Finite Group Databasebeta

← #14769320

Subgroups — #14769320

Order 2816.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623248C211yesmaximal, characteristic
2C2×#10622449C211yesmaximal, characteristic, complemented
3C2×#10622383C211yesmaximal, characteristic, complemented
4C2×D11×#102C211yesmaximal, characteristic, complemented
5#13071548C211yesmaximal, characteristic, complemented
6#13069441C211yesmaximal, characteristic, complemented
7#13069051C211yesmaximal, characteristic, complemented
8#13069041C211yesmaximal, characteristic, complemented
9#13068935C211yesmaximal, characteristic, complemented
10#13068930C211yesmaximal, characteristic, complemented
11#13068627C211yesmaximal, characteristic, complemented
12#13068545C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068444C211yesmaximal, characteristic, complemented
15C11×#1982C211yesmaximal, characteristic, complemented
16C22×D4×D11—21no—
17C22×D4×D11C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C2×C11×#127C2211yescharacteristic
20C2×#66991—21no—
21C2×#66991C2211yescharacteristic
22C2×#66991C2211yescharacteristic
23C2×#66990—21no—
24C2×#66990—21no—
25C22×#4313C2211yescharacteristic, complemented
26C22×C8×D11C2211yescharacteristic, complemented
27#10623248—24no—
28#10623248C418yescomplemented
29C2×#66945C2211yescharacteristic, complemented
30C2×C4⋊C4×D11C2211yescharacteristic, complemented
31C2×C4×D44C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×C11×C4⋊C8C2211yescharacteristic, complemented
34C2×C11×#102C2211yescharacteristic, complemented
35C2×C11×#102C2211yescharacteristic, complemented
36C2×C11×#102C2211yescharacteristic, complemented
37C2×C11×#102C2211yescharacteristic, complemented
38C4×C11×C4⋊C4C2211yescharacteristic, complemented
39C2×#66896C2211yescharacteristic, complemented
40C2×#66896C2211yescharacteristic, complemented
41C2×#66896C2211yescharacteristic, complemented
42C2×#66896C2211yescharacteristic, complemented
43C2×#66885C2211yescharacteristic
44C2×#66885C2211yescharacteristic
45C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
46C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
47#10622600C2211yescharacteristic, complemented
48#10622600C2211yescharacteristic, complemented
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51#10622553—21no—
52C4×(C2×D11)⋊C4—21no—
53#10622549C2211yescharacteristic, complemented
54C2×#66867C2211yescharacteristic, complemented
55#10622449—24no—
56#10622383—24no—
57D11×#102—24no—
58#10622278—21no—
59#10622266—21no—
60#10622189C2211yescharacteristic, complemented
61#10622189C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C24×D11—21no—
66C22×D4×C11—21no—
67C22×D4×C11—21no—
68C22×D4×C11C2311yescharacteristic
69C22×D4×C11C2311yescharacteristic
70C22×C22⋊D11—21no—
71C22×C22⋊D11—21no—
72C22×C22⋊D11—21no—
73C22×C22⋊D11—21no—
74C2×D4×D11—28no—
75C2×D4×D11—22no—
76C2×D4×D11—22no—
77C2×D4×D11—22no—
78C2×D4×D11—22no—
79C2×D4×D11—22no—
80C2×D4×D11—22no—
81C2×D4×D11—41no—
82C2×D4×D11—41no—
83C2×D4×D11—41no—
84C2×D4×D11—41no—
85C2×D4×D11—44no—
86C2×D4×D11—44no—
87C2×D4×D11C2×C414yes—
88C2×D4×D11C2×C414yescomplemented
89C22×D44D411yescharacteristic
90C22×D44C2311yescharacteristic
91C22×C4×D11—21no—
92C22×C4×D11—21no—
93C22×C4×D11C2311yescharacteristic
94C22×C4×D11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C11×#127—22no—
98C11×#127C2×C414yescomplemented
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C42×C11—21no—
102C2×C42×C11C2311yescharacteristic
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105#66991—22no—
106#66991—22no—
107#66991—28no—
108#66991C2×C414yes—
109#66991C2×C414yescomplemented
110#66990—28no—
111#66990—28no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4D411yescharacteristic
117C2×(C2×D11)⋊C4D411yescharacteristic
118C2×C4⋊Dic11D411yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×Dic11⋊C4—21no—
123C2×C4×Dic11—21no—
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C2×#4313—22no—
127C2×#4313—22no—
128C2×#4313—41no—
129C2×C8×D11—22no—
130C2×C8×D11—22no—
131C2×C8×D11—41no—
132#66945—22no—
133#66945—41no—
134C4⋊C4×D11—22no—
135C4⋊C4×D11—41no—
136C4×D44—22no—
137C4×D44C2×C414yes—
138C4×D44C2×C414yescomplemented
139C4×D44D414yes—
140C11×C4⋊C8—22no—
141C11×#102—22no—
142C11×#102—22no—
143C11×#102—41no—
144C11×#102—41no—
145C11×#95—21no—
146#66896—22no—
147#66896—22no—
148#66896—41no—
149#66896—41no—
150C11⋊#95—21no—
151C11⋊#95—21no—
152C11⋊#95—21no—
153C11⋊#95—21no—
154#66885—22no—
155#66885—22no—
156(C2×D11)⋊C8—22no—
157(C2×D11)⋊C8—22no—
158#66873—22no—
159#66873D414yescomplemented
160#66867—22no—
161#22423—111nomaximal, Sylow
162C24×C11—21no—
163C24×C11—21no—
164C23×D11—21no—
165C23×D11—24no—
166C23×D11—24no—
167C23×D11—42no—
168C23×D11—42no—
169C23×D11—42no—
170C23×D11—42no—
171C23×D11—42no—
172C23×D11—42no—
173C23×D11—42no—
174C23×D11—42no—
175C23×D11—81no—
176C23×D11—81no—
177C23×D11—81no—
178C23×D11—81no—
179C23×D11C2×D411yescharacteristic
180C23×D11C2×D411yescharacteristic
181C2×D4×C11—24no—
182C2×D4×C11—24no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—42no—
194C2×D4×C11—42no—
195C2×D4×C11—81no—
196C2×D4×C11—81no—
197C2×D4×C11C22×C412yes—
198C2×D4×C11C22×C412yes—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2411yescharacteristic
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—42no—
209C2×C22⋊D11—42no—
210C2×C22⋊D11—42no—
211C2×C22⋊D11—42no—
212C2×C22⋊D11—42no—
213C2×C22⋊D11—42no—
214C2×C22⋊D11—42no—
215C2×C22⋊D11—42no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221D4×D11—28no—
222D4×D11—28no—
223D4×D11—44no—
224D4×D11—44no—
225D4×D11—44no—
226D4×D11—44no—
227D4×D11—44no—
228D4×D11—44no—
229D4×D11—432no—
230C2×D44—22no—
231C2×D44—22no—
232C2×D44—21no—
233C2×D44—21no—
234C2×D44—21no—
235C2×D44C22⋊C414yes—
236C2×D44C22×C412yes—
237C2×D44C2×D412yes—
238C2×D44#4112yes—
239C2×C4×D11—24no—
240C2×C4×D11—21no—
241C2×C4×D11—21no—
242C2×C4×D11—21no—
243C2×C4×D11—21no—
244C2×C4×D11—21no—
245C2×C4×D11—21no—
246C2×C4×D11—21no—
247C2×C4×D11—21no—
248C2×C4×D11—42no—
249C2×C4×D11—42no—
250C2×C4×D11—42no—
251C2×C4×D11—42no—
252C2×C4×D11—81no—
253C2×C4×D11C22×C412yes—
254C2×C4×D11C22×C412yes—
255C2×C4×D11C2×D412yes—
256C2×C4×D11C2×D412yes—
257C2×C8×C11—21no—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—21no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4C2×D412yescomplemented
267C42×C11—81no—
268C42×C11C22×C412yes—
269C42×C11C2×D412yes—
270C22⋊Dic11—24no—
271C22⋊Dic11—24no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—42no—
274(C2×D11)⋊C4—42no—
275(C2×D11)⋊C4—81no—
276(C2×D11)⋊C4C22⋊C414yes—
277(C2×D11)⋊C4C22⋊C414yes—
278C4⋊Dic11—21no—
279C4⋊Dic11—21no—
280C4⋊Dic11—21no—
281C4⋊Dic11—21no—
282C4⋊Dic11—21no—
283C4⋊Dic11C22⋊C414yes—
284C4⋊Dic11C22×C412yes—
285Dic11⋊C4—42no—
286C4×Dic11—42no—
287C2×C11⋊C8—21no—
288C2×C11⋊C8—21no—
289C2×C11⋊C8—21no—
290C2×C11⋊C8—21no—
291C2×C11⋊C8—21no—
292C2×C11⋊C8C2×D412yescomplemented
293#4313—44no—
294C8×D11—44no—
295C2×D42—111no—
296C2×#435—111no—
297C2×#418—111no—
298C22×#102—111no—
299#2352—111no—
300#1982D1111yescharacteristic, complemented
301#1961—111no—
302#1895—111no—
303#1893—111no—
304#1875—111no—
305#1874—111no—
306#1804—111no—
307#1786—111no—
308#1786—111no—
309#1762—111no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11C22×D411yescharacteristic
325C22×D11—21no—
326C22×D11—21no—
327C22×D11—21no—
328C22×D11—21no—
329C22×D11—22no—
330C22×D11—21no—
331C22×D11—22no—
332C22×D11—21no—
333C22×D11—22no—
334C22×D11—21no—
335C22×D11—21no—
336C22×D11—21no—
337C22×D11—21no—
338C22×D11—48no—
339C22×D11—48no—
340C22×D11—48no—
341C22×D11—41no—
342C22×D11—41no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—48no—
346C22×D11—84no—
347C22×D11—84no—
348C22×D11—84no—
349C22×D11—84no—
350C22×D11—84no—
351C22×D11—84no—
352C22×D11—84no—
353C22×D11—84no—
354C22×D11—84no—
355C22×D11—84no—
356C22×D11C2×C22⋊C412yes—
357C22×D11C2×C22⋊C412yes—
358C22×D11AGL(1,ℤ/8)12yes—
359C22×D11AGL(1,ℤ/8)12yes—
360D4×C11—22no—
361D4×C11—22no—
362D4×C11—22no—
363D4×C11—22no—
364D4×C11—48no—
365D4×C11—41no—
366D4×C11—41no—
367D4×C11—41no—
368D4×C11—41no—
369D4×C11—84no—
370C2×C4×C11—21no—
371C2×C4×C11—21no—
372C2×C4×C11—21no—
373C2×C4×C11—21no—
374C2×C4×C11—22no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11C2×C22⋊C412yes—
381C2×C4×C11C2×C22⋊C412yes—
382C2×C4×C11C23×C411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11C2×#4111yescharacteristic
386C2×C4×C11H(5,𝔽2)11yescharacteristic
387C2×C4×C11H(5,𝔽2)11yescharacteristic
388C22⋊D11—48no—
389C22⋊D11—48no—
390C22⋊D11—48no—
391C22⋊D11—48no—
392C2×Dic11—21no—
393C2×Dic11—21no—
394C2×Dic11—21no—
395C2×Dic11—21no—
396C2×Dic11—22no—
397C2×Dic11—41no—
398C2×Dic11—41no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11—41no—
402C2×Dic11—41no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405C2×Dic11C2×C22⋊C412yes—
406C2×Dic11C2×C22⋊C412yes—
407D44—28no—
408D44—22no—
409D44—22no—
410D44—22no—
411D44C4×D414yes—
412C4×D11—22no—
413C4×D11—22no—
414C4×D11—22no—
415C4×D11—22no—
416C4×D11—22no—
417C4×D11—22no—
418C4×D11—22no—
419C4×D11—22no—
420C4×D11—48no—
421C4×D11—84no—
422C8×C11—41no—
423C8×C11—41no—
424C11⋊C8—22no—
425C11⋊C8—41no—
426C23×D4—111no—
427C23×D4—111no—
428C23×D4—221no—
429C22×M16—111no—
430C23×C8—111no—
431D42—118no—
432D42—224no—
433C2×#127C2×D1111yescharacteristic
434C2×#121—111no—
435C2×#121—111no—
436C2×#121—221no—
437C2×#120—221no—
438C2×#120—221no—
439C2×C4×D4—111no—
440C2×C4×D4—111no—
441C2×#117—111no—
442C22×C4⋊C4—111no—
443#435—224no—
444C2×C4⋊C8C2×D1111yescharacteristic, complemented
445#418—224no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102—111no—
449C2×#102—111no—
450C2×#102—111no—
451C2×#102—111no—
452C2×#102—111no—
453C2×#102—111no—
454C2×#102—224no—
455C2×#102C2×D1111yescharacteristic, complemented
456C2×#102C2×D1111yescharacteristic, complemented
457C2×#102C2×D1111yescharacteristic, complemented
458C2×#102C2×D1111yescharacteristic, complemented
459C2×C22⋊C8—111no—
460C2×C22⋊C8—111no—
461C2×#97—111no—
462#388—221no—
463#387—221no—
464#386—221no—
465#382—111no—
466#380—111no—
467#380—111no—
468C4×C4⋊C4C2×D1111yescharacteristic, complemented
469C4×C22⋊C4—221no—
470#340—111no—
471#340—111no—
472#340—111no—
473#340—111no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—81no—
481C22×C11—81no—
482C22×C11—81no—
483C22×C11—81no—
484C22×C11—81no—
485C22×C11—81no—
486C22×C11—81no—
487C22×C11—81no—
488C22×C11C22×C22⋊C411yescharacteristic
489C22×C11D4211yescharacteristic
490C22×C11#54611yescharacteristic
491C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
492C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
493C22×C11#57611yescharacteristic
494C22×C11#57711yescharacteristic
495C2×D11—22no—
496C2×D11—22no—
497C2×D11—22no—
498C2×D11—22no—
499C2×D11—22no—
500C2×D11—22no—
501C2×D11—24no—
502C2×D11—22no—
503C2×D11—22no—
504C2×D11—22no—
505C2×D11—42no—
506C2×D11—42no—
507C2×D11—41no—
508C2×D11—42no—
509C2×D11—41no—
510C2×D11—42no—
511C2×D11—41no—
512C2×D11—42no—
513C2×D11—41no—
514C2×D11—42no—
515C2×D11—816no—
516C2×D11—816no—
517C2×D11#41814yescomplemented
518C4×C11—22no—
519C4×C11—22no—
520C4×C11—42no—
521C4×C11—81no—
522C4×C11C2×C4×D411yescharacteristic
523C4×C11#51811yescharacteristic
524C4×C11D4211yescharacteristic
525C4×C11#54611yescharacteristic
526Dic11—22no—
527Dic11—22no—
528Dic11—42no—
529Dic11—81no—
530Dic11—81no—
531C25—221no—
532C25—221no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—114no—
536C22×D4—114no—
537C22×D4—111no—
538C22×D4—111no—
539C22×D4—222no—
540C22×D4—222no—
541C22×D4—221no—
542C22×D4—221no—
543C22×D4—222no—
544C22×D4—222no—
545C22×D4—222no—
546C22×D4—222no—
547C22×D4—228no—
548C22×D4—221no—
549C22×D4—221no—
550C22×D4—441no—
551C22×D4—441no—
552C22×D4—441no—
553C22×D4—441no—
554C22×D4—444no—
555C22×D4—444no—
556C22×D4C22×D1111yescharacteristic
557C22×D4C22×D1111yescharacteristic
558C23×C4—111no—
559C23×C4—111no—
560C23×C4—221no—
561C23×C4—221no—
562C2×M16—222no—
563C2×M16—222no—
564C2×M16—441no—
565C22×C8—111no—
566C22×C8—111no—
567C22×C8—222no—
568C22×C8—222no—
569C22×C8—441no—
570C22×C8C22×D1111yescharacteristic
571C22×C8C22×D1111yescharacteristic
572#127—22no—
573#127C4×D1114yescomplemented
574#121—114no—
575#121—114no—
576#121—228no—
577#121—222no—
578#121—222no—
579#120—228no—
580#120—228no—
581C4×D4—114no—
582C4×D4—114no—
583C4×D4—114no—
584C4×D4—222no—
585#117—222no—
586#117—441no—
587C2×C4⋊C4—111no—
588C2×C4⋊C4—111no—
589C2×C4⋊C4—111no—
590C2×C4⋊C4—111no—
591C2×C4⋊C4—222no—
592C2×C4⋊C4—221no—
593C2×C4⋊C4—441no—
594C2×C4⋊C4C22×D1111yescharacteristic
595C2×C4⋊C4C22×D1111yescharacteristic
596C2×C22⋊C4—111no—
597C2×C22⋊C4—111no—
598C2×C22⋊C4—221no—
599C2×C22⋊C4—221no—
600C2×C22⋊C4—221no—
601C2×C22⋊C4—221no—
602C2×C22⋊C4—221no—
603C2×C22⋊C4—221no—
604C2×C42—21no—
605C2×C42—221no—
606C2×C42C22×D1111yescharacteristic
607C4⋊C8—22no—
608#102—22no—
609#102—22no—
610#102—41no—
611#102—41no—
612#102—114no—
613#102—222no—
614#102—222no—
615#102—222no—
616#102—222no—
617#102—222no—
618#102—441no—
619#102—441no—
620C22⋊C8—222no—
621C22⋊C8—222no—
622#97—222no—
623#95—21no—
624#95—221no—
625#95—221no—
626#95—221no—
627#95—221no—
628C2×C11—82no—
629C2×C11—82no—
630C2×C11D4×C22⋊C411yescharacteristic
631C2×C11C2×#41811yescharacteristic
632C2×C11#289711yescharacteristic
633C2×C11#326411yescharacteristic
634C2×C11#326511yescharacteristic
635C2×C11#331011yescharacteristic
636C2×C11#331811yescharacteristic
637D11—24no—
638D11—42no—
639D11—44no—
640C24—21no—
641C24—21no—
642C24—111no—
643C24—111no—
644C24—224no—
645C24—224no—
646C24—221no—
647C24—442no—
648C24—442no—
649C24—442no—
650C24—442no—
651C24—442no—
652C24—442no—
653C24—442no—
654C24—442no—
655C24—881no—
656C24—881no—
657C24—881no—
658C24—881no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—81no—
674C2×D4—81no—
675C2×D4—114no—
676C2×D4—112no—
677C2×D4—112no—
678C2×D4—112no—
679C2×D4—222no—
680C2×D4—222no—
681C2×D4—224no—
682C2×D4—224no—
683C2×D4—228no—
684C2×D4—228no—
685C2×D4—224no—
686C2×D4—224no—
687C2×D4—221no—
688C2×D4—221no—
689C2×D4—221no—
690C2×D4—444no—
691C2×D4—444no—
692C2×D4—444no—
693C2×D4—444no—
694C2×D4—444no—
695C2×D4—444no—
696C2×D4—442no—
697C2×D4—442no—
698C2×D4—442no—
699C2×D4—442no—
700C2×D4—4432no—
701C2×D4—442no—
702C2×D4—442no—
703C2×D4—442no—
704C2×D4—442no—
705C2×D4C2×C4×D1112yes—
706C2×D4C2×C4×D1112yes—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—111no—
710C22×C4—111no—
711C22×C4—112no—
712C22×C4—112no—
713C22×C4—112no—
714C22×C4—112no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—224no—
725C22×C4—221no—
726C22×C4—221no—
727C22×C4—442no—
728C22×C4—442no—
729C22×C4—442no—
730C22×C4—442no—
731C22×C4—881no—
732C22×C4D4×D1111yescharacteristic
733C22×C4D4×D1111yescharacteristic
734C22×C4C23×D1111yescharacteristic
735M16—444no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—112no—
743C2×C8—221no—
744C2×C8—221no—
745C2×C8—221no—
746C2×C8—221no—
747C2×C8—221no—
748C2×C8—444no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—114no—
753C4⋊C4—112no—
754C4⋊C4—221no—
755C4⋊C4—221no—
756C4⋊C4—221no—
757C4⋊C4—221no—
758C4⋊C4—221no—
759C4⋊C4—442no—
760C4⋊C4D4×D1112yescomplemented
761C22⋊C4—114no—
762C22⋊C4—114no—
763C22⋊C4—224no—
764C22⋊C4—224no—
765C22⋊C4—224no—
766C22⋊C4—442no—
767C22⋊C4—442no—
768C22⋊C4—881no—
769C42—81no—
770C42—442no—
771C42C2×C4×D1112yes—
772C42D4×D1112yes—
773C11#2242311yescharacteristic, complemented, Sylow
774C23—22no—
775C23—22no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—112no—
789C23—112no—
790C23—112no—
791C23—112no—
792C23—221no—
793C23—221no—
794C23—221no—
795C23—221no—
796C23—222no—
797C23—221no—
798C23—221no—
799C23—221no—
800C23—221no—
801C23—221no—
802C23—222no—
803C23—221no—
804C23—222no—
805C23—448no—
806C23—448no—
807C23—448no—
808C23—448no—
809C23—441no—
810C23—441no—
811C23—441no—
812C23—441no—
813C23—884no—
814C23—884no—
815C23—884no—
816C23—884no—
817C23—884no—
818C23—884no—
819C23—884no—
820C23—884no—
821C23—884no—
822C23—884no—
823C23C2×D4×D1111yescharacteristic
824D4—22no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—48no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—84no—
834D4—114no—
835D4—228no—
836D4—222no—
837D4—222no—
838D4—222no—
839D4—448no—
840D4—448no—
841D4—448no—
842D4—448no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—112no—
854C2×C4—112no—
855C2×C4—221no—
856C2×C4—221no—
857C2×C4—221no—
858C2×C4—221no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—448no—
869C2×C4—441no—
870C2×C4—441no—
871C2×C4—441no—
872C2×C4—441no—
873C2×C4—441no—
874C2×C4—441no—
875C2×C4—441no—
876C2×C4—441no—
877C2×C4—884no—
878C2×C4C22⋊C4×D1112yes—
879C2×C4C22⋊C4×D1112yes—
880C2×C4C22×C4×D1111yescharacteristic
881C2×C4C2×D4×D1111yescharacteristic
882C2×C4C2×D4×D1111yescharacteristic
883C2×C4#6703711yescharacteristic
884C2×C4#41×D1111yescharacteristic
885C2×C4#6704211yescharacteristic
886C8—41no—
887C8—41no—
888C8—222no—
889C8—441no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—81no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22—81no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—114no—
905C22—222no—
906C22—222no—
907C22—222no—
908C22—222no—
909C22—222no—
910C22—222no—
911C22—222no—
912C22—224no—
913C22—222no—
914C22—222no—
915C22—441no—
916C22—442no—
917C22—441no—
918C22—442no—
919C22—441no—
920C22—442no—
921C22—442no—
922C22—442no—
923C22—441no—
924C22—442no—
925C22—8816no—
926C22—8816no—
927C22C2×C22⋊C4×D1111yescharacteristic
928C22#1062314011yescharacteristic
929C22#1062314311yescharacteristic
930C22#1062328811yescharacteristic
931C22#1062329311yescharacteristic
932C22D11×AGL(1,ℤ/8)11yescharacteristic
933C22D11×AGL(1,ℤ/8)11yescharacteristic
934C4—22no—
935C4—22no—
936C4—42no—
937C4—81no—
938C4—222no—
939C4—222no—
940C4—442no—
941C4—881no—
942C4—881no—
943C4C4×D4×D1111yescharacteristic
944C4#1062307611yescharacteristic
945C4#1062320711yescharacteristic
946C4#1062324811yescharacteristic
947C2—82no—
948C2—82no—
949C2—224no—
950C2—442no—
951C2—444no—
952C2#1307143711yescharacteristic
953C2D11×#41811yescharacteristic
954C2#1307713711yescharacteristic
955C2#1308009111yescharacteristic
956C2#1308010611yescharacteristic
957C2#1308064411yescharacteristic
958C2#1308076411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1982C2
socleC23×C11C22×D4
prime radicalC2×#10623248C2
cosocleC22×C4×C11C24
hypercenter#1982D11
hypocenterC11#22423
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
2. C2×#10622449C2semidirect
3. C2×#10622383C2semidirect
4. C2×D11×#102C2semidirect
5. #13071548C2semidirect
6. #13069441C2semidirect
7. #13069051C2semidirect
8. #13069041C2semidirect
9. #13068935C2semidirect
10. #13068930C2semidirect
11. #13068627C2semidirect
12. #13068545C2semidirect
13. #13068545C2semidirect
14. #13068444C2semidirect
15. C11×#1982C2semidirect
25. C22×#4313C22semidirect
26. C22×C8×D11C22semidirect
28. #10623248C4semidirect
29. C2×#66945C22semidirect
30. C2×C4⋊C4×D11C22semidirect
33. C2×C11×C4⋊C8C22semidirect
34. C2×C11×#102C22semidirect
35. C2×C11×#102C22semidirect
36. C2×C11×#102C22semidirect
37. C2×C11×#102C22semidirect
38. C4×C11×C4⋊C4C22semidirect
39. C2×#66896C22semidirect
40. C2×#66896C22semidirect
41. C2×#66896C22semidirect
42. C2×#66896C22semidirect
45. C2×(C2×D11)⋊C8C22semidirect
46. C2×(C2×D11)⋊C8C22semidirect
47. #10622600C22semidirect
48. #10622600C22semidirect
53. #10622549C22semidirect
54. C2×#66867C22semidirect
60. #10622189C22semidirect
61. #10622189C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
88. C2×D4×D11C2×C4semidirect
98. C11×#127C2×C4semidirect
109. #66991C2×C4semidirect
138. C4×D44C2×C4semidirect
159. #66873D4semidirect
266. C11×C4⋊C4C2×D4semidirect
292. C2×C11⋊C8C2×D4semidirect
300. #1982D11semidirect
444. C2×C4⋊C8C2×D11semidirect
455. C2×#102C2×D11semidirect
456. C2×#102C2×D11semidirect
457. C2×#102C2×D11semidirect
458. C2×#102C2×D11semidirect
468. C4×C4⋊C4C2×D11semidirect
517. C2×D11#418semidirect
573. #127C4×D11semidirect
760. C4⋊C4D4×D11semidirect
773. C11#22423semidirect

Maximal subgroups

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

subgroupindex
C2×#106232482
C2×#106224492
C2×#106223832
C2×D11×#1022
#130715482
#130694412
#130690512
#130690412
#130689352
#130689302
#130686272
#130685452
#130684442
C11×#19822
#2242311