Finite Group Databasebeta

← #14960611

Subgroups — #14960611

Order 2816.

2910 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×#10623128C211yesmaximal, characteristic, complemented
2C22×#66982C211yesmaximal, characteristic, complemented
3#13076898C211yesmaximal, characteristic, complemented
4#13075170C214yesmaximal, complemented
5#13075166C214yesmaximal, complemented
6#13074886C214yesmaximal, complemented
7#13074878C214yesmaximal, complemented
8#13074353C211yesmaximal, characteristic, complemented
9#13074352C211yesmaximal, characteristic, complemented
10#13074095C212yesmaximal, complemented
11#13072251C212yesmaximal, complemented
12#13071934C212yesmaximal, complemented
13#13071932C212yesmaximal, complemented
14#13071218C211yesmaximal, characteristic, complemented
15C11×#2847C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C22×#4341C2212yes—
19C2×C11×#121C2211yescharacteristic
20C2×C11×#121C2212yescomplemented
21C2×C11×#120C2212yes—
22C2×#67006C2212yes—
23C22×C22⋊Dic11C2211yescharacteristic
24C2×#66993C2214yes—
25C2×#66992C2212yes—
26C2×#66992C2212yescomplemented
27C2×#66990C2212yes—
28C2×#66983C2211yescharacteristic
29C2×#66983C2212yescomplemented
30C2×#66982—28no—
31C2×#66982C2214yes—
32C2×#66982C2214yes—
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37#10623128—28no—
38C2×#66949C2212yescomplemented
39C2×#66937C2212yescomplemented
40C2×#66935C2212yes—
41C2×#66931C2212yescomplemented
42C11×#386C2212yes—
43C11×#386C2214yescomplemented
44C11×#380C2211yescharacteristic
45C11×#380C2212yescomplemented
46#10622836C2214yes—
47#10622836C2214yescomplemented
48#10622836C2212yescomplemented
49#10622833C2212yes—
50#10622833C2214yescomplemented
51#10622826C2212yes—
52#10622826C2214yescomplemented
53#10622825C2211yescharacteristic
54#10622825C2212yescomplemented
55#10622606C2212yescomplemented
56#10622604C2214yescomplemented
57#10622591C2214yescomplemented
58#10622574C2214yescomplemented
59#10622573C2214yes—
60#10622573C2214yescomplemented
61#10622572C2214yescomplemented
62#10622571C2212yes—
63#10622571C2214yescomplemented
64#10622570C2214yes—
65#10622569C2214yescomplemented
66#10622560C2214yescomplemented
67#10622557C2214yescomplemented
68#10622556C2212yes—
69C22⋊C4×Dic11C2212yes—
70#10622287C2212yescomplemented
71#10622286C2214yescomplemented
72#10622284C2212yescomplemented
73#10622282C2214yescomplemented
74#10622278C2214yescomplemented
75#10622271C2214yescomplemented
76#10622268C2214yescomplemented
77C25×C11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C22×D4×C11C2312yes—
80C22×D4×C11C2311yescharacteristic
81C22×D4×C11C2314yes—
82C23×C4×C11—24no—
83C23×C4×C11—44no—
84C23×C4×C11C2312yes—
85C23×C4×C11C2312yes—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—24no—
89C22×C22⋊D11—44no—
90C22×C22⋊D11C2312yes—
91C22×C22⋊D11C2314yes—
92C22×C22⋊D11C2312yes—
93C22×C22⋊D11C2312yes—
94C22×C22⋊D11C2314yes—
95C22×C22⋊D11C2314yes—
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2312yes—
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C2×#4341—28no—
101C2×#4341—44no—
102C2×#4341—44no—
103C22×D44C2311yescharacteristic
104C22×D44C2314yes—
105C22×C4×D11C2312yes—
106C22×Dic22C2312yes—
107C11×#121—24no—
108C11×#121—44no—
109C11×#120—44no—
110C2×C11×C4⋊C4C2311yescharacteristic
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⋊Dic11—24no—
118C2×C22⋊Dic11C2312yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2312yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123#66993—48no—
124#66992—28no—
125#66992—28no—
126#66990—44no—
127#66983—24no—
128#66983—44no—
129#66982—216no—
130#66982—216no—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4—24no—
133C2×(C2×D11)⋊C4C2312yes—
134C2×(C2×D11)⋊C4C2312yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2312yes—
137C2×(C2×D11)⋊C4C2312yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2312yes—
144C2×Dic11⋊C4—24no—
145C2×Dic11⋊C4D418yescomplemented
146C2×Dic11⋊C4C2312yes—
147C2×Dic11⋊C4C2314yes—
148C2×Dic11⋊C4C2312yes—
149C2×Dic11⋊C4C2312yes—
150C2×C4×Dic11C2314yes—
151#66949—28no—
152#66937—28no—
153#66935—44no—
154#66931—28no—
155C11×#95C2312yes—
156C11×#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2312yes—
164#36710—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—22no—
176C23×D11—42no—
177C23×D11—42no—
178C23×D11C2412yes—
179C23×D11C2412yes—
180C2×D4×C11—24no—
181C2×D4×C11—24no—
182C2×D4×C11—24no—
183C2×D4×C11—28no—
184C2×D4×C11—22no—
185C2×D4×C11—44no—
186C2×D4×C11—42no—
187C2×D4×C11—44no—
188C22×C4×C11—22no—
189C22×C4×C11—24no—
190C22×C4×C11—24no—
191C22×C4×C11—24no—
192C22×C4×C11—24no—
193C22×C4×C11—42no—
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
204C2×C22⋊D11—24no—
205C2×C22⋊D11—28no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—24no—
209C2×C22⋊D11—28no—
210C2×C22⋊D11—24no—
211C2×C22⋊D11—28no—
212C2×C22⋊D11—42no—
213C2×C22⋊D11—42no—
214C2×C22⋊D11—44no—
215C2×C22⋊D11—44no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—44no—
219C2×C22⋊D11—44no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—416no—
222C22×Dic11—24no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—42no—
227C22×Dic11—42no—
228C22×Dic11—42no—
229C22×Dic11—42no—
230C22×Dic11C2×D414yes—
231C22×Dic11C2×D414yes—
232C22×Dic11C2414yes—
233C22×Dic11C2412yes—
234C22×Dic11C2412yes—
235C22×Dic11C2412yes—
236C22×Dic11C2412yes—
237#4341—432no—
238C2×D44—22no—
239C2×D44—44no—
240C2×D44—42no—
241C2×D44—44no—
242C2×D44—44no—
243C2×C4×D11—24no—
244C2×C4×D11—42no—
245C2×C4×D11—42no—
246C2×Dic22—24no—
247C2×Dic22—42no—
248C2×Dic22—42no—
249C11×C4⋊C4—22no—
250C11×C4⋊C4—42no—
251C11×C22⋊C4—24no—
252C11×C22⋊C4—24no—
253C11×C22⋊C4—44no—
254C11×C22⋊C4—44no—
255C22⋊Dic11—24no—
256C22⋊Dic11—28no—
257C22⋊Dic11—24no—
258C22⋊Dic11—44no—
259C22⋊Dic11—44no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—44no—
266(C2×D11)⋊C4—44no—
267(C2×D11)⋊C4—44no—
268(C2×D11)⋊C4—44no—
269C4⋊Dic11—22no—
270C4⋊Dic11—42no—
271Dic11⋊C4—24no—
272Dic11⋊C4—28no—
273Dic11⋊C4C2×D418yes—
274Dic11⋊C4C2×D418yes—
275C4×Dic11—44no—
276C2×#537—111no—
277C22×#123—111no—
278#2847—111no—
279#2847D1111yescharacteristic, complemented
280#2696—114no—
281#2696—114no—
282#2673—114no—
283#2673—114no—
284#2617—111no—
285#2617—111no—
286#2591—112no—
287#2433—112no—
288#2404—112no—
289#2404—112no—
290#2313—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—24no—
302C23×C11—22no—
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—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—24no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—24no—
322C22×D11—24no—
323C22×D11—24no—
324C22×D11—44no—
325C22×D11—44no—
326C22×D11—44no—
327C22×D11—84no—
328C22×D11—84no—
329D4×C11—48no—
330D4×C11—82no—
331D4×C11—88no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—24no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—24no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—24no—
343C2×C4×C11—44no—
344C2×C4×C11—48no—
345C2×C4×C11—48no—
346C2×C4×C11—44no—
347C2×C4×C11C22×D412yes—
348C2×C4×C11C22×D412yes—
349C22⋊D11—416no—
350C22⋊D11—48no—
351C22⋊D11—48no—
352C22⋊D11—84no—
353C22⋊D11—88no—
354C22⋊D11—88no—
355C2×Dic11—28no—
356C2×Dic11—24no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—24no—
362C2×Dic11—22no—
363C2×Dic11—24no—
364C2×Dic11—22no—
365C2×Dic11—24no—
366C2×Dic11—24no—
367C2×Dic11—44no—
368C2×Dic11—48no—
369C2×Dic11—44no—
370C2×Dic11C22×D414yes—
371C2×Dic11C22×D414yes—
372D44—82no—
373D44—88no—
374C4×D11—48no—
375Dic22—48no—
376C22×#41—112no—
377C23×D4—111no—
378C24×C4C2×D1111yescharacteristic
379#537—228no—
380C2×#127—114no—
381C2×#123—114no—
382C2×#123—114no—
383C2×#123—228no—
384C2×C22⋊Q8—112no—
385C2×C22⋊Q8—112no—
386C2×#121—112no—
387C2×#121—112no—
388C2×#121—111no—
389C2×#121—112no—
390C2×#121—112no—
391C2×#121C2×D1111yescharacteristic
392C2×#121C2×D1112yescomplemented
393C2×#120—112no—
394C2×#120—112no—
395C2×#120—112no—
396C2×#120C2×D1112yes—
397C22×C4⋊C4—111no—
398C22×C4⋊C4—111no—
399C22×C22⋊C4—111no—
400C22×C22⋊C4—111no—
401C22×C22⋊C4—111no—
402#400—114no—
403#397—112no—
404#397—112no—
405#394—114no—
406#394—114no—
407#394—114no—
408#393—114no—
409#393—114no—
410#392—112no—
411#392—114no—
412#392—114no—
413#392—114no—
414#392—114no—
415#392—112no—
416#390—114no—
417#388—114no—
418#388—114no—
419#387—114no—
420#387—114no—
421#386—112no—
422#386—114no—
423#386—112no—
424#386—114no—
425#386—112no—
426#386—114no—
427#386—114no—
428#386—114no—
429#386C2×D1112yes—
430#386C2×D1114yescomplemented
431#381—112no—
432#380—111no—
433#380—112no—
434#380C2×D1111yescharacteristic
435#380C2×D1112yescomplemented
436C4×C22⋊C4—112no—
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—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—44no—
453C22×C11—44no—
454C22×C11#53514yes—
455C22×C11C23×D411yescharacteristic
456C22×C11C2×H(5,𝔽2)11yescharacteristic
457C22×C11C2×H(5,𝔽2)12yes—
458C22×C11C2×H(5,𝔽2)11yescharacteristic
459C22×C11#58512yes—
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—
471C4×C11—22no—
472C4×C11—22no—
473C4×C11—42no—
474C4×C11—42no—
475C4×C11—44no—
476Dic11—24no—
477Dic11—24no—
478Dic11—42no—
479Dic11—42no—
480Dic11—44no—
481C25—111no—
482C25C22×D1111yescharacteristic
483C2×#41—228no—
484C2×#41—444no—
485C2×#41—444no—
486C22×Q8—112no—
487C22×D4—112no—
488C22×D4—114no—
489C22×D4—114no—
490C22×D4—112no—
491C22×D4—112no—
492C22×D4—114no—
493C22×D4—111no—
494C22×D4—114no—
495C22×D4—224no—
496C22×D4—444no—
497C22×D4C22×D1112yes—
498C22×D4C22×D1114yes—
499C22×D4C22×D1111yescharacteristic
500C23×C4—24no—
501C23×C4—44no—
502C23×C4—111no—
503C23×C4—111no—
504C23×C4—111no—
505C23×C4—112no—
506C23×C4—112no—
507C23×C4C22×D1112yes—
508C23×C4C22×D1112yes—
509C23×C4C22×D1111yescharacteristic
510C23×C4C22×D1111yescharacteristic
511#127—448no—
512#123—2216no—
513#123—2216no—
514C22⋊Q8—228no—
515C22⋊Q8—228no—
516#121—24no—
517#121—44no—
518#121—228no—
519#121—228no—
520#121—228no—
521#121—224no—
522#121—444no—
523#120—44no—
524#120—444no—
525#120—444no—
526#120—444no—
527C2×C4⋊C4—118no—
528C2×C4⋊C4—112no—
529C2×C4⋊C4—112no—
530C2×C4⋊C4—114no—
531C2×C4⋊C4—111no—
532C2×C4⋊C4—112no—
533C2×C4⋊C4—112no—
534C2×C4⋊C4—224no—
535C2×C4⋊C4C22×D1111yescharacteristic
536C2×C4⋊C4C22×D1112yes—
537C2×C22⋊C4—114no—
538C2×C22⋊C4—112no—
539C2×C22⋊C4—112no—
540C2×C22⋊C4—114no—
541C2×C22⋊C4—112no—
542C2×C22⋊C4—112no—
543C2×C22⋊C4—112no—
544C2×C22⋊C4—112no—
545C2×C22⋊C4—114no—
546C2×C22⋊C4—114no—
547C2×C22⋊C4—114no—
548C2×C22⋊C4—114no—
549C2×C22⋊C4—114no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—224no—
552C2×C22⋊C4—224no—
553C2×C22⋊C4—224no—
554C2×C22⋊C4C22×D1112yes—
555C2×C22⋊C4C22×D1112yes—
556C2×C22⋊C4C22×D1114yes—
557C2×C22⋊C4C22×D1114yes—
558C2×C42—114no—
559#95—114no—
560#95—114no—
561#95—112no—
562#95—114no—
563#95—114no—
564#95—114no—
565#95—114no—
566#95C22×D1112yes—
567#95C22×D1114yes—
568C2×C11—24no—
569C2×C11—44no—
570C2×C11—82no—
571C2×C11C2×#53511yescharacteristic
572C2×C11#348411yescharacteristic
573C2×C11#348711yescharacteristic
574C2×C11#353412yes—
575C2×C11#353412yes—
576D11—82no—
577D11—82no—
578C24—22no—
579C24—24no—
580C24—22no—
581C24—22no—
582C24—42no—
583C24—112no—
584C24—112no—
585C24—222no—
586C24—222no—
587C24—222no—
588C24—442no—
589C24—442no—
590C24C23×D1112yes—
591C24C23×D1112yes—
592C24C23×D1111yescharacteristic
593#41—4432no—
594C2×Q8—224no—
595C2×Q8—442no—
596C2×Q8—442no—
597C2×D4—24no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—28no—
601C2×D4—22no—
602C2×D4—44no—
603C2×D4—42no—
604C2×D4—44no—
605C2×D4—224no—
606C2×D4—228no—
607C2×D4—224no—
608C2×D4—224no—
609C2×D4—224no—
610C2×D4—228no—
611C2×D4—224no—
612C2×D4—228no—
613C2×D4—222no—
614C2×D4—444no—
615C2×D4—442no—
616C2×D4—444no—
617C2×D4—444no—
618C2×D4—444no—
619C2×D4—442no—
620C2×D4—442no—
621C2×D4—444no—
622C2×D4—444no—
623C2×D4—444no—
624C2×D4—444no—
625C2×D4—444no—
626C2×D4—444no—
627C2×D4—4416no—
628C22×C4—22no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—416no—
638C22×C4—114no—
639C22×C4—112no—
640C22×C4—112no—
641C22×C4—114no—
642C22×C4—114no—
643C22×C4—112no—
644C22×C4—112no—
645C22×C4—224no—
646C22×C4—224no—
647C22×C4—222no—
648C22×C4—222no—
649C22×C4—222no—
650C22×C4—442no—
651C22×C4—442no—
652C22×C4—442no—
653C22×C4—442no—
654C22×C4—442no—
655C22×C4—442no—
656C22×C4D4×D1114yes—
657C22×C4C23×D1114yes—
658C22×C4C23×D1112yes—
659C22×C4C23×D1112yes—
660C22×C4C23×D1111yescharacteristic
661C22×C4C23×D1111yescharacteristic
662C4⋊C4—22no—
663C4⋊C4—42no—
664C4⋊C4—118no—
665C4⋊C4—118no—
666C4⋊C4—228no—
667C4⋊C4—224no—
668C4⋊C4—222no—
669C4⋊C4—442no—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—228no—
675C22⋊C4—224no—
676C22⋊C4—228no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4—224no—
682C22⋊C4—444no—
683C22⋊C4—444no—
684C22⋊C4—444no—
685C22⋊C4—444no—
686C22⋊C4—444no—
687C22⋊C4—444no—
688C42—444no—
689C11#3671011yescharacteristic, complemented, Sylow
690C23—22no—
691C23—22no—
692C23—28no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—24no—
701C23—22no—
702C23—22no—
703C23—24no—
704C23—48no—
705C23—48no—
706C23—44no—
707C23—44no—
708C23—222no—
709C23—222no—
710C23—222no—
711C23—224no—
712C23—222no—
713C23—224no—
714C23—222no—
715C23—222no—
716C23—224no—
717C23—224no—
718C23—444no—
719C23—444no—
720C23—444no—
721C23—884no—
722C23—884no—
723C23C2×D4×D1112yes—
724C23#6703714yes—
725C23#6703712yes—
726C23#6704212yes—
727C23C24×D1111yescharacteristic
728Q8—448no—
729D4—48no—
730D4—82no—
731D4—88no—
732D4—4416no—
733D4—448no—
734D4—448no—
735D4—882no—
736D4—888no—
737D4—884no—
738D4—888no—
739D4—888no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—44no—
752C2×C4—48no—
753C2×C4—48no—
754C2×C4—44no—
755C2×C4—114no—
756C2×C4—114no—
757C2×C4—228no—
758C2×C4—224no—
759C2×C4—222no—
760C2×C4—222no—
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—448no—
770C2×C4—444no—
771C2×C4—448no—
772C2×C4—444no—
773C2×C4C2×D4×D1112yes—
774C2×C4C2×D4×D1112yes—
775C22—22no—
776C22—22no—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—416no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—44no—
791C22—44no—
792C22—442no—
793C22—442no—
794C22—442no—
795C22—442no—
796C22—442no—
797C22—442no—
798C22—444no—
799C22—444no—
800C22—444no—
801C22—444no—
802C22—888no—
803C22#1062313814yes—
804C22C22×D4×D1111yescharacteristic
805C22C2×#6703711yescharacteristic
806C22C2×#6703712yes—
807C22C2×#6704211yescharacteristic
808C22#1062345312yes—
809C4—22no—
810C4—22no—
811C4—42no—
812C4—42no—
813C4—44no—
814C4—224no—
815C4—224no—
816C4—442no—
817C4—442no—
818C4—444no—
819C2—24no—
820C2—44no—
821C2—82no—
822C2—882no—
823C2—882no—
824C2C2×#1062313811yescharacteristic
825C2#1308224511yescharacteristic
826C2#1308227011yescharacteristic
827C2#1308280012yes—
828C2#1308280612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2847C2
hypercenter#2847D11
hypocenterC11#36710
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. C2×#10623128C2semidirect
2. C22×#66982C2semidirect
3. #13076898C2semidirect
4. #13075170C2semidirect
5. #13075166C2semidirect
6. #13074886C2semidirect
7. #13074878C2semidirect
8. #13074353C2semidirect
9. #13074352C2semidirect
10. #13074095C2semidirect
11. #13072251C2semidirect
12. #13071934C2semidirect
13. #13071932C2semidirect
14. #13071218C2semidirect
15. C11×#2847C2semidirect
20. C2×C11×#121C22semidirect
26. C2×#66992C22semidirect
29. C2×#66983C22semidirect
38. C2×#66949C22semidirect
39. C2×#66937C22semidirect
41. C2×#66931C22semidirect
43. C11×#386C22semidirect
45. C11×#380C22semidirect
47. #10622836C22semidirect
48. #10622836C22semidirect
50. #10622833C22semidirect
52. #10622826C22semidirect
54. #10622825C22semidirect
55. #10622606C22semidirect
56. #10622604C22semidirect
57. #10622591C22semidirect
58. #10622574C22semidirect
60. #10622573C22semidirect
61. #10622572C22semidirect
63. #10622571C22semidirect
65. #10622569C22semidirect
66. #10622560C22semidirect
67. #10622557C22semidirect
70. #10622287C22semidirect
71. #10622286C22semidirect
72. #10622284C22semidirect
73. #10622282C22semidirect
74. #10622278C22semidirect
75. #10622271C22semidirect
76. #10622268C22semidirect
145. C2×Dic11⋊C4D4semidirect
279. #2847D11semidirect
392. C2×#121C2×D11semidirect
430. #386C2×D11semidirect
435. #380C2×D11semidirect
689. C11#36710semidirect

Maximal subgroups

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

subgroupindex
C2×#106231282
C22×#669822
#130768982
#130751702
#130751662
#130748862
#130748782
#130743532
#130743522
#130740952
#130722512
#130719342
#130719322
#130712182
C11×#28472
#3671011