Finite Group Databasebeta

← #14926392

Subgroups — #14926392

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×#10623046C211yesmaximal, characteristic, complemented
2#13076938C212yesmaximal, complemented
3#13076903C211yesmaximal, characteristic, complemented
4#13076898C211yesmaximal, characteristic, complemented
5#13074421C211yesmaximal, characteristic, complemented
6#13074350C211yesmaximal, characteristic, complemented
7#13074328C212yesmaximal, complemented
8#13072661C214yesmaximal, complemented
9#13072607C214yesmaximal, complemented
10#13072562C214yesmaximal, complemented
11#13072502C214yesmaximal, complemented
12#13071274C212yesmaximal, complemented
13#13071219C211yesmaximal, characteristic, complemented
14C4×#67006C212yesmaximal, complemented
15C22×C4×D4×C11C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C2×C4×D4×C11—28no—
20C2×C4×D4×C11C2214yes—
21C2×C4×D4×C11C2214yes—
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C2×#67006C2212yes—
27C2×#67006C2212yes—
28C2×#66983C2211yescharacteristic
29C2×#66983C2212yescomplemented
30C2×#66982C2212yes—
31C2×C4×C22⋊D11C2212yes—
32C2×C4×C22⋊D11C2214yescomplemented
33C2×#66977C2211yescharacteristic
34C2×#66977C2212yescomplemented
35#10623046—28no—
36C2×#66951C2212yescomplemented
37C2×#66949C2212yescomplemented
38C2×#66947C2212yescomplemented
39C2×#66942C2212yescomplemented
40#10622860C2212yes—
41#10622860C2212yes—
42#10622836C2214yes—
43#10622836C2214yes—
44#10622835C2214yes—
45#10622835C2214yes—
46#10622826C2212yes—
47#10622826C2212yes—
48#10622826C2214yescomplemented
49#10622826C2214yescomplemented
50#10622825C2211yescharacteristic
51#10622825C2211yescharacteristic
52#10622825C2212yescomplemented
53#10622825C2212yescomplemented
54#10622824C2212yes—
55#10622823C2212yes—
56#10622823C2212yes—
57#10622823C2214yescomplemented
58#10622823C2214yescomplemented
59C4×C22⋊Dic11C2212yes—
60C4×C22⋊Dic11C2214yescomplemented
61#10622594C2214yescomplemented
62#10622594C2214yescomplemented
63#10622574C2214yescomplemented
64#10622573C2212yescomplemented
65#10622570C2214yescomplemented
66#10622569C2214yescomplemented
67#10622566C2212yescomplemented
68#10622562C2212yescomplemented
69#10622561C2214yescomplemented
70#10622560C2212yescomplemented
71#10622558C2214yescomplemented
72#10622557C2214yescomplemented
73#10622553C2214yescomplemented
74#10622553C2214yescomplemented
75#10622546C2214yescomplemented
76#10622546C2214yescomplemented
77C25×C11C2311yescharacteristic
78C25×C11C2311yescharacteristic
79C22×D4×C11—24no—
80C22×D4×C11—24no—
81C22×D4×C11—24no—
82C22×D4×C11C2314yes—
83C23×C4×C11—24no—
84C23×C4×C11—24no—
85C23×C4×C11—44no—
86C23×C4×C11—44no—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2312yes—
89C23×C4×C11C2314yes—
90C23×C4×C11C2312yes—
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C22×C22⋊D11C2312yes—
96C22×C22⋊D11C2314yes—
97C22×C22⋊D11C2314yes—
98C22×D44C2311yescharacteristic
99C22×C4×D11C2312yes—
100C22×Dic22C2311yescharacteristic
101C4×D4×C11—216no—
102C4×D4×C11—216no—
103C2×C11×C4⋊C4D418yescomplemented
104C2×C11×C4⋊C4C2312yes—
105C2×C11×C4⋊C4C2312yes—
106C2×C11×C22⋊C4—24no—
107C2×C11×C22⋊C4—24no—
108C2×C11×C22⋊C4C2314yes—
109C2×C11×C22⋊C4C2312yes—
110C2×C11×C22⋊C4C2312yes—
111C2×C42×C11—24no—
112C2×C42×C11C2314yes—
113#67006—28no—
114#67006—28no—
115C2×C22⋊Dic11C2312yes—
116C2×C22⋊Dic11C2314yes—
117C2×C22⋊Dic11C2314yes—
118C2×C22⋊Dic11C2312yes—
119C2×C22⋊Dic11C2312yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124#66983—24no—
125#66983—44no—
126#66982—28no—
127C4×C22⋊D11—28no—
128C4×C22⋊D11—48no—
129C2×(C2×D11)⋊C4C2312yes—
130C2×(C2×D11)⋊C4C2312yes—
131C2×(C2×D11)⋊C4C2312yes—
132C2×(C2×D11)⋊C4C2312yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×C4⋊Dic11C2312yes—
138C2×C4⋊Dic11C2312yes—
139#66977—24no—
140#66977—44no—
141C2×Dic11⋊C4C2312yes—
142C2×Dic11⋊C4C2312yes—
143C2×Dic11⋊C4C2312yes—
144C2×Dic11⋊C4C2312yes—
145C2×Dic11⋊C4C2314yes—
146C2×Dic11⋊C4C2314yes—
147C2×C4×Dic11C2312yes—
148C2×C4×Dic11C2314yes—
149#66951—28no—
150#66949—28no—
151#66947—28no—
152#66942—28no—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2312yes—
161C11⋊#95C2312yes—
162#34987—111nomaximal, Sylow
163C24×C11—22no—
164C24×C11—22no—
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—42no—
168C24×C11—42no—
169C24×C11—42no—
170C24×C11—42no—
171C24×C11#4114yes—
172C24×C11#4114yes—
173C24×C11C2412yes—
174C24×C11C2412yes—
175C24×C11C2411yescharacteristic
176C23×D11C2412yes—
177C2×D4×C11—232no—
178C2×D4×C11—28no—
179C2×D4×C11—28no—
180C2×D4×C11—28no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—24no—
185C22×C4×C11—22no—
186C22×C4×C11—28no—
187C22×C4×C11—24no—
188C22×C4×C11—24no—
189C22×C4×C11—24no—
190C22×C4×C11—28no—
191C22×C4×C11—24no—
192C22×C4×C11—42no—
193C22×C4×C11—44no—
194C22×C4×C11—42no—
195C22×C4×C11—42no—
196C22×C4×C11—42no—
197C22×C4×C11—42no—
198C22×C4×C11—416no—
199C22×C4×C11—416no—
200C22×C4×C11C2×D414yes—
201C22×C4×C11C2×D414yes—
202C22×C4×C11C2×D414yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2411yescharacteristic
207C22×C4×C11C2411yescharacteristic
208C22×C4×C11C2412yes—
209C2×C22⋊D11—24no—
210C2×C22⋊D11—28no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—28no—
214C2×C22⋊D11—44no—
215C2×C22⋊D11—44no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—44no—
218C22×Dic11C2414yes—
219C22×Dic11C2414yes—
220C22×Dic11C2412yes—
221C22×Dic11C2412yes—
222C22×Dic11C2412yes—
223C2×D44—22no—
224C2×D44—42no—
225C2×C4×D11—24no—
226C2×C4×D11—44no—
227C2×Dic22—22no—
228C2×Dic22—42no—
229C11×C4⋊C4C2×D418yes—
230C11×C4⋊C4C2×D418yes—
231C11×C22⋊C4—28no—
232C11×C22⋊C4—24no—
233C11×C22⋊C4—24no—
234C42×C11—28no—
235C22⋊Dic11—24no—
236C22⋊Dic11—28no—
237C22⋊Dic11—28no—
238C22⋊Dic11—24no—
239C22⋊Dic11—24no—
240C22⋊Dic11—44no—
241C22⋊Dic11—44no—
242C22⋊Dic11—44no—
243C22⋊Dic11—44no—
244(C2×D11)⋊C4—24no—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—28no—
249(C2×D11)⋊C4—44no—
250C4⋊Dic11—22no—
251C4⋊Dic11—22no—
252C4⋊Dic11—42no—
253C4⋊Dic11—42no—
254Dic11⋊C4—24no—
255Dic11⋊C4—24no—
256Dic11⋊C4—24no—
257Dic11⋊C4—24no—
258Dic11⋊C4—28no—
259Dic11⋊C4—44no—
260C4×Dic11—24no—
261C4×Dic11—44no—
262C2×#539—111no—
263C22×C4×D4D1111yescharacteristic, complemented
264#2853—112no—
265#2848—111no—
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—28no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—24no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—24no—
290C23×C11—22no—
291C23×C11—48no—
292C23×C11—48no—
293C23×C11—44no—
294C23×C11—44no—
295C23×C11—48no—
296C23×C11—44no—
297C23×C11—44no—
298C23×C11—48no—
299C23×C11C22×D412yes—
300C23×C11C2×#4114yes—
301C23×C11C2×#4114yes—
302C23×C11C2×#4112yes—
303C23×C11C2×#4112yes—
304C23×C11C2511yescharacteristic
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—24no—
309C22×D11—24no—
310D4×C11—232no—
311C2×C4×C11—28no—
312C2×C4×C11—28no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—24no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—24no—
322C2×C4×C11—44no—
323C2×C4×C11—44no—
324C2×C4×C11—48no—
325C2×C4×C11—416no—
326C2×C4×C11—48no—
327C2×C4×C11—44no—
328C2×C4×C11C22×D414yes—
329C2×C4×C11C22×D412yes—
330C2×C4×C11C22×D414yes—
331C2×C4×C11C22×D412yes—
332C2×C4×C11H(5,𝔽2)14yes—
333C22⋊D11—416no—
334C22⋊D11—48no—
335C22⋊D11—88no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—24no—
342C2×Dic11—24no—
343C2×Dic11—24no—
344C2×Dic11—24no—
345C2×Dic11—24no—
346C2×Dic11—24no—
347C2×Dic11—24no—
348C2×Dic11—24no—
349D44—82no—
350C4×D11—84no—
351Dic22—82no—
352C23×D4C2×D1111yescharacteristic
353C24×C4C2×D1111yescharacteristic
354C24×C4C2×D1111yescharacteristic
355#539—228no—
356C2×#126—112no—
357C2×#125—112no—
358C2×#123—112no—
359C2×#123—112no—
360C2×C22⋊Q8—111no—
361C2×C22⋊Q8—112no—
362C2×C22⋊Q8—112no—
363C2×#121—111no—
364C2×#121—112no—
365C2×#120—112no—
366C2×#120—112no—
367C2×C4×D4—28no—
368C2×C4×D4—112no—
369C2×C4×D4—114no—
370C2×C4×D4C2×D1114yes—
371C2×C4×D4C2×D1114yes—
372C22×C4⋊C4C2×D1111yescharacteristic
373C22×C22⋊C4C2×D1111yescharacteristic
374C22×C22⋊C4C2×D1111yescharacteristic
375C22×C42C2×D1111yescharacteristic
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—112no—
397#386—114no—
398#386—114no—
399#386—114no—
400#385—112no—
401#385—112no—
402#385—114no—
403#385—114no—
404#381—112no—
405#380—111no—
406#380—111no—
407#380—112no—
408#380—112no—
409#379—112no—
410#379—112no—
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—28no—
420C22×C11—24no—
421C22×C11—24no—
422C22×C11—416no—
423C22×C11—416no—
424C22×C11—42no—
425C22×C11—42no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—44no—
431C22×C11#52514yes—
432C22×C11C23×D411yescharacteristic
433C22×C11C22×#4111yescharacteristic
434C22×C11C22×#4111yescharacteristic
435C22×C11C2×H(5,𝔽2)12yes—
436C22×C11#58512yes—
437C2×D11—42no—
438C2×D11—44no—
439C2×D11—42no—
440C2×D11—42no—
441C2×D11—44no—
442C4×C11—24no—
443C4×C11—24no—
444C4×C11—22no—
445C4×C11—24no—
446C4×C11—22no—
447C4×C11—42no—
448Dic11—42no—
449Dic11—44no—
450Dic11—42no—
451Dic11—42no—
452Dic11—44no—
453C25C22×D1111yescharacteristic
454C25C22×D1111yescharacteristic
455C22×Q8—111no—
456C22×D4—24no—
457C22×D4—24no—
458C22×D4—24no—
459C22×D4—112no—
460C22×D4—114no—
461C22×D4—114no—
462C22×D4—111no—
463C22×D4C22×D1114yes—
464C23×C4—24no—
465C23×C4—24no—
466C23×C4—44no—
467C23×C4—44no—
468C23×C4—112no—
469C23×C4C22×D1111yescharacteristic
470C23×C4C22×D1114yes—
471C23×C4C22×D1112yes—
472C23×C4C22×D1112yes—
473C23×C4C22×D1111yescharacteristic
474C23×C4C22×D1111yescharacteristic
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1111yescharacteristic
477#126—228no—
478#125—228no—
479#123—228no—
480#123—228no—
481C22⋊Q8—224no—
482C22⋊Q8—228no—
483C22⋊Q8—444no—
484#121—224no—
485#121—444no—
486#120—228no—
487#120—228no—
488C4×D4—216no—
489C4×D4—216no—
490C4×D4—228no—
491C4×D4—448no—
492C2×C4⋊C4—112no—
493C2×C4⋊C4—114no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—112no—
496C2×C4⋊C4—112no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—112no—
499C2×C4⋊C4—112no—
500C2×C4⋊C4—112no—
501C2×C4⋊C4—114no—
502C2×C4⋊C4C22⋊D1118yescomplemented
503C2×C4⋊C4C22×D1112yes—
504C2×C4⋊C4C22×D1112yes—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—112no—
508C2×C22⋊C4—112no—
509C2×C22⋊C4—112no—
510C2×C22⋊C4—114no—
511C2×C22⋊C4—114no—
512C2×C22⋊C4—114no—
513C2×C22⋊C4—112no—
514C2×C22⋊C4—112no—
515C2×C22⋊C4—112no—
516C2×C22⋊C4—112no—
517C2×C22⋊C4—114no—
518C2×C22⋊C4—114no—
519C2×C22⋊C4—114no—
520C2×C22⋊C4—114no—
521C2×C22⋊C4—114no—
522C2×C22⋊C4C22×D1114yes—
523C2×C22⋊C4C22×D1112yes—
524C2×C22⋊C4C22×D1112yes—
525C2×C42—24no—
526C2×C42—112no—
527C2×C42—114no—
528C2×C42C22×D1114yes—
529#95—114no—
530#95—114no—
531#95—114no—
532#95—112no—
533#95—112no—
534#95—114no—
535#95—114no—
536#95—114no—
537#95—114no—
538C2×C11—24no—
539C2×C11—44no—
540C2×C11—44no—
541C2×C11C2×#52511yescharacteristic
542C2×C11#345912yes—
543C2×C11#348411yescharacteristic
544C2×C11#348711yescharacteristic
545C2×C11#350512yes—
546D11—82no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—42no—
552C24—42no—
553C24—42no—
554C24—42no—
555C24—112no—
556C24#433914yes—
557C24#433914yes—
558C24C23×D1112yes—
559C24C23×D1112yes—
560C24C23×D1111yescharacteristic
561C2×Q8—222no—
562C2×Q8—442no—
563C2×D4—232no—
564C2×D4—28no—
565C2×D4—28no—
566C2×D4—28no—
567C2×D4—228no—
568C2×D4—224no—
569C2×D4—224no—
570C2×D4—224no—
571C2×D4—228no—
572C2×D4—222no—
573C2×D4—442no—
574C2×D4—444no—
575C2×D4—444no—
576C2×D4—444no—
577C2×D4—444no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—22no—
583C22×C4—28no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—28no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—42no—
590C22×C4—44no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—416no—
596C22×C4—416no—
597C22×C4—114no—
598C22×C4—114no—
599C22×C4—112no—
600C22×C4—112no—
601C22×C4—112no—
602C22×C4—224no—
603C22×C4—444no—
604C22×C4C2×C22⋊D1114yes—
605C22×C4C2×C22⋊D1114yes—
606C22×C4C2×C22⋊D1114yes—
607C22×C4C23×D1112yes—
608C22×C4C23×D1112yes—
609C22×C4C23×D1112yes—
610C22×C4C23×D1112yes—
611C22×C4C23×D1111yescharacteristic
612C22×C4C23×D1111yescharacteristic
613C4⋊C4—228no—
614C4⋊C4—224no—
615C4⋊C4—222no—
616C4⋊C4—224no—
617C4⋊C4—224no—
618C4⋊C4—222no—
619C4⋊C4—224no—
620C4⋊C4—442no—
621C4⋊C4—442no—
622C4⋊C4—444no—
623C4⋊C4C2×C22⋊D1118yes—
624C4⋊C4C2×C22⋊D1118yes—
625C22⋊C4—28no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—228no—
629C22⋊C4—228no—
630C22⋊C4—224no—
631C22⋊C4—224no—
632C22⋊C4—224no—
633C22⋊C4—228no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C22⋊C4—444no—
639C22⋊C4—444no—
640C22⋊C4—444no—
641C22⋊C4—444no—
642C22⋊C4—444no—
643C42—28no—
644C42—224no—
645C42—444no—
646C11#3498711yescharacteristic, complemented, Sylow
647C23—22no—
648C23—22no—
649C23—28no—
650C23—28no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—48no—
662C23—48no—
663C23—44no—
664C23—44no—
665C23—48no—
666C23—44no—
667C23—44no—
668C23—48no—
669C23—222no—
670C23—222no—
671C23—224no—
672C23—224no—
673C23—222no—
674C23C2×#433914yes—
675C23C2×#433914yes—
676C23C2×#433912yes—
677C23C2×#433912yes—
678C23C22×C22⋊D1112yes—
679C23C24×D1111yescharacteristic
680Q8—882no—
681D4—232no—
682D4—4416no—
683D4—448no—
684D4—882no—
685D4—888no—
686C2×C4—28no—
687C2×C4—28no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—416no—
700C2×C4—48no—
701C2×C4—48no—
702C2×C4—44no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—224no—
706C2×C4—224no—
707C2×C4—224no—
708C2×C4—224no—
709C2×C4—224no—
710C2×C4—224no—
711C2×C4—224no—
712C2×C4—224no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—884no—
717C2×C4#6703714yes—
718C2×C4C22×C22⋊D1114yes—
719C2×C4C22×C22⋊D1114yes—
720C2×C4C22×C22⋊D1112yes—
721C2×C4C22×C22⋊D1112yes—
722C22—24no—
723C22—22no—
724C22—22no—
725C22—24no—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—28no—
731C22—416no—
732C22—416no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—442no—
741C22—444no—
742C22—442no—
743C22—442no—
744C22—444no—
745C22#1062332214yes—
746C22C22×#433911yescharacteristic
747C22C22×#433911yescharacteristic
748C22C2×#6703712yes—
749C22#1062345312yes—
750C22C23×C22⋊D1111yescharacteristic
751C4—24no—
752C4—24no—
753C4—24no—
754C4—22no—
755C4—22no—
756C4—42no—
757C4—442no—
758C4—444no—
759C4—442no—
760C4—442no—
761C4—444no—
762C2—24no—
763C2—44no—
764C2—44no—
765C2—882no—
766C2C2×#1062332211yescharacteristic
767C2#1308202512yes—
768C2#1308225111yescharacteristic
769C2#1308227411yescharacteristic
770C2#1308245512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC22×C4×D4×C11C2
hypercenterC22×C4×D4D11
hypocenterC11#34987
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10623046C2semidirect
2. #13076938C2semidirect
3. #13076903C2semidirect
4. #13076898C2semidirect
5. #13074421C2semidirect
6. #13074350C2semidirect
7. #13074328C2semidirect
8. #13072661C2semidirect
9. #13072607C2semidirect
10. #13072562C2semidirect
11. #13072502C2semidirect
12. #13071274C2semidirect
13. #13071219C2semidirect
14. C4×#67006C2semidirect
15. C22×C4×D4×C11C2semidirect
29. C2×#66983C22semidirect
32. C2×C4×C22⋊D11C22semidirect
34. C2×#66977C22semidirect
36. C2×#66951C22semidirect
37. C2×#66949C22semidirect
38. C2×#66947C22semidirect
39. C2×#66942C22semidirect
48. #10622826C22semidirect
49. #10622826C22semidirect
52. #10622825C22semidirect
53. #10622825C22semidirect
57. #10622823C22semidirect
58. #10622823C22semidirect
60. C4×C22⋊Dic11C22semidirect
61. #10622594C22semidirect
62. #10622594C22semidirect
63. #10622574C22semidirect
64. #10622573C22semidirect
65. #10622570C22semidirect
66. #10622569C22semidirect
67. #10622566C22semidirect
68. #10622562C22semidirect
69. #10622561C22semidirect
70. #10622560C22semidirect
71. #10622558C22semidirect
72. #10622557C22semidirect
73. #10622553C22semidirect
74. #10622553C22semidirect
75. #10622546C22semidirect
76. #10622546C22semidirect
103. C2×C11×C4⋊C4D4semidirect
263. C22×C4×D4D11semidirect
502. C2×C4⋊C4C22⋊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×#106230462
#130769382
#130769032
#130768982
#130744212
#130743502
#130743282
#130726612
#130726072
#130725622
#130725022
#130712742
#130712192
C4×#670062
C22×C4×D4×C112
#3498711