Finite Group Databasebeta

← #14724882

Subgroups — #14724882

Order 2816.

660 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078677C211yesmaximal, characteristic
2#13077633C211yesmaximal, characteristic, complemented
3#13077359C211yesmaximal, characteristic, complemented
4#13067529C211yesmaximal, characteristic, complemented
5#13067500C211yesmaximal, characteristic, complemented
6#13067493C211yesmaximal, characteristic, complemented
7#13067479C211yesmaximal, characteristic, complemented
8#13067458C211yesmaximal, characteristic, complemented
9#13067444C211yesmaximal, characteristic, complemented
10#13067427C211yesmaximal, characteristic, complemented
11#13067415C211yesmaximal, characteristic, complemented
12#13067084C211yesmaximal, characteristic, complemented
13#13067001C211yesmaximal, characteristic, complemented
14#13066911C211yesmaximal, characteristic, complemented
15C11×#1573C211yesmaximal, characteristic, complemented
16C2×#66954—21no—
17#10623008C2211yescharacteristic
18C4×#4339C2211yescharacteristic
19C11×#432C2211yescharacteristic
20C11×#431C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22#10622723—21no—
23#10622538C2211yescharacteristic
24C4×#4318C2211yescharacteristic
25#10622463C411yescharacteristic
26#10622461C411yescharacteristic
27#10622456C411yescharacteristic
28#10622455C411yescharacteristic
29#10622451C2211yescharacteristic
30#10622451C2211yescharacteristic
31#10622451C2211yescharacteristic
32#10622451C2211yescharacteristic
33#10622449—21no—
34#10622449—21no—
35#10622447C2211yescharacteristic
36#10622447C2211yescharacteristic
37#10622443C2211yescharacteristic
38#10622443C2211yescharacteristic
39#10622350C411yescharacteristic
40#10622350C411yescharacteristic
41#10622347C411yescharacteristic
42#10622347C411yescharacteristic
43#10622342—21no—
44#10622342—21no—
45#10622320—21no—
46#10622318—21no—
47C4×D88C2211yescharacteristic
48C4×D88C2211yescharacteristic
49C4×#4314C2211yescharacteristic
50C4×#4314C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×#335C2211yescharacteristic
53C11×#334C2211yescharacteristic
54C11×#334C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622121C2211yescharacteristic
60#10622121C2211yescharacteristic
61#10622121C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4339—21no—
68C2×#4339C2×C411yescharacteristic
69C22×C8×C11—21no—
70C2×C42×C11C2311yescharacteristic
71#66983—21no—
72#66983C2×C411yescharacteristic
73#66983C2×C411yescharacteristic
74C4×C22⋊D11—21no—
75C4×C22⋊D11—21no—
76#66979C2×C411yescharacteristic
77C2×#4318D411yescharacteristic
78C2×#4318D411yescharacteristic
79C2×D88C2×C411yescharacteristic
80C2×D88C2×C411yescharacteristic
81C2×#4314C2×C411yescharacteristic
82C2×#4314C2×C411yescharacteristic
83#66954—44no—
84C2×#4313—21no—
85C2×#4313—21no—
86C2×#4313—21no—
87C2×#4313—21no—
88C2×C8×D11—21no—
89C2×C8×D11—21no—
90#66928—21no—
91#66927C2×C411yescharacteristic
92C4×D44—21no—
93C4×D44C2×C411yescharacteristic
94C4×D44C2311yescharacteristic
95C4×D44C2311yescharacteristic
96C4×D44C2311yescharacteristic
97#66925—21no—
98C42×D11—21no—
99#66922C2×C411yescharacteristic
100C4×Dic22C2×C411yescharacteristic
101C4×Dic22C2311yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8C2×C411yescharacteristic
104C11×C4⋊C8C2×C411yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×C22⋊C8—21no—
110C11×C22⋊C8C2×C411yescharacteristic
111C11×C22⋊C8C2×C411yescharacteristic
112C11×#97—21no—
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115C22⋊(C11⋊C8)—21no—
116#66885C2×C411yescharacteristic
117#66885C2×C411yescharacteristic
118#66885C2×C411yescharacteristic
119#66885C2×C411yescharacteristic
120#66885C2×C411yescharacteristic
121#66885C2×C411yescharacteristic
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8—21no—
127(C2×D11)⋊C8—21no—
128#66882C2×C411yescharacteristic
129#66882C2×C411yescharacteristic
130#66881C2×C411yescharacteristic
131#66881C2×C411yescharacteristic
132#66880C2×C411yescharacteristic
133#66880C2×C411yescharacteristic
134Dic11⋊C8—21no—
135Dic11⋊C8—21no—
136C8×Dic11—21no—
137C8×Dic11—21no—
138C4⋊(C11⋊C8)—21no—
139#66867D411yescharacteristic
140#66867D411yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18011—111nomaximal, Sylow
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151C2×C22⋊D11—21no—
152#4339—22no—
153#4339—41no—
154#4339—42no—
155#4339—42no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44C22×C411yescharacteristic
159C2×D44C22×C411yescharacteristic
160C2×D44C22×C411yescharacteristic
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×Dic22—21no—
167C2×Dic22C22×C411yescharacteristic
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—42no—
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C22×C411yescharacteristic
175C2×C8×C11C22×C411yescharacteristic
176C2×C8×C11C22×C411yescharacteristic
177C42×C11C22×C411yescharacteristic
178C42×C11C2×D411yescharacteristic
179C42×C11#4111yescharacteristic
180C42×C11C2411yescharacteristic
181C22⋊Dic11—21no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11C22×C411yescharacteristic
190C4⋊Dic11C22×C411yescharacteristic
191C4⋊Dic11C22×C411yescharacteristic
192C4⋊Dic11C22×C411yescharacteristic
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198#4318—22no—
199#4318—41no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C2×D411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206D88—41no—
207D88—41no—
208#4314—22no—
209#4314—22no—
210#4313—42no—
211#4313—42no—
212#4313—42no—
213#4313—42no—
214C8×D11—42no—
215C8×D11—42no—
216#3106—111no—
217#2971—111no—
218#2935—111no—
219#1594—111no—
220#1589—111no—
221#1588—111no—
222#1586—111no—
223#1583—111no—
224#1581—111no—
225SD16⋊C8—111no—
226C8×SD16—111no—
227#1573D1111yescharacteristic, complemented
228#1496—111no—
229#1477—111no—
230#1453—111no—
231C23×C11C4×D411yescharacteristic
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11C4×D411yescharacteristic
241C2×C4×C11C4×D411yescharacteristic
242C2×C4×C11C4×D411yescharacteristic
243C2×C4×C11C23×C411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C22⋊D11—42no—
247C22⋊D11—42no—
248C22⋊D11—42no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254D44—21no—
255D44—21no—
256D44—21no—
257D44—21no—
258D44—21no—
259D44—21no—
260D44—42no—
261D44—81no—
262C4×D11—42no—
263C4×D11—41no—
264C4×D11—41no—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—41no—
268C4×D11—41no—
269C4×D11—81no—
270Dic22—21no—
271Dic22—42no—
272Dic22#13112yescomplemented
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—21no—
276C8×C11—21no—
277C8×C11—41no—
278C8×C11—41no—
279C8×C11—41no—
280C8×C11—41no—
281C11⋊C8—21no—
282C11⋊C8—21no—
283C11⋊C8—21no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C11⋊C8AGL(1,ℤ/8)12yes—
287C2×#131—221no—
288#532—111no—
289C4×#41—111no—
290#482—111no—
291#482—111no—
292#477—111no—
293#476—111no—
294#460—111no—
295#459—111no—
296#449—111no—
297#449—111no—
298C8×Q8—111no—
299C8×Q8—111no—
300C4×SD16—111no—
301C4×SD16—111no—
302C4×D8—111no—
303C4×D8—111no—
304#436—111no—
305#436—111no—
306#436—111no—
307#436—111no—
308#436—221no—
309#436—221no—
310#435—221no—
311#435—221no—
312C8×D4—111no—
313C8×D4—111no—
314#432—221no—
315#432C2×D1111yescharacteristic
316#431—111no—
317#431C2×D1111yescharacteristic
318C2×C4⋊C8C2×D1111yescharacteristic
319#408—221no—
320C4×M16—111no—
321C4×M16—221no—
322#335C2×D1111yescharacteristic
323#335C2×D1111yescharacteristic
324#334C2×D1111yescharacteristic
325#334C2×D1111yescharacteristic
326Q8⋊C8—111no—
327Q8⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8—111no—
332D4⋊C8—111no—
333D4⋊C8—111no—
334#322—111no—
335#322—111no—
336#322—111no—
337C82—111no—
338C22×C11—21no—
339C22×C11—21no—
340C22×C11—21no—
341C22×C11C2×C4×D411yescharacteristic
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—41no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—21no—
355C4×C11C2×#13111yescharacteristic
356C4×C11#56811yescharacteristic
357C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
358C4×C11#57511yescharacteristic
359Dic11—22no—
360Dic11—41no—
361Dic11—41no—
362Dic11—41no—
363Dic11—41no—
364C2×#41—111no—
365C2×#41—221no—
366C2×SD16—111no—
367C2×SD16—111no—
368C2×D8—111no—
369C2×D8—111no—
370#131—444no—
371C2×M16—111no—
372C2×M16—111no—
373C2×M16—221no—
374C2×M16—221no—
375C2×M16—221no—
376C2×M16—221no—
377C22×C8—21no—
378C22×C8—221no—
379C22×C8—221no—
380C4⋊Q8—111no—
381#127—111no—
382#124—221no—
383#121—111no—
384#121—111no—
385#121—221no—
386C4×Q8—111no—
387C4×Q8—111no—
388C4×D4—111no—
389C4×D4—111no—
390C4×D4—111no—
391C4×D4—111no—
392C4×D4—221no—
393C4×D4—221no—
394C4×D4—221no—
395#117—111no—
396#117—221no—
397C2×C42—221no—
398C2×C42C22×D1111yescharacteristic
399#107—111no—
400#107—111no—
401#106—111no—
402#106—111no—
403C4⋊C8—21no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406C4⋊C8—221no—
407C4⋊C8C4×D1111yescharacteristic
408C4⋊C8C4×D1111yescharacteristic
409C4⋊C8C22×D1111yescharacteristic
410C4⋊C8C22×D1111yescharacteristic
411C4⋊C8C22×D1111yescharacteristic
412C4⋊C8C22×D1111yescharacteristic
413#103—111no—
414#103—111no—
415#102—111no—
416#102—111no—
417#102—111no—
418#102—111no—
419#102—111no—
420#102—111no—
421C22⋊C8—21no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8—221no—
429C22⋊C8C4×D1111yescharacteristic
430C22⋊C8C4×D1111yescharacteristic
431#97—21no—
432#97—111no—
433#97—111no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—111no—
437C4×C8—111no—
438C4×C8—221no—
439C4×C8—221no—
440C4×C8C22×D1111yescharacteristic
441C4×C8C22×D1111yescharacteristic
442C2×C11—41no—
443C2×C11#293311yescharacteristic
444C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
445C2×C11#295711yescharacteristic
446D11—81no—
447D11—81no—
448D11—81no—
449#41—222no—
450#41—441no—
451#41—442no—
452#41—442no—
453C2×Q8—111no—
454C2×Q8—221no—
455C2×D4—111no—
456C2×D4—111no—
457C2×D4—111no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4C2×C4×D1111yescharacteristic
469C22×C4D4×D1111yescharacteristic
470C22×C4#434311yescharacteristic
471SD16—222no—
472SD16—222no—
473D8—441no—
474D8—441no—
475M16—222no—
476M16—442no—
477M16—442no—
478M16—442no—
479M16—442no—
480M16—441no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—42no—
486C2×C8—111no—
487C2×C8—111no—
488C2×C8—111no—
489C2×C8—111no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—442no—
493C2×C8—442no—
494C2×C8C2×C4×D1111yescharacteristic
495C2×C8C2×C4×D1111yescharacteristic
496C2×C8C2×C4×D1111yescharacteristic
497C2×C8C2×C4×D1111yescharacteristic
498C4⋊C4—111no—
499C4⋊C4—111no—
500C4⋊C4—111no—
501C4⋊C4—111no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C22⋊C4—221no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C22⋊C4—221no—
511C22⋊C4—221no—
512C42—221no—
513C42—221no—
514C42—221no—
515C42C2×C4×D1111yescharacteristic
516C42D4×D1111yescharacteristic
517C42#434311yescharacteristic
518C42C23×D1111yescharacteristic
519C11#1801111yescharacteristic, complemented, Sylow
520C23—221no—
521C23—221no—
522C23—221no—
523C23#6694611yescharacteristic
524Q8—112no—
525Q8—221no—
526Q8—442no—
527D4—221no—
528D4—221no—
529D4—221no—
530D4—221no—
531D4—221no—
532D4—221no—
533D4—442no—
534D4—442no—
535D4—442no—
536D4—442no—
537D4—881no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—442no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—881no—
556C2×C4#6694611yescharacteristic
557C2×C4#6694611yescharacteristic
558C2×C4#6694611yescharacteristic
559C2×C4C22×C4×D1111yescharacteristic
560C2×C4C2×D4×D1111yescharacteristic
561C2×C4C2×#434311yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—112no—
571C8—221no—
572C8—221no—
573C8—221no—
574C8—441no—
575C8—441no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—441no—
580C22—441no—
581C22—441no—
582C22—441no—
583C22—441no—
584C22—441no—
585C22—441no—
586C22—441no—
587C22—441no—
588C22C2×#6694611yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—21no—
593C4—222no—
594C4—441no—
595C4—441no—
596C4—441no—
597C4—441no—
598C4D11×#13111yescharacteristic
599C4#1062328111yescharacteristic
600C4D11×AGL(1,ℤ/8)11yescharacteristic
601C4#1062330811yescharacteristic
602C2—41no—
603C2—881no—
604C2—881no—
605C2—881no—
606C2#1307734011yescharacteristic
607C2#1307742311yescharacteristic
608C2#1307753211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1573C2
socleC22×C11C2×C4×D4
prime radical#13078677C2
cosocleC42×C11C24
hypercenter#1573D11
hypocenterC11#18011
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
2. #13077633C2semidirect
3. #13077359C2semidirect
4. #13067529C2semidirect
5. #13067500C2semidirect
6. #13067493C2semidirect
7. #13067479C2semidirect
8. #13067458C2semidirect
9. #13067444C2semidirect
10. #13067427C2semidirect
11. #13067415C2semidirect
12. #13067084C2semidirect
13. #13067001C2semidirect
14. #13066911C2semidirect
15. C11×#1573C2semidirect
227. #1573D11semidirect
272. Dic22#131semidirect
519. C11#18011semidirect

Maximal subgroups

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

subgroupindex
#130786772
#130776332
#130773592
#130675292
#130675002
#130674932
#130674792
#130674582
#130674442
#130674272
#130674152
#130670842
#130670012
#130669112
C11×#15732
#1801111