Finite Group Databasebeta

← #14725101

Subgroups — #14725101

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078624C211yesmaximal, characteristic
2#13077717C211yesmaximal, characteristic, complemented
3#13077651C211yesmaximal, characteristic
4#13067515C211yesmaximal, characteristic, complemented
5#13067509C211yesmaximal, characteristic, complemented
6#13067497C211yesmaximal, characteristic, complemented
7#13067470C211yesmaximal, characteristic, complemented
8#13067462C211yesmaximal, characteristic, complemented
9#13067449C211yesmaximal, characteristic, complemented
10#13067425C211yesmaximal, characteristic, complemented
11#13067419C211yesmaximal, characteristic, complemented
12#13067394C211yesmaximal, characteristic, complemented
13#13067090C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#1478C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17#10623001C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C11×#431C2211yescharacteristic
20#10622831C411yescharacteristic
21#10622831C411yescharacteristic
22#10622820—21no—
23C2×C22⋊(C11⋊C8)—21no—
24#10622632C411yescharacteristic
25#10622632C411yescharacteristic
26C4×#4324C2211yescharacteristic
27C4×#4324C2211yescharacteristic
28C4×#4324C2211yescharacteristic
29C4×#4324C2211yescharacteristic
30#10622625C2211yescharacteristic
31#10622625C2211yescharacteristic
32#10622624—21no—
33#10622624—21no—
34D4×C11⋊C8C2211yescharacteristic
35D4×C11⋊C8C2211yescharacteristic
36#10622621C411yescharacteristic
37#10622621C411yescharacteristic
38#10622584C411yescharacteristic
39#10622584C411yescharacteristic
40#10622539C2211yescharacteristic
41#10622538C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622444C2211yescharacteristic, complemented
44#10622444C2211yescharacteristic, complemented
45#10622443C2211yescharacteristic, complemented
46#10622443C2211yescharacteristic, complemented
47#10622333—21no—
48#10622333—21no—
49#10622292—21no—
50C8×Dic22—21no—
51C11×D4⋊C8C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×D4⋊C8C2211yescharacteristic
55#10622118C2211yescharacteristic, complemented
56#10622118C2211yescharacteristic, complemented
57#10622117C2211yescharacteristic, complemented
58#10622117C2211yescharacteristic, complemented
59#10622094C2211yescharacteristic, complemented
60#10622094C2211yescharacteristic, complemented
61#10622094C2211yescharacteristic, complemented
62#10622094C2211yescharacteristic, complemented
63#10622093C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×D4×C11C2×C411yescharacteristic
68C23×C4×C11—21no—
69C4×D4×C11—21no—
70C4×D4×C11—21no—
71C4×D4×C11C2×C411yescharacteristic
72C4×D4×C11C2×C411yescharacteristic
73C4×D4×C11C2311yescharacteristic
74C4×D4×C11C2311yescharacteristic
75C2×C11×C4⋊C4C2×C411yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C42×C11C2311yescharacteristic
78C2×#4324C2×C411yescharacteristic
79C2×#4324C2×C411yescharacteristic
80C2×#4324C2×C411yescharacteristic
81C2×#4324C2×C411yescharacteristic
82#66979—21no—
83#66977—21no—
84#66977C2×C411yescharacteristic
85#66977C2×C411yescharacteristic
86C2×#4318—21no—
87C2×#4318—21no—
88C22×C11⋊C8—21no—
89C22×C11⋊C8—21no—
90#66923—21no—
91#66922C2×C411yescharacteristic
92#66922C2×C411yescharacteristic
93C4×Dic22—21no—
94C4×Dic22C2311yescharacteristic
95C4×Dic22C2311yescharacteristic
96C11×C4⋊C8—21no—
97C11×C4⋊C8C2311yescharacteristic
98C11×C4⋊C8C2311yescharacteristic
99C11×C22⋊C8—21no—
100C11×C22⋊C8—21no—
101C4×C8×C11—21no—
102C4×C8×C11C2311yescharacteristic
103C4×C8×C11C2311yescharacteristic
104#66896C2×C411yescharacteristic
105#66896C2×C411yescharacteristic
106#66896C2×C411yescharacteristic
107#66896C2×C411yescharacteristic
108C22⋊(C11⋊C8)—21no—
109C22⋊(C11⋊C8)—21no—
110C22⋊(C11⋊C8)—21no—
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)C2×C411yescharacteristic
114C22⋊(C11⋊C8)C2×C411yescharacteristic
115C22⋊(C11⋊C8)D411yescharacteristic
116C22⋊(C11⋊C8)D411yescharacteristic
117#66879—21no—
118#66879—21no—
119Dic11⋊C8—21no—
120Dic11⋊C8—21no—
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123C8×Dic11—21no—
124C8×Dic11—21no—
125#66874C2×C411yescharacteristic
126#66874C2×C411yescharacteristic
127#66874C2×C411yescharacteristic
128#66874C2×C411yescharacteristic
129#66872C2×C411yescharacteristic
130#66872C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66872C2×C411yescharacteristic
133C4⋊(C11⋊C8)C2×C411yescharacteristic
134C4⋊(C11⋊C8)C2×C411yescharacteristic
135C4⋊(C11⋊C8)D411yescharacteristic
136C4⋊(C11⋊C8)D411yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139#66867—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18028—111nomaximal, Sylow
145C24×C11—21no—
146C2×D4×C11—22no—
147C2×D4×C11—21no—
148C2×D4×C11—41no—
149C2×D4×C11C22×C411yescharacteristic
150C2×D4×C11C22×C411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—81no—
157C22×C4×C11—81no—
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11#4111yescharacteristic
161C2×Dic22—21no—
162C2×Dic22C22×C411yescharacteristic
163C2×Dic22C22×C411yescharacteristic
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4C22×C411yescharacteristic
170C11×C4⋊C4C22×C411yescharacteristic
171C11×C22⋊C4—21no—
172C11×C22⋊C4—21no—
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C42×C11C22×C411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11#4111yescharacteristic
178C42×C11C2411yescharacteristic
179C22⋊Dic11—21no—
180C22⋊Dic11—21no—
181#4324—22no—
182#4324—22no—
183#4324—41no—
184#4324—41no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11C22×C411yescharacteristic
189C4⋊Dic11C22×C411yescharacteristic
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196#4318—81no—
197#4318—81no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—81no—
201C2×C11⋊C8—81no—
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210#3101—111no—
211#2986—111no—
212#2974—111no—
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#1497—111no—
223#1478D1111yescharacteristic
224#1454—111no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—81no—
230C23×C11C4×D411yescharacteristic
231D4×C11—21no—
232D4×C11—21no—
233D4×C11—21no—
234D4×C11—42no—
235D4×C11#13112yes—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—81no—
248C2×C4×C11—81no—
249C2×C4×C11—81no—
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C4×D411yescharacteristic
252C2×C4×C11C4×D411yescharacteristic
253C2×C4×C11C23×C411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260Dic22—21no—
261Dic22—21no—
262Dic22—21no—
263Dic22—21no—
264Dic22—42no—
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—21no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279#533—111no—
280C2×C4×D4C2×D1111yescharacteristic
281#483—111no—
282#483—111no—
283#476—111no—
284#476—111no—
285#461—111no—
286#461—111no—
287#450—111no—
288#450—111no—
289#446—111no—
290#446—111no—
291#446—221no—
292C8×Q8—111no—
293C8×Q8—111no—
294C8×Q8—221no—
295C4×SD16—111no—
296C4×SD16—111no—
297C4×SD16—111no—
298C4×SD16—111no—
299#436—111no—
300#436—111no—
301#435—221no—
302#435—221no—
303C8×D4—111no—
304C8×D4—111no—
305#433—221no—
306#433—221no—
307#432—111no—
308#431—111no—
309#431—111no—
310#431C2×D1111yescharacteristic
311#431C2×D1111yescharacteristic
312#407—221no—
313C2×C22⋊C8—221no—
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⋊C8C2×D1111yescharacteristic
323D4⋊C8C2×D1111yescharacteristic
324D4⋊C8C2×D1111yescharacteristic
325D4⋊C8C2×D1111yescharacteristic
326#322—111no—
327#322—111no—
328#322—111no—
329C82—111no—
330C22×C11—21no—
331C22×C11—22no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—84no—
340C22×C11C2×C4×D411yescharacteristic
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11C2×#13111yescharacteristic
348C4×C11#56811yescharacteristic
349C4×C11#57711yescharacteristic
350C4×C11#57711yescharacteristic
351Dic11—41no—
352Dic11—41no—
353Dic11—41no—
354Dic11—41no—
355C22×D4C4×D1111yescharacteristic
356C23×C4—21no—
357C2×SD16—111no—
358C2×SD16—111no—
359C2×SD16—111no—
360C2×SD16—111no—
361C2×M16—221no—
362C2×M16—221no—
363C22×C8—221no—
364C22×C8—221no—
365C4⋊Q8—111no—
366C4⋊Q8—111no—
367#125—221no—
368C22⋊Q8—111no—
369C22⋊Q8—111no—
370C22⋊Q8—221no—
371C4×Q8—111no—
372C4×Q8—111no—
373C4×Q8—221no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4C4×D1111yescharacteristic
377C4×D4C4×D1111yescharacteristic
378C4×D4C22×D1111yescharacteristic
379C4×D4C22×D1111yescharacteristic
380#117—221no—
381C2×C4⋊C4C4×D1111yescharacteristic
382C2×C22⋊C4—21no—
383C2×C42C22×D1111yescharacteristic
384#106—111no—
385#106—111no—
386#106—111no—
387#106—111no—
388C4⋊C8—21no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—111no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8—221no—
399C4⋊C8C22×D1111yescharacteristic
400C4⋊C8C22×D1111yescharacteristic
401#103—111no—
402#103—111no—
403#103—111no—
404#103—111no—
405#102—111no—
406#102—111no—
407#102—111no—
408#102—111no—
409C22⋊C8—21no—
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—221no—
421#97—221no—
422#97—221no—
423C4×C8—21no—
424C4×C8—111no—
425C4×C8—111no—
426C4×C8—111no—
427C4×C8—111no—
428C4×C8—221no—
429C4×C8—221no—
430C4×C8C22×D1111yescharacteristic
431C4×C8C22×D1111yescharacteristic
432C2×C11—41no—
433C2×C11—42no—
434C2×C11—81no—
435C2×C11#293311yescharacteristic
436C2×C11#294911yescharacteristic
437C2×C11#295511yescharacteristic
438C24—21no—
439C2×Q8—111no—
440C2×Q8—111no—
441C2×Q8—221no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4C2×C4×D1111yescharacteristic
446C2×D4C2×C4×D1111yescharacteristic
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—81no—
453C22×C4—81no—
454C22×C4C2×C4×D1111yescharacteristic
455C22×C4D4×D1111yescharacteristic
456C22×C4#434111yescharacteristic
457SD16—222no—
458SD16—222no—
459SD16—441no—
460SD16—441no—
461M16—881no—
462M16—881no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—111no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—111no—
471C2×C8—111no—
472C2×C8—111no—
473C2×C8—111no—
474C2×C8—111no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—881no—
478C2×C8—881no—
479C4⋊C4—21no—
480C4⋊C4—111no—
481C4⋊C4—111no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4C2×C4×D1111yescharacteristic
490C4⋊C4C2×C4×D1111yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—221no—
496C22⋊C4—221no—
497C42—221no—
498C42—221no—
499C42C2×C4×D1111yescharacteristic
500C42D4×D1111yescharacteristic
501C42#434111yescharacteristic
502C42C23×D1111yescharacteristic
503C11#1802811yescharacteristic, complemented, Sylow
504C23—21no—
505C23—21no—
506C23—42no—
507C23—42no—
508C23—81no—
509C23(C22⋊D11)⋊C411yescharacteristic
510Q8—221no—
511Q8—221no—
512Q8—221no—
513Q8—221no—
514Q8—442no—
515D4—21no—
516D4—21no—
517D4—21no—
518D4—42no—
519D4#6695412yes—
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—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4(C22⋊D11)⋊C411yescharacteristic
539C2×C4(C22⋊D11)⋊C411yescharacteristic
540C2×C4(C22⋊D11)⋊C411yescharacteristic
541C2×C4C22×C4×D1111yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4C2×#434111yescharacteristic
544C8—41no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8—221no—
549C8—221no—
550C8—221no—
551C8—221no—
552C8—221no—
553C8—221no—
554C8—221no—
555C8—221no—
556C8—441no—
557C8—441no—
558C22—21no—
559C22—21no—
560C22—22no—
561C22—21no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—84no—
568C22C2×(C22⋊D11)⋊C411yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—441no—
576C4—441no—
577C4—441no—
578C4—441no—
579C4C2×#6695411yescharacteristic
580C4#1062327611yescharacteristic
581C4#1062330611yescharacteristic
582C4#1062330611yescharacteristic
583C2—41no—
584C2—42no—
585C2—81no—
586C2#1307733711yescharacteristic
587C2#1307747811yescharacteristic
588C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1478C2
socleC22×C11C2×C4×D4
prime radicalC22×D4×C11C2×C4
cosocleC42×C11C24
hypercenter#1478D11
hypocenterC11#18028
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #13077717C2semidirect
4. #13067515C2semidirect
5. #13067509C2semidirect
6. #13067497C2semidirect
7. #13067470C2semidirect
8. #13067462C2semidirect
9. #13067449C2semidirect
10. #13067425C2semidirect
11. #13067419C2semidirect
12. #13067394C2semidirect
13. #13067090C2semidirect
14. #13066916C2semidirect
43. #10622444C22semidirect
44. #10622444C22semidirect
45. #10622443C22semidirect
46. #10622443C22semidirect
55. #10622118C22semidirect
56. #10622118C22semidirect
57. #10622117C22semidirect
58. #10622117C22semidirect
59. #10622094C22semidirect
60. #10622094C22semidirect
61. #10622094C22semidirect
62. #10622094C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
503. C11#18028semidirect

Maximal subgroups

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

subgroupindex
#130786242
#130777172
#130776512
#130675152
#130675092
#130674972
#130674702
#130674622
#130674492
#130674252
#130674192
#130673942
#130670902
#130669162
C11×#14782
#1802811