Finite Group Databasebeta

← #14727985

Subgroups — #14727985

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079437C211yesmaximal, characteristic, complemented
2#13079422C211yesmaximal, characteristic, complemented
3#13073774C211yesmaximal, characteristic, complemented
4#13067630C214yesmaximal, complemented
5#13067596C214yesmaximal, complemented
6#13067136C211yesmaximal, characteristic, complemented
7#13067132C211yesmaximal, characteristic, complemented
8#13066943C211yesmaximal, characteristic, complemented
9C2×C11×#538C211yesmaximal, characteristic
10C11×#538—22no—
11C11×#538—22no—
12C11×#538—22no—
13C11×#538C2214yes—
14C2×C11×#126—21no—
15C2×C11×#124—21no—
16C2×C11×#123—21no—
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#121—21no—
19C2×C11×#121C2211yescharacteristic
20C2×C11×#120—21no—
21C2×C4×D4×C11—21no—
22C22×C11×C22⋊C4C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24#10622860—21no—
25#10622841—21no—
26#10622831—21no—
27#10622824—21no—
28C4×C22⋊Dic11C2211yescharacteristic
29#10622820C2211yescharacteristic
30#10622820C2211yescharacteristic
31#10622665—22no—
32#10622663C2212yescomplemented
33#10622656C2212yescomplemented
34#10622655—22no—
35#10622653C2212yescomplemented
36#10622646C2212yescomplemented
37#10622584—21no—
38#10622583—21no—
39#10622566C2212yescomplemented
40#10622560C2212yescomplemented
41#10622558—22no—
42#10622176C2214yescomplemented
43#10622175C2214yescomplemented
44#10622163C2214yescomplemented
45C25×C11D411yescharacteristic
46C22×Q8×C11D411yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11D411yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11D411yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C22×Dic22C2311yescharacteristic
55C11×#126—24no—
56C11×#126—24no—
57C11×#124—24no—
58C11×#124—24no—
59C11×#123—24no—
60C11×#123—24no—
61C11×C22⋊Q8—21no—
62C11×C22⋊Q8—21no—
63C11×C22⋊Q8D412yes—
64C11×C22⋊Q8C2312yes—
65C11×#121—24no—
66C11×#121—24no—
67C11×#121—21no—
68C11×#121—21no—
69C11×#121D412yes—
70C11×#121C2312yes—
71C11×#120—24no—
72C11×#120—24no—
73C4×D4×C11—24no—
74C4×D4×C11—24no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4D412yes—
89C2×C11×C22⋊C4C2312yes—
90C2×C42×C11—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—22no—
95C2×#4326—22no—
96C2×#4324—22no—
97C2×C4⋊Dic11C2311yescharacteristic
98#66977—21no—
99#66977—21no—
100#66977—21no—
101#66977—21no—
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11—21no—
104C2×#4318—21no—
105C2×#4318—21no—
106#66899—22no—
107#66896—22no—
108C11⋊#95—22no—
109C11⋊#95—22no—
110C11⋊#95C2312yes—
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)C2312yes—
114C22⋊(C11⋊C8)C2312yes—
115#66874—22no—
116#66874—22no—
117#66872—22no—
118#66871—22no—
119#18329—111nomaximal, Sylow
120C24×C11—21no—
121C24×C11—21no—
122C24×C11—21no—
123C24×C11—42no—
124C24×C11—42no—
125C24×C11—81no—
126C24×C11C2×D411yescharacteristic
127C24×C11C2×D412yes—
128C2×Q8×C11—21no—
129C2×Q8×C11—81no—
130C2×Q8×C11C2×D412yes—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—24no—
134C2×D4×C11—24no—
135C2×D4×C11—21no—
136C2×D4×C11—44no—
137C2×D4×C11—81no—
138C2×D4×C11—82no—
139C2×D4×C11—82no—
140C2×D4×C11C2×D412yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—24no—
146C22×C4×C11—21no—
147C22×C4×C11—42no—
148C22×C4×C11—81no—
149C22×C4×C11—82no—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—22no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—81no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4C2×D412yes—
169C11×C4⋊C4C2×D412yes—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—22no—
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—
181C42×C11—24no—
182C22⋊Dic11—42no—
183C22⋊Dic11—44no—
184C22⋊Dic11—41no—
185C22⋊Dic11—41no—
186C22⋊Dic11—82no—
187#4326—82no—
188#4324—82no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191Dic11⋊C4—41no—
192Dic11⋊C4—41no—
193C4×Dic11—81no—
194#4318—81no—
195#4318—81no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×#538D1111yescharacteristic
199#3195—111no—
200#3193—111no—
201#2561—111no—
202#1612—114no—
203#1606—114no—
204#1508—111no—
205#1507—111no—
206#1462—111no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—41no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—81no—
224C23×C11—81no—
225C23×C11—88no—
226C23×C11#12011yescharacteristic
227C23×C11#12011yescharacteristic
228C23×C11C22×D411yescharacteristic
229Q8×C11—42no—
230Q8×C11—81no—
231D4×C11—42no—
232D4×C11—44no—
233D4×C11—44no—
234D4×C11—81no—
235D4×C11—84no—
236D4×C11—84no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—81no—
253C2×C4×C11—84no—
254C2×C4×C11#12011yescharacteristic
255C2×C4×C11#12011yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265Dic22—42no—
266Dic22—42no—
267C11⋊C8—42no—
268C11⋊C8—42no—
269#538—22no—
270#538—22no—
271#538—22no—
272#538C2×D1114yes—
273C2×#126—21no—
274C2×#124—21no—
275C2×#123—21no—
276C2×C22⋊Q8—111no—
277C2×C22⋊Q8C2×D1111yescharacteristic
278C2×#121—21no—
279C2×#121C2×D1111yescharacteristic
280C2×#120—21no—
281C2×C4×D4—21no—
282C22×C22⋊C4C2×D1111yescharacteristic
283#484—221no—
284#483—112no—
285#483—221no—
286#480—112no—
287#470—222no—
288#468—222no—
289#451—112no—
290#451—221no—
291#450—221no—
292#448—112no—
293#407—111no—
294#407—111no—
295#397—112no—
296#393—112no—
297#388—222no—
298#381—221no—
299#379—221no—
300C4×C22⋊C4—111no—
301#328—114no—
302#327—114no—
303#323—114no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—21no—
311C22×C11—44no—
312C22×C11—44no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—82no—
320C22×C11—84no—
321C22×C11—84no—
322C22×C11—84no—
323C22×C11#45512yes—
324C22×C11C2×#12011yescharacteristic
325C22×C11#57512yes—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—42no—
331C4×C11—42no—
332C4×C11—42no—
333C4×C11—42no—
334Dic11—82no—
335Dic11—81no—
336Dic11—81no—
337C25C22⋊D1111yescharacteristic
338C22×Q8—111no—
339C22×Q8C22⋊D1111yescharacteristic
340C22×D4—21no—
341C22×D4—21no—
342C22×D4—21no—
343C22×D4C22⋊D1111yescharacteristic
344C23×C4—21no—
345C23×C4C22⋊D1111yescharacteristic
346C23×C4C22×D1111yescharacteristic
347C2×Q16—222no—
348C2×SD16—222no—
349C2×M16—221no—
350C2×M16—221no—
351#126—24no—
352#126—24no—
353#124—24no—
354#124—24no—
355#123—24no—
356#123—24no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—221no—
360C22⋊Q8—221no—
361C22⋊Q8—221no—
362C22⋊Q8—221no—
363C22⋊Q8C22⋊D1112yes—
364C22⋊Q8C22×D1112yes—
365#121—24no—
366#121—24no—
367#121—21no—
368#121—21no—
369#121C22⋊D1112yes—
370#121C22×D1112yes—
371#120—24no—
372#120—24no—
373C4×D4—24no—
374C4×D4—24no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4C22⋊D1111yescharacteristic
380C2×C4⋊C4C22⋊D1111yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4—222no—
393C2×C22⋊C4—222no—
394C2×C22⋊C4C22⋊D1112yes—
395C2×C22⋊C4C22×D1112yes—
396C2×C42—21no—
397C2×C42—221no—
398#107—222no—
399#106—222no—
400#103—222no—
401#103—222no—
402#103—222no—
403#102—222no—
404C22⋊C8—112no—
405C22⋊C8—112no—
406C22⋊C8—221no—
407C22⋊C8—221no—
408#95—112no—
409#95—222no—
410#95—222no—
411C2×C11—22no—
412C2×C11—22no—
413C2×C11—41no—
414C2×C11—82no—
415C2×C11—82no—
416C2×C11#300511yescharacteristic
417C2×C11C2×#45511yescharacteristic
418C2×C11#302611yescharacteristic
419C24—21no—
420C24—21no—
421C24—21no—
422C24—42no—
423C24—42no—
424C24—81no—
425C24C2×C22⋊D1111yescharacteristic
426C24C2×C22⋊D1112yes—
427C2×Q8—21no—
428C2×Q8—81no—
429C2×Q8—221no—
430C2×Q8—221no—
431C2×Q8—881no—
432C2×Q8C2×C22⋊D1112yes—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—24no—
436C2×D4—24no—
437C2×D4—21no—
438C2×D4—44no—
439C2×D4—81no—
440C2×D4—82no—
441C2×D4—82no—
442C2×D4C2×C22⋊D1112yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—24no—
448C22×C4—21no—
449C22×C4—42no—
450C22×C4—81no—
451C22×C4—82no—
452C22×C4—222no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4C2×C22⋊D1112yes—
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C2×C22⋊D1111yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C23×D1111yescharacteristic
462Q16—882no—
463SD16—882no—
464M16—881no—
465M16—881no—
466C2×C8—222no—
467C2×C8—222no—
468C4⋊C4—24no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—441no—
476C4⋊C4—441no—
477C4⋊C4C2×C22⋊D1112yes—
478C4⋊C4C2×C22⋊D1112yes—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—442no—
491C22⋊C4—444no—
492C22⋊C4—441no—
493C22⋊C4—441no—
494C22⋊C4—882no—
495C42—24no—
496C42—881no—
497C11#1832911yescharacteristic, complemented, Sylow
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—41no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—81no—
515C23—81no—
516C23—88no—
517C23#6700611yescharacteristic
518C23#6700611yescharacteristic
519C23C22×C22⋊D1111yescharacteristic
520Q8—42no—
521Q8—81no—
522Q8—442no—
523Q8—442no—
524D4—42no—
525D4—44no—
526D4—44no—
527D4—81no—
528D4—84no—
529D4—84no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—81no—
546C2×C4—84no—
547C2×C4—442no—
548C2×C4—442no—
549C2×C4—442no—
550C2×C4—442no—
551C2×C4—442no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4#6700611yescharacteristic
555C2×C4#6700611yescharacteristic
556C2×C4C22×C22⋊D1111yescharacteristic
557C2×C4C22×C22⋊D1111yescharacteristic
558C8—442no—
559C8—442no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—44no—
568C22—44no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—82no—
576C22—84no—
577C22—84no—
578C22—84no—
579C22#1062285512yes—
580C22#1062335312yes—
581C22C2×#6700611yescharacteristic
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—42no—
587C4—42no—
588C4—42no—
589C4—42no—
590C4—882no—
591C4—881no—
592C4—881no—
593C2—22no—
594C2—22no—
595C2—41no—
596C2—82no—
597C2—82no—
598C2#1307785811yescharacteristic
599C2C2×#1062285511yescharacteristic
600C2#1307801311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#538C2
socleC22×C11C2×#120
hypercenterC2×#538D11
hypocenterC11#18329
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#538

Complements

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

NH ≅ G/Ntype
1. #13079437C2semidirect
2. #13079422C2semidirect
3. #13073774C2semidirect
4. #13067630C2semidirect
5. #13067596C2semidirect
6. #13067136C2semidirect
7. #13067132C2semidirect
8. #13066943C2semidirect
32. #10622663C22semidirect
33. #10622656C22semidirect
35. #10622653C22semidirect
36. #10622646C22semidirect
39. #10622566C22semidirect
40. #10622560C22semidirect
42. #10622176C22semidirect
43. #10622175C22semidirect
44. #10622163C22semidirect
497. C11#18329semidirect

Maximal subgroups

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

subgroupindex
#130794372
#130794222
#130737742
#130676302
#130675962
#130671362
#130671322
#130669432
C2×C11×#5382
#1832911