Finite Group Databasebeta

← #14926396

Subgroups — #14926396

Order 2816.

2902 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623176C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3#13076941C212yesmaximal, complemented
4#13076898C211yesmaximal, characteristic, complemented
5#13074423C211yesmaximal, characteristic, complemented
6#13074353C211yesmaximal, characteristic, complemented
7#13074331C212yesmaximal, complemented
8#13072674C214yesmaximal, complemented
9#13072609C214yesmaximal, complemented
10#13072575C214yesmaximal, complemented
11#13072515C214yesmaximal, complemented
12#13071271C212yesmaximal, complemented
13#13071218C211yesmaximal, characteristic, complemented
14#13071117C212yesmaximal, complemented
15C11×#2848C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×C22⋊Q8C2212yescomplemented
21C2×#67006C2212yes—
22C22×C22⋊Dic11C2211yescharacteristic
23C2×#66999C2212yescomplemented
24C2×#66983C2211yescharacteristic
25C2×#66983C2212yescomplemented
26C2×C4×C22⋊D11—28no—
27C2×C4×C22⋊D11C2214yes—
28C2×C4×C22⋊D11C2214yes—
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32#10623176—28no—
33C2×#66951C2212yescomplemented
34C2×#66947C2212yescomplemented
35C2×#66946C2214yescomplemented
36C2×#66943C2212yescomplemented
37C2×#66939C2212yes—
38C2×#66935C2212yes—
39C2×(C22⋊D11)⋊C4C2212yes—
40C11×#385C2212yes—
41C11×#385C2214yescomplemented
42C11×#380C2211yescharacteristic
43C11×#380C2212yescomplemented
44C11×#379C2212yes—
45#10622844C2212yescomplemented
46#10622826C2212yes—
47#10622826C2214yescomplemented
48#10622825C2211yescharacteristic
49#10622825C2212yescomplemented
50#10622607C2214yescomplemented
51#10622605C2212yescomplemented
52#10622604C2214yescomplemented
53#10622603C2214yescomplemented
54#10622602C2214yescomplemented
55#10622594C2214yescomplemented
56#10622591C2214yescomplemented
57#10622574C2214yes—
58#10622574C2214yes—
59#10622573C2214yes—
60#10622573C2214yes—
61#10622571C2212yes—
62#10622570C2214yescomplemented
63#10622569C2214yescomplemented
64#10622568C2212yes—
65#10622559C2212yes—
66#10622558C2214yescomplemented
67#10622557C2214yescomplemented
68#10622556C2212yes—
69C22⋊C4×Dic11C2212yes—
70#10622287C2212yescomplemented
71#10622284C2212yescomplemented
72#10622282C2214yescomplemented
73#10622279C2214yescomplemented
74#10622278C2214yescomplemented
75#10622268C2214yescomplemented
76#10622268C2214yescomplemented
77C25×C11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C23×C4×C11—24no—
81C23×C4×C11—44no—
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2312yes—
84C23×C4×C11C2312yes—
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11C2312yes—
90C22×C22⋊D11C2314yes—
91C22×C22⋊D11C2314yes—
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C22×D44C2314yes—
96C22×D44C2311yescharacteristic
97C22×C4×D11—24no—
98C22×C4×D11—44no—
99C22×C4×D11C2314yes—
100C22×C4×D11C2312yes—
101C11×C22⋊Q8—24no—
102C11×C22⋊Q8—44no—
103C2×C11×C4⋊C4C2312yes—
104C2×C11×C4⋊C4C2314yes—
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2312yes—
107C2×C11×C22⋊C4C2312yes—
108C2×C11×C22⋊C4C2312yes—
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2314yes—
111#67006—28no—
112C2×C22⋊Dic11—24no—
113C2×C22⋊Dic11C2314yes—
114C2×C22⋊Dic11C2312yes—
115C2×C22⋊Dic11C2314yes—
116#66999—28no—
117#66983—24no—
118#66983—44no—
119C4×C22⋊D11—216no—
120C4×C22⋊D11—216no—
121C2×(C2×D11)⋊C4—24no—
122C2×(C2×D11)⋊C4C2312yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2312yes—
125C2×(C2×D11)⋊C4C2312yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2312yes—
128C2×(C2×D11)⋊C4C2312yes—
129C2×(C2×D11)⋊C4C2312yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×C4⋊Dic11C2312yes—
134C2×C4⋊Dic11C2312yes—
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2312yes—
137C2×Dic11⋊C4D418yescomplemented
138C2×Dic11⋊C4C2312yes—
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2312yes—
141C2×Dic11⋊C4C2312yes—
142C2×C4×Dic11—24no—
143C2×C4×Dic11C2312yes—
144C2×C4×Dic11C2314yes—
145C2×C4×Dic11C2314yes—
146#66951—28no—
147#66947—28no—
148#66946—48no—
149#66943—28no—
150#66939—28no—
151#66935—28no—
152(C22⋊D11)⋊C4—28no—
153C11×#95C2312yes—
154C11×#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2312yes—
162#34987—111nomaximal, Sylow
163C24×C11—22no—
164C24×C11—22no—
165C24×C11—42no—
166C24×C11—42no—
167C24×C11#4114yes—
168C24×C11C2412yes—
169C24×C11C2411yescharacteristic
170C23×D11—22no—
171C23×D11—22no—
172C23×D11—42no—
173C23×D11—42no—
174C23×D11#4114yes—
175C23×D11C2412yes—
176C23×D11C2412yes—
177C2×Q8×C11—22no—
178C2×Q8×C11—42no—
179C22×C4×C11—22no—
180C22×C4×C11—24no—
181C22×C4×C11—24no—
182C22×C4×C11—24no—
183C22×C4×C11—24no—
184C22×C4×C11—24no—
185C22×C4×C11—42no—
186C22×C4×C11—42no—
187C22×C4×C11—42no—
188C22×C4×C11—416no—
189C22×C4×C11C2×D414yes—
190C22×C4×C11C2414yes—
191C22×C4×C11C2412yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2411yescharacteristic
194C22×C4×C11C2411yescharacteristic
195C22×C4×C11C2412yes—
196C2×C22⋊D11—232no—
197C2×C22⋊D11—28no—
198C2×C22⋊D11—24no—
199C2×C22⋊D11—28no—
200C2×C22⋊D11—24no—
201C2×C22⋊D11—24no—
202C2×C22⋊D11—28no—
203C2×C22⋊D11—28no—
204C2×C22⋊D11—44no—
205C2×C22⋊D11—44no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—42no—
210C22×Dic11—42no—
211C22×Dic11C2×D414yes—
212C22×Dic11C2×D414yes—
213C22×Dic11C2414yes—
214C22×Dic11C2412yes—
215C22×Dic11C2412yes—
216C22×Dic11C2412yes—
217C22×Dic11C2412yes—
218C2×D44—28no—
219C2×D44—22no—
220C2×D44—44no—
221C2×D44—44no—
222C2×D44—42no—
223C2×C4×D11—28no—
224C2×C4×D11—24no—
225C2×C4×D11—28no—
226C2×C4×D11—44no—
227C2×C4×D11—44no—
228C2×C4×D11—416no—
229C11×C4⋊C4—24no—
230C11×C4⋊C4—22no—
231C11×C4⋊C4—28no—
232C11×C4⋊C4—42no—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—44no—
236C11×C22⋊C4—44no—
237C22⋊Dic11—28no—
238C22⋊Dic11—28no—
239C22⋊Dic11—24no—
240(C2×D11)⋊C4—24no—
241(C2×D11)⋊C4—24no—
242(C2×D11)⋊C4—24no—
243(C2×D11)⋊C4—28no—
244(C2×D11)⋊C4—24no—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—28no—
248(C2×D11)⋊C4—44no—
249(C2×D11)⋊C4—44no—
250(C2×D11)⋊C4—44no—
251C4⋊Dic11—24no—
252C4⋊Dic11—24no—
253C4⋊Dic11—22no—
254C4⋊Dic11—42no—
255Dic11⋊C4—24no—
256Dic11⋊C4—44no—
257Dic11⋊C4C2×D418yes—
258Dic11⋊C4C2×D418yes—
259C4×Dic11—24no—
260C4×Dic11—28no—
261C4×Dic11—44no—
262C2×#539—111no—
263C22×C4×D4—111no—
264#2853—112no—
265#2848D1111yescharacteristic, complemented
266#2847—111no—
267#2626—111no—
268#2617—111no—
269#2613—112no—
270#2467—114no—
271#2463—114no—
272#2460—114no—
273#2456—114no—
274#2321—112no—
275#2313—111no—
276C4×#120—112no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—28no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—48no—
287C23×C11—44no—
288C23×C11—48no—
289C23×C11—44no—
290C23×C11C22×D412yes—
291C23×C11C2×#4114yes—
292C23×C11C2×#4112yes—
293C23×C11C2×#4112yes—
294C23×C11C2511yescharacteristic
295C22×D11—28no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—24no—
299C22×D11—24no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—24no—
304C22×D11—24no—
305C22×D11—48no—
306C22×D11—44no—
307C22×D11—44no—
308C22×D11—48no—
309C22×D11C2×#4114yes—
310Q8×C11—82no—
311C2×C4×C11—28no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—24no—
319C2×C4×C11—24no—
320C2×C4×C11—24no—
321C2×C4×C11—24no—
322C2×C4×C11—24no—
323C2×C4×C11—44no—
324C2×C4×C11—48no—
325C2×C4×C11—48no—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D412yes—
328C2×C4×C11H(5,𝔽2)14yes—
329C22⋊D11—232no—
330C22⋊D11—48no—
331C22⋊D11—88no—
332C2×Dic11—28no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—24no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—24no—
343C2×Dic11—24no—
344C2×Dic11—44no—
345C2×Dic11—44no—
346C2×Dic11C22×D414yes—
347C2×Dic11C22×D414yes—
348D44—416no—
349D44—82no—
350C4×D11—416no—
351C4×D11—84no—
352C23×D4—111no—
353C24×C4—111no—
354C24×C4C2×D1111yescharacteristic
355#539—228no—
356C2×#126—112no—
357C2×#125—112no—
358C2×#123—112no—
359C2×#123—112no—
360C2×C22⋊Q8—112no—
361C2×C22⋊Q8C2×D1111yescharacteristic
362C2×C22⋊Q8C2×D1112yescomplemented
363C2×#121—111no—
364C2×#121—112no—
365C2×#120—112no—
366C2×#120—112no—
367C2×C4×D4—114no—
368C2×C4×D4—114no—
369C2×C4×D4—114no—
370C2×C4×D4—112no—
371C2×C4×D4—228no—
372C22×C4⋊C4—111no—
373C22×C22⋊C4—111no—
374C22×C22⋊C4—111no—
375C22×C42—111no—
376#399—112no—
377#397—112no—
378#396—114no—
379#394—114no—
380#394—114no—
381#394—114no—
382#393—112no—
383#392—114no—
384#392—114no—
385#392—112no—
386#390—114no—
387#388—114no—
388#388—114no—
389#388—114no—
390#388—114no—
391#387—114no—
392#387—114no—
393#387—114no—
394#387—114no—
395#386—112no—
396#386—114no—
397#386—112no—
398#386—114no—
399#386—114no—
400#385—114no—
401#385—112no—
402#385C2×D1112yes—
403#385C2×D1114yescomplemented
404#381—112no—
405#380—111no—
406#380—112no—
407#380C2×D1111yescharacteristic
408#380C2×D1112yescomplemented
409#379—112no—
410#379C2×D1112yes—
411C4×C22⋊C4—112no—
412C4×C22⋊C4—114no—
413C22×C11—24no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—24no—
417C22×C11—24no—
418C22×C11—24no—
419C22×C11—24no—
420C22×C11—416no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11#52514yes—
426C22×C11C23×D411yescharacteristic
427C22×C11C22×#4111yescharacteristic
428C22×C11C22×#4111yescharacteristic
429C22×C11C2×H(5,𝔽2)12yes—
430C22×C11#58512yes—
431C2×D11—24no—
432C2×D11—28no—
433C2×D11—416no—
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—44no—
437C2×D11—42no—
438C2×D11—44no—
439C2×D11—42no—
440C2×D11—42no—
441C2×D11—44no—
442C4×C11—24no—
443C4×C11—22no—
444C4×C11—22no—
445C4×C11—44no—
446C4×C11—42no—
447C4×C11—42no—
448Dic11—24no—
449Dic11—24no—
450Dic11—42no—
451Dic11—42no—
452Dic11—44no—
453C25—111no—
454C25C22×D1111yescharacteristic
455C22×Q8C22×D1111yescharacteristic
456C22×D4—114no—
457C22×D4—112no—
458C22×D4—114no—
459C22×D4—114no—
460C22×D4—111no—
461C22×D4—224no—
462C22×D4—224no—
463C22×D4—224no—
464C23×C4—24no—
465C23×C4—44no—
466C23×C4—111no—
467C23×C4—111no—
468C23×C4—111no—
469C23×C4—114no—
470C23×C4—112no—
471C23×C4—224no—
472C23×C4—444no—
473C23×C4C22×D1111yescharacteristic
474C23×C4C22×D1112yes—
475C23×C4C22×D1112yes—
476C23×C4C22×D1111yescharacteristic
477#126—228no—
478#125—228no—
479#123—228no—
480#123—228no—
481C22⋊Q8—24no—
482C22⋊Q8—44no—
483C22⋊Q8—228no—
484#121—224no—
485#121—444no—
486#120—228no—
487#120—228no—
488C4×D4—228no—
489C4×D4—2216no—
490C4×D4—2216no—
491C4×D4—448no—
492C2×C4⋊C4—118no—
493C2×C4⋊C4—112no—
494C2×C4⋊C4—112no—
495C2×C4⋊C4—112no—
496C2×C4⋊C4—111no—
497C2×C4⋊C4—112no—
498C2×C4⋊C4—112no—
499C2×C4⋊C4—112no—
500C2×C4⋊C4—114no—
501C2×C4⋊C4C22×D1114yes—
502C2×C4⋊C4C22×D1112yes—
503C2×C4⋊C4C22×D1111yescharacteristic
504C2×C4⋊C4C22×D1112yes—
505C2×C22⋊C4—114no—
506C2×C22⋊C4—112no—
507C2×C22⋊C4—114no—
508C2×C22⋊C4—112no—
509C2×C22⋊C4—112no—
510C2×C22⋊C4—114no—
511C2×C22⋊C4—112no—
512C2×C22⋊C4—114no—
513C2×C22⋊C4—112no—
514C2×C22⋊C4—112no—
515C2×C22⋊C4—112no—
516C2×C22⋊C4—114no—
517C2×C22⋊C4—114no—
518C2×C22⋊C4—114no—
519C2×C22⋊C4—224no—
520C2×C22⋊C4—224no—
521C2×C22⋊C4C22×D1112yes—
522C2×C22⋊C4C22×D1112yes—
523C2×C22⋊C4C22×D1114yes—
524C2×C22⋊C4C22×D1114yes—
525C2×C42—114no—
526C2×C42—112no—
527C2×C42—114no—
528C2×C42—224no—
529#95—114no—
530#95—114no—
531#95—112no—
532#95—114no—
533#95—114no—
534#95—114no—
535#95—114no—
536#95C22×D1114yes—
537#95C22×D1112yes—
538C2×C11—24no—
539C2×C11—44no—
540C2×C11C2×#52511yescharacteristic
541C2×C11#345912yes—
542C2×C11#348411yescharacteristic
543C2×C11#348711yescharacteristic
544C2×C11#350512yes—
545D11—44no—
546D11—82no—
547C24—22no—
548C24—22no—
549C24—42no—
550C24—42no—
551C24—112no—
552C24—114no—
553C24—112no—
554C24—222no—
555C24—222no—
556C24—442no—
557C24—442no—
558C24#434314yes—
559C24C23×D1112yes—
560C24C23×D1111yescharacteristic
561C2×Q8—22no—
562C2×Q8—42no—
563C2×D4—228no—
564C2×D4—228no—
565C2×D4—228no—
566C2×D4—2232no—
567C2×D4—228no—
568C2×D4—224no—
569C2×D4—224no—
570C2×D4—224no—
571C2×D4—228no—
572C2×D4—222no—
573C2×D4—444no—
574C2×D4—444no—
575C2×D4—442no—
576C2×D4—444no—
577C2×D4—444no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—416no—
588C22×C4—114no—
589C22×C4—112no—
590C22×C4—112no—
591C22×C4—114no—
592C22×C4—114no—
593C22×C4—112no—
594C22×C4—112no—
595C22×C4—228no—
596C22×C4—224no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—228no—
601C22×C4—444no—
602C22×C4—444no—
603C22×C4—4416no—
604C22×C4—442no—
605C22×C4—442no—
606C22×C4D4×D1114yes—
607C22×C4C23×D1114yes—
608C22×C4C23×D1112yes—
609C22×C4C23×D1112yes—
610C22×C4C23×D1111yescharacteristic
611C22×C4C23×D1111yescharacteristic
612C22×C4C23×D1112yes—
613C4⋊C4—24no—
614C4⋊C4—22no—
615C4⋊C4—28no—
616C4⋊C4—42no—
617C4⋊C4—118no—
618C4⋊C4—118no—
619C4⋊C4—224no—
620C4⋊C4—224no—
621C4⋊C4—224no—
622C4⋊C4—222no—
623C4⋊C4—442no—
624C4⋊C4—444no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—224no—
630C22⋊C4—224no—
631C22⋊C4—224no—
632C22⋊C4—228no—
633C22⋊C4—228no—
634C22⋊C4—228no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C22⋊C4—224no—
639C22⋊C4—228no—
640C22⋊C4—444no—
641C22⋊C4—444no—
642C22⋊C4—444no—
643C42—228no—
644C42—224no—
645C42—444no—
646C11#3498711yescharacteristic, complemented, Sylow
647C23—22no—
648C23—22no—
649C23—28no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—48no—
657C23—44no—
658C23—44no—
659C23—48no—
660C23—114no—
661C23—228no—
662C23—222no—
663C23—224no—
664C23—222no—
665C23—224no—
666C23—222no—
667C23—224no—
668C23—222no—
669C23—222no—
670C23—224no—
671C23—448no—
672C23—444no—
673C23—448no—
674C23—444no—
675C23C2×D4×D1112yes—
676C23C2×#434314yes—
677C23C2×#434312yes—
678C23#41×D1112yes—
679C23C24×D1111yescharacteristic
680Q8—82no—
681D4—2232no—
682D4—4416no—
683D4—448no—
684D4—882no—
685D4—888no—
686C2×C4—28no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—44no—
699C2×C4—48no—
700C2×C4—48no—
701C2×C4—114no—
702C2×C4—114no—
703C2×C4—228no—
704C2×C4—224no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—224no—
710C2×C4—222no—
711C2×C4—224no—
712C2×C4—222no—
713C2×C4—224no—
714C2×C4—224no—
715C2×C4—4416no—
716C2×C4—444no—
717C2×C4—444no—
718C2×C4—884no—
719C2×C4C2×D4×D1112yes—
720C2×C4C2×D4×D1112yes—
721C2×C4#6703714yes—
722C22—24no—
723C22—22no—
724C22—22no—
725C22—24no—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—416no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—224no—
735C22—228no—
736C22—4416no—
737C22—444no—
738C22—442no—
739C22—442no—
740C22—442no—
741C22—444no—
742C22—442no—
743C22—442no—
744C22—444no—
745C22#1062315814yes—
746C22C22×D4×D1111yescharacteristic
747C22C2×#6703712yes—
748C22C22×#434311yescharacteristic
749C22C2×#41×D1111yescharacteristic
750C22#1062345312yes—
751C4—24no—
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—44no—
757C4—224no—
758C4—224no—
759C4—442no—
760C4—444no—
761C4—442no—
762C2—24no—
763C2—44no—
764C2—444no—
765C2—882no—
766C2C2×#1062315811yescharacteristic
767C2#1308202312yes—
768C2#1308224511yescharacteristic
769C2#1308227011yescharacteristic
770C2#1308245712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2848C2
hypercenter#2848D11
hypocenterC11#34987
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2848

Complements

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

NH ≅ G/Ntype
1. C2×#10623176C2semidirect
2. C22×C4×C22⋊D11C2semidirect
3. #13076941C2semidirect
4. #13076898C2semidirect
5. #13074423C2semidirect
6. #13074353C2semidirect
7. #13074331C2semidirect
8. #13072674C2semidirect
9. #13072609C2semidirect
10. #13072575C2semidirect
11. #13072515C2semidirect
12. #13071271C2semidirect
13. #13071218C2semidirect
14. #13071117C2semidirect
15. C11×#2848C2semidirect
20. C2×C11×C22⋊Q8C22semidirect
23. C2×#66999C22semidirect
25. C2×#66983C22semidirect
33. C2×#66951C22semidirect
34. C2×#66947C22semidirect
35. C2×#66946C22semidirect
36. C2×#66943C22semidirect
41. C11×#385C22semidirect
43. C11×#380C22semidirect
45. #10622844C22semidirect
47. #10622826C22semidirect
49. #10622825C22semidirect
50. #10622607C22semidirect
51. #10622605C22semidirect
52. #10622604C22semidirect
53. #10622603C22semidirect
54. #10622602C22semidirect
55. #10622594C22semidirect
56. #10622591C22semidirect
62. #10622570C22semidirect
63. #10622569C22semidirect
66. #10622558C22semidirect
67. #10622557C22semidirect
70. #10622287C22semidirect
71. #10622284C22semidirect
72. #10622282C22semidirect
73. #10622279C22semidirect
74. #10622278C22semidirect
75. #10622268C22semidirect
76. #10622268C22semidirect
137. C2×Dic11⋊C4D4semidirect
265. #2848D11semidirect
362. C2×C22⋊Q8C2×D11semidirect
403. #385C2×D11semidirect
408. #380C2×D11semidirect
646. C11#34987semidirect

Maximal subgroups

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

subgroupindex
C2×#106231762
C22×C4×C22⋊D112
#130769412
#130768982
#130744232
#130743532
#130743312
#130726742
#130726092
#130725752
#130725152
#130712712
#130712182
#130711172
C11×#28482
#3498711