×D1111yescharacteristic
345C22×C8—221no—
346C22×C8—221no—
347#121—221no—
348#121—221no—
349#121—221no—
350#121—221no—
351#120—442no—
352#120—442no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—111no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—221no—
369C2×C22⋊C4—221no—
370C2×C22⋊C4—221no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374#107—442no—
375#102—442no—
376C22⋊C8—112no—
377C22⋊C8—221no—
378C22⋊C8—221no—
379C22⋊C8—221no—
380#95—21no—
381#95—21no—
382#95—42no—
383#95—221no—
384#95—221no—
385#95—221no—
386C2×C11—21no—
387C2×C11—21no—
388C2×C11—21no—
389C2×C11—21no—
390C2×C11—82no—
391C2×C11#159511yescharacteristic
392C2×C11#160611yescharacteristic
393C2×C11#160711yescharacteristic
394C2×C11#161811yescharacteristic
395C2×C11#203311yescharacteristic
396C2×C11#203711yescharacteristic
397C2×C11#204411yescharacteristic
398D11—161no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—41no—
406C24—41no—
407C24—41no—
408C24—41no—
409C24—221no—
410C24#432312yes—
411C24C2×C22⋊D1111yescharacteristic
412C2×D4—221no—
413C2×D4—221no—
414C2×D4—441no—
415C2×D4—441no—
416C2×D4—442no—
417C2×D4—442no—
418C2×D4—441no—
419C2×D4—441no—
420C2×D4—441no—
421C2×D4—441no—
422C2×D4—441no—
423C2×D4—441no—
424C2×D4—881no—
425C2×D4—881no—
426C2×D4—881no—
427C2×D4—881no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4#433911yescharacteristic
453C22×C4#433911yescharacteristic
454C22×C4D4×D1111yescharacteristic
455C22×C4D4×D1111yescharacteristic
456C22×C4D4×D1111yescharacteristic
457C22×C4#434111yescharacteristic
458C2×C8—222no—
459C2×C8—441no—
460C2×C8—441no—
461C2×C8—441no—
462C2×C8—441no—
463C2×C8—441no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—441no—
471C4⋊C4—441no—
472C22⋊C4—48no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—442no—
478C22⋊C4—442no—
479C22⋊C4—441no—
480C22⋊C4—441no—
481C22⋊C4—441no—
482C22⋊C4—441no—
483C22⋊C4—881no—
484C22⋊C4—881no—
485C11#1039411yescharacteristic, complemented, Sylow
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—81no—
508C23—81no—
509C23—81no—
510C23—81no—
511C23—81no—
512C23—81no—
513C23—441no—
514C23—441no—
515C23—441no—
516C23—441no—
517C23—441no—
518C23—441no—
519C23—441no—
520C23#6698211yescharacteristic
521C23C2×#432311yescharacteristic
522C23#6699011yescharacteristic
523C23#6699211yescharacteristic
524C23#6699511yescharacteristic
525C23#6700211yescharacteristic
526C23#6700311yescharacteristic
527D4—442no—
528D4—881no—
529D4—884no—
530D4—884no—
531D4—881no—
532D4—881no—
533D4—881no—
534D4—881no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—81no—
554C2×C4—81no—
555C2×C4—81no—
556C2×C4—81no—
557C2×C4—81no—
558C2×C4—81no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4—81no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4#6693611yescharacteristic
572C2×C4#6693711yescharacteristic
573C2×C4#6693711yescharacteristic
574C2×C4#6693811yescharacteristic
575C8—442no—
576C8—881no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—44no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—881no—
601C22—881no—
602C22—881no—
603C22—881no—
604C22—881no—
605C22—881no—
606C22—881no—
607C22#1062257211yescharacteristic
608C22#1062258011yescharacteristic
609C22#1062261611yescharacteristic
610C22#1062264511yescharacteristic
611C22#1062264911yescharacteristic
612C22#1062265111yescharacteristic
613C22#1062266011yescharacteristic
614C22#1062266211yescharacteristic
615C22#1062266611yescharacteristic
616C22#1062267411yescharacteristic
617C22#1062269011yescharacteristic
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—82no—
623C4—81no—
624C4—82no—
625C4—881no—
626C4—881no—
627C4—881no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—82no—
633C2—1761no—
634C2#1306753311yescharacteristic
635C2#1306759411yescharacteristic
636C2#1306760111yescharacteristic
637C2#1306766211yescharacteristic
638C2#1306979811yescharacteristic
639C2#1306982611yescharacteristic
640C2#1306986511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1439C2
socleC23×C11#120
prime radical#13074350C2
hypercenter#1439D11
hypocenterC11#10394
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. #13068933C2semidirect
3. #13068804C2semidirect
4. C2×#10622089C2semidirect
5. C2×#10622163C2semidirect
6. #13066495C2semidirect
7. C11×#1439C2semidirect
76. C22⋊(C11⋊C8)D4semidirect
171. #1439D11semidirect
485. C11#10394semidirect

Maximal subgroups

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

subgroupindex
#130743502
#130689332
#130688042
C2×#106220892
C2×#106221632
#130664952
C11×#14392
#1039411