Finite Group Databasebeta

← #14769246

Subgroups — #14769246

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×#10623360C211yesmaximal, characteristic
2C2×#10622341C211yesmaximal, characteristic, complemented
3C2×#10622845C211yesmaximal, characteristic, complemented
4C2×D11×#102C211yesmaximal, characteristic, complemented
5#13071512C211yesmaximal, characteristic, complemented
6#13069545C211yesmaximal, characteristic, complemented
7#13069429C211yesmaximal, characteristic, complemented
8#13069052C211yesmaximal, characteristic, complemented
9#13069036C211yesmaximal, characteristic, complemented
10#13068931C211yesmaximal, characteristic, complemented
11#13068920C211yesmaximal, characteristic, complemented
12#13068614C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068443C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18#10623360—24no—
19#10623360C418yescomplemented
20C2×#67000C2211yescharacteristic
21C2×#66999C2211yescharacteristic
22C2×#66992—21no—
23C2×#66990—21no—
24C2×D4×Dic11C2211yescharacteristic
25C2×#66983C2211yescharacteristic
26C2×#66982—21no—
27C2×C4×C22⋊D11C2211yescharacteristic
28C22×(C2×D11)⋊C4—21no—
29C22×C4⋊Dic11C2211yescharacteristic, complemented
30C22×#4318C2211yescharacteristic, complemented
31C22×C8×D11C2211yescharacteristic
32C2×C4⋊C4×D11C2211yescharacteristic
33C2×(C22⋊D11)⋊C4—21no—
34C2×C11×#103C2211yescharacteristic, complemented
35C2×C11×#103C2211yescharacteristic, complemented
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic, complemented
39C11×#380C2211yescharacteristic, complemented
40#10622845—24no—
41C2×#66899C2211yescharacteristic, complemented
42C2×#66899C2211yescharacteristic, complemented
43C2×#66896C2211yescharacteristic
44C2×#66896C2211yescharacteristic
45C2×#66885C2211yescharacteristic
46C2×#66885C2211yescharacteristic
47C2×(C2×D11)⋊C8C2211yescharacteristic
48C2×#66879C2211yescharacteristic, complemented
49C2×Dic11⋊C8C2211yescharacteristic, complemented
50#10622600C2211yescharacteristic
51#10622589C2211yescharacteristic, complemented
52C4⋊C4×Dic11C2211yescharacteristic, complemented
53C2×#66873C2211yescharacteristic
54C2×#66873C2211yescharacteristic
55#10622559—21no—
56D11×#102—24no—
57#10622341—24no—
58#10622281—21no—
59#10622260—21no—
60#10622189C2211yescharacteristic, complemented
61#10622189C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—41no—
69C2×C11×#41—41no—
70C2×C11×#41C2×C414yescomplemented
71C22×Q8×C11C2311yescharacteristic
72C22×D4×C11—21no—
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C22×C22⋊D11—21no—
77C22×C22⋊D11—21no—
78C22×C22⋊D11D411yescharacteristic
79C23×Dic11—21no—
80C23×Dic11—21no—
81C2×D4×D11—22no—
82C2×D4×D11—22no—
83C2×D4×D11—22no—
84C2×D4×D11—41no—
85C2×D4×D11—41no—
86C2×D4×D11C2×C414yescomplemented
87C22×D44C2311yescharacteristic
88C22×C4×D11—21no—
89C22×C4×D11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11D411yescharacteristic
97#67000—22no—
98#67000C2×C414yescomplemented
99#66999—22no—
100#66999C2×C414yescomplemented
101#66992—28no—
102#66990—28no—
103D4×Dic11—22no—
104D4×Dic11C2×C414yescomplemented
105#66983—22no—
106#66983C2×C414yescomplemented
107#66982—28no—
108C4×C22⋊D11C2×C414yes—
109C4×C22⋊D11D414yes—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—28no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4D411yescharacteristic
117C2×C4⋊Dic11—22no—
118C2×C4⋊Dic11—21no—
119C2×C4⋊Dic11—41no—
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4D411yescharacteristic
128C2×C4×Dic11—21no—
129C2×C4×Dic11C2311yescharacteristic
130C2×#4318—22no—
131C2×#4318—22no—
132C2×#4318—41no—
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C2×C8×D11—22no—
136C2×C8×D11—22no—
137C2×C8×D11—41no—
138C4⋊C4×D11—22no—
139C4⋊C4×D11—41no—
140(C22⋊D11)⋊C4—44no—
141C11×#103—41no—
142C11×#103—41no—
143C11×#102—22no—
144C11×#102—22no—
145C11×C22⋊C8—22no—
146C11×#95—21no—
147#66899—22no—
148#66899—22no—
149#66896—22no—
150#66896D414yescomplemented
151C11⋊#95—21no—
152C11⋊#95—21no—
153#66885—22no—
154#66885—41no—
155(C2×D11)⋊C8—22no—
156#66879—22no—
157Dic11⋊C8—22no—
158#66873—22no—
159#66873—41no—
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
172C11×#41—28no—
173C11×#41—44no—
174C11×#41—44no—
175C11×#41—44no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11C22×C412yes—
182C2×D4×C11—24no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—42no—
187C2×D4×C11—42no—
188C2×D4×C11C22×C412yes—
189C2×D4×C11C2×D412yes—
190C2×D4×C11#4112yes—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—24no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—42no—
200C22×C4×C11—42no—
201C22×C4×C11C22×C412yes—
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D412yes—
204C22×C4×C11C2411yescharacteristic
205C2×C22⋊D11—24no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—22no—
208C2×C22⋊D11—22no—
209C2×C22⋊D11—42no—
210C2×C22⋊D11—42no—
211C2×C22⋊D11—81no—
212C2×C22⋊D11—81no—
213C2×C22⋊D11C22⋊C414yes—
214C22×Dic11—24no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—42no—
219C22×Dic11—42no—
220C22×Dic11—81no—
221C22×Dic11—81no—
222C22×Dic11—81no—
223C22×Dic11C2×D411yescharacteristic
224C22×Dic11C2×D411yescharacteristic
225C22×Dic11C2×D411yescharacteristic
226D4×D11—28no—
227D4×D11—44no—
228D4×D11—44no—
229D4×D11—44no—
230C2×D44—21no—
231C2×D44—21no—
232C2×D44—21no—
233C2×D44—21no—
234C2×D44—21no—
235C2×D44C22×C412yes—
236C2×C4×D11—21no—
237C2×C4×D11—21no—
238C2×C4×D11—21no—
239C2×C4×D11—21no—
240C2×C4×D11—42no—
241C2×C4×D11—42no—
242C2×C4×D11—81no—
243C2×C4×D11C22×C412yes—
244C2×C4×D11C2×D412yes—
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×C22⋊C4—42no—
256C22⋊Dic11—24no—
257C22⋊Dic11C22⋊C414yes—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—42no—
263(C2×D11)⋊C4C22⋊C414yes—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11—42no—
269C4⋊Dic11C22×C412yes—
270C4⋊Dic11C2×D412yes—
271Dic11⋊C4—24no—
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#1874—111no—
297#1872—111no—
298#1802—111no—
299#1788D1111yescharacteristic, complemented
300#1786—111no—
301#1762—111no—
302C23×C11—22no—
303C23×C11—21no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—21no—
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—48no—
323C22×D11—41no—
324C22×D11—41no—
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—
338Q8×C11—22no—
339Q8×C11—22no—
340Q8×C11—41no—
341Q8×C11—41no—
342D4×C11—22no—
343D4×C11—22no—
344D4×C11—22no—
345D4×C11—48no—
346D4×C11C4×D414yescomplemented
347C2×C4×C11—21no—
348C2×C4×C11—21no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—48no—
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—41no—
363C2×C4×C11C2×C22⋊C412yes—
364C2×C4×C11C23×C411yescharacteristic
365C2×C4×C11C22×D411yescharacteristic
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11C2×#4111yescharacteristic
368C2×C4×C11H(5,𝔽2)11yescharacteristic
369C2×C4×C11H(5,𝔽2)11yescharacteristic
370C22⋊D11—28no—
371C22⋊D11—48no—
372C22⋊D11—84no—
373C2×Dic11—21no—
374C2×Dic11—21no—
375C2×Dic11—21no—
376C2×Dic11—21no—
377C2×Dic11—21no—
378C2×Dic11—21no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384C2×Dic11—41no—
385C2×Dic11—41no—
386C2×Dic11—41no—
387C2×Dic11—41no—
388C2×Dic11—84no—
389C2×Dic11—84no—
390C2×Dic11C2×C22⋊C412yes—
391C2×Dic11C2×C22⋊C412yes—
392C2×Dic11C2×C22⋊C412yes—
393D44—22no—
394D44—22no—
395D44—41no—
396D44—41no—
397C4×D11—22no—
398C4×D11—22no—
399C4×D11—22no—
400C4×D11—22no—
401C4×D11—84no—
402C8×C11—41no—
403C8×C11—41no—
404C11⋊C8—22no—
405C11⋊C8—41no—
406C22×#41C2×D1111yescharacteristic
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—111no—
419C2×C4×D4—111no—
420C2×C4×D4—221no—
421C22×C4⋊C4—111no—
422C22×C4⋊C4—111no—
423C22×C22⋊C4—221no—
424#435—224no—
425C2×C4⋊C8—111no—
426#417—224no—
427C2×#103—111no—
428C2×#103—111no—
429C2×#103C2×D1111yescharacteristic, complemented
430C2×#103C2×D1111yescharacteristic, complemented
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#380C2×D1111yescharacteristic, complemented
449C4×C4⋊C4—111no—
450#340—111no—
451#340—111no—
452#340—111no—
453#340—111no—
454C22×C11—22no—
455C22×C11—24no—
456C22×C11—22no—
457C22×C11—22no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—41no—
462C22×C11—42no—
463C22×C11—41no—
464C22×C11—42no—
465C22×C11—41no—
466C22×C11—42no—
467C22×C11—41no—
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—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—816no—
485C2×D11—81no—
486C2×D11—81no—
487C2×D11—81no—
488C2×D11—81no—
489C2×D11#41714yescomplemented
490C4×C11—22no—
491C4×C11—42no—
492C4×C11—81no—
493C4×C11—81no—
494C4×C11C2×C4×D411yescharacteristic
495C4×C11#51811yescharacteristic
496C4×C11D4211yescharacteristic
497C4×C11#54611yescharacteristic
498Dic11—22no—
499Dic11—22no—
500Dic11—22no—
501Dic11—42no—
502Dic11—42no—
503Dic11—81no—
504C25—221no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41C4×D1114yescomplemented
511C22×Q8C22×D1111yescharacteristic
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—114no—
546#121—228no—
547#121—222no—
548#120—228no—
549C4×D4—114no—
550C4×D4—114no—
551C4×D4—114no—
552C4×D4—222no—
553C4×D4—444no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—111no—
557C2×C4⋊C4—111no—
558C2×C4⋊C4—222no—
559C2×C4⋊C4—222no—
560C2×C4⋊C4—221no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4—221no—
563C2×C4⋊C4—221no—
564C2×C4⋊C4—221no—
565C2×C4⋊C4—441no—
566C2×C4⋊C4—441no—
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—41no—
583#103—41no—
584#103—222no—
585#103—222no—
586#102—22no—
587#102—22no—
588#102—114no—
589#102—222no—
590#102—222no—
591#102—222no—
592#102—441no—
593#102—441no—
594C22⋊C8—22no—
595C22⋊C8—222no—
596#97—222no—
597#95—21no—
598#95—221no—
599#95—221no—
600C2×C11—44no—
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—24no—
610D11—82no—
611C24—21no—
612C24—111no—
613C24—224no—
614C24—221no—
615C24—442no—
616C24—442no—
617C24—442no—
618C24—442no—
619C24—881no—
620C24—881no—
621C24D4×D1111yescharacteristic
622#41—28no—
623#41—44no—
624#41—44no—
625#41—44no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8C2×C4×D1112yes—
632C2×D4—24no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—114no—
639C2×D4—112no—
640C2×D4—224no—
641C2×D4—222no—
642C2×D4—222no—
643C2×D4—228no—
644C2×D4—224no—
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—881no—
656C2×D4—881no—
657C2×D4C2×C4×D1112yes—
658C2×D4D4×D1112yes—
659C2×D4#434112yes—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—24no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—42no—
669C22×C4—42no—
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—221no—
682C22×C4—221no—
683C22×C4—442no—
684C22×C4—442no—
685C22×C4—442no—
686C22×C4—442no—
687C22×C4—881no—
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—114no—
714C4⋊C4—112no—
715C4⋊C4—112no—
716C4⋊C4—224no—
717C4⋊C4—221no—
718C4⋊C4—221no—
719C4⋊C4—221no—
720C4⋊C4—221no—
721C4⋊C4—442no—
722C4⋊C4—442no—
723C4⋊C4—442no—
724C4⋊C4—881no—
725C22⋊C4—42no—
726C22⋊C4—114no—
727C22⋊C4—114no—
728C22⋊C4—224no—
729C22⋊C4—224no—
730C22⋊C4—224no—
731C22⋊C4—224no—
732C22⋊C4—224no—
733C22⋊C4—442no—
734C42—112no—
735C42—112no—
736C42—442no—
737C11#2241911yescharacteristic, complemented, Sylow
738C23—22no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—22no—
745C23—21no—
746C23—22no—
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—448no—
760C23—448no—
761C23—441no—
762C23—441no—
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—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—48no—
782D4—228no—
783D4—222no—
784D4—222no—
785D4—448no—
786D4—441no—
787D4—441no—
788D4—884no—
789D4(C22⋊D11)⋊C414yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—48no—
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—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—222no—
821C2×C4—441no—
822C2×C4—441no—
823C2×C4—441no—
824C2×C4—441no—
825C2×C4—441no—
826C2×C4—441no—
827C2×C4—441no—
828C2×C4—884no—
829C2×C4—884no—
830C2×C4—884no—
831C2×C4C22⋊C4×D1112yes—
832C2×C4C22×C4×D1111yescharacteristic
833C2×C4C2×D4×D1111yescharacteristic
834C2×C4C2×D4×D1111yescharacteristic
835C2×C4C2×#434111yescharacteristic
836C2×C4#6703711yescharacteristic
837C2×C4#6703711yescharacteristic
838C8—41no—
839C8—41no—
840C8—222no—
841C8—441no—
842C22—22no—
843C22—24no—
844C22—22no—
845C22—22no—
846C22—41no—
847C22—42no—
848C22—41no—
849C22—42no—
850C22—41no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—41no—
855C22—42no—
856C22—114no—
857C22—222no—
858C22—222no—
859C22—222no—
860C22—222no—
861C22—222no—
862C22—222no—
863C22—442no—
864C22—442no—
865C22—442no—
866C22—8816no—
867C22—881no—
868C22—881no—
869C22—881no—
870C22—881no—
871C22C2×C22⋊C4×D1111yescharacteristic
872C22#1062312111yescharacteristic
873C22#1062312211yescharacteristic
874C22#1062330011yescharacteristic
875C22#1062330111yescharacteristic
876C22D11×AGL(1,ℤ/8)11yescharacteristic
877C22D11×#13711yescharacteristic
878C4—22no—
879C4—42no—
880C4—81no—
881C4—81no—
882C4—222no—
883C4—222no—
884C4—222no—
885C4—442no—
886C4—442no—
887C4—881no—
888C4C2×(C22⋊D11)⋊C411yescharacteristic
889C4#1062301711yescharacteristic
890C4#1062312111yescharacteristic
891C4#1062312211yescharacteristic
892C2—42no—
893C2—44no—
894C2—224no—
895C2—882no—
896C2#1307143211yescharacteristic
897C2D11×#41711yescharacteristic
898C2#1307713811yescharacteristic
899C2#1308009911yescharacteristic
900C2#1308012411yescharacteristic
901C2#1308057011yescharacteristic
902C2#1308069011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1788C2
socleC23×C11C22×D4
prime radicalC2×#10623360C2
cosocleC22×C4×C11C24
hypercenter#1788D11
hypocenterC11#22419
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#10622341C2semidirect
3. C2×#10622845C2semidirect
4. C2×D11×#102C2semidirect
5. #13071512C2semidirect
6. #13069545C2semidirect
7. #13069429C2semidirect
8. #13069052C2semidirect
9. #13069036C2semidirect
10. #13068931C2semidirect
11. #13068920C2semidirect
12. #13068614C2semidirect
13. #13068545C2semidirect
14. #13068443C2semidirect
15. C11×#1788C2semidirect
19. #10623360C4semidirect
29. C22×C4⋊Dic11C22semidirect
30. C22×#4318C22semidirect
34. C2×C11×#103C22semidirect
35. C2×C11×#103C22semidirect
38. C2×C11×C22⋊C8C22semidirect
39. C11×#380C22semidirect
41. C2×#66899C22semidirect
42. C2×#66899C22semidirect
48. C2×#66879C22semidirect
49. C2×Dic11⋊C8C22semidirect
51. #10622589C22semidirect
52. C4⋊C4×Dic11C22semidirect
60. #10622189C22semidirect
61. #10622189C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
70. C2×C11×#41C2×C4semidirect
86. C2×D4×D11C2×C4semidirect
98. #67000C2×C4semidirect
100. #66999C2×C4semidirect
104. D4×Dic11C2×C4semidirect
106. #66983C2×C4semidirect
150. #66896D4semidirect
299. #1788D11semidirect
346. D4×C11C4×D4semidirect
429. C2×#103C2×D11semidirect
430. C2×#103C2×D11semidirect
441. C2×C22⋊C8C2×D11semidirect
448. #380C2×D11semidirect
489. C2×D11#417semidirect
510. C2×#41C4×D11semidirect
737. C11#22419semidirect
789. D4(C22⋊D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#106233602
C2×#106223412
C2×#106228452
C2×D11×#1022
#130715122
#130695452
#130694292
#130690522
#130690362
#130689312
#130689202
#130686142
#130685452
#130684432
C11×#17882
#2241911