Finite Group Databasebeta

← #14769367

Subgroups — #14769367

Order 2816.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623081C211yesmaximal, characteristic
2C2×#10622625C211yesmaximal, characteristic, complemented
3C2×#10622579C211yesmaximal, characteristic, complemented
4C2×#10622614C211yesmaximal, characteristic, complemented
5#13069548C211yesmaximal, characteristic, complemented
6#13069425C211yesmaximal, characteristic, complemented
7#13069052C211yesmaximal, characteristic, complemented
8#13069047C211yesmaximal, characteristic, complemented
9#13068933C211yesmaximal, characteristic, complemented
10#13068928C211yesmaximal, characteristic, complemented
11#13068623C211yesmaximal, characteristic, complemented
12#13068554C211yesmaximal, characteristic, complemented
13#13068546C211yesmaximal, characteristic, complemented
14C4×#66873C211yesmaximal, characteristic, complemented
15C11×#2352C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic, complemented
21C2×#66990—21no—
22C2×#66983C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C22×#4318C2211yescharacteristic, complemented
26#10623081—24no—
27#10623081C418yescomplemented
28C2×#66947—21no—
29C2×#66937—21no—
30C2×C22⋊C4×D11—21no—
31C2×#66928C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C11×#388—21no—
34C11×#387—21no—
35C11×#386—21no—
36C11×#382C2211yescharacteristic, complemented
37C11×#380C2211yescharacteristic
38C11×#380C2211yescharacteristic, complemented
39C4×C11×C4⋊C4C2211yescharacteristic, complemented
40C4×C11×C22⋊C4—21no—
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
43#10622625—24no—
44#10622614—24no—
45C2×#66874C2211yescharacteristic, complemented
46C2×#66874C2211yescharacteristic, complemented
47C2×#66874C2211yescharacteristic, complemented
48C2×#66874C2211yescharacteristic, complemented
49#10622579—24no—
50C2×#66873C2211yescharacteristic
51C2×#66873C2211yescharacteristic
52C2×#66873C2211yescharacteristic
53C2×#66873C2211yescharacteristic
54C2×#66873C2211yescharacteristic
55C2×#66873C2211yescharacteristic
56C2×#66873C2211yescharacteristic
57C2×#66873C2211yescharacteristic
58C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
59C2×C4×C11⋊C8C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×D4×C11D411yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—21no—
70C22×C22⋊D11—21no—
71C2×#4339—22no—
72C2×#4339—22no—
73C2×#4339—22no—
74C2×#4339—41no—
75C2×#4339—41no—
76C2×#4339C2×C414yes—
77C22×D44—22no—
78C22×D44—22no—
79C22×D44—21no—
80C22×D44—22no—
81C22×D44—41no—
82C22×D44—41no—
83C22×D44C2×C414yescomplemented
84C22×D44C2311yescharacteristic
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×Dic22C2311yescharacteristic
89C4×D4×C11C2×C414yes—
90C4×D4×C11D414yes—
91C11×#117—22no—
92C11×#117—41no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—41no—
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4D411yescharacteristic
105C2×C11×C22⋊C4D411yescharacteristic
106C2×C42×C11—21no—
107C2×C42×C11—21no—
108C2×C42×C11C2311yescharacteristic
109C2×C22⋊Dic11—21no—
110#66990—28no—
111#66983—22no—
112#66983C2×C414yes—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×C4⋊Dic11C2311yescharacteristic
118#66977—22no—
119#66977C2×C414yescomplemented
120C2×Dic11⋊C4—21no—
121C2×#4318—22no—
122C2×#4318—22no—
123C2×#4318—22no—
124C2×#4318—22no—
125C2×#4318—41no—
126C2×#4318—41no—
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131#66947—28no—
132#66937—28no—
133C22⋊C4×D11—28no—
134#66928—22no—
135#66928C2×C414yescomplemented
136C4×D44—22no—
137C4×D44C2×C414yescomplemented
138C11×#95—21no—
139C11×#95—21no—
140C11×#95—21no—
141C11×#95—21no—
142C11×#95—21no—
143C22⋊(C11⋊C8)—22no—
144C22⋊(C11⋊C8)—22no—
145#66874—22no—
146#66874—22no—
147#66874—41no—
148#66874—41no—
149#66873—22no—
150#66873—22no—
151#66873—22no—
152#66873—22no—
153#66873—22no—
154#66873—41no—
155#66873—41no—
156#66873D414yescomplemented
157C4⋊(C11⋊C8)—22no—
158C4×C11⋊C8—22no—
159#22427—111nomaximal, Sylow
160C24×C11C2×D411yescharacteristic
161C24×C11C2×D411yescharacteristic
162C23×D11—21no—
163C23×D11—21no—
164C23×D11—24no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—42no—
168C23×D11—42no—
169C23×D11—81no—
170C23×D11—81no—
171C2×D4×C11—41no—
172C2×D4×C11—41no—
173C2×D4×C11C22⋊C414yes—
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×C11—21no—
186C22×C4×C11—42no—
187C22×C4×C11—42no—
188C22×C4×C11—81no—
189C22×C4×C11C22×C412yes—
190C22×C4×C11C22×C412yes—
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D412yes—
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2411yescharacteristic
198C2×C22⋊D11—24no—
199C2×C22⋊D11—24no—
200C2×C22⋊D11—42no—
201C2×C22⋊D11—42no—
202C2×C22⋊D11—81no—
203C2×C22⋊D11—81no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206#4339—28no—
207#4339—44no—
208#4339—44no—
209#4339—44no—
210C2×D44—28no—
211C2×D44—24no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44—21no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—42no—
221C2×D44—42no—
222C2×D44—44no—
223C2×D44—44no—
224C2×D44—44no—
225C2×D44C22×C412yes—
226C2×D44C22×C412yes—
227C2×D44C2×D412yes—
228C2×D44#4112yes—
229C2×C4×D11—24no—
230C2×C4×D11—24no—
231C2×C4×D11—42no—
232C2×C4×D11—42no—
233C2×C4×D11—81no—
234C2×C4×D11—81no—
235C2×Dic22—21no—
236C2×Dic22—21no—
237C2×Dic22—21no—
238C2×Dic22—21no—
239C2×Dic22—21no—
240C2×Dic22C22×C412yes—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—42no—
249C11×C4⋊C4C22⋊C414yes—
250C11×C4⋊C4C2×D412yes—
251C11×C22⋊C4—42no—
252C11×C22⋊C4—42no—
253C11×C22⋊C4—81no—
254C11×C22⋊C4C22⋊C414yes—
255C11×C22⋊C4C22⋊C414yes—
256C42×C11—42no—
257C42×C11—81no—
258C42×C11C22×C412yes—
259C42×C11C2×D412yes—
260C22⋊Dic11—24no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265C4⋊Dic11—21no—
266C4⋊Dic11C22×C412yes—
267Dic11⋊C4—24no—
268#4318—44no—
269#4318—44no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8—21no—
281C2×C11⋊C8C2×D412yes—
282C2×#546—111no—
283C2×#436—111no—
284C2×#417—111no—
285C2×#418—111no—
286#2352D1111yescharacteristic, complemented
287#1983—111no—
288#1958—111no—
289#1895—111no—
290#1894—111no—
291#1874—111no—
292#1873—111no—
293#1804—111no—
294#1788—111no—
295#1786—111no—
296C4×#102—111no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11C2×C22⋊C412yes—
310C23×C11C2×C22⋊C412yes—
311C23×C11C22×D411yescharacteristic
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—48no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—41no—
320C22×D11—41no—
321C22×D11—48no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11—84no—
331C22×D11—84no—
332C22×D11—84no—
333D4×C11—44no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—84no—
363C2×C4×C11C2×C22⋊C412yes—
364C2×C4×C11C2×C22⋊C412yes—
365C2×C4×C11C2×C22⋊C412yes—
366C2×C4×C11C2×C22⋊C412yes—
367C2×C4×C11C23×C411yescharacteristic
368C2×C4×C11C22×D411yescharacteristic
369C2×C4×C11C22×D411yescharacteristic
370C2×C4×C11C2×#4111yescharacteristic
371C2×C4×C11H(5,𝔽2)11yescharacteristic
372C2×C4×C11H(5,𝔽2)11yescharacteristic
373C22⋊D11—48no—
374C22⋊D11—84no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381D44—22no—
382D44—22no—
383D44—22no—
384D44—22no—
385D44—22no—
386D44—48no—
387D44—41no—
388D44—41no—
389D44C4×D414yes—
390C4×D11—48no—
391C4×D11—84no—
392Dic22—22no—
393Dic22—22no—
394Dic22—41no—
395Dic22—41no—
396C11⋊C8—22no—
397C11⋊C8—41no—
398C11⋊C8—41no—
399C11⋊C8—41no—
400C22×#41—111no—
401C23×D4—111no—
402C22×M16—111no—
403C22×M16—111no—
404#546—118no—
405#546—224no—
406C2×#124—111no—
407C2×#123—221no—
408C2×C22⋊Q8—111no—
409C2×#121—111no—
410C2×#121—221no—
411C2×#120—221no—
412C2×C4×D4—111no—
413C2×C4×D4C2×D1111yescharacteristic
414C2×#117C2×D1111yescharacteristic
415C22×C4⋊C4C2×D1111yescharacteristic, complemented
416C22×C22⋊C4—221no—
417#436—224no—
418C2×C4⋊C8—111no—
419#418—224no—
420#417—224no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#103—111no—
424C2×#103—111no—
425C2×#102—111no—
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102—111no—
432C2×#102—111no—
433C2×C22⋊C8—111no—
434C2×C22⋊C8—111no—
435C2×C4×C8—111no—
436#388—21no—
437#387—21no—
438#386—21no—
439#382C2×D1111yescharacteristic, complemented
440#380C2×D1111yescharacteristic
441#380C2×D1111yescharacteristic, complemented
442C4×C4⋊C4C2×D1111yescharacteristic, complemented
443C4×C22⋊C4—21no—
444#340—111no—
445#340—111no—
446#340—111no—
447#340—111no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—41no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11—41no—
458C22×C11—41no—
459C22×C11—41no—
460C22×C11—41no—
461C22×C11—41no—
462C22×C11C22×C22⋊C411yescharacteristic
463C22×C11D4211yescharacteristic
464C22×C11#54611yescharacteristic
465C22×C11#57511yescharacteristic
466C22×C11#57511yescharacteristic
467C22×C11#57611yescharacteristic
468C22×C11#57711yescharacteristic
469C2×D11—24no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—816no—
480C2×D11—81no—
481C2×D11—81no—
482C2×D11—81no—
483C2×D11—81no—
484C4×C11—22no—
485C4×C11—22no—
486C4×C11—22no—
487C4×C11—22no—
488C4×C11—42no—
489C4×C11—81no—
490C4×C11—81no—
491C4×C11—81no—
492C4×C11C2×C4×D411yescharacteristic
493C4×C11#51811yescharacteristic
494C4×C11D4211yescharacteristic
495C4×C11#54611yescharacteristic
496Dic11—42no—
497Dic11—42no—
498C25—221no—
499C2×#41—114no—
500C2×#41—222no—
501C2×#41—222no—
502C2×#41—222no—
503C2×#41—441no—
504C2×#41—441no—
505C22×Q8—111no—
506C22×D4—114no—
507C22×D4—111no—
508C22×D4—111no—
509C22×D4—222no—
510C22×D4—222no—
511C22×D4—221no—
512C22×D4—221no—
513C22×D4—222no—
514C22×D4—221no—
515C22×D4—441no—
516C22×D4—441no—
517C22×D4C22⋊D1111yescharacteristic
518C23×C4—21no—
519C23×C4—221no—
520C23×C4—221no—
521C23×C4C22×D1111yescharacteristic
522C23×C4C22×D1111yescharacteristic
523C2×M16—222no—
524C2×M16—222no—
525C2×M16—222no—
526C2×M16—222no—
527C2×M16—441no—
528C2×M16—441no—
529C22×C8—111no—
530C22×C8—111no—
531C22×C8—111no—
532C22×C8—111no—
533#124—114no—
534#124—222no—
535#123—228no—
536C22⋊Q8—114no—
537C22⋊Q8—222no—
538#121—114no—
539#121—222no—
540#121—228no—
541#120—228no—
542C4×D4—114no—
543C4×D4—222no—
544C4×D4C4×D1114yes—
545C4×D4D4414yes—
546#117—22no—
547#117—41no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4C22⋊D1111yescharacteristic
554C2×C4⋊C4C22×D1111yescharacteristic
555C2×C4⋊C4C22×D1111yescharacteristic
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C4⋊C4C22×D1111yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—228no—
567C2×C22⋊C4C22⋊D1111yescharacteristic
568C2×C22⋊C4C22⋊D1111yescharacteristic
569C2×C42—21no—
570C2×C42—21no—
571C2×C42C22×D1111yescharacteristic
572C4⋊C8—222no—
573#103—222no—
574#103—222no—
575#103—441no—
576#103—441no—
577#102—114no—
578#102—222no—
579#102—222no—
580#102—222no—
581#102—222no—
582#102—222no—
583#102—441no—
584#102—441no—
585C22⋊C8—222no—
586C22⋊C8—222no—
587C4×C8—222no—
588#95—21no—
589#95—21no—
590#95—21no—
591#95—21no—
592#95—21no—
593C2×C11—42no—
594C2×C11—42no—
595C2×C11D4×C22⋊C411yescharacteristic
596C2×C11#289611yescharacteristic
597C2×C11#289711yescharacteristic
598C2×C11#327311yescharacteristic
599C2×C11#327511yescharacteristic
600C2×C11#332211yescharacteristic
601C2×C11#332311yescharacteristic
602D11—44no—
603D11—82no—
604C24—221no—
605C24—221no—
606C24—224no—
607C24—442no—
608C24—442no—
609C24—442no—
610C24—442no—
611C24—881no—
612C24—881no—
613C24C2×C22⋊D1111yescharacteristic
614C24C2×C22⋊D1111yescharacteristic
615#41—228no—
616#41—444no—
617#41—444no—
618#41—444no—
619C2×Q8—112no—
620C2×Q8—221no—
621C2×Q8—221no—
622C2×Q8—221no—
623C2×Q8—221no—
624C2×Q8—221no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—112no—
628C2×D4—112no—
629C2×D4—112no—
630C2×D4—112no—
631C2×D4—228no—
632C2×D4—224no—
633C2×D4—224no—
634C2×D4—224no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—221no—
642C2×D4—221no—
643C2×D4—444no—
644C2×D4—444no—
645C2×D4—444no—
646C2×D4—442no—
647C2×D4—442no—
648C2×D4—442no—
649C2×D4—442no—
650C2×D4—881no—
651C2×D4—881no—
652C2×D4(C2×D11)⋊C414yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—81no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—224no—
671C22×C4—224no—
672C22×C4—442no—
673C22×C4—442no—
674C22×C4—881no—
675C22×C4—881no—
676C22×C4C2×C4×D1112yes—
677C22×C4C2×C4×D1112yes—
678C22×C4C2×D4412yes—
679C22×C4C2×D4412yes—
680C22×C4C2×C22⋊D1111yescharacteristic
681C22×C4C2×C22⋊D1111yescharacteristic
682C22×C4C2×C22⋊D1111yescharacteristic
683C22×C4C2×C22⋊D1111yescharacteristic
684C22×C4C23×D1111yescharacteristic
685M16—444no—
686M16—444no—
687C2×C8—112no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8—221no—
695C2×C8—221no—
696C2×C8—221no—
697C2×C8—221no—
698C2×C8—221no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—42no—
707C4⋊C4—112no—
708C4⋊C4—224no—
709C4⋊C4—221no—
710C4⋊C4(C2×D11)⋊C414yes—
711C4⋊C4D4×D1112yes—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—81no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4—224no—
719C22⋊C4—224no—
720C22⋊C4(C2×D11)⋊C414yes—
721C22⋊C4(C2×D11)⋊C414yes—
722C42—42no—
723C42—81no—
724C42C2×C4×D1112yes—
725C42C2×D4412yes—
726C11#2242711yescharacteristic, complemented, Sylow
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—448no—
744C23—448no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23—441no—
749C23—441no—
750C23—441no—
751C23—441no—
752C23—441no—
753C23—441no—
754C23—441no—
755C23—884no—
756C23—884no—
757C23—884no—
758C23—884no—
759C23—884no—
760C23C2×(C2×D11)⋊C412yes—
761C23C2×(C2×D11)⋊C412yes—
762C23C22×C22⋊D1111yescharacteristic
763Q8—222no—
764Q8—222no—
765Q8—441no—
766Q8—441no—
767D4—44no—
768D4—114no—
769D4—222no—
770D4—222no—
771D4—222no—
772D4—222no—
773D4—222no—
774D4—448no—
775D4—448no—
776D4—441no—
777D4—441no—
778D4—884no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—84no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—448no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—441no—
815C2×C4—884no—
816C2×C4C2×(C2×D11)⋊C412yes—
817C2×C4C2×(C2×D11)⋊C412yes—
818C2×C4C2×(C2×D11)⋊C412yes—
819C2×C4C2×(C2×D11)⋊C412yes—
820C2×C4C22×C4×D1111yescharacteristic
821C2×C4C22×D4411yescharacteristic
822C2×C4C2×D4×D1111yescharacteristic
823C2×C4#6703711yescharacteristic
824C2×C4#41×D1111yescharacteristic
825C2×C4#6704211yescharacteristic
826C8—222no—
827C8—441no—
828C8—441no—
829C8—441no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—224no—
845C22—442no—
846C22—442no—
847C22—442no—
848C22—442no—
849C22—442no—
850C22—442no—
851C22—442no—
852C22—442no—
853C22—442no—
854C22—8816no—
855C22—881no—
856C22—881no—
857C22—881no—
858C22—881no—
859C22C22×(C2×D11)⋊C411yescharacteristic
860C22D4×C22⋊D1111yescharacteristic
861C22#1062335311yescharacteristic
862C22#1062335311yescharacteristic
863C22#1062336011yescharacteristic
864C22#1062336611yescharacteristic
865C22#1062336811yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4—442no—
875C4—442no—
876C4C4×D4×D1111yescharacteristic
877C4#1062307611yescharacteristic
878C4D4×D4411yescharacteristic
879C4#1062308511yescharacteristic
880C2—42no—
881C2—42no—
882C2—444no—
883C2—882no—
884C2D4×(C2×D11)⋊C411yescharacteristic
885C2#1307713311yescharacteristic
886C2#1307713911yescharacteristic
887C2#1308022311yescharacteristic
888C2#1308024811yescharacteristic
889C2#1308081111yescharacteristic
890C2#1308082611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2352C2
socleC23×C11C22×D4
prime radicalC2×#10623081C2
cosocleC22×C4×C11C24
hypercenter#2352D11
hypocenterC11#22427
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#10622625C2semidirect
3. C2×#10622579C2semidirect
4. C2×#10622614C2semidirect
5. #13069548C2semidirect
6. #13069425C2semidirect
7. #13069052C2semidirect
8. #13069047C2semidirect
9. #13068933C2semidirect
10. #13068928C2semidirect
11. #13068623C2semidirect
12. #13068554C2semidirect
13. #13068546C2semidirect
14. C4×#66873C2semidirect
15. C11×#2352C2semidirect
20. C22×C11×C4⋊C4C22semidirect
25. C22×#4318C22semidirect
27. #10623081C4semidirect
36. C11×#382C22semidirect
38. C11×#380C22semidirect
39. C4×C11×C4⋊C4C22semidirect
42. C2×C22⋊(C11⋊C8)C22semidirect
45. C2×#66874C22semidirect
46. C2×#66874C22semidirect
47. C2×#66874C22semidirect
48. C2×#66874C22semidirect
58. C2×C4⋊(C11⋊C8)C22semidirect
59. C2×C4×C11⋊C8C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
83. C22×D44C2×C4semidirect
119. #66977C2×C4semidirect
135. #66928C2×C4semidirect
137. C4×D44C2×C4semidirect
156. #66873D4semidirect
286. #2352D11semidirect
415. C22×C4⋊C4C2×D11semidirect
439. #382C2×D11semidirect
441. #380C2×D11semidirect
442. C4×C4⋊C4C2×D11semidirect
726. C11#22427semidirect

Maximal subgroups

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

subgroupindex
C2×#106230812
C2×#106226252
C2×#106225792
C2×#106226142
#130695482
#130694252
#130690522
#130690472
#130689332
#130689282
#130686232
#130685542
#130685462
C4×#668732
C11×#23522
#2242711