Finite Group Databasebeta

← #14723852

Subgroups — #14723852

Order 2816.

596 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078698C211yesmaximal, characteristic
2#13077767C211yesmaximal, characteristic
3#13077696C211yesmaximal, characteristic, complemented
4#13067496C211yesmaximal, characteristic, complemented
5#13067489C211yesmaximal, characteristic, complemented
6#13067468C211yesmaximal, characteristic, complemented
7#13067461C211yesmaximal, characteristic, complemented
8#13067436C211yesmaximal, characteristic, complemented
9#13067430C211yesmaximal, characteristic, complemented
10C8×Dic44C211yesmaximal, characteristic, complemented
11C8×#4314C211yesmaximal, characteristic, complemented
12#13067405C211yesmaximal, characteristic, complemented
13#13067046C211yesmaximal, characteristic, complemented
14#13067025C211yesmaximal, characteristic
15C11×#1454C211yesmaximal, characteristic, complemented
16#10623010C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21#10622538C2211yescharacteristic
22#10622537C2211yescharacteristic
23#10622458C411yescharacteristic
24#10622458C411yescharacteristic
25#10622453—21no—
26#10622452—21no—
27#10622443—21no—
28#10622443—21no—
29#10622442C411yescharacteristic
30#10622442C411yescharacteristic
31#10622352C411yescharacteristic
32#10622351C411yescharacteristic
33#10622349C411yescharacteristic
34#10622342—21no—
35#10622341—21no—
36#10622334C411yescharacteristic
37#10622331—21no—
38#10622331—21no—
39C4×Dic44C2211yescharacteristic
40C4×Dic44C2211yescharacteristic
41C4×#4314C2211yescharacteristic
42C4×#4314C2211yescharacteristic
43#10622301C2211yescharacteristic
44C8×D44C2211yescharacteristic
45#10622292C2211yescharacteristic
46C8×Dic22C2211yescharacteristic
47C8×Dic22C2211yescharacteristic
48C8×Dic22C2211yescharacteristic
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#322C2211yescharacteristic
52C11×#322C2211yescharacteristic
53C11×#322C2211yescharacteristic
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
67C22×Dic22C2×C411yescharacteristic
68C2×C42×C11C2311yescharacteristic
69#66983C2×C411yescharacteristic
70#66982—21no—
71C4×C22⋊D11—21no—
72C2×C4⋊Dic11C2×C411yescharacteristic
73#66977C2×C411yescharacteristic
74C2×Dic11⋊C4—21no—
75C2×C4×Dic11—21no—
76C2×#4318—21no—
77C2×Dic44C2×C411yescharacteristic
78C2×Dic44C2×C411yescharacteristic
79C2×#4314C2×C411yescharacteristic
80C2×#4314C2×C411yescharacteristic
81C2×#4313—21no—
82C2×C8×D11—21no—
83#66929—21no—
84#66928C2×C411yescharacteristic
85C4×D44C2311yescharacteristic
86#66925—21no—
87#66923C2×C411yescharacteristic
88C4×Dic22—21no—
89C4×Dic22—21no—
90C4×Dic22C2×C411yescharacteristic
91C4×Dic22C2×C411yescharacteristic
92C4×Dic22C2311yescharacteristic
93C4×Dic22C2311yescharacteristic
94C4×Dic22C2311yescharacteristic
95C11×C4⋊C8—21no—
96C11×C4⋊C8C2×C411yescharacteristic
97C11×C4⋊C8C2×C411yescharacteristic
98C11×C4⋊C8D411yescharacteristic
99C11×C4⋊C8D411yescharacteristic
100C11×C22⋊C8—21no—
101C11×C22⋊C8C2×C411yescharacteristic
102C11×C22⋊C8C2×C411yescharacteristic
103C11×C22⋊C8D411yescharacteristic
104C11×C22⋊C8D411yescharacteristic
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—
127Dic11⋊C8—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133C8×Dic11—21no—
134C8×Dic11—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
143C4×C11⋊C8—21no—
144#17919—111nomaximal, Sylow
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C2×C22⋊D11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C2×D44C22×C411yescharacteristic
152C2×C4×D11—21no—
153C2×Dic22—22no—
154C2×Dic22—22no—
155C2×Dic22—21no—
156C2×Dic22C22×C411yescharacteristic
157C2×Dic22C22×C411yescharacteristic
158C2×Dic22C22×C411yescharacteristic
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11C22×C411yescharacteristic
162C2×C8×C11C22×C411yescharacteristic
163C2×C8×C11C22×C411yescharacteristic
164C2×C8×C11C22×C411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C42×C11C22×C411yescharacteristic
170C42×C11C2×D411yescharacteristic
171C42×C11#4111yescharacteristic
172C42×C11C2411yescharacteristic
173C22⋊Dic11—21no—
174(C2×D11)⋊C4—21no—
175(C2×D11)⋊C4—21no—
176(C2×D11)⋊C4—21no—
177(C2×D11)⋊C4—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11C22×C411yescharacteristic
180C4⋊Dic11C22×C411yescharacteristic
181C4⋊Dic11C22×C411yescharacteristic
182C4⋊Dic11C22×C411yescharacteristic
183Dic11⋊C4—21no—
184Dic11⋊C4—21no—
185Dic11⋊C4—21no—
186Dic11⋊C4—21no—
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×Dic11—21no—
196#4318—81no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201Dic44—22no—
202Dic44—22no—
203#4314—22no—
204#4314—22no—
205#4313—81no—
206C8×D11—81no—
207#3108—111no—
208#2993—111no—
209#2982—111no—
210#1588—111no—
211#1587—111no—
212#1584—111no—
213#1583—111no—
214#1579—111no—
215SD16⋊C8—111no—
216C8×Q16—111no—
217C8×SD16—111no—
218#1574—111no—
219#1487—111no—
220#1482—111no—
221#1454D1111yescharacteristic, complemented
222C23×C11C4×D411yescharacteristic
223C22×D11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—41no—
229C2×C4×C11C4×D411yescharacteristic
230C2×C4×C11C4×D411yescharacteristic
231C2×C4×C11C4×D411yescharacteristic
232C2×C4×C11C23×C411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C22⋊D11—81no—
236C2×Dic11—24no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—81no—
245D44—21no—
246D44—21no—
247C4×D11—41no—
248C4×D11—41no—
249Dic22—24no—
250Dic22—21no—
251Dic22—21no—
252Dic22—21no—
253Dic22—21no—
254Dic22#13112yes—
255Dic22#13112yes—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—41no—
265C8×C11—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270#529—111no—
271C2×C4×Q8—111no—
272#483—111no—
273#480—111no—
274#479—111no—
275#479—111no—
276#464—111no—
277#464—111no—
278#451—111no—
279#448—111no—
280#446—111no—
281C8×Q8—111no—
282C8×Q8—111no—
283C8×Q8—111no—
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8—221no—
287C8×Q8—221no—
288C4×Q16—111no—
289C4×Q16—111no—
290C4×SD16—111no—
291C4×SD16—111no—
292#436—111no—
293#436—221no—
294#435—221no—
295C8×D4—111no—
296#433—221no—
297#431—111no—
298#431—221no—
299#431—221no—
300#431C2×D1111yescharacteristic
301#431C2×D1111yescharacteristic
302#431C2×D1111yescharacteristic
303#424—221no—
304#423—111no—
305#335—111no—
306#335—111no—
307#334—111no—
308#334—111no—
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315D4⋊C8—111no—
316D4⋊C8—111no—
317#322C2×D1111yescharacteristic
318#322C2×D1111yescharacteristic
319#322C2×D1111yescharacteristic
320C82C2×D1111yescharacteristic
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11C2×C4×D411yescharacteristic
325C2×D11—41no—
326C2×D11—41no—
327C2×D11—41no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11C2×#13111yescharacteristic
333C4×C11C2×#13111yescharacteristic
334C4×C11#57711yescharacteristic
335C4×C11#57811yescharacteristic
336Dic11—22no—
337Dic11—22no—
338Dic11—41no—
339Dic11—41no—
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343C22×Q8—111no—
344C2×Q16—111no—
345C2×Q16—111no—
346C2×SD16—111no—
347C2×SD16—111no—
348C2×M16—221no—
349C2×M16—221no—
350C22×C8—221no—
351#126—221no—
352#125—111no—
353#124—111no—
354#123—221no—
355C22⋊Q8—111no—
356#121—111no—
357C4×Q8—111no—
358C4×Q8—111no—
359C4×Q8—111no—
360C4×Q8—111no—
361C4×Q8—111no—
362C4×Q8—221no—
363C4×Q8—221no—
364C4×D4—111no—
365C4×D4—221no—
366#117—221no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—221no—
369C2×C42—221no—
370C2×C42C22×D1111yescharacteristic
371#107—111no—
372#107—111no—
373#106—111no—
374#106—111no—
375C4⋊C8—21no—
376C4⋊C8—111no—
377C4⋊C8—111no—
378C4⋊C8—111no—
379C4⋊C8—111no—
380C4⋊C8—221no—
381C4⋊C8—221no—
382C4⋊C8—221no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8C4×D1111yescharacteristic
388C4⋊C8C4×D1111yescharacteristic
389C4⋊C8D4411yescharacteristic
390C4⋊C8D4411yescharacteristic
391#103—111no—
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#102—111no—
398#102—111no—
399C22⋊C8—21no—
400C22⋊C8—221no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403C22⋊C8C4×D1111yescharacteristic
404C22⋊C8C4×D1111yescharacteristic
405C22⋊C8D4411yescharacteristic
406C22⋊C8D4411yescharacteristic
407#97—221no—
408C4×C8—221no—
409C4×C8—221no—
410C4×C8—221no—
411C4×C8—221no—
412C4×C8—221no—
413C4×C8—221no—
414C4×C8C22×D1111yescharacteristic
415C4×C8C22×D1111yescharacteristic
416C4×C8C22×D1111yescharacteristic
417C4×C8C22×D1111yescharacteristic
418C4×C8C22×D1111yescharacteristic
419C4×C8C22×D1111yescharacteristic
420C2×C11—41no—
421C2×C11#292911yescharacteristic
422C2×C11#294711yescharacteristic
423C2×C11#295711yescharacteristic
424D11—81no—
425C2×Q8—111no—
426C2×Q8—111no—
427C2×Q8—111no—
428C2×Q8—222no—
429C2×Q8—222no—
430C2×Q8—221no—
431C2×D4—111no—
432C2×D4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4C2×C4×D1111yescharacteristic
437C22×C4C2×D4411yescharacteristic
438C22×C4#433911yescharacteristic
439Q16—222no—
440Q16—222no—
441SD16—222no—
442SD16—222no—
443M16—881no—
444M16—881no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—881no—
452C2×C8C2×C4×D1111yescharacteristic
453C2×C8C2×C4×D1111yescharacteristic
454C2×C8C2×C4×D1111yescharacteristic
455C2×C8C2×C4×D1111yescharacteristic
456C2×C8C2×D4411yescharacteristic
457C2×C8C2×D4411yescharacteristic
458C2×C8C2×D4411yescharacteristic
459C2×C8C2×D4411yescharacteristic
460C4⋊C4—111no—
461C4⋊C4—111no—
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⋊C4—221no—
472C4⋊C4—221no—
473C22⋊C4—221no—
474C22⋊C4—221no—
475C22⋊C4—221no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C42—221no—
479C42—221no—
480C42—221no—
481C42—221no—
482C42—221no—
483C42C2×C4×D1111yescharacteristic
484C42C2×D4411yescharacteristic
485C42#433911yescharacteristic
486C42C23×D1111yescharacteristic
487C11#1791911yescharacteristic, complemented, Sylow
488C23—221no—
489C23C4×D4411yescharacteristic
490Q8—112no—
491Q8—112no—
492Q8—224no—
493Q8—221no—
494Q8—221no—
495Q8—221no—
496Q8—221no—
497D4—221no—
498D4—221no—
499D4—881no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—224no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—881no—
516C2×C4C4×D4411yescharacteristic
517C2×C4C4×D4411yescharacteristic
518C2×C4C4×D4411yescharacteristic
519C2×C4C22×C4×D1111yescharacteristic
520C2×C4C22×D4411yescharacteristic
521C2×C4C2×#433911yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—41no—
531C8—41no—
532C8—441no—
533C8—441no—
534C8—441no—
535C8—441no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—441no—
540C22—441no—
541C22—441no—
542C22C2×C4×D4411yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—222no—
548C4—222no—
549C4—441no—
550C4—441no—
551C4—441no—
552C4—441no—
553C4—441no—
554C4D11×#13111yescharacteristic
555C4D11×#13111yescharacteristic
556C4#1062328211yescharacteristic
557C4#1062328411yescharacteristic
558C2—41no—
559C2—881no—
560C2#1307731211yescharacteristic
561C2#1307746111yescharacteristic
562C2#1307753411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1454C2
socleC22×C11C2×C4×D4
prime radical#66983C2×C4
cosocleC42×C11C24
hypercenter#1454D11
hypocenterC11#17919
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
3. #13077696C2semidirect
4. #13067496C2semidirect
5. #13067489C2semidirect
6. #13067468C2semidirect
7. #13067461C2semidirect
8. #13067436C2semidirect
9. #13067430C2semidirect
10. C8×Dic44C2semidirect
11. C8×#4314C2semidirect
12. #13067405C2semidirect
13. #13067046C2semidirect
15. C11×#1454C2semidirect
221. #1454D11semidirect
487. C11#17919semidirect

Maximal subgroups

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

subgroupindex
#130786982
#130777672
#130776962
#130674962
#130674892
#130674682
#130674612
#130674362
#130674302
C8×Dic442
C8×#43142
#130674052
#130670462
#130670252
C11×#14542
#1791911