Finite Group Databasebeta

← #14960579

Subgroups — #14960579

Order 2816.

2782 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623041C211yesmaximal, characteristic, complemented
2#13076898C212yesmaximal, complemented
3#13075108C218yesmaximal, complemented
4#13074913C218yesmaximal, complemented
5#13074358C212yesmaximal, complemented
6#13073547C212yesmaximal, complemented
7#13072270C212yesmaximal, complemented
8#13071951C212yesmaximal, complemented
9#13071935C212yesmaximal, complemented
10#13071219C211yesmaximal, characteristic, complemented
11C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C22×#4339C2212yes—
15C2×C11×C22⋊Q8—28no—
16C2×C11×C22⋊Q8C2218yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C2×#67006C2214yes—
23C2×#67000C2214yescomplemented
24C2×#66983C2212yes—
25C2×#66983C2212yes—
26C2×#66983C2214yes—
27C2×#66982C2214yes—
28#10623041—28no—
29C2×#66950C2214yescomplemented
30C2×#66948C2214yescomplemented
31#10622844C2218yescomplemented
32#10622843C2214yescomplemented
33#10622826C2214yes—
34#10622826C2214yes—
35#10622826C2218yes—
36#10622825C2212yes—
37#10622825C2214yes—
38#10622824C2212yes—
39C4×C22⋊Dic11C2212yes—
40#10622607C2218yescomplemented
41#10622604C2214yescomplemented
42#10622604C2214yescomplemented
43#10622602C2218yescomplemented
44#10622596C2214yescomplemented
45#10622594C2218yescomplemented
46#10622592C2214yescomplemented
47#10622573C2214yes—
48#10622573C2214yes—
49#10622570C2218yes—
50#10622569C2218yes—
51#10622562C2214yes—
52#10622560C2214yes—
53C25×C11C2311yescharacteristic
54C22×Q8×C11—24no—
55C22×Q8×C11—44no—
56C22×Q8×C11C2314yes—
57C23×C4×C11—24no—
58C23×C4×C11—44no—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2314yes—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2314yes—
67C22×C22⋊D11C2318yes—
68C2×#4339—28no—
69C2×#4339—48no—
70C22×D44C2312yes—
71C22×D44C2312yes—
72C22×D44C2312yes—
73C22×C4×D11C2314yes—
74C22×Dic22C2312yes—
75C11×C22⋊Q8—232no—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4D418yescomplemented
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C11×C22⋊C4—24no—
83C2×C11×C22⋊C4—24no—
84C2×C11×C22⋊C4C2314yes—
85C2×C11×C22⋊C4C2314yes—
86#67006—48no—
87C2×C22⋊Dic11C2314yes—
88C2×C22⋊Dic11C2318yes—
89#67000—48no—
90#66983—28no—
91#66983—28no—
92#66983—48no—
93#66982—48no—
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2314yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×(C2×D11)⋊C4C2318yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×C4⋊Dic11C2312yes—
100C2×C4⋊Dic11C2312yes—
101C2×C4⋊Dic11C2314yes—
102C2×Dic11⋊C4C2318yes—
103C2×C4×Dic11C2314yes—
104#66950—216no—
105#66948—216no—
106C11⋊#95C2314yes—
107C11⋊#95C2318yes—
108C11⋊#95C2314yes—
109C11⋊#95C2314yes—
110C11⋊#95C2318yes—
111C11⋊#95C2314yes—
112#36707—111nomaximal, Sylow
113C24×C11—22no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11—42no—
117C24×C11C2412yes—
118C24×C11C2411yescharacteristic
119C23×D11C2414yes—
120C2×Q8×C11—28no—
121C2×Q8×C11—28no—
122C2×Q8×C11—44no—
123C2×Q8×C11—416no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—24no—
130C22×C4×C11—28no—
131C22×C4×C11—28no—
132C22×C4×C11—42no—
133C22×C4×C11—44no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—416no—
137C22×C4×C11C2×D414yes—
138C22×C4×C11C2×D414yes—
139C22×C4×C11C2×D414yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2412yes—
142C22×C4×C11C2412yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2412yes—
145C22×C4×C11C2412yes—
146C2×C22⋊D11—28no—
147C2×C22⋊D11—28no—
148C2×C22⋊D11—28no—
149C2×C22⋊D11—216no—
150C2×C22⋊D11—48no—
151C2×C22⋊D11—48no—
152C22×Dic11C2418yes—
153C22×Dic11C2414yes—
154#4339—432no—
155C2×D44—24no—
156C2×D44—24no—
157C2×D44—24no—
158C2×D44—44no—
159C2×D44—44no—
160C2×D44—44no—
161C2×C4×D11—28no—
162C2×C4×D11—44no—
163C2×C4×D11—44no—
164C2×Dic22—24no—
165C2×Dic22—44no—
166C11×C4⋊C4—28no—
167C11×C4⋊C4—28no—
168C11×C4⋊C4C2×D4116yes—
169C11×C22⋊C4—28no—
170C11×C22⋊C4—28no—
171C22⋊Dic11—28no—
172C22⋊Dic11—48no—
173(C2×D11)⋊C4—28no—
174(C2×D11)⋊C4—28no—
175(C2×D11)⋊C4—216no—
176(C2×D11)⋊C4—48no—
177(C2×D11)⋊C4—48no—
178C4⋊Dic11—24no—
179C4⋊Dic11—24no—
180C4⋊Dic11—44no—
181Dic11⋊C4—48no—
182C4×Dic11—44no—
183C2×#537—111no—
184C22×C22⋊Q8D1111yescharacteristic, complemented
185#2847—112no—
186#2692—118no—
187#2676—118no—
188#2618—112no—
189#2539—112no—
190#2436—112no—
191#2406—112no—
192#2404—112no—
193#2313—111no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—28no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—22no—
201C23×C11—416no—
202C23×C11—44no—
203C23×C11—44no—
204C23×C11C22×D412yes—
205C23×C11H(5,𝔽2)14yes—
206C23×C112−1+414yes—
207C23×C11C2511yescharacteristic
208C22×D11—24no—
209C22×D11—28no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—28no—
213Q8×C11—416no—
214C2×C4×C11—28no—
215C2×C4×C11—28no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—44no—
226C2×C4×C11—44no—
227C2×C4×C11—416no—
228C2×C4×C11—44no—
229C2×C4×C11—44no—
230C2×C4×C11C22×D414yes—
231C2×C4×C11C22×D414yes—
232C2×C4×C11C22×D414yes—
233C2×C4×C11H(5,𝔽2)14yes—
234C22⋊D11—416no—
235C22⋊D11—816no—
236C2×Dic11—24no—
237C2×Dic11—28no—
238C2×Dic11—24no—
239C2×Dic11—28no—
240C2×Dic11—24no—
241C2×Dic11—28no—
242D44—48no—
243D44—84no—
244D44—84no—
245C4×D11—416no—
246Dic22—48no—
247C22×#41—112no—
248C23×Q8C2×D1111yescharacteristic
249C24×C4C2×D1111yescharacteristic
250#537—228no—
251C2×#124—114no—
252C2×#123—114no—
253C2×C22⋊Q8—28no—
254C2×C22⋊Q8—114no—
255C2×C22⋊Q8C2×D1118yes—
256C2×#121—112no—
257C2×#121—112no—
258C2×#121—114no—
259C2×#121—114no—
260C2×#120—114no—
261C22×C4⋊C4C2×D1111yescharacteristic
262C22×C4⋊C4C2×D1111yescharacteristic
263C22×C4⋊C4C2×D1111yescharacteristic
264C22×C22⋊C4C2×D1111yescharacteristic
265C22×C22⋊C4C2×D1111yescharacteristic
266#399—114no—
267#398—114no—
268#396—118no—
269#395—114no—
270#394—114no—
271#394—114no—
272#393—118no—
273#393—114no—
274#392—114no—
275#392—114no—
276#391—114no—
277#390—118no—
278#387—118no—
279#386—114no—
280#386—118no—
281#386—114no—
282#386—118no—
283#385—118no—
284#381—112no—
285#380—112no—
286#380—114no—
287C4×C22⋊C4—112no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—28no—
291C22×C11—24no—
292C22×C11—28no—
293C22×C11—416no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—44no—
297C22×C11#53514yes—
298C22×C11C23×D411yescharacteristic
299C22×C11C2×H(5,𝔽2)12yes—
300C22×C11C2×H(5,𝔽2)12yes—
301C22×C11C2×2−1+412yes—
302C2×D11—44no—
303C2×D11—44no—
304C2×D11—44no—
305C2×D11—48no—
306C2×D11—48no—
307C4×C11—24no—
308C4×C11—24no—
309C4×C11—24no—
310C4×C11—24no—
311C4×C11—42no—
312C4×C11—42no—
313Dic11—44no—
314Dic11—48no—
315C25C22×D1111yescharacteristic
316C2×#41—228no—
317C2×#41—448no—
318C22×Q8—24no—
319C22×Q8—44no—
320C22×Q8—112no—
321C22×Q8C22×D1114yes—
322C22×D4—114no—
323C22×D4—118no—
324C22×D4—112no—
325C22×D4—112no—
326C22×D4—112no—
327C23×C4—24no—
328C23×C4—44no—
329C23×C4—114no—
330C23×C4C22×D1111yescharacteristic
331C23×C4C22×D1111yescharacteristic
332C23×C4C22×D1114yes—
333C23×C4C22×D1111yescharacteristic
334C23×C4C22×D1111yescharacteristic
335C23×C4C22×D1111yescharacteristic
336C23×C4C22×D1111yescharacteristic
337#124—448no—
338#123—448no—
339C22⋊Q8—232no—
340C22⋊Q8—2216no—
341#121—228no—
342#121—228no—
343#121—2216no—
344#121—448no—
345#120—448no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—112no—
349C2×C4⋊C4—112no—
350C2×C4⋊C4—114no—
351C2×C4⋊C4—118no—
352C2×C4⋊C4C22⋊D1118yescomplemented
353C2×C4⋊C4C22×D1114yes—
354C2×C4⋊C4C22×D1114yes—
355C2×C4⋊C4C22×D1114yes—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—114no—
359C2×C22⋊C4—114no—
360C2×C22⋊C4—114no—
361C2×C22⋊C4—118no—
362C2×C22⋊C4—118no—
363C2×C22⋊C4—118no—
364C2×C22⋊C4—118no—
365C2×C22⋊C4C22×D1114yes—
366C2×C22⋊C4C22×D1114yes—
367C2×C42—114no—
368#95—114no—
369#95—118no—
370#95—114no—
371#95—114no—
372#95—114no—
373#95—118no—
374C2×C11—24no—
375C2×C11—44no—
376C2×C11C2×#53511yescharacteristic
377C2×C11#348411yescharacteristic
378C2×C11#348611yescharacteristic
379C2×C11#353614yes—
380D11—84no—
381C24—24no—
382C24—22no—
383C24—24no—
384C24—42no—
385C24—114no—
386C24C23×D1112yes—
387C24C23×D1111yescharacteristic
388#41—4432no—
389C2×Q8—28no—
390C2×Q8—28no—
391C2×Q8—44no—
392C2×Q8—416no—
393C2×Q8—224no—
394C2×Q8—444no—
395C2×D4—228no—
396C2×D4—228no—
397C2×D4—228no—
398C2×D4—2216no—
399C2×D4—224no—
400C2×D4—224no—
401C2×D4—224no—
402C2×D4—444no—
403C2×D4—444no—
404C2×D4—444no—
405C2×D4—448no—
406C2×D4—448no—
407C22×C4—24no—
408C22×C4—22no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—28no—
414C22×C4—28no—
415C22×C4—42no—
416C22×C4—44no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—416no—
420C22×C4—118no—
421C22×C4—114no—
422C22×C4—228no—
423C22×C4—444no—
424C22×C4—444no—
425C22×C4C2×C22⋊D1114yes—
426C22×C4C2×C22⋊D1114yes—
427C22×C4C2×C22⋊D1114yes—
428C22×C4C23×D1112yes—
429C22×C4C23×D1112yes—
430C22×C4C23×D1112yes—
431C22×C4C23×D1112yes—
432C22×C4C23×D1112yes—
433C22×C4C23×D1112yes—
434C4⋊C4—28no—
435C4⋊C4—28no—
436C4⋊C4—224no—
437C4⋊C4—224no—
438C4⋊C4—444no—
439C4⋊C4—448no—
440C4⋊C4C2×C22⋊D11116yes—
441C22⋊C4—28no—
442C22⋊C4—28no—
443C22⋊C4—228no—
444C22⋊C4—2216no—
445C22⋊C4—228no—
446C22⋊C4—228no—
447C22⋊C4—448no—
448C22⋊C4—448no—
449C22⋊C4—448no—
450C42—444no—
451C11#3670711yescharacteristic, complemented, Sylow
452C23—22no—
453C23—22no—
454C23—28no—
455C23—24no—
456C23—22no—
457C23—24no—
458C23—22no—
459C23—416no—
460C23—44no—
461C23—44no—
462C23—228no—
463C23—228no—
464C23—224no—
465C23—224no—
466C23—224no—
467C23#6704014yes—
468C23#6704214yes—
469C23C22×C22⋊D1112yes—
470C23C24×D1111yescharacteristic
471Q8—416no—
472Q8—448no—
473D4—448no—
474D4—4416no—
475D4—884no—
476D4—884no—
477D4—8816no—
478C2×C4—28no—
479C2×C4—28no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—44no—
490C2×C4—44no—
491C2×C4—416no—
492C2×C4—44no—
493C2×C4—44no—
494C2×C4—228no—
495C2×C4—228no—
496C2×C4—228no—
497C2×C4—224no—
498C2×C4—224no—
499C2×C4—224no—
500C2×C4—4416no—
501C2×C4#6703714yes—
502C2×C4C22×C22⋊D1114yes—
503C2×C4C22×C22⋊D1114yes—
504C2×C4C22×C22⋊D1114yes—
505C22—22no—
506C22—22no—
507C22—28no—
508C22—24no—
509C22—28no—
510C22—416no—
511C22—42no—
512C22—42no—
513C22—44no—
514C22—444no—
515C22—444no—
516C22—444no—
517C22—448no—
518C22—448no—
519C22#1062336114yes—
520C22C2×#6703712yes—
521C22C2×#6704012yes—
522C22C2×#6704212yes—
523C22C23×C22⋊D1111yescharacteristic
524C4—24no—
525C4—24no—
526C4—24no—
527C4—24no—
528C4—42no—
529C4—42no—
530C4—444no—
531C4—448no—
532C2—24no—
533C2—44no—
534C2—884no—
535C2C2×#1062336111yescharacteristic
536C2#1308225111yescharacteristic
537C2#1308226711yescharacteristic
538C2#1308284514yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC22×C11×C22⋊Q8C2
hypercenterC22×C22⋊Q8D11
hypocenterC11#36707
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#10623041C2semidirect
2. #13076898C2semidirect
3. #13075108C2semidirect
4. #13074913C2semidirect
5. #13074358C2semidirect
6. #13073547C2semidirect
7. #13072270C2semidirect
8. #13071951C2semidirect
9. #13071935C2semidirect
10. #13071219C2semidirect
11. C22×C11×C22⋊Q8C2semidirect
23. C2×#67000C22semidirect
29. C2×#66950C22semidirect
30. C2×#66948C22semidirect
31. #10622844C22semidirect
32. #10622843C22semidirect
40. #10622607C22semidirect
41. #10622604C22semidirect
42. #10622604C22semidirect
43. #10622602C22semidirect
44. #10622596C22semidirect
45. #10622594C22semidirect
46. #10622592C22semidirect
78. C2×C11×C4⋊C4D4semidirect
184. C22×C22⋊Q8D11semidirect
352. C2×C4⋊C4C22⋊D11semidirect
451. C11#36707semidirect

Maximal subgroups

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

subgroupindex
C2×#106230412
#130768982
#130751082
#130749132
#130743582
#130735472
#130722702
#130719512
#130719352
#130712192
C22×C11×C22⋊Q82
#3670711