Finite Group Databasebeta

← #14769247

Subgroups — #14769247

Order 2816.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623081C211yesmaximal, characteristic
2C2×#10622624C211yesmaximal, characteristic, complemented
3C2×#10622579C211yesmaximal, characteristic, complemented
4C22×#66873C211yesmaximal, characteristic, complemented
5#13069548C211yesmaximal, characteristic, complemented
6#13069430C211yesmaximal, characteristic, complemented
7#13069052C211yesmaximal, characteristic, complemented
8#13069037C211yesmaximal, characteristic, complemented
9#13068933C211yesmaximal, characteristic, complemented
10#13068923C211yesmaximal, characteristic, complemented
11#13068613C211yesmaximal, characteristic, complemented
12#13068554C211yesmaximal, characteristic, complemented
13#13068546C211yesmaximal, characteristic, complemented
14#13068444C211yesmaximal, characteristic, complemented
15D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C2×C4×D4×C11—21no—
19C2×C4×D4×C11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic, complemented
22C2×#66990—21no—
23C2×#66983C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C22×#4318C2211yescharacteristic, complemented
26C23×C11⋊C8C2211yescharacteristic
27#10623081—24no—
28#10623081C418yescomplemented
29C2×#66947—21no—
30C2×#66937—21no—
31C2×C22⋊C4×D11—21no—
32C2×#66928C2211yescharacteristic
33C2×C4×D44C2211yescharacteristic
34C11×#389—21no—
35C11×#385—21no—
36C11×#385—21no—
37C11×#384C2211yescharacteristic, complemented
38C11×#380C2211yescharacteristic
39C11×#380C2211yescharacteristic, complemented
40C4×C11×C4⋊C4C2211yescharacteristic, complemented
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
43#10622624—24no—
44C2×#66874C2211yescharacteristic, complemented
45C2×#66874C2211yescharacteristic, complemented
46C2×#66874C2211yescharacteristic, complemented
47C2×#66874C2211yescharacteristic, complemented
48#10622579—24no—
49C2×#66873—24no—
50C2×#66873C2211yescharacteristic
51C2×#66873C2211yescharacteristic
52C2×#66873C2211yescharacteristic
53C2×#66873C2211yescharacteristic
54C2×#66873C2211yescharacteristic
55C2×#66873C2211yescharacteristic
56C2×#66873C2211yescharacteristic
57C2×#66873C2211yescharacteristic
58C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
59C2×#66867C2211yescharacteristic, 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×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C22×C22⋊D11—21no—
71C22×C22⋊D11—21no—
72C2×#4339—22no—
73C2×#4339—22no—
74C2×#4339—22no—
75C2×#4339—41no—
76C2×#4339—41no—
77C2×#4339C2×C414yescomplemented
78C22×D44—22no—
79C22×D44—22no—
80C22×D44—21no—
81C22×D44—22no—
82C22×D44—41no—
83C22×D44—41no—
84C22×D44C2×C414yescomplemented
85C22×D44C2311yescharacteristic
86C22×D44C2311yescharacteristic
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×Dic22C2311yescharacteristic
90C4×D4×C11—44no—
91C4×D4×C11C2×C414yes—
92C4×D4×C11D414yes—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—41no—
100C2×C11×C4⋊C4—41no—
101C2×C11×C4⋊C4D411yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4D411yescharacteristic
109C2×C11×C22⋊C4D411yescharacteristic
110C2×C42×C11—21no—
111C2×C42×C11C2311yescharacteristic
112C2×C22⋊Dic11—21no—
113#66990—28no—
114#66983—22no—
115#66983C2×C414yescomplemented
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×C4⋊Dic11C2311yescharacteristic
121#66977—22no—
122#66977C2×C414yescomplemented
123C2×Dic11⋊C4—21no—
124C2×#4318—22no—
125C2×#4318—22no—
126C2×#4318—41no—
127C22×C11⋊C8—22no—
128C22×C11⋊C8—22no—
129C22×C11⋊C8—41no—
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134#66947—28no—
135#66937—28no—
136C22⋊C4×D11—28no—
137#66928—22no—
138#66928C2×C414yescomplemented
139C4×D44—22no—
140C4×D44C2×C414yescomplemented
141C11×#95—21no—
142C11×#95—21no—
143C11×#95—21no—
144C22⋊(C11⋊C8)—22no—
145C22⋊(C11⋊C8)—22no—
146#66874—22no—
147#66874—22no—
148#66874—41no—
149#66874—41no—
150#66873—22no—
151#66873—22no—
152#66873—22no—
153#66873—22no—
154#66873—22no—
155#66873—41no—
156#66873—41no—
157#66873D414yescomplemented
158C4⋊(C11⋊C8)—22no—
159#66867—22no—
160#22419—111nomaximal, Sylow
161C24×C11C2×D411yescharacteristic
162C24×C11C2×D411yescharacteristic
163C23×D11—21no—
164C23×D11—21no—
165C23×D11—24no—
166C23×D11—42no—
167C23×D11—42no—
168C23×D11—42no—
169C23×D11—42no—
170C23×D11—81no—
171C23×D11—81no—
172C2×D4×C11—22no—
173C2×D4×C11—22no—
174C2×D4×C11C22⋊C414yes—
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—21no—
187C22×C4×C11—42no—
188C22×C4×C11—42no—
189C22×C4×C11—42no—
190C22×C4×C11—42no—
191C22×C4×C11—81no—
192C22×C4×C11—81no—
193C22×C4×C11C22×C412yes—
194C22×C4×C11C22×C412yes—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2411yescharacteristic
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—42no—
205C2×C22⋊D11—42no—
206C2×C22⋊D11—81no—
207C2×C22⋊D11—81no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210#4339—28no—
211#4339—44no—
212#4339—44no—
213#4339—44no—
214C2×D44—28no—
215C2×D44—24no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44—21no—
222C2×D44—21no—
223C2×D44—21no—
224C2×D44—42no—
225C2×D44—42no—
226C2×D44—44no—
227C2×D44—44no—
228C2×D44—44no—
229C2×D44C22×C412yes—
230C2×D44C22×C412yes—
231C2×D44C2×D412yes—
232C2×D44#4112yes—
233C2×C4×D11—24no—
234C2×C4×D11—24no—
235C2×C4×D11—42no—
236C2×C4×D11—42no—
237C2×C4×D11—81no—
238C2×C4×D11—81no—
239C2×Dic22—21no—
240C2×Dic22—21no—
241C2×Dic22—21no—
242C2×Dic22—21no—
243C2×Dic22—21no—
244C2×Dic22C22×C412yes—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—42no—
253C11×C4⋊C4—42no—
254C11×C4⋊C4—42no—
255C11×C4⋊C4—81no—
256C11×C4⋊C4C22⋊C414yes—
257C11×C4⋊C4C2×D412yes—
258C11×C22⋊C4—42no—
259C11×C22⋊C4—42no—
260C11×C22⋊C4C22⋊C414yes—
261C11×C22⋊C4C22⋊C414yes—
262C42×C11—42no—
263C42×C11C22×C412yes—
264C42×C11C2×D412yes—
265C22⋊Dic11—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270C4⋊Dic11—21no—
271C4⋊Dic11C22×C412yes—
272Dic11⋊C4—24no—
273#4318—44no—
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⋊C8—21no—
282C2×C11⋊C8—21no—
283C2×C11⋊C8—21no—
284C2×C11⋊C8—21no—
285C2×C11⋊C8—44no—
286C2×C11⋊C8C2×D412yes—
287C2×#546—111no—
288C2×#435—111no—
289C2×#417—111no—
290C22×#102—111no—
291D4×C4⋊C4D1111yescharacteristic, complemented
292#1983—111no—
293#1959—111no—
294#1895—111no—
295#1892—111no—
296#1874—111no—
297#1872—111no—
298#1802—111no—
299#1788—111no—
300#1786—111no—
301#1762—111no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11C2×C22⋊C412yes—
313C23×C11C2×C22⋊C412yes—
314C23×C11AGL(1,ℤ/8)12yes—
315C23×C11#13712yes—
316C23×C11C22×D411yescharacteristic
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—48no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—41no—
330C22×D11—41no—
331C22×D11—41no—
332C22×D11—48no—
333C22×D11—84no—
334C22×D11—84no—
335C22×D11—84no—
336C22×D11—84no—
337C22×D11—84no—
338D4×C11—28no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
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—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—84no—
368C2×C4×C11—84no—
369C2×C4×C11C2×C22⋊C412yes—
370C2×C4×C11C2×C22⋊C412yes—
371C2×C4×C11C2×C22⋊C412yes—
372C2×C4×C11C2×C22⋊C412yes—
373C2×C4×C11C23×C411yescharacteristic
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C2×#4111yescharacteristic
377C2×C4×C11H(5,𝔽2)11yescharacteristic
378C2×C4×C11H(5,𝔽2)11yescharacteristic
379C22⋊D11—48no—
380C22⋊D11—84no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—41no—
384C2×Dic11—41no—
385C2×Dic11—41no—
386C2×Dic11—41no—
387D44—22no—
388D44—22no—
389D44—22no—
390D44—22no—
391D44—22no—
392D44—48no—
393D44—41no—
394D44—41no—
395D44C4×D414yescomplemented
396C4×D11—48no—
397C4×D11—84no—
398Dic22—22no—
399Dic22—22no—
400Dic22—41no—
401Dic22—41no—
402C11⋊C8—22no—
403C11⋊C8—41no—
404C11⋊C8—41no—
405C11⋊C8—41no—
406C22×#41—111no—
407C23×D4—111no—
408C22×M16—111no—
409C23×C8—111no—
410#546—118no—
411#546—224no—
412C2×#124—111no—
413C2×#123—221no—
414C2×C22⋊Q8—111no—
415C2×#121—111no—
416C2×#121—221no—
417C2×#120—221no—
418C2×C4×D4—21no—
419C2×C4×D4—111no—
420C2×C4×D4C2×D1111yescharacteristic
421C22×C4⋊C4C2×D1111yescharacteristic
422C22×C4⋊C4C2×D1111yescharacteristic, complemented
423C22×C22⋊C4—221no—
424#435—224no—
425C2×C4⋊C8—111no—
426#417—224no—
427C2×#103—111no—
428C2×#103—111no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#102—111no—
432C2×#102—111no—
433C2×#102—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×#102—111no—
437C2×#102—111no—
438C2×#102—111no—
439C2×#102—224no—
440C2×C22⋊C8—111no—
441C2×C22⋊C8—111no—
442C2×#97—111no—
443#389—21no—
444#385—21no—
445#385—21no—
446#384C2×D1111yescharacteristic, complemented
447#380C2×D1111yescharacteristic
448#380C2×D1111yescharacteristic, complemented
449C4×C4⋊C4C2×D1111yescharacteristic, complemented
450#340—111no—
451#340—111no—
452#340—111no—
453#340—111no—
454C22×C11—22no—
455C22×C11—22no—
456C22×C11—22no—
457C22×C11—22no—
458C22×C11—22no—
459C22×C11—22no—
460C22×C11—22no—
461C22×C11—22no—
462C22×C11—22no—
463C22×C11—41no—
464C22×C11—41no—
465C22×C11—41no—
466C22×C11—41no—
467C22×C11#41714yescomplemented
468C22×C11C22×C22⋊C411yescharacteristic
469C22×C11D4211yescharacteristic
470C22×C11#54611yescharacteristic
471C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
472C22×C11C2×#13711yescharacteristic
473C22×C11#57611yescharacteristic
474C22×C11#57711yescharacteristic
475C2×D11—24no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—816no—
486C2×D11—81no—
487C2×D11—81no—
488C2×D11—81no—
489C2×D11—81no—
490C4×C11—22no—
491C4×C11—22no—
492C4×C11—22no—
493C4×C11—22no—
494C4×C11—42no—
495C4×C11—81no—
496C4×C11—81no—
497C4×C11—81no—
498C4×C11C2×C4×D411yescharacteristic
499C4×C11#51811yescharacteristic
500C4×C11D4211yescharacteristic
501C4×C11#54611yescharacteristic
502Dic11—42no—
503Dic11—42no—
504C25—221no—
505C2×#41—114no—
506C2×#41—222no—
507C2×#41—222no—
508C2×#41—222no—
509C2×#41—441no—
510C2×#41—441no—
511C22×Q8—111no—
512C22×D4—114no—
513C22×D4—111no—
514C22×D4—111no—
515C22×D4—222no—
516C22×D4—222no—
517C22×D4—221no—
518C22×D4—221no—
519C22×D4—222no—
520C22×D4—221no—
521C22×D4—441no—
522C22×D4—441no—
523C22×D4C22⋊D1111yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—221no—
527C23×C4—221no—
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1111yescharacteristic
530C2×M16—222no—
531C2×M16—222no—
532C2×M16—441no—
533C22×C8—111no—
534C22×C8—111no—
535C22×C8—111no—
536C22×C8—111no—
537C22×C8—222no—
538C22×C8—222no—
539C22×C8—441no—
540#124—114no—
541#124—222no—
542#123—228no—
543C22⋊Q8—114no—
544C22⋊Q8—222no—
545#121—114no—
546#121—222no—
547#121—228no—
548#120—228no—
549C4×D4—44no—
550C4×D4—114no—
551C4×D4—222no—
552C4×D4C4×D1114yes—
553C4×D4D4414yes—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—41no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4—111no—
563C2×C4⋊C4—221no—
564C2×C4⋊C4C22⋊D1111yescharacteristic
565C2×C4⋊C4C22×D1111yescharacteristic
566C2×C4⋊C4C22×D1111yescharacteristic
567C2×C4⋊C4C22×D1111yescharacteristic
568C2×C4⋊C4C22×D1111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—221no—
572C2×C22⋊C4—221no—
573C2×C22⋊C4—221no—
574C2×C22⋊C4—221no—
575C2×C22⋊C4—221no—
576C2×C22⋊C4—228no—
577C2×C22⋊C4C22⋊D1111yescharacteristic
578C2×C22⋊C4C22⋊D1111yescharacteristic
579C2×C42—21no—
580C2×C42C22×D1111yescharacteristic
581C4⋊C8—222no—
582#103—222no—
583#103—222no—
584#103—441no—
585#103—441no—
586#102—114no—
587#102—222no—
588#102—222no—
589#102—222no—
590#102—222no—
591#102—222no—
592#102—441no—
593#102—441no—
594C22⋊C8—222no—
595C22⋊C8—222no—
596#97—222no—
597#95—21no—
598#95—21no—
599#95—21no—
600C2×C11—24no—
601C2×C11—42no—
602C2×C11D4×C22⋊C411yescharacteristic
603C2×C11C2×#41711yescharacteristic
604C2×C11#289711yescharacteristic
605C2×C11#326411yescharacteristic
606C2×C11#326611yescharacteristic
607C2×C11#330611yescharacteristic
608C2×C11#331411yescharacteristic
609D11—44no—
610D11—82no—
611C24—221no—
612C24—221no—
613C24—224no—
614C24—442no—
615C24—442no—
616C24—442no—
617C24—442no—
618C24—881no—
619C24—881no—
620C24C2×C22⋊D1111yescharacteristic
621C24C2×C22⋊D1111yescharacteristic
622#41—228no—
623#41—444no—
624#41—444no—
625#41—444no—
626C2×Q8—112no—
627C2×Q8—221no—
628C2×Q8—221no—
629C2×Q8—221no—
630C2×Q8—221no—
631C2×Q8—221no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—112no—
635C2×D4—112no—
636C2×D4—112no—
637C2×D4—112no—
638C2×D4—228no—
639C2×D4—224no—
640C2×D4—224no—
641C2×D4—224no—
642C2×D4—221no—
643C2×D4—221no—
644C2×D4—221no—
645C2×D4—221no—
646C2×D4—221no—
647C2×D4—221no—
648C2×D4—221no—
649C2×D4—221no—
650C2×D4—444no—
651C2×D4—444no—
652C2×D4—444no—
653C2×D4—442no—
654C2×D4—442no—
655C2×D4—442no—
656C2×D4—442no—
657C2×D4—881no—
658C2×D4—881no—
659C2×D4(C2×D11)⋊C414yes—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—81no—
677C22×C4—81no—
678C22×C4—221no—
679C22×C4—221no—
680C22×C4—224no—
681C22×C4—224no—
682C22×C4—442no—
683C22×C4—442no—
684C22×C4—881no—
685C22×C4—881no—
686C22×C4C2×C4×D1112yes—
687C22×C4C2×C4×D1112yes—
688C22×C4C2×D4412yes—
689C22×C4C2×D4412yes—
690C22×C4C2×C22⋊D1111yescharacteristic
691C22×C4C2×C22⋊D1111yescharacteristic
692C22×C4C2×C22⋊D1111yescharacteristic
693C22×C4C2×C22⋊D1111yescharacteristic
694C22×C4C23×D1111yescharacteristic
695M16—444no—
696C2×C8—112no—
697C2×C8—221no—
698C2×C8—221no—
699C2×C8—221no—
700C2×C8—221no—
701C2×C8—221no—
702C2×C8—221no—
703C2×C8—221no—
704C2×C8—221no—
705C2×C8—221no—
706C2×C8—221no—
707C2×C8—221no—
708C2×C8—444no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—42no—
717C4⋊C4—42no—
718C4⋊C4—42no—
719C4⋊C4—81no—
720C4⋊C4—112no—
721C4⋊C4—224no—
722C4⋊C4—221no—
723C4⋊C4(C2×D11)⋊C414yes—
724C4⋊C4D4×D1112yes—
725C22⋊C4—42no—
726C22⋊C4—42no—
727C22⋊C4—224no—
728C22⋊C4—224no—
729C22⋊C4—224no—
730C22⋊C4—224no—
731C22⋊C4—224no—
732C22⋊C4(C2×D11)⋊C414yes—
733C22⋊C4(C2×D11)⋊C414yes—
734C42—42no—
735C42C2×C4×D1112yes—
736C42C2×D4412yes—
737C11#2241911yescharacteristic, complemented, Sylow
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—222no—
749C23—222no—
750C23—222no—
751C23—222no—
752C23—448no—
753C23—441no—
754C23—441no—
755C23—441no—
756C23—441no—
757C23—441no—
758C23—441no—
759C23—441no—
760C23—448no—
761C23—441no—
762C23—441no—
763C23—441no—
764C23—884no—
765C23—884no—
766C23—884no—
767C23—884no—
768C23—884no—
769C23C2×(C2×D11)⋊C412yes—
770C23C2×(C2×D11)⋊C412yes—
771C23#6698512yes—
772C23#6699512yes—
773C23C22×C22⋊D1111yescharacteristic
774Q8—222no—
775Q8—222no—
776Q8—441no—
777Q8—441no—
778D4—28no—
779D4—114no—
780D4—222no—
781D4—222no—
782D4—222no—
783D4—222no—
784D4—222no—
785D4—448no—
786D4—448no—
787D4—441no—
788D4—441no—
789D4—884no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—84no—
819C2×C4—84no—
820C2×C4—222no—
821C2×C4—222no—
822C2×C4—448no—
823C2×C4—441no—
824C2×C4—441no—
825C2×C4—441no—
826C2×C4—441no—
827C2×C4—884no—
828C2×C4C2×(C2×D11)⋊C412yes—
829C2×C4C2×(C2×D11)⋊C412yes—
830C2×C4C2×(C2×D11)⋊C412yes—
831C2×C4C2×(C2×D11)⋊C412yes—
832C2×C4C22×C4×D1111yescharacteristic
833C2×C4C22×D4411yescharacteristic
834C2×C4C2×D4×D1111yescharacteristic
835C2×C4#6703711yescharacteristic
836C2×C4#41×D1111yescharacteristic
837C2×C4#6704211yescharacteristic
838C8—222no—
839C8—441no—
840C8—441no—
841C8—441no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—224no—
856C22—442no—
857C22—442no—
858C22—442no—
859C22—442no—
860C22—442no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—8816no—
866C22—881no—
867C22—881no—
868C22—881no—
869C22—881no—
870C22#1062257914yescomplemented
871C22C22×(C2×D11)⋊C411yescharacteristic
872C22C2×#6698511yescharacteristic
873C22D4×C22⋊D1111yescharacteristic
874C22C2×#6699511yescharacteristic
875C22#1062336011yescharacteristic
876C22#1062336611yescharacteristic
877C22#1062336811yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—81no—
884C4—81no—
885C4—81no—
886C4—442no—
887C4—442no—
888C4C4×D4×D1111yescharacteristic
889C4#1062307611yescharacteristic
890C4D4×D4411yescharacteristic
891C4#1062308511yescharacteristic
892C2—24no—
893C2—42no—
894C2—444no—
895C2—882no—
896C2D4×(C2×D11)⋊C411yescharacteristic
897C2C2×#1062257911yescharacteristic
898C2#1307713911yescharacteristic
899C2#1308009211yescharacteristic
900C2#1308012711yescharacteristic
901C2#1308057111yescharacteristic
902C2#1308069111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC2×#10623081C2
cosocleC22×C4×C11C24
hypercenterD4×C4⋊C4D11
hypocenterC11#22419
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622624C2semidirect
3. C2×#10622579C2semidirect
4. C22×#66873C2semidirect
5. #13069548C2semidirect
6. #13069430C2semidirect
7. #13069052C2semidirect
8. #13069037C2semidirect
9. #13068933C2semidirect
10. #13068923C2semidirect
11. #13068613C2semidirect
12. #13068554C2semidirect
13. #13068546C2semidirect
14. #13068444C2semidirect
15. D4×C11×C4⋊C4C2semidirect
21. C22×C11×C4⋊C4C22semidirect
25. C22×#4318C22semidirect
28. #10623081C4semidirect
37. C11×#384C22semidirect
39. C11×#380C22semidirect
40. C4×C11×C4⋊C4C22semidirect
42. C2×C22⋊(C11⋊C8)C22semidirect
44. C2×#66874C22semidirect
45. C2×#66874C22semidirect
46. C2×#66874C22semidirect
47. C2×#66874C22semidirect
58. C2×C4⋊(C11⋊C8)C22semidirect
59. C2×#66867C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
77. C2×#4339C2×C4semidirect
84. C22×D44C2×C4semidirect
115. #66983C2×C4semidirect
122. #66977C2×C4semidirect
138. #66928C2×C4semidirect
140. C4×D44C2×C4semidirect
157. #66873D4semidirect
291. D4×C4⋊C4D11semidirect
395. D44C4×D4semidirect
422. C22×C4⋊C4C2×D11semidirect
446. #384C2×D11semidirect
448. #380C2×D11semidirect
449. C4×C4⋊C4C2×D11semidirect
467. C22×C11#417semidirect
737. C11#22419semidirect
870. C22#10622579semidirect

Maximal subgroups

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

subgroupindex
C2×#106230812
C2×#106226242
C2×#106225792
C22×#668732
#130695482
#130694302
#130690522
#130690372
#130689332
#130689232
#130686132
#130685542
#130685462
#130684442
D4×C11×C4⋊C42
#2241911