Finite Group Databasebeta

← #14754550

Subgroups — #14754550

Order 2816.

1462 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623358C211yesmaximal, characteristic
2C2×#10622734C211yesmaximal, characteristic, complemented
3C2×#10622719C211yesmaximal, characteristic, complemented
4#13071208C211yesmaximal, characteristic
5#13068817C212yesmaximal, complemented
6#13068817C212yesmaximal, complemented
7#13068811C212yesmaximal, complemented
8#13068806C212yesmaximal, complemented
9#13068336C211yesmaximal, characteristic, complemented
10C2×#10622189C211yesmaximal, characteristic, complemented
11C2×C11×#408C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15#10623358—24no—
16#10623358—24no—
17C2×Q8×Dic11—21no—
18C2×D4×Dic11—22no—
19C2×D4×Dic11—21no—
20C2×#66979C2212yes—
21C2×#66979C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C22×C4⋊Dic11C2212yes—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C11×#408C418yescomplemented
27C2×C11×C22⋊C8C2212yes—
28C2×C11×C22⋊C8C2212yes—
29#10622843—21no—
30#10622834—21no—
31#10622833—22no—
32#10622825C2212yes—
33#10622825C2212yes—
34#10622734—24no—
35#10622719—24no—
36C2×#66882C2211yescharacteristic
37C2×#66882C2212yes—
38C2×#66882C2211yescharacteristic
39C2×#66881C2211yescharacteristic
40C2×#66881C2212yes—
41C2×#66881C2211yescharacteristic
42#10622189C2212yes—
43#10622189C2212yes—
44#10622189C2212yes—
45#10622189C2212yes—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41C2×C414yes—
51C2×C11×#41Q814yes—
52C22×Q8×C11D411yescharacteristic
53C22×D4×C11D412yes—
54C22×D4×C11D411yescharacteristic
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×Dic11—22no—
58C23×Dic11—21no—
59C23×Dic11—21no—
60C2×C11×M16—22no—
61C2×C11×M16—22no—
62C2×C11×M16C2×C414yescomplemented
63C22×C8×C11—22no—
64C22×C8×C11—22no—
65C22×C8×C11C2×C414yescomplemented
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2312yes—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—22no—
74Q8×Dic11—28no—
75D4×Dic11—216no—
76D4×Dic11—28no—
77#66979—22no—
78#66979—24no—
79#66979—24no—
80#66979—22no—
81#66979—22no—
82#66979D414yes—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—24no—
87C2×C4⋊Dic11—24no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11D414yes—
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2312yes—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4×Dic11—22no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C11×C22⋊C8C2×C418yescomplemented
102C11×C22⋊C8C2×C418yescomplemented
103C11⋊#95—22no—
104C11⋊#95—22no—
105#66882—24no—
106#66882—22no—
107#66882—22no—
108#66881—24no—
109#66881—22no—
110#66881—22no—
111#20849—111nomaximal, Sylow
112C24×C11C2×D412yes—
113C24×C11C2×D411yescharacteristic
114C11×#41—28no—
115C11×#41—28no—
116C11×#41—28no—
117C11×#41—28no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11C4⋊C414yes—
121C2×D4×C11—24no—
122C2×D4×C11—24no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11C4⋊C418yes—
126C2×D4×C11C4⋊C414yes—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11C22×C414yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×Q814yes—
138C22×C4×C11C2×Q812yes—
139C22×C4×C11#4112yes—
140C22×C4×C11#4112yes—
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—28no—
143C22×Dic11—24no—
144C22×Dic11—21no—
145C22×Dic11—22no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—22no—
150C22×Dic11—42no—
151C22×Dic11—81no—
152C22×Dic11—81no—
153C22×Dic11—81no—
154C22×Dic11—81no—
155C22×Dic11—82no—
156C22×Dic11—82no—
157C11×M16—28no—
158C2×C8×C11—28no—
159C2×C8×C11—21no—
160C2×C8×C11—22no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—22no—
165C2×C8×C11C22×C412yes—
166C2×C8×C11C22×C412yes—
167C2×C8×C11C22×C414yes—
168C22⋊Dic11—28no—
169C22⋊Dic11—24no—
170C22⋊Dic11—42no—
171C22⋊Dic11—82no—
172C22⋊Dic11—82no—
173C4⋊Dic11—28no—
174C4⋊Dic11—24no—
175C4⋊Dic11—22no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—22no—
183C4⋊Dic11—22no—
184C4⋊Dic11—42no—
185C4⋊Dic11C2×D412yes—
186C4⋊Dic11C2×D414yes—
187C4⋊Dic11C2×D412yes—
188C4×Dic11—28no—
189C4×Dic11—24no—
190C4×Dic11—42no—
191C2×#520—111no—
192C2×#428—111no—
193C2×#427—111no—
194C2×#408D1111yescharacteristic
195#2311—111no—
196#1854—112no—
197#1854—112no—
198#1853—112no—
199#1852—112no—
200#1736—111no—
201C2×#340—111no—
202C23×C11—21no—
203C23×C11—21no—
204C23×C11—21no—
205C23×C11—21no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11C2×C4⋊C414yes—
213C23×C11C2×C4⋊C412yes—
214C23×C11#12012yes—
215C23×C11#12312yes—
216C23×C11C22×D411yescharacteristic
217Q8×C11—28no—
218D4×C11—216no—
219D4×C11—28no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11C2×C4⋊C414yes—
227C2×C4×C11C2×C4⋊C412yes—
228C2×C4×C11C4×D414yes—
229C2×C4×C11C4×D414yes—
230C2×C4×C11#12012yes—
231C2×C4×C11C22⋊Q814yes—
232C2×C4×C11C22⋊Q814yes—
233C2×C4×C11#12312yes—
234C2×C4×C11C23×C411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×Q811yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×Dic11—22no—
241C2×Dic11—24no—
242C2×Dic11—22no—
243C2×Dic11—42no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—42no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—42no—
252C2×Dic11—41no—
253C2×Dic11—42no—
254C2×Dic11—41no—
255C2×Dic11—42no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—84no—
259C2×Dic11—88no—
260C2×Dic11—84no—
261C8×C11—22no—
262C8×C11—22no—
263C8×C11—24no—
264C22×#41C2×D1111yescharacteristic
265C22×M16C2×D1111yescharacteristic
266C23×C8C2×D1111yescharacteristic
267#520—224no—
268#520—224no—
269C2×C4×Q8—221no—
270C2×C4×D4—222no—
271C2×C4×D4—221no—
272C2×#117—111no—
273C2×#117—111no—
274C2×#117—112no—
275C22×C4⋊C4—111no—
276C22×C4⋊C4—111no—
277C22×C4⋊C4—112no—
278#428—224no—
279#427—224no—
280C2×#107—111no—
281C2×#107—112no—
282C2×#107—111no—
283C2×#106—111no—
284C2×#106—112no—
285C2×#106—111no—
286#408Dic1118yescomplemented
287C2×C22⋊C8C2×D1112yes—
288C2×C22⋊C8C2×D1112yes—
289#391—221no—
290#390—221no—
291#386—222no—
292#380—112no—
293#380—112no—
294#340—112no—
295#340—112no—
296#340—112no—
297#340—112no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—22no—
301C22×C11—22no—
302C22×C11—22no—
303C22×C11—22no—
304C22×C11—24no—
305C22×C11—24no—
306C22×C11—24no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11#38514yes—
312C22×C11C22×C4⋊C411yescharacteristic
313C22×C11C2×#12011yescharacteristic
314C22×C11C2×#12311yescharacteristic
315C22×C11#57611yescharacteristic
316C22×C11#57711yescharacteristic
317C22×C11#57711yescharacteristic
318C22×C11#57811yescharacteristic
319C4×C11—24no—
320C4×C11#38514yes—
321C4×C11C2×C4×D411yescharacteristic
322C4×C11C2×C4×D411yescharacteristic
323C4×C11C2×C22⋊Q811yescharacteristic
324C4×C11C2×C22⋊Q811yescharacteristic
325Dic11—44no—
326Dic11—42no—
327Dic11—42no—
328Dic11—82no—
329Dic11—81no—
330Dic11—81no—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41Dic2214yes—
336C2×#41C2×Dic1114yes—
337C22×Q8D4411yescharacteristic
338C22×D4D4412yes—
339C22×D4D4411yescharacteristic
340C23×C4—222no—
341C23×C4—221no—
342C23×C4—221no—
343C23×C4C22×D1112yes—
344C23×C4C22×D1111yescharacteristic
345C2×M16—22no—
346C2×M16—22no—
347C2×M16C2×Dic1114yescomplemented
348C22×C8—22no—
349C22×C8—22no—
350C22×C8C2×Dic1114yescomplemented
351C22×C8C22×D1111yescharacteristic
352C22×C8C22×D1111yescharacteristic
353C22×C8C22×D1112yes—
354C4×Q8—228no—
355C4×D4—2216no—
356C4×D4—228no—
357#117—114no—
358#117—224no—
359#117—224no—
360#117—222no—
361#117—222no—
362#117—222no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—112no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—112no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—224no—
371C2×C4⋊C4—224no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—222no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—221no—
378C2×C22⋊C4—222no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—222no—
383C2×C42—222no—
384C2×C42—221no—
385C2×C42—221no—
386#107—222no—
387#107—222no—
388#107—224no—
389#106—222no—
390#106—222no—
391#106—224no—
392C22⋊C8C2×Dic1118yescomplemented
393C22⋊C8C2×Dic1118yescomplemented
394#95—222no—
395#95—222no—
396C2×C11—24no—
397C2×C11—44no—
398C2×C11C2×#38511yescharacteristic
399C2×C11#291211yescharacteristic
400C2×C11#291311yescharacteristic
401C2×C11#301211yescharacteristic
402C2×C11#301311yescharacteristic
403C2×C11#309611yescharacteristic
404C2×C11#309711yescharacteristic
405C24C2×D4412yes—
406C24C2×D4411yescharacteristic
407#41—28no—
408#41—28no—
409#41—28no—
410#41—28no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8C4⋊Dic1114yes—
414C2×D4—24no—
415C2×D4—24no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4C4⋊Dic1118yes—
419C2×D4C4⋊Dic1114yes—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—221no—
425C22×C4—222no—
426C22×C4—221no—
427C22×C4—228no—
428C22×C4—224no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—222no—
432C22×C4—442no—
433C22×C4—881no—
434C22×C4—882no—
435C22×C4—881no—
436C22×C4—882no—
437C22×C4—881no—
438C22×C4—881no—
439C22×C4C2×Dic2214yes—
440C22×C4C2×Dic2212yes—
441C22×C4C2×D4412yes—
442C22×C4C2×D4411yescharacteristic
443C22×C4D4×D1112yes—
444C22×C4D4×D1112yes—
445C22×C4#434112yes—
446C22×C4#434112yes—
447C22×C4C22×Dic1114yes—
448C22×C4C22×Dic1112yes—
449C22×C4C23×D1111yescharacteristic
450M16—28no—
451C2×C8—28no—
452C2×C8—21no—
453C2×C8—22no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—22no—
458C2×C8C22×Dic1112yes—
459C2×C8C22×Dic1112yes—
460C2×C8C22×Dic1114yes—
461C4⋊C4—114no—
462C4⋊C4—112no—
463C4⋊C4—112no—
464C4⋊C4—228no—
465C4⋊C4—224no—
466C4⋊C4—221no—
467C4⋊C4—222no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—222no—
474C4⋊C4—222no—
475C4⋊C4—442no—
476C22⋊C4—228no—
477C22⋊C4—224no—
478C22⋊C4—442no—
479C22⋊C4—882no—
480C22⋊C4—882no—
481C42—228no—
482C42—224no—
483C42—442no—
484C11#2084911yescharacteristic, complemented, Sylow
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23#6693512yes—
496C23#6693912yes—
497C23C2×C4⋊Dic1114yes—
498C23C2×C4⋊Dic1112yes—
499C23C22×D4411yescharacteristic
500Q8—28no—
501D4—216no—
502D4—28no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—222no—
510C2×C4—224no—
511C2×C4—222no—
512C2×C4—442no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—442no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—441no—
520C2×C4—442no—
521C2×C4—441no—
522C2×C4—442no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—442no—
526C2×C4—441no—
527C2×C4—884no—
528C2×C4—888no—
529C2×C4—884no—
530C2×C4#6693114yes—
531C2×C4#6693114yes—
532C2×C4#6693512yes—
533C2×C4#6693912yes—
534C2×C4C2×C4⋊Dic1114yes—
535C2×C4C2×C4⋊Dic1112yes—
536C2×C4D4×Dic1114yes—
537C2×C4D4×Dic1114yes—
538C2×C4C22×Dic2211yescharacteristic
539C2×C4C2×D4×D1111yescharacteristic
540C2×C4C2×D4×D1111yescharacteristic
541C2×C4C2×#434111yescharacteristic
542C2×C4C2×#434111yescharacteristic
543C2×C4C23×Dic1111yescharacteristic
544C8—22no—
545C8—22no—
546C8—24no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—24no—
554C22—24no—
555C22—24no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22#1062256314yes—
561C22C2×#6693511yescharacteristic
562C22C2×#6693911yescharacteristic
563C22#1062328211yescharacteristic
564C22#1062328211yescharacteristic
565C22#1062328311yescharacteristic
566C22#1062328411yescharacteristic
567C22C22×C4⋊Dic1111yescharacteristic
568C4—24no—
569C4—444no—
570C4—442no—
571C4—442no—
572C4—882no—
573C4—881no—
574C4—881no—
575C4#1062256314yes—
576C4C2×#6693111yescharacteristic
577C4C2×#6693111yescharacteristic
578C4C2×D4×Dic1111yescharacteristic
579C4C2×D4×Dic1111yescharacteristic
580C2—24no—
581C2—44no—
582C2C2×#1062256311yescharacteristic
583C2#1307721111yescharacteristic
584C2#1307721611yescharacteristic
585C2#1307792311yescharacteristic
586C2#1307793411yescharacteristic
587C2#1307857511yescharacteristic
588C2#1307858611yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#408C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC2×#408D11
hypocenterC11#20849
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. C2×#10622734C2semidirect
3. C2×#10622719C2semidirect
5. #13068817C2semidirect
6. #13068817C2semidirect
7. #13068811C2semidirect
8. #13068806C2semidirect
9. #13068336C2semidirect
10. C2×#10622189C2semidirect
26. C11×#408C4semidirect
62. C2×C11×M16C2×C4semidirect
65. C22×C8×C11C2×C4semidirect
101. C11×C22⋊C8C2×C4semidirect
102. C11×C22⋊C8C2×C4semidirect
286. #408Dic11semidirect
347. C2×M16C2×Dic11semidirect
350. C22×C8C2×Dic11semidirect
392. C22⋊C8C2×Dic11semidirect
393. C22⋊C8C2×Dic11semidirect
484. C11#20849semidirect

Maximal subgroups

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

subgroupindex
C2×#106233582
C2×#106227342
C2×#106227192
#130712082
#130688172
#130688112
#130688062
#130683362
C2×#106221892
C2×C11×#4082
#2084911