Finite Group Databasebeta

← #14810264

Subgroups — #14810264

Order 2816.

1432 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623081C211yesmaximal, characteristic
2C2×#10622681C211yesmaximal, characteristic, complemented
3C2×#10622679C211yesmaximal, characteristic, complemented
4#13069819C211yesmaximal, characteristic, complemented
5#13069812C211yesmaximal, characteristic, complemented
6#13069805C211yesmaximal, characteristic, complemented
7#13069798C211yesmaximal, characteristic, complemented
8#13069548C211yesmaximal, characteristic, complemented
9#13069411C211yesmaximal, characteristic, complemented
10#13068554C211yesmaximal, characteristic, complemented
11#13068554C211yesmaximal, characteristic, complemented
12#13068546C211yesmaximal, characteristic, complemented
13#13068546C211yesmaximal, characteristic, complemented
14C4×#66873C211yesmaximal, characteristic, complemented
15C11×#2562C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C2×C11×#125C2211yescharacteristic, complemented
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66990—21no—
21C2×#66983C2211yescharacteristic
22C2×#66977C2211yescharacteristic
23#10623081—24no—
24#10623081—24no—
25C2×#66947—21no—
26C2×#66937—21no—
27C2×C22⋊C4×D11—21no—
28C2×#66928C2211yescharacteristic
29C2×C4×D44C2211yescharacteristic
30C11×#400—21no—
31C11×#394—21no—
32C11×#388—21no—
33C11×#388—21no—
34C11×#380C2211yescharacteristic
35C11×#380C2211yescharacteristic
36C11×#380C2211yescharacteristic, complemented
37C11×#380C2211yescharacteristic, complemented
38C4×C11×C4⋊C4C2211yescharacteristic, complemented
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
42C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
43#10622681—24no—
44#10622679—24no—
45C2×#66874C2211yescharacteristic, complemented
46C2×#66874C2211yescharacteristic, complemented
47C2×#66874C2211yescharacteristic, complemented
48C2×#66874C2211yescharacteristic, complemented
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C2×#66873C2211yescharacteristic
52C2×#66873C2211yescharacteristic
53C2×#66873C2211yescharacteristic
54C2×#66873C2211yescharacteristic
55C2×#66873C2211yescharacteristic
56C2×#66873C2211yescharacteristic
57C2×#66872C2211yescharacteristic, complemented
58C2×#66871C2211yescharacteristic, complemented
59C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
60C2×C4×C11⋊C8C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63C24×D11—21no—
64C22×D4×C11D411yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C22×C22⋊D11—21no—
69C2×#4339—22no—
70C2×#4339—22no—
71C2×#4339—22no—
72C2×#4339—22no—
73C2×#4339—41no—
74C2×#4339—41no—
75C22×D44—21no—
76C22×D44—22no—
77C22×D44—22no—
78C22×D44—22no—
79C22×D44—22no—
80C22×D44—41no—
81C22×D44—41no—
82C22×D44C2311yescharacteristic
83C22×D44C2311yescharacteristic
84C22×C4×D11—21no—
85C22×C4×D11—21no—
86C22×Dic22C2311yescharacteristic
87C11×#125—22no—
88C11×#125—22no—
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C42×C11—21no—
105C2×C42×C11C2311yescharacteristic
106C2×C22⋊Dic11—21no—
107#66990—28no—
108#66983—22no—
109#66983—22no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×C4⋊Dic11C2311yescharacteristic
115#66977—22no—
116#66977—22no—
117C2×Dic11⋊C4—21no—
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122#66947—28no—
123#66937—28no—
124C22⋊C4×D11—28no—
125#66928—22no—
126#66928D414yes—
127C4×D44—22no—
128C4×D44D414yes—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C22⋊(C11⋊C8)—41no—
135C22⋊(C11⋊C8)—41no—
136C22⋊(C11⋊C8)—41no—
137C22⋊(C11⋊C8)—41no—
138#66874—22no—
139#66874—22no—
140#66874—41no—
141#66874—41no—
142#66873—22no—
143#66873—22no—
144#66873—22no—
145#66873—22no—
146#66873—22no—
147#66873—22no—
148#66873—41no—
149#66873—41no—
150#66872—22no—
151#66871—22no—
152C4⋊(C11⋊C8)—22no—
153C4×C11⋊C8—22no—
154#25890—111nomaximal, Sylow
155C24×C11C2×D411yescharacteristic
156C24×C11C2×D411yescharacteristic
157C23×D11—21no—
158C23×D11—21no—
159C23×D11—24no—
160C23×D11—42no—
161C23×D11—42no—
162C23×D11—42no—
163C23×D11—42no—
164C23×D11—81no—
165C23×D11—81no—
166C2×D4×C11—22no—
167C2×D4×C11—22no—
168C2×D4×C11—41no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2411yescharacteristic
190C2×C22⋊D11—24no—
191C2×C22⋊D11—24no—
192C2×C22⋊D11—42no—
193C2×C22⋊D11—42no—
194C2×C22⋊D11—81no—
195C2×C22⋊D11—81no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198#4339—44no—
199#4339—44no—
200#4339—44no—
201#4339—44no—
202C2×D44—24no—
203C2×D44—21no—
204C2×D44—21no—
205C2×D44—21no—
206C2×D44—21no—
207C2×D44—21no—
208C2×D44—21no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—42no—
212C2×D44—42no—
213C2×D44—44no—
214C2×D44—44no—
215C2×D44—44no—
216C2×D44—44no—
217C2×D44C2×D412yes—
218C2×D44C2×D412yes—
219C2×D44#4112yes—
220C2×D44#4112yes—
221C2×C4×D11—24no—
222C2×C4×D11—24no—
223C2×C4×D11—42no—
224C2×C4×D11—42no—
225C2×C4×D11—81no—
226C2×C4×D11—81no—
227C2×Dic22—21no—
228C2×Dic22—21no—
229C2×Dic22—21no—
230C2×Dic22—21no—
231C2×Dic22—21no—
232C2×Dic22C2×D412yes—
233C11×C4⋊C4—22no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—42no—
243C11×C4⋊C4—42no—
244C11×C22⋊C4—22no—
245C11×C22⋊C4—22no—
246C11×C22⋊C4—42no—
247C11×C22⋊C4—42no—
248C11×C22⋊C4—81no—
249C11×C22⋊C4—81no—
250C42×C11—81no—
251C42×C11C2×D412yes—
252C42×C11C2×D412yes—
253C22⋊Dic11—24no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258C4⋊Dic11—21no—
259C4⋊Dic11C2×D412yes—
260Dic11⋊C4—24no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×#546—111no—
274C2×#488—111no—
275C2×#478—111no—
276#2562D1111yescharacteristic, complemented
277#2036—111no—
278#2035—111no—
279#2034—111no—
280#2033—111no—
281#1983—111no—
282#1954—111no—
283#1788—111no—
284#1788—111no—
285#1786—111no—
286#1786—111no—
287C4×#102—111no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11#13512yes—
302C23×C11C22×D411yescharacteristic
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—48no—
308C22×D11—41no—
309C22×D11—41no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11—48no—
313C22×D11—41no—
314C22×D11—41no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—84no—
320C22×D11—84no—
321C22×D11—84no—
322C22×D11—84no—
323C22×D11—84no—
324D4×C11—44no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11#12012yes—
356C2×C4×C11#12012yes—
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11C22×D411yescharacteristic
359C2×C4×C11C2×#4111yescharacteristic
360C2×C4×C11C2×#4111yescharacteristic
361C2×C4×C11H(5,𝔽2)11yescharacteristic
362C2×C4×C11H(5,𝔽2)11yescharacteristic
363C22⋊D11—48no—
364C22⋊D11—84no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371D44—22no—
372D44—22no—
373D44—22no—
374D44—22no—
375D44—22no—
376D44—48no—
377D44—41no—
378D44—41no—
379D44#12414yes—
380C4×D11—48no—
381C4×D11—84no—
382Dic22—22no—
383Dic22—22no—
384Dic22—41no—
385Dic22—41no—
386C11⋊C8—41no—
387C11⋊C8—41no—
388C11⋊C8—41no—
389C11⋊C8—41no—
390C22×#41—111no—
391C23×D4—111no—
392#546—224no—
393#546—224no—
394C2×#125C2×D1111yescharacteristic, complemented
395C2×#124—111no—
396C2×#123—221no—
397C2×C22⋊Q8—111no—
398C2×#121—111no—
399C2×#121—221no—
400C2×#120—221no—
401C2×C4×D4—111no—
402C2×C4×D4C2×D1111yescharacteristic
403C22×C22⋊C4—221no—
404#488—224no—
405#478—224no—
406C2×#107—111no—
407C2×#106—111no—
408C2×C4⋊C8—111no—
409C2×#103—111no—
410C2×#103—111no—
411C2×#103—111no—
412C2×#103—111no—
413C2×#102—111no—
414C2×#102—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×C22⋊C8—111no—
422C2×C22⋊C8—111no—
423C2×C22⋊C8—111no—
424C2×C22⋊C8—111no—
425C2×C4×C8—111no—
426#400—21no—
427#394—21no—
428#388—21no—
429#388—21no—
430#380C2×D1111yescharacteristic
431#380C2×D1111yescharacteristic
432#380C2×D1111yescharacteristic, complemented
433#380C2×D1111yescharacteristic, complemented
434C4×C4⋊C4C2×D1111yescharacteristic, complemented
435#340—111no—
436#340—111no—
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—22no—
440C22×C11—41no—
441C22×C11—41no—
442C22×C11—41no—
443C22×C11—41no—
444C22×C11—41no—
445C22×C11—41no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—41no—
451C22×C11C2×#12011yescharacteristic
452C22×C11#54611yescharacteristic
453C22×C11#54611yescharacteristic
454C22×C11C2×#13511yescharacteristic
455C22×C11#57511yescharacteristic
456C22×C11#57611yescharacteristic
457C22×C11#57711yescharacteristic
458C2×D11—24no—
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—42no—
464C2×D11—42no—
465C2×D11—42no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—816no—
469C2×D11—81no—
470C2×D11—81no—
471C2×D11—81no—
472C2×D11—81no—
473C4×C11—22no—
474C4×C11—22no—
475C4×C11—41no—
476C4×C11—41no—
477C4×C11—81no—
478C4×C11—81no—
479C4×C11—81no—
480C4×C11—81no—
481C4×C11C2×#12411yescharacteristic
482C4×C11#53511yescharacteristic
483C4×C11#54611yescharacteristic
484C4×C11#54611yescharacteristic
485Dic11—42no—
486Dic11—42no—
487C25—221no—
488C2×#41—222no—
489C2×#41—222no—
490C2×#41—222no—
491C2×#41—222no—
492C2×#41—441no—
493C2×#41—441no—
494C22×Q8—111no—
495C22×D4—111no—
496C22×D4—111no—
497C22×D4—222no—
498C22×D4—222no—
499C22×D4—222no—
500C22×D4—222no—
501C22×D4—221no—
502C22×D4—221no—
503C22×D4—221no—
504C22×D4—441no—
505C22×D4—441no—
506C22×D4C22⋊D1111yescharacteristic
507C23×C4—221no—
508C23×C4—221no—
509C23×C4C22×D1111yescharacteristic
510C23×C4C22×D1111yescharacteristic
511C22×C8—111no—
512C22×C8—111no—
513C22×C8—111no—
514C22×C8—111no—
515#125—22no—
516#125—22no—
517#124—114no—
518#124—222no—
519#123—228no—
520C22⋊Q8—222no—
521C22⋊Q8—222no—
522#121—228no—
523#121—222no—
524#121—222no—
525#120—228no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—114no—
529C4×D4—222no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—111no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4C22⋊D1111yescharacteristic
535C2×C4⋊C4C22×D1111yescharacteristic
536C2×C4⋊C4C22×D1111yescharacteristic
537C2×C4⋊C4C22×D1111yescharacteristic
538C2×C4⋊C4C22×D1111yescharacteristic
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—228no—
544C2×C22⋊C4—221no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4—221no—
548C2×C22⋊C4—221no—
549C2×C22⋊C4C22⋊D1111yescharacteristic
550C2×C22⋊C4C22⋊D1111yescharacteristic
551C2×C42—21no—
552C2×C42C22×D1111yescharacteristic
553#107—222no—
554#106—222no—
555C4⋊C8—222no—
556#103—222no—
557#103—222no—
558#103—441no—
559#103—441no—
560#102—222no—
561#102—222no—
562#102—222no—
563#102—222no—
564#102—222no—
565#102—222no—
566#102—441no—
567#102—441no—
568C22⋊C8—441no—
569C22⋊C8—441no—
570C22⋊C8—441no—
571C22⋊C8—441no—
572C4×C8—222no—
573#95—21no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578C2×C11—42no—
579C2×C11—81no—
580C2×C11#243511yescharacteristic
581C2×C11#300211yescharacteristic
582C2×C11#301211yescharacteristic
583C2×C11#329611yescharacteristic
584C2×C11#329711yescharacteristic
585C2×C11#332211yescharacteristic
586C2×C11#332311yescharacteristic
587D11—44no—
588D11—82no—
589C24—224no—
590C24—221no—
591C24—221no—
592C24—442no—
593C24—442no—
594C24—442no—
595C24—442no—
596C24—881no—
597C24—881no—
598C24C2×C22⋊D1111yescharacteristic
599C24C2×C22⋊D1111yescharacteristic
600#41—444no—
601#41—444no—
602#41—444no—
603#41—444no—
604C2×Q8—112no—
605C2×Q8—221no—
606C2×Q8—221no—
607C2×Q8—221no—
608C2×Q8—221no—
609C2×Q8—221no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—41no—
613C2×D4—112no—
614C2×D4—112no—
615C2×D4—112no—
616C2×D4—112no—
617C2×D4—224no—
618C2×D4—224no—
619C2×D4—224no—
620C2×D4—221no—
621C2×D4—221no—
622C2×D4—221no—
623C2×D4—221no—
624C2×D4—221no—
625C2×D4—221no—
626C2×D4—221no—
627C2×D4—221no—
628C2×D4—442no—
629C2×D4—442no—
630C2×D4—444no—
631C2×D4—444no—
632C2×D4—444no—
633C2×D4—444no—
634C2×D4—442no—
635C2×D4—442no—
636C2×D4—881no—
637C2×D4—881no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—224no—
655C22×C4—221no—
656C22×C4—221no—
657C22×C4—224no—
658C22×C4—442no—
659C22×C4—442no—
660C22×C4—881no—
661C22×C4—881no—
662C22×C4C2×C22⋊D1111yescharacteristic
663C22×C4C2×C22⋊D1111yescharacteristic
664C22×C4C2×C22⋊D1111yescharacteristic
665C22×C4C2×C22⋊D1111yescharacteristic
666C22×C4C23×D1111yescharacteristic
667C2×C8—221no—
668C2×C8—221no—
669C2×C8—221no—
670C2×C8—221no—
671C2×C8—221no—
672C2×C8—221no—
673C2×C8—221no—
674C2×C8—221no—
675C2×C8—221no—
676C2×C8—221no—
677C2×C8—221no—
678C2×C8—221no—
679C4⋊C4—22no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—112no—
691C4⋊C4—224no—
692C4⋊C4—221no—
693C22⋊C4—22no—
694C22⋊C4—22no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—81no—
698C22⋊C4—81no—
699C22⋊C4—224no—
700C22⋊C4—224no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C22⋊C4—224no—
704C42—81no—
705C42D4×D1112yes—
706C42D4×D1112yes—
707C11#2589011yescharacteristic, complemented, Sylow
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—222no—
722C23—222no—
723C23—222no—
724C23—222no—
725C23—448no—
726C23—448no—
727C23—441no—
728C23—441no—
729C23—441no—
730C23—441no—
731C23—441no—
732C23—441no—
733C23—441no—
734C23—441no—
735C23—441no—
736C23—441no—
737C23—884no—
738C23—884no—
739C23—884no—
740C23—884no—
741C23—884no—
742C23#6700312yes—
743C23C22×C22⋊D1111yescharacteristic
744Q8—222no—
745Q8—222no—
746Q8—441no—
747Q8—441no—
748D4—44no—
749D4—114no—
750D4—222no—
751D4—222no—
752D4—222no—
753D4—222no—
754D4—222no—
755D4—448no—
756D4—448no—
757D4—441no—
758D4—441no—
759D4—884no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—222no—
791C2×C4—222no—
792C2×C4—448no—
793C2×C4—441no—
794C2×C4—441no—
795C2×C4—441no—
796C2×C4—441no—
797C2×C4—884no—
798C2×C4#6699012yes—
799C2×C4#6699012yes—
800C2×C4C2×D4×D1111yescharacteristic
801C2×C4C2×D4×D1111yescharacteristic
802C2×C4#41×D1111yescharacteristic
803C2×C4#41×D1111yescharacteristic
804C2×C4#6704211yescharacteristic
805C2×C4#6704211yescharacteristic
806C8—441no—
807C8—441no—
808C8—441no—
809C8—441no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—224no—
825C22—442no—
826C22—442no—
827C22—442no—
828C22—442no—
829C22—442no—
830C22—442no—
831C22—442no—
832C22—442no—
833C22—442no—
834C22—8816no—
835C22—881no—
836C22—881no—
837C22—881no—
838C22—881no—
839C22C2×#6699011yescharacteristic
840C22C2×#6700311yescharacteristic
841C22#1062335311yescharacteristic
842C22#1062336011yescharacteristic
843C22#1062336011yescharacteristic
844C22#1062336611yescharacteristic
845C22#1062336811yescharacteristic
846C4—22no—
847C4—22no—
848C4—41no—
849C4—41no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—81no—
854C4—442no—
855C4—442no—
856C4D11×#12411yescharacteristic
857C4#1062320511yescharacteristic
858C4#1062320711yescharacteristic
859C4#1062320711yescharacteristic
860C2—42no—
861C2—81no—
862C2—444no—
863C2—882no—
864C2#1307226411yescharacteristic
865C2#1307783211yescharacteristic
866C2#1307791711yescharacteristic
867C2#1308044511yescharacteristic
868C2#1308046011yescharacteristic
869C2#1308081111yescharacteristic
870C2#1308082611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2562C2
socleC23×C11C22×D4
prime radicalC2×#10623081C2
hypercenter#2562D11
hypocenterC11#25890
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2562

Complements

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

NH ≅ G/Ntype
2. C2×#10622681C2semidirect
3. C2×#10622679C2semidirect
4. #13069819C2semidirect
5. #13069812C2semidirect
6. #13069805C2semidirect
7. #13069798C2semidirect
8. #13069548C2semidirect
9. #13069411C2semidirect
10. #13068554C2semidirect
11. #13068554C2semidirect
12. #13068546C2semidirect
13. #13068546C2semidirect
14. C4×#66873C2semidirect
15. C11×#2562C2semidirect
18. C2×C11×#125C22semidirect
36. C11×#380C22semidirect
37. C11×#380C22semidirect
38. C4×C11×C4⋊C4C22semidirect
41. C2×C22⋊(C11⋊C8)C22semidirect
42. C2×C22⋊(C11⋊C8)C22semidirect
45. C2×#66874C22semidirect
46. C2×#66874C22semidirect
47. C2×#66874C22semidirect
48. C2×#66874C22semidirect
57. C2×#66872C22semidirect
58. C2×#66871C22semidirect
59. C2×C4⋊(C11⋊C8)C22semidirect
60. C2×C4×C11⋊C8C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
276. #2562D11semidirect
394. C2×#125C2×D11semidirect
432. #380C2×D11semidirect
433. #380C2×D11semidirect
434. C4×C4⋊C4C2×D11semidirect
707. C11#25890semidirect

Maximal subgroups

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

subgroupindex
C2×#106230812
C2×#106226812
C2×#106226792
#130698192
#130698122
#130698052
#130697982
#130695482
#130694112
#130685542
#130685462
C4×#668732
C11×#25622
#2589011