Finite Group Databasebeta

← #14960568

Subgroups — #14960568

Order 2816.

3038 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×#10623175C211yesmaximal, characteristic, complemented
2C22×#66983C211yesmaximal, characteristic, complemented
3#13076898C211yesmaximal, characteristic, complemented
4#13075101C214yesmaximal, complemented
5#13074913C214yesmaximal, complemented
6#13074907C214yesmaximal, complemented
7#13074849C214yesmaximal, complemented
8#13074423C211yesmaximal, characteristic, complemented
9#13074353C211yesmaximal, characteristic, complemented
10#13073966C212yesmaximal, complemented
11#13071992C212yesmaximal, complemented
12#13071988C212yesmaximal, complemented
13#13071971C212yesmaximal, complemented
14#13071229C211yesmaximal, characteristic, complemented
15C11×#2848C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×C22⋊Q8C2212yescomplemented
22C2×#67006C2212yes—
23C2×#67000C2212yescomplemented
24C2×#66983—28no—
25C2×#66983C2211yescharacteristic
26C2×#66983C2214yes—
27C2×#66983C2214yes—
28C2×#66983C2212yescomplemented
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32#10623175—28no—
33C2×#66951C2212yescomplemented
34C2×#66948C2212yescomplemented
35C2×#66948C2214yescomplemented
36C2×#66947C2212yescomplemented
37C2×#66937C2214yescomplemented
38C2×#66937C2214yescomplemented
39C2×#66935C2212yes—
40C2×#66935C2212yes—
41C2×(C22⋊D11)⋊C4C2212yes—
42C2×C22⋊C4×D11C2212yes—
43C11×#385C2212yes—
44C11×#385C2214yescomplemented
45C11×#380C2211yescharacteristic
46C11×#380C2212yescomplemented
47C11×#379C2212yes—
48#10622844C2212yescomplemented
49#10622826C2212yes—
50#10622826C2214yescomplemented
51#10622825C2211yescharacteristic
52#10622825C2212yescomplemented
53#10622607C2214yescomplemented
54#10622607C2214yescomplemented
55#10622605C2212yescomplemented
56#10622604C2214yescomplemented
57#10622604C2214yescomplemented
58#10622602C2214yescomplemented
59#10622594C2214yescomplemented
60#10622573C2214yescomplemented
61#10622573C2214yescomplemented
62#10622572C2214yescomplemented
63#10622572C2214yescomplemented
64#10622571C2212yes—
65#10622570C2214yescomplemented
66#10622569C2214yescomplemented
67#10622568C2212yes—
68#10622559C2212yes—
69#10622555C2212yes—
70#10622287C2212yescomplemented
71#10622284C2214yescomplemented
72#10622284C2212yescomplemented
73#10622281C2214yescomplemented
74#10622281C2214yescomplemented
75#10622278C2214yescomplemented
76#10622270C2214yescomplemented
77C25×C11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C24×D11C2311yescharacteristic
80C22×Q8×C11C2311yescharacteristic
81C23×C4×C11—24no—
82C23×C4×C11—44no—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2312yes—
85C23×C4×C11C2312yes—
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—44no—
90C22×C22⋊D11—44no—
91C22×C22⋊D11C2312yes—
92C22×C22⋊D11C2314yes—
93C22×C22⋊D11C2314yes—
94C22×C22⋊D11C2314yes—
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C22×D44—24no—
98C22×D44—44no—
99C22×D44C2314yes—
100C22×D44C2312yes—
101C22×D44C2312yes—
102C22×D44C2311yescharacteristic
103C22×D44C2314yes—
104C22×C4×D11C2312yes—
105C22×C4×D11C2314yes—
106C11×C22⋊Q8—24no—
107C11×C22⋊Q8—44no—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2312yes—
110C2×C11×C4⋊C4C2314yes—
111C2×C11×C4⋊C4C2312yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2312yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C11×C22⋊C4C2314yes—
116#67006—44no—
117C2×C22⋊Dic11C2312yes—
118C2×C22⋊Dic11C2314yes—
119#67000—28no—
120#66983—24no—
121#66983—216no—
122#66983—216no—
123#66983—44no—
124C2×(C2×D11)⋊C4—24no—
125C2×(C2×D11)⋊C4D418yescomplemented
126C2×(C2×D11)⋊C4C2312yes—
127C2×(C2×D11)⋊C4C2312yes—
128C2×(C2×D11)⋊C4C2312yes—
129C2×(C2×D11)⋊C4C2312yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2312yes—
132C2×(C2×D11)⋊C4C2312yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2312yes—
139C2×(C2×D11)⋊C4C2312yes—
140C2×C4⋊Dic11—24no—
141C2×C4⋊Dic11C2314yes—
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2312yes—
144C2×Dic11⋊C4C2312yes—
145C2×Dic11⋊C4C2314yes—
146C2×Dic11⋊C4C2314yes—
147C2×C4×Dic11C2312yes—
148#66951—28no—
149#66948—28no—
150#66948—48no—
151#66947—28no—
152#66937—48no—
153#66937—48no—
154#66935—28no—
155#66935—44no—
156(C22⋊D11)⋊C4—28no—
157C22⋊C4×D11—44no—
158C11×#95C2314yes—
159C11×#95C2312yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2312yes—
165#36706—111nomaximal, Sylow
166C24×C11—22no—
167C24×C11—24no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—42no—
171C24×C11C2412yes—
172C24×C11C2411yescharacteristic
173C23×D11—22no—
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—42no—
179C23×D11—42no—
180C23×D11—42no—
181C23×D11—42no—
182C23×D11C2×D414yes—
183C23×D11C2412yes—
184C23×D11C2412yes—
185C23×D11C2412yes—
186C2×Q8×C11—22no—
187C2×Q8×C11—42no—
188C22×C4×C11—22no—
189C22×C4×C11—24no—
190C22×C4×C11—24no—
191C22×C4×C11—24no—
192C22×C4×C11—24no—
193C22×C4×C11—24no—
194C22×C4×C11—42no—
195C22×C4×C11—42no—
196C22×C4×C11—42no—
197C22×C4×C11—416no—
198C22×C4×C11C2×D414yes—
199C22×C4×C11C2414yes—
200C22×C4×C11C2412yes—
201C22×C4×C11C2412yes—
202C22×C4×C11C2411yescharacteristic
203C22×C4×C11C2411yescharacteristic
204C22×C4×C11C2412yes—
205C2×C22⋊D11—28no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—28no—
209C2×C22⋊D11—28no—
210C2×C22⋊D11—28no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—28no—
213C2×C22⋊D11—44no—
214C2×C22⋊D11—44no—
215C2×C22⋊D11—44no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—416no—
218C2×C22⋊D11—416no—
219C22×Dic11—22no—
220C22×Dic11—42no—
221C22×Dic11—42no—
222C22×Dic11C2×D414yes—
223C22×Dic11C2412yes—
224C22×Dic11C2412yes—
225C22×Dic11C2414yes—
226C22×Dic11C2412yes—
227C2×D44—28no—
228C2×D44—24no—
229C2×D44—24no—
230C2×D44—22no—
231C2×D44—28no—
232C2×D44—44no—
233C2×D44—44no—
234C2×D44—44no—
235C2×D44—44no—
236C2×D44—44no—
237C2×D44—44no—
238C2×D44—42no—
239C2×D44—416no—
240C2×C4×D11—24no—
241C2×C4×D11—44no—
242C2×C4×D11—44no—
243C2×C4×D11—44no—
244C2×C4×D11—44no—
245C11×C4⋊C4—22no—
246C11×C4⋊C4—24no—
247C11×C4⋊C4—28no—
248C11×C4⋊C4—42no—
249C11×C22⋊C4—24no—
250C11×C22⋊C4—24no—
251C11×C22⋊C4—28no—
252C11×C22⋊C4—44no—
253C22⋊Dic11—24no—
254C22⋊Dic11—44no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—44no—
263(C2×D11)⋊C4—44no—
264(C2×D11)⋊C4—44no—
265(C2×D11)⋊C4—44no—
266(C2×D11)⋊C4—44no—
267(C2×D11)⋊C4C2×D418yes—
268(C2×D11)⋊C4C2×D418yes—
269C4⋊Dic11—28no—
270C4⋊Dic11—22no—
271C4⋊Dic11—42no—
272Dic11⋊C4—24no—
273Dic11⋊C4—44no—
274Dic11⋊C4—44no—
275C4×Dic11—24no—
276C2×#538—111no—
277C22×#121—111no—
278#2848D1111yescharacteristic, complemented
279#2847—111no—
280#2691—114no—
281#2676—114no—
282#2675—114no—
283#2671—114no—
284#2626—111no—
285#2617—111no—
286#2579—112no—
287#2410—112no—
288#2410—112no—
289#2408—112no—
290#2315—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—48no—
301C23×C11—48no—
302C23×C11—44no—
303C23×C11—44no—
304C23×C11C22×D412yes—
305C23×C11H(5,𝔽2)14yes—
306C23×C11H(5,𝔽2)12yes—
307C23×C112−1+412yes—
308C23×C11C2511yescharacteristic
309C22×D11—22no—
310C22×D11—24no—
311C22×D11—24no—
312C22×D11—22no—
313C22×D11—28no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—24no—
317C22×D11—22no—
318C22×D11—24no—
319C22×D11—24no—
320C22×D11—24no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—44no—
325C22×D11—44no—
326C22×D11—44no—
327C22×D11—44no—
328C22×D11—44no—
329C22×D11—84no—
330C22×D11—84no—
331C22×D11—84no—
332C22×D11—84no—
333C22×D11C22×D414yes—
334Q8×C11—82no—
335C2×C4×C11—28no—
336C2×C4×C11—22no—
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—24no—
345C2×C4×C11—24no—
346C2×C4×C11—24no—
347C2×C4×C11—44no—
348C2×C4×C11—48no—
349C2×C4×C11—48no—
350C2×C4×C11C22×D412yes—
351C2×C4×C11C22×D412yes—
352C2×C4×C11H(5,𝔽2)14yes—
353C22⋊D11—416no—
354C22⋊D11—416no—
355C22⋊D11—48no—
356C22⋊D11—88no—
357C2×Dic11—24no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—24no—
361C2×Dic11—24no—
362C2×Dic11—24no—
363C2×Dic11—22no—
364C2×Dic11—24no—
365C2×Dic11—22no—
366C2×Dic11—44no—
367C2×Dic11—44no—
368C2×Dic11C22×D414yes—
369D44—416no—
370D44—82no—
371D44—84no—
372D44—84no—
373D44—88no—
374C4×D11—84no—
375C4×D11—88no—
376C23×D4—111no—
377C23×D4—111no—
378C23×D4—111no—
379C24×C4C2×D1111yescharacteristic
380#538—228no—
381C2×#126—112no—
382C2×#124—112no—
383C2×#123—112no—
384C2×C22⋊Q8C2×D1111yescharacteristic
385C2×C22⋊Q8C2×D1112yescomplemented
386C2×#121—111no—
387C2×#121—114no—
388C2×#121—114no—
389C2×#121—112no—
390C2×#121—112no—
391C2×#121—114no—
392C2×#121—114no—
393C2×#121—114no—
394C2×#121—228no—
395C2×#120—112no—
396C2×#120—112no—
397C2×#120—112no—
398C2×C4×D4—112no—
399C22×C4⋊C4—111no—
400C22×C22⋊C4—111no—
401C22×C22⋊C4—111no—
402C22×C22⋊C4—112no—
403#399—112no—
404#398—114no—
405#397—112no—
406#396—114no—
407#396—114no—
408#394—114no—
409#394—114no—
410#394—114no—
411#394—114no—
412#393—112no—
413#392—114no—
414#392—114no—
415#392—112no—
416#392—114no—
417#390—114no—
418#387—114no—
419#386—112no—
420#386—114no—
421#386—112no—
422#386—114no—
423#386—114no—
424#385—114no—
425#385—112no—
426#385—114no—
427#385—114no—
428#385C2×D1112yes—
429#385C2×D1114yescomplemented
430#380—111no—
431#380—112no—
432#380—112no—
433#380C2×D1111yescharacteristic
434#380C2×D1112yescomplemented
435#379—112no—
436#379C2×D1112yes—
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—24no—
440C22×C11—24no—
441C22×C11—24no—
442C22×C11—24no—
443C22×C11—24no—
444C22×C11—416no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—42no—
449C22×C11#53714yes—
450C22×C11C23×D411yescharacteristic
451C22×C11C2×H(5,𝔽2)12yes—
452C22×C11C2×H(5,𝔽2)11yescharacteristic
453C22×C11C2×H(5,𝔽2)12yes—
454C22×C11C2×2−1+411yescharacteristic
455C2×D11—24no—
456C2×D11—24no—
457C2×D11—24no—
458C2×D11—44no—
459C2×D11—44no—
460C2×D11—42no—
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—42no—
464C2×D11—42no—
465C2×D11—42no—
466C2×D11—44no—
467C2×D11—44no—
468C2×D11—44no—
469C2×D11—44no—
470C2×D11—88no—
471C2×D11—88no—
472C4×C11—24no—
473C4×C11—22no—
474C4×C11—22no—
475C4×C11—42no—
476C4×C11—42no—
477C4×C11—44no—
478Dic11—24no—
479Dic11—42no—
480Dic11—42no—
481Dic11—44no—
482C25—111no—
483C25—111no—
484C25C22×D1111yescharacteristic
485C22×Q8C22×D1111yescharacteristic
486C22×D4—112no—
487C22×D4—114no—
488C22×D4—114no—
489C22×D4—114no—
490C22×D4—114no—
491C22×D4—112no—
492C22×D4—112no—
493C22×D4—111no—
494C22×D4—114no—
495C22×D4—224no—
496C22×D4—224no—
497C22×D4—224no—
498C22×D4—444no—
499C22×D4—444no—
500C22×D4—444no—
501C23×C4—24no—
502C23×C4—44no—
503C23×C4—111no—
504C23×C4—111no—
505C23×C4—112no—
506C23×C4—114no—
507C23×C4C22×D1111yescharacteristic
508C23×C4C22×D1112yes—
509C23×C4C22×D1112yes—
510C23×C4C22×D1111yescharacteristic
511#126—228no—
512#124—228no—
513#123—228no—
514C22⋊Q8—24no—
515C22⋊Q8—44no—
516#121—228no—
517#121—2216no—
518#121—2216no—
519#121—224no—
520#121—448no—
521#121—448no—
522#121—444no—
523#121—448no—
524#120—228no—
525#120—444no—
526#120—444no—
527C4×D4—228no—
528C2×C4⋊C4—114no—
529C2×C4⋊C4—112no—
530C2×C4⋊C4—111no—
531C2×C4⋊C4—112no—
532C2×C4⋊C4—114no—
533C2×C4⋊C4—114no—
534C2×C4⋊C4—224no—
535C2×C4⋊C4C22×D1112yes—
536C2×C4⋊C4C22×D1114yes—
537C2×C4⋊C4C22×D1111yescharacteristic
538C2×C4⋊C4C22×D1112yes—
539C2×C22⋊C4—118no—
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—112no—
547C2×C22⋊C4—112no—
548C2×C22⋊C4—114no—
549C2×C22⋊C4—112no—
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—224no—
557C2×C22⋊C4—444no—
558C2×C22⋊C4C22×D1112yes—
559C2×C22⋊C4C22×D1112yes—
560C2×C22⋊C4C22×D1114yes—
561C2×C22⋊C4C22×D1114yes—
562C2×C42—112no—
563#95—114no—
564#95—112no—
565#95—114no—
566#95—114no—
567#95—114no—
568#95C22×D1112yes—
569#95C22×D1114yes—
570C2×C11—24no—
571C2×C11—44no—
572C2×C11C2×#53711yescharacteristic
573C2×C11#348411yescharacteristic
574C2×C11#348411yescharacteristic
575C2×C11#353612yes—
576C2×C11#353712yes—
577D11—44no—
578D11—82no—
579D11—82no—
580C24—22no—
581C24—24no—
582C24—22no—
583C24—22no—
584C24—42no—
585C24—112no—
586C24—114no—
587C24—112no—
588C24—112no—
589C24—222no—
590C24—222no—
591C24—222no—
592C24—222no—
593C24—222no—
594C24—442no—
595C24—442no—
596C24—442no—
597C24—442no—
598C24C23×D1112yes—
599C24C23×D1111yescharacteristic
600C2×Q8—22no—
601C2×Q8—42no—
602C2×D4—228no—
603C2×D4—224no—
604C2×D4—224no—
605C2×D4—228no—
606C2×D4—228no—
607C2×D4—224no—
608C2×D4—224no—
609C2×D4—224no—
610C2×D4—228no—
611C2×D4—228no—
612C2×D4—228no—
613C2×D4—222no—
614C2×D4—228no—
615C2×D4—444no—
616C2×D4—4416no—
617C2×D4—444no—
618C2×D4—442no—
619C2×D4—444no—
620C2×D4—444no—
621C2×D4—444no—
622C2×D4—444no—
623C2×D4—444no—
624C2×D4—444no—
625C2×D4—444no—
626C2×D4—444no—
627C2×D4—4416no—
628C2×D4—4416no—
629C22×C4—22no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—416no—
639C22×C4—112no—
640C22×C4—114no—
641C22×C4—112no—
642C22×C4—114no—
643C22×C4—112no—
644C22×C4—224no—
645C22×C4—222no—
646C22×C4—444no—
647C22×C4—444no—
648C22×C4—444no—
649C22×C4—444no—
650C22×C4—442no—
651C22×C4—442no—
652C22×C4D4×D1114yes—
653C22×C4C23×D1114yes—
654C22×C4C23×D1112yes—
655C22×C4C23×D1112yes—
656C22×C4C23×D1111yescharacteristic
657C22×C4C23×D1111yescharacteristic
658C22×C4C23×D1112yes—
659C4⋊C4—24no—
660C4⋊C4—22no—
661C4⋊C4—28no—
662C4⋊C4—42no—
663C4⋊C4—228no—
664C4⋊C4—224no—
665C4⋊C4—222no—
666C4⋊C4—444no—
667C4⋊C4—444no—
668C4⋊C4—442no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—28no—
672C22⋊C4—44no—
673C22⋊C4—118no—
674C22⋊C4—118no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4—224no—
682C22⋊C4—228no—
683C22⋊C4—444no—
684C22⋊C4—444no—
685C22⋊C4—444no—
686C22⋊C4—444no—
687C22⋊C4—444no—
688C22⋊C4—444no—
689C42—224no—
690C11#3670611yescharacteristic, complemented, Sylow
691C23—22no—
692C23—22no—
693C23—28no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—48no—
701C23—48no—
702C23—44no—
703C23—44no—
704C23—114no—
705C23—224no—
706C23—222no—
707C23—222no—
708C23—224no—
709C23—228no—
710C23—222no—
711C23—222no—
712C23—224no—
713C23—224no—
714C23—222no—
715C23—222no—
716C23—222no—
717C23—224no—
718C23—224no—
719C23—222no—
720C23—444no—
721C23—444no—
722C23—444no—
723C23—444no—
724C23—444no—
725C23—884no—
726C23—884no—
727C23—884no—
728C23—884no—
729C23C2×D4×D1112yes—
730C23#6704012yes—
731C23#6704214yes—
732C23#6704212yes—
733C23C24×D1111yescharacteristic
734Q8—82no—
735D4—4416no—
736D4—4416no—
737D4—4416no—
738D4—448no—
739D4—882no—
740D4—884no—
741D4—884no—
742D4—888no—
743D4—888no—
744C2×C4—28no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—44no—
757C2×C4—48no—
758C2×C4—48no—
759C2×C4—114no—
760C2×C4—224no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—224no—
764C2×C4—222no—
765C2×C4—224no—
766C2×C4—222no—
767C2×C4—224no—
768C2×C4—224no—
769C2×C4—444no—
770C2×C4—444no—
771C2×C4—884no—
772C2×C4—888no—
773C2×C4C2×D4×D1112yes—
774C2×C4C2×D4×D1112yes—
775C2×C4#6703714yes—
776C22—22no—
777C22—22no—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—416no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—224no—
789C22—224no—
790C22—224no—
791C22—444no—
792C22—444no—
793C22—442no—
794C22—442no—
795C22—442no—
796C22—442no—
797C22—442no—
798C22—442no—
799C22—444no—
800C22—444no—
801C22—444no—
802C22—444no—
803C22—888no—
804C22—888no—
805C22#1062316014yes—
806C22C22×D4×D1111yescharacteristic
807C22C2×#6703712yes—
808C22C2×#6704011yescharacteristic
809C22C2×#6704211yescharacteristic
810C22C2×#6704212yes—
811C4—24no—
812C4—22no—
813C4—22no—
814C4—42no—
815C4—42no—
816C4—44no—
817C4—224no—
818C4—442no—
819C4—442no—
820C4—444no—
821C2—24no—
822C2—44no—
823C2—444no—
824C2—882no—
825C2—882no—
826C2C2×#1062316011yescharacteristic
827C2#1308224511yescharacteristic
828C2#1308224911yescharacteristic
829C2#1308284512yes—
830C2#1308285512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2848C2
hypercenter#2848D11
hypocenterC11#36706
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2848

Complements

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

NH ≅ G/Ntype
1. C2×#10623175C2semidirect
2. C22×#66983C2semidirect
3. #13076898C2semidirect
4. #13075101C2semidirect
5. #13074913C2semidirect
6. #13074907C2semidirect
7. #13074849C2semidirect
8. #13074423C2semidirect
9. #13074353C2semidirect
10. #13073966C2semidirect
11. #13071992C2semidirect
12. #13071988C2semidirect
13. #13071971C2semidirect
14. #13071229C2semidirect
15. C11×#2848C2semidirect
21. C2×C11×C22⋊Q8C22semidirect
23. C2×#67000C22semidirect
28. C2×#66983C22semidirect
33. C2×#66951C22semidirect
34. C2×#66948C22semidirect
35. C2×#66948C22semidirect
36. C2×#66947C22semidirect
37. C2×#66937C22semidirect
38. C2×#66937C22semidirect
44. C11×#385C22semidirect
46. C11×#380C22semidirect
48. #10622844C22semidirect
50. #10622826C22semidirect
52. #10622825C22semidirect
53. #10622607C22semidirect
54. #10622607C22semidirect
55. #10622605C22semidirect
56. #10622604C22semidirect
57. #10622604C22semidirect
58. #10622602C22semidirect
59. #10622594C22semidirect
60. #10622573C22semidirect
61. #10622573C22semidirect
62. #10622572C22semidirect
63. #10622572C22semidirect
65. #10622570C22semidirect
66. #10622569C22semidirect
70. #10622287C22semidirect
71. #10622284C22semidirect
72. #10622284C22semidirect
73. #10622281C22semidirect
74. #10622281C22semidirect
75. #10622278C22semidirect
76. #10622270C22semidirect
125. C2×(C2×D11)⋊C4D4semidirect
278. #2848D11semidirect
385. C2×C22⋊Q8C2×D11semidirect
429. #385C2×D11semidirect
434. #380C2×D11semidirect
690. C11#36706semidirect

Maximal subgroups

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

subgroupindex
C2×#106231752
C22×#669832
#130768982
#130751012
#130749132
#130749072
#130748492
#130744232
#130743532
#130739662
#130719922
#130719882
#130719712
#130712292
C11×#28482
#3670611