Finite Group Databasebeta

← #14736811

Subgroups — #14736811

Order 2816.

668 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079350C211yesmaximal, characteristic, complemented
2#13078071C211yesmaximal, characteristic, complemented
3#13077636C211yesmaximal, characteristic, complemented
4#13068175C211yesmaximal, characteristic, complemented
5#13068151C211yesmaximal, characteristic, complemented
6#13068117C211yesmaximal, characteristic, complemented
7#13068093C211yesmaximal, characteristic, complemented
8#13068058C211yesmaximal, characteristic, complemented
9#13068034C211yesmaximal, characteristic, complemented
10#13068000C211yesmaximal, characteristic, complemented
11#13067974C211yesmaximal, characteristic, complemented
12#13067369C211yesmaximal, characteristic, complemented
13#13067319C211yesmaximal, characteristic, complemented
14#13067311C211yesmaximal, characteristic, complemented
15C11×#3106C211yesmaximal, characteristic, complemented
16C11×#532C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C2×#67003—21no—
19#10623008C2211yescharacteristic
20C11×#482—21no—
21C11×#477C2211yescharacteristic
22C11×#476C2211yescharacteristic
23C11×#460C2211yescharacteristic
24C11×#459C2211yescharacteristic
25C11×#449—21no—
26C4×C11×SD16—21no—
27C4×C11×D8—21no—
28C11×#431C2211yescharacteristic
29#10622701C2211yescharacteristic
30#10622692C2211yescharacteristic
31#10622686C2211yescharacteristic
32#10622683C2211yescharacteristic
33#10622652—21no—
34#10622652—21no—
35#10622644C2211yescharacteristic
36#10622641—21no—
37#10622640C2211yescharacteristic
38Q8×C11⋊C8C2211yescharacteristic
39Q8×C11⋊C8C2211yescharacteristic
40#10622632C2211yescharacteristic
41#10622629—21no—
42#10622628C2211yescharacteristic
43#10622627—21no—
44#10622627—21no—
45#10622625—21no—
46#10622625—21no—
47#10622625C2211yescharacteristic
48#10622625C2211yescharacteristic
49#10622615—21no—
50#10622539—21no—
51#10622539C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C4×#4318—21no—
54C4×#4318C2211yescharacteristic
55#10622184C2211yescharacteristic
56#10622184C2211yescharacteristic
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×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
89#67003—44no—
90C2×#4326—21no—
91C2×#4325—21no—
92C2×#4324—21no—
93C2×#4323—21no—
94C2×#4323—21no—
95C2×#4323—21no—
96#66983—21no—
97#66983—21no—
98C2×#4318—21no—
99C2×#4318—21no—
100C2×#4318D411yescharacteristic
101C2×#4318D411yescharacteristic
102C22×C11⋊C8—21no—
103#66928—21no—
104#66927C2311yescharacteristic
105C4×D44—21no—
106C4×D44—21no—
107#66922C2311yescharacteristic
108C11×#107—21no—
109C11×#106—21no—
110C11×C4⋊C8C2311yescharacteristic
111C11×C4⋊C8C2311yescharacteristic
112C11×#103—21no—
113C11×#102—21no—
114C11×#102—21no—
115C11×#102—21no—
116C11×C22⋊C8—21no—
117C4×C8×C11—21no—
118#66896—21no—
119#66896—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122C22⋊(C11⋊C8)—21no—
123#66874—21no—
124#66874—21no—
125#66873—21no—
126#66873—21no—
127#66873—21no—
128#66873—21no—
129#66872—21no—
130#66872—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)—21no—
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138#66867—21no—
139#66867D411yescharacteristic
140#66867D411yescharacteristic
141C4×C11⋊C8—21no—
142C4×C11⋊C8—21no—
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19184—111nomaximal, Sylow
146C11×#41—22no—
147C11×#41—41no—
148C11×#41—82no—
149C2×Q8×C11—21no—
150C2×Q8×C11C2×D411yescharacteristic
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—41no—
156C2×D4×C11C2×D411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—41no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C2×C22⋊D11—41no—
165#4339—42no—
166#4339—42no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—21no—
170C2×C4×D11—41no—
171C2×Dic22—21no—
172C11×SD16—42no—
173C11×D8—42no—
174C2×C8×C11—21no—
175C2×C8×C11—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—41no—
186C11×C22⋊C4—41no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11C2×D411yescharacteristic
191C42×C11C2×D411yescharacteristic
192C42×C11#4111yescharacteristic
193C42×C11C2411yescharacteristic
194#4326—42no—
195#4325—42no—
196#4324—42no—
197#4323—42no—
198#4323—42no—
199#4323—42no—
200(C2×D11)⋊C4—41no—
201(C2×D11)⋊C4—41no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204#4318—22no—
205#4318—41no—
206#4318—42no—
207#4318—42no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—42no—
213C2×C11⋊C8C2×D411yescharacteristic
214C2×C11⋊C8C2×D411yescharacteristic
215C2×C11⋊C8C2×D411yescharacteristic
216C2×C11⋊C8C2×D411yescharacteristic
217#3184—111no—
218#3106D1111yescharacteristic, complemented
219#3035—111no—
220#2971—111no—
221#1701—111no—
222#1697—111no—
223#1691—111no—
224#1687—111no—
225#1682—111no—
226#1678—111no—
227#1672—111no—
228#1668—111no—
229#1565—111no—
230#1553—111no—
231#1551—111no—
232C23×C11—21no—
233C23×C11—41no—
234C23×C11#12111yescharacteristic
235C22×D11—41no—
236Q8×C11—21no—
237Q8×C11—81no—
238Q8×C11AGL(1,ℤ/8)12yes—
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—42no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—81no—
261C2×C4×C11—82no—
262C2×C4×C11#12111yescharacteristic
263C2×C4×C11#12111yescharacteristic
264C2×C4×C11#12111yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C22⋊D11—82no—
269C2×Dic11—41no—
270D44—41no—
271D44—41no—
272D44—41no—
273D44—41no—
274D44—81no—
275C4×D11—82no—
276Dic22—41no—
277Dic22—41no—
278C8×C11—41no—
279C8×C11—41no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—21no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C11⋊C8—41no—
287C11⋊C8#13512yescomplemented
288C2×#135—221no—
289#532—111no—
290#532C2×D1111yescharacteristic
291C4×#41C2×D1111yescharacteristic
292#498—111no—
293#493—111no—
294#486—111no—
295#486—111no—
296#482—21no—
297#477C2×D1111yescharacteristic
298#476C2×D1111yescharacteristic
299#469—221no—
300#469—221no—
301#464—221no—
302#463—221no—
303#462—111no—
304#461—111no—
305#460—111no—
306#460C2×D1111yescharacteristic
307#459—111no—
308#459C2×D1111yescharacteristic
309#449—21no—
310C8×Q8—111no—
311C8×Q8—111no—
312#442—221no—
313#442—221no—
314C4×SD16—21no—
315C4×D8—21no—
316#436—111no—
317#436—111no—
318#436—221no—
319#436—221no—
320#432—111no—
321#432—221no—
322#431C2×D1111yescharacteristic
323C2×C4⋊C8—111no—
324#416—221no—
325C4×M16—111no—
326C4×M16—221no—
327#335—111no—
328#335—111no—
329#334—111no—
330#334—111no—
331#333—111no—
332#333—111no—
333#332—111no—
334#332—111no—
335#331—111no—
336#331—111no—
337#331—111no—
338#331—111no—
339C22×C11—21no—
340C22×C11—21no—
341C22×C11—21no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11C2×#12111yescharacteristic
349C2×D11—81no—
350C2×D11—81no—
351C2×D11—81no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—22no—
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11—81no—
360C4×C11C2×#13511yescharacteristic
361C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
362C4×C11#57511yescharacteristic
363C4×C11#57511yescharacteristic
364Dic11—81no—
365C2×#41—21no—
366C2×#41—221no—
367C2×#41C22⋊D1111yescharacteristic
368#135—444no—
369C2×Q16—221no—
370C2×SD16—21no—
371C2×SD16—221no—
372C2×SD16—221no—
373C2×D8—21no—
374C2×D8—221no—
375C2×D8—221no—
376C2×D8—221no—
377C2×M16—111no—
378C2×M16—111no—
379C2×M16—221no—
380C2×M16—221no—
381C22×C8—221no—
382C4⋊Q8—111no—
383C4⋊Q8C22×D1111yescharacteristic
384#127—111no—
385#127C22×D1111yescharacteristic
386#124—21no—
387#124—221no—
388#121—21no—
389#121—21no—
390#121—221no—
391#121—221no—
392C4×Q8C22⋊D1111yescharacteristic
393C4×Q8C22×D1111yescharacteristic
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—221no—
399C4×D4—221no—
400C4×D4C22⋊D1111yescharacteristic
401C4×D4C22×D1111yescharacteristic
402#117—21no—
403#117C22⋊D1111yescharacteristic
404C2×C42—21no—
405C2×C42C22×D1111yescharacteristic
406#107—21no—
407#106—21no—
408#106—221no—
409#106—221no—
410C4⋊C8—111no—
411C4⋊C8—111no—
412C4⋊C8—111no—
413C4⋊C8—111no—
414C4⋊C8—221no—
415C4⋊C8—221no—
416C4⋊C8—221no—
417C4⋊C8C22×D1111yescharacteristic
418C4⋊C8C22×D1111yescharacteristic
419#103—21no—
420#103—221no—
421#103—221no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—221no—
426#102—221no—
427#102—221no—
428#102—221no—
429#102—221no—
430#102—221no—
431C22⋊C8—21no—
432C22⋊C8—221no—
433C22⋊C8—221no—
434C22⋊C8—221no—
435#97—111no—
436#97—111no—
437#97—221no—
438C4×C8—21no—
439C4×C8—111no—
440C4×C8—111no—
441C4×C8—221no—
442C4×C8—221no—
443C2×C11—41no—
444C2×C11—81no—
445C2×C11—161no—
446C2×C11#303511yescharacteristic
447C2×C11#305511yescharacteristic
448C2×C11#306811yescharacteristic
449D11—161no—
450#41—22no—
451#41—41no—
452#41—82no—
453#41—442no—
454#41—442no—
455C2×Q8—21no—
456C2×Q8—221no—
457C2×Q8C2×C22⋊D1111yescharacteristic
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—41no—
463C2×D4—221no—
464C2×D4—221no—
465C2×D4—221no—
466C2×D4—441no—
467C2×D4C2×C22⋊D1111yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—41no—
472C22×C4—441no—
473C22×C4D4×D1111yescharacteristic
474C22×C4#434111yescharacteristic
475C22×C4C2×C22⋊D1111yescharacteristic
476Q16—442no—
477SD16—42no—
478SD16—442no—
479SD16—442no—
480D8—42no—
481D8—442no—
482D8—442no—
483D8—442no—
484M16—222no—
485M16—442no—
486M16—441no—
487M16—442no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—111no—
491C2×C8—111no—
492C2×C8—111no—
493C2×C8—111no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—442no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4C2×C22⋊D1111yescharacteristic
506C4⋊C4C2×C22⋊D1111yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—441no—
513C22⋊C4—441no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42D4×D1111yescharacteristic
518C42#434111yescharacteristic
519C42C2×C22⋊D1111yescharacteristic
520C42C23×D1111yescharacteristic
521C11#1918411yescharacteristic, complemented, Sylow
522C23—21no—
523C23—41no—
524C23—441no—
525C23#6699211yescharacteristic
526Q8—21no—
527Q8—81no—
528Q8—441no—
529Q8—441no—
530Q8#6700212yes—
531D4—21no—
532D4—21no—
533D4—42no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—81no—
539D4—82no—
540D4—441no—
541D4—441no—
542D4—441no—
543D4—441no—
544D4—881no—
545D4—882no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—81no—
559C2×C4—82no—
560C2×C4—441no—
561C2×C4—882no—
562C2×C4#6699211yescharacteristic
563C2×C4#6699211yescharacteristic
564C2×C4#6699211yescharacteristic
565C2×C4C2×D4×D1111yescharacteristic
566C2×C4C2×#434111yescharacteristic
567C2×C4C22×C22⋊D1111yescharacteristic
568C8—41no—
569C8—41no—
570C8—112no—
571C8—221no—
572C8—221no—
573C8—221no—
574C8—441no—
575C8—441no—
576C8—441no—
577C8—441no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—881no—
588C22—881no—
589C22—881no—
590C22C2×#6699211yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—22no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—881no—
600C4D11×#13511yescharacteristic
601C4#1062329911yescharacteristic
602C4C2×#6700211yescharacteristic
603C4#1062335311yescharacteristic
604C2—41no—
605C2—81no—
606C2—161no—
607C2—1761no—
608C2#1307806711yescharacteristic
609C2#1307823711yescharacteristic
610C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3106C2
socleC22×C11C2×#121
hypercenter#3106D11
hypocenterC11#19184
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #13079350C2semidirect
2. #13078071C2semidirect
3. #13077636C2semidirect
4. #13068175C2semidirect
5. #13068151C2semidirect
6. #13068117C2semidirect
7. #13068093C2semidirect
8. #13068058C2semidirect
9. #13068034C2semidirect
10. #13068000C2semidirect
11. #13067974C2semidirect
12. #13067369C2semidirect
13. #13067319C2semidirect
14. #13067311C2semidirect
15. C11×#3106C2semidirect
218. #3106D11semidirect
287. C11⋊C8#135semidirect
521. C11#19184semidirect

Maximal subgroups

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

subgroupindex
#130793502
#130780712
#130776362
#130681752
#130681512
#130681172
#130680932
#130680582
#130680342
#130680002
#130679742
#130673692
#130673192
#130673112
C11×#31062
#1918411