Finite Group Databasebeta

← #14725398

Subgroups — #14725398

Order 2816.

674 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#13077747C211yesmaximal, characteristic, complemented
2#13077649C211yesmaximal, characteristic, complemented
3C4×#66967C211yesmaximal, characteristic
4#13067531C211yesmaximal, characteristic, complemented
5#13067500C211yesmaximal, characteristic, complemented
6#13067491C211yesmaximal, characteristic, complemented
7#13067477C211yesmaximal, characteristic, complemented
8#13067459C211yesmaximal, characteristic, complemented
9#13067445C211yesmaximal, characteristic, complemented
10SD16×C11⋊C8C211yesmaximal, characteristic, complemented
11#13067382C211yesmaximal, characteristic, complemented
12#13067049C211yesmaximal, characteristic, complemented
13#13067039C211yesmaximal, characteristic, complemented
14#13066914C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×#66967C411yescharacteristic
17C4×#4343C2211yescharacteristic
18C4×D4×D11C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic, complemented
20C4×C11×SD16C2211yescharacteristic
21C8×D4×C11C2211yescharacteristic
22#10622777C411yescharacteristic
23#10622724—21no—
24C2×(C2×D11)⋊C8—21no—
25C4×#4325C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic, complemented
27C4×#4323C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622482C411yescharacteristic
30#10622474C411yescharacteristic
31#10622451—21no—
32#10622451C2211yescharacteristic
33#10622451C2211yescharacteristic, complemented
34#10622450—21no—
35#10622450C2211yescharacteristic
36#10622448C2211yescharacteristic
37#10622430C411yescharacteristic
38#10622416C411yescharacteristic
39#10622398C411yescharacteristic
40#10622383C411yescharacteristic
41#10622343—21no—
42#10622339—21no—
43C4×D88C2211yescharacteristic
44#10622301—21no—
45#10622301C2211yescharacteristic
46#10622301C2211yescharacteristic, complemented
47C4×#4313C2211yescharacteristic
48#10622298—21no—
49#10622298C2211yescharacteristic
50#10622298C2211yescharacteristic
51C11×#335C2211yescharacteristic, 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#10622095C2211yescharacteristic, complemented
64#10622093C2211yescharacteristic, complemented
65#10622093C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, 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×#4313—21no—
85C2×#4313—21no—
86C2×#4313—21no—
87C2×#4313C2×C411yescharacteristic
88C2×#4313C2×C411yescharacteristic
89#66946—21no—
90#66946C2×C411yescharacteristic
91#66946C2×C411yescharacteristic
92#66945—21no—
93#66945C2×C411yescharacteristic
94C4⋊C4×D11C2×C411yescharacteristic
95(C22⋊D11)⋊C4—21no—
96C22⋊C4×D11—21no—
97C4×D44—21no—
98C4×D44C2311yescharacteristic
99C4×D44C2311yescharacteristic
100C42×D11—21no—
101C42×D11C2311yescharacteristic
102C11×#106C2×C411yescharacteristic
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×#103C2×C411yescharacteristic
107C11×#102C2×C411yescharacteristic
108C11×C22⋊C8—21no—
109C4×C8×C11—21no—
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113#66899C2×C411yescharacteristic
114#66896C2×C411yescharacteristic
115C22⋊(C11⋊C8)—21no—
116#66885C2×C411yescharacteristic
117#66885C2×C411yescharacteristic
118(C2×D11)⋊C8—21no—
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#66879—21no—
128#66879C2×C411yescharacteristic
129#66879C2×C411yescharacteristic
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8D411yescharacteristic
133Dic11⋊C8D411yescharacteristic
134#66873C2×C411yescharacteristic
135#66873C2×C411yescharacteristic
136#66872C2×C411yescharacteristic
137#66871C2×C411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18052—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—41no—
154D4×D11—22no—
155D4×D11—41no—
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×SD16M1614yescomplemented
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—41no—
213#4313—81no—
214#4313—81no—
215#4313—81no—
216#4313—81no—
217#4313—81no—
218#2991—111no—
219#2974—111no—
220C4×AGL(1,ℤ/8)—111no—
221#1594—111no—
222#1589—111no—
223#1588—111no—
224#1586—111no—
225#1583—111no—
226#1581—111no—
227SD16⋊C8D1111yescharacteristic, complemented
228C8×SD16—111no—
229#1569—111no—
230#1488—111no—
231#1486—111no—
232#1453—111no—
233C23×C11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—42no—
237C22×D11—42no—
238C22×D11—81no—
239C22×D11C4×D411yescharacteristic
240Q8×C11—21no—
241Q8×C11C2×M1612yes—
242D4×C11—21no—
243D4×C11C2×M1612yes—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11C23×C411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C22⋊D11—42no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—81no—
256C2×Dic11C4×D411yescharacteristic
257C2×Dic11C4×D411yescharacteristic
258C2×Dic11C4×D411yescharacteristic
259D44—21no—
260D44—21no—
261D44—21no—
262D44—21no—
263D44—42no—
264C4×D11—21no—
265C4×D11—21no—
266C4×D11—21no—
267C4×D11—21no—
268C4×D11—41no—
269C4×D11—42no—
270C4×D11—42no—
271C4×D11—41no—
272C4×D11—41no—
273C4×D11—41no—
274C4×D11—41no—
275C4×D11—81no—
276C4×D11—81no—
277C8×C11—21no—
278C8×C11—21no—
279C8×C11—21no—
280C8×C11—41no—
281C8×C11—41no—
282C8×C11—41no—
283C8×C11C2×M1612yes—
284C11⋊C8—21no—
285C11⋊C8—21no—
286C11⋊C8—21no—
287C11⋊C8—21no—
288C11⋊C8—41no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C2×AGL(1,ℤ/8)—111no—
292C4×#41—111no—
293C2×C4×D4—111no—
294C8×Q8—111no—
295C8×Q8C2×D1111yescharacteristic, complemented
296#442—111no—
297#442—111no—
298#440—111no—
299#440—111no—
300C4×SD16—111no—
301C4×SD16C2×D1111yescharacteristic
302C4×D8—111no—
303C4×D8—111no—
304#436—111no—
305#436—111no—
306#436—111no—
307#436—111no—
308#436—221no—
309#436—221no—
310#435—221no—
311#435—221no—
312C8×D4—111no—
313C8×D4C2×D1111yescharacteristic
314#432—111no—
315#431—111no—
316#431—111no—
317#431—221no—
318#428—111no—
319#423—111no—
320#423—221no—
321#418—111no—
322#417—111no—
323#407—221no—
324C2×C22⋊C8—221no—
325C4×M16—111no—
326#335—111no—
327#335C2×D1111yescharacteristic, complemented
328#334—111no—
329#334—111no—
330Q8⋊C8—111no—
331Q8⋊C8C2×D1111yescharacteristic, complemented
332D4⋊C8—111no—
333D4⋊C8—111no—
334D4⋊C8—111no—
335D4⋊C8—111no—
336D4⋊C8—111no—
337D4⋊C8C2×D1111yescharacteristic
338#322—111no—
339#322—111no—
340#322C2×D1111yescharacteristic, complemented
341C82—111no—
342C22×C11—22no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11C2×C4×D411yescharacteristic
346C2×D11—21no—
347C2×D11—21no—
348C2×D11—21no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—41no—
352C2×D11—41no—
353C2×D11—41no—
354C2×D11—41no—
355C2×D11—84no—
356C4×C11—22no—
357C4×C11—21no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11C22×M1611yescharacteristic
361C4×C11#56811yescharacteristic
362C4×C11#57611yescharacteristic
363C4×C11#57711yescharacteristic
364Dic11—21no—
365Dic11—21no—
366Dic11—21no—
367Dic11—41no—
368Dic11—41no—
369C2×#41—111no—
370C22×D4—111no—
371C23×C4—221no—
372AGL(1,ℤ/8)—224no—
373C2×SD16—111no—
374C2×SD16C4×D1111yescharacteristic
375C2×D8—111no—
376C2×D8—111no—
377C2×M16—111no—
378C2×M16—111no—
379C2×M16—221no—
380C2×M16—221no—
381C2×M16—221no—
382C2×M16—221no—
383C2×M16—221no—
384C22×C8—21no—
385C22×C8—221no—
386C4×Q8—111no—
387C4×Q8C22×D1111yescharacteristic
388C4×D4—111no—
389C4×D4—111no—
390C4×D4—111no—
391C4×D4—111no—
392C4×D4—111no—
393C4×D4—221no—
394C4×D4—221no—
395C4×D4—221no—
396C4×D4—221no—
397C4×D4C22×D1111yescharacteristic
398#117—111no—
399#117—221no—
400C2×C4⋊C4—111no—
401C2×C22⋊C4—221no—
402C2×C42—111no—
403C2×C42—221no—
404#107—111no—
405#107—111no—
406#106—111no—
407#106C4×D1111yescharacteristic
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#103C4×D1111yescharacteristic
420#102—111no—
421#102—111no—
422#102—111no—
423#102—111no—
424#102—111no—
425#102C4×D1111yescharacteristic
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—
439C4×C8—21no—
440C4×C8—111no—
441C4×C8—111no—
442C4×C8—111no—
443C4×C8—221no—
444C4×C8C22×D1111yescharacteristic
445C4×C8C22×D1111yescharacteristic
446C4×C8C22×D1111yescharacteristic
447C2×C11—42no—
448C2×C11D4×M1611yescharacteristic
449C2×C11#294611yescharacteristic
450C2×C11#295511yescharacteristic
451D11—41no—
452D11—81no—
453D11—81no—
454C24—221no—
455#41—222no—
456#41—441no—
457C2×Q8C2×C4×D1111yescharacteristic
458C2×D4—111no—
459C2×D4—111no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—222no—
463C2×D4—441no—
464C2×D4C2×C4×D1111yescharacteristic
465C22×C4—21no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—881no—
477C22×C4—881no—
478SD16—222no—
479SD16#431314yescomplemented
480D8—222no—
481D8—222no—
482M16—222no—
483M16—441no—
484M16—881no—
485M16—881no—
486M16—881no—
487M16—881no—
488M16—881no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—81no—
493C2×C8—111no—
494C2×C8—111no—
495C2×C8—111no—
496C2×C8—111no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—881no—
501C2×C8C2×C4×D1111yescharacteristic
502C2×C8C2×C4×D1111yescharacteristic
503C2×C8D4×D1111yescharacteristic
504C2×C8D4×D1111yescharacteristic
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—221no—
514C22⋊C4—221no—
515C22⋊C4—221no—
516C22⋊C4—221no—
517C22⋊C4—221no—
518C22⋊C4—221no—
519C42—21no—
520C42—111no—
521C42—111no—
522C42—111no—
523C42—221no—
524C42—221no—
525C42C23×D1111yescharacteristic
526C11#1805211yescharacteristic, complemented, Sylow
527C23—21no—
528C23—111no—
529C23—221no—
530C23—221no—
531C23—442no—
532C23—442no—
533C23—881no—
534Q8—21no—
535Q8C2×#431312yes—
536D4—21no—
537D4—221no—
538D4—221no—
539D4—221no—
540D4—221no—
541D4—442no—
542D4—442no—
543D4C2×#431312yes—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—111no—
550C2×C4—111no—
551C2×C4—111no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—441no—
559C2×C4—442no—
560C2×C4—442no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—881no—
566C2×C4—881no—
567C2×C4—881no—
568C2×C4C22×C4×D1111yescharacteristic
569C2×C4C2×D4×D1111yescharacteristic
570C2×C4#41×D1111yescharacteristic
571C8—21no—
572C8—21no—
573C8—21no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—221no—
578C8—221no—
579C8—221no—
580C8—221no—
581C8—441no—
582C8—441no—
583C8—441no—
584C8C2×#431312yes—
585C22—22no—
586C22—41no—
587C22—41no—
588C22—221no—
589C22—221no—
590C22—221no—
591C22—441no—
592C22—441no—
593C22—441no—
594C22—441no—
595C22—441no—
596C22—441no—
597C22—884no—
598C22C4×D4×D1111yescharacteristic
599C4—21no—
600C4—22no—
601C4—41no—
602C4—41no—
603C4—221no—
604C4—221no—
605C4—221no—
606C4—441no—
607C4—441no—
608C4C22×#431311yescharacteristic
609C4#1062328111yescharacteristic
610C4#1062330511yescharacteristic
611C4#1062330911yescharacteristic
612C2—42no—
613C2—441no—
614C2—881no—
615C2—881no—
616C2D4×#431311yescharacteristic
617C2#1307744711yescharacteristic
618C2#1307751611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×SD16⋊C8C2
socleC22×C11C2×C4×D4
prime radicalC2×#66967C4
cosocleC42×C11C24
hypercenterSD16⋊C8D11
hypocenterC11#18052
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
1. #13077747C2semidirect
2. #13077649C2semidirect
4. #13067531C2semidirect
5. #13067500C2semidirect
6. #13067491C2semidirect
7. #13067477C2semidirect
8. #13067459C2semidirect
9. #13067445C2semidirect
10. SD16×C11⋊C8C2semidirect
11. #13067382C2semidirect
12. #13067049C2semidirect
13. #13067039C2semidirect
14. #13066914C2semidirect
15. C11×SD16⋊C8C2semidirect
19. C8×Q8×C11C22semidirect
26. Q8×C11⋊C8C22semidirect
33. #10622451C22semidirect
46. #10622301C22semidirect
51. C11×#335C22semidirect
52. C11×Q8⋊C8C22semidirect
54. C11×#322C22semidirect
55. Q8⋊(C11⋊C8)C22semidirect
58. #10622121C22semidirect
59. #10622118C22semidirect
60. #10622117C22semidirect
62. #10622097C22semidirect
63. #10622095C22semidirect
64. #10622093C22semidirect
65. #10622093C22semidirect
66. C8×C11⋊C8C22semidirect
170. C11×SD16M16semidirect
227. SD16⋊C8D11semidirect
295. C8×Q8C2×D11semidirect
327. #335C2×D11semidirect
331. Q8⋊C8C2×D11semidirect
340. #322C2×D11semidirect
479. SD16#4313semidirect
526. C11#18052semidirect

Maximal subgroups

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

subgroupindex
#130777472
#130776492
C4×#669672
#130675312
#130675002
#130674912
#130674772
#130674592
#130674452
SD16×C11⋊C82
#130673822
#130670492
#130670392
#130669142
C11×SD16⋊C82
#1805211