Finite Group Databasebeta

← #14926036

Subgroups — #14926036

Order 2816.

3270 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623053C211yesmaximal, characteristic, complemented
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3#13074180C214yesmaximal, complemented
4#13073971C212yesmaximal, complemented
5#13073514C212yesmaximal, complemented
6#13072932C212yesmaximal, complemented
7#13072886C211yesmaximal, characteristic, complemented
8#13071971C212yesmaximal, complemented
9#13071937C211yesmaximal, characteristic, complemented
10#13071935C211yesmaximal, characteristic, complemented
11#13071901C212yesmaximal, complemented
12#13071896C212yesmaximal, complemented
13#13071128C214yesmaximal, complemented
14#13071117C212yesmaximal, complemented
15#13071115C212yesmaximal, complemented
16#13071007C211yesmaximal, characteristic, complemented
17C11×#2482C211yesmaximal, characteristic, complemented
18C23×C22⋊D11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C22×#4339C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C2×#67006C2212yes—
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28#10623053—28no—
29C2×#66946C2211yescharacteristic, complemented
30C2×#66946C2211yescharacteristic, complemented
31C2×#66946C2214yescomplemented
32C2×#66940C2211yescharacteristic, complemented
33C2×#66940C2211yescharacteristic, complemented
34C2×#66937C2214yes—
35C2×#66935C2212yes—
36C2×(C22⋊D11)⋊C4—28no—
37C2×(C22⋊D11)⋊C4C2212yes—
38C2×(C22⋊D11)⋊C4C2212yes—
39C2×(C22⋊D11)⋊C4C2212yes—
40C2×(C22⋊D11)⋊C4C2212yes—
41C2×(C22⋊D11)⋊C4C2212yes—
42C2×(C22⋊D11)⋊C4C2212yes—
43C2×(C22⋊D11)⋊C4C2214yescomplemented
44C2×#66925C2212yescomplemented
45C2×C42×D11C2212yescomplemented
46C11×#399C2212yescomplemented
47C11×#397C2212yescomplemented
48C11×#388C2214yescomplemented
49C11×#385C2212yes—
50C11×#381C2211yescharacteristic
51C11×#379C2212yes—
52#10622826C2212yes—
53#10622824C2211yescharacteristic
54#10622606C2212yescomplemented
55#10622605C2214yescomplemented
56#10622605C2212yescomplemented
57#10622602C2214yescomplemented
58#10622585C2214yescomplemented
59#10622573C2214yes—
60#10622573C2212yescomplemented
61#10622572C2214yes—
62#10622571C2212yes—
63#10622571C2214yescomplemented
64#10622570C2214yes—
65#10622569C2214yescomplemented
66#10622568C2212yes—
67#10622560C2212yescomplemented
68#10622559C2212yes—
69#10622559C2214yescomplemented
70#10622555C2212yes—
71C22⋊C4×Dic11C2212yes—
72C22⋊C4×Dic11C2214yescomplemented
73#10622553C2214yescomplemented
74#10622286C2212yescomplemented
75#10622284C2212yescomplemented
76#10622280C2214yescomplemented
77#10622279C2214yescomplemented
78#10622278C2214yescomplemented
79#10622278C2214yescomplemented
80#10622271C2214yescomplemented
81#10622264C2212yescomplemented
82#10622263C2212yescomplemented
83#10622262C2212yescomplemented
84#10622261C2212yescomplemented
85C25×C11C2311yescharacteristic
86C24×D11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11—28no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11C2312yes—
92C22×C22⋊D11C2314yes—
93C22×C22⋊D11C2312yes—
94C22×C22⋊D11C2312yes—
95C23×Dic11—24no—
96C23×Dic11—44no—
97C23×Dic11C2312yes—
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2312yes—
101C23×Dic11C2311yescharacteristic
102C2×#4339—24no—
103C2×#4339—28no—
104C22×D44C2311yescharacteristic
105C22×D44C2314yes—
106C22×C4×D11—24no—
107C22×C4×D11—44no—
108C22×C4×D11C2312yes—
109C22×C4×D11C2312yes—
110C22×C4×D11C2312yes—
111C22×C4×D11C2312yes—
112C22×C4×D11C2312yes—
113C22×Dic22C2311yescharacteristic
114C11×#117—24no—
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2314yes—
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4C2312yes—
120C2×C11×C22⋊C4C2312yes—
121C2×C11×C22⋊C4C2312yes—
122C2×C11×C22⋊C4C2312yes—
123C2×C11×C22⋊C4C2314yes—
124C2×C11×C22⋊C4C2314yes—
125C2×C42×C11C2312yes—
126#67006—28no—
127C2×C22⋊Dic11C2312yes—
128C2×C22⋊Dic11C2314yes—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4C2312yes—
131C2×(C2×D11)⋊C4C2312yes—
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×Dic11⋊C4—24no—
140C2×Dic11⋊C4C2312yes—
141C2×Dic11⋊C4C2312yes—
142C2×Dic11⋊C4C2312yes—
143C2×Dic11⋊C4C2312yes—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×C4×Dic11D418yescomplemented
147C2×C4×Dic11C2312yes—
148C2×C4×Dic11C2312yes—
149C2×C4×Dic11C2314yes—
150C2×C4×Dic11C2311yescharacteristic
151C2×C4×Dic11C2311yescharacteristic
152C2×C4×Dic11C2311yescharacteristic
153C2×C4×Dic11C2311yescharacteristic
154#66946—24no—
155#66946—24no—
156#66946—48no—
157#66940—24no—
158#66940—24no—
159#66937—216no—
160#66935—28no—
161(C22⋊D11)⋊C4—28no—
162(C22⋊D11)⋊C4—28no—
163(C22⋊D11)⋊C4—28no—
164(C22⋊D11)⋊C4—28no—
165(C22⋊D11)⋊C4—28no—
166(C22⋊D11)⋊C4—28no—
167(C22⋊D11)⋊C4—48no—
168#66925—28no—
169C42×D11—28no—
170C11×#95C2312yes—
171C11×#95C2312yes—
172C11×#95C2314yes—
173C11⋊#95C2312yes—
174C11⋊#95C2314yes—
175C11⋊#95C2312yes—
176C11⋊#95C2314yes—
177C11⋊#95C2314yes—
178C11⋊#95C2314yes—
179C11⋊#95C2314yes—
180#34963—111nomaximal, Sylow
181C24×C11—22no—
182C24×C11—24no—
183C24×C11—24no—
184C24×C11—42no—
185C24×C11C2412yes—
186C24×C11C2411yescharacteristic
187C23×D11—22no—
188C23×D11—24no—
189C23×D11—24no—
190C23×D11—42no—
191C23×D11C2412yes—
192C23×D11C2412yes—
193C22×C4×C11—24no—
194C22×C4×C11—22no—
195C22×C4×C11—42no—
196C22×C4×C11C2×D414yes—
197C22×C4×C11C2414yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2412yes—
200C22×C4×C11C2412yes—
201C22×C4×C11C2411yescharacteristic
202C22×C4×C11C2411yescharacteristic
203C2×C22⋊D11—232no—
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—28no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—28no—
213C2×C22⋊D11—44no—
214C2×C22⋊D11#4118yes—
215C2×C22⋊D11#4118yescomplemented
216C22×Dic11—24no—
217C22×Dic11—24no—
218C22×Dic11—24no—
219C22×Dic11—24no—
220C22×Dic11—28no—
221C22×Dic11—22no—
222C22×Dic11—42no—
223C22×Dic11—44no—
224C22×Dic11—416no—
225C22×Dic11C2×D414yes—
226C22×Dic11C2×D414yes—
227C22×Dic11C2414yes—
228C22×Dic11C2412yes—
229C22×Dic11C2411yescharacteristic
230C22×Dic11C2411yescharacteristic
231C22×Dic11C2412yes—
232C22×Dic11C2411yescharacteristic
233C22×Dic11C2411yescharacteristic
234#4339—232no—
235C2×D44—24no—
236C2×D44—28no—
237C2×D44—28no—
238C2×D44—22no—
239C2×D44—44no—
240C2×C4×D11—24no—
241C2×C4×D11—24no—
242C2×C4×D11—24no—
243C2×C4×D11—24no—
244C2×C4×D11—24no—
245C2×C4×D11—28no—
246C2×C4×D11—28no—
247C2×C4×D11—28no—
248C2×C4×D11—24no—
249C2×C4×D11—24no—
250C2×C4×D11—44no—
251C2×C4×D11—416no—
252C2×Dic22—24no—
253C2×Dic22—22no—
254C11×C4⋊C4—22no—
255C11×C4⋊C4—22no—
256C11×C4⋊C4—44no—
257C11×C22⋊C4—24no—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—28no—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—24no—
262C11×C22⋊C4—44no—
263C42×C11—24no—
264C22⋊Dic11—28no—
265C22⋊Dic11—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—28no—
269(C2×D11)⋊C4—28no—
270(C2×D11)⋊C4—24no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—44no—
273(C2×D11)⋊C4—44no—
274(C2×D11)⋊C4—44no—
275Dic11⋊C4—24no—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279Dic11⋊C4—28no—
280Dic11⋊C4—44no—
281C4×Dic11—24no—
282C4×Dic11—24no—
283C4×Dic11—28no—
284C4×Dic11C2×D414yes—
285C4×Dic11C2×D414yes—
286C4×Dic11C2×D414yes—
287C4×Dic11C2×D414yes—
288C2×C4×#41—111no—
289C22×C4×D4—111no—
290#2598—114no—
291#2580—112no—
292#2535—112no—
293#2487—112no—
294#2482—111no—
295#2482D1111yescharacteristic, complemented
296#2408—112no—
297#2404—111no—
298#2404—111no—
299#2398—112no—
300#2397—112no—
301C4×#121—114no—
302C4×#120—112no—
303C4×#120—112no—
304#2283—111no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—28no—
308C23×C11—22no—
309C23×C11—24no—
310C23×C11—22no—
311C23×C11—24no—
312C23×C11—416no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11C22×D412yes—
316C23×C11C2×#4114yes—
317C23×C11C2×#4114yes—
318C23×C11C2511yescharacteristic
319C22×D11—28no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—24no—
323C22×D11—22no—
324C22×D11—24no—
325C22×D11—22no—
326C22×D11—24no—
327C22×D11—24no—
328C22×D11—416no—
329C22×D11—44no—
330C22×D11—44no—
331C22×D11C2×#4114yes—
332C22×D11C2×#4114yes—
333C2×C4×C11—28no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—24no—
340C2×C4×C11—24no—
341C2×C4×C11—24no—
342C2×C4×C11—24no—
343C2×C4×C11—24no—
344C2×C4×C11—24no—
345C2×C4×C11—44no—
346C2×C4×C11C22×D412yes—
347C2×C4×C11C22×D412yes—
348C22⋊D11—216no—
349C22⋊D11—216no—
350C22⋊D11—216no—
351C22⋊D11—416no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—28no—
357C2×Dic11—28no—
358C2×Dic11—22no—
359C2×Dic11—24no—
360C2×Dic11—24no—
361C2×Dic11—24no—
362C2×Dic11—24no—
363C2×Dic11—48no—
364C2×Dic11—44no—
365C2×Dic11—48no—
366C2×Dic11C22×D412yes—
367C2×Dic11C22×D412yes—
368C2×Dic11C22×D412yes—
369C2×Dic11C22×D412yes—
370C2×Dic11C2×#4114yes—
371C2×Dic11C2×#4114yes—
372C2×Dic11H(5,𝔽2)14yes—
373D44—28no—
374D44—416no—
375C4×D11—216no—
376C4×D11—48no—
377C4×D11—48no—
378C4×D11—48no—
379C4×D11—48no—
380Dic22—28no—
381C22×#41—111no—
382C23×D4—111no—
383C24×C4—111no—
384C24×C4—111no—
385C2×#121—114no—
386C2×#120—112no—
387C2×#120—112no—
388C4×#41—228no—
389C2×C4×Q8—111no—
390C2×C4×Q8—111no—
391C2×C4×D4—111no—
392C2×C4×D4—111no—
393C2×C4×D4—114no—
394C2×C4×D4—112no—
395C2×C4×D4—112no—
396C2×C4×D4—112no—
397C2×C4×D4—112no—
398C2×C4×D4—112no—
399C2×C4×D4—112no—
400C2×C4×D4—114no—
401C2×C4×D4—228no—
402C2×#117—112no—
403C2×#117C2×D1111yescharacteristic
404C22×C4⋊C4—111no—
405C22×C22⋊C4—111no—
406C22×C22⋊C4C2×D1111yescharacteristic
407C22×C42—111no—
408C22×C42—112no—
409#400—114no—
410#399—112no—
411#399—114no—
412#399C2×D1112yescomplemented
413#397—112no—
414#397C2×D1112yescomplemented
415#394—114no—
416#393—112no—
417#393—112no—
418#392—114no—
419#392—112no—
420#392—112no—
421#390—114no—
422#389—114no—
423#388—114no—
424#388C2×D1114yescomplemented
425#386—112no—
426#386—114no—
427#386—114no—
428#386—112no—
429#386—114no—
430#386—114no—
431#385—114no—
432#385—114no—
433#385—112no—
434#385C2×D1112yes—
435#383—112no—
436#382—112no—
437#381—111no—
438#381C2×D1111yescharacteristic
439#380—112no—
440#380—114no—
441#379—112no—
442#379C2×D1112yes—
443C4×C4⋊C4—112no—
444C4×C22⋊C4—112no—
445C4×C22⋊C4—114no—
446C4×C22⋊C4—114no—
447#376—112no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—28no—
451C22×C11—24no—
452C22×C11—28no—
453C22×C11—416no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—44no—
457C22×C11#52514yes—
458C22×C11C23×D411yescharacteristic
459C22×C11C22×#4112yes—
460C22×C11C22×#4112yes—
461C22×C11C2×H(5,𝔽2)12yes—
462C2×D11—24no—
463C2×D11—24no—
464C2×D11—28no—
465C2×D11—28no—
466C2×D11—416no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—44no—
472C2×D11—44no—
473C4×C11—22no—
474C4×C11—22no—
475C4×C11—42no—
476C4×C11—42no—
477C4×C11—42no—
478C4×C11—44no—
479Dic11—24no—
480Dic11—22no—
481Dic11—22no—
482Dic11—42no—
483Dic11—44no—
484Dic11#52514yes—
485Dic11#53514yes—
486C25—111no—
487C25C22×D1111yescharacteristic
488C2×#41—228no—
489C2×#41—224no—
490C22×Q8—111no—
491C22×D4—112no—
492C22×D4—112no—
493C22×D4—112no—
494C22×D4—114no—
495C22×D4—111no—
496C22×D4—114no—
497C22×D4—224no—
498C22×D4—228no—
499C23×C4—111no—
500C23×C4—111no—
501C23×C4—112no—
502C23×C4—111no—
503C23×C4—112no—
504C23×C4—112no—
505C23×C4—112no—
506C23×C4—112no—
507C23×C4—112no—
508C23×C4—112no—
509C23×C4—224no—
510C23×C4—224no—
511C23×C4—444no—
512C23×C4—444no—
513C23×C4C22×D1111yescharacteristic
514C23×C4C22×D1111yescharacteristic
515#121—2216no—
516#120—228no—
517#120—228no—
518C4×Q8—224no—
519C4×Q8—224no—
520C4×D4—228no—
521C4×D4—228no—
522C4×D4—228no—
523C4×D4—228no—
524C4×D4—224no—
525C4×D4—224no—
526C4×D4—228no—
527C4×D4—228no—
528C4×D4—448no—
529C4×D4—448no—
530#117—24no—
531#117—228no—
532C2×C4⋊C4—112no—
533C2×C4⋊C4—112no—
534C2×C4⋊C4—112no—
535C2×C4⋊C4—112no—
536C2×C4⋊C4—114no—
537C2×C4⋊C4—114no—
538C2×C4⋊C4—224no—
539C2×C4⋊C4C22×D1111yescharacteristic
540C2×C4⋊C4C22×D1111yescharacteristic
541C2×C4⋊C4C22×D1114yes—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—112no—
544C2×C22⋊C4—114no—
545C2×C22⋊C4—112no—
546C2×C22⋊C4—112no—
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—224no—
555C2×C22⋊C4C22×D1112yes—
556C2×C22⋊C4C22×D1112yes—
557C2×C22⋊C4C22×D1112yes—
558C2×C22⋊C4C22×D1112yes—
559C2×C22⋊C4C22×D1114yes—
560C2×C22⋊C4C22×D1114yes—
561C2×C42—118no—
562C2×C42—111no—
563C2×C42—111no—
564C2×C42—111no—
565C2×C42—111no—
566C2×C42—114no—
567C2×C42—112no—
568C2×C42—112no—
569C2×C42—228no—
570C2×C42C22×D1112yes—
571#95—114no—
572#95—112no—
573#95—114no—
574#95—114no—
575#95—114no—
576#95—114no—
577#95—112no—
578#95C22×D1112yes—
579#95C22×D1114yes—
580#95C22×D1112yes—
581C2×C11—24no—
582C2×C11—44no—
583C2×C11C2×#52511yescharacteristic
584C2×C11C2×#52511yescharacteristic
585C2×C11C2×#53511yescharacteristic
586C2×C11#348114yes—
587D11—44no—
588D11—44no—
589C24—22no—
590C24—24no—
591C24—24no—
592C24—42no—
593C24—112no—
594C24—112no—
595C24—224no—
596C24—222no—
597C24—224no—
598C24—442no—
599C24C23×D1112yes—
600C24C23×D1111yescharacteristic
601#41—2232no—
602C2×Q8—224no—
603C2×Q8—222no—
604C2×D4—118no—
605C2×D4—118no—
606C2×D4—224no—
607C2×D4—228no—
608C2×D4—228no—
609C2×D4—224no—
610C2×D4—224no—
611C2×D4—224no—
612C2×D4—224no—
613C2×D4—2232no—
614C2×D4—224no—
615C2×D4—224no—
616C2×D4—224no—
617C2×D4—228no—
618C2×D4—228no—
619C2×D4—222no—
620C2×D4—444no—
621C2×D4—444no—
622C22×C4—24no—
623C22×C4—22no—
624C22×C4—42no—
625C22×C4—111no—
626C22×C4—111no—
627C22×C4—114no—
628C22×C4—114no—
629C22×C4—112no—
630C22×C4—111no—
631C22×C4—111no—
632C22×C4—114no—
633C22×C4—112no—
634C22×C4—224no—
635C22×C4—224no—
636C22×C4—224no—
637C22×C4—224no—
638C22×C4—224no—
639C22×C4—228no—
640C22×C4—228no—
641C22×C4—228no—
642C22×C4—224no—
643C22×C4—224no—
644C22×C4—224no—
645C22×C4—224no—
646C22×C4—224no—
647C22×C4—228no—
648C22×C4—224no—
649C22×C4—222no—
650C22×C4—444no—
651C22×C4—4416no—
652C22×C4—444no—
653C22×C4—442no—
654C22×C4—4416no—
655C22×C4D4×D1114yes—
656C22×C4C23×D1114yes—
657C22×C4C23×D1112yes—
658C22×C4C23×D1112yes—
659C22×C4C23×D1112yes—
660C22×C4C23×D1111yescharacteristic
661C22×C4C23×D1111yescharacteristic
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—44no—
665C4⋊C4—224no—
666C4⋊C4—224no—
667C4⋊C4—224no—
668C4⋊C4—224no—
669C4⋊C4—228no—
670C4⋊C4—444no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—28no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—44no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—228no—
680C22⋊C4—228no—
681C22⋊C4—228no—
682C22⋊C4—224no—
683C22⋊C4—224no—
684C22⋊C4—224no—
685C22⋊C4—444no—
686C22⋊C4—444no—
687C22⋊C4—444no—
688C42—24no—
689C42—114no—
690C42—114no—
691C42—114no—
692C42—114no—
693C42—224no—
694C42—224no—
695C42—228no—
696C11#3496311yescharacteristic, complemented, Sylow
697C23—22no—
698C23—22no—
699C23—28no—
700C23—22no—
701C23—24no—
702C23—22no—
703C23—24no—
704C23—416no—
705C23—44no—
706C23—44no—
707C23—114no—
708C23—114no—
709C23—228no—
710C23—222no—
711C23—222no—
712C23—224no—
713C23—224no—
714C23—222no—
715C23—222no—
716C23—224no—
717C23—224no—
718C23—4416no—
719C23—444no—
720C23—444no—
721C23C2×D4×D1112yes—
722C23#41×D1114yes—
723C23#41×D1114yes—
724C23C24×D1111yescharacteristic
725Q8—228no—
726D4—228no—
727D4—2216no—
728D4—2216no—
729D4—2216no—
730D4—4416no—
731D4—4416no—
732C2×C4—28no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—44no—
745C2×C4—112no—
746C2×C4—112no—
747C2×C4—114no—
748C2×C4—114no—
749C2×C4—112no—
750C2×C4—112no—
751C2×C4—114no—
752C2×C4—2216no—
753C2×C4—228no—
754C2×C4—228no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—224no—
761C2×C4—224no—
762C2×C4—224no—
763C2×C4—224no—
764C2×C4—448no—
765C2×C4—448no—
766C2×C4—448no—
767C2×C4—448no—
768C2×C4—448no—
769C2×C4—448no—
770C2×C4—444no—
771C2×C4C2×D4×D1112yes—
772C2×C4C2×D4×D1112yes—
773C22—22no—
774C22—28no—
775C22—22no—
776C22—28no—
777C22—24no—
778C22—416no—
779C22—42no—
780C22—44no—
781C22—42no—
782C22—228no—
783C22—228no—
784C22—224no—
785C22—224no—
786C22—4416no—
787C22—442no—
788C22—442no—
789C22—444no—
790C22—444no—
791C22—442no—
792C22—442no—
793C22#1062318714yes—
794C22C22×D4×D1111yescharacteristic
795C22C2×#41×D1112yes—
796C22C2×#41×D1112yes—
797C22D11×H(5,𝔽2)12yes—
798C4—22no—
799C4—22no—
800C4—42no—
801C4—42no—
802C4—44no—
803C4—42no—
804C4—114no—
805C4—114no—
806C4—222no—
807C4—222no—
808C4—224no—
809C4—442no—
810C4—444no—
811C2—24no—
812C2—44no—
813C2—444no—
814C2—444no—
815C2D11×#52511yescharacteristic
816C2C2×#1062318711yescharacteristic
817C2D11×#53511yescharacteristic
818C2#1308221914yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2482C2
hypercenter#2482D11
hypocenterC11#34963
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2482

Complements

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

NH ≅ G/Ntype
1. C2×#10623053C2semidirect
2. C22×(C22⋊D11)⋊C4C2semidirect
3. #13074180C2semidirect
4. #13073971C2semidirect
5. #13073514C2semidirect
6. #13072932C2semidirect
7. #13072886C2semidirect
8. #13071971C2semidirect
9. #13071937C2semidirect
10. #13071935C2semidirect
11. #13071901C2semidirect
12. #13071896C2semidirect
13. #13071128C2semidirect
14. #13071117C2semidirect
15. #13071115C2semidirect
16. #13071007C2semidirect
17. C11×#2482C2semidirect
29. C2×#66946C22semidirect
30. C2×#66946C22semidirect
31. C2×#66946C22semidirect
32. C2×#66940C22semidirect
33. C2×#66940C22semidirect
43. C2×(C22⋊D11)⋊C4C22semidirect
44. C2×#66925C22semidirect
45. C2×C42×D11C22semidirect
46. C11×#399C22semidirect
47. C11×#397C22semidirect
48. C11×#388C22semidirect
54. #10622606C22semidirect
55. #10622605C22semidirect
56. #10622605C22semidirect
57. #10622602C22semidirect
58. #10622585C22semidirect
60. #10622573C22semidirect
63. #10622571C22semidirect
65. #10622569C22semidirect
67. #10622560C22semidirect
69. #10622559C22semidirect
72. C22⋊C4×Dic11C22semidirect
73. #10622553C22semidirect
74. #10622286C22semidirect
75. #10622284C22semidirect
76. #10622280C22semidirect
77. #10622279C22semidirect
78. #10622278C22semidirect
79. #10622278C22semidirect
80. #10622271C22semidirect
81. #10622264C22semidirect
82. #10622263C22semidirect
83. #10622262C22semidirect
84. #10622261C22semidirect
146. C2×C4×Dic11D4semidirect
215. C2×C22⋊D11#41semidirect
295. #2482D11semidirect
412. #399C2×D11semidirect
414. #397C2×D11semidirect
424. #388C2×D11semidirect
696. C11#34963semidirect

Maximal subgroups

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

subgroupindex
C2×#106230532
C22×(C22⋊D11)⋊C42
#130741802
#130739712
#130735142
#130729322
#130728862
#130719712
#130719372
#130719352
#130719012
#130718962
#130711282
#130711172
#130711152
#130710072
C11×#24822
#3496311