Finite Group Databasebeta

← #14725371

Subgroups — #14725371

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#13077741C211yesmaximal, characteristic, complemented
2#13077653C211yesmaximal, characteristic, complemented
3C4×#67002C211yesmaximal, characteristic
4#13067521C211yesmaximal, characteristic, complemented
5#13067503C211yesmaximal, characteristic, complemented
6#13067477C211yesmaximal, characteristic, complemented
7#13067476C211yesmaximal, characteristic, complemented
8#13067455C211yesmaximal, characteristic, complemented
9#13067442C211yesmaximal, characteristic, complemented
10#13067437C211yesmaximal, characteristic, complemented
11#13067408C211yesmaximal, characteristic, complemented
12#13067384C211yesmaximal, characteristic, complemented
13#13067042C211yesmaximal, characteristic, complemented
14#13066911C211yesmaximal, characteristic, complemented
15C11×#1488C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17C2×#67002C411yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C11×#432C2211yescharacteristic
20C11×#431C2211yescharacteristic
21#10622845C411yescharacteristic
22#10622639C411yescharacteristic
23#10622639C411yescharacteristic
24C4×#4325C2211yescharacteristic
25C4×#4325C2211yescharacteristic
26#10622637C2211yescharacteristic, complemented
27#10622637C2211yescharacteristic, complemented
28#10622627C411yescharacteristic
29#10622627C411yescharacteristic
30C4×#4323C2211yescharacteristic
31C4×#4323C2211yescharacteristic
32#10622624—21no—
33#10622624—21no—
34D4×C11⋊C8C2211yescharacteristic, complemented
35D4×C11⋊C8C2211yescharacteristic, complemented
36#10622614C411yescharacteristic
37#10622608C411yescharacteristic
38#10622539—21no—
39#10622538C2211yescharacteristic
40#10622537C2211yescharacteristic
41C2×C4⋊(C11⋊C8)—21no—
42C4×#4318C2211yescharacteristic
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×D4⋊C8C2211yescharacteristic, complemented
54C11×D4⋊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
67C2×C11×#41C2×C411yescharacteristic
68C22×D44C2×C411yescharacteristic
69C22×C4×D11—21no—
70C4×Q8×C11C2×C411yescharacteristic
71C4×Q8×C11C2311yescharacteristic
72C4×D4×C11—21no—
73C4×D4×C11—21no—
74C4×D4×C11C2×C411yescharacteristic
75C4×D4×C11C2311yescharacteristic
76C11×#117—21no—
77C11×#117C2×C411yescharacteristic
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80#67002—24no—
81C2×#4325C2×C411yescharacteristic
82C2×#4325C2×C411yescharacteristic
83C2×#4323C2×C411yescharacteristic
84C2×#4323C2×C411yescharacteristic
85C2×(C2×D11)⋊C4—21no—
86C2×C4⋊Dic11C2×C411yescharacteristic
87C2×#4318—21no—
88C2×#4318C2×C411yescharacteristic
89C2×#4318C2×C411yescharacteristic
90C22×C11⋊C8—21no—
91C22×C11⋊C8—21no—
92C2×#4313—21no—
93C2×#4313—21no—
94C2×C8×D11—21no—
95C2×C8×D11—21no—
96C4×D44—21no—
97C4×D44—21no—
98C4×D44C2×C411yescharacteristic
99C4×D44C2×C411yescharacteristic
100C4×D44C2311yescharacteristic
101C4×D44C2311yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C22⋊C8—21no—
106C11×C22⋊C8—21no—
107C11×#97—21no—
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110#66899C2×C411yescharacteristic
111#66899C2×C411yescharacteristic
112#66896C2×C411yescharacteristic
113#66896C2×C411yescharacteristic
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)D411yescharacteristic
117C22⋊(C11⋊C8)D411yescharacteristic
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122#66873C2×C411yescharacteristic
123#66873C2×C411yescharacteristic
124#66873C2×C411yescharacteristic
125#66873C2×C411yescharacteristic
126#66872C2×C411yescharacteristic
127#66872C2×C411yescharacteristic
128#66871C2×C411yescharacteristic
129#66871C2×C411yescharacteristic
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)D411yescharacteristic
134C4⋊(C11⋊C8)D411yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137#66867—21no—
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
146C23×D11—21no—
147C11×#41—22no—
148C11×#41—41no—
149C2×Q8×C11C22×C411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11C22×C411yescharacteristic
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C22×Dic11—21no—
159C2×D44—22no—
160C2×D44—21no—
161C2×D44—41no—
162C2×D44C22×C411yescharacteristic
163C2×D44C22×C411yescharacteristic
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—81no—
169C2×C4×D11—81no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C11×C4⋊C4—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—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11C22×C411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11#4111yescharacteristic
187C42×C11C2411yescharacteristic
188#4325—22no—
189#4325—22no—
190#4323—22no—
191#4323M1614yescomplemented
192(C2×D11)⋊C4—21no—
193(C2×D11)⋊C4—21no—
194(C2×D11)⋊C4—21no—
195(C2×D11)⋊C4—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11C22×C411yescharacteristic
198C4⋊Dic11C22×C411yescharacteristic
199#4318—22no—
200#4318—41no—
201#4318—81no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—81no—
205C2×C11⋊C8—81no—
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C22×C411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214#4313—81no—
215#4313—81no—
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#1488D1111yescharacteristic, complemented
231#1486—111no—
232#1453—111no—
233C23×C11—21no—
234C23×C11C4×D411yescharacteristic
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—42no—
238C22×D11—42no—
239C22×D11—81no—
240Q8×C11—21no—
241Q8×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—21no—
252C2×C4×C11—41no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11C4×D411yescharacteristic
258C2×C4×C11C4×D411yescharacteristic
259C2×C4×C11C4×D411yescharacteristic
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—81no—
266D44—21no—
267D44—21no—
268D44—21no—
269D44—42no—
270D44C2×M1612yes—
271C4×D11—41no—
272C4×D11—41no—
273C4×D11—41no—
274C4×D11—41no—
275C4×D11—81no—
276C4×D11—81no—
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×#41C2×D1111yescharacteristic
293C2×C4×D4—111no—
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—221no—
315#432C2×D1111yescharacteristic
316#431—111no—
317#431C2×D1111yescharacteristic
318#428—111no—
319#423—111no—
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⋊C8C2×D1111yescharacteristic, complemented
331Q8⋊C8C2×D1111yescharacteristic, complemented
332D4⋊C8—111no—
333D4⋊C8—111no—
334D4⋊C8—111no—
335D4⋊C8—111no—
336D4⋊C8C2×D1111yescharacteristic, complemented
337D4⋊C8C2×D1111yescharacteristic, complemented
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×C11C2×C4×D411yescharacteristic
349C2×D11—22no—
350C2×D11—41no—
351C2×D11—41no—
352C2×D11—41no—
353C2×D11—41no—
354C2×D11—41no—
355C2×D11—84no—
356C4×C11—21no—
357C4×C11—21no—
358C4×C11—21no—
359C4×C11—21no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11C22×M1611yescharacteristic
364C4×C11#56811yescharacteristic
365C4×C11#57611yescharacteristic
366C4×C11#57711yescharacteristic
367Dic11—41no—
368Dic11—41no—
369C2×#41C4×D1111yescharacteristic
370C22×D4—111no—
371C23×C4—221no—
372AGL(1,ℤ/8)—224no—
373C2×SD16—111no—
374C2×SD16—111no—
375C2×D8—111no—
376C2×D8—111no—
377C2×M16—111no—
378C2×M16—111no—
379C2×M16—221no—
380C2×M16—221no—
381C2×M16—221no—
382C22×C8—221no—
383C22×C8—221no—
384C22×C8—221no—
385C22×C8—221no—
386C4×Q8C4×D1111yescharacteristic
387C4×Q8C22×D1111yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—111no—
391C4×D4—111no—
392C4×D4—111no—
393C4×D4—111no—
394C4×D4—221no—
395C4×D4—221no—
396C4×D4C4×D1111yescharacteristic
397C4×D4C22×D1111yescharacteristic
398#117—21no—
399#117C4×D1111yescharacteristic
400C2×C4⋊C4—111no—
401C2×C22⋊C4—221no—
402C2×C42—21no—
403C2×C42C22×D1111yescharacteristic
404#107—111no—
405#107—111no—
406#106—111no—
407#106—111no—
408C4⋊C8—21no—
409C4⋊C8—111no—
410C4⋊C8—111no—
411C4⋊C8—111no—
412C4⋊C8—111no—
413C4⋊C8—221no—
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—21no—
428C22⋊C8—111no—
429C22⋊C8—111no—
430C22⋊C8—221no—
431C22⋊C8—221no—
432C22⋊C8—221no—
433C22⋊C8—221no—
434C22⋊C8—221no—
435C22⋊C8—221no—
436#97—21no—
437#97—111no—
438#97—111no—
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×C11D4×M1611yescharacteristic
450C2×C11#294611yescharacteristic
451C2×C11#295511yescharacteristic
452D11—42no—
453D11—81no—
454C24—221no—
455#41—22no—
456#41—41no—
457C2×Q8C2×C4×D1111yescharacteristic
458C2×D4—21no—
459C2×D4—111no—
460C2×D4—111no—
461C2×D4—222no—
462C2×D4—221no—
463C2×D4—441no—
464C2×D4C2×C4×D1111yescharacteristic
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—881no—
474C22×C4—881no—
475C22×C4C2×C4×D1111yescharacteristic
476C22×C4D4×D1111yescharacteristic
477C22×C4#434111yescharacteristic
478SD16—222no—
479SD16—222no—
480D8—114no—
481D8—222no—
482M16—222no—
483M16—441no—
484M16—881no—
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—21no—
507C4⋊C4—111no—
508C4⋊C4—111no—
509C4⋊C4—221no—
510C4⋊C4C2×C4×D1111yescharacteristic
511C4⋊C4C2×C4×D1111yescharacteristic
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—221no—
516C22⋊C4—221no—
517C22⋊C4—221no—
518C22⋊C4—221no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42C2×C4×D1111yescharacteristic
523C42D4×D1111yescharacteristic
524C42#434111yescharacteristic
525C42C23×D1111yescharacteristic
526C11#1805011yescharacteristic, complemented, Sylow
527C23—21no—
528C23—221no—
529C23—221no—
530C23—442no—
531C23—442no—
532C23—881no—
533C23(C22⋊D11)⋊C411yescharacteristic
534Q8—21no—
535Q8—21no—
536D4—21no—
537D4—42no—
538D4—112no—
539D4—221no—
540D4—221no—
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—21no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—881no—
563C2×C4—881no—
564C2×C4—881no—
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—222no—
592C22—441no—
593C22—441no—
594C22—441no—
595C22—441no—
596C22—441no—
597C22—884no—
598C22C2×(C22⋊D11)⋊C411yescharacteristic
599C4—21no—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—441no—
607C4—441no—
608C4C2×M16×D1111yescharacteristic
609C4#1062327611yescharacteristic
610C4#1062330011yescharacteristic
611C4#1062330111yescharacteristic
612C2—41no—
613C2—42no—
614C2—442no—
615C2—881no—
616C2#1307734811yescharacteristic
617C2#1307745111yescharacteristic
618C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1488C2
socleC22×C11C2×C4×D4
prime radicalC2×#67002C4
cosocleC42×C11C24
hypercenter#1488D11
hypocenterC11#18050
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
1. #13077741C2semidirect
2. #13077653C2semidirect
4. #13067521C2semidirect
5. #13067503C2semidirect
6. #13067477C2semidirect
7. #13067476C2semidirect
8. #13067455C2semidirect
9. #13067442C2semidirect
10. #13067437C2semidirect
11. #13067408C2semidirect
12. #13067384C2semidirect
13. #13067042C2semidirect
14. #13066911C2semidirect
15. C11×#1488C2semidirect
26. #10622637C22semidirect
27. #10622637C22semidirect
34. D4×C11⋊C8C22semidirect
35. D4×C11⋊C8C22semidirect
51. C11×Q8⋊C8C22semidirect
52. C11×Q8⋊C8C22semidirect
53. C11×D4⋊C8C22semidirect
54. C11×D4⋊C8C22semidirect
55. #10622118C22semidirect
56. #10622118C22semidirect
57. #10622117C22semidirect
58. #10622117C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
191. #4323M16semidirect
230. #1488D11semidirect
330. Q8⋊C8C2×D11semidirect
331. Q8⋊C8C2×D11semidirect
336. D4⋊C8C2×D11semidirect
337. D4⋊C8C2×D11semidirect
526. C11#18050semidirect

Maximal subgroups

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

subgroupindex
#130777412
#130776532
C4×#670022
#130675212
#130675032
#130674772
#130674762
#130674552
#130674422
#130674372
#130674082
#130673842
#130670422
#130669112
C11×#14882
#1805011