Finite Group Databasebeta

← #14723728

Subgroups — #14723728

Order 2816.

626 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#13078636C211yesmaximal, characteristic
2#13077585C211yesmaximal, characteristic, complemented
3#13077572C211yesmaximal, characteristic, complemented
4#13067493C211yesmaximal, characteristic, complemented
5#13067486C211yesmaximal, characteristic, complemented
6#13067479C211yesmaximal, characteristic, complemented
7#13067472C211yesmaximal, characteristic, complemented
8#13067439C211yesmaximal, characteristic, complemented
9#13067434C211yesmaximal, characteristic, complemented
10#13067427C211yesmaximal, characteristic, complemented
11#13067427C211yesmaximal, characteristic, complemented
12#13067048C211yesmaximal, characteristic, complemented
13#13067022C211yesmaximal, characteristic, complemented
14#13066909C211yesmaximal, characteristic, complemented
15C11×#1572C211yesmaximal, characteristic, complemented
16#10623010C2211yescharacteristic
17C4×#4339C2211yescharacteristic
18C11×#432C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21#10622538C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622460C411yescharacteristic
24#10622458C411yescharacteristic
25#10622457C411yescharacteristic
26#10622451C2211yescharacteristic
27#10622447C2211yescharacteristic
28#10622447C2211yescharacteristic
29#10622447C2211yescharacteristic
30#10622444C2211yescharacteristic
31#10622443C2211yescharacteristic
32#10622443C2211yescharacteristic
33#10622443C2211yescharacteristic
34#10622442C411yescharacteristic
35#10622350C411yescharacteristic
36#10622347C411yescharacteristic
37#10622346C411yescharacteristic
38#10622343—21no—
39(C22⋊D11)⋊C8—21no—
40(C22⋊D11)⋊C8—21no—
41(C22⋊D11)⋊C8—21no—
42#10622336C411yescharacteristic
43#10622322—21no—
44#10622321—21no—
45C4×Dic44C2211yescharacteristic
46C4×D88C2211yescharacteristic
47C4×#4314C2211yescharacteristic
48C4×#4314C2211yescharacteristic
49#10622298—21no—
50C4×C8×D11—21no—
51C11×#335C2211yescharacteristic
52C11×#335C2211yescharacteristic
53C11×#334C2211yescharacteristic
54C11×#334C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622121C2211yescharacteristic
60#10622121C2211yescharacteristic
61#10622121C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×#4339C2×C411yescharacteristic
68C2×C42×C11C2311yescharacteristic
69#66983C2×C411yescharacteristic
70#66982—21no—
71C4×C22⋊D11—21no—
72C4×C22⋊D11—21no—
73C4×C22⋊D11—21no—
74#66979C2×C411yescharacteristic
75#66977C2×C411yescharacteristic
76C22×C11⋊C8D411yescharacteristic
77C22×C11⋊C8D411yescharacteristic
78C2×Dic44C2×C411yescharacteristic
79C2×D88C2×C411yescharacteristic
80C2×#4314C2×C411yescharacteristic
81C2×#4314C2×C411yescharacteristic
82C2×#4313—21no—
83C2×C8×D11—21no—
84C2×C8×D11—21no—
85C2×C8×D11—21no—
86#66929—21no—
87#66928C2×C411yescharacteristic
88C4×D44C2×C411yescharacteristic
89C4×D44C2311yescharacteristic
90C4×D44C2311yescharacteristic
91#66925—21no—
92#66925—21no—
93C42×D11—21no—
94#66923C2×C411yescharacteristic
95C4×Dic22C2×C411yescharacteristic
96C4×Dic22C2311yescharacteristic
97C4×Dic22C2311yescharacteristic
98C11×C4⋊C8C2×C411yescharacteristic
99C11×C4⋊C8C2×C411yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C22⋊C8—21no—
105C11×C22⋊C8—21no—
106C11×C22⋊C8C2×C411yescharacteristic
107C11×C22⋊C8C2×C411yescharacteristic
108C11×#97—21no—
109C4×C8×C11—21no—
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C22⋊(C11⋊C8)—21no—
113#66885C2×C411yescharacteristic
114#66885C2×C411yescharacteristic
115#66885C2×C411yescharacteristic
116#66885C2×C411yescharacteristic
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121#66882C2×C411yescharacteristic
122#66882C2×C411yescharacteristic
123#66881C2×C411yescharacteristic
124#66881C2×C411yescharacteristic
125#66880C2×C411yescharacteristic
126#66880C2×C411yescharacteristic
127#66880C2×C411yescharacteristic
128#66880C2×C411yescharacteristic
129#66879—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134C8×Dic11—21no—
135C8×Dic11—21no—
136C8×Dic11—21no—
137C4⋊(C11⋊C8)—21no—
138C4×C11⋊C8D411yescharacteristic
139C4×C11⋊C8D411yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17909—111nomaximal, Sylow
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C2×C22⋊D11—21no—
149C2×C22⋊D11—21no—
150#4339—22no—
151#4339—22no—
152C2×D44C22×C411yescharacteristic
153C2×D44C22×C411yescharacteristic
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×Dic22C22×C411yescharacteristic
159C2×Dic22C22×C411yescharacteristic
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11C22×C411yescharacteristic
165C2×C8×C11C22×C411yescharacteristic
166C2×C8×C11C22×C411yescharacteristic
167C2×C8×C11C22×C411yescharacteristic
168C42×C11C22×C411yescharacteristic
169C42×C11C2×D411yescharacteristic
170C42×C11#4111yescharacteristic
171C42×C11C2411yescharacteristic
172C22⋊Dic11—21no—
173C22⋊Dic11—21no—
174(C2×D11)⋊C4—21no—
175(C2×D11)⋊C4—21no—
176(C2×D11)⋊C4—21no—
177(C2×D11)⋊C4—21no—
178(C2×D11)⋊C4—21no—
179(C2×D11)⋊C4—21no—
180C4⋊Dic11C22×C411yescharacteristic
181C4⋊Dic11C22×C411yescharacteristic
182C4⋊Dic11C22×C411yescharacteristic
183C4⋊Dic11C22×C411yescharacteristic
184Dic11⋊C4—21no—
185Dic11⋊C4—21no—
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—41no—
197C2×C11⋊C8—41no—
198C2×C11⋊C8C2×D411yescharacteristic
199C2×C11⋊C8C2×D411yescharacteristic
200C2×C11⋊C8C2×D411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202Dic44—22no—
203D88—22no—
204#4314—22no—
205#4314—22no—
206#4313—42no—
207C8×D11—42no—
208C8×D11—42no—
209C8×D11—42no—
210#3102—111no—
211#2966—111no—
212C8×#41—111no—
213#1588—111no—
214#1587—111no—
215#1586—111no—
216#1585—111no—
217#1580—111no—
218#1579—111no—
219SD16⋊C8—111no—
220SD16⋊C8—111no—
221#1572D1111yescharacteristic, complemented
222#1488—111no—
223#1482—111no—
224#1452—111no—
225C23×C11C4×D411yescharacteristic
226C22×D11—21no—
227C22×D11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—41no—
233C2×C4×C11C4×D411yescharacteristic
234C2×C4×C11C4×D411yescharacteristic
235C2×C4×C11C4×D411yescharacteristic
236C2×C4×C11C23×C411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C22⋊D11—24no—
240C22⋊D11—42no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247D44—21no—
248D44—21no—
249D44—21no—
250D44#13112yes—
251C4×D11—24no—
252C4×D11—42no—
253C4×D11—41no—
254C4×D11—41no—
255C4×D11—41no—
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—
268C8×C11—41no—
269C11⋊C8—21no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—21no—
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×D8—111no—
293#436—111no—
294#435—221no—
295C8×D4—111no—
296C8×D4—111no—
297C8×D4—111no—
298C8×D4—221no—
299C8×D4—221no—
300C8×D4—221no—
301#433—221no—
302#432C2×D1111yescharacteristic
303#431—111no—
304#431—221no—
305#431C2×D1111yescharacteristic
306#431C2×D1111yescharacteristic
307#405—221no—
308C2×C4×C8—111no—
309C2×C4×C8—221no—
310#335C2×D1111yescharacteristic
311#335C2×D1111yescharacteristic
312#334C2×D1111yescharacteristic
313#334C2×D1111yescharacteristic
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318D4⋊C8—111no—
319D4⋊C8—111no—
320D4⋊C8—111no—
321D4⋊C8—111no—
322#322—111no—
323#322—111no—
324#322—111no—
325#322—111no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11C2×C4×D411yescharacteristic
330C2×D11—22no—
331C2×D11—41no—
332C2×D11—41no—
333C2×D11—41no—
334C2×D11—41no—
335C2×D11—41no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11C2×#13111yescharacteristic
341C4×C11C2×#13111yescharacteristic
342C4×C11#57511yescharacteristic
343C4×C11#57511yescharacteristic
344Dic11—22no—
345Dic11—41no—
346Dic11—41no—
347Dic11—41no—
348Dic11—41no—
349Dic11—41no—
350C2×#41—111no—
351C2×Q16—111no—
352C2×SD16—111no—
353C2×SD16—111no—
354C2×D8—111no—
355C2×M16—221no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8—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—111no—
372C4×D4—111no—
373C4×D4—221no—
374C4×D4—221no—
375C4×D4—221no—
376#117—111no—
377#117—221no—
378#117—221no—
379C2×C42—221no—
380C2×C42C22×D1111yescharacteristic
381#107—111no—
382#107—111no—
383#106—111no—
384#106—111no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8C4×D1111yescharacteristic
391C4⋊C8C4×D1111yescharacteristic
392C4⋊C8C22×D1111yescharacteristic
393C4⋊C8C22×D1111yescharacteristic
394C4⋊C8C22×D1111yescharacteristic
395C4⋊C8C22×D1111yescharacteristic
396#103—111no—
397#103—111no—
398#103—111no—
399#103—111no—
400#102—111no—
401#102—111no—
402#102—111no—
403#102—111no—
404C22⋊C8—21no—
405C22⋊C8—21no—
406C22⋊C8—221no—
407C22⋊C8—221no—
408C22⋊C8—221no—
409C22⋊C8—221no—
410C22⋊C8—221no—
411C22⋊C8C4×D1111yescharacteristic
412C22⋊C8C4×D1111yescharacteristic
413#97—21no—
414#97—221no—
415C4×C8—21no—
416C4×C8—111no—
417C4×C8—111no—
418C4×C8—111no—
419C4×C8—111no—
420C4×C8—111no—
421C4×C8—111no—
422C4×C8—221no—
423C4×C8—221no—
424C4×C8—221no—
425C4×C8C22×D1111yescharacteristic
426C4×C8C22×D1111yescharacteristic
427C2×C11—41no—
428C2×C11#292911yescharacteristic
429C2×C11#294311yescharacteristic
430C2×C11#295511yescharacteristic
431D11—42no—
432D11—81no—
433#41—222no—
434#41—222no—
435C2×Q8—111no—
436C2×Q8—111no—
437C2×D4—111no—
438C2×D4—111no—
439C2×D4—221no—
440C2×D4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4C2×C4×D1111yescharacteristic
446C22×C4D4×D1111yescharacteristic
447C22×C4#434311yescharacteristic
448Q16—222no—
449SD16—222no—
450SD16—222no—
451D8—222no—
452M16—442no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—111no—
458C2×C8—111no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—442no—
464C2×C8—442no—
465C2×C8—442no—
466C2×C8—441no—
467C2×C8—441no—
468C2×C8C2×C4×D1111yescharacteristic
469C2×C8C2×C4×D1111yescharacteristic
470C2×C8C2×C4×D1111yescharacteristic
471C2×C8C2×C4×D1111yescharacteristic
472C4⋊C4—111no—
473C4⋊C4—111no—
474C4⋊C4—111no—
475C4⋊C4—111no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊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—221no—
491C42—221no—
492C42—221no—
493C42—221no—
494C42C2×C4×D1111yescharacteristic
495C42D4×D1111yescharacteristic
496C42#434311yescharacteristic
497C42C23×D1111yescharacteristic
498C11#1790911yescharacteristic, complemented, Sylow
499C23—221no—
500C23—221no—
501C23#6694611yescharacteristic
502Q8—112no—
503Q8—221no—
504Q8—221no—
505Q8—221no—
506D4—112no—
507D4—224no—
508D4—221no—
509D4—221no—
510D4—221no—
511D4—442no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—224no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—442no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4#6694611yescharacteristic
530C2×C4#6694611yescharacteristic
531C2×C4#6694611yescharacteristic
532C2×C4C22×C4×D1111yescharacteristic
533C2×C4C2×D4×D1111yescharacteristic
534C2×C4C2×#434311yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—221no—
544C8—221no—
545C8—221no—
546C8—221no—
547C8—441no—
548C8—441no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—222no—
553C22—441no—
554C22—441no—
555C22—441no—
556C22—441no—
557C22—441no—
558C22C2×#6694611yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—222no—
564C4—441no—
565C4—441no—
566C4—441no—
567C4—441no—
568C4—441no—
569C4D11×#13111yescharacteristic
570C4D11×#13111yescharacteristic
571C4#1062329911yescharacteristic
572C4#1062329911yescharacteristic
573C2—41no—
574C2—442no—
575C2—881no—
576C2#1307730911yescharacteristic
577C2#1307741611yescharacteristic
578C2#1307751811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1572C2
socleC22×C11C2×C4×D4
prime radical#10622347C4
cosocleC42×C11C24
hypercenter#1572D11
hypocenterC11#17909
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
2. #13077585C2semidirect
3. #13077572C2semidirect
4. #13067493C2semidirect
5. #13067486C2semidirect
6. #13067479C2semidirect
7. #13067472C2semidirect
8. #13067439C2semidirect
9. #13067434C2semidirect
10. #13067427C2semidirect
11. #13067427C2semidirect
12. #13067048C2semidirect
13. #13067022C2semidirect
14. #13066909C2semidirect
15. C11×#1572C2semidirect
221. #1572D11semidirect
498. C11#17909semidirect

Maximal subgroups

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

subgroupindex
#130786362
#130775852
#130775722
#130674932
#130674862
#130674792
#130674722
#130674392
#130674342
#130674272
#130670482
#130670222
#130669092
C11×#15722
#1790911