Finite Group Databasebeta

← #14725107

Subgroups — #14725107

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#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#13067397C211yesmaximal, characteristic, complemented
12#13067088C211yesmaximal, characteristic, complemented
13#13067007C211yesmaximal, characteristic
14#13066916C211yesmaximal, characteristic, complemented
15C11×#2974C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17#10623001C2211yescharacteristic
18C11×#436C2211yescharacteristic
19C11×#436C2211yescharacteristic
20C11×#435—21no—
21C11×#435—21no—
22C8×D4×C11C2211yescharacteristic
23C8×D4×C11C2211yescharacteristic
24C11×#432C2211yescharacteristic
25C11×#431C2211yescharacteristic
26C11×#407—21no—
27C2×C11×C22⋊C8—21no—
28#10622831C411yescharacteristic
29#10622831C411yescharacteristic
30#10622632C411yescharacteristic
31#10622632C411yescharacteristic
32C4×#4324C2211yescharacteristic
33C4×#4324C2211yescharacteristic
34C4×#4324C2211yescharacteristic
35C4×#4324C2211yescharacteristic
36#10622621C411yescharacteristic
37#10622621C411yescharacteristic
38#10622584C411yescharacteristic
39#10622584C411yescharacteristic
40#10622538C2211yescharacteristic
41#10622538C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622444—21no—
44#10622443—21no—
45#10622333—21no—
46#10622333—21no—
47#10622292C2211yescharacteristic, complemented
48#10622292C2211yescharacteristic, complemented
49C8×Dic22C2211yescharacteristic, complemented
50C8×Dic22C2211yescharacteristic, complemented
51D4⋊(C11⋊C8)C2211yescharacteristic
52D4⋊(C11⋊C8)C2211yescharacteristic
53D4⋊(C11⋊C8)C2211yescharacteristic
54D4⋊(C11⋊C8)C2211yescharacteristic
55#10622122C2211yescharacteristic, complemented
56#10622122C2211yescharacteristic, complemented
57#10622122C2211yescharacteristic, complemented
58#10622122C2211yescharacteristic, complemented
59#10622118C2211yescharacteristic, complemented
60#10622118C2211yescharacteristic, complemented
61#10622117C2211yescharacteristic, complemented
62#10622117C2211yescharacteristic, complemented
63#10622093C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×D4×C11C2×C411yescharacteristic
68C23×C4×C11—21no—
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C22×C8×C11—21no—
72C22×C8×C11—21no—
73C4×D4×C11—21no—
74C4×D4×C11—21no—
75C4×D4×C11C2×C411yescharacteristic
76C4×D4×C11C2×C411yescharacteristic
77C4×D4×C11C2311yescharacteristic
78C4×D4×C11C2311yescharacteristic
79C2×C11×C4⋊C4C2×C411yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4324C2×C411yescharacteristic
83C2×#4324C2×C411yescharacteristic
84C2×#4324C2×C411yescharacteristic
85C2×#4324C2×C411yescharacteristic
86#66979—21no—
87#66977—21no—
88#66977C2×C411yescharacteristic
89#66977C2×C411yescharacteristic
90#66923—21no—
91#66922C2×C411yescharacteristic
92#66922C2×C411yescharacteristic
93C4×Dic22—21no—
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
107C11×#97—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
139C4×C11⋊C8—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
164C11×M16—81no—
165C11×M16—81no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—81no—
169C2×C8×C11—81no—
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C11×C4⋊C4—21no—
175C11×C4⋊C4C22×C411yescharacteristic
176C11×C4⋊C4C22×C411yescharacteristic
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C42×C11C22×C411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11#4111yescharacteristic
184C42×C11C2411yescharacteristic
185C22⋊Dic11—21no—
186C22⋊Dic11—21no—
187#4324—22no—
188#4324—22no—
189#4324—41no—
190#4324—41no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11C22×C411yescharacteristic
195C4⋊Dic11C22×C411yescharacteristic
196Dic11⋊C4—21no—
197Dic11⋊C4—21no—
198Dic11⋊C4—21no—
199Dic11⋊C4—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#3101—111no—
211#2986—111no—
212#2974D1111yescharacteristic
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#1478—111no—
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—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#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#436C2×D1111yescharacteristic
300#436C2×D1111yescharacteristic
301#435—21no—
302#435—21no—
303C8×D4C2×D1111yescharacteristic
304C8×D4C2×D1111yescharacteristic
305#433—221no—
306#433—221no—
307#432C2×D1111yescharacteristic
308#431—111no—
309#431—111no—
310#431—111no—
311#431C2×D1111yescharacteristic
312#407—21no—
313C2×C22⋊C8—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—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—21no—
362C2×M16—21no—
363C22×C8—21no—
364C22×C8—21no—
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—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8C22⋊D1111yescharacteristic
398C4⋊C8C22⋊D1111yescharacteristic
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—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—111no—
415C22⋊C8—111no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8C22⋊D1111yescharacteristic
419C22⋊C8C22⋊D1111yescharacteristic
420#97—21no—
421#97—221no—
422#97—221no—
423C4×C8—111no—
424C4×C8—111no—
425C4×C8—111no—
426C4×C8—111no—
427C4×C8—221no—
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×C4#433911yescharacteristic
456C22×C4C2×C22⋊D1111yescharacteristic
457SD16—222no—
458SD16—222no—
459SD16—441no—
460SD16—441no—
461M16—81no—
462M16—81no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—81no—
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—221no—
475C2×C8C2×C22⋊D1111yescharacteristic
476C2×C8C2×C22⋊D1111yescharacteristic
477C2×C8C2×C22⋊D1111yescharacteristic
478C2×C8C2×C22⋊D1111yescharacteristic
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
500C42#433911yescharacteristic
501C42C2×C22⋊D1111yescharacteristic
502C42C23×D1111yescharacteristic
503C11#1802811yescharacteristic, complemented, Sylow
504C23—21no—
505C23—21no—
506C23—42no—
507C23—42no—
508C23—81no—
509C23C4×C22⋊D1111yescharacteristic
510Q8—221no—
511Q8—221no—
512Q8—221no—
513Q8—221no—
514Q8—442no—
515D4—21no—
516D4—21no—
517D4—21no—
518D4—42no—
519D4#6696012yes—
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×C4C4×C22⋊D1111yescharacteristic
539C2×C4C4×C22⋊D1111yescharacteristic
540C2×C4C4×C22⋊D1111yescharacteristic
541C2×C4C22×C4×D1111yescharacteristic
542C2×C4C2×#433911yescharacteristic
543C2×C4C22×C22⋊D1111yescharacteristic
544C8—21no—
545C8—21no—
546C8—21no—
547C8—21no—
548C8—41no—
549C8—41no—
550C8—221no—
551C8—221no—
552C8—221no—
553C8—221no—
554C8—441no—
555C8—441no—
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×C4×C22⋊D1111yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—441no—
576C4—441no—
577C4—441no—
578C4—441no—
579C4C2×#6696011yescharacteristic
580C4#1062327611yescharacteristic
581C4#1062336711yescharacteristic
582C4#1062336711yescharacteristic
583C2—41no—
584C2—42no—
585C2—81no—
586C2#1307734111yescharacteristic
587C2#1307747311yescharacteristic
588C2#1307751711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2974C2
socleC22×C11C2×C4×D4
prime radicalC22×D4×C11C2×C4
cosocleC42×C11C24
hypercenter#2974D11
hypocenterC11#18028
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #13077717C2semidirect
3. #13067518C2semidirect
4. #13067504C2semidirect
5. #13067492C2semidirect
6. #13067473C2semidirect
7. #13067457C2semidirect
8. #13067452C2semidirect
9. #13067428C2semidirect
10. C8×#4324C2semidirect
11. #13067397C2semidirect
12. #13067088C2semidirect
14. #13066916C2semidirect
47. #10622292C22semidirect
48. #10622292C22semidirect
49. C8×Dic22C22semidirect
50. C8×Dic22C22semidirect
55. #10622122C22semidirect
56. #10622122C22semidirect
57. #10622122C22semidirect
58. #10622122C22semidirect
59. #10622118C22semidirect
60. #10622118C22semidirect
61. #10622117C22semidirect
62. #10622117C22semidirect
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
#130675182
#130675042
#130674922
#130674732
#130674572
#130674522
#130674282
C8×#43242
#130673972
#130670882
#130670072
#130669162
C11×#29742
#1802811