Finite Group Databasebeta

← #14725378

Subgroups — #14725378

Order 2816.

626 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#13077742C211yesmaximal, characteristic
2#13077706C211yesmaximal, characteristic, complemented
3C4×#66962C211yesmaximal, characteristic
4#13067524C211yesmaximal, characteristic, complemented
5#13067512C211yesmaximal, characteristic, complemented
6#13067486C211yesmaximal, characteristic, complemented
7#13067472C211yesmaximal, characteristic, complemented
8#13067465C211yesmaximal, characteristic, complemented
9#13067451C211yesmaximal, characteristic, complemented
10#13067427C211yesmaximal, characteristic, complemented
11#13067415C211yesmaximal, characteristic, complemented
12#13067048C211yesmaximal, characteristic
13#13067044C211yesmaximal, characteristic, complemented
14#13066913C211yesmaximal, characteristic, complemented
15C11×#1569C211yesmaximal, characteristic, complemented
16C2×#66962C411yescharacteristic
17C4×#4339C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C11×#432C2211yescharacteristic
20C11×#423C2211yescharacteristic
21C4×C11×M16C2211yescharacteristic
22#10622746C411yescharacteristic
23#10622740—21no—
24#10622740—21no—
25#10622734C411yescharacteristic
26#10622733C411yescharacteristic
27#10622538C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622448—21no—
30#10622447C2211yescharacteristic
31#10622447C2211yescharacteristic
32D11×C4⋊C8—21no—
33#10622444C2211yescharacteristic
34#10622444C2211yescharacteristic
35#10622444C2211yescharacteristic
36#10622444C2211yescharacteristic
37#10622443C2211yescharacteristic
38#10622443C2211yescharacteristic
39#10622332—21no—
40#10622331—21no—
41#10622329C411yescharacteristic
42#10622329C411yescharacteristic
43#10622323C411yescharacteristic
44#10622323C411yescharacteristic
45#10622314—21no—
46#10622314—21no—
47C4×Dic44C2211yescharacteristic
48C4×Dic44C2211yescharacteristic
49C4×#4314C2211yescharacteristic
50C4×#4314C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×#335C2211yescharacteristic
53C11×#334C2211yescharacteristic
54C11×#334C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622122C2211yescharacteristic
60#10622122C2211yescharacteristic
61#10622121C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4339C2×C411yescharacteristic
68C22×Dic22C2×C411yescharacteristic
69C2×C11×M16—21no—
70C2×C11×M16C2×C411yescharacteristic
71C2×C11×M16C2×C411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C4×C22⋊D11—21no—
74C4×C22⋊D11—21no—
75#66979C2×C411yescharacteristic
76C2×C4⋊Dic11C2×C411yescharacteristic
77C2×Dic11⋊C4—21no—
78C2×C4×Dic11—21no—
79#66962—24no—
80C2×Dic44C2×C411yescharacteristic
81C2×Dic44C2×C411yescharacteristic
82C2×#4314C2×C411yescharacteristic
83C2×#4314C2×C411yescharacteristic
84C2×C8×D11—21no—
85C2×C8×D11—21no—
86C4×D44C2×C411yescharacteristic
87C4×D44C2311yescharacteristic
88#66925—21no—
89C42×D11—21no—
90C4×Dic22—21no—
91C4×Dic22—21no—
92C4×Dic22C2×C411yescharacteristic
93C4×Dic22C2×C411yescharacteristic
94C4×Dic22C2×C411yescharacteristic
95C4×Dic22C2311yescharacteristic
96C4×Dic22C2311yescharacteristic
97C4×Dic22C2311yescharacteristic
98C11×C4⋊C8—21no—
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×C22⋊C8—21no—
104C11×#97—21no—
105C11×#97C2×C411yescharacteristic
106C11×#97C2×C411yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C22⋊(C11⋊C8)—21no—
110C22⋊(C11⋊C8)D411yescharacteristic
111C22⋊(C11⋊C8)D411yescharacteristic
112#66885C2×C411yescharacteristic
113#66885C2×C411yescharacteristic
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8—21no—
116#66882C2×C411yescharacteristic
117#66882C2×C411yescharacteristic
118#66881C2×C411yescharacteristic
119#66881C2×C411yescharacteristic
120#66880C2×C411yescharacteristic
121#66880C2×C411yescharacteristic
122#66880C2×C411yescharacteristic
123#66880C2×C411yescharacteristic
124#66880C2×C411yescharacteristic
125#66880C2×C411yescharacteristic
126#66879—21no—
127#66879—21no—
128#66879—21no—
129#66879—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134Dic11⋊C8—21no—
135Dic11⋊C8—21no—
136C8×Dic11—21no—
137C8×Dic11—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)D411yescharacteristic
140C4⋊(C11⋊C8)D411yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18051—111nomaximal, Sylow
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C2×C22⋊D11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152#4339—22no—
153#4339—41no—
154C2×D44C22×C411yescharacteristic
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×Dic22—22no—
159C2×Dic22—21no—
160C2×Dic22—41no—
161C2×Dic22C22×C411yescharacteristic
162C2×Dic22C22×C411yescharacteristic
163C2×Dic22C22×C411yescharacteristic
164C11×M16—22no—
165C11×M16—41no—
166C11×M16—81no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C22×C411yescharacteristic
175C42×C11C22×C411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11#4111yescharacteristic
178C42×C11C2411yescharacteristic
179C22⋊Dic11—21no—
180(C2×D11)⋊C4—21no—
181(C2×D11)⋊C4—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11C22×C411yescharacteristic
184C4⋊Dic11C22×C411yescharacteristic
185C4⋊Dic11C22×C411yescharacteristic
186C4⋊Dic11C22×C411yescharacteristic
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C2×D411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206Dic44—22no—
207Dic44—22no—
208#4314—22no—
209#4314M1614yescomplemented
210C8×D11—81no—
211C8×D11—81no—
212#2990—111no—
213#2984—111no—
214C4×#137—111no—
215#1593—111no—
216#1591—111no—
217#1587—111no—
218#1585—111no—
219#1584—111no—
220#1582—111no—
221SD16⋊C8—111no—
222C8×SD16—111no—
223#1569D1111yescharacteristic, complemented
224#1488—111no—
225#1487—111no—
226#1453—111no—
227C23×C11C4×D411yescharacteristic
228C22×D11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—41no—
234C2×C4×C11C4×D411yescharacteristic
235C2×C4×C11C4×D411yescharacteristic
236C2×C4×C11C4×D411yescharacteristic
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C22⋊D11—42no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250D44—21no—
251D44C2×M1612yes—
252C4×D11—42no—
253C4×D11—42no—
254C4×D11—41no—
255C4×D11—41no—
256Dic22—21no—
257Dic22—21no—
258Dic22—21no—
259Dic22—21no—
260Dic22—21no—
261Dic22—42no—
262Dic22C2×M1612yes—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—41no—
267C8×C11—41no—
268C8×C11—41no—
269C8×C11—41no—
270C8×C11C2×M1612yes—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C2×#137—111no—
278C4×#41—111no—
279C2×C4×Q8—111no—
280#446—111no—
281#446—111no—
282#446—111no—
283#446—111no—
284#446—221no—
285#446—221no—
286C8×Q8—111no—
287C8×Q8—111no—
288#441—111no—
289#441—111no—
290#440—111no—
291#440—111no—
292C4×Q16—111no—
293C4×Q16—111no—
294C4×SD16—111no—
295C4×SD16—111no—
296#435—221no—
297#435—221no—
298C8×D4—111no—
299C8×D4—111no—
300#432—221no—
301#432—221no—
302#432C2×D1111yescharacteristic
303#431—111no—
304#431—111no—
305#431—221no—
306#428—111no—
307#423C2×D1111yescharacteristic
308C2×C4⋊C8—221no—
309#419—111no—
310#417—111no—
311C4×M16C2×D1111yescharacteristic
312#335C2×D1111yescharacteristic
313#335C2×D1111yescharacteristic
314#334C2×D1111yescharacteristic
315#334C2×D1111yescharacteristic
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318Q8⋊C8—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322D4⋊C8—111no—
323D4⋊C8—111no—
324#322—111no—
325#322—111no—
326#322—111no—
327C82—111no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11C2×C4×D411yescharacteristic
332C2×D11—22no—
333C2×D11—41no—
334C2×D11—41no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11C22×M1611yescharacteristic
340C4×C11#56811yescharacteristic
341C4×C11#57711yescharacteristic
342C4×C11#57811yescharacteristic
343Dic11—22no—
344Dic11—41no—
345Dic11—41no—
346Dic11—41no—
347Dic11—41no—
348Dic11—41no—
349Dic11—41no—
350C2×#41—111no—
351C22×Q8—111no—
352#137—224no—
353C2×Q16—111no—
354C2×Q16—111no—
355C2×SD16—111no—
356C2×SD16—111no—
357C2×M16—21no—
358C2×M16C4×D1111yescharacteristic
359C2×M16C4×D1111yescharacteristic
360C22×C8—221no—
361C22×C8—221no—
362C4×Q8—111no—
363C4×Q8—111no—
364C4×Q8—111no—
365C4×Q8—111no—
366C4×Q8—111no—
367C4×Q8—111no—
368C4×Q8—221no—
369C4×Q8—221no—
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—221no—
379C2×C42—221no—
380C2×C42C22×D1111yescharacteristic
381#107—111no—
382#107—111no—
383#106—111no—
384#106—111no—
385C4⋊C8—21no—
386C4⋊C8—111no—
387C4⋊C8—111no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8—221no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8C22×D1111yescharacteristic
396C4⋊C8C22×D1111yescharacteristic
397C4⋊C8C22×D1111yescharacteristic
398C4⋊C8C22×D1111yescharacteristic
399#103—111no—
400#103—111no—
401#103—111no—
402#103—111no—
403#103—111no—
404#103—111no—
405#102—111no—
406#102—111no—
407C22⋊C8—21no—
408C22⋊C8—111no—
409C22⋊C8—111no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—21no—
414#97—221no—
415#97—221no—
416#97—221no—
417#97—221no—
418#97C4×D1111yescharacteristic
419#97C4×D1111yescharacteristic
420C4×C8—111no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—111no—
424C4×C8—221no—
425C4×C8—221no—
426C4×C8C22×D1111yescharacteristic
427C4×C8C22×D1111yescharacteristic
428C2×C11—41no—
429C2×C11D4×M1611yescharacteristic
430C2×C11#294711yescharacteristic
431C2×C11#295511yescharacteristic
432D11—42no—
433#41—222no—
434#41—441no—
435C2×Q8—111no—
436C2×Q8—111no—
437C2×Q8—111no—
438C2×Q8—222no—
439C2×Q8—221no—
440C2×Q8—441no—
441C2×D4—111no—
442C2×D4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4C2×C4×D1111yescharacteristic
449C22×C4D4×D1111yescharacteristic
450C22×C4#434311yescharacteristic
451Q16—222no—
452Q16—222no—
453SD16—114no—
454SD16—222no—
455M16—22no—
456M16—41no—
457M16—81no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—111no—
463C2×C8—111no—
464C2×C8—111no—
465C2×C8—111no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—881no—
469C2×C8—881no—
470C2×C8C2×C4×D1111yescharacteristic
471C2×C8C2×C4×D1111yescharacteristic
472C2×C8C2×C4×D1111yescharacteristic
473C2×C8C2×C4×D1111yescharacteristic
474C4⋊C4—111no—
475C4⋊C4—111no—
476C4⋊C4—111no—
477C4⋊C4—111no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C22⋊C4—221no—
486C22⋊C4—221no—
487C22⋊C4—221no—
488C42—221no—
489C42—221no—
490C42—221no—
491C42—221no—
492C42—221no—
493C42—221no—
494C42—221no—
495C42C2×C4×D1111yescharacteristic
496C42D4×D1111yescharacteristic
497C42#434311yescharacteristic
498C42C23×D1111yescharacteristic
499C11#1805111yescharacteristic, complemented, Sylow
500C23—221no—
501C23#6694611yescharacteristic
502Q8—112no—
503Q8—221no—
504Q8—221no—
505Q8—221no—
506Q8—221no—
507Q8—221no—
508Q8—442no—
509D4—112no—
510D4—221no—
511D4—442no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4#6694611yescharacteristic
531C2×C4#6694611yescharacteristic
532C2×C4#6694611yescharacteristic
533C2×C4C22×C4×D1111yescharacteristic
534C2×C4C2×D4×D1111yescharacteristic
535C2×C4C2×#434311yescharacteristic
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—221no—
544C8—221no—
545C8—221no—
546C8—221no—
547C8—441no—
548C8—441no—
549C8M16×D1112yes—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—222no—
554C22—441no—
555C22—441no—
556C22C2×#6694611yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—222no—
562C4—441no—
563C4—441no—
564C4—441no—
565C4—441no—
566C4—441no—
567C4—441no—
568C4C2×M16×D1111yescharacteristic
569C4#1062327611yescharacteristic
570C4#1062330611yescharacteristic
571C4#1062331011yescharacteristic
572C2—41no—
573C2—442no—
574C2#1307735111yescharacteristic
575C2#1307745711yescharacteristic
576C2#1307751811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1569C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenter#1569D11
hypocenterC11#18051
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
2. #13077706C2semidirect
4. #13067524C2semidirect
5. #13067512C2semidirect
6. #13067486C2semidirect
7. #13067472C2semidirect
8. #13067465C2semidirect
9. #13067451C2semidirect
10. #13067427C2semidirect
11. #13067415C2semidirect
13. #13067044C2semidirect
14. #13066913C2semidirect
15. C11×#1569C2semidirect
209. #4314M16semidirect
223. #1569D11semidirect
499. C11#18051semidirect

Maximal subgroups

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

subgroupindex
#130777422
#130777062
C4×#669622
#130675242
#130675122
#130674862
#130674722
#130674652
#130674512
#130674272
#130674152
#130670482
#130670442
#130669132
C11×#15692
#1805111