Finite Group Databasebeta

← #14723397

Subgroups — #14723397

Order 2816.

700 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077732C211yesmaximal, characteristic, complemented
2#13077637C211yesmaximal, characteristic, complemented
3C4×#66967C211yesmaximal, characteristic
4#13067480C211yesmaximal, characteristic, complemented
5#13067479C211yesmaximal, characteristic, complemented
6#13067474C211yesmaximal, characteristic, complemented
7#13067471C211yesmaximal, characteristic, complemented
8#13067455C211yesmaximal, characteristic, complemented
9#13067447C211yesmaximal, characteristic, complemented
10#13067442C211yesmaximal, characteristic, complemented
11#13067365C211yesmaximal, characteristic, complemented
12#13066997C211yesmaximal, characteristic, complemented
13D11×D4⋊C8C211yesmaximal, characteristic, complemented
14#13066904C211yesmaximal, characteristic, complemented
15C11×#1582C211yesmaximal, characteristic, complemented
16C2×#66967C411yescharacteristic
17C4×#4343C2211yescharacteristic
18C4×D4×D11C2211yescharacteristic
19C11×#446C2211yescharacteristic, complemented
20C4×C11×SD16C2211yescharacteristic
21C8×D4×C11C2211yescharacteristic
22#10622777C411yescharacteristic
23C8×C22⋊D11—21no—
24C2×(C2×D11)⋊C8—21no—
25C4×#4325C2211yescharacteristic
26#10622637C2211yescharacteristic, complemented
27C4×#4323C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622482C411yescharacteristic
30#10622474C411yescharacteristic
31#10622451C2211yescharacteristic, complemented
32#10622450—21no—
33#10622449—21no—
34#10622447C2211yescharacteristic
35#10622446C2211yescharacteristic
36D11×C4⋊C8C2211yescharacteristic
37#10622430C411yescharacteristic
38#10622416C411yescharacteristic
39#10622398C411yescharacteristic
40#10622383C411yescharacteristic
41(C22⋊D11)⋊C8—21no—
42D11×C22⋊C8—21no—
43#10622319—21no—
44#10622318—21no—
45C4×D88C2211yescharacteristic
46#10622301C2211yescharacteristic, complemented
47C4×#4313C2211yescharacteristic
48C8×D44C2211yescharacteristic
49#10622298C2211yescharacteristic
50C4×C8×D11C2211yescharacteristic
51C11×#334C2211yescharacteristic, complemented
52C11×Q8⋊C8C2211yescharacteristic, complemented
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic, complemented
55Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic, complemented
59#10622118C2211yescharacteristic, complemented
60#10622117C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic, complemented
63#10622096C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C2×#4343C2×C411yescharacteristic
68C2×D4×D11C2×C411yescharacteristic
69C22×C4×D11—21no—
70C2×C11×SD16C2×C411yescharacteristic
71C22×C8×C11—21no—
72C4×Q8×C11C2311yescharacteristic
73C4×D4×C11C2311yescharacteristic
74Q8×Dic11C2×C411yescharacteristic
75C2×#4325C2×C411yescharacteristic
76D4×Dic11C2×C411yescharacteristic
77C2×#4323C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C22×C11⋊C8—21no—
80#66967—24no—
81C2×D88C2×C411yescharacteristic
82C2×#4313—21no—
83C2×#4313—21no—
84C2×#4313C2×C411yescharacteristic
85C2×#4313C2×C411yescharacteristic
86C2×C8×D11—21no—
87C2×C8×D11—21no—
88C2×C8×D11—21no—
89C2×C8×D11—21no—
90#66946—21no—
91#66946C2×C411yescharacteristic
92#66946C2×C411yescharacteristic
93#66945—21no—
94#66945C2×C411yescharacteristic
95C4⋊C4×D11C2×C411yescharacteristic
96(C22⋊D11)⋊C4—21no—
97C22⋊C4×D11—21no—
98C4×D44—21no—
99C4×D44C2311yescharacteristic
100C4×D44C2311yescharacteristic
101C42×D11—21no—
102C42×D11C2311yescharacteristic
103C11×#106C2×C411yescharacteristic
104C11×C4⋊C8—21no—
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×#103C2×C411yescharacteristic
108C11×#102C2×C411yescharacteristic
109C11×C22⋊C8—21no—
110C11×#97—21no—
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114#66899C2×C411yescharacteristic
115#66896C2×C411yescharacteristic
116C22⋊(C11⋊C8)—21no—
117#66885C2×C411yescharacteristic
118#66885C2×C411yescharacteristic
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8D411yescharacteristic
125(C2×D11)⋊C8D411yescharacteristic
126#66882C2×C411yescharacteristic
127#66879C2×C411yescharacteristic
128#66879C2×C411yescharacteristic
129Dic11⋊C8—21no—
130Dic11⋊C8D411yescharacteristic
131Dic11⋊C8D411yescharacteristic
132C8×Dic11—21no—
133C8×Dic11—21no—
134#66873C2×C411yescharacteristic
135#66873C2×C411yescharacteristic
136#66872C2×C411yescharacteristic
137#66871C2×C411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141#66867—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#17873—111nomaximal, Sylow
146C23×D11—21no—
147C2×Q8×C11C22×C411yescharacteristic
148C2×D4×C11C22×C411yescharacteristic
149C22×C4×C11—21no—
150C2×C22⋊D11—21no—
151C22×Dic11—21no—
152#4343—22no—
153#4343—22no—
154D4×D11—22no—
155D4×D11M1614yescomplemented
156C2×D44—21no—
157C2×D44C22×C411yescharacteristic
158C2×D44C22×C411yescharacteristic
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—81no—
166C2×C4×D11—81no—
167C2×C4×D11C22×C411yescharacteristic
168C2×C4×D11C2×D411yescharacteristic
169C2×C4×D11#4111yescharacteristic
170C11×SD16—22no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—81no—
175C2×C8×C11C22×C411yescharacteristic
176C2×C8×C11C22×C411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C11×C4⋊C4—21no—
180C11×C4⋊C4C22×C411yescharacteristic
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C22⋊C4—21no—
183C42×C11—21no—
184C42×C11C2411yescharacteristic
185C22⋊Dic11—21no—
186#4325—22no—
187#4323—22no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11C22×C411yescharacteristic
195C4⋊Dic11C22×C411yescharacteristic
196Dic11⋊C4—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11C22×C411yescharacteristic
200C4×Dic11C2×D411yescharacteristic
201C4×Dic11#4111yescharacteristic
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—81no—
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210D88—22no—
211#4313—22no—
212#4313—22no—
213#4313—81no—
214#4313—81no—
215C8×D11—42no—
216C8×D11—81no—
217C8×D11—81no—
218C8×D11—81no—
219#2989—111no—
220#2972—111no—
221C4×AGL(1,ℤ/8)—111no—
222#1586—111no—
223#1586—111no—
224#1585—111no—
225#1585—111no—
226#1582—111no—
227#1582D1111yescharacteristic, complemented
228#1581—111no—
229#1581—111no—
230#1565—111no—
231#1476—111no—
232C2×D4⋊C8—111no—
233#1451—111no—
234C23×C11—21no—
235C22×D11—21no—
236C22×D11—24no—
237C22×D11—21no—
238C22×D11—81no—
239C22×D11—81no—
240C22×D11C4×D411yescharacteristic
241Q8×C11—21no—
242Q8×C11—21no—
243D4×C11—21no—
244D4×C11C2×M1612yes—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11C23×C411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C22⋊D11—24no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—81no—
257C2×Dic11C4×D411yescharacteristic
258C2×Dic11C4×D411yescharacteristic
259C2×Dic11C4×D411yescharacteristic
260D44—21no—
261D44—21no—
262D44—21no—
263D44—42no—
264D44C2×M1612yes—
265C4×D11—21no—
266C4×D11—21no—
267C4×D11—41no—
268C4×D11—41no—
269C4×D11—41no—
270C4×D11—41no—
271C4×D11—41no—
272C4×D11—42no—
273C4×D11—81no—
274C4×D11—81no—
275C4×D11—81no—
276C4×D11C2×M1612yes—
277C4×D11#13112yes—
278C8×C11—21no—
279C8×C11—21no—
280C8×C11—21no—
281C8×C11—21no—
282C8×C11—41no—
283C8×C11—41no—
284C8×C11—41no—
285C11⋊C8—22no—
286C11⋊C8—21no—
287C11⋊C8—21no—
288C11⋊C8—21no—
289C11⋊C8—21no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C2×AGL(1,ℤ/8)—111no—
293C4×#41—111no—
294C2×C4×D4—111no—
295#446—111no—
296#446C2×D1111yescharacteristic, complemented
297#442—111no—
298#442—111no—
299#440—111no—
300#440—111no—
301C4×SD16—111no—
302C4×SD16C2×D1111yescharacteristic
303C4×D8—111no—
304C4×D8—111no—
305#436—111no—
306#436—111no—
307#435—221no—
308#435—221no—
309C8×D4—111no—
310C8×D4—111no—
311C8×D4—111no—
312C8×D4—221no—
313C8×D4—221no—
314C8×D4C2×D1111yescharacteristic
315#432—221no—
316#431—111no—
317#431—111no—
318#428—111no—
319#423—221no—
320C2×C4⋊C8—111no—
321#418—111no—
322#417—111no—
323C2×C22⋊C8—221no—
324C2×C22⋊C8—221no—
325C4×M16—111no—
326C2×C4×C8—111no—
327#335—111no—
328#335—111no—
329#334—111no—
330#334C2×D1111yescharacteristic, complemented
331Q8⋊C8—111no—
332Q8⋊C8C2×D1111yescharacteristic, complemented
333D4⋊C8—111no—
334D4⋊C8—111no—
335D4⋊C8—111no—
336D4⋊C8—111no—
337D4⋊C8—111no—
338D4⋊C8C2×D1111yescharacteristic
339#322—111no—
340#322—111no—
341#322—111no—
342#322C2×D1111yescharacteristic, complemented
343C22×C11—22no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11C2×C4×D411yescharacteristic
347C2×D11—21no—
348C2×D11—21no—
349C2×D11—22no—
350C2×D11—41no—
351C2×D11—41no—
352C2×D11—41no—
353C2×D11—41no—
354C2×D11—41no—
355C2×D11—84no—
356C2×D11#43512yes—
357C4×C11—21no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11C22×M1611yescharacteristic
362C4×C11C2×#13111yescharacteristic
363C4×C11#57611yescharacteristic
364C4×C11#57711yescharacteristic
365Dic11—21no—
366Dic11—21no—
367Dic11—41no—
368Dic11—41no—
369Dic11#43512yes—
370C2×#41—111no—
371C22×D4—111no—
372C23×C4—221no—
373AGL(1,ℤ/8)—224no—
374C2×SD16—111no—
375C2×SD16C4×D1111yescharacteristic
376C2×D8—111no—
377C2×D8—111no—
378C2×M16—111no—
379C2×M16—111no—
380C2×M16—221no—
381C2×M16—221no—
382C22×C8—21no—
383C22×C8—221no—
384C22×C8—221no—
385C22×C8—221no—
386C22×C8—221no—
387C22×C8—221no—
388C4×Q8—111no—
389C4×Q8C22×D1111yescharacteristic
390C4×D4—111no—
391C4×D4—111no—
392C4×D4—111no—
393C4×D4—111no—
394C4×D4—111no—
395C4×D4—221no—
396C4×D4—221no—
397C4×D4—221no—
398C4×D4—221no—
399C4×D4C22×D1111yescharacteristic
400#117—111no—
401#117—221no—
402C2×C4⋊C4—111no—
403C2×C22⋊C4—221no—
404C2×C42—111no—
405C2×C42—221no—
406#107—111no—
407#107—111no—
408#106—111no—
409#106C4×D1111yescharacteristic
410C4⋊C8—21no—
411C4⋊C8—111no—
412C4⋊C8—111no—
413C4⋊C8—111no—
414C4⋊C8—111no—
415C4⋊C8—221no—
416C4⋊C8—221no—
417C4⋊C8C22×D1111yescharacteristic
418C4⋊C8C22×D1111yescharacteristic
419#103—111no—
420#103C4×D1111yescharacteristic
421#102—111no—
422#102—111no—
423#102—111no—
424#102—111no—
425#102—111no—
426#102C4×D1111yescharacteristic
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—
440C4×C8—111no—
441C4×C8—111no—
442C4×C8—111no—
443C4×C8—221no—
444C4×C8—221no—
445C4×C8C22×D1111yescharacteristic
446C4×C8C22×D1111yescharacteristic
447C4×C8C22×D1111yescharacteristic
448C2×C11—42no—
449C2×C11C2×#43511yescharacteristic
450C2×C11#294611yescharacteristic
451C2×C11#295611yescharacteristic
452D11—22no—
453D11—42no—
454D11—81no—
455C24—221no—
456#41—222no—
457#41—222no—
458C2×Q8C2×C4×D1111yescharacteristic
459C2×D4—114no—
460C2×D4—111no—
461C2×D4—111no—
462C2×D4—221no—
463C2×D4—222no—
464C2×D4—221no—
465C2×D4C2×C4×D1111yescharacteristic
466C22×C4—21no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—881no—
478C22×C4—881no—
479SD16—22no—
480SD16—222no—
481D8—222no—
482D8—222no—
483M16—222no—
484M16—222no—
485M16—881no—
486M16—881no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—81no—
491C2×C8—111no—
492C2×C8—111no—
493C2×C8—111no—
494C2×C8—111no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—442no—
499C2×C8—881no—
500C2×C8—881no—
501C2×C8—881no—
502C2×C8—881no—
503C2×C8C2×C4×D1111yescharacteristic
504C2×C8C2×C4×D1111yescharacteristic
505C2×C8D4×D1111yescharacteristic
506C2×C8D4×D1111yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—111no—
509C4⋊C4—111no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4C2×C4×D1111yescharacteristic
513C4⋊C4C2×C4×D1111yescharacteristic
514C22⋊C4—21no—
515C22⋊C4—221no—
516C22⋊C4—221no—
517C22⋊C4—221no—
518C22⋊C4—221no—
519C22⋊C4—221no—
520C22⋊C4—221no—
521C42—21no—
522C42—111no—
523C42—111no—
524C42—111no—
525C42—221no—
526C42—221no—
527C42C23×D1111yescharacteristic
528C11#1787311yescharacteristic, complemented, Sylow
529C23—21no—
530C23—111no—
531C23—224no—
532C23—221no—
533C23—221no—
534C23—881no—
535C23—881no—
536Q8—21no—
537Q8—21no—
538D4—21no—
539D4—112no—
540D4—224no—
541D4—221no—
542D4—221no—
543D4—221no—
544D4—442no—
545D4M16×D1112yes—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—111no—
552C2×C4—112no—
553C2×C4—112no—
554C2×C4—111no—
555C2×C4—111no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—441no—
561C2×C4—442no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—881no—
567C2×C4—881no—
568C2×C4—881no—
569C2×C4—881no—
570C2×C4C22×C4×D1111yescharacteristic
571C2×C4C2×D4×D1111yescharacteristic
572C2×C4#41×D1111yescharacteristic
573C8—21no—
574C8—21no—
575C8—21no—
576C8—21no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—222no—
581C8—221no—
582C8—221no—
583C8—221no—
584C8—221no—
585C8—441no—
586C8—441no—
587C22—22no—
588C22—41no—
589C22—41no—
590C22—112no—
591C22—221no—
592C22—221no—
593C22—222no—
594C22—441no—
595C22—441no—
596C22—441no—
597C22—441no—
598C22—441no—
599C22—884no—
600C22C4×D4×D1111yescharacteristic
601C4—21no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—112no—
606C4—221no—
607C4—221no—
608C4—441no—
609C4—441no—
610C4C2×M16×D1111yescharacteristic
611C4D11×#13111yescharacteristic
612C4#1062329311yescharacteristic
613C4#1062330011yescharacteristic
614C2—42no—
615C2—222no—
616C2—442no—
617C2—881no—
618C2D11×#43511yescharacteristic
619C2#1307744311yescharacteristic
620C2#1307752411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1582C2
socleC22×C11C2×C4×D4
prime radicalC2×#66967C4
cosocleC42×C11C24
hypercenter#1582D11
hypocenterC11#17873
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
1. #13077732C2semidirect
2. #13077637C2semidirect
4. #13067480C2semidirect
5. #13067479C2semidirect
6. #13067474C2semidirect
7. #13067471C2semidirect
8. #13067455C2semidirect
9. #13067447C2semidirect
10. #13067442C2semidirect
11. #13067365C2semidirect
12. #13066997C2semidirect
13. D11×D4⋊C8C2semidirect
14. #13066904C2semidirect
15. C11×#1582C2semidirect
19. C11×#446C22semidirect
26. #10622637C22semidirect
31. #10622451C22semidirect
46. #10622301C22semidirect
51. C11×#334C22semidirect
52. C11×Q8⋊C8C22semidirect
54. C11×#322C22semidirect
55. Q8⋊(C11⋊C8)C22semidirect
58. #10622121C22semidirect
59. #10622118C22semidirect
60. #10622117C22semidirect
62. #10622097C22semidirect
63. #10622096C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. #10622092C22semidirect
155. D4×D11M16semidirect
227. #1582D11semidirect
296. #446C2×D11semidirect
330. #334C2×D11semidirect
332. Q8⋊C8C2×D11semidirect
342. #322C2×D11semidirect
528. C11#17873semidirect

Maximal subgroups

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

subgroupindex
#130777322
#130776372
C4×#669672
#130674802
#130674792
#130674742
#130674712
#130674552
#130674472
#130674422
#130673652
#130669972
D11×D4⋊C82
#130669042
C11×#15822
#1787311