Finite Group Databasebeta

← #14723935

Subgroups — #14723935

Order 2816.

620 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078636C211yesmaximal, characteristic
2#13077761C211yesmaximal, characteristic, complemented
3#13077725C211yesmaximal, characteristic, complemented
4#13067493C211yesmaximal, characteristic, complemented
5#13067472C211yesmaximal, characteristic, complemented
6#13067465C211yesmaximal, characteristic, complemented
7#13067444C211yesmaximal, characteristic, complemented
8#13067427C211yesmaximal, characteristic, complemented
9#13067427C211yesmaximal, characteristic, complemented
10#13067422C211yesmaximal, characteristic, complemented
11#13067410C211yesmaximal, characteristic, complemented
12#13067053C211yesmaximal, characteristic, complemented
13#13067027C211yesmaximal, characteristic, complemented
14#13066911C211yesmaximal, characteristic, complemented
15C11×#1571C211yesmaximal, characteristic, complemented
16#10623010C2211yescharacteristic
17C4×#4339C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C11×#423C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21#10622741—21no—
22#10622740—21no—
23C8×C22⋊D11—21no—
24C8×C22⋊D11—21no—
25#10622538C2211yescharacteristic
26C4×#4318C2211yescharacteristic
27#10622460C411yescharacteristic
28#10622458C411yescharacteristic
29#10622457C411yescharacteristic
30#10622453—21no—
31#10622452—21no—
32#10622451C2211yescharacteristic
33#10622447C2211yescharacteristic
34#10622447C2211yescharacteristic
35#10622447C2211yescharacteristic
36#10622446—21no—
37D11×C4⋊C8—21no—
38#10622444C2211yescharacteristic
39#10622443C2211yescharacteristic
40#10622443C2211yescharacteristic
41#10622443C2211yescharacteristic
42#10622442C411yescharacteristic
43#10622350C411yescharacteristic
44#10622347C411yescharacteristic
45#10622346C411yescharacteristic
46#10622336C411yescharacteristic
47C4×Dic44C2211yescharacteristic
48C4×D88C2211yescharacteristic
49C4×#4314C2211yescharacteristic
50C4×#4314C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×#335C2211yescharacteristic
53C11×#335C2211yescharacteristic
54C11×#335C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622121C2211yescharacteristic
60#10622121C2211yescharacteristic
61#10622121C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4339C2×C411yescharacteristic
68C2×C11×M16—21no—
69C22×C8×C11—21no—
70C2×C42×C11C2311yescharacteristic
71#66983C2×C411yescharacteristic
72#66982—21no—
73C4×C22⋊D11—21no—
74C4×C22⋊D11—21no—
75C4×C22⋊D11—21no—
76#66979C2×C411yescharacteristic
77#66977C2×C411yescharacteristic
78C2×#4318—21no—
79C2×Dic44C2×C411yescharacteristic
80C2×D88C2×C411yescharacteristic
81C2×#4314C2×C411yescharacteristic
82C2×#4314C2×C411yescharacteristic
83C2×#4313—21no—
84C2×C8×D11—21no—
85C2×C8×D11—21no—
86C2×C8×D11—21no—
87#66929—21no—
88#66928C2×C411yescharacteristic
89C4×D44C2×C411yescharacteristic
90C4×D44C2311yescharacteristic
91C4×D44C2311yescharacteristic
92#66925—21no—
93#66925—21no—
94C42×D11—21no—
95#66923C2×C411yescharacteristic
96C4×Dic22C2×C411yescharacteristic
97C4×Dic22C2311yescharacteristic
98C4×Dic22C2311yescharacteristic
99C11×C4⋊C8—21no—
100C11×C4⋊C8—21no—
101C11×C4⋊C8C2×C411yescharacteristic
102C11×C4⋊C8C2×C411yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×C22⋊C8C2×C411yescharacteristic
108C11×C22⋊C8C2×C411yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C22⋊(C11⋊C8)D411yescharacteristic
112C22⋊(C11⋊C8)D411yescharacteristic
113#66885C2×C411yescharacteristic
114#66885C2×C411yescharacteristic
115#66885C2×C411yescharacteristic
116#66885C2×C411yescharacteristic
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121#66882C2×C411yescharacteristic
122#66882C2×C411yescharacteristic
123#66881C2×C411yescharacteristic
124#66881C2×C411yescharacteristic
125#66880C2×C411yescharacteristic
126#66880C2×C411yescharacteristic
127#66880C2×C411yescharacteristic
128#66880C2×C411yescharacteristic
129#66879—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134C8×Dic11—21no—
135C8×Dic11—21no—
136C8×Dic11—21no—
137C4⋊(C11⋊C8)D411yescharacteristic
138C4⋊(C11⋊C8)D411yescharacteristic
139#66867—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17926—111nomaximal, Sylow
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C2×C22⋊D11—21no—
149C2×C22⋊D11—21no—
150#4339—22no—
151#4339—22no—
152C2×D44C22×C411yescharacteristic
153C2×D44C22×C411yescharacteristic
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×Dic22C22×C411yescharacteristic
159C2×Dic22C22×C411yescharacteristic
160C11×M16—81no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—81no—
166C2×C8×C11C22×C411yescharacteristic
167C2×C8×C11C22×C411yescharacteristic
168C2×C8×C11C22×C411yescharacteristic
169C2×C8×C11C22×C411yescharacteristic
170C42×C11C22×C411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11#4111yescharacteristic
173C42×C11C2411yescharacteristic
174C22⋊Dic11—21no—
175C22⋊Dic11—21no—
176(C2×D11)⋊C4—21no—
177(C2×D11)⋊C4—21no—
178(C2×D11)⋊C4—21no—
179(C2×D11)⋊C4—21no—
180(C2×D11)⋊C4—21no—
181(C2×D11)⋊C4—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—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196#4318—42no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C2×D411yescharacteristic
200C2×C11⋊C8C2×D411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203Dic44—22no—
204D88—22no—
205#4314—22no—
206#4314—22no—
207#4313—81no—
208C8×D11—81no—
209C8×D11—81no—
210C8×D11—81no—
211#3102—111no—
212#2993—111no—
213#2988—111no—
214#1588—111no—
215#1585—111no—
216#1584—111no—
217#1581—111no—
218SD16⋊C8—111no—
219SD16⋊C8—111no—
220C8×Q16—111no—
221C8×D8—111no—
222#1571D1111yescharacteristic, complemented
223#1489—111no—
224#1483—111no—
225#1453—111no—
226C23×C11C4×D411yescharacteristic
227C22×D11—21no—
228C22×D11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—41no—
234C2×C4×C11C4×D411yescharacteristic
235C2×C4×C11C4×D411yescharacteristic
236C2×C4×C11C4×D411yescharacteristic
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C22⋊D11—24no—
241C22⋊D11—81no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248D44—21no—
249D44—21no—
250D44—21no—
251D44#13112yes—
252C4×D11—24no—
253C4×D11—41no—
254C4×D11—41no—
255C4×D11—41no—
256C4×D11—41no—
257C4×D11—81no—
258Dic22—21no—
259Dic22—21no—
260Dic22—21no—
261Dic22#13112yes—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—41no—
267C8×C11—41no—
268C8×C11—41no—
269C8×C11—41no—
270C11⋊C8—22no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—41no—
276#529—111no—
277C4×#41—111no—
278#485—111no—
279#482—111no—
280#479—111no—
281#478—111no—
282#464—111no—
283#463—111no—
284#452—111no—
285#449—111no—
286#446—111no—
287C8×Q8—111no—
288C8×Q8—111no—
289C8×Q8—111no—
290C4×Q16—111no—
291C4×SD16—111no—
292C4×SD16—111no—
293C4×D8—111no—
294#436—111no—
295#436—221no—
296#435—221no—
297C8×D4—111no—
298C8×D4—111no—
299C8×D4—111no—
300C8×D4—221no—
301C8×D4—221no—
302#433—221no—
303#431—111no—
304#431—221no—
305#431C2×D1111yescharacteristic
306#424—221no—
307#423C2×D1111yescharacteristic
308C2×C4⋊C8—221no—
309C2×C4⋊C8C2×D1111yescharacteristic
310C4×M16—111no—
311#335C2×D1111yescharacteristic
312#335C2×D1111yescharacteristic
313#335C2×D1111yescharacteristic
314#335C2×D1111yescharacteristic
315Q8⋊C8—111no—
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318Q8⋊C8—111no—
319D4⋊C8—111no—
320D4⋊C8—111no—
321D4⋊C8—111no—
322D4⋊C8—111no—
323#322—111no—
324#322—111no—
325#322—111no—
326C82—111no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11C2×C4×D411yescharacteristic
331C2×D11—22no—
332C2×D11—41no—
333C2×D11—41no—
334C2×D11—41no—
335C2×D11—41no—
336C2×D11—41no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11C2×#13111yescharacteristic
342C4×C11C2×#13111yescharacteristic
343C4×C11#57611yescharacteristic
344C4×C11#57811yescharacteristic
345Dic11—22no—
346Dic11—41no—
347Dic11—41no—
348Dic11—41no—
349Dic11—41no—
350Dic11—41no—
351C2×#41—111no—
352C2×Q16—111no—
353C2×SD16—111no—
354C2×SD16—111no—
355C2×D8—111no—
356C2×M16—21no—
357C2×M16—221no—
358C2×M16—221no—
359C22×C8—21no—
360C22×C8—221no—
361C22×C8—221no—
362C22×C8—221no—
363#126—221no—
364#125—111no—
365#124—111no—
366#123—221no—
367C22⋊Q8—111no—
368#121—111no—
369C4×Q8—111no—
370C4×Q8—111no—
371C4×Q8—111no—
372C4×D4—111no—
373C4×D4—111no—
374C4×D4—111no—
375C4×D4—221no—
376C4×D4—221no—
377C4×D4—221no—
378#117—111no—
379#117—221no—
380#117—221no—
381C2×C42—221no—
382C2×C42C22×D1111yescharacteristic
383#107—111no—
384#107—111no—
385#106—111no—
386#106—111no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8C4×D1111yescharacteristic
396C4⋊C8C4×D1111yescharacteristic
397C4⋊C8C22×D1111yescharacteristic
398C4⋊C8C22×D1111yescharacteristic
399C4⋊C8C22×D1111yescharacteristic
400C4⋊C8C22×D1111yescharacteristic
401#103—111no—
402#103—111no—
403#103—111no—
404#103—111no—
405#102—111no—
406#102—111no—
407#102—111no—
408#102—111no—
409C22⋊C8—111no—
410C22⋊C8—111no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413C22⋊C8—221no—
414C22⋊C8—221no—
415C22⋊C8C4×D1111yescharacteristic
416C22⋊C8C4×D1111yescharacteristic
417#97—221no—
418#97—221no—
419C4×C8—111no—
420C4×C8—111no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—221no—
424C4×C8—221no—
425C4×C8—221no—
426C4×C8C22×D1111yescharacteristic
427C4×C8C22×D1111yescharacteristic
428C2×C11—41no—
429C2×C11#292911yescharacteristic
430C2×C11#295111yescharacteristic
431C2×C11#295611yescharacteristic
432D11—42no—
433D11—81no—
434#41—222no—
435#41—222no—
436C2×Q8—111no—
437C2×Q8—111no—
438C2×D4—111no—
439C2×D4—111no—
440C2×D4—221no—
441C2×D4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4C2×C4×D1111yescharacteristic
447C22×C4D4×D1111yescharacteristic
448C22×C4#434311yescharacteristic
449Q16—222no—
450SD16—222no—
451SD16—222no—
452D8—222no—
453M16—81no—
454M16—442no—
455M16—881no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—81no—
461C2×C8—111no—
462C2×C8—111no—
463C2×C8—111no—
464C2×C8—111no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—881no—
468C2×C8—881no—
469C2×C8—881no—
470C2×C8C2×C4×D1111yescharacteristic
471C2×C8C2×C4×D1111yescharacteristic
472C2×C8C2×C4×D1111yescharacteristic
473C2×C8C2×C4×D1111yescharacteristic
474C4⋊C4—111no—
475C4⋊C4—111no—
476C4⋊C4—111no—
477C4⋊C4—111no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C22⋊C4—221no—
485C22⋊C4—221no—
486C22⋊C4—221no—
487C22⋊C4—221no—
488C22⋊C4—221no—
489C22⋊C4—221no—
490C22⋊C4—221no—
491C22⋊C4—221no—
492C42—221no—
493C42—221no—
494C42—221no—
495C42—221no—
496C42C2×C4×D1111yescharacteristic
497C42D4×D1111yescharacteristic
498C42#434311yescharacteristic
499C42C23×D1111yescharacteristic
500C11#1792611yescharacteristic, complemented, Sylow
501C23—221no—
502C23—221no—
503C23#6694611yescharacteristic
504Q8—112no—
505Q8—221no—
506Q8—221no—
507Q8—221no—
508D4—112no—
509D4—224no—
510D4—221no—
511D4—221no—
512D4—221no—
513D4—881no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—224no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—881no—
531C2×C4#6694611yescharacteristic
532C2×C4#6694611yescharacteristic
533C2×C4#6694611yescharacteristic
534C2×C4C22×C4×D1111yescharacteristic
535C2×C4C2×D4×D1111yescharacteristic
536C2×C4C2×#434311yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—222no—
546C8—221no—
547C8—221no—
548C8—221no—
549C8—221no—
550C8—441no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—222no—
555C22—441no—
556C22—441no—
557C22—441no—
558C22—441no—
559C22—441no—
560C22C2×#6694611yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—222no—
566C4—441no—
567C4—441no—
568C4—441no—
569C4—441no—
570C4—441no—
571C4D11×#13111yescharacteristic
572C4D11×#13111yescharacteristic
573C4#1062328811yescharacteristic
574C4#1062329711yescharacteristic
575C2—41no—
576C2—442no—
577C2—881no—
578C2#1307730911yescharacteristic
579C2#1307749011yescharacteristic
580C2#1307752511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1571C2
socleC22×C11C2×C4×D4
prime radical#10622347C4
cosocleC42×C11C24
hypercenter#1571D11
hypocenterC11#17926
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
2. #13077761C2semidirect
3. #13077725C2semidirect
4. #13067493C2semidirect
5. #13067472C2semidirect
6. #13067465C2semidirect
7. #13067444C2semidirect
8. #13067427C2semidirect
9. #13067427C2semidirect
10. #13067422C2semidirect
11. #13067410C2semidirect
12. #13067053C2semidirect
13. #13067027C2semidirect
14. #13066911C2semidirect
15. C11×#1571C2semidirect
222. #1571D11semidirect
500. C11#17926semidirect

Maximal subgroups

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

subgroupindex
#130786362
#130777612
#130777252
#130674932
#130674722
#130674652
#130674442
#130674272
#130674222
#130674102
#130670532
#130670272
#130669112
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