Finite Group Databasebeta

← #14725113

Subgroups — #14725113

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#13078620C211yesmaximal, characteristic
2#13077718C211yesmaximal, characteristic, complemented
3#13077653C211yesmaximal, characteristic
4#13067521C211yesmaximal, characteristic, complemented
5#13067503C211yesmaximal, characteristic, complemented
6#13067491C211yesmaximal, characteristic, complemented
7#13067476C211yesmaximal, characteristic, complemented
8#13067456C211yesmaximal, characteristic, complemented
9#13067455C211yesmaximal, characteristic, complemented
10#13067431C211yesmaximal, characteristic, complemented
11#13067413C211yesmaximal, characteristic, complemented
12#13067397C211yesmaximal, characteristic, complemented
13#13067008C211yesmaximal, characteristic
14#13066916C211yesmaximal, characteristic, complemented
15C11×#1497C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C11×#432C2211yescharacteristic
19C11×#431C2211yescharacteristic
20#10622697C411yescharacteristic
21#10622697C411yescharacteristic
22#10622696C411yescharacteristic
23#10622696C411yescharacteristic
24#10622659C411yescharacteristic
25#10622659C411yescharacteristic
26#10622656C411yescharacteristic
27#10622656C411yescharacteristic
28C4×#4325C2211yescharacteristic
29C4×#4325C2211yescharacteristic
30C4×#4325C2211yescharacteristic
31C4×#4325C2211yescharacteristic
32#10622637—21no—
33#10622637C2211yescharacteristic, complemented
34#10622637C2211yescharacteristic, complemented
35Q8×C11⋊C8—21no—
36Q8×C11⋊C8C2211yescharacteristic, complemented
37Q8×C11⋊C8C2211yescharacteristic, complemented
38#10622613—21no—
39#10622613—21no—
40#10622538C2211yescharacteristic
41#10622538C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622451C2211yescharacteristic
44#10622451C2211yescharacteristic
45#10622447C2211yescharacteristic
46#10622447C2211yescharacteristic
47#10622339—21no—
48D11×C22⋊C8—21no—
49#10622319—21no—
50#10622319—21no—
51C11×Q8⋊C8C2211yescharacteristic, complemented
52C11×Q8⋊C8C2211yescharacteristic, complemented
53C11×Q8⋊C8C2211yescharacteristic, complemented
54C11×Q8⋊C8C2211yescharacteristic, complemented
55#10622118C2211yescharacteristic, complemented
56#10622118C2211yescharacteristic, complemented
57#10622117C2211yescharacteristic, complemented
58#10622117C2211yescharacteristic, complemented
59#10622097C2211yescharacteristic
60#10622097C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic
63#10622093C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×D44C2×C411yescharacteristic
68C22×C4×D11—21no—
69C11×C4⋊Q8C2×C411yescharacteristic
70C11×C4⋊Q8C2×C411yescharacteristic
71C11×#125—21no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8C2×C411yescharacteristic
74C11×C22⋊Q8C2×C411yescharacteristic
75C4×Q8×C11—21no—
76C4×Q8×C11C2311yescharacteristic
77C4×Q8×C11C2311yescharacteristic
78C11×#117—21no—
79C2×C42×C11C2311yescharacteristic
80C2×#4325C2×C411yescharacteristic
81C2×#4325C2×C411yescharacteristic
82C2×#4325C2×C411yescharacteristic
83C2×#4325C2×C411yescharacteristic
84C2×(C2×D11)⋊C4—21no—
85C2×C4⋊Dic11C2×C411yescharacteristic
86C2×#4313—21no—
87C2×#4313—21no—
88C2×C8×D11—21no—
89C2×C8×D11—21no—
90C4×D44—21no—
91C4×D44—21no—
92C4×D44C2×C411yescharacteristic
93C4×D44C2×C411yescharacteristic
94C4×D44C2311yescharacteristic
95C4×D44C2311yescharacteristic
96C11×C4⋊C8—21no—
97C11×C4⋊C8C2311yescharacteristic
98C11×C4⋊C8C2311yescharacteristic
99C11×C22⋊C8—21no—
100C11×C22⋊C8—21no—
101C11×#97—21no—
102C4×C8×C11C2311yescharacteristic
103C4×C8×C11C2311yescharacteristic
104#66899C2×C411yescharacteristic
105#66899C2×C411yescharacteristic
106#66899C2×C411yescharacteristic
107#66899C2×C411yescharacteristic
108C22⋊(C11⋊C8)—21no—
109C22⋊(C11⋊C8)C2×C411yescharacteristic
110C22⋊(C11⋊C8)C2×C411yescharacteristic
111C22⋊(C11⋊C8)D411yescharacteristic
112C22⋊(C11⋊C8)D411yescharacteristic
113(C2×D11)⋊C8—21no—
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8—21no—
117#66873C2×C411yescharacteristic
118#66873C2×C411yescharacteristic
119#66873C2×C411yescharacteristic
120#66873C2×C411yescharacteristic
121#66872C2×C411yescharacteristic
122#66872C2×C411yescharacteristic
123#66872C2×C411yescharacteristic
124#66872C2×C411yescharacteristic
125C4⋊(C11⋊C8)—21no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)—21no—
129C4⋊(C11⋊C8)C2×C411yescharacteristic
130C4⋊(C11⋊C8)C2×C411yescharacteristic
131C4⋊(C11⋊C8)D411yescharacteristic
132C4⋊(C11⋊C8)D411yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135#66867—21no—
136#66867—21no—
137C4×C11⋊C8—21no—
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18028—111nomaximal, Sylow
145C23×D11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11C22×C411yescharacteristic
148C2×Q8×C11C22×C411yescharacteristic
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C22×Dic11—21no—
153C2×D44—22no—
154C2×D44—21no—
155C2×D44—41no—
156C2×D44C22×C411yescharacteristic
157C2×D44C22×C411yescharacteristic
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—81no—
163C2×C4×D11—81no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C22×C411yescharacteristic
176C11×C4⋊C4C22×C411yescharacteristic
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11C22×C411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11#4111yescharacteristic
184C42×C11C2411yescharacteristic
185#4325—22no—
186#4325—22no—
187#4325—41no—
188#4325—41no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11C22×C411yescharacteristic
195C4⋊Dic11C22×C411yescharacteristic
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8C22×C411yescharacteristic
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206#4313—81no—
207#4313—81no—
208C8×D11—81no—
209C8×D11—81no—
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#1497D1111yescharacteristic, complemented
223#1478—111no—
224#1454—111no—
225C23×C11C4×D411yescharacteristic
226C22×D11—21no—
227C22×D11—21no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—81no—
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11—21no—
234Q8×C11—21no—
235Q8×C11—42no—
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—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C4×D411yescharacteristic
247C2×C4×C11C4×D411yescharacteristic
248C2×C4×C11C23×C411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—81no—
254D44—21no—
255D44—21no—
256D44—21no—
257D44—42no—
258D44#13112yes—
259C4×D11—41no—
260C4×D11—41no—
261C4×D11—41no—
262C4×D11—41no—
263C4×D11—81no—
264C4×D11—81no—
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#533C2×D1111yescharacteristic
280C2×C4×D4—111no—
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#432C2×D1111yescharacteristic
308#431—111no—
309#431—111no—
310#431—111no—
311#431C2×D1111yescharacteristic
312#407—221no—
313C2×C22⋊C8—221no—
314#335—111no—
315#335—111no—
316#334—111no—
317#334—111no—
318Q8⋊C8C2×D1111yescharacteristic, complemented
319Q8⋊C8C2×D1111yescharacteristic, complemented
320Q8⋊C8C2×D1111yescharacteristic, complemented
321Q8⋊C8C2×D1111yescharacteristic, complemented
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×C11C2×C4×D411yescharacteristic
334C2×D11—22no—
335C2×D11—41no—
336C2×D11—41no—
337C2×D11—41no—
338C2×D11—41no—
339C2×D11—41no—
340C2×D11—84no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11C2×#13111yescharacteristic
350C4×C11#56811yescharacteristic
351C4×C11#57711yescharacteristic
352C4×C11#57711yescharacteristic
353Dic11—41no—
354Dic11—41no—
355C22×D4—111no—
356C23×C4—221no—
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⋊Q8C4×D1111yescharacteristic
366C4⋊Q8C4×D1111yescharacteristic
367#125—21no—
368C22⋊Q8—21no—
369C22⋊Q8C4×D1111yescharacteristic
370C22⋊Q8C4×D1111yescharacteristic
371C4×Q8—21no—
372C4×Q8C22×D1111yescharacteristic
373C4×Q8C22×D1111yescharacteristic
374C4×D4—111no—
375C4×D4—111no—
376C4×D4—111no—
377C4×D4—111no—
378C4×D4—221no—
379C4×D4—221no—
380#117—21no—
381C2×C4⋊C4—111no—
382C2×C22⋊C4—221no—
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—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#293311yescharacteristic
434C2×C11#294911yescharacteristic
435C2×C11#295511yescharacteristic
436D11—42no—
437D11—81no—
438C24—221no—
439C2×Q8—21no—
440C2×Q8C2×C4×D1111yescharacteristic
441C2×Q8C2×C4×D1111yescharacteristic
442C2×D4—111no—
443C2×D4—111no—
444C2×D4—222no—
445C2×D4—221no—
446C2×D4—441no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—881no—
453C22×C4—881no—
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—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—111no—
487C4⋊C4—111no—
488C4⋊C4—221no—
489C4⋊C4C2×C4×D1111yescharacteristic
490C4⋊C4C2×C4×D1111yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—221no—
494C22⋊C4—221no—
495C22⋊C4—221no—
496C22⋊C4—221no—
497C42—21no—
498C42—21no—
499C42C2×C4×D1111yescharacteristic
500C42D4×D1111yescharacteristic
501C42#434111yescharacteristic
502C42C23×D1111yescharacteristic
503C11#1802811yescharacteristic, complemented, Sylow
504C23—221no—
505C23—221no—
506C23—442no—
507C23—442no—
508C23—881no—
509C23(C22⋊D11)⋊C411yescharacteristic
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—42no—
515D4—112no—
516D4—221no—
517D4—221no—
518D4—221no—
519D4—442no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—881no—
536C2×C4—881no—
537C2×C4—881no—
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—21no—
561C22—222no—
562C22—441no—
563C22—441no—
564C22—441no—
565C22—441no—
566C22—441no—
567C22—884no—
568C22C2×(C22⋊D11)⋊C411yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—441no—
578C4—441no—
579C4D11×#13111yescharacteristic
580C4#1062328111yescharacteristic
581C4#1062330911yescharacteristic
582C4#1062330911yescharacteristic
583C2—41no—
584C2—442no—
585C2—881no—
586C2#1307734611yescharacteristic
587C2#1307747111yescharacteristic
588C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1497C2
socleC22×C11C2×C4×D4
prime radicalC22×D44C2×C4
cosocleC42×C11C24
hypercenter#1497D11
hypocenterC11#18028
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
2. #13077718C2semidirect
4. #13067521C2semidirect
5. #13067503C2semidirect
6. #13067491C2semidirect
7. #13067476C2semidirect
8. #13067456C2semidirect
9. #13067455C2semidirect
10. #13067431C2semidirect
11. #13067413C2semidirect
12. #13067397C2semidirect
14. #13066916C2semidirect
15. C11×#1497C2semidirect
33. #10622637C22semidirect
34. #10622637C22semidirect
36. Q8×C11⋊C8C22semidirect
37. Q8×C11⋊C8C22semidirect
51. C11×Q8⋊C8C22semidirect
52. C11×Q8⋊C8C22semidirect
53. C11×Q8⋊C8C22semidirect
54. C11×Q8⋊C8C22semidirect
55. #10622118C22semidirect
56. #10622118C22semidirect
57. #10622117C22semidirect
58. #10622117C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
222. #1497D11semidirect
318. Q8⋊C8C2×D11semidirect
319. Q8⋊C8C2×D11semidirect
320. Q8⋊C8C2×D11semidirect
321. Q8⋊C8C2×D11semidirect
503. C11#18028semidirect

Maximal subgroups

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

subgroupindex
#130786202
#130777182
#130776532
#130675212
#130675032
#130674912
#130674762
#130674562
#130674552
#130674312
#130674132
#130673972
#130670082
#130669162
C11×#14972
#1802811