Finite Group Databasebeta

← #14725359

Subgroups — #14725359

Order 2816.

676 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077742C211yesmaximal, characteristic, complemented
2#13077651C211yesmaximal, characteristic, complemented
3C4×#66985C211yesmaximal, characteristic
4#13067515C211yesmaximal, characteristic, complemented
5#13067509C211yesmaximal, characteristic, complemented
6#13067483C211yesmaximal, characteristic, complemented
7#13067470C211yesmaximal, characteristic, complemented
8#13067449C211yesmaximal, characteristic, complemented
9#13067448C211yesmaximal, characteristic, complemented
10#13067437C211yesmaximal, characteristic, complemented
11#13067408C211yesmaximal, characteristic, complemented
12#13067381C211yesmaximal, characteristic, complemented
13#13067051C211yesmaximal, characteristic, complemented
14#13066911C211yesmaximal, characteristic, complemented
15C11×#1486C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66985C411yescharacteristic
18C4×#4339C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C11×#423C2211yescharacteristic
21#10622828C411yescharacteristic
22#10622820—21no—
23C2×C22⋊(C11⋊C8)—21no—
24#10622740—21no—
25#10622740—21no—
26#10622631C411yescharacteristic
27#10622631C411yescharacteristic
28C4×#4324C2211yescharacteristic
29C4×#4324C2211yescharacteristic
30#10622627C411yescharacteristic
31#10622627C411yescharacteristic
32C4×#4323C2211yescharacteristic
33C4×#4323C2211yescharacteristic
34#10622625C2211yescharacteristic
35#10622625C2211yescharacteristic
36#10622624—21no—
37#10622624—21no—
38D4×C11⋊C8C2211yescharacteristic
39D4×C11⋊C8C2211yescharacteristic
40#10622579C411yescharacteristic
41#10622577C411yescharacteristic
42#10622539C2211yescharacteristic
43#10622538C2211yescharacteristic
44C4×#4318C2211yescharacteristic
45#10622448—21no—
46#10622447C2211yescharacteristic, complemented
47#10622447C2211yescharacteristic, complemented
48D11×C4⋊C8—21no—
49#10622444C2211yescharacteristic, complemented
50#10622444C2211yescharacteristic, complemented
51C11×D4⋊C8C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×D4⋊C8C2211yescharacteristic
55#10622118C2211yescharacteristic, complemented
56#10622118C2211yescharacteristic, complemented
57#10622117C2211yescharacteristic, complemented
58#10622117C2211yescharacteristic, complemented
59#10622097C2211yescharacteristic, complemented
60#10622097C2211yescharacteristic, complemented
61#10622094C2211yescharacteristic, complemented
62#10622094C2211yescharacteristic, complemented
63#10622093C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×D4×C11C2×C411yescharacteristic
68C23×C4×C11—21no—
69C2×#4339C2×C411yescharacteristic
70C2×C11×M16—21no—
71C4×D4×C11—21no—
72C4×D4×C11—21no—
73C4×D4×C11C2×C411yescharacteristic
74C4×D4×C11C2×C411yescharacteristic
75C4×D4×C11C2311yescharacteristic
76C4×D4×C11C2311yescharacteristic
77C2×C11×C4⋊C4C2×C411yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C42×C11C2311yescharacteristic
80C2×#4324C2×C411yescharacteristic
81C2×#4324C2×C411yescharacteristic
82#66985—24no—
83C2×#4323C2×C411yescharacteristic
84C2×#4323C2×C411yescharacteristic
85C4×C22⋊D11—21no—
86C4×C22⋊D11—21no—
87#66979C2×C411yescharacteristic
88C2×#4318—21no—
89C2×#4318—21no—
90C2×#4318C2×C411yescharacteristic
91C2×#4318C2×C411yescharacteristic
92C22×C11⋊C8—21no—
93C22×C11⋊C8—21no—
94C2×C8×D11—21no—
95C2×C8×D11—21no—
96C4×D44C2×C411yescharacteristic
97C4×D44C2311yescharacteristic
98#66925—21no—
99C42×D11—21no—
100C4×Dic22C2×C411yescharacteristic
101C4×Dic22C2311yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×C22⋊C8—21no—
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109#66896C2×C411yescharacteristic
110#66896C2×C411yescharacteristic
111#66896C2×C411yescharacteristic
112#66896C2×C411yescharacteristic
113C22⋊(C11⋊C8)—21no—
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117C22⋊(C11⋊C8)—21no—
118C22⋊(C11⋊C8)D411yescharacteristic
119C22⋊(C11⋊C8)D411yescharacteristic
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122#66879—21no—
123#66879—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126#66874C2×C411yescharacteristic
127#66874C2×C411yescharacteristic
128#66873C2×C411yescharacteristic
129#66873C2×C411yescharacteristic
130#66872C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66871C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134C4⋊(C11⋊C8)D411yescharacteristic
135C4⋊(C11⋊C8)D411yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138#66867—21no—
139#66867C2×C411yescharacteristic
140#66867C2×C411yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18050—111nomaximal, Sylow
146C24×C11—21no—
147C2×D4×C11—22no—
148C2×D4×C11—21no—
149C2×D4×C11—41no—
150C2×D4×C11C22×C411yescharacteristic
151C2×D4×C11C22×C411yescharacteristic
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—81no—
158C22×C4×C11—81no—
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11#4111yescharacteristic
162C2×C22⋊D11—21no—
163#4339—22no—
164#4339—41no—
165C2×D44C22×C411yescharacteristic
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×Dic22C22×C411yescharacteristic
170C11×M16—81no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4C22×C411yescharacteristic
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C42×C11C22×C411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11#4111yescharacteristic
185C42×C11C2411yescharacteristic
186C22⋊Dic11—21no—
187#4324—22no—
188#4324—22no—
189#4323—22no—
190#4323M1614yescomplemented
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193C4⋊Dic11C22×C411yescharacteristic
194C4⋊Dic11C22×C411yescharacteristic
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200#4318—22no—
201#4318—41no—
202#4318—81no—
203#4318—81no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—81no—
207C2×C11⋊C8—81no—
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C22×C411yescharacteristic
210C2×C11⋊C8C22×C411yescharacteristic
211C2×C11⋊C8C22×C411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214C2×C11⋊C8C2×D411yescharacteristic
215C2×C11⋊C8C2×D411yescharacteristic
216C8×D11—81no—
217C8×D11—81no—
218#2990—111no—
219#2974—111no—
220C4×AGL(1,ℤ/8)—111no—
221#1592—111no—
222#1590—111no—
223#1586—111no—
224#1585—111no—
225#1582—111no—
226#1581—111no—
227#1580—111no—
228C8×D8—111no—
229#1569—111no—
230#1488—111no—
231#1486D1111yescharacteristic, complemented
232#1453—111no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11—81no—
238C23×C11C4×D411yescharacteristic
239C22×D11—21no—
240D4×C11—21no—
241D4×C11—21no—
242D4×C11—21no—
243D4×C11—42no—
244D4×C11C2×M1612yes—
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
265C22⋊D11—42no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269D44—21no—
270D44C2×M1612yes—
271C4×D11—42no—
272C4×D11—42no—
273C4×D11—41no—
274C4×D11—41no—
275Dic22—21no—
276Dic22—21no—
277C8×C11—41no—
278C8×C11—41no—
279C8×C11—41no—
280C8×C11—41no—
281C11⋊C8—21no—
282C11⋊C8—21no—
283C11⋊C8—21no—
284C11⋊C8—21no—
285C11⋊C8—21no—
286C11⋊C8—21no—
287C11⋊C8—21no—
288C11⋊C8—41no—
289C11⋊C8—41no—
290C11⋊C8C2×M1612yes—
291C2×AGL(1,ℤ/8)—111no—
292C4×#41—111no—
293C2×C4×D4C2×D1111yescharacteristic
294#446—111no—
295#446—111no—
296#442—111no—
297#442—111no—
298#440—111no—
299#440—111no—
300C4×SD16—111no—
301C4×SD16—111no—
302C4×D8—111no—
303C4×D8—111no—
304#436—111no—
305#436—111no—
306#435—221no—
307#435—221no—
308#435—221no—
309#435—221no—
310C8×D4—111no—
311C8×D4—111no—
312C8×D4—111no—
313C8×D4—111no—
314#432—111no—
315#432—221no—
316#431—111no—
317#431C2×D1111yescharacteristic
318#428—111no—
319#423C2×D1111yescharacteristic
320C2×C4⋊C8—221no—
321#418—111no—
322#417—111no—
323#407—221no—
324C2×C22⋊C8—221no—
325C4×M16—111no—
326#335—111no—
327#335—111no—
328#334—111no—
329#334—111no—
330Q8⋊C8—111no—
331Q8⋊C8—111no—
332D4⋊C8—111no—
333D4⋊C8—111no—
334D4⋊C8C2×D1111yescharacteristic
335D4⋊C8C2×D1111yescharacteristic
336D4⋊C8C2×D1111yescharacteristic
337D4⋊C8C2×D1111yescharacteristic
338#322—111no—
339#322—111no—
340#322—111no—
341C82—111no—
342C22×C11—21no—
343C22×C11—22no—
344C22×C11—21no—
345C22×C11—21no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—84no—
352C22×C11C2×C4×D411yescharacteristic
353C2×D11—22no—
354C2×D11—41no—
355C2×D11—41no—
356C4×C11—21no—
357C4×C11—21no—
358C4×C11—21no—
359C4×C11—21no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11C22×M1611yescharacteristic
363C4×C11#56811yescharacteristic
364C4×C11#57611yescharacteristic
365C4×C11#57711yescharacteristic
366Dic11—41no—
367Dic11—41no—
368Dic11—41no—
369C2×#41—111no—
370C22×D4C4×D1111yescharacteristic
371C23×C4—21no—
372AGL(1,ℤ/8)—224no—
373C2×SD16—111no—
374C2×SD16—111no—
375C2×D8—111no—
376C2×D8—111no—
377C2×M16—21no—
378C2×M16—111no—
379C2×M16—111no—
380C2×M16—221no—
381C2×M16—221no—
382C22×C8—221no—
383C22×C8—221no—
384C22×C8—221no—
385C22×C8—221no—
386C4×Q8—111no—
387C4×Q8—111no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—111no—
391C4×D4—111no—
392C4×D4—221no—
393C4×D4—221no—
394C4×D4C4×D1111yescharacteristic
395C4×D4C4×D1111yescharacteristic
396C4×D4C22×D1111yescharacteristic
397C4×D4C22×D1111yescharacteristic
398#117—111no—
399#117—221no—
400C2×C4⋊C4C4×D1111yescharacteristic
401C2×C22⋊C4—21no—
402C2×C42—221no—
403C2×C42C22×D1111yescharacteristic
404#107—111no—
405#107—111no—
406#106—111no—
407#106—111no—
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8—111no—
411C4⋊C8—111no—
412C4⋊C8—111no—
413C4⋊C8—111no—
414C4⋊C8—221no—
415C4⋊C8—221no—
416C4⋊C8C22×D1111yescharacteristic
417C4⋊C8C22×D1111yescharacteristic
418#103—111no—
419#103—111no—
420#102—111no—
421#102—111no—
422#102—111no—
423#102—111no—
424#102—111no—
425#102—111no—
426C22⋊C8—21no—
427C22⋊C8—111no—
428C22⋊C8—111no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431C22⋊C8—221no—
432C22⋊C8—221no—
433C22⋊C8—221no—
434C22⋊C8—221no—
435C22⋊C8—221no—
436#97—111no—
437#97—111no—
438#97—221no—
439#97—221no—
440#97—221no—
441C4×C8—111no—
442C4×C8—111no—
443C4×C8—111no—
444C4×C8—111no—
445C4×C8C22×D1111yescharacteristic
446C4×C8C22×D1111yescharacteristic
447C2×C11—41no—
448C2×C11—42no—
449C2×C11—81no—
450C2×C11D4×M1611yescharacteristic
451C2×C11#294611yescharacteristic
452C2×C11#295511yescharacteristic
453D11—42no—
454C24—21no—
455#41—222no—
456#41—441no—
457C2×Q8—111no—
458C2×D4—22no—
459C2×D4—21no—
460C2×D4—41no—
461C2×D4—111no—
462C2×D4—221no—
463C2×D4C2×C4×D1111yescharacteristic
464C2×D4C2×C4×D1111yescharacteristic
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—81no—
471C22×C4—81no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4C2×C4×D1111yescharacteristic
476C22×C4D4×D1111yescharacteristic
477C22×C4#434111yescharacteristic
478SD16—222no—
479SD16—222no—
480D8—114no—
481D8—222no—
482M16—81no—
483M16—222no—
484M16—441no—
485M16—881no—
486M16—881no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—111no—
492C2×C8—111no—
493C2×C8—111no—
494C2×C8—111no—
495C2×C8—111no—
496C2×C8—111no—
497C2×C8—111no—
498C2×C8—111no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—881no—
502C2×C8—881no—
503C2×C8—881no—
504C2×C8—881no—
505C4⋊C4—21no—
506C4⋊C4—111no—
507C4⋊C4—111no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4C2×C4×D1111yescharacteristic
511C4⋊C4C2×C4×D1111yescharacteristic
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—221no—
517C22⋊C4—221no—
518C22⋊C4—221no—
519C42—221no—
520C42—221no—
521C42—221no—
522C42C2×C4×D1111yescharacteristic
523C42D4×D1111yescharacteristic
524C42#434111yescharacteristic
525C42C23×D1111yescharacteristic
526C11#1805011yescharacteristic, complemented, Sylow
527C23—21no—
528C23—21no—
529C23—42no—
530C23—42no—
531C23—81no—
532C23—221no—
533C23(C22⋊D11)⋊C411yescharacteristic
534Q8—221no—
535Q8—221no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—42no—
540D4—112no—
541D4—221no—
542D4—442no—
543D4M16×D1112yes—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—81no—
556C2×C4—81no—
557C2×C4—81no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—442no—
562C2×C4—442no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4(C22⋊D11)⋊C411yescharacteristic
566C2×C4(C22⋊D11)⋊C411yescharacteristic
567C2×C4(C22⋊D11)⋊C411yescharacteristic
568C2×C4C22×C4×D1111yescharacteristic
569C2×C4C2×D4×D1111yescharacteristic
570C2×C4C2×#434111yescharacteristic
571C8—41no—
572C8—41no—
573C8—41no—
574C8—41no—
575C8—112no—
576C8—221no—
577C8—221no—
578C8—221no—
579C8—221no—
580C8—221no—
581C8—221no—
582C8—221no—
583C8—441no—
584C8—441no—
585C22—21no—
586C22—21no—
587C22—22no—
588C22—21no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—84no—
595C22—222no—
596C22—441no—
597C22—441no—
598C22C2×(C22⋊D11)⋊C411yescharacteristic
599C4—21no—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—41no—
604C4—41no—
605C4—441no—
606C4—441no—
607C4—441no—
608C4C2×M16×D1111yescharacteristic
609C4#1062327611yescharacteristic
610C4#1062328811yescharacteristic
611C4#1062329311yescharacteristic
612C2—41no—
613C2—42no—
614C2—81no—
615C2—442no—
616C2#1307734811yescharacteristic
617C2#1307744211yescharacteristic
618C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1486C2
socleC22×C11C2×C4×D4
prime radicalC2×#66985C4
cosocleC42×C11C24
hypercenter#1486D11
hypocenterC11#18050
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
1. #13077742C2semidirect
2. #13077651C2semidirect
4. #13067515C2semidirect
5. #13067509C2semidirect
6. #13067483C2semidirect
7. #13067470C2semidirect
8. #13067449C2semidirect
9. #13067448C2semidirect
10. #13067437C2semidirect
11. #13067408C2semidirect
12. #13067381C2semidirect
13. #13067051C2semidirect
14. #13066911C2semidirect
15. C11×#1486C2semidirect
46. #10622447C22semidirect
47. #10622447C22semidirect
49. #10622444C22semidirect
50. #10622444C22semidirect
55. #10622118C22semidirect
56. #10622118C22semidirect
57. #10622117C22semidirect
58. #10622117C22semidirect
59. #10622097C22semidirect
60. #10622097C22semidirect
61. #10622094C22semidirect
62. #10622094C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
190. #4323M16semidirect
231. #1486D11semidirect
526. C11#18050semidirect

Maximal subgroups

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

subgroupindex
#130777422
#130776512
C4×#669852
#130675152
#130675092
#130674832
#130674702
#130674492
#130674482
#130674372
#130674082
#130673812
#130670512
#130669112
C11×#14862
#1805011