Finite Group Databasebeta

← #14720040

Subgroups — #14720040

Order 2816.

1346 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623081C211yesmaximal, characteristic
2#13077653C212yesmaximal, complemented
3#13066974C214yesmaximal, complemented
4#13066969C212yesmaximal, complemented
5#13066941C212yesmaximal, complemented
6#13066937C211yesmaximal, characteristic, complemented
7D11×#323C212yesmaximal, complemented
8C11×#1466C211yesmaximal, characteristic, complemented
9C22×#4339C411yescharacteristic
10C23×D44C411yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C2×#66990C412yes—
13C2×#66983C411yescharacteristic
14C2×#66977C411yescharacteristic
15#10623081—24no—
16#10623081—22no—
17#10623081—22no—
18C2×#66947C412yes—
19C2×#66937C2212yes—
20C2×C22⋊C4×D11C2212yes—
21C2×#66928C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C11×#432C2212yescomplemented
24#10622538C2212yescomplemented
25#10622451—22no—
26#10622447—22no—
27#10622339C2214yescomplemented
28D11×C22⋊C8C2214yescomplemented
29#10622319—24no—
30C11×#323C2212yes—
31C11×#323C2212yescomplemented
32#10622163C2211yescharacteristic
33#10622163C2211yescharacteristic
34#10622163C2212yescomplemented
35#10622106C2214yescomplemented
36#10622106C2214yescomplemented
37C24×D11C2×C412yes—
38C22×D4×C11C2×C411yescharacteristic
39C23×C4×C11C2×C411yescharacteristic
40C23×C4×C11C2×C411yescharacteristic
41C22×C22⋊D11C2×C412yes—
42C22×C22⋊D11C2×C412yes—
43C2×#4339—22no—
44C2×#4339—21no—
45C2×#4339—21no—
46C2×#4339—44no—
47C22×D44—21no—
48C22×D44—22no—
49C22×D44—21no—
50C22×D44—44no—
51C22×D44C2×C411yescharacteristic
52C22×D44C2×C411yescharacteristic
53C22×D44C2×C412yes—
54C22×C4×D11C2×C412yes—
55C22×C4×D11C2312yes—
56C22×Dic22C2×C411yescharacteristic
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C2×C11×C4⋊C4C2×C411yescharacteristic
60C2×C11×C22⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4C2311yescharacteristic
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11C2×C412yes—
64#66990—24no—
65#66990—24no—
66#66983—22no—
67#66983—22no—
68C2×(C2×D11)⋊C4C2×C412yes—
69C2×(C2×D11)⋊C4C2×C412yes—
70C2×(C2×D11)⋊C4C2×C412yes—
71C2×(C2×D11)⋊C4C2312yes—
72C2×C4⋊Dic11C2×C411yescharacteristic
73#66977—22no—
74#66977—22no—
75C2×Dic11⋊C4C2×C412yes—
76C2×#4313—24no—
77C2×C8×D11—24no—
78#66947—24no—
79#66947—24no—
80#66937—24no—
81#66937—24no—
82C22⋊C4×D11—24no—
83C22⋊C4×D11—24no—
84#66928—22no—
85#66928—22no—
86C4×D44D414yes—
87C4×D44D412yes—
88C4×D44D412yes—
89C11×C4⋊C8—22no—
90C11×C22⋊C8C2314yes—
91C11×#97—22no—
92C22⋊(C11⋊C8)C2312yes—
93C22⋊(C11⋊C8)C2312yes—
94(C2×D11)⋊C8—24no—
95(C2×D11)⋊C8—24no—
96C4⋊(C11⋊C8)—22no—
97C4×C11⋊C8—22no—
98#17421—111nomaximal, Sylow
99C24×C11C22×C411yescharacteristic
100C24×C11C22×C411yescharacteristic
101C23×D11—24no—
102C23×D11—22no—
103C23×D11—22no—
104C23×D11—42no—
105C23×D11—44no—
106C23×D11—82no—
107C23×D11C22×C412yes—
108C23×D11C22×C412yes—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—41no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C2×C22⋊D11—24no—
124C2×C22⋊D11—22no—
125C2×C22⋊D11—22no—
126C2×C22⋊D11—44no—
127C2×C22⋊D11—82no—
128C22×Dic11C22×C412yes—
129C22×Dic11C22×C412yes—
130#4339—48no—
131#4339—44no—
132#4339—44no—
133C2×D44—24no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—42no—
139C2×D44—44no—
140C2×D44—48no—
141C2×D44—44no—
142C2×D44—44no—
143C2×D44C22⋊C412yes—
144C2×D44C22⋊C411yescharacteristic
145C2×D44C22⋊C411yescharacteristic
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—44no—
149C2×C4×D11—82no—
150C2×C4×D11C2×D414yes—
151C2×C4×D11C2×D414yes—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—42no—
155C2×C8×C11—24no—
156C11×C4⋊C4—22no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—22no—
159C42×C11C2×D412yes—
160C42×C11C2×D412yes—
161C22⋊Dic11—24no—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—24no—
165(C2×D11)⋊C4C22⋊C414yes—
166(C2×D11)⋊C4C22⋊C414yes—
167C4⋊Dic11C22⋊C412yes—
168C4⋊Dic11C22⋊C412yes—
169Dic11⋊C4—24no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172#4313—84no—
173C8×D11—84no—
174C2×#546—111no—
175#2974—112no—
176#1471—114no—
177#1469—112no—
178#1466D1111yescharacteristic, complemented
179#1462—112no—
180#1460—111no—
181C2×#323—112no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11#13112yes—
192C23×C11C23×C411yescharacteristic
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—24no—
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—22no—
199C22×D11—42no—
200C22×D11—44no—
201C22×D11—44no—
202C22×D11—44no—
203C22×D11—44no—
204C22×D11—42no—
205C22×D11—42no—
206C22×D11—82no—
207C22×D11—82no—
208C22×D11—88no—
209C22×D11—88no—
210C22×D11C2×C22⋊C412yes—
211C22×D11C2×C22⋊C412yes—
212D4×C11—44no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—22no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11C2×C22⋊C411yescharacteristic
226C2×C4×C11C2×C22⋊C412yes—
227C2×C4×C11C2×C22⋊C411yescharacteristic
228C2×C4×C11C22×D412yes—
229C22⋊D11—44no—
230C22⋊D11—44no—
231C22⋊D11—84no—
232C2×Dic11—22no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11C2×C22⋊C414yes—
236D44—24no—
237D44—22no—
238D44—42no—
239D44—44no—
240D44—44no—
241D44—42no—
242D44#10014yes—
243C4×D11—44no—
244C4×D11—44no—
245C4×D11—44no—
246C4×D11—44no—
247Dic22—42no—
248Dic22—42no—
249C8×C11—44no—
250C11⋊C8—42no—
251C11⋊C8—42no—
252C22×#41—111no—
253C23×D4—111no—
254#546—222no—
255#546—224no—
256#546—222no—
257C2×#124—111no—
258C2×#123—112no—
259C2×C22⋊Q8—111no—
260C2×#121—111no—
261C2×#121—112no—
262C2×#120—112no—
263C2×C4×D4—111no—
264C2×C4×D4C2×D1111yescharacteristic
265C22×C22⋊C4—112no—
266#436—222no—
267#435—224no—
268C8×D4—222no—
269#432C2×D1112yescomplemented
270#431—112no—
271#407—114no—
272C2×C22⋊C8—114no—
273#323—111no—
274#323—111no—
275#323—112no—
276#323—114no—
277#323—114no—
278#323C2×D1112yes—
279#323C2×D1112yescomplemented
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—22no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—41no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11—41no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11C22×C22⋊C411yescharacteristic
293C22×C11C2×#13111yescharacteristic
294C22×C11#56811yescharacteristic
295C2×D11—22no—
296C2×D11—22no—
297C2×D11—22no—
298C2×D11—22no—
299C2×D11—22no—
300C2×D11—44no—
301C2×D11—44no—
302C2×D11—42no—
303C2×D11—42no—
304C2×D11—42no—
305C2×D11—88no—
306C2×D11—88no—
307C2×D11—82no—
308C2×D11—82no—
309C2×D11C2×#10014yes—
310C4×C11—22no—
311C4×C11—22no—
312C4×C11—21no—
313C4×C11—41no—
314C4×C11—41no—
315C4×C11C2×#10012yes—
316Dic11—24no—
317Dic11—42no—
318C25—112no—
319C2×#41—221no—
320C2×#41—222no—
321C2×#41—221no—
322C2×#41—444no—
323C22×Q8—111no—
324C22×D4—112no—
325C22×D4—112no—
326C22×D4—111no—
327C22×D4—112no—
328C22×D4—111no—
329C22×D4—221no—
330C22×D4—222no—
331C22×D4—221no—
332C22×D4—444no—
333C22×D4C4×D1111yescharacteristic
334C23×C4—112no—
335C23×C4—112no—
336C23×C4C4×D1111yescharacteristic
337C23×C4C4×D1111yescharacteristic
338C2×M16—224no—
339C22×C8—224no—
340#124—222no—
341#124—222no—
342#123—224no—
343#123—224no—
344C22⋊Q8—222no—
345C22⋊Q8—222no—
346#121—224no—
347#121—224no—
348#121—222no—
349#121—222no—
350#120—224no—
351#120—224no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—112no—
355C4×D4—114no—
356C4×D4—112no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—112no—
359C2×C4⋊C4C4×D1111yescharacteristic
360C2×C22⋊C4—112no—
361C2×C22⋊C4—112no—
362C2×C22⋊C4—112no—
363C2×C22⋊C4—112no—
364C2×C22⋊C4—112no—
365C2×C22⋊C4—224no—
366C2×C22⋊C4—224no—
367C2×C22⋊C4C22×D1111yescharacteristic
368C2×C22⋊C4C22×D1111yescharacteristic
369C2×C42C22×D1111yescharacteristic
370C4⋊C8—22no—
371C4⋊C8—222no—
372C22⋊C8—112no—
373C22⋊C8—112no—
374C22⋊C8—224no—
375C22⋊C8—224no—
376C22⋊C8C22×D1114yes—
377#97—22no—
378C4×C8—222no—
379C2×C11—21no—
380C2×C11—21no—
381C2×C11—42no—
382C2×C11—81no—
383C2×C11#288011yescharacteristic
384C2×C11#288311yescharacteristic
385C2×C11C22×#10011yescharacteristic
386D11—24no—
387D11—42no—
388D11—82no—
389C24—112no—
390C24—112no—
391C24—222no—
392C24—222no—
393C24—224no—
394C24—442no—
395C24—444no—
396C24—882no—
397C24C2×C4×D1111yescharacteristic
398C24C2×C4×D1111yescharacteristic
399#41—444no—
400#41—448no—
401#41—444no—
402C2×Q8—221no—
403C2×Q8—221no—
404C2×Q8—442no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—41no—
408C2×D4—111no—
409C2×D4—112no—
410C2×D4—111no—
411C2×D4—224no—
412C2×D4—222no—
413C2×D4—222no—
414C2×D4—224no—
415C2×D4—222no—
416C2×D4—222no—
417C2×D4—221no—
418C2×D4—221no—
419C2×D4—442no—
420C2×D4—444no—
421C2×D4—448no—
422C2×D4—444no—
423C2×D4—444no—
424C2×D4—444no—
425C2×D4—882no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—112no—
433C22×C4—114no—
434C22×C4—114no—
435C22×C4—112no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—444no—
439C22×C4—882no—
440C22×C4C2×C4×D1111yescharacteristic
441C22×C4C2×C4×D1111yescharacteristic
442C22×C4C2×C4×D1111yescharacteristic
443C22×C4C2×C4×D1111yescharacteristic
444C22×C4C23×D1111yescharacteristic
445M16—884no—
446C2×C8—24no—
447C2×C8—222no—
448C2×C8—222no—
449C2×C8—884no—
450C4⋊C4—22no—
451C4⋊C4—112no—
452C4⋊C4—112no—
453C4⋊C4—224no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—114no—
457C22⋊C4—114no—
458C22⋊C4—224no—
459C22⋊C4—224no—
460C22⋊C4—224no—
461C22⋊C4—224no—
462C42D4×D1112yes—
463C42D4×D1112yes—
464C11#1742111yescharacteristic, complemented, Sylow
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—112no—
475C23—112no—
476C23—224no—
477C23—222no—
478C23—222no—
479C23—222no—
480C23—222no—
481C23—222no—
482C23—442no—
483C23—444no—
484C23—444no—
485C23—442no—
486C23—442no—
487C23—444no—
488C23—444no—
489C23—882no—
490C23—882no—
491C23—888no—
492C23—888no—
493C23#6696012yes—
494C23C22×C4×D1111yescharacteristic
495Q8—442no—
496Q8—442no—
497D4—44no—
498D4—114no—
499D4—224no—
500D4—222no—
501D4—442no—
502D4—444no—
503D4—444no—
504D4—444no—
505D4—444no—
506D4—442no—
507D4—884no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—114no—
521C2×C4—222no—
522C2×C4—444no—
523C2×C4—444no—
524C2×C4—444no—
525C2×C4—444no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4C22⋊C4×D1112yes—
529C2×C4C22⋊C4×D1111yescharacteristic
530C2×C4C22⋊C4×D1111yescharacteristic
531C2×C4C2×D4×D1112yes—
532C8—44no—
533C8—442no—
534C8—442no—
535C22—21no—
536C22—21no—
537C22—22no—
538C22—42no—
539C22—42no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—81no—
546C22—81no—
547C22—114no—
548C22—222no—
549C22—222no—
550C22—222no—
551C22—222no—
552C22—222no—
553C22—444no—
554C22—444no—
555C22—442no—
556C22—442no—
557C22—442no—
558C22—882no—
559C22—882no—
560C22—888no—
561C22—888no—
562C22C2×C22⋊C4×D1111yescharacteristic
563C22C2×#6696011yescharacteristic
564C22#1062327611yescharacteristic
565C4—22no—
566C4—22no—
567C4—21no—
568C4—41no—
569C4—41no—
570C4—224no—
571C4—442no—
572C4D11×#10012yes—
573C2—21no—
574C2—21no—
575C2—42no—
576C2—81no—
577C2—224no—
578C2—442no—
579C2—882no—
580C2#1307706611yescharacteristic
581C2#1307707511yescharacteristic
582C2C2×D11×#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1466C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623081C2
cosocleC22×C4×C11C24
hypercenter#1466D11
hypocenterC11#17421
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
2. #13077653C2semidirect
3. #13066974C2semidirect
4. #13066969C2semidirect
5. #13066941C2semidirect
6. #13066937C2semidirect
7. D11×#323C2semidirect
8. C11×#1466C2semidirect
23. C11×#432C22semidirect
24. #10622538C22semidirect
27. #10622339C22semidirect
28. D11×C22⋊C8C22semidirect
31. C11×#323C22semidirect
34. #10622163C22semidirect
35. #10622106C22semidirect
36. #10622106C22semidirect
178. #1466D11semidirect
269. #432C2×D11semidirect
279. #323C2×D11semidirect
464. C11#17421semidirect

Maximal subgroups

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

subgroupindex
C2×#106230812
#130776532
#130669742
#130669692
#130669412
#130669372
D11×#3232
C11×#14662
#1742111