Finite Group Databasebeta

← #14724425

Subgroups — #14724425

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#13079218C211yesmaximal, characteristic
2#13077760C211yesmaximal, characteristic
3#13077712C211yesmaximal, characteristic, complemented
4#13067523C211yesmaximal, characteristic, complemented
5#13067518C211yesmaximal, characteristic, complemented
6#13067514C211yesmaximal, characteristic, complemented
7#13067434C211yesmaximal, characteristic, complemented
8SD16⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
9#13067420C211yesmaximal, characteristic, complemented
10#13067419C211yesmaximal, characteristic, complemented
11#13067380C211yesmaximal, characteristic, complemented
12#13067073C211yesmaximal, characteristic
13#13067069C211yesmaximal, characteristic, complemented
14C8×#4313C211yesmaximal, characteristic, complemented
15C11×#1590C211yesmaximal, characteristic, complemented
16#10623109C2211yescharacteristic
17#10623088C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C4×C11×SD16C2211yescharacteristic
20C11×#436C2211yescharacteristic
21#10622787C411yescharacteristic
22#10622780C411yescharacteristic
23#10622741—21no—
24#10622732—21no—
25C4×#4326C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27C4×#4324C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622481C411yescharacteristic
30#10622469C411yescharacteristic
31#10622453—21no—
32#10622450C2211yescharacteristic
33#10622448C2211yescharacteristic
34#10622444—21no—
35#10622443C2211yescharacteristic
36#10622443C2211yescharacteristic
37#10622429C411yescharacteristic
38#10622410C411yescharacteristic
39#10622393C411yescharacteristic
40#10622378C411yescharacteristic
41#10622343—21no—
42#10622333—21no—
43#10622322—21no—
44#10622314—21no—
45C4×Dic44C2211yescharacteristic
46C4×#4313C2211yescharacteristic
47#10622298C2211yescharacteristic
48C4×C8×D11C2211yescharacteristic
49#10622292C2211yescharacteristic
50#10622292C2211yescharacteristic
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#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×SD16C2×C411yescharacteristic
68C2×C11×M16—21no—
69C4×Q8×C11C2311yescharacteristic
70C4×D4×C11C2311yescharacteristic
71#66999C2×C411yescharacteristic
72#66997C2×C411yescharacteristic
73C2×#4326C2×C411yescharacteristic
74#66991C2×C411yescharacteristic
75#66989C2×C411yescharacteristic
76C2×#4324C2×C411yescharacteristic
77C4×C22⋊D11—21no—
78#66979—21no—
79C22×C11⋊C8—21no—
80C2×Dic44C2×C411yescharacteristic
81C2×#4313—21no—
82C2×#4313C2×C411yescharacteristic
83C2×#4313C2×C411yescharacteristic
84C2×C8×D11—21no—
85#66950C2×C411yescharacteristic
86#66950C2×C411yescharacteristic
87#66949—21no—
88#66943C2×C411yescharacteristic
89#66942—21no—
90#66941C2×C411yescharacteristic
91#66936—21no—
92#66932—21no—
93#66925—21no—
94C42×D11C2311yescharacteristic
95C4×Dic22—21no—
96C4×Dic22C2311yescharacteristic
97C4×Dic22C2311yescharacteristic
98C11×#106C2×C411yescharacteristic
99C11×C4⋊C8—21no—
100C11×C4⋊C8C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×#103C2×C411yescharacteristic
103C11×#102C2×C411yescharacteristic
104C11×C22⋊C8—21no—
105C11×#97—21no—
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109#66899C2×C411yescharacteristic
110#66896C2×C411yescharacteristic
111C22⋊(C11⋊C8)—21no—
112(C2×D11)⋊C8—21no—
113(C2×D11)⋊C8D411yescharacteristic
114(C2×D11)⋊C8D411yescharacteristic
115#66882C2×C411yescharacteristic
116#66880C2×C411yescharacteristic
117#66880C2×C411yescharacteristic
118#66879—21no—
119#66879—21no—
120#66879—21no—
121#66879C2×C411yescharacteristic
122#66879C2×C411yescharacteristic
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8D411yescharacteristic
129Dic11⋊C8D411yescharacteristic
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#17969—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×D4×C11C22×C411yescharacteristic
147C22×C4×C11—21no—
148C2×C22⋊D11—21no—
149C2×C4×D11C22×C411yescharacteristic
150C2×C4×D11C2×D411yescharacteristic
151C2×C4×D11#4111yescharacteristic
152C2×Dic22—21no—
153C2×Dic22C22×C411yescharacteristic
154C2×Dic22C22×C411yescharacteristic
155C11×SD16—22no—
156C11×M16—81no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11C22×C411yescharacteristic
161C2×C8×C11C22×C411yescharacteristic
162C2×C8×C11C2×D411yescharacteristic
163C2×C8×C11C2×D411yescharacteristic
164C11×C4⋊C4—21no—
165C11×C4⋊C4C22×C411yescharacteristic
166C11×C4⋊C4C22×C411yescharacteristic
167C11×C22⋊C4—21no—
168C42×C11—21no—
169C42×C11C2411yescharacteristic
170C22⋊Dic11—21no—
171C22⋊Dic11—21no—
172C22⋊Dic11—21no—
173#4326—22no—
174#4324—22no—
175(C2×D11)⋊C4—21no—
176(C2×D11)⋊C4—21no—
177(C2×D11)⋊C4—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
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—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11C22×C411yescharacteristic
193C4×Dic11C2×D411yescharacteristic
194C4×Dic11#4111yescharacteristic
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—81no—
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203Dic44—22no—
204#4313—22no—
205#4313—22no—
206#4313—81no—
207C8×D11—42no—
208#3172—111no—
209#2993—111no—
210#2985—111no—
211#1593—111no—
212#1592—111no—
213#1591—111no—
214#1590D1111yescharacteristic, complemented
215#1579—111no—
216SD16⋊C8—111no—
217C8×Q16—111no—
218C8×SD16—111no—
219#1569—111no—
220#1494—111no—
221#1493—111no—
222C8×M16—111no—
223C23×C11—21no—
224C22×D11C4×D411yescharacteristic
225Q8×C11—21no—
226Q8×C11—21no—
227D4×C11—21no—
228D4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11C23×C411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C22⋊D11—81no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11C4×D411yescharacteristic
243C2×Dic11C4×D411yescharacteristic
244C2×Dic11C4×D411yescharacteristic
245C4×D11—21no—
246C4×D11—21no—
247C4×D11—21no—
248C4×D11—21no—
249C4×D11—41no—
250Dic22—21no—
251Dic22—21no—
252Dic22—21no—
253Dic22—21no—
254Dic22—81no—
255C8×C11—22no—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11—41no—
260C8×C11—41no—
261C8×C11#13112yes—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8#13112yes—
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—221no—
282#446—221no—
283#446C2×D1111yescharacteristic
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8—111no—
287C4×Q16—111no—
288C4×Q16—111no—
289C4×SD16—111no—
290C4×SD16C2×D1111yescharacteristic
291#436—221no—
292#436C2×D1111yescharacteristic
293#435—221no—
294C8×D4—111no—
295#433—221no—
296#433—221no—
297#433—221no—
298#432—111no—
299#431—111no—
300#424—221no—
301#423—111no—
302C4×M16—111no—
303C2×C4×C8—111no—
304#335—111no—
305#335—111no—
306#334—111no—
307#334C2×D1111yescharacteristic
308Q8⋊C8—111no—
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8C2×D1111yescharacteristic
314D4⋊C8—111no—
315D4⋊C8C2×D1111yescharacteristic
316#322—111no—
317#322—111no—
318C82—111no—
319C82C2×D1111yescharacteristic
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11C2×C4×D411yescharacteristic
324C2×D11—21no—
325C2×D11—21no—
326C2×D11—21no—
327C4×C11—21no—
328C4×C11—41no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11C2×#13111yescharacteristic
332C4×C11C2×#13111yescharacteristic
333C4×C11#57711yescharacteristic
334C4×C11#57811yescharacteristic
335Dic11—21no—
336Dic11—21no—
337Dic11—21no—
338Dic11—41no—
339Dic11—41no—
340Dic11—41no—
341Dic11—41no—
342C2×Q16—111no—
343C2×Q16—111no—
344C2×SD16—111no—
345C2×SD16C4×D1111yescharacteristic
346C2×M16—21no—
347C2×M16—111no—
348C2×M16—111no—
349C2×M16—221no—
350C22×C8—221no—
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—221no—
367C4×Q8C22×D1111yescharacteristic
368C4×D4—221no—
369C4×D4C22×D1111yescharacteristic
370#117—221no—
371#117—221no—
372C2×C42—111no—
373#107—111no—
374#107—111no—
375#106—111no—
376#106C4×D1111yescharacteristic
377C4⋊C8—21no—
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⋊C8C22×D1111yescharacteristic
389C4⋊C8C22×D1111yescharacteristic
390#103—111no—
391#103—111no—
392#103—111no—
393#103—111no—
394#103—111no—
395#103C4×D1111yescharacteristic
396#102—111no—
397#102C4×D1111yescharacteristic
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—111no—
410C4×C8—111no—
411C4×C8—111no—
412C4×C8—221no—
413C4×C8—221no—
414C4×C8—221no—
415C4×C8—221no—
416C4×C8C22×D1111yescharacteristic
417C4×C8C22×D1111yescharacteristic
418C4×C8C22×D1111yescharacteristic
419C2×C11—81no—
420C2×C11#293111yescharacteristic
421C2×C11#294711yescharacteristic
422C2×C11#295611yescharacteristic
423D11—41no—
424C2×Q8—111no—
425C2×Q8—111no—
426C2×Q8—221no—
427C2×Q8C2×C4×D1111yescharacteristic
428C2×D4—221no—
429C2×D4C2×C4×D1111yescharacteristic
430C22×C4—21no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—111no—
434Q16—222no—
435Q16—222no—
436SD16—22no—
437SD16—222no—
438M16—81no—
439M16—222no—
440M16—222no—
441M16—881no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—111no—
446C2×C8—111no—
447C2×C8—111no—
448C2×C8—111no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—442no—
453C2×C8—881no—
454C2×C8C2×C4×D1111yescharacteristic
455C2×C8C2×C4×D1111yescharacteristic
456C2×C8D4×D1111yescharacteristic
457C2×C8D4×D1111yescharacteristic
458C4⋊C4—21no—
459C4⋊C4—111no—
460C4⋊C4—111no—
461C4⋊C4—221no—
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⋊C4C2×C4×D1111yescharacteristic
472C4⋊C4C2×C4×D1111yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—221no—
475C22⋊C4—221no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C22⋊C4—221no—
479C22⋊C4—221no—
480C42—21no—
481C42—111no—
482C42—111no—
483C42—111no—
484C42—221no—
485C42—221no—
486C42C23×D1111yescharacteristic
487C11#1796911yescharacteristic, complemented, Sylow
488C23—21no—
489C23—111no—
490Q8—21no—
491Q8—21no—
492Q8—221no—
493Q8—221no—
494Q8—221no—
495Q8—221no—
496Q8—881no—
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—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—441no—
517C2×C4C22×C4×D1111yescharacteristic
518C2×C4C2×D4×D1111yescharacteristic
519C2×C4#41×D1111yescharacteristic
520C8—22no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—112no—
527C8—221no—
528C8—221no—
529C8—221no—
530C8—441no—
531C8—441no—
532C8—441no—
533C8#6696012yes—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—221no—
538C22—221no—
539C22—221no—
540C22C4×D4×D1111yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—221no—
546C4—221no—
547C4—221no—
548C4—441no—
549C4—441no—
550C4—441no—
551C4—441no—
552C4C2×#6696011yescharacteristic
553C4D11×#13111yescharacteristic
554C4#1062329311yescharacteristic
555C4#1062330211yescharacteristic
556C2—81no—
557C2—441no—
558C2#1307732511yescharacteristic
559C2#1307745211yescharacteristic
560C2#1307752111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1590C2
socleC22×C11C2×C4×D4
prime radical#66991C2×C4
cosocleC42×C11C24
hypercenter#1590D11
hypocenterC11#17969
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
3. #13077712C2semidirect
4. #13067523C2semidirect
5. #13067518C2semidirect
6. #13067514C2semidirect
7. #13067434C2semidirect
8. SD16⋊(C11⋊C8)C2semidirect
9. #13067420C2semidirect
10. #13067419C2semidirect
11. #13067380C2semidirect
13. #13067069C2semidirect
14. C8×#4313C2semidirect
15. C11×#1590C2semidirect
214. #1590D11semidirect
487. C11#17969semidirect

Maximal subgroups

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

subgroupindex
#130792182
#130777602
#130777122
#130675232
#130675182
#130675142
#130674342
SD16⋊(C11⋊C8)2
#130674202
#130674192
#130673802
#130670732
#130670692
C8×#43132
C11×#15902
#1796911