Finite Group Databasebeta

← #14737194

Subgroups — #14737194

Order 2816.

630 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#13079588C211yesmaximal, characteristic, complemented
2#13079191C211yesmaximal, characteristic, complemented
3#13077592C211yesmaximal, characteristic, complemented
4#13068132C211yesmaximal, characteristic, complemented
5#13068127C211yesmaximal, characteristic, complemented
6#13068098C211yesmaximal, characteristic, complemented
7#13068093C211yesmaximal, characteristic, complemented
8#13068062C211yesmaximal, characteristic, complemented
9#13068058C211yesmaximal, characteristic, complemented
10#13068055C211yesmaximal, characteristic, complemented
11#13068051C211yesmaximal, characteristic, complemented
12#13067362C211yesmaximal, characteristic, complemented
13#13067321C211yesmaximal, characteristic, complemented
14#13067319C211yesmaximal, characteristic, complemented
15C11×#3212C211yesmaximal, characteristic, complemented
16C11×#532C2211yescharacteristic
17C11×#529C2211yescharacteristic
18#10623008C2211yescharacteristic
19C11×#495—21no—
20C11×#488—21no—
21C11×#462C2211yescharacteristic
22C11×#461C2211yescharacteristic
23C11×#460C2211yescharacteristic
24C11×#459C2211yescharacteristic
25C11×#452—21no—
26C11×#449—21no—
27C11×#431C2211yescharacteristic
28#10622701C2211yescharacteristic
29#10622691C2211yescharacteristic
30#10622686C2211yescharacteristic
31#10622683C2211yescharacteristic
32#10622681—21no—
33#10622672—21no—
34#10622660—21no—
35#10622651—21no—
36#10622651—21no—
37#10622650—21no—
38#10622644C2211yescharacteristic
39#10622640C2211yescharacteristic
40#10622637C2211yescharacteristic
41Q8×C11⋊C8C2211yescharacteristic
42#10622632C2211yescharacteristic
43#10622628C2211yescharacteristic
44C4×#4323—21no—
45C4×#4323—21no—
46#10622625C2211yescharacteristic
47#10622624—21no—
48D4×C11⋊C8—21no—
49D4×C11⋊C8C2211yescharacteristic
50#10622613—21no—
51#10622610—21no—
52#10622539C2211yescharacteristic
53#10622538C2211yescharacteristic
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#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41—21no—
68C2×#4339—21no—
69C2×C11×Q16—21no—
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C2×C11×D8—21no—
73C11×C4⋊Q8C2311yescharacteristic
74C11×#127C2311yescharacteristic
75C11×#126—21no—
76C11×#125D411yescharacteristic
77C11×#124—21no—
78C11×#124D411yescharacteristic
79C11×#123—21no—
80C11×C22⋊Q8D411yescharacteristic
81C11×#121—21no—
82C11×#121—21no—
83C11×#121D411yescharacteristic
84C4×Q8×C11C2311yescharacteristic
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11—21no—
88C4×D4×C11C2311yescharacteristic
89C11×#117—21no—
90C2×C42×C11C2311yescharacteristic
91C2×#4326—21no—
92C2×#4325—21no—
93C2×#4324—21no—
94C2×#4323—21no—
95C2×#4323—21no—
96C2×#4323—21no—
97#66983—21no—
98#66983—21no—
99C2×#4318—21no—
100C22×C11⋊C8—21no—
101C22×C11⋊C8D411yescharacteristic
102C22×C11⋊C8D411yescharacteristic
103#66928—21no—
104#66927C2311yescharacteristic
105C4×D44—21no—
106C4×D44—21no—
107#66922C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×C4⋊C8C2311yescharacteristic
110C11×#103—21no—
111C11×#103—21no—
112C11×#102—21no—
113C11×#102—21no—
114C11×C22⋊C8—21no—
115C4×C8×C11—21no—
116#66896—21no—
117#66896—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122#66874—21no—
123#66874—21no—
124#66873—21no—
125#66873—21no—
126#66873—21no—
127#66873—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
136#66867—21no—
137#66867—21no—
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8D411yescharacteristic
141C4×C11⋊C8D411yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19225—111nomaximal, Sylow
145C11×#41—81no—
146C11×#41—81no—
147C2×Q8×C11—21no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—41no—
154C2×D4×C11C2×D411yescharacteristic
155C22×C4×C11—21no—
156C22×C4×C11—41no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C2×C22⋊D11—41no—
161#4339—81no—
162#4339—81no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×C4×D11—41no—
167C2×Dic22—21no—
168C11×Q16—81no—
169C11×SD16—81no—
170C11×SD16—81no—
171C11×D8—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⋊C4C2×D411yescharacteristic
181C11×C4⋊C4C2×D411yescharacteristic
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—41no—
188C11×C22⋊C4—41no—
189C42×C11—21no—
190C42×C11C2×D411yescharacteristic
191C42×C11C2×D411yescharacteristic
192C42×C11#4111yescharacteristic
193C42×C11C2411yescharacteristic
194#4326—81no—
195#4325—81no—
196#4324—81no—
197#4323—42no—
198#4323—42no—
199#4323—81no—
200(C2×D11)⋊C4—41no—
201(C2×D11)⋊C4—41no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204#4318—42no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—41no—
211C2×C11⋊C8—42no—
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214C2×C11⋊C8C2×D411yescharacteristic
215C2×C11⋊C8C2×D411yescharacteristic
216#3212—111no—
217#3212D1111yescharacteristic, complemented
218#3169—111no—
219#2966—111no—
220#1694—111no—
221#1693—111no—
222#1688—111no—
223#1687—111no—
224#1682—111no—
225#1682—111no—
226#1681—111no—
227#1681—111no—
228#1564—111no—
229#1553—111no—
230#1553—111no—
231C23×C11—21no—
232C23×C11—41no—
233C23×C11#12111yescharacteristic
234C22×D11—41no—
235Q8×C11—21no—
236Q8×C11—21no—
237Q8×C11—41no—
238Q8×C11—41no—
239D4×C11—21no—
240D4×C11—21no—
241D4×C11—42no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—81no—
247D4×C11—82no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—82no—
260C2×C4×C11#12111yescharacteristic
261C2×C4×C11#12111yescharacteristic
262C2×C4×C11#12111yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C22⋊D11—82no—
267C2×Dic11—41no—
268D44—41no—
269D44—41no—
270D44—41no—
271D44—41no—
272D44—81no—
273C4×D11—82no—
274Dic22—41no—
275Dic22—41no—
276C8×C11—41no—
277C8×C11—41no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C11⋊C8#13512yes—
286#532—111no—
287#532C2×D1111yescharacteristic
288#529C2×D1111yescharacteristic
289#500—111no—
290#495—21no—
291#495—221no—
292#493—111no—
293#488—21no—
294#488—221no—
295#486—111no—
296#486—111no—
297#466—221no—
298#466—221no—
299#462—111no—
300#462C2×D1111yescharacteristic
301#461—111no—
302#461C2×D1111yescharacteristic
303#460—111no—
304#460C2×D1111yescharacteristic
305#459—111no—
306#459C2×D1111yescharacteristic
307#452—21no—
308#452—221no—
309#449—21no—
310#449—221no—
311#446—111no—
312C8×Q8—111no—
313C4×D8—221no—
314C4×D8—221no—
315#436—111no—
316#435—221no—
317C8×D4—111no—
318C8×D4—221no—
319#433—221no—
320#432—111no—
321#431—111no—
322#431C2×D1111yescharacteristic
323#405—221no—
324C2×C4×C8—111no—
325#335—111no—
326#335—111no—
327#334—111no—
328#334—111no—
329#332—111no—
330#332—111no—
331#332—111no—
332#332—111no—
333#331—111no—
334#331—111no—
335#331—111no—
336#331—111no—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—21no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11C2×#12111yescharacteristic
347C2×D11—81no—
348C2×D11—81no—
349C2×D11—81no—
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×C11C2×#13511yescharacteristic
359C4×C11#57511yescharacteristic
360C4×C11#57611yescharacteristic
361C4×C11#57611yescharacteristic
362Dic11—81no—
363C2×#41—21no—
364C2×#41—221no—
365C2×Q16—21no—
366C2×Q16—221no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—221no—
370C2×SD16—221no—
371C2×D8—21no—
372C2×D8—221no—
373C2×D8—221no—
374C2×D8—221no—
375C2×M16—221no—
376C22×C8—111no—
377C22×C8—111no—
378C22×C8—221no—
379C4⋊Q8—111no—
380C4⋊Q8C22×D1111yescharacteristic
381#127—111no—
382#127C22×D1111yescharacteristic
383#126—21no—
384#125C22⋊D1111yescharacteristic
385#124—21no—
386#124—221no—
387#124C22⋊D1111yescharacteristic
388#123—21no—
389C22⋊Q8C22⋊D1111yescharacteristic
390#121—21no—
391#121—21no—
392#121—221no—
393#121—221no—
394#121C22⋊D1111yescharacteristic
395C4×Q8C22×D1111yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—221no—
400C4×D4—221no—
401C4×D4C22×D1111yescharacteristic
402#117—21no—
403C2×C42C22×D1111yescharacteristic
404#107—221no—
405#107—221no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—111no—
410C4⋊C8—221no—
411C4⋊C8—221no—
412C4⋊C8C22×D1111yescharacteristic
413C4⋊C8C22×D1111yescharacteristic
414#103—21no—
415#103—21no—
416#103—221no—
417#103—221no—
418#102—21no—
419#102—21no—
420#102—221no—
421#102—221no—
422#102—221no—
423#102—221no—
424#102—221no—
425#102—221no—
426C22⋊C8—21no—
427C22⋊C8—221no—
428C22⋊C8—221no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431#97—221no—
432#97—221no—
433C4×C8—21no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—111no—
437C4×C8—111no—
438C4×C8—221no—
439C4×C8—221no—
440C2×C11—41no—
441C2×C11—81no—
442C2×C11—161no—
443C2×C11#303511yescharacteristic
444C2×C11#305811yescharacteristic
445C2×C11#306711yescharacteristic
446D11—161no—
447#41—81no—
448#41—81no—
449#41—881no—
450#41—881no—
451C2×Q8—21no—
452C2×Q8—221no—
453C2×Q8C2×C22⋊D1111yescharacteristic
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—41no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—441no—
463C2×D4C2×C22⋊D1111yescharacteristic
464C22×C4—21no—
465C22×C4—41no—
466C22×C4—441no—
467C22×C4D4×D1111yescharacteristic
468C22×C4#434111yescharacteristic
469C22×C4C2×C22⋊D1111yescharacteristic
470Q16—81no—
471Q16—881no—
472SD16—81no—
473SD16—81no—
474SD16—881no—
475SD16—881no—
476D8—81no—
477D8—442no—
478D8—442no—
479D8—881no—
480M16—442no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—111no—
484C2×C8—111no—
485C2×C8—111no—
486C2×C8—111no—
487C2×C8—222no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—441no—
493C2×C8—442no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—221no—
501C4⋊C4—221no—
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—
510C22⋊C4—41no—
511C22⋊C4—441no—
512C22⋊C4—441no—
513C42—21no—
514C42D4×D1111yescharacteristic
515C42#434111yescharacteristic
516C42C2×C22⋊D1111yescharacteristic
517C42C23×D1111yescharacteristic
518C11#1922511yescharacteristic, complemented, Sylow
519C23—21no—
520C23—41no—
521C23—441no—
522C23#6699211yescharacteristic
523Q8—21no—
524Q8—21no—
525Q8—41no—
526Q8—41no—
527Q8—441no—
528Q8—441no—
529D4—21no—
530D4—21no—
531D4—42no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—81no—
537D4—82no—
538D4—441no—
539D4—441no—
540D4—441no—
541D4—441no—
542D4—881no—
543D4—882no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—82no—
556C2×C4—441no—
557C2×C4—882no—
558C2×C4#6699211yescharacteristic
559C2×C4#6699211yescharacteristic
560C2×C4#6699211yescharacteristic
561C2×C4C2×D4×D1111yescharacteristic
562C2×C4C2×#434111yescharacteristic
563C2×C4C22×C22⋊D1111yescharacteristic
564C8—41no—
565C8—41no—
566C8—112no—
567C8—221no—
568C8—221no—
569C8—221no—
570C8—441no—
571C8—441no—
572C8—441no—
573C8—441no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—881no—
584C22—881no—
585C22—881no—
586C22C2×#6699211yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—81no—
595C4—881no—
596C4D11×#13511yescharacteristic
597C4#1062329911yescharacteristic
598C4#1062336611yescharacteristic
599C4#1062336611yescharacteristic
600C2—41no—
601C2—81no—
602C2—161no—
603C2—1761no—
604C2#1307806711yescharacteristic
605C2#1307826111yescharacteristic
606C2#1307833311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3212C2
socleC22×C11C2×#121
hypercenter#3212D11
hypocenterC11#19225
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3212

Complements

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

NH ≅ G/Ntype
1. #13079588C2semidirect
2. #13079191C2semidirect
3. #13077592C2semidirect
4. #13068132C2semidirect
5. #13068127C2semidirect
6. #13068098C2semidirect
7. #13068093C2semidirect
8. #13068062C2semidirect
9. #13068058C2semidirect
10. #13068055C2semidirect
11. #13068051C2semidirect
12. #13067362C2semidirect
13. #13067321C2semidirect
14. #13067319C2semidirect
15. C11×#3212C2semidirect
217. #3212D11semidirect
518. C11#19225semidirect

Maximal subgroups

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

subgroupindex
#130795882
#130791912
#130775922
#130681322
#130681272
#130680982
#130680932
#130680622
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