Finite Group Databasebeta

← #14730951

Subgroups — #14730951

Order 2816.

1088 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079531C211yesmaximal, characteristic, complemented
2C2×#10622698C211yesmaximal, characteristic, complemented
3#13078096C211yesmaximal, characteristic, complemented
4#13067699C214yesmaximal, complemented
5#13067688C214yesmaximal, complemented
6#13067297C211yesmaximal, characteristic, complemented
7#13067067C211yesmaximal, characteristic, complemented
8#13066998C211yesmaximal, characteristic, complemented
9C11×#3511C211yesmaximal, characteristic, complemented
10C11×#556—21no—
11C11×#555C2212yescomplemented
12C11×#554C2212yescomplemented
13C11×#553—22no—
14C11×#548—22no—
15C11×#547—21no—
16C11×#542—22no—
17C11×#537—21no—
18C11×#533—21no—
19C11×#532—21no—
20C11×#532C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C11×#520—21no—
23C4×C11×#41C2211yescharacteristic
24C2×#67002—21no—
25C22×#4325—22no—
26C2×#66927C2211yescharacteristic
27#10622701—21no—
28#10622698—22no—
29#10622698C2214yes—
30#10622686—21no—
31#10622649—22no—
32#10622640—21no—
33#10622640C2212yes—
34#10622628—21no—
35#10622628C2212yes—
36#10622628C2214yes—
37#10622614—21no—
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622184C2214yescomplemented
42Q8⋊(C11⋊C8)C2212yescomplemented
43D4⋊(C11⋊C8)C2214yescomplemented
44D4⋊(C11⋊C8)C2212yescomplemented
45C2×C11×#41—22no—
46C2×C11×#41—21no—
47C2×C11×#41D411yescharacteristic
48C22×Q8×C11D412yes—
49C22×D44—21no—
50C22×D44—21no—
51C22×D44—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8D412yes—
55C11×C4⋊Q8D411yescharacteristic
56C11×C4⋊Q8C2312yes—
57C11×#127D411yescharacteristic
58C11×#126—24no—
59C11×#125—22no—
60C11×#124—22no—
61C11×#124—24no—
62C11×#124—21no—
63C11×#123—24no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—24no—
68C11×#121—22no—
69C11×#121—24no—
70C11×#121—22no—
71C11×#121—22no—
72C11×#121—21no—
73C11×#121D412yes—
74C4×Q8×C11—22no—
75C4×Q8×C11—22no—
76C4×Q8×C11D411yescharacteristic
77C4×Q8×C11C2311yescharacteristic
78C4×D4×C11—22no—
79C4×D4×C11—24no—
80C4×D4×C11—22no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11D411yescharacteristic
85C4×D4×C11C2311yescharacteristic
86C4×D4×C11C2312yes—
87C11×#117—22no—
88C11×#117—22no—
89C11×#117—21no—
90C11×#117D411yescharacteristic
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—22no—
94C2×C42×C11—21no—
95C2×C42×C11C2311yescharacteristic
96#67002—44no—
97C2×#4325—28no—
98C2×#4325—22no—
99C2×#4325—48no—
100C2×#4323—22no—
101C2×#4323—24no—
102C2×#4318—21no—
103C22×C11⋊C8—21no—
104#66927—21no—
105#66927—21no—
106#66927—21no—
107#66927C2312yes—
108C22⋊(C11⋊C8)—21no—
109#66873—22no—
110#66873—22no—
111#66873—24no—
112C4⋊(C11⋊C8)—21no—
113C4⋊(C11⋊C8)C2312yes—
114C4⋊(C11⋊C8)C2312yes—
115C4×C11⋊C8—21no—
116C4×C11⋊C8—21no—
117C4×C11⋊C8C2312yes—
118#18626—111nomaximal, Sylow
119C23×D11—41no—
120C11×#41—22no—
121C11×#41—22no—
122C11×#41—42no—
123C11×#41—42no—
124C11×#41—84no—
125C2×Q8×C11—21no—
126C2×Q8×C11—22no—
127C2×Q8×C11—44no—
128C2×Q8×C11C2×D411yescharacteristic
129C2×Q8×C11C2×D414yes—
130C2×D4×C11—21no—
131C2×D4×C11—22no—
132C2×D4×C11—24no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11C2×D412yes—
136C2×D4×C11C2×D411yescharacteristic
137C22×C4×C11—24no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44—44no—
150C2×D44—41no—
151C2×D44—41no—
152C2×D44—41no—
153C2×D44—42no—
154C2×D44—42no—
155C2×D44—82no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4C2×D411yescharacteristic
166C11×C4⋊C4C2×D411yescharacteristic
167C11×C4⋊C4C2×D412yes—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—21no—
172C11×C22⋊C4—21no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—22no—
176C42×C11—24no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11C2411yescharacteristic
184#4325—44no—
185#4325—416no—
186#4323—44no—
187#4323—84no—
188#4318—42no—
189C2×C11⋊C8—24no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193#3511D1111yescharacteristic, complemented
194#3205—111no—
195C2×#492—111no—
196#3038—111no—
197#1624—114no—
198#1622—114no—
199#1548—111no—
200#1492—111no—
201#1476—111no—
202C23×C11—21no—
203C23×C11—22no—
204C23×C11#12011yescharacteristic
205C22×D11—42no—
206C22×D11—82no—
207C22×D11—82no—
208C22×D11—82no—
209Q8×C11—21no—
210Q8×C11—21no—
211Q8×C11—44no—
212Q8×C11—42no—
213Q8×C11—44no—
214D4×C11—21no—
215D4×C11—21no—
216D4×C11—24no—
217D4×C11—42no—
218D4×C11—44no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—84no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—22no—
227C2×C4×C11—21no—
228C2×C4×C11—24no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—82no—
235C2×C4×C11—84no—
236C2×C4×C11#12011yescharacteristic
237C2×C4×C11#12011yescharacteristic
238C2×C4×C11#12011yescharacteristic
239C2×C4×C11#13512yes—
240C2×C4×C11AGL(1,ℤ/8)12yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244D44—44no—
245D44—42no—
246D44—42no—
247D44—44no—
248D44—82no—
249D44—82no—
250D44—82no—
251C11⋊C8—24no—
252C11⋊C8—42no—
253C11⋊C8—42no—
254C2×AGL(1,ℤ/8)—221no—
255C22×SD16—222no—
256#556—21no—
257#555C2×D1112yescomplemented
258#554C2×D1112yescomplemented
259#553—22no—
260#548—22no—
261#547—21no—
262#542—22no—
263#537—21no—
264#533—21no—
265#532—21no—
266#532C2×D1111yescharacteristic
267C2×C4⋊Q8C2×D1111yescharacteristic
268C2×#127—111no—
269#520—21no—
270C4×#41C2×D1111yescharacteristic
271#493—221no—
272#492—114no—
273#492—222no—
274#486—221no—
275#460—112no—
276#460—221no—
277#459—114no—
278#459—112no—
279#459—221no—
280#447—222no—
281#431—111no—
282#423—111no—
283#418—221no—
284C2×C4×C8—111no—
285#333—114no—
286Q8⋊C8—112no—
287D4⋊C8—114no—
288D4⋊C8—112no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—41no—
292C22×C11—42no—
293C22×C11—41no—
294C22×C11—42no—
295C22×C11—41no—
296C22×C11—42no—
297C22×C11#44912yes—
298C22×C11C2×#12011yescharacteristic
299C2×D11—82no—
300C2×D11—82no—
301C2×D11—82no—
302C2×D11—164no—
303C4×C11—21no—
304C4×C11—21no—
305C4×C11—41no—
306C4×C11—42no—
307C4×C11—41no—
308C4×C11—41no—
309C4×C11—44no—
310C4×C11#44912yes—
311C4×C11#45312yes—
312C4×C11C2×#13511yescharacteristic
313C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
314C4×C11#57712yes—
315C2×#41—22no—
316C2×#41—21no—
317C2×#41C22⋊D1111yescharacteristic
318C22×Q8C22⋊D1112yes—
319C22×D4—221no—
320C22×D4—221no—
321C22×D4—221no—
322AGL(1,ℤ/8)—444no—
323C2×SD16—228no—
324C2×SD16—222no—
325C2×SD16—448no—
326C2×D8—222no—
327C2×D8—224no—
328C2×M16—221no—
329C22×C8—221no—
330C4⋊Q8—21no—
331C4⋊Q8—21no—
332C4⋊Q8C22⋊D1112yes—
333C4⋊Q8C22⋊D1111yescharacteristic
334C4⋊Q8C22×D1112yes—
335#127—112no—
336#127—221no—
337#127—221no—
338#127—221no—
339#127C22⋊D1111yescharacteristic
340#126—24no—
341#125—22no—
342#124—22no—
343#124—24no—
344#124—21no—
345#123—24no—
346C22⋊Q8—22no—
347C22⋊Q8—22no—
348C22⋊Q8—22no—
349C22⋊Q8—24no—
350#121—22no—
351#121—24no—
352#121—22no—
353#121—22no—
354#121—21no—
355#121C22⋊D1112yes—
356C4×Q8—22no—
357C4×Q8—22no—
358C4×Q8C22⋊D1111yescharacteristic
359C4×Q8C22×D1111yescharacteristic
360C4×D4—22no—
361C4×D4—24no—
362C4×D4—22no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4C22⋊D1111yescharacteristic
367C4×D4C22×D1111yescharacteristic
368C4×D4C22×D1112yes—
369#117—22no—
370#117—22no—
371#117—21no—
372#117C22⋊D1111yescharacteristic
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C42—21no—
377C2×C42C22×D1111yescharacteristic
378C4⋊C8—112no—
379C4⋊C8—112no—
380C4⋊C8—221no—
381#102—222no—
382#102—222no—
383#102—224no—
384C22⋊C8—221no—
385C4×C8—112no—
386C4×C8—221no—
387C4×C8—221no—
388C2×C11—22no—
389C2×C11—81no—
390C2×C11—82no—
391C2×C11C2×#44911yescharacteristic
392C2×C11#301011yescharacteristic
393C2×C11C2×#45311yescharacteristic
394D11—162no—
395C24—441no—
396#41—22no—
397#41—22no—
398#41—42no—
399#41—42no—
400#41—84no—
401C2×Q8—21no—
402C2×Q8—22no—
403C2×Q8—44no—
404C2×Q8C2×C22⋊D1111yescharacteristic
405C2×Q8C2×C22⋊D1114yes—
406C2×D4—21no—
407C2×D4—22no—
408C2×D4—24no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—222no—
412C2×D4—222no—
413C2×D4—222no—
414C2×D4—444no—
415C2×D4—442no—
416C2×D4—442no—
417C2×D4—441no—
418C2×D4—441no—
419C2×D4—441no—
420C2×D4—882no—
421C2×D4C2×C22⋊D1112yes—
422C2×D4C2×C22⋊D1111yescharacteristic
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C2×C22⋊D1111yescharacteristic
432SD16—4416no—
433SD16—444no—
434D8—444no—
435D8—884no—
436M16—442no—
437C2×C8—224no—
438C2×C8—222no—
439C2×C8—222no—
440C2×C8—222no—
441C4⋊C4—24no—
442C4⋊C4—24no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4C2×C22⋊D1111yescharacteristic
451C4⋊C4C2×C22⋊D1111yescharacteristic
452C4⋊C4C2×C22⋊D1112yes—
453C22⋊C4—24no—
454C22⋊C4—24no—
455C22⋊C4—24no—
456C22⋊C4—21no—
457C22⋊C4—21no—
458C22⋊C4—22no—
459C22⋊C4—21no—
460C22⋊C4—22no—
461C42—24no—
462C42—21no—
463C42—21no—
464C42—21no—
465C42C2×C22⋊D1111yescharacteristic
466C42C2×C22⋊D1111yescharacteristic
467C42C2×C22⋊D1111yescharacteristic
468C42C23×D1111yescharacteristic
469C11#1862611yescharacteristic, complemented, Sylow
470C23—21no—
471C23—22no—
472C23—442no—
473C23—882no—
474C23—882no—
475C23—882no—
476C23#6700611yescharacteristic
477Q8—21no—
478Q8—21no—
479Q8—44no—
480Q8—42no—
481Q8—44no—
482D4—21no—
483D4—21no—
484D4—24no—
485D4—42no—
486D4—44no—
487D4—42no—
488D4—42no—
489D4—84no—
490D4—444no—
491D4—442no—
492D4—442no—
493D4—444no—
494D4—882no—
495D4—882no—
496D4—882no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—24no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—82no—
510C2×C4—84no—
511C2×C4#6700212yes—
512C2×C4#6700312yes—
513C2×C4#6700611yescharacteristic
514C2×C4#6700611yescharacteristic
515C2×C4#6700611yescharacteristic
516C2×C4C22×C22⋊D1111yescharacteristic
517C2×C4C22×C22⋊D1111yescharacteristic
518C2×C4C22×C22⋊D1111yescharacteristic
519C8—224no—
520C8—442no—
521C8—442no—
522C22—21no—
523C22—21no—
524C22—41no—
525C22—42no—
526C22—41no—
527C22—42no—
528C22—41no—
529C22—42no—
530C22—882no—
531C22—882no—
532C22—882no—
533C22—1764no—
534C22#1062285112yes—
535C22C2×#6700611yescharacteristic
536C4—21no—
537C4—21no—
538C4—41no—
539C4—42no—
540C4—41no—
541C4—41no—
542C4—44no—
543C4#1062285112yes—
544C4#1062285412yes—
545C4C2×#6700211yescharacteristic
546C4C2×#6700311yescharacteristic
547C4#1062336812yes—
548C2—22no—
549C2—81no—
550C2—82no—
551C2—1762no—
552C2C2×#1062285111yescharacteristic
553C2#1307790211yescharacteristic
554C2C2×#1062285411yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3511C2
socleC22×C11C2×#120
hypercenter#3511D11
hypocenterC11#18626
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #13079531C2semidirect
2. C2×#10622698C2semidirect
3. #13078096C2semidirect
4. #13067699C2semidirect
5. #13067688C2semidirect
6. #13067297C2semidirect
7. #13067067C2semidirect
8. #13066998C2semidirect
9. C11×#3511C2semidirect
11. C11×#555C22semidirect
12. C11×#554C22semidirect
41. #10622184C22semidirect
42. Q8⋊(C11⋊C8)C22semidirect
43. D4⋊(C11⋊C8)C22semidirect
44. D4⋊(C11⋊C8)C22semidirect
193. #3511D11semidirect
257. #555C2×D11semidirect
258. #554C2×D11semidirect
469. C11#18626semidirect

Maximal subgroups

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

subgroupindex
#130795312
C2×#106226982
#130780962
#130676992
#130676882
#130672972
#130670672
#130669982
C11×#35112
#1862611