Finite Group Databasebeta

← #14769485

Subgroups — #14769485

Order 2816.

1602 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
1C23×#4325C211yesmaximal, characteristic
2C2×#10622430C212yesmaximal, complemented
3Q8×C22⋊Dic11C211yesmaximal, characteristic, complemented
4#13071436C211yesmaximal, characteristic
5#13069494C212yesmaximal, complemented
6#13068969C212yesmaximal, complemented
7#13068947C212yesmaximal, complemented
8#13068643C211yesmaximal, characteristic, complemented
9#13068548C211yesmaximal, characteristic
10#13068395C211yesmaximal, characteristic, complemented
11C11×#1787C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C23×D44C2211yescharacteristic
14C2×Q8×Dic11C2212yescomplemented
15C22×#4325—28no—
16C22×#4325C418yescomplemented
17C22×#4325C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C2×#66946C2212yes—
23C2×C22⋊C4×D11—21no—
24C2×C11×#103C2212yescomplemented
25C2×C11×#103C2212yescomplemented
26C2×C11×C22⋊C8C2211yescharacteristic
27C11×#380C2211yescharacteristic
28#10622843—22no—
29#10622843C2212yescomplemented
30#10622825—21no—
31#10622825C2211yescharacteristic
32C4×C22⋊Dic11—21no—
33C4×C22⋊Dic11C2211yescharacteristic
34C2×#66885C2212yes—
35C2×#66885C2212yes—
36C2×#66879C2212yescomplemented
37#10622601C2212yes—
38C2×#66871C2212yescomplemented
39#10622568—21no—
40#10622430—28no—
41#10622278—22no—
42#10622188C2212yescomplemented
43#10622167C2212yescomplemented
44C24×D11—21no—
45C22×Q8×C11—21no—
46C22×Q8×C11—22no—
47C22×Q8×C11—24no—
48C22×Q8×C11—42no—
49C22×Q8×C11C2×C414yescomplemented
50C22×Q8×C11C2311yescharacteristic
51C22×Q8×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C22×D44—24no—
55C22×D44—21no—
56C22×D44—22no—
57C22×D44—42no—
58C22×D44C2×C414yes—
59C22×D44C2311yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—22no—
62C22×C8×C11C2312yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C22⋊C4—21no—
65C2×C22⋊Dic11—21no—
66C2×C22⋊Dic11D411yescharacteristic
67C2×C22⋊Dic11D411yescharacteristic
68Q8×Dic11—24no—
69Q8×Dic11—42no—
70C2×#4325—24no—
71C2×#4325—24no—
72C2×#4325—232no—
73C2×#4325—24no—
74C2×#4325C2×C414yes—
75C2×#4325C2×C414yes—
76C2×#4325C2×C414yescomplemented
77C2×#4325C2×C414yescomplemented
78C2×#4325D418yes—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—22no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11C2312yes—
84C2×C4×Dic11—22no—
85C2×C4×Dic11C2312yes—
86C22×C11⋊C8—24no—
87C22×C11⋊C8C2×C414yescomplemented
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90#66946—24no—
91#66946—42no—
92C22⋊C4×D11—44no—
93C11×#103—24no—
94C11×#103—42no—
95C11×C22⋊C8—22no—
96C11×#95—21no—
97C11⋊#95—21no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100C11⋊#95D412yes—
101#66885—24no—
102#66885—42no—
103#66879—24no—
104#66871—24no—
105#22437—111nomaximal, Sylow
106C24×C11C2×D411yescharacteristic
107C23×D11—21no—
108C23×D11—21no—
109C23×D11—24no—
110C23×D11—44no—
111C23×D11—42no—
112C23×D11—42no—
113C23×D11—82no—
114C2×Q8×C11—24no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11—28no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—44no—
122C2×Q8×C11—44no—
123C2×Q8×C11—48no—
124C2×Q8×C11C22×C412yes—
125C2×Q8×C11C22×C412yes—
126C2×Q8×C11C2×D414yes—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—44no—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11#4112yes—
137C22×C4×C11C2411yescharacteristic
138C22×Dic11—22no—
139C22×Dic11C2×D412yes—
140C22×Dic11C2×D412yes—
141C2×D44—28no—
142C2×D44—24no—
143C2×D44—22no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—44no—
149C2×D44—44no—
150C2×D44—48no—
151C2×D44C22×C412yes—
152C2×D44C22×C412yes—
153C2×D44C2×D414yes—
154C2×C4×D11—44no—
155C2×C4×D11—44no—
156C2×C4×D11—82no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C22⋊C4—42no—
163C22⋊Dic11—22no—
164C22⋊Dic11—22no—
165C22⋊Dic11—42no—
166#4325—28no—
167#4325—28no—
168#4325—28no—
169#4325C22⋊C4116yescomplemented
170(C2×D11)⋊C4—44no—
171(C2×D11)⋊C4—44no—
172(C2×D11)⋊C4—82no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11—44no—
176C4×Dic11—22no—
177C4×Dic11—22no—
178C4×Dic11—44no—
179C2×C11⋊C8—28no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8C22×C412yes—
182C2×C11⋊C8C22×C412yes—
183C2×C11⋊C8C2×D414yes—
184C23×SD16—111no—
185C2×#440—112no—
186Q8×C22⋊C4—111no—
187D4×C22⋊C4—111no—
188#1973—112no—
189#1880—112no—
190#1877—112no—
191#1808—111no—
192#1787D1111yescharacteristic, complemented
193#1786—111no—
194#1752—111no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11C4×D412yes—
198C23×C11AGL(1,ℤ/8)12yes—
199C23×C11#13712yes—
200C23×C11C22×D411yescharacteristic
201C22×D11—22no—
202C22×D11—24no—
203C22×D11—22no—
204C22×D11—48no—
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—42no—
212C22×D11—48no—
213C22×D11—84no—
214C22×D11—88no—
215C22×D11—88no—
216Q8×C11—22no—
217Q8×C11—24no—
218Q8×C11—22no—
219Q8×C11—22no—
220Q8×C11—48no—
221Q8×C11—42no—
222Q8×C11C2×C22⋊C414yescomplemented
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—48no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11C4×D412yes—
236C2×C4×C11C23×C411yescharacteristic
237C2×C4×C11C22×D412yes—
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11H(5,𝔽2)12yes—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249D44—22no—
250D44—22no—
251D44—22no—
252D44—24no—
253D44—48no—
254D44—42no—
255D44C2×C22⋊C414yes—
256C4×D11—88no—
257C8×C11—42no—
258C11⋊C8—22no—
259C11⋊C8C2×C22⋊C414yescomplemented
260C23×Q8C2×D1111yescharacteristic
261C23×D4—111no—
262C22×SD16—111no—
263C22×SD16—111no—
264C22×SD16—111no—
265C22×SD16—111no—
266C22×SD16—118no—
267C22×SD16—228no—
268C23×C8—111no—
269C2×C4×Q8—112no—
270C2×C4×D4—112no—
271C22×C22⋊C4—221no—
272#440—228no—
273C2×#107—112no—
274C2×#103C2×D1112yescomplemented
275C2×#103C2×D1112yescomplemented
276C2×#102—112no—
277C2×#102—112no—
278C2×C22⋊C8C2×D1111yescharacteristic
279C2×#97—112no—
280#391—112no—
281#391—222no—
282#390—112no—
283#386—222no—
284#380—111no—
285#380—221no—
286#380C2×D1111yescharacteristic
287#379—221no—
288C4×C22⋊C4—111no—
289C4×C22⋊C4—221no—
290#340—112no—
291#336—112no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11#44014yescomplemented
297C22×C11C2×C4×D411yescharacteristic
298C22×C11D4212yes—
299C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C11C2×#13711yescharacteristic
301C22×C11#57712yes—
302C2×D11—24no—
303C2×D11—42no—
304C2×D11—42no—
305C2×D11—44no—
306C2×D11—44no—
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—42no—
310C2×D11—816no—
311C2×D11—82no—
312C2×D11—82no—
313C4×C11—22no—
314C4×C11—24no—
315C4×C11—42no—
316C4×C11—82no—
317C4×C11C22×C22⋊C411yescharacteristic
318C4×C11#51811yescharacteristic
319C4×C11#54612yes—
320Dic11—42no—
321Dic11—42no—
322Dic11—82no—
323C25—221no—
324C22×Q8—21no—
325C22×Q8—22no—
326C22×Q8—24no—
327C22×Q8—42no—
328C22×Q8C4×D1114yescomplemented
329C22×Q8C22×D1111yescharacteristic
330C22×Q8C22×D1111yescharacteristic
331C22×D4—114no—
332C22×D4—111no—
333C22×D4—111no—
334C22×D4—224no—
335C22×D4—221no—
336C22×D4—222no—
337C22×D4—442no—
338C23×C4—21no—
339C23×C4—222no—
340C23×C4C22×D1111yescharacteristic
341C2×SD16—114no—
342C2×SD16—118no—
343C2×SD16—114no—
344C2×SD16—114no—
345C2×SD16—114no—
346C2×SD16—224no—
347C2×SD16—2232no—
348C2×SD16—224no—
349C2×SD16—224no—
350C22×C8—111no—
351C22×C8—114no—
352C22×C8—111no—
353C22×C8—224no—
354C22×C8C22×D1112yes—
355C4×Q8—224no—
356C4×Q8—442no—
357C4×D4—224no—
358C4×D4—442no—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4C22×D1112yes—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—111no—
364C2×C22⋊C4—111no—
365C2×C22⋊C4—222no—
366C2×C22⋊C4—222no—
367C2×C22⋊C4—221no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4—444no—
370C2×C42—112no—
371C2×C42—222no—
372#107—224no—
373#103—24no—
374#103—42no—
375#102—224no—
376#102—442no—
377C22⋊C8—22no—
378#97—224no—
379#95—21no—
380#95—112no—
381#95—222no—
382#95—222no—
383#95—221no—
384C2×C11—24no—
385C2×C11D4×C22⋊C411yescharacteristic
386C2×C11C2×#44011yescharacteristic
387C2×C11#294911yescharacteristic
388C2×C11#326512yes—
389C2×C11#326612yes—
390D11—44no—
391D11—82no—
392C24—221no—
393C24—221no—
394C24—224no—
395C24—444no—
396C24—442no—
397C24—442no—
398C24—882no—
399C24D4×D1111yescharacteristic
400C2×Q8—24no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—22no—
404C2×Q8—28no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—44no—
408C2×Q8—44no—
409C2×Q8—48no—
410C2×Q8C2×C4×D1112yes—
411C2×Q8C2×C4×D1112yes—
412C2×Q8D4×D1114yes—
413C2×D4—112no—
414C2×D4—112no—
415C2×D4—114no—
416C2×D4—228no—
417C2×D4—224no—
418C2×D4—222no—
419C2×D4—221no—
420C2×D4—221no—
421C2×D4—222no—
422C2×D4—222no—
423C2×D4—444no—
424C2×D4—448no—
425C2×D4—444no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—44no—
433C22×C4—112no—
434C22×C4—112no—
435C22×C4—222no—
436C22×C4—444no—
437C22×C4—444no—
438C22×C4—882no—
439C22×C4C2×C4×D1112yes—
440C22×C4D4×D1111yescharacteristic
441C22×C4#434112yes—
442C22×C4C23×D1111yescharacteristic
443SD16—1116no—
444SD16—228no—
445SD16—228no—
446SD16—228no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—112no—
451C2×C8—114no—
452C2×C8—112no—
453C2×C8—228no—
454C2×C8—222no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—222no—
458C4⋊C4—222no—
459C4⋊C4—444no—
460C22⋊C4—42no—
461C22⋊C4—222no—
462C22⋊C4—222no—
463C22⋊C4—444no—
464C22⋊C4—444no—
465C22⋊C4—442no—
466C22⋊C4—882no—
467C42—222no—
468C42—222no—
469C42—444no—
470C11#2243711yescharacteristic, complemented, Sylow
471C23—22no—
472C23—22no—
473C23—222no—
474C23—224no—
475C23—222no—
476C23—448no—
477C23—441no—
478C23—441no—
479C23—442no—
480C23—441no—
481C23—441no—
482C23—442no—
483C23—442no—
484C23—448no—
485C23—884no—
486C23—888no—
487C23—888no—
488C23(C22⋊D11)⋊C412yes—
489C23#6696712yes—
490C23#6697112yes—
491C23C2×D4×D1111yescharacteristic
492Q8—22no—
493Q8—24no—
494Q8—22no—
495Q8—22no—
496Q8—48no—
497Q8—42no—
498Q8C22⋊C4×D1114yescomplemented
499D4—114no—
500D4—222no—
501D4—222no—
502D4—222no—
503D4—224no—
504D4—448no—
505D4—442no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—48no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—888no—
528C2×C4(C22⋊D11)⋊C412yes—
529C2×C4C22×C4×D1111yescharacteristic
530C2×C4C2×D4×D1112yes—
531C2×C4C2×#434111yescharacteristic
532C2×C4#6703712yes—
533C8—42no—
534C8—114no—
535C8—222no—
536C22—24no—
537C22—24no—
538C22—22no—
539C22—22no—
540C22—224no—
541C22—444no—
542C22—444no—
543C22—442no—
544C22—442no—
545C22—442no—
546C22—442no—
547C22—442no—
548C22—8816no—
549C22—882no—
550C22—882no—
551C22#1062243014yescomplemented
552C22C2×(C22⋊D11)⋊C411yescharacteristic
553C22#1062312112yes—
554C22C2×#6696711yescharacteristic
555C22C2×#6697111yescharacteristic
556C22#1062330912yes—
557C4—22no—
558C4—24no—
559C4—42no—
560C4—82no—
561C4—442no—
562C4—442no—
563C4—882no—
564C4C2×C22⋊C4×D1111yescharacteristic
565C4#1062301711yescharacteristic
566C4#1062312212yes—
567C2—24no—
568C2—444no—
569C2—882no—
570C2#1307143211yescharacteristic
571C2C2×#1062243011yescharacteristic
572C2#1307747111yescharacteristic
573C2#1308010412yes—
574C2#1308011912yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1787C2
socleC23×C11C22×D4
prime radicalC23×D44C22
cosocleC22×C4×C11C24
hypercenter#1787D11
hypocenterC11#22437
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
2. C2×#10622430C2semidirect
3. Q8×C22⋊Dic11C2semidirect
5. #13069494C2semidirect
6. #13068969C2semidirect
7. #13068947C2semidirect
8. #13068643C2semidirect
10. #13068395C2semidirect
11. C11×#1787C2semidirect
14. C2×Q8×Dic11C22semidirect
16. C22×#4325C4semidirect
24. C2×C11×#103C22semidirect
25. C2×C11×#103C22semidirect
29. #10622843C22semidirect
36. C2×#66879C22semidirect
38. C2×#66871C22semidirect
42. #10622188C22semidirect
43. #10622167C22semidirect
49. C22×Q8×C11C2×C4semidirect
76. C2×#4325C2×C4semidirect
77. C2×#4325C2×C4semidirect
87. C22×C11⋊C8C2×C4semidirect
169. #4325C22⋊C4semidirect
192. #1787D11semidirect
222. Q8×C11C2×C22⋊C4semidirect
259. C11⋊C8C2×C22⋊C4semidirect
274. C2×#103C2×D11semidirect
275. C2×#103C2×D11semidirect
296. C22×C11#440semidirect
328. C22×Q8C4×D11semidirect
470. C11#22437semidirect
498. Q8C22⋊C4×D11semidirect
551. C22#10622430semidirect

Maximal subgroups

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

subgroupindex
C23×#43252
C2×#106224302
Q8×C22⋊Dic112
#130714362
#130694942
#130689692
#130689472
#130686432
#130685482
#130683952
C11×#17872
#2243711