Finite Group Databasebeta

← #14723841

Subgroups — #14723841

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#13078694C211yesmaximal, characteristic
2#13077766C211yesmaximal, characteristic
3#13077695C211yesmaximal, characteristic, complemented
4#13067495C211yesmaximal, characteristic, complemented
5#13067486C211yesmaximal, characteristic, complemented
6#13067463C211yesmaximal, characteristic, complemented
7#13067462C211yesmaximal, characteristic, complemented
8#13067433C211yesmaximal, characteristic, complemented
9#13067428C211yesmaximal, characteristic, complemented
10C8×Dic44C211yesmaximal, characteristic, complemented
11#13067403C211yesmaximal, characteristic, complemented
12#13067043C211yesmaximal, characteristic, complemented
13#13067021C211yesmaximal, characteristic
14#13066915C211yesmaximal, characteristic, complemented
15C8×C11×SD16C211yesmaximal, characteristic, complemented
16C4×Q8×D11C2211yescharacteristic
17#10623088C2211yescharacteristic
18C8×Q8×C11C2211yescharacteristic
19C4×C11×SD16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622783C411yescharacteristic
22#10622779C411yescharacteristic
23#10622724—21no—
24#10622715—21no—
25C4×#4326C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27C4×#4324C2211yescharacteristic
28#10622625C2211yescharacteristic
29#10622475C411yescharacteristic
30#10622470C411yescharacteristic
31#10622450C2211yescharacteristic
32#10622446—21no—
33#10622446C2211yescharacteristic
34#10622444C2211yescharacteristic
35#10622443—21no—
36#10622443C2211yescharacteristic
37#10622421C411yescharacteristic
38#10622409C411yescharacteristic
39#10622387C411yescharacteristic
40#10622380C411yescharacteristic
41#10622342—21no—
42#10622333—21no—
43C4×Dic44C2211yescharacteristic
44#10622298—21no—
45#10622298C2211yescharacteristic
46#10622298C2211yescharacteristic
47#10622298C2211yescharacteristic
48C8×Dic22—21no—
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C82×C11C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622096C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×Q8×D11C2×C411yescharacteristic
68C2×C11×SD16C2×C411yescharacteristic
69C22×C8×C11—21no—
70C4×Q8×C11C2311yescharacteristic
71C4×D4×C11C2311yescharacteristic
72Q8×Dic11C2×C411yescharacteristic
73C2×#4326C2×C411yescharacteristic
74#66991C2×C411yescharacteristic
75#66989C2×C411yescharacteristic
76C2×#4324C2×C411yescharacteristic
77C4×C22⋊D11—21no—
78#66979—21no—
79C2×#4318—21no—
80C2×Dic44C2×C411yescharacteristic
81C2×#4313—21no—
82#66950C2×C411yescharacteristic
83C4⋊C4×D11—21no—
84C4⋊C4×D11C2×C411yescharacteristic
85#66943C2×C411yescharacteristic
86#66940—21no—
87#66940C2×C411yescharacteristic
88#66936—21no—
89#66932—21no—
90C42×D11—21no—
91C42×D11C2311yescharacteristic
92C4×Dic22—21no—
93C4×Dic22C2311yescharacteristic
94C4×Dic22C2311yescharacteristic
95C11×#106C2×C411yescharacteristic
96C11×C4⋊C8—21no—
97C11×C4⋊C8C2311yescharacteristic
98C11×C4⋊C8C2311yescharacteristic
99C11×#103C2×C411yescharacteristic
100C11×#102C2×C411yescharacteristic
101C11×C22⋊C8—21no—
102C4×C8×C11—21no—
103C4×C8×C11C2311yescharacteristic
104C4×C8×C11C2311yescharacteristic
105C4×C8×C11C2311yescharacteristic
106#66899C2×C411yescharacteristic
107#66896C2×C411yescharacteristic
108C22⋊(C11⋊C8)—21no—
109(C2×D11)⋊C8—21no—
110(C2×D11)⋊C8—21no—
111(C2×D11)⋊C8C2×C411yescharacteristic
112(C2×D11)⋊C8C2×C411yescharacteristic
113(C2×D11)⋊C8D411yescharacteristic
114(C2×D11)⋊C8D411yescharacteristic
115#66882C2×C411yescharacteristic
116#66880C2×C411yescharacteristic
117#66880C2×C411yescharacteristic
118#66879—21no—
119Dic11⋊C8—21no—
120Dic11⋊C8—21no—
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8C2×C411yescharacteristic
126Dic11⋊C8C2×C411yescharacteristic
127Dic11⋊C8D411yescharacteristic
128Dic11⋊C8D411yescharacteristic
129C8×Dic11—21no—
130C8×Dic11—21no—
131C8×Dic11—21no—
132C8×Dic11—21no—
133#66874C2×C411yescharacteristic
134#66874C2×C411yescharacteristic
135#66872C2×C411yescharacteristic
136#66871C2×C411yescharacteristic
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17919—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×D4×C11C22×C411yescharacteristic
147C22×C4×C11—21no—
148C2×C22⋊D11—21no—
149Q8×D11—22no—
150Q8×D11—22no—
151C2×C4×D11—21no—
152C2×C4×D11—21no—
153C2×C4×D11C22×C411yescharacteristic
154C2×C4×D11C2×D411yescharacteristic
155C2×C4×D11#4111yescharacteristic
156C2×Dic22—21no—
157C2×Dic22C22×C411yescharacteristic
158C2×Dic22C22×C411yescharacteristic
159C11×SD16—22no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—81no—
164C2×C8×C11C22×C411yescharacteristic
165C2×C8×C11C22×C411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C11×C4⋊C4—21no—
169C11×C4⋊C4C22×C411yescharacteristic
170C11×C4⋊C4C22×C411yescharacteristic
171C11×C22⋊C4—21no—
172C42×C11—21no—
173C42×C11C2411yescharacteristic
174C22⋊Dic11—21no—
175C22⋊Dic11—21no—
176C22⋊Dic11—21no—
177#4326—22no—
178#4324—22no—
179(C2×D11)⋊C4—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11C22×C411yescharacteristic
184C4⋊Dic11C22×C411yescharacteristic
185Dic11⋊C4—21no—
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11C22×C411yescharacteristic
195C4×Dic11C2×D411yescharacteristic
196C4×Dic11#4111yescharacteristic
197#4318—81no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205Dic44—22no—
206#4313—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×SD16D1111yescharacteristic, complemented
218#1574—111no—
219#1487—111no—
220#1482—111no—
221#1454—111no—
222C23×C11—21no—
223C22×D11C4×D411yescharacteristic
224Q8×C11—21no—
225Q8×C11#13112yes—
226D4×C11—21no—
227D4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
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×Dic11C4×D411yescharacteristic
242C2×Dic11C4×D411yescharacteristic
243C2×Dic11C4×D411yescharacteristic
244C4×D11—24no—
245C4×D11—21no—
246C4×D11—21no—
247C4×D11—21no—
248C4×D11—21no—
249C4×D11—41no—
250C4×D11—81no—
251Dic22—24no—
252Dic22—21no—
253Dic22—21no—
254Dic22—21no—
255Dic22#13112yes—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—41no—
261C8×C11—41no—
262C8×C11—41no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—21no—
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—221no—
286C8×Q8—221no—
287C8×Q8C2×D1111yescharacteristic
288C4×Q16—111no—
289C4×Q16—111no—
290C4×SD16—111no—
291C4×SD16C2×D1111yescharacteristic
292#436—111no—
293#436—221no—
294#435—221no—
295C8×D4C2×D1111yescharacteristic
296#433—221no—
297#431—111no—
298#431—111no—
299#431—111no—
300#431—111no—
301#431—221no—
302#431—221no—
303#424—221no—
304#423—111no—
305#335—111no—
306#335—111no—
307#334—111no—
308#334C2×D1111yescharacteristic
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8C2×D1111yescharacteristic
315D4⋊C8—111no—
316D4⋊C8C2×D1111yescharacteristic
317#322—111no—
318#322—111no—
319#322—111no—
320C82C2×D1111yescharacteristic
321C22×C11—41no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11C2×C4×D411yescharacteristic
325C2×D11—21no—
326C2×D11—21no—
327C2×D11—21no—
328C4×C11—22no—
329C4×C11—21no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11C2×#13111yescharacteristic
333C4×C11C2×#13111yescharacteristic
334C4×C11#57711yescharacteristic
335C4×C11#57811yescharacteristic
336Dic11—21no—
337Dic11—22no—
338Dic11—21no—
339Dic11—21no—
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343C22×Q8—111no—
344C2×Q16—111no—
345C2×Q16—111no—
346C2×SD16—111no—
347C2×SD16C4×D1111yescharacteristic
348C2×M16—221no—
349C2×M16—221no—
350C22×C8—21no—
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—221no—
362C4×Q8—221no—
363C4×Q8C22×D1111yescharacteristic
364C4×D4—221no—
365C4×D4C22×D1111yescharacteristic
366#117—221no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—221no—
369C2×C42—111no—
370C2×C42—221no—
371#107—111no—
372#107—111no—
373#106—111no—
374#106C4×D1111yescharacteristic
375C4⋊C8—21no—
376C4⋊C8—111no—
377C4⋊C8—111no—
378C4⋊C8—111no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—111no—
382C4⋊C8—221no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8C22×D1111yescharacteristic
390C4⋊C8C22×D1111yescharacteristic
391#103—111no—
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#103C4×D1111yescharacteristic
397#102—111no—
398#102C4×D1111yescharacteristic
399C22⋊C8—21no—
400C22⋊C8—111no—
401C22⋊C8—111no—
402C22⋊C8—111no—
403C22⋊C8—111no—
404C22⋊C8—221no—
405C22⋊C8—221no—
406C22⋊C8—221no—
407#97—221no—
408C4×C8—21no—
409C4×C8—111no—
410C4×C8—111no—
411C4×C8—111no—
412C4×C8—221no—
413C4×C8—221no—
414C4×C8—221no—
415C4×C8—221no—
416C4×C8—221no—
417C4×C8C22×D1111yescharacteristic
418C4×C8C22×D1111yescharacteristic
419C4×C8C22×D1111yescharacteristic
420C2×C11—81no—
421C2×C11#292911yescharacteristic
422C2×C11#294711yescharacteristic
423C2×C11#295711yescharacteristic
424D11—41no—
425C2×Q8—111no—
426C2×Q8—111no—
427C2×Q8—221no—
428C2×Q8—222no—
429C2×Q8—222no—
430C2×Q8C2×C4×D1111yescharacteristic
431C2×D4—221no—
432C2×D4C2×C4×D1111yescharacteristic
433C22×C4—21no—
434C22×C4—111no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—221no—
438C22×C4—221no—
439Q16—222no—
440Q16—222no—
441SD16—22no—
442SD16—222no—
443M16—881no—
444M16—881no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—81no—
449C2×C8—111no—
450C2×C8—111no—
451C2×C8—111no—
452C2×C8—111no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8C2×C4×D1111yescharacteristic
457C2×C8C2×C4×D1111yescharacteristic
458C2×C8D4×D1111yescharacteristic
459C2×C8D4×D1111yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—111no—
462C4⋊C4—111no—
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⋊C4C2×C4×D1111yescharacteristic
472C4⋊C4C2×C4×D1111yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—221no—
475C22⋊C4—221no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C42—21no—
479C42—111no—
480C42—111no—
481C42—111no—
482C42—221no—
483C42—221no—
484C42—221no—
485C42—221no—
486C42C23×D1111yescharacteristic
487C11#1791911yescharacteristic, complemented, Sylow
488C23—21no—
489C23—111no—
490Q8—21no—
491Q8—112no—
492Q8—224no—
493Q8—221no—
494Q8—221no—
495Q8—221no—
496Q8#6695412yes—
497D4—21no—
498D4—21no—
499D4—881no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—111no—
506C2×C4—111no—
507C2×C4—111no—
508C2×C4—224no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—441no—
518C2×C4—881no—
519C2×C4C22×C4×D1111yescharacteristic
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4#41×D1111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—221no—
530C8—221no—
531C8—221no—
532C8—221no—
533C8—441no—
534C8—441no—
535C8—441no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—221no—
540C22—221no—
541C22—221no—
542C22C4×D4×D1111yescharacteristic
543C4—21no—
544C4—22no—
545C4—41no—
546C4—41no—
547C4—221no—
548C4—221no—
549C4—222no—
550C4—221no—
551C4—441no—
552C4—441no—
553C4—441no—
554C4C2×#6695411yescharacteristic
555C4D11×#13111yescharacteristic
556C4#1062329311yescharacteristic
557C4#1062330211yescharacteristic
558C2—81no—
559C2—441no—
560C2#1307730511yescharacteristic
561C2#1307745211yescharacteristic
562C2#1307752811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC8×C11×SD16C2
socleC22×C11C2×C4×D4
prime radical#66991C2×C4
cosocleC42×C11C24
hypercenterC8×SD16D11
hypocenterC11#17919
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
3. #13077695C2semidirect
4. #13067495C2semidirect
5. #13067486C2semidirect
6. #13067463C2semidirect
7. #13067462C2semidirect
8. #13067433C2semidirect
9. #13067428C2semidirect
10. C8×Dic44C2semidirect
11. #13067403C2semidirect
12. #13067043C2semidirect
14. #13066915C2semidirect
15. C8×C11×SD16C2semidirect
217. C8×SD16D11semidirect
487. C11#17919semidirect

Maximal subgroups

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

subgroupindex
#130786942
#130777662
#130776952
#130674952
#130674862
#130674632
#130674622
#130674332
#130674282
C8×Dic442
#130674032
#130670432
#130670212
#130669152
C8×C11×SD162
#1791911