Finite Group Databasebeta

← #14741607

Subgroups — #14741607

Order 2816.

712 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079202C211yesmaximal, characteristic, complemented
2#13079198C211yesmaximal, characteristic, complemented
3#13079171C211yesmaximal, characteristic
4#13079126C211yesmaximal, characteristic, complemented
5#13078938C211yesmaximal, characteristic
6#13068295C211yesmaximal, characteristic, complemented
7#13068289C211yesmaximal, characteristic, complemented
8#13068275C211yesmaximal, characteristic, complemented
9#13068267C211yesmaximal, characteristic, complemented
10#13068265C211yesmaximal, characteristic, complemented
11#13068260C211yesmaximal, characteristic, complemented
12#13068248C211yesmaximal, characteristic, complemented
13#13068236C211yesmaximal, characteristic, complemented
14C2×#10622092C211yesmaximal, characteristic, complemented
15C11×#3167C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18#10623001C2211yescharacteristic
19#10623001C2211yescharacteristic
20C11×#498C2211yescharacteristic
21C11×#492C2211yescharacteristic
22C11×#487C2211yescharacteristic
23C11×#486C2211yescharacteristic
24C11×#465—22no—
25C4×C11×SD16—22no—
26C2×C4×C8×C11C2211yescharacteristic
27#10622846—22no—
28#10622729—22no—
29#10622706C2211yescharacteristic
30#10622706C2211yescharacteristic
31#10622705C2211yescharacteristic
32#10622694C2211yescharacteristic
33#10622694C2211yescharacteristic
34#10622694C2211yescharacteristic
35#10622692C2211yescharacteristic
36#10622692C2211yescharacteristic
37#10622692C2211yescharacteristic
38#10622691C2211yescharacteristic
39#10622691C2211yescharacteristic
40#10622691C2211yescharacteristic
41#10622689C2211yescharacteristic
42#10622683C2211yescharacteristic
43#10622683C2211yescharacteristic
44#10622683C2211yescharacteristic
45#10622677—22no—
46#10622669—22no—
47#10622664—22no—
48#10622654—22no—
49C4×#4326—22no—
50C4×#4324—22no—
51#10622611—22no—
52C2×C4×C11⋊C8C2211yescharacteristic
53C2×C4×C11⋊C8C2211yescharacteristic
54#10622312C2211yescharacteristic
55C4×Dic44—22no—
56#10622295C2211yescharacteristic
57#10622294C2211yescharacteristic
58#10622294C2211yescharacteristic
59#10622092C2211yescharacteristic
60#10622092C2211yescharacteristic
61#10622092C2211yescharacteristic
62#10622092C2211yescharacteristic
63C2×C11×#41—21no—
64C2×C11×SD16—22no—
65C22×C8×C11D412yes—
66C11×C4⋊Q8C2311yescharacteristic
67C11×C4⋊Q8C2311yescharacteristic
68C11×C4⋊Q8C2311yescharacteristic
69C11×#127C2311yescharacteristic
70C11×#125—21no—
71C11×#124—21no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8—21no—
74C11×#121—21no—
75C11×#121—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×D4×C11—21no—
79C4×D4×C11—21no—
80C11×#117—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4326—22no—
83C2×#4324—22no—
84#66979—21no—
85#66979—21no—
86#66977—21no—
87#66977—21no—
88#66977—21no—
89#66977—21no—
90C22×C11⋊C8D412yes—
91C22×C11⋊C8D412yes—
92C2×Dic44—22no—
93#66923—21no—
94#66923—21no—
95#66922C2311yescharacteristic
96#66922C2311yescharacteristic
97#66922C2311yescharacteristic
98#66922C2311yescharacteristic
99C4×Dic22—21no—
100C4×Dic22—21no—
101C4×Dic22—21no—
102C4×Dic22—21no—
103C11×#106—22no—
104C11×#103—22no—
105C11×#102—22no—
106C4×C8×C11D412yes—
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109#66899—22no—
110#66899—22no—
111#66899—22no—
112#66896—22no—
113#66896—22no—
114#66896—22no—
115#66882—22no—
116#66880—22no—
117#66880—22no—
118#66874—22no—
119#66874—22no—
120#66872—22no—
121#66872—22no—
122#66872—22no—
123#66871—22no—
124#66871—22no—
125#66871—22no—
126C4×C11⋊C8D412yes—
127C4×C11⋊C8D412yes—
128C4×C11⋊C8C2311yescharacteristic
129C4×C11⋊C8C2311yescharacteristic
130C4×C11⋊C8C2311yescharacteristic
131C4×C11⋊C8C2311yescharacteristic
132#19620—111nomaximal, Sylow
133C11×#41—44no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—41no—
141C22×C4×C11—41no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C11×SD16—44no—
150C2×C8×C11—42no—
151C2×C8×C11C2×D412yes—
152C2×C8×C11C2×D412yes—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—41no—
160C11×C4⋊C4—41no—
161C11×C22⋊C4—41no—
162C11×C22⋊C4—41no—
163C11×C22⋊C4—41no—
164C42×C11—41no—
165C42×C11C2×D411yescharacteristic
166C42×C11C2×D411yescharacteristic
167C42×C11C2×D411yescharacteristic
168C42×C11C2411yescharacteristic
169C22⋊Dic11—41no—
170C22⋊Dic11—41no—
171#4326—44no—
172#4324—44no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181Dic11⋊C4—41no—
182Dic11⋊C4—41no—
183Dic11⋊C4—41no—
184Dic11⋊C4—41no—
185C4×Dic11—41no—
186C4×Dic11—41no—
187C2×C11⋊C8—24no—
188C2×C11⋊C8—24no—
189C2×C11⋊C8C2×D412yes—
190C2×C11⋊C8C2×D412yes—
191C2×C11⋊C8C2×D412yes—
192C2×C11⋊C8C2×D412yes—
193Dic44—44no—
194#3170—111no—
195#3170—111no—
196#3167—111no—
197#3167D1111yescharacteristic
198#3160—111no—
199#3131—111no—
200#1723—111no—
201#1722—111no—
202#1720—111no—
203#1719—111no—
204#1718—111no—
205#1718—111no—
206#1716—111no—
207#1714—111no—
208C2×#322—111no—
209C23×C11—41no—
210C23×C11#12711yescharacteristic
211Q8×C11—42no—
212Q8×C11—42no—
213Q8×C11—42no—
214D4×C11—42no—
215D4×C11—42no—
216D4×C11—42no—
217D4×C11—82no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—82no—
224C2×C4×C11#12711yescharacteristic
225C2×C4×C11#12711yescharacteristic
226C2×C4×C11#12711yescharacteristic
227C2×C4×C11#13714yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235Dic22—42no—
236Dic22—42no—
237Dic22—42no—
238Dic22—42no—
239C8×C11—22no—
240C8×C11—22no—
241C11⋊C8—22no—
242C11⋊C8—22no—
243C11⋊C8—22no—
244C11⋊C8#13514yes—
245#533—111no—
246#533—111no—
247#533C2×D1111yescharacteristic
248#532C2×D1111yescharacteristic
249#500—111no—
250#500—111no—
251#500—111no—
252#500—111no—
253#499—222no—
254#498—111no—
255#498—111no—
256#498—111no—
257#498C2×D1111yescharacteristic
258#494—111no—
259#494—111no—
260#492—111no—
261#492C2×D1111yescharacteristic
262#488—222no—
263#487—111no—
264#487—111no—
265#487—111no—
266#487—111no—
267#487—111no—
268#487—111no—
269#487—111no—
270#487C2×D1111yescharacteristic
271#486—111no—
272#486—111no—
273#486—111no—
274#486C2×D1111yescharacteristic
275#467—222no—
276#467—222no—
277#465—22no—
278#465—222no—
279C4×Q16—222no—
280C4×Q16—222no—
281C4×SD16—22no—
282C4×SD16—222no—
283#427—222no—
284#416—222no—
285C2×C4×C8—111no—
286C2×C4×C8—111no—
287C2×C4×C8C2×D1111yescharacteristic
288#322—111no—
289#322—111no—
290#322—111no—
291#322—111no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11#49712yes—
298C22×C11C2×#12711yescharacteristic
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—81no—
302C4×C11—81no—
303C4×C11—81no—
304C4×C11#49712yes—
305C4×C11C2×#13512yes—
306C4×C11C2×#13712yes—
307C4×C11#57512yes—
308Dic11—81no—
309Dic11—81no—
310Dic11—81no—
311Dic11—81no—
312C2×#41—21no—
313C2×Q16—222no—
314C2×Q16—222no—
315C2×SD16—22no—
316C2×SD16—222no—
317C22×C8—112no—
318C22×C8—112no—
319C22×C8C22⋊D1112yes—
320C4⋊Q8—111no—
321C4⋊Q8—111no—
322C4⋊Q8—111no—
323C4⋊Q8—111no—
324C4⋊Q8C22×D1111yescharacteristic
325C4⋊Q8C22×D1111yescharacteristic
326C4⋊Q8C22×D1111yescharacteristic
327#127C22×D1111yescharacteristic
328#125—21no—
329#125—221no—
330#125—221no—
331#124—21no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—221no—
335C22⋊Q8—221no—
336C22⋊Q8—221no—
337C22⋊Q8—221no—
338#121—21no—
339#121—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8—221no—
343C4×Q8—221no—
344C4×Q8—221no—
345C4×Q8—221no—
346C4×D4—21no—
347C4×D4—21no—
348#117—21no—
349#117—221no—
350#117—221no—
351C2×C42C22×D1111yescharacteristic
352#107—222no—
353#107—222no—
354#107—222no—
355#107—222no—
356#106—22no—
357#106—222no—
358#106—222no—
359#106—222no—
360#103—22no—
361#103—222no—
362#103—222no—
363#103—222no—
364#103—222no—
365#103—222no—
366#103—222no—
367#103—222no—
368#102—22no—
369#102—222no—
370#102—222no—
371#102—222no—
372C4×C8—112no—
373C4×C8—112no—
374C4×C8—111no—
375C4×C8—111no—
376C4×C8—111no—
377C4×C8—111no—
378C4×C8C22⋊D1112yes—
379C4×C8C22×D1111yescharacteristic
380C4×C8C22×D1111yescharacteristic
381C2×C11—22no—
382C2×C11—161no—
383C2×C11#314711yescharacteristic
384C2×C11C2×#49711yescharacteristic
385C2×C11#315011yescharacteristic
386#41—44no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—221no—
391C2×Q8—221no—
392C2×Q8—221no—
393C2×Q8—221no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—41no—
398C22×C4—41no—
399C22×C4D4×D1111yescharacteristic
400C22×C4D4×D1111yescharacteristic
401C22×C4C2×C22⋊D1111yescharacteristic
402Q16—444no—
403Q16—444no—
404SD16—44no—
405SD16—444no—
406C2×C8—42no—
407C2×C8—112no—
408C2×C8—112no—
409C2×C8—112no—
410C2×C8—112no—
411C2×C8—224no—
412C2×C8—224no—
413C2×C8C2×C22⋊D1112yes—
414C2×C8C2×C22⋊D1112yes—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—221no—
424C4⋊C4—221no—
425C4⋊C4—221no—
426C4⋊C4—221no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—221no—
430C4⋊C4—221no—
431C4⋊C4—441no—
432C4⋊C4—441no—
433C4⋊C4—441no—
434C4⋊C4—441no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—441no—
439C22⋊C4—441no—
440C42—41no—
441C42—441no—
442C42—441no—
443C42D4×D1111yescharacteristic
444C42D4×D1111yescharacteristic
445C42C2×C22⋊D1111yescharacteristic
446C42C23×D1111yescharacteristic
447C11#1962011yescharacteristic, complemented, Sylow
448C23—41no—
449C23#6699311yescharacteristic
450Q8—42no—
451Q8—42no—
452Q8—42no—
453Q8—442no—
454Q8—442no—
455Q8—442no—
456Q8—442no—
457D4—42no—
458D4—42no—
459D4—42no—
460D4—82no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—82no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4#6696814yes—
472C2×C4#6699311yescharacteristic
473C2×C4#6699311yescharacteristic
474C2×C4#6699311yescharacteristic
475C2×C4C2×D4×D1111yescharacteristic
476C2×C4C2×D4×D1111yescharacteristic
477C2×C4C22×C22⋊D1111yescharacteristic
478C8—22no—
479C8—22no—
480C8—114no—
481C8—222no—
482C8—222no—
483C8—222no—
484C22—21no—
485C22—21no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22#1062278012yes—
490C22C2×#6699311yescharacteristic
491C4—21no—
492C4—21no—
493C4—81no—
494C4—81no—
495C4—81no—
496C4—881no—
497C4—881no—
498C4—881no—
499C4—881no—
500C4#1062278012yes—
501C4C2×#6696812yes—
502C4D11×#13512yes—
503C4#1062335312yes—
504C2—22no—
505C2—161no—
506C2#1307904011yescharacteristic
507C2C2×#1062278011yescharacteristic
508C2#1307906111yescharacteristic
subgroupG/H
centerC2×C4#66993
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3167C2
socleC22×C11C2×#127
prime radicalC11×#532C22
hypercenter#3167D11
hypocenterC11#19620
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. #13079202C2semidirect
2. #13079198C2semidirect
4. #13079126C2semidirect
6. #13068295C2semidirect
7. #13068289C2semidirect
8. #13068275C2semidirect
9. #13068267C2semidirect
10. #13068265C2semidirect
11. #13068260C2semidirect
12. #13068248C2semidirect
13. #13068236C2semidirect
14. C2×#10622092C2semidirect
447. C11#19620semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130791982
#130791712
#130791262
#130789382
#130682952
#130682892
#130682752
#130682672
#130682652
#130682602
#130682482
#130682362
C2×#106220922
C11×#31672
#1962011