Finite Group Databasebeta

← #14727841

Subgroups — #14727841

Order 2816.

930 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#13079757C211yesmaximal, characteristic, complemented
2#13079734C211yesmaximal, characteristic, complemented
3#13074382C211yesmaximal, characteristic, complemented
4#13067630C214yesmaximal, complemented
5#13067613C214yesmaximal, complemented
6#13067180C211yesmaximal, characteristic, complemented
7#13067176C211yesmaximal, characteristic, complemented
8#13066930C211yesmaximal, characteristic, complemented
9C11×#3455C211yesmaximal, characteristic
10C11×#542—21no—
11C11×#542—21no—
12C11×#541—21no—
13C11×#540—21no—
14C11×#539—21no—
15C11×#539C2212yes—
16C11×#538—21no—
17C11×#538C2212yes—
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C11×#529—22no—
21C11×#529—22no—
22C11×#525—21no—
23C4×C11×#41—21no—
24C2×C11×#117C2211yescharacteristic
25C2×#66977—21no—
26C2×#66922C2211yescharacteristic
27#10622694—21no—
28#10622692—21no—
29#10622691—21no—
30#10622683—21no—
31#10622656C2214yes—
32#10622646C2214yes—
33#10622633—22no—
34#10622620—22no—
35#10622596—21no—
36#10622596C2212yes—
37#10622566—21no—
38#10622566C2212yes—
39#10622549C2211yescharacteristic
40#10622542—21no—
41#10622538C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622176C2214yes—
44#10622175C2214yes—
45#10622166C2212yes—
46#10622163C2212yes—
47C2×C11×#41—21no—
48C23×C4×C11D411yescharacteristic
49C22×Dic22—21no—
50C11×C4⋊Q8D411yescharacteristic
51C11×C4⋊Q8D411yescharacteristic
52C11×C4⋊Q8D411yescharacteristic
53C11×#127D411yescharacteristic
54C11×#126—22no—
55C11×#126—22no—
56C11×#126—22no—
57C11×#126—22no—
58C11×#125—22no—
59C11×#125—22no—
60C11×#125—21no—
61C11×#124—22no—
62C11×#124—22no—
63C11×#124—21no—
64C11×#123—22no—
65C11×#123—22no—
66C11×#123—22no—
67C11×#123—22no—
68C11×#123—22no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8C2312yes—
75C11×#121—21no—
76C11×#121—21no—
77C11×#121—22no—
78C11×#121—22no—
79C11×#121—21no—
80C11×#121C2312yes—
81C11×#120—22no—
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11—21no—
85C4×Q8×C11D412yes—
86C4×D4×C11—21no—
87C4×D4×C11—21no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—21no—
93C4×D4×C11D412yes—
94C11×#117—22no—
95C11×#117—21no—
96C11×#117—21no—
97C11×#117—21no—
98C11×#117—21no—
99C11×#117—21no—
100C2×C11×C4⋊C4D411yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C11×C22⋊C4C2311yescharacteristic
104C2×C42×C11—22no—
105C2×C42×C11D411yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C22⋊Dic11—22no—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11C2312yes—
111#66977—44no—
112C2×Dic11⋊C4—22no—
113#66922—21no—
114#66922—21no—
115#66922—21no—
116#66922—21no—
117#66899—24no—
118#66896—24no—
119C11⋊#95—22no—
120C11⋊#95—22no—
121C11⋊#95—21no—
122C11⋊#95C2312yes—
123C22⋊(C11⋊C8)C2312yes—
124C22⋊(C11⋊C8)C2312yes—
125#66872—24no—
126#66871—24no—
127C4⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)—21no—
129C4×C11⋊C8—21no—
130C4×C11⋊C8—21no—
131#18312—111nomaximal, Sylow
132C24×C11C2×D411yescharacteristic
133C11×#41—42no—
134C11×#41—42no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11C2×D412yes—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11C2×D412yes—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
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—22no—
159C2×Dic22—41no—
160C2×Dic22—41no—
161C2×Dic22—42no—
162C2×Dic22—42no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4C2×D412yes—
178C11×C4⋊C4C2×D412yes—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—21no—
191C11×C22⋊C4—22no—
192C42×C11—22no—
193C42×C11—22no—
194C42×C11—21no—
195C42×C11—22no—
196C42×C11—21no—
197C42×C11C2×D411yescharacteristic
198C42×C11C2×D411yescharacteristic
199C42×C11C2×D411yescharacteristic
200C42×C11C2×D411yescharacteristic
201C22⋊Dic11—44no—
202C4⋊Dic11—22no—
203C4⋊Dic11—22no—
204C4⋊Dic11—41no—
205C4⋊Dic11—41no—
206C4⋊Dic11—42no—
207Dic11⋊C4—44no—
208C2×C11⋊C8—22no—
209C2×C11⋊C8—22no—
210#3455D1111yescharacteristic
211#3229—111no—
212#3226—111no—
213#2621—111no—
214#1612—114no—
215#1609—114no—
216#1518—111no—
217#1517—111no—
218#1458—111no—
219C23×C11—21no—
220C23×C11—22no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11C22×D411yescharacteristic
226Q8×C11—42no—
227Q8×C11—42no—
228Q8×C11—81no—
229D4×C11—42no—
230D4×C11—42no—
231D4×C11—42no—
232D4×C11—42no—
233D4×C11—81no—
234D4×C11—82no—
235D4×C11—82no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—44no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—82no—
252C2×C4×C11—82no—
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11#12011yescharacteristic
255C2×C4×C11#12011yescharacteristic
256C2×C4×C11#12011yescharacteristic
257C2×C4×C11#13512yes—
258C2×C4×C11AGL(1,ℤ/8)12yes—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267Dic22—82no—
268Dic22—82no—
269C11⋊C8—42no—
270C11⋊C8—42no—
271#542—21no—
272#542—21no—
273#541—21no—
274#540—21no—
275#539—21no—
276#539C2×D1112yes—
277#538—21no—
278#538C2×D1112yes—
279#533C2×D1111yescharacteristic
280#532C2×D1111yescharacteristic
281C2×C4⋊Q8—111no—
282#529—22no—
283#529—22no—
284#525—21no—
285C2×C22⋊Q8—221no—
286C4×#41—21no—
287C2×#117C2×D1111yescharacteristic
288#500—221no—
289#498—221no—
290#487—221no—
291#486—221no—
292#483—114no—
293#480—114no—
294#475—222no—
295#474—222no—
296#431—111no—
297#431—111no—
298#398—112no—
299#398—221no—
300#397—112no—
301#397—221no—
302#391—221no—
303#382—111no—
304#328—114no—
305#327—114no—
306#324—112no—
307#323—112no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—42no—
311C22×C11—41no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—41no—
315C22×C11—42no—
316C22×C11—41no—
317C22×C11—81no—
318C22×C11C2×#12011yescharacteristic
319C22×C11C2×#13511yescharacteristic
320C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—21no—
325C4×C11—41no—
326C4×C11—42no—
327C4×C11—41no—
328C4×C11—42no—
329C4×C11—41no—
330C4×C11—42no—
331C4×C11#44912yes—
332C4×C11#44912yes—
333Dic11—82no—
334Dic11—82no—
335C2×#41—21no—
336C22×Q8—221no—
337C23×C4C22⋊D1111yescharacteristic
338C4⋊Q8—221no—
339C4⋊Q8—221no—
340C4⋊Q8—221no—
341C4⋊Q8—221no—
342C4⋊Q8C22⋊D1111yescharacteristic
343C4⋊Q8C22⋊D1111yescharacteristic
344C4⋊Q8C22⋊D1111yescharacteristic
345#127C22⋊D1111yescharacteristic
346#126—22no—
347#126—22no—
348#126—22no—
349#126—22no—
350#125—22no—
351#125—22no—
352#125—21no—
353#124—22no—
354#124—22no—
355#124—21no—
356#123—22no—
357#123—22no—
358#123—22no—
359#123—22no—
360#123—22no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—22no—
364C22⋊Q8—22no—
365C22⋊Q8—21no—
366C22⋊Q8—444no—
367C22⋊Q8C22×D1112yes—
368#121—21no—
369#121—21no—
370#121—22no—
371#121—22no—
372#121—21no—
373#121C22×D1112yes—
374#120—22no—
375C4×Q8—21no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8C22⋊D1112yes—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—22no—
384C4×D4—22no—
385C4×D4—21no—
386C4×D4C22⋊D1112yes—
387#117—22no—
388#117—21no—
389#117—21no—
390#117—21no—
391#117—21no—
392#117—21no—
393C2×C4⋊C4—112no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4C22⋊D1111yescharacteristic
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C22⋊C4—222no—
400C2×C22⋊C4C22⋊D1111yescharacteristic
401C2×C22⋊C4C22×D1111yescharacteristic
402C2×C42—22no—
403C2×C42C22⋊D1111yescharacteristic
404C2×C42C22×D1111yescharacteristic
405#107—224no—
406#106—224no—
407C4⋊C8—221no—
408C4⋊C8—221no—
409#103—224no—
410#102—224no—
411C22⋊C8—112no—
412C22⋊C8—112no—
413C4×C8—221no—
414C4×C8—221no—
415#95—112no—
416#95—221no—
417#95—222no—
418#95—222no—
419C2×C11—21no—
420C2×C11—21no—
421C2×C11—82no—
422C2×C11—81no—
423C2×C11C2×#44911yescharacteristic
424C2×C11#302211yescharacteristic
425C2×C11#302811yescharacteristic
426C24C2×C22⋊D1111yescharacteristic
427#41—42no—
428#41—42no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—442no—
432C2×Q8—442no—
433C2×Q8—441no—
434C2×Q8—441no—
435C2×Q8C2×C22⋊D1112yes—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C2×C22⋊D1112yes—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C23×D1111yescharacteristic
457C2×C8—222no—
458C2×C8—222no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4—222no—
474C4⋊C4—222no—
475C4⋊C4—444no—
476C4⋊C4—442no—
477C4⋊C4—441no—
478C4⋊C4—441no—
479C4⋊C4C2×C22⋊D1112yes—
480C4⋊C4C2×C22⋊D1112yes—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—22no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—22no—
494C22⋊C4—444no—
495C42—22no—
496C42—22no—
497C42—21no—
498C42—22no—
499C42—21no—
500C42C2×C22⋊D1111yescharacteristic
501C42C2×C22⋊D1111yescharacteristic
502C42C2×C22⋊D1111yescharacteristic
503C42C2×C22⋊D1111yescharacteristic
504C11#1831211yescharacteristic, complemented, Sylow
505C23—21no—
506C23—21no—
507C23—22no—
508C23—21no—
509C23—41no—
510C23—41no—
511C23C22×C22⋊D1111yescharacteristic
512Q8—42no—
513Q8—42no—
514Q8—81no—
515Q8—882no—
516Q8—882no—
517D4—42no—
518D4—42no—
519D4—42no—
520D4—42no—
521D4—81no—
522D4—82no—
523D4—82no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—44no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4#6700212yes—
548C2×C4#6700312yes—
549C2×C4#6700611yescharacteristic
550C2×C4#6700611yescharacteristic
551C2×C4#6700611yescharacteristic
552C2×C4#6700611yescharacteristic
553C2×C4C22×C22⋊D1111yescharacteristic
554C2×C4C22×C22⋊D1111yescharacteristic
555C8—442no—
556C8—442no—
557C22—21no—
558C22—21no—
559C22—42no—
560C22—42no—
561C22—41no—
562C22—41no—
563C22—42no—
564C22—42no—
565C22—41no—
566C22—81no—
567C22C2×#6700211yescharacteristic
568C22C2×#6700311yescharacteristic
569C22C2×#6700611yescharacteristic
570C4—21no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—41no—
575C4—42no—
576C4—41no—
577C4—42no—
578C4—41no—
579C4—42no—
580C4—882no—
581C4—882no—
582C4#1062285112yes—
583C4#1062285112yes—
584C2—21no—
585C2—21no—
586C2—81no—
587C2—82no—
588C2C2×#1062285111yescharacteristic
589C2#1307799511yescharacteristic
590C2#1307802211yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3455C2
socleC22×C11C2×#120
hypercenter#3455D11
hypocenterC11#18312
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3455

Complements

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

NH ≅ G/Ntype
1. #13079757C2semidirect
2. #13079734C2semidirect
3. #13074382C2semidirect
4. #13067630C2semidirect
5. #13067613C2semidirect
6. #13067180C2semidirect
7. #13067176C2semidirect
8. #13066930C2semidirect
504. C11#18312semidirect

Maximal subgroups

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

subgroupindex
#130797572
#130797342
#130743822
#130676302
#130676132
#130671802
#130671762
#130669302
C11×#34552
#1831211