Finite Group Databasebeta

← #14754757

Subgroups — #14754757

Order 2816.

1598 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623076C211yesmaximal, characteristic
2C2×#10622474C211yesmaximal, characteristic, complemented
3C2×#10622383C211yesmaximal, characteristic
4C2×D11×#102C211yesmaximal, characteristic
5#13071238C211yesmaximal, characteristic, complemented
6#13068878C211yesmaximal, characteristic, complemented
7#13068877C211yesmaximal, characteristic, complemented
8#13068874C211yesmaximal, characteristic, complemented
9#13068866C211yesmaximal, characteristic, complemented
10#13068865C211yesmaximal, characteristic, complemented
11#13068862C211yesmaximal, characteristic, complemented
12#13068861C211yesmaximal, characteristic, complemented
13#13068331C211yesmaximal, characteristic, complemented
14#13068311C211yesmaximal, characteristic, complemented
15C11×#1864C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×C4×C22⋊D11—21no—
20C22×(C2×D11)⋊C4—21no—
21C22×#4313C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23#10623076—24no—
24#10623076—24no—
25C2×#66946C2211yescharacteristic
26C2×#66945C2211yescharacteristic
27C2×#66945C2211yescharacteristic
28C2×C4⋊C4×D11C2211yescharacteristic
29C2×(C22⋊D11)⋊C4—21no—
30C2×C22⋊C4×D11—21no—
31C2×C4×D44C2211yescharacteristic
32C2×#66925C2211yescharacteristic
33C2×C11×#106C2211yescharacteristic, complemented
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C11×#389C2211yescharacteristic, complemented
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×#66885C2211yescharacteristic
41C2×#66882C2211yescharacteristic, complemented
42#10622602—21no—
43#10622598C2211yescharacteristic, complemented
44#10622589—21no—
45#10622586C2211yescharacteristic, complemented
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66872C2211yescharacteristic, complemented
49C2×#66871C2211yescharacteristic, complemented
50#10622541C2211yescharacteristic, complemented
51#10622474—24no—
52#10622383C418yescomplemented
53D11×#102—24no—
54#10622281—21no—
55#10622263—21no—
56C11×#340C2211yescharacteristic, complemented
57C11×#336C2211yescharacteristic, complemented
58#10622189C2211yescharacteristic, complemented
59#10622188C2211yescharacteristic, complemented
60#10622188C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622162C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11—21no—
67C22×C22⋊D11—21no—
68C23×Dic11—21no—
69C2×D4×D11—22no—
70C2×D4×D11—22no—
71C2×D4×D11—22no—
72C2×D4×D11C2×C414yes—
73C2×D4×D11D414yes—
74C2×D4×D11Q814yes—
75C22×D44C2311yescharacteristic
76C22×C4×D11—21no—
77C22×C4×D11—21no—
78C22×C4×D11—21no—
79C22×C4×D11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—21no—
89C2×C42×C11C2311yescharacteristic
90C2×C22⋊Dic11—21no—
91D4×Dic11—22no—
92D4×Dic11—22no—
93C4×C22⋊D11—28no—
94C2×(C2×D11)⋊C4—28no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4D411yescharacteristic
100C2×(C2×D11)⋊C4D411yescharacteristic
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4D411yescharacteristic
109C2×Dic11⋊C4D411yescharacteristic
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C2×#4313—22no—
116C2×#4313—22no—
117C2×#4313C2×C414yescomplemented
118C2×C8×D11—22no—
119C2×C8×D11—22no—
120C2×C8×D11—22no—
121#66946—22no—
122#66946—22no—
123#66945—22no—
124#66945—22no—
125#66945C2×C414yescomplemented
126#66945D414yes—
127C4⋊C4×D11—22no—
128C4⋊C4×D11—22no—
129(C22⋊D11)⋊C4—28no—
130C22⋊C4×D11—28no—
131C4×D44—22no—
132C4×D44—22no—
133#66925—22no—
134#66925—22no—
135C11×#106—22no—
136C11×#102—22no—
137C11×#102C2×C414yescomplemented
138C11×#95—21no—
139#66896—22no—
140#66896C2×C414yescomplemented
141C11⋊#95—21no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144#66885—22no—
145#66885C2×C414yescomplemented
146#66882—22no—
147#66873—22no—
148#66873C2×C414yescomplemented
149#66872—22no—
150#66871—22no—
151#20876—111nomaximal, Sylow
152C24×C11—21no—
153C23×D11—21no—
154C23×D11—24no—
155C23×D11—24no—
156C23×D11—24no—
157C23×D11—81no—
158C23×D11—81no—
159C23×D11—81no—
160C23×D11—81no—
161C23×D11C2×D411yescharacteristic
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11C22×C412yes—
166C2×D4×C11C2×D412yes—
167C2×D4×C11C2×Q812yes—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—24no—
171C22×C4×C11—21no—
172C22×C4×C11—81no—
173C22×C4×C11—81no—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2411yescharacteristic
177C2×C22⋊D11—24no—
178C2×C22⋊D11—24no—
179C2×C22⋊D11—24no—
180C22×Dic11—24no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—81no—
185C22×Dic11—81no—
186C22×Dic11C2×D411yescharacteristic
187C22×Dic11C2×D411yescharacteristic
188C22×Dic11C2×D411yescharacteristic
189D4×D11—28no—
190D4×D11—28no—
191D4×D11—28no—
192D4×D11C4⋊C4116yescomplemented
193C2×D44—21no—
194C2×D44—21no—
195C2×D44—21no—
196C2×D44C22×C412yes—
197C2×D44C2×D412yes—
198C2×D44C2×Q812yes—
199C2×C4×D11—24no—
200C2×C4×D11—24no—
201C2×C4×D11—42no—
202C2×C4×D11—81no—
203C2×C4×D11—81no—
204C2×C4×D11—81no—
205C2×C4×D11—81no—
206C2×C4×D11—81no—
207C2×C4×D11—81no—
208C2×C4×D11C22×C412yes—
209C2×C4×D11C2×D412yes—
210C2×C4×D11C2×D412yes—
211C2×C4×D11C2×Q812yes—
212C2×C4×D11#4112yes—
213C2×C4×D11#4112yes—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11—21no—
218C2×C8×C11—21no—
219C2×C8×C11C22×C412yes—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—81no—
225C11×C4⋊C4C22×C412yes—
226C11×C4⋊C4C2×D412yes—
227C11×C22⋊C4—24no—
228C42×C11—21no—
229C42×C11—21no—
230C22⋊Dic11—24no—
231(C2×D11)⋊C4—24no—
232(C2×D11)⋊C4—24no—
233(C2×D11)⋊C4—24no—
234(C2×D11)⋊C4—22no—
235(C2×D11)⋊C4—22no—
236(C2×D11)⋊C4—24no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11—21no—
241C4⋊Dic11—81no—
242C4⋊Dic11C22×C412yes—
243C4⋊Dic11C2×D412yes—
244Dic11⋊C4—22no—
245Dic11⋊C4—22no—
246Dic11⋊C4—42no—
247Dic11⋊C4—81no—
248Dic11⋊C4—81no—
249C4×Dic11—24no—
250C4×Dic11—24no—
251C4×Dic11—21no—
252C4×Dic11—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8C22×C412yes—
259#4313—28no—
260C8×D11—44no—
261C2×#518—111no—
262C2×#428—111no—
263C2×#418—111no—
264C22×#102—111no—
265#2317—111no—
266#1864—111no—
267#1864—111no—
268#1864—111no—
269#1864D1111yescharacteristic, complemented
270#1862—111no—
271#1862—111no—
272#1862—111no—
273#1862—111no—
274#1735—111no—
275#1729—111no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11C22×D411yescharacteristic
284C22×D11—21no—
285C22×D11—21no—
286C22×D11—21no—
287C22×D11—21no—
288C22×D11—22no—
289C22×D11—22no—
290C22×D11—22no—
291C22×D11—216no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11—84no—
297C22×D11—84no—
298C22×D11—84no—
299C22×D11—84no—
300C22×D11—84no—
301C22×D11—84no—
302C22×D11C4×D412yes—
303C22×D11#12012yes—
304C22×D11C22⋊Q812yes—
305D4×C11—22no—
306D4×C11—22no—
307D4×C11—22no—
308D4×C11C2×C4⋊C414yes—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—84no—
325C2×C4×C11C23×C411yescharacteristic
326C2×C4×C11C22×D411yescharacteristic
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C22×Q811yescharacteristic
329C2×C4×C11C2×#4111yescharacteristic
330C2×C4×C11C2×#4111yescharacteristic
331C22⋊D11—216no—
332C2×Dic11—22no—
333C2×Dic11—21no—
334C2×Dic11—21no—
335C2×Dic11—22no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—21no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—84no—
348C2×Dic11C4×D412yes—
349C2×Dic11#12012yes—
350C2×Dic11C22⋊Q812yes—
351D44—22no—
352D44—22no—
353D44—22no—
354D44C2×C4⋊C414yes—
355C4×D11—84no—
356C4×D11—84no—
357C4×D11—84no—
358C4×D11C2×C4⋊C414yes—
359C4×D11C4×D414yes—
360C4×D11C22⋊Q814yes—
361C4×D11#12314yes—
362C8×C11—22no—
363C8×C11—41no—
364C11⋊C8—22no—
365C11⋊C8—41no—
366C23×D4—111no—
367C22×M16—111no—
368C23×C8—111no—
369#518—224no—
370#518—224no—
371C2×C4×D4—111no—
372C2×C4×D4—111no—
373C2×C4×D4—111no—
374C2×C4×D4—221no—
375C2×C4×D4—221no—
376C2×C4×D4C2×D1111yescharacteristic
377C2×#117—111no—
378C2×#117—111no—
379C2×#117—111no—
380C22×C4⋊C4—111no—
381C22×C22⋊C4—221no—
382C22×C22⋊C4—221no—
383#428—224no—
384C2×#107—111no—
385C2×#107—111no—
386C2×#106—111no—
387C2×#106C2×D1111yescharacteristic, complemented
388#418—118no—
389C2×#102—111no—
390C2×#102—111no—
391C2×#102—111no—
392C2×#102—111no—
393C2×#102—111no—
394C2×#102—111no—
395C2×#102—224no—
396C2×#102C2×D1111yescharacteristic
397C2×#102C2×D1111yescharacteristic
398#389—111no—
399#389—111no—
400#389—111no—
401#389C2×D1111yescharacteristic, complemented
402#385—221no—
403#385—221no—
404#384—221no—
405#382—221no—
406#340—111no—
407#340—111no—
408#340—111no—
409#340C2×D1111yescharacteristic, complemented
410#336—111no—
411#336—111no—
412#336—111no—
413#336C2×D1111yescharacteristic, complemented
414C22×C11—24no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11C2×C4×D411yescharacteristic
422C22×C11C2×#12011yescharacteristic
423C22×C11C2×C22⋊Q811yescharacteristic
424C22×C11#57611yescharacteristic
425C22×C11#57611yescharacteristic
426C22×C11#57711yescharacteristic
427C22×C11#57711yescharacteristic
428C2×D11—22no—
429C2×D11—22no—
430C2×D11—22no—
431C2×D11—22no—
432C2×D11—22no—
433C2×D11—22no—
434C2×D11—24no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—42no—
440C2×D11—42no—
441C2×D11—816no—
442C2×D11#38514yes—
443C4×C11—42no—
444C4×C11—41no—
445C4×C11—41no—
446C4×C11—42no—
447C4×C11—81no—
448C4×C11C22×C4⋊C411yescharacteristic
449C4×C11C2×C4×D411yescharacteristic
450C4×C11C2×C22⋊Q811yescharacteristic
451C4×C11C2×#12311yescharacteristic
452Dic11—42no—
453Dic11—42no—
454Dic11—41no—
455Dic11—41no—
456Dic11—81no—
457Dic11#38514yes—
458C25—221no—
459C22×D4—114no—
460C22×D4—114no—
461C22×D4—114no—
462C22×D4—111no—
463C22×D4—222no—
464C22×D4—222no—
465C22×D4—222no—
466C22×D4—221no—
467C22×D4C22×D1111yescharacteristic
468C23×C4—21no—
469C23×C4—111no—
470C23×C4—221no—
471C23×C4—221no—
472C23×C4—221no—
473C23×C4—221no—
474C2×M16—114no—
475C2×M16—222no—
476C2×M16—222no—
477C22×C8—111no—
478C22×C8—111no—
479C22×C8—222no—
480C22×C8—222no—
481C22×C8—222no—
482C22×C8C22×D1111yescharacteristic
483C22×C8C22×D1111yescharacteristic
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—222no—
487C4×D4—222no—
488C4×D4—228no—
489C4×D4—222no—
490C4×D4—222no—
491C4×D4—228no—
492C4×D4—222no—
493C4×D4—222no—
494#117—114no—
495#117—114no—
496#117—222no—
497#117—222no—
498#117—222no—
499#117—222no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—111no—
506C2×C4⋊C4—222no—
507C2×C4⋊C4—222no—
508C2×C4⋊C4—221no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4C22×D1111yescharacteristic
513C2×C4⋊C4C22×D1111yescharacteristic
514C2×C4⋊C4C22×D1111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—111no—
517C2×C22⋊C4—111no—
518C2×C22⋊C4—228no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4—228no—
523C2×C22⋊C4—221no—
524C2×C22⋊C4—221no—
525C2×C42—111no—
526C2×C42—221no—
527C2×C42—221no—
528C2×C42C22×D1111yescharacteristic
529#107—222no—
530#107—222no—
531#106—22no—
532#106—222no—
533#102—22no—
534#102—114no—
535#102—114no—
536#102—114no—
537#102—222no—
538#102—222no—
539#102—222no—
540#102C4×D1114yescomplemented
541#95—21no—
542#95—221no—
543#95—221no—
544#95—221no—
545C2×C11—44no—
546C2×C11C2×#38511yescharacteristic
547C2×C11#294611yescharacteristic
548C2×C11#294611yescharacteristic
549C2×C11#300811yescharacteristic
550C2×C11#300911yescharacteristic
551C2×C11#308111yescharacteristic
552C2×C11#308111yescharacteristic
553D11—24no—
554D11—44no—
555C24—21no—
556C24—111no—
557C24—224no—
558C24—224no—
559C24—224no—
560C24—221no—
561C24—881no—
562C24—881no—
563C24—881no—
564C24—881no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—1116no—
569C2×D4—112no—
570C2×D4—112no—
571C2×D4—112no—
572C2×D4—228no—
573C2×D4—228no—
574C2×D4—228no—
575C2×D4—224no—
576C2×D4—224no—
577C2×D4—224no—
578C2×D4—221no—
579C2×D4—221no—
580C2×D4—221no—
581C2×D4C2×C4×D1112yes—
582C2×D4D4×D1112yes—
583C2×D4Q8×D1112yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—21no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4—111no—
591C22×C4—112no—
592C22×C4—112no—
593C22×C4—112no—
594C22×C4—112no—
595C22×C4—112no—
596C22×C4—112no—
597C22×C4—111no—
598C22×C4—111no—
599C22×C4—224no—
600C22×C4—224no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—224no—
604C22×C4—221no—
605C22×C4—442no—
606C22×C4—881no—
607C22×C4—881no—
608C22×C4—881no—
609C22×C4—881no—
610C22×C4—881no—
611C22×C4—881no—
612C22×C4—881no—
613C22×C4—881no—
614C22×C4D4×D1111yescharacteristic
615C22×C4D4×D1111yescharacteristic
616C22×C4C23×D1111yescharacteristic
617M16—228no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—112no—
624C2×C8—221no—
625C2×C8—221no—
626C2×C8—221no—
627C2×C8—221no—
628C2×C8—221no—
629C2×C8—444no—
630C2×C8C2×C4×D1112yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—81no—
636C4⋊C4—112no—
637C4⋊C4—112no—
638C4⋊C4—222no—
639C4⋊C4—222no—
640C4⋊C4—221no—
641C4⋊C4—221no—
642C4⋊C4—221no—
643C4⋊C4—221no—
644C4⋊C4—442no—
645C4⋊C4—881no—
646C4⋊C4—881no—
647C4⋊C4—881no—
648C4⋊C4C2×C4×D1112yes—
649C4⋊C4D4×D1112yes—
650C22⋊C4—24no—
651C22⋊C4—222no—
652C22⋊C4—222no—
653C22⋊C4—224no—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C22⋊C4—224no—
657C22⋊C4—224no—
658C42—21no—
659C42—21no—
660C42—224no—
661C42—224no—
662C42—221no—
663C42—221no—
664C11#2087611yescharacteristic, complemented, Sylow
665C23—22no—
666C23—22no—
667C23—22no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—112no—
673C23—112no—
674C23—112no—
675C23—2216no—
676C23—221no—
677C23—221no—
678C23—221no—
679C23—221no—
680C23—222no—
681C23—222no—
682C23—222no—
683C23—441no—
684C23—441no—
685C23—441no—
686C23—441no—
687C23—884no—
688C23—884no—
689C23—884no—
690C23—884no—
691C23—884no—
692C23—884no—
693C23C2×D4×D1111yescharacteristic
694D4—22no—
695D4—22no—
696D4—22no—
697D4—114no—
698D4—2216no—
699D4—222no—
700D4—222no—
701D4—222no—
702D4C4⋊C4×D1114yes—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—84no—
719C2×C4—112no—
720C2×C4—112no—
721C2×C4—112no—
722C2×C4—114no—
723C2×C4—114no—
724C2×C4—114no—
725C2×C4—114no—
726C2×C4—221no—
727C2×C4—221no—
728C2×C4—221no—
729C2×C4—221no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—221no—
733C2×C4—221no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—884no—
742C2×C4—884no—
743C2×C4—884no—
744C2×C4—884no—
745C2×C4C22×C4×D1111yescharacteristic
746C2×C4C2×D4×D1111yescharacteristic
747C2×C4C2×D4×D1111yescharacteristic
748C2×C4C2×Q8×D1111yescharacteristic
749C2×C4#41×D1111yescharacteristic
750C2×C4#41×D1111yescharacteristic
751C8—22no—
752C8—41no—
753C8—222no—
754C8—441no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—114no—
763C22—222no—
764C22—222no—
765C22—222no—
766C22—222no—
767C22—222no—
768C22—222no—
769C22—224no—
770C22—442no—
771C22—442no—
772C22—442no—
773C22—442no—
774C22—442no—
775C22—442no—
776C22—8816no—
777C22C4×D4×D1111yescharacteristic
778C22D11×#12011yescharacteristic
779C22D11×C22⋊Q811yescharacteristic
780C22#1062329311yescharacteristic
781C22#1062330011yescharacteristic
782C22#1062330511yescharacteristic
783C22#1062330611yescharacteristic
784C4—41no—
785C4—41no—
786C4—42no—
787C4—42no—
788C4—81no—
789C4—114no—
790C4—441no—
791C4—442no—
792C4—441no—
793C4—442no—
794C4—881no—
795C4C2×C4⋊C4×D1111yescharacteristic
796C4C4×D4×D1111yescharacteristic
797C4D11×C22⋊Q811yescharacteristic
798C4D11×#12311yescharacteristic
799C2—44no—
800C2—224no—
801C2—444no—
802C2D11×#38511yescharacteristic
803C2#1307744311yescharacteristic
804C2#1307744511yescharacteristic
805C2#1307788111yescharacteristic
806C2#1307788811yescharacteristic
807C2#1307844211yescharacteristic
808C2#1307844411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1864C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
cosocleC22×C4×C11C24
hypercenter#1864D11
hypocenterC11#20876
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. C2×#10622474C2semidirect
5. #13071238C2semidirect
6. #13068878C2semidirect
7. #13068877C2semidirect
8. #13068874C2semidirect
9. #13068866C2semidirect
10. #13068865C2semidirect
11. #13068862C2semidirect
12. #13068861C2semidirect
13. #13068331C2semidirect
14. #13068311C2semidirect
15. C11×#1864C2semidirect
33. C2×C11×#106C22semidirect
36. C11×#389C22semidirect
41. C2×#66882C22semidirect
43. #10622598C22semidirect
45. #10622586C22semidirect
48. C2×#66872C22semidirect
49. C2×#66871C22semidirect
50. #10622541C22semidirect
52. #10622383C4semidirect
56. C11×#340C22semidirect
57. C11×#336C22semidirect
58. #10622189C22semidirect
59. #10622188C22semidirect
60. #10622188C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
63. #10622162C22semidirect
117. C2×#4313C2×C4semidirect
125. #66945C2×C4semidirect
137. C11×#102C2×C4semidirect
140. #66896C2×C4semidirect
145. #66885C2×C4semidirect
148. #66873C2×C4semidirect
192. D4×D11C4⋊C4semidirect
269. #1864D11semidirect
387. C2×#106C2×D11semidirect
401. #389C2×D11semidirect
409. #340C2×D11semidirect
413. #336C2×D11semidirect
540. #102C4×D11semidirect
664. C11#20876semidirect

Maximal subgroups

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

subgroupindex
C2×#106230762
C2×#106224742
C2×#106223832
C2×D11×#1022
#130712382
#130688782
#130688772
#130688742
#130688662
#130688652
#130688622
#130688612
#130683312
#130683112
C11×#18642
#2087611