Finite Group Databasebeta

← #14809940

Subgroups — #14809940

Order 2816.

2026 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#127C211yesmaximal, characteristic
2C2×#10622701C211yesmaximal, characteristic, complemented
3#13076963C211yesmaximal, characteristic, complemented
4#13069848C214yesmaximal, complemented
5#13069423C211yesmaximal, characteristic, complemented
6#13069422C211yesmaximal, characteristic, complemented
7#13068545C214yesmaximal, complemented
8C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
9C2×C11×#486C211yesmaximal, characteristic, complemented
10C22×D4×D11—21no—
11C22×D4×D11—21no—
12C22×D4×D11C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic, complemented
14C2×C11×#127C2211yescharacteristic
15C2×#66999—21no—
16C2×#66993—21no—
17C2×#66993—21no—
18C2×#66993C2212yes—
19D11×#127—24no—
20D11×#127—24no—
21C2×#66927C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C11×#486—24no—
24C2×C11×#102C2214yescomplemented
25C2×C4×C8×C11C2211yescharacteristic, complemented
26#10622843—21no—
27C2×#66896C2214yescomplemented
28C2×#66885C2214yescomplemented
29C2×(C2×D11)⋊C8C2212yes—
30#10622701—24no—
31#10622600—21no—
32#10622600C2212yes—
33#10622586—21no—
34#10622586C2212yescomplemented
35C2×#66873C2214yescomplemented
36#10622548C2211yescharacteristic, complemented
37C2×C4×C11⋊C8C2211yescharacteristic, complemented
38#10622188C2212yescomplemented
39C24×D11—22no—
40C22×Q8×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11C2312yes—
44C22×C22⋊D11—22no—
45C22×C22⋊D11—22no—
46C22×C22⋊D11—22no—
47C2×D4×D11—28no—
48C2×D4×D11—28no—
49C2×D4×D11—24no—
50C2×D4×D11—24no—
51C2×D4×D11—28no—
52C2×D4×D11—44no—
53C2×D4×D11—44no—
54C2×D4×D11—44no—
55C2×D4×D11—44no—
56C2×D4×D11—44no—
57C22×D44—21no—
58C22×D44—21no—
59C22×D44C2312yes—
60C22×C4×D11D411yescharacteristic
61C22×C4×D11D411yescharacteristic
62C22×C4×D11C2311yescharacteristic
63C22×C8×C11C2312yes—
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8—22no—
66C11×#127—22no—
67C11×#127D414yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2312yes—
70C2×C42×C11C2311yescharacteristic
71#66999—44no—
72#66993—28no—
73#66993—28no—
74#66993—24no—
75#66993—24no—
76C2×(C2×D11)⋊C4—22no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2312yes—
80C2×Dic11⋊C4—22no—
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C22×C11⋊C8C2312yes—
85#66927—22no—
86#66927D414yes—
87C42×D11—22no—
88C42×D11—22no—
89C11×#102—28no—
90C4×C8×C11—22no—
91#66896—44no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94#66885—44no—
95(C2×D11)⋊C8—24no—
96#66873—28no—
97C4×C11⋊C8—22no—
98#25855—111nomaximal, Sylow
99C24×C11—22no—
100C23×D11—28no—
101C23×D11—22no—
102C23×D11—44no—
103C23×D11—44no—
104C23×D11—44no—
105C23×D11—44no—
106C23×D11—44no—
107C23×D11—44no—
108C23×D11C2×D411yescharacteristic
109C2×Q8×C11—42no—
110C2×Q8×C11—42no—
111C2×Q8×C11—42no—
112C2×D4×C11—24no—
113C2×D4×C11—24no—
114C2×D4×C11—22no—
115C2×D4×C11—24no—
116C2×D4×C11—24no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11C2×D414yes—
122C22×C4×C11—22no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C2×C22⋊D11—28no—
127C2×C22⋊D11—28no—
128C2×C22⋊D11—28no—
129C2×C22⋊D11—44no—
130C2×C22⋊D11—44no—
131C2×C22⋊D11—44no—
132C2×C22⋊D11—44no—
133C2×C22⋊D11—44no—
134C2×C22⋊D11—44no—
135C22×Dic11—22no—
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139D4×D11—416no—
140D4×D11—416no—
141D4×D11—432no—
142D4×D11—432no—
143C2×D44—24no—
144C2×D44—24no—
145C2×D44—22no—
146C2×D44—24no—
147C2×D44—24no—
148C2×D44—42no—
149C2×D44—42no—
150C2×D44—42no—
151C2×D44—42no—
152C2×D44C2×D414yes—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—22no—
160C2×C4×D11D814yes—
161C2×C4×D11SD1614yes—
162C2×C4×D11#4114yes—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—42no—
169C42×C11C2×D412yes—
170C42×C11C2×D412yes—
171(C2×D11)⋊C4—44no—
172C4⋊Dic11—24no—
173C4⋊Dic11—42no—
174C4⋊Dic11—42no—
175Dic11⋊C4—44no—
176C4×Dic11—22no—
177C4×Dic11—22no—
178C4×Dic11—21no—
179C4×Dic11—21no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C22×#127—111no—
184C2×#486—111no—
185C2×#486D1111yescharacteristic, complemented
186#2857—111no—
187#2041—114no—
188#1957—111no—
189#1957—111no—
190#1786—114no—
191C4×C22⋊C8—111no—
192C23×C11—24no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11C22×D411yescharacteristic
200C22×D11—21no—
201C22×D11—21no—
202C22×D11—21no—
203C22×D11—21no—
204C22×D11—24no—
205C22×D11—416no—
206C22×D11—416no—
207C22×D11—416no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—88no—
215C22×D11—88no—
216C22×D11—88no—
217C22×D11—88no—
218C22×D11#12412yes—
219C22×D11C2×D812yes—
220C22×D11C2×SD1612yes—
221Q8×C11—84no—
222D4×C11—28no—
223D4×C11—44no—
224D4×C11—48no—
225D4×C11—48no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11#12012yes—
230C2×C4×C11#12012yes—
231C2×C4×C11C2×D812yes—
232C2×C4×C11C2×SD1612yes—
233C2×C4×C11AGL(1,ℤ/8)12yes—
234C2×C4×C11AGL(1,ℤ/8)12yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C2×#4112yes—
238C2×C4×C11H(5,𝔽2)12yes—
239C22⋊D11—416no—
240C22⋊D11—416no—
241C22⋊D11—416no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11#12412yes—
252C2×Dic11C2×D812yes—
253C2×Dic11C2×SD1612yes—
254D44—28no—
255D44—44no—
256D44—48no—
257D44—48no—
258C4×D11—24no—
259C4×D11—24no—
260C4×D11—28no—
261C4×D11—28no—
262C8×C11—42no—
263C11⋊C8—42no—
264C23×D4—112no—
265C23×D4—221no—
266C23×D4—221no—
267C2×C4⋊Q8C2×D1111yescharacteristic, complemented
268C2×#127—112no—
269C2×#127—111no—
270C2×#127—221no—
271C2×#127—221no—
272C2×#127—224no—
273C2×#127—224no—
274C2×#127C2×D1111yescharacteristic
275C2×C22⋊Q8—221no—
276C22×C42—111no—
277#486—24no—
278#486—224no—
279C2×#102—114no—
280C2×#102—114no—
281C2×#102—114no—
282C2×#102C2×D1114yescomplemented
283C2×C22⋊C8—112no—
284C2×C4×C8—111no—
285C2×C4×C8C2×D1111yescharacteristic, complemented
286#391—221no—
287#389—112no—
288#389—221no—
289#384—111no—
290#380—112no—
291#380—221no—
292#336—112no—
293C22×C11—44no—
294C22×C11—44no—
295C22×C11—44no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11—82no—
300C22×C11C2×#12011yescharacteristic
301C22×C11C2×#12411yescharacteristic
302C22×C11#53511yescharacteristic
303C22×C11C22×D811yescharacteristic
304C22×C11C22×SD1611yescharacteristic
305C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
306C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
307C2×D11—22no—
308C2×D11—22no—
309C2×D11—22no—
310C2×D11—22no—
311C2×D11—22no—
312C2×D11—22no—
313C2×D11—44no—
314C2×D11—44no—
315C2×D11—44no—
316C2×D11—832no—
317C2×D11—82no—
318C2×D11—82no—
319C2×D11—82no—
320C2×D11—82no—
321C2×D11#48614yescomplemented
322C4×C11—82no—
323C4×C11#44714yes—
324C4×C11#45014yes—
325C4×C11#54612yes—
326C4×C11#54612yes—
327Dic11—22no—
328Dic11—22no—
329Dic11—22no—
330Dic11—82no—
331C25—222no—
332C22×Q8—21no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—112no—
336C22×D4—228no—
337C22×D4—222no—
338C22×D4—222no—
339C22×D4—222no—
340C22×D4—224no—
341C22×D4—228no—
342C22×D4—228no—
343C22×D4—224no—
344C22×D4—221no—
345C22×D4—221no—
346C22×D4—444no—
347C22×D4—444no—
348C22×D4—444no—
349C22×D4—444no—
350C22×D4—444no—
351C22×D4C22×D1112yes—
352C23×C4—111no—
353C23×C4—111no—
354C23×C4—111no—
355C22×C8—112no—
356C22×C8C22×D1112yes—
357C4⋊Q8—22no—
358C4⋊Q8—22no—
359#127—22no—
360#127—114no—
361#127—224no—
362#127—228no—
363#127—228no—
364#127—224no—
365#127—222no—
366#127C22⋊D1114yes—
367C22⋊Q8—444no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—112no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4C22×D1112yes—
374C2×C22⋊C4—222no—
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—222no—
379C2×C42—222no—
380C2×C42C22×D1111yescharacteristic
381#102—28no—
382#102—228no—
383#102—444no—
384#102—444no—
385C22⋊C8—224no—
386C4×C8—22no—
387C4×C8—222no—
388#95—222no—
389#95—222no—
390C2×C11—84no—
391C2×C11#243511yescharacteristic
392C2×C11C2×#44711yescharacteristic
393C2×C11C2×#45011yescharacteristic
394C2×C11C2×#48611yescharacteristic
395C2×C11#313811yescharacteristic
396C2×C11#320511yescharacteristic
397C2×C11#320811yescharacteristic
398D11—24no—
399D11—84no—
400C24—22no—
401C24—111no—
402C24—228no—
403C24—222no—
404C24—444no—
405C24—444no—
406C24—444no—
407C24—444no—
408C24—444no—
409C24—444no—
410C2×Q8—42no—
411C2×Q8—42no—
412C2×Q8—42no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—22no—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—114no—
423C2×D4—228no—
424C2×D4—228no—
425C2×D4—228no—
426C2×D4—224no—
427C2×D4—224no—
428C2×D4—224no—
429C2×D4—224no—
430C2×D4—222no—
431C2×D4—444no—
432C2×D4—444no—
433C2×D4—444no—
434C2×D4—4416no—
435C2×D4—4416no—
436C2×D4—4432no—
437C2×D4—4432no—
438C2×D4—444no—
439C2×D4—444no—
440C2×D4—444no—
441C2×D4—442no—
442C2×D4—442no—
443C2×D4—442no—
444C2×D4—442no—
445C2×D4C2×C22⋊D1114yes—
446C22×C4—22no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—114no—
451C22×C4—114no—
452C22×C4—114no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—221no—
458C22×C4—222no—
459C22×C4—221no—
460C22×C4—222no—
461C22×C4D4×D1111yescharacteristic
462C22×C4D4×D1111yescharacteristic
463C22×C4C23×D1111yescharacteristic
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—222no—
468C2×C8—222no—
469C2×C8—222no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—42no—
473C4⋊C4—224no—
474C4⋊C4—444no—
475C4⋊C4—442no—
476C4⋊C4—442no—
477C22⋊C4—444no—
478C42—222no—
479C42—222no—
480C42—221no—
481C42—221no—
482C42D4×D1112yes—
483C42C2×C22⋊D1112yes—
484C11#2585511yescharacteristic, complemented, Sylow
485C23—24no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—112no—
493C23—112no—
494C23—112no—
495C23—221no—
496C23—221no—
497C23—221no—
498C23—221no—
499C23—224no—
500C23—4416no—
501C23—4416no—
502C23—4416no—
503C23—442no—
504C23—442no—
505C23—442no—
506C23—442no—
507C23—442no—
508C23—442no—
509C23—888no—
510C23—888no—
511C23—888no—
512C23—888no—
513C23C2×D4×D1111yescharacteristic
514Q8—84no—
515D4—28no—
516D4—48no—
517D4—48no—
518D4—44no—
519D4—228no—
520D4—4416no—
521D4—4416no—
522D4—4416no—
523D4—448no—
524D4—448no—
525D4—444no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—112no—
530C2×C4—112no—
531C2×C4—112no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—228no—
539C2×C4—228no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4D8×D1112yes—
546C2×C4#6696412yes—
547C2×C4SD16×D1112yes—
548C2×C4#6696712yes—
549C2×C4#6699012yes—
550C2×C4#6699012yes—
551C2×C4C2×D4×D1111yescharacteristic
552C2×C4#41×D1112yes—
553C2×C4#6704212yes—
554C2×C4C22×C22⋊D1111yescharacteristic
555C8—42no—
556C8—442no—
557C22—44no—
558C22—44no—
559C22—44no—
560C22—82no—
561C22—82no—
562C22—82no—
563C22—82no—
564C22—114no—
565C22—222no—
566C22—222no—
567C22—222no—
568C22—222no—
569C22—222no—
570C22—222no—
571C22—444no—
572C22—444no—
573C22—444no—
574C22—8832no—
575C22—882no—
576C22—882no—
577C22—882no—
578C22—882no—
579C22D11×#12411yescharacteristic
580C22#1062320511yescharacteristic
581C22C2×D8×D1111yescharacteristic
582C22C2×#6696411yescharacteristic
583C22C2×SD16×D1111yescharacteristic
584C22C2×#6696711yescharacteristic
585C22C2×#6699011yescharacteristic
586C4—82no—
587C4—222no—
588C4—222no—
589C4—222no—
590C4—882no—
591C4#1062276914yes—
592C4#1062278214yes—
593C4#1062320712yes—
594C4#1062336012yes—
595C2—84no—
596C2—224no—
597C2—884no—
598C2#1307226411yescharacteristic
599C2C2×#1062276911yescharacteristic
600C2C2×#1062278211yescharacteristic
601C2D11×#48611yescharacteristic
602C2#1307898711yescharacteristic
603C2#1307953511yescharacteristic
604C2#1307955811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#486C2
socleC23×C11C22×D4
prime radicalC2×D11×#127C2
hypercenterC2×#486D11
hypocenterC11#25855
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
2. C2×#10622701C2semidirect
3. #13076963C2semidirect
4. #13069848C2semidirect
5. #13069423C2semidirect
6. #13069422C2semidirect
7. #13068545C2semidirect
8. C4×(C2×D11)⋊C8C2semidirect
9. C2×C11×#486C2semidirect
13. C2×C11×C4⋊Q8C22semidirect
24. C2×C11×#102C22semidirect
25. C2×C4×C8×C11C22semidirect
27. C2×#66896C22semidirect
28. C2×#66885C22semidirect
34. #10622586C22semidirect
35. C2×#66873C22semidirect
36. #10622548C22semidirect
37. C2×C4×C11⋊C8C22semidirect
38. #10622188C22semidirect
185. C2×#486D11semidirect
267. C2×C4⋊Q8C2×D11semidirect
282. C2×#102C2×D11semidirect
285. C2×C4×C8C2×D11semidirect
321. C2×D11#486semidirect
484. C11#25855semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1272
C2×#106227012
#130769632
#130698482
#130694232
#130694222
#130685452
C4×(C2×D11)⋊C82
C2×C11×#4862
#2585511