Finite Group Databasebeta

← #14769289

Subgroups — #14769289

Order 2816.

1530 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623129C211yesmaximal, characteristic
2C2×#10622724C211yesmaximal, characteristic, complemented
3C2×#10622384C211yesmaximal, characteristic, complemented
4C22×#66880C211yesmaximal, characteristic, complemented
5#13071512C211yesmaximal, characteristic, complemented
6#13069547C211yesmaximal, characteristic, complemented
7#13069431C211yesmaximal, characteristic, complemented
8#13069048C211yesmaximal, characteristic, complemented
9#13068934C211yesmaximal, characteristic, complemented
10#13068922C211yesmaximal, characteristic, complemented
11#13068620C211yesmaximal, characteristic, complemented
12#13068553C211yesmaximal, characteristic, complemented
13#13068550C211yesmaximal, characteristic, complemented
14#13068445C211yesmaximal, characteristic, complemented
15C11×#1893C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×#66992—21no—
21C2×#66989C2211yescharacteristic
22C2×D4×Dic11—21no—
23C2×C4×C22⋊D11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×#4313C2211yescharacteristic
26#10623129—24no—
27#10623129C418yescomplemented
28C2×#66950C2211yescharacteristic
29C2×C4⋊C4×D11C2211yescharacteristic
30C2×#66940C2211yescharacteristic
31C2×#66938—21no—
32C2×(C22⋊D11)⋊C4—21no—
33C2×#66931—21no—
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C11×#380C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40#10622724—24no—
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×#66880—24no—
43C2×#66880C2211yescharacteristic
44C2×#66880C2211yescharacteristic
45C2×#66880C2211yescharacteristic
46C2×#66880C2211yescharacteristic
47C2×#66879C2211yescharacteristic
48C2×Dic11⋊C8C2211yescharacteristic
49#10622600C2211yescharacteristic
50#10622589C2211yescharacteristic
51C4⋊C4×Dic11C2211yescharacteristic
52C2×#66874C2211yescharacteristic
53C2×#66874C2211yescharacteristic
54C2×#66874C2211yescharacteristic
55C2×#66874C2211yescharacteristic
56#10622559—21no—
57#10622384—24no—
58#10622281—21no—
59#10622260—21no—
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C22×D4×C11—21no—
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C22×C22⋊D11D411yescharacteristic
69C23×Dic11—21no—
70C23×Dic11—21no—
71C23×Dic11—21no—
72C2×#4341—22no—
73C2×#4341—22no—
74C2×#4341—22no—
75C2×#4341—41no—
76C2×#4341—41no—
77C2×#4341C2×C414yescomplemented
78C22×C4×D11—21no—
79C22×C4×D11C2311yescharacteristic
80C22×Dic22—22no—
81C22×Dic22—22no—
82C22×Dic22—21no—
83C22×Dic22—22no—
84C22×Dic22—41no—
85C22×Dic22—41no—
86C22×Dic22C2×C414yescomplemented
87C22×Dic22C2311yescharacteristic
88C22×Dic22C2311yescharacteristic
89C22×C8×C11—22no—
90C22×C8×C11—22no—
91C22×C8×C11—41no—
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C11×#121—22no—
95C11×#121C2×C414yescomplemented
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#66992—28no—
105#66989—22no—
106#66989C2×C414yescomplemented
107D4×Dic11—28no—
108C4×C22⋊D11C2×C414yes—
109C4×C22⋊D11D414yes—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4D411yescharacteristic
113C2×C4⋊Dic11—21no—
114C2×C4⋊Dic11—22no—
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11—41no—
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4D411yescharacteristic
124C2×C4×Dic11—21no—
125C2×C4×Dic11—21no—
126C2×C4×Dic11C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C2×#4313—22no—
130C2×#4313—22no—
131C2×#4313—41no—
132#66950—22no—
133#66950C2×C414yescomplemented
134C4⋊C4×D11—22no—
135C4⋊C4×D11—41no—
136#66940—22no—
137#66940C2×C414yescomplemented
138#66938—28no—
139(C22⋊D11)⋊C4—44no—
140#66931—28no—
141C11×#102—22no—
142C11×#102—41no—
143C11×#95—21no—
144#66896—22no—
145#66896—41no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C22⋊(C11⋊C8)—22no—
149(C2×D11)⋊C8—22no—
150#66880—22no—
151#66880—22no—
152#66880—22no—
153#66880D414yescomplemented
154#66879—22no—
155Dic11⋊C8—22no—
156#66874—22no—
157#66874—22no—
158#66874—41no—
159#66874—41no—
160#22421—111nomaximal, Sylow
161C24×C11—21no—
162C24×C11C2×D411yescharacteristic
163C23×D11C2×D411yescharacteristic
164C2×D4×C11—24no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—42no—
171C2×D4×C11—42no—
172C2×D4×C11C22×C412yes—
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×C11C22×C412yes—
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D412yes—
183C22×C4×C11C2411yescharacteristic
184C2×C22⋊D11—22no—
185C2×C22⋊D11—22no—
186C2×C22⋊D11—24no—
187C2×C22⋊D11—42no—
188C2×C22⋊D11—42no—
189C2×C22⋊D11C22⋊C414yes—
190C22×Dic11—24no—
191C22×Dic11—24no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—42no—
197C22×Dic11—42no—
198C22×Dic11—42no—
199C22×Dic11—42no—
200C22×Dic11—42no—
201C22×Dic11—42no—
202C22×Dic11—81no—
203C22×Dic11C2×D411yescharacteristic
204C22×Dic11C2×D411yescharacteristic
205C22×Dic11C2×D411yescharacteristic
206#4341—28no—
207#4341—44no—
208#4341—44no—
209#4341—44no—
210C2×C4×D11—21no—
211C2×C4×D11—21no—
212C2×C4×D11—21no—
213C2×C4×D11—21no—
214C2×C4×D11—42no—
215C2×C4×D11—42no—
216C2×C4×D11—81no—
217C2×C4×D11C22×C412yes—
218C2×C4×D11C2×D412yes—
219C2×Dic22—28no—
220C2×Dic22—24no—
221C2×Dic22—21no—
222C2×Dic22—21no—
223C2×Dic22—21no—
224C2×Dic22—21no—
225C2×Dic22—21no—
226C2×Dic22—21no—
227C2×Dic22—21no—
228C2×Dic22—21no—
229C2×Dic22—44no—
230C2×Dic22—44no—
231C2×Dic22—44no—
232C2×Dic22—42no—
233C2×Dic22—42no—
234C2×Dic22C22×C412yes—
235C2×Dic22C22×C412yes—
236C2×Dic22C2×D412yes—
237C2×Dic22#4112yes—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—44no—
244C2×C8×C11C2×D412yes—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4C22×C412yes—
251C11×C22⋊C4—24no—
252C11×C22⋊C4—42no—
253C22⋊Dic11—24no—
254C22⋊Dic11—24no—
255C22⋊Dic11C22⋊C414yes—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—42no—
258(C2×D11)⋊C4C22⋊C414yes—
259C4⋊Dic11—24no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11—42no—
264C4⋊Dic11C2×D412yes—
265Dic11⋊C4—24no—
266Dic11⋊C4—42no—
267Dic11⋊C4—42no—
268Dic11⋊C4—81no—
269Dic11⋊C4C22⋊C414yes—
270C4×Dic11—24no—
271C4×Dic11—42no—
272C4×Dic11C22×C412yes—
273C4×Dic11C2×D412yes—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280#4313—44no—
281C2×#548—111no—
282C2×#435—111no—
283C2×#417—111no—
284C22×#103—111no—
285D4×C4⋊C4—111no—
286#1983—111no—
287#1959—111no—
288#1894—111no—
289#1893D1111yescharacteristic, complemented
290#1874—111no—
291#1872—111no—
292#1803—111no—
293#1788—111no—
294#1787—111no—
295#1763—111no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—22no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11C2×C22⋊C412yes—
308C23×C11AGL(1,ℤ/8)12yes—
309C23×C11#13712yes—
310C23×C11C22×D411yescharacteristic
311C22×D11—21no—
312C22×D11—21no—
313C22×D11—21no—
314C22×D11—21no—
315C22×D11—21no—
316C22×D11—21no—
317C22×D11C2×C22⋊C412yes—
318D4×C11—22no—
319D4×C11—22no—
320D4×C11—48no—
321D4×C11—41no—
322D4×C11—41no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
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×C11C2×C22⋊C412yes—
339C2×C4×C11C23×C411yescharacteristic
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C2×#4111yescharacteristic
343C2×C4×C11H(5,𝔽2)11yescharacteristic
344C2×C4×C11H(5,𝔽2)11yescharacteristic
345C22⋊D11—28no—
346C22⋊D11—48no—
347C2×Dic11—22no—
348C2×Dic11—21no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—21no—
352C2×Dic11—21no—
353C2×Dic11—21no—
354C2×Dic11—21no—
355C2×Dic11—21no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—48no—
359C2×Dic11—48no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—84no—
368C2×Dic11C2×C22⋊C412yes—
369C2×Dic11C2×C22⋊C412yes—
370C2×Dic11C2×C22⋊C412yes—
371C4×D11—22no—
372C4×D11—22no—
373C4×D11—22no—
374C4×D11—22no—
375C4×D11—84no—
376Dic22—22no—
377Dic22—22no—
378Dic22—22no—
379Dic22—22no—
380Dic22—22no—
381Dic22—48no—
382Dic22—41no—
383Dic22—41no—
384Dic22C4×D414yescomplemented
385C8×C11—22no—
386C8×C11—41no—
387C11⋊C8—41no—
388C11⋊C8—41no—
389C22×#41—111no—
390C23×Q8—111no—
391C22×M16—111no—
392C23×C8C2×D1111yescharacteristic
393#548—118no—
394#548—224no—
395C2×#124—111no—
396C2×#124—221no—
397C2×C22⋊Q8—111no—
398C2×C22⋊Q8—221no—
399C2×#121—221no—
400C2×#121C2×D1111yescharacteristic
401C2×C4×Q8—111no—
402C2×C4×D4—111no—
403C2×C4×D4—221no—
404C2×C4×D4—221no—
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
407#435—224no—
408C2×C4⋊C8—111no—
409#417—224no—
410C2×#103—111no—
411C2×#103—111no—
412C2×#103—111no—
413C2×#103—111no—
414C2×#103—111no—
415C2×#103—111no—
416C2×#103—111no—
417C2×#103—111no—
418C2×#103—224no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102C2×D1111yescharacteristic
422C2×#102C2×D1111yescharacteristic
423C2×C22⋊C8—111no—
424C2×C22⋊C8—111no—
425C2×#97—111no—
426#389—221no—
427#385—221no—
428#385—221no—
429#384—111no—
430#380—111no—
431#380C2×D1111yescharacteristic
432C4×C4⋊C4—111no—
433#340—111no—
434#340—111no—
435#340C2×D1111yescharacteristic
436#340C2×D1111yescharacteristic
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—22no—
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—42no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—81no—
447C22×C11—81no—
448C22×C11—81no—
449C22×C11—81no—
450C22×C11#41714yescomplemented
451C22×C11C22×C22⋊C411yescharacteristic
452C22×C11D4211yescharacteristic
453C22×C11#54611yescharacteristic
454C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
455C22×C11C2×#13711yescharacteristic
456C22×C11#57711yescharacteristic
457C22×C11#57811yescharacteristic
458C2×D11—22no—
459C2×D11—22no—
460C2×D11—22no—
461C2×D11—41no—
462C2×D11—41no—
463C2×D11—41no—
464C2×D11—41no—
465C4×C11—22no—
466C4×C11—42no—
467C4×C11—81no—
468C4×C11—81no—
469C4×C11C2×C4×D411yescharacteristic
470C4×C11#51811yescharacteristic
471C4×C11D4211yescharacteristic
472C4×C11#54611yescharacteristic
473Dic11—24no—
474Dic11—22no—
475Dic11—22no—
476Dic11—22no—
477Dic11—42no—
478Dic11—42no—
479Dic11—81no—
480C2×#41—114no—
481C2×#41—222no—
482C2×#41—222no—
483C2×#41—222no—
484C2×#41—441no—
485C2×#41—441no—
486C22×Q8—114no—
487C22×Q8—111no—
488C22×Q8—111no—
489C22×Q8—222no—
490C22×Q8—222no—
491C22×Q8—221no—
492C22×Q8—222no—
493C22×Q8—441no—
494C22×Q8—441no—
495C22×D4—21no—
496C22×D4—111no—
497C22×D4—221no—
498C22×D4C22×D1111yescharacteristic
499C23×C4—111no—
500C23×C4—221no—
501C23×C4—221no—
502C23×C4—221no—
503C23×C4—221no—
504C23×C4C22×D1111yescharacteristic
505C2×M16—222no—
506C2×M16—222no—
507C2×M16—441no—
508C22×C8—22no—
509C22×C8—22no—
510C22×C8—41no—
511C22×C8—111no—
512C22×C8—111no—
513C22×C8C22×D1111yescharacteristic
514C22×C8C22×D1111yescharacteristic
515#124—114no—
516#124—222no—
517#124—228no—
518C22⋊Q8—114no—
519C22⋊Q8—228no—
520C22⋊Q8—222no—
521#121—22no—
522#121—228no—
523#121C4×D1114yescomplemented
524C4×Q8—114no—
525C4×Q8—222no—
526C4×D4—114no—
527C4×D4—114no—
528C4×D4—228no—
529C4×D4—444no—
530C2×C4⋊C4—111no—
531C2×C4⋊C4—111no—
532C2×C4⋊C4—111no—
533C2×C4⋊C4—222no—
534C2×C4⋊C4—222no—
535C2×C4⋊C4—221no—
536C2×C4⋊C4—221no—
537C2×C4⋊C4—221no—
538C2×C4⋊C4—221no—
539C2×C4⋊C4—221no—
540C2×C4⋊C4—221no—
541C2×C4⋊C4—441no—
542C2×C4⋊C4—441no—
543C2×C4⋊C4C22×D1111yescharacteristic
544C2×C4⋊C4C22×D1111yescharacteristic
545C2×C4⋊C4C22×D1111yescharacteristic
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—111no—
549C2×C22⋊C4—111no—
550C2×C22⋊C4—221no—
551C2×C22⋊C4—221no—
552C2×C22⋊C4—221no—
553C2×C22⋊C4—221no—
554C2×C42—111no—
555C2×C42—221no—
556C2×C42—221no—
557C4⋊C8—222no—
558#103—114no—
559#103—222no—
560#103—222no—
561#103—222no—
562#103—222no—
563#103—222no—
564#103—441no—
565#103—441no—
566#102—22no—
567#102—41no—
568#102—222no—
569#102—441no—
570C22⋊C8—222no—
571C22⋊C8—222no—
572#97—222no—
573#95—21no—
574#95—221no—
575#95—221no—
576C2×C11—24no—
577C2×C11—82no—
578C2×C11D4×C22⋊C411yescharacteristic
579C2×C11C2×#41711yescharacteristic
580C2×C11#289811yescharacteristic
581C2×C11#326511yescharacteristic
582C2×C11#327011yescharacteristic
583C2×C11#330811yescharacteristic
584C2×C11#331611yescharacteristic
585D11—42no—
586C24—21no—
587C24—111no—
588C24D4×D1111yescharacteristic
589#41—228no—
590#41—444no—
591#41—444no—
592#41—444no—
593C2×Q8—112no—
594C2×Q8—112no—
595C2×Q8—112no—
596C2×Q8—112no—
597C2×Q8—228no—
598C2×Q8—224no—
599C2×Q8—221no—
600C2×Q8—221no—
601C2×Q8—221no—
602C2×Q8—221no—
603C2×Q8—221no—
604C2×Q8—221no—
605C2×Q8—221no—
606C2×Q8—221no—
607C2×Q8—442no—
608C2×Q8—442no—
609C2×Q8—444no—
610C2×Q8—444no—
611C2×Q8—444no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—114no—
621C2×D4—222no—
622C2×D4—222no—
623C2×D4—224no—
624C2×D4—442no—
625C2×D4—442no—
626C2×D4C2×C4×D1112yes—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—111no—
635C22×C4—111no—
636C22×C4—111no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—224no—
640C22×C4—221no—
641C22×C4—221no—
642C22×C4—221no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—224no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—442no—
650C22×C4—442no—
651C22×C4—442no—
652C22×C4—442no—
653C22×C4—442no—
654C22×C4—442no—
655C22×C4—442no—
656C22×C4—442no—
657C22×C4—881no—
658C22×C4—881no—
659C22×C4C2×C4×D1112yes—
660C22×C4D4×D1111yescharacteristic
661C22×C4D4×D1112yes—
662C22×C4C23×D1111yescharacteristic
663M16—444no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—44no—
670C2×C8—221no—
671C2×C8—221no—
672C2×C8—221no—
673C2×C8—221no—
674C2×C8—221no—
675C2×C8—221no—
676C2×C8D4×D1112yes—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—114no—
683C4⋊C4—112no—
684C4⋊C4—224no—
685C4⋊C4—224no—
686C4⋊C4—221no—
687C4⋊C4—221no—
688C4⋊C4—221no—
689C4⋊C4—442no—
690C4⋊C4—442no—
691C4⋊C4—442no—
692C4⋊C4—881no—
693C4⋊C4C2×C4×D1112yes—
694C22⋊C4—24no—
695C22⋊C4—42no—
696C22⋊C4—114no—
697C22⋊C4—114no—
698C22⋊C4—224no—
699C22⋊C4—224no—
700C22⋊C4—224no—
701C22⋊C4—442no—
702C42—112no—
703C42—112no—
704C42—224no—
705C42—442no—
706C11#2242111yescharacteristic, complemented, Sylow
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—22no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—112no—
719C23—221no—
720C23—221no—
721C23—221no—
722C23—221no—
723C23—221no—
724C23—221no—
725C23C22⋊C4×D1112yes—
726C23#6696412yes—
727C23#6696812yes—
728C23C2×D4×D1111yescharacteristic
729Q8—114no—
730Q8—222no—
731Q8—222no—
732Q8—222no—
733Q8—222no—
734Q8—222no—
735Q8—448no—
736Q8—441no—
737Q8—441no—
738D4—22no—
739D4—22no—
740D4—48no—
741D4—41no—
742D4—41no—
743D4—228no—
744D4—448no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—112no—
761C2×C4—112no—
762C2×C4—112no—
763C2×C4—222no—
764C2×C4—221no—
765C2×C4—221no—
766C2×C4—221no—
767C2×C4—221no—
768C2×C4—221no—
769C2×C4—222no—
770C2×C4—221no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—448no—
779C2×C4—448no—
780C2×C4—441no—
781C2×C4—441no—
782C2×C4—441no—
783C2×C4—441no—
784C2×C4—441no—
785C2×C4—441no—
786C2×C4—441no—
787C2×C4—884no—
788C2×C4—884no—
789C2×C4C22⋊C4×D1112yes—
790C2×C4C22×C4×D1111yescharacteristic
791C2×C4C2×D4×D1111yescharacteristic
792C2×C4C2×D4×D1111yescharacteristic
793C2×C4#6703711yescharacteristic
794C2×C4#41×D1111yescharacteristic
795C2×C4#6704211yescharacteristic
796C8—22no—
797C8—41no—
798C8—441no—
799C8—441no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—222no—
814C22—222no—
815C22—222no—
816C22—441no—
817C22—441no—
818C22—441no—
819C22—441no—
820C22#1062238414yescomplemented
821C22C2×C22⋊C4×D1111yescharacteristic
822C22#1062314011yescharacteristic
823C22#1062314111yescharacteristic
824C22C2×#6696411yescharacteristic
825C22C2×#6696811yescharacteristic
826C22#1062330111yescharacteristic
827C22#1062330211yescharacteristic
828C4—22no—
829C4—42no—
830C4—81no—
831C4—81no—
832C4—222no—
833C4—224no—
834C4—222no—
835C4—222no—
836C4—442no—
837C4—442no—
838C4—881no—
839C4C4×D4×D1111yescharacteristic
840C4#1062307611yescharacteristic
841C4#1062312111yescharacteristic
842C4#1062318511yescharacteristic
843C2—24no—
844C2—82no—
845C2—442no—
846C2#1307143411yescharacteristic
847C2C2×#1062238411yescharacteristic
848C2#1307714511yescharacteristic
849C2#1308010811yescharacteristic
850C2#1308018311yescharacteristic
851C2#1308061311yescharacteristic
852C2#1308073311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1893C2
socleC23×C11C22×D4
prime radicalC2×#10623129C2
cosocleC22×C4×C11C24
hypercenter#1893D11
hypocenterC11#22421
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×#10622724C2semidirect
3. C2×#10622384C2semidirect
4. C22×#66880C2semidirect
5. #13071512C2semidirect
6. #13069547C2semidirect
7. #13069431C2semidirect
8. #13069048C2semidirect
9. #13068934C2semidirect
10. #13068922C2semidirect
11. #13068620C2semidirect
12. #13068553C2semidirect
13. #13068550C2semidirect
14. #13068445C2semidirect
15. C11×#1893C2semidirect
27. #10623129C4semidirect
77. C2×#4341C2×C4semidirect
86. C22×Dic22C2×C4semidirect
95. C11×#121C2×C4semidirect
106. #66989C2×C4semidirect
133. #66950C2×C4semidirect
137. #66940C2×C4semidirect
153. #66880D4semidirect
289. #1893D11semidirect
384. Dic22C4×D4semidirect
450. C22×C11#417semidirect
523. #121C4×D11semidirect
706. C11#22421semidirect
820. C22#10622384semidirect

Maximal subgroups

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

subgroupindex
C2×#106231292
C2×#106227242
C2×#106223842
C22×#668802
#130715122
#130695472
#130694312
#130690482
#130689342
#130689222
#130686202
#130685532
#130685502
#130684452
C11×#18932
#2242111