Finite Group Databasebeta

← #14809098

Subgroups — #14809098

Order 2816.

1656 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622781C212yesmaximal, complemented
2C2×#10622727C211yesmaximal, characteristic, complemented
3C2×#10622841C211yesmaximal, characteristic, complemented
4C2×#10622830C211yesmaximal, characteristic
5#13072270C211yesmaximal, characteristic, complemented
6#13072263C211yesmaximal, characteristic, complemented
7#13069708C212yesmaximal, complemented
8#13069690C212yesmaximal, complemented
9#13069472C212yesmaximal, complemented
10C8×C22⋊Dic11C211yesmaximal, characteristic, complemented
11C23×C11×SD16C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C22×C11×SD16—28no—
15C22×C11×SD16—24no—
16C22×C11×SD16C2212yes—
17C22×C11×SD16C2212yes—
18C23×C8×C11C2211yescharacteristic
19C2×#67000C2212yescomplemented
20C22×#4326C2212yescomplemented
21C2×#66989C2212yes—
22C22×#4323C2212yes—
23C2×#66983C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C22×#4314C2211yescharacteristic, complemented
26#10622860—22no—
27#10622844—22no—
28#10622843C2212yescomplemented
29#10622841—24no—
30C2×#66899C2212yescomplemented
31#10622835—22no—
32#10622834C2212yes—
33#10622830—24no—
34C2×#66896C2212yes—
35#10622826—22no—
36C4×C22⋊Dic11C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38#10622781—28no—
39#10622727—24no—
40C2×#66885C2211yescharacteristic, complemented
41C2×#66881C2211yescharacteristic, complemented
42C2×#66880C2211yescharacteristic, complemented
43C2×C8×Dic11C2212yescomplemented
44#10622188C2212yescomplemented
45C25×C11—21no—
46C22×Q8×C11—21no—
47C22×Q8×C11—24no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11—42no—
51C22×Q8×C11C2312yes—
52C22×D4×C11—24no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11—21no—
56C22×D4×C11—42no—
57C22×D4×C11C2312yes—
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C22×D44C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
63C2×C11×SD16—232no—
64C2×C11×SD16—24no—
65C2×C11×SD16—24no—
66C2×C11×SD16—24no—
67C2×C11×SD16—24no—
68C2×C11×SD16—24no—
69C2×C11×SD16D418yescomplemented
70C22×C8×C11—24no—
71C22×C8×C11D414yes—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—24no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11D412yes—
78#67000—24no—
79#67000—42no—
80C2×#4326—24no—
81C2×#4326—24no—
82C2×#4326—42no—
83#66989—24no—
84#66989—42no—
85C2×#4323—24no—
86C2×#4323—24no—
87C2×#4323—42no—
88#66983—22no—
89#66983—22no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—24no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94#66977—22no—
95#66977—22no—
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11C2312yes—
98C22×C11⋊C8C2312yes—
99C2×#4314—22no—
100C2×#4314—24no—
101#66899—24no—
102#66896—24no—
103C11⋊#95—24no—
104C11⋊#95D412yes—
105C22⋊(C11⋊C8)D414yes—
106#66885—22no—
107#66881—22no—
108#66880—22no—
109C8×Dic11—24no—
110#25776—111nomaximal, Sylow
111C24×C11—22no—
112C24×C11—44no—
113C24×C11—42no—
114C24×C11—44no—
115C24×C11—82no—
116C24×C11C2×D411yescharacteristic
117C23×D11—21no—
118C2×Q8×C11—22no—
119C2×Q8×C11—28no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—44no—
125C2×Q8×C11—48no—
126C2×Q8×C11—44no—
127C2×Q8×C11—42no—
128C2×Q8×C11C2×D414yes—
129C2×D4×C11—28no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—48no—
136C2×D4×C11—44no—
137C2×D4×C11—44no—
138C2×D4×C11—42no—
139C2×D4×C11C2×D414yes—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—44no—
144C22×C4×C11—42no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2411yescharacteristic
149C2×C22⋊D11—42no—
150C2×C22⋊D11—44no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11C2×D414yes—
155C2×D44—21no—
156C2×D44—22no—
157C2×D44—21no—
158C2×D44—22no—
159C2×Dic22—21no—
160C2×Dic22—22no—
161C2×Dic22—21no—
162C2×Dic22—22no—
163C11×SD16—216no—
164C11×SD16—216no—
165C2×C8×C11—28no—
166C2×C8×C11—22no—
167C2×C8×C11C2×D412yes—
168C2×C8×C11C2×D414yes—
169C2×C8×C11C2×D412yes—
170C22⋊Dic11—24no—
171C22⋊Dic11—48no—
172C22⋊Dic11—42no—
173C22⋊Dic11—84no—
174#4326—48no—
175#4323—48no—
176(C2×D11)⋊C4—48no—
177(C2×D11)⋊C4—42no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182Dic11⋊C4—42no—
183C4×Dic11—22no—
184C4×Dic11—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8C2×D414yes—
188#4314—44no—
189C23×SD16D1111yescharacteristic, complemented
190C2×#495—112no—
191C2×#465—111no—
192C2×#451—111no—
193C2×#447—111no—
194#2436—111no—
195#2435—111no—
196#2015—112no—
197#2012—112no—
198#1968—112no—
199C8×C22⋊C4—111no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—24no—
203C23×C11—48no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—44no—
207C23×C11—44no—
208C23×C11—816no—
209C23×C11—84no—
210C23×C11—84no—
211C23×C11#12712yes—
212C23×C11#13514yes—
213C23×C11C22×D411yescharacteristic
214C22×D11—41no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218Q8×C11—24no—
219Q8×C11—24no—
220Q8×C11—48no—
221Q8×C11—42no—
222Q8×C11—42no—
223D4×C11—24no—
224D4×C11—24no—
225D4×C11—48no—
226D4×C11—42no—
227D4×C11—42no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—48no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11#12712yes—
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D412yes—
240C2×C4×C11H(5,𝔽2)12yes—
241C22⋊D11—84no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251D44—41no—
252D44—41no—
253D44—42no—
254Dic22—41no—
255Dic22—41no—
256Dic22—42no—
257C8×C11—22no—
258C8×C11#12014yes—
259C11⋊C8—24no—
260C23×Q8C2×D1111yescharacteristic
261C23×D4C2×D1111yescharacteristic
262C22×Q16—112no—
263C22×SD16—28no—
264C22×SD16—24no—
265C22×SD16—111no—
266C22×SD16C2×D1112yes—
267C22×SD16C2×D1112yes—
268C22×D8—112no—
269C23×C8C2×D1111yescharacteristic
270C2×#124—112no—
271C2×#124—112no—
272C2×C22⋊Q8—111no—
273C2×#121—111no—
274#495—228no—
275#465—224no—
276#451—224no—
277#447—224no—
278C2×#106—111no—
279C2×#103—112no—
280C2×#103—111no—
281C2×#102—112no—
282C2×#102—111no—
283C2×C22⋊C8—111no—
284C2×C4×C8—112no—
285#394—222no—
286#393—222no—
287#391—112no—
288#390—112no—
289#386—222no—
290#379—222no—
291C4×C22⋊C4—111no—
292#336—112no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—28no—
296C22×C11—44no—
297C22×C11—48no—
298C22×C11—816no—
299C22×C11—82no—
300C22×C11—82no—
301C22×C11—84no—
302C22×C11#49514yescomplemented
303C22×C11C2×#12711yescharacteristic
304C22×C11D4212yes—
305C22×C11C2×#13512yes—
306C22×C11#57712yes—
307C2×D11—81no—
308C2×D11—81no—
309C2×D11—81no—
310C2×D11—84no—
311C4×C11—22no—
312C4×C11—44no—
313C4×C11C2×#12011yescharacteristic
314C4×C11#53511yescharacteristic
315C4×C11D4212yes—
316Dic11—44no—
317Dic11—81no—
318Dic11—81no—
319Dic11—81no—
320C25—21no—
321C22×Q8—21no—
322C22×Q8—24no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8—42no—
326C22×Q8—111no—
327C22×Q8C22×D1112yes—
328C22×D4—24no—
329C22×D4—22no—
330C22×D4—21no—
331C22×D4—22no—
332C22×D4—42no—
333C22×D4—111no—
334C22×D4—221no—
335C22×D4C22×D1112yes—
336C23×C4—21no—
337C23×C4C22×D1111yescharacteristic
338C2×Q16—224no—
339C2×Q16—224no—
340C2×Q16—442no—
341C2×SD16—232no—
342C2×SD16—24no—
343C2×SD16—24no—
344C2×SD16—24no—
345C2×SD16—24no—
346C2×SD16—24no—
347C2×SD16—222no—
348C2×SD16—224no—
349C2×SD16C22⋊D1118yescomplemented
350C2×D8—224no—
351C2×D8—224no—
352C2×D8—442no—
353C22×C8—24no—
354C22×C8—112no—
355C22×C8C22⋊D1114yes—
356C22×C8C22×D1111yescharacteristic
357C22×C8C22×D1111yescharacteristic
358#124—224no—
359#124—224no—
360#124—442no—
361#124—442no—
362C22⋊Q8—222no—
363C22⋊Q8—222no—
364#121—222no—
365#121—222no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—221no—
369C2×C22⋊C4—112no—
370C2×C22⋊C4—224no—
371C2×C22⋊C4—224no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—224no—
375C2×C42—112no—
376#106—222no—
377#103—224no—
378#103—222no—
379#102—224no—
380#102—222no—
381C22⋊C8—114no—
382C4×C8—224no—
383#95—112no—
384#95—224no—
385C2×C11—24no—
386C2×C11—84no—
387C2×C11#243311yescharacteristic
388C2×C11C2×#49511yescharacteristic
389C2×C11#315411yescharacteristic
390C2×C11#328214yes—
391D11—161no—
392C24—22no—
393C24—44no—
394C24—42no—
395C24—44no—
396C24—82no—
397C24—221no—
398C24D4×D1111yescharacteristic
399C2×Q8—22no—
400C2×Q8—28no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—44no—
406C2×Q8—48no—
407C2×Q8—44no—
408C2×Q8—42no—
409C2×Q8—221no—
410C2×Q8—222no—
411C2×Q8—221no—
412C2×Q8—222no—
413C2×Q8C2×C22⋊D1114yes—
414C2×D4—28no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—48no—
421C2×D4—44no—
422C2×D4—44no—
423C2×D4—42no—
424C2×D4—221no—
425C2×D4—222no—
426C2×D4—221no—
427C2×D4—222no—
428C2×D4—444no—
429C2×D4—442no—
430C2×D4C2×C22⋊D1114yes—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—44no—
435C22×C4—42no—
436C22×C4—114no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4D4×D1111yescharacteristic
441C22×C4D4×D1112yes—
442C22×C4C2×C22⋊D1112yes—
443C22×C4C23×D1111yescharacteristic
444Q16—448no—
445SD16—216no—
446SD16—216no—
447SD16—444no—
448D8—448no—
449C2×C8—22no—
450C2×C8—28no—
451C2×C8—114no—
452C2×C8—222no—
453C2×C8—222no—
454C2×C8C2×C22⋊D1112yes—
455C2×C8C2×C22⋊D1114yes—
456C2×C8C2×C22⋊D1112yes—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—442no—
462C22⋊C4—224no—
463C22⋊C4—448no—
464C22⋊C4—448no—
465C22⋊C4—442no—
466C22⋊C4—442no—
467C22⋊C4—884no—
468C42—222no—
469C42—222no—
470C11#2577611yescharacteristic, complemented, Sylow
471C23—22no—
472C23—22no—
473C23—24no—
474C23—48no—
475C23—44no—
476C23—44no—
477C23—42no—
478C23—42no—
479C23—816no—
480C23—84no—
481C23—84no—
482C23—442no—
483C23—442no—
484C23—442no—
485C23—441no—
486C23#6696914yes—
487C23#6699312yes—
488C23C2×D4×D1111yescharacteristic
489Q8—24no—
490Q8—24no—
491Q8—48no—
492Q8—42no—
493Q8—42no—
494Q8—442no—
495Q8—441no—
496Q8—441no—
497D4—24no—
498D4—24no—
499D4—48no—
500D4—42no—
501D4—42no—
502D4—442no—
503D4—441no—
504D4—441no—
505D4—884no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—48no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4#6699312yes—
524C2×C4C2×D4×D1111yescharacteristic
525C2×C4#6703712yes—
526C2×C4C22×C22⋊D1112yes—
527C2×C4C22×C22⋊D1111yescharacteristic
528C8—22no—
529C8—224no—
530C8#6700614yes—
531C22—28no—
532C22—22no—
533C22—22no—
534C22—48no—
535C22—44no—
536C22—816no—
537C22—84no—
538C22—82no—
539C22—82no—
540C22—884no—
541C22—881no—
542C22—881no—
543C22—881no—
544C22#1062278114yescomplemented
545C22C2×#6696912yes—
546C22#1062329312yes—
547C22D4×C22⋊D1112yes—
548C22C2×#6699311yescharacteristic
549C4—22no—
550C4—44no—
551C4—444no—
552C4—881no—
553C4—881no—
554C4—881no—
555C4D4×C22⋊D1112yes—
556C4#1062333611yescharacteristic
557C4C2×#6700611yescharacteristic
558C2—24no—
559C2—84no—
560C2—1761no—
561C2#1307224911yescharacteristic
562C2C2×#1062278111yescharacteristic
563C2#1307908611yescharacteristic
564C2#1308032314yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC23×C11×SD16C2
socleC23×C11C22×D4
prime radicalC2×#10622830C2
hypercenterC23×SD16D11
hypocenterC11#25776
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10622781C2semidirect
2. C2×#10622727C2semidirect
3. C2×#10622841C2semidirect
5. #13072270C2semidirect
6. #13072263C2semidirect
7. #13069708C2semidirect
8. #13069690C2semidirect
9. #13069472C2semidirect
10. C8×C22⋊Dic11C2semidirect
11. C23×C11×SD16C2semidirect
19. C2×#67000C22semidirect
20. C22×#4326C22semidirect
25. C22×#4314C22semidirect
28. #10622843C22semidirect
30. C2×#66899C22semidirect
40. C2×#66885C22semidirect
41. C2×#66881C22semidirect
42. C2×#66880C22semidirect
43. C2×C8×Dic11C22semidirect
44. #10622188C22semidirect
69. C2×C11×SD16D4semidirect
189. C23×SD16D11semidirect
302. C22×C11#495semidirect
349. C2×SD16C22⋊D11semidirect
470. C11#25776semidirect
544. C22#10622781semidirect

Maximal subgroups

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

subgroupindex
C2×#106227812
C2×#106227272
C2×#106228412
C2×#106228302
#130722702
#130722632
#130697082
#130696902
#130694722
C8×C22⋊Dic112
C23×C11×SD162
#2577611