Finite Group Databasebeta

← #14763591

Subgroups — #14763591

Order 2816.

1254 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623148C211yesmaximal, characteristic
2#13071229C211yesmaximal, characteristic, complemented
3#13071211C211yesmaximal, characteristic, complemented
4#13069601C211yesmaximal, characteristic, complemented
5#13069600C211yesmaximal, characteristic, complemented
6#13069453C211yesmaximal, characteristic, complemented
7#13069066C214yesmaximal, complemented
8#13068602C214yesmaximal, complemented
9C11×#1964C211yesmaximal, characteristic, complemented
10C2×C11×#121C2211yescharacteristic
11C2×#66992C412yescomplemented
12C2×#66990C2212yes—
13C2×D4×Dic11C2212yes—
14C22×(C2×D11)⋊C4C2211yescharacteristic
15C2×#66977C2211yescharacteristic
16#10623148—22no—
17#10623148—22no—
18#10623148—22no—
19#10623148—22no—
20C2×#66951C412yescomplemented
21C2×#66939C412yescomplemented
22C2×#66938C412yescomplemented
23C2×C22⋊C4×D11C2212yes—
24C2×C11×#99C2214yes—
25C11×#380C2211yescharacteristic
26C4×C11×C22⋊C4C2211yescharacteristic
27C2×#66898C2214yes—
28#10622825C2211yescharacteristic
29C4×C22⋊Dic11C2211yescharacteristic
30#10622602—22no—
31#10622568C2212yes—
32#10622555C2212yes—
33#10622555C2212yes—
34#10622553—22no—
35#10622282—22no—
36#10622281—22no—
37#10622165C2214yes—
38#10622165C2214yes—
39C24×D11C2311yescharacteristic
40C22×D4×C11C2×C411yescharacteristic, complemented
41C22×D4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C22×C22⋊D11C2×C412yes—
44C22×C22⋊D11C2×C412yes—
45C23×Dic11C2×C412yescomplemented
46C23×Dic11C2311yescharacteristic
47C22×C4×D11—22no—
48C22×Dic22C2×C411yescharacteristic, complemented
49C11×#121—21no—
50C11×#121—21no—
51C11×#121—21no—
52C11×#121—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
55C2×C11×C22⋊C4C2×C412yescomplemented
56C2×C11×C22⋊C4C2312yes—
57C2×C11×C22⋊C4C2312yes—
58C2×C42×C11—21no—
59C2×C22⋊Dic11C2×C412yescomplemented
60C2×C22⋊Dic11C2312yes—
61C2×C22⋊Dic11C2312yes—
62C2×C22⋊Dic11C2312yes—
63#66992—24no—
64#66992—24no—
65#66990—24no—
66#66990—24no—
67D4×Dic11—24no—
68D4×Dic11—24no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4C2×C412yes—
73C2×(C2×D11)⋊C4C2×C412yes—
74C2×(C2×D11)⋊C4C2×C412yes—
75C2×(C2×D11)⋊C4C2×C412yes—
76C2×(C2×D11)⋊C4D412yes—
77C2×(C2×D11)⋊C4D412yes—
78C2×(C2×D11)⋊C4D412yes—
79C2×(C2×D11)⋊C4D412yes—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2×C411yescharacteristic, complemented
82C2×C4⋊Dic11C2×C412yescomplemented
83#66977—21no—
84#66977—21no—
85#66977—21no—
86#66977—21no—
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4C2×C412yescomplemented
90C2×C4×Dic11—21no—
91C2×C4×Dic11C2×C412yescomplemented
92#66951—24no—
93#66951—24no—
94#66939—24no—
95#66939—24no—
96#66938—24no—
97#66938—24no—
98C22⋊C4×D11—44no—
99C11×#99—44no—
100C11×#95—21no—
101C11×#95—21no—
102#66898—44no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—22no—
106C11⋊#95—22no—
107#21876—111nomaximal, Sylow
108C24×C11C22×C412yes—
109C24×C11C2411yescharacteristic
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—81no—
113C23×D11—81no—
114C23×D11C22×C412yes—
115C23×D11C2×D412yes—
116C23×D11C2×D412yes—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—24no—
120C2×D4×C11—24no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—81no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—81no—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C22×C411yescharacteristic
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C2×C22⋊D11—24no—
135C2×C22⋊D11—24no—
136C2×C22⋊D11—82no—
137C2×C22⋊D11—82no—
138C22×Dic11—24no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—81no—
142C22×Dic11—82no—
143C22×Dic11C22×C412yes—
144C22×Dic11C22×C412yes—
145C22×Dic11C22×C412yes—
146C22×Dic11C2×D412yes—
147C22×Dic11C2×D412yes—
148C2×C4×D11—44no—
149C2×C4×D11—82no—
150C2×C4×D11—82no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—81no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—81no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—22no—
162C42×C11—81no—
163C22⋊Dic11—24no—
164C22⋊Dic11—22no—
165C22⋊Dic11—22no—
166C22⋊Dic11—22no—
167C22⋊Dic11—24no—
168C22⋊Dic11—22no—
169(C2×D11)⋊C4—24no—
170(C2×D11)⋊C4—24no—
171(C2×D11)⋊C4—44no—
172(C2×D11)⋊C4—82no—
173(C2×D11)⋊C4—82no—
174(C2×D11)⋊C4C22⋊C414yes—
175(C2×D11)⋊C4C22⋊C414yes—
176(C2×D11)⋊C4C22⋊C414yes—
177(C2×D11)⋊C4C22⋊C414yes—
178C4⋊Dic11—24no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—81no—
182Dic11⋊C4—22no—
183Dic11⋊C4—22no—
184Dic11⋊C4—82no—
185Dic11⋊C4—82no—
186C4×Dic11—24no—
187C4×Dic11—81no—
188C2×#538—111no—
189#2315—111no—
190#2312—111no—
191#1996—111no—
192#1996—111no—
193#1964—111no—
194#1964D1111yescharacteristic, complemented
195#1898—114no—
196#1799—114no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11C23×C411yescharacteristic
204C23×C11C22×D411yescharacteristic
205C23×C11C22×D411yescharacteristic
206C23×C11H(5,𝔽2)12yes—
207C23×C112−1+412yes—
208C22×D11—22no—
209C22×D11—22no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—84no—
219C22×D11—84no—
220C22×D11C2×C22⋊C414yes—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—44no—
224D4×C11—81no—
225D4×C11—81no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11C2×C22⋊C411yescharacteristic
241C2×C4×C11C2×C22⋊C411yescharacteristic
242C2×C4×C11C2×C22⋊C411yescharacteristic
243C2×C4×C11C2×C22⋊C411yescharacteristic
244C22⋊D11—84no—
245C22⋊D11—84no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—84no—
260C2×Dic11C2×C22⋊C414yes—
261C4×D11—88no—
262Dic22—81no—
263Dic22—81no—
264#538—222no—
265#538—222no—
266#538—222no—
267#538—222no—
268C2×#126—112no—
269C2×#124—112no—
270C2×#123—112no—
271C2×C22⋊Q8—111no—
272C2×#121—112no—
273C2×#121C2×D1111yescharacteristic
274C2×#120—112no—
275C2×C4×D4—112no—
276C22×C22⋊C4—111no—
277C22×C22⋊C4—112no—
278C2×#99—114no—
279C2×#99C2×D1114yes—
280#388—222no—
281#388—222no—
282#385—222no—
283#385—222no—
284#380—111no—
285#380—112no—
286#380—112no—
287#380C2×D1111yescharacteristic
288#379—112no—
289C4×C22⋊C4—111no—
290C4×C22⋊C4C2×D1111yescharacteristic
291#342—114no—
292#342—114no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—21no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—84no—
305C22×C11C22×C22⋊C411yescharacteristic
306C22×C11#52012yes—
307C22×C11#53511yescharacteristic
308C22×C11#53611yescharacteristic
309C22×C11#53712yes—
310C2×D11—24no—
311C2×D11—24no—
312C2×D11—24no—
313C2×D11—44no—
314C2×D11—44no—
315C2×D11—84no—
316C2×D11—84no—
317C4×C11—21no—
318C4×C11—21no—
319C4×C11—21no—
320C4×C11—21no—
321C4×C11—42no—
322C4×C11—82no—
323C4×C11—82no—
324Dic11—24no—
325Dic11—42no—
326Dic11—42no—
327Dic11—82no—
328Dic11—82no—
329C25—111no—
330C22×Q8—111no—
331C22×D4—112no—
332C22×D4—112no—
333C22×D4C4×D1111yescharacteristic, complemented
334C22×D4C22×D1112yes—
335C23×C4—111no—
336C23×C4—112no—
337C23×C4—222no—
338C23×C4C22×D1111yescharacteristic
339#126—224no—
340#126—224no—
341#124—224no—
342#124—224no—
343#123—224no—
344#123—224no—
345C22⋊Q8—221no—
346C22⋊Q8—221no—
347C22⋊Q8—221no—
348C22⋊Q8—221no—
349#121—21no—
350#121—21no—
351#121—21no—
352#121—21no—
353#121—224no—
354#121—224no—
355#120—224no—
356#120—224no—
357C4×D4—224no—
358C4×D4—224no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4C4×D1111yescharacteristic, complemented
367C2×C22⋊C4—112no—
368C2×C22⋊C4—112no—
369C2×C22⋊C4—112no—
370C2×C22⋊C4—112no—
371C2×C22⋊C4—112no—
372C2×C22⋊C4—112no—
373C2×C22⋊C4—112no—
374C2×C22⋊C4—112no—
375C2×C22⋊C4—112no—
376C2×C22⋊C4—112no—
377C2×C22⋊C4—112no—
378C2×C22⋊C4—112no—
379C2×C22⋊C4—222no—
380C2×C22⋊C4—222no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—444no—
383C2×C22⋊C4C4×D1112yescomplemented
384C2×C22⋊C4C22×D1112yes—
385C2×C22⋊C4C22×D1112yes—
386C2×C42—21no—
387C2×C42—112no—
388C2×C42—221no—
389#99—44no—
390#99—444no—
391#95—21no—
392#95—21no—
393#95—222no—
394#95—222no—
395#95—221no—
396#95—221no—
397C2×C11—21no—
398C2×C11—22no—
399C2×C11—21no—
400C2×C11—22no—
401C2×C11—82no—
402C2×C11#231111yescharacteristic
403C2×C11#288311yescharacteristic
404C2×C11#288311yescharacteristic
405D11—44no—
406C24—112no—
407C24—112no—
408C24—112no—
409C24—222no—
410C24—222no—
411C24—881no—
412C24—881no—
413C24C2×C4×D1112yes—
414C24C23×D1111yescharacteristic
415C2×Q8—221no—
416C2×Q8—221no—
417C2×Q8—881no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—24no—
421C2×D4—24no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—81no—
425C2×D4—224no—
426C2×D4—224no—
427C2×D4—882no—
428C2×D4—882no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—81no—
432C22×C4—112no—
433C22×C4—112no—
434C22×C4—112no—
435C22×C4—112no—
436C22×C4—112no—
437C22×C4—224no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—444no—
441C22×C4—882no—
442C22×C4—882no—
443C22×C4—881no—
444C22×C4—882no—
445C22×C4C2×C4×D1112yes—
446C22×C4C2×C4×D1111yescharacteristic
447C22×C4C2×C4×D1111yescharacteristic
448C22×C4D4×D1111yescharacteristic
449C22×C4D4×D1111yescharacteristic
450C22×C4D4×D1111yescharacteristic
451C22×C4D4×D1111yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—81no—
455C4⋊C4—224no—
456C4⋊C4—222no—
457C4⋊C4—222no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—882no—
461C4⋊C4—882no—
462C4⋊C4—881no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—24no—
467C22⋊C4—22no—
468C22⋊C4—114no—
469C22⋊C4—114no—
470C22⋊C4—114no—
471C22⋊C4—114no—
472C22⋊C4—224no—
473C22⋊C4—224no—
474C22⋊C4—224no—
475C22⋊C4—222no—
476C22⋊C4—222no—
477C22⋊C4—222no—
478C22⋊C4—224no—
479C22⋊C4—222no—
480C22⋊C4—444no—
481C22⋊C4—882no—
482C22⋊C4—882no—
483C42—81no—
484C42—224no—
485C42—881no—
486C11#2187611yescharacteristic, complemented, Sylow
487C23—22no—
488C23—24no—
489C23—41no—
490C23—41no—
491C23—42no—
492C23—42no—
493C23—114no—
494C23—222no—
495C23—222no—
496C23—224no—
497C23—224no—
498C23—442no—
499C23—442no—
500C23—442no—
501C23—442no—
502C23—442no—
503C23—442no—
504C23—884no—
505C23—884no—
506C23C22×C4×D1111yescharacteristic
507C23C2×D4×D1111yescharacteristic
508C23C2×D4×D1111yescharacteristic
509C23#6703712yes—
510C23#6704312yes—
511Q8—881no—
512Q8—881no—
513D4—42no—
514D4—44no—
515D4—42no—
516D4—81no—
517D4—81no—
518D4—884no—
519D4—884no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—114no—
535C2×C4—222no—
536C2×C4—222no—
537C2×C4—442no—
538C2×C4—442no—
539C2×C4—442no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4—442no—
548C2×C4—888no—
549C2×C4—884no—
550C2×C4C22⋊C4×D1111yescharacteristic
551C2×C4C22⋊C4×D1111yescharacteristic
552C2×C4C22⋊C4×D1111yescharacteristic
553C2×C4C22⋊C4×D1111yescharacteristic
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—84no—
566C22—224no—
567C22—224no—
568C22—224no—
569C22—444no—
570C22—444no—
571C22—884no—
572C22—884no—
573C22C2×C22⋊C4×D1111yescharacteristic
574C22#1062307712yes—
575C22#1062313912yes—
576C22#1062320611yescharacteristic
577C22#1062324611yescharacteristic
578C4—21no—
579C4—21no—
580C4—21no—
581C4—21no—
582C4—42no—
583C4—82no—
584C4—82no—
585C4—224no—
586C4—442no—
587C4—442no—
588C4—882no—
589C4—882no—
590C2—21no—
591C2—22no—
592C2—22no—
593C2—21no—
594C2—82no—
595C2—444no—
596C2#1307120611yescharacteristic
597C2#1307707411yescharacteristic
598C2#1307707511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#1964C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623148C2
cosocleC24×C11C24
hypercenter#1964D11
hypocenterC11#21876
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #13071229C2semidirect
3. #13071211C2semidirect
4. #13069601C2semidirect
5. #13069600C2semidirect
6. #13069453C2semidirect
7. #13069066C2semidirect
8. #13068602C2semidirect
9. C11×#1964C2semidirect
11. C2×#66992C4semidirect
20. C2×#66951C4semidirect
21. C2×#66939C4semidirect
22. C2×#66938C4semidirect
40. C22×D4×C11C2×C4semidirect
45. C23×Dic11C2×C4semidirect
48. C22×Dic22C2×C4semidirect
54. C2×C11×C4⋊C4C2×C4semidirect
55. C2×C11×C22⋊C4C2×C4semidirect
59. C2×C22⋊Dic11C2×C4semidirect
81. C2×C4⋊Dic11C2×C4semidirect
82. C2×C4⋊Dic11C2×C4semidirect
89. C2×Dic11⋊C4C2×C4semidirect
91. C2×C4×Dic11C2×C4semidirect
194. #1964D11semidirect
333. C22×D4C4×D11semidirect
366. C2×C4⋊C4C4×D11semidirect
383. C2×C22⋊C4C4×D11semidirect
486. C11#21876semidirect

Maximal subgroups

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

subgroupindex
C2×#106231482
#130712292
#130712112
#130696012
#130696002
#130694532
#130690662
#130686022
C11×#19642
#2187611