Finite Group Databasebeta

← #14754652

Subgroups — #14754652

Order 2816.

1422 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077205C211yesmaximal, characteristic, complemented
2C2×#10622849C211yesmaximal, characteristic
3#13077135C211yesmaximal, characteristic
4#13071240C211yesmaximal, characteristic, complemented
5#13068849C214yesmaximal, complemented
6#13068842C214yesmaximal, complemented
7C2×#10622168C211yesmaximal, characteristic, complemented
8#13068325C211yesmaximal, characteristic, complemented
9C2×C11×#520C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C11×#520—22no—
12C11×#520—22no—
13C11×#520—22no—
14C11×#520C2214yes—
15C2×C4×Q8×C11—21no—
16C2×C4×D4×C11—21no—
17C2×C4×D4×C11—22no—
18C2×C11×#117—21no—
19C2×C11×#117C2211yescharacteristic
20C22×C11×C4⋊C4—21no—
21C22×C11×C4⋊C4C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26#10622849C418yescomplemented
27C2×#66901C2214yes—
28#10622846—22no—
29#10622845C2212yes—
30#10622845C2212yes—
31#10622838—21no—
32#10622828—21no—
33#10622823—22no—
34#10622611—22no—
35#10622608C2212yescomplemented
36#10622608C2212yescomplemented
37#10622590C2212yescomplemented
38#10622589C2212yescomplemented
39#10622586—22no—
40#10622577—21no—
41#10622577—21no—
42#10622170C2214yescomplemented
43#10622168C2214yescomplemented
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41C2×C414yes—
49C2×C11×#41D412yes—
50C2×C11×#41Q814yes—
51C2×C11×#41C2312yes—
52C22×Q8×C11D411yescharacteristic
53C22×D4×C11—21no—
54C22×D4×C11D411yescharacteristic
55C23×C4×C11—21no—
56C23×C4×C11—22no—
57C23×C4×C11D412yes—
58C23×C4×C11C2311yescharacteristic
59C4×Q8×C11—24no—
60C4×Q8×C11—24no—
61C4×D4×C11—28no—
62C4×D4×C11—24no—
63C4×D4×C11—24no—
64C4×D4×C11—28no—
65C11×#117—24no—
66C11×#117—21no—
67C11×#117—21no—
68C11×#117—24no—
69C11×#117D412yes—
70C11×#117C2312yes—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4D412yes—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—21no—
84C2×C42×C11—22no—
85C2×C42×C11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88#66979—22no—
89#66979—21no—
90#66979—21no—
91#66979—21no—
92#66979—21no—
93#66979C2×C414yescomplemented
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—24no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2312yes—
100C2×#4318—21no—
101C2×#4318—22no—
102C2×#4318—21no—
103C2×#4318—22no—
104C2×#4318—22no—
105C2×#4318C2×C414yescomplemented
106C2×#4318C2312yes—
107C2×#4318C2312yes—
108C22×C11⋊C8—21no—
109C22×C11⋊C8—21no—
110#66901C2×C4116yescomplemented
111#66899—22no—
112#66899—22no—
113#66896—22no—
114#66896—22no—
115C11⋊#95—24no—
116#66872—22no—
117#66872—22no—
118#66871—22no—
119#66871—22no—
120#20864—111nomaximal, Sylow
121C24×C11—21no—
122C24×C11C2×D411yescharacteristic
123C11×#41—24no—
124C11×#41—24no—
125C11×#41—24no—
126C11×#41—24no—
127C11×#41—24no—
128C11×#41—22no—
129C11×#41—22no—
130C11×#41C4⋊C418yescomplemented
131C11×#41C22×C414yes—
132C11×#41C2×Q814yes—
133C2×Q8×C11—21no—
134C2×Q8×C11—22no—
135C2×Q8×C11C4⋊C414yescomplemented
136C2×Q8×C11C2×D412yes—
137C2×D4×C11—24no—
138C2×D4×C11—22no—
139C2×D4×C11—24no—
140C2×D4×C11—22no—
141C2×D4×C11—21no—
142C2×D4×C11—22no—
143C2×D4×C11C4⋊C414yescomplemented
144C2×D4×C11C2×D412yes—
145C22×C4×C11—21no—
146C22×C4×C11—24no—
147C22×C4×C11—22no—
148C22×C4×C11—24no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—21no—
153C22×C4×C11—28no—
154C22×C4×C11—22no—
155C22×C4×C11—82no—
156C22×C4×C11—84no—
157C22×C4×C11C22×C412yes—
158C22×C4×C11C2×D414yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×Q812yes—
165C22×C4×C11#4112yes—
166C22×C4×C11#4112yes—
167C22×C4×C11C2411yescharacteristic
168C22×Dic11—22no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C11×C4⋊C4—28no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4C2×D412yes—
179C11×C4⋊C4C2×D412yes—
180C11×C22⋊C4—28no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C42×C11—28no—
184C42×C11—22no—
185C42×C11—22no—
186C22⋊Dic11—24no—
187C22⋊Dic11—41no—
188C22⋊Dic11—41no—
189C4⋊Dic11—24no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194Dic11⋊C4—84no—
195C4×Dic11—22no—
196C4×Dic11—41no—
197C4×Dic11—41no—
198C4×Dic11C22×C414yescomplemented
199#4318—24no—
200#4318—22no—
201#4318—22no—
202#4318—22no—
203#4318—42no—
204#4318C22×C414yescomplemented
205C2×C11⋊C8—24no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—22no—
208C2×C11⋊C8—42no—
209C2×#520D1111yescharacteristic
210#2911—111no—
211C2×#421—111no—
212#2896—111no—
213#2317—111no—
214#1860—114no—
215#1859—114no—
216C2×#343—111no—
217#1733—111no—
218C23×C11—22no—
219C23×C11—24no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11C4×D412yes—
225C23×C11#12011yescharacteristic
226C23×C11#12011yescharacteristic
227C23×C11C22⋊Q812yes—
228C23×C11C22×D411yescharacteristic
229Q8×C11—22no—
230Q8×C11—24no—
231Q8×C11C2×C4⋊C414yes—
232D4×C11—24no—
233D4×C11—24no—
234D4×C11—28no—
235D4×C11—22no—
236D4×C11—24no—
237D4×C11C2×C4⋊C414yes—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—28no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—22no—
246C2×C4×C11—42no—
247C2×C4×C11—44no—
248C2×C4×C11—42no—
249C2×C4×C11—44no—
250C2×C4×C11—82no—
251C2×C4×C11—88no—
252C2×C4×C11C2×C4⋊C412yes—
253C2×C4×C11C2×C4⋊C412yes—
254C2×C4×C11C4×D412yes—
255C2×C4×C11C4×D412yes—
256C2×C4×C11C4×D412yes—
257C2×C4×C11#12011yescharacteristic
258C2×C4×C11#12011yescharacteristic
259C2×C4×C11C22⋊Q812yes—
260C2×C4×C11C22⋊Q812yes—
261C2×C4×C11C22⋊Q812yes—
262C2×C4×C11#12312yes—
263C2×C4×C11#12312yes—
264C2×C4×C11C23×C411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C22×Q811yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×Dic11—24no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C11⋊C8—24no—
278C11⋊C8—42no—
279C22×#41C2×D1111yescharacteristic
280C22×M16—111no—
281C22×M16—111no—
282#520—22no—
283#520—22no—
284#520—22no—
285#520C2×D1114yes—
286C2×C4×Q8—21no—
287C2×C4×D4—21no—
288C2×C4×D4—22no—
289C2×#117—21no—
290C2×#117—111no—
291C2×#117—111no—
292C2×#117C2×D1111yescharacteristic
293C22×C4⋊C4—21no—
294C22×C4⋊C4C2×D1111yescharacteristic
295#428—112no—
296#428—112no—
297#428—221no—
298#428—221no—
299#427—222no—
300#421—118no—
301C2×#104—114no—
302#419—221no—
303#418—221no—
304#417—112no—
305#417—112no—
306#416—222no—
307#389—222no—
308#385—222no—
309#384—112no—
310#382—112no—
311#343—114no—
312#339—114no—
313C22×C11—21no—
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—24no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—48no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11#38512yes—
326C22×C11#38512yes—
327C22×C11C2×C4×D411yescharacteristic
328C22×C11C2×#12011yescharacteristic
329C22×C11C2×C22⋊Q811yescharacteristic
330C4×C11—24no—
331C4×C11—44no—
332C4×C11—42no—
333C4×C11—42no—
334C4×C11#38512yes—
335C4×C11#38512yes—
336C4×C11C22×C4⋊C411yescharacteristic
337C4×C11C2×C4×D411yescharacteristic
338C4×C11C2×C22⋊Q811yescharacteristic
339C4×C11C2×#12311yescharacteristic
340Dic11—44no—
341Dic11—81no—
342Dic11—81no—
343C2×#41—22no—
344C2×#41—22no—
345C2×#41—21no—
346C2×#41—21no—
347C2×#41Dic2214yes—
348C2×#41C4×D1114yes—
349C2×#41C22⋊D1112yes—
350C2×#41C22×D1112yes—
351C22×Q8C22⋊D1111yescharacteristic
352C22×D4—21no—
353C22×D4C22⋊D1111yescharacteristic
354C23×C4—21no—
355C23×C4—22no—
356C23×C4C22⋊D1112yes—
357C23×C4C22×D1111yescharacteristic
358C2×M16—114no—
359C2×M16—112no—
360C2×M16—112no—
361C2×M16—222no—
362C2×M16—221no—
363C2×M16—221no—
364C2×M16—222no—
365C2×M16—222no—
366C22×C8—221no—
367C22×C8—221no—
368C4×Q8—24no—
369C4×Q8—24no—
370C4×D4—28no—
371C4×D4—24no—
372C4×D4—24no—
373C4×D4—28no—
374#117—24no—
375#117—21no—
376#117—21no—
377#117—24no—
378#117—114no—
379#117—222no—
380#117—221no—
381#117—221no—
382#117—221no—
383#117—221no—
384#117C22⋊D1112yes—
385#117C22×D1112yes—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—224no—
397C2×C4⋊C4C22⋊D1112yes—
398C2×C4⋊C4C22⋊D1111yescharacteristic
399C2×C4⋊C4C22⋊D1111yescharacteristic
400C2×C4⋊C4C22×D1112yes—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—221no—
404C2×C22⋊C4—221no—
405C2×C42—22no—
406C2×C42—21no—
407C2×C42—112no—
408C2×C42—221no—
409#107—222no—
410#107—222no—
411#106—222no—
412#106—222no—
413#104—1116no—
414#103—222no—
415#103—222no—
416#102—222no—
417#102—222no—
418#95—224no—
419C2×C11—21no—
420C2×C11—22no—
421C2×C11—21no—
422C2×C11—22no—
423C2×C11—44no—
424C2×C11C2×#38511yescharacteristic
425C2×C11#301911yescharacteristic
426C2×C11#302011yescharacteristic
427C24—21no—
428C24C2×C22⋊D1111yescharacteristic
429#41—24no—
430#41—24no—
431#41—24no—
432#41—24no—
433#41—24no—
434#41—22no—
435#41—22no—
436#41Dic11⋊C418yescomplemented
437#41C2×Dic2214yes—
438#41C2×C4×D1114yes—
439C2×Q8—22no—
440C2×Q8—21no—
441C2×Q8Dic11⋊C414yescomplemented
442C2×Q8C2×C22⋊D1112yes—
443C2×D4—24no—
444C2×D4—24no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—21no—
449C2×D4Dic11⋊C414yescomplemented
450C2×D4C2×C22⋊D1112yes—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—28no—
460C22×C4—22no—
461C22×C4—82no—
462C22×C4—84no—
463C22×C4—222no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4C2×Dic2212yes—
467C22×C4C2×C4×D1112yes—
468C22×C4#433912yes—
469C22×C4#433912yes—
470C22×C4C2×C22⋊D1114yes—
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C2×C22⋊D1111yescharacteristic
474C22×C4C2×C22⋊D1111yescharacteristic
475C22×C4C2×C22⋊D1111yescharacteristic
476C22×C4C23×D1111yescharacteristic
477M16—114no—
478M16—224no—
479M16—222no—
480M16—222no—
481M16—222no—
482M16—442no—
483C2×C8—224no—
484C2×C8—222no—
485C2×C8—222no—
486C2×C8—442no—
487C4⋊C4—28no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—224no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—884no—
500C4⋊C4C2×C22⋊D1112yes—
501C4⋊C4C2×C22⋊D1112yes—
502C22⋊C4—28no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—224no—
506C22⋊C4—441no—
507C22⋊C4—441no—
508C42—28no—
509C42—22no—
510C42—22no—
511C42—114no—
512C42—222no—
513C42—441no—
514C42—441no—
515C11#2086411yescharacteristic, complemented, Sylow
516C23—24no—
517C23—22no—
518C23—41no—
519C23—41no—
520C23—42no—
521C23—42no—
522C23#6697712yes—
523C23C4×C22⋊D1112yes—
524C23#6700611yescharacteristic
525C23#6700611yescharacteristic
526C23C22×C22⋊D1111yescharacteristic
527Q8—22no—
528Q8—24no—
529Q8C2×Dic11⋊C414yes—
530D4—24no—
531D4—24no—
532D4—28no—
533D4—22no—
534D4—24no—
535D4C2×Dic11⋊C414yes—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—28no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—42no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—44no—
548C2×C4—82no—
549C2×C4—88no—
550C2×C4—224no—
551C2×C4—442no—
552C2×C4—442no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4C2×Dic11⋊C412yes—
558C2×C4C2×Dic11⋊C412yes—
559C2×C4#6697712yes—
560C2×C4#6697712yes—
561C2×C4#6697712yes—
562C2×C4C4×C22⋊D1112yes—
563C2×C4C4×C22⋊D1112yes—
564C2×C4C4×C22⋊D1112yes—
565C2×C4#6698212yes—
566C2×C4#6698212yes—
567C2×C4#6700611yescharacteristic
568C2×C4#6700611yescharacteristic
569C2×C4C22×Dic2211yescharacteristic
570C2×C4C22×C4×D1111yescharacteristic
571C2×C4C2×#433911yescharacteristic
572C2×C4C2×#433911yescharacteristic
573C2×C4C22×C22⋊D1111yescharacteristic
574C2×C4C22×C22⋊D1111yescharacteristic
575C8—224no—
576C8—442no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—24no—
584C22—42no—
585C22—42no—
586C22—48no—
587C22—42no—
588C22—42no—
589C22#1062282312yes—
590C22#1062282312yes—
591C22C2×#6697711yescharacteristic
592C22C2×C4×C22⋊D1111yescharacteristic
593C22C2×#6700611yescharacteristic
594C4—24no—
595C4—44no—
596C4—42no—
597C4—42no—
598C4—444no—
599C4—881no—
600C4—881no—
601C4#1062282312yes—
602C4#1062282312yes—
603C4C22×Dic11⋊C411yescharacteristic
604C4C2×#6697711yescharacteristic
605C4C2×C4×C22⋊D1111yescharacteristic
606C4C2×#6698211yescharacteristic
607C2—21no—
608C2—22no—
609C2—21no—
610C2—22no—
611C2—44no—
612C2C2×#1062282311yescharacteristic
613C2#1307797311yescharacteristic
614C2#1307798011yescharacteristic
subgroupG/H
centerC22C2×#67006
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#520C2
socleC22×C11C2×#120
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC2×#520D11
hypocenterC11#20864
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #13077205C2semidirect
4. #13071240C2semidirect
5. #13068849C2semidirect
6. #13068842C2semidirect
7. C2×#10622168C2semidirect
8. #13068325C2semidirect
26. #10622849C4semidirect
35. #10622608C22semidirect
36. #10622608C22semidirect
37. #10622590C22semidirect
38. #10622589C22semidirect
42. #10622170C22semidirect
43. #10622168C22semidirect
93. #66979C2×C4semidirect
105. C2×#4318C2×C4semidirect
110. #66901C2×C4semidirect
130. C11×#41C4⋊C4semidirect
135. C2×Q8×C11C4⋊C4semidirect
143. C2×D4×C11C4⋊C4semidirect
198. C4×Dic11C22×C4semidirect
204. #4318C22×C4semidirect
436. #41Dic11⋊C4semidirect
441. C2×Q8Dic11⋊C4semidirect
449. C2×D4Dic11⋊C4semidirect
515. C11#20864semidirect

Maximal subgroups

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

subgroupindex
#130772052
C2×#106228492
#130771352
#130712402
#130688492
#130688422
C2×#106221682
#130683252
C2×C11×#5202
#2086411