Finite Group Databasebeta

← #14960752

Subgroups — #14960752

Order 2816.

2842 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623014C211yesmaximal, characteristic, complemented
2#13076903C212yesmaximal, complemented
3#13074962C218yesmaximal, complemented
4#13074861C218yesmaximal, complemented
5#13074421C212yesmaximal, complemented
6#13073996C212yesmaximal, complemented
7#13072263C212yesmaximal, complemented
8#13071939C212yesmaximal, complemented
9#13071939C212yesmaximal, complemented
10#13071214C211yesmaximal, characteristic, complemented
11C22×C11×#121C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C2×C11×#121—28no—
17C2×C11×#121C2218yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C2×#66989C2214yescomplemented
23C2×#66988C2214yescomplemented
24C2×#66988C2214yescomplemented
25C2×#66977C2212yes—
26C2×#66977C2212yes—
27C2×#66977C2214yescomplemented
28#10623014—28no—
29C2×#66931C2214yescomplemented
30C2×#66931C2214yescomplemented
31#10622860C2212yes—
32#10622860C2214yes—
33#10622860C2214yes—
34#10622835C2218yescomplemented
35#10622835C2218yescomplemented
36#10622835C2218yescomplemented
37#10622834C2214yescomplemented
38#10622833C2214yescomplemented
39#10622833C2214yescomplemented
40#10622825C2212yes—
41#10622825C2214yescomplemented
42#10622823C2214yes—
43#10622823C2214yes—
44#10622823C2218yescomplemented
45C4×C22⋊Dic11C2212yes—
46#10622596C2214yescomplemented
47#10622592C2214yescomplemented
48#10622585C2218yescomplemented
49#10622564C2218yescomplemented
50#10622562C2214yescomplemented
51#10622561C2218yescomplemented
52#10622560C2214yescomplemented
53C25×C11C2311yescharacteristic
54C25×C11C2311yescharacteristic
55C25×C11C2311yescharacteristic
56C22×D4×C11—24no—
57C22×D4×C11—24no—
58C22×D4×C11—24no—
59C22×D4×C11—44no—
60C22×D4×C11—44no—
61C22×D4×C11—44no—
62C22×D4×C11C2314yes—
63C22×D4×C11C2314yes—
64C22×D4×C11C2314yes—
65C23×C4×C11—24no—
66C23×C4×C11—44no—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2314yes—
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×Dic11C2312yes—
73C23×Dic11C2312yes—
74C22×Dic22C2312yes—
75C22×Dic22C2312yes—
76C11×#121—232no—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4D418yes—
81C2×C11×C22⋊C4C2314yes—
82C2×C11×C22⋊C4C2314yes—
83C2×C22⋊Dic11—28no—
84C2×C22⋊Dic11C2314yes—
85C2×C22⋊Dic11C2314yes—
86C2×C22⋊Dic11C2318yes—
87C2×C22⋊Dic11C2314yes—
88C2×C22⋊Dic11C2318yes—
89C2×C22⋊Dic11C2318yes—
90C2×C22⋊Dic11C2314yes—
91C2×C22⋊Dic11C2314yes—
92C2×C22⋊Dic11C2318yes—
93#66989—48no—
94#66988—48no—
95#66988—48no—
96C2×C4⋊Dic11C2312yes—
97C2×C4⋊Dic11C2312yes—
98C2×C4⋊Dic11C2314yes—
99#66977—28no—
100#66977—28no—
101#66977—48no—
102C2×Dic11⋊C4C2314yes—
103C2×Dic11⋊C4C2314yes—
104C2×Dic11⋊C4C2318yes—
105C2×Dic11⋊C4C2318yes—
106C2×C4×Dic11C2314yes—
107#66931—216no—
108#66931—216no—
109C11⋊#95C2318yes—
110C11⋊#95C2314yes—
111C11⋊#95C2314yes—
112C11⋊#95C2318yes—
113#36718—111nomaximal, Sylow
114C24×C11—22no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11—22no—
118C24×C11—24no—
119C24×C11—24no—
120C24×C11—42no—
121C24×C11—42no—
122C24×C11—42no—
123C24×C11—42no—
124C24×C11—42no—
125C24×C11C2×D414yes—
126C24×C11C2412yes—
127C24×C11C2412yes—
128C24×C11C2412yes—
129C24×C11C2411yescharacteristic
130C2×D4×C11—28no—
131C2×D4×C11—28no—
132C2×D4×C11—28no—
133C2×D4×C11—28no—
134C2×D4×C11—28no—
135C2×D4×C11—28no—
136C2×D4×C11—44no—
137C2×D4×C11—44no—
138C2×D4×C11—44no—
139C2×D4×C11—416no—
140C2×D4×C11—416no—
141C2×D4×C11—416no—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—28no—
146C22×C4×C11—28no—
147C22×C4×C11—42no—
148C22×C4×C11—44no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—416no—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2412yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2412yes—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—44no—
161C22×Dic11—44no—
162C22×Dic11C2418yes—
163C22×Dic11C2414yes—
164C22×Dic11C2414yes—
165C2×Dic22—24no—
166C2×Dic22—24no—
167C2×Dic22—44no—
168C2×Dic22—44no—
169C11×C4⋊C4—28no—
170C11×C22⋊C4—28no—
171C11×C22⋊C4C2×D4116yes—
172C22⋊Dic11—28no—
173C22⋊Dic11—28no—
174C22⋊Dic11—216no—
175C22⋊Dic11—28no—
176C22⋊Dic11—48no—
177C22⋊Dic11—44no—
178C22⋊Dic11—44no—
179C22⋊Dic11—48no—
180C22⋊Dic11—48no—
181C4⋊Dic11—24no—
182C4⋊Dic11—24no—
183C4⋊Dic11—44no—
184Dic11⋊C4—28no—
185Dic11⋊C4—28no—
186Dic11⋊C4—216no—
187Dic11⋊C4—48no—
188C4×Dic11—44no—
189C2×#543—111no—
190C22×#121D1111yescharacteristic
191#2848—112no—
192#2681—118no—
193#2672—118no—
194#2626—112no—
195#2583—112no—
196#2435—112no—
197#2405—112no—
198#2405—112no—
199#2312—111no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—28no—
203C23×C11—22no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—22no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—28no—
211C23×C11—22no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—24no—
215C23×C11—44no—
216C23×C11—44no—
217C23×C11—416no—
218C23×C11—44no—
219C23×C11—44no—
220C23×C11—44no—
221C23×C11—44no—
222C23×C11—44no—
223C23×C11—88no—
224C23×C11—88no—
225C23×C11C22×D414yes—
226C23×C11C22×D412yes—
227C23×C11H(5,𝔽2)14yes—
228C23×C112−1+414yes—
229C23×C11C2511yescharacteristic
230D4×C11—416no—
231D4×C11—416no—
232D4×C11—416no—
233C2×C4×C11—28no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—44no—
241C2×C4×C11—44no—
242C2×C4×C11—416no—
243C2×C4×C11—44no—
244C2×C4×C11C22×D414yes—
245C2×C4×C11C22×D414yes—
246C2×C4×C11H(5,𝔽2)14yes—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—28no—
250C2×Dic11—28no—
251C2×Dic11—28no—
252C2×Dic11—28no—
253C2×Dic11—28no—
254C2×Dic11—84no—
255C2×Dic11—84no—
256Dic22—84no—
257Dic22—84no—
258C23×D4C2×D1111yescharacteristic
259C23×D4C2×D1111yescharacteristic
260C23×D4C2×D1111yescharacteristic
261C24×C4C2×D1111yescharacteristic
262#543—228no—
263C2×#124—114no—
264C2×#123—114no—
265C2×#123—114no—
266C2×C22⋊Q8—112no—
267C2×C22⋊Q8—112no—
268C2×C22⋊Q8—114no—
269C2×C22⋊Q8—114no—
270C2×C22⋊Q8—114no—
271C2×#121—28no—
272C2×#121C2×D1118yes—
273C22×C4⋊C4C2×D1111yescharacteristic
274C22×C22⋊C4—112no—
275C22×C22⋊C4C2×D1111yescharacteristic
276C22×C22⋊C4C2×D1111yescharacteristic
277#399—114no—
278#398—114no—
279#396—118no—
280#395—114no—
281#394—118no—
282#394—118no—
283#394—118no—
284#393—114no—
285#390—114no—
286#389—118no—
287#388—118no—
288#386—114no—
289#386—114no—
290#385—114no—
291#385—114no—
292#385—118no—
293#380—112no—
294#380—114no—
295#379—112no—
296#379—114no—
297#379—114no—
298C4×C22⋊C4—112no—
299C22×C11—22no—
300C22×C11—22no—
301C22×C11—28no—
302C22×C11—24no—
303C22×C11—24no—
304C22×C11—24no—
305C22×C11—24no—
306C22×C11—28no—
307C22×C11—416no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—44no—
311C22×C11—48no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—48no—
316C22×C11—88no—
317C22×C11—88no—
318C22×C11#53614yes—
319C22×C11C23×D411yescharacteristic
320C22×C11C2×H(5,𝔽2)12yes—
321C22×C11C2×H(5,𝔽2)12yes—
322C22×C11C2×2−1+412yes—
323C4×C11—24no—
324C4×C11—24no—
325C4×C11—24no—
326C4×C11—42no—
327Dic11—44no—
328Dic11—44no—
329Dic11—48no—
330C25C22×D1111yescharacteristic
331C25C22×D1111yescharacteristic
332C25C22×D1111yescharacteristic
333C22×Q8—112no—
334C22×Q8—112no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—44no—
339C22×D4—44no—
340C22×D4—44no—
341C22×D4C22×D1114yes—
342C22×D4C22×D1114yes—
343C22×D4C22×D1114yes—
344C23×C4—24no—
345C23×C4—44no—
346C23×C4—112no—
347C23×C4—112no—
348C23×C4C22×D1111yescharacteristic
349C23×C4C22×D1114yes—
350C23×C4C22×D1111yescharacteristic
351C23×C4C22×D1111yescharacteristic
352C23×C4C22×D1111yescharacteristic
353#124—448no—
354#123—448no—
355#123—448no—
356C22⋊Q8—228no—
357C22⋊Q8—228no—
358C22⋊Q8—2216no—
359C22⋊Q8—2216no—
360C22⋊Q8—448no—
361#121—232no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—112no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—112no—
367C2×C4⋊C4—118no—
368C2×C4⋊C4—114no—
369C2×C4⋊C4—118no—
370C2×C4⋊C4C22×D1114yes—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—114no—
373C2×C22⋊C4—114no—
374C2×C22⋊C4—118no—
375C2×C22⋊C4—114no—
376C2×C22⋊C4—118no—
377C2×C22⋊C4—114no—
378C2×C22⋊C4—114no—
379C2×C22⋊C4—118no—
380C2×C22⋊C4—118no—
381C2×C22⋊C4—228no—
382C2×C22⋊C4C22⋊D1118yes—
383C2×C22⋊C4C22×D1114yes—
384C2×C22⋊C4C22×D1114yes—
385C2×C42—114no—
386#95—114no—
387#95—118no—
388#95—114no—
389#95—118no—
390C2×C11—24no—
391C2×C11—44no—
392C2×C11—44no—
393C2×C11—82no—
394C2×C11C2×#53611yescharacteristic
395C2×C11#348411yescharacteristic
396C2×C11#348411yescharacteristic
397C2×C11#353614yes—
398C24—24no—
399C24—22no—
400C24—24no—
401C24—24no—
402C24—22no—
403C24—24no—
404C24—42no—
405C24—42no—
406C24—42no—
407C24—42no—
408C24—42no—
409C24C2×C22⋊D1114yes—
410C24C23×D1112yes—
411C24C23×D1112yes—
412C24C23×D1112yes—
413C24C23×D1111yescharacteristic
414C2×Q8—224no—
415C2×Q8—224no—
416C2×Q8—444no—
417C2×Q8—444no—
418C2×D4—28no—
419C2×D4—28no—
420C2×D4—28no—
421C2×D4—28no—
422C2×D4—28no—
423C2×D4—28no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—44no—
427C2×D4—416no—
428C2×D4—416no—
429C2×D4—416no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—28no—
434C22×C4—28no—
435C22×C4—42no—
436C22×C4—44no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—416no—
440C22×C4—118no—
441C22×C4—114no—
442C22×C4—114no—
443C22×C4—224no—
444C22×C4—224no—
445C22×C4—444no—
446C22×C4—444no—
447C22×C4C2×C22⋊D1114yes—
448C22×C4C2×C22⋊D1114yes—
449C22×C4C23×D1112yes—
450C22×C4C23×D1112yes—
451C22×C4C23×D1112yes—
452C22×C4C23×D1112yes—
453C4⋊C4—28no—
454C4⋊C4—2216no—
455C4⋊C4—228no—
456C4⋊C4—228no—
457C4⋊C4—224no—
458C4⋊C4—224no—
459C4⋊C4—444no—
460C4⋊C4—448no—
461C22⋊C4—28no—
462C22⋊C4—2216no—
463C22⋊C4—228no—
464C22⋊C4—228no—
465C22⋊C4—228no—
466C22⋊C4—448no—
467C22⋊C4—444no—
468C22⋊C4—444no—
469C22⋊C4—448no—
470C22⋊C4—448no—
471C22⋊C4C2×C22⋊D11116yes—
472C42—444no—
473C11#3671811yescharacteristic, complemented, Sylow
474C23—22no—
475C23—22no—
476C23—28no—
477C23—24no—
478C23—24no—
479C23—24no—
480C23—22no—
481C23—24no—
482C23—24no—
483C23—22no—
484C23—28no—
485C23—24no—
486C23—24no—
487C23—24no—
488C23—22no—
489C23—44no—
490C23—44no—
491C23—416no—
492C23—44no—
493C23—44no—
494C23—44no—
495C23—44no—
496C23—44no—
497C23—88no—
498C23—88no—
499C23#6703714yes—
500C23#6704314yes—
501C23C22×C22⋊D1114yes—
502C23C22×C22⋊D1112yes—
503C23C24×D1111yescharacteristic
504Q8—884no—
505Q8—884no—
506D4—416no—
507D4—416no—
508D4—416no—
509C2×C4—28no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—44no—
517C2×C4—44no—
518C2×C4—416no—
519C2×C4—44no—
520C2×C4—228no—
521C2×C4—228no—
522C2×C4—228no—
523C2×C4—228no—
524C2×C4—228no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—884no—
528C2×C4—884no—
529C2×C4#6703714yes—
530C2×C4C22×C22⋊D1114yes—
531C2×C4C22×C22⋊D1114yes—
532C22—22no—
533C22—22no—
534C22—28no—
535C22—24no—
536C22—24no—
537C22—24no—
538C22—24no—
539C22—28no—
540C22—416no—
541C22—42no—
542C22—42no—
543C22—44no—
544C22—48no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—48no—
549C22—88no—
550C22—88no—
551C22#1062335614yes—
552C22C2×#6703712yes—
553C22C2×#6703712yes—
554C22C2×#6704312yes—
555C22C23×C22⋊D1111yescharacteristic
556C4—24no—
557C4—24no—
558C4—24no—
559C4—42no—
560C4—444no—
561C4—444no—
562C4—448no—
563C2—24no—
564C2—44no—
565C2—44no—
566C2—82no—
567C2C2×#1062335611yescharacteristic
568C2#1308225111yescharacteristic
569C2#1308225111yescharacteristic
570C2#1308283814yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
Fitting, prime radicalC22×C11×#121C2
hypercenterC22×#121D11
hypocenterC11#36718
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10623014C2semidirect
2. #13076903C2semidirect
3. #13074962C2semidirect
4. #13074861C2semidirect
5. #13074421C2semidirect
6. #13073996C2semidirect
7. #13072263C2semidirect
8. #13071939C2semidirect
9. #13071939C2semidirect
10. #13071214C2semidirect
22. C2×#66989C22semidirect
23. C2×#66988C22semidirect
24. C2×#66988C22semidirect
27. C2×#66977C22semidirect
29. C2×#66931C22semidirect
30. C2×#66931C22semidirect
34. #10622835C22semidirect
35. #10622835C22semidirect
36. #10622835C22semidirect
37. #10622834C22semidirect
38. #10622833C22semidirect
39. #10622833C22semidirect
41. #10622825C22semidirect
44. #10622823C22semidirect
46. #10622596C22semidirect
47. #10622592C22semidirect
48. #10622585C22semidirect
49. #10622564C22semidirect
50. #10622562C22semidirect
51. #10622561C22semidirect
52. #10622560C22semidirect
473. C11#36718semidirect

Maximal subgroups

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

subgroupindex
C2×#106230142
#130769032
#130749622
#130748612
#130744212
#130739962
#130722632
#130719392
#130712142
C22×C11×#1212
#3671811