Finite Group Databasebeta

← #14960785

Subgroups — #14960785

Order 2816.

2970 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623136C211yesmaximal, characteristic, complemented
2C22×#66982C211yesmaximal, characteristic, complemented
3#13076898C211yesmaximal, characteristic, complemented
4#13075308C214yesmaximal, complemented
5#13075304C214yesmaximal, complemented
6#13074944C214yesmaximal, complemented
7#13074942C214yesmaximal, complemented
8#13074361C211yesmaximal, characteristic, complemented
9#13074360C211yesmaximal, characteristic, complemented
10#13073544C212yesmaximal, complemented
11#13073106C212yesmaximal, complemented
12#13071942C212yesmaximal, complemented
13#13071927C212yesmaximal, complemented
14#13071213C211yesmaximal, characteristic, complemented
15C11×#2847C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C22×D4×D11C2212yes—
19C2×C11×#121C2211yescharacteristic
20C2×C11×#121C2212yescomplemented
21C2×C11×#120C2212yescomplemented
22C2×#67006C2212yescomplemented
23C22×C22⋊Dic11C2211yescharacteristic, complemented
24C2×#66992C2212yes—
25C2×#66990C2212yescomplemented
26C2×#66990C2214yescomplemented
27C2×#66988C2212yescomplemented
28C2×#66983C2211yescharacteristic
29C2×#66983C2212yescomplemented
30C2×#66982—28no—
31C2×#66982C2214yescomplemented
32C2×#66982C2214yescomplemented
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic, complemented
36C22×Dic11⋊C4C2211yescharacteristic, complemented
37#10623136—28no—
38C2×#66947C2212yescomplemented
39C2×#66939C2212yescomplemented
40C2×#66936C2212yescomplemented
41C2×#66935C2212yescomplemented
42C11×#386C2212yescomplemented
43C11×#386C2214yescomplemented
44C11×#380C2212yescomplemented
45C11×#380C2211yescharacteristic, complemented
46#10622836C2214yes—
47#10622836C2214yescomplemented
48#10622835C2212yescomplemented
49#10622834C2214yescomplemented
50#10622833C2212yescomplemented
51#10622826C2214yescomplemented
52#10622826C2212yescomplemented
53#10622825C2212yescomplemented
54#10622825C2211yescharacteristic, complemented
55#10622607C2214yescomplemented
56#10622603C2214yescomplemented
57#10622593C2212yescomplemented
58#10622574C2214yescomplemented
59#10622573C2214yes—
60#10622571C2212yescomplemented
61#10622570C2214yescomplemented
62#10622570C2214yescomplemented
63#10622569C2214yescomplemented
64#10622568C2212yes—
65#10622568C2214yescomplemented
66#10622565C2214yescomplemented
67#10622562C2214yescomplemented
68#10622561C2214yescomplemented
69C22⋊C4×Dic11C2212yescomplemented
70#10622288C2214yescomplemented
71#10622285C2214yescomplemented
72#10622285C2212yescomplemented
73#10622283C2214yescomplemented
74#10622281C2214yescomplemented
75#10622274C2212yescomplemented
76#10622263C2214yescomplemented
77C25×C11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C24×D11C2312yes—
80C22×D4×C11C2312yes—
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2314yes—
83C23×C4×C11—24no—
84C23×C4×C11—44no—
85C23×C4×C11C2312yes—
86C23×C4×C11C2312yes—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11—24no—
90C22×C22⋊D11—44no—
91C22×C22⋊D11C2312yes—
92C22×C22⋊D11C2314yes—
93C22×C22⋊D11C2312yes—
94C22×C22⋊D11C2312yes—
95C22×C22⋊D11C2314yes—
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C2×D4×D11—28no—
100C2×D4×D11—44no—
101C2×D4×D11—44no—
102C22×D44C2311yescharacteristic
103C22×D44C2312yes—
104C22×C4×D11C2312yes—
105C11×#121—24no—
106C11×#121—44no—
107C11×#120—44no—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2312yes—
110C2×C11×C22⋊C4C2312yes—
111C2×C11×C22⋊C4C2312yes—
112C2×C11×C22⋊C4C2314yes—
113C2×C11×C22⋊C4C2314yes—
114#67006—44no—
115C2×C22⋊Dic11—24no—
116C2×C22⋊Dic11C2312yes—
117C2×C22⋊Dic11C2314yes—
118C2×C22⋊Dic11C2312yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122#66992—28no—
123#66990—28no—
124#66990—48no—
125#66988—44no—
126#66983—24no—
127#66983—44no—
128#66982—216no—
129#66982—216no—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4D418yescomplemented
132C2×(C2×D11)⋊C4C2312yes—
133C2×(C2×D11)⋊C4C2312yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2312yes—
141C2×(C2×D11)⋊C4C2312yes—
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2314yes—
144C2×C4⋊Dic11C2312yes—
145C2×Dic11⋊C4—24no—
146C2×Dic11⋊C4—24no—
147C2×Dic11⋊C4C2312yes—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2312yes—
150C2×Dic11⋊C4C2312yes—
151C2×Dic11⋊C4C2314yes—
152C2×C4×Dic11C2314yes—
153#66947—28no—
154#66939—44no—
155#66936—28no—
156#66935—28no—
157C11×#95C2314yes—
158C11×#95C2312yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2312yes—
164#36721—111nomaximal, Sylow
165C24×C11—22no—
166C24×C11—24no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—42no—
170C24×C11C2412yes—
171C24×C11C2412yes—
172C24×C11C2411yescharacteristic
173C23×D11—22no—
174C23×D11—22no—
175C23×D11—24no—
176C23×D11—42no—
177C23×D11—42no—
178C23×D11—42no—
179C23×D11—42no—
180C23×D11—44no—
181C23×D11—44no—
182C23×D11C2×D414yes—
183C23×D11C2412yes—
184C23×D11C2412yes—
185C2×D4×C11—24no—
186C2×D4×C11—24no—
187C2×D4×C11—24no—
188C2×D4×C11—28no—
189C2×D4×C11—22no—
190C2×D4×C11—44no—
191C2×D4×C11—42no—
192C2×D4×C11—44no—
193C22×C4×C11—22no—
194C22×C4×C11—24no—
195C22×C4×C11—24no—
196C22×C4×C11—24no—
197C22×C4×C11—24no—
198C22×C4×C11—42no—
199C22×C4×C11—42no—
200C22×C4×C11—42no—
201C22×C4×C11—42no—
202C22×C4×C11—416no—
203C22×C4×C11C2×D414yes—
204C22×C4×C11C2414yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2411yescharacteristic
208C22×C4×C11C2411yescharacteristic
209C2×C22⋊D11—24no—
210C2×C22⋊D11—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—28no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—28no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—28no—
217C2×C22⋊D11—42no—
218C2×C22⋊D11—42no—
219C2×C22⋊D11—44no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—44no—
223C2×C22⋊D11—416no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—42no—
229C22×Dic11—42no—
230C22×Dic11C2×D414yes—
231C22×Dic11C2414yes—
232C22×Dic11C2412yes—
233C22×Dic11C2412yes—
234C22×Dic11C2412yes—
235C22×Dic11C2412yes—
236D4×D11—432no—
237C2×D44—24no—
238C2×D44—22no—
239C2×D44—42no—
240C2×D44—42no—
241C2×D44—42no—
242C2×C4×D11—24no—
243C2×C4×D11—42no—
244C2×C4×D11—42no—
245C11×C4⋊C4—22no—
246C11×C4⋊C4—42no—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—24no—
249C11×C22⋊C4—44no—
250C11×C22⋊C4—44no—
251C22⋊Dic11—24no—
252C22⋊Dic11—28no—
253C22⋊Dic11—24no—
254C22⋊Dic11—44no—
255C22⋊Dic11—44no—
256C22⋊Dic11—44no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—28no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—44no—
261(C2×D11)⋊C4—44no—
262(C2×D11)⋊C4—44no—
263(C2×D11)⋊C4—44no—
264(C2×D11)⋊C4—44no—
265(C2×D11)⋊C4C2×D418yes—
266(C2×D11)⋊C4C2×D418yes—
267C4⋊Dic11—22no—
268C4⋊Dic11—44no—
269C4⋊Dic11—42no—
270Dic11⋊C4—24no—
271Dic11⋊C4—28no—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
274Dic11⋊C4—44no—
275C4×Dic11—44no—
276C2×#534—111no—
277C22×#123—111no—
278#2847—111no—
279#2847D1111yescharacteristic, complemented
280#2706—114no—
281#2706—114no—
282#2678—114no—
283#2678—114no—
284#2618—111no—
285#2618—111no—
286#2539—112no—
287#2504—112no—
288#2405—112no—
289#2403—112no—
290#2312—111no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—28no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—24no—
303C23×C11—22no—
304C23×C11—24no—
305C23×C11—48no—
306C23×C11—48no—
307C23×C11—44no—
308C23×C11—44no—
309C23×C11C22×D412yes—
310C23×C11H(5,𝔽2)14yes—
311C23×C11H(5,𝔽2)12yes—
312C23×C11H(5,𝔽2)12yes—
313C23×C11C2511yescharacteristic
314C22×D11—24no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—24no—
318C22×D11—28no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—24no—
322C22×D11—22no—
323C22×D11—24no—
324C22×D11—44no—
325C22×D11—44no—
326C22×D11—48no—
327C22×D11—84no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11—84no—
331C22×D11—88no—
332C22×D11—88no—
333C22×D11C22×D414yes—
334D4×C11—48no—
335D4×C11—82no—
336D4×C11—88no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—24no—
343C2×C4×C11—24no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—24no—
348C2×C4×C11—44no—
349C2×C4×C11—48no—
350C2×C4×C11—48no—
351C2×C4×C11—44no—
352C2×C4×C11C22×D412yes—
353C2×C4×C11C22×D412yes—
354C22⋊D11—416no—
355C22⋊D11—48no—
356C22⋊D11—48no—
357C22⋊D11—84no—
358C22⋊D11—88no—
359C2×Dic11—24no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—24no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—24no—
368C2×Dic11—24no—
369C2×Dic11—22no—
370C2×Dic11—24no—
371C2×Dic11—44no—
372C2×Dic11—44no—
373C2×Dic11—44no—
374C2×Dic11C22×D414yes—
375D44—48no—
376D44—82no—
377C4×D11—48no—
378C23×D4—111no—
379C23×D4—112no—
380C24×C4C2×D1111yescharacteristic, complemented
381#534—228no—
382C2×#123—114no—
383C2×#123—114no—
384C2×#123—112no—
385C2×#123—112no—
386C2×#123—112no—
387C2×#123—112no—
388C2×#123—228no—
389C2×#121—112no—
390C2×#121—111no—
391C2×#121—112no—
392C2×#121C2×D1111yescharacteristic
393C2×#121C2×D1112yescomplemented
394C2×#120—112no—
395C2×#120—112no—
396C2×#120—114no—
397C2×#120—112no—
398C2×#120C2×D1112yescomplemented
399C22×C4⋊C4—111no—
400C22×C4⋊C4—111no—
401C22×C22⋊C4—111no—
402C22×C22⋊C4—111no—
403C22×C22⋊C4—111no—
404#399—114no—
405#398—112no—
406#398—112no—
407#397—114no—
408#397—114no—
409#396—114no—
410#396—114no—
411#394—112no—
412#394—114no—
413#394—112no—
414#394—114no—
415#392—114no—
416#392—114no—
417#392—114no—
418#390—114no—
419#390—114no—
420#390—114no—
421#388—114no—
422#388—114no—
423#386—112no—
424#386—112no—
425#386—114no—
426#386—112no—
427#386—114no—
428#386C2×D1112yescomplemented
429#386C2×D1114yescomplemented
430#385—114no—
431#382—114no—
432#380—111no—
433#380—112no—
434#380C2×D1111yescharacteristic, complemented
435#380C2×D1112yescomplemented
436#379—112no—
437#379—114no—
438C4×C22⋊C4—112no—
439C22×C11—22no—
440C22×C11—22no—
441C22×C11—24no—
442C22×C11—24no—
443C22×C11—24no—
444C22×C11—24no—
445C22×C11—24no—
446C22×C11—416no—
447C22×C11—42no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—44no—
455C22×C11—44no—
456C22×C11#53514yes—
457C22×C11C23×D411yescharacteristic
458C22×C11C2×H(5,𝔽2)11yescharacteristic
459C22×C11C2×H(5,𝔽2)12yes—
460C22×C11C2×H(5,𝔽2)11yescharacteristic
461C22×C11#58512yes—
462C2×D11—24no—
463C2×D11—24no—
464C2×D11—24no—
465C2×D11—44no—
466C2×D11—44no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—44no—
471C2×D11—44no—
472C2×D11—88no—
473C2×D11—816no—
474C4×C11—22no—
475C4×C11—22no—
476C4×C11—42no—
477C4×C11—42no—
478C4×C11—44no—
479Dic11—24no—
480Dic11—42no—
481Dic11—42no—
482Dic11—42no—
483Dic11—44no—
484C25—111no—
485C25—112no—
486C25C22×D1111yescharacteristic
487C22×D4—112no—
488C22×D4—114no—
489C22×D4—114no—
490C22×D4—112no—
491C22×D4—112no—
492C22×D4—111no—
493C22×D4—112no—
494C22×D4—228no—
495C22×D4—224no—
496C22×D4—444no—
497C22×D4—444no—
498C22×D4—444no—
499C22×D4C22×D1112yes—
500C22×D4C22×D1111yescharacteristic
501C22×D4C22×D1114yes—
502C23×C4—24no—
503C23×C4—44no—
504C23×C4—111no—
505C23×C4—111no—
506C23×C4—111no—
507C23×C4—112no—
508C23×C4C22×D1112yes—
509C23×C4C22×D1112yes—
510C23×C4C22×D1111yescharacteristic
511C23×C4C22×D1111yescharacteristic
512#123—228no—
513#123—228no—
514#123—2216no—
515#123—2216no—
516#123—444no—
517#123—444no—
518#121—24no—
519#121—44no—
520#121—228no—
521#121—224no—
522#121—444no—
523#120—44no—
524#120—228no—
525#120—228no—
526#120—444no—
527#120—448no—
528C2×C4⋊C4—114no—
529C2×C4⋊C4—112no—
530C2×C4⋊C4—112no—
531C2×C4⋊C4—111no—
532C2×C4⋊C4—112no—
533C2×C4⋊C4—112no—
534C2×C4⋊C4—114no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—224no—
537C2×C4⋊C4—224no—
538C2×C4⋊C4C22×D1111yescharacteristic
539C2×C4⋊C4C22×D1112yes—
540C2×C22⋊C4—118no—
541C2×C22⋊C4—112no—
542C2×C22⋊C4—112no—
543C2×C22⋊C4—114no—
544C2×C22⋊C4—112no—
545C2×C22⋊C4—112no—
546C2×C22⋊C4—114no—
547C2×C22⋊C4—112no—
548C2×C22⋊C4—112no—
549C2×C22⋊C4—114no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—114no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—114no—
557C2×C22⋊C4—224no—
558C2×C22⋊C4—224no—
559C2×C22⋊C4C22×D1112yes—
560C2×C22⋊C4C22×D1112yes—
561C2×C22⋊C4C22×D1114yes—
562C2×C22⋊C4C22×D1114yes—
563C2×C42—114no—
564#95—114no—
565#95—114no—
566#95—112no—
567#95—114no—
568#95—114no—
569#95C22×D1114yes—
570#95C22×D1112yes—
571C2×C11—24no—
572C2×C11—44no—
573C2×C11—82no—
574C2×C11C2×#53511yescharacteristic
575C2×C11#348411yescharacteristic
576C2×C11#348511yescharacteristic
577C2×C11#353412yes—
578C2×C11#353412yes—
579D11—44no—
580D11—82no—
581C24—22no—
582C24—24no—
583C24—22no—
584C24—22no—
585C24—42no—
586C24—112no—
587C24—114no—
588C24—112no—
589C24—224no—
590C24—222no—
591C24—222no—
592C24—442no—
593C24—442no—
594C24—442no—
595C24—442no—
596C24—444no—
597C24—444no—
598C24C23×D1112yes—
599C24C23×D1112yes—
600C24C23×D1111yescharacteristic
601C2×D4—24no—
602C2×D4—24no—
603C2×D4—24no—
604C2×D4—28no—
605C2×D4—22no—
606C2×D4—44no—
607C2×D4—42no—
608C2×D4—44no—
609C2×D4—224no—
610C2×D4—224no—
611C2×D4—224no—
612C2×D4—228no—
613C2×D4—224no—
614C2×D4—228no—
615C2×D4—224no—
616C2×D4—224no—
617C2×D4—228no—
618C2×D4—222no—
619C2×D4—442no—
620C2×D4—442no—
621C2×D4—442no—
622C2×D4—444no—
623C2×D4—442no—
624C2×D4—442no—
625C2×D4—444no—
626C2×D4—444no—
627C2×D4—444no—
628C2×D4—4432no—
629C2×D4—4416no—
630C22×C4—22no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—416no—
640C22×C4—112no—
641C22×C4—114no—
642C22×C4—114no—
643C22×C4—112no—
644C22×C4—112no—
645C22×C4—112no—
646C22×C4—224no—
647C22×C4—222no—
648C22×C4—222no—
649C22×C4—222no—
650C22×C4—222no—
651C22×C4—442no—
652C22×C4—442no—
653C22×C4—442no—
654C22×C4—442no—
655C22×C4D4×D1114yes—
656C22×C4C23×D1114yes—
657C22×C4C23×D1112yes—
658C22×C4C23×D1112yes—
659C22×C4C23×D1111yescharacteristic
660C22×C4C23×D1111yescharacteristic
661C4⋊C4—22no—
662C4⋊C4—42no—
663C4⋊C4—228no—
664C4⋊C4—224no—
665C4⋊C4—224no—
666C4⋊C4—224no—
667C4⋊C4—222no—
668C4⋊C4—442no—
669C4⋊C4—444no—
670C4⋊C4—444no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—118no—
676C22⋊C4—118no—
677C22⋊C4—224no—
678C22⋊C4—228no—
679C22⋊C4—228no—
680C22⋊C4—224no—
681C22⋊C4—224no—
682C22⋊C4—224no—
683C22⋊C4—444no—
684C22⋊C4—444no—
685C22⋊C4—444no—
686C22⋊C4—444no—
687C22⋊C4—444no—
688C22⋊C4—444no—
689C22⋊C4—444no—
690C22⋊C4—444no—
691C42—444no—
692C11#3672111yescharacteristic, complemented, Sylow
693C23—22no—
694C23—22no—
695C23—28no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—24no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—48no—
708C23—48no—
709C23—44no—
710C23—44no—
711C23—114no—
712C23—224no—
713C23—222no—
714C23—222no—
715C23—224no—
716C23—228no—
717C23—222no—
718C23—222no—
719C23—224no—
720C23—222no—
721C23—224no—
722C23—444no—
723C23—444no—
724C23—448no—
725C23—884no—
726C23—884no—
727C23—884no—
728C23—884no—
729C23—888no—
730C23—888no—
731C23C2×D4×D1112yes—
732C23#6703714yes—
733C23#6703712yes—
734C23#6704212yes—
735C23C24×D1111yescharacteristic
736D4—48no—
737D4—82no—
738D4—88no—
739D4—448no—
740D4—4416no—
741D4—448no—
742D4—448no—
743D4—882no—
744D4—884no—
745D4—888no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—44no—
758C2×C4—48no—
759C2×C4—48no—
760C2×C4—44no—
761C2×C4—114no—
762C2×C4—224no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—224no—
767C2×C4—222no—
768C2×C4—224no—
769C2×C4—222no—
770C2×C4—224no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—224no—
774C2×C4—448no—
775C2×C4—444no—
776C2×C4—444no—
777C2×C4—444no—
778C2×C4C2×D4×D1112yes—
779C2×C4C2×D4×D1112yes—
780C22—22no—
781C22—22no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—416no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—44no—
796C22—44no—
797C22—224no—
798C22—224no—
799C22—224no—
800C22—444no—
801C22—444no—
802C22—442no—
803C22—442no—
804C22—442no—
805C22—444no—
806C22—444no—
807C22—888no—
808C22—8816no—
809C22#1062313814yes—
810C22C22×D4×D1111yescharacteristic
811C22C2×#6703711yescharacteristic
812C22C2×#6703712yes—
813C22C2×#6704211yescharacteristic
814C22#1062345312yes—
815C4—22no—
816C4—22no—
817C4—42no—
818C4—42no—
819C4—44no—
820C4—224no—
821C4—442no—
822C4—442no—
823C4—442no—
824C4—444no—
825C2—24no—
826C2—44no—
827C2—82no—
828C2—444no—
829C2—882no—
830C2C2×#1062313811yescharacteristic
831C2#1308224511yescharacteristic
832C2#1308225811yescharacteristic
833C2#1308280012yes—
834C2#1308280612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2847C2
hypercenter#2847D11
hypocenterC11#36721
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. C2×#10623136C2semidirect
2. C22×#66982C2semidirect
3. #13076898C2semidirect
4. #13075308C2semidirect
5. #13075304C2semidirect
6. #13074944C2semidirect
7. #13074942C2semidirect
8. #13074361C2semidirect
9. #13074360C2semidirect
10. #13073544C2semidirect
11. #13073106C2semidirect
12. #13071942C2semidirect
13. #13071927C2semidirect
14. #13071213C2semidirect
15. C11×#2847C2semidirect
16. C24×C4×C11C22semidirect
20. C2×C11×#121C22semidirect
21. C2×C11×#120C22semidirect
22. C2×#67006C22semidirect
23. C22×C22⋊Dic11C22semidirect
25. C2×#66990C22semidirect
26. C2×#66990C22semidirect
27. C2×#66988C22semidirect
29. C2×#66983C22semidirect
31. C2×#66982C22semidirect
32. C2×#66982C22semidirect
35. C22×Dic11⋊C4C22semidirect
36. C22×Dic11⋊C4C22semidirect
38. C2×#66947C22semidirect
39. C2×#66939C22semidirect
40. C2×#66936C22semidirect
41. C2×#66935C22semidirect
42. C11×#386C22semidirect
43. C11×#386C22semidirect
44. C11×#380C22semidirect
45. C11×#380C22semidirect
47. #10622836C22semidirect
48. #10622835C22semidirect
49. #10622834C22semidirect
50. #10622833C22semidirect
51. #10622826C22semidirect
52. #10622826C22semidirect
53. #10622825C22semidirect
54. #10622825C22semidirect
55. #10622607C22semidirect
56. #10622603C22semidirect
57. #10622593C22semidirect
58. #10622574C22semidirect
60. #10622571C22semidirect
61. #10622570C22semidirect
62. #10622570C22semidirect
63. #10622569C22semidirect
65. #10622568C22semidirect
66. #10622565C22semidirect
67. #10622562C22semidirect
68. #10622561C22semidirect
69. C22⋊C4×Dic11C22semidirect
70. #10622288C22semidirect
71. #10622285C22semidirect
72. #10622285C22semidirect
73. #10622283C22semidirect
74. #10622281C22semidirect
75. #10622274C22semidirect
76. #10622263C22semidirect
131. C2×(C2×D11)⋊C4D4semidirect
279. #2847D11semidirect
380. C24×C4C2×D11semidirect
393. C2×#121C2×D11semidirect
398. C2×#120C2×D11semidirect
428. #386C2×D11semidirect
429. #386C2×D11semidirect
434. #380C2×D11semidirect
435. #380C2×D11semidirect
692. C11#36721semidirect

Maximal subgroups

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

subgroupindex
C2×#106231362
C22×#669822
#130768982
#130753082
#130753042
#130749442
#130749422
#130743612
#130743602
#130735442
#130731062
#130719422
#130719272
#130712132
C11×#28472
#3672111