Finite Group Databasebeta

← #14809105

Subgroups — #14809105

Order 2816.

1656 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4314C211yesmaximal, characteristic, complemented
2C2×#10622781C212yesmaximal, complemented
3C2×#10622663C211yesmaximal, characteristic, complemented
4C2×#10622649C211yesmaximal, characteristic
5#13072275C211yesmaximal, characteristic, complemented
6#13072268C211yesmaximal, characteristic, complemented
7#13069711C212yesmaximal, complemented
8#13069695C212yesmaximal, complemented
9#13069468C212yesmaximal, complemented
10C8×C22⋊Dic11C211yesmaximal, characteristic, complemented
11C2×C11×#465C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C22×C11×SD16C2211yescharacteristic, complemented
15C23×C8×C11C2211yescharacteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×#67000C2212yes—
19C22×#4326C2212yescomplemented
20C2×#66989C2212yescomplemented
21C22×#4323C2212yes—
22C22×#4314—24no—
23C22×#4314—28no—
24C22×#4314C2212yes—
25C22×#4314C2212yes—
26C11×#465—24no—
27C2×C11×#106C2211yescharacteristic, complemented
28C2×C11×#103C2211yescharacteristic, complemented
29C2×C11×#102C2211yescharacteristic, complemented
30#10622833—22no—
31C4×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33#10622781—28no—
34C2×C8×Dic11C2212yescomplemented
35#10622663—24no—
36#10622649—24no—
37#10622604—22no—
38#10622601C2212yes—
39#10622587C2212yescomplemented
40C2×#66874C2212yescomplemented
41C2×#66873C2212yes—
42#10622568—22no—
43#10622560—22no—
44#10622188C2212yescomplemented
45C24×D11—21no—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×Dic11—21no—
51C22×D44—22no—
52C22×D44—24no—
53C22×D44—22no—
54C22×D44—21no—
55C22×D44—42no—
56C22×D44C2312yes—
57C22×Dic22—22no—
58C22×Dic22—24no—
59C22×Dic22—22no—
60C22×Dic22—21no—
61C22×Dic22—42no—
62C22×Dic22C2312yes—
63C2×C11×SD16—24no—
64C2×C11×SD16—22no—
65C22×C8×C11—24no—
66C22×C8×C11D414yes—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—22no—
71C11×#121—22no—
72C11×#121—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C22⋊Dic11—24no—
79C2×C22⋊Dic11D412yes—
80#67000—24no—
81#67000—42no—
82C2×#4326—24no—
83C2×#4326—24no—
84C2×#4326—42no—
85#66989—24no—
86#66989—42no—
87C2×#4323—24no—
88C2×#4323—24no—
89C2×#4323—42no—
90C2×(C2×D11)⋊C4—24no—
91C2×(C2×D11)⋊C4—24no—
92C2×C4×Dic11C2312yes—
93C22×C11⋊C8C2312yes—
94C2×#4314—232no—
95C2×#4314—24no—
96C2×#4314—24no—
97C2×#4314—24no—
98C2×#4314—24no—
99C2×#4314—24no—
100C2×#4314D418yescomplemented
101C11×#106—22no—
102C11×#103—22no—
103C11×#102—22no—
104C11⋊#95—24no—
105C11⋊#95D412yes—
106C22⋊(C11⋊C8)D414yes—
107C8×Dic11—24no—
108#66874—24no—
109#66873—24no—
110#25776—111nomaximal, Sylow
111C24×C11—21no—
112C24×C11C2×D411yescharacteristic
113C23×D11—22no—
114C23×D11—44no—
115C23×D11—42no—
116C23×D11—44no—
117C23×D11—82no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—42no—
127C2×D4×C11—44no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—22no—
138C22×Dic11—44no—
139C22×Dic11—42no—
140C22×Dic11C2×D414yes—
141C2×D44—28no—
142C2×D44—22no—
143C2×D44—22no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44—44no—
148C2×D44—48no—
149C2×D44—44no—
150C2×D44—42no—
151C2×D44C2×D414yes—
152C2×Dic22—28no—
153C2×Dic22—22no—
154C2×Dic22—22no—
155C2×Dic22—22no—
156C2×Dic22—22no—
157C2×Dic22—22no—
158C2×Dic22—48no—
159C2×Dic22—44no—
160C2×Dic22—44no—
161C2×Dic22—42no—
162C2×Dic22C2×D414yes—
163C11×SD16—44no—
164C2×C8×C11—28no—
165C2×C8×C11—22no—
166C2×C8×C11C2×D414yes—
167C2×C8×C11C2×D412yes—
168C2×C8×C11C2×D412yes—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—42no—
174C11×C22⋊C4—42no—
175C11×C22⋊C4—42no—
176C22⋊Dic11—24no—
177C22⋊Dic11—48no—
178#4326—48no—
179#4323—48no—
180(C2×D11)⋊C4—48no—
181(C2×D11)⋊C4—84no—
182C4×Dic11—22no—
183C4×Dic11—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8C2×D414yes—
187#4314—216no—
188#4314—216no—
189C23×SD16—111no—
190C2×#495—112no—
191C2×#465D1111yescharacteristic, complemented
192C2×#451—111no—
193C2×#447—111no—
194#2436—111no—
195#2435—111no—
196#2015—112no—
197#2012—112no—
198#1968—112no—
199C8×C22⋊C4—111no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—41no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11#12712yes—
207C23×C11#13514yes—
208C23×C11C22×D411yescharacteristic
209C22×D11—24no—
210C22×D11—48no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—44no—
214C22×D11—44no—
215C22×D11—816no—
216C22×D11—84no—
217C22×D11—84no—
218Q8×C11—41no—
219Q8×C11—41no—
220Q8×C11—42no—
221D4×C11—41no—
222D4×C11—41no—
223D4×C11—42no—
224D4×C11—84no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11#12712yes—
236C2×C4×C11C22×D412yes—
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11H(5,𝔽2)12yes—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—48no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247D44—24no—
248D44—24no—
249D44—48no—
250D44—42no—
251D44—42no—
252Dic22—24no—
253Dic22—24no—
254Dic22—48no—
255Dic22—42no—
256Dic22—42no—
257C8×C11—22no—
258C8×C11#12014yes—
259C11⋊C8—24no—
260C23×Q8—111no—
261C23×D4—111no—
262C22×Q16—112no—
263C22×SD16—112no—
264C22×SD16—112no—
265C22×SD16—228no—
266C22×SD16—224no—
267C22×SD16C2×D1111yescharacteristic, complemented
268C22×D8—112no—
269C23×C8C2×D1111yescharacteristic
270C2×#124—112no—
271C2×#124—112no—
272C2×C22⋊Q8C2×D1111yescharacteristic
273C2×#121C2×D1111yescharacteristic
274#495—228no—
275#465—24no—
276#451—224no—
277#447—224no—
278C2×#106C2×D1111yescharacteristic, complemented
279C2×#103—112no—
280C2×#103C2×D1111yescharacteristic, complemented
281C2×#102—112no—
282C2×#102C2×D1111yescharacteristic, complemented
283C2×C22⋊C8—111no—
284C2×C4×C8—112no—
285#394—222no—
286#393—222no—
287#391—112no—
288#390—112no—
289#386—222no—
290#379—222no—
291C4×C22⋊C4—111no—
292#336—112no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—28no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—84no—
300C22×C11#49514yescomplemented
301C22×C11C2×#12711yescharacteristic
302C22×C11D4212yes—
303C22×C11C2×#13512yes—
304C22×C11#57712yes—
305C2×D11—44no—
306C2×D11—48no—
307C2×D11—816no—
308C2×D11—82no—
309C2×D11—82no—
310C2×D11—84no—
311C4×C11—22no—
312C4×C11—81no—
313C4×C11—81no—
314C4×C11—81no—
315C4×C11C2×#12011yescharacteristic
316C4×C11#53511yescharacteristic
317C4×C11D4212yes—
318Dic11—44no—
319Dic11—44no—
320C25—221no—
321C22×Q8—112no—
322C22×Q8—224no—
323C22×Q8—221no—
324C22×Q8—222no—
325C22×Q8—222no—
326C22×Q8—442no—
327C22×Q8C22×D1111yescharacteristic
328C22×D4—21no—
329C22×D4—112no—
330C22×D4—224no—
331C22×D4—222no—
332C22×D4—221no—
333C22×D4—222no—
334C22×D4—442no—
335C22×D4C22×D1111yescharacteristic
336C23×C4—221no—
337C23×C4C22×D1111yescharacteristic
338C2×Q16—224no—
339C2×Q16—224no—
340C2×Q16—442no—
341C2×SD16—24no—
342C2×SD16—22no—
343C2×SD16—118no—
344C2×SD16—224no—
345C2×SD16—224no—
346C2×SD16—2232no—
347C2×SD16—224no—
348C2×SD16—224no—
349C2×SD16—224no—
350C2×D8—224no—
351C2×D8—224no—
352C2×D8—442no—
353C22×C8—24no—
354C22×C8—112no—
355C22×C8C22⋊D1114yes—
356C22×C8C22×D1111yescharacteristic
357C22×C8C22×D1111yescharacteristic
358#124—224no—
359#124—224no—
360#124—442no—
361#124—442no—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364#121—22no—
365#121—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—112no—
372C2×C22⋊C4—224no—
373C2×C22⋊C4—224no—
374C2×C22⋊C4—224no—
375C2×C42—112no—
376#106—22no—
377#103—22no—
378#103—224no—
379#102—22no—
380#102—224no—
381C22⋊C8—114no—
382C4×C8—224no—
383#95—112no—
384#95—224no—
385C2×C11—24no—
386C2×C11—161no—
387C2×C11#243311yescharacteristic
388C2×C11C2×#49511yescharacteristic
389C2×C11#315411yescharacteristic
390C2×C11#328214yes—
391D11—84no—
392C24—21no—
393C24—222no—
394C24—444no—
395C24—442no—
396C24—444no—
397C24—882no—
398C24D4×D1111yescharacteristic
399C2×Q8—21no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—21no—
403C2×Q8—114no—
404C2×Q8—228no—
405C2×Q8—222no—
406C2×Q8—222no—
407C2×Q8—222no—
408C2×Q8—222no—
409C2×Q8—222no—
410C2×Q8—444no—
411C2×Q8—448no—
412C2×Q8—444no—
413C2×Q8—442no—
414C2×D4—21no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—44no—
419C2×D4—42no—
420C2×D4—114no—
421C2×D4—228no—
422C2×D4—222no—
423C2×D4—222no—
424C2×D4—222no—
425C2×D4—222no—
426C2×D4—222no—
427C2×D4—448no—
428C2×D4—444no—
429C2×D4—444no—
430C2×D4—442no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—114no—
437C22×C4—222no—
438C22×C4—444no—
439C22×C4—442no—
440C22×C4D4×D1111yescharacteristic
441C22×C4D4×D1112yes—
442C22×C4C2×C22⋊D1112yes—
443C22×C4C23×D1111yescharacteristic
444Q16—448no—
445SD16—44no—
446SD16—2216no—
447SD16—2216no—
448D8—448no—
449C2×C8—22no—
450C2×C8—28no—
451C2×C8—114no—
452C2×C8—222no—
453C2×C8—222no—
454C2×C8D4×D1114yes—
455C2×C8C2×C22⋊D1112yes—
456C2×C8C2×C22⋊D1112yes—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—42no—
462C22⋊C4—42no—
463C22⋊C4—42no—
464C22⋊C4—224no—
465C22⋊C4—448no—
466C22⋊C4—448no—
467C22⋊C4—884no—
468C42—222no—
469C42—222no—
470C11#2577611yescharacteristic, complemented, Sylow
471C23—22no—
472C23—22no—
473C23—42no—
474C23—42no—
475C23—41no—
476C23—42no—
477C23—224no—
478C23—448no—
479C23—444no—
480C23—444no—
481C23—442no—
482C23—442no—
483C23—8816no—
484C23—884no—
485C23—884no—
486C23#6696914yes—
487C23#6699312yes—
488C23C2×D4×D1111yescharacteristic
489Q8—41no—
490Q8—41no—
491Q8—42no—
492Q8—224no—
493Q8—224no—
494Q8—448no—
495Q8—442no—
496Q8—442no—
497D4—41no—
498D4—41no—
499D4—42no—
500D4—84no—
501D4—224no—
502D4—224no—
503D4—448no—
504D4—442no—
505D4—442no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—448no—
521C2×C4—442no—
522C2×C4—442no—
523C2×C4#6699312yes—
524C2×C4C2×D4×D1112yes—
525C2×C4C2×D4×D1111yescharacteristic
526C2×C4#6704212yes—
527C2×C4C22×C22⋊D1111yescharacteristic
528C8—22no—
529C8—224no—
530C8#6699014yes—
531C22—28no—
532C22—22no—
533C22—22no—
534C22—84no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—448no—
539C22—444no—
540C22—8816no—
541C22—884no—
542C22—882no—
543C22—882no—
544C22#1062278114yescomplemented
545C22#1062314012yes—
546C22C2×#6696912yes—
547C22#1062330112yes—
548C22C2×#6699311yescharacteristic
549C4—22no—
550C4—81no—
551C4—81no—
552C4—81no—
553C4—444no—
554C4—444no—
555C4#1062314012yes—
556C4C2×#6699011yescharacteristic
557C4#1062336111yescharacteristic
558C2—24no—
559C2—161no—
560C2—884no—
561C2#1307225411yescharacteristic
562C2C2×#1062278111yescharacteristic
563C2#1307909311yescharacteristic
564C2#1308032014yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#465C2
socleC23×C11C22×D4
prime radicalC2×#10622649C2
hypercenterC2×#465D11
hypocenterC11#25776
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C23×#4314C2semidirect
2. C2×#10622781C2semidirect
3. C2×#10622663C2semidirect
5. #13072275C2semidirect
6. #13072268C2semidirect
7. #13069711C2semidirect
8. #13069695C2semidirect
9. #13069468C2semidirect
10. C8×C22⋊Dic11C2semidirect
11. C2×C11×#465C2semidirect
14. C22×C11×SD16C22semidirect
19. C22×#4326C22semidirect
20. C2×#66989C22semidirect
27. C2×C11×#106C22semidirect
28. C2×C11×#103C22semidirect
29. C2×C11×#102C22semidirect
34. C2×C8×Dic11C22semidirect
39. #10622587C22semidirect
40. C2×#66874C22semidirect
44. #10622188C22semidirect
100. C2×#4314D4semidirect
191. C2×#465D11semidirect
267. C22×SD16C2×D11semidirect
278. C2×#106C2×D11semidirect
280. C2×#103C2×D11semidirect
282. C2×#102C2×D11semidirect
300. C22×C11#495semidirect
470. C11#25776semidirect
544. C22#10622781semidirect

Maximal subgroups

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

subgroupindex
C23×#43142
C2×#106227812
C2×#106226632
C2×#106226492
#130722752
#130722682
#130697112
#130696952
#130694682
C8×C22⋊Dic112
C2×C11×#4652
#2577611