Finite Group Databasebeta

← #14724752

Subgroups — #14724752

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078630C211yesmaximal, characteristic
2#13077624C211yesmaximal, characteristic, complemented
3#13077617C211yesmaximal, characteristic, complemented
4#13067526C211yesmaximal, characteristic, complemented
5#13067515C211yesmaximal, characteristic, complemented
6#13067486C211yesmaximal, characteristic, complemented
7#13067481C211yesmaximal, characteristic, complemented
8#13067473C211yesmaximal, characteristic, complemented
9#13067473C211yesmaximal, characteristic, complemented
10#13067425C211yesmaximal, characteristic, complemented
11#13067393C211yesmaximal, characteristic, complemented
12#13067073C211yesmaximal, characteristic, complemented
13#13066995C211yesmaximal, characteristic, complemented
14#13066904C211yesmaximal, characteristic, complemented
15C11×#1580C211yesmaximal, characteristic, complemented
16#10623088C2211yescharacteristic
17C4×#4341C2211yescharacteristic
18C4×C11×D8C2211yescharacteristic
19C8×D4×C11C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622771C411yescharacteristic
22#10622766C411yescharacteristic
23#10622724—21no—
24#10622724—21no—
25#10622714—21no—
26C2×#66879—21no—
27C4×#4324C2211yescharacteristic
28C4×#4324C2211yescharacteristic
29#10622625C2211yescharacteristic
30D4×C11⋊C8C2211yescharacteristic
31#10622501C411yescharacteristic
32#10622490C411yescharacteristic
33#10622448C2211yescharacteristic
34#10622446C2211yescharacteristic
35#10622444C2211yescharacteristic
36#10622443C2211yescharacteristic
37#10622397C411yescharacteristic
38#10622396C411yescharacteristic
39#10622380C411yescharacteristic
40#10622379C411yescharacteristic
41#10622343—21no—
42#10622342—21no—
43#10622333—21no—
44#10622332—21no—
45C4×Dic44C2211yescharacteristic
46C4×#4313C2211yescharacteristic
47#10622298C2211yescharacteristic
48C4×C8×D11C2211yescharacteristic
49#10622292C2211yescharacteristic
50#10622292C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622117C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622095C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×#4341C2×C411yescharacteristic
68C2×C11×D8C2×C411yescharacteristic
69C22×C8×C11—21no—
70C22×C8×C11—21no—
71C4×D4×C11C2311yescharacteristic
72C4×D4×C11C2311yescharacteristic
73#66991C2×C411yescharacteristic
74#66989C2×C411yescharacteristic
75D4×Dic11C2×C411yescharacteristic
76C2×#4324C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C4×C22⋊D11—21no—
80#66979—21no—
81C2×C4×Dic11—21no—
82C2×#4318—21no—
83C22×C11⋊C8—21no—
84C2×Dic44C2×C411yescharacteristic
85C2×#4313D411yescharacteristic
86C2×#4313D411yescharacteristic
87C2×C8×D11—21no—
88#66950C2×C411yescharacteristic
89#66945C2×C411yescharacteristic
90#66943C2×C411yescharacteristic
91#66940C2×C411yescharacteristic
92#66936—21no—
93(C22⋊D11)⋊C4—21no—
94#66932—21no—
95#66930—21no—
96C42×D11C2311yescharacteristic
97C4×Dic22C2311yescharacteristic
98C4×Dic22C2311yescharacteristic
99C11×#107C2×C411yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×#102C2×C411yescharacteristic
103C11×#102C2×C411yescharacteristic
104C11×C22⋊C8—21no—
105C11×C22⋊C8—21no—
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109#66896C2×C411yescharacteristic
110#66896C2×C411yescharacteristic
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)—21no—
113(C2×D11)⋊C8—21no—
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8C2×C411yescharacteristic
116(C2×D11)⋊C8C2×C411yescharacteristic
117#66882C2×C411yescharacteristic
118#66880C2×C411yescharacteristic
119#66880C2×C411yescharacteristic
120#66879—21no—
121#66879—21no—
122#66879—21no—
123#66879—21no—
124#66879D411yescharacteristic
125#66879D411yescharacteristic
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8C2×C411yescharacteristic
131Dic11⋊C8C2×C411yescharacteristic
132C8×Dic11—21no—
133C8×Dic11—21no—
134C8×Dic11—21no—
135#66874C2×C411yescharacteristic
136#66874C2×C411yescharacteristic
137#66872C2×C411yescharacteristic
138#66872C2×C411yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18002—111nomaximal, Sylow
145C2×D4×C11C22×C411yescharacteristic
146C2×D4×C11C22×C411yescharacteristic
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153#4341—22no—
154#4341—41no—
155C2×C4×D11C22×C411yescharacteristic
156C2×C4×D11C2×D411yescharacteristic
157C2×C4×D11#4111yescharacteristic
158C2×Dic22C22×C411yescharacteristic
159C2×Dic22C22×C411yescharacteristic
160C11×D8—22no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—42no—
165C2×C8×C11—42no—
166C2×C8×C11C22×C411yescharacteristic
167C2×C8×C11C22×C411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C11×C4⋊C4C22×C411yescharacteristic
171C11×C4⋊C4C22×C411yescharacteristic
172C11×C22⋊C4—21no—
173C11×C22⋊C4—21no—
174C42×C11C2411yescharacteristic
175C22⋊Dic11—21no—
176C22⋊Dic11—21no—
177C22⋊Dic11—21no—
178C22⋊Dic11—21no—
179#4324—22no—
180#4324—41no—
181(C2×D11)⋊C4—21no—
182(C2×D11)⋊C4—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11C22×C411yescharacteristic
186C4⋊Dic11C22×C411yescharacteristic
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11C22×C411yescharacteristic
196C4×Dic11C2×D411yescharacteristic
197C4×Dic11#4111yescharacteristic
198#4318—42no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—42no—
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207Dic44—41no—
208#4313—41no—
209#4313—41no—
210C8×D11—42no—
211#3102—111no—
212#2970—111no—
213#2969—111no—
214#1593—111no—
215#1592—111no—
216#1587—111no—
217#1586—111no—
218#1585—111no—
219#1585—111no—
220#1580D1111yescharacteristic, complemented
221SD16⋊C8—111no—
222#1572—111no—
223#1494—111no—
224#1476—111no—
225#1451—111no—
226C23×C11—21no—
227C23×C11—21no—
228C22×D11C4×D411yescharacteristic
229D4×C11—21no—
230D4×C11—21no—
231D4×C11—21no—
232D4×C11#13112yes—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11C23×C411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C22⋊D11—42no—
243C22⋊D11—81no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—42no—
249C2×Dic11—81no—
250C2×Dic11C4×D411yescharacteristic
251C2×Dic11C4×D411yescharacteristic
252C2×Dic11C4×D411yescharacteristic
253C4×D11—21no—
254C4×D11—21no—
255C4×D11—21no—
256C4×D11—21no—
257C4×D11—41no—
258Dic22—21no—
259Dic22—21no—
260Dic22—21no—
261Dic22—21no—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—41no—
267C8×C11—41no—
268C8×C11—41no—
269C11⋊C8—22no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276#529—111no—
277C4×#41—111no—
278#485—111no—
279#482—111no—
280#479—111no—
281#478—111no—
282#464—111no—
283#463—111no—
284#452—111no—
285#449—111no—
286#446—111no—
287#446—111no—
288#446—111no—
289C8×Q8—111no—
290C4×Q16—111no—
291C4×SD16—111no—
292C4×SD16—111no—
293C4×D8C2×D1111yescharacteristic
294#436—111no—
295#436—221no—
296#435—221no—
297#435—221no—
298#435—221no—
299C8×D4—111no—
300C8×D4C2×D1111yescharacteristic
301C8×D4C2×D1111yescharacteristic
302#433—221no—
303#432—111no—
304#432—221no—
305#431—111no—
306#431—111no—
307#405—221no—
308C4×M16—111no—
309C2×#97—221no—
310C2×C4×C8—111no—
311#335—111no—
312#335—111no—
313#334—111no—
314#334C2×D1111yescharacteristic
315Q8⋊C8—111no—
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318Q8⋊C8—111no—
319D4⋊C8—111no—
320D4⋊C8—111no—
321D4⋊C8C2×D1111yescharacteristic
322D4⋊C8C2×D1111yescharacteristic
323#322—111no—
324#322—111no—
325#322—111no—
326#322C2×D1111yescharacteristic
327C22×C11—22no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11C2×C4×D411yescharacteristic
334C2×D11—21no—
335C2×D11—21no—
336C2×D11—21no—
337C4×C11—21no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11C2×#13111yescharacteristic
341C4×C11#56811yescharacteristic
342C4×C11#57511yescharacteristic
343C4×C11#57511yescharacteristic
344Dic11—21no—
345Dic11—21no—
346Dic11—21no—
347Dic11—41no—
348Dic11—41no—
349Dic11—41no—
350Dic11—41no—
351C2×#41—111no—
352C2×Q16—111no—
353C2×SD16—111no—
354C2×SD16—111no—
355C2×D8C4×D1111yescharacteristic
356C2×M16—111no—
357C2×M16—111no—
358C2×M16—221no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—221no—
362C22×C8—221no—
363#126—221no—
364#125—111no—
365#124—111no—
366#123—221no—
367C22⋊Q8—111no—
368#121—111no—
369C4×Q8—111no—
370C4×Q8—111no—
371C4×Q8—111no—
372C4×D4—111no—
373C4×D4—221no—
374C4×D4—221no—
375C4×D4—221no—
376C4×D4C22×D1111yescharacteristic
377C4×D4C22×D1111yescharacteristic
378#117—111no—
379#117—221no—
380#117—221no—
381C2×C42—111no—
382C2×C42—221no—
383#107—111no—
384#107C4×D1111yescharacteristic
385#106—111no—
386#106—111no—
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⋊C8C22×D1111yescharacteristic
396C4⋊C8C22×D1111yescharacteristic
397#103—111no—
398#103—111no—
399#103—111no—
400#103—111no—
401#102—111no—
402#102—111no—
403#102C4×D1111yescharacteristic
404#102C4×D1111yescharacteristic
405C22⋊C8—21no—
406C22⋊C8—21no—
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—
418#97—221no—
419C4×C8—111no—
420C4×C8—111no—
421C4×C8—111no—
422C4×C8—221no—
423C4×C8—221no—
424C4×C8—221no—
425C4×C8C22×D1111yescharacteristic
426C4×C8C22×D1111yescharacteristic
427C4×C8C22×D1111yescharacteristic
428C2×C11—42no—
429C2×C11—81no—
430C2×C11#293311yescharacteristic
431C2×C11#294311yescharacteristic
432C2×C11#295611yescharacteristic
433D11—41no—
434#41—222no—
435#41—441no—
436C2×Q8—111no—
437C2×Q8—111no—
438C2×D4—221no—
439C2×D4—221no—
440C2×D4C2×C4×D1111yescharacteristic
441C2×D4C2×C4×D1111yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—221no—
448C22×C4—221no—
449Q16—441no—
450SD16—222no—
451SD16—441no—
452D8—22no—
453M16—441no—
454M16—441no—
455M16—442no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—42no—
460C2×C8—42no—
461C2×C8—111no—
462C2×C8—111no—
463C2×C8—111no—
464C2×C8—111no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—442no—
469C2×C8—442no—
470C2×C8C2×C4×D1111yescharacteristic
471C2×C8C2×C4×D1111yescharacteristic
472C2×C8D4×D1111yescharacteristic
473C2×C8D4×D1111yescharacteristic
474C4⋊C4—111no—
475C4⋊C4—111no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4C2×C4×D1111yescharacteristic
483C4⋊C4C2×C4×D1111yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—221no—
487C22⋊C4—221no—
488C22⋊C4—221no—
489C22⋊C4—221no—
490C22⋊C4—221no—
491C22⋊C4—221no—
492C42—111no—
493C42—111no—
494C42—111no—
495C42—221no—
496C42—221no—
497C42—221no—
498C42—221no—
499C42C23×D1111yescharacteristic
500C11#1800211yescharacteristic, complemented, Sylow
501C23—21no—
502C23—21no—
503C23—111no—
504Q8—221no—
505Q8—221no—
506Q8—221no—
507Q8—221no—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—442no—
512D4—881no—
513D4#6695412yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—111no—
521C2×C4—111no—
522C2×C4—111no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—441no—
532C2×C4—442no—
533C2×C4—881no—
534C2×C4C22×C4×D1111yescharacteristic
535C2×C4C2×D4×D1111yescharacteristic
536C2×C4#41×D1111yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—222no—
545C8—221no—
546C8—221no—
547C8—221no—
548C8—221no—
549C8—441no—
550C8—441no—
551C22—22no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—221no—
558C22—221no—
559C22—221no—
560C22C4×D4×D1111yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—221no—
565C4—221no—
566C4—221no—
567C4—441no—
568C4—441no—
569C4—441no—
570C4—441no—
571C4C2×#6695411yescharacteristic
572C4#1062328111yescharacteristic
573C4#1062330411yescharacteristic
574C4#1062330411yescharacteristic
575C2—42no—
576C2—81no—
577C2—441no—
578C2#1307733611yescharacteristic
579C2#1307741311yescharacteristic
580C2#1307752411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1580C2
socleC22×C11C2×C4×D4
prime radical#10622771C4
cosocleC42×C11C24
hypercenter#1580D11
hypocenterC11#18002
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1580

Complements

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

NH ≅ G/Ntype
2. #13077624C2semidirect
3. #13077617C2semidirect
4. #13067526C2semidirect
5. #13067515C2semidirect
6. #13067486C2semidirect
7. #13067481C2semidirect
8. #13067473C2semidirect
9. #13067473C2semidirect
10. #13067425C2semidirect
11. #13067393C2semidirect
12. #13067073C2semidirect
13. #13066995C2semidirect
14. #13066904C2semidirect
15. C11×#1580C2semidirect
220. #1580D11semidirect
500. C11#18002semidirect

Maximal subgroups

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

subgroupindex
#130786302
#130776242
#130776172
#130675262
#130675152
#130674862
#130674812
#130674732
#130674252
#130673932
#130670732
#130669952
#130669042
C11×#15802
#1800211