Finite Group Databasebeta

← #15625220

Subgroups — #15625220

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081913C211yesmaximal, characteristic
2C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
3#13079644C218yesmaximal, complemented
4#13079565C214yesmaximal, complemented
5#13079542C214yesmaximal, complemented
6#13079075C211yesmaximal, characteristic, complemented
7#13079073C211yesmaximal, characteristic, complemented
8#13078998C211yesmaximal, characteristic, complemented
9#13078102C214yesmaximal, complemented
10#13077852C214yesmaximal, complemented
11#13077247C211yesmaximal, characteristic, complemented
12C11×#3139C211yesmaximal, characteristic, complemented
13C22×Q8×D11C2212yes—
14C11×#533C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×#66997C2212yes—
17C2×#66995C2214yes—
18C2×#66962C2214yes—
19#10623259C2212yes—
20#10623256C2212yes—
21D11×C4⋊Q8—22no—
22D11×C4⋊Q8—22no—
23D11×C4⋊Q8C2214yes—
24D11×C4⋊Q8C2214yes—
25#10623222C2214yes—
26#10623158—22no—
27#10623155—22no—
28#10623111—22no—
29C4×#4343—22no—
30#10623055C2212yes—
31#10623053C2212yes—
32C2×C4⋊C4×D11—22no—
33C2×#66941—22no—
34#10623008C2211yescharacteristic
35C2×C42×D11C2211yescharacteristic
36C2×#66922C2211yescharacteristic
37C11×#491C2214yescomplemented
38C11×#487C2214yescomplemented
39C11×#419C2214yes—
40C4×C11×M16C2211yescharacteristic
41#10622739C2212yes—
42#10622731C2212yes—
43#10622706C2214yescomplemented
44#10622705C2212yescomplemented
45#10622699C2214yescomplemented
46#10622698C2212yescomplemented
47#10622682C2214yescomplemented
48#10622617C2214yes—
49C4×#4318C2211yescharacteristic
50#10622431C22116yescomplemented
51#10622421C22116yes—
52#10622419C22116yes—
53#10622406C22116yescomplemented
54#10622328C2214yescomplemented
55#10622318C2214yes—
56#10622312C2212yescomplemented
57#10622306C2212yescomplemented
58#10622298C2214yes—
59C22×Q8×C11C2312yes—
60C2×#4343—22no—
61C2×Q8×D11—24no—
62C2×Q8×D11—48no—
63C2×Q8×D11C2318yes—
64C2×#4339C2312yes—
65C22×C4×D11—22no—
66C22×C4×D11D412yes—
67C22×C4×D11C2311yescharacteristic
68C22×Dic22—22no—
69C22×Dic22C2312yes—
70C2×C11×M16C2312yes—
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8C2312yes—
73C11×C4⋊Q8C2312yes—
74C11×C4⋊Q8C2312yes—
75C11×#125C2312yes—
76C11×C22⋊Q8—22no—
77C4×Q8×C11—22no—
78C11×#117C2312yes—
79C2×C11×C4⋊C4—22no—
80C2×C42×C11C2311yescharacteristic
81#67000—22no—
82#66999—22no—
83Q8×Dic11—22no—
84#66997—22no—
85#66997—22no—
86#66997C2318yes—
87C2×#4326C2318yes—
88#66995—48no—
89C2×#4325C2318yes—
90#66983—22no—
91C2×C4⋊Dic11—22no—
92C2×Dic11⋊C4—24no—
93C2×C4×Dic11D412yes—
94C2×C4×Dic11C2311yescharacteristic
95C2×#4318C2312yes—
96#66962—48no—
97C2×Dic44C2318yes—
98C2×#4314C2318yes—
99#66951—24no—
100#66950C2314yes—
101#66948—22no—
102#66948C2314yes—
103#66947—24no—
104#66946—24no—
105#66946—22no—
106#66946C2314yes—
107#66945—22no—
108#66945—24no—
109C4⋊C4×D11—24no—
110C4⋊C4×D11—24no—
111C4⋊C4×D11—24no—
112C4⋊C4×D11—24no—
113#66943—22no—
114#66941—24no—
115#66941—24no—
116#66941—24no—
117#66941—24no—
118#66940C2314yes—
119#66939—22no—
120#66935—22no—
121(C22⋊D11)⋊C4—24no—
122#66928C2312yes—
123#66927C2311yescharacteristic
124C4×D44—24no—
125C4×D44—22no—
126#66925—22no—
127C42×D11—22no—
128C42×D11D412yes—
129C42×D11D412yes—
130C42×D11C2312yes—
131C42×D11C2312yes—
132#66922—22no—
133#66922C2312yes—
134#66922C2312yes—
135#66922C2311yescharacteristic
136C11×#103C23116yes—
137C11×#97C2312yes—
138C4×C8×C11C2312yes—
139(C2×D11)⋊C8C2318yes—
140Dic11⋊C8C2318yes—
141#66874C23116yes—
142#66867C2312yes—
143C4×C11⋊C8C2312yes—
144#60800—111nomaximal, Sylow
145C23×D11C2×D411yescharacteristic
146C2×Q8×C11—22no—
147C2×Q8×C11—22no—
148C2×Q8×C11—28no—
149C2×Q8×C11C2414yes—
150C22×C4×C11—22no—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—22no—
154C22×Dic11—22no—
155C22×Dic11C2×D412yes—
156C22×Dic11C2×D411yescharacteristic
157#4343—48no—
158Q8×D11—416no—
159Q8×D11—416no—
160#4339—28no—
161C2×D44—24no—
162C2×D44—22no—
163C2×D44C2412yes—
164C2×C4×D11—28no—
165C2×C4×D11—24no—
166C2×C4×D11—28no—
167C2×C4×D11—22no—
168C2×C4×D11—24no—
169C2×C4×D11—48no—
170C2×C4×D11C2×D412yes—
171C2×C4×D11C2×D412yes—
172C2×C4×D11C2×D412yes—
173C2×C4×D11C2×D412yes—
174C2×C4×D11C2×D412yes—
175C2×C4×D11C2412yes—
176C2×Dic22—28no—
177C2×Dic22—22no—
178C2×Dic22—28no—
179C2×Dic22—48no—
180C2×Dic22C2414yes—
181C2×Dic22C2412yes—
182C11×M16—24no—
183C2×C8×C11C2414yes—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4C2414yes—
189C11×C22⋊C4—22no—
190C42×C11—22no—
191C42×C11C2×D412yes—
192C42×C11C2411yescharacteristic
193C42×C11C2411yescharacteristic
194#4326—48no—
195#4325—48no—
196(C2×D11)⋊C4—24no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—24no—
199(C2×D11)⋊C4—24no—
200C4⋊Dic11—24no—
201C4⋊Dic11—24no—
202C4⋊Dic11—24no—
203C4⋊Dic11—22no—
204Dic11⋊C4—24no—
205Dic11⋊C4—28no—
206Dic11⋊C4—28no—
207C4×Dic11—24no—
208C4×Dic11C2×D411yescharacteristic
209C4×Dic11C2×D411yescharacteristic
210C4×Dic11C2×D412yes—
211C4×Dic11C2×D412yes—
212C4×Dic11C2×D412yes—
213C4×Dic11C2×D412yes—
214C4×Dic11C2412yes—
215#4318—24no—
216C2×C11⋊C8C2414yes—
217Dic44—48no—
218#4314—48no—
219#3444—111no—
220C22×C4⋊Q8—111no—
221#3218—118no—
222#3209—114no—
223#3206—114no—
224#3152—111no—
225#3152—111no—
226#3139—111no—
227#3139D1111yescharacteristic, complemented
228#3039—114no—
229#3004—114no—
230#2920—111no—
231C23×C11C22×D411yescharacteristic
232C22×D11—22no—
233C22×D11—24no—
234C22×D11—22no—
235C22×D11C22×D412yes—
236Q8×C11—28no—
237Q8×C11—44no—
238Q8×C11—44no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—44no—
243C2×C4×C11C22×D412yes—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D412yes—
246C2×C4×C11H(5,𝔽2)14yes—
247C2×C4×C11C2511yescharacteristic
248C22⋊D11—44no—
249C2×Dic11—22no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—44no—
254C2×Dic11C22×D412yes—
255C2×Dic11C22×D412yes—
256C2×Dic11C22×D412yes—
257D44—24no—
258D44—48no—
259D44—44no—
260C4×D11—24no—
261C4×D11—24no—
262C4×D11—24no—
263C4×D11—24no—
264C4×D11—24no—
265C4×D11—416no—
266C4×D11—44no—
267C4×D11—48no—
268C4×D11#13718yescomplemented
269Dic22—28no—
270Dic22—24no—
271Dic22—416no—
272Dic22—44no—
273C8×C11—24no—
274C11⋊C8—24no—
275C23×Q8—112no—
276C2×#137—114no—
277C2×#137—114no—
278#533—112no—
279#533C2×D1111yescharacteristic
280#532—112no—
281#532—111no—
282C2×C4⋊Q8—112no—
283C2×C4⋊Q8—114no—
284C2×C4⋊Q8—114no—
285C2×C4⋊Q8—111no—
286C2×C4⋊Q8—222no—
287C2×C4⋊Q8—222no—
288C2×C4⋊Q8—222no—
289C2×C4⋊Q8C2×D1111yescharacteristic
290#529—114no—
291#529—222no—
292#529—222no—
293#525—112no—
294#525—222no—
295C4×#41—112no—
296C4×#41—222no—
297C22×C4⋊C4—222no—
298C22×C42—111no—
299#497—114no—
300#497—114no—
301#494—112no—
302#494—112no—
303#492—112no—
304#492—112no—
305#491—114no—
306#491C2×D1114yescomplemented
307#487—114no—
308#487C2×D1114yescomplemented
309#462—1116no—
310#461—1116no—
311#451—1116no—
312#448—1116no—
313#432—114no—
314#431—114no—
315#423—112no—
316#419—114no—
317#419C2×D1114yes—
318#407—112no—
319C4×M16—111no—
320C4×M16C2×D1111yescharacteristic
321C22×C11—22no—
322C22×C11#53512yes—
323C22×C11C23×D411yescharacteristic
324C2×D11—28no—
325C2×D11—22no—
326C2×D11—22no—
327C2×D11—42no—
328C2×D11—44no—
329C2×D11C2×#13714yes—
330C4×C11—22no—
331C4×C11—44no—
332C4×C11—44no—
333C4×C11#53512yes—
334C4×C11C2×#13714yes—
335C4×C11C2×H(5,𝔽2)12yes—
336Dic11—22no—
337Dic11—22no—
338Dic11—44no—
339Dic11—42no—
340Dic11C2×#13714yes—
341C2×#41—112no—
342C2×#41—222no—
343C22×Q8—118no—
344C22×Q8—112no—
345C22×Q8—222no—
346C22×Q8—224no—
347C22×Q8—448no—
348C22×Q8C22×D1112yes—
349C23×C4—112no—
350C23×C4—111no—
351C23×C4—222no—
352#137—448no—
353#137—448no—
354C2×Q16—118no—
355C2×Q16—118no—
356C2×SD16—118no—
357C2×SD16—118no—
358C2×M16—112no—
359C2×M16C22×D1112yes—
360C4⋊Q8—22no—
361C4⋊Q8—118no—
362C4⋊Q8—112no—
363C4⋊Q8—112no—
364C4⋊Q8—111no—
365C4⋊Q8—224no—
366C4⋊Q8—224no—
367C4⋊Q8—224no—
368C4⋊Q8—224no—
369C4⋊Q8—222no—
370C4⋊Q8—222no—
371C4⋊Q8—222no—
372C4⋊Q8C22×D1112yes—
373C4⋊Q8C22×D1112yes—
374C4⋊Q8C22×D1112yes—
375#127—111no—
376#126—224no—
377#125—222no—
378#125C22×D1112yes—
379#124—112no—
380#124—222no—
381#123—222no—
382#123—224no—
383C22⋊Q8—22no—
384C22⋊Q8—114no—
385C22⋊Q8—222no—
386#121—114no—
387#121—222no—
388#121—222no—
389#120—222no—
390C4×Q8—22no—
391C4×Q8—114no—
392C4×Q8—222no—
393C4×D4—114no—
394C4×D4—224no—
395C4×D4—222no—
396C4×D4—224no—
397C4×D4—224no—
398C4×D4—222no—
399#117—222no—
400#117—224no—
401#117—222no—
402#117C22×D1112yes—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—224no—
405C2×C4⋊C4—224no—
406C2×C4⋊C4—224no—
407C2×C4⋊C4—224no—
408C2×C4⋊C4—224no—
409C2×C4⋊C4—222no—
410C2×C42—112no—
411C2×C42—111no—
412C2×C42—112no—
413C2×C42—112no—
414C2×C42—112no—
415C2×C42—112no—
416C2×C42—222no—
417C2×C42C22×D1111yescharacteristic
418C4⋊C8—118no—
419#103—1116no—
420#103C22×D11116yes—
421C22⋊C8—118no—
422#97—112no—
423#97C22×D1112yes—
424C4×C8—112no—
425C4×C8C22×D1112yes—
426C2×C11—22no—
427C2×C11C2×#53511yescharacteristic
428C2×C11C22×#13712yes—
429D11—24no—
430D11—82no—
431C24—111no—
432#41—228no—
433#41—448no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—28no—
437C2×Q8—114no—
438C2×Q8—112no—
439C2×Q8—228no—
440C2×Q8—222no—
441C2×Q8—228no—
442C2×Q8—448no—
443C2×Q8—4416no—
444C2×Q8—4416no—
445C2×Q8C23×D1114yes—
446C2×D4—112no—
447C2×D4—224no—
448C2×D4—222no—
449C2×D4—222no—
450C22×C4—22no—
451C22×C4—112no—
452C22×C4—112no—
453C22×C4—111no—
454C22×C4—112no—
455C22×C4—112no—
456C22×C4—112no—
457C22×C4—112no—
458C22×C4—112no—
459C22×C4—228no—
460C22×C4—224no—
461C22×C4—228no—
462C22×C4—224no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—448no—
466C22×C4D4×D1112yes—
467C22×C4C23×D1111yescharacteristic
468Q16—448no—
469Q16—448no—
470SD16—448no—
471SD16—448no—
472M16—24no—
473M16—224no—
474C2×C8—114no—
475C2×C8C23×D1114yes—
476C4⋊C4—24no—
477C4⋊C4—24no—
478C4⋊C4—22no—
479C4⋊C4—24no—
480C4⋊C4—228no—
481C4⋊C4—228no—
482C4⋊C4—224no—
483C4⋊C4—224no—
484C4⋊C4—224no—
485C4⋊C4—224no—
486C4⋊C4—222no—
487C4⋊C4C23×D1114yes—
488C22⋊C4—22no—
489C22⋊C4—224no—
490C22⋊C4—224no—
491C22⋊C4—224no—
492C22⋊C4—224no—
493C42—22no—
494C42—111no—
495C42—112no—
496C42—111no—
497C42—112no—
498C42—112no—
499C42—112no—
500C42—112no—
501C42—224no—
502C42D4×D1112yes—
503C42C23×D1111yescharacteristic
504C42C23×D1111yescharacteristic
505C11#6080011yescharacteristic, complemented, Sylow
506C23—112no—
507C23—224no—
508C23—222no—
509C23—222no—
510C23C2×D4×D1111yescharacteristic
511Q8—28no—
512Q8—44no—
513Q8—44no—
514Q8—228no—
515Q8—224no—
516Q8—4416no—
517Q8—444no—
518D4—224no—
519D4—448no—
520D4—444no—
521D4—444no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—44no—
526C2×C4—112no—
527C2×C4—118no—
528C2×C4—112no—
529C2×C4—112no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—222no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—222no—
538C2×C4—224no—
539C2×C4—448no—
540C2×C4—4416no—
541C2×C4—444no—
542C2×C4—444no—
543C2×C4C2×D4×D1112yes—
544C2×C4C2×D4×D1112yes—
545C2×C4C2×D4×D1111yescharacteristic
546C2×C4#6704214yes—
547C2×C4C24×D1111yescharacteristic
548C8—24no—
549C8—224no—
550C22—22no—
551C22—114no—
552C22—228no—
553C22—222no—
554C22—222no—
555C22—442no—
556C22—444no—
557C22#1062320512yes—
558C22C22×D4×D1111yescharacteristic
559C4—22no—
560C4—44no—
561C4—44no—
562C4—114no—
563C4—222no—
564C4—222no—
565C4—444no—
566C4—442no—
567C4#1062320512yes—
568C4D11×#13714yes—
569C4C2×#6704212yes—
570C2—22no—
571C2—224no—
572C2—882no—
573C2C2×#1062320511yescharacteristic
574C2C2×D11×#13712yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3139C2
socleC22×C11C23×D4
prime radical#13081913C2
hypercenter#3139D11
hypocenterC11#60800
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

Complements

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

NH ≅ G/Ntype
2. C2×D11×C4⋊Q8C2semidirect
3. #13079644C2semidirect
4. #13079565C2semidirect
5. #13079542C2semidirect
6. #13079075C2semidirect
7. #13079073C2semidirect
8. #13078998C2semidirect
9. #13078102C2semidirect
10. #13077852C2semidirect
11. #13077247C2semidirect
12. C11×#3139C2semidirect
37. C11×#491C22semidirect
38. C11×#487C22semidirect
43. #10622706C22semidirect
44. #10622705C22semidirect
45. #10622699C22semidirect
46. #10622698C22semidirect
47. #10622682C22semidirect
50. #10622431C22semidirect
53. #10622406C22semidirect
54. #10622328C22semidirect
56. #10622312C22semidirect
57. #10622306C22semidirect
227. #3139D11semidirect
268. C4×D11#137semidirect
306. #491C2×D11semidirect
308. #487C2×D11semidirect
505. C11#60800semidirect

Maximal subgroups

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

subgroupindex
#130819132
C2×D11×C4⋊Q82
#130796442
#130795652
#130795422
#130790752
#130790732
#130789982
#130781022
#130778522
#130772472
C11×#31392
#6080011