Finite Group Databasebeta

← #14724908

Subgroups — #14724908

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078687C211yesmaximal, characteristic
2#13077636C211yesmaximal, characteristic
3#13077559C211yesmaximal, characteristic, complemented
4#13067515C211yesmaximal, characteristic, complemented
5#13067509C211yesmaximal, characteristic, complemented
6#13067497C211yesmaximal, characteristic, complemented
7#13067484C211yesmaximal, characteristic, complemented
8#13067463C211yesmaximal, characteristic, complemented
9#13067462C211yesmaximal, characteristic, complemented
10#13067432C211yesmaximal, characteristic, complemented
11#13067420C211yesmaximal, characteristic, complemented
12#13067399C211yesmaximal, characteristic, complemented
13#13067090C211yesmaximal, characteristic, complemented
14#13066911C211yesmaximal, characteristic, complemented
15C11×#1477C211yesmaximal, characteristic
16C4×C11×#41C2211yescharacteristic
17#10623001C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20#10622852C411yescharacteristic
21#10622852C411yescharacteristic
22#10622715—21no—
23#10622714—21no—
24#10622644C411yescharacteristic
25C4×#4326C2211yescharacteristic
26C4×#4326C2211yescharacteristic
27Q8×C11⋊C8C2211yescharacteristic
28Q8×C11⋊C8C2211yescharacteristic
29#10622633C411yescharacteristic
30#10622632C411yescharacteristic
31C4×#4324C2211yescharacteristic
32C4×#4324C2211yescharacteristic
33#10622625—21no—
34#10622625—21no—
35#10622625C2211yescharacteristic
36#10622625C2211yescharacteristic
37#10622620C411yescharacteristic
38#10622609C411yescharacteristic
39#10622609C411yescharacteristic
40#10622539—21no—
41#10622539C2211yescharacteristic
42#10622538C2211yescharacteristic
43C4×#4318—21no—
44C4×#4318C2211yescharacteristic
45#10622444C2211yescharacteristic
46#10622444C2211yescharacteristic
47#10622443C2211yescharacteristic
48#10622443C2211yescharacteristic
49#10622441—21no—
50#10622441—21no—
51C11×Q8⋊C8C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×D4⋊C8C2211yescharacteristic
55#10622118C2211yescharacteristic
56#10622118C2211yescharacteristic
57#10622117C2211yescharacteristic
58#10622117C2211yescharacteristic
59#10622094C2211yescharacteristic
60#10622094C2211yescharacteristic
61#10622094C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×#41C2×C411yescharacteristic
68C22×C8×C11—21no—
69C4×Q8×C11C2×C411yescharacteristic
70C4×Q8×C11C2311yescharacteristic
71C4×D4×C11—21no—
72C4×D4×C11—21no—
73C4×D4×C11C2×C411yescharacteristic
74C4×D4×C11C2311yescharacteristic
75C11×#117—21no—
76C11×#117C2×C411yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×#4326C2×C411yescharacteristic
80C2×#4326C2×C411yescharacteristic
81C2×#4324C2×C411yescharacteristic
82C2×#4324C2×C411yescharacteristic
83#66979—21no—
84#66977—21no—
85#66977C2×C411yescharacteristic
86#66977C2×C411yescharacteristic
87C2×#4318—21no—
88C2×#4318—21no—
89C2×#4318D411yescharacteristic
90C2×#4318D411yescharacteristic
91#66923—21no—
92#66922C2×C411yescharacteristic
93#66922C2×C411yescharacteristic
94C4×Dic22—21no—
95C4×Dic22C2311yescharacteristic
96C4×Dic22C2311yescharacteristic
97C11×C4⋊C8—21no—
98C11×C4⋊C8—21no—
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×C22⋊C8—21no—
102C4×C8×C11C2311yescharacteristic
103C4×C8×C11C2311yescharacteristic
104#66899C2×C411yescharacteristic
105#66899C2×C411yescharacteristic
106#66896C2×C411yescharacteristic
107#66896C2×C411yescharacteristic
108C22⋊(C11⋊C8)—21no—
109C22⋊(C11⋊C8)—21no—
110C22⋊(C11⋊C8)—21no—
111C22⋊(C11⋊C8)C2×C411yescharacteristic
112C22⋊(C11⋊C8)C2×C411yescharacteristic
113#66879—21no—
114#66879—21no—
115Dic11⋊C8—21no—
116Dic11⋊C8—21no—
117Dic11⋊C8—21no—
118Dic11⋊C8—21no—
119C8×Dic11—21no—
120C8×Dic11—21no—
121#66874C2×C411yescharacteristic
122#66874C2×C411yescharacteristic
123#66874C2×C411yescharacteristic
124#66874C2×C411yescharacteristic
125#66872C2×C411yescharacteristic
126#66872C2×C411yescharacteristic
127#66871C2×C411yescharacteristic
128#66871C2×C411yescharacteristic
129C4⋊(C11⋊C8)—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)C2×C411yescharacteristic
132C4⋊(C11⋊C8)C2×C411yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135#66867—21no—
136#66867D411yescharacteristic
137#66867D411yescharacteristic
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18013—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—41no—
147C2×Q8×C11C22×C411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11C22×C411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C2×Dic22—21no—
157C2×Dic22C22×C411yescharacteristic
158C2×Dic22C22×C411yescharacteristic
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—42no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4C22×C411yescharacteristic
167C11×C4⋊C4C22×C411yescharacteristic
168C11×C22⋊C4—21no—
169C11×C22⋊C4—21no—
170C11×C22⋊C4—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11C22×C411yescharacteristic
175C42×C11C2×D411yescharacteristic
176C42×C11#4111yescharacteristic
177C42×C11C2411yescharacteristic
178C22⋊Dic11—21no—
179C22⋊Dic11—21no—
180#4326—22no—
181#4326—22no—
182#4324—41no—
183#4324—41no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11C22×C411yescharacteristic
188C4⋊Dic11C22×C411yescharacteristic
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195#4318—22no—
196#4318—41no—
197#4318—42no—
198#4318—42no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209#3107—111no—
210#2971—111no—
211#2962—111no—
212#1592—111no—
213#1590—111no—
214#1588—111no—
215#1587—111no—
216#1584—111no—
217#1583—111no—
218#1579—111no—
219C8×Q16—111no—
220#1573—111no—
221#1497—111no—
222#1477D1111yescharacteristic
223#1453—111no—
224C23×C11—21no—
225C23×C11C4×D411yescharacteristic
226Q8×C11—21no—
227Q8×C11#13112yes—
228D4×C11—21no—
229D4×C11—21no—
230D4×C11—42no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—81no—
243C2×C4×C11C4×D411yescharacteristic
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253Dic22—21no—
254Dic22—21no—
255Dic22—21no—
256Dic22—21no—
257Dic22—81no—
258C8×C11—41no—
259C8×C11—41no—
260C8×C11—41no—
261C8×C11—41no—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8#13712yes—
272#533—111no—
273C4×#41C2×D1111yescharacteristic
274#485—111no—
275#485—111no—
276#475—111no—
277#474—111no—
278#462—111no—
279#461—111no—
280#452—111no—
281#452—111no—
282#446—111no—
283#446—111no—
284#446—221no—
285#446—221no—
286C8×Q8—111no—
287C8×Q8—111no—
288C8×Q8—111no—
289C8×Q8—111no—
290C4×Q16—111no—
291C4×Q16—111no—
292C4×SD16—111no—
293C4×SD16—111no—
294#436—111no—
295#436—111no—
296#436—221no—
297#436—221no—
298#432—111no—
299#432—221no—
300#431—111no—
301#431C2×D1111yescharacteristic
302#424—221no—
303C2×C4⋊C8C2×D1111yescharacteristic
304#405—221no—
305C4×M16—111no—
306C4×M16—221no—
307#335—111no—
308#335—111no—
309#334—111no—
310#334—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315Q8⋊C8C2×D1111yescharacteristic
316Q8⋊C8C2×D1111yescharacteristic
317D4⋊C8C2×D1111yescharacteristic
318D4⋊C8C2×D1111yescharacteristic
319#322—111no—
320#322—111no—
321#322—111no—
322C82—111no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11C2×C4×D411yescharacteristic
330C4×C11—21no—
331C4×C11—22no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11C2×#13111yescharacteristic
338C4×C11#56811yescharacteristic
339C4×C11C2×#13711yescharacteristic
340C4×C11#57511yescharacteristic
341Dic11—41no—
342Dic11—41no—
343Dic11—41no—
344Dic11—41no—
345C2×#41C4×D1111yescharacteristic
346C2×Q16—111no—
347C2×Q16—111no—
348C2×SD16—111no—
349C2×SD16—111no—
350C2×M16—111no—
351C2×M16—111no—
352C2×M16—221no—
353C2×M16—221no—
354C22×C8—21no—
355C4⋊Q8—111no—
356C4⋊Q8—111no—
357#125—221no—
358C22⋊Q8—111no—
359C22⋊Q8—111no—
360C22⋊Q8—221no—
361C4×Q8—111no—
362C4×Q8—111no—
363C4×Q8—221no—
364C4×Q8C4×D1111yescharacteristic
365C4×Q8C22×D1111yescharacteristic
366C4×D4—21no—
367C4×D4—21no—
368C4×D4C4×D1111yescharacteristic
369C4×D4C22×D1111yescharacteristic
370#117—21no—
371#117—221no—
372#117C4×D1111yescharacteristic
373C2×C42—21no—
374C2×C42C22×D1111yescharacteristic
375#107—111no—
376#107—111no—
377#106—111no—
378#106—111no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8—111no—
382C4⋊C8—111no—
383C4⋊C8—111no—
384C4⋊C8—111no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8—221no—
391C4⋊C8C22×D1111yescharacteristic
392C4⋊C8C22×D1111yescharacteristic
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#103—111no—
398#103—111no—
399#102—111no—
400#102—111no—
401C22⋊C8—21no—
402C22⋊C8—111no—
403C22⋊C8—111no—
404C22⋊C8—221no—
405C22⋊C8—221no—
406C22⋊C8—221no—
407#97—111no—
408#97—111no—
409#97—221no—
410#97—221no—
411#97—221no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—221no—
417C4×C8—221no—
418C4×C8—221no—
419C4×C8—221no—
420C4×C8C22×D1111yescharacteristic
421C4×C8C22×D1111yescharacteristic
422C2×C11—41no—
423C2×C11—81no—
424C2×C11#293311yescharacteristic
425C2×C11C4×#13711yescharacteristic
426C2×C11#295711yescharacteristic
427#41—22no—
428#41—41no—
429C2×Q8—111no—
430C2×Q8—111no—
431C2×Q8—221no—
432C2×Q8C2×C4×D1111yescharacteristic
433C2×D4—21no—
434C2×D4C2×C4×D1111yescharacteristic
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4C2×C4×D1111yescharacteristic
439C22×C4D4×D1111yescharacteristic
440C22×C4#434111yescharacteristic
441Q16—222no—
442Q16—222no—
443SD16—441no—
444SD16—441no—
445M16—222no—
446M16—442no—
447M16—441no—
448M16—442no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—42no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—111no—
457C2×C8—111no—
458C2×C8—111no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—111no—
462C2×C8—221no—
463C2×C8—221no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—111no—
467C4⋊C4—111no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4C2×C4×D1111yescharacteristic
476C4⋊C4C2×C4×D1111yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—221no—
481C22⋊C4—221no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—221no—
486C42—221no—
487C42C2×C4×D1111yescharacteristic
488C42D4×D1111yescharacteristic
489C42#434111yescharacteristic
490C42C23×D1111yescharacteristic
491C11#1801311yescharacteristic, complemented, Sylow
492C23—21no—
493C23(C22⋊D11)⋊C411yescharacteristic
494Q8—21no—
495Q8—221no—
496Q8—221no—
497Q8—221no—
498Q8—221no—
499Q8—881no—
500Q8#6695412yes—
501D4—21no—
502D4—21no—
503D4—42no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—81no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4(C22⋊D11)⋊C411yescharacteristic
521C2×C4(C22⋊D11)⋊C411yescharacteristic
522C2×C4(C22⋊D11)⋊C411yescharacteristic
523C2×C4C22×C4×D1111yescharacteristic
524C2×C4C2×D4×D1111yescharacteristic
525C2×C4C2×#434111yescharacteristic
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—112no—
531C8—221no—
532C8—221no—
533C8—221no—
534C8—221no—
535C8—221no—
536C8—221no—
537C8—221no—
538C8—441no—
539C8—441no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22C2×(C22⋊D11)⋊C411yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—22no—
551C4—21no—
552C4—41no—
553C4—41no—
554C4—441no—
555C4—441no—
556C4—441no—
557C4—441no—
558C4C2×#6695411yescharacteristic
559C4#1062327611yescharacteristic
560C4#1062330411yescharacteristic
561C4D11×#13711yescharacteristic
562C2—41no—
563C2—81no—
564C2#1307733711yescharacteristic
565C2#1307744011yescharacteristic
566C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1477C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#41C2×C4
cosocleC42×C11C24
hypercenter#1477D11
hypocenterC11#18013
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1477

Complements

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

NH ≅ G/Ntype
3. #13077559C2semidirect
4. #13067515C2semidirect
5. #13067509C2semidirect
6. #13067497C2semidirect
7. #13067484C2semidirect
8. #13067463C2semidirect
9. #13067462C2semidirect
10. #13067432C2semidirect
11. #13067420C2semidirect
12. #13067399C2semidirect
13. #13067090C2semidirect
14. #13066911C2semidirect
491. C11#18013semidirect

Maximal subgroups

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

subgroupindex
#130786872
#130776362
#130775592
#130675152
#130675092
#130674972
#130674842
#130674632
#130674622
#130674322
#130674202
#130673992
#130670902
#130669112
C11×#14772
#1801311