Finite Group Databasebeta

← #14960781

Subgroups — #14960781

Order 2816.

2970 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623335C211yesmaximal, characteristic, complemented
2C22×#66936C211yesmaximal, characteristic, complemented
3#13076897C212yesmaximal, complemented
4#13075309C214yesmaximal, complemented
5#13075305C214yesmaximal, complemented
6#13074947C214yesmaximal, complemented
7#13074945C214yesmaximal, complemented
8#13074362C212yesmaximal, complemented
9#13073546C212yesmaximal, complemented
10#13073106C212yesmaximal, complemented
11#13071943C211yesmaximal, characteristic, complemented
12#13071929C211yesmaximal, characteristic, complemented
13#13071926C211yesmaximal, characteristic, complemented
14#13071212C211yesmaximal, characteristic, complemented
15C11×#2405C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic, complemented
20C2×C11×#123C2212yescomplemented
21C22×C11×C22⋊C4C2211yescharacteristic
22C2×#67006C2212yescomplemented
23C2×#67006C2212yescomplemented
24C22×C22⋊Dic11C2211yescharacteristic
25#10623335—28no—
26C2×#66992C2212yes—
27C2×#66992C2212yes—
28C2×#66990C2212yescomplemented
29C2×#66990C2212yescomplemented
30C2×#66988C2212yescomplemented
31C2×#66982C2212yescomplemented
32C2×#66982C2212yescomplemented
33C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
34C22×C4⋊Dic11C2211yescharacteristic, complemented
35C22×Dic11⋊C4C2211yescharacteristic, complemented
36C2×#66937C2214yescomplemented
37C2×#66936—28no—
38C2×#66936C2214yescomplemented
39C2×#66936C2214yescomplemented
40C2×#66935C2212yescomplemented
41C2×#66935C2212yescomplemented
42C11×#394C2214yescomplemented
43C11×#386C2212yescomplemented
44C11×#385C2212yescomplemented
45C11×#379C2211yescharacteristic
46C11×#379C2212yescomplemented
47#10622860C2211yescharacteristic
48#10622836C2214yes—
49#10622833C2212yescomplemented
50#10622826C2212yescomplemented
51#10622826C2212yescomplemented
52#10622607C2214yescomplemented
53#10622605C2214yescomplemented
54#10622601C2214yescomplemented
55#10622597C2214yescomplemented
56#10622574C2214yescomplemented
57#10622573C2214yes—
58#10622573C2214yescomplemented
59#10622572C2214yescomplemented
60#10622571C2212yescomplemented
61#10622571C2212yescomplemented
62#10622570C2214yescomplemented
63#10622570C2214yescomplemented
64#10622569C2214yescomplemented
65#10622568C2212yescomplemented
66#10622565C2214yescomplemented
67#10622561C2214yescomplemented
68#10622559C2212yescomplemented
69#10622558C2214yescomplemented
70#10622557C2214yescomplemented
71#10622555C2212yescomplemented
72C22⋊C4×Dic11C2212yescomplemented
73#10622288C2214yescomplemented
74#10622280C2214yescomplemented
75#10622278C2214yescomplemented
76#10622263C2214yescomplemented
77C25×C11C2311yescharacteristic
78C25×C11C2311yescharacteristic
79C24×D11C2311yescharacteristic
80C24×D11C2311yescharacteristic
81C22×D4×C11—24no—
82C22×D4×C11—44no—
83C22×D4×C11C2312yes—
84C22×D4×C11C2312yes—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—44no—
91C22×C22⋊D11—44no—
92C22×C22⋊D11C2312yes—
93C22×C22⋊D11C2312yes—
94C22×C22⋊D11C2312yes—
95C22×C22⋊D11C2312yes—
96C22×C22⋊D11C2314yes—
97C22×C22⋊D11C2312yes—
98C22×C22⋊D11C2312yes—
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C22×D44C2314yes—
104C22×C4×D11—24no—
105C22×C4×D11—44no—
106C22×C4×D11C2314yes—
107C11×#123—44no—
108C2×C11×C4⋊C4C2314yes—
109C2×C11×C22⋊C4—24no—
110C2×C11×C22⋊C4C2312yes—
111C2×C11×C22⋊C4C2312yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2312yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C11×C22⋊C4C2312yes—
116C2×C11×C22⋊C4C2314yes—
117#67006—28no—
118#67006—44no—
119C2×C22⋊Dic11D418yescomplemented
120C2×C22⋊Dic11C2312yes—
121C2×C22⋊Dic11C2312yes—
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2312yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2312yes—
127C2×C22⋊Dic11C2312yes—
128#66992—28no—
129#66992—28no—
130#66990—28no—
131#66990—44no—
132#66988—28no—
133#66982—28no—
134#66982—44no—
135C2×(C2×D11)⋊C4—24no—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2312yes—
138C2×(C2×D11)⋊C4C2312yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×C4⋊Dic11—24no—
145C2×C4⋊Dic11C2314yes—
146C2×Dic11⋊C4—24no—
147C2×Dic11⋊C4C2314yes—
148C2×Dic11⋊C4C2312yes—
149C2×Dic11⋊C4C2312yes—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×C4×Dic11C2314yes—
153#66937—48no—
154#66936—216no—
155#66936—216no—
156#66935—44no—
157#66935—44no—
158C11×#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164#36721—111nomaximal, Sylow
165C24×C11—24no—
166C24×C11—22no—
167C24×C11—42no—
168C24×C11—42no—
169C24×C11—42no—
170C24×C11—42no—
171C24×C11—42no—
172C24×C11C2×D414yes—
173C24×C11C2412yes—
174C24×C11C2411yescharacteristic
175C24×C11C2411yescharacteristic
176C24×C11C2411yescharacteristic
177C23×D11—22no—
178C23×D11—24no—
179C23×D11—24no—
180C23×D11—22no—
181C23×D11—42no—
182C23×D11—42no—
183C23×D11—42no—
184C23×D11—42no—
185C23×D11C2412yes—
186C23×D11C2412yes—
187C2×D4×C11—24no—
188C2×D4×C11—24no—
189C2×D4×C11—24no—
190C2×D4×C11—24no—
191C2×D4×C11—42no—
192C2×D4×C11—42no—
193C2×D4×C11—416no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—24no—
198C22×C4×C11—42no—
199C22×C4×C11—42no—
200C22×C4×C11C2414yes—
201C22×C4×C11C2412yes—
202C22×C4×C11C2412yes—
203C22×C4×C11C2412yes—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—24no—
209C2×C22⋊D11—24no—
210C2×C22⋊D11—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—28no—
215C2×C22⋊D11—42no—
216C2×C22⋊D11—42no—
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—
224C2×C22⋊D11—416no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—42no—
228C22×Dic11—42no—
229C22×Dic11—42no—
230C22×Dic11—42no—
231C22×Dic11C2×D414yes—
232C22×Dic11C2×D414yes—
233C22×Dic11C2414yes—
234C22×Dic11C2412yes—
235C22×Dic11C2412yes—
236C22×Dic11C2412yes—
237C22×Dic11C2412yes—
238C2×D44—28no—
239C2×D44—44no—
240C2×D44—44no—
241C2×C4×D11—28no—
242C2×C4×D11—28no—
243C2×C4×D11—44no—
244C2×C4×D11—416no—
245C11×C4⋊C4—44no—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—24no—
249C11×C22⋊C4—42no—
250C11×C22⋊C4—44no—
251C11×C22⋊C4—42no—
252C11×C22⋊C4—44no—
253C22⋊Dic11—24no—
254C22⋊Dic11—24no—
255C22⋊Dic11—24no—
256C22⋊Dic11—42no—
257C22⋊Dic11—42no—
258C22⋊Dic11—44no—
259C22⋊Dic11C2×D418yes—
260C22⋊Dic11C2×D418yes—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—44no—
265(C2×D11)⋊C4—44no—
266(C2×D11)⋊C4—44no—
267(C2×D11)⋊C4—44no—
268(C2×D11)⋊C4—44no—
269C4⋊Dic11—28no—
270Dic11⋊C4—28no—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273Dic11⋊C4—44no—
274Dic11⋊C4—44no—
275C4×Dic11—44no—
276C2×#534—111no—
277C22×#123—111no—
278#2847—112no—
279#2706—114no—
280#2706—114no—
281#2678—114no—
282#2678—114no—
283#2618—112no—
284#2539—112no—
285#2504—112no—
286#2405—111no—
287#2405D1111yescharacteristic, complemented
288#2403—111no—
289#2403—111no—
290#2312—111no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—28no—
300C23×C11—22no—
301C23×C11—24no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—24no—
305C23×C11—44no—
306C23×C11—44no—
307C23×C11—44no—
308C23×C11—88no—
309C23×C11—82no—
310C23×C11—82no—
311C23×C11—88no—
312C23×C11C22×D412yes—
313C23×C11C22×D412yes—
314C23×C11C22×D412yes—
315C23×C11H(5,𝔽2)14yes—
316C23×C11C2511yescharacteristic
317C22×D11—28no—
318C22×D11—22no—
319C22×D11—24no—
320C22×D11—22no—
321C22×D11—24no—
322C22×D11—22no—
323C22×D11—24no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—24no—
327C22×D11—416no—
328C22×D11—44no—
329C22×D11—44no—
330C22×D11—44no—
331C22×D11—82no—
332C22×D11—82no—
333C22×D11—88no—
334C22×D11H(5,𝔽2)14yes—
335D4×C11—48no—
336D4×C11—48no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—24no—
341C2×C4×C11—24no—
342C2×C4×C11—22no—
343C2×C4×C11—24no—
344C2×C4×C11—24no—
345C2×C4×C11—22no—
346C2×C4×C11—24no—
347C2×C4×C11—44no—
348C2×C4×C11—44no—
349C2×C4×C11—44no—
350C22⋊D11—48no—
351C22⋊D11—48no—
352C22⋊D11—48no—
353C22⋊D11—48no—
354C22⋊D11—84no—
355C22⋊D11—84no—
356C22⋊D11—88no—
357C2×Dic11—24no—
358C2×Dic11—24no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—24no—
363C2×Dic11—24no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—24no—
368C2×Dic11—44no—
369C2×Dic11—44no—
370C2×Dic11—44no—
371C2×Dic11—44no—
372C2×Dic11C22×D414yes—
373C2×Dic11C22×D414yes—
374D44—88no—
375C4×D11—416no—
376C23×D4—111no—
377C23×D4—111no—
378C23×D4C2×D1111yescharacteristic
379C24×C4—111no—
380#534—228no—
381C2×#123—112no—
382C2×#123—112no—
383C2×#123—112no—
384C2×#123—114no—
385C2×#123—114no—
386C2×#123—228no—
387C2×#123C2×D1112yescomplemented
388C2×#121—112no—
389C2×#121—112no—
390C2×#121—114no—
391C2×#120—112no—
392C2×#120—112no—
393C2×#120—112no—
394C2×#120—112no—
395C2×#120—112no—
396C2×#120—112no—
397C22×C4⋊C4—111no—
398C22×C4⋊C4—111no—
399C22×C22⋊C4—111no—
400C22×C22⋊C4—111no—
401C22×C22⋊C4C2×D1111yescharacteristic
402#399—114no—
403#398—114no—
404#397—114no—
405#397—114no—
406#396—114no—
407#396—114no—
408#394—114no—
409#394—114no—
410#394C2×D1114yescomplemented
411#392—114no—
412#392—114no—
413#392—114no—
414#390—114no—
415#390—114no—
416#390—114no—
417#388—114no—
418#388—114no—
419#386—112no—
420#386—112no—
421#386—112no—
422#386—114no—
423#386—112no—
424#386—112no—
425#386—114no—
426#386C2×D1112yescomplemented
427#385—112no—
428#385C2×D1112yescomplemented
429#382—114no—
430#380—112no—
431#380—114no—
432#379—111no—
433#379—112no—
434#379C2×D1111yescharacteristic
435#379C2×D1112yescomplemented
436C4×C22⋊C4—112no—
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—28no—
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—44no—
447C22×C11—44no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—44no—
452C22×C11—44no—
453C22×C11—88no—
454C22×C11—88no—
455C22×C11#53514yes—
456C22×C11C23×D411yescharacteristic
457C22×C11C2×H(5,𝔽2)12yes—
458C22×C11C2×H(5,𝔽2)12yes—
459C22×C11#58512yes—
460C2×D11—24no—
461C2×D11—28no—
462C2×D11—416no—
463C2×D11—42no—
464C2×D11—42no—
465C2×D11—44no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—44no—
470C2×D11—44no—
471C2×D11—88no—
472C4×C11—42no—
473C4×C11—42no—
474C4×C11—42no—
475C4×C11—44no—
476Dic11—24no—
477Dic11—24no—
478Dic11—42no—
479Dic11—42no—
480Dic11—44no—
481C25—111no—
482C25—111no—
483C25C22×D1111yescharacteristic
484C25C22×D1111yescharacteristic
485C22×D4—24no—
486C22×D4—44no—
487C22×D4—112no—
488C22×D4—112no—
489C22×D4—112no—
490C22×D4—112no—
491C22×D4—114no—
492C22×D4—112no—
493C22×D4—112no—
494C22×D4—114no—
495C22×D4—224no—
496C22×D4—224no—
497C22×D4—444no—
498C22×D4—444no—
499C22×D4C22×D1112yes—
500C22×D4C22×D1112yes—
501C23×C4—111no—
502C23×C4—111no—
503C23×C4—111no—
504C23×C4—111no—
505C23×C4—114no—
506C23×C4—224no—
507C23×C4—444no—
508C23×C4C22×D1111yescharacteristic
509C23×C4C22×D1111yescharacteristic
510C23×C4C22×D1111yescharacteristic
511#123—44no—
512#123—2216no—
513#123—2216no—
514#123—228no—
515#123—228no—
516#123—444no—
517#121—228no—
518#121—228no—
519#121—448no—
520#120—228no—
521#120—228no—
522#120—444no—
523#120—444no—
524#120—444no—
525#120—444no—
526C2×C4⋊C4—114no—
527C2×C4⋊C4—114no—
528C2×C4⋊C4—112no—
529C2×C4⋊C4—112no—
530C2×C4⋊C4—114no—
531C2×C4⋊C4—114no—
532C2×C4⋊C4—224no—
533C2×C4⋊C4—224no—
534C2×C4⋊C4C22×D1114yes—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—118no—
537C2×C22⋊C4—112no—
538C2×C22⋊C4—112no—
539C2×C22⋊C4—112no—
540C2×C22⋊C4—112no—
541C2×C22⋊C4—112no—
542C2×C22⋊C4—114no—
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—114no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—224no—
554C2×C22⋊C4C22×D1112yes—
555C2×C22⋊C4C22×D1112yes—
556C2×C22⋊C4C22×D1112yes—
557C2×C22⋊C4C22×D1112yes—
558C2×C22⋊C4C22×D1114yes—
559C2×C22⋊C4C22×D1114yes—
560C2×C22⋊C4C22×D1112yes—
561C2×C42—114no—
562#95—114no—
563#95—114no—
564#95—114no—
565#95—114no—
566#95—114no—
567#95C22×D1114yes—
568C2×C11—24no—
569C2×C11—42no—
570C2×C11—42no—
571C2×C11—82no—
572C2×C11C2×#53511yescharacteristic
573C2×C11#348411yescharacteristic
574C2×C11#348511yescharacteristic
575C2×C11#353414yes—
576D11—44no—
577D11—82no—
578C24—24no—
579C24—22no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—112no—
586C24—112no—
587C24—224no—
588C24—222no—
589C24—224no—
590C24—222no—
591C24—442no—
592C24—442no—
593C24—442no—
594C24—442no—
595C24D4×D1114yes—
596C24C23×D1112yes—
597C24C23×D1111yescharacteristic
598C24C23×D1111yescharacteristic
599C24C23×D1111yescharacteristic
600C2×D4—24no—
601C2×D4—24no—
602C2×D4—24no—
603C2×D4—24no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—416no—
607C2×D4—228no—
608C2×D4—224no—
609C2×D4—224no—
610C2×D4—224no—
611C2×D4—224no—
612C2×D4—224no—
613C2×D4—224no—
614C2×D4—224no—
615C2×D4—224no—
616C2×D4—224no—
617C2×D4—224no—
618C2×D4—228no—
619C2×D4—444no—
620C2×D4—444no—
621C2×D4—442no—
622C2×D4—442no—
623C2×D4—442no—
624C2×D4—442no—
625C2×D4—444no—
626C2×D4—444no—
627C2×D4—444no—
628C2×D4—444no—
629C2×D4—4416no—
630C2×D4—4416no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—24no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—114no—
640C22×C4—114no—
641C22×C4—114no—
642C22×C4—112no—
643C22×C4—112no—
644C22×C4—228no—
645C22×C4—228no—
646C22×C4—222no—
647C22×C4—222no—
648C22×C4—444no—
649C22×C4—4416no—
650C22×C4—442no—
651C22×C4—442no—
652C22×C4—442no—
653C22×C4—442no—
654C22×C4C23×D1114yes—
655C22×C4C23×D1112yes—
656C22×C4C23×D1112yes—
657C22×C4C23×D1112yes—
658C4⋊C4—44no—
659C4⋊C4—228no—
660C4⋊C4—228no—
661C4⋊C4—224no—
662C4⋊C4—224no—
663C4⋊C4—444no—
664C4⋊C4—444no—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—42no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—42no—
672C22⋊C4—118no—
673C22⋊C4—118no—
674C22⋊C4—228no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—444no—
681C22⋊C4—444no—
682C22⋊C4—444no—
683C22⋊C4—444no—
684C22⋊C4—444no—
685C22⋊C4—442no—
686C22⋊C4—444no—
687C22⋊C4—442no—
688C42—444no—
689C11#3672111yescharacteristic, complemented, Sylow
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—28no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—24no—
703C23—24no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—88no—
708C23—82no—
709C23—82no—
710C23—88no—
711C23—114no—
712C23—228no—
713C23—222no—
714C23—224no—
715C23—224no—
716C23—222no—
717C23—222no—
718C23—222no—
719C23—222no—
720C23—224no—
721C23—224no—
722C23—4416no—
723C23—444no—
724C23—444no—
725C23—444no—
726C23—882no—
727C23—882no—
728C23—888no—
729C23C2×D4×D1112yes—
730C23C2×D4×D1112yes—
731C23C2×D4×D1112yes—
732C23#6703714yes—
733C23C24×D1111yescharacteristic
734D4—48no—
735D4—48no—
736D4—448no—
737D4—448no—
738D4—448no—
739D4—448no—
740D4—888no—
741D4—884no—
742D4—884no—
743D4—888no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—114no—
758C2×C4—114no—
759C2×C4—224no—
760C2×C4—224no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—224no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—224no—
767C2×C4—224no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—4416no—
771C2×C4—444no—
772C2×C4—444no—
773C2×C4—444no—
774C2×C4—444no—
775C22—22no—
776C22—22no—
777C22—28no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—44no—
785C22—44no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—44no—
790C22—44no—
791C22—88no—
792C22—88no—
793C22—224no—
794C22—228no—
795C22—4416no—
796C22—442no—
797C22—442no—
798C22—444no—
799C22—442no—
800C22—442no—
801C22—442no—
802C22—444no—
803C22—444no—
804C22—888no—
805C22#1062312314yes—
806C22C22×D4×D1111yescharacteristic
807C22C2×#6703712yes—
808C22#1062345312yes—
809C22D11×H(5,𝔽2)12yes—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—44no—
814C4—224no—
815C4—224no—
816C4—442no—
817C4—442no—
818C4—444no—
819C2—24no—
820C2—42no—
821C2—42no—
822C2—82no—
823C2—444no—
824C2—882no—
825C2C2×#1062312311yescharacteristic
826C2#1308224811yescharacteristic
827C2#1308225411yescharacteristic
828C2#1308280114yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2405C2
hypercenter#2405D11
hypocenterC11#36721
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2405

Complements

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

NH ≅ G/Ntype
1. C2×#10623335C2semidirect
2. C22×#66936C2semidirect
3. #13076897C2semidirect
4. #13075309C2semidirect
5. #13075305C2semidirect
6. #13074947C2semidirect
7. #13074945C2semidirect
8. #13074362C2semidirect
9. #13073546C2semidirect
10. #13073106C2semidirect
11. #13071943C2semidirect
12. #13071929C2semidirect
13. #13071926C2semidirect
14. #13071212C2semidirect
15. C11×#2405C2semidirect
19. C23×C4×D11C22semidirect
20. C2×C11×#123C22semidirect
22. C2×#67006C22semidirect
23. C2×#67006C22semidirect
28. C2×#66990C22semidirect
29. C2×#66990C22semidirect
30. C2×#66988C22semidirect
31. C2×#66982C22semidirect
32. C2×#66982C22semidirect
33. C22×(C2×D11)⋊C4C22semidirect
34. C22×C4⋊Dic11C22semidirect
35. C22×Dic11⋊C4C22semidirect
36. C2×#66937C22semidirect
38. C2×#66936C22semidirect
39. C2×#66936C22semidirect
40. C2×#66935C22semidirect
41. C2×#66935C22semidirect
42. C11×#394C22semidirect
43. C11×#386C22semidirect
44. C11×#385C22semidirect
46. C11×#379C22semidirect
49. #10622833C22semidirect
50. #10622826C22semidirect
51. #10622826C22semidirect
52. #10622607C22semidirect
53. #10622605C22semidirect
54. #10622601C22semidirect
55. #10622597C22semidirect
56. #10622574C22semidirect
58. #10622573C22semidirect
59. #10622572C22semidirect
60. #10622571C22semidirect
61. #10622571C22semidirect
62. #10622570C22semidirect
63. #10622570C22semidirect
64. #10622569C22semidirect
65. #10622568C22semidirect
66. #10622565C22semidirect
67. #10622561C22semidirect
68. #10622559C22semidirect
69. #10622558C22semidirect
70. #10622557C22semidirect
71. #10622555C22semidirect
72. C22⋊C4×Dic11C22semidirect
73. #10622288C22semidirect
74. #10622280C22semidirect
75. #10622278C22semidirect
76. #10622263C22semidirect
119. C2×C22⋊Dic11D4semidirect
287. #2405D11semidirect
387. C2×#123C2×D11semidirect
410. #394C2×D11semidirect
426. #386C2×D11semidirect
428. #385C2×D11semidirect
435. #379C2×D11semidirect
689. C11#36721semidirect

Maximal subgroups

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

subgroupindex
C2×#106233352
C22×#669362
#130768972
#130753092
#130753052
#130749472
#130749452
#130743622
#130735462
#130731062
#130719432
#130719292
#130719262
#130712122
C11×#24052
#3672111