Finite Group Databasebeta

← #14723914

Subgroups — #14723914

Order 2816.

638 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078622C211yesmaximal, characteristic
2#13077712C211yesmaximal, characteristic, complemented
3#13077637C211yesmaximal, characteristic
4#13067473C211yesmaximal, characteristic, complemented
5#13067471C211yesmaximal, characteristic, complemented
6#13067454C211yesmaximal, characteristic, complemented
7#13067431C211yesmaximal, characteristic, complemented
8#13067425C211yesmaximal, characteristic, complemented
9SD16×C11⋊C8C211yesmaximal, characteristic, complemented
10#13067415C211yesmaximal, characteristic, complemented
11#13067393C211yesmaximal, characteristic, complemented
12#13067057C211yesmaximal, characteristic
13#13067035C211yesmaximal, characteristic, complemented
14#13066912C211yesmaximal, characteristic, complemented
15C11×#1582C211yesmaximal, characteristic, complemented
16#10623109C2211yescharacteristic
17C4×D4×D11C2211yescharacteristic
18C11×#446C2211yescharacteristic, complemented
19C4×C11×SD16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622782C411yescharacteristic
22#10622775C411yescharacteristic
23C8×C22⋊D11—21no—
24C2×(C2×D11)⋊C8—21no—
25C4×#4325C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic, complemented
27C4×#4324C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622483C411yescharacteristic
30#10622475C411yescharacteristic
31#10622453—21no—
32#10622448C2211yescharacteristic
33#10622447C2211yescharacteristic
34#10622446C2211yescharacteristic
35#10622444—21no—
36#10622443C2211yescharacteristic, complemented
37#10622431C411yescharacteristic
38#10622418C411yescharacteristic
39#10622389C411yescharacteristic
40#10622374C411yescharacteristic
41(C22⋊D11)⋊C8—21no—
42D11×C22⋊C8—21no—
43#10622322—21no—
44#10622314—21no—
45C4×#4314C2211yescharacteristic
46C4×#4313C2211yescharacteristic
47C8×D44C2211yescharacteristic
48#10622298C2211yescharacteristic
49#10622298C2211yescharacteristic
50#10622292C2211yescharacteristic, complemented
51C11×#334C2211yescharacteristic, complemented
52C11×Q8⋊C8C2211yescharacteristic, complemented
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic, complemented
55Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic, complemented
58#10622121C2211yescharacteristic
59#10622117C2211yescharacteristic, complemented
60#10622117C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic
62#10622095C2211yescharacteristic, complemented
63#10622094C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×D4×D11C2×C411yescharacteristic
68C22×C4×D11—21no—
69C2×C11×SD16C2×C411yescharacteristic
70C22×C8×C11—21no—
71C4×Q8×C11C2311yescharacteristic
72C4×D4×C11C2311yescharacteristic
73#66999C2×C411yescharacteristic
74#66997C2×C411yescharacteristic
75C2×#4325C2×C411yescharacteristic
76D4×Dic11C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C22×C11⋊C8—21no—
80C2×#4314C2×C411yescharacteristic
81C2×#4313—21no—
82C2×C8×D11—21no—
83C2×C8×D11—21no—
84#66950C2×C411yescharacteristic
85#66949—21no—
86#66946C2×C411yescharacteristic
87C4⋊C4×D11C2×C411yescharacteristic
88#66942—21no—
89#66941C2×C411yescharacteristic
90(C22⋊D11)⋊C4—21no—
91C22⋊C4×D11—21no—
92C4×D44C2311yescharacteristic
93#66925—21no—
94C42×D11C2311yescharacteristic
95C4×Dic22—21no—
96C4×Dic22C2311yescharacteristic
97C11×#106C2×C411yescharacteristic
98C11×C4⋊C8—21no—
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×#103C2×C411yescharacteristic
102C11×#102C2×C411yescharacteristic
103C11×C22⋊C8—21no—
104C11×#97—21no—
105C4×C8×C11C2311yescharacteristic
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108#66899C2×C411yescharacteristic
109#66896C2×C411yescharacteristic
110C22⋊(C11⋊C8)—21no—
111#66885C2×C411yescharacteristic
112(C2×D11)⋊C8—21no—
113(C2×D11)⋊C8—21no—
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8C2×C411yescharacteristic
117(C2×D11)⋊C8C2×C411yescharacteristic
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⋊C8C2×C411yescharacteristic
128Dic11⋊C8C2×C411yescharacteristic
129Dic11⋊C8D411yescharacteristic
130Dic11⋊C8D411yescharacteristic
131C8×Dic11—21no—
132C8×Dic11—21no—
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#17924—111nomaximal, Sylow
145C23×D11—21no—
146C2×Q8×C11C22×C411yescharacteristic
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C2×C22⋊D11—21no—
150C22×Dic11—21no—
151D4×D11—22no—
152D4×D11—22no—
153C2×D44C22×C411yescharacteristic
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—81no—
158C2×C4×D11—81no—
159C2×C4×D11C22×C411yescharacteristic
160C2×C4×D11C2×D411yescharacteristic
161C2×C4×D11#4111yescharacteristic
162C2×Dic22—21no—
163C2×Dic22C22×C411yescharacteristic
164C11×SD16—22no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—81no—
169C2×C8×C11C22×C411yescharacteristic
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C11×C4⋊C4—21no—
174C11×C4⋊C4C22×C411yescharacteristic
175C11×C4⋊C4C22×C411yescharacteristic
176C11×C22⋊C4—21no—
177C42×C11—21no—
178C42×C11C2411yescharacteristic
179C22⋊Dic11—21no—
180#4325—22no—
181#4324—22no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11C22×C411yescharacteristic
188C4⋊Dic11C22×C411yescharacteristic
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195C4×Dic11—21no—
196C4×Dic11C22×C411yescharacteristic
197C4×Dic11C2×D411yescharacteristic
198C4×Dic11#4111yescharacteristic
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
207#4314—22no—
208#4313—42no—
209C8×D11—81no—
210C8×D11—81no—
211#3101—111no—
212#2985—111no—
213#2972—111no—
214#1585—111no—
215#1585—111no—
216#1582—111no—
217#1582D1111yescharacteristic, complemented
218SD16⋊C8—111no—
219SD16⋊C8—111no—
220C8×SD16—111no—
221C8×SD16—111no—
222#1572—111no—
223#1490—111no—
224#1485—111no—
225#1453—111no—
226C23×C11—21no—
227C22×D11—21no—
228C22×D11—24no—
229C22×D11—81no—
230C22×D11—81no—
231C22×D11C4×D411yescharacteristic
232Q8×C11—21no—
233Q8×C11—21no—
234D4×C11—21no—
235D4×C11#13112yes—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C22⋊D11—24no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—81no—
249C2×Dic11C4×D411yescharacteristic
250C2×Dic11C4×D411yescharacteristic
251C2×Dic11C4×D411yescharacteristic
252D44—21no—
253D44#13112yes—
254C4×D11—21no—
255C4×D11—21no—
256C4×D11—21no—
257C4×D11—21no—
258C4×D11—41no—
259C4×D11—41no—
260C4×D11—41no—
261C4×D11—81no—
262C4×D11—81no—
263Dic22—21no—
264Dic22—21no—
265Dic22—81no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—41no—
271C8×C11—41no—
272C8×C11—41no—
273C11⋊C8—22no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280#533—111no—
281C2×C4×D4—111no—
282#483—111no—
283#483—111no—
284#476—111no—
285#476—111no—
286#461—111no—
287#461—111no—
288#450—111no—
289#450—111no—
290#446—111no—
291#446—221no—
292#446—221no—
293#446C2×D1111yescharacteristic, complemented
294C8×Q8—111no—
295C8×Q8—111no—
296C4×SD16—111no—
297C4×SD16—111no—
298C4×SD16—111no—
299C4×SD16C2×D1111yescharacteristic
300C8×D4—111no—
301C8×D4—111no—
302C8×D4—111no—
303C8×D4—221no—
304C8×D4—221no—
305C8×D4C2×D1111yescharacteristic
306#433—221no—
307#433—221no—
308#432—111no—
309#431—111no—
310#431—111no—
311#431—111no—
312C2×C22⋊C8—221no—
313C2×C22⋊C8—221no—
314C4×M16—111no—
315#335—111no—
316#335—111no—
317#334—111no—
318#334C2×D1111yescharacteristic, complemented
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322Q8⋊C8C2×D1111yescharacteristic, complemented
323D4⋊C8—111no—
324D4⋊C8—111no—
325D4⋊C8—111no—
326D4⋊C8C2×D1111yescharacteristic
327#322—111no—
328#322—111no—
329#322C2×D1111yescharacteristic, complemented
330C82—111no—
331C22×C11—22no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11C2×C4×D411yescharacteristic
335C2×D11—21no—
336C2×D11—22no—
337C2×D11—21no—
338C2×D11—21no—
339C2×D11—41no—
340C2×D11—41no—
341C2×D11—84no—
342C4×C11—21no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11C2×#13111yescharacteristic
347C4×C11C2×#13111yescharacteristic
348C4×C11#57711yescharacteristic
349C4×C11#57711yescharacteristic
350Dic11—21no—
351Dic11—21no—
352Dic11—21no—
353Dic11—41no—
354Dic11—41no—
355Dic11—41no—
356C22×D4—111no—
357C23×C4—221no—
358C2×SD16—111no—
359C2×SD16—111no—
360C2×SD16—111no—
361C2×SD16C4×D1111yescharacteristic
362C2×M16—221no—
363C22×C8—21no—
364C22×C8—221no—
365C22×C8—221no—
366C22×C8—221no—
367C4⋊Q8—111no—
368C4⋊Q8—111no—
369#125—221no—
370C22⋊Q8—111no—
371C22⋊Q8—111no—
372C22⋊Q8—221no—
373C4×Q8—111no—
374C4×Q8—221no—
375C4×Q8C22×D1111yescharacteristic
376C4×D4—111no—
377C4×D4—111no—
378C4×D4—111no—
379C4×D4—221no—
380C4×D4—221no—
381C4×D4C22×D1111yescharacteristic
382#117—221no—
383C2×C4⋊C4—111no—
384C2×C22⋊C4—221no—
385C2×C42—111no—
386#106—111no—
387#106—111no—
388#106—111no—
389#106C4×D1111yescharacteristic
390C4⋊C8—21no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—111no—
395C4⋊C8—111no—
396C4⋊C8—111no—
397C4⋊C8—221no—
398C4⋊C8—221no—
399C4⋊C8—221no—
400C4⋊C8C22×D1111yescharacteristic
401C4⋊C8C22×D1111yescharacteristic
402#103—111no—
403#103—111no—
404#103—111no—
405#103C4×D1111yescharacteristic
406#102—111no—
407#102—111no—
408#102—111no—
409#102C4×D1111yescharacteristic
410C22⋊C8—21no—
411C22⋊C8—111no—
412C22⋊C8—111no—
413C22⋊C8—111no—
414C22⋊C8—111no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419C22⋊C8—221no—
420#97—21no—
421#97—221no—
422#97—221no—
423#97—221no—
424C4×C8—111no—
425C4×C8—111no—
426C4×C8—111no—
427C4×C8—221no—
428C4×C8—221no—
429C4×C8—221no—
430C4×C8C22×D1111yescharacteristic
431C4×C8C22×D1111yescharacteristic
432C4×C8C22×D1111yescharacteristic
433C2×C11—42no—
434C2×C11#292911yescharacteristic
435C2×C11#294911yescharacteristic
436C2×C11#295611yescharacteristic
437D11—41no—
438D11—42no—
439C24—221no—
440C2×Q8—111no—
441C2×Q8—221no—
442C2×Q8C2×C4×D1111yescharacteristic
443C2×D4—111no—
444C2×D4—221no—
445C2×D4—222no—
446C2×D4—222no—
447C2×D4C2×C4×D1111yescharacteristic
448C22×C4—21no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—881no—
457C22×C4—881no—
458SD16—22no—
459SD16—222no—
460SD16—222no—
461SD16—222no—
462M16—442no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—81no—
467C2×C8—111no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—111no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—881no—
475C2×C8—881no—
476C2×C8—881no—
477C2×C8C2×C4×D1111yescharacteristic
478C2×C8C2×C4×D1111yescharacteristic
479C2×C8D4×D1111yescharacteristic
480C2×C8D4×D1111yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—111no—
483C4⋊C4—111no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4C2×C4×D1111yescharacteristic
492C4⋊C4C2×C4×D1111yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—221no—
495C22⋊C4—221no—
496C22⋊C4—221no—
497C22⋊C4—221no—
498C22⋊C4—221no—
499C42—21no—
500C42—111no—
501C42—111no—
502C42—111no—
503C42—221no—
504C42C23×D1111yescharacteristic
505C11#1792411yescharacteristic, complemented, Sylow
506C23—21no—
507C23—111no—
508C23—224no—
509C23—221no—
510C23—881no—
511C23—881no—
512Q8—21no—
513Q8—21no—
514Q8—221no—
515Q8—221no—
516Q8—881no—
517D4—21no—
518D4—112no—
519D4—224no—
520D4—221no—
521D4#6696012yes—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—111no—
528C2×C4—111no—
529C2×C4—111no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—881no—
541C2×C4—881no—
542C2×C4—881no—
543C2×C4C22×C4×D1111yescharacteristic
544C2×C4C2×D4×D1111yescharacteristic
545C2×C4#41×D1111yescharacteristic
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—222no—
554C8—221no—
555C8—221no—
556C8—221no—
557C8—221no—
558C8—441no—
559C8—441no—
560C22—22no—
561C22—41no—
562C22—41no—
563C22—221no—
564C22—221no—
565C22—222no—
566C22—221no—
567C22—441no—
568C22—441no—
569C22—884no—
570C22C4×D4×D1111yescharacteristic
571C4—21no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—221no—
576C4—221no—
577C4—221no—
578C4—441no—
579C4—441no—
580C4—441no—
581C4C2×#6696011yescharacteristic
582C4D11×#13111yescharacteristic
583C4#1062329311yescharacteristic
584C4#1062330111yescharacteristic
585C2—42no—
586C2—441no—
587C2—442no—
588C2#1307730711yescharacteristic
589C2#1307747011yescharacteristic
590C2#1307752411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1582C2
socleC22×C11C2×C4×D4
prime radicalC2×D4×D11C2×C4
cosocleC42×C11C24
hypercenter#1582D11
hypocenterC11#17924
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
2. #13077712C2semidirect
4. #13067473C2semidirect
5. #13067471C2semidirect
6. #13067454C2semidirect
7. #13067431C2semidirect
8. #13067425C2semidirect
9. SD16×C11⋊C8C2semidirect
10. #13067415C2semidirect
11. #13067393C2semidirect
13. #13067035C2semidirect
14. #13066912C2semidirect
15. C11×#1582C2semidirect
18. C11×#446C22semidirect
26. Q8×C11⋊C8C22semidirect
36. #10622443C22semidirect
50. #10622292C22semidirect
51. C11×#334C22semidirect
52. C11×Q8⋊C8C22semidirect
54. C11×#322C22semidirect
55. Q8⋊(C11⋊C8)C22semidirect
57. #10622122C22semidirect
59. #10622117C22semidirect
60. #10622117C22semidirect
62. #10622095C22semidirect
63. #10622094C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
217. #1582D11semidirect
293. #446C2×D11semidirect
318. #334C2×D11semidirect
322. Q8⋊C8C2×D11semidirect
329. #322C2×D11semidirect
505. C11#17924semidirect

Maximal subgroups

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

subgroupindex
#130786222
#130777122
#130776372
#130674732
#130674712
#130674542
#130674312
#130674252
SD16×C11⋊C82
#130674152
#130673932
#130670572
#130670352
#130669122
C11×#15822
#1792411