Finite Group Databasebeta

← #14725413

Subgroups — #14725413

Order 2816.

624 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077747C211yesmaximal, characteristic
2#13077704C211yesmaximal, characteristic, complemented
3C4×#66971C211yesmaximal, characteristic
4#13067520C211yesmaximal, characteristic, complemented
5#13067505C211yesmaximal, characteristic, complemented
6#13067491C211yesmaximal, characteristic, complemented
7#13067484C211yesmaximal, characteristic, complemented
8#13067466C211yesmaximal, characteristic, complemented
9#13067459C211yesmaximal, characteristic, complemented
10Q16×C11⋊C8C211yesmaximal, characteristic, complemented
11#13067380C211yesmaximal, characteristic, complemented
12#13067049C211yesmaximal, characteristic
13#13067043C211yesmaximal, characteristic, complemented
14#13066914C211yesmaximal, characteristic, complemented
15C11×#1579C211yesmaximal, characteristic, complemented
16C2×#66971C411yescharacteristic
17C4×#4343C2211yescharacteristic
18C4×Q8×D11C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic
22#10622797C411yescharacteristic
23C4×#4326C2211yescharacteristic
24C4×#4325C2211yescharacteristic
25Q8×C11⋊C8C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27#10622502C411yescharacteristic
28#10622494C411yescharacteristic
29#10622451—21no—
30#10622451C2211yescharacteristic
31#10622450—21no—
32#10622450C2211yescharacteristic
33#10622448—21no—
34#10622448C2211yescharacteristic
35#10622444—21no—
36#10622444C2211yescharacteristic
37#10622430C411yescharacteristic
38#10622416C411yescharacteristic
39#10622415C411yescharacteristic
40#10622402C411yescharacteristic
41C4×#4314C2211yescharacteristic
42#10622301—21no—
43#10622301C2211yescharacteristic
44C4×#4313C2211yescharacteristic
45#10622298—21no—
46#10622298—21no—
47#10622298C2211yescharacteristic
48#10622298C2211yescharacteristic
49#10622292—21no—
50#10622292C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622096C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622093C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4343C2×C411yescharacteristic
68C2×Q8×D11C2×C411yescharacteristic
69C2×C11×Q16C2×C411yescharacteristic
70C4×Q8×C11C2311yescharacteristic
71C4×Q8×C11C2311yescharacteristic
72Q8×Dic11C2×C411yescharacteristic
73Q8×Dic11C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75C2×#4325C2×C411yescharacteristic
76#66971—24no—
77C2×#4314C2×C411yescharacteristic
78C2×#4313—21no—
79C2×#4313—21no—
80C2×#4313—21no—
81C2×#4313C2×C411yescharacteristic
82C2×#4313C2×C411yescharacteristic
83#66946—21no—
84#66946C2×C411yescharacteristic
85#66945—21no—
86#66945C2×C411yescharacteristic
87C4⋊C4×D11—21no—
88C4⋊C4×D11C2×C411yescharacteristic
89#66940—21no—
90#66940C2×C411yescharacteristic
91C4×D44—21no—
92C4×D44C2311yescharacteristic
93C42×D11—21no—
94C42×D11—21no—
95C42×D11C2311yescharacteristic
96C4×Dic22—21no—
97C4×Dic22C2311yescharacteristic
98C11×#107C2×C411yescharacteristic
99C11×C4⋊C8—21no—
100C11×C4⋊C8—21no—
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×#103C2×C411yescharacteristic
104C11×#103C2×C411yescharacteristic
105C4×C8×C11—21no—
106C4×C8×C11—21no—
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110#66899C2×C411yescharacteristic
111#66899C2×C411yescharacteristic
112#66885C2×C411yescharacteristic
113(C2×D11)⋊C8—21no—
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8—21no—
117(C2×D11)⋊C8D411yescharacteristic
118(C2×D11)⋊C8D411yescharacteristic
119#66881C2×C411yescharacteristic
120#66880C2×C411yescharacteristic
121#66879—21no—
122#66879—21no—
123#66879—21no—
124#66879C2×C411yescharacteristic
125#66879C2×C411yescharacteristic
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8D411yescharacteristic
131Dic11⋊C8D411yescharacteristic
132#66874C2×C411yescharacteristic
133#66873C2×C411yescharacteristic
134#66872C2×C411yescharacteristic
135#66871C2×C411yescharacteristic
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18053—111nomaximal, Sylow
146C2×Q8×C11C22×C411yescharacteristic
147C2×Q8×C11C22×C411yescharacteristic
148#4343—22no—
149#4343—41no—
150Q8×D11—22no—
151Q8×D11—41no—
152C2×D44—21no—
153C2×D44C22×C411yescharacteristic
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11C22×C411yescharacteristic
160C2×C4×D11C2×D411yescharacteristic
161C2×C4×D11#4111yescharacteristic
162C2×Dic22—21no—
163C2×Dic22C22×C411yescharacteristic
164C11×Q16M1614yescomplemented
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11C22×C411yescharacteristic
169C2×C8×C11C22×C411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4C22×C411yescharacteristic
175C11×C4⋊C4C22×C411yescharacteristic
176C42×C11—21no—
177C42×C11—21no—
178C42×C11C2411yescharacteristic
179#4326—22no—
180#4325—22no—
181(C2×D11)⋊C4—21no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11C22×C411yescharacteristic
187C4⋊Dic11C22×C411yescharacteristic
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191C4×Dic11—21no—
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
206#4314—22no—
207#4313—22no—
208#4313—41no—
209#4313—81no—
210#4313—81no—
211#4313—81no—
212#2991—111no—
213#2984—111no—
214C4×#137—111no—
215#1592—111no—
216#1590—111no—
217#1588—111no—
218#1587—111no—
219#1584—111no—
220#1583—111no—
221#1579D1111yescharacteristic, complemented
222C8×Q16—111no—
223#1569—111no—
224#1488—111no—
225#1487—111no—
226#1453—111no—
227C22×D11—21no—
228C22×D11C4×D411yescharacteristic
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11C2×M1612yes—
232Q8×C11C2×M1612yes—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11C4×D411yescharacteristic
244C2×Dic11C4×D411yescharacteristic
245C2×Dic11C4×D411yescharacteristic
246D44—21no—
247D44—21no—
248D44—42no—
249C4×D11—21no—
250C4×D11—21no—
251C4×D11—21no—
252C4×D11—21no—
253C4×D11—41no—
254C4×D11—42no—
255C4×D11—42no—
256C4×D11—42no—
257C4×D11—42no—
258C4×D11—41no—
259C4×D11—41no—
260Dic22—21no—
261Dic22—21no—
262Dic22—42no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—41no—
267C8×C11—41no—
268C8×C11—41no—
269C8×C11C2×M1612yes—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C2×#137—111no—
278C4×#41—111no—
279C2×C4×Q8—111no—
280#446—111no—
281#446—111no—
282#446—221no—
283#446—221no—
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8C2×D1111yescharacteristic
287C8×Q8C2×D1111yescharacteristic
288#441—111no—
289#441—111no—
290#440—111no—
291#440—111no—
292C4×Q16—111no—
293C4×Q16C2×D1111yescharacteristic
294C4×SD16—111no—
295C4×SD16—111no—
296#436—111no—
297#436—111no—
298#436—221no—
299#436—221no—
300#432—111no—
301#432—221no—
302#431—111no—
303#431—111no—
304#431—221no—
305#431—221no—
306#428—111no—
307#423—111no—
308#423—221no—
309#419—111no—
310#417—111no—
311C4×M16—111no—
312#335—111no—
313#335—111no—
314#334—111no—
315#334C2×D1111yescharacteristic
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318Q8⋊C8—111no—
319Q8⋊C8—111no—
320Q8⋊C8C2×D1111yescharacteristic
321Q8⋊C8C2×D1111yescharacteristic
322D4⋊C8—111no—
323D4⋊C8—111no—
324#322—111no—
325#322—111no—
326#322C2×D1111yescharacteristic
327C82—111no—
328C22×C11C2×C4×D411yescharacteristic
329C2×D11—21no—
330C2×D11—21no—
331C2×D11—21no—
332C2×D11—41no—
333C2×D11—41no—
334C2×D11—41no—
335C4×C11—22no—
336C4×C11—22no—
337C4×C11—21no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11C22×M1611yescharacteristic
341C4×C11#56811yescharacteristic
342C4×C11#57711yescharacteristic
343C4×C11#57811yescharacteristic
344Dic11—21no—
345Dic11—21no—
346Dic11—21no—
347Dic11—41no—
348Dic11—41no—
349Dic11—41no—
350C2×#41—111no—
351C22×Q8—111no—
352#137—224no—
353C2×Q16—111no—
354C2×Q16C4×D1111yescharacteristic
355C2×SD16—111no—
356C2×SD16—111no—
357C2×M16—111no—
358C2×M16—111no—
359C2×M16—221no—
360C2×M16—221no—
361C2×M16—221no—
362C4×Q8—111no—
363C4×Q8—111no—
364C4×Q8—111no—
365C4×Q8—111no—
366C4×Q8—221no—
367C4×Q8—221no—
368C4×Q8C22×D1111yescharacteristic
369C4×Q8C22×D1111yescharacteristic
370C4×D4—111no—
371C4×D4—111no—
372C4×D4—221no—
373C4×D4—221no—
374#117—111no—
375#117—221no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—221no—
378C2×C42—111no—
379C2×C42—221no—
380C2×C42—221no—
381#107—111no—
382#107C4×D1111yescharacteristic
383#106—111no—
384#106—111no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8C22×D1111yescharacteristic
398C4⋊C8C22×D1111yescharacteristic
399#103—111no—
400#103—111no—
401#103—111no—
402#103—111no—
403#103C4×D1111yescharacteristic
404#103C4×D1111yescharacteristic
405#102—111no—
406#102—111no—
407C22⋊C8—111no—
408C22⋊C8—111no—
409C22⋊C8—221no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—111no—
414#97—111no—
415#97—221no—
416#97—221no—
417#97—221no—
418C4×C8—21no—
419C4×C8—21no—
420C4×C8—111no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—221no—
424C4×C8—221no—
425C4×C8C22×D1111yescharacteristic
426C4×C8C22×D1111yescharacteristic
427C4×C8C22×D1111yescharacteristic
428C2×C11D4×M1611yescharacteristic
429C2×C11#294711yescharacteristic
430C2×C11#295511yescharacteristic
431D11—41no—
432D11—81no—
433#41—222no—
434#41—441no—
435C2×Q8—111no—
436C2×Q8—221no—
437C2×Q8—222no—
438C2×Q8—441no—
439C2×Q8C2×C4×D1111yescharacteristic
440C2×Q8C2×C4×D1111yescharacteristic
441C2×D4—111no—
442C2×D4—221no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451Q16—222no—
452Q16#431314yescomplemented
453SD16—222no—
454SD16—222no—
455M16—222no—
456M16—441no—
457M16—881no—
458M16—881no—
459M16—881no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—111no—
464C2×C8—111no—
465C2×C8—111no—
466C2×C8—111no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8C2×C4×D1111yescharacteristic
471C2×C8C2×C4×D1111yescharacteristic
472C2×C8D4×D1111yescharacteristic
473C2×C8D4×D1111yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—111no—
477C4⋊C4—111no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4C2×C4×D1111yescharacteristic
484C4⋊C4C2×C4×D1111yescharacteristic
485C22⋊C4—221no—
486C22⋊C4—221no—
487C22⋊C4—221no—
488C42—21no—
489C42—21no—
490C42—111no—
491C42—111no—
492C42—111no—
493C42—221no—
494C42—221no—
495C42—221no—
496C42—221no—
497C42—221no—
498C42C23×D1111yescharacteristic
499C11#1805311yescharacteristic, complemented, Sylow
500C23—111no—
501C23—221no—
502Q8—21no—
503Q8—21no—
504Q8—221no—
505Q8—221no—
506Q8—442no—
507Q8C2×#431312yes—
508Q8C2×#431312yes—
509D4—221no—
510D4—221no—
511D4—442no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—111no—
517C2×C4—111no—
518C2×C4—111no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—441no—
527C2×C4—442no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4C22×C4×D1111yescharacteristic
534C2×C4C2×D4×D1111yescharacteristic
535C2×C4#41×D1111yescharacteristic
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—221no—
543C8—221no—
544C8—221no—
545C8—221no—
546C8—441no—
547C8—441no—
548C8—441no—
549C8C2×#431312yes—
550C22—221no—
551C22—221no—
552C22—221no—
553C22—441no—
554C22—441no—
555C22—441no—
556C22C4×D4×D1111yescharacteristic
557C4—21no—
558C4—22no—
559C4—22no—
560C4—41no—
561C4—41no—
562C4—221no—
563C4—221no—
564C4—221no—
565C4—441no—
566C4—441no—
567C4—441no—
568C4C22×#431311yescharacteristic
569C4#1062328111yescharacteristic
570C4#1062330911yescharacteristic
571C4#1062331011yescharacteristic
572C2—441no—
573C2—881no—
574C2D4×#431311yescharacteristic
575C2#1307745811yescharacteristic
576C2#1307751611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1579C2
socleC22×C11C2×C4×D4
prime radicalC2×#4343C2×C4
cosocleC42×C11C24
hypercenter#1579D11
hypocenterC11#18053
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1579

Complements

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

NH ≅ G/Ntype
2. #13077704C2semidirect
4. #13067520C2semidirect
5. #13067505C2semidirect
6. #13067491C2semidirect
7. #13067484C2semidirect
8. #13067466C2semidirect
9. #13067459C2semidirect
10. Q16×C11⋊C8C2semidirect
11. #13067380C2semidirect
13. #13067043C2semidirect
14. #13066914C2semidirect
15. C11×#1579C2semidirect
164. C11×Q16M16semidirect
221. #1579D11semidirect
452. Q16#4313semidirect
499. C11#18053semidirect

Maximal subgroups

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

subgroupindex
#130777472
#130777042
C4×#669712
#130675202
#130675052
#130674912
#130674842
#130674662
#130674592
Q16×C11⋊C82
#130673802
#130670492
#130670432
#130669142
C11×#15792
#1805311