Finite Group Databasebeta

← #14725322

Subgroups — #14725322

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077630C211yesmaximal, characteristic
2Q8×#4318C211yesmaximal, characteristic, complemented
3#13067525C211yesmaximal, characteristic, complemented
4#13067513C211yesmaximal, characteristic, complemented
5#13067488C211yesmaximal, characteristic, complemented
6#13067474C211yesmaximal, characteristic, complemented
7#13067467C211yesmaximal, characteristic, complemented
8#13067453C211yesmaximal, characteristic, complemented
9SD16⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
10SD16×C11⋊C8C211yesmaximal, characteristic, complemented
11#13067383C211yesmaximal, characteristic, complemented
12#13067063C211yesmaximal, characteristic, complemented
13#13067055C211yesmaximal, characteristic
14#13066919C211yesmaximal, characteristic, complemented
15C4×C11×#137C211yesmaximal, characteristic
16C2×C11×#137C411yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C11×#441C411yescharacteristic
20C11×#441C411yescharacteristic
21C11×#440C411yescharacteristic
22C11×#440C411yescharacteristic
23C4×C11×Q16C2211yescharacteristic
24C4×C11×Q16C2211yescharacteristic
25C4×C11×SD16C2211yescharacteristic
26C4×C11×SD16C2211yescharacteristic
27C11×#428C411yescharacteristic
28C11×#419C411yescharacteristic
29C11×#417C411yescharacteristic
30C4×C11×M16C2211yescharacteristic
31#10622637—21no—
32#10622637—21no—
33#10622637C2211yescharacteristic
34#10622637C2211yescharacteristic
35#10622637C2211yescharacteristic
36#10622637C2211yescharacteristic
37Q8×C11⋊C8C2211yescharacteristic
38Q8×C11⋊C8C2211yescharacteristic
39#10622624—21no—
40#10622624—21no—
41D4×C11⋊C8C2211yescharacteristic
42D4×C11⋊C8C2211yescharacteristic
43#10622539—21no—
44#10622539C2211yescharacteristic
45#10622537—21no—
46#10622537C2211yescharacteristic
47C4×#4318—21no—
48C4×#4318C2211yescharacteristic
49C4×#4318C2211yescharacteristic
50C2×#66867—21no—
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#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×#41C2×C411yescharacteristic
68C22×Q8×C11C2×C411yescharacteristic
69C11×#137—24no—
70C2×C11×Q16C2×C411yescharacteristic
71C2×C11×Q16C2×C411yescharacteristic
72C2×C11×SD16C2×C411yescharacteristic
73C2×C11×SD16C2×C411yescharacteristic
74C2×C11×M16C2×C411yescharacteristic
75C2×C11×M16C2×C411yescharacteristic
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11C2×C411yescharacteristic
79C4×Q8×C11C2×C411yescharacteristic
80C4×Q8×C11C2×C411yescharacteristic
81C4×Q8×C11C2311yescharacteristic
82C4×Q8×C11C2311yescharacteristic
83C4×Q8×C11C2311yescharacteristic
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11C2×C411yescharacteristic
87C4×D4×C11C2311yescharacteristic
88C11×#117—21no—
89C11×#117C2×C411yescharacteristic
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4C2×C411yescharacteristic
92C2×C42×C11—21no—
93C2×C42×C11—21no—
94C2×C42×C11C2311yescharacteristic
95C2×#4318—21no—
96C2×#4318—21no—
97C2×#4318D411yescharacteristic
98C2×#4318D411yescharacteristic
99C22×C11⋊C8—21no—
100C22×C11⋊C8—21no—
101C11×#107C2×C411yescharacteristic
102C11×#107C2×C411yescharacteristic
103C11×#106C2×C411yescharacteristic
104C11×#106C2×C411yescharacteristic
105C11×#103C2×C411yescharacteristic
106C11×#103C2×C411yescharacteristic
107C11×#103C2×C411yescharacteristic
108C11×#103C2×C411yescharacteristic
109C11×#103C2×C411yescharacteristic
110C11×#103C2×C411yescharacteristic
111C11×#102C2×C411yescharacteristic
112C11×#102C2×C411yescharacteristic
113C11×#97C2×C411yescharacteristic
114C11×#97C2×C411yescharacteristic
115C4×C8×C11C2311yescharacteristic
116C4×C8×C11C2311yescharacteristic
117C22⋊(C11⋊C8)—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(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)—21no—
127C4⋊(C11⋊C8)C2311yescharacteristic
128C4⋊(C11⋊C8)C2311yescharacteristic
129C4⋊(C11⋊C8)C2311yescharacteristic
130C4⋊(C11⋊C8)C2311yescharacteristic
131#66867—21no—
132#66867—21no—
133#66867—21no—
134#66867—21no—
135#66867—21no—
136#66867—21no—
137#66867D411yescharacteristic
138#66867D411yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18047—111nomaximal, Sylow
146C11×#41—22no—
147C11×#41—41no—
148C2×Q8×C11—21no—
149C2×Q8×C11—22no—
150C2×Q8×C11—41no—
151C2×Q8×C11C22×C411yescharacteristic
152C2×Q8×C11C22×C411yescharacteristic
153C2×Q8×C11C22×C411yescharacteristic
154C2×D4×C11—21no—
155C2×D4×C11C22×C411yescharacteristic
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C11×Q16—22no—
165C11×Q16—22no—
166C11×SD16—22no—
167C11×SD16M1614yescomplemented
168C11×M16—22no—
169C11×M16—41no—
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C22×C411yescharacteristic
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⋊C4—21no—
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C4⋊C4C22×C411yescharacteristic
183C11×C4⋊C4C22×C411yescharacteristic
184C11×C4⋊C4C22×C411yescharacteristic
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11C22×C411yescharacteristic
196C42×C11C2×D411yescharacteristic
197C42×C11#4111yescharacteristic
198C42×C11C2411yescharacteristic
199#4318—22no—
200#4318—41no—
201#4318—42no—
202#4318—42no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—42no—
210C2×C11⋊C8—42no—
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214C2×C11⋊C8C2×D411yescharacteristic
215#2970—111no—
216Q8×M16—111no—
217C4×#137D1111yescharacteristic
218#1593—111no—
219#1591—111no—
220#1587—111no—
221#1585—111no—
222#1584—111no—
223#1582—111no—
224SD16⋊C8—111no—
225C8×SD16—111no—
226#1569—111no—
227#1491—111no—
228#1489—111no—
229#1455—111no—
230C23×C11—21no—
231C23×C11C4×D411yescharacteristic
232Q8×C11—21no—
233Q8×C11—21no—
234Q8×C11—21no—
235Q8×C11—21no—
236Q8×C11—21no—
237Q8×C11—42no—
238Q8×C11C2×M1612yes—
239D4×C11—21no—
240D4×C11—42no—
241D4×C11C2×M1612yes—
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—21no—
252C2×C4×C11—21no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—81no—
259C2×C4×C11—81no—
260C2×C4×C11C4×D411yescharacteristic
261C2×C4×C11C4×D411yescharacteristic
262C2×C4×C11C4×D411yescharacteristic
263C2×C4×C11C23×C411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11C2×M1612yes—
270C11⋊C8—22no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8#13712yescomplemented
280C2×#137Dic1111yescharacteristic
281C4×#41C2×D1111yescharacteristic
282C2×C4×Q8C2×D1111yescharacteristic
283#446—111no—
284#446—111no—
285#446—111no—
286#446—111no—
287#446—221no—
288#446—221no—
289C8×Q8—111no—
290C8×Q8—111no—
291#441Dic1111yescharacteristic
292#441Dic1111yescharacteristic
293#440Dic1111yescharacteristic
294#440Dic1111yescharacteristic
295C4×Q16C2×D1111yescharacteristic
296C4×Q16C2×D1111yescharacteristic
297C4×SD16C2×D1111yescharacteristic
298C4×SD16C2×D1111yescharacteristic
299#435—221no—
300#435—221no—
301C8×D4—111no—
302C8×D4—111no—
303#432—111no—
304#432—221no—
305#428Dic1111yescharacteristic
306#423—111no—
307#423—221no—
308#419Dic1111yescharacteristic
309#417Dic1111yescharacteristic
310C4×M16—111no—
311C4×M16—111no—
312C4×M16—221no—
313C4×M16C2×D1111yescharacteristic
314C2×#97—221no—
315#335—111no—
316#335—111no—
317#334—111no—
318#334—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322Q8⋊C8—111no—
323Q8⋊C8—111no—
324Q8⋊C8—111no—
325D4⋊C8—111no—
326D4⋊C8—111no—
327#322—111no—
328#322—111no—
329#322—111no—
330C82—111no—
331C22×C11—21no—
332C22×C11—22no—
333C22×C11—21no—
334C22×C11—21no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11C2×C4×D411yescharacteristic
338C4×C11—21no—
339C4×C11—22no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11C22×M1611yescharacteristic
350C4×C11#56811yescharacteristic
351C4×C11C2×#13711yescharacteristic
352C4×C11#57511yescharacteristic
353C2×#41C2×Dic1111yescharacteristic
354C22×Q8C2×Dic1111yescharacteristic
355#137—24no—
356C2×Q16C2×Dic1111yescharacteristic
357C2×Q16C2×Dic1111yescharacteristic
358C2×SD16C2×Dic1111yescharacteristic
359C2×SD16C2×Dic1111yescharacteristic
360C2×M16—111no—
361C2×M16—111no—
362C2×M16—221no—
363C2×M16—221no—
364C2×M16C2×Dic1111yescharacteristic
365C2×M16C2×Dic1111yescharacteristic
366C22×C8—221no—
367C22×C8—221no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8C2×Dic1111yescharacteristic
371C4×Q8C2×Dic1111yescharacteristic
372C4×Q8C2×Dic1111yescharacteristic
373C4×Q8C22×D1111yescharacteristic
374C4×Q8C22×D1111yescharacteristic
375C4×Q8C22×D1111yescharacteristic
376C4×D4—21no—
377C4×D4—21no—
378C4×D4C2×Dic1111yescharacteristic
379C4×D4C22×D1111yescharacteristic
380#117—21no—
381#117C2×Dic1111yescharacteristic
382C2×C4⋊C4—21no—
383C2×C4⋊C4C2×Dic1111yescharacteristic
384C2×C42—21no—
385C2×C42—21no—
386C2×C42C22×D1111yescharacteristic
387#107C2×Dic1111yescharacteristic
388#107C2×Dic1111yescharacteristic
389#106C2×Dic1111yescharacteristic
390#106C2×Dic1111yescharacteristic
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⋊C8—221no—
400C4⋊C8—221no—
401C4⋊C8—221no—
402#103C2×Dic1111yescharacteristic
403#103C2×Dic1111yescharacteristic
404#103C2×Dic1111yescharacteristic
405#103C2×Dic1111yescharacteristic
406#103C2×Dic1111yescharacteristic
407#103C2×Dic1111yescharacteristic
408#102C2×Dic1111yescharacteristic
409#102C2×Dic1111yescharacteristic
410C22⋊C8—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—111no—
414#97—111no—
415#97—221no—
416#97—221no—
417#97—221no—
418#97—221no—
419#97—221no—
420#97—221no—
421#97C2×Dic1111yescharacteristic
422#97C2×Dic1111yescharacteristic
423C4×C8—111no—
424C4×C8—111no—
425C4×C8—111no—
426C4×C8—111no—
427C4×C8—221no—
428C4×C8—221no—
429C4×C8C22×D1111yescharacteristic
430C4×C8C22×D1111yescharacteristic
431C2×C11—41no—
432C2×C11—42no—
433C2×C11D4×M1611yescharacteristic
434C2×C11C4×#13711yescharacteristic
435C2×C11#295611yescharacteristic
436#41—22no—
437#41—41no—
438C2×Q8—21no—
439C2×Q8—22no—
440C2×Q8—41no—
441C2×Q8C22×Dic1111yescharacteristic
442C2×Q8C22×Dic1111yescharacteristic
443C2×Q8C22×Dic1111yescharacteristic
444C2×D4—21no—
445C2×D4C22×Dic1111yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4D4×D1111yescharacteristic
452C22×C4#434111yescharacteristic
453C22×C4C22×Dic1111yescharacteristic
454Q16—22no—
455Q16—22no—
456SD16—22no—
457SD16#431814yescomplemented
458M16—22no—
459M16—41no—
460M16—222no—
461M16—441no—
462M16—442no—
463M16—442no—
464C2×C8—111no—
465C2×C8—111no—
466C2×C8—111no—
467C2×C8—111no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—442no—
475C2×C8—442no—
476C2×C8C22×Dic1111yescharacteristic
477C2×C8C22×Dic1111yescharacteristic
478C2×C8C22×Dic1111yescharacteristic
479C2×C8C22×Dic1111yescharacteristic
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—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42D4×D1111yescharacteristic
502C42#434111yescharacteristic
503C42C22×Dic1111yescharacteristic
504C42C23×D1111yescharacteristic
505C11#1804711yescharacteristic, complemented, Sylow
506C23—21no—
507C23D4×Dic1111yescharacteristic
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—42no—
514Q8C2×#431812yes—
515D4—21no—
516D4—42no—
517D4C2×#431812yes—
518C2×C4—21no—
519C2×C4—21no—
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—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4D4×Dic1111yescharacteristic
537C2×C4D4×Dic1111yescharacteristic
538C2×C4D4×Dic1111yescharacteristic
539C2×C4C2×D4×D1111yescharacteristic
540C2×C4C2×#434111yescharacteristic
541C2×C4C23×Dic1111yescharacteristic
542C8—21no—
543C8—21no—
544C8—21no—
545C8—112no—
546C8—222no—
547C8—221no—
548C8—221no—
549C8—221no—
550C8—441no—
551C8—441no—
552C8—441no—
553C8—441no—
554C8—441no—
555C8C2×#431812yes—
556C22—21no—
557C22—21no—
558C22—22no—
559C22—21no—
560C22—41no—
561C22—41no—
562C22C2×D4×Dic1111yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—22no—
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4D11×#13711yescharacteristic
575C4#1062330811yescharacteristic
576C4C22×#431811yescharacteristic
577C4#1062335011yescharacteristic
578C2—41no—
579C2—42no—
580C2D4×#431811yescharacteristic
581C2#137×Dic1111yescharacteristic
582C2#1307752611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC4×C11×#137C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#41C2×C4
cosocleC42×C11C24
hypercenterC4×#137D11
hypocenterC11#18047
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#137

Complements

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

NH ≅ G/Ntype
2. Q8×#4318C2semidirect
3. #13067525C2semidirect
4. #13067513C2semidirect
5. #13067488C2semidirect
6. #13067474C2semidirect
7. #13067467C2semidirect
8. #13067453C2semidirect
9. SD16⋊(C11⋊C8)C2semidirect
10. SD16×C11⋊C8C2semidirect
11. #13067383C2semidirect
12. #13067063C2semidirect
14. #13066919C2semidirect
167. C11×SD16M16semidirect
279. C11⋊C8#137semidirect
457. SD16#4318semidirect
505. C11#18047semidirect

Maximal subgroups

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

subgroupindex
#130776302
Q8×#43182
#130675252
#130675132
#130674882
#130674742
#130674672
#130674532
SD16⋊(C11⋊C8)2
SD16×C11⋊C82
#130673832
#130670632
#130670552
#130669192
C4×C11×#1372
#1804711