Finite Group Databasebeta

← #14769377

Subgroups — #14769377

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×#10623337C211yesmaximal, characteristic
2C2×#10622342C211yesmaximal, characteristic, complemented
3C2×#10622384C211yesmaximal, characteristic, complemented
4C2×#10622828C211yesmaximal, characteristic, complemented
5#13071538C211yesmaximal, characteristic, complemented
6#13069547C211yesmaximal, characteristic, complemented
7#13069426C211yesmaximal, characteristic, complemented
8#13069051C211yesmaximal, characteristic, complemented
9#13069047C211yesmaximal, characteristic, complemented
10#13068930C211yesmaximal, characteristic, complemented
11#13068926C211yesmaximal, characteristic, complemented
12#13068624C211yesmaximal, characteristic, complemented
13#13068553C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C22×#4341C2211yescharacteristic
18C2×#67006—21no—
19C22×C22⋊Dic11—21no—
20#10623337—24no—
21#10623337C418yescomplemented
22C2×#66992—21no—
23C2×#66991C2211yescharacteristic
24C2×#66989C2211yescharacteristic
25C2×#66988—21no—
26C2×D4×Dic11C2211yescharacteristic
27C2×C4×C22⋊D11C2211yescharacteristic
28C2×#66979C2211yescharacteristic
29C2×#66977C2211yescharacteristic
30C22×#4318C2211yescharacteristic
31C22×#4313C2211yescharacteristic, complemented
32C2×C4⋊C4×D11C2211yescharacteristic, complemented
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C11×#380C2211yescharacteristic
39#10622828—24no—
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43C2×#66896C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
45C2×#66880C2211yescharacteristic, complemented
46C2×#66880C2211yescharacteristic, complemented
47C2×Dic11⋊C8C2211yescharacteristic, complemented
48C2×C8×Dic11C2211yescharacteristic, complemented
49#10622600C2211yescharacteristic, complemented
50#10622590C2211yescharacteristic, complemented
51C4⋊C4×Dic11C2211yescharacteristic, complemented
52C2×#66874C2211yescharacteristic, complemented
53C2×#66874C2211yescharacteristic, complemented
54#10622569—21no—
55#10622557—21no—
56#10622384—24no—
57#10622342—24no—
58#10622279—21no—
59#10622265—21no—
60#10622189C2211yescharacteristic, complemented
61#10622189C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C25×C11—21no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—21no—
68C22×D4×C11—22no—
69C22×D4×C11—41no—
70C22×D4×C11—41no—
71C22×D4×C11C2×C414yescomplemented
72C22×D4×C11C2311yescharacteristic
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11—21no—
76C22×C22⋊D11—21no—
77C22×C22⋊D11D411yescharacteristic
78C23×Dic11—21no—
79C23×Dic11—21no—
80C2×#4341—22no—
81C2×#4341—22no—
82C2×#4341—22no—
83C2×#4341—41no—
84C2×#4341—41no—
85C2×#4341C2×C414yes—
86C22×C4×D11—21no—
87C22×C4×D11C2311yescharacteristic
88C22×Dic22C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—21no—
94#67006—28no—
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11—21no—
98C2×C22⋊Dic11—21no—
99C2×C22⋊Dic11—21no—
100C2×C22⋊Dic11—28no—
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11D411yescharacteristic
103#66992—28no—
104#66991—22no—
105#66991C2×C414yes—
106#66989—22no—
107#66989C2×C414yescomplemented
108#66988—28no—
109D4×Dic11—22no—
110D4×Dic11C2×C414yescomplemented
111C4×C22⋊D11C2×C414yes—
112C4×C22⋊D11D414yes—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4D411yescharacteristic
115#66979—22no—
116#66979—41no—
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120#66977—22no—
121#66977C2×C414yescomplemented
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4D411yescharacteristic
125C2×C4×Dic11—21no—
126C2×C4×Dic11—21no—
127C2×C4×Dic11C2311yescharacteristic
128C2×#4318—22no—
129C2×#4318—22no—
130C2×#4318—41no—
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C2×#4313—22no—
134C2×#4313—22no—
135C2×#4313—41no—
136C4⋊C4×D11—22no—
137C4⋊C4×D11—41no—
138C11×#102—22no—
139C11×#102—22no—
140C11×#102—41no—
141C11×#102—41no—
142C11×C22⋊C8—22no—
143C11×#95—21no—
144#66896—22no—
145#66896—22no—
146#66896—22no—
147#66896D414yescomplemented
148C11⋊#95—21no—
149C11⋊#95—21no—
150C11⋊#95—21no—
151C11⋊#95—21no—
152(C2×D11)⋊C8—22no—
153#66880—22no—
154#66880—41no—
155Dic11⋊C8—22no—
156C8×Dic11—22no—
157#66874—22no—
158#66874—41no—
159#22427—111nomaximal, Sylow
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—24no—
163C24×C11—42no—
164C24×C11—42no—
165C24×C11—42no—
166C24×C11—42no—
167C24×C11—81no—
168C24×C11—81no—
169C24×C11C2×D411yescharacteristic
170C23×D11C2×D411yescharacteristic
171C2×D4×C11—28no—
172C2×D4×C11—24no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11—21no—
181C2×D4×C11—44no—
182C2×D4×C11—44no—
183C2×D4×C11—44no—
184C2×D4×C11—42no—
185C2×D4×C11—42no—
186C2×D4×C11C22×C412yes—
187C2×D4×C11C22×C412yes—
188C2×D4×C11C2×D412yes—
189C2×D4×C11#4112yes—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D412yes—
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11—24no—
201C2×C22⋊D11—24no—
202C2×C22⋊D11—41no—
203C2×C22⋊D11—41no—
204C2×C22⋊D11—42no—
205C2×C22⋊D11—42no—
206C2×C22⋊D11—81no—
207C2×C22⋊D11—81no—
208C2×C22⋊D11C22⋊C414yes—
209C22×Dic11—24no—
210C22×Dic11—24no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—42no—
216C22×Dic11—42no—
217C22×Dic11—81no—
218C22×Dic11—81no—
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D411yescharacteristic
222#4341—28no—
223#4341—44no—
224#4341—44no—
225#4341—44no—
226C2×C4×D11—21no—
227C2×C4×D11—21no—
228C2×C4×D11—21no—
229C2×C4×D11—21no—
230C2×C4×D11—42no—
231C2×C4×D11—42no—
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—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C22⋊C4—81no—
252C22⋊Dic11—24no—
253C22⋊Dic11—24no—
254C22⋊Dic11—24no—
255C22⋊Dic11—24no—
256C22⋊Dic11—24no—
257C22⋊Dic11—42no—
258C22⋊Dic11C22⋊C414yes—
259(C2×D11)⋊C4—42no—
260(C2×D11)⋊C4C22⋊C414yes—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11C22×C412yes—
266C4⋊Dic11C2×D412yes—
267Dic11⋊C4—24no—
268Dic11⋊C4—42no—
269Dic11⋊C4C22⋊C414yes—
270C4×Dic11—42no—
271C4×Dic11—81no—
272C4×Dic11C22×C412yes—
273C4×Dic11C2×D412yes—
274#4318—44no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8C2×D412yes—
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#1895—111no—
290#1894—111no—
291#1874—111no—
292#1873—111no—
293#1804—111no—
294#1788—111no—
295#1786D1111yescharacteristic, complemented
296C4×#102—111no—
297C23×C11—22no—
298C23×C11—21no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—22no—
307C23×C11—48no—
308C23×C11—48no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—84no—
320C23×C11—84no—
321C23×C11—84no—
322C23×C11—84no—
323C23×C11—84no—
324C23×C11C2×C22⋊C412yes—
325C23×C11C22×D411yescharacteristic
326C22×D11—21no—
327C22×D11—21no—
328C22×D11—21no—
329C22×D11—21no—
330C22×D11—21no—
331C22×D11—21no—
332C22×D11C2×C22⋊C412yes—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—22no—
338D4×C11—48no—
339D4×C11—41no—
340D4×C11—41no—
341D4×C11C4×D414yes—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11C2×C22⋊C412yes—
355C2×C4×C11C23×C411yescharacteristic
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11C2×#4111yescharacteristic
359C2×C4×C11H(5,𝔽2)11yescharacteristic
360C2×C4×C11H(5,𝔽2)11yescharacteristic
361C22⋊D11—44no—
362C22⋊D11—48no—
363C22⋊D11—84no—
364C2×Dic11—21no—
365C2×Dic11—21no—
366C2×Dic11—21no—
367C2×Dic11—21no—
368C2×Dic11—21no—
369C2×Dic11—21no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—48no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—84no—
384C2×Dic11C2×C22⋊C412yes—
385C2×Dic11C2×C22⋊C412yes—
386C2×Dic11C2×C22⋊C412yes—
387C4×D11—22no—
388C4×D11—22no—
389C4×D11—22no—
390C4×D11—22no—
391C4×D11—84no—
392Dic22—22no—
393Dic22—22no—
394Dic22—41no—
395Dic22—41no—
396C8×C11—41no—
397C8×C11—41no—
398C11⋊C8—22no—
399C11⋊C8—41no—
400C22×#41—111no—
401C23×D4C2×D1111yescharacteristic
402C22×M16—111no—
403C22×M16—111no—
404#546—118no—
405#546—224no—
406C2×#124—111no—
407C2×#123—221no—
408C2×C22⋊Q8—111no—
409C2×#121—111no—
410C2×#121—221no—
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×#102C2×D1111yescharacteristic
430C2×#102C2×D1111yescharacteristic
431C2×#102C2×D1111yescharacteristic
432C2×#102C2×D1111yescharacteristic
433C2×C22⋊C8—111no—
434C2×C22⋊C8C2×D1111yescharacteristic
435C2×C4×C8—111no—
436#388—221no—
437#387—221no—
438#386—221no—
439#382—111no—
440#380—111no—
441#380C2×D1111yescharacteristic
442C4×C4⋊C4—111no—
443C4×C22⋊C4—221no—
444#340—111no—
445#340—111no—
446#340—111no—
447#340—111no—
448C22×C11—22no—
449C22×C11—24no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—41no—
455C22×C11—42no—
456C22×C11—41no—
457C22×C11—42no—
458C22×C11—41no—
459C22×C11—42no—
460C22×C11—41no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—816no—
466C22×C11—81no—
467C22×C11—81no—
468C22×C11—81no—
469C22×C11—81no—
470C22×C11C22×C22⋊C411yescharacteristic
471C22×C11D4211yescharacteristic
472C22×C11#54611yescharacteristic
473C22×C11#57511yescharacteristic
474C22×C11#57511yescharacteristic
475C22×C11#57611yescharacteristic
476C22×C11#57711yescharacteristic
477C2×D11—22no—
478C2×D11—22no—
479C2×D11—22no—
480C2×D11—41no—
481C2×D11—41no—
482C2×D11—41no—
483C2×D11—41no—
484C4×C11—22no—
485C4×C11—81no—
486C4×C11—81no—
487C4×C11C2×C4×D411yescharacteristic
488C4×C11#51811yescharacteristic
489C4×C11D4211yescharacteristic
490C4×C11#54611yescharacteristic
491Dic11—22no—
492Dic11—22no—
493Dic11—22no—
494Dic11—42no—
495Dic11—42no—
496Dic11—42no—
497Dic11—81no—
498C25—21no—
499C2×#41—114no—
500C2×#41—222no—
501C2×#41—222no—
502C2×#41—222no—
503C2×#41—441no—
504C2×#41—441no—
505C22×Q8—111no—
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—111no—
513C22×D4—221no—
514C22×D4—221no—
515C22×D4C4×D1114yescomplemented
516C22×D4C22×D1111yescharacteristic
517C22×D4C22×D1111yescharacteristic
518C23×C4—111no—
519C23×C4—221no—
520C23×C4—221no—
521C23×C4—221no—
522C23×C4C22×D1111yescharacteristic
523C2×M16—222no—
524C2×M16—222no—
525C2×M16—222no—
526C2×M16—222no—
527C2×M16—441no—
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—114no—
539#121—228no—
540#121—222no—
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—111no—
552C2×C4⋊C4—222no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4—441no—
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C4⋊C4C22×D1111yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—111no—
560C2×C22⋊C4—111no—
561C2×C22⋊C4—228no—
562C2×C22⋊C4—221no—
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—22no—
579#102—41no—
580#102—41no—
581#102—114no—
582#102—222no—
583#102—222no—
584#102—222no—
585C22⋊C8—22no—
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—44no—
595C2×C11—82no—
596C2×C11D4×C22⋊C411yescharacteristic
597C2×C11#289611yescharacteristic
598C2×C11#289711yescharacteristic
599C2×C11#327311yescharacteristic
600C2×C11#327511yescharacteristic
601C2×C11#332211yescharacteristic
602C2×C11#332311yescharacteristic
603D11—42no—
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24—111no—
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—28no—
626C2×D4—24no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—44no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—114no—
641C2×D4—224no—
642C2×D4—224no—
643C2×D4—441no—
644C2×D4—441no—
645C2×D4—442no—
646C2×D4—442no—
647C2×D4—881no—
648C2×D4—881no—
649C2×D4C2×C4×D1112yes—
650C2×D4C2×C4×D1112yes—
651C2×D4D4×D1112yes—
652C2×D4#434112yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—111no—
660C22×C4—111no—
661C22×C4—111no—
662C22×C4—112no—
663C22×C4—112no—
664C22×C4—224no—
665C22×C4—224no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
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—444no—
686M16—444no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—112no—
694C2×C8—221no—
695C2×C8—221no—
696C2×C8—221no—
697C2×C8—221no—
698C2×C8—221no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—114no—
704C4⋊C4—112no—
705C4⋊C4—112no—
706C4⋊C4—224no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4—221no—
710C4⋊C4—221no—
711C4⋊C4—442no—
712C22⋊C4—81no—
713C22⋊C4—114no—
714C22⋊C4—114no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4—224no—
719C22⋊C4—224no—
720C22⋊C4—442no—
721C22⋊C4—442no—
722C42—112no—
723C42—112no—
724C42—442no—
725C42—881no—
726C11#2242711yescharacteristic, complemented, Sylow
727C23—22no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—21no—
735C23—22no—
736C23—22no—
737C23—48no—
738C23—48no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—84no—
750C23—84no—
751C23—84no—
752C23—84no—
753C23—84no—
754C23—112no—
755C23—221no—
756C23—221no—
757C23—221no—
758C23—221no—
759C23—221no—
760C23—221no—
761C23C22⋊C4×D1112yes—
762C23C2×D4×D1111yescharacteristic
763Q8—222no—
764Q8—222no—
765Q8—441no—
766Q8—441no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—48no—
773D4—41no—
774D4—41no—
775D4—444no—
776D4—448no—
777D4—884no—
778D4(C22⋊D11)⋊C414yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—112no—
792C2×C4—112no—
793C2×C4—112no—
794C2×C4—221no—
795C2×C4—221no—
796C2×C4—221no—
797C2×C4—221no—
798C2×C4—221no—
799C2×C4—221no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—448no—
808C2×C4—441no—
809C2×C4—441no—
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×C4C2×#434111yescharacteristic
824C2×C4#6703711yescharacteristic
825C2×C4#6703711yescharacteristic
826C8—41no—
827C8—41no—
828C8—222no—
829C8—441no—
830C22—22no—
831C22—24no—
832C22—22no—
833C22—22no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—816no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—222no—
853C22—222no—
854C22—222no—
855C22—441no—
856C22—441no—
857C22—441no—
858C22—441no—
859C22C2×C22⋊C4×D1111yescharacteristic
860C22#1062312111yescharacteristic
861C22#1062312211yescharacteristic
862C22#1062328811yescharacteristic
863C22#1062329311yescharacteristic
864C22#1062330411yescharacteristic
865C22#1062330411yescharacteristic
866C4—22no—
867C4—81no—
868C4—81no—
869C4—222no—
870C4—222no—
871C4—222no—
872C4—442no—
873C4—442no—
874C4—442no—
875C4—881no—
876C4C2×(C22⋊D11)⋊C411yescharacteristic
877C4#1062301711yescharacteristic
878C4#1062312111yescharacteristic
879C4#1062312211yescharacteristic
880C2—42no—
881C2—44no—
882C2—82no—
883C2—442no—
884C2#1307143211yescharacteristic
885C2#1307713011yescharacteristic
886C2#1307713711yescharacteristic
887C2#1308022711yescharacteristic
888C2#1308025111yescharacteristic
889C2#1308082111yescharacteristic
890C2#1308083611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1786C2
socleC23×C11C22×D4
prime radicalC2×#10623337C2
cosocleC22×C4×C11C24
hypercenter#1786D11
hypocenterC11#22427
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. C2×#10622342C2semidirect
3. C2×#10622384C2semidirect
4. C2×#10622828C2semidirect
5. #13071538C2semidirect
6. #13069547C2semidirect
7. #13069426C2semidirect
8. #13069051C2semidirect
9. #13069047C2semidirect
10. #13068930C2semidirect
11. #13068926C2semidirect
12. #13068624C2semidirect
13. #13068553C2semidirect
14. #102×Dic11C2semidirect
15. C11×#1786C2semidirect
21. #10623337C4semidirect
31. C22×#4313C22semidirect
32. C2×C4⋊C4×D11C22semidirect
44. C2×(C2×D11)⋊C8C22semidirect
45. C2×#66880C22semidirect
46. C2×#66880C22semidirect
47. C2×Dic11⋊C8C22semidirect
48. C2×C8×Dic11C22semidirect
49. #10622600C22semidirect
50. #10622590C22semidirect
51. C4⋊C4×Dic11C22semidirect
52. C2×#66874C22semidirect
53. C2×#66874C22semidirect
60. #10622189C22semidirect
61. #10622189C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
71. C22×D4×C11C2×C4semidirect
107. #66989C2×C4semidirect
110. D4×Dic11C2×C4semidirect
121. #66977C2×C4semidirect
147. #66896D4semidirect
295. #1786D11semidirect
515. C22×D4C4×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×#106233372
C2×#106223422
C2×#106223842
C2×#106228282
#130715382
#130695472
#130694262
#130690512
#130690472
#130689302
#130689262
#130686242
#130685532
#102×Dic112
C11×#17862
#2242711