Finite Group Databasebeta

← #14724437

Subgroups — #14724437

Order 2816.

600 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079172C211yesmaximal, characteristic
2#13077712C211yesmaximal, characteristic, complemented
3#13077693C211yesmaximal, characteristic
4#13067520C211yesmaximal, characteristic, complemented
5#13067506C211yesmaximal, characteristic, complemented
6#13067504C211yesmaximal, characteristic, complemented
7SD16⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
8#13067427C211yesmaximal, characteristic, complemented
9#13067419C211yesmaximal, characteristic, complemented
10#13067413C211yesmaximal, characteristic, complemented
11#13067378C211yesmaximal, characteristic, complemented
12#13067087C211yesmaximal, characteristic, complemented
13#13067083C211yesmaximal, characteristic
14#13066901C211yesmaximal, characteristic, complemented
15C11×#1592C211yesmaximal, characteristic, complemented
16#10623109C2211yescharacteristic
17#10623079C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C4×C11×SD16C2211yescharacteristic
20C11×#436C2211yescharacteristic
21#10622788C411yescharacteristic
22#10622784C411yescharacteristic
23#10622742—21no—
24#10622740—21no—
25C4×#4325C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27C4×#4324C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622477C411yescharacteristic
30#10622468C411yescharacteristic
31#10622453—21no—
32#10622448C2211yescharacteristic
33#10622448C2211yescharacteristic
34#10622447C2211yescharacteristic
35#10622444—21no—
36#10622443C2211yescharacteristic
37#10622420C411yescharacteristic
38#10622405C411yescharacteristic
39#10622391C411yescharacteristic
40#10622373C411yescharacteristic
41#10622343—21no—
42#10622340—21no—
43#10622322—21no—
44#10622314—21no—
45C4×#4314C2211yescharacteristic
46#10622301C2211yescharacteristic
47#10622298C2211yescharacteristic
48#10622298C2211yescharacteristic
49C4×C8×D11C2211yescharacteristic
50#10622292C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622096C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4339—21no—
68C2×C11×SD16C2×C411yescharacteristic
69C2×C11×M16—21no—
70C4×Q8×C11C2311yescharacteristic
71C4×D4×C11C2311yescharacteristic
72#66999C2×C411yescharacteristic
73#66997C2×C411yescharacteristic
74C2×#4325C2×C411yescharacteristic
75#66993C2×C411yescharacteristic
76#66991C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C22×C11⋊C8—21no—
80C2×#4314C2×C411yescharacteristic
81C2×#4313—21no—
82C2×C8×D11—21no—
83C2×C8×D11C2×C411yescharacteristic
84C2×C8×D11C2×C411yescharacteristic
85#66950C2×C411yescharacteristic
86#66949—21no—
87#66948C2×C411yescharacteristic
88#66942—21no—
89#66941C2×C411yescharacteristic
90#66941C2×C411yescharacteristic
91#66938—21no—
92#66937—21no—
93C4×D44C2311yescharacteristic
94#66925—21no—
95C42×D11C2311yescharacteristic
96C4×Dic22—21no—
97C4×Dic22C2311yescharacteristic
98C11×#106C2×C411yescharacteristic
99C11×C4⋊C8—21no—
100C11×C4⋊C8C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×#103C2×C411yescharacteristic
103C11×#102C2×C411yescharacteristic
104C11×C22⋊C8—21no—
105C11×#97—21no—
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109#66899C2×C411yescharacteristic
110#66896C2×C411yescharacteristic
111C22⋊(C11⋊C8)—21no—
112#66885C2×C411yescharacteristic
113(C2×D11)⋊C8—21no—
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8—21no—
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8D411yescharacteristic
119(C2×D11)⋊C8D411yescharacteristic
120#66881C2×C411yescharacteristic
121#66880C2×C411yescharacteristic
122#66879—21no—
123#66879—21no—
124#66879—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8D411yescharacteristic
129Dic11⋊C8D411yescharacteristic
130C8×Dic11—21no—
131C8×Dic11C2×C411yescharacteristic
132C8×Dic11C2×C411yescharacteristic
133#66874C2×C411yescharacteristic
134#66873C2×C411yescharacteristic
135#66872C2×C411yescharacteristic
136#66872C2×C411yescharacteristic
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17971—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×D4×C11C22×C411yescharacteristic
147C22×C4×C11—21no—
148C2×C22⋊D11—21no—
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151#4339—81no—
152#4339—81no—
153C2×D44—21no—
154C2×D44C22×C411yescharacteristic
155C2×C4×D11—21no—
156C2×C4×D11C22×C411yescharacteristic
157C2×C4×D11C2×D411yescharacteristic
158C2×C4×D11#4111yescharacteristic
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22C22×C411yescharacteristic
162C11×SD16—22no—
163C11×M16—81no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11C22×C411yescharacteristic
168C2×C8×C11C22×C411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C11×C4⋊C4—21no—
172C11×C4⋊C4C22×C411yescharacteristic
173C11×C4⋊C4C22×C411yescharacteristic
174C11×C22⋊C4—21no—
175C42×C11—21no—
176C42×C11C2411yescharacteristic
177C22⋊Dic11—21no—
178#4325—22no—
179#4324—22no—
180(C2×D11)⋊C4—21no—
181(C2×D11)⋊C4—21no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11C22×C411yescharacteristic
186C4⋊Dic11C22×C411yescharacteristic
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193C4×Dic11—21no—
194C4×Dic11C22×C411yescharacteristic
195C4×Dic11C2×D411yescharacteristic
196C4×Dic11#4111yescharacteristic
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—81no—
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205#4314—22no—
206#4313—81no—
207C8×D11—22no—
208C8×D11—22no—
209C8×D11—81no—
210#3167—111no—
211#2985—111no—
212#2981—111no—
213#1592—111no—
214#1592D1111yescharacteristic, complemented
215#1590—111no—
216#1590—111no—
217SD16⋊C8—111no—
218SD16⋊C8—111no—
219C8×SD16—111no—
220C8×SD16—111no—
221#1568—111no—
222#1497—111no—
223#1496—111no—
224#1450—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—
241C22⋊D11—81no—
242C22⋊D11—81no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11C4×D411yescharacteristic
247C2×Dic11C4×D411yescharacteristic
248C2×Dic11C4×D411yescharacteristic
249D44—21no—
250D44—21no—
251D44—81no—
252C4×D11—21no—
253C4×D11—21no—
254C4×D11—21no—
255C4×D11—21no—
256C4×D11—41no—
257C4×D11—41no—
258C4×D11—41no—
259Dic22—21no—
260Dic22—21no—
261Dic22—81no—
262Dic22—81no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—41no—
267C8×C11—41no—
268C8×C11—41no—
269C8×C11#13112yes—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8#13112yes—
277#533—111no—
278#532—111no—
279#498—111no—
280#492—111no—
281#487—111no—
282#486—111no—
283#465—111no—
284#465—111no—
285#465—111no—
286#465—111no—
287#446—111no—
288#446—221no—
289#446—221no—
290#446C2×D1111yescharacteristic
291C8×Q8—111no—
292C8×Q8—111no—
293C4×SD16—111no—
294C4×SD16—111no—
295C4×SD16—111no—
296C4×SD16C2×D1111yescharacteristic
297#436—111no—
298#436C2×D1111yescharacteristic
299#435—221no—
300#435—221no—
301C8×D4—111no—
302C8×D4—111no—
303#433—221no—
304#433—221no—
305#432—111no—
306#432—111no—
307#431—111no—
308#431—111no—
309#408—221no—
310#408—221no—
311C2×C4×C8—111no—
312#335—111no—
313#335C2×D1111yescharacteristic
314#334—111no—
315#334—111no—
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318Q8⋊C8—111no—
319Q8⋊C8C2×D1111yescharacteristic
320D4⋊C8—111no—
321D4⋊C8—111no—
322D4⋊C8—111no—
323D4⋊C8C2×D1111yescharacteristic
324#322—111no—
325#322C2×D1111yescharacteristic
326C82—111no—
327C82—111no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11C2×C4×D411yescharacteristic
332C2×D11—21no—
333C2×D11—21no—
334C2×D11—21no—
335C2×D11—41no—
336C2×D11—41no—
337C2×D11—41no—
338C4×C11—21no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11C2×#13111yescharacteristic
343C4×C11C2×#13111yescharacteristic
344C4×C11#57711yescharacteristic
345C4×C11#57711yescharacteristic
346Dic11—21no—
347Dic11—21no—
348Dic11—21no—
349Dic11—41no—
350Dic11—41no—
351Dic11—41no—
352C2×#41—221no—
353C2×SD16—111no—
354C2×SD16—111no—
355C2×SD16—111no—
356C2×SD16C4×D1111yescharacteristic
357C2×M16—21no—
358C2×M16—221no—
359C22×C8—111no—
360C22×C8—111no—
361C22×C8—221no—
362C22×C8—221no—
363C4⋊Q8—111no—
364C4⋊Q8—111no—
365C4⋊Q8—111no—
366#127—111no—
367#125—221no—
368#124—221no—
369C22⋊Q8—111no—
370C22⋊Q8—111no—
371C22⋊Q8—221no—
372#121—111no—
373#121—111no—
374#121—221no—
375C4×Q8—111no—
376C4×Q8—221no—
377C4×Q8C22×D1111yescharacteristic
378C4×D4—111no—
379C4×D4—221no—
380C4×D4C22×D1111yescharacteristic
381#117—221no—
382C2×C42—111no—
383#106—111no—
384#106—111no—
385#106—111no—
386#106C4×D1111yescharacteristic
387C4⋊C8—21no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8C22×D1111yescharacteristic
397C4⋊C8C22×D1111yescharacteristic
398#103—111no—
399#103—111no—
400#103—111no—
401#103C4×D1111yescharacteristic
402#102—111no—
403#102—111no—
404#102—111no—
405#102C4×D1111yescharacteristic
406C22⋊C8—21no—
407C22⋊C8—111no—
408C22⋊C8—111no—
409C22⋊C8—221no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413C22⋊C8—221no—
414C22⋊C8—221no—
415#97—21no—
416#97—221no—
417#97—221no—
418#97—221no—
419C4×C8—111no—
420C4×C8—111no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—111no—
424C4×C8—221no—
425C4×C8—221no—
426C4×C8C22×D1111yescharacteristic
427C4×C8C22×D1111yescharacteristic
428C4×C8C22×D1111yescharacteristic
429C2×C11—81no—
430C2×C11#293111yescharacteristic
431C2×C11#294911yescharacteristic
432C2×C11#295711yescharacteristic
433D11—41no—
434D11—81no—
435#41—881no—
436#41—881no—
437C2×Q8—111no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×Q8C2×C4×D1111yescharacteristic
441C2×D4—111no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4C2×C4×D1111yescharacteristic
447C22×C4—21no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—221no—
452SD16—22no—
453SD16—222no—
454SD16—222no—
455SD16—222no—
456M16—81no—
457M16—881no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—111no—
462C2×C8—111no—
463C2×C8—111no—
464C2×C8—111no—
465C2×C8—222no—
466C2×C8—222no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—881no—
471C2×C8—881no—
472C2×C8C2×C4×D1111yescharacteristic
473C2×C8C2×C4×D1111yescharacteristic
474C2×C8D4×D1111yescharacteristic
475C2×C8D4×D1111yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—111no—
478C4⋊C4—111no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4C2×C4×D1111yescharacteristic
487C4⋊C4C2×C4×D1111yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—221no—
490C22⋊C4—221no—
491C22⋊C4—221no—
492C22⋊C4—221no—
493C22⋊C4—221no—
494C42—21no—
495C42—111no—
496C42—111no—
497C42—111no—
498C42—221no—
499C42C23×D1111yescharacteristic
500C11#1797111yescharacteristic, complemented, Sylow
501C23—21no—
502C23—111no—
503C23—221no—
504Q8—21no—
505Q8—21no—
506Q8—221no—
507Q8—221no—
508Q8—881no—
509Q8—881no—
510D4—21no—
511D4—21no—
512D4—221no—
513D4—221no—
514D4—881no—
515D4—881no—
516D4—881no—
517D4—881no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—111no—
524C2×C4—111no—
525C2×C4—111no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4C22×C4×D1111yescharacteristic
537C2×C4C2×D4×D1111yescharacteristic
538C2×C4#41×D1111yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—112no—
546C8—221no—
547C8—221no—
548C8—221no—
549C8—441no—
550C8—441no—
551C8—441no—
552C8#6696012yes—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—221no—
557C22—221no—
558C22—221no—
559C22—441no—
560C22—441no—
561C22—441no—
562C22C4×D4×D1111yescharacteristic
563C4—21no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—221no—
568C4—221no—
569C4—221no—
570C4—441no—
571C4—441no—
572C4—441no—
573C4C2×#6696011yescharacteristic
574C4D11×#13111yescharacteristic
575C4#1062330611yescharacteristic
576C4#1062330911yescharacteristic
577C2—81no—
578C2—441no—
579C2—881no—
580C2#1307732511yescharacteristic
581C2#1307747211yescharacteristic
582C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1592C2
socleC22×C11C2×C4×D4
prime radical#10623079C22
cosocleC42×C11C24
hypercenter#1592D11
hypocenterC11#17971
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1592

Complements

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

NH ≅ G/Ntype
2. #13077712C2semidirect
4. #13067520C2semidirect
5. #13067506C2semidirect
6. #13067504C2semidirect
7. SD16⋊(C11⋊C8)C2semidirect
8. #13067427C2semidirect
9. #13067419C2semidirect
10. #13067413C2semidirect
11. #13067378C2semidirect
12. #13067087C2semidirect
14. #13066901C2semidirect
15. C11×#1592C2semidirect
214. #1592D11semidirect
500. C11#17971semidirect

Maximal subgroups

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

subgroupindex
#130791722
#130777122
#130776932
#130675202
#130675062
#130675042
SD16⋊(C11⋊C8)2
#130674272
#130674192
#130674132
#130673782
#130670872
#130670832
#130669012
C11×#15922
#1797111