Finite Group Databasebeta

← #14723486

Subgroups — #14723486

Order 2816.

660 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077731C211yesmaximal, characteristic, complemented
2#13077726C211yesmaximal, characteristic, complemented
3C4×#66969C211yesmaximal, characteristic
4#13067487C211yesmaximal, characteristic, complemented
5#13067484C211yesmaximal, characteristic, complemented
6#13067483C211yesmaximal, characteristic, complemented
7#13067478C211yesmaximal, characteristic, complemented
8#13067460C211yesmaximal, characteristic, complemented
9#13067454C211yesmaximal, characteristic, complemented
10#13067451C211yesmaximal, characteristic, complemented
11D11×#334C211yesmaximal, characteristic, complemented
12#13067002C211yesmaximal, characteristic, complemented
13#13067000C211yesmaximal, characteristic, complemented
14#13066907C211yesmaximal, characteristic, complemented
15C11×#1583C211yesmaximal, characteristic, complemented
16C2×#66969C411yescharacteristic
17C4×#4343C2211yescharacteristic
18C4×#4341C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C4×C11×SD16C2211yescharacteristic
21C11×#436C2211yescharacteristic
22SD16×Dic11C411yescharacteristic
23#10622740—21no—
24#10622731—21no—
25C4×#4326C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27C4×#4323C2211yescharacteristic
28#10622625C2211yescharacteristic
29#10622473C411yescharacteristic
30#10622465C411yescharacteristic
31#10622447—21no—
32#10622447C2211yescharacteristic
33D11×C4⋊C8—21no—
34D11×C4⋊C8C2211yescharacteristic
35D11×C4⋊C8C2211yescharacteristic
36#10622444C2211yescharacteristic
37#10622417C411yescharacteristic
38#10622403C411yescharacteristic
39#10622385C411yescharacteristic
40#10622369C411yescharacteristic
41#10622341—21no—
42#10622332—21no—
43C4×#4314C2211yescharacteristic
44C8×D44—21no—
45C8×D44C2211yescharacteristic
46#10622298—21no—
47#10622298C2211yescharacteristic
48#10622298C2211yescharacteristic
49C4×C8×D11C2211yescharacteristic
50#10622292C2211yescharacteristic
51C11×#334C2211yescharacteristic
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#10622095C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×#4343C2×C411yescharacteristic
68C2×#4341C2×C411yescharacteristic
69C2×C11×SD16C2×C411yescharacteristic
70C2×C11×M16—21no—
71C4×Q8×C11C2311yescharacteristic
72C4×D4×C11C2311yescharacteristic
73Q8×Dic11C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75D4×Dic11C2×C411yescharacteristic
76C2×#4323C2×C411yescharacteristic
77C4×C22⋊D11—21no—
78C2×C4×Dic11—21no—
79C2×#4318—21no—
80#66969—24no—
81C2×#4314C2×C411yescharacteristic
82C2×C8×D11—21no—
83C2×C8×D11—21no—
84C2×C8×D11—21no—
85C2×C8×D11—21no—
86C2×C8×D11C2×C411yescharacteristic
87C2×C8×D11C2×C411yescharacteristic
88#66946—21no—
89#66946C2×C411yescharacteristic
90#66945—21no—
91#66945C2×C411yescharacteristic
92#66945C2×C411yescharacteristic
93#66940C2×C411yescharacteristic
94(C22⋊D11)⋊C4—21no—
95#66930—21no—
96C4×D44—21no—
97C4×D44C2311yescharacteristic
98C42×D11—21no—
99C42×D11C2311yescharacteristic
100C4×Dic22C2311yescharacteristic
101C11×#106C2×C411yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×#103C2×C411yescharacteristic
106C11×#102C2×C411yescharacteristic
107C11×C22⋊C8—21no—
108C4×C8×C11—21no—
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112#66899C2×C411yescharacteristic
113#66896C2×C411yescharacteristic
114C22⋊(C11⋊C8)—21no—
115#66885C2×C411yescharacteristic
116(C2×D11)⋊C8—21no—
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8D411yescharacteristic
120(C2×D11)⋊C8D411yescharacteristic
121#66881C2×C411yescharacteristic
122#66880C2×C411yescharacteristic
123#66879—21no—
124#66879—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8D411yescharacteristic
131Dic11⋊C8D411yescharacteristic
132C8×Dic11C2×C411yescharacteristic
133C8×Dic11C2×C411yescharacteristic
134#66874C2×C411yescharacteristic
135#66873C2×C411yescharacteristic
136#66871C2×C411yescharacteristic
137#66871C2×C411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#17882—111nomaximal, Sylow
146C2×Q8×C11C22×C411yescharacteristic
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C2×C22⋊D11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152#4343—22no—
153#4343M1614yescomplemented
154#4341—22no—
155#4341—22no—
156C2×D44—21no—
157C2×D44C22×C411yescharacteristic
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11C22×C411yescharacteristic
162C2×C4×D11C2×D411yescharacteristic
163C2×C4×D11#4111yescharacteristic
164C2×Dic22C22×C411yescharacteristic
165C11×SD16—22no—
166C11×M16—81no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C11×C4⋊C4—21no—
175C11×C4⋊C4C22×C411yescharacteristic
176C11×C4⋊C4C22×C411yescharacteristic
177C11×C22⋊C4—21no—
178C42×C11—21no—
179C42×C11C2411yescharacteristic
180C22⋊Dic11—21no—
181#4326—22no—
182#4323—22no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11C22×C411yescharacteristic
189C4⋊Dic11C22×C411yescharacteristic
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11C22×C411yescharacteristic
198C4×Dic11C2×D411yescharacteristic
199C4×Dic11#4111yescharacteristic
200#4318—81no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208#4314—22no—
209C8×D11—22no—
210C8×D11—22no—
211C8×D11—81no—
212C8×D11—81no—
213C8×D11—81no—
214C8×D11—81no—
215#2989—111no—
216#2988—111no—
217C4×#135—111no—
218#1587—111no—
219#1587—111no—
220#1586—111no—
221#1586—111no—
222#1583—111no—
223#1583D1111yescharacteristic, complemented
224#1582—111no—
225#1582—111no—
226C2×#334—111no—
227#1477—111no—
228#1477—111no—
229#1452—111no—
230C23×C11—21no—
231C22×D11—21no—
232C22×D11C4×D411yescharacteristic
233Q8×C11—21no—
234Q8×C11C2×M1612yes—
235D4×C11—21no—
236D4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11C23×C411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C22⋊D11—42no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—42no—
250C2×Dic11—81no—
251C2×Dic11C4×D411yescharacteristic
252C2×Dic11C4×D411yescharacteristic
253C2×Dic11C4×D411yescharacteristic
254D44—24no—
255D44—21no—
256D44C2×M1612yes—
257C4×D11—21no—
258C4×D11—21no—
259C4×D11—24no—
260C4×D11—41no—
261C4×D11—41no—
262C4×D11—41no—
263C4×D11—81no—
264C4×D11C2×M1612yes—
265C4×D11#13112yes—
266Dic22—21no—
267Dic22—21no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—41no—
273C8×C11—41no—
274C8×C11—41no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C2×#135—111no—
283C4×#41—111no—
284C4×#41—111no—
285#446—111no—
286#446—111no—
287C8×Q8—111no—
288C8×Q8C2×D1111yescharacteristic
289C4×Q16—111no—
290C4×Q16—111no—
291C4×SD16—111no—
292C4×SD16—111no—
293C4×SD16—111no—
294C4×SD16C2×D1111yescharacteristic
295C4×D8—111no—
296C4×D8—111no—
297#436—111no—
298#436C2×D1111yescharacteristic
299#435—221no—
300#435—221no—
301C8×D4—111no—
302C8×D4—111no—
303C8×D4—221no—
304C8×D4—221no—
305#432—221no—
306#431—111no—
307#431—111no—
308#431—221no—
309#427—111no—
310#423—221no—
311C2×C4⋊C8—111no—
312C2×C4⋊C8—111no—
313C2×C4⋊C8—221no—
314#416—111no—
315#416—111no—
316C2×C4×C8—111no—
317#334—111no—
318#334—111no—
319#334—111no—
320#334C2×D1111yescharacteristic
321Q8⋊C8—111no—
322Q8⋊C8—111no—
323Q8⋊C8—111no—
324Q8⋊C8C2×D1111yescharacteristic
325D4⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8C2×D1111yescharacteristic
329#322—111no—
330#322—111no—
331#322—111no—
332#322C2×D1111yescharacteristic
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11C2×C4×D411yescharacteristic
337C2×D11—21no—
338C2×D11—21no—
339C2×D11—22no—
340C2×D11—41no—
341C2×D11—41no—
342C2×D11#43512yes—
343C4×C11—22no—
344C4×C11—21no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11C22×M1611yescharacteristic
348C4×C11C2×#13111yescharacteristic
349C4×C11#57711yescharacteristic
350C4×C11#57711yescharacteristic
351Dic11—21no—
352Dic11—21no—
353Dic11—41no—
354Dic11—41no—
355Dic11—41no—
356Dic11#43512yes—
357C2×#41—111no—
358C2×#41—111no—
359#135—224no—
360C2×Q16—111no—
361C2×SD16—111no—
362C2×SD16C4×D1111yescharacteristic
363C2×D8—111no—
364C2×M16—21no—
365C2×M16—221no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8—221no—
369C22×C8—221no—
370C22×C8—221no—
371C22×C8—221no—
372C4×Q8—111no—
373C4×Q8—111no—
374C4×Q8—111no—
375C4×Q8C22×D1111yescharacteristic
376C4×D4—111no—
377C4×D4—111no—
378C4×D4—111no—
379C4×D4—221no—
380C4×D4—221no—
381C4×D4—221no—
382C4×D4—221no—
383C4×D4C22×D1111yescharacteristic
384#117—111no—
385#117—111no—
386#117—221no—
387#117—221no—
388C2×C42—111no—
389C2×C42—221no—
390C2×C42—221no—
391#107—111no—
392#107—111no—
393#106—111no—
394#106C4×D1111yescharacteristic
395C4⋊C8—21no—
396C4⋊C8—111no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—221no—
401C4⋊C8—221no—
402C4⋊C8—221no—
403C4⋊C8—221no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406C4⋊C8C22×D1111yescharacteristic
407C4⋊C8C22×D1111yescharacteristic
408#103—111no—
409#103—111no—
410#103—111no—
411#103C4×D1111yescharacteristic
412#102—111no—
413#102—111no—
414#102—111no—
415#102C4×D1111yescharacteristic
416C22⋊C8—21no—
417C22⋊C8—111no—
418C22⋊C8—111no—
419C22⋊C8—221no—
420C22⋊C8—221no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423#97—221no—
424#97—221no—
425C4×C8—21no—
426C4×C8—111no—
427C4×C8—111no—
428C4×C8—111no—
429C4×C8—111no—
430C4×C8—111no—
431C4×C8—221no—
432C4×C8C22×D1111yescharacteristic
433C4×C8C22×D1111yescharacteristic
434C4×C8C22×D1111yescharacteristic
435C2×C11—81no—
436C2×C11C2×#43511yescharacteristic
437C2×C11#295211yescharacteristic
438C2×C11#295711yescharacteristic
439D11—22no—
440D11—42no—
441#41—114no—
442#41—222no—
443#41—222no—
444#41—222no—
445C2×Q8—111no—
446C2×Q8C2×C4×D1111yescharacteristic
447C2×D4—111no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4C2×C4×D1111yescharacteristic
451C22×C4—21no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460Q16—222no—
461SD16—22no—
462SD16—222no—
463D8—222no—
464M16—81no—
465M16—881no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—111no—
470C2×C8—111no—
471C2×C8—111no—
472C2×C8—111no—
473C2×C8—222no—
474C2×C8—222no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—881no—
479C2×C8—881no—
480C2×C8—881no—
481C2×C8—881no—
482C2×C8C2×C4×D1111yescharacteristic
483C2×C8C2×C4×D1111yescharacteristic
484C2×C8D4×D1111yescharacteristic
485C2×C8D4×D1111yescharacteristic
486C4⋊C4—21no—
487C4⋊C4—111no—
488C4⋊C4—111no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4C2×C4×D1111yescharacteristic
493C4⋊C4C2×C4×D1111yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—221no—
496C22⋊C4—221no—
497C22⋊C4—221no—
498C22⋊C4—221no—
499C22⋊C4—221no—
500C42—21no—
501C42—111no—
502C42—111no—
503C42—111no—
504C42—221no—
505C42—221no—
506C42—221no—
507C42—221no—
508C42—221no—
509C42C23×D1111yescharacteristic
510C11#1788211yescharacteristic, complemented, Sylow
511C23—21no—
512C23—111no—
513C23—221no—
514Q8—21no—
515Q8—221no—
516Q8—221no—
517Q8M16×D1112yes—
518D4—21no—
519D4—21no—
520D4—112no—
521D4—224no—
522D4—221no—
523D4—442no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—111no—
530C2×C4—112no—
531C2×C4—112no—
532C2×C4—111no—
533C2×C4—111no—
534C2×C4—224no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—441no—
541C2×C4—442no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—881no—
545C2×C4—881no—
546C2×C4C22×C4×D1111yescharacteristic
547C2×C4C2×D4×D1111yescharacteristic
548C2×C4#41×D1111yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—221no—
557C8—221no—
558C8—221no—
559C8—221no—
560C8—441no—
561C8—441no—
562C8—441no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—112no—
567C22—221no—
568C22—221no—
569C22—222no—
570C22—441no—
571C22—441no—
572C22C4×D4×D1111yescharacteristic
573C4—21no—
574C4—22no—
575C4—41no—
576C4—41no—
577C4—112no—
578C4—221no—
579C4—221no—
580C4—441no—
581C4—441no—
582C4—441no—
583C4C2×M16×D1111yescharacteristic
584C4D11×#13111yescharacteristic
585C4#1062329311yescharacteristic
586C4#1062330111yescharacteristic
587C2—81no—
588C2—222no—
589C2—442no—
590C2D11×#43511yescharacteristic
591C2#1307749411yescharacteristic
592C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1583C2
socleC22×C11C2×C4×D4
prime radicalC2×#66969C4
cosocleC42×C11C24
hypercenter#1583D11
hypocenterC11#17882
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
1. #13077731C2semidirect
2. #13077726C2semidirect
4. #13067487C2semidirect
5. #13067484C2semidirect
6. #13067483C2semidirect
7. #13067478C2semidirect
8. #13067460C2semidirect
9. #13067454C2semidirect
10. #13067451C2semidirect
11. D11×#334C2semidirect
12. #13067002C2semidirect
13. #13067000C2semidirect
14. #13066907C2semidirect
15. C11×#1583C2semidirect
153. #4343M16semidirect
223. #1583D11semidirect
510. C11#17882semidirect

Maximal subgroups

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

subgroupindex
#130777312
#130777262
C4×#669692
#130674872
#130674842
#130674832
#130674782
#130674602
#130674542
#130674512
D11×#3342
#130670022
#130670002
#130669072
C11×#15832
#1788211