Finite Group Databasebeta

← #14754552

Subgroups — #14754552

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×#10623035C211yesmaximal, characteristic
2C2×#10622577C211yesmaximal, characteristic, complemented
3C2×#10622719C211yesmaximal, characteristic, complemented
4C2×#10622723C211yesmaximal, characteristic
5#13071209C211yesmaximal, characteristic
6#13068818C212yesmaximal, complemented
7#13068816C212yesmaximal, complemented
8#13068810C212yesmaximal, complemented
9#13068805C212yesmaximal, complemented
10#13068335C211yesmaximal, characteristic, complemented
11C2×C11×#340C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C2×C4×C22⋊D11—22no—
17C2×#66979C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20#10623035—24no—
21#10623035—24no—
22C2×#66946—21no—
23C2×#66945C2212yes—
24C2×C4⋊C4×D11C2212yes—
25C2×#66940—21no—
26#10622826—22no—
27#10622723C418yescomplemented
28C2×(C2×D11)⋊C8C2212yes—
29C2×(C2×D11)⋊C8C2212yes—
30#10622719—24no—
31C2×#66882C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35#10622601—21no—
36#10622600C2212yes—
37#10622600C2212yes—
38#10622587—21no—
39#10622577—24no—
40C2×#66872C2212yes—
41C2×#66871C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11D412yes—
50C2×#4339—22no—
51C2×#4339—22no—
52C2×#4339—22no—
53C2×#4339—22no—
54C2×#4339C2×C414yes—
55C2×#4339Q814yes—
56C22×D44D411yescharacteristic
57C22×C4×D11—22no—
58C22×C4×D11C2312yes—
59C22×Dic22D411yescharacteristic
60C22×C8×C11—22no—
61C22×C8×C11—22no—
62C22×C8×C11C2×C414yescomplemented
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4D414yes—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2312yes—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C4×C22⋊D11—216no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79#66979—22no—
80#66979—22no—
81#66979—22no—
82#66979D414yes—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—22no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—22no—
90C2×C4×Dic11—21no—
91C2×#4318—22no—
92C2×#4318—22no—
93C2×#4318C2×C414yescomplemented
94C22×C11⋊C8C2312yes—
95#66946—28no—
96#66945—24no—
97#66945—24no—
98C4⋊C4×D11—24no—
99C4⋊C4×D11—24no—
100#66940—28no—
101C11⋊#95—22no—
102C11⋊#95—22no—
103(C2×D11)⋊C8C2×C418yescomplemented
104(C2×D11)⋊C8C2×C418yescomplemented
105#66882—22no—
106#66882—22no—
107#66881—22no—
108#66881—22no—
109#66872—24no—
110#66871—24no—
111#20849—111nomaximal, Sylow
112C24×C11C2×D411yescharacteristic
113C23×D11C2×D412yes—
114C22×C4×C11—22no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—42no—
118C22×C4×C11—81no—
119C22×C4×C11—81no—
120C22×C4×C11—81no—
121C22×C4×C11—81no—
122C22×C4×C11C22×C412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×Q812yes—
127C22×C4×C11#4112yes—
128C22×C4×C11#4112yes—
129C22×C4×C11C2411yescharacteristic
130C2×C22⋊D11—24no—
131C2×C22⋊D11—24no—
132C2×C22⋊D11C4⋊C418yes—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11C2×D412yes—
138#4339—28no—
139#4339—28no—
140#4339—28no—
141#4339—28no—
142C2×D44—22no—
143C2×D44—22no—
144C2×D44C4⋊C414yes—
145C2×C4×D11—28no—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—82no—
151C2×C4×D11—82no—
152C2×C4×D11C22×C414yes—
153C2×C4×D11C2×Q814yes—
154C2×Dic22—22no—
155C2×Dic22—22no—
156C2×Dic22C4⋊C414yes—
157C2×C8×C11—28no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11C22×C412yes—
163C2×C8×C11C22×C412yes—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4C2×D414yes—
170C22⋊Dic11—24no—
171C22⋊Dic11—42no—
172(C2×D11)⋊C4—28no—
173(C2×D11)⋊C4—82no—
174(C2×D11)⋊C4—82no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11C2×D412yes—
182C4⋊Dic11C2×D412yes—
183Dic11⋊C4—28no—
184C4×Dic11—28no—
185C4×Dic11—24no—
186C4×Dic11—42no—
187#4318—28no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8C22×C414yes—
191C2×#520—111no—
192C2×#428—111no—
193C2×#427—111no—
194C2×#408—111no—
195#2311—111no—
196#1854—112no—
197#1854—112no—
198#1853—112no—
199#1852—112no—
200#1736—111no—
201C2×#340D1111yescharacteristic, complemented
202C23×C11—21no—
203C23×C11—21no—
204C23×C11—21no—
205C23×C11—21no—
206C23×C11C2×C4⋊C412yes—
207C23×C11#12012yes—
208C23×C11#12312yes—
209C23×C11C22×D411yescharacteristic
210C22×D11—22no—
211C22×D11—22no—
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—22no—
215C22×D11—22no—
216C22×D11C2×C4⋊C414yes—
217C2×C4×C11—24no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—84no—
224C2×C4×C11—84no—
225C2×C4×C11C2×C4⋊C412yes—
226C2×C4×C11C4×D414yes—
227C2×C4×C11C4×D414yes—
228C2×C4×C11#12012yes—
229C2×C4×C11C22⋊Q814yes—
230C2×C4×C11C22⋊Q814yes—
231C2×C4×C11#12312yes—
232C2×C4×C11C23×C411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×Q811yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C22⋊D11—216no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11C2×C4⋊C414yes—
254D44—28no—
255C4×D11—24no—
256C4×D11—24no—
257C4×D11—24no—
258C4×D11—24no—
259C4×D11—88no—
260Dic22—28no—
261C8×C11—22no—
262C8×C11—22no—
263C11⋊C8—24no—
264C22×#41—111no—
265C22×M16—111no—
266C23×C8C2×D1111yescharacteristic
267#520—224no—
268#520—224no—
269C2×C4×Q8—221no—
270C2×C4×D4—221no—
271C2×C4×D4—222no—
272C2×#117—111no—
273C2×#117—111no—
274C2×#117—112no—
275C22×C4⋊C4—112no—
276C22×C4⋊C4C2×D1111yescharacteristic
277C22×C4⋊C4C2×D1111yescharacteristic
278#428—224no—
279#427—224no—
280C2×#107—111no—
281C2×#107—111no—
282C2×#107—112no—
283C2×#106—111no—
284C2×#106—111no—
285C2×#106—112no—
286#408—118no—
287C2×C22⋊C8—112no—
288C2×C22⋊C8—112no—
289#391—221no—
290#390—221no—
291#386—222no—
292#380—112no—
293#380—112no—
294#340—112no—
295#340—112no—
296#340C2×D1112yes—
297#340C2×D1112yes—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—22no—
301C22×C11—22no—
302C22×C11—22no—
303C22×C11—22no—
304C22×C11#38514yes—
305C22×C11C22×C4⋊C411yescharacteristic
306C22×C11C2×#12011yescharacteristic
307C22×C11C2×#12311yescharacteristic
308C22×C11#57611yescharacteristic
309C22×C11#57711yescharacteristic
310C22×C11#57711yescharacteristic
311C22×C11#57811yescharacteristic
312C2×D11—24no—
313C2×D11—24no—
314C2×D11—24no—
315C2×D11—42no—
316C2×D11—42no—
317C2×D11—42no—
318C2×D11—42no—
319C4×C11—44no—
320C4×C11—82no—
321C4×C11#38514yes—
322C4×C11C2×C4×D411yescharacteristic
323C4×C11C2×C4×D411yescharacteristic
324C4×C11C2×C22⋊Q811yescharacteristic
325C4×C11C2×C22⋊Q811yescharacteristic
326Dic11—24no—
327Dic11—42no—
328Dic11—42no—
329Dic11—81no—
330Dic11—81no—
331C2×#41—114no—
332C2×#41—114no—
333C2×#41—222no—
334C2×#41—222no—
335C2×#41—222no—
336C2×#41—222no—
337C22×Q8—111no—
338C22×D4—112no—
339C22×D4—111no—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—112no—
343C23×C4—222no—
344C23×C4C22×D1111yescharacteristic
345C2×M16—114no—
346C2×M16—222no—
347C2×M16—222no—
348C22×C8—22no—
349C22×C8—22no—
350C22×C8—112no—
351C22×C8C4×D1114yescomplemented
352C22×C8C22×D1111yescharacteristic
353C22×C8C22×D1111yescharacteristic
354C4×Q8—228no—
355C4×D4—228no—
356C4×D4—2216no—
357#117—114no—
358#117—224no—
359#117—222no—
360#117—224no—
361#117—222no—
362#117—222no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—224no—
373C2×C4⋊C4—222no—
374C2×C4⋊C4—224no—
375C2×C4⋊C4D4414yes—
376C2×C4⋊C4C22×D1112yes—
377C2×C4⋊C4C22×D1112yes—
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⋊C8—118no—
393C22⋊C8—118no—
394#95—222no—
395#95—222no—
396C2×C11—24no—
397C2×C11C2×#38511yescharacteristic
398C2×C11#291211yescharacteristic
399C2×C11#291311yescharacteristic
400C2×C11#301211yescharacteristic
401C2×C11#301311yescharacteristic
402C2×C11#309611yescharacteristic
403C2×C11#309711yescharacteristic
404D11—44no—
405C24—112no—
406C24D4×D1111yescharacteristic
407#41—228no—
408#41—228no—
409#41—228no—
410#41—228no—
411C2×Q8—114no—
412C2×Q8—222no—
413C2×Q8—222no—
414C2×D4—118no—
415C2×D4—114no—
416C2×D4—224no—
417C2×D4—224no—
418C2×D4—222no—
419C2×D4—222no—
420C22×C4—22no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—42no—
424C22×C4—81no—
425C22×C4—81no—
426C22×C4—81no—
427C22×C4—81no—
428C22×C4—112no—
429C22×C4—114no—
430C22×C4—114no—
431C22×C4—228no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—882no—
441C22×C4—882no—
442C22×C4C2×C4×D1112yes—
443C22×C4C2×D4412yes—
444C22×C4#433912yes—
445C22×C4D4×D1112yes—
446C22×C4D4×D1111yescharacteristic
447C22×C4#434112yes—
448C22×C4Q8×D1112yes—
449C22×C4C23×D1111yescharacteristic
450M16—228no—
451C2×C8—28no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—114no—
457C2×C8—222no—
458C2×C8—222no—
459C2×C8C2×C4×D1112yes—
460C2×C8C2×C4×D1112yes—
461C4⋊C4—24no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—42no—
466C4⋊C4—112no—
467C4⋊C4—112no—
468C4⋊C4—228no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4C2×D4414yes—
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—114no—
490C23—222no—
491C23—222no—
492C23—222no—
493C23—222no—
494C23—222no—
495C23—222no—
496C23#6693512yes—
497C23#6693612yes—
498C23C4⋊C4×D1112yes—
499C23C2×D4×D1111yescharacteristic
500Q8—228no—
501D4—2216no—
502D4—228no—
503C2×C4—24no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—84no—
510C2×C4—84no—
511C2×C4—114no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—888no—
531C2×C4C4×D4414yes—
532C2×C4(C22⋊D11)⋊C414yes—
533C2×C4#6693512yes—
534C2×C4#6693612yes—
535C2×C4C4⋊C4×D1112yes—
536C2×C4#6694914yes—
537C2×C4#6695014yes—
538C2×C4C22×C4×D1111yescharacteristic
539C2×C4C22×D4411yescharacteristic
540C2×C4C2×#433911yescharacteristic
541C2×C4C2×D4×D1111yescharacteristic
542C2×C4C2×#434111yescharacteristic
543C2×C4C2×Q8×D1111yescharacteristic
544C8—22no—
545C8—22no—
546C8—224no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—224no—
554C22—224no—
555C22—224no—
556C22—442no—
557C22—442no—
558C22—442no—
559C22—442no—
560C22#1062228114yes—
561C22C2×#6693511yescharacteristic
562C22C2×#6693611yescharacteristic
563C22C2×C4⋊C4×D1111yescharacteristic
564C22#1062328811yescharacteristic
565C22#1062329311yescharacteristic
566C22#1062329311yescharacteristic
567C22#1062329711yescharacteristic
568C4—44no—
569C4—82no—
570C4—224no—
571C4—442no—
572C4—442no—
573C4—881no—
574C4—881no—
575C4#1062228114yes—
576C4C2×C4×D4411yescharacteristic
577C4C2×(C22⋊D11)⋊C411yescharacteristic
578C4C2×#6694911yescharacteristic
579C4C2×#6695011yescharacteristic
580C2—24no—
581C2—444no—
582C2C2×#1062228111yescharacteristic
583C2#1307720711yescharacteristic
584C2#1307721211yescharacteristic
585C2#1307792511yescharacteristic
586C2#1307793611yescharacteristic
587C2#1307857011yescharacteristic
588C2#1307858111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#340C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenterC2×#340D11
hypocenterC11#20849
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C2×#10622577C2semidirect
3. C2×#10622719C2semidirect
6. #13068818C2semidirect
7. #13068816C2semidirect
8. #13068810C2semidirect
9. #13068805C2semidirect
10. #13068335C2semidirect
11. C2×C11×#340C2semidirect
27. #10622723C4semidirect
62. C22×C8×C11C2×C4semidirect
93. C2×#4318C2×C4semidirect
103. (C2×D11)⋊C8C2×C4semidirect
104. (C2×D11)⋊C8C2×C4semidirect
201. C2×#340D11semidirect
351. C22×C8C4×D11semidirect
484. C11#20849semidirect

Maximal subgroups

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

subgroupindex
C2×#106230352
C2×#106225772
C2×#106227192
C2×#106227232
#130712092
#130688182
#130688162
#130688102
#130688052
#130683352
C2×C11×#3402
#2084911