Finite Group Databasebeta

← #14769322

Subgroups — #14769322

Order 2816.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623081C211yesmaximal, characteristic
2C2×#10622624C211yesmaximal, characteristic, complemented
3C2×#10622614C211yesmaximal, characteristic, complemented
4C2×#10622615C211yesmaximal, characteristic, complemented
5#13069548C211yesmaximal, characteristic, complemented
6#13069430C211yesmaximal, characteristic, complemented
7#13069047C211yesmaximal, characteristic, complemented
8#13069042C211yesmaximal, characteristic, complemented
9#13068938C211yesmaximal, characteristic, complemented
10#13068928C211yesmaximal, characteristic, complemented
11#13068613C211yesmaximal, characteristic, complemented
12#13068554C211yesmaximal, characteristic, complemented
13#13068546C211yesmaximal, characteristic, complemented
14#13068444C211yesmaximal, characteristic, complemented
15C11×#2354C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic, complemented
21C2×#66990—21no—
22C2×#66983C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C23×C11⋊C8C2211yescharacteristic, complemented
26#10623081—24no—
27#10623081C418yescomplemented
28C2×#66947—21no—
29C2×#66937—21no—
30C2×C22⋊C4×D11—21no—
31C2×#66928C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C11×#390—21no—
34C11×#388—21no—
35C11×#388—21no—
36C11×#384C2211yescharacteristic, complemented
37C11×#380C2211yescharacteristic
38C11×#380C2211yescharacteristic, complemented
39C4×C11×C4⋊C4—21no—
40C4×C11×C4⋊C4C2211yescharacteristic, complemented
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
43#10622624—24no—
44#10622615—24no—
45#10622614—24no—
46C2×#66874C2211yescharacteristic, complemented
47C2×#66874C2211yescharacteristic, complemented
48C2×#66874C2211yescharacteristic, complemented
49C2×#66874C2211yescharacteristic, complemented
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×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—21no—
69C22×C22⋊D11—21no—
70C2×#4339—22no—
71C2×#4339—22no—
72C2×#4339—22no—
73C2×#4339—41no—
74C2×#4339—41no—
75C2×#4339C2×C414yes—
76C22×D44—22no—
77C22×D44—22no—
78C22×D44—21no—
79C22×D44—22no—
80C22×D44—41no—
81C22×D44—41no—
82C22×D44C2×C414yes—
83C22×D44C2311yescharacteristic
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×Dic22C2311yescharacteristic
88C4×D4×C11C2×C414yes—
89C4×D4×C11D414yes—
90C11×#117—22no—
91C11×#117—22no—
92C11×#117—41no—
93C11×#117—41no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4D411yescharacteristic
106C2×C11×C22⋊C4D411yescharacteristic
107C2×C42×C11—21no—
108C2×C42×C11—21no—
109C2×C42×C11—21no—
110C2×C42×C11C2311yescharacteristic
111C2×C22⋊Dic11—21no—
112#66990—28no—
113#66983—22no—
114#66983C2×C414yes—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×C4⋊Dic11C2311yescharacteristic
120#66977—22no—
121#66977C2×C414yes—
122C2×Dic11⋊C4—21no—
123C2×#4318—22no—
124C2×#4318—22no—
125C2×#4318—41no—
126C22×C11⋊C8—22no—
127C22×C11⋊C8—22no—
128C22×C11⋊C8—41no—
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133#66947—28no—
134#66937—28no—
135C22⋊C4×D11—28no—
136#66928—22no—
137#66928C2×C414yes—
138C4×D44—22no—
139C4×D44C2×C414yes—
140C11×#95—21no—
141C11×#95—21no—
142C11×#95—21no—
143C22⋊(C11⋊C8)—22no—
144C22⋊(C11⋊C8)—22no—
145#66874—22no—
146#66874—22no—
147#66874—41no—
148#66874—41no—
149#66873—22no—
150#66873—22no—
151#66873—22no—
152#66873—22no—
153#66873—22no—
154#66873—41no—
155#66873—41no—
156#66873D414yescomplemented
157C4⋊(C11⋊C8)—22no—
158#66867—22no—
159#22424—111nomaximal, Sylow
160C24×C11C2×D411yescharacteristic
161C24×C11C2×D411yescharacteristic
162C23×D11—21no—
163C23×D11—21no—
164C23×D11—24no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—42no—
168C23×D11—42no—
169C23×D11—81no—
170C23×D11—81no—
171C2×D4×C11—41no—
172C2×D4×C11—41no—
173C2×D4×C11C22⋊C414yes—
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×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11C22×C412yes—
187C22×C4×C11C22×C412yes—
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D412yes—
193C22×C4×C11C2×D412yes—
194C22×C4×C11C2411yescharacteristic
195C2×C22⋊D11—24no—
196C2×C22⋊D11—24no—
197C2×C22⋊D11—42no—
198C2×C22⋊D11—42no—
199C2×C22⋊D11—81no—
200C2×C22⋊D11—81no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203#4339—28no—
204#4339—44no—
205#4339—44no—
206#4339—44no—
207C2×D44—28no—
208C2×D44—24no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44—21no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—42no—
218C2×D44—42no—
219C2×D44—44no—
220C2×D44—44no—
221C2×D44—44no—
222C2×D44C22×C412yes—
223C2×D44C22×C412yes—
224C2×D44C2×D412yes—
225C2×D44#4112yes—
226C2×C4×D11—24no—
227C2×C4×D11—24no—
228C2×C4×D11—42no—
229C2×C4×D11—42no—
230C2×C4×D11—81no—
231C2×C4×D11—81no—
232C2×Dic22—21no—
233C2×Dic22—21no—
234C2×Dic22—21no—
235C2×Dic22—21no—
236C2×Dic22—21no—
237C2×Dic22C22×C412yes—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4—42no—
246C11×C4⋊C4—81no—
247C11×C4⋊C4C22⋊C414yes—
248C11×C4⋊C4C2×D412yes—
249C11×C22⋊C4—42no—
250C11×C22⋊C4—42no—
251C11×C22⋊C4—81no—
252C11×C22⋊C4—81no—
253C11×C22⋊C4C22⋊C414yes—
254C11×C22⋊C4C22⋊C414yes—
255C42×C11—42no—
256C42×C11—42no—
257C42×C11—42no—
258C42×C11C22×C412yes—
259C42×C11C2×D412yes—
260C22⋊Dic11—24no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265C4⋊Dic11—21no—
266C4⋊Dic11C22×C412yes—
267Dic11⋊C4—24no—
268#4318—44no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
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—44no—
281C2×C11⋊C8C2×D412yes—
282C2×#546—111no—
283C2×#435—111no—
284C2×#418—111no—
285C2×#416—111no—
286#2354D1111yescharacteristic, complemented
287#1983—111no—
288#1959—111no—
289#1894—111no—
290#1893—111no—
291#1875—111no—
292#1873—111no—
293#1802—111no—
294#1788—111no—
295#1786—111no—
296#1762—111no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11C2×C22⋊C412yes—
310C23×C11C2×C22⋊C412yes—
311C23×C11C22×D411yescharacteristic
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—48no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—41no—
320C22×D11—41no—
321C22×D11—48no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11—84no—
331C22×D11—84no—
332C22×D11—84no—
333D4×C11—44no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
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—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11C2×C22⋊C412yes—
363C2×C4×C11C2×C22⋊C412yes—
364C2×C4×C11C2×C22⋊C412yes—
365C2×C4×C11C2×C22⋊C412yes—
366C2×C4×C11C23×C411yescharacteristic
367C2×C4×C11C22×D411yescharacteristic
368C2×C4×C11C22×D411yescharacteristic
369C2×C4×C11C2×#4111yescharacteristic
370C2×C4×C11H(5,𝔽2)11yescharacteristic
371C2×C4×C11H(5,𝔽2)11yescharacteristic
372C22⋊D11—48no—
373C22⋊D11—84no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380D44—22no—
381D44—22no—
382D44—22no—
383D44—22no—
384D44—22no—
385D44—48no—
386D44—41no—
387D44—41no—
388D44C4×D414yes—
389C4×D11—48no—
390C4×D11—84no—
391Dic22—22no—
392Dic22—22no—
393Dic22—41no—
394Dic22—41no—
395C11⋊C8—22no—
396C11⋊C8—41no—
397C11⋊C8—41no—
398C11⋊C8—41no—
399C22×#41—111no—
400C23×D4—111no—
401C22×M16—111no—
402C23×C8—111no—
403#546—118no—
404#546—224no—
405C2×#124—111no—
406C2×#123—221no—
407C2×C22⋊Q8—111no—
408C2×#121—111no—
409C2×#121—221no—
410C2×#120—221no—
411C2×C4×D4—111no—
412C2×C4×D4C2×D1111yescharacteristic
413C2×#117C2×D1111yescharacteristic
414C2×#117C2×D1111yescharacteristic, complemented
415C22×C22⋊C4—221no—
416#435—224no—
417C2×C4⋊C8—111no—
418#418—224no—
419#416—224no—
420C2×#103—111no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#103—111no—
424C2×#102—111no—
425C2×#102—111no—
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102—111no—
432C2×C22⋊C8—111no—
433C2×C22⋊C8—111no—
434C2×#97—111no—
435#390—21no—
436#388—21no—
437#388—21no—
438#384C2×D1111yescharacteristic, complemented
439#380C2×D1111yescharacteristic
440#380C2×D1111yescharacteristic, complemented
441C4×C4⋊C4—21no—
442C4×C4⋊C4C2×D1111yescharacteristic, complemented
443#340—111no—
444#340—111no—
445#340—111no—
446#340—111no—
447C22×C11—22no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11—41no—
458C22×C11—41no—
459C22×C11—41no—
460C22×C11—41no—
461C22×C11C22×C22⋊C411yescharacteristic
462C22×C11D4211yescharacteristic
463C22×C11#54611yescharacteristic
464C22×C11#57511yescharacteristic
465C22×C11#57511yescharacteristic
466C22×C11#57611yescharacteristic
467C22×C11#57711yescharacteristic
468C2×D11—24no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—816no—
479C2×D11—81no—
480C2×D11—81no—
481C2×D11—81no—
482C2×D11—81no—
483C4×C11—22no—
484C4×C11—22no—
485C4×C11—22no—
486C4×C11—22no—
487C4×C11—42no—
488C4×C11—81no—
489C4×C11—81no—
490C4×C11—81no—
491C4×C11C2×C4×D411yescharacteristic
492C4×C11#51811yescharacteristic
493C4×C11D4211yescharacteristic
494C4×C11#54611yescharacteristic
495Dic11—42no—
496Dic11—42no—
497C25—221no—
498C2×#41—114no—
499C2×#41—222no—
500C2×#41—222no—
501C2×#41—222no—
502C2×#41—441no—
503C2×#41—441no—
504C22×Q8—111no—
505C22×D4—114no—
506C22×D4—111no—
507C22×D4—111no—
508C22×D4—222no—
509C22×D4—222no—
510C22×D4—221no—
511C22×D4—221no—
512C22×D4—222no—
513C22×D4—221no—
514C22×D4—441no—
515C22×D4—441no—
516C22×D4C22⋊D1111yescharacteristic
517C23×C4—221no—
518C23×C4—221no—
519C23×C4C22×D1111yescharacteristic
520C23×C4C22×D1111yescharacteristic
521C2×M16—222no—
522C2×M16—222no—
523C2×M16—441no—
524C22×C8—111no—
525C22×C8—111no—
526C22×C8—111no—
527C22×C8—111no—
528C22×C8—222no—
529C22×C8—222no—
530C22×C8—441no—
531#124—114no—
532#124—222no—
533#123—228no—
534C22⋊Q8—114no—
535C22⋊Q8—222no—
536#121—114no—
537#121—222no—
538#121—228no—
539#120—228no—
540C4×D4—114no—
541C4×D4—222no—
542C4×D4C4×D1114yes—
543C4×D4D4414yes—
544#117—22no—
545#117—22no—
546#117—41no—
547#117—41no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—221no—
552C2×C4⋊C4C22⋊D1111yescharacteristic
553C2×C4⋊C4C22×D1111yescharacteristic
554C2×C4⋊C4C22×D1111yescharacteristic
555C2×C4⋊C4C22×D1111yescharacteristic
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—228no—
567C2×C22⋊C4C22⋊D1111yescharacteristic
568C2×C22⋊C4C22⋊D1111yescharacteristic
569C2×C42—21no—
570C2×C42—21no—
571C2×C42—21no—
572C2×C42C22×D1111yescharacteristic
573C4⋊C8—222no—
574#103—222no—
575#103—222no—
576#103—441no—
577#103—441no—
578#102—114no—
579#102—222no—
580#102—222no—
581#102—222no—
582#102—222no—
583#102—222no—
584#102—441no—
585#102—441no—
586C22⋊C8—222no—
587C22⋊C8—222no—
588#97—222no—
589#95—21no—
590#95—21no—
591#95—21no—
592C2×C11—42no—
593C2×C11—42no—
594C2×C11D4×C22⋊C411yescharacteristic
595C2×C11#289611yescharacteristic
596C2×C11#289711yescharacteristic
597C2×C11#326711yescharacteristic
598C2×C11#326811yescharacteristic
599C2×C11#331111yescharacteristic
600C2×C11#331911yescharacteristic
601D11—44no—
602D11—82no—
603C24—221no—
604C24—221no—
605C24—224no—
606C24—442no—
607C24—442no—
608C24—442no—
609C24—442no—
610C24—881no—
611C24—881no—
612C24C2×C22⋊D1111yescharacteristic
613C24C2×C22⋊D1111yescharacteristic
614#41—228no—
615#41—444no—
616#41—444no—
617#41—444no—
618C2×Q8—112no—
619C2×Q8—221no—
620C2×Q8—221no—
621C2×Q8—221no—
622C2×Q8—221no—
623C2×Q8—221no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—112no—
627C2×D4—112no—
628C2×D4—112no—
629C2×D4—112no—
630C2×D4—228no—
631C2×D4—224no—
632C2×D4—224no—
633C2×D4—224no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—221no—
642C2×D4—444no—
643C2×D4—444no—
644C2×D4—444no—
645C2×D4—442no—
646C2×D4—442no—
647C2×D4—442no—
648C2×D4—442no—
649C2×D4—881no—
650C2×D4—881no—
651C2×D4(C2×D11)⋊C414yes—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—221no—
665C22×C4—221no—
666C22×C4—224no—
667C22×C4—224no—
668C22×C4—442no—
669C22×C4—442no—
670C22×C4—881no—
671C22×C4—881no—
672C22×C4C2×C4×D1112yes—
673C22×C4C2×C4×D1112yes—
674C22×C4C2×D4412yes—
675C22×C4C2×D4412yes—
676C22×C4C2×C22⋊D1111yescharacteristic
677C22×C4C2×C22⋊D1111yescharacteristic
678C22×C4C2×C22⋊D1111yescharacteristic
679C22×C4C2×C22⋊D1111yescharacteristic
680C22×C4C23×D1111yescharacteristic
681M16—444no—
682C2×C8—112no—
683C2×C8—221no—
684C2×C8—221no—
685C2×C8—221no—
686C2×C8—221no—
687C2×C8—221no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8—444no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—42no—
703C4⋊C4—81no—
704C4⋊C4—112no—
705C4⋊C4—224no—
706C4⋊C4—221no—
707C4⋊C4(C2×D11)⋊C414yes—
708C4⋊C4D4×D1112yes—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—81no—
712C22⋊C4—81no—
713C22⋊C4—224no—
714C22⋊C4—224no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4(C2×D11)⋊C414yes—
719C22⋊C4(C2×D11)⋊C414yes—
720C42—42no—
721C42—42no—
722C42—42no—
723C42C2×C4×D1112yes—
724C42C2×D4412yes—
725C11#2242411yescharacteristic, complemented, Sylow
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—448no—
743C23—448no—
744C23—441no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23—441no—
749C23—441no—
750C23—441no—
751C23—441no—
752C23—441no—
753C23—441no—
754C23—884no—
755C23—884no—
756C23—884no—
757C23—884no—
758C23—884no—
759C23C2×(C2×D11)⋊C412yes—
760C23C2×(C2×D11)⋊C412yes—
761C23C22×C22⋊D1111yescharacteristic
762Q8—222no—
763Q8—222no—
764Q8—441no—
765Q8—441no—
766D4—44no—
767D4—114no—
768D4—222no—
769D4—222no—
770D4—222no—
771D4—222no—
772D4—222no—
773D4—448no—
774D4—448no—
775D4—441no—
776D4—441no—
777D4—884no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
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—222no—
807C2×C4—222no—
808C2×C4—448no—
809C2×C4—441no—
810C2×C4—441no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—884no—
814C2×C4C2×(C2×D11)⋊C412yes—
815C2×C4C2×(C2×D11)⋊C412yes—
816C2×C4C2×(C2×D11)⋊C412yes—
817C2×C4C2×(C2×D11)⋊C412yes—
818C2×C4C22×C4×D1111yescharacteristic
819C2×C4C22×D4411yescharacteristic
820C2×C4C2×D4×D1111yescharacteristic
821C2×C4#6703711yescharacteristic
822C2×C4#41×D1111yescharacteristic
823C2×C4#6704211yescharacteristic
824C8—222no—
825C8—441no—
826C8—441no—
827C8—441no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—224no—
843C22—442no—
844C22—442no—
845C22—442no—
846C22—442no—
847C22—442no—
848C22—442no—
849C22—442no—
850C22—442no—
851C22—442no—
852C22—8816no—
853C22—881no—
854C22—881no—
855C22—881no—
856C22—881no—
857C22C22×(C2×D11)⋊C411yescharacteristic
858C22D4×C22⋊D1111yescharacteristic
859C22#1062335311yescharacteristic
860C22#1062335311yescharacteristic
861C22#1062336011yescharacteristic
862C22#1062336611yescharacteristic
863C22#1062336811yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—81no—
870C4—81no—
871C4—81no—
872C4—442no—
873C4—442no—
874C4C4×D4×D1111yescharacteristic
875C4#1062307611yescharacteristic
876C4D4×D4411yescharacteristic
877C4#1062308511yescharacteristic
878C2—42no—
879C2—42no—
880C2—444no—
881C2—882no—
882C2D4×(C2×D11)⋊C411yescharacteristic
883C2#1307713311yescharacteristic
884C2#1307713911yescharacteristic
885C2#1308014211yescharacteristic
886C2#1308015711yescharacteristic
887C2#1308064611yescharacteristic
888C2#1308076611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2354C2
socleC23×C11C22×D4
prime radicalC2×#10623081C2
cosocleC22×C4×C11C24
hypercenter#2354D11
hypocenterC11#22424
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. C2×#10622624C2semidirect
3. C2×#10622614C2semidirect
4. C2×#10622615C2semidirect
5. #13069548C2semidirect
6. #13069430C2semidirect
7. #13069047C2semidirect
8. #13069042C2semidirect
9. #13068938C2semidirect
10. #13068928C2semidirect
11. #13068613C2semidirect
12. #13068554C2semidirect
13. #13068546C2semidirect
14. #13068444C2semidirect
15. C11×#2354C2semidirect
20. C2×C11×#117C22semidirect
25. C23×C11⋊C8C22semidirect
27. #10623081C4semidirect
36. C11×#384C22semidirect
38. C11×#380C22semidirect
40. C4×C11×C4⋊C4C22semidirect
42. C2×C22⋊(C11⋊C8)C22semidirect
46. C2×#66874C22semidirect
47. C2×#66874C22semidirect
48. C2×#66874C22semidirect
49. C2×#66874C22semidirect
58. C2×C4⋊(C11⋊C8)C22semidirect
59. C2×#66867C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
156. #66873D4semidirect
286. #2354D11semidirect
414. C2×#117C2×D11semidirect
438. #384C2×D11semidirect
440. #380C2×D11semidirect
442. C4×C4⋊C4C2×D11semidirect
725. C11#22424semidirect

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×#106226142
C2×#106226152
#130695482
#130694302
#130690472
#130690422
#130689382
#130689282
#130686132
#130685542
#130685462
#130684442
C11×#23542
#2242411