Finite Group Databasebeta

← #14926384

Subgroups — #14926384

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
1C22×#66946C211yesmaximal, characteristic, complemented
2#13076935C212yesmaximal, complemented
3#13076900C211yesmaximal, characteristic, complemented
4#13076895C211yesmaximal, characteristic, complemented
5#13074423C211yesmaximal, characteristic, complemented
6#13074352C211yesmaximal, characteristic, complemented
7#13074332C212yesmaximal, complemented
8#13072663C214yesmaximal, complemented
9#13072609C214yesmaximal, complemented
10#13072564C214yesmaximal, complemented
11#13072504C214yesmaximal, complemented
12#13071270C212yesmaximal, complemented
13#13071219C211yesmaximal, characteristic, complemented
14C4×#66990C212yesmaximal, complemented
15C2×C11×#539C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C11×#539—28no—
20C2×C11×#126C2212yescomplemented
21C2×C11×#125C2212yescomplemented
22C2×C11×#123C2212yes—
23C2×C11×#123C2212yescomplemented
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×C22⋊Q8C2212yescomplemented
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11C2212yes—
28C22×C11×C4⋊C4C2211yescharacteristic
29C2×#66999C2212yescomplemented
30C2×#66991C2212yescomplemented
31C2×#66990C2212yes—
32C2×#66990C2212yes—
33C2×C4×C22⋊D11C2214yescomplemented
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C2×#66946—28no—
38C2×#66946C2214yes—
39C2×#66946C2214yes—
40#10622844C2212yescomplemented
41#10622836C2212yescomplemented
42#10622833C2212yes—
43#10622833C2212yes—
44#10622826C2214yescomplemented
45#10622825C2211yescharacteristic
46#10622825C2211yescharacteristic
47#10622824C2212yes—
48C4×C22⋊Dic11C2212yes—
49#10622607C2214yescomplemented
50#10622606C2212yescomplemented
51#10622605C2212yescomplemented
52#10622604C2214yes—
53#10622604C2214yes—
54#10622603C2214yescomplemented
55#10622602C2214yescomplemented
56#10622602C2214yescomplemented
57#10622600C2212yescomplemented
58#10622600C2212yescomplemented
59#10622594C2214yescomplemented
60#10622594C2214yescomplemented
61#10622591C2214yescomplemented
62#10622591C2214yescomplemented
63#10622574C2214yescomplemented
64#10622573C2214yes—
65#10622573C2214yes—
66#10622570C2214yescomplemented
67#10622569C2214yescomplemented
68#10622569C2214yescomplemented
69#10622568C2212yes—
70#10622568C2212yes—
71#10622559C2212yes—
72#10622559C2212yes—
73#10622557C2214yescomplemented
74#10622557C2214yescomplemented
75#10622553C2214yescomplemented
76C4×(C2×D11)⋊C4C2214yescomplemented
77C24×D11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2312yes—
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2312yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11C2314yes—
87C22×C22⋊D11C2314yes—
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C22×D44—24no—
91C22×D44—24no—
92C22×D44—24no—
93C22×D44C2314yes—
94C22×C4×D11—24no—
95C22×C4×D11—24no—
96C22×C4×D11—44no—
97C22×C4×D11—44no—
98C22×C4×D11C2314yes—
99C22×C4×D11C2312yes—
100C22×C4×D11C2312yes—
101C11×#126—28no—
102C11×#125—28no—
103C11×#123—28no—
104C11×#123—28no—
105C11×C22⋊Q8—24no—
106C11×C22⋊Q8—28no—
107C11×#121—24no—
108C4×D4×C11—28no—
109C2×C11×C4⋊C4D418yescomplemented
110C2×C11×C4⋊C4C2312yes—
111C2×C11×C4⋊C4C2312yes—
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2312yes—
115C2×C11×C4⋊C4C2312yes—
116C2×C11×C4⋊C4C2312yes—
117C2×C11×C4⋊C4C2312yes—
118C2×C11×C22⋊C4C2312yes—
119C2×C11×C22⋊C4C2312yes—
120C2×C11×C22⋊C4C2312yes—
121C2×C11×C22⋊C4C2312yes—
122C2×C11×C22⋊C4C2312yes—
123C2×C42×C11C2312yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2312yes—
126C2×C22⋊Dic11C2312yes—
127C2×C22⋊Dic11C2314yes—
128#66999—44no—
129#66991—44no—
130#66990—28no—
131#66990—28no—
132C4×C22⋊D11—48no—
133C2×(C2×D11)⋊C4—24no—
134C2×(C2×D11)⋊C4—24no—
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×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×C4⋊Dic11C2312yes—
145C2×C4⋊Dic11C2312yes—
146C2×Dic11⋊C4C2314yes—
147C2×Dic11⋊C4C2314yes—
148C2×C4×Dic11—24no—
149C2×C4×Dic11C2314yes—
150C2×C4×Dic11C2314yes—
151#66946—216no—
152#66946—216no—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2312yes—
161C11⋊#95C2312yes—
162#34987—111nomaximal, Sylow
163C24×C11C2412yes—
164C24×C11C2411yescharacteristic
165C23×D11—22no—
166C23×D11—22no—
167C23×D11—22no—
168C23×D11—22no—
169C23×D11—42no—
170C23×D11—42no—
171C23×D11—42no—
172C23×D11—42no—
173C23×D11#4114yes—
174C23×D11#4114yes—
175C23×D11C2412yes—
176C23×D11C2412yes—
177C2×Q8×C11—22no—
178C2×Q8×C11—42no—
179C2×D4×C11—24no—
180C2×D4×C11—24no—
181C2×D4×C11—24no—
182C2×D4×C11—22no—
183C2×D4×C11—42no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—24no—
187C22×C4×C11—42no—
188C22×C4×C11—42no—
189C22×C4×C11—44no—
190C22×C4×C11C2×D414yes—
191C22×C4×C11C2×D414yes—
192C22×C4×C11C2×D414yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2411yescharacteristic
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11—28no—
201C2×C22⋊D11—28no—
202C2×C22⋊D11—44no—
203C2×C22⋊D11—44no—
204C2×C22⋊D11—44no—
205C2×C22⋊D11—44no—
206C22×Dic11—24no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—42no—
210C22×Dic11C2414yes—
211C22×Dic11C2414yes—
212C22×Dic11C2412yes—
213C22×Dic11C2412yes—
214C2×D44—232no—
215C2×D44—28no—
216C2×D44—28no—
217C2×D44—28no—
218C2×C4×D11—28no—
219C2×C4×D11—24no—
220C2×C4×D11—24no—
221C2×C4×D11—28no—
222C2×C4×D11—24no—
223C2×C4×D11—24no—
224C2×C4×D11—44no—
225C2×C4×D11—42no—
226C2×C4×D11—42no—
227C2×C4×D11—416no—
228C2×C4×D11—416no—
229C11×C4⋊C4—24no—
230C11×C4⋊C4—22no—
231C11×C4⋊C4—24no—
232C11×C4⋊C4—24no—
233C11×C4⋊C4—22no—
234C11×C4⋊C4—24no—
235C11×C4⋊C4C2×D418yes—
236C11×C4⋊C4C2×D418yes—
237C11×C22⋊C4—24no—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—24no—
241C11×C22⋊C4—24no—
242C42×C11—24no—
243C22⋊Dic11—28no—
244C22⋊Dic11—24no—
245C22⋊Dic11—24no—
246C22⋊Dic11—44no—
247(C2×D11)⋊C4—28no—
248(C2×D11)⋊C4—28no—
249(C2×D11)⋊C4—28no—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—44no—
253(C2×D11)⋊C4—44no—
254(C2×D11)⋊C4—44no—
255(C2×D11)⋊C4—44no—
256C4⋊Dic11—42no—
257C4⋊Dic11—42no—
258Dic11⋊C4—28no—
259Dic11⋊C4—44no—
260C4×Dic11—28no—
261C4×Dic11—44no—
262C2×#539D1111yescharacteristic, complemented
263C22×C4×D4—111no—
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—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—24no—
283C23×C11—24no—
284C23×C11C22×D412yes—
285C23×C11C2×#4112yes—
286C23×C11C2×#4112yes—
287C23×C11C2511yescharacteristic
288C22×D11—28no—
289C22×D11—28no—
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—24no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—24no—
299C22×D11—22no—
300C22×D11—48no—
301C22×D11—48no—
302C22×D11—44no—
303C22×D11—44no—
304C22×D11—48no—
305C22×D11—44no—
306C22×D11—44no—
307C22×D11—48no—
308C22×D11C2×#4114yes—
309C22×D11C2×#4114yes—
310Q8×C11—82no—
311D4×C11—48no—
312D4×C11—82no—
313C2×C4×C11—28no—
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—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—24no—
325C2×C4×C11—24no—
326C2×C4×C11—44no—
327C2×C4×C11—44no—
328C2×C4×C11—84no—
329C2×C4×C11C22×D414yes—
330C2×C4×C11C22×D414yes—
331C2×C4×C11C22×D412yes—
332C2×C4×C11C22×D412yes—
333C22⋊D11—416no—
334C22⋊D11—88no—
335C2×Dic11—28no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—24no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—24no—
343C2×Dic11—24no—
344C2×Dic11—24no—
345C2×Dic11—24no—
346C2×Dic11—44no—
347C2×Dic11H(5,𝔽2)14yes—
348D44—232no—
349C4×D11—416no—
350C4×D11—48no—
351C4×D11—48no—
352C23×D4—111no—
353C24×C4—111no—
354C24×C4—111no—
355#539—28no—
356C2×#126C2×D1112yescomplemented
357C2×#125C2×D1112yescomplemented
358C2×#123C2×D1112yes—
359C2×#123C2×D1112yescomplemented
360C2×C22⋊Q8—112no—
361C2×C22⋊Q8C2×D1111yescharacteristic
362C2×C22⋊Q8C2×D1112yescomplemented
363C2×#121—112no—
364C2×#121C2×D1111yescharacteristic
365C2×#120—112no—
366C2×#120—112no—
367C2×C4×D4—114no—
368C2×C4×D4—114no—
369C2×C4×D4—114no—
370C2×C4×D4—228no—
371C2×C4×D4C2×D1112yes—
372C22×C4⋊C4C2×D1111yescharacteristic
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—112no—
384#392—114no—
385#392—114no—
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—114no—
401#385—114no—
402#385—112no—
403#385—112no—
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—42no—
418C22×C11—44no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—44no—
422C22×C11#52514yes—
423C22×C11C23×D411yescharacteristic
424C22×C11C22×#4111yescharacteristic
425C22×C11C22×#4111yescharacteristic
426C22×C11C2×H(5,𝔽2)12yes—
427C22×C11#58512yes—
428C2×D11—24no—
429C2×D11—24no—
430C2×D11—28no—
431C2×D11—24no—
432C2×D11—24no—
433C2×D11—416no—
434C2×D11—416no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—42no—
440C2×D11—42no—
441C2×D11—44no—
442C4×C11—24no—
443C4×C11—24no—
444C4×C11—22no—
445C4×C11—22no—
446C4×C11—42no—
447C4×C11—42no—
448C4×C11—42no—
449Dic11—24no—
450Dic11—44no—
451Dic11—42no—
452Dic11—44no—
453C25—111no—
454C25—111no—
455C22×Q8C22×D1111yescharacteristic
456C22×D4—114no—
457C22×D4—114no—
458C22×D4—114no—
459C22×D4—224no—
460C22×D4—224no—
461C22×D4—224no—
462C22×D4C22×D1112yes—
463C22×D4C22×D1111yescharacteristic
464C23×C4—111no—
465C23×C4—111no—
466C23×C4—114no—
467C23×C4—112no—
468C23×C4—112no—
469C23×C4—224no—
470C23×C4—224no—
471C23×C4—444no—
472C23×C4—444no—
473C23×C4C22×D1111yescharacteristic
474C23×C4C22×D1112yes—
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1111yescharacteristic
477#126—28no—
478#125—28no—
479#123—28no—
480#123—28no—
481C22⋊Q8—24no—
482C22⋊Q8—28no—
483C22⋊Q8—444no—
484#121—24no—
485#121—444no—
486#120—228no—
487#120—228no—
488C4×D4—28no—
489C4×D4—2216no—
490C4×D4—2216no—
491C4×D4—448no—
492C2×C4⋊C4—114no—
493C2×C4⋊C4—112no—
494C2×C4⋊C4—112no—
495C2×C4⋊C4—114no—
496C2×C4⋊C4C22⋊D1118yescomplemented
497C2×C4⋊C4C22×D1112yes—
498C2×C4⋊C4C22×D1111yescharacteristic
499C2×C4⋊C4C22×D1112yes—
500C2×C4⋊C4C22×D1111yescharacteristic
501C2×C4⋊C4C22×D1112yes—
502C2×C4⋊C4C22×D1112yes—
503C2×C4⋊C4C22×D1112yes—
504C2×C4⋊C4C22×D1112yes—
505C2×C22⋊C4—114no—
506C2×C22⋊C4—112no—
507C2×C22⋊C4—112no—
508C2×C22⋊C4—114no—
509C2×C22⋊C4—112no—
510C2×C22⋊C4—112no—
511C2×C22⋊C4—114no—
512C2×C22⋊C4—114no—
513C2×C22⋊C4—114no—
514C2×C22⋊C4—114no—
515C2×C22⋊C4—114no—
516C2×C22⋊C4—114no—
517C2×C22⋊C4—114no—
518C2×C22⋊C4—224no—
519C2×C22⋊C4—224no—
520C2×C22⋊C4C22×D1112yes—
521C2×C22⋊C4C22×D1112yes—
522C2×C22⋊C4C22×D1112yes—
523C2×C22⋊C4C22×D1112yes—
524C2×C22⋊C4C22×D1112yes—
525C2×C42—114no—
526C2×C42—114no—
527C2×C42—224no—
528C2×C42C22×D1112yes—
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—82no—
540C2×C11C2×#52511yescharacteristic
541C2×C11#345912yes—
542C2×C11#348411yescharacteristic
543C2×C11#348711yescharacteristic
544C2×C11#350512yes—
545D11—44no—
546D11—44no—
547C24—112no—
548C24—112no—
549C24—114no—
550C24—114no—
551C24—222no—
552C24—222no—
553C24—222no—
554C24—222no—
555C24—442no—
556C24—442no—
557C24—442no—
558C24—442no—
559C24C23×D1112yes—
560C24C23×D1111yescharacteristic
561C2×Q8—22no—
562C2×Q8—42no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—22no—
567C2×D4—42no—
568C2×D4—228no—
569C2×D4—228no—
570C2×D4—2232no—
571C2×D4—228no—
572C2×D4—228no—
573C2×D4—228no—
574C2×D4—444no—
575C2×D4—444no—
576C2×D4—444no—
577C2×D4—444no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—44no—
584C22×C4—112no—
585C22×C4—114no—
586C22×C4—114no—
587C22×C4—112no—
588C22×C4—228no—
589C22×C4—224no—
590C22×C4—224no—
591C22×C4—224no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—228no—
595C22×C4—224no—
596C22×C4—224no—
597C22×C4—444no—
598C22×C4—442no—
599C22×C4—442no—
600C22×C4—4416no—
601C22×C4—4416no—
602C22×C4—442no—
603C22×C4C2×C22⋊D1114yes—
604C22×C4C2×C22⋊D1114yes—
605C22×C4C2×C22⋊D1114yes—
606C22×C4C23×D1112yes—
607C22×C4C23×D1112yes—
608C22×C4C23×D1112yes—
609C22×C4C23×D1112yes—
610C22×C4C23×D1112yes—
611C22×C4C23×D1111yescharacteristic
612C22×C4C23×D1111yescharacteristic
613C4⋊C4—24no—
614C4⋊C4—22no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—22no—
618C4⋊C4—24no—
619C4⋊C4—228no—
620C4⋊C4—442no—
621C4⋊C4—442no—
622C4⋊C4—444no—
623C4⋊C4C2×C22⋊D1118yes—
624C4⋊C4C2×C22⋊D1118yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—228no—
631C22⋊C4—228no—
632C22⋊C4—228no—
633C22⋊C4—224no—
634C22⋊C4—224no—
635C22⋊C4—228no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C22⋊C4—444no—
639C22⋊C4—444no—
640C22⋊C4—444no—
641C22⋊C4—444no—
642C22⋊C4—444no—
643C42—24no—
644C42—228no—
645C42—444no—
646C11#3498711yescharacteristic, complemented, Sylow
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—24no—
653C23—22no—
654C23—114no—
655C23—114no—
656C23—228no—
657C23—228no—
658C23—222no—
659C23—222no—
660C23—222no—
661C23—224no—
662C23—222no—
663C23—222no—
664C23—224no—
665C23—222no—
666C23—222no—
667C23—222no—
668C23—448no—
669C23—448no—
670C23—444no—
671C23—444no—
672C23—448no—
673C23—444no—
674C23—444no—
675C23—448no—
676C23#41×D1112yes—
677C23#41×D1112yes—
678C23C22×C22⋊D1112yes—
679C23C24×D1111yescharacteristic
680Q8—82no—
681D4—48no—
682D4—82no—
683D4—2232no—
684D4—4416no—
685D4—888no—
686C2×C4—28no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—84no—
702C2×C4—114no—
703C2×C4—228no—
704C2×C4—222no—
705C2×C4—222no—
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—4416no—
715C2×C4—448no—
716C2×C4—448no—
717C2×C4—444no—
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—44no—
727C22—42no—
728C22—42no—
729C22—44no—
730C22—42no—
731C22—224no—
732C22—224no—
733C22—228no—
734C22—224no—
735C22—224no—
736C22—4416no—
737C22—4416no—
738C22—444no—
739C22—442no—
740C22—442no—
741C22—442no—
742C22—442no—
743C22—442no—
744C22—442no—
745C22#1062335914yes—
746C22C2×#41×D1111yescharacteristic
747C22C2×#41×D1111yescharacteristic
748C22D11×H(5,𝔽2)12yes—
749C22#1062345712yes—
750C22C23×C22⋊D1111yescharacteristic
751C4—24no—
752C4—22no—
753C4—22no—
754C4—24no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—224no—
759C4—444no—
760C4—442no—
761C4—444no—
762C2—24no—
763C2—82no—
764C2—444no—
765C2—444no—
766C2C2×#1062335911yescharacteristic
767C2#1308202412yes—
768C2#1308224711yescharacteristic
769C2#1308227111yescharacteristic
770C2#1308244812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#539C2
hypercenterC2×#539D11
hypocenterC11#34987
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#539

Complements

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

NH ≅ G/Ntype
1. C22×#66946C2semidirect
2. #13076935C2semidirect
3. #13076900C2semidirect
4. #13076895C2semidirect
5. #13074423C2semidirect
6. #13074352C2semidirect
7. #13074332C2semidirect
8. #13072663C2semidirect
9. #13072609C2semidirect
10. #13072564C2semidirect
11. #13072504C2semidirect
12. #13071270C2semidirect
13. #13071219C2semidirect
14. C4×#66990C2semidirect
15. C2×C11×#539C2semidirect
20. C2×C11×#126C22semidirect
21. C2×C11×#125C22semidirect
23. C2×C11×#123C22semidirect
25. C2×C11×C22⋊Q8C22semidirect
29. C2×#66999C22semidirect
30. C2×#66991C22semidirect
33. C2×C4×C22⋊D11C22semidirect
40. #10622844C22semidirect
41. #10622836C22semidirect
44. #10622826C22semidirect
49. #10622607C22semidirect
50. #10622606C22semidirect
51. #10622605C22semidirect
54. #10622603C22semidirect
55. #10622602C22semidirect
56. #10622602C22semidirect
57. #10622600C22semidirect
58. #10622600C22semidirect
59. #10622594C22semidirect
60. #10622594C22semidirect
61. #10622591C22semidirect
62. #10622591C22semidirect
63. #10622574C22semidirect
66. #10622570C22semidirect
67. #10622569C22semidirect
68. #10622569C22semidirect
73. #10622557C22semidirect
74. #10622557C22semidirect
75. #10622553C22semidirect
76. C4×(C2×D11)⋊C4C22semidirect
109. C2×C11×C4⋊C4D4semidirect
262. C2×#539D11semidirect
356. C2×#126C2×D11semidirect
357. C2×#125C2×D11semidirect
359. C2×#123C2×D11semidirect
362. C2×C22⋊Q8C2×D11semidirect
496. 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
C22×#669462
#130769352
#130769002
#130768952
#130744232
#130743522
#130743322
#130726632
#130726092
#130725642
#130725042
#130712702
#130712192
C4×#669902
C2×C11×#5392
#3498711