Finite Group Databasebeta

← #14738879

Subgroups — #14738879

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#13079631C211yesmaximal, characteristic
2#13078992C211yesmaximal, characteristic, complemented
3#13077621C211yesmaximal, characteristic, complemented
4#13068186C211yesmaximal, characteristic, complemented
5#13068179C211yesmaximal, characteristic, complemented
6#13068158C211yesmaximal, characteristic, complemented
7#13068151C211yesmaximal, characteristic, complemented
8#13068062C211yesmaximal, characteristic, complemented
9#13068055C211yesmaximal, characteristic, complemented
10#13068034C211yesmaximal, characteristic, complemented
11#13068027C211yesmaximal, characteristic, complemented
12#13067381C211yesmaximal, characteristic, complemented
13#13067326C211yesmaximal, characteristic, complemented
14#13067285C211yesmaximal, characteristic, complemented
15C11×#3252C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#529C2211yescharacteristic
18C2×#66927C2211yescharacteristic
19C11×#479—21no—
20C11×#477C2211yescharacteristic, complemented
21C11×#476C2211yescharacteristic, complemented
22C11×#470—21no—
23C11×#468—21no—
24C11×#464—21no—
25C11×#462C2211yescharacteristic, complemented
26C11×#461C2211yescharacteristic, complemented
27C11×#423C2211yescharacteristic
28#10622701C2211yescharacteristic
29#10622701C2211yescharacteristic
30#10622701C2211yescharacteristic
31#10622701C2211yescharacteristic
32#10622680—21no—
33#10622680—21no—
34#10622680—21no—
35#10622671—21no—
36#10622659—21no—
37#10622649—21no—
38#10622640C2211yescharacteristic
39#10622640C2211yescharacteristic
40#10622637C2211yescharacteristic, complemented
41Q8×C11⋊C8C2211yescharacteristic, complemented
42#10622628C2211yescharacteristic
43#10622628C2211yescharacteristic
44#10622625—21no—
45#10622625C2211yescharacteristic, complemented
46#10622624—21no—
47D4×C11⋊C8C2211yescharacteristic, complemented
48#10622614—21no—
49#10622614—21no—
50#10622613—21no—
51#10622610—21no—
52#10622539C2211yescharacteristic
53#10622538C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622185C2211yescharacteristic, complemented
56#10622185C2211yescharacteristic, complemented
57#10622184C2211yescharacteristic, complemented
58#10622184C2211yescharacteristic, complemented
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622123C2211yescharacteristic
62#10622123C2211yescharacteristic
63#10622118C2211yescharacteristic, complemented
64#10622118C2211yescharacteristic, complemented
65#10622117C2211yescharacteristic, complemented
66#10622117C2211yescharacteristic, complemented
67C22×D44—21no—
68C22×D44—21no—
69C22×D44—21no—
70C2×C11×Q16—21no—
71C2×C11×SD16—21no—
72C2×C11×M16—21no—
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×#126—21no—
76C11×#125—21no—
77C11×#125D411yescharacteristic
78C11×#124D411yescharacteristic
79C11×#123—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8D411yescharacteristic
83C11×#121D411yescharacteristic
84C4×Q8×C11—21no—
85C4×Q8×C11—21no—
86C4×Q8×C11C2311yescharacteristic
87C4×D4×C11—21no—
88C4×D4×C11C2311yescharacteristic
89C11×#117—21no—
90C11×#117—21no—
91C2×C42×C11C2311yescharacteristic
92C2×#4325—21no—
93C2×#4325—21no—
94C2×#4323—21no—
95C2×#4323—21no—
96C2×#4318—21no—
97C2×#4318D411yescharacteristic
98C2×#4318D411yescharacteristic
99C22×C11⋊C8—21no—
100#66927—21no—
101#66927—21no—
102#66927—21no—
103#66927C2311yescharacteristic
104#66927C2311yescharacteristic
105C11×#107—21no—
106C11×#106—21no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8C2311yescharacteristic
109C11×C4⋊C8C2311yescharacteristic
110C11×#103—21no—
111C11×#103—21no—
112C11×#103—21no—
113C11×#102—21no—
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117C22⋊(C11⋊C8)—21no—
118#66873—21no—
119#66873—21no—
120#66873—21no—
121#66873—21no—
122#66873—21no—
123#66873—21no—
124#66873—21no—
125#66873—21no—
126#66873—21no—
127#66873—21no—
128#66873—21no—
129#66873—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
136#66867—21no—
137#66867—21no—
138#66867D411yescharacteristic
139#66867D411yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19380—111nomaximal, Sylow
145C23×D11—41no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11C2×D411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—42no—
162C2×D44—42no—
163C2×D44—41no—
164C2×D44—41no—
165C2×D44—41no—
166C2×D44—81no—
167C2×D44—81no—
168C2×D44—82no—
169C11×Q16—81no—
170C11×SD16—81no—
171C11×M16—81no—
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⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—41no—
183C11×C4⋊C4—41no—
184C11×C4⋊C4C2×D411yescharacteristic
185C11×C4⋊C4C2×D411yescharacteristic
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—21no—
191C11×C22⋊C4—41no—
192C42×C11—21no—
193C42×C11—41no—
194C42×C11C2×D411yescharacteristic
195C42×C11C2×D411yescharacteristic
196C42×C11#4111yescharacteristic
197C42×C11C2411yescharacteristic
198#4325—81no—
199#4325—81no—
200#4323—81no—
201#4323—81no—
202#4318—41no—
203#4318—41no—
204#4318—42no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—42no—
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214#3252D1111yescharacteristic, complemented
215#3217—111no—
216#3138—111no—
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—21no—
230C23×C11#12111yescharacteristic
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—82no—
234C22×D11—82no—
235C22×D11—82no—
236Q8×C11—21no—
237Q8×C11—21no—
238Q8×C11—41no—
239Q8×C11—41no—
240Q8×C11—81no—
241D4×C11—21no—
242D4×C11—21no—
243D4×C11—81no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262D44—41no—
263D44—41no—
264D44—41no—
265D44—41no—
266D44—41no—
267D44—41no—
268D44—41no—
269D44—41no—
270D44—81no—
271D44—81no—
272D44—82no—
273D44—82no—
274D44—82no—
275C8×C11—41no—
276C8×C11—41no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285#533C2×D1111yescharacteristic
286C2×#127—111no—
287#529C2×D1111yescharacteristic
288#496—221no—
289#490—221no—
290#490—221no—
291#490—221no—
292#486—111no—
293#486—111no—
294#486—111no—
295#486—111no—
296#479—21no—
297#477C2×D1111yescharacteristic, complemented
298#476C2×D1111yescharacteristic, complemented
299#470—21no—
300#468—21no—
301#464—21no—
302#462C2×D1111yescharacteristic, complemented
303#461C2×D1111yescharacteristic, complemented
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#423C2×D1111yescharacteristic
320#418—221no—
321#418—221no—
322#405—221no—
323C4×M16—111no—
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—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11C2×#12111yescharacteristic
343C2×D11—81no—
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—81no—
347C2×D11—81no—
348C2×D11—81no—
349C2×D11—164no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11#57511yescharacteristic
360C4×C11#57511yescharacteristic
361C4×C11#57611yescharacteristic
362C4×C11#57711yescharacteristic
363C22×D4—221no—
364C22×D4—221no—
365C22×D4—221no—
366C2×Q16—21no—
367C2×SD16—21no—
368C2×SD16—221no—
369C2×SD16—221no—
370C2×D8—221no—
371C2×D8—221no—
372C2×M16—21no—
373C2×M16—111no—
374C2×M16—111no—
375C2×M16—221no—
376C22×C8—221no—
377C4⋊Q8C22×D1111yescharacteristic
378C4⋊Q8C22×D1111yescharacteristic
379#127—111no—
380#127—111no—
381#127—221no—
382#127—221no—
383#127—221no—
384#126—21no—
385#125—21no—
386#125C22⋊D1111yescharacteristic
387#124C22⋊D1111yescharacteristic
388#123—21no—
389C22⋊Q8—21no—
390C22⋊Q8—21no—
391C22⋊Q8C22⋊D1111yescharacteristic
392#121C22⋊D1111yescharacteristic
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8C22×D1111yescharacteristic
396C4×D4—21no—
397C4×D4C22×D1111yescharacteristic
398#117—21no—
399#117—21no—
400C2×C42C22×D1111yescharacteristic
401#107—21no—
402#106—21no—
403C4⋊C8—21no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—221no—
409C4⋊C8—221no—
410C4⋊C8C22×D1111yescharacteristic
411C4⋊C8C22×D1111yescharacteristic
412#103—21no—
413#103—21no—
414#103—21no—
415#102—21no—
416#102—221no—
417#102—221no—
418#102—221no—
419#102—221no—
420#102—221no—
421#102—221no—
422#102—221no—
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—111no—
433#97—111no—
434#97—221no—
435#97—221no—
436C4×C8—111no—
437C4×C8—111no—
438C4×C8—221no—
439C4×C8—221no—
440C2×C11—41no—
441C2×C11—81no—
442C2×C11#304011yescharacteristic
443C2×C11#306211yescharacteristic
444C2×C11#306811yescharacteristic
445D11—161no—
446D11—161no—
447C24—441no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8C2×C22⋊D1111yescharacteristic
451C2×D4—21no—
452C2×D4—221no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—442no—
459C2×D4—442no—
460C2×D4—441no—
461C2×D4—441no—
462C2×D4—441no—
463C2×D4—881no—
464C2×D4—881no—
465C2×D4—882no—
466C2×D4C2×C22⋊D1111yescharacteristic
467C22×C4—21no—
468C22×C4D4×D1111yescharacteristic
469C22×C4#434111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471Q16—81no—
472SD16—81no—
473SD16—881no—
474SD16—881no—
475D8—881no—
476D8—881no—
477M16—81no—
478M16—441no—
479M16—441no—
480M16—442no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—111no—
484C2×C8—111no—
485C2×C8—111no—
486C2×C8—111no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—442no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4C2×C22⋊D1111yescharacteristic
503C4⋊C4C2×C22⋊D1111yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—41no—
510C42—21no—
511C42—41no—
512C42D4×D1111yescharacteristic
513C42#434111yescharacteristic
514C42C2×C22⋊D1111yescharacteristic
515C42C23×D1111yescharacteristic
516C11#1938011yescharacteristic, complemented, Sylow
517C23—21no—
518C23—441no—
519C23—441no—
520C23—882no—
521C23—882no—
522C23—882no—
523C23#6699211yescharacteristic
524Q8—21no—
525Q8—21no—
526Q8—41no—
527Q8—41no—
528Q8—81no—
529D4—21no—
530D4—21no—
531D4—81no—
532D4—441no—
533D4—441no—
534D4—441no—
535D4—441no—
536D4—441no—
537D4—441no—
538D4—441no—
539D4—441no—
540D4—881no—
541D4—881no—
542D4—882no—
543D4—882no—
544D4—882no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4#6699211yescharacteristic
558C2×C4#6699211yescharacteristic
559C2×C4#6699211yescharacteristic
560C2×C4C2×D4×D1111yescharacteristic
561C2×C4C2×#434111yescharacteristic
562C2×C4C22×C22⋊D1111yescharacteristic
563C8—41no—
564C8—41no—
565C8—221no—
566C8—221no—
567C8—221no—
568C8—221no—
569C8—441no—
570C8—441no—
571C8—441no—
572C8—441no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—881no—
580C22—881no—
581C22—881no—
582C22—881no—
583C22—881no—
584C22—881no—
585C22—1764no—
586C22C2×#6699211yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—81no—
595C4—81no—
596C4#1062330811yescharacteristic
597C4#1062330811yescharacteristic
598C4#1062336611yescharacteristic
599C4#1062336811yescharacteristic
600C2—41no—
601C2—81no—
602C2—1761no—
603C2—1761no—
604C2#1307811211yescharacteristic
605C2#1307829811yescharacteristic
606C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3252C2
socleC22×C11C2×#121
prime radical#13079631C2
hypercenter#3252D11
hypocenterC11#19380
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3252

Complements

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

NH ≅ G/Ntype
2. #13078992C2semidirect
3. #13077621C2semidirect
4. #13068186C2semidirect
5. #13068179C2semidirect
6. #13068158C2semidirect
7. #13068151C2semidirect
8. #13068062C2semidirect
9. #13068055C2semidirect
10. #13068034C2semidirect
11. #13068027C2semidirect
12. #13067381C2semidirect
13. #13067326C2semidirect
14. #13067285C2semidirect
15. C11×#3252C2semidirect
20. C11×#477C22semidirect
21. C11×#476C22semidirect
25. C11×#462C22semidirect
26. C11×#461C22semidirect
40. #10622637C22semidirect
41. Q8×C11⋊C8C22semidirect
45. #10622625C22semidirect
47. D4×C11⋊C8C22semidirect
55. #10622185C22semidirect
56. #10622185C22semidirect
57. #10622184C22semidirect
58. #10622184C22semidirect
63. #10622118C22semidirect
64. #10622118C22semidirect
65. #10622117C22semidirect
66. #10622117C22semidirect
214. #3252D11semidirect
297. #477C2×D11semidirect
298. #476C2×D11semidirect
302. #462C2×D11semidirect
303. #461C2×D11semidirect
516. C11#19380semidirect

Maximal subgroups

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

subgroupindex
#130796312
#130789922
#130776212
#130681862
#130681792
#130681582
#130681512
#130680622
#130680552
#130680342
#130680272
#130673812
#130673262
#130672852
C11×#32522
#1938011