Finite Group Databasebeta

← #14724424

Subgroups — #14724424

Order 2816.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079223C211yesmaximal, characteristic
2#13077765C211yesmaximal, characteristic
3#13077713C211yesmaximal, characteristic, complemented
4#13067522C211yesmaximal, characteristic, complemented
5#13067515C211yesmaximal, characteristic, complemented
6#13067510C211yesmaximal, characteristic, complemented
7#13067509C211yesmaximal, characteristic, complemented
8#13067432C211yesmaximal, characteristic, complemented
9#13067425C211yesmaximal, characteristic, complemented
10#13067420C211yesmaximal, characteristic, complemented
11#13067419C211yesmaximal, characteristic, complemented
12#13067384C211yesmaximal, characteristic, complemented
13#13067072C211yesmaximal, characteristic, complemented
14C8×#4318C211yesmaximal, characteristic, complemented
15C11×#1494C211yesmaximal, characteristic
16C11×#529C2211yescharacteristic
17#10623001C2211yescharacteristic
18C11×#432C2211yescharacteristic
19C2×C4×C8×C11C2211yescharacteristic
20#10622682C411yescharacteristic
21#10622678C411yescharacteristic
22#10622673C411yescharacteristic
23#10622668C411yescharacteristic
24#10622665C411yescharacteristic
25#10622665C411yescharacteristic
26#10622655C411yescharacteristic
27#10622655C411yescharacteristic
28C4×#4326C2211yescharacteristic
29C4×#4326C2211yescharacteristic
30#10622637C2211yescharacteristic
31Q8×C11⋊C8C2211yescharacteristic
32C4×#4324C2211yescharacteristic
33C4×#4324C2211yescharacteristic
34#10622625—21no—
35#10622625C2211yescharacteristic
36#10622624—21no—
37D4×C11⋊C8C2211yescharacteristic
38#10622613—21no—
39#10622612—21no—
40#10622538C2211yescharacteristic
41#10622537C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622444C2211yescharacteristic
44#10622444C2211yescharacteristic
45#10622443C2211yescharacteristic
46#10622443C2211yescharacteristic
47#10622333—21no—
48#10622333—21no—
49#10622314—21no—
50#10622314—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#10622092C2211yescharacteristic
64#10622092C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C22×C8×C11—21no—
68C11×#126—21no—
69C11×#125C2×C411yescharacteristic
70C11×#124C2×C411yescharacteristic
71C11×#123—21no—
72C11×C22⋊Q8C2×C411yescharacteristic
73C11×#121C2×C411yescharacteristic
74C4×Q8×C11C2311yescharacteristic
75C4×D4×C11—21no—
76C4×D4×C11C2311yescharacteristic
77C11×#117—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×#4318C2×C411yescharacteristic
90C2×#4318C2×C411yescharacteristic
91C22×C11⋊C8—21no—
92#66923—21no—
93#66922C2×C411yescharacteristic
94#66922C2×C411yescharacteristic
95C4×Dic22—21no—
96C4×Dic22C2311yescharacteristic
97C4×Dic22C2311yescharacteristic
98C11×C4⋊C8C2311yescharacteristic
99C11×C4⋊C8C2311yescharacteristic
100C11×C22⋊C8—21no—
101C11×#97—21no—
102C4×C8×C11—21no—
103C4×C8×C11C2311yescharacteristic
104C4×C8×C11C2311yescharacteristic
105#66899C2×C411yescharacteristic
106#66899C2×C411yescharacteristic
107#66896C2×C411yescharacteristic
108#66896C2×C411yescharacteristic
109C22⋊(C11⋊C8)—21no—
110C22⋊(C11⋊C8)—21no—
111C22⋊(C11⋊C8)D411yescharacteristic
112C22⋊(C11⋊C8)D411yescharacteristic
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)—21no—
132C4⋊(C11⋊C8)D411yescharacteristic
133C4⋊(C11⋊C8)D411yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136#66867—21no—
137#66867C2×C411yescharacteristic
138#66867C2×C411yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17969—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×D4×C11—21no—
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C2×Dic22—21no—
153C2×Dic22C22×C411yescharacteristic
154C2×Dic22C22×C411yescharacteristic
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—42no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4C22×C411yescharacteristic
165C11×C4⋊C4C22×C411yescharacteristic
166C11×C22⋊C4—21no—
167C11×C22⋊C4—21no—
168C11×C22⋊C4—21no—
169C11×C22⋊C4—21no—
170C11×C22⋊C4—21no—
171C42×C11—21no—
172C42×C11C22×C411yescharacteristic
173C42×C11C2×D411yescharacteristic
174C42×C11#4111yescharacteristic
175C42×C11C2411yescharacteristic
176C22⋊Dic11—21no—
177C22⋊Dic11—21no—
178#4326—22no—
179#4326—22no—
180#4324—22no—
181#4324—22no—
182C4⋊Dic11—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—
193#4318—22no—
194#4318—22no—
195#4318—81no—
196#4318—81no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—81no—
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208#3172—111no—
209#2993—111no—
210#2985—111no—
211#1593—111no—
212#1592—111no—
213#1591—111no—
214#1590—111no—
215#1579—111no—
216SD16⋊C8—111no—
217C8×Q16—111no—
218C8×SD16—111no—
219#1569—111no—
220#1494D1111yescharacteristic
221#1493—111no—
222C8×M16—111no—
223C23×C11—21no—
224C23×C11C4×D411yescharacteristic
225Q8×C11—21no—
226Q8×C11—21no—
227D4×C11—21no—
228D4×C11—21no—
229D4×C11—81no—
230C2×C4×C11—21no—
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—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11C4×D411yescharacteristic
241C2×C4×C11C4×D411yescharacteristic
242C2×C4×C11C4×D411yescharacteristic
243C2×C4×C11C23×C411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250Dic22—21no—
251Dic22—21no—
252Dic22—21no—
253Dic22—21no—
254Dic22—81no—
255C8×C11—22no—
256C8×C11—41no—
257C8×C11—41no—
258C8×C11—41no—
259C11⋊C8—21no—
260C11⋊C8—21no—
261C11⋊C8—21no—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8#13112yes—
268C11⋊C8#13112yes—
269#533—111no—
270#529C2×D1111yescharacteristic
271#501—111no—
272#497—111no—
273#491—111no—
274#489—111no—
275#470—111no—
276#470—111no—
277#468—111no—
278#468—111no—
279#446—111no—
280#446—111no—
281#446—111no—
282#446—221no—
283#446—221no—
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8—111no—
287C4×Q16—111no—
288C4×Q16—111no—
289C4×SD16—111no—
290C4×SD16—111no—
291#436—111no—
292#436—221no—
293#435—221no—
294C8×D4—111no—
295#433—221no—
296#433—221no—
297#433—221no—
298#432C2×D1111yescharacteristic
299#431—111no—
300#424—221no—
301#423—111no—
302C4×M16—111no—
303C2×C4×C8C2×D1111yescharacteristic
304#335—111no—
305#335—111no—
306#334—111no—
307#334—111no—
308Q8⋊C8—111no—
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8C2×D1111yescharacteristic
313Q8⋊C8C2×D1111yescharacteristic
314D4⋊C8C2×D1111yescharacteristic
315D4⋊C8C2×D1111yescharacteristic
316#322—111no—
317#322—111no—
318C82—111no—
319C82—111no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11C2×C4×D411yescharacteristic
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11C2×#13111yescharacteristic
335C4×C11C2×#13111yescharacteristic
336C4×C11#57711yescharacteristic
337C4×C11#57811yescharacteristic
338Dic11—41no—
339Dic11—41no—
340Dic11—41no—
341Dic11—41no—
342C2×Q16—111no—
343C2×Q16—111no—
344C2×SD16—111no—
345C2×SD16—111no—
346C2×M16—111no—
347C2×M16—111no—
348C2×M16—221no—
349C2×M16—221no—
350C22×C8—21no—
351C22×C8—221no—
352C4⋊Q8—111no—
353C4⋊Q8—111no—
354#126—21no—
355#125—221no—
356#125C4×D1111yescharacteristic
357#124C4×D1111yescharacteristic
358#123—21no—
359C22⋊Q8—111no—
360C22⋊Q8—111no—
361C22⋊Q8—221no—
362C22⋊Q8C4×D1111yescharacteristic
363#121C4×D1111yescharacteristic
364C4×Q8—111no—
365C4×Q8—111no—
366C4×Q8—221no—
367C4×Q8C22×D1111yescharacteristic
368C4×D4—21no—
369C4×D4C22×D1111yescharacteristic
370#117—21no—
371#117—221no—
372C2×C42C22×D1111yescharacteristic
373#107—111no—
374#107—111no—
375#106—111no—
376#106—111no—
377C4⋊C8—111no—
378C4⋊C8—111no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—221no—
382C4⋊C8—221no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8C22×D1111yescharacteristic
389C4⋊C8C22×D1111yescharacteristic
390#103—111no—
391#103—111no—
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#102—111no—
397#102—111no—
398C22⋊C8—21no—
399C22⋊C8—111no—
400C22⋊C8—111no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403#97—21no—
404#97—111no—
405#97—111no—
406#97—221no—
407#97—221no—
408#97—221no—
409C4×C8—21no—
410C4×C8—111no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—221no—
415C4×C8—221no—
416C4×C8—221no—
417C4×C8C22×D1111yescharacteristic
418C4×C8C22×D1111yescharacteristic
419C2×C11—41no—
420C2×C11—81no—
421C2×C11#293111yescharacteristic
422C2×C11#294711yescharacteristic
423C2×C11#295611yescharacteristic
424C2×Q8—111no—
425C2×Q8—111no—
426C2×Q8—221no—
427C2×Q8C2×C4×D1111yescharacteristic
428C2×D4—21no—
429C2×D4C2×C4×D1111yescharacteristic
430C22×C4—21no—
431C22×C4C2×C4×D1111yescharacteristic
432C22×C4D4×D1111yescharacteristic
433C22×C4#434111yescharacteristic
434Q16—222no—
435Q16—222no—
436SD16—222no—
437SD16—222no—
438M16—222no—
439M16—222no—
440M16—881no—
441M16—881no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—42no—
447C2×C8—111no—
448C2×C8—111no—
449C2×C8—111no—
450C2×C8—111no—
451C2×C8—111no—
452C2×C8—111no—
453C2×C8—111no—
454C2×C8—111no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—881no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—111no—
463C4⋊C4—111no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4C2×C4×D1111yescharacteristic
472C4⋊C4C2×C4×D1111yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—221no—
479C22⋊C4—221no—
480C42—21no—
481C42—221no—
482C42—221no—
483C42C2×C4×D1111yescharacteristic
484C42D4×D1111yescharacteristic
485C42#434111yescharacteristic
486C42C23×D1111yescharacteristic
487C11#1796911yescharacteristic, complemented, Sylow
488C23—21no—
489C23(C22⋊D11)⋊C411yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—221no—
493Q8—221no—
494Q8—221no—
495Q8—221no—
496Q8—881no—
497D4—21no—
498D4—21no—
499D4—81no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4(C22⋊D11)⋊C411yescharacteristic
515C2×C4(C22⋊D11)⋊C411yescharacteristic
516C2×C4(C22⋊D11)⋊C411yescharacteristic
517C2×C4C22×C4×D1111yescharacteristic
518C2×C4C2×D4×D1111yescharacteristic
519C2×C4C2×#434111yescharacteristic
520C8—22no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—112no—
525C8—112no—
526C8—221no—
527C8—221no—
528C8—221no—
529C8—221no—
530C8—221no—
531C8—221no—
532C8—441no—
533C8—441no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22C2×(C22⋊D11)⋊C411yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—441no—
549C4—441no—
550C4—441no—
551C4—441no—
552C4D11×#13111yescharacteristic
553C4D11×#13111yescharacteristic
554C4#1062330111yescharacteristic
555C4#1062330211yescharacteristic
556C2—41no—
557C2—81no—
558C2#1307732411yescharacteristic
559C2#1307746211yescharacteristic
560C2#1307752211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1494C2
socleC22×C11C2×C4×D4
prime radicalC11×#121C2×C4
cosocleC42×C11C24
hypercenter#1494D11
hypocenterC11#17969
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
3. #13077713C2semidirect
4. #13067522C2semidirect
5. #13067515C2semidirect
6. #13067510C2semidirect
7. #13067509C2semidirect
8. #13067432C2semidirect
9. #13067425C2semidirect
10. #13067420C2semidirect
11. #13067419C2semidirect
12. #13067384C2semidirect
13. #13067072C2semidirect
14. C8×#4318C2semidirect
487. C11#17969semidirect

Maximal subgroups

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

subgroupindex
#130792232
#130777652
#130777132
#130675222
#130675152
#130675102
#130675092
#130674322
#130674252
#130674202
#130674192
#130673842
#130670722
C8×#43182
C11×#14942
#1796911