Finite Group Databasebeta

← #14725555

Subgroups — #14725555

Order 2816.

600 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079182C211yesmaximal, characteristic
2#13077623C211yesmaximal, characteristic, complemented
3#13077619C211yesmaximal, characteristic, complemented
4#13067510C211yesmaximal, characteristic, complemented
5#13067499C211yesmaximal, characteristic, complemented
6#13067461C211yesmaximal, characteristic, complemented
7#13067453C211yesmaximal, characteristic, complemented
8#13067451C211yesmaximal, characteristic, complemented
9C8×#4326C211yesmaximal, characteristic, complemented
10#13067408C211yesmaximal, characteristic, complemented
11#13067361C211yesmaximal, characteristic, complemented
12#13067023C211yesmaximal, characteristic, complemented
13#13067021C211yesmaximal, characteristic, complemented
14#13066895C211yesmaximal, characteristic, complemented
15C11×#1583C211yesmaximal, characteristic, complemented
16#10623111C2211yescharacteristic
17#10623088C2211yescharacteristic
18C8×Q8×C11C2211yescharacteristic
19C4×C11×SD16C2211yescharacteristic
20C11×#436C2211yescharacteristic
21#10622784C411yescharacteristic
22#10622781C411yescharacteristic
23#10622741—21no—
24#10622735—21no—
25C4×#4326C2211yescharacteristic
26#10622637C2211yescharacteristic
27C4×#4323C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622477C411yescharacteristic
30#10622471C411yescharacteristic
31#10622453—21no—
32#10622449—21no—
33#10622447C2211yescharacteristic
34#10622446C2211yescharacteristic
35#10622446C2211yescharacteristic
36#10622444C2211yescharacteristic
37#10622426C411yescharacteristic
38#10622413C411yescharacteristic
39#10622388C411yescharacteristic
40#10622381C411yescharacteristic
41#10622343—21no—
42#10622333—21no—
43C4×#4314C2211yescharacteristic
44#10622302—21no—
45#10622301—21no—
46#10622301C2211yescharacteristic
47C4×#4313C2211yescharacteristic
48#10622298C2211yescharacteristic
49C4×C8×D11C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622117C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622092C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×SD16C2×C411yescharacteristic
68C2×C11×M16—21no—
69C4×Q8×C11C2311yescharacteristic
70C4×D4×C11C2311yescharacteristic
71#67000C2×C411yescharacteristic
72#66999C2×C411yescharacteristic
73C2×#4326C2×C411yescharacteristic
74#66991C2×C411yescharacteristic
75#66989C2×C411yescharacteristic
76C2×#4323C2×C411yescharacteristic
77C4×C22⋊D11—21no—
78#66979—21no—
79C22×C11⋊C8—21no—
80C2×#4314C2×C411yescharacteristic
81C2×#4313—21no—
82C2×#4313D411yescharacteristic
83C2×#4313D411yescharacteristic
84C2×C8×D11—21no—
85C2×C8×D11C2×C411yescharacteristic
86C2×C8×D11C2×C411yescharacteristic
87#66951—21no—
88#66950C2×C411yescharacteristic
89#66948C2×C411yescharacteristic
90#66947—21no—
91#66943C2×C411yescharacteristic
92#66943C2×C411yescharacteristic
93#66936—21no—
94#66932—21no—
95C4×D44—21no—
96C4×D44C2311yescharacteristic
97#66925—21no—
98C42×D11C2311yescharacteristic
99C4×Dic22C2311yescharacteristic
100C11×#106C2×C411yescharacteristic
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×#103C2×C411yescharacteristic
105C11×#102C2×C411yescharacteristic
106C11×C22⋊C8—21no—
107C4×C8×C11—21no—
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111#66899C2×C411yescharacteristic
112#66896C2×C411yescharacteristic
113C22⋊(C11⋊C8)—21no—
114#66885C2×C411yescharacteristic
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8—21no—
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120#66881C2×C411yescharacteristic
121#66880C2×C411yescharacteristic
122#66879—21no—
123#66879D411yescharacteristic
124#66879D411yescharacteristic
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128C8×Dic11—21no—
129C8×Dic11—21no—
130C8×Dic11—21no—
131C8×Dic11C2×C411yescharacteristic
132C8×Dic11C2×C411yescharacteristic
133#66874C2×C411yescharacteristic
134#66873C2×C411yescharacteristic
135#66871C2×C411yescharacteristic
136#66871C2×C411yescharacteristic
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140#66867—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18069—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×D4×C11C22×C411yescharacteristic
147C22×C4×C11—21no—
148C2×C22⋊D11—21no—
149C2×D44—21no—
150C2×D44C22×C411yescharacteristic
151C2×C4×D11—21no—
152C2×C4×D11C22×C411yescharacteristic
153C2×C4×D11C2×D411yescharacteristic
154C2×C4×D11#4111yescharacteristic
155C2×Dic22C22×C411yescharacteristic
156C11×SD16—41no—
157C11×M16—42no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11C22×C411yescharacteristic
162C2×C8×C11C22×C411yescharacteristic
163C2×C8×C11C2×D411yescharacteristic
164C2×C8×C11C2×D411yescharacteristic
165C11×C4⋊C4—21no—
166C11×C4⋊C4C22×C411yescharacteristic
167C11×C4⋊C4C22×C411yescharacteristic
168C11×C22⋊C4—21no—
169C42×C11—21no—
170C42×C11C2411yescharacteristic
171C22⋊Dic11—21no—
172C22⋊Dic11—21no—
173C22⋊Dic11—21no—
174#4326—22no—
175#4323—22no—
176(C2×D11)⋊C4—21no—
177(C2×D11)⋊C4—21no—
178(C2×D11)⋊C4—21no—
179(C2×D11)⋊C4—21no—
180(C2×D11)⋊C4—21no—
181(C2×D11)⋊C4—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11C22×C411yescharacteristic
186C4⋊Dic11C22×C411yescharacteristic
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191C4×Dic11—21no—
192C4×Dic11C22×C411yescharacteristic
193C4×Dic11C2×D411yescharacteristic
194C4×Dic11#4111yescharacteristic
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—42no—
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203#4314—41no—
204#4313—22no—
205#4313—22no—
206#4313—42no—
207C8×D11—22no—
208C8×D11—41no—
209C8×D11—42no—
210#3168—111no—
211#2969—111no—
212#2969—111no—
213#1591—111no—
214#1589—111no—
215#1583—111no—
216#1583D1111yescharacteristic, complemented
217#1582—111no—
218#1582—111no—
219C8×Q16—111no—
220C8×D8—111no—
221#1564—111no—
222#1482—111no—
223#1482—111no—
224C8×M16—111no—
225C23×C11—21no—
226C22×D11—21no—
227C22×D11C4×D411yescharacteristic
228Q8×C11—21no—
229Q8×C11—21no—
230D4×C11—21no—
231D4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C22⋊D11—81no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11C4×D411yescharacteristic
245C2×Dic11C4×D411yescharacteristic
246C2×Dic11C4×D411yescharacteristic
247D44—21no—
248D44—21no—
249D44—81no—
250C4×D11—21no—
251C4×D11—21no—
252C4×D11—21no—
253C4×D11—21no—
254C4×D11—41no—
255C4×D11—41no—
256C4×D11—41no—
257Dic22—21no—
258Dic22—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—41no—
263C8×C11—41no—
264C8×C11—41no—
265C8×C11#13512yes—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8#13112yes—
272C11⋊C8#13512yes—
273#529—111no—
274#529—111no—
275#499—111no—
276#495—111no—
277#488—111no—
278#488—111no—
279#467—111no—
280#466—111no—
281#465—111no—
282#465—111no—
283#446—111no—
284#446—111no—
285C8×Q8—111no—
286C8×Q8C2×D1111yescharacteristic
287C4×Q16—111no—
288C4×SD16—111no—
289C4×SD16C2×D1111yescharacteristic
290C4×D8—111no—
291#436—111no—
292#436—221no—
293#436—221no—
294#436C2×D1111yescharacteristic
295#435—221no—
296#435—221no—
297C8×D4—111no—
298C8×D4—111no—
299#433—221no—
300#433—221no—
301#431—111no—
302#431—111no—
303#431—111no—
304#405—221no—
305#405—221no—
306C4×M16—111no—
307C2×C4×C8—111no—
308#335—111no—
309#335—111no—
310#334—111no—
311#334C2×D1111yescharacteristic
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315Q8⋊C8C2×D1111yescharacteristic
316D4⋊C8—111no—
317D4⋊C8—111no—
318D4⋊C8—111no—
319D4⋊C8C2×D1111yescharacteristic
320#322—111no—
321#322C2×D1111yescharacteristic
322C82—111no—
323C82—111no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11C2×C4×D411yescharacteristic
328C2×D11—21no—
329C2×D11—21no—
330C2×D11—21no—
331C2×D11—41no—
332C2×D11—41no—
333C2×D11—41no—
334C4×C11—21no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11C2×#13111yescharacteristic
339C4×C11#56811yescharacteristic
340C4×C11C2×#13511yescharacteristic
341C4×C11C2×#13511yescharacteristic
342Dic11—21no—
343Dic11—21no—
344Dic11—21no—
345Dic11—41no—
346Dic11—41no—
347Dic11—41no—
348C2×Q16—111no—
349C2×SD16—111no—
350C2×SD16C4×D1111yescharacteristic
351C2×D8—111no—
352C2×M16—21no—
353C2×M16—111no—
354C2×M16—111no—
355C2×M16—221no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8—221no—
359C22×C8—221no—
360#126—221no—
361#126—221no—
362#125—111no—
363#125—111no—
364#124—111no—
365#124—111no—
366#123—221no—
367#123—221no—
368C22⋊Q8—111no—
369C22⋊Q8—111no—
370#121—111no—
371#121—111no—
372C4×Q8—111no—
373C4×Q8C22×D1111yescharacteristic
374C4×D4—111no—
375C4×D4—221no—
376C4×D4—221no—
377C4×D4C22×D1111yescharacteristic
378#117—221no—
379#117—221no—
380C2×C42—111no—
381#107—111no—
382#107—111no—
383#106—111no—
384#106C4×D1111yescharacteristic
385C4⋊C8—21no—
386C4⋊C8—111no—
387C4⋊C8—111no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8—221no—
391C4⋊C8—221no—
392C4⋊C8C22×D1111yescharacteristic
393C4⋊C8C22×D1111yescharacteristic
394#103—111no—
395#103—111no—
396#103—111no—
397#103C4×D1111yescharacteristic
398#102—111no—
399#102—111no—
400#102—111no—
401#102C4×D1111yescharacteristic
402C22⋊C8—21no—
403C22⋊C8—221no—
404C22⋊C8—221no—
405C22⋊C8—221no—
406C22⋊C8—221no—
407C22⋊C8—221no—
408C22⋊C8—221no—
409#97—111no—
410#97—111no—
411#97—221no—
412#97—221no—
413C4×C8—21no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—111no—
417C4×C8—111no—
418C4×C8—111no—
419C4×C8—221no—
420C4×C8—221no—
421C4×C8—221no—
422C4×C8C22×D1111yescharacteristic
423C4×C8C22×D1111yescharacteristic
424C4×C8C22×D1111yescharacteristic
425C2×C11—81no—
426C2×C11#293511yescharacteristic
427C2×C11C4×#13511yescharacteristic
428C2×C11#295711yescharacteristic
429D11—41no—
430D11—81no—
431C2×Q8—111no—
432C2×Q8C2×C4×D1111yescharacteristic
433C2×D4—111no—
434C2×D4—221no—
435C2×D4—221no—
436C2×D4C2×C4×D1111yescharacteristic
437C22×C4—21no—
438C22×C4—111no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—221no—
442Q16—222no—
443SD16—41no—
444SD16—441no—
445D8—222no—
446M16—42no—
447M16—222no—
448M16—222no—
449M16—442no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—111no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—111no—
457C2×C8—222no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—441no—
462C2×C8—442no—
463C2×C8—442no—
464C2×C8C2×C4×D1111yescharacteristic
465C2×C8C2×C4×D1111yescharacteristic
466C2×C8D4×D1111yescharacteristic
467C2×C8D4×D1111yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—111no—
470C4⋊C4—111no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4C2×C4×D1111yescharacteristic
479C4⋊C4C2×C4×D1111yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—221no—
482C22⋊C4—221no—
483C22⋊C4—221no—
484C22⋊C4—221no—
485C22⋊C4—221no—
486C22⋊C4—221no—
487C22⋊C4—221no—
488C22⋊C4—221no—
489C22⋊C4—221no—
490C42—21no—
491C42—111no—
492C42—111no—
493C42—111no—
494C42—221no—
495C42C23×D1111yescharacteristic
496C11#1806911yescharacteristic, complemented, Sylow
497C23—21no—
498C23—111no—
499C23—221no—
500Q8—21no—
501Q8—21no—
502Q8—221no—
503Q8—221no—
504D4—21no—
505D4—21no—
506D4—221no—
507D4—221no—
508D4—881no—
509D4—881no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—111no—
516C2×C4—111no—
517C2×C4—111no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4C22×C4×D1111yescharacteristic
529C2×C4C2×D4×D1111yescharacteristic
530C2×C4#41×D1111yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—112no—
538C8—112no—
539C8—221no—
540C8—221no—
541C8—441no—
542C8—441no—
543C8—441no—
544C8#6696912yes—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—221no—
549C22—221no—
550C22—221no—
551C22—441no—
552C22—441no—
553C22—441no—
554C22C4×D4×D1111yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—221no—
560C4—221no—
561C4—221no—
562C4—441no—
563C4—441no—
564C4—441no—
565C4#1062327611yescharacteristic
566C4D11×#13111yescharacteristic
567C4C2×#6696911yescharacteristic
568C4D11×#13511yescharacteristic
569C2—81no—
570C2—441no—
571C2—881no—
572C2#1307735711yescharacteristic
573C2C4×#6696911yescharacteristic
574C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1583C2
socleC22×C11C2×C4×D4
prime radical#10622388C4
cosocleC42×C11C24
hypercenter#1583D11
hypocenterC11#18069
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
2. #13077623C2semidirect
3. #13077619C2semidirect
4. #13067510C2semidirect
5. #13067499C2semidirect
6. #13067461C2semidirect
7. #13067453C2semidirect
8. #13067451C2semidirect
9. C8×#4326C2semidirect
10. #13067408C2semidirect
11. #13067361C2semidirect
12. #13067023C2semidirect
13. #13067021C2semidirect
14. #13066895C2semidirect
15. C11×#1583C2semidirect
216. #1583D11semidirect
496. C11#18069semidirect

Maximal subgroups

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

subgroupindex
#130791822
#130776232
#130776192
#130675102
#130674992
#130674612
#130674532
#130674512
C8×#43262
#130674082
#130673612
#130670232
#130670212
#130668952
C11×#15832
#1806911