Finite Group Databasebeta

← #14725109

Subgroups — #14725109

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#13077718C211yesmaximal, characteristic, complemented
2#13077651C211yesmaximal, characteristic
3#13067519C211yesmaximal, characteristic, complemented
4#13067507C211yesmaximal, characteristic, complemented
5#13067495C211yesmaximal, characteristic, complemented
6#13067474C211yesmaximal, characteristic, complemented
7#13067460C211yesmaximal, characteristic, complemented
8#13067453C211yesmaximal, characteristic, complemented
9SD16⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
10SD16×C11⋊C8C211yesmaximal, characteristic, complemented
11#13067396C211yesmaximal, characteristic, complemented
12#13067089C211yesmaximal, characteristic, complemented
13#13067007C211yesmaximal, characteristic
14#13066916C211yesmaximal, characteristic, complemented
15C11×#3101C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C11×#483C411yescharacteristic
19C11×#483C411yescharacteristic
20C11×#476C411yescharacteristic
21C11×#476C411yescharacteristic
22C11×#461C411yescharacteristic
23C11×#461C411yescharacteristic
24C11×#450C411yescharacteristic
25C11×#450C411yescharacteristic
26C4×C11×SD16C2211yescharacteristic
27C4×C11×SD16C2211yescharacteristic
28C4×C11×SD16C2211yescharacteristic
29C4×C11×SD16C2211yescharacteristic
30C11×#431C2211yescharacteristic
31#10622820—21no—
32C2×C22⋊(C11⋊C8)—21no—
33#10622637—21no—
34#10622637C2211yescharacteristic, complemented
35#10622637C2211yescharacteristic, complemented
36Q8×C11⋊C8—21no—
37Q8×C11⋊C8C2211yescharacteristic, complemented
38Q8×C11⋊C8C2211yescharacteristic, complemented
39#10622625C2211yescharacteristic
40#10622625C2211yescharacteristic
41#10622624—21no—
42#10622624—21no—
43D4×C11⋊C8C2211yescharacteristic
44D4×C11⋊C8C2211yescharacteristic
45#10622613—21no—
46#10622613—21no—
47#10622539C2211yescharacteristic
48#10622538C2211yescharacteristic
49#10622538C2211yescharacteristic
50#10622538C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
52Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
53Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
54Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57D4⋊(C11⋊C8)C2211yescharacteristic
58D4⋊(C11⋊C8)C2211yescharacteristic
59#10622096C2211yescharacteristic, complemented
60#10622096C2211yescharacteristic, complemented
61#10622095C2211yescharacteristic, complemented
62#10622095C2211yescharacteristic, complemented
63#10622093C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×D4×C11C2×C411yescharacteristic
68C23×C4×C11—21no—
69C2×C11×SD16C2×C411yescharacteristic
70C2×C11×SD16C2×C411yescharacteristic
71C2×C11×SD16C2×C411yescharacteristic
72C2×C11×SD16C2×C411yescharacteristic
73C11×C4⋊Q8C2×C411yescharacteristic
74C11×C4⋊Q8C2×C411yescharacteristic
75C11×#125—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8C2×C411yescharacteristic
78C11×C22⋊Q8C2×C411yescharacteristic
79C4×Q8×C11—21no—
80C4×Q8×C11C2311yescharacteristic
81C4×Q8×C11C2311yescharacteristic
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11C2×C411yescharacteristic
85C4×D4×C11C2×C411yescharacteristic
86C4×D4×C11C2311yescharacteristic
87C4×D4×C11C2311yescharacteristic
88C11×#117—21no—
89C2×C11×C4⋊C4C2×C411yescharacteristic
90C2×C11×C22⋊C4—21no—
91C2×C42×C11C2311yescharacteristic
92C2×#4318—21no—
93C2×#4318—21no—
94C22×C11⋊C8—21no—
95C22×C11⋊C8—21no—
96C11×#106C2×C411yescharacteristic
97C11×#106C2×C411yescharacteristic
98C11×#106C2×C411yescharacteristic
99C11×#106C2×C411yescharacteristic
100C11×C4⋊C8C2×C411yescharacteristic
101C11×C4⋊C8C2×C411yescharacteristic
102C11×#103C2×C411yescharacteristic
103C11×#103C2×C411yescharacteristic
104C11×#103C2×C411yescharacteristic
105C11×#103C2×C411yescharacteristic
106C11×#102C2×C411yescharacteristic
107C11×#102C2×C411yescharacteristic
108C11×#102C2×C411yescharacteristic
109C11×#102C2×C411yescharacteristic
110C11×C22⋊C8C2×C411yescharacteristic
111C11×C22⋊C8C2×C411yescharacteristic
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117C22⋊(C11⋊C8)—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)D411yescharacteristic
122C22⋊(C11⋊C8)D411yescharacteristic
123C4⋊(C11⋊C8)—21no—
124C4⋊(C11⋊C8)—21no—
125C4⋊(C11⋊C8)—21no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)D411yescharacteristic
129C4⋊(C11⋊C8)D411yescharacteristic
130C4⋊(C11⋊C8)C2311yescharacteristic
131C4⋊(C11⋊C8)C2311yescharacteristic
132C4⋊(C11⋊C8)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134#66867—21no—
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
145C24×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11C22×C411yescharacteristic
148C2×Q8×C11C22×C411yescharacteristic
149C2×D4×C11—22no—
150C2×D4×C11—21no—
151C2×D4×C11—41no—
152C2×D4×C11C22×C411yescharacteristic
153C2×D4×C11C22×C411yescharacteristic
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—81no—
160C22×C4×C11—81no—
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C11×SD16—22no—
165C11×SD16—22no—
166C11×SD16—41no—
167C11×SD16—41no—
168C2×C8×C11C22×C411yescharacteristic
169C2×C8×C11C22×C411yescharacteristic
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C22×C411yescharacteristic
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4C22×C411yescharacteristic
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C4⋊C4C22×C411yescharacteristic
183C11×C4⋊C4C22×C411yescharacteristic
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11C22×C411yescharacteristic
193C42×C11C2×D411yescharacteristic
194C42×C11#4111yescharacteristic
195C42×C11C2411yescharacteristic
196#4318—81no—
197#4318—81no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—81no—
205C2×C11⋊C8—81no—
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210#3101D1111yescharacteristic
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#1478—111no—
224#1454—111no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—81no—
230C23×C11C4×D411yescharacteristic
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11—21no—
234Q8×C11—21no—
235Q8×C11—42no—
236D4×C11—21no—
237D4×C11—21no—
238D4×C11—21no—
239D4×C11—42no—
240D4×C11#13112yes—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—81no—
257C2×C4×C11—81no—
258C2×C4×C11—81no—
259C2×C4×C11C4×D411yescharacteristic
260C2×C4×C11C4×D411yescharacteristic
261C2×C4×C11C4×D411yescharacteristic
262C2×C4×C11C23×C411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—21no—
269C11⋊C8—21no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279#533C2×D1111yescharacteristic
280C2×C4×D4C2×D1111yescharacteristic
281#483Dic1111yescharacteristic
282#483Dic1111yescharacteristic
283#476Dic1111yescharacteristic
284#476Dic1111yescharacteristic
285#461Dic1111yescharacteristic
286#461Dic1111yescharacteristic
287#450Dic1111yescharacteristic
288#450Dic1111yescharacteristic
289#446—111no—
290#446—111no—
291#446—221no—
292C8×Q8—111no—
293C8×Q8—111no—
294C8×Q8—221no—
295C4×SD16C2×D1111yescharacteristic
296C4×SD16C2×D1111yescharacteristic
297C4×SD16C2×D1111yescharacteristic
298C4×SD16C2×D1111yescharacteristic
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#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⋊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×C11—41no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11C2×#13111yescharacteristic
352C4×C11#56811yescharacteristic
353C4×C11#57711yescharacteristic
354C4×C11#57711yescharacteristic
355C22×D4C2×Dic1111yescharacteristic
356C23×C4—21no—
357C2×SD16C2×Dic1111yescharacteristic
358C2×SD16C2×Dic1111yescharacteristic
359C2×SD16C2×Dic1111yescharacteristic
360C2×SD16C2×Dic1111yescharacteristic
361C2×M16—221no—
362C2×M16—221no—
363C22×C8—221no—
364C22×C8—221no—
365C4⋊Q8C2×Dic1111yescharacteristic
366C4⋊Q8C2×Dic1111yescharacteristic
367#125—21no—
368C22⋊Q8—21no—
369C22⋊Q8C2×Dic1111yescharacteristic
370C22⋊Q8C2×Dic1111yescharacteristic
371C4×Q8—21no—
372C4×Q8C22×D1111yescharacteristic
373C4×Q8C22×D1111yescharacteristic
374C4×D4—21no—
375C4×D4—21no—
376C4×D4C2×Dic1111yescharacteristic
377C4×D4C2×Dic1111yescharacteristic
378C4×D4C22×D1111yescharacteristic
379C4×D4C22×D1111yescharacteristic
380#117—21no—
381C2×C4⋊C4C2×Dic1111yescharacteristic
382C2×C22⋊C4—21no—
383C2×C42C22×D1111yescharacteristic
384#106C2×Dic1111yescharacteristic
385#106C2×Dic1111yescharacteristic
386#106C2×Dic1111yescharacteristic
387#106C2×Dic1111yescharacteristic
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8—221no—
399C4⋊C8C2×Dic1111yescharacteristic
400C4⋊C8C2×Dic1111yescharacteristic
401#103C2×Dic1111yescharacteristic
402#103C2×Dic1111yescharacteristic
403#103C2×Dic1111yescharacteristic
404#103C2×Dic1111yescharacteristic
405#102C2×Dic1111yescharacteristic
406#102C2×Dic1111yescharacteristic
407#102C2×Dic1111yescharacteristic
408#102C2×Dic1111yescharacteristic
409C22⋊C8—111no—
410C22⋊C8—111no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413C22⋊C8—221no—
414C22⋊C8—221no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8C2×Dic1111yescharacteristic
419C22⋊C8C2×Dic1111yescharacteristic
420#97—221no—
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—21no—
440C2×Q8C22×Dic1111yescharacteristic
441C2×Q8C22×Dic1111yescharacteristic
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4C22×Dic1111yescharacteristic
446C2×D4C22×Dic1111yescharacteristic
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—81no—
453C22×C4—81no—
454C22×C4D4×D1111yescharacteristic
455C22×C4#434111yescharacteristic
456C22×C4C22×Dic1111yescharacteristic
457SD16—22no—
458SD16—22no—
459SD16—41no—
460SD16—41no—
461M16—881no—
462M16—881no—
463C2×C8—111no—
464C2×C8—111no—
465C2×C8—111no—
466C2×C8—111no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—881no—
474C2×C8—881no—
475C2×C8C22×Dic1111yescharacteristic
476C2×C8C22×Dic1111yescharacteristic
477C2×C8C22×Dic1111yescharacteristic
478C2×C8C22×Dic1111yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4C22×Dic1111yescharacteristic
488C4⋊C4C22×Dic1111yescharacteristic
489C4⋊C4C22×Dic1111yescharacteristic
490C4⋊C4C22×Dic1111yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—21no—
497C42—21no—
498C42—21no—
499C42D4×D1111yescharacteristic
500C42#434111yescharacteristic
501C42C22×Dic1111yescharacteristic
502C42C23×D1111yescharacteristic
503C11#1802811yescharacteristic, complemented, Sylow
504C23—21no—
505C23—21no—
506C23—42no—
507C23—42no—
508C23—81no—
509C23D4×Dic1111yescharacteristic
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—42no—
515D4—21no—
516D4—21no—
517D4—21no—
518D4—42no—
519D4#6700112yes—
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—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—81no—
536C2×C4—81no—
537C2×C4—81no—
538C2×C4D4×Dic1111yescharacteristic
539C2×C4D4×Dic1111yescharacteristic
540C2×C4D4×Dic1111yescharacteristic
541C2×C4C2×D4×D1111yescharacteristic
542C2×C4C2×#434111yescharacteristic
543C2×C4C23×Dic1111yescharacteristic
544C8—21no—
545C8—21no—
546C8—21no—
547C8—21no—
548C8—221no—
549C8—221no—
550C8—221no—
551C8—221no—
552C8—441no—
553C8—441no—
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×D4×Dic1111yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4#1062329311yescharacteristic
580C4#1062329311yescharacteristic
581C4C2×#6700111yescharacteristic
582C4#1062335011yescharacteristic
583C2—41no—
584C2—42no—
585C2—81no—
586C2#1307734311yescharacteristic
587C2#1307747611yescharacteristic
588C2#1307751911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#3101C2
socleC22×C11C2×C4×D4
prime radicalC22×D4×C11C2×C4
cosocleC42×C11C24
hypercenter#3101D11
hypocenterC11#18028
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3101

Complements

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

NH ≅ G/Ntype
1. #13077718C2semidirect
3. #13067519C2semidirect
4. #13067507C2semidirect
5. #13067495C2semidirect
6. #13067474C2semidirect
7. #13067460C2semidirect
8. #13067453C2semidirect
9. SD16⋊(C11⋊C8)C2semidirect
10. SD16×C11⋊C8C2semidirect
11. #13067396C2semidirect
12. #13067089C2semidirect
14. #13066916C2semidirect
34. #10622637C22semidirect
35. #10622637C22semidirect
37. Q8×C11⋊C8C22semidirect
38. Q8×C11⋊C8C22semidirect
51. Q8⋊(C11⋊C8)C22semidirect
52. Q8⋊(C11⋊C8)C22semidirect
53. Q8⋊(C11⋊C8)C22semidirect
54. Q8⋊(C11⋊C8)C22semidirect
59. #10622096C22semidirect
60. #10622096C22semidirect
61. #10622095C22semidirect
62. #10622095C22semidirect
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
#130777182
#130776512
#130675192
#130675072
#130674952
#130674742
#130674602
#130674532
SD16⋊(C11⋊C8)2
SD16×C11⋊C82
#130673962
#130670892
#130670072
#130669162
C11×#31012
#1802811