Finite Group Databasebeta

← #14736243

Subgroups — #14736243

Order 2816.

664 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079191C211yesmaximal, characteristic, complemented
2#13078676C211yesmaximal, characteristic, complemented
3#41×C11⋊C8C211yesmaximal, characteristic, complemented
4#13068034C211yesmaximal, characteristic, complemented
5#13068030C211yesmaximal, characteristic, complemented
6#13068027C211yesmaximal, characteristic, complemented
7#13068023C211yesmaximal, characteristic, complemented
8#13068018C211yesmaximal, characteristic, complemented
9#13068013C211yesmaximal, characteristic, complemented
10#13067974C211yesmaximal, characteristic, complemented
11#13067969C211yesmaximal, characteristic, complemented
12#13067362C211yesmaximal, characteristic, complemented
13#13067278C211yesmaximal, characteristic, complemented
14#13067276C211yesmaximal, characteristic, complemented
15C11×#3106C211yesmaximal, characteristic, complemented
16C11×#532C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18#10623008C2211yescharacteristic
19C11×#482—21no—
20C11×#477C2211yescharacteristic
21C11×#476C2211yescharacteristic
22C11×#460C2211yescharacteristic
23C11×#459C2211yescharacteristic
24C11×#449—21no—
25C4×C11×SD16—21no—
26C4×C11×D8—21no—
27C11×#431C2211yescharacteristic
28#10622851—21no—
29#10622701C2211yescharacteristic
30#10622691C2211yescharacteristic
31#10622686C2211yescharacteristic
32#10622683C2211yescharacteristic
33#10622651—21no—
34#10622651—21no—
35#10622640C2211yescharacteristic
36C4×#4325—21no—
37Q8×C11⋊C8C2211yescharacteristic
38Q8×C11⋊C8C2211yescharacteristic
39#10622634C2211yescharacteristic
40#10622628C2211yescharacteristic
41C4×#4323—21no—
42C4×#4323—21no—
43C4×#4323—21no—
44D4×C11⋊C8—21no—
45D4×C11⋊C8—21no—
46D4×C11⋊C8C2211yescharacteristic
47D4×C11⋊C8C2211yescharacteristic
48#10622621C2211yescharacteristic
49#10622616—21no—
50#10622538—21no—
51#10622538C2211yescharacteristic
52#10622538C2211yescharacteristic
53C2×C4×C11⋊C8—21no—
54C2×C4×C11⋊C8C2211yescharacteristic
55#10622184C2211yescharacteristic
56#10622184C2211yescharacteristic
57#10622182C2211yescharacteristic
58#10622182C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×#41D411yescharacteristic
69C2×#4339—21no—
70C2×C11×SD16—21no—
71C2×C11×D8—21no—
72C11×C4⋊Q8C2311yescharacteristic
73C11×#127C2311yescharacteristic
74C11×#124—21no—
75C11×#121—21no—
76C11×#121—21no—
77C4×Q8×C11D411yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11D411yescharacteristic
84C4×D4×C11C2311yescharacteristic
85C11×#117—21no—
86C11×#117D411yescharacteristic
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89C2×#4325—21no—
90C2×#4323—21no—
91C2×#4323—21no—
92C2×#4323—21no—
93#66983—21no—
94#66983—21no—
95C22×C11⋊C8—21no—
96C22×C11⋊C8—21no—
97C22×C11⋊C8D411yescharacteristic
98C22×C11⋊C8D411yescharacteristic
99#66928—21no—
100#66927C2311yescharacteristic
101C4×D44—21no—
102C4×D44—21no—
103#66922C2311yescharacteristic
104C11×#107—21no—
105C11×#106—21no—
106C11×C4⋊C8C2311yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×#103—21no—
109C11×#102—21no—
110C11×#102—21no—
111C11×#102—21no—
112C11×C22⋊C8—21no—
113C4×C8×C11—21no—
114#66899—21no—
115#66896—21no—
116#66896—21no—
117#66896—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122#66873—21no—
123#66873—21no—
124#66873—21no—
125#66873—21no—
126#66872—21no—
127#66871—21no—
128#66871—21no—
129#66871—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4×C11⋊C8—21no—
137C4×C11⋊C8—21no—
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8D411yescharacteristic
141C4×C11⋊C8D411yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19128—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—22no—
147C11×#41—82no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—41no—
155C2×D4×C11C2×D411yescharacteristic
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—41no—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11#4111yescharacteristic
163C2×C22⋊D11—41no—
164#4339—82no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×C4×D11—41no—
169C2×Dic22—21no—
170C11×SD16—42no—
171C11×D8—42no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—41no—
184C11×C22⋊C4—41no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11#4111yescharacteristic
191C42×C11C2411yescharacteristic
192#4325—42no—
193#4323—42no—
194#4323—42no—
195#4323—42no—
196(C2×D11)⋊C4—41no—
197(C2×D11)⋊C4—41no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—41no—
206C2×C11⋊C8—42no—
207C2×C11⋊C8—42no—
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212#3169—111no—
213#3106—111no—
214#3106D1111yescharacteristic, complemented
215C8×#41—111no—
216#1678—111no—
217#1678—111no—
218#1677—111no—
219#1677—111no—
220#1676—111no—
221#1675—111no—
222#1668—111no—
223#1667—111no—
224#1564—111no—
225#1543—111no—
226#1543—111no—
227C23×C11—21no—
228C23×C11—41no—
229C23×C11#12111yescharacteristic
230C22×D11—41no—
231Q8×C11—21no—
232Q8×C11—81no—
233Q8×C11#13512yes—
234D4×C11—24no—
235D4×C11—21no—
236D4×C11—41no—
237D4×C11—41no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—81no—
241D4×C11—82no—
242D4×C11#13512yes—
243C2×C4×C11—24no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—82no—
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C22⋊D11—82no—
264C2×Dic11—41no—
265D44—41no—
266D44—41no—
267D44—41no—
268D44—41no—
269D44—81no—
270C4×D11—82no—
271Dic22—81no—
272C8×C11—41no—
273C8×C11—41no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8#13512yes—
282#532—111no—
283#532C2×D1111yescharacteristic
284C4×#41C2×D1111yescharacteristic
285#500—111no—
286#493—111no—
287#486—111no—
288#486—111no—
289#482—21no—
290#482—221no—
291#477—111no—
292#477C2×D1111yescharacteristic
293#476—111no—
294#476C2×D1111yescharacteristic
295#466—221no—
296#466—221no—
297#460—111no—
298#460C2×D1111yescharacteristic
299#459—111no—
300#459C2×D1111yescharacteristic
301#449—21no—
302#449—221no—
303C8×Q8—111no—
304C8×Q8—111no—
305C4×SD16—21no—
306C4×SD16—221no—
307C4×D8—21no—
308C4×D8—221no—
309C4×D8—221no—
310C4×D8—221no—
311C8×D4—111no—
312C8×D4—111no—
313C8×D4—221no—
314C8×D4—221no—
315#431—111no—
316#431—111no—
317#431—221no—
318#431C2×D1111yescharacteristic
319C2×C4×C8—111no—
320C2×C4×C8—221no—
321#335—111no—
322#335—111no—
323#334—111no—
324#334—111no—
325#333—111no—
326#333—111no—
327#333—111no—
328#333—111no—
329#331—111no—
330#331—111no—
331#331—111no—
332#331—111no—
333C22×C11—21no—
334C22×C11—21no—
335C22×C11—22no—
336C22×C11—21no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11C2×#12111yescharacteristic
343C2×D11—81no—
344C2×D11—81no—
345C2×D11—81no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—22no—
349C4×C11—21no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—81no—
353C4×C11#47212yes—
354C4×C11C2×#13511yescharacteristic
355C4×C11C2×#13511yescharacteristic
356C4×C11C2×#13511yescharacteristic
357C4×C11#57511yescharacteristic
358Dic11—81no—
359C2×#41—21no—
360C2×#41—221no—
361C2×#41C22⋊D1111yescharacteristic
362C2×SD16—21no—
363C2×SD16—221no—
364C2×D8—21no—
365C2×D8—221no—
366C2×D8—221no—
367C2×D8—221no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8—221no—
371C22×C8—221no—
372C4⋊Q8—111no—
373C4⋊Q8C22×D1111yescharacteristic
374#127—111no—
375#127C22×D1111yescharacteristic
376#124—21no—
377#124—221no—
378#121—21no—
379#121—21no—
380#121—221no—
381#121—221no—
382C4×Q8C22⋊D1111yescharacteristic
383C4×Q8C22×D1111yescharacteristic
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—221no—
389C4×D4—221no—
390C4×D4C22⋊D1111yescharacteristic
391C4×D4C22×D1111yescharacteristic
392#117—21no—
393#117C22⋊D1111yescharacteristic
394C2×C42—21no—
395C2×C42C22×D1111yescharacteristic
396#107—21no—
397#107—221no—
398#107—221no—
399#107—221no—
400#106—21no—
401#106—221no—
402C4⋊C8—111no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—221no—
407C4⋊C8—221no—
408C4⋊C8C22×D1111yescharacteristic
409C4⋊C8C22×D1111yescharacteristic
410#103—21no—
411#103—221no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—221no—
416#102—221no—
417#102—221no—
418#102—221no—
419#102—221no—
420#102—221no—
421#102—221no—
422C22⋊C8—21no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C4×C8—21no—
428C4×C8—111no—
429C4×C8—111no—
430C4×C8—111no—
431C4×C8—111no—
432C4×C8—221no—
433C4×C8—221no—
434C4×C8—221no—
435C4×C8—221no—
436C2×C11—41no—
437C2×C11—42no—
438C2×C11—161no—
439C2×C11#303511yescharacteristic
440C2×C11#305011yescharacteristic
441C2×C11C2×#47211yescharacteristic
442D11—161no—
443#41—22no—
444#41—22no—
445#41—82no—
446#41—882no—
447C2×Q8—21no—
448C2×Q8—221no—
449C2×Q8C2×C22⋊D1111yescharacteristic
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—441no—
459C2×D4C2×C22⋊D1111yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—41no—
464C22×C4—441no—
465C22×C4D4×D1111yescharacteristic
466C22×C4#434111yescharacteristic
467C22×C4C2×C22⋊D1111yescharacteristic
468SD16—42no—
469SD16—442no—
470D8—42no—
471D8—442no—
472D8—442no—
473D8—442no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—111no—
477C2×C8—111no—
478C2×C8—111no—
479C2×C8—111no—
480C2×C8—222no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—442no—
486C2×C8—441no—
487C2×C8—442no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4C2×C22⋊D1111yescharacteristic
495C4⋊C4C2×C22⋊D1111yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—441no—
502C22⋊C4—441no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42D4×D1111yescharacteristic
507C42#434111yescharacteristic
508C42C2×C22⋊D1111yescharacteristic
509C42C23×D1111yescharacteristic
510C11#1912811yescharacteristic, complemented, Sylow
511C23—21no—
512C23—41no—
513C23—441no—
514C23#6699211yescharacteristic
515Q8—21no—
516Q8—81no—
517Q8—881no—
518Q8#6700312yes—
519D4—24no—
520D4—21no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—81no—
526D4—82no—
527D4—441no—
528D4—441no—
529D4—441no—
530D4—441no—
531D4—881no—
532D4—882no—
533D4#6700312yes—
534C2×C4—24no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—82no—
548C2×C4—441no—
549C2×C4—882no—
550C2×C4#6699211yescharacteristic
551C2×C4#6699211yescharacteristic
552C2×C4#6699211yescharacteristic
553C2×C4C2×D4×D1111yescharacteristic
554C2×C4C2×#434111yescharacteristic
555C2×C4C22×C22⋊D1111yescharacteristic
556C8—41no—
557C8—41no—
558C8—112no—
559C8—221no—
560C8—221no—
561C8—221no—
562C8—441no—
563C8—441no—
564C8—441no—
565C8—441no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—22no—
570C22—41no—
571C22—41no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—881no—
576C22—881no—
577C22—881no—
578C22C2×#6699211yescharacteristic
579C4—21no—
580C4—21no—
581C4—21no—
582C4—22no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—881no—
587C4#1062281212yes—
588C4D11×#13511yescharacteristic
589C4#1062329911yescharacteristic
590C4C2×#6700311yescharacteristic
591C4C2×#6700311yescharacteristic
592C2—41no—
593C2—42no—
594C2—161no—
595C2—1761no—
596C2#1307806711yescharacteristic
597C2#1307819411yescharacteristic
598C2C2×#1062281211yescharacteristic
subgroupG/H
centerC2×C4#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3106C2
socleC22×C11C2×#121
hypercenter#3106D11
hypocenterC11#19128
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #13079191C2semidirect
2. #13078676C2semidirect
3. #41×C11⋊C8C2semidirect
4. #13068034C2semidirect
5. #13068030C2semidirect
6. #13068027C2semidirect
7. #13068023C2semidirect
8. #13068018C2semidirect
9. #13068013C2semidirect
10. #13067974C2semidirect
11. #13067969C2semidirect
12. #13067362C2semidirect
13. #13067278C2semidirect
14. #13067276C2semidirect
15. C11×#3106C2semidirect
214. #3106D11semidirect
510. C11#19128semidirect

Maximal subgroups

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

subgroupindex
#130791912
#130786762
#41×C11⋊C82
#130680342
#130680302
#130680272
#130680232
#130680182
#130680132
#130679742
#130679692
#130673622
#130672782
#130672762
C11×#31062
#1912811