Finite Group Databasebeta

← #14741504

Subgroups — #14741504

Order 2816.

798 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079176C211yesmaximal, characteristic, complemented
2#13079175C211yesmaximal, characteristic, complemented
3#13079171C211yesmaximal, characteristic, complemented
4#13079126C211yesmaximal, characteristic, complemented
5#13079042C211yesmaximal, characteristic
6#13068251C211yesmaximal, characteristic, complemented
7#13068248C211yesmaximal, characteristic, complemented
8#13068246C211yesmaximal, characteristic, complemented
9#13068243C211yesmaximal, characteristic, complemented
10#13068241C211yesmaximal, characteristic, complemented
11#13068240C211yesmaximal, characteristic, complemented
12#13068237C211yesmaximal, characteristic, complemented
13#13068236C211yesmaximal, characteristic, complemented
14C2×#10622092C211yesmaximal, characteristic, complemented
15C11×#3167C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C2×#67003—22no—
19#10623008C2211yescharacteristic
20#10623001C2211yescharacteristic
21C11×#498C2211yescharacteristic
22C11×#492C2211yescharacteristic
23C11×#487C2211yescharacteristic
24C11×#486C2211yescharacteristic
25C11×#465—22no—
26C4×C11×SD16—22no—
27C2×C4×C8×C11C2211yescharacteristic
28#10622727—22no—
29#10622706C2211yescharacteristic
30#10622705C2211yescharacteristic
31#10622701C2211yescharacteristic
32#10622698C2211yescharacteristic
33#10622698C2211yescharacteristic
34#10622694C2211yescharacteristic
35#10622692C2211yescharacteristic
36#10622692C2211yescharacteristic
37#10622692C2211yescharacteristic
38#10622692C2211yescharacteristic
39#10622691C2211yescharacteristic
40#10622691C2211yescharacteristic
41#10622689C2211yescharacteristic
42#10622689C2211yescharacteristic
43#10622686C2211yescharacteristic
44#10622683C2211yescharacteristic
45#10622677—22no—
46#10622672—22no—
47#10622661—22no—
48#10622654—22no—
49C4×#4325—22no—
50C4×#4324—22no—
51#10622611—22no—
52C2×C4×C11⋊C8C2211yescharacteristic
53C2×C4×C11⋊C8C2211yescharacteristic
54#10622307C2211yescharacteristic
55#10622306C2211yescharacteristic
56C4×#4314—22no—
57#10622294C2211yescharacteristic
58#10622293C2211yescharacteristic
59#10622092C2211yescharacteristic
60#10622092C2211yescharacteristic
61#10622092C2211yescharacteristic
62#10622092C2211yescharacteristic
63C2×C11×#41—21no—
64C2×#4339—21no—
65C2×C11×SD16—22no—
66C22×C8×C11D412yes—
67C11×C4⋊Q8C2311yescharacteristic
68C11×C4⋊Q8C2311yescharacteristic
69C11×C4⋊Q8C2311yescharacteristic
70C11×#127C2311yescharacteristic
71C11×#125—21no—
72C11×#124—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—21no—
75C11×#121—21no—
76C11×#121—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C11×#117—21no—
82C2×C42×C11C2311yescharacteristic
83#67003—48no—
84C2×#4326—22no—
85C2×#4325—22no—
86C2×#4325—22no—
87C2×#4324—22no—
88C2×#4324—22no—
89C2×#4323—22no—
90#66983—21no—
91#66983—21no—
92#66979—21no—
93#66977—21no—
94#66977—21no—
95C22×C11⋊C8D412yes—
96C22×C11⋊C8D412yes—
97C2×#4314—22no—
98#66928—21no—
99#66927C2311yescharacteristic
100C4×D44—21no—
101C4×D44—21no—
102#66923—21no—
103#66922C2311yescharacteristic
104#66922C2311yescharacteristic
105#66922C2311yescharacteristic
106C4×Dic22—21no—
107C4×Dic22—21no—
108C11×#106—22no—
109C11×#103—22no—
110C11×#102—22no—
111C4×C8×C11D412yes—
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114#66899—22no—
115#66896—22no—
116#66885—22no—
117#66881—22no—
118#66880—22no—
119#66874—22no—
120#66873—22no—
121#66872—22no—
122#66872—22no—
123#66872—22no—
124#66872—22no—
125#66871—22no—
126#66871—22no—
127C4×C11⋊C8D412yes—
128C4×C11⋊C8D412yes—
129C4×C11⋊C8C2311yescharacteristic
130C4×C11⋊C8C2311yescharacteristic
131C4×C11⋊C8C2311yescharacteristic
132C4×C11⋊C8C2311yescharacteristic
133#19608—111nomaximal, Sylow
134C11×#41—44no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—41no—
142C22×C4×C11—41no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C2×C22⋊D11—41no—
147#4339—44no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×C4×D11—41no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C11×SD16—44no—
156C2×C8×C11—42no—
157C2×C8×C11C2×D412yes—
158C2×C8×C11C2×D412yes—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—41no—
166C11×C4⋊C4—41no—
167C11×C22⋊C4—41no—
168C11×C22⋊C4—41no—
169C11×C22⋊C4—41no—
170C42×C11—41no—
171C42×C11C2×D411yescharacteristic
172C42×C11C2×D411yescharacteristic
173C42×C11C2×D411yescharacteristic
174C42×C11C2411yescharacteristic
175C22⋊Dic11—41no—
176#4326—44no—
177#4325—44no—
178#4325—44no—
179#4324—44no—
180#4324—44no—
181#4323—44no—
182(C2×D11)⋊C4—41no—
183(C2×D11)⋊C4—41no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190Dic11⋊C4—41no—
191Dic11⋊C4—41no—
192C4×Dic11—41no—
193C2×C11⋊C8—42no—
194C2×C11⋊C8SD1618yescomplemented
195C2×C11⋊C8C2×D412yes—
196C2×C11⋊C8C2×D412yes—
197C2×C11⋊C8C2×D412yes—
198C2×C11⋊C8C2×D412yes—
199#4314—44no—
200#3167—111no—
201#3167—111no—
202#3167—111no—
203#3167D1111yescharacteristic, complemented
204#3160—111no—
205#3147—111no—
206#1716—111no—
207#1716—111no—
208#1715—111no—
209#1715—111no—
210#1714—111no—
211#1714—111no—
212#1714—111no—
213#1714—111no—
214C2×#322—111no—
215C23×C11—41no—
216C23×C11#12711yescharacteristic
217C22×D11—41no—
218Q8×C11—42no—
219Q8×C11—42no—
220Q8×C11—42no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—42no—
224D4×C11—82no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—82no—
231C2×C4×C11#12711yescharacteristic
232C2×C4×C11#12711yescharacteristic
233C2×C4×C11#12711yescharacteristic
234C2×C4×C11C2×SD1614yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C22⋊D11—82no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242D44—42no—
243D44—42no—
244D44—42no—
245C4×D11—82no—
246Dic22—42no—
247Dic22—42no—
248Dic22—42no—
249C8×C11—22no—
250C8×C11—22no—
251C11⋊C8—22no—
252C11⋊C8—22no—
253C11⋊C8C2×SD1614yes—
254C11⋊C8C2×SD1614yes—
255C2×#135—222no—
256#533—111no—
257#533C2×D1111yescharacteristic
258#532—111no—
259#532C2×D1111yescharacteristic
260#500—111no—
261#500—111no—
262#499—222no—
263#498—111no—
264#498—111no—
265#498—111no—
266#498—111no—
267#498—111no—
268#498C2×D1111yescharacteristic
269#495—222no—
270#494—111no—
271#493—111no—
272#492—111no—
273#492—111no—
274#492—111no—
275#492—111no—
276#492—111no—
277#492C2×D1111yescharacteristic
278#487—111no—
279#487—111no—
280#487—111no—
281#487C2×D1111yescharacteristic
282#486—111no—
283#486—111no—
284#486—111no—
285#486C2×D1111yescharacteristic
286#465—22no—
287#465—222no—
288#465—222no—
289#465—222no—
290C4×SD16—22no—
291C4×SD16—222no—
292C4×SD16—222no—
293C4×SD16—222no—
294#427—222no—
295C2×C4×C8—111no—
296C2×C4×C8—111no—
297C2×C4×C8C2×D1111yescharacteristic
298#322—111no—
299#322—111no—
300#322—111no—
301#322—111no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—81no—
305C22×C11—81no—
306C22×C11—81no—
307C22×C11#49212yes—
308C22×C11C2×#12711yescharacteristic
309C2×D11—81no—
310C2×D11—81no—
311C2×D11—81no—
312C4×C11—21no—
313C4×C11—21no—
314C4×C11—81no—
315C4×C11—81no—
316C4×C11—81no—
317C4×C11#49212yes—
318C4×C11C22×SD1612yes—
319C4×C11#57512yes—
320C4×C11#57512yes—
321Dic11—81no—
322Dic11—81no—
323Dic11—81no—
324C2×#41—21no—
325C2×#41—221no—
326#135—448no—
327C2×Q16—222no—
328C2×SD16—22no—
329C2×SD16—222no—
330C2×SD16—222no—
331C2×SD16—222no—
332C2×SD16—222no—
333C2×SD16—222no—
334C2×D8—222no—
335C22×C8—112no—
336C22×C8—112no—
337C22×C8C22⋊D1112yes—
338C4⋊Q8—111no—
339C4⋊Q8—111no—
340C4⋊Q8—111no—
341C4⋊Q8C22×D1111yescharacteristic
342C4⋊Q8C22×D1111yescharacteristic
343C4⋊Q8C22×D1111yescharacteristic
344#127—111no—
345#127C22×D1111yescharacteristic
346#125—21no—
347#125—221no—
348#124—21no—
349#124—221no—
350C22⋊Q8—21no—
351C22⋊Q8—21no—
352C22⋊Q8—221no—
353C22⋊Q8—221no—
354#121—21no—
355#121—21no—
356#121—221no—
357#121—221no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—221no—
361C4×Q8—221no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—221no—
365C4×D4—221no—
366#117—21no—
367#117—221no—
368C2×C42C22×D1111yescharacteristic
369#107—222no—
370#107—222no—
371#106—22no—
372#106—222no—
373#106—222no—
374#106—222no—
375#106—222no—
376#106—222no—
377#103—22no—
378#103—222no—
379#103—222no—
380#103—222no—
381#102—22no—
382#102—222no—
383#102—222no—
384#102—222no—
385C4×C8—112no—
386C4×C8—112no—
387C4×C8—111no—
388C4×C8—111no—
389C4×C8—111no—
390C4×C8—111no—
391C4×C8C22⋊D1112yes—
392C4×C8C22×D1111yescharacteristic
393C4×C8C22×D1111yescharacteristic
394C2×C11—22no—
395C2×C11—161no—
396C2×C11C2×#49211yescharacteristic
397C2×C11#315011yescharacteristic
398C2×C11#315011yescharacteristic
399D11—161no—
400#41—44no—
401#41—444no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—221no—
406C2×Q8—221no—
407C2×Q8—221no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—41no—
412C2×D4—221no—
413C2×D4—221no—
414C2×D4—221no—
415C2×D4—441no—
416C22×C4—41no—
417C22×C4—441no—
418C22×C4D4×D1111yescharacteristic
419C22×C4D4×D1111yescharacteristic
420C22×C4C2×C22⋊D1111yescharacteristic
421Q16—444no—
422SD16—44no—
423SD16—444no—
424SD16—444no—
425SD16—444no—
426SD16—444no—
427SD16—444no—
428D8—444no—
429C2×C8—42no—
430C2×C8—118no—
431C2×C8—112no—
432C2×C8—112no—
433C2×C8—112no—
434C2×C8—112no—
435C2×C8—442no—
436C2×C8C2×C22⋊D1112yes—
437C2×C8C2×C22⋊D1112yes—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—41no—
445C4⋊C4—41no—
446C4⋊C4—221no—
447C4⋊C4—221no—
448C4⋊C4—221no—
449C4⋊C4—221no—
450C4⋊C4—221no—
451C4⋊C4—221no—
452C4⋊C4—441no—
453C4⋊C4—441no—
454C22⋊C4—41no—
455C22⋊C4—41no—
456C22⋊C4—41no—
457C22⋊C4—441no—
458C22⋊C4—441no—
459C22⋊C4—441no—
460C42—41no—
461C42—441no—
462C42D4×D1111yescharacteristic
463C42D4×D1111yescharacteristic
464C42C2×C22⋊D1111yescharacteristic
465C42C23×D1111yescharacteristic
466C11#1960811yescharacteristic, complemented, Sylow
467C23—41no—
468C23—441no—
469C23#6699311yescharacteristic
470Q8—42no—
471Q8—42no—
472Q8—42no—
473Q8—442no—
474Q8—442no—
475Q8—442no—
476D4—42no—
477D4—42no—
478D4—42no—
479D4—82no—
480D4—442no—
481D4—442no—
482D4—442no—
483D4—882no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—82no—
490C2×C4—441no—
491C2×C4—441no—
492C2×C4—441no—
493C2×C4—882no—
494C2×C4SD16×D1114yes—
495C2×C4#6699311yescharacteristic
496C2×C4#6699311yescharacteristic
497C2×C4#6699311yescharacteristic
498C2×C4C2×D4×D1111yescharacteristic
499C2×C4C2×D4×D1111yescharacteristic
500C2×C4C22×C22⋊D1111yescharacteristic
501C8—22no—
502C8—22no—
503C8—114no—
504C8—114no—
505C8—222no—
506C8—222no—
507C22—21no—
508C22—21no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—881no—
513C22—881no—
514C22—881no—
515C22#1062278812yes—
516C22C2×#6699311yescharacteristic
517C4—21no—
518C4—21no—
519C4—81no—
520C4—81no—
521C4—81no—
522C4—881no—
523C4—881no—
524C4—881no—
525C4#1062278812yes—
526C4C2×SD16×D1112yes—
527C4#1062329912yes—
528C4#1062335312yes—
529C2—22no—
530C2—161no—
531C2—1761no—
532C2C2×#1062278811yescharacteristic
533C2#1307905911yescharacteristic
534C2#1307906111yescharacteristic
subgroupG/H
centerC2×C4#66993
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3167C2
socleC22×C11C2×#127
prime radical#13079042C2
hypercenter#3167D11
hypocenterC11#19608
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #13079176C2semidirect
2. #13079175C2semidirect
3. #13079171C2semidirect
4. #13079126C2semidirect
6. #13068251C2semidirect
7. #13068248C2semidirect
8. #13068246C2semidirect
9. #13068243C2semidirect
10. #13068241C2semidirect
11. #13068240C2semidirect
12. #13068237C2semidirect
13. #13068236C2semidirect
14. C2×#10622092C2semidirect
15. C11×#3167C2semidirect
194. C2×C11⋊C8SD16semidirect
203. #3167D11semidirect
466. C11#19608semidirect

Maximal subgroups

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

subgroupindex
#130791762
#130791752
#130791712
#130791262
#130790422
#130682512
#130682482
#130682462
#130682432
#130682412
#130682402
#130682372
#130682362
C2×#106220922
C11×#31672
#1960811