Finite Group Databasebeta

← #14960713

Subgroups — #14960713

Order 2816.

3034 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623335C211yesmaximal, characteristic, complemented
2#13076908C212yesmaximal, complemented
3#13075225C214yesmaximal, complemented
4#13075199C214yesmaximal, complemented
5#13074977C214yesmaximal, complemented
6#13074944C214yesmaximal, complemented
7#13074328C212yesmaximal, complemented
8#13072894C211yesmaximal, characteristic, complemented
9#13072023C212yesmaximal, complemented
10#13072001C212yesmaximal, complemented
11#13071943C211yesmaximal, characteristic, complemented
12#13071939C211yesmaximal, characteristic, complemented
13#13071926C211yesmaximal, characteristic, complemented
14#13071198C211yesmaximal, characteristic, complemented
15C22×C11×#121C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic, complemented
19C24×C4×C11C2211yescharacteristic, complemented
20C23×C22⋊D11C2211yescharacteristic
21C2×C11×#121—28no—
22C2×C11×#121C2214yes—
23C2×C11×#121C2214yescomplemented
24C22×C11×C4⋊C4C2211yescharacteristic, complemented
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic, complemented
27C2×#67006C2212yes—
28C2×#67006C2212yes—
29C22×C22⋊Dic11C2211yescharacteristic
30#10623335—28no—
31C2×#66992C2212yescomplemented
32C2×#66992C2212yescomplemented
33C2×#66990C2212yescomplemented
34C2×#66990C2212yescomplemented
35C2×#66988C2212yescomplemented
36C2×#66988C2212yescomplemented
37C2×#66982C2212yes—
38C2×#66982C2212yes—
39C2×#66982C2214yescomplemented
40C2×#66979C2212yescomplemented
41#10622860C2211yescharacteristic
42#10622860C2211yescharacteristic
43#10622860C2212yescomplemented
44#10622860C2212yescomplemented
45#10622836C2214yescomplemented
46#10622836C2214yescomplemented
47#10622836C2214yescomplemented
48#10622835C2214yescomplemented
49#10622835C2214yescomplemented
50#10622835C2214yescomplemented
51#10622834C2214yescomplemented
52#10622834C2214yescomplemented
53#10622833C2212yescomplemented
54#10622833C2212yescomplemented
55#10622826C2212yes—
56#10622826C2212yes—
57#10622826C2214yescomplemented
58#10622824C2214yescomplemented
59#10622824C2212yescomplemented
60#10622823C2214yescomplemented
61#10622823C2212yescomplemented
62#10622823C2212yescomplemented
63#10622607C2214yescomplemented
64#10622603C2214yescomplemented
65#10622597C2214yescomplemented
66#10622585C2214yescomplemented
67#10622574C2214yescomplemented
68#10622572C2214yescomplemented
69#10622570C2214yescomplemented
70#10622568C2212yescomplemented
71#10622565C2214yescomplemented
72#10622561C2214yescomplemented
73#10622559C2212yescomplemented
74#10622559C2212yescomplemented
75#10622558C2214yescomplemented
76#10622556C2212yescomplemented
77C25×C11C2311yescharacteristic
78C25×C11C2311yescharacteristic
79C25×C11C2311yescharacteristic
80C24×D11C2311yescharacteristic
81C22×D4×C11—24no—
82C22×D4×C11—24no—
83C22×D4×C11—44no—
84C22×D4×C11—44no—
85C22×D4×C11—44no—
86C22×D4×C11D418yescomplemented
87C22×D4×C11C2312yes—
88C22×D4×C11C2312yes—
89C22×D4×C11C2314yes—
90C22×D4×C11C2312yes—
91C22×D4×C11C2312yes—
92C23×C4×C11—24no—
93C23×C4×C11—44no—
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2314yes—
97C23×C4×C11C2311yescharacteristic
98C23×C4×C11C2311yescharacteristic
99C22×C22⋊D11—24no—
100C22×C22⋊D11—44no—
101C22×C22⋊D11C2312yes—
102C22×C22⋊D11C2312yes—
103C22×C22⋊D11C2312yes—
104C22×C22⋊D11C2312yes—
105C22×C22⋊D11C2314yes—
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C11×#121—216no—
110C11×#121—216no—
111C2×C11×C4⋊C4—24no—
112C2×C11×C4⋊C4C2314yes—
113C2×C11×C22⋊C4—24no—
114C2×C11×C22⋊C4—24no—
115C2×C11×C22⋊C4C2312yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C11×C22⋊C4C2312yes—
118#67006—28no—
119#67006—44no—
120C2×C22⋊Dic11—24no—
121C2×C22⋊Dic11C2312yes—
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2312yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2312yes—
126C2×C22⋊Dic11C2312yes—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2312yes—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2312yes—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2312yes—
134C2×C22⋊Dic11C2312yes—
135C2×C22⋊Dic11C2314yes—
136#66992—28no—
137#66992—28no—
138#66990—28no—
139#66990—44no—
140#66988—28no—
141#66988—44no—
142#66982—28no—
143#66982—48no—
144#66982—44no—
145C2×(C2×D11)⋊C4C2312yes—
146C2×(C2×D11)⋊C4C2312yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150#66979—44no—
151C2×C4⋊Dic11C2314yes—
152C2×Dic11⋊C4C2312yes—
153C2×Dic11⋊C4C2312yes—
154C2×Dic11⋊C4C2314yes—
155C2×Dic11⋊C4C2314yes—
156C2×Dic11⋊C4C2314yes—
157C2×C4×Dic11C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164#36715—111nomaximal, Sylow
165C24×C11—24no—
166C24×C11—24no—
167C24×C11—22no—
168C24×C11—24no—
169C24×C11—42no—
170C24×C11—42no—
171C24×C11—42no—
172C24×C11—42no—
173C24×C11—42no—
174C24×C11—42no—
175C24×C11C2×D414yes—
176C24×C11C2×D414yes—
177C24×C11C2412yes—
178C24×C11C2411yescharacteristic
179C24×C11C2412yes—
180C24×C11C2411yescharacteristic
181C24×C11C2411yescharacteristic
182C23×D11—22no—
183C23×D11—42no—
184C23×D11—42no—
185C23×D11—42no—
186C23×D11C2412yes—
187C2×D4×C11—24no—
188C2×D4×C11—24no—
189C2×D4×C11—28no—
190C2×D4×C11—24no—
191C2×D4×C11—24no—
192C2×D4×C11—416no—
193C2×D4×C11—42no—
194C2×D4×C11—42no—
195C2×D4×C11—42no—
196C2×D4×C11—42no—
197C2×D4×C11—42no—
198C2×D4×C11—42no—
199C2×D4×C11—44no—
200C2×D4×C11—44no—
201C2×D4×C11—416no—
202C2×D4×C11—416no—
203C2×D4×C11C2×D418yes—
204C2×D4×C11C2×D418yes—
205C22×C4×C11—22no—
206C22×C4×C11—24no—
207C22×C4×C11—24no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—28no—
211C22×C4×C11—24no—
212C22×C4×C11—28no—
213C22×C4×C11—44no—
214C22×C4×C11—42no—
215C22×C4×C11—416no—
216C22×C4×C11C2×D414yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2412yes—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—24no—
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—42no—
228C2×C22⋊D11—42no—
229C2×C22⋊D11—44no—
230C2×C22⋊D11—44no—
231C2×C22⋊D11—44no—
232C2×C22⋊D11—44no—
233C2×C22⋊D11—44no—
234C2×C22⋊D11—416no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—22no—
238C22×Dic11—42no—
239C22×Dic11—42no—
240C22×Dic11—42no—
241C22×Dic11C2412yes—
242C22×Dic11C2414yes—
243C22×Dic11C2412yes—
244C22×Dic11C2414yes—
245C22×Dic11C2412yes—
246C11×C4⋊C4—28no—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—24no—
249C11×C22⋊C4—28no—
250C22⋊Dic11—24no—
251C22⋊Dic11—24no—
252C22⋊Dic11—24no—
253C22⋊Dic11—24no—
254C22⋊Dic11—24no—
255C22⋊Dic11—24no—
256C22⋊Dic11—44no—
257C22⋊Dic11—42no—
258C22⋊Dic11—44no—
259C22⋊Dic11—42no—
260C22⋊Dic11—42no—
261C22⋊Dic11—44no—
262C22⋊Dic11—42no—
263C22⋊Dic11—44no—
264C22⋊Dic11—44no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—28no—
268(C2×D11)⋊C4—44no—
269(C2×D11)⋊C4—44no—
270C4⋊Dic11—44no—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273Dic11⋊C4—28no—
274Dic11⋊C4—44no—
275Dic11⋊C4—44no—
276C4×Dic11—44no—
277C2×#534—111no—
278C22×#121D1111yescharacteristic, complemented
279#2849—112no—
280#2701—114no—
281#2699—114no—
282#2682—114no—
283#2678—114no—
284#2613—112no—
285#2483—111no—
286#2413—112no—
287#2411—112no—
288#2405—111no—
289#2405—111no—
290#2403—111no—
291#2309—111no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—28no—
295C23×C11—22no—
296C23×C11—24no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—24no—
304C23×C11—22no—
305C23×C11—28no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—24no—
309C23×C11—22no—
310C23×C11—24no—
311C23×C11—44no—
312C23×C11—44no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11—416no—
316C23×C11—44no—
317C23×C11—44no—
318C23×C11—44no—
319C23×C11—88no—
320C23×C11—88no—
321C23×C11C22×D412yes—
322C23×C11C22×D414yes—
323C23×C11C22×D412yes—
324C23×C11C22×D412yes—
325C23×C11H(5,𝔽2)14yes—
326C23×C11C2511yescharacteristic
327C22×D11—22no—
328C22×D11—24no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—24no—
332C22×D11—44no—
333C22×D11—82no—
334C22×D11—82no—
335C22×D11—88no—
336D4×C11—48no—
337D4×C11—48no—
338D4×C11—48no—
339D4×C11—48no—
340D4×C11—416no—
341C2×C4×C11—28no—
342C2×C4×C11—28no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—24no—
350C2×C4×C11—24no—
351C2×C4×C11—416no—
352C2×C4×C11—44no—
353C2×C4×C11—44no—
354C2×C4×C11C22×D414yes—
355C2×C4×C11H(5,𝔽2)14yes—
356C22⋊D11—48no—
357C22⋊D11—48no—
358C22⋊D11—84no—
359C22⋊D11—84no—
360C22⋊D11—88no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—24no—
365C2×Dic11—24no—
366C2×Dic11—24no—
367C2×Dic11—24no—
368C2×Dic11—22no—
369C2×Dic11—24no—
370C2×Dic11—22no—
371C2×Dic11—24no—
372C2×Dic11—24no—
373C2×Dic11—24no—
374C2×Dic11—44no—
375C2×Dic11—82no—
376C2×Dic11—82no—
377C23×D4—111no—
378C23×D4C2×D1111yescharacteristic
379C23×D4C2×D1111yescharacteristic
380C23×D4C2×D1111yescharacteristic, complemented
381C24×C4C2×D1111yescharacteristic, complemented
382#534—228no—
383C2×#123—112no—
384C2×#123—112no—
385C2×#123—112no—
386C2×#123—114no—
387C2×#123—112no—
388C2×#121—28no—
389C2×#121—112no—
390C2×#121—112no—
391C2×#121C2×D1114yes—
392C2×#121C2×D1114yescomplemented
393C2×#120—112no—
394C2×#120—112no—
395C2×#120—112no—
396C2×#120—112no—
397C2×#117—112no—
398C22×C4⋊C4C2×D1111yescharacteristic, complemented
399C22×C22⋊C4—111no—
400C22×C22⋊C4C2×D1111yescharacteristic
401C22×C22⋊C4C2×D1111yescharacteristic, complemented
402#398—114no—
403#397—114no—
404#396—114no—
405#396—114no—
406#394—114no—
407#394—114no—
408#394—114no—
409#394—114no—
410#394—114no—
411#392—114no—
412#392—114no—
413#392—114no—
414#390—114no—
415#390—114no—
416#390—114no—
417#389—114no—
418#388—114no—
419#388—114no—
420#386—112no—
421#386—112no—
422#386—112no—
423#386—112no—
424#386—114no—
425#385—112no—
426#385—112no—
427#385—114no—
428#385—112no—
429#385—112no—
430#381—114no—
431#381—112no—
432#381—112no—
433#379—112no—
434#379—111no—
435#379—111no—
436#379—112no—
437#379—112no—
438C22×C11—22no—
439C22×C11—22no—
440C22×C11—28no—
441C22×C11—24no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—24no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—22no—
448C22×C11—22no—
449C22×C11—24no—
450C22×C11—416no—
451C22×C11—44no—
452C22×C11—44no—
453C22×C11—44no—
454C22×C11—44no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—44no—
459C22×C11—44no—
460C22×C11—88no—
461C22×C11—88no—
462C22×C11#53414yes—
463C22×C11C23×D411yescharacteristic
464C22×C11C2×H(5,𝔽2)12yes—
465C22×C11C2×H(5,𝔽2)12yes—
466C22×C11#58512yes—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—44no—
471C2×D11—44no—
472C2×D11—88no—
473C4×C11—24no—
474C4×C11—24no—
475C4×C11—42no—
476C4×C11—42no—
477Dic11—42no—
478Dic11—42no—
479Dic11—42no—
480Dic11—44no—
481Dic11—44no—
482C25—111no—
483C25C22×D1111yescharacteristic
484C25C22×D1111yescharacteristic
485C25C22×D1111yescharacteristic
486C22×D4—24no—
487C22×D4—24no—
488C22×D4—44no—
489C22×D4—44no—
490C22×D4—44no—
491C22×D4—112no—
492C22×D4—112no—
493C22×D4—112no—
494C22×D4—112no—
495C22×D4—114no—
496C22×D4—224no—
497C22×D4—444no—
498C22×D4C22⋊D1118yescomplemented
499C22×D4C22×D1112yes—
500C22×D4C22×D1112yes—
501C22×D4C22×D1114yes—
502C22×D4C22×D1112yes—
503C22×D4C22×D1112yes—
504C23×C4—24no—
505C23×C4—44no—
506C23×C4—111no—
507C23×C4—111no—
508C23×C4—111no—
509C23×C4C22×D1111yescharacteristic
510C23×C4C22×D1111yescharacteristic
511C23×C4C22×D1114yes—
512C23×C4C22×D1111yescharacteristic
513C23×C4C22×D1111yescharacteristic
514#123—228no—
515#123—228no—
516#123—448no—
517#123—444no—
518#123—444no—
519#121—216no—
520#121—216no—
521#121—228no—
522#121—228no—
523#120—228no—
524#120—228no—
525#120—444no—
526#120—444no—
527#117—444no—
528C2×C4⋊C4—24no—
529C2×C4⋊C4—112no—
530C2×C4⋊C4—112no—
531C2×C4⋊C4—114no—
532C2×C4⋊C4—114no—
533C2×C4⋊C4—114no—
534C2×C4⋊C4—114no—
535C2×C4⋊C4C22×D1114yes—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—112no—
539C2×C22⋊C4—112no—
540C2×C22⋊C4—112no—
541C2×C22⋊C4—112no—
542C2×C22⋊C4—112no—
543C2×C22⋊C4—112no—
544C2×C22⋊C4—112no—
545C2×C22⋊C4—112no—
546C2×C22⋊C4—114no—
547C2×C22⋊C4—112no—
548C2×C22⋊C4—114no—
549C2×C22⋊C4—114no—
550C2×C22⋊C4—112no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—112no—
553C2×C22⋊C4—112no—
554C2×C22⋊C4—114no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—114no—
557C2×C22⋊C4—114no—
558C2×C22⋊C4—224no—
559C2×C22⋊C4C22×D1112yes—
560C2×C22⋊C4C22×D1112yes—
561C2×C22⋊C4C22×D1114yes—
562C2×C42—114no—
563#95—114no—
564#95—114no—
565#95—114no—
566#95—114no—
567#95—114no—
568#95—114no—
569C2×C11—24no—
570C2×C11—42no—
571C2×C11—44no—
572C2×C11—42no—
573C2×C11—82no—
574C2×C11C2×#53411yescharacteristic
575C2×C11#348411yescharacteristic
576C2×C11#348511yescharacteristic
577C2×C11#354214yes—
578D11—82no—
579C24—24no—
580C24—24no—
581C24—22no—
582C24—24no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—42no—
589C24—112no—
590C24—222no—
591C24—442no—
592C24—442no—
593C24—442no—
594C24C2×C22⋊D1114yes—
595C24C2×C22⋊D1114yes—
596C24C23×D1112yes—
597C24C23×D1111yescharacteristic
598C24C23×D1112yes—
599C24C23×D1111yescharacteristic
600C24C23×D1111yescharacteristic
601C2×D4—24no—
602C2×D4—24no—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—416no—
615C2×D4—416no—
616C2×D4—416no—
617C2×D4—224no—
618C2×D4—224no—
619C2×D4—224no—
620C2×D4—224no—
621C2×D4—224no—
622C2×D4—224no—
623C2×D4—442no—
624C2×D4—442no—
625C2×D4—444no—
626C2×D4—444no—
627C2×D4—444no—
628C2×D4—444no—
629C2×D4—444no—
630C2×D4—4416no—
631C2×D4C2×C22⋊D1118yes—
632C2×D4C2×C22⋊D1118yes—
633C22×C4—24no—
634C22×C4—22no—
635C22×C4—24no—
636C22×C4—24no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—28no—
640C22×C4—28no—
641C22×C4—44no—
642C22×C4—42no—
643C22×C4—416no—
644C22×C4—112no—
645C22×C4—114no—
646C22×C4—112no—
647C22×C4—114no—
648C22×C4—112no—
649C22×C4—222no—
650C22×C4—222no—
651C22×C4—222no—
652C22×C4—442no—
653C22×C4—442no—
654C22×C4—442no—
655C22×C4C2×C22⋊D1114yes—
656C22×C4C23×D1112yes—
657C22×C4C23×D1112yes—
658C22×C4C23×D1112yes—
659C22×C4C23×D1112yes—
660C4⋊C4—28no—
661C4⋊C4—228no—
662C4⋊C4—224no—
663C4⋊C4—224no—
664C4⋊C4—444no—
665C4⋊C4—444no—
666C4⋊C4—444no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—28no—
670C22⋊C4—224no—
671C22⋊C4—224no—
672C22⋊C4—224no—
673C22⋊C4—224no—
674C22⋊C4—224no—
675C22⋊C4—224no—
676C22⋊C4—228no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—444no—
680C22⋊C4—444no—
681C22⋊C4—444no—
682C22⋊C4—442no—
683C22⋊C4—444no—
684C22⋊C4—442no—
685C22⋊C4—444no—
686C22⋊C4—442no—
687C22⋊C4—444no—
688C22⋊C4—444no—
689C22⋊C4—442no—
690C42—444no—
691C11#3671511yescharacteristic, complemented, Sylow
692C23—22no—
693C23—22no—
694C23—28no—
695C23—24no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—24no—
704C23—22no—
705C23—28no—
706C23—22no—
707C23—24no—
708C23—22no—
709C23—24no—
710C23—22no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—416no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—88no—
720C23—88no—
721C23—224no—
722C23—222no—
723C23—222no—
724C23—224no—
725C23—222no—
726C23—444no—
727C23—882no—
728C23—882no—
729C23—888no—
730C23#6703714yes—
731C23C22×C22⋊D1112yes—
732C23C22×C22⋊D1112yes—
733C23C22×C22⋊D1114yes—
734C23C22×C22⋊D1112yes—
735C23C24×D1111yescharacteristic
736D4—48no—
737D4—48no—
738D4—48no—
739D4—48no—
740D4—416no—
741D4—448no—
742D4—448no—
743D4—884no—
744D4—884no—
745D4—888no—
746C2×C4—28no—
747C2×C4—28no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—416no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—224no—
760C2×C4—224no—
761C2×C4—224no—
762C2×C4—224no—
763C2×C4—222no—
764C2×C4—224no—
765C2×C4—222no—
766C2×C4—224no—
767C2×C4—224no—
768C2×C4—224no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—444no—
773C2×C4—882no—
774C2×C4—882no—
775C2×C4#6703714yes—
776C2×C4C22×C22⋊D1114yes—
777C22—28no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—24no—
782C22—22no—
783C22—24no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—24no—
788C22—22no—
789C22—416no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—88no—
800C22—88no—
801C22—444no—
802C22—444no—
803C22—442no—
804C22—442no—
805C22—442no—
806C22—888no—
807C22#1062333514yes—
808C22C2×#6703712yes—
809C22C2×#6703712yes—
810C22#1062345312yes—
811C22C23×C22⋊D1111yescharacteristic
812C4—24no—
813C4—24no—
814C4—42no—
815C4—42no—
816C4—444no—
817C4—444no—
818C4—442no—
819C4—442no—
820C4—442no—
821C2—24no—
822C2—44no—
823C2—42no—
824C2—42no—
825C2—82no—
826C2—882no—
827C2C2×#1062333511yescharacteristic
828C2#1308225111yescharacteristic
829C2#1308226011yescharacteristic
830C2#1308293614yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC22×C11×#121C2
hypercenterC22×#121D11
hypocenterC11#36715
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10623335C2semidirect
2. #13076908C2semidirect
3. #13075225C2semidirect
4. #13075199C2semidirect
5. #13074977C2semidirect
6. #13074944C2semidirect
7. #13074328C2semidirect
8. #13072894C2semidirect
9. #13072023C2semidirect
10. #13072001C2semidirect
11. #13071943C2semidirect
12. #13071939C2semidirect
13. #13071926C2semidirect
14. #13071198C2semidirect
15. C22×C11×#121C2semidirect
18. C23×D4×C11C22semidirect
19. C24×C4×C11C22semidirect
23. C2×C11×#121C22semidirect
24. C22×C11×C4⋊C4C22semidirect
26. C22×C11×C22⋊C4C22semidirect
31. C2×#66992C22semidirect
32. C2×#66992C22semidirect
33. C2×#66990C22semidirect
34. C2×#66990C22semidirect
35. C2×#66988C22semidirect
36. C2×#66988C22semidirect
39. C2×#66982C22semidirect
40. C2×#66979C22semidirect
43. #10622860C22semidirect
44. #10622860C22semidirect
45. #10622836C22semidirect
46. #10622836C22semidirect
47. #10622836C22semidirect
48. #10622835C22semidirect
49. #10622835C22semidirect
50. #10622835C22semidirect
51. #10622834C22semidirect
52. #10622834C22semidirect
53. #10622833C22semidirect
54. #10622833C22semidirect
57. #10622826C22semidirect
58. #10622824C22semidirect
59. #10622824C22semidirect
60. #10622823C22semidirect
61. #10622823C22semidirect
62. #10622823C22semidirect
63. #10622607C22semidirect
64. #10622603C22semidirect
65. #10622597C22semidirect
66. #10622585C22semidirect
67. #10622574C22semidirect
68. #10622572C22semidirect
69. #10622570C22semidirect
70. #10622568C22semidirect
71. #10622565C22semidirect
72. #10622561C22semidirect
73. #10622559C22semidirect
74. #10622559C22semidirect
75. #10622558C22semidirect
76. #10622556C22semidirect
86. C22×D4×C11D4semidirect
278. C22×#121D11semidirect
380. C23×D4C2×D11semidirect
381. C24×C4C2×D11semidirect
392. C2×#121C2×D11semidirect
398. C22×C4⋊C4C2×D11semidirect
401. C22×C22⋊C4C2×D11semidirect
498. C22×D4C22⋊D11semidirect
691. C11#36715semidirect

Maximal subgroups

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

subgroupindex
C2×#106233352
#130769082
#130752252
#130751992
#130749772
#130749442
#130743282
#130728942
#130720232
#130720012
#130719432
#130719392
#130719262
#130711982
C22×C11×#1212
#3671511