Finite Group Databasebeta

← #14725244

Subgroups — #14725244

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#4313C211yesmaximal, characteristic, complemented
2C4×SD16×D11C211yesmaximal, characteristic
3D4×#4313C211yesmaximal, characteristic
4#13067520C211yesmaximal, characteristic, complemented
5#13067517C211yesmaximal, characteristic, complemented
6#13067494C211yesmaximal, characteristic, complemented
7#13067491C211yesmaximal, characteristic, complemented
8#13067473C211yesmaximal, characteristic, complemented
9#13067470C211yesmaximal, characteristic, complemented
10SD16⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11#13067373C211yesmaximal, characteristic, complemented
12#13067043C211yesmaximal, characteristic, complemented
13#13067039C211yesmaximal, characteristic
14#13066902C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×SD16×D11C411yescharacteristic
17C22×#4313—21no—
18C4×Q8×D11C2211yescharacteristic
19C4×D4×D11C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic, complemented
21C4×C11×SD16C2211yescharacteristic
22C8×D4×C11C2211yescharacteristic
23SD16×Dic11C411yescharacteristic
24#10622724—21no—
25C4×#4325C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic, complemented
27C4×#4324C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29D11×#106C411yescharacteristic
30#10622465C411yescharacteristic
31#10622451C2211yescharacteristic
32#10622450—21no—
33#10622450C2211yescharacteristic
34#10622450C2211yescharacteristic
35#10622444—21no—
36#10622444C2211yescharacteristic, complemented
37D11×#103C411yescharacteristic
38#10622401C411yescharacteristic
39D11×#102C411yescharacteristic
40#10622371C411yescharacteristic
41#10622343—21no—
42#10622339—21no—
43C4×#4314C2211yescharacteristic
44#10622301C2211yescharacteristic
45C4×#4313—21no—
46C4×#4313C2211yescharacteristic
47#10622298C2211yescharacteristic
48C4×C8×D11C2211yescharacteristic
49#10622292—21no—
50#10622292C2211yescharacteristic, complemented
51C11×#335C2211yescharacteristic, complemented
52C11×Q8⋊C8C2211yescharacteristic, complemented
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic, complemented
55Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic, complemented
58#10622121C2211yescharacteristic
59#10622117C2211yescharacteristic, complemented
60#10622117C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic
62#10622096C2211yescharacteristic, complemented
63#10622094C2211yescharacteristic, complemented
64#10622093C2211yescharacteristic, complemented
65#10622093C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C2×Q8×D11C2×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×#4324C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C22×C11⋊C8—21no—
80SD16×D11—24no—
81C2×#4314C2×C411yescharacteristic
82C2×#4313—21no—
83C2×#4313—21no—
84C2×#4313—21no—
85C2×#4313—21no—
86C2×#4313—44no—
87C2×#4313D411yescharacteristic
88C2×#4313D411yescharacteristic
89C2×C8×D11C2×C411yescharacteristic
90C2×C8×D11C2×C411yescharacteristic
91#66946C2×C411yescharacteristic
92C4⋊C4×D11—21no—
93C4⋊C4×D11C2×C411yescharacteristic
94C4⋊C4×D11C2×C411yescharacteristic
95#66940—21no—
96#66940C2×C411yescharacteristic
97(C22⋊D11)⋊C4—21no—
98C22⋊C4×D11—21no—
99C4×D44C2311yescharacteristic
100C42×D11—21no—
101C42×D11C2311yescharacteristic
102C4×Dic22—21no—
103C4×Dic22C2311yescharacteristic
104C11×#106C2×C411yescharacteristic
105C11×C4⋊C8—21no—
106C11×C4⋊C8C2311yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×#103C2×C411yescharacteristic
109C11×#102C2×C411yescharacteristic
110C11×C22⋊C8—21no—
111C4×C8×C11—21no—
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115#66899C2×C411yescharacteristic
116#66896C2×C411yescharacteristic
117C22⋊(C11⋊C8)—21no—
118#66885C2×C411yescharacteristic
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122#66881C2×C411yescharacteristic
123#66880C2×C411yescharacteristic
124#66879—21no—
125#66879—21no—
126#66879D411yescharacteristic
127#66879D411yescharacteristic
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133C8×Dic11C2×C411yescharacteristic
134C8×Dic11C2×C411yescharacteristic
135#66874C2×C411yescharacteristic
136#66873C2×C411yescharacteristic
137#66872C2×C411yescharacteristic
138#66872C2×C411yescharacteristic
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8—21no—
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#18040—111nomaximal, Sylow
147C23×D11—21no—
148C2×Q8×C11C22×C411yescharacteristic
149C2×D4×C11C22×C411yescharacteristic
150C22×C4×C11—21no—
151C2×C22⋊D11—21no—
152C22×Dic11—21no—
153Q8×D11—22no—
154Q8×D11—41no—
155D4×D11—22no—
156D4×D11—41no—
157C2×D44C22×C411yescharacteristic
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11C22×C411yescharacteristic
166C2×C4×D11C2×D411yescharacteristic
167C2×C4×D11#4111yescharacteristic
168C2×Dic22—21no—
169C2×Dic22C22×C411yescharacteristic
170C11×SD16M1614yescomplemented
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—42no—
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#4324—22no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11C22×C411yescharacteristic
192C4⋊Dic11C22×C411yescharacteristic
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11C22×C411yescharacteristic
201C4×Dic11C2×D411yescharacteristic
202C4×Dic11#4111yescharacteristic
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—42no—
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211#4314—22no—
212#4313—22no—
213#4313—22no—
214#4313—42no—
215#4313—42no—
216#4313—42no—
217#4313—42no—
218C8×D11—22no—
219C8×D11—41no—
220Q8×M16—111no—
221C2×C4×SD16—111no—
222D4×M16—111no—
223#1592—111no—
224#1592—111no—
225#1588—111no—
226#1588—111no—
227#1585—111no—
228#1585—111no—
229SD16⋊C8—111no—
230SD16⋊C8D1111yescharacteristic, complemented
231#1567—111no—
232#1487—111no—
233#1486—111no—
234#1451—111no—
235C23×C11—21no—
236C22×D11—21no—
237C22×D11—42no—
238C22×D11—42no—
239C22×D11—81no—
240C22×D11C4×D411yescharacteristic
241Q8×C11—21no—
242Q8×C11C2×M1612yescomplemented
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—42no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—42no—
258C2×Dic11C4×D411yescharacteristic
259C2×Dic11C4×D411yescharacteristic
260C2×Dic11C4×D411yescharacteristic
261D44—21no—
262D44—21no—
263C4×D11—21no—
264C4×D11—21no—
265C4×D11—41no—
266C4×D11—42no—
267C4×D11—42no—
268C4×D11—41no—
269C4×D11—41no—
270C4×D11—42no—
271C4×D11—81no—
272C4×D11AGL(1,ℤ/8)12yes—
273C4×D11#13712yes—
274Dic22—21no—
275Dic22—21no—
276Dic22—42no—
277C8×C11—21no—
278C8×C11—21no—
279C8×C11—21no—
280C8×C11—41no—
281C8×C11—41no—
282C8×C11—41no—
283C8×C11C2×M1612yescomplemented
284C11⋊C8—21no—
285C11⋊C8—21no—
286C11⋊C8—21no—
287C11⋊C8—21no—
288C11⋊C8—41no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C22×SD16—111no—
292C22×M16—221no—
293C2×C4×Q8—111no—
294C2×C4×D4—111no—
295#446—111no—
296#446—111no—
297#446—221no—
298#446—221no—
299C8×Q8—111no—
300C8×Q8C2×D1111yescharacteristic, complemented
301C4×SD16—111no—
302C4×SD16—111no—
303C4×SD16—111no—
304C4×SD16—111no—
305C4×SD16—111no—
306C4×SD16—111no—
307C4×SD16—111no—
308C4×SD16C2×D1111yescharacteristic
309#436—111no—
310#436—111no—
311#435—221no—
312#435—221no—
313C8×D4—111no—
314C8×D4C2×D1111yescharacteristic
315#431—111no—
316C2×#106—111no—
317#423—111no—
318#423—111no—
319#423—221no—
320C2×#103—111no—
321C2×#102—111no—
322#407—221no—
323C4×M16—111no—
324C4×M16—221no—
325C2×C4×C8—111no—
326#335—111no—
327#335—111no—
328#335—111no—
329#335C2×D1111yescharacteristic, complemented
330Q8⋊C8—111no—
331Q8⋊C8—111no—
332Q8⋊C8—111no—
333Q8⋊C8C2×D1111yescharacteristic, complemented
334D4⋊C8—111no—
335D4⋊C8—111no—
336D4⋊C8—111no—
337D4⋊C8C2×D1111yescharacteristic
338#322—111no—
339#322—111no—
340#322—111no—
341#322C2×D1111yescharacteristic, complemented
342C22×C11—22no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11C2×C4×D411yescharacteristic
346C2×D11—21no—
347C2×D11—21no—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—84no—
352C2×D11#44012yes—
353C4×C11—22no—
354C4×C11—21no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11C22×M1611yescharacteristic
358C4×C11#56811yescharacteristic
359C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
360C4×C11C2×#13711yescharacteristic
361Dic11—21no—
362Dic11—21no—
363Dic11—41no—
364Dic11—41no—
365Dic11—41no—
366Dic11#44012yes—
367C22×Q8—111no—
368C22×D4—111no—
369C23×C4—221no—
370C2×SD16—111no—
371C2×SD16—111no—
372C2×SD16—111no—
373C2×SD16—224no—
374C2×SD16C4×D1111yescharacteristic
375C2×M16—111no—
376C2×M16—111no—
377C2×M16—221no—
378C2×M16—221no—
379C2×M16—221no—
380C2×M16—221no—
381C2×M16—444no—
382C22×C8—21no—
383C22×C8—111no—
384C22×C8—111no—
385C22×C8—221no—
386C4×Q8—111no—
387C4×Q8—111no—
388C4×Q8—111no—
389C4×Q8—221no—
390C4×Q8—221no—
391C4×Q8C22×D1111yescharacteristic
392C4×D4—111no—
393C4×D4—111no—
394C4×D4—111no—
395C4×D4—221no—
396C4×D4—221no—
397C4×D4C22×D1111yescharacteristic
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C42—111no—
403C2×C42—221no—
404#106—111no—
405#106—111no—
406#106—111no—
407#106C4×D1111yescharacteristic
408C4⋊C8—21no—
409C4⋊C8—111no—
410C4⋊C8—111no—
411C4⋊C8—221no—
412C4⋊C8—221no—
413C4⋊C8—221no—
414C4⋊C8—221no—
415C4⋊C8—221no—
416C4⋊C8—221no—
417C4⋊C8C22×D1111yescharacteristic
418C4⋊C8C22×D1111yescharacteristic
419#103—111no—
420#103—111no—
421#103—111no—
422#103C4×D1111yescharacteristic
423#102—111no—
424#102—111no—
425#102—111no—
426#102C4×D1111yescharacteristic
427C22⋊C8—21no—
428C22⋊C8—221no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431C22⋊C8—221no—
432#97—111no—
433#97—111no—
434#97—221no—
435#97—221no—
436C4×C8—21no—
437C4×C8—111no—
438C4×C8—111no—
439C4×C8—111no—
440C4×C8—111no—
441C4×C8—111no—
442C4×C8—221no—
443C4×C8C22×D1111yescharacteristic
444C4×C8C22×D1111yescharacteristic
445C4×C8C22×D1111yescharacteristic
446C2×C11—42no—
447C2×C11D4×M1611yescharacteristic
448C2×C11C2×#44011yescharacteristic
449C2×C11#295711yescharacteristic
450D11—22no—
451D11—81no—
452C24—221no—
453C2×Q8—111no—
454C2×Q8—221no—
455C2×Q8—222no—
456C2×Q8—441no—
457C2×Q8C2×C4×D1111yescharacteristic
458C2×D4—111no—
459C2×D4—221no—
460C2×D4—222no—
461C2×D4—441no—
462C2×D4C2×C4×D1111yescharacteristic
463C22×C4—21no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—442no—
474C22×C4—442no—
475SD16—222no—
476SD16—222no—
477SD16—222no—
478SD16#431314yescomplemented
479M16—222no—
480M16—222no—
481M16—442no—
482M16—442no—
483M16—442no—
484M16—442no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—42no—
489C2×C8—111no—
490C2×C8—111no—
491C2×C8—111no—
492C2×C8—111no—
493C2×C8—222no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—441no—
498C2×C8—442no—
499C2×C8C2×C4×D1111yescharacteristic
500C2×C8C2×C4×D1111yescharacteristic
501C2×C8D4×D1111yescharacteristic
502C2×C8D4×D1111yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—111no—
505C4⋊C4—111no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4C2×C4×D1111yescharacteristic
512C4⋊C4C2×C4×D1111yescharacteristic
513C22⋊C4—21no—
514C22⋊C4—221no—
515C22⋊C4—221no—
516C22⋊C4—221no—
517C42—21no—
518C42—111no—
519C42—111no—
520C42—111no—
521C42—221no—
522C42—221no—
523C42—221no—
524C42C23×D1111yescharacteristic
525C11#1804011yescharacteristic, complemented, Sylow
526C23—21no—
527C23—111no—
528C23—221no—
529C23—442no—
530C23—442no—
531C23—881no—
532Q8—21no—
533Q8—221no—
534Q8—221no—
535Q8—442no—
536Q8C2×#431312yescomplemented
537D4—21no—
538D4—221no—
539D4—221no—
540D4—442no—
541D4C2×#431312yes—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—111no—
548C2×C4—112no—
549C2×C4—112no—
550C2×C4—111no—
551C2×C4—111no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—441no—
558C2×C4—442no—
559C2×C4—442no—
560C2×C4—442no—
561C2×C4—442no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—881no—
565C2×C4C22×C4×D1111yescharacteristic
566C2×C4C2×D4×D1111yescharacteristic
567C2×C4#41×D1111yescharacteristic
568C8—21no—
569C8—21no—
570C8—21no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—221no—
575C8—221no—
576C8—221no—
577C8—221no—
578C8—441no—
579C8—441no—
580C8—441no—
581C8C2×#431312yescomplemented
582C22—22no—
583C22—41no—
584C22—41no—
585C22—112no—
586C22—221no—
587C22—221no—
588C22—441no—
589C22—441no—
590C22—441no—
591C22—884no—
592C22C4×D4×D1111yescharacteristic
593C4—21no—
594C4—22no—
595C4—41no—
596C4—41no—
597C4—112no—
598C4—221no—
599C4—221no—
600C4—441no—
601C4—441no—
602C4—441no—
603C4C22×#431311yescharacteristic
604C4#1062328111yescharacteristic
605C4D11×AGL(1,ℤ/8)11yescharacteristic
606C4D11×#13711yescharacteristic
607C2—42no—
608C2—222no—
609C2—881no—
610C2D4×#431311yescharacteristic
611C2D11×#44011yescharacteristic
612C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×SD16⋊C8C2
socleC22×C11C2×C4×D4
prime radicalC2×D4×D11C2×C4
cosocleC42×C11C24
hypercenterSD16⋊C8D11
hypocenterC11#18040
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. Q8×#4313C2semidirect
4. #13067520C2semidirect
5. #13067517C2semidirect
6. #13067494C2semidirect
7. #13067491C2semidirect
8. #13067473C2semidirect
9. #13067470C2semidirect
10. SD16⋊(C11⋊C8)C2semidirect
11. #13067373C2semidirect
12. #13067043C2semidirect
14. #13066902C2semidirect
15. C11×SD16⋊C8C2semidirect
20. C8×Q8×C11C22semidirect
26. Q8×C11⋊C8C22semidirect
36. #10622444C22semidirect
50. #10622292C22semidirect
51. C11×#335C22semidirect
52. C11×Q8⋊C8C22semidirect
54. C11×#322C22semidirect
55. Q8⋊(C11⋊C8)C22semidirect
57. #10622122C22semidirect
59. #10622117C22semidirect
60. #10622117C22semidirect
62. #10622096C22semidirect
63. #10622094C22semidirect
64. #10622093C22semidirect
65. #10622093C22semidirect
66. #10622092C22semidirect
170. C11×SD16M16semidirect
230. SD16⋊C8D11semidirect
242. Q8×C11C2×M16semidirect
283. C8×C11C2×M16semidirect
300. C8×Q8C2×D11semidirect
329. #335C2×D11semidirect
333. Q8⋊C8C2×D11semidirect
341. #322C2×D11semidirect
478. SD16#4313semidirect
525. C11#18040semidirect
536. Q8C2×#4313semidirect
581. C8C2×#4313semidirect

Maximal subgroups

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

subgroupindex
Q8×#43132
C4×SD16×D112
D4×#43132
#130675202
#130675172
#130674942
#130674912
#130674732
#130674702
SD16⋊(C11⋊C8)2
#130673732
#130670432
#130670392
#130669022
C11×SD16⋊C82
#1804011