Finite Group Databasebeta

← #14724422

Subgroups — #14724422

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#13079222C211yesmaximal, characteristic
2#13077767C211yesmaximal, characteristic
3#13077710C211yesmaximal, characteristic, complemented
4#13067526C211yesmaximal, characteristic, complemented
5#13067520C211yesmaximal, characteristic, complemented
6#13067514C211yesmaximal, characteristic, complemented
7#13067508C211yesmaximal, characteristic, complemented
8#13067436C211yesmaximal, characteristic, complemented
9#13067430C211yesmaximal, characteristic, complemented
10C8×Dic44C211yesmaximal, characteristic, complemented
11C8×#4314C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067077C211yesmaximal, characteristic
14#13067072C211yesmaximal, characteristic, complemented
15C8×C11×M16C211yesmaximal, characteristic, complemented
16#10623010C2211yescharacteristic
17#10623001C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C4×C11×M16C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21#10622750C411yescharacteristic
22#10622750C411yescharacteristic
23#10622747C411yescharacteristic
24#10622747C411yescharacteristic
25#10622539C2211yescharacteristic
26#10622537C2211yescharacteristic
27#10622453—21no—
28#10622452—21no—
29#10622441—21no—
30#10622441—21no—
31#10622342—21no—
32#10622341—21no—
33#10622333—21no—
34#10622333—21no—
35#10622328C411yescharacteristic
36#10622327C411yescharacteristic
37#10622316C411yescharacteristic
38#10622315C411yescharacteristic
39C4×Dic44C2211yescharacteristic
40C4×Dic44C2211yescharacteristic
41C4×#4314C2211yescharacteristic
42C4×#4314C2211yescharacteristic
43#10622301C2211yescharacteristic
44C8×D44C2211yescharacteristic
45#10622292C2211yescharacteristic
46#10622292C2211yescharacteristic
47#10622292C2211yescharacteristic
48C8×Dic22C2211yescharacteristic
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#322C2211yescharacteristic
52C11×#322C2211yescharacteristic
53C82×C11C2211yescharacteristic
54C82×C11C2211yescharacteristic
55#10622097C2211yescharacteristic
56#10622097C2211yescharacteristic
57#10622096C2211yescharacteristic
58#10622096C2211yescharacteristic
59#10622095C2211yescharacteristic
60#10622095C2211yescharacteristic
61#10622094C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622094C2211yescharacteristic
65#10622094C2211yescharacteristic
66#10622094C2211yescharacteristic
67C2×C11×M16C2×C411yescharacteristic
68C2×C11×M16C2×C411yescharacteristic
69C22×C8×C11—21no—
70C2×C42×C11C2311yescharacteristic
71#66983C2×C411yescharacteristic
72#66982—21no—
73C4×C22⋊D11—21no—
74#66979—21no—
75#66977—21no—
76#66977C2×C411yescharacteristic
77#66977C2×C411yescharacteristic
78#66977C2×C411yescharacteristic
79C2×#4318—21no—
80C2×Dic44C2×C411yescharacteristic
81C2×Dic44C2×C411yescharacteristic
82C2×#4314C2×C411yescharacteristic
83C2×#4314C2×C411yescharacteristic
84C2×#4313—21no—
85C2×C8×D11—21no—
86#66929—21no—
87#66928C2×C411yescharacteristic
88C4×D44C2311yescharacteristic
89#66925—21no—
90#66923—21no—
91#66923C2×C411yescharacteristic
92#66922C2×C411yescharacteristic
93#66922C2×C411yescharacteristic
94C4×Dic22—21no—
95C4×Dic22C2311yescharacteristic
96C4×Dic22C2311yescharacteristic
97C4×Dic22C2311yescharacteristic
98C11×C4⋊C8D411yescharacteristic
99C11×C4⋊C8D411yescharacteristic
100C11×C22⋊C8D411yescharacteristic
101C11×C22⋊C8D411yescharacteristic
102C11×#97C2×C411yescharacteristic
103C11×#97C2×C411yescharacteristic
104C4×C8×C11—21no—
105C4×C8×C11C2311yescharacteristic
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C22⋊(C11⋊C8)—21no—
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—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134Dic11⋊C8—21no—
135C8×Dic11—21no—
136C8×Dic11—21no—
137C8×Dic11—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143#66867—21no—
144#17969—111nomaximal, Sylow
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C2×C22⋊D11—21no—
149C2×D44C22×C411yescharacteristic
150C2×C4×D11—21no—
151C2×Dic22—21no—
152C2×Dic22C22×C411yescharacteristic
153C2×Dic22C22×C411yescharacteristic
154C2×Dic22C22×C411yescharacteristic
155C11×M16—22no—
156C11×M16—22no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—42no—
160C2×C8×C11C22×C411yescharacteristic
161C2×C8×C11C22×C411yescharacteristic
162C2×C8×C11C22×C411yescharacteristic
163C2×C8×C11C22×C411yescharacteristic
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C42×C11C22×C411yescharacteristic
169C42×C11C2×D411yescharacteristic
170C42×C11#4111yescharacteristic
171C42×C11C2411yescharacteristic
172C22⋊Dic11—21no—
173C22⋊Dic11—21no—
174C22⋊Dic11—21no—
175(C2×D11)⋊C4—21no—
176(C2×D11)⋊C4—21no—
177(C2×D11)⋊C4—21no—
178(C2×D11)⋊C4—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11C22×C411yescharacteristic
183C4⋊Dic11C22×C411yescharacteristic
184C4⋊Dic11C22×C411yescharacteristic
185C4⋊Dic11C22×C411yescharacteristic
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197#4318—81no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202Dic44—22no—
203Dic44—22no—
204#4314—22no—
205#4314—22no—
206#4313—81no—
207C8×D11—81no—
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#1494—111no—
221#1493—111no—
222C8×M16D1111yescharacteristic, complemented
223C23×C11C4×D411yescharacteristic
224C22×D11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—41no—
230C2×C4×C11C4×D411yescharacteristic
231C2×C4×C11C4×D411yescharacteristic
232C2×C4×C11C4×D411yescharacteristic
233C2×C4×C11C23×C411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C22⋊D11—81no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244D44—21no—
245D44—21no—
246C4×D11—41no—
247C4×D11—41no—
248Dic22—21no—
249Dic22—21no—
250Dic22—21no—
251Dic22—21no—
252Dic22—21no—
253Dic22—21no—
254Dic22—81no—
255C8×C11—22no—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—41no—
263C8×C11#13112yes—
264C8×C11#13112yes—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269#533—111no—
270#529—111no—
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#432—111no—
299#431C2×D1111yescharacteristic
300#424—221no—
301#423—111no—
302C4×M16C2×D1111yescharacteristic
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⋊C8—111no—
313Q8⋊C8—111no—
314D4⋊C8—111no—
315D4⋊C8—111no—
316#322C2×D1111yescharacteristic
317#322C2×D1111yescharacteristic
318C82C2×D1111yescharacteristic
319C82C2×D1111yescharacteristic
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11C2×C4×D411yescharacteristic
324C2×D11—41no—
325C2×D11—41no—
326C2×D11—41no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11C2×#13111yescharacteristic
332C4×C11C2×#13111yescharacteristic
333C4×C11#57711yescharacteristic
334C4×C11#57811yescharacteristic
335Dic11—41no—
336Dic11—41no—
337Dic11—41no—
338Dic11—41no—
339Dic11—41no—
340Dic11—41no—
341Dic11—41no—
342C2×Q16—111no—
343C2×Q16—111no—
344C2×SD16—111no—
345C2×SD16—111no—
346C2×M16—221no—
347C2×M16—221no—
348C2×M16C4×D1111yescharacteristic
349C2×M16C4×D1111yescharacteristic
350C22×C8—21no—
351C22×C8—221no—
352C4⋊Q8—111no—
353C4⋊Q8—111no—
354#126—221no—
355#125—111no—
356#125—221no—
357#124—111no—
358#123—221no—
359C22⋊Q8—111no—
360C22⋊Q8—111no—
361C22⋊Q8—111no—
362C22⋊Q8—221no—
363#121—111no—
364C4×Q8—111no—
365C4×Q8—111no—
366C4×Q8—111no—
367C4×Q8—221no—
368C4×D4—111no—
369C4×D4—221no—
370#117—221no—
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⋊C8D4411yescharacteristic
389C4⋊C8D4411yescharacteristic
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—221no—
399C22⋊C8—221no—
400C22⋊C8—221no—
401C22⋊C8D4411yescharacteristic
402C22⋊C8D4411yescharacteristic
403#97—221no—
404#97—221no—
405#97—221no—
406#97—221no—
407#97C4×D1111yescharacteristic
408#97C4×D1111yescharacteristic
409C4×C8—21no—
410C4×C8—221no—
411C4×C8—221no—
412C4×C8—221no—
413C4×C8C22×D1111yescharacteristic
414C4×C8C22×D1111yescharacteristic
415C4×C8C22×D1111yescharacteristic
416C4×C8C22×D1111yescharacteristic
417C4×C8C22×D1111yescharacteristic
418C4×C8C22×D1111yescharacteristic
419C2×C11—41no—
420C2×C11#293111yescharacteristic
421C2×C11#294711yescharacteristic
422C2×C11#295611yescharacteristic
423D11—81no—
424C2×Q8—111no—
425C2×Q8—111no—
426C2×Q8—111no—
427C2×Q8—221no—
428C2×D4—111no—
429C2×D4—221no—
430C22×C4—221no—
431C22×C4C2×C4×D1111yescharacteristic
432C22×C4C2×D4411yescharacteristic
433C22×C4#433911yescharacteristic
434Q16—222no—
435Q16—222no—
436SD16—222no—
437SD16—222no—
438M16—22no—
439M16—22no—
440M16—881no—
441M16—881no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—42no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—881no—
450C2×C8C2×C4×D1111yescharacteristic
451C2×C8C2×C4×D1111yescharacteristic
452C2×C8C2×C4×D1111yescharacteristic
453C2×C8C2×C4×D1111yescharacteristic
454C2×C8C2×D4411yescharacteristic
455C2×C8C2×D4411yescharacteristic
456C2×C8C2×D4411yescharacteristic
457C2×C8C2×D4411yescharacteristic
458C4⋊C4—111no—
459C4⋊C4—111no—
460C4⋊C4—111no—
461C4⋊C4—111no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C22⋊C4—221no—
474C22⋊C4—221no—
475C22⋊C4—221no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C22⋊C4—221no—
479C22⋊C4—221no—
480C42—221no—
481C42—221no—
482C42—221no—
483C42C2×C4×D1111yescharacteristic
484C42C2×D4411yescharacteristic
485C42#433911yescharacteristic
486C42C23×D1111yescharacteristic
487C11#1796911yescharacteristic, complemented, Sylow
488C23—221no—
489C23C4×D4411yescharacteristic
490Q8—221no—
491Q8—221no—
492Q8—221no—
493Q8—221no—
494Q8—221no—
495Q8—221no—
496Q8—881no—
497D4—221no—
498D4—221no—
499D4—881no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4C4×D4411yescharacteristic
515C2×C4C4×D4411yescharacteristic
516C2×C4C4×D4411yescharacteristic
517C2×C4C22×C4×D1111yescharacteristic
518C2×C4C22×D4411yescharacteristic
519C2×C4C2×#433911yescharacteristic
520C8—22no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—21no—
527C8—41no—
528C8—441no—
529C8—441no—
530C8—441no—
531C8—441no—
532C8#6695412yes—
533C8#6695412yes—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—441no—
538C22—441no—
539C22—441no—
540C22C2×C4×D4411yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—441no—
546C4—441no—
547C4—441no—
548C4—441no—
549C4—441no—
550C4—441no—
551C4—441no—
552C4C2×#6695411yescharacteristic
553C4C2×#6695411yescharacteristic
554C4#1062328211yescharacteristic
555C4#1062328411yescharacteristic
556C2—41no—
557C2—881no—
558C2#1307732911yescharacteristic
559C2#1307746111yescharacteristic
560C2#1307752711yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC8×C11×M16C2
socleC22×C11C2×C4×D4
prime radical#66983C2×C4
cosocleC42×C11C24
hypercenterC8×M16D11
hypocenterC11#17969
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ C8×M16

Complements

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

NH ≅ G/Ntype
3. #13077710C2semidirect
4. #13067526C2semidirect
5. #13067520C2semidirect
6. #13067514C2semidirect
7. #13067508C2semidirect
8. #13067436C2semidirect
9. #13067430C2semidirect
10. C8×Dic44C2semidirect
11. C8×#4314C2semidirect
12. #13067383C2semidirect
14. #13067072C2semidirect
15. C8×C11×M16C2semidirect
222. C8×M16D11semidirect
487. C11#17969semidirect

Maximal subgroups

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

subgroupindex
#130792222
#130777672
#130777102
#130675262
#130675202
#130675142
#130675082
#130674362
#130674302
C8×Dic442
C8×#43142
#130673832
#130670772
#130670722
C8×C11×M162
#1796911