Finite Group Databasebeta

← #14725187

Subgroups — #14725187

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078630C211yesmaximal, characteristic
2#13077777C211yesmaximal, characteristic, complemented
3#13077744C211yesmaximal, characteristic, complemented
4#13067515C211yesmaximal, characteristic, complemented
5#13067492C211yesmaximal, characteristic, complemented
6#13067492C211yesmaximal, characteristic, complemented
7#13067465C211yesmaximal, characteristic, complemented
8#13067446C211yesmaximal, characteristic, complemented
9#13067425C211yesmaximal, characteristic, complemented
10C8×Dic44C211yesmaximal, characteristic, complemented
11#13067389C211yesmaximal, characteristic, complemented
12#13067078C211yesmaximal, characteristic, complemented
13#13067000C211yesmaximal, characteristic, complemented
14#13066915C211yesmaximal, characteristic, complemented
15C11×#1589C211yesmaximal, characteristic, complemented
16#10623088C2211yescharacteristic
17C4×#4341C2211yescharacteristic
18C4×C11×D8C2211yescharacteristic
19C11×#436C2211yescharacteristic
20C11×#436C2211yescharacteristic
21#10622771C411yescharacteristic
22#10622766C411yescharacteristic
23#10622741—21no—
24#10622740—21no—
25#10622732—21no—
26#10622731—21no—
27C4×#4324C2211yescharacteristic
28C4×#4324C2211yescharacteristic
29#10622625C2211yescharacteristic
30D4×C11⋊C8C2211yescharacteristic
31#10622501C411yescharacteristic
32#10622490C411yescharacteristic
33#10622450C2211yescharacteristic
34D11×C4⋊C8C2211yescharacteristic
35#10622444C2211yescharacteristic
36#10622443C2211yescharacteristic
37#10622397C411yescharacteristic
38#10622396C411yescharacteristic
39#10622380C411yescharacteristic
40#10622379C411yescharacteristic
41#10622342—21no—
42(C22⋊D11)⋊C8—21no—
43#10622333—21no—
44#10622331—21no—
45C4×Dic44C2211yescharacteristic
46#10622298C2211yescharacteristic
47#10622298C2211yescharacteristic
48#10622298C2211yescharacteristic
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C82×C11C2211yescharacteristic
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622117C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622096C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×#4341C2×C411yescharacteristic
68C2×C11×D8C2×C411yescharacteristic
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C4×D4×C11C2311yescharacteristic
72C4×D4×C11C2311yescharacteristic
73#66991C2×C411yescharacteristic
74#66989C2×C411yescharacteristic
75D4×Dic11C2×C411yescharacteristic
76C2×#4324C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C4×C22⋊D11—21no—
80#66979—21no—
81C2×C4×Dic11—21no—
82C2×#4318—21no—
83C22×C11⋊C8—21no—
84C2×Dic44C2×C411yescharacteristic
85C2×#4313—21no—
86C2×C8×D11—21no—
87#66950C2×C411yescharacteristic
88#66945C2×C411yescharacteristic
89#66943C2×C411yescharacteristic
90#66940C2×C411yescharacteristic
91#66936—21no—
92(C22⋊D11)⋊C4—21no—
93#66932—21no—
94#66930—21no—
95C42×D11C2311yescharacteristic
96C4×Dic22C2311yescharacteristic
97C4×Dic22C2311yescharacteristic
98C11×#107C2×C411yescharacteristic
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×#102C2×C411yescharacteristic
102C11×#102C2×C411yescharacteristic
103C11×C22⋊C8—21no—
104C11×C22⋊C8—21no—
105C4×C8×C11C2311yescharacteristic
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108#66896C2×C411yescharacteristic
109#66896C2×C411yescharacteristic
110C22⋊(C11⋊C8)—21no—
111C22⋊(C11⋊C8)—21no—
112(C2×D11)⋊C8—21no—
113(C2×D11)⋊C8C2×C411yescharacteristic
114(C2×D11)⋊C8C2×C411yescharacteristic
115(C2×D11)⋊C8D411yescharacteristic
116(C2×D11)⋊C8D411yescharacteristic
117#66882C2×C411yescharacteristic
118#66880C2×C411yescharacteristic
119#66880C2×C411yescharacteristic
120#66879—21no—
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8C2×C411yescharacteristic
129Dic11⋊C8C2×C411yescharacteristic
130Dic11⋊C8D411yescharacteristic
131Dic11⋊C8D411yescharacteristic
132C8×Dic11—21no—
133C8×Dic11—21no—
134C8×Dic11—21no—
135#66874C2×C411yescharacteristic
136#66874C2×C411yescharacteristic
137#66872C2×C411yescharacteristic
138#66872C2×C411yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18033—111nomaximal, Sylow
145C2×D4×C11C22×C411yescharacteristic
146C2×D4×C11C22×C411yescharacteristic
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153#4341—22no—
154#4341—41no—
155C2×C4×D11C22×C411yescharacteristic
156C2×C4×D11C2×D411yescharacteristic
157C2×C4×D11#4111yescharacteristic
158C2×Dic22C22×C411yescharacteristic
159C2×Dic22C22×C411yescharacteristic
160C11×D8—41no—
161C11×M16—81no—
162C11×M16—81no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11C22×C411yescharacteristic
167C2×C8×C11C22×C411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C11×C4⋊C4C22×C411yescharacteristic
171C11×C4⋊C4C22×C411yescharacteristic
172C11×C22⋊C4—21no—
173C11×C22⋊C4—21no—
174C42×C11C2411yescharacteristic
175C22⋊Dic11—21no—
176C22⋊Dic11—21no—
177C22⋊Dic11—21no—
178C22⋊Dic11—21no—
179#4324—22no—
180#4324—41no—
181(C2×D11)⋊C4—21no—
182(C2×D11)⋊C4—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×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11C22×C411yescharacteristic
196C4×Dic11C2×D411yescharacteristic
197C4×Dic11#4111yescharacteristic
198#4318—81no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—81no—
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207Dic44—22no—
208#4313—81no—
209C8×D11—81no—
210#3102—111no—
211#2994—111no—
212#2991—111no—
213#1592—111no—
214#1589D1111yescharacteristic, complemented
215#1588—111no—
216#1588—111no—
217#1584—111no—
218#1581—111no—
219SD16⋊C8—111no—
220C8×Q16—111no—
221#1571—111no—
222#1495—111no—
223#1477—111no—
224#1454—111no—
225C23×C11—21no—
226C23×C11—21no—
227C22×D11C4×D411yescharacteristic
228D4×C11—21no—
229D4×C11—21no—
230D4×C11—21no—
231D4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11C23×C411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C22⋊D11—42no—
242C22⋊D11—42no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11C4×D411yescharacteristic
250C2×Dic11C4×D411yescharacteristic
251C2×Dic11C4×D411yescharacteristic
252C4×D11—21no—
253C4×D11—21no—
254C4×D11—21no—
255C4×D11—21no—
256C4×D11—41no—
257Dic22—21no—
258Dic22—21no—
259Dic22—21no—
260Dic22#13112yes—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—41no—
266C8×C11—41no—
267C8×C11—41no—
268C11⋊C8—21no—
269C11⋊C8—21no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275#529—111no—
276C4×#41—111no—
277#485—111no—
278#482—111no—
279#479—111no—
280#478—111no—
281#464—111no—
282#463—111no—
283#452—111no—
284#449—111no—
285#446—111no—
286C8×Q8—111no—
287C8×Q8—111no—
288C8×Q8—111no—
289C4×Q16—111no—
290C4×SD16—111no—
291C4×SD16—111no—
292C4×D8C2×D1111yescharacteristic
293#436—111no—
294#436—221no—
295#436—221no—
296#436C2×D1111yescharacteristic
297#436C2×D1111yescharacteristic
298#435—221no—
299C8×D4—111no—
300C8×D4—221no—
301#433—221no—
302#431—111no—
303#431—111no—
304#431—111no—
305#431—221no—
306#424—221no—
307#423—111no—
308#423—221no—
309C2×C4⋊C8—111no—
310#335—111no—
311#335—111no—
312#335—111no—
313#335C2×D1111yescharacteristic
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318D4⋊C8—111no—
319D4⋊C8—111no—
320D4⋊C8C2×D1111yescharacteristic
321D4⋊C8C2×D1111yescharacteristic
322#322—111no—
323#322—111no—
324#322—111no—
325C82C2×D1111yescharacteristic
326C22×C11—41no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11C2×C4×D411yescharacteristic
333C2×D11—21no—
334C2×D11—21no—
335C2×D11—21no—
336C4×C11—21no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11C2×#13111yescharacteristic
340C4×C11#56811yescharacteristic
341C4×C11#57611yescharacteristic
342C4×C11#57811yescharacteristic
343Dic11—22no—
344Dic11—21no—
345Dic11—21no—
346Dic11—21no—
347Dic11—41no—
348Dic11—41no—
349Dic11—41no—
350C2×#41—111no—
351C2×Q16—111no—
352C2×SD16—111no—
353C2×SD16—111no—
354C2×D8C4×D1111yescharacteristic
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—221no—
358C2×M16—221no—
359C22×C8—221no—
360C22×C8—221no—
361#126—221no—
362#125—111no—
363#124—111no—
364#123—221no—
365C22⋊Q8—111no—
366#121—111no—
367C4×Q8—111no—
368C4×Q8—111no—
369C4×Q8—111no—
370C4×D4—111no—
371C4×D4—221no—
372C4×D4—221no—
373C4×D4—221no—
374C4×D4C22×D1111yescharacteristic
375C4×D4C22×D1111yescharacteristic
376#117—111no—
377#117—221no—
378#117—221no—
379C2×C42—111no—
380C2×C42—221no—
381#107—111no—
382#107C4×D1111yescharacteristic
383#106—111no—
384#106—111no—
385C4⋊C8—111no—
386C4⋊C8—111no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8C22×D1111yescharacteristic
399C4⋊C8C22×D1111yescharacteristic
400#103—111no—
401#103—111no—
402#103—111no—
403#103—111no—
404#102—111no—
405#102—111no—
406#102C4×D1111yescharacteristic
407#102C4×D1111yescharacteristic
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—111no—
411C22⋊C8—111no—
412C22⋊C8—111no—
413C22⋊C8—111no—
414C22⋊C8—221no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417#97—221no—
418C4×C8—111no—
419C4×C8—111no—
420C4×C8—111no—
421C4×C8—221no—
422C4×C8—221no—
423C4×C8—221no—
424C4×C8C22×D1111yescharacteristic
425C4×C8C22×D1111yescharacteristic
426C4×C8C22×D1111yescharacteristic
427C2×C11—81no—
428C2×C11—81no—
429C2×C11#293311yescharacteristic
430C2×C11#295111yescharacteristic
431C2×C11#295511yescharacteristic
432D11—41no—
433#41—222no—
434#41—441no—
435C2×Q8—111no—
436C2×Q8—111no—
437C2×D4—221no—
438C2×D4—221no—
439C2×D4C2×C4×D1111yescharacteristic
440C2×D4C2×C4×D1111yescharacteristic
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—221no—
447C22×C4—221no—
448Q16—222no—
449SD16—222no—
450SD16—441no—
451D8—41no—
452M16—81no—
453M16—81no—
454M16—881no—
455M16—881no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—111no—
462C2×C8—111no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—881no—
467C2×C8—881no—
468C2×C8C2×C4×D1111yescharacteristic
469C2×C8C2×C4×D1111yescharacteristic
470C2×C8D4×D1111yescharacteristic
471C2×C8D4×D1111yescharacteristic
472C4⋊C4—111no—
473C4⋊C4—111no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4C2×C4×D1111yescharacteristic
481C4⋊C4C2×C4×D1111yescharacteristic
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—221no—
485C22⋊C4—221no—
486C22⋊C4—221no—
487C22⋊C4—221no—
488C22⋊C4—221no—
489C22⋊C4—221no—
490C42—111no—
491C42—111no—
492C42—111no—
493C42—221no—
494C42—221no—
495C42—221no—
496C42—221no—
497C42C23×D1111yescharacteristic
498C11#1803311yescharacteristic, complemented, Sylow
499C23—21no—
500C23—21no—
501C23—111no—
502Q8—112no—
503Q8—221no—
504Q8—221no—
505Q8—221no—
506D4—21no—
507D4—21no—
508D4—21no—
509D4—21no—
510D4—442no—
511D4—442no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—111no—
519C2×C4—111no—
520C2×C4—111no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—441no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4C22×C4×D1111yescharacteristic
533C2×C4C2×D4×D1111yescharacteristic
534C2×C4#41×D1111yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—221no—
543C8—221no—
544C8—221no—
545C8—221no—
546C8—441no—
547C8—441no—
548C8—441no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—221no—
556C22—221no—
557C22—221no—
558C22C4×D4×D1111yescharacteristic
559C4—21no—
560C4—41no—
561C4—41no—
562C4—221no—
563C4—221no—
564C4—222no—
565C4—221no—
566C4—441no—
567C4—441no—
568C4—441no—
569C4#1062327611yescharacteristic
570C4D11×#13111yescharacteristic
571C4#1062328811yescharacteristic
572C4#1062330211yescharacteristic
573C2—81no—
574C2—81no—
575C2—441no—
576C2#1307734511yescharacteristic
577C2#1307748611yescharacteristic
578C2#1307751411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1589C2
socleC22×C11C2×C4×D4
prime radical#10622771C4
cosocleC42×C11C24
hypercenter#1589D11
hypocenterC11#18033
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1589

Complements

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

NH ≅ G/Ntype
2. #13077777C2semidirect
3. #13077744C2semidirect
4. #13067515C2semidirect
5. #13067492C2semidirect
6. #13067492C2semidirect
7. #13067465C2semidirect
8. #13067446C2semidirect
9. #13067425C2semidirect
10. C8×Dic44C2semidirect
11. #13067389C2semidirect
12. #13067078C2semidirect
13. #13067000C2semidirect
14. #13066915C2semidirect
15. C11×#1589C2semidirect
214. #1589D11semidirect
498. C11#18033semidirect

Maximal subgroups

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

subgroupindex
#130786302
#130777772
#130777442
#130675152
#130674922
#130674652
#130674462
#130674252
C8×Dic442
#130673892
#130670782
#130670002
#130669152
C11×#15892
#1803311