Finite Group Databasebeta

← #14755041

Subgroups — #14755041

Order 2816.

1970 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623336C211yesmaximal, characteristic
2C2×#10623054C211yesmaximal, characteristic, complemented
3C22×#66896C211yesmaximal, characteristic, complemented
4C2×#10622742C211yesmaximal, characteristic, complemented
5#13068935C214yesmaximal, complemented
6#13068930C214yesmaximal, complemented
7#13068336C211yesmaximal, characteristic, complemented
8#13068332C211yesmaximal, characteristic, complemented
9C2×C11×#418C211yesmaximal, characteristic, complemented
10C23×D4×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×#67006—22no—
15#10623336—24no—
16#10623336C418yescomplemented
17C2×#66993—21no—
18C2×#66991C2214yes—
19C2×#66989—21no—
20C2×#66979C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23#10623054—24no—
24#10623054—24no—
25C2×#66945C2212yescomplemented
26C2×C4⋊C4×D11C2212yescomplemented
27C2×(C22⋊D11)⋊C4—22no—
28C2×C4×D44—21no—
29C2×C4×Dic22—21no—
30C11×#418—24no—
31C2×C11×#102C2212yes—
32C2×C11×#102C2212yes—
33C2×#66896—24no—
34C2×#66896C2214yes—
35#10622742—24no—
36C2×(C2×D11)⋊C8C2214yescomplemented
37#10622189C2214yescomplemented
38#10622167C2212yescomplemented
39#10622167C2212yescomplemented
40C25×C11—21no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—21no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11C2×C414yescomplemented
48C22×D4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C22×C22⋊D11—24no—
51C22×C22⋊D11D412yes—
52C23×Dic11—21no—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339—22no—
57C2×#4339C2×C414yes—
58C2×#4339D414yes—
59C22×D44D411yescharacteristic
60C22×C4×D11—22no—
61C22×C4×D11C2312yes—
62C22×Dic22D411yescharacteristic
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16—22no—
66C22×C8×C11C2312yes—
67C11×#117—22no—
68C11×#117D414yescomplemented
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C42×C11—21no—
73#67006—216no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—24no—
76#66993—28no—
77#66991—28no—
78#66991C2×C4116yescomplemented
79#66989—28no—
80C2×(C2×D11)⋊C4—22no—
81#66979—22no—
82#66979C2×C414yescomplemented
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11D414yescomplemented
86C2×C4⋊Dic11C2312yes—
87C2×C4⋊Dic11C2312yes—
88C2×Dic11⋊C4—22no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—22no—
91C22×C11⋊C8—22no—
92C22×C11⋊C8—22no—
93C22×C11⋊C8—22no—
94C22×C11⋊C8C2312yes—
95#66945—24no—
96#66945—24no—
97C4⋊C4×D11—24no—
98C4⋊C4×D11—24no—
99(C22⋊D11)⋊C4—216no—
100C4×D44—28no—
101C4×Dic22—28no—
102C11×#102—24no—
103C11×#102—24no—
104#66896—28no—
105(C2×D11)⋊C8—28no—
106#20914—111nomaximal, Sylow
107C24×C11—22no—
108C24×C11—24no—
109C24×C11—42no—
110C24×C11—42no—
111C24×C11—82no—
112C24×C11—82no—
113C24×C11C2×D411yescharacteristic
114C23×D11C2×D412yes—
115C2×D4×C11—24no—
116C2×D4×C11—28no—
117C2×D4×C11—28no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—42no—
124C2×D4×C11—44no—
125C2×D4×C11—44no—
126C2×D4×C11—42no—
127C2×D4×C11C22×C414yes—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11#4112yes—
136C22×C4×C11#4112yes—
137C22×C4×C11C2411yescharacteristic
138C2×C22⋊D11—24no—
139C2×C22⋊D11—24no—
140C2×C22⋊D11—216no—
141C2×C22⋊D11—84no—
142C2×C22⋊D11—84no—
143C2×C22⋊D11C22⋊C418yes—
144C22×Dic11—24no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—82no—
148C22×Dic11C2×D412yes—
149#4339—28no—
150#4339—28no—
151#4339—28no—
152#4339—28no—
153C2×D44—22no—
154C2×D44—22no—
155C2×D44C22⋊C414yes—
156C2×C4×D11—28no—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×C4×D11—84no—
162C2×C4×D11C22×C414yes—
163C2×C4×D11C2×D414yes—
164C2×Dic22—22no—
165C2×Dic22—22no—
166C2×Dic22C22⋊C414yes—
167C11×M16—44no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4C2×D412yes—
174C11×C4⋊C4C2×D412yes—
175C11×C22⋊C4—24no—
176C42×C11—24no—
177C22⋊Dic11—216no—
178C22⋊Dic11—24no—
179(C2×D11)⋊C4—28no—
180C4⋊Dic11—24no—
181C4⋊Dic11—22no—
182C4⋊Dic11—22no—
183C4⋊Dic11C22×C414yes—
184C4⋊Dic11C2×D414yes—
185Dic11⋊C4—28no—
186C4×Dic11—28no—
187C4×Dic11—24no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—44no—
192C2×#535—111no—
193C2×#520—111no—
194C2×#418D1111yescharacteristic, complemented
195C22×#102—111no—
196C2×#408—111no—
197#1875—114no—
198#1874—114no—
199#1736—111no—
200#1735—111no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—24no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—44no—
207C23×C11—44no—
208C23×C11—48no—
209C23×C11—88no—
210C23×C11—88no—
211C23×C11—84no—
212C23×C11—84no—
213C23×C11C2×C22⋊C412yes—
214C23×C11#12012yes—
215C23×C11#12312yes—
216C23×C11C22×D411yescharacteristic
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11C2×C22⋊C414yes—
222D4×C11—24no—
223D4×C11—24no—
224D4×C11—42no—
225D4×C11—42no—
226D4×C11—48no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11C2×C22⋊C412yes—
232C2×C4×C11C4×D414yes—
233C2×C4×C11C4×D414yes—
234C2×C4×C11#12012yes—
235C2×C4×C11#12114yes—
236C2×C4×C11#12114yes—
237C2×C4×C11#12312yes—
238C2×C4×C11C23×C411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C22⋊D11—216no—
245C22⋊D11—816no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—44no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—84no—
254C2×Dic11C2×C22⋊C414yes—
255D44—28no—
256C4×D11—24no—
257C4×D11—24no—
258C4×D11—24no—
259C4×D11—24no—
260C4×D11—88no—
261Dic22—28no—
262C8×C11—42no—
263C11⋊C8—42no—
264C22×#41—111no—
265C23×D4C2×D1111yescharacteristic
266C22×M16C2×D1111yescharacteristic
267C23×C8—111no—
268#535—118no—
269#535—224no—
270C2×#127—221no—
271C2×#124—221no—
272C2×#121—114no—
273C2×#120—222no—
274#520—224no—
275#520—224no—
276C2×C4×Q8—221no—
277C2×C4×D4—221no—
278C2×C4×D4—222no—
279C2×#117—111no—
280C2×#117—112no—
281C2×#117C2×D1111yescharacteristic
282C22×C4⋊C4—111no—
283C22×C4⋊C4—112no—
284#418—24no—
285C2×#102—114no—
286C2×#102—224no—
287C2×#102C2×D1112yes—
288C2×#102C2×D1112yes—
289#408—224no—
290C2×C22⋊C8—114no—
291#340—114no—
292#340—112no—
293#340—112no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11—22no—
297C22×C11—22no—
298C22×C11—48no—
299C22×C11—44no—
300C22×C11—816no—
301C22×C11—84no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11#38614yes—
305C22×C11C22×C22⋊C411yescharacteristic
306C22×C11C2×#12011yescharacteristic
307C22×C11C2×#12311yescharacteristic
308C22×C11#57612yes—
309C22×C11#57712yes—
310C2×D11—28no—
311C2×D11—24no—
312C2×D11—44no—
313C2×D11—42no—
314C2×D11—42no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11#38614yes—
318C4×C11C2×C4×D411yescharacteristic
319C4×C11C2×C4×D411yescharacteristic
320C4×C11C2×#12111yescharacteristic
321C4×C11C2×#12111yescharacteristic
322Dic11—24no—
323Dic11—44no—
324Dic11—44no—
325C25—21no—
326C2×#41—114no—
327C2×#41—114no—
328C2×#41—222no—
329C2×#41—222no—
330C2×#41—222no—
331C2×#41—222no—
332C22×Q8—111no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—21no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—112no—
340C22×D4—111no—
341C22×D4—224no—
342C22×D4C4×D1114yescomplemented
343C22×D4C22×D1112yes—
344C23×C4—112no—
345C23×C4—222no—
346C23×C4—221no—
347C23×C4C22×D1111yescharacteristic
348C2×M16—22no—
349C2×M16—22no—
350C2×M16—22no—
351C22×C8—112no—
352C22×C8—222no—
353C22×C8—222no—
354C22×C8—222no—
355C22×C8C22×D1112yes—
356#127—228no—
357#124—228no—
358#121—1116no—
359#121—228no—
360#120—2216no—
361C4×Q8—228no—
362C4×D4—228no—
363C4×D4—2216no—
364#117—22no—
365#117—114no—
366#117—224no—
367#117—222no—
368#117—224no—
369#117C22⋊D1114yescomplemented
370C2×C4⋊C4—114no—
371C2×C4⋊C4—112no—
372C2×C4⋊C4—112no—
373C2×C4⋊C4—224no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—224no—
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—224no—
383C2×C22⋊C4—221no—
384C2×C42—21no—
385C2×C42—222no—
386C2×C42—221no—
387#102—24no—
388#102—24no—
389#102—228no—
390C22⋊C8—228no—
391C2×C11—24no—
392C2×C11—84no—
393C2×C11C2×#38611yescharacteristic
394C2×C11#289712yes—
395C2×C11#300811yescharacteristic
396C2×C11#301011yescharacteristic
397C2×C11#309612yes—
398D11—44no—
399C24—22no—
400C24—24no—
401C24—42no—
402C24—42no—
403C24—82no—
404C24—82no—
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—24no—
415C2×D4—28no—
416C2×D4—28no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—42no—
423C2×D4—44no—
424C2×D4—42no—
425C2×D4—44no—
426C2×D4—118no—
427C2×D4—114no—
428C2×D4—224no—
429C2×D4—224no—
430C2×D4—2216no—
431C2×D4—222no—
432C2×D4—222no—
433C2×D4—884no—
434C2×D4—884no—
435C2×D4C2×C4×D1114yes—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—112no—
439C22×C4—114no—
440C22×C4—114no—
441C22×C4—228no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—224no—
449C22×C4—884no—
450C22×C4—882no—
451C22×C4C2×C4×D1112yes—
452C22×C4#433912yes—
453C22×C4D4×D1111yescharacteristic
454C22×C4D4×D1112yes—
455C22×C4D4×D1112yes—
456C22×C4#434112yes—
457C22×C4C2×C22⋊D1112yes—
458C22×C4C23×D1111yescharacteristic
459M16—44no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—222no—
464C2×C8—222no—
465C2×C8—222no—
466C2×C8—444no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—114no—
470C4⋊C4—114no—
471C4⋊C4—228no—
472C4⋊C4—224no—
473C4⋊C4—222no—
474C4⋊C4—222no—
475C4⋊C4C2×C22⋊D1112yes—
476C4⋊C4C2×C22⋊D1112yes—
477C22⋊C4—24no—
478C22⋊C4—228no—
479C22⋊C4—2216no—
480C22⋊C4—224no—
481C42—24no—
482C42—228no—
483C42—224no—
484C11#2091411yescharacteristic, complemented, Sylow
485C23—22no—
486C23—22no—
487C23—24no—
488C23—42no—
489C23—44no—
490C23—44no—
491C23—42no—
492C23—48no—
493C23—88no—
494C23—88no—
495C23—84no—
496C23—84no—
497C23—114no—
498C23—222no—
499C23—224no—
500C23—224no—
501C23—222no—
502C23C22⋊C4×D1112yes—
503C23#6693612yes—
504C23#6699012yes—
505C23C2×D4×D1111yescharacteristic
506Q8—228no—
507D4—24no—
508D4—24no—
509D4—42no—
510D4—42no—
511D4—48no—
512D4—2216no—
513D4—228no—
514D4—8816no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—114no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—224no—
528C2×C4—444no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—888no—
532C2×C4—884no—
533C2×C4C22⋊C4×D1112yes—
534C2×C4(C22⋊D11)⋊C414yes—
535C2×C4#6693612yes—
536C2×C4#6693714yes—
537C2×C4C4×C22⋊D1114yes—
538C2×C4#6699012yes—
539C2×C4#6699114yes—
540C2×C4C22×C4×D1111yescharacteristic
541C2×C4C2×#433911yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4C2×D4×D1111yescharacteristic
544C2×C4C2×#434111yescharacteristic
545C2×C4C22×C22⋊D1111yescharacteristic
546C8—42no—
547C8—442no—
548C22—24no—
549C22—22no—
550C22—22no—
551C22—24no—
552C22—48no—
553C22—44no—
554C22—816no—
555C22—84no—
556C22—82no—
557C22—82no—
558C22—228no—
559C22—224no—
560C22—444no—
561C22—442no—
562C22—442no—
563C22#1062256914yes—
564C22C2×C22⋊C4×D1111yescharacteristic
565C22C2×#6693611yescharacteristic
566C22#1062330512yes—
567C22#1062330612yes—
568C22C2×#6699011yescharacteristic
569C4—42no—
570C4—42no—
571C4—224no—
572C4—444no—
573C4—444no—
574C4#1062256914yes—
575C4C2×(C22⋊D11)⋊C411yescharacteristic
576C4C2×#6693711yescharacteristic
577C4C2×C4×C22⋊D1111yescharacteristic
578C4C2×#6699111yescharacteristic
579C2—24no—
580C2—84no—
581C2—444no—
582C2C2×#1062256911yescharacteristic
583C2#1307714112yes—
584C2#1307788311yescharacteristic
585C2#1307790111yescharacteristic
586C2#1307857212yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#418C2
socleC23×C11C22×D4
prime radicalC2×#10623336C2
cosocleC22×C4×C11C24
hypercenterC2×#418D11
hypocenterC11#20914
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
2. C2×#10623054C2semidirect
3. C22×#66896C2semidirect
4. C2×#10622742C2semidirect
5. #13068935C2semidirect
6. #13068930C2semidirect
7. #13068336C2semidirect
8. #13068332C2semidirect
9. C2×C11×#418C2semidirect
16. #10623336C4semidirect
25. C2×#66945C22semidirect
26. C2×C4⋊C4×D11C22semidirect
36. C2×(C2×D11)⋊C8C22semidirect
37. #10622189C22semidirect
38. #10622167C22semidirect
39. #10622167C22semidirect
47. C22×D4×C11C2×C4semidirect
68. C11×#117D4semidirect
78. #66991C2×C4semidirect
82. #66979C2×C4semidirect
85. C2×C4⋊Dic11D4semidirect
194. C2×#418D11semidirect
342. C22×D4C4×D11semidirect
369. #117C22⋊D11semidirect
484. C11#20914semidirect

Maximal subgroups

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

subgroupindex
C2×#106233362
C2×#106230542
C22×#668962
C2×#106227422
#130689352
#130689302
#130683362
#130683322
C2×C11×#4182
#2091411