Finite Group Databasebeta

← #14736478

Subgroups — #14736478

Order 2816.

704 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079191C211yesmaximal, characteristic, complemented
2#13078071C211yesmaximal, characteristic, complemented
3#13077583C211yesmaximal, characteristic, complemented
4#13068186C211yesmaximal, characteristic, complemented
5#13068182C211yesmaximal, characteristic, complemented
6#13068179C211yesmaximal, characteristic, complemented
7#13068175C211yesmaximal, characteristic, complemented
8#13068132C211yesmaximal, characteristic, complemented
9#13068127C211yesmaximal, characteristic, complemented
10#13068098C211yesmaximal, characteristic, complemented
11#13068093C211yesmaximal, characteristic, complemented
12C2×#10622118C211yesmaximal, characteristic, complemented
13#13067266C211yesmaximal, characteristic, complemented
14#13067265C211yesmaximal, characteristic, complemented
15C11×#3035C211yesmaximal, characteristic, complemented
16C2×C11×#135—21no—
17C11×#532C2211yescharacteristic
18C4×C11×#41C2211yescharacteristic
19C2×#67003—21no—
20#10623008C2211yescharacteristic
21C11×#464—21no—
22C11×#463—21no—
23C11×#462C2211yescharacteristic
24C11×#461C2211yescharacteristic
25C11×#460C2211yescharacteristic
26C11×#459C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C11×#416—21no—
29#10622701C2211yescharacteristic
30#10622691C2211yescharacteristic
31#10622686C2211yescharacteristic
32#10622683C2211yescharacteristic
33#10622651—21no—
34#10622651—21no—
35#10622644C2211yescharacteristic
36#10622641—21no—
37#10622640C2211yescharacteristic
38#10622637C2211yescharacteristic
39#10622637C2211yescharacteristic
40#10622632C2211yescharacteristic
41#10622629—21no—
42#10622628C2211yescharacteristic
43C4×#4323—21no—
44C4×#4323—21no—
45#10622625C2211yescharacteristic
46#10622625C2211yescharacteristic
47#10622624—21no—
48#10622624—21no—
49#10622615—21no—
50#10622538—21no—
51#10622538C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C4×#4318—21no—
54C2×C4×C11⋊C8C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622182C2211yescharacteristic
58#10622182C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622118C2211yescharacteristic
66#10622118C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×#41D411yescharacteristic
69C2×#4339—21no—
70C11×#135—44no—
71C2×C11×Q16—21no—
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×D8—21no—
75C22×C8×C11—21no—
76C11×C4⋊Q8C2311yescharacteristic
77C11×#127C2311yescharacteristic
78C11×#124—21no—
79C11×#121—21no—
80C11×#121—21no—
81C4×Q8×C11D411yescharacteristic
82C4×Q8×C11C2311yescharacteristic
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11D411yescharacteristic
88C4×D4×C11C2311yescharacteristic
89C11×#117—21no—
90C11×#117D411yescharacteristic
91C2×C42×C11—21no—
92C2×C42×C11C2311yescharacteristic
93#67003—44no—
94C2×#4326—21no—
95C2×#4325—21no—
96C2×#4324—21no—
97C2×#4323—21no—
98C2×#4323—21no—
99C2×#4323—21no—
100#66983—21no—
101#66983—21no—
102C2×#4318—21no—
103C2×#4318—21no—
104C22×C11⋊C8—21no—
105C22×C11⋊C8D411yescharacteristic
106C22×C11⋊C8D411yescharacteristic
107#66928—21no—
108#66927C2311yescharacteristic
109C4×D44—21no—
110C4×D44—21no—
111#66922C2311yescharacteristic
112C11×C4⋊C8—21no—
113C11×C4⋊C8C2311yescharacteristic
114C11×C4⋊C8C2311yescharacteristic
115C11×#103—21no—
116C11×#103—21no—
117C11×#102—21no—
118C11×#102—21no—
119#66896—21no—
120#66896—21no—
121C22⋊(C11⋊C8)—21no—
122C22⋊(C11⋊C8)—21no—
123C22⋊(C11⋊C8)—21no—
124#66874—21no—
125#66874—21no—
126#66873—21no—
127#66873—21no—
128#66873—21no—
129#66873—21no—
130#66871—21no—
131#66871—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)—21no—
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139#66867—21no—
140#66867—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8D411yescharacteristic
143C4×C11⋊C8D411yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#19157—111nomaximal, Sylow
147C11×#41—22no—
148C11×#41—22no—
149C11×#41—42no—
150C11×#41—42no—
151C2×Q8×C11—21no—
152C2×Q8×C11C2×D411yescharacteristic
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—41no—
158C2×D4×C11C2×D411yescharacteristic
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—41no—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11#4111yescharacteristic
166C2×C22⋊D11—41no—
167#4339—42no—
168#4339—42no—
169C2×D44—21no—
170C2×D44—21no—
171C2×D44—21no—
172C2×C4×D11—41no—
173C2×Dic22—21no—
174C11×Q16—42no—
175C11×SD16—42no—
176C11×SD16—42no—
177C11×D8—42no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—42no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4C2×D411yescharacteristic
186C11×C4⋊C4C2×D411yescharacteristic
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—41no—
191C11×C22⋊C4—41no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11C2×D411yescharacteristic
196C42×C11C2×D411yescharacteristic
197C42×C11#4111yescharacteristic
198C42×C11C2411yescharacteristic
199#4326—42no—
200#4325—42no—
201#4324—42no—
202#4323—42no—
203#4323—42no—
204#4323—42no—
205(C2×D11)⋊C4—41no—
206(C2×D11)⋊C4—41no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209#4318—42no—
210#4318—42no—
211C2×C11⋊C8—22no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—41no—
217C2×C11⋊C8—42no—
218C2×C11⋊C8C2×D411yescharacteristic
219C2×C11⋊C8C2×D411yescharacteristic
220C2×C11⋊C8C2×D411yescharacteristic
221C2×C11⋊C8C2×D411yescharacteristic
222#3169—111no—
223#3035—111no—
224#3035D1111yescharacteristic, complemented
225#2965—111no—
226#1702—111no—
227#1702—111no—
228#1701—111no—
229#1701—111no—
230#1694—111no—
231#1693—111no—
232#1688—111no—
233#1687—111no—
234C2×#334—111no—
235#1540—111no—
236#1540—111no—
237C23×C11—21no—
238C23×C11—41no—
239C23×C11#12111yescharacteristic
240C22×D11—41no—
241Q8×C11—21no—
242Q8×C11—21no—
243Q8×C11—41no—
244Q8×C11—41no—
245D4×C11—21no—
246D4×C11—21no—
247D4×C11—42no—
248D4×C11—41no—
249D4×C11—41no—
250D4×C11—41no—
251D4×C11—41no—
252D4×C11—81no—
253D4×C11—82no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—41no—
260C2×C4×C11—42no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—41no—
265C2×C4×C11—82no—
266C2×C4×C11#12111yescharacteristic
267C2×C4×C11#12111yescharacteristic
268C2×C4×C11#12111yescharacteristic
269C2×C4×C11AGL(1,ℤ/8)12yes—
270C2×C4×C11AGL(1,ℤ/8)12yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C22⋊D11—82no—
275C2×Dic11—41no—
276D44—41no—
277D44—41no—
278D44—41no—
279D44—41no—
280D44—81no—
281C4×D11—82no—
282Dic22—41no—
283Dic22—41no—
284C8×C11—41no—
285C8×C11—41no—
286C11⋊C8—21no—
287C11⋊C8—21no—
288C11⋊C8—21no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293C11⋊C8#13512yescomplemented
294C2×#135—21no—
295C2×#135—221no—
296#532—111no—
297#532C2×D1111yescharacteristic
298C4×#41C2×D1111yescharacteristic
299#500—111no—
300#493—111no—
301#486—111no—
302#486—111no—
303#466—221no—
304#466—221no—
305#464—21no—
306#464—221no—
307#463—21no—
308#463—221no—
309#462—111no—
310#462C2×D1111yescharacteristic
311#461—111no—
312#461C2×D1111yescharacteristic
313#460—111no—
314#460C2×D1111yescharacteristic
315#459—111no—
316#459C2×D1111yescharacteristic
317#446—111no—
318#446—111no—
319C4×D8—221no—
320C4×D8—221no—
321#436—111no—
322#436—111no—
323#435—221no—
324#435—221no—
325#431—111no—
326#431—221no—
327C2×C4⋊C8—111no—
328C2×C4⋊C8C2×D1111yescharacteristic
329#416—21no—
330#416—221no—
331C4×M16—221no—
332C2×C4×C8—111no—
333#334—111no—
334#334—111no—
335#334—111no—
336#334—111no—
337#332—111no—
338#332—111no—
339#332—111no—
340#332—111no—
341#331—111no—
342#331—111no—
343#331—111no—
344#331—111no—
345C22×C11—21no—
346C22×C11—21no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11#46912yes—
354C22×C11C2×#12111yescharacteristic
355C2×D11—81no—
356C2×D11—81no—
357C2×D11—81no—
358C4×C11—21no—
359C4×C11—21no—
360C4×C11—21no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—81no—
365C4×C11#46912yes—
366C4×C11C2×#13511yescharacteristic
367C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
368C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
369C4×C11#57511yescharacteristic
370Dic11—81no—
371C2×#41—21no—
372C2×#41—221no—
373C2×#41C22⋊D1111yescharacteristic
374#135—44no—
375#135—444no—
376C2×Q16—21no—
377C2×Q16—221no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—221no—
381C2×SD16—221no—
382C2×D8—21no—
383C2×D8—221no—
384C2×D8—221no—
385C2×D8—221no—
386C2×M16—221no—
387C2×M16—221no—
388C22×C8—21no—
389C22×C8—111no—
390C22×C8—111no—
391C22×C8—221no—
392C4⋊Q8—111no—
393C4⋊Q8C22×D1111yescharacteristic
394#127—111no—
395#127C22×D1111yescharacteristic
396#124—21no—
397#124—221no—
398#121—21no—
399#121—21no—
400#121—221no—
401#121—221no—
402C4×Q8C22⋊D1111yescharacteristic
403C4×Q8C22×D1111yescharacteristic
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4—221no—
409C4×D4—221no—
410C4×D4C22⋊D1111yescharacteristic
411C4×D4C22×D1111yescharacteristic
412#117—21no—
413#117C22⋊D1111yescharacteristic
414C2×C42—21no—
415C2×C42C22×D1111yescharacteristic
416#107—221no—
417#107—221no—
418C4⋊C8—21no—
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
428#103—21no—
429#103—21no—
430#103—221no—
431#103—221no—
432#102—21no—
433#102—21no—
434#102—221no—
435#102—221no—
436#102—221no—
437#102—221no—
438#102—221no—
439#102—221no—
440C22⋊C8—221no—
441C22⋊C8—221no—
442C22⋊C8—221no—
443#97—221no—
444#97—221no—
445C4×C8—111no—
446C4×C8—111no—
447C4×C8—111no—
448C4×C8—111no—
449C4×C8—221no—
450C2×C11—22no—
451C2×C11—81no—
452C2×C11—161no—
453C2×C11#303511yescharacteristic
454C2×C11C2×#46911yescharacteristic
455C2×C11#306711yescharacteristic
456D11—161no—
457#41—22no—
458#41—22no—
459#41—42no—
460#41—42no—
461#41—442no—
462#41—442no—
463C2×Q8—21no—
464C2×Q8—221no—
465C2×Q8C2×C22⋊D1111yescharacteristic
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—41no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—441no—
475C2×D4C2×C22⋊D1111yescharacteristic
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—41no—
480C22×C4—441no—
481C22×C4D4×D1111yescharacteristic
482C22×C4#434111yescharacteristic
483C22×C4C2×C22⋊D1111yescharacteristic
484Q16—42no—
485Q16—442no—
486SD16—42no—
487SD16—42no—
488SD16—442no—
489SD16—442no—
490D8—42no—
491D8—442no—
492D8—442no—
493D8—442no—
494M16—442no—
495M16—442no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—42no—
499C2×C8—111no—
500C2×C8—111no—
501C2×C8—111no—
502C2×C8—111no—
503C2×C8—222no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—441no—
509C2×C8—442no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4C2×C22⋊D1111yescharacteristic
517C4⋊C4C2×C22⋊D1111yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—441no—
524C22⋊C4—441no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42D4×D1111yescharacteristic
529C42#434111yescharacteristic
530C42C2×C22⋊D1111yescharacteristic
531C42C23×D1111yescharacteristic
532C11#1915711yescharacteristic, complemented, Sylow
533C23—21no—
534C23—41no—
535C23—441no—
536C23#6699211yescharacteristic
537Q8—21no—
538Q8—21no—
539Q8—41no—
540Q8—41no—
541Q8—441no—
542Q8—441no—
543D4—21no—
544D4—21no—
545D4—42no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—81no—
551D4—82no—
552D4—441no—
553D4—441no—
554D4—441no—
555D4—441no—
556D4—881no—
557D4—882no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—82no—
570C2×C4—441no—
571C2×C4—882no—
572C2×C4#6698512yes—
573C2×C4#6699211yescharacteristic
574C2×C4#6699211yescharacteristic
575C2×C4#6699211yescharacteristic
576C2×C4#6700212yes—
577C2×C4C2×D4×D1111yescharacteristic
578C2×C4C2×#434111yescharacteristic
579C2×C4C22×C22⋊D1111yescharacteristic
580C8—41no—
581C8—41no—
582C8—112no—
583C8—221no—
584C8—221no—
585C8—221no—
586C8—441no—
587C8—441no—
588C8—441no—
589C8—441no—
590C22—21no—
591C22—21no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—881no—
599C22—881no—
600C22—881no—
601C22#1062265212yes—
602C22C2×#6699211yescharacteristic
603C4—21no—
604C4—21no—
605C4—21no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—81no—
610C4—881no—
611C4#1062265212yes—
612C4D11×#13511yescharacteristic
613C4#1062329911yescharacteristic
614C4C2×#6698511yescharacteristic
615C4C2×#6700211yescharacteristic
616C2—22no—
617C2—81no—
618C2—161no—
619C2—1761no—
620C2#1307806711yescharacteristic
621C2C2×#1062265211yescharacteristic
622C2#1307833311yescharacteristic
subgroupG/H
centerC2×C4#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3035C2
socleC22×C11C2×#121
hypercenter#3035D11
hypocenterC11#19157
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. #13079191C2semidirect
2. #13078071C2semidirect
3. #13077583C2semidirect
4. #13068186C2semidirect
5. #13068182C2semidirect
6. #13068179C2semidirect
7. #13068175C2semidirect
8. #13068132C2semidirect
9. #13068127C2semidirect
10. #13068098C2semidirect
11. #13068093C2semidirect
12. C2×#10622118C2semidirect
13. #13067266C2semidirect
14. #13067265C2semidirect
15. C11×#3035C2semidirect
224. #3035D11semidirect
293. C11⋊C8#135semidirect
532. C11#19157semidirect

Maximal subgroups

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

subgroupindex
#130791912
#130780712
#130775832
#130681862
#130681822
#130681792
#130681752
#130681322
#130681272
#130680982
#130680932
C2×#106221182
#130672662
#130672652
C11×#30352
#1915711