Finite Group Databasebeta

← #14725133

Subgroups — #14725133

Order 2816.

606 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078643C211yesmaximal, characteristic
2#13077703C211yesmaximal, characteristic, complemented
3#13067518C211yesmaximal, characteristic, complemented
4#13067504C211yesmaximal, characteristic, complemented
5#13067492C211yesmaximal, characteristic, complemented
6#13067473C211yesmaximal, characteristic, complemented
7#13067457C211yesmaximal, characteristic, complemented
8#13067452C211yesmaximal, characteristic, complemented
9#13067428C211yesmaximal, characteristic, complemented
10C8×#4324C211yesmaximal, characteristic, complemented
11#13067394C211yesmaximal, characteristic, complemented
12#13067085C211yesmaximal, characteristic
13#13067010C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#2979C211yesmaximal, characteristic
16C11×#532C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18C11×#436—21no—
19C11×#436C2211yescharacteristic
20C11×#436C2211yescharacteristic
21C8×D4×C11—21no—
22C8×D4×C11C2211yescharacteristic
23C8×D4×C11C2211yescharacteristic
24C11×#431C2211yescharacteristic
25C11×#431C2211yescharacteristic
26C11×#408—21no—
27C11×#408—21no—
28#10622707C411yescharacteristic
29#10622707C411yescharacteristic
30#10622688C411yescharacteristic
31#10622688C411yescharacteristic
32#10622653C411yescharacteristic
33#10622653C411yescharacteristic
34#10622647C411yescharacteristic
35#10622647C411yescharacteristic
36C4×#4324C2211yescharacteristic
37C4×#4324C2211yescharacteristic
38C4×#4324C2211yescharacteristic
39C4×#4324C2211yescharacteristic
40#10622539C2211yescharacteristic
41#10622538C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622441—21no—
44#10622441—21no—
45#10622332—21no—
46#10622331—21no—
47#10622292C2211yescharacteristic
48#10622292C2211yescharacteristic
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51D4⋊(C11⋊C8)C2211yescharacteristic
52D4⋊(C11⋊C8)C2211yescharacteristic
53D4⋊(C11⋊C8)C2211yescharacteristic
54D4⋊(C11⋊C8)C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×#41—21no—
68C22×Dic22C2×C411yescharacteristic
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C22×C8×C11—21no—
72C22×C8×C11—21no—
73C11×C4⋊Q8C2×C411yescharacteristic
74C11×#127C2×C411yescharacteristic
75C11×#124—21no—
76C11×#121—21no—
77C11×#121C2×C411yescharacteristic
78C11×#121C2×C411yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11C2311yescharacteristic
81C4×D4×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×#4324C2×C411yescharacteristic
84C2×#4324C2×C411yescharacteristic
85C2×#4324C2×C411yescharacteristic
86C2×#4324C2×C411yescharacteristic
87C2×C4⋊Dic11C2×C411yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C4×Dic22—21no—
91C4×Dic22—21no—
92C4×Dic22C2×C411yescharacteristic
93C4×Dic22C2×C411yescharacteristic
94C4×Dic22C2311yescharacteristic
95C4×Dic22C2311yescharacteristic
96C11×C4⋊C8D411yescharacteristic
97C11×C4⋊C8D411yescharacteristic
98C11×C4⋊C8C2311yescharacteristic
99C11×C4⋊C8C2311yescharacteristic
100C11×C22⋊C8—21no—
101C11×C22⋊C8—21no—
102C11×C22⋊C8—21no—
103C11×C22⋊C8—21no—
104C11×C22⋊C8—21no—
105C11×C22⋊C8D411yescharacteristic
106C11×C22⋊C8D411yescharacteristic
107C4×C8×C11—21no—
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110#66896C2×C411yescharacteristic
111#66896C2×C411yescharacteristic
112#66896C2×C411yescharacteristic
113#66896C2×C411yescharacteristic
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)C2×C411yescharacteristic
117C22⋊(C11⋊C8)C2×C411yescharacteristic
118#66879—21no—
119#66879—21no—
120Dic11⋊C8—21no—
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124C8×Dic11—21no—
125C8×Dic11—21no—
126#66874C2×C411yescharacteristic
127#66874C2×C411yescharacteristic
128#66874C2×C411yescharacteristic
129#66874C2×C411yescharacteristic
130#66872C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66872C2×C411yescharacteristic
133#66872C2×C411yescharacteristic
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)C2×C411yescharacteristic
136C4⋊(C11⋊C8)C2×C411yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139#66867—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18030—111nomaximal, Sylow
145C11×#41—81no—
146C11×#41—81no—
147C2×Q8×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11C22×C411yescharacteristic
153C2×D4×C11C22×C411yescharacteristic
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C22×Dic11—21no—
160C22×Dic11—21no—
161C2×Dic22—22no—
162C2×Dic22—21no—
163C2×Dic22—41no—
164C2×Dic22C22×C411yescharacteristic
165C2×Dic22C22×C411yescharacteristic
166C11×M16—81no—
167C11×M16—81no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—81no—
171C2×C8×C11—81no—
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C11×C4⋊C4—21no—
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C42×C11C22×C411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11#4111yescharacteristic
186C42×C11C2411yescharacteristic
187#4324—22no—
188#4324—22no—
189#4324—41no—
190#4324—41no—
191C4⋊Dic11—21no—
192C4⋊Dic11C22×C411yescharacteristic
193C4⋊Dic11C22×C411yescharacteristic
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197Dic11⋊C4—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C22×C411yescharacteristic
210#3103—111no—
211#2984—111no—
212#2979D1111yescharacteristic
213#1592—111no—
214#1590—111no—
215#1588—111no—
216#1585—111no—
217#1583—111no—
218#1582—111no—
219SD16⋊C8—111no—
220C8×SD16—111no—
221#1572—111no—
222#1496—111no—
223#1479—111no—
224#1454—111no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11C4×D411yescharacteristic
228Q8×C11—81no—
229D4×C11—21no—
230D4×C11—21no—
231D4×C11—21no—
232D4×C11—21no—
233D4×C11—42no—
234D4×C11—81no—
235D4×C11—81no—
236D4×C11—81no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C23×C411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260Dic22—21no—
261Dic22—21no—
262Dic22—21no—
263Dic22—42no—
264Dic22#13112yes—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—41no—
270C8×C11—41no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279#532C2×D1111yescharacteristic
280C2×C4×Q8—111no—
281#481—111no—
282#481—111no—
283#475—111no—
284#475—111no—
285#460—111no—
286#460—111no—
287#448—111no—
288#448—111no—
289#446—111no—
290#446—111no—
291#446—221no—
292#446—221no—
293C8×Q8—111no—
294C8×Q8—111no—
295C4×SD16—111no—
296C4×SD16—111no—
297C4×SD16—111no—
298C4×SD16—111no—
299#436—21no—
300#436C2×D1111yescharacteristic
301#436C2×D1111yescharacteristic
302C8×D4—21no—
303C8×D4C2×D1111yescharacteristic
304C8×D4C2×D1111yescharacteristic
305#432—111no—
306#432—221no—
307#431—111no—
308#431—111no—
309#431—221no—
310#431C2×D1111yescharacteristic
311#431C2×D1111yescharacteristic
312#408—21no—
313#408—21no—
314#335—111no—
315#335—111no—
316#334—111no—
317#334—111no—
318Q8⋊C8—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322D4⋊C8—111no—
323D4⋊C8—111no—
324D4⋊C8—111no—
325D4⋊C8—111no—
326#322—111no—
327#322—111no—
328#322—111no—
329C82—111no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11C2×C4×D411yescharacteristic
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11C2×#13111yescharacteristic
347C4×C11#56811yescharacteristic
348C4×C11#57711yescharacteristic
349C4×C11#57711yescharacteristic
350Dic11—22no—
351Dic11—41no—
352Dic11—41no—
353Dic11—41no—
354C2×#41—21no—
355C22×Q8—111no—
356C2×SD16—111no—
357C2×SD16—111no—
358C2×SD16—111no—
359C2×SD16—111no—
360C2×M16—21no—
361C2×M16—21no—
362C22×C8—21no—
363C22×C8—21no—
364C4⋊Q8C4×D1111yescharacteristic
365#127C4×D1111yescharacteristic
366#124—21no—
367#121—21no—
368#121C4×D1111yescharacteristic
369#121C4×D1111yescharacteristic
370C4×Q8—111no—
371C4×Q8—111no—
372C4×Q8—111no—
373C4×Q8—111no—
374C4×Q8—221no—
375C4×Q8—221no—
376C4×D4—21no—
377C4×D4C22×D1111yescharacteristic
378C4×D4C22×D1111yescharacteristic
379C2×C4⋊C4—111no—
380C2×C4⋊C4—221no—
381C2×C42—221no—
382C2×C42C22×D1111yescharacteristic
383#106—111no—
384#106—111no—
385#106—111no—
386#106—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⋊C8C22⋊D1111yescharacteristic
397C4⋊C8C22⋊D1111yescharacteristic
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#102—111no—
407#102—111no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—111no—
414C22⋊C8—111no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417C22⋊C8C22⋊D1111yescharacteristic
418C22⋊C8C22⋊D1111yescharacteristic
419#97—221no—
420#97—221no—
421#97—221no—
422C4×C8—21no—
423C4×C8—111no—
424C4×C8—111no—
425C4×C8—111no—
426C4×C8—111no—
427C4×C8—221no—
428C4×C8—221no—
429C4×C8C22×D1111yescharacteristic
430C4×C8C22×D1111yescharacteristic
431C2×C11—41no—
432C2×C11—81no—
433C2×C11—81no—
434C2×C11#293311yescharacteristic
435C2×C11#294911yescharacteristic
436C2×C11#295511yescharacteristic
437#41—81no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—111no—
441C2×Q8—111no—
442C2×Q8—222no—
443C2×Q8—221no—
444C2×Q8—441no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4C2×C4×D1111yescharacteristic
450C2×D4C2×C4×D1111yescharacteristic
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4C2×C4×D1111yescharacteristic
456C22×C4#433911yescharacteristic
457C22×C4C2×C22⋊D1111yescharacteristic
458SD16—222no—
459SD16—222no—
460SD16—441no—
461SD16—441no—
462M16—81no—
463M16—81no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—81no—
467C2×C8—81no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—111no—
471C2×C8—111no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8C2×C22⋊D1111yescharacteristic
477C2×C8C2×C22⋊D1111yescharacteristic
478C2×C8C2×C22⋊D1111yescharacteristic
479C2×C8C2×C22⋊D1111yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—111no—
482C4⋊C4—111no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4C2×C4×D1111yescharacteristic
489C4⋊C4C2×C4×D1111yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C42—221no—
495C42—221no—
496C42—221no—
497C42—221no—
498C42C2×C4×D1111yescharacteristic
499C42#433911yescharacteristic
500C42C2×C22⋊D1111yescharacteristic
501C42C23×D1111yescharacteristic
502C11#1803011yescharacteristic, complemented, Sylow
503C23—21no—
504C23—21no—
505C23C4×C22⋊D1111yescharacteristic
506Q8—81no—
507Q8—112no—
508Q8—221no—
509Q8—221no—
510Q8—221no—
511Q8—442no—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—42no—
517D4—81no—
518D4—81no—
519D4—81no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—442no—
536C2×C4—442no—
537C2×C4C4×C22⋊D1111yescharacteristic
538C2×C4C4×C22⋊D1111yescharacteristic
539C2×C4C4×C22⋊D1111yescharacteristic
540C2×C4C22×C4×D1111yescharacteristic
541C2×C4C2×#433911yescharacteristic
542C2×C4C22×C22⋊D1111yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—221no—
550C8—221no—
551C8—221no—
552C8—221no—
553C8—441no—
554C8—441no—
555C8—441no—
556C8—441no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22C2×C4×C22⋊D1111yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—41no—
572C4—41no—
573C4—222no—
574C4—441no—
575C4—441no—
576C4—441no—
577C4D11×#13111yescharacteristic
578C4#1062328111yescharacteristic
579C4#1062336711yescharacteristic
580C4#1062336711yescharacteristic
581C2—41no—
582C2—81no—
583C2—81no—
584C2#1307733811yescharacteristic
585C2#1307747311yescharacteristic
586C2#1307751711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2979C2
socleC22×C11C2×C4×D4
prime radicalC11×#532C22
cosocleC42×C11C24
hypercenter#2979D11
hypocenterC11#18030
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2979

Complements

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

NH ≅ G/Ntype
2. #13077703C2semidirect
3. #13067518C2semidirect
4. #13067504C2semidirect
5. #13067492C2semidirect
6. #13067473C2semidirect
7. #13067457C2semidirect
8. #13067452C2semidirect
9. #13067428C2semidirect
10. C8×#4324C2semidirect
11. #13067394C2semidirect
13. #13067010C2semidirect
14. #13066916C2semidirect
502. C11#18030semidirect

Maximal subgroups

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

subgroupindex
#130786432
#130777032
#130675182
#130675042
#130674922
#130674732
#130674572
#130674522
#130674282
C8×#43242
#130673942
#130670852
#130670102
#130669162
C11×#29792
#1803011