Finite Group Databasebeta

← #14723488

Subgroups — #14723488

Order 2816.

660 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077732C211yesmaximal, characteristic, complemented
2#13077726C211yesmaximal, characteristic, complemented
3C4×#66972C211yesmaximal, characteristic
4#13067488C211yesmaximal, characteristic, complemented
5#13067482C211yesmaximal, characteristic, complemented
6#13067479C211yesmaximal, characteristic, complemented
7#13067459C211yesmaximal, characteristic, complemented
8#13067456C211yesmaximal, characteristic, complemented
9#13067455C211yesmaximal, characteristic, complemented
10#13067450C211yesmaximal, characteristic, complemented
11D11×#334C211yesmaximal, characteristic, complemented
12#13067002C211yesmaximal, characteristic, complemented
13#13067002C211yesmaximal, characteristic, complemented
14#13066907C211yesmaximal, characteristic, complemented
15C11×#1587C211yesmaximal, characteristic, complemented
16C2×#66972C411yescharacteristic
17C4×#4343C2211yescharacteristic
18C4×#4343C2211yescharacteristic
19C11×#446C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic
22Q16×Dic11C411yescharacteristic
23C4×#4325C2211yescharacteristic
24C4×#4325C2211yescharacteristic
25#10622637C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27#10622493C411yescharacteristic
28#10622485C411yescharacteristic
29#10622451C2211yescharacteristic
30#10622450—21no—
31#10622449—21no—
32#10622447—21no—
33#10622447C2211yescharacteristic
34D11×C4⋊C8—21no—
35D11×C4⋊C8C2211yescharacteristic
36D11×C4⋊C8C2211yescharacteristic
37#10622417C411yescharacteristic
38#10622417C411yescharacteristic
39#10622401C411yescharacteristic
40#10622401C411yescharacteristic
41#10622319—21no—
42#10622318—21no—
43C4×D88C2211yescharacteristic
44#10622301C2211yescharacteristic
45C8×D44—21no—
46C8×D44C2211yescharacteristic
47#10622298—21no—
48#10622298C2211yescharacteristic
49#10622298C2211yescharacteristic
50C4×C8×D11C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic
63#10622095C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×#4343C2×C411yescharacteristic
68C2×#4343C2×C411yescharacteristic
69C2×C11×Q16C2×C411yescharacteristic
70C4×Q8×C11C2311yescharacteristic
71C4×Q8×C11C2311yescharacteristic
72Q8×Dic11C2×C411yescharacteristic
73Q8×Dic11C2×C411yescharacteristic
74C2×#4325C2×C411yescharacteristic
75C2×#4325C2×C411yescharacteristic
76#66972—24no—
77C2×D88C2×C411yescharacteristic
78C2×#4313—21no—
79C2×#4313—21no—
80C2×C8×D11—21no—
81C2×C8×D11—21no—
82C2×C8×D11—21no—
83C2×C8×D11—21no—
84C2×C8×D11C2×C411yescharacteristic
85C2×C8×D11C2×C411yescharacteristic
86#66946—21no—
87#66946—21no—
88#66946C2×C411yescharacteristic
89#66946C2×C411yescharacteristic
90#66945—21no—
91#66945—21no—
92#66945C2×C411yescharacteristic
93#66945C2×C411yescharacteristic
94C4×D44—21no—
95C4×D44—21no—
96C4×D44C2311yescharacteristic
97C4×D44C2311yescharacteristic
98C42×D11—21no—
99C42×D11—21no—
100C42×D11C2311yescharacteristic
101C11×#107C2×C411yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×#103C2×C411yescharacteristic
107C11×#103C2×C411yescharacteristic
108C11×#97—21no—
109C4×C8×C11—21no—
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113#66899C2×C411yescharacteristic
114#66899C2×C411yescharacteristic
115#66885C2×C411yescharacteristic
116#66885C2×C411yescharacteristic
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8D411yescharacteristic
123(C2×D11)⋊C8D411yescharacteristic
124#66882C2×C411yescharacteristic
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8D411yescharacteristic
129Dic11⋊C8D411yescharacteristic
130C8×Dic11C2×C411yescharacteristic
131C8×Dic11C2×C411yescharacteristic
132#66873C2×C411yescharacteristic
133#66873C2×C411yescharacteristic
134#66872C2×C411yescharacteristic
135#66872C2×C411yescharacteristic
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140#66867—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#17882—111nomaximal, Sylow
146C2×Q8×C11C22×C411yescharacteristic
147C2×Q8×C11C22×C411yescharacteristic
148#4343—22no—
149#4343—22no—
150#4343—22no—
151#4343M1614yescomplemented
152C2×D44—21no—
153C2×D44—21no—
154C2×D44C22×C411yescharacteristic
155C2×D44C22×C411yescharacteristic
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11C22×C411yescharacteristic
163C2×C4×D11C2×D411yescharacteristic
164C2×C4×D11#4111yescharacteristic
165C11×Q16—22no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11C22×C411yescharacteristic
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C22×C411yescharacteristic
176C11×C4⋊C4C22×C411yescharacteristic
177C42×C11—21no—
178C42×C11—21no—
179C42×C11C2411yescharacteristic
180#4325—22no—
181#4325—22no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11C22×C411yescharacteristic
191C4⋊Dic11C22×C411yescharacteristic
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11C22×C411yescharacteristic
197C4×Dic11C2×D411yescharacteristic
198C4×Dic11#4111yescharacteristic
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206D88—22no—
207#4313—81no—
208#4313—81no—
209C8×D11—22no—
210C8×D11—22no—
211C8×D11—81no—
212C8×D11—81no—
213C8×D11—81no—
214C8×D11—81no—
215#2989—111no—
216#2988—111no—
217C4×#135—111no—
218#1587—111no—
219#1587D1111yescharacteristic, complemented
220#1586—111no—
221#1586—111no—
222#1583—111no—
223#1583—111no—
224#1582—111no—
225#1582—111no—
226C2×#334—111no—
227#1477—111no—
228#1477—111no—
229#1452—111no—
230C22×D11—21no—
231C22×D11—21no—
232C22×D11C4×D411yescharacteristic
233Q8×C11—21no—
234Q8×C11—21no—
235Q8×C11—21no—
236Q8×C11C2×M1612yes—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11C4×D411yescharacteristic
247C2×Dic11C4×D411yescharacteristic
248C2×Dic11C4×D411yescharacteristic
249D44—24no—
250D44—21no—
251D44—21no—
252D44—21no—
253D44—42no—
254D44C2×M1612yes—
255C4×D11—21no—
256C4×D11—21no—
257C4×D11—24no—
258C4×D11—41no—
259C4×D11—41no—
260C4×D11—41no—
261C4×D11—41no—
262C4×D11—41no—
263C4×D11—42no—
264C4×D11—81no—
265C4×D11—81no—
266C4×D11C2×M1612yes—
267C4×D11#13112yes—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—41no—
273C8×C11—41no—
274C8×C11—41no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C2×#135—111no—
283C4×#41—111no—
284C4×#41—111no—
285#446—111no—
286#446C2×D1111yescharacteristic
287C8×Q8—111no—
288C8×Q8C2×D1111yescharacteristic
289C4×Q16—111no—
290C4×Q16C2×D1111yescharacteristic
291C4×SD16—111no—
292C4×SD16—111no—
293C4×SD16—111no—
294C4×SD16—111no—
295C4×D8—111no—
296C4×D8—111no—
297#436—111no—
298#436—111no—
299#435—221no—
300#435—221no—
301C8×D4—111no—
302C8×D4—111no—
303C8×D4—221no—
304C8×D4—221no—
305#432—221no—
306#431—111no—
307#431—111no—
308#431—221no—
309#427—111no—
310#423—221no—
311C2×C4⋊C8—111no—
312C2×C4⋊C8—111no—
313C2×C4⋊C8—221no—
314#416—111no—
315#416—111no—
316C2×C4×C8—111no—
317#334—111no—
318#334—111no—
319#334—111no—
320#334C2×D1111yescharacteristic
321Q8⋊C8—111no—
322Q8⋊C8—111no—
323Q8⋊C8C2×D1111yescharacteristic
324Q8⋊C8C2×D1111yescharacteristic
325D4⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329#322—111no—
330#322—111no—
331#322—111no—
332#322C2×D1111yescharacteristic
333C22×C11C2×C4×D411yescharacteristic
334C2×D11—21no—
335C2×D11—21no—
336C2×D11—22no—
337C2×D11—41no—
338C2×D11—41no—
339C2×D11—41no—
340C2×D11—41no—
341C2×D11—41no—
342C2×D11#43512yes—
343C4×C11—22no—
344C4×C11—21no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11C22×M1611yescharacteristic
349C4×C11C2×#13111yescharacteristic
350C4×C11#57711yescharacteristic
351C4×C11#57711yescharacteristic
352Dic11—21no—
353Dic11—21no—
354Dic11—41no—
355Dic11—41no—
356Dic11#43512yes—
357C2×#41—111no—
358C2×#41—111no—
359#135—224no—
360C2×Q16C4×D1111yescharacteristic
361C2×SD16—111no—
362C2×SD16—111no—
363C2×D8—111no—
364C2×M16—221no—
365C2×M16—221no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8—221no—
369C22×C8—221no—
370C22×C8—221no—
371C22×C8—221no—
372C4×Q8—111no—
373C4×Q8—111no—
374C4×Q8C22×D1111yescharacteristic
375C4×Q8C22×D1111yescharacteristic
376C4×D4—111no—
377C4×D4—111no—
378C4×D4—111no—
379C4×D4—111no—
380C4×D4—221no—
381C4×D4—221no—
382C4×D4—221no—
383C4×D4—221no—
384#117—111no—
385#117—111no—
386#117—221no—
387#117—221no—
388C2×C42—111no—
389C2×C42—221no—
390C2×C42—221no—
391#107—111no—
392#107C4×D1111yescharacteristic
393#106—111no—
394#106—111no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—221no—
402C4⋊C8—221no—
403C4⋊C8—221no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406C4⋊C8C22×D1111yescharacteristic
407C4⋊C8C22×D1111yescharacteristic
408#103—111no—
409#103—111no—
410#103C4×D1111yescharacteristic
411#103C4×D1111yescharacteristic
412#102—111no—
413#102—111no—
414#102—111no—
415#102—111no—
416C22⋊C8—111no—
417C22⋊C8—111no—
418C22⋊C8—221no—
419C22⋊C8—221no—
420C22⋊C8—221no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423#97—21no—
424#97—221no—
425C4×C8—21no—
426C4×C8—111no—
427C4×C8—111no—
428C4×C8—111no—
429C4×C8—111no—
430C4×C8—111no—
431C4×C8—221no—
432C4×C8C22×D1111yescharacteristic
433C4×C8C22×D1111yescharacteristic
434C4×C8C22×D1111yescharacteristic
435C2×C11C2×#43511yescharacteristic
436C2×C11#295211yescharacteristic
437C2×C11#295711yescharacteristic
438D11—22no—
439D11—42no—
440D11—81no—
441#41—114no—
442#41—222no—
443#41—222no—
444#41—222no—
445C2×Q8C2×C4×D1111yescharacteristic
446C2×Q8C2×C4×D1111yescharacteristic
447C2×D4—111no—
448C2×D4—111no—
449C2×D4—221no—
450C2×D4—221no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460Q16—22no—
461SD16—222no—
462SD16—222no—
463D8—222no—
464M16—881no—
465M16—881no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—111no—
470C2×C8—111no—
471C2×C8—111no—
472C2×C8—111no—
473C2×C8—222no—
474C2×C8—222no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—881no—
479C2×C8—881no—
480C2×C8—881no—
481C2×C8—881no—
482C2×C8C2×C4×D1111yescharacteristic
483C2×C8C2×C4×D1111yescharacteristic
484C2×C8D4×D1111yescharacteristic
485C2×C8D4×D1111yescharacteristic
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—111no—
489C4⋊C4—111no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4C2×C4×D1111yescharacteristic
493C4⋊C4C2×C4×D1111yescharacteristic
494C22⋊C4—221no—
495C22⋊C4—221no—
496C22⋊C4—221no—
497C22⋊C4—221no—
498C22⋊C4—221no—
499C22⋊C4—221no—
500C42—21no—
501C42—21no—
502C42—111no—
503C42—111no—
504C42—111no—
505C42—221no—
506C42—221no—
507C42—221no—
508C42—221no—
509C42C23×D1111yescharacteristic
510C11#1788211yescharacteristic, complemented, Sylow
511C23—111no—
512C23—221no—
513C23—221no—
514Q8—21no—
515Q8—21no—
516Q8—21no—
517Q8M16×D1112yes—
518D4—112no—
519D4—224no—
520D4—221no—
521D4—221no—
522D4—221no—
523D4—442no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—111no—
529C2×C4—112no—
530C2×C4—112no—
531C2×C4—111no—
532C2×C4—111no—
533C2×C4—224no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—441no—
539C2×C4—442no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—881no—
545C2×C4—881no—
546C2×C4C22×C4×D1111yescharacteristic
547C2×C4C2×D4×D1111yescharacteristic
548C2×C4#41×D1111yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—221no—
557C8—221no—
558C8—221no—
559C8—221no—
560C8—441no—
561C8—441no—
562C8—441no—
563C22—112no—
564C22—221no—
565C22—221no—
566C22—222no—
567C22—441no—
568C22—441no—
569C22—441no—
570C22—441no—
571C22—441no—
572C22C4×D4×D1111yescharacteristic
573C4—21no—
574C4—22no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—112no—
579C4—221no—
580C4—221no—
581C4—441no—
582C4—441no—
583C4C2×M16×D1111yescharacteristic
584C4D11×#13111yescharacteristic
585C4#1062330911yescharacteristic
586C4#1062330911yescharacteristic
587C2—222no—
588C2—442no—
589C2—881no—
590C2D11×#43511yescharacteristic
591C2#1307749611yescharacteristic
592C2#1307752811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1587C2
socleC22×C11C2×C4×D4
prime radicalC2×#66972C4
cosocleC42×C11C24
hypercenter#1587D11
hypocenterC11#17882
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
1. #13077732C2semidirect
2. #13077726C2semidirect
4. #13067488C2semidirect
5. #13067482C2semidirect
6. #13067479C2semidirect
7. #13067459C2semidirect
8. #13067456C2semidirect
9. #13067455C2semidirect
10. #13067450C2semidirect
11. D11×#334C2semidirect
12. #13067002C2semidirect
13. #13067002C2semidirect
14. #13066907C2semidirect
15. C11×#1587C2semidirect
151. #4343M16semidirect
219. #1587D11semidirect
510. C11#17882semidirect

Maximal subgroups

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

subgroupindex
#130777322
#130777262
C4×#669722
#130674882
#130674822
#130674792
#130674592
#130674562
#130674552
#130674502
D11×#3342
#130670022
#130669072
C11×#15872
#1788211