Finite Group Databasebeta

← #14738869

Subgroups — #14738869

Order 2816.

636 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079983C211yesmaximal, characteristic, complemented
2#13079634C211yesmaximal, characteristic
3#13077620C211yesmaximal, characteristic, complemented
4#13068181C211yesmaximal, characteristic, complemented
5#13068174C211yesmaximal, characteristic, complemented
6#13068153C211yesmaximal, characteristic, complemented
7#13068146C211yesmaximal, characteristic, complemented
8#13068057C211yesmaximal, characteristic, complemented
9#13068050C211yesmaximal, characteristic, complemented
10#13068029C211yesmaximal, characteristic, complemented
11#13068022C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067326C211yesmaximal, characteristic, complemented
14#13067284C211yesmaximal, characteristic, complemented
15C11×#3138C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C2×C11×#127C2211yescharacteristic
18#10623010C2211yescharacteristic
19C11×#490—21no—
20C11×#490—21no—
21C11×#486C2211yescharacteristic
22C11×#486C2211yescharacteristic
23C11×#486C2211yescharacteristic
24C11×#486C2211yescharacteristic
25C11×#418—21no—
26C11×#418—21no—
27C4×C11×M16C2211yescharacteristic
28#10622831—21no—
29#10622830—21no—
30#10622741—21no—
31#10622740—21no—
32#10622704C2211yescharacteristic, complemented
33#10622703C2211yescharacteristic, complemented
34#10622697C2211yescharacteristic, complemented
35#10622696C2211yescharacteristic, complemented
36#10622688C2211yescharacteristic
37#10622688C2211yescharacteristic
38#10622687—21no—
39#10622685C2211yescharacteristic
40#10622685C2211yescharacteristic
41#10622684—21no—
42#10622665—21no—
43#10622662—21no—
44#10622641—21no—
45#10622635—21no—
46#10622539C2211yescharacteristic
47#10622538C2211yescharacteristic
48#10622537C2211yescharacteristic
49#10622322—21no—
50#10622321—21no—
51#10622301C2211yescharacteristic, complemented
52C8×D44C2211yescharacteristic, complemented
53#10622292C2211yescharacteristic, complemented
54C8×Dic22C2211yescharacteristic, complemented
55#10622185C2211yescharacteristic, complemented
56#10622185C2211yescharacteristic, complemented
57#10622184C2211yescharacteristic, complemented
58#10622184C2211yescharacteristic, complemented
59#10622182C2211yescharacteristic
60#10622182C2211yescharacteristic
61#10622182C2211yescharacteristic
62#10622182C2211yescharacteristic
63#10622096C2211yescharacteristic, complemented
64#10622096C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66#10622095C2211yescharacteristic, complemented
67C22×D4×C11—21no—
68C22×D4×C11—21no—
69C22×D4×C11—21no—
70C2×C11×M16D411yescharacteristic
71C2×C11×M16D411yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×#127—21no—
75C11×#127—21no—
76C11×#127—21no—
77C11×#127C2311yescharacteristic
78C11×#127C2311yescharacteristic
79C11×#125—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—21no—
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C11×#117—21no—
85C2×C42×C11C2311yescharacteristic
86C2×#4326—21no—
87C2×#4325—21no—
88C2×#4324—21no—
89C2×#4324—21no—
90C2×#4323—21no—
91C2×#4323—21no—
92#66983D411yescharacteristic
93#66982—21no—
94C4×C22⋊D11—21no—
95#66977D411yescharacteristic
96C2×#4318—21no—
97C2×#4313—21no—
98C2×C8×D11—21no—
99#66929—21no—
100#66928D411yescharacteristic
101C4×D44C2311yescharacteristic
102#66925—21no—
103#66923D411yescharacteristic
104C4×Dic22C2311yescharacteristic
105C11×#102—21no—
106C11×#102—21no—
107C11×#102—21no—
108C11×#102—21no—
109C11×#102—21no—
110C11×#102—21no—
111C11×#102—21no—
112C11×#102—21no—
113C11×#97D411yescharacteristic
114C11×#97D411yescharacteristic
115C4×C8×C11C2311yescharacteristic
116C4×C8×C11C2311yescharacteristic
117#66899—21no—
118#66899—21no—
119#66896—21no—
120#66896—21no—
121#66896—21no—
122#66896—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8—21no—
127#66879—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130C8×Dic11—21no—
131#66874—21no—
132#66873—21no—
133#66872—21no—
134#66871—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142#66867—21no—
143C4×C11⋊C8—21no—
144#19380—111nomaximal, Sylow
145C24×C11—41no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—42no—
155C2×D4×C11—42no—
156C2×D4×C11—41no—
157C2×D4×C11—41no—
158C2×D4×C11—41no—
159C2×D4×C11—81no—
160C2×D4×C11—81no—
161C2×D4×C11—82no—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11#4111yescharacteristic
165C2×C22⋊D11—21no—
166C2×D44C2×D411yescharacteristic
167C2×C4×D11—21no—
168C2×Dic22C2×D411yescharacteristic
169C11×M16—41no—
170C11×M16—41no—
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4—41no—
181C11×C22⋊C4—41no—
182C42×C11—41no—
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11#4111yescharacteristic
186C42×C11C2411yescharacteristic
187C22⋊Dic11—21no—
188#4326—81no—
189#4325—81no—
190#4324—81no—
191#4324—81no—
192#4323—81no—
193#4323—81no—
194(C2×D11)⋊C4—21no—
195(C2×D11)⋊C4—21no—
196(C2×D11)⋊C4—21no—
197(C2×D11)⋊C4—21no—
198C4⋊Dic11C2×D411yescharacteristic
199C4⋊Dic11C2×D411yescharacteristic
200Dic11⋊C4—21no—
201Dic11⋊C4—21no—
202Dic11⋊C4—21no—
203Dic11⋊C4—21no—
204C4×Dic11—21no—
205#4318—81no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212#4313—42no—
213C8×D11—42no—
214#3252—111no—
215#3217—111no—
216#3138D1111yescharacteristic, complemented
217#2969—111no—
218#1702—111no—
219#1701—111no—
220#1698—111no—
221#1697—111no—
222#1682—111no—
223#1681—111no—
224#1678—111no—
225#1677—111no—
226#1569—111no—
227#1554—111no—
228#1545—111no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—82no—
232C23×C11—82no—
233C23×C11—82no—
234C23×C11#12111yescharacteristic
235C22×D11—21no—
236Q8×C11—41no—
237Q8×C11—41no—
238Q8×C11—81no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—81no—
248D4×C11—81no—
249D4×C11—82no—
250D4×C11—82no—
251D4×C11—82no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11#12111yescharacteristic
261C2×C4×C11#12111yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C22⋊D11—81no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269D44—21no—
270D44—21no—
271C4×D11—41no—
272C4×D11—41no—
273Dic22—21no—
274Dic22—21no—
275C8×C11—21no—
276C8×C11—21no—
277C8×C11—21no—
278C8×C11—21no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285#533C2×D1111yescharacteristic
286C2×#127C2×D1111yescharacteristic
287#529—111no—
288#496—221no—
289#490—21no—
290#490—21no—
291#490—221no—
292#486C2×D1111yescharacteristic
293#486C2×D1111yescharacteristic
294#486C2×D1111yescharacteristic
295#486C2×D1111yescharacteristic
296#479—221no—
297#477—111no—
298#476—111no—
299#470—221no—
300#468—221no—
301#464—221no—
302#462—111no—
303#461—111no—
304#460—111no—
305#460—111no—
306#459—111no—
307#459—111no—
308#450—221no—
309#447—221no—
310#446—111no—
311C8×Q8—111no—
312#436—111no—
313#436—221no—
314#435—221no—
315C8×D4—111no—
316#433—221no—
317#432—111no—
318#431—111no—
319#423—111no—
320#418—21no—
321#418—21no—
322#405—221no—
323C4×M16C2×D1111yescharacteristic
324#335—111no—
325#335—111no—
326#334—111no—
327#334—111no—
328#333—111no—
329#333—111no—
330#332—111no—
331#332—111no—
332#331—111no—
333#331—111no—
334#331—111no—
335#331—111no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—164no—
346C22×C11C2×#12111yescharacteristic
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—41no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—81no—
355C4×C11—81no—
356C4×C11#57511yescharacteristic
357C4×C11#57511yescharacteristic
358C4×C11#57611yescharacteristic
359C4×C11#57711yescharacteristic
360Dic11—41no—
361Dic11—41no—
362Dic11—41no—
363C22×D4—21no—
364C22×D4—21no—
365C22×D4—21no—
366C2×Q16—221no—
367C2×SD16—221no—
368C2×SD16—221no—
369C2×SD16—221no—
370C2×D8—221no—
371C2×D8—221no—
372C2×M16—221no—
373C2×M16—221no—
374C2×M16C22⋊D1111yescharacteristic
375C2×M16C22⋊D1111yescharacteristic
376C22×C8—221no—
377C4⋊Q8C22×D1111yescharacteristic
378C4⋊Q8C22×D1111yescharacteristic
379#127—21no—
380#127—21no—
381#127—21no—
382#127C22×D1111yescharacteristic
383#127C22×D1111yescharacteristic
384#126—221no—
385#125—21no—
386#125—111no—
387#124—111no—
388#123—221no—
389C22⋊Q8—21no—
390C22⋊Q8—21no—
391C22⋊Q8—111no—
392#121—111no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—111no—
396C4×D4—111no—
397C4×D4—221no—
398#117—21no—
399#117—221no—
400C2×C42C22×D1111yescharacteristic
401#107—221no—
402#106—221no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—221no—
410C4⋊C8—221no—
411C4⋊C8—221no—
412#103—221no—
413#103—221no—
414#103—221no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—221no—
424#102—221no—
425#102—221no—
426#102—221no—
427#102—221no—
428C22⋊C8—221no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431C22⋊C8—221no—
432#97—221no—
433#97—221no—
434#97C22⋊D1111yescharacteristic
435#97C22⋊D1111yescharacteristic
436C4×C8—221no—
437C4×C8—221no—
438C4×C8C22×D1111yescharacteristic
439C4×C8C22×D1111yescharacteristic
440C2×C11—41no—
441C2×C11—161no—
442C2×C11—161no—
443C2×C11#304011yescharacteristic
444C2×C11#306211yescharacteristic
445C2×C11#306811yescharacteristic
446D11—81no—
447C24—41no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—111no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—42no—
458C2×D4—42no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—81no—
463C2×D4—81no—
464C2×D4—82no—
465C2×D4—111no—
466C2×D4—221no—
467C22×C4—221no—
468C22×C4D4×D1111yescharacteristic
469C22×C4#434111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471Q16—881no—
472SD16—881no—
473SD16—881no—
474SD16—881no—
475D8—881no—
476D8—881no—
477M16—41no—
478M16—41no—
479M16—442no—
480M16—881no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—442no—
488C2×C8C2×C22⋊D1111yescharacteristic
489C2×C8C2×C22⋊D1111yescharacteristic
490C2×C8C2×C22⋊D1111yescharacteristic
491C2×C8C2×C22⋊D1111yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—111no—
499C4⋊C4—111no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C22⋊C4—41no—
505C22⋊C4—221no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C42—41no—
511C42—221no—
512C42D4×D1111yescharacteristic
513C42#434111yescharacteristic
514C42C2×C22⋊D1111yescharacteristic
515C42C23×D1111yescharacteristic
516C11#1938011yescharacteristic, complemented, Sylow
517C23—41no—
518C23—41no—
519C23—82no—
520C23—82no—
521C23—82no—
522C23—221no—
523C23#6699111yescharacteristic
524Q8—41no—
525Q8—41no—
526Q8—81no—
527Q8—221no—
528Q8—221no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—81no—
538D4—81no—
539D4—82no—
540D4—82no—
541D4—82no—
542D4—221no—
543D4—221no—
544D4—881no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4#6699111yescharacteristic
558C2×C4#6699111yescharacteristic
559C2×C4#6699111yescharacteristic
560C2×C4C2×D4×D1111yescharacteristic
561C2×C4C2×#434111yescharacteristic
562C2×C4C22×C22⋊D1111yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—441no—
568C8—441no—
569C8—441no—
570C8—441no—
571C8—441no—
572C8—441no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—164no—
583C22—441no—
584C22—441no—
585C22—441no—
586C22C2×#6699111yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—81no—
592C4—81no—
593C4—441no—
594C4—441no—
595C4—441no—
596C4#1062330511yescharacteristic
597C4#1062330611yescharacteristic
598C4#1062335311yescharacteristic
599C4#1062335311yescharacteristic
600C2—41no—
601C2—161no—
602C2—161no—
603C2—881no—
604C2#1307810611yescharacteristic
605C2#1307829011yescharacteristic
606C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3138C2
socleC22×C11C2×#121
prime radical#13079634C2
hypercenter#3138D11
hypocenterC11#19380
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3138

Complements

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

NH ≅ G/Ntype
1. #13079983C2semidirect
3. #13077620C2semidirect
4. #13068181C2semidirect
5. #13068174C2semidirect
6. #13068153C2semidirect
7. #13068146C2semidirect
8. #13068057C2semidirect
9. #13068050C2semidirect
10. #13068029C2semidirect
11. #13068022C2semidirect
12. #13067383C2semidirect
13. #13067326C2semidirect
14. #13067284C2semidirect
15. C11×#3138C2semidirect
32. #10622704C22semidirect
33. #10622703C22semidirect
34. #10622697C22semidirect
35. #10622696C22semidirect
51. #10622301C22semidirect
52. C8×D44C22semidirect
53. #10622292C22semidirect
54. C8×Dic22C22semidirect
55. #10622185C22semidirect
56. #10622185C22semidirect
57. #10622184C22semidirect
58. #10622184C22semidirect
63. #10622096C22semidirect
64. #10622096C22semidirect
65. #10622095C22semidirect
66. #10622095C22semidirect
216. #3138D11semidirect
516. C11#19380semidirect

Maximal subgroups

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

subgroupindex
#130799832
#130796342
#130776202
#130681812
#130681742
#130681532
#130681462
#130680572
#130680502
#130680292
#130680222
#130673832
#130673262
#130672842
C11×#31382
#1938011