Finite Group Databasebeta

← #14786409

Subgroups — #14786409

Order 2816.

1500 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C22⋊Q8C211yesmaximal, characteristic
2C2×#10622475C211yesmaximal, characteristic, complemented
3C2×#10622418C211yesmaximal, characteristic, complemented
4D11×#380C211yesmaximal, characteristic
5#13069813C211yesmaximal, characteristic, complemented
6#13069812C211yesmaximal, characteristic, complemented
7#13069809C211yesmaximal, characteristic, complemented
8#13068922C211yesmaximal, characteristic, complemented
9#13068920C211yesmaximal, characteristic, complemented
10#13068810C211yesmaximal, characteristic, complemented
11#13068807C211yesmaximal, characteristic, complemented
12#13068549C211yesmaximal, characteristic, complemented
13#13068549C211yesmaximal, characteristic, complemented
14#13068525C211yesmaximal, characteristic
15C11×#2035C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×#66999C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21D11×C22⋊Q8—24no—
22D11×C22⋊Q8—24no—
23C2×#66950C2211yescharacteristic
24C2×#66949—21no—
25C2×C4⋊C4×D11—21no—
26C2×C4⋊C4×D11C2211yescharacteristic
27C2×C4⋊C4×D11C2211yescharacteristic
28C2×C4⋊C4×D11C2211yescharacteristic
29C2×C22⋊C4×D11—21no—
30C2×C22⋊C4×D11—21no—
31C2×#66931—21no—
32C2×C11×#106C2211yescharacteristic, complemented
33C2×C11×#103C2211yescharacteristic, complemented
34C2×C11×#103C2211yescharacteristic, complemented
35C2×C11×C22⋊C8C2211yescharacteristic
36C11×#380C2211yescharacteristic
37C2×#66899C2211yescharacteristic, complemented
38C2×#66899C2211yescharacteristic, complemented
39#10622825C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×(C2×D11)⋊C8C2211yescharacteristic
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×#66881C2211yescharacteristic, complemented
46C2×#66880C2211yescharacteristic, complemented
47C2×#66880C2211yescharacteristic, complemented
48#10622600C2211yescharacteristic
49#10622600C2211yescharacteristic
50C2×#66874C2211yescharacteristic, complemented
51C2×#66874C2211yescharacteristic, complemented
52C2×#66872C2211yescharacteristic, complemented
53C2×#66872C2211yescharacteristic, complemented
54#10622555—21no—
55#10622475—24no—
56#10622418—24no—
57#10622280—21no—
58D11×#95—21no—
59C11×#340C2211yescharacteristic, complemented
60#10622189C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63C24×D11D411yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×Dic11D411yescharacteristic
67C2×Q8×D11—22no—
68C2×Q8×D11—22no—
69C2×Q8×D11—22no—
70C2×Q8×D11—22no—
71C2×Q8×D11—41no—
72C2×Q8×D11—41no—
73C22×C4×D11—21no—
74C22×C4×D11—21no—
75C22×C4×D11—22no—
76C22×C4×D11—22no—
77C22×C4×D11—22no—
78C22×C4×D11—22no—
79C22×C4×D11—21no—
80C22×C4×D11—21no—
81C22×C4×D11—41no—
82C22×C4×D11—41no—
83C22×C4×D11D411yescharacteristic
84C22×C4×D11D411yescharacteristic
85C22×C4×D11C2311yescharacteristic
86C22×C4×D11C2311yescharacteristic
87C22×Dic22—21no—
88C22×Dic22C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C11×C22⋊Q8—22no—
92C11×C22⋊Q8—22no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C22⋊Dic11—21no—
100C2×C22⋊Dic11—21no—
101#66999—22no—
102#66999D414yes—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111#66977—22no—
112#66977—22no—
113C2×Dic11⋊C4—21no—
114C2×Dic11⋊C4—21no—
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120#66950—22no—
121#66950D414yes—
122#66949—28no—
123C4⋊C4×D11—28no—
124C4⋊C4×D11—22no—
125C4⋊C4×D11—22no—
126C4⋊C4×D11—22no—
127C4⋊C4×D11—22no—
128C4⋊C4×D11—41no—
129C4⋊C4×D11—41no—
130C22⋊C4×D11—28no—
131C22⋊C4×D11—44no—
132#66931—28no—
133C11×#106—22no—
134C11×#103—22no—
135C11×#103—41no—
136C11×C22⋊C8—41no—
137C11×#95—21no—
138#66899—22no—
139#66899—41no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C11⋊#95—21no—
143C22⋊(C11⋊C8)—41no—
144(C2×D11)⋊C8—22no—
145(C2×D11)⋊C8—22no—
146(C2×D11)⋊C8—22no—
147(C2×D11)⋊C8—22no—
148#66881—22no—
149#66880—22no—
150#66880—41no—
151#66874—22no—
152#66874—41no—
153#66872—22no—
154#66872—22no—
155#24003—111nomaximal, Sylow
156C24×C11C2×D411yescharacteristic
157C23×D11—22no—
158C23×D11—22no—
159C23×D11—22no—
160C23×D11—22no—
161C23×D11—41no—
162C23×D11—41no—
163C23×D11SD1614yes—
164C23×D11C2×D411yescharacteristic
165C23×D11C2×D411yescharacteristic
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11C2×D412yes—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
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×C11C2×D411yescharacteristic
183C22×C4×C11C2411yescharacteristic
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—41no—
191C22×Dic11C2×D411yescharacteristic
192C22×Dic11C2×D411yescharacteristic
193Q8×D11—44no—
194Q8×D11—44no—
195Q8×D11—44no—
196Q8×D11—44no—
197C2×C4×D11—24no—
198C2×C4×D11—24no—
199C2×C4×D11—22no—
200C2×C4×D11—22no—
201C2×C4×D11—22no—
202C2×C4×D11—22no—
203C2×C4×D11—21no—
204C2×C4×D11—21no—
205C2×C4×D11—21no—
206C2×C4×D11—21no—
207C2×C4×D11—21no—
208C2×C4×D11—21no—
209C2×C4×D11—21no—
210C2×C4×D11—21no—
211C2×C4×D11—41no—
212C2×C4×D11—41no—
213C2×C4×D11—42no—
214C2×C4×D11—42no—
215C2×C4×D11—42no—
216C2×C4×D11—42no—
217C2×C4×D11—44no—
218C2×C4×D11—44no—
219C2×C4×D11—44no—
220C2×C4×D11—44no—
221C2×C4×D11—42no—
222C2×C4×D11—42no—
223C2×C4×D11—42no—
224C2×C4×D11—42no—
225C2×C4×D11—42no—
226C2×C4×D11—42no—
227C2×C4×D11C2×D412yes—
228C2×C4×D11C2×D412yes—
229C2×C4×D11#4112yes—
230C2×C4×D11#4112yes—
231C2×Dic22—24no—
232C2×Dic22—21no—
233C2×Dic22—21no—
234C2×Dic22—21no—
235C2×Dic22—21no—
236C2×Dic22—21no—
237C2×Dic22—42no—
238C2×Dic22—42no—
239C2×Dic22C2×D412yes—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C11×C4⋊C4—24no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4C2×D412yes—
253C11×C22⋊C4—24no—
254C11×C22⋊C4—42no—
255C22⋊Dic11—24no—
256C22⋊Dic11—42no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—42no—
260(C2×D11)⋊C4—42no—
261C4⋊Dic11—24no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11C2×D412yes—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270Dic11⋊C4—24no—
271Dic11⋊C4—42no—
272Dic11⋊C4—42no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C22×C22⋊Q8—111no—
280C2×#483—111no—
281C2×#483—111no—
282C2×#380—111no—
283#2035—111no—
284#2035—111no—
285#2035—111no—
286#2035D1111yescharacteristic, complemented
287#1872—111no—
288#1872—111no—
289#1853—111no—
290#1853—111no—
291#1787—111no—
292#1787—111no—
293#1779—111no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11C2×SD1612yes—
301C23×C11C22×D411yescharacteristic
302C22×D11—21no—
303C22×D11—21no—
304C22×D11—21no—
305C22×D11—21no—
306C22×D11—21no—
307C22×D11—21no—
308C22×D11—21no—
309C22×D11—21no—
310C22×D11—28no—
311C22×D11—28no—
312C22×D11—44no—
313C22×D11—44no—
314C22×D11—44no—
315C22×D11—44no—
316C22×D11—44no—
317C22×D11#12012yes—
318C22×D11#12312yes—
319C22×D11C2×SD1612yes—
320C22×D11C2×SD1612yes—
321C22×D11#13712yes—
322C22×D11#13712yes—
323Q8×C11—22no—
324Q8×C11—22no—
325Q8×C11—41no—
326Q8×C11—41no—
327C2×C4×C11—21no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C22×D411yescharacteristic
348C2×C4×C11C2×#4111yescharacteristic
349C2×C4×C11C2×#4111yescharacteristic
350C2×C4×C11H(5,𝔽2)11yescharacteristic
351C2×C4×C11H(5,𝔽2)11yescharacteristic
352C2×Dic11—21no—
353C2×Dic11—21no—
354C2×Dic11—21no—
355C2×Dic11—21no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—44no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C2×Dic11#12012yes—
370C2×Dic11#12312yes—
371C4×D11—22no—
372C4×D11—22no—
373C4×D11—22no—
374C4×D11—22no—
375C4×D11—22no—
376C4×D11—22no—
377C4×D11—22no—
378C4×D11—22no—
379C4×D11—44no—
380C4×D11—44no—
381C4×D11—48no—
382C4×D11—48no—
383C4×D11—84no—
384C4×D11—84no—
385Dic22—22no—
386Dic22—22no—
387Dic22—48no—
388Dic22—41no—
389Dic22—41no—
390C8×C11—41no—
391C8×C11—41no—
392C11⋊C8—41no—
393C11⋊C8—41no—
394C23×Q8—111no—
395C24×C4—111no—
396C2×C22⋊Q8—111no—
397C2×C22⋊Q8—111no—
398C2×C22⋊Q8—111no—
399C2×C22⋊Q8—221no—
400C2×C22⋊Q8—221no—
401C2×C22⋊Q8—224no—
402C2×C22⋊Q8—224no—
403C2×C22⋊Q8C2×D1111yescharacteristic
404C22×C4⋊C4—111no—
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
407C22×C4⋊C4—221no—
408C22×C22⋊C4—221no—
409C22×C22⋊C4—221no—
410#483—224no—
411#483—224no—
412C2×#106—111no—
413C2×#106—111no—
414C2×#106—111no—
415C2×#106C2×D1111yescharacteristic, complemented
416C2×#103—111no—
417C2×#103—111no—
418C2×#103—111no—
419C2×#103—111no—
420C2×#103—111no—
421C2×#103—111no—
422C2×#103C2×D1111yescharacteristic, complemented
423C2×#103C2×D1111yescharacteristic, complemented
424C2×C22⋊C8—111no—
425C2×C22⋊C8—111no—
426C2×C22⋊C8—111no—
427C2×C22⋊C8—111no—
428C2×C22⋊C8—111no—
429C2×C22⋊C8C2×D1111yescharacteristic
430#380—111no—
431#380—111no—
432#380—111no—
433#380—221no—
434#380—221no—
435#380C2×D1111yescharacteristic
436C2×#95—221no—
437#340—111no—
438#340—111no—
439#340—111no—
440#340C2×D1111yescharacteristic, complemented
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—41no—
445C22×C11—41no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11C2×#12011yescharacteristic
449C22×C11C2×#12311yescharacteristic
450C22×C11#53411yescharacteristic
451C22×C11C22×SD1611yescharacteristic
452C22×C11C2×#13711yescharacteristic
453C22×C11C2×#13711yescharacteristic
454C22×C11#57511yescharacteristic
455C2×D11—22no—
456C2×D11—22no—
457C2×D11—22no—
458C2×D11—22no—
459C2×D11—22no—
460C2×D11—22no—
461C2×D11—22no—
462C2×D11—22no—
463C2×D11—22no—
464C2×D11—22no—
465C2×D11—22no—
466C2×D11—22no—
467C2×D11—416no—
468C2×D11#44814yes—
469C2×D11#48314yescomplemented
470C4×C11—41no—
471C4×C11—42no—
472C4×C11—42no—
473C4×C11—81no—
474C4×C11—81no—
475C4×C11#54611yescharacteristic
476C4×C11#54611yescharacteristic
477C4×C11#54611yescharacteristic
478C4×C11#54611yescharacteristic
479Dic11—22no—
480Dic11—22no—
481Dic11—42no—
482Dic11—42no—
483Dic11—81no—
484Dic11—81no—
485C25—111no—
486C22×Q8—111no—
487C22×Q8—221no—
488C22×Q8—222no—
489C22×Q8—222no—
490C22×Q8—222no—
491C22×Q8—222no—
492C22×Q8—441no—
493C22×Q8—441no—
494C22×Q8C22×D1111yescharacteristic
495C23×C4—111no—
496C23×C4—111no—
497C23×C4—111no—
498C23×C4—111no—
499C23×C4—111no—
500C23×C4—222no—
501C23×C4—222no—
502C23×C4—222no—
503C23×C4—222no—
504C23×C4—221no—
505C23×C4—221no—
506C23×C4—221no—
507C23×C4—221no—
508C23×C4—441no—
509C23×C4—441no—
510C23×C4C22×D1111yescharacteristic
511C22×C8—111no—
512C22×C8—111no—
513C22×C8C22×D1111yescharacteristic
514C22×C8C22×D1111yescharacteristic
515C22⋊Q8—22no—
516C22⋊Q8—22no—
517C22⋊Q8—114no—
518C22⋊Q8—114no—
519C22⋊Q8—228no—
520C22⋊Q8—222no—
521C22⋊Q8—228no—
522C22⋊Q8—222no—
523C22⋊Q8—222no—
524C22⋊Q8—222no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4—111no—
529C2×C4⋊C4—222no—
530C2×C4⋊C4—228no—
531C2×C4⋊C4—222no—
532C2×C4⋊C4—222no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4—221no—
535C2×C4⋊C4—221no—
536C2×C4⋊C4—221no—
537C2×C4⋊C4—222no—
538C2×C4⋊C4—221no—
539C2×C4⋊C4—221no—
540C2×C4⋊C4—441no—
541C2×C4⋊C4—441no—
542C2×C4⋊C4C22×D1111yescharacteristic
543C2×C4⋊C4C22×D1111yescharacteristic
544C2×C4⋊C4C22×D1111yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—228no—
548C2×C22⋊C4—221no—
549C2×C22⋊C4—221no—
550C2×C22⋊C4—221no—
551C2×C22⋊C4—221no—
552C2×C22⋊C4—221no—
553C2×C22⋊C4—221no—
554C2×C22⋊C4—444no—
555#106—22no—
556#106—222no—
557#106—222no—
558#106—222no—
559#103—22no—
560#103—41no—
561#103—222no—
562#103—222no—
563#103—222no—
564#103—441no—
565#103—441no—
566#103—441no—
567C22⋊C8—41no—
568C22⋊C8—222no—
569C22⋊C8—222no—
570C22⋊C8—222no—
571C22⋊C8—222no—
572C22⋊C8—441no—
573#95—21no—
574#95—221no—
575#95—221no—
576#95—221no—
577C2×C11—42no—
578C2×C11#240511yescharacteristic
579C2×C11C2×#44811yescharacteristic
580C2×C11#300711yescharacteristic
581C2×C11C2×#48311yescharacteristic
582C2×C11#309511yescharacteristic
583C2×C11#318711yescharacteristic
584C2×C11#319511yescharacteristic
585D11—24no—
586D11—24no—
587C24—111no—
588C24—111no—
589C24—114no—
590C24—222no—
591C24—222no—
592C24—222no—
593C24—222no—
594C24—441no—
595C24—441no—
596C24D4×D1111yescharacteristic
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—112no—
603C2×Q8—224no—
604C2×Q8—221no—
605C2×Q8—221no—
606C2×Q8—221no—
607C2×Q8—221no—
608C2×Q8—221no—
609C2×Q8—442no—
610C2×Q8—442no—
611C2×Q8—444no—
612C2×Q8—444no—
613C2×Q8—444no—
614C2×Q8—444no—
615C2×Q8D4×D1112yes—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—111no—
627C22×C4—111no—
628C22×C4—112no—
629C22×C4—112no—
630C22×C4—112no—
631C22×C4—112no—
632C22×C4—222no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—222no—
636C22×C4—224no—
637C22×C4—224no—
638C22×C4—222no—
639C22×C4—222no—
640C22×C4—221no—
641C22×C4—221no—
642C22×C4—221no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—221no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—221no—
650C22×C4—221no—
651C22×C4—221no—
652C22×C4—441no—
653C22×C4—441no—
654C22×C4—444no—
655C22×C4—444no—
656C22×C4—444no—
657C22×C4—444no—
658C22×C4—442no—
659C22×C4—442no—
660C22×C4—442no—
661C22×C4—442no—
662C22×C4—442no—
663C22×C4—442no—
664C22×C4—442no—
665C22×C4—442no—
666C22×C4—442no—
667C22×C4—442no—
668C22×C4—441no—
669C22×C4D4×D1111yescharacteristic
670C22×C4C23×D1111yescharacteristic
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—221no—
678C2×C8—221no—
679C2×C8—221no—
680C2×C8—221no—
681C2×C8—221no—
682C2×C8—221no—
683C4⋊C4—24no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—112no—
690C4⋊C4—224no—
691C4⋊C4—224no—
692C4⋊C4—224no—
693C4⋊C4—224no—
694C4⋊C4—221no—
695C4⋊C4—221no—
696C4⋊C4—221no—
697C4⋊C4—221no—
698C4⋊C4—221no—
699C4⋊C4—442no—
700C4⋊C4—442no—
701C4⋊C4D4×D1112yes—
702C22⋊C4—24no—
703C22⋊C4—42no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C22⋊C4—442no—
708C22⋊C4—442no—
709C22⋊C4—442no—
710C11#2400311yescharacteristic, complemented, Sylow
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—112no—
718C23—112no—
719C23—112no—
720C23—112no—
721C23—112no—
722C23—112no—
723C23—228no—
724C23—228no—
725C23—221no—
726C23—221no—
727C23—221no—
728C23—221no—
729C23—221no—
730C23—221no—
731C23—221no—
732C23—221no—
733C23—444no—
734C23—444no—
735C23—444no—
736C23—444no—
737C23—444no—
738C23SD16×D1112yes—
739C23C2×D4×D1111yescharacteristic
740Q8—22no—
741Q8—22no—
742Q8—41no—
743Q8—41no—
744Q8—222no—
745Q8—222no—
746Q8—448no—
747Q8—441no—
748Q8—441no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—112no—
769C2×C4—112no—
770C2×C4—221no—
771C2×C4—221no—
772C2×C4—221no—
773C2×C4—221no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—222no—
784C2×C4—444no—
785C2×C4—444no—
786C2×C4—448no—
787C2×C4—448no—
788C2×C4—444no—
789C2×C4—441no—
790C2×C4—441no—
791C2×C4—441no—
792C2×C4—441no—
793C2×C4—441no—
794C2×C4—441no—
795C2×C4—441no—
796C2×C4—441no—
797C2×C4—441no—
798C2×C4—441no—
799C2×C4—884no—
800C2×C4—884no—
801C2×C4C2×D4×D1111yescharacteristic
802C2×C4C2×D4×D1111yescharacteristic
803C2×C4#6703711yescharacteristic
804C2×C4#41×D1111yescharacteristic
805C2×C4#41×D1111yescharacteristic
806C2×C4#6704211yescharacteristic
807C8—41no—
808C8—41no—
809C8—441no—
810C8—441no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—114no—
819C22—114no—
820C22—222no—
821C22—222no—
822C22—222no—
823C22—222no—
824C22—222no—
825C22—222no—
826C22—222no—
827C22—222no—
828C22—222no—
829C22—222no—
830C22—222no—
831C22—222no—
832C22—4416no—
833C22D11×#12011yescharacteristic
834C22#1062313611yescharacteristic
835C22D11×#12311yescharacteristic
836C22C2×SD16×D1111yescharacteristic
837C22#1062329911yescharacteristic
838C22D11×#13711yescharacteristic
839C22D11×#13711yescharacteristic
840C4—41no—
841C4—42no—
842C4—42no—
843C4—81no—
844C4—81no—
845C4—222no—
846C4—222no—
847C4—442no—
848C4—442no—
849C4—881no—
850C4—881no—
851C4#1062314111yescharacteristic
852C4#1062314311yescharacteristic
853C4#1062318511yescharacteristic
854C4#1062320711yescharacteristic
855C2—42no—
856C2—224no—
857C2—224no—
858C2#1307193811yescharacteristic
859C2D11×#44811yescharacteristic
860C2#1307787311yescharacteristic
861C2D11×#48311yescharacteristic
862C2#1307856311yescharacteristic
863C2#1307936811yescharacteristic
864C2#1307943611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2035C2
socleC23×C11C22×D4
prime radicalC24×D11D4
hypercenter#2035D11
hypocenterC11#24003
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2035

Complements

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

NH ≅ G/Ntype
2. C2×#10622475C2semidirect
3. C2×#10622418C2semidirect
5. #13069813C2semidirect
6. #13069812C2semidirect
7. #13069809C2semidirect
8. #13068922C2semidirect
9. #13068920C2semidirect
10. #13068810C2semidirect
11. #13068807C2semidirect
12. #13068549C2semidirect
13. #13068549C2semidirect
15. C11×#2035C2semidirect
32. C2×C11×#106C22semidirect
33. C2×C11×#103C22semidirect
34. C2×C11×#103C22semidirect
37. C2×#66899C22semidirect
38. C2×#66899C22semidirect
45. C2×#66881C22semidirect
46. C2×#66880C22semidirect
47. C2×#66880C22semidirect
50. C2×#66874C22semidirect
51. C2×#66874C22semidirect
52. C2×#66872C22semidirect
53. C2×#66872C22semidirect
59. C11×#340C22semidirect
60. #10622189C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
286. #2035D11semidirect
415. C2×#106C2×D11semidirect
422. C2×#103C2×D11semidirect
423. C2×#103C2×D11semidirect
440. #340C2×D11semidirect
469. C2×D11#483semidirect
710. C11#24003semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C22⋊Q82
C2×#106224752
C2×#106224182
D11×#3802
#130698132
#130698122
#130698092
#130689222
#130689202
#130688102
#130688072
#130685492
#130685252
C11×#20352
#2400311