Finite Group Databasebeta

← #14769368

Subgroups — #14769368

Order 2816.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623143C211yesmaximal, characteristic
2C2×#10622741C211yesmaximal, characteristic, complemented
3C2×#10622746C211yesmaximal, characteristic, complemented
4C2×#10622383C211yesmaximal, characteristic, complemented
5#13071547C211yesmaximal, characteristic, complemented
6#13069547C211yesmaximal, characteristic, complemented
7#13069426C211yesmaximal, characteristic, complemented
8#13069048C211yesmaximal, characteristic, complemented
9#13068934C211yesmaximal, characteristic, complemented
10#13068927C211yesmaximal, characteristic, complemented
11#13068625C211yesmaximal, characteristic, complemented
12#13068554C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068430C211yesmaximal, characteristic, complemented
15C11×#1895C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic, complemented
19C2×C11×#121C2211yescharacteristic
20C2×#66991—21no—
21C2×#66990—21no—
22C2×#66989C2211yescharacteristic
23C2×C4×C22⋊D11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic, complemented
25C22×#4313C2211yescharacteristic
26#10623143—24no—
27#10623143C418yescomplemented
28C2×#66950C2211yescharacteristic
29C2×#66946C2211yescharacteristic
30C2×#66945C2211yescharacteristic
31C2×#66936—21no—
32C2×C22⋊C4×D11—21no—
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C11×#380C2211yescharacteristic, complemented
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
39#10622746—24no—
40#10622741—24no—
41C2×#66885C2211yescharacteristic
42C2×#66885C2211yescharacteristic
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×#66880C2211yescharacteristic, complemented
45C2×#66880C2211yescharacteristic, complemented
46C2×Dic11⋊C8C2211yescharacteristic, complemented
47C2×C8×Dic11C2211yescharacteristic, complemented
48#10622600C2211yescharacteristic
49#10622590C2211yescharacteristic, complemented
50C4⋊C4×Dic11C2211yescharacteristic, complemented
51C2×#66874C2211yescharacteristic, complemented
52C2×#66874C2211yescharacteristic, complemented
53C2×#66873C2211yescharacteristic
54C2×#66873C2211yescharacteristic
55#10622571—21no—
56C22⋊C4×Dic11—21no—
57#10622383—24no—
58#10622283—21no—
59#10622268—21no—
60C11×#340C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×D4×C11—21no—
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—21no—
69C22×C22⋊D11—21no—
70C22×C22⋊D11D411yescharacteristic
71C23×Dic11—21no—
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×C414yes—
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×C4×D11C2311yescharacteristic
88C22×Dic22C2311yescharacteristic
89C2×C11×M16—22no—
90C2×C11×M16—22no—
91C2×C11×M16—41no—
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C11×#121—22no—
95C11×#121C2×C414yes—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11D411yescharacteristic
104#66991—28no—
105#66990—28no—
106#66989—22no—
107#66989C2×C414yescomplemented
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)⋊C4D411yescharacteristic
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11—22no—
117C2×C4⋊Dic11—21no—
118C2×C4⋊Dic11—41no—
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121C2×Dic11⋊C4D411yescharacteristic
122C2×C4×Dic11—21no—
123C2×C4×Dic11—21no—
124C2×C4×Dic11C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C2×#4313—22no—
128C2×#4313—22no—
129C2×#4313—41no—
130#66950—22no—
131#66950C2×C414yescomplemented
132#66946—22no—
133#66946C2×C414yescomplemented
134#66945—22no—
135#66945—41no—
136#66936—28no—
137C22⋊C4×D11—28no—
138C11×#102—22no—
139C11×#102—41no—
140C11×#95—21no—
141#66896—22no—
142#66896—41no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C22⋊(C11⋊C8)—22no—
148#66885—22no—
149#66885D414yescomplemented
150(C2×D11)⋊C8—22no—
151#66880—22no—
152#66880—22no—
153Dic11⋊C8—22no—
154C8×Dic11—22no—
155#66874—41no—
156#66874—41no—
157#66873—22no—
158#66873—22no—
159#22427—111nomaximal, Sylow
160C24×C11—21no—
161C24×C11C2×D411yescharacteristic
162C23×D11—21no—
163C23×D11—24no—
164C23×D11—42no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—42no—
168C23×D11—81no—
169C23×D11—81no—
170C23×D11C2×D411yescharacteristic
171C2×D4×C11—24no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11—81no—
178C2×D4×C11—81no—
179C2×D4×C11C22×C412yes—
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×C11—21no—
187C22×C4×C11C22×C412yes—
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D412yes—
190C22×C4×C11C2411yescharacteristic
191C2×C22⋊D11—24no—
192C2×C22⋊D11—24no—
193C2×C22⋊D11—41no—
194C2×C22⋊D11—41no—
195C2×C22⋊D11—42no—
196C2×C22⋊D11—42no—
197C2×C22⋊D11—42no—
198C2×C22⋊D11—42no—
199C2×C22⋊D11C22⋊C414yes—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—42no—
204C22×Dic11—42no—
205C22×Dic11—81no—
206C22×Dic11C2×D411yescharacteristic
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209D4×D11—28no—
210D4×D11—44no—
211D4×D11—44no—
212D4×D11—44no—
213#4339—28no—
214#4339—44no—
215#4339—44no—
216#4339—44no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44C22×C412yes—
221C2×D44C2×D412yes—
222C2×D44#4112yes—
223C2×C4×D11—24no—
224C2×C4×D11—24no—
225C2×C4×D11—21no—
226C2×C4×D11—21no—
227C2×C4×D11—21no—
228C2×C4×D11—21no—
229C2×C4×D11—42no—
230C2×C4×D11—42no—
231C2×C4×D11—81no—
232C2×C4×D11—81no—
233C2×C4×D11C22×C412yes—
234C2×C4×D11C2×D412yes—
235C2×Dic22—21no—
236C2×Dic22—21no—
237C2×Dic22—21no—
238C2×Dic22—21no—
239C2×Dic22—21no—
240C2×Dic22C22×C412yes—
241C11×M16—44no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11C2×D412yes—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4C22×C412yes—
254C11×C22⋊C4—24no—
255C11×C22⋊C4—42no—
256C22⋊Dic11—24no—
257C22⋊Dic11—24no—
258C22⋊Dic11C22⋊C414yes—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—42no—
262(C2×D11)⋊C4—81no—
263(C2×D11)⋊C4C22⋊C414yes—
264C4⋊Dic11—24no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11—42no—
269C4⋊Dic11C2×D412yes—
270Dic11⋊C4C22⋊C414yes—
271C4×Dic11—42no—
272C4×Dic11—81no—
273C4×Dic11C22×C412yes—
274C4×Dic11C2×D412yes—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8—21no—
281#4313—44no—
282C2×#546—111no—
283C2×#436—111no—
284C2×#417—111no—
285C2×#418—111no—
286#2352—111no—
287#1983—111no—
288#1958—111no—
289#1895D1111yescharacteristic, complemented
290#1894—111no—
291#1874—111no—
292#1873—111no—
293#1804—111no—
294#1788—111no—
295#1786—111no—
296C4×#102—111no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—22no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11C2×C22⋊C412yes—
311C23×C11C22×D411yescharacteristic
312C22×D11—22no—
313C22×D11—21no—
314C22×D11—22no—
315C22×D11—21no—
316C22×D11—22no—
317C22×D11—21no—
318C22×D11—21no—
319C22×D11—21no—
320C22×D11—21no—
321C22×D11—48no—
322C22×D11—48no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—84no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11—84no—
331C22×D11—84no—
332C22×D11C2×C22⋊C412yes—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—41no—
336D4×C11—41no—
337D4×C11—84no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11C2×C22⋊C412yes—
354C2×C4×C11C23×C411yescharacteristic
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11C2×#4111yescharacteristic
358C2×C4×C11H(5,𝔽2)11yescharacteristic
359C2×C4×C11H(5,𝔽2)11yescharacteristic
360C22⋊D11—44no—
361C22⋊D11—48no—
362C22⋊D11—48no—
363C2×Dic11—21no—
364C2×Dic11—21no—
365C2×Dic11—21no—
366C2×Dic11—21no—
367C2×Dic11—21no—
368C2×Dic11—21no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—84no—
379C2×Dic11C2×C22⋊C412yes—
380C2×Dic11C2×C22⋊C412yes—
381C2×Dic11C2×C22⋊C412yes—
382D44—22no—
383D44—22no—
384D44—22no—
385D44C4×D414yes—
386C4×D11—22no—
387C4×D11—22no—
388C4×D11—22no—
389C4×D11—22no—
390C4×D11—48no—
391C4×D11—84no—
392Dic22—22no—
393Dic22—22no—
394Dic22—41no—
395Dic22—41no—
396C8×C11—22no—
397C8×C11—41no—
398C11⋊C8—41no—
399C11⋊C8—41no—
400C22×#41—111no—
401C23×D4—111no—
402C22×M16—111no—
403C22×M16C2×D1111yescharacteristic, complemented
404#546—118no—
405#546—224no—
406C2×#124—111no—
407C2×#123—221no—
408C2×C22⋊Q8—111no—
409C2×#121—221no—
410C2×#121C2×D1111yescharacteristic
411C2×#120—221no—
412C2×C4×D4—111no—
413C2×C4×D4—111no—
414C2×#117—111no—
415C22×C4⋊C4—111no—
416C22×C22⋊C4—221no—
417#436—224no—
418C2×C4⋊C8—111no—
419#418—224no—
420#417—224no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#103—111no—
424C2×#103—111no—
425C2×#102—111no—
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102C2×D1111yescharacteristic
432C2×#102C2×D1111yescharacteristic
433C2×C22⋊C8—111no—
434C2×C22⋊C8—111no—
435C2×C4×C8—111no—
436#388—221no—
437#387—221no—
438#386—221no—
439#382—111no—
440#380—111no—
441#380C2×D1111yescharacteristic, complemented
442C4×C4⋊C4—111no—
443C4×C22⋊C4—221no—
444#340—111no—
445#340—111no—
446#340C2×D1111yescharacteristic, complemented
447#340C2×D1111yescharacteristic, complemented
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—41no—
452C22×C11—41no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—81no—
459C22×C11—81no—
460C22×C11—81no—
461C22×C11—81no—
462C22×C11C22×C22⋊C411yescharacteristic
463C22×C11D4211yescharacteristic
464C22×C11#54611yescharacteristic
465C22×C11#57511yescharacteristic
466C22×C11#57511yescharacteristic
467C22×C11#57611yescharacteristic
468C22×C11#57711yescharacteristic
469C2×D11—24no—
470C2×D11—22no—
471C2×D11—22no—
472C2×D11—22no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—41no—
476C2×D11—42no—
477C2×D11—41no—
478C2×D11—42no—
479C2×D11—41no—
480C2×D11—42no—
481C2×D11—41no—
482C2×D11—42no—
483C2×D11—816no—
484C4×C11—22no—
485C4×C11—42no—
486C4×C11—81no—
487C4×C11—81no—
488C4×C11C2×C4×D411yescharacteristic
489C4×C11#51811yescharacteristic
490C4×C11D4211yescharacteristic
491C4×C11#54611yescharacteristic
492Dic11—22no—
493Dic11—22no—
494Dic11—22no—
495Dic11—42no—
496Dic11—42no—
497Dic11—81no—
498C25—221no—
499C2×#41—114no—
500C2×#41—222no—
501C2×#41—222no—
502C2×#41—222no—
503C2×#41—441no—
504C2×#41—441no—
505C22×Q8—111no—
506C22×D4—21no—
507C22×D4—111no—
508C22×D4—114no—
509C22×D4—111no—
510C22×D4—222no—
511C22×D4—221no—
512C22×D4—222no—
513C22×D4—222no—
514C22×D4—221no—
515C22×D4—441no—
516C22×D4—441no—
517C22×D4C22×D1111yescharacteristic
518C23×C4—111no—
519C23×C4—221no—
520C23×C4—221no—
521C23×C4—221no—
522C23×C4C22×D1111yescharacteristic
523C2×M16—22no—
524C2×M16—22no—
525C2×M16—41no—
526C2×M16—222no—
527C2×M16—222no—
528C2×M16—441no—
529C22×C8—111no—
530C22×C8—111no—
531C22×C8C22×D1111yescharacteristic
532C22×C8C22×D1111yescharacteristic
533#124—114no—
534#124—222no—
535#123—228no—
536C22⋊Q8—114no—
537C22⋊Q8—222no—
538#121—22no—
539#121—228no—
540#121C4×D1114yes—
541#120—228no—
542C4×D4—114no—
543C4×D4—114no—
544C4×D4—114no—
545C4×D4—222no—
546#117—222no—
547#117—441no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—222no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4—441no—
555C2×C4⋊C4C22×D1111yescharacteristic
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C4⋊C4C22×D1111yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—111no—
561C2×C22⋊C4—111no—
562C2×C22⋊C4—228no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C42—111no—
570C2×C42—221no—
571C2×C42—221no—
572C4⋊C8—222no—
573#103—222no—
574#103—222no—
575#103—441no—
576#103—441no—
577#102—22no—
578#102—41no—
579#102—114no—
580#102—222no—
581#102—222no—
582#102—222no—
583#102—222no—
584#102—441no—
585C22⋊C8—222no—
586C22⋊C8—222no—
587C4×C8—222no—
588#95—21no—
589#95—221no—
590#95—221no—
591#95—221no—
592#95—221no—
593C2×C11—42no—
594C2×C11—82no—
595C2×C11D4×C22⋊C411yescharacteristic
596C2×C11#289611yescharacteristic
597C2×C11#289711yescharacteristic
598C2×C11#327311yescharacteristic
599C2×C11#327511yescharacteristic
600C2×C11#332211yescharacteristic
601C2×C11#332311yescharacteristic
602D11—42no—
603D11—44no—
604C24—21no—
605C24—111no—
606C24—224no—
607C24—221no—
608C24—442no—
609C24—442no—
610C24—442no—
611C24—442no—
612C24—881no—
613C24—881no—
614C24D4×D1111yescharacteristic
615#41—228no—
616#41—444no—
617#41—444no—
618#41—444no—
619C2×Q8—112no—
620C2×Q8—221no—
621C2×Q8—221no—
622C2×Q8—221no—
623C2×Q8—221no—
624C2×Q8—221no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—114no—
634C2×D4—112no—
635C2×D4—112no—
636C2×D4—112no—
637C2×D4—224no—
638C2×D4—228no—
639C2×D4—224no—
640C2×D4—221no—
641C2×D4—221no—
642C2×D4—221no—
643C2×D4—444no—
644C2×D4—444no—
645C2×D4—444no—
646C2×D4—441no—
647C2×D4—441no—
648C2×D4—442no—
649C2×D4—442no—
650C2×D4—442no—
651C2×D4—442no—
652C2×D4C2×C4×D1112yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—111no—
661C22×C4—111no—
662C22×C4—111no—
663C22×C4—112no—
664C22×C4—112no—
665C22×C4—224no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—224no—
673C22×C4—221no—
674C22×C4—442no—
675C22×C4—442no—
676C22×C4—442no—
677C22×C4—442no—
678C22×C4—881no—
679C22×C4—881no—
680C22×C4—881no—
681C22×C4C2×C4×D1112yes—
682C22×C4D4×D1111yescharacteristic
683C22×C4D4×D1112yes—
684C22×C4C23×D1111yescharacteristic
685M16—44no—
686M16—444no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8—221no—
695C2×C8—221no—
696C2×C8—221no—
697C2×C8—221no—
698C2×C8D4×D1112yes—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—114no—
705C4⋊C4—112no—
706C4⋊C4—224no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4—221no—
710C4⋊C4—442no—
711C4⋊C4C2×C4×D1112yes—
712C22⋊C4—24no—
713C22⋊C4—42no—
714C22⋊C4—114no—
715C22⋊C4—114no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4—224no—
719C22⋊C4—224no—
720C22⋊C4—442no—
721C22⋊C4—881no—
722C42—112no—
723C42—112no—
724C42—442no—
725C42—881no—
726C11#2242711yescharacteristic, complemented, Sylow
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—112no—
741C23—222no—
742C23—221no—
743C23—221no—
744C23—221no—
745C23—221no—
746C23—221no—
747C23—222no—
748C23—221no—
749C23—222no—
750C23—448no—
751C23—448no—
752C23—441no—
753C23—441no—
754C23—441no—
755C23—441no—
756C23—884no—
757C23—884no—
758C23—884no—
759C23—884no—
760C23—884no—
761C23C22⋊C4×D1112yes—
762C23C2×D4×D1111yescharacteristic
763Q8—222no—
764Q8—222no—
765Q8—441no—
766Q8—441no—
767D4—22no—
768D4—22no—
769D4—41no—
770D4—41no—
771D4—84no—
772D4—114no—
773D4—222no—
774D4—222no—
775D4—222no—
776D4—444no—
777D4—448no—
778D4—448no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—112no—
795C2×C4—112no—
796C2×C4—112no—
797C2×C4—221no—
798C2×C4—221no—
799C2×C4—221no—
800C2×C4—221no—
801C2×C4—221no—
802C2×C4—221no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—448no—
810C2×C4—441no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—441no—
815C2×C4—441no—
816C2×C4—441no—
817C2×C4—884no—
818C2×C4—884no—
819C2×C4C22⋊C4×D1112yes—
820C2×C4C22×C4×D1111yescharacteristic
821C2×C4C2×D4×D1111yescharacteristic
822C2×C4C2×D4×D1111yescharacteristic
823C2×C4#6703711yescharacteristic
824C2×C4#41×D1111yescharacteristic
825C2×C4#6704211yescharacteristic
826C8—22no—
827C8—41no—
828C8—441no—
829C8—441no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—222no—
845C22—224no—
846C22—222no—
847C22—222no—
848C22—442no—
849C22—442no—
850C22—441no—
851C22—442no—
852C22—441no—
853C22—442no—
854C22—441no—
855C22—442no—
856C22—441no—
857C22—442no—
858C22—8816no—
859C22C2×C22⋊C4×D1111yescharacteristic
860C22#1062314011yescharacteristic
861C22#1062314111yescharacteristic
862C22#1062330411yescharacteristic
863C22#1062330511yescharacteristic
864C22#1062330611yescharacteristic
865C22#1062330811yescharacteristic
866C4—22no—
867C4—42no—
868C4—81no—
869C4—81no—
870C4—222no—
871C4—222no—
872C4—222no—
873C4—442no—
874C4—442no—
875C4—881no—
876C4C4×D4×D1111yescharacteristic
877C4#1062307611yescharacteristic
878C4#1062312111yescharacteristic
879C4#1062318511yescharacteristic
880C2—42no—
881C2—82no—
882C2—442no—
883C2—444no—
884C2#1307143411yescharacteristic
885C2#1307713211yescharacteristic
886C2#1307714111yescharacteristic
887C2#1308022411yescharacteristic
888C2#1308025411yescharacteristic
889C2#1308081211yescharacteristic
890C2#1308082711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1895C2
socleC23×C11C22×D4
prime radicalC2×#10623143C2
cosocleC22×C4×C11C24
hypercenter#1895D11
hypocenterC11#22427
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
2. C2×#10622741C2semidirect
3. C2×#10622746C2semidirect
4. C2×#10622383C2semidirect
5. #13071547C2semidirect
6. #13069547C2semidirect
7. #13069426C2semidirect
8. #13069048C2semidirect
9. #13068934C2semidirect
10. #13068927C2semidirect
11. #13068625C2semidirect
12. #13068554C2semidirect
13. #13068545C2semidirect
14. #13068430C2semidirect
15. C11×#1895C2semidirect
18. C22×C11×M16C22semidirect
24. C22×C4⋊Dic11C22semidirect
27. #10623143C4semidirect
35. C11×#380C22semidirect
38. C2×C22⋊(C11⋊C8)C22semidirect
44. C2×#66880C22semidirect
45. C2×#66880C22semidirect
46. C2×Dic11⋊C8C22semidirect
47. C2×C8×Dic11C22semidirect
49. #10622590C22semidirect
50. C4⋊C4×Dic11C22semidirect
51. C2×#66874C22semidirect
52. C2×#66874C22semidirect
60. C11×#340C22semidirect
61. C11×#340C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
77. C2×D4×D11C2×C4semidirect
107. #66989C2×C4semidirect
131. #66950C2×C4semidirect
133. #66946C2×C4semidirect
149. #66885D4semidirect
289. #1895D11semidirect
403. C22×M16C2×D11semidirect
441. #380C2×D11semidirect
446. #340C2×D11semidirect
447. #340C2×D11semidirect
726. C11#22427semidirect

Maximal subgroups

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

subgroupindex
C2×#106231432
C2×#106227412
C2×#106227462
C2×#106223832
#130715472
#130695472
#130694262
#130690482
#130689342
#130689272
#130686252
#130685542
#130685452
#130684302
C11×#18952
#2242711