Finite Group Databasebeta

← #14724420

Subgroups — #14724420

Order 2816.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077765C211yesmaximal, characteristic
2#13077711C211yesmaximal, characteristic, complemented
3#13067525C211yesmaximal, characteristic, complemented
4#13067519C211yesmaximal, characteristic, complemented
5#13067513C211yesmaximal, characteristic, complemented
6#13067507C211yesmaximal, characteristic, complemented
7#13067435C211yesmaximal, characteristic, complemented
8SD16⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
9Q16×C11⋊C8C211yesmaximal, characteristic, complemented
10SD16×C11⋊C8C211yesmaximal, characteristic, complemented
11#13067383C211yesmaximal, characteristic, complemented
12#13067076C211yesmaximal, characteristic
13#13067071C211yesmaximal, characteristic, complemented
14M16×C11⋊C8C211yesmaximal, characteristic, complemented
15C11×#3172C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C11×#529C2211yescharacteristic
18C11×#501C411yescharacteristic
19C11×#497C411yescharacteristic
20C11×#491C411yescharacteristic
21C11×#489C411yescharacteristic
22C11×#470C411yescharacteristic
23C11×#470C411yescharacteristic
24C11×#468C411yescharacteristic
25C11×#468C411yescharacteristic
26C4×C11×Q16C2211yescharacteristic
27C4×C11×Q16C2211yescharacteristic
28C4×C11×SD16C2211yescharacteristic
29C4×C11×SD16C2211yescharacteristic
30C4×C11×M16C2211yescharacteristic
31#10622637—21no—
32#10622637—21no—
33#10622637C2211yescharacteristic
34#10622637C2211yescharacteristic
35#10622637C2211yescharacteristic
36Q8×C11⋊C8C2211yescharacteristic
37Q8×C11⋊C8C2211yescharacteristic
38Q8×C11⋊C8C2211yescharacteristic
39#10622625—21no—
40#10622625C2211yescharacteristic
41#10622624—21no—
42D4×C11⋊C8C2211yescharacteristic
43#10622613—21no—
44#10622613—21no—
45#10622613—21no—
46#10622612—21no—
47#10622539C2211yescharacteristic
48#10622538C2211yescharacteristic
49#10622537C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic
52Q8⋊(C11⋊C8)C2211yescharacteristic
53Q8⋊(C11⋊C8)C2211yescharacteristic
54Q8⋊(C11⋊C8)C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57D4⋊(C11⋊C8)C2211yescharacteristic
58D4⋊(C11⋊C8)C2211yescharacteristic
59#10622096C2211yescharacteristic
60#10622096C2211yescharacteristic
61#10622095C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622093C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×Q16C2×C411yescharacteristic
68C2×C11×Q16C2×C411yescharacteristic
69C2×C11×SD16C2×C411yescharacteristic
70C2×C11×SD16C2×C411yescharacteristic
71C2×C11×M16C2×C411yescharacteristic
72C2×C11×M16C2×C411yescharacteristic
73C11×C4⋊Q8C2×C411yescharacteristic
74C11×C4⋊Q8C2×C411yescharacteristic
75C11×#126—21no—
76C11×#125—21no—
77C11×#125C2×C411yescharacteristic
78C11×#124C2×C411yescharacteristic
79C11×#123—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8C2×C411yescharacteristic
82C11×C22⋊Q8C2×C411yescharacteristic
83C11×C22⋊Q8C2×C411yescharacteristic
84C11×#121C2×C411yescharacteristic
85C4×Q8×C11—21no—
86C4×Q8×C11C2311yescharacteristic
87C4×Q8×C11C2311yescharacteristic
88C4×Q8×C11C2311yescharacteristic
89C4×D4×C11—21no—
90C4×D4×C11C2311yescharacteristic
91C11×#117—21no—
92C11×#117—21no—
93C2×C42×C11C2311yescharacteristic
94C2×#4318—21no—
95C2×#4318—21no—
96C22×C11⋊C8—21no—
97C22×C11⋊C8—21no—
98C11×#107C2×C411yescharacteristic
99C11×#107C2×C411yescharacteristic
100C11×#106C2×C411yescharacteristic
101C11×#106C2×C411yescharacteristic
102C11×#103C2×C411yescharacteristic
103C11×#103C2×C411yescharacteristic
104C11×#103C2×C411yescharacteristic
105C11×#103C2×C411yescharacteristic
106C11×#103C2×C411yescharacteristic
107C11×#103C2×C411yescharacteristic
108C11×#102C2×C411yescharacteristic
109C11×#102C2×C411yescharacteristic
110C11×#97C2×C411yescharacteristic
111C11×#97C2×C411yescharacteristic
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117C22⋊(C11⋊C8)D411yescharacteristic
118C22⋊(C11⋊C8)D411yescharacteristic
119C4⋊(C11⋊C8)—21no—
120C4⋊(C11⋊C8)—21no—
121C4⋊(C11⋊C8)—21no—
122C4⋊(C11⋊C8)—21no—
123C4⋊(C11⋊C8)—21no—
124C4⋊(C11⋊C8)—21no—
125C4⋊(C11⋊C8)—21no—
126C4⋊(C11⋊C8)D411yescharacteristic
127C4⋊(C11⋊C8)D411yescharacteristic
128C4⋊(C11⋊C8)C2311yescharacteristic
129C4⋊(C11⋊C8)C2311yescharacteristic
130C4⋊(C11⋊C8)C2311yescharacteristic
131C4⋊(C11⋊C8)C2311yescharacteristic
132#66867—21no—
133#66867—21no—
134#66867—21no—
135#66867—21no—
136C4×C11⋊C8—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#17969—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11C22×C411yescharacteristic
147C2×Q8×C11C22×C411yescharacteristic
148C2×Q8×C11C22×C411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11C22×C411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C11×Q16—22no—
156C11×Q16—22no—
157C11×SD16—22no—
158C11×SD16—22no—
159C11×M16—22no—
160C11×M16—22no—
161C2×C8×C11C22×C411yescharacteristic
162C2×C8×C11C22×C411yescharacteristic
163C2×C8×C11C22×C411yescharacteristic
164C2×C8×C11C22×C411yescharacteristic
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—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⋊C4—21no—
176C11×C4⋊C4C22×C411yescharacteristic
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C4⋊C4C22×C411yescharacteristic
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11C22×C411yescharacteristic
191C42×C11C2×D411yescharacteristic
192C42×C11#4111yescharacteristic
193C42×C11C2411yescharacteristic
194#4318—81no—
195#4318—81no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—42no—
203C2×C11⋊C8—81no—
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208#3172D1111yescharacteristic
209#2993—111no—
210#2985—111no—
211#1593—111no—
212#1592—111no—
213#1591—111no—
214#1590—111no—
215#1579—111no—
216SD16⋊C8—111no—
217C8×Q16—111no—
218C8×SD16—111no—
219#1569—111no—
220#1494—111no—
221#1493—111no—
222C8×M16—111no—
223C23×C11—21no—
224C23×C11C4×D411yescharacteristic
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—81no—
232D4×C11—21no—
233D4×C11—21no—
234D4×C11—81no—
235C2×C4×C11—21no—
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—21no—
245C2×C4×C11—21no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C4×D411yescharacteristic
252C2×C4×C11C23×C411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C8×C11—21no—
256C8×C11—21no—
257C8×C11#13112yes—
258C8×C11#13112yes—
259C11⋊C8—22no—
260C11⋊C8—21no—
261C11⋊C8—21no—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269#533C2×D1111yescharacteristic
270#529C2×D1111yescharacteristic
271#501Dic1111yescharacteristic
272#497Dic1111yescharacteristic
273#491Dic1111yescharacteristic
274#489Dic1111yescharacteristic
275#470Dic1111yescharacteristic
276#470Dic1111yescharacteristic
277#468Dic1111yescharacteristic
278#468Dic1111yescharacteristic
279#446—111no—
280#446—111no—
281#446—111no—
282#446—221no—
283#446—221no—
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8—111no—
287C4×Q16C2×D1111yescharacteristic
288C4×Q16C2×D1111yescharacteristic
289C4×SD16C2×D1111yescharacteristic
290C4×SD16C2×D1111yescharacteristic
291#436—111no—
292#436—221no—
293#435—221no—
294C8×D4—111no—
295#433—221no—
296#433—221no—
297#433—221no—
298#432—111no—
299#431—111no—
300#424—221no—
301#423—111no—
302C4×M16C2×D1111yescharacteristic
303C2×C4×C8—111no—
304#335—111no—
305#335—111no—
306#334—111no—
307#334—111no—
308Q8⋊C8—111no—
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314D4⋊C8—111no—
315D4⋊C8—111no—
316#322—111no—
317#322—111no—
318C82—111no—
319C82—111no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11C2×C4×D411yescharacteristic
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11C2×#13111yescharacteristic
339C4×C11C2×#13111yescharacteristic
340C4×C11#57711yescharacteristic
341C4×C11#57811yescharacteristic
342C2×Q16C2×Dic1111yescharacteristic
343C2×Q16C2×Dic1111yescharacteristic
344C2×SD16C2×Dic1111yescharacteristic
345C2×SD16C2×Dic1111yescharacteristic
346C2×M16—221no—
347C2×M16—221no—
348C2×M16C2×Dic1111yescharacteristic
349C2×M16C2×Dic1111yescharacteristic
350C22×C8—221no—
351C22×C8—221no—
352C4⋊Q8C2×Dic1111yescharacteristic
353C4⋊Q8C2×Dic1111yescharacteristic
354#126—21no—
355#125—21no—
356#125C2×Dic1111yescharacteristic
357#124C2×Dic1111yescharacteristic
358#123—21no—
359C22⋊Q8—21no—
360C22⋊Q8C2×Dic1111yescharacteristic
361C22⋊Q8C2×Dic1111yescharacteristic
362C22⋊Q8C2×Dic1111yescharacteristic
363#121C2×Dic1111yescharacteristic
364C4×Q8—21no—
365C4×Q8C22×D1111yescharacteristic
366C4×Q8C22×D1111yescharacteristic
367C4×Q8C22×D1111yescharacteristic
368C4×D4—21no—
369C4×D4C22×D1111yescharacteristic
370#117—21no—
371#117—21no—
372C2×C42C22×D1111yescharacteristic
373#107C2×Dic1111yescharacteristic
374#107C2×Dic1111yescharacteristic
375#106C2×Dic1111yescharacteristic
376#106C2×Dic1111yescharacteristic
377C4⋊C8—111no—
378C4⋊C8—111no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—111no—
382C4⋊C8—111no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390#103C2×Dic1111yescharacteristic
391#103C2×Dic1111yescharacteristic
392#103C2×Dic1111yescharacteristic
393#103C2×Dic1111yescharacteristic
394#103C2×Dic1111yescharacteristic
395#103C2×Dic1111yescharacteristic
396#102C2×Dic1111yescharacteristic
397#102C2×Dic1111yescharacteristic
398C22⋊C8—111no—
399C22⋊C8—111no—
400C22⋊C8—221no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403#97—221no—
404#97—221no—
405#97—221no—
406#97—221no—
407#97C2×Dic1111yescharacteristic
408#97C2×Dic1111yescharacteristic
409C4×C8—111no—
410C4×C8—111no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8—221no—
414C4×C8—221no—
415C4×C8—221no—
416C4×C8—221no—
417C4×C8C22×D1111yescharacteristic
418C4×C8C22×D1111yescharacteristic
419C2×C11—41no—
420C2×C11—81no—
421C2×C11#293111yescharacteristic
422C2×C11#294711yescharacteristic
423C2×C11#295611yescharacteristic
424C2×Q8—21no—
425C2×Q8C22×Dic1111yescharacteristic
426C2×Q8C22×Dic1111yescharacteristic
427C2×Q8C22×Dic1111yescharacteristic
428C2×D4—21no—
429C2×D4C22×Dic1111yescharacteristic
430C22×C4—21no—
431C22×C4D4×D1111yescharacteristic
432C22×C4#434111yescharacteristic
433C22×C4C22×Dic1111yescharacteristic
434Q16—22no—
435Q16—22no—
436SD16—22no—
437SD16—22no—
438M16—22no—
439M16—22no—
440M16—881no—
441M16—881no—
442C2×C8—111no—
443C2×C8—111no—
444C2×C8—111no—
445C2×C8—111no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—442no—
453C2×C8—881no—
454C2×C8C22×Dic1111yescharacteristic
455C2×C8C22×Dic1111yescharacteristic
456C2×C8C22×Dic1111yescharacteristic
457C2×C8C22×Dic1111yescharacteristic
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4C22×Dic1111yescharacteristic
470C4⋊C4C22×Dic1111yescharacteristic
471C4⋊C4C22×Dic1111yescharacteristic
472C4⋊C4C22×Dic1111yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42D4×D1111yescharacteristic
484C42#434111yescharacteristic
485C42C22×Dic1111yescharacteristic
486C42C23×D1111yescharacteristic
487C11#1796911yescharacteristic, complemented, Sylow
488C23—21no—
489C23D4×Dic1111yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—81no—
497D4—21no—
498D4—21no—
499D4—81no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4D4×Dic1111yescharacteristic
515C2×C4D4×Dic1111yescharacteristic
516C2×C4D4×Dic1111yescharacteristic
517C2×C4C2×D4×D1111yescharacteristic
518C2×C4C2×#434111yescharacteristic
519C2×C4C23×Dic1111yescharacteristic
520C8—21no—
521C8—21no—
522C8—222no—
523C8—221no—
524C8—221no—
525C8—221no—
526C8—221no—
527C8—441no—
528C8—441no—
529C8—441no—
530C8—441no—
531C8—441no—
532C8#6700112yes—
533C8#6700112yes—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22C2×D4×Dic1111yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4#1062330911yescharacteristic
553C4#1062331011yescharacteristic
554C4C2×#6700111yescharacteristic
555C4C2×#6700111yescharacteristic
556C2—41no—
557C2—81no—
558C2#1307732811yescharacteristic
559C2#1307746011yescharacteristic
560C2#1307752611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#3172C2
socleC22×C11C2×C4×D4
prime radicalC11×#121C2×C4
cosocleC42×C11C24
hypercenter#3172D11
hypocenterC11#17969
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3172

Complements

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

NH ≅ G/Ntype
2. #13077711C2semidirect
3. #13067525C2semidirect
4. #13067519C2semidirect
5. #13067513C2semidirect
6. #13067507C2semidirect
7. #13067435C2semidirect
8. SD16⋊(C11⋊C8)C2semidirect
9. Q16×C11⋊C8C2semidirect
10. SD16×C11⋊C8C2semidirect
11. #13067383C2semidirect
13. #13067071C2semidirect
14. M16×C11⋊C8C2semidirect
487. C11#17969semidirect

Maximal subgroups

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

subgroupindex
#130777652
#130777112
#130675252
#130675192
#130675132
#130675072
#130674352
SD16⋊(C11⋊C8)2
Q16×C11⋊C82
SD16×C11⋊C82
#130673832
#130670762
#130670712
M16×C11⋊C82
C11×#31722
#1796911