Finite Group Databasebeta

← #14769191

Subgroups — #14769191

Order 2816.

1638 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×#10623360C211yesmaximal, characteristic
2C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
3C2×D11×#102C211yesmaximal, characteristic, complemented
4#13071546C211yesmaximal, characteristic, complemented
5#13069545C211yesmaximal, characteristic, complemented
6#13069424C211yesmaximal, characteristic, complemented
7#13069044C211yesmaximal, characteristic, complemented
8#13069036C211yesmaximal, characteristic, complemented
9#13068938C211yesmaximal, characteristic, complemented
10#13068920C211yesmaximal, characteristic, complemented
11#13068624C211yesmaximal, characteristic, complemented
12#13068556C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, characteristic, complemented
15C2×C11×#416C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic, complemented
19C2×C11×#117C2211yescharacteristic, complemented
20#10623360—24no—
21#10623360C418yescomplemented
22C2×#67000C2211yescharacteristic
23C2×#66999C2211yescharacteristic
24C2×#66992—21no—
25C2×#66990—21no—
26C2×D4×Dic11C2211yescharacteristic
27C2×#66983C2211yescharacteristic
28C2×#66982—21no—
29C2×C4×C22⋊D11C2211yescharacteristic
30C22×(C2×D11)⋊C4—21no—
31C22×C8×D11C2211yescharacteristic
32C2×C4⋊C4×D11C2211yescharacteristic
33C11×#416—24no—
34C2×C11×#103C2211yescharacteristic, complemented
35C2×C11×#103C2211yescharacteristic, complemented
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×#66899C2211yescharacteristic, complemented
39C2×#66899C2211yescharacteristic, complemented
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42#10622825C2211yescharacteristic, complemented
43C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
44C2×#66885C2211yescharacteristic
45C2×#66885C2211yescharacteristic
46C8×C22⋊D11—24no—
47C2×(C2×D11)⋊C8C2211yescharacteristic
48C2×Dic11⋊C8C2211yescharacteristic, complemented
49C2×C8×Dic11C2211yescharacteristic, complemented
50#10622600C2211yescharacteristic
51#10622590C2211yescharacteristic, complemented
52C4⋊C4×Dic11C2211yescharacteristic, complemented
53C2×#66873C2211yescharacteristic
54C2×#66873C2211yescharacteristic
55#10622569—21no—
56#10622558—21no—
57C4×(C2×D11)⋊C4—21no—
58#10622546—21no—
59D11×#102—24no—
60#10622189C2211yescharacteristic, complemented
61#10622189C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—41no—
69C2×C11×#41—41no—
70C2×C11×#41C2×C414yescomplemented
71C22×Q8×C11C2311yescharacteristic
72C22×D4×C11—21no—
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C22×C22⋊D11—21no—
77C22×C22⋊D11—21no—
78C22×C22⋊D11D411yescharacteristic
79C23×Dic11—21no—
80C2×D4×D11—22no—
81C2×D4×D11—22no—
82C2×D4×D11—22no—
83C2×D4×D11—41no—
84C2×D4×D11—41no—
85C2×D4×D11C2×C414yes—
86C22×D44C2311yescharacteristic
87C22×C4×D11—21no—
88C22×C4×D11C2311yescharacteristic
89C22×C8×C11—22no—
90C22×C8×C11—22no—
91C22×C8×C11—41no—
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C11×#117—22no—
95C11×#117—41no—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C42×C11—21no—
100C2×C22⋊Dic11—21no—
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11D411yescharacteristic
103#67000—22no—
104#67000C2×C414yescomplemented
105#66999—22no—
106#66999C2×C414yes—
107#66992—28no—
108#66990—28no—
109D4×Dic11—22no—
110D4×Dic11C2×C414yescomplemented
111#66983—22no—
112#66983C2×C414yescomplemented
113#66982—28no—
114C4×C22⋊D11C2×C414yes—
115C4×C22⋊D11D414yes—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—28no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4D411yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4D411yescharacteristic
129C2×C4×Dic11—21no—
130C2×C4×Dic11C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C2×C8×D11—22no—
134C2×C8×D11—22no—
135C2×C8×D11—41no—
136C4⋊C4×D11—22no—
137C4⋊C4×D11—41no—
138C11×#103—22no—
139C11×#103—22no—
140C11×#102—22no—
141C11×#102D414yescomplemented
142#66899—41no—
143#66899—41no—
144#66896—22no—
145#66896—22no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C11⋊#95—21no—
149C11⋊#95—21no—
150C11⋊#95—21no—
151C22⋊(C11⋊C8)—22no—
152#66885—22no—
153#66885—41no—
154(C2×D11)⋊C8—22no—
155Dic11⋊C8—22no—
156C8×Dic11—22no—
157#66873—22no—
158#66873—41no—
159#22414—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
171C11×#41—28no—
172C11×#41—44no—
173C11×#41—44no—
174C11×#41—44no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11C22×C412yes—
181C2×D4×C11—24no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—42no—
186C2×D4×C11—42no—
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×C11—24no—
197C22×C4×C11—21no—
198C22×C4×C11—42no—
199C22×C4×C11—42no—
200C22×C4×C11C22×C412yes—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2411yescharacteristic
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—22no—
207C2×C22⋊D11—22no—
208C2×C22⋊D11—42no—
209C2×C22⋊D11—42no—
210C2×C22⋊D11—81no—
211C2×C22⋊D11—81no—
212C2×C22⋊D11C22⋊C414yes—
213C22×Dic11—24no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—81no—
218C22×Dic11—81no—
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D411yescharacteristic
222D4×D11—28no—
223D4×D11—44no—
224D4×D11—44no—
225D4×D11—44no—
226C2×D44—21no—
227C2×D44—21no—
228C2×D44—21no—
229C2×D44—21no—
230C2×D44—21no—
231C2×D44C22×C412yes—
232C2×C4×D11—21no—
233C2×C4×D11—21no—
234C2×C4×D11—21no—
235C2×C4×D11—21no—
236C2×C4×D11—42no—
237C2×C4×D11—42no—
238C2×C4×D11—81no—
239C2×C4×D11C22×C412yes—
240C2×C4×D11C2×D412yes—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—44no—
247C2×C8×C11C2×D412yes—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4C2×D412yes—
252C11×C22⋊C4—42no—
253C42×C11—42no—
254C22⋊Dic11—24no—
255C22⋊Dic11—81no—
256C22⋊Dic11C22⋊C414yes—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—42no—
262(C2×D11)⋊C4C22⋊C414yes—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11C22×C412yes—
269Dic11⋊C4—24no—
270Dic11⋊C4—42no—
271Dic11⋊C4C22⋊C414yes—
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—
281C8×D11—44no—
282C2×#546—111no—
283C2×C8×D4—111no—
284C2×#416D1111yescharacteristic, complemented
285C22×#102—111no—
286#2352—111no—
287#1983—111no—
288#1958—111no—
289#1893—111no—
290#1892—111no—
291#1875—111no—
292#1872—111no—
293#1804—111no—
294#1788—111no—
295#1786—111no—
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—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11C2×C22⋊C412yes—
311C23×C11C22×D411yescharacteristic
312C22×D11—21no—
313C22×D11—21no—
314C22×D11—21no—
315C22×D11—21no—
316C22×D11—22no—
317C22×D11—48no—
318C22×D11—41no—
319C22×D11—41no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—48no—
325C22×D11—84no—
326C22×D11—84no—
327C22×D11—84no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11C2×C22⋊C412yes—
331C22×D11#13512yes—
332C22×D11#13512yes—
333Q8×C11—22no—
334Q8×C11—22no—
335Q8×C11—41no—
336Q8×C11—41no—
337D4×C11—22no—
338D4×C11—22no—
339D4×C11—22no—
340D4×C11—48no—
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—22no—
349C2×C4×C11—22no—
350C2×C4×C11—48no—
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×C11C2×C22⋊C412yes—
359C2×C4×C11C23×C411yescharacteristic
360C2×C4×C11C22×D411yescharacteristic
361C2×C4×C11C22×D411yescharacteristic
362C2×C4×C11C2×#4111yescharacteristic
363C2×C4×C11H(5,𝔽2)11yescharacteristic
364C2×C4×C11H(5,𝔽2)11yescharacteristic
365C22⋊D11—28no—
366C22⋊D11—48no—
367C22⋊D11—84no—
368C2×Dic11—21no—
369C2×Dic11—21no—
370C2×Dic11—21no—
371C2×Dic11—21no—
372C2×Dic11—21no—
373C2×Dic11—21no—
374C2×Dic11—22no—
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—
387D44—22no—
388D44—22no—
389D44—41no—
390D44—41no—
391C4×D11—22no—
392C4×D11—22no—
393C4×D11—22no—
394C4×D11—22no—
395C4×D11—84no—
396C8×C11—22no—
397C8×C11—41no—
398C11⋊C8—41no—
399C11⋊C8—41no—
400C22×#41C2×D1111yescharacteristic
401C23×D4—111no—
402C23×C8—111no—
403C23×C8C2×D1111yescharacteristic, complemented
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×#117C2×D1111yescharacteristic, complemented
415C22×C4⋊C4—111no—
416C22×C22⋊C4—221no—
417C8×D4—224no—
418C2×C4⋊C8—111no—
419#416—24no—
420C2×#103—111no—
421C2×#103—111no—
422C2×#103C2×D1111yescharacteristic, complemented
423C2×#103C2×D1111yescharacteristic, complemented
424C2×#102—111no—
425C2×#102—111no—
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—224no—
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#380—111no—
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—42no—
455C22×C11—41no—
456C22×C11—42no—
457C22×C11—41no—
458C22×C11—42no—
459C22×C11—41no—
460C22×C11—42no—
461C22×C11—41no—
462C22×C11C22×C22⋊C411yescharacteristic
463C22×C11D4211yescharacteristic
464C22×C11#54611yescharacteristic
465C22×C11C2×#13511yescharacteristic
466C22×C11C2×#13511yescharacteristic
467C22×C11#57611yescharacteristic
468C22×C11#57711yescharacteristic
469C2×D11—22no—
470C2×D11—22no—
471C2×D11—22no—
472C2×D11—22no—
473C2×D11—22no—
474C2×D11—22no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—816no—
479C2×D11—81no—
480C2×D11—81no—
481C2×D11—81no—
482C2×D11—81no—
483C2×D11#41614yescomplemented
484C4×C11—22no—
485C4×C11—42no—
486C4×C11—42no—
487C4×C11—81no—
488C4×C11C2×C4×D411yescharacteristic
489C4×C11#51811yescharacteristic
490C4×C11D4211yescharacteristic
491C4×C11#54611yescharacteristic
492Dic11—22no—
493Dic11—22no—
494Dic11—22no—
495Dic11—42no—
496Dic11—81no—
497Dic11—81no—
498C25—221no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41C4×D1114yescomplemented
505C22×Q8C22×D1111yescharacteristic
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—21no—
519C23×C4—111no—
520C23×C4—221no—
521C23×C4—221no—
522C23×C4C22×D1111yescharacteristic
523C22×C8—22no—
524C22×C8—22no—
525C22×C8—41no—
526C22×C8—111no—
527C22×C8—111no—
528C22×C8—222no—
529C22×C8—222no—
530C22×C8—441no—
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—22no—
547#117—41no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4—222no—
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—21no—
570C2×C42—111no—
571C2×C42—221no—
572C4⋊C8—222no—
573#103—22no—
574#103—22no—
575#103—441no—
576#103—441no—
577#102—22no—
578#102—222no—
579#102—222no—
580#102—222no—
581#102—222no—
582#102—441no—
583#102—441no—
584#102C22⋊D1114yescomplemented
585C22⋊C8—222no—
586C22⋊C8—222no—
587C4×C8—222no—
588#95—221no—
589#95—221no—
590#95—221no—
591#95—221no—
592#95—221no—
593C2×C11—44no—
594C2×C11—42no—
595C2×C11D4×C22⋊C411yescharacteristic
596C2×C11C2×#41611yescharacteristic
597C2×C11#289711yescharacteristic
598C2×C11#328011yescharacteristic
599C2×C11#328211yescharacteristic
600C2×C11#329611yescharacteristic
601C2×C11#329711yescharacteristic
602D11—24no—
603D11—82no—
604C24—21no—
605C24—111no—
606C24—224no—
607C24—221no—
608C24—442no—
609C24—442no—
610C24—442no—
611C24—442no—
612C24—881no—
613C24—881no—
614C24D4×D1111yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C2×C4×D1112yes—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—114no—
632C2×D4—112no—
633C2×D4—224no—
634C2×D4—222no—
635C2×D4—222no—
636C2×D4—228no—
637C2×D4—224no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—221no—
642C2×D4—221no—
643C2×D4—444no—
644C2×D4—444no—
645C2×D4—444no—
646C2×D4—442no—
647C2×D4—442no—
648C2×D4—881no—
649C2×D4—881no—
650C2×D4C2×C4×D1112yes—
651C2×D4#433912yes—
652C2×D4C2×C22⋊D1112yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—24no—
660C22×C4—21no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—111no—
664C22×C4—111no—
665C22×C4—111no—
666C22×C4—112no—
667C22×C4—112no—
668C22×C4—224no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—221no—
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
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—44no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8—221no—
695C2×C8—221no—
696C2×C8—221no—
697C2×C8—444no—
698C2×C8C2×C22⋊D1112yes—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—114no—
703C4⋊C4—112no—
704C4⋊C4—224no—
705C4⋊C4—221no—
706C4⋊C4—221no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4—221no—
710C4⋊C4—442no—
711C4⋊C4C2×C22⋊D1112yes—
712C22⋊C4—42no—
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—881no—
722C42—42no—
723C42—112no—
724C42—112no—
725C42—881no—
726C11#2241411yescharacteristic, complemented, Sylow
727C23—22no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—112no—
741C23—112no—
742C23—112no—
743C23—221no—
744C23—221no—
745C23—221no—
746C23—221no—
747C23—222no—
748C23—448no—
749C23—448no—
750C23—441no—
751C23—441no—
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—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—48no—
771D4—228no—
772D4—222no—
773D4—222no—
774D4—448no—
775D4—441no—
776D4—441no—
777D4—884no—
778D4C4×C22⋊D1114yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—48no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—112no—
796C2×C4—112no—
797C2×C4—112no—
798C2×C4—221no—
799C2×C4—221no—
800C2×C4—221no—
801C2×C4—221no—
802C2×C4—221no—
803C2×C4—221no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
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×#433911yescharacteristic
822C2×C4C2×D4×D1111yescharacteristic
823C2×C4#6703711yescharacteristic
824C2×C4#6703711yescharacteristic
825C2×C4C22×C22⋊D1111yescharacteristic
826C8—22no—
827C8—41no—
828C8—441no—
829C8—441no—
830C22—22no—
831C22—24no—
832C22—22no—
833C22—22no—
834C22—42no—
835C22—41no—
836C22—42no—
837C22—42no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—42no—
844C22—114no—
845C22—222no—
846C22—222no—
847C22—222no—
848C22—222no—
849C22—222no—
850C22—222no—
851C22—442no—
852C22—442no—
853C22—442no—
854C22—8816no—
855C22—881no—
856C22—881no—
857C22—881no—
858C22—881no—
859C22C2×C22⋊C4×D1111yescharacteristic
860C22#1062302111yescharacteristic
861C22D11×#13511yescharacteristic
862C22D11×#13511yescharacteristic
863C22#1062330011yescharacteristic
864C22#1062330111yescharacteristic
865C22D4×C22⋊D1111yescharacteristic
866C4—22no—
867C4—42no—
868C4—42no—
869C4—81no—
870C4—222no—
871C4—222no—
872C4—222no—
873C4—442no—
874C4—881no—
875C4—881no—
876C4#1062301711yescharacteristic
877C4#1062302111yescharacteristic
878C4C2×C4×C22⋊D1111yescharacteristic
879C4D4×C22⋊D1111yescharacteristic
880C2—42no—
881C2—44no—
882C2—224no—
883C2—882no—
884C2C22⋊C4×C22⋊D1111yescharacteristic
885C2D11×#41611yescharacteristic
886C2#1307713811yescharacteristic
887C2#1308029511yescharacteristic
888C2#1308031711yescharacteristic
889C2#1308045211yescharacteristic
890C2#1308046711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC2×#10623360C2
cosocleC22×C4×C11C24
hypercenterC2×#416D11
hypocenterC11#22414
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×C8×C22⋊D11C2semidirect
3. C2×D11×#102C2semidirect
4. #13071546C2semidirect
5. #13069545C2semidirect
6. #13069424C2semidirect
7. #13069044C2semidirect
8. #13069036C2semidirect
9. #13068938C2semidirect
10. #13068920C2semidirect
11. #13068624C2semidirect
12. #13068556C2semidirect
13. #13068545C2semidirect
14. #102×Dic11C2semidirect
15. C2×C11×#416C2semidirect
18. C23×C8×C11C22semidirect
19. C2×C11×#117C22semidirect
21. #10623360C4semidirect
34. C2×C11×#103C22semidirect
35. C2×C11×#103C22semidirect
38. C2×#66899C22semidirect
39. C2×#66899C22semidirect
42. #10622825C22semidirect
43. C2×C22⋊(C11⋊C8)C22semidirect
48. C2×Dic11⋊C8C22semidirect
49. C2×C8×Dic11C22semidirect
51. #10622590C22semidirect
52. C4⋊C4×Dic11C22semidirect
60. #10622189C22semidirect
61. #10622189C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
70. C2×C11×#41C2×C4semidirect
104. #67000C2×C4semidirect
110. D4×Dic11C2×C4semidirect
112. #66983C2×C4semidirect
141. C11×#102D4semidirect
284. C2×#416D11semidirect
403. C23×C8C2×D11semidirect
414. C2×#117C2×D11semidirect
422. C2×#103C2×D11semidirect
423. C2×#103C2×D11semidirect
483. C2×D11#416semidirect
504. C2×#41C4×D11semidirect
584. #102C22⋊D11semidirect
726. C11#22414semidirect

Maximal subgroups

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

subgroupindex
C2×#106233602
C2×C8×C22⋊D112
C2×D11×#1022
#130715462
#130695452
#130694242
#130690442
#130690362
#130689382
#130689202
#130686242
#130685562
#130685452
#102×Dic112
C2×C11×#4162
#2241411