Finite Group Databasebeta

← #14769256

Subgroups — #14769256

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×#10623143C211yesmaximal, characteristic
2C2×#10622341C211yesmaximal, characteristic, complemented
3C2×#10622579C211yesmaximal, characteristic, complemented
4C2×D11×#102C211yesmaximal, characteristic, complemented
5C4⋊C4×C22⋊D11C211yesmaximal, characteristic, complemented
6#13069547C211yesmaximal, characteristic, complemented
7#13069431C211yesmaximal, characteristic, complemented
8#13069055C211yesmaximal, characteristic, complemented
9#13069038C211yesmaximal, characteristic, complemented
10#13068922C211yesmaximal, characteristic, complemented
11#13068615C211yesmaximal, characteristic, complemented
12#13068557C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068440C211yesmaximal, characteristic, complemented
15C11×#1874C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic, complemented
20C2×#66991—21no—
21C2×#66990—21no—
22C2×#66989C2211yescharacteristic
23C2×C4×C22⋊D11—21no—
24C2×C4×C22⋊D11C2211yescharacteristic
25C22×#4318C2211yescharacteristic, complemented
26C22×C8×D11C2211yescharacteristic
27#10623143—24no—
28#10623143C418yescomplemented
29C2×#66950C2211yescharacteristic
30C2×#66946C2211yescharacteristic
31C2×C4⋊C4×D11C2211yescharacteristic
32C2×#66936—21no—
33C2×C22⋊C4×D11—21no—
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic, complemented
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39#10622825C2211yescharacteristic, complemented
40#10622823—21no—
41C2×#66885C2211yescharacteristic
42C2×#66885C2211yescharacteristic
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×#66880C2211yescharacteristic, complemented
45C2×#66880C2211yescharacteristic, complemented
46C2×#66879C2211yescharacteristic, complemented
47C2×Dic11⋊C8C2211yescharacteristic, complemented
48#10622602—21no—
49#10622600C2211yescharacteristic
50#10622589C2211yescharacteristic, complemented
51C4⋊C4×Dic11C2211yescharacteristic, complemented
52#10622585—21no—
53C2×#66874C2211yescharacteristic, complemented
54C2×#66874C2211yescharacteristic, complemented
55#10622579—24no—
56C2×#66873C2211yescharacteristic
57C2×#66873C2211yescharacteristic
58D11×#102—24no—
59#10622341—24no—
60C11×#340C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×D4×C11—21no—
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—21no—
70C22×C22⋊D11—21no—
71C22×C22⋊D11D411yescharacteristic
72C2×D4×D11—22no—
73C2×D4×D11—22no—
74C2×D4×D11—22no—
75C2×D4×D11—41no—
76C2×D4×D11—41no—
77C2×D4×D11C2×C414yescomplemented
78C2×#4339—22no—
79C2×#4339—22no—
80C2×#4339—22no—
81C2×#4339—41no—
82C2×#4339—41no—
83C2×#4339C2×C414yescomplemented
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×C4×D11C2311yescharacteristic
89C22×Dic22C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C11×#121—22no—
93C11×#121C2×C414yescomplemented
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—41no—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—21no—
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11D411yescharacteristic
105#66991—28no—
106#66990—28no—
107#66989—22no—
108#66989C2×C414yescomplemented
109C4×C22⋊D11—44no—
110C4×C22⋊D11C2×C414yes—
111C4×C22⋊D11D414yes—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4D411yescharacteristic
116C2×C4⋊Dic11—21no—
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4D411yescharacteristic
123C2×C4×Dic11—21no—
124C2×C4×Dic11C2311yescharacteristic
125C2×#4318—22no—
126C2×#4318—22no—
127C2×#4318—41no—
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C2×C8×D11—22no—
131C2×C8×D11—22no—
132C2×C8×D11—41no—
133#66950—22no—
134#66950C2×C414yescomplemented
135#66946—22no—
136#66946C2×C414yescomplemented
137C4⋊C4×D11—22no—
138C4⋊C4×D11—41no—
139#66936—28no—
140C22⋊C4×D11—28no—
141C11×#102—22no—
142C11×#102—41no—
143C11×C22⋊C8—22no—
144#66896—22no—
145#66896—41no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C11⋊#95—21no—
149#66885—22no—
150#66885—22no—
151(C2×D11)⋊C8—22no—
152#66880—41no—
153#66880—41no—
154#66879—22no—
155Dic11⋊C8—22no—
156#66874—22no—
157#66874—22no—
158#66873—22no—
159#66873D414yescomplemented
160#22419—111nomaximal, Sylow
161C24×C11—21no—
162C24×C11C2×D411yescharacteristic
163C23×D11—21no—
164C23×D11—24no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—42no—
168C23×D11—42no—
169C23×D11—81no—
170C23×D11—81no—
171C23×D11C2×D411yescharacteristic
172C2×D4×C11—24no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—81no—
179C2×D4×C11—81no—
180C2×D4×C11C22×C412yes—
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—21no—
188C22×C4×C11—42no—
189C22×C4×C11—42no—
190C22×C4×C11—81no—
191C22×C4×C11C22×C412yes—
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D412yes—
194C22×C4×C11C2411yescharacteristic
195C2×C22⋊D11—24no—
196C2×C22⋊D11—24no—
197C2×C22⋊D11—22no—
198C2×C22⋊D11—22no—
199C2×C22⋊D11—42no—
200C2×C22⋊D11—42no—
201C2×C22⋊D11—42no—
202C2×C22⋊D11—42no—
203C2×C22⋊D11C22⋊C414yes—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209C22×Dic11C2×D411yescharacteristic
210D4×D11—28no—
211D4×D11—44no—
212D4×D11—44no—
213D4×D11—44no—
214#4339—28no—
215#4339—44no—
216#4339—44no—
217#4339—44no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44C22×C412yes—
222C2×D44C2×D412yes—
223C2×D44#4112yes—
224C2×C4×D11—24no—
225C2×C4×D11—24no—
226C2×C4×D11—21no—
227C2×C4×D11—21no—
228C2×C4×D11—21no—
229C2×C4×D11—21no—
230C2×C4×D11—42no—
231C2×C4×D11—42no—
232C2×C4×D11—42no—
233C2×C4×D11—42no—
234C2×C4×D11—81no—
235C2×C4×D11—81no—
236C2×C4×D11—81no—
237C2×C4×D11C22×C412yes—
238C2×C4×D11C2×D412yes—
239C2×Dic22—21no—
240C2×Dic22—21no—
241C2×Dic22—21no—
242C2×Dic22—21no—
243C2×Dic22—21no—
244C2×Dic22C22×C412yes—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C2×C8×C11—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—42no—
256C11×C4⋊C4C22×C412yes—
257C11×C4⋊C4C2×D412yes—
258C11×C22⋊C4—24no—
259C22⋊Dic11—24no—
260C22⋊Dic11—24no—
261C22⋊Dic11—42no—
262C22⋊Dic11C22⋊C414yes—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—42no—
266(C2×D11)⋊C4C22⋊C414yes—
267C4⋊Dic11—24no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272Dic11⋊C4—42no—
273Dic11⋊C4—42no—
274Dic11⋊C4—81no—
275Dic11⋊C4C22⋊C414yes—
276C4×Dic11—42no—
277C4×Dic11C22×C412yes—
278C4×Dic11C2×D412yes—
279#4318—44no—
280C2×C11⋊C8—21no—
281C2×C11⋊C8—21no—
282C2×C11⋊C8—21no—
283C2×C11⋊C8—21no—
284C2×C11⋊C8—21no—
285C2×C11⋊C8C2×D412yes—
286C8×D11—44no—
287C2×#546—111no—
288C2×#435—111no—
289C2×#417—111no—
290C22×#102—111no—
291D4×C4⋊C4—111no—
292#1983—111no—
293#1959—111no—
294#1895—111no—
295#1892—111no—
296#1874D1111yescharacteristic, complemented
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—22no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11C2×C22⋊C412yes—
316C23×C11C22×D411yescharacteristic
317C22×D11—21no—
318C22×D11—21no—
319C22×D11—21no—
320C22×D11—21no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—48no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—48no—
330C22×D11—84no—
331C22×D11—84no—
332C22×D11—84no—
333C22×D11—84no—
334C22×D11—84no—
335C22×D11C2×C22⋊C412yes—
336C22×D11AGL(1,ℤ/8)12yes—
337C22×D11#13712yes—
338D4×C11—22no—
339D4×C11—22no—
340D4×C11—41no—
341D4×C11—41no—
342D4×C11—84no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
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—84no—
359C2×C4×C11C2×C22⋊C412yes—
360C2×C4×C11C23×C411yescharacteristic
361C2×C4×C11C22×D411yescharacteristic
362C2×C4×C11C22×D411yescharacteristic
363C2×C4×C11C2×#4111yescharacteristic
364C2×C4×C11H(5,𝔽2)11yescharacteristic
365C2×C4×C11H(5,𝔽2)11yescharacteristic
366C22⋊D11—28no—
367C22⋊D11—48no—
368C22⋊D11—48no—
369C2×Dic11—21no—
370C2×Dic11—21no—
371C2×Dic11—21no—
372C2×Dic11—21no—
373C2×Dic11—21no—
374C2×Dic11—21no—
375C2×Dic11—22no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384C2×Dic11C2×C22⋊C412yes—
385C2×Dic11C2×C22⋊C412yes—
386C2×Dic11C2×C22⋊C412yes—
387D44—22no—
388D44—22no—
389D44—22no—
390D44C4×D414yescomplemented
391C4×D11—22no—
392C4×D11—22no—
393C4×D11—22no—
394C4×D11—22no—
395C4×D11—48no—
396C4×D11—84no—
397C4×D11—84no—
398Dic22—22no—
399Dic22—22no—
400Dic22—41no—
401Dic22—41no—
402C8×C11—41no—
403C8×C11—41no—
404C11⋊C8—22no—
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—221no—
416C2×#121C2×D1111yescharacteristic
417C2×#120—221no—
418C2×C4×D4—111no—
419C2×C4×D4—111no—
420C2×C4×D4—221no—
421C22×C4⋊C4—111no—
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—224no—
438C2×#102C2×D1111yescharacteristic
439C2×#102C2×D1111yescharacteristic
440C2×C22⋊C8—111no—
441C2×C22⋊C8C2×D1111yescharacteristic, complemented
442C2×#97—111no—
443#389—221no—
444#385—221no—
445#385—221no—
446#384—111no—
447#380—111no—
448#380—111no—
449C4×C4⋊C4—111no—
450#340—111no—
451#340—111no—
452#340C2×D1111yescharacteristic, complemented
453#340C2×D1111yescharacteristic, complemented
454C22×C11—22no—
455C22×C11—22no—
456C22×C11—22no—
457C22×C11—41no—
458C22×C11—41no—
459C22×C11—41no—
460C22×C11—41no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—81no—
465C22×C11—81no—
466C22×C11—81no—
467C22×C11—81no—
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—22no—
476C2×D11—22no—
477C2×D11—22no—
478C2×D11—22no—
479C2×D11—22no—
480C2×D11—22no—
481C2×D11—24no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—816no—
489C2×D11#41714yescomplemented
490C4×C11—22no—
491C4×C11—42no—
492C4×C11—42no—
493C4×C11—81no—
494C4×C11C2×C4×D411yescharacteristic
495C4×C11#51811yescharacteristic
496C4×C11D4211yescharacteristic
497C4×C11#54611yescharacteristic
498Dic11—22no—
499Dic11—22no—
500Dic11—22no—
501Dic11—42no—
502Dic11—81no—
503Dic11—81no—
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—21no—
513C22×D4—111no—
514C22×D4—114no—
515C22×D4—111no—
516C22×D4—222no—
517C22×D4—221no—
518C22×D4—222no—
519C22×D4—222no—
520C22×D4—221no—
521C22×D4—441no—
522C22×D4—441no—
523C22×D4C22×D1111yescharacteristic
524C23×C4—21no—
525C23×C4—111no—
526C23×C4—221no—
527C23×C4—221no—
528C23×C4—221no—
529C23×C4C22×D1111yescharacteristic
530C2×M16—222no—
531C2×M16—222no—
532C2×M16—441no—
533C22×C8—111no—
534C22×C8—111no—
535C22×C8—222no—
536C22×C8—222no—
537C22×C8—441no—
538C22×C8C22×D1111yescharacteristic
539C22×C8C22×D1111yescharacteristic
540#124—114no—
541#124—222no—
542#123—228no—
543C22⋊Q8—114no—
544C22⋊Q8—222no—
545#121—22no—
546#121—228no—
547#121C4×D1114yescomplemented
548#120—228no—
549C4×D4—114no—
550C4×D4—114no—
551C4×D4—114no—
552C4×D4—222no—
553C4×D4—444no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—41no—
557C2×C4⋊C4—111no—
558C2×C4⋊C4—111no—
559C2×C4⋊C4—111no—
560C2×C4⋊C4—221no—
561C2×C4⋊C4—222no—
562C2×C4⋊C4—221no—
563C2×C4⋊C4—221no—
564C2×C4⋊C4—221no—
565C2×C4⋊C4—441no—
566C2×C4⋊C4C22×D1111yescharacteristic
567C2×C4⋊C4C22×D1111yescharacteristic
568C2×C4⋊C4C22×D1111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—111no—
571C2×C22⋊C4—111no—
572C2×C22⋊C4—228no—
573C2×C22⋊C4—221no—
574C2×C22⋊C4—221no—
575C2×C22⋊C4—221no—
576C2×C22⋊C4—221no—
577C2×C22⋊C4—221no—
578C2×C22⋊C4—221no—
579C2×C42—111no—
580C2×C42—221no—
581C4⋊C8—222no—
582#103—222no—
583#103—222no—
584#103—441no—
585#103—441no—
586#102—22no—
587#102—41no—
588#102—114no—
589#102—222no—
590#102—222no—
591#102—222no—
592#102—222no—
593#102—441no—
594C22⋊C8—22no—
595C22⋊C8—222no—
596#97—222no—
597#95—221no—
598#95—221no—
599#95—221no—
600C2×C11—42no—
601C2×C11—82no—
602C2×C11D4×C22⋊C411yescharacteristic
603C2×C11C2×#41711yescharacteristic
604C2×C11#289711yescharacteristic
605C2×C11#326411yescharacteristic
606C2×C11#326611yescharacteristic
607C2×C11#330611yescharacteristic
608C2×C11#331411yescharacteristic
609D11—24no—
610D11—44no—
611C24—21no—
612C24—111no—
613C24—224no—
614C24—221no—
615C24—442no—
616C24—442no—
617C24—442no—
618C24—442no—
619C24—881no—
620C24—881no—
621C24D4×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—24no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—81no—
639C2×D4—81no—
640C2×D4—114no—
641C2×D4—112no—
642C2×D4—112no—
643C2×D4—112no—
644C2×D4—224no—
645C2×D4—228no—
646C2×D4—222no—
647C2×D4—222no—
648C2×D4—224no—
649C2×D4—221no—
650C2×D4—221no—
651C2×D4—221no—
652C2×D4—444no—
653C2×D4—444no—
654C2×D4—444no—
655C2×D4—442no—
656C2×D4—442no—
657C2×D4—442no—
658C2×D4—442no—
659C2×D4C2×C4×D1112yes—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—81no—
670C22×C4—111no—
671C22×C4—111no—
672C22×C4—111no—
673C22×C4—112no—
674C22×C4—112no—
675C22×C4—224no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4—221no—
679C22×C4—221no—
680C22×C4—221no—
681C22×C4—224no—
682C22×C4—221no—
683C22×C4—221no—
684C22×C4—442no—
685C22×C4—442no—
686C22×C4—442no—
687C22×C4—442no—
688C22×C4—881no—
689C22×C4—881no—
690C22×C4—881no—
691C22×C4C2×C4×D1112yes—
692C22×C4D4×D1111yescharacteristic
693C22×C4D4×D1112yes—
694C22×C4C23×D1111yescharacteristic
695M16—444no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—112no—
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—42no—
714C4⋊C4—114no—
715C4⋊C4—224no—
716C4⋊C4—221no—
717C4⋊C4—221no—
718C4⋊C4—221no—
719C4⋊C4—221no—
720C4⋊C4—442no—
721C4⋊C4—442no—
722C4⋊C4—881no—
723C4⋊C4C2×C4×D1112yes—
724C4⋊C4D4×D1112yes—
725C22⋊C4—24no—
726C22⋊C4—114no—
727C22⋊C4—114no—
728C22⋊C4—224no—
729C22⋊C4—224no—
730C22⋊C4—224no—
731C22⋊C4—224no—
732C22⋊C4—442no—
733C22⋊C4—442no—
734C42—112no—
735C42—112no—
736C42—442no—
737C11#2241911yescharacteristic, complemented, Sylow
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—22no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—112no—
752C23—112no—
753C23—112no—
754C23—221no—
755C23—221no—
756C23—221no—
757C23—221no—
758C23—222no—
759C23—222no—
760C23—222no—
761C23—448no—
762C23—448no—
763C23—441no—
764C23—441no—
765C23—441no—
766C23—441no—
767C23—884no—
768C23—884no—
769C23—884no—
770C23—884no—
771C23—884no—
772C23C22⋊C4×D1112yes—
773C23C2×D4×D1111yescharacteristic
774Q8—222no—
775Q8—222no—
776Q8—441no—
777Q8—441no—
778D4—22no—
779D4—22no—
780D4—41no—
781D4—41no—
782D4—84no—
783D4—114no—
784D4—228no—
785D4—222no—
786D4—222no—
787D4—222no—
788D4—448no—
789D4—448no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—84no—
806C2×C4—112no—
807C2×C4—112no—
808C2×C4—112no—
809C2×C4—221no—
810C2×C4—221no—
811C2×C4—221no—
812C2×C4—221no—
813C2×C4—221no—
814C2×C4—221no—
815C2×C4—222no—
816C2×C4—222no—
817C2×C4—222no—
818C2×C4—222no—
819C2×C4—222no—
820C2×C4—448no—
821C2×C4—441no—
822C2×C4—441no—
823C2×C4—441no—
824C2×C4—441no—
825C2×C4—441no—
826C2×C4—441no—
827C2×C4—441no—
828C2×C4—441no—
829C2×C4—884no—
830C2×C4—884no—
831C2×C4C22⋊C4×D1112yes—
832C2×C4C22×C4×D1111yescharacteristic
833C2×C4C2×D4×D1111yescharacteristic
834C2×C4C2×D4×D1111yescharacteristic
835C2×C4#6703711yescharacteristic
836C2×C4#41×D1111yescharacteristic
837C2×C4#6704211yescharacteristic
838C8—41no—
839C8—41no—
840C8—222no—
841C8—441no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—114no—
857C22—222no—
858C22—222no—
859C22—222no—
860C22—222no—
861C22—222no—
862C22—222no—
863C22—224no—
864C22—442no—
865C22—442no—
866C22—442no—
867C22—442no—
868C22—442no—
869C22—442no—
870C22—8816no—
871C22C2×C22⋊C4×D1111yescharacteristic
872C22#1062312111yescharacteristic
873C22#1062318511yescharacteristic
874C22#1062328811yescharacteristic
875C22#1062329311yescharacteristic
876C22D11×AGL(1,ℤ/8)11yescharacteristic
877C22D11×#13711yescharacteristic
878C4—22no—
879C4—42no—
880C4—42no—
881C4—81no—
882C4—222no—
883C4—222no—
884C4—222no—
885C4—442no—
886C4—881no—
887C4—881no—
888C4C4×D4×D1111yescharacteristic
889C4#1062307611yescharacteristic
890C4#1062314011yescharacteristic
891C4#1062314111yescharacteristic
892C2—42no—
893C2—82no—
894C2—224no—
895C2—444no—
896C2#1307143411yescharacteristic
897C2D11×#41711yescharacteristic
898C2#1307713711yescharacteristic
899C2#1308009411yescharacteristic
900C2#1308012911yescharacteristic
901C2#1308058011yescharacteristic
902C2#1308070011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1874C2
socleC23×C11C22×D4
prime radicalC2×#10623143C2
cosocleC22×C4×C11C24
hypercenter#1874D11
hypocenterC11#22419
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C2×#10622341C2semidirect
3. C2×#10622579C2semidirect
4. C2×D11×#102C2semidirect
5. C4⋊C4×C22⋊D11C2semidirect
6. #13069547C2semidirect
7. #13069431C2semidirect
8. #13069055C2semidirect
9. #13069038C2semidirect
10. #13068922C2semidirect
11. #13068615C2semidirect
12. #13068557C2semidirect
13. #13068545C2semidirect
14. #13068440C2semidirect
15. C11×#1874C2semidirect
19. C22×C11×C4⋊C4C22semidirect
25. C22×#4318C22semidirect
28. #10623143C4semidirect
36. C2×C11×C22⋊C8C22semidirect
39. #10622825C22semidirect
44. C2×#66880C22semidirect
45. C2×#66880C22semidirect
46. C2×#66879C22semidirect
47. C2×Dic11⋊C8C22semidirect
50. #10622589C22semidirect
51. C4⋊C4×Dic11C22semidirect
53. C2×#66874C22semidirect
54. C2×#66874C22semidirect
60. C11×#340C22semidirect
61. C11×#340C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
77. C2×D4×D11C2×C4semidirect
83. C2×#4339C2×C4semidirect
93. C11×#121C2×C4semidirect
108. #66989C2×C4semidirect
134. #66950C2×C4semidirect
136. #66946C2×C4semidirect
159. #66873D4semidirect
296. #1874D11semidirect
390. D44C4×D4semidirect
422. C22×C4⋊C4C2×D11semidirect
441. C2×C22⋊C8C2×D11semidirect
452. #340C2×D11semidirect
453. #340C2×D11semidirect
489. C2×D11#417semidirect
547. #121C4×D11semidirect
737. C11#22419semidirect

Maximal subgroups

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

subgroupindex
C2×#106231432
C2×#106223412
C2×#106225792
C2×D11×#1022
C4⋊C4×C22⋊D112
#130695472
#130694312
#130690552
#130690382
#130689222
#130686152
#130685572
#130685452
#130684402
C11×#18742
#2241911