Finite Group Databasebeta

← #14726275

Subgroups — #14726275

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078560C211yesmaximal, characteristic, complemented
2#13078552C211yesmaximal, characteristic, complemented
3#13072890C211yesmaximal, characteristic, complemented
4#13067664C214yesmaximal, complemented
5#13067630C214yesmaximal, complemented
6#13067149C211yesmaximal, characteristic, complemented
7#13067145C211yesmaximal, 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×#66979C2211yescharacteristic
24#10622860—21no—
25#10622838—21no—
26#10622828—21no—
27#10622824C2211yescharacteristic
28#10622823—21no—
29#10622820C2211yescharacteristic
30#10622820C2211yescharacteristic
31#10622658—22no—
32#10622657C2212yescomplemented
33#10622656C2212yescomplemented
34#10622648—22no—
35#10622647C2212yescomplemented
36#10622646C2212yescomplemented
37#10622577—21no—
38#10622577—21no—
39#10622566C2212yescomplemented
40#10622562C2212yescomplemented
41#10622557—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
54C11×#126—24no—
55C11×#126—24no—
56C11×#124—24no—
57C11×#124—24no—
58C11×#123—24no—
59C11×#123—24no—
60C11×C22⋊Q8—21no—
61C11×C22⋊Q8—21no—
62C11×C22⋊Q8D412yes—
63C11×C22⋊Q8C2312yes—
64C11×#121—24no—
65C11×#121—24no—
66C11×#121—21no—
67C11×#121—21no—
68C11×#121D412yes—
69C11×#121C2312yes—
70C11×#120—24no—
71C11×#120—24no—
72C4×D4×C11—24no—
73C4×D4×C11—24no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C22⋊C4—21no—
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⋊C4D412yes—
88C2×C11×C22⋊C4C2312yes—
89C2×C42×C11—21no—
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11—22no—
94#66979—21no—
95#66979—21no—
96#66979—21no—
97#66979—21no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—22no—
101C2×C4×Dic11—21no—
102C2×#4318—21no—
103C2×#4318—21no—
104#66899—22no—
105#66899—22no—
106#66896—22no—
107#66896—22no—
108C11⋊#95—21no—
109C11⋊#95—22no—
110C11⋊#95C2312yes—
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)C2312yes—
114C22⋊(C11⋊C8)C2312yes—
115#66872—22no—
116#66872—22no—
117#66871—22no—
118#66871—22no—
119#18149—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—42no—
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—42no—
137C2×D4×C11—44no—
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×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—22no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4C2×D412yes—
166C11×C4⋊C4C2×D412yes—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C42×C11—24no—
179C22⋊Dic11—42no—
180C22⋊Dic11—44no—
181C22⋊Dic11—41no—
182C22⋊Dic11—41no—
183C22⋊Dic11—82no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188Dic11⋊C4—82no—
189C4×Dic11—41no—
190C4×Dic11—41no—
191#4318—42no—
192#4318—42no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×#538D1111yescharacteristic
196#3095—111no—
197#3094—111no—
198#2482—111no—
199#1618—114no—
200#1612—114no—
201#1511—111no—
202#1510—111no—
203#1462—111no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—41no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—81no—
221C23×C11—81no—
222C23×C11—88no—
223C23×C11#12011yescharacteristic
224C23×C11#12011yescharacteristic
225C23×C11C22×D411yescharacteristic
226Q8×C11—42no—
227Q8×C11—81no—
228D4×C11—42no—
229D4×C11—44no—
230D4×C11—44no—
231D4×C11—81no—
232D4×C11—84no—
233D4×C11—84no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—81no—
250C2×C4×C11—84no—
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C11⋊C8—42no—
263C11⋊C8—42no—
264#538—22no—
265#538—22no—
266#538—22no—
267#538C2×D1114yes—
268C2×#126—21no—
269C2×#124—21no—
270C2×#123—21no—
271C2×C22⋊Q8C2×D1111yescharacteristic
272C2×#121—21no—
273C2×#121C2×D1111yescharacteristic
274C2×#120—21no—
275C2×C4×D4—21no—
276C2×#117—111no—
277C22×C22⋊C4C2×D1111yescharacteristic
278#485—222no—
279#484—112no—
280#483—112no—
281#482—222no—
282#481—112no—
283#480—112no—
284#428—221no—
285#428—221no—
286#419—221no—
287#418—221no—
288#407—111no—
289#407—111no—
290#399—112no—
291#397—112no—
292#388—222no—
293#385—221no—
294#381—111no—
295#379—221no—
296#328—114no—
297#327—114no—
298#323—114no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—82no—
315C22×C11—84no—
316C22×C11—84no—
317C22×C11—84no—
318C22×C11#45812yes—
319C22×C11C2×#12011yescharacteristic
320C22×C11#57512yes—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—21no—
325C4×C11—42no—
326C4×C11—42no—
327C4×C11—42no—
328C4×C11—42no—
329Dic11—82no—
330Dic11—81no—
331Dic11—81no—
332C25C22⋊D1111yescharacteristic
333C22×Q8C22⋊D1111yescharacteristic
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—21no—
337C22×D4C22⋊D1111yescharacteristic
338C23×C4—21no—
339C23×C4C22⋊D1111yescharacteristic
340C23×C4C22×D1111yescharacteristic
341C2×M16—221no—
342C2×M16—221no—
343#126—24no—
344#126—24no—
345#124—24no—
346#124—24no—
347#123—24no—
348#123—24no—
349C22⋊Q8—21no—
350C22⋊Q8—21no—
351C22⋊Q8C22⋊D1112yes—
352C22⋊Q8C22×D1112yes—
353#121—24no—
354#121—24no—
355#121—21no—
356#121—21no—
357#121C22⋊D1112yes—
358#121C22×D1112yes—
359#120—24no—
360#120—24no—
361C4×D4—24no—
362C4×D4—24no—
363#117—221no—
364#117—221no—
365#117—221no—
366#117—221no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4C22⋊D1111yescharacteristic
373C2×C4⋊C4C22⋊D1111yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—222no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4C22⋊D1112yes—
388C2×C22⋊C4C22×D1112yes—
389C2×C42—21no—
390C2×C42—221no—
391#107—222no—
392#107—222no—
393#106—222no—
394#106—222no—
395#103—222no—
396#103—222no—
397#102—222no—
398#102—222no—
399C22⋊C8—112no—
400C22⋊C8—112no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403#95—112no—
404#95—221no—
405#95—222no—
406C2×C11—22no—
407C2×C11—22no—
408C2×C11—41no—
409C2×C11—82no—
410C2×C11—82no—
411C2×C11#300511yescharacteristic
412C2×C11#301911yescharacteristic
413C2×C11C2×#45811yescharacteristic
414C24—21no—
415C24—21no—
416C24—21no—
417C24—42no—
418C24—42no—
419C24—81no—
420C24C2×C22⋊D1111yescharacteristic
421C24C2×C22⋊D1112yes—
422C2×Q8—21no—
423C2×Q8—42no—
424C2×Q8C2×C22⋊D1112yes—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—24no—
428C2×D4—24no—
429C2×D4—21no—
430C2×D4—42no—
431C2×D4—44no—
432C2×D4—82no—
433C2×D4—82no—
434C2×D4C2×C22⋊D1112yes—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—24no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—81no—
443C22×C4—82no—
444C22×C4—222no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4C2×C22⋊D1111yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C2×C22⋊D1112yes—
450C22×C4C2×C22⋊D1111yescharacteristic
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C23×D1111yescharacteristic
454M16—442no—
455M16—442no—
456C2×C8—222no—
457C2×C8—222no—
458C4⋊C4—24no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—22no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—882no—
468C4⋊C4C2×C22⋊D1112yes—
469C4⋊C4C2×C22⋊D1112yes—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—442no—
482C22⋊C4—444no—
483C22⋊C4—441no—
484C22⋊C4—441no—
485C22⋊C4—882no—
486C42—24no—
487C42—441no—
488C42—441no—
489C11#1814911yescharacteristic, complemented, Sylow
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—41no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—81no—
507C23—81no—
508C23—88no—
509C23#6700611yescharacteristic
510C23#6700611yescharacteristic
511C23C22×C22⋊D1111yescharacteristic
512Q8—42no—
513Q8—81no—
514D4—42no—
515D4—44no—
516D4—44no—
517D4—81no—
518D4—84no—
519D4—84no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—81no—
536C2×C4—84no—
537C2×C4—442no—
538C2×C4—442no—
539C2×C4—442no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4#6700611yescharacteristic
545C2×C4#6700611yescharacteristic
546C2×C4C22×C22⋊D1111yescharacteristic
547C2×C4C22×C22⋊D1111yescharacteristic
548C8—442no—
549C8—442no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—44no—
558C22—44no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—82no—
566C22—84no—
567C22—84no—
568C22—84no—
569C22#1062285612yes—
570C22#1062335312yes—
571C22C2×#6700611yescharacteristic
572C4—21no—
573C4—21no—
574C4—21no—
575C4—21no—
576C4—42no—
577C4—42no—
578C4—42no—
579C4—42no—
580C4—882no—
581C4—881no—
582C4—881no—
583C2—22no—
584C2—22no—
585C2—41no—
586C2—82no—
587C2—82no—
588C2#1307785811yescharacteristic
589C2#1307797311yescharacteristic
590C2C2×#1062285611yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#538C2
socleC22×C11C2×#120
hypercenterC2×#538D11
hypocenterC11#18149
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. #13078560C2semidirect
2. #13078552C2semidirect
3. #13072890C2semidirect
4. #13067664C2semidirect
5. #13067630C2semidirect
6. #13067149C2semidirect
7. #13067145C2semidirect
8. #13066943C2semidirect
32. #10622657C22semidirect
33. #10622656C22semidirect
35. #10622647C22semidirect
36. #10622646C22semidirect
39. #10622566C22semidirect
40. #10622562C22semidirect
42. #10622176C22semidirect
43. #10622175C22semidirect
44. #10622163C22semidirect
489. C11#18149semidirect

Maximal subgroups

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

subgroupindex
#130785602
#130785522
#130728902
#130676642
#130676302
#130671492
#130671452
#130669432
C2×C11×#5382
#1814911