Finite Group Databasebeta

← #14769337

Subgroups — #14769337

Order 2816.

1446 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic22C211yesmaximal, characteristic
2C2×#10622624C211yesmaximal, characteristic
3C2×#10622617C211yesmaximal, characteristic, complemented
4C22×#66874C211yesmaximal, characteristic, complemented
5#13069539C211yesmaximal, characteristic, complemented
6#13069435C211yesmaximal, characteristic, complemented
7#13069047C211yesmaximal, characteristic, complemented
8#13069037C211yesmaximal, characteristic, complemented
9#13068928C211yesmaximal, characteristic, complemented
10#13068923C211yesmaximal, characteristic, complemented
11#13068628C211yesmaximal, characteristic, complemented
12#13068550C211yesmaximal, characteristic, complemented
13#13068550C211yesmaximal, characteristic, complemented
14#13068449C211yesmaximal, characteristic, complemented
15C11×#2352C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C2×D4×Dic11—21no—
22C2×#66977C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C23×C11⋊C8C2211yescharacteristic
26D4×Dic22—24no—
27D4×Dic22C418yescomplemented
28C2×#66941—21no—
29C2×#66931—21no—
30C2×#66931—21no—
31C2×#66922C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C11×#388—21no—
34C11×#387—21no—
35C11×#386—21no—
36C11×#382C2211yescharacteristic
37C11×#380C2211yescharacteristic
38C11×#380C2211yescharacteristic
39C4×C11×C4⋊C4C2211yescharacteristic
40C4×C11×C22⋊C4—21no—
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622624—24no—
44#10622617—24no—
45C2×#66874—24no—
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49C2×#66874C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×#66874C2211yescharacteristic
52C2×#66874C2211yescharacteristic
53C2×#66874C2211yescharacteristic
54C2×#66874C2211yescharacteristic
55C2×#66874C2211yescharacteristic
56C2×#66874C2211yescharacteristic
57C2×#66874C2211yescharacteristic
58C2×C4⋊(C11⋊C8)C2211yescharacteristic
59C2×#66867C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C22×D4×C11D411yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×Dic11—21no—
69C23×Dic11—21no—
70C22×Dic22—22no—
71C22×Dic22—22no—
72C22×Dic22—22no—
73C22×Dic22—22no—
74C22×Dic22—21no—
75C22×Dic22—21no—
76C22×Dic22—22no—
77C22×Dic22—22no—
78C22×Dic22—41no—
79C22×Dic22—41no—
80C22×Dic22—41no—
81C22×Dic22—41no—
82C22×Dic22C2×C414yes—
83C22×Dic22C2×C414yescomplemented
84C22×Dic22C2311yescharacteristic
85C22×Dic22C2311yescharacteristic
86C22×Dic22C2311yescharacteristic
87C4×D4×C11C2×C414yes—
88C4×D4×C11D414yes—
89C11×#117—22no—
90C11×#117—41no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—41no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C42×C11—21no—
105C2×C42×C11—21no—
106C2×C42×C11C2311yescharacteristic
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109D4×Dic11—28no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11C2311yescharacteristic
113#66977—22no—
114#66977—22no—
115#66977C2×C414yes—
116#66977C2×C414yescomplemented
117C2×Dic11⋊C4—21no—
118C2×Dic11⋊C4—21no—
119C2×Dic11⋊C4—21no—
120C2×C4×Dic11—21no—
121C2×#4318—22no—
122C2×#4318—22no—
123C2×#4318—41no—
124C22×C11⋊C8—22no—
125C22×C11⋊C8—22no—
126C22×C11⋊C8—41no—
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131#66941—28no—
132#66931—28no—
133#66931—28no—
134#66922—22no—
135#66922C2×C414yescomplemented
136C4×Dic22—22no—
137C4×Dic22C2×C414yescomplemented
138C11×#95—21no—
139C11×#95—21no—
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—22no—
148#66874—22no—
149#66874—22no—
150#66874—22no—
151#66874—22no—
152#66874—41no—
153#66874—41no—
154#66874—41no—
155#66874—41no—
156#66874D414yescomplemented
157C4⋊(C11⋊C8)—22no—
158#66867—22no—
159#22425—111nomaximal, Sylow
160C24×C11C2×D411yescharacteristic
161C24×C11C2×D411yescharacteristic
162C2×D4×C11—22no—
163C2×D4×C11—22no—
164C2×D4×C11C22⋊C414yes—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11—81no—
180C22×C4×C11C22×C412yes—
181C22×C4×C11C22×C412yes—
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D412yes—
187C22×C4×C11C2×D412yes—
188C22×C4×C11C2411yescharacteristic
189C22×Dic11—24no—
190C22×Dic11—24no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—42no—
196C22×Dic11—42no—
197C22×Dic11—42no—
198C22×Dic11—42no—
199C2×Dic22—28no—
200C2×Dic22—28no—
201C2×Dic22—24no—
202C2×Dic22—24no—
203C2×Dic22—21no—
204C2×Dic22—21no—
205C2×Dic22—21no—
206C2×Dic22—21no—
207C2×Dic22—21no—
208C2×Dic22—21no—
209C2×Dic22—21no—
210C2×Dic22—21no—
211C2×Dic22—21no—
212C2×Dic22—21no—
213C2×Dic22—21no—
214C2×Dic22—21no—
215C2×Dic22—21no—
216C2×Dic22—44no—
217C2×Dic22—44no—
218C2×Dic22—44no—
219C2×Dic22—44no—
220C2×Dic22—44no—
221C2×Dic22—44no—
222C2×Dic22—42no—
223C2×Dic22—42no—
224C2×Dic22—42no—
225C2×Dic22—42no—
226C2×Dic22C22×C412yes—
227C2×Dic22C22×C412yes—
228C2×Dic22C22×C412yes—
229C2×Dic22C2×D412yes—
230C2×Dic22#4112yes—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—42no—
239C11×C4⋊C4C22⋊C414yes—
240C11×C4⋊C4C2×D412yes—
241C11×C22⋊C4—42no—
242C11×C22⋊C4—42no—
243C11×C22⋊C4—81no—
244C11×C22⋊C4C22⋊C414yes—
245C11×C22⋊C4C22⋊C414yes—
246C42×C11—42no—
247C42×C11—81no—
248C42×C11C22×C412yes—
249C42×C11C2×D412yes—
250C22⋊Dic11—24no—
251C22⋊Dic11—24no—
252C4⋊Dic11—24no—
253C4⋊Dic11—24no—
254C4⋊Dic11—21no—
255C4⋊Dic11C22×C412yes—
256Dic11⋊C4—24no—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259C4×Dic11—24no—
260#4318—44no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—44no—
273C2×C11⋊C8C2×D412yes—
274C2×D4×Q8—111no—
275C2×#435—111no—
276C2×#419—111no—
277C22×#103—111no—
278#2352D1111yescharacteristic
279#1981—111no—
280#1960—111no—
281#1894—111no—
282#1892—111no—
283#1873—111no—
284#1872—111no—
285#1805—111no—
286#1787—111no—
287#1787—111no—
288#1763—111no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11C2×C22⋊C412yes—
300C23×C11C2×C22⋊C412yes—
301C23×C11#13712yes—
302C23×C11#13712yes—
303C23×C11C22×D411yescharacteristic
304D4×C11—28no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—84no—
334C2×C4×C11C2×C22⋊C412yes—
335C2×C4×C11C2×C22⋊C412yes—
336C2×C4×C11C2×C22⋊C412yes—
337C2×C4×C11C2×C22⋊C412yes—
338C2×C4×C11C23×C411yescharacteristic
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C2×#4111yescharacteristic
342C2×C4×C11H(5,𝔽2)11yescharacteristic
343C2×C4×C11H(5,𝔽2)11yescharacteristic
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—48no—
351C2×Dic11—48no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—41no—
358Dic22—22no—
359Dic22—22no—
360Dic22—22no—
361Dic22—22no—
362Dic22—22no—
363Dic22—22no—
364Dic22—22no—
365Dic22—48no—
366Dic22—48no—
367Dic22—41no—
368Dic22—41no—
369Dic22—41no—
370Dic22—41no—
371Dic22C4×D414yes—
372C11⋊C8—22no—
373C11⋊C8—41no—
374C11⋊C8—41no—
375C11⋊C8—41no—
376C23×Q8—111no—
377C23×Q8—111no—
378C22×M16—111no—
379C23×C8—111no—
380D4×Q8—118no—
381D4×Q8—224no—
382C2×C4⋊Q8—111no—
383C2×C4⋊Q8—221no—
384C2×C22⋊Q8—111no—
385C2×C22⋊Q8—111no—
386C2×C22⋊Q8—221no—
387C2×C22⋊Q8—221no—
388C2×C4×Q8—111no—
389C2×C4×D4—221no—
390C2×C4×D4C2×D1111yescharacteristic
391C2×#117C2×D1111yescharacteristic
392C22×C4⋊C4C2×D1111yescharacteristic
393#435—224no—
394C2×C4⋊C8—111no—
395#419—224no—
396C2×#103—111no—
397C2×#103—111no—
398C2×#103—111no—
399C2×#103—111no—
400C2×#103—111no—
401C2×#103—111no—
402C2×#103—111no—
403C2×#103—111no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103—111no—
408C2×#103—224no—
409C2×C22⋊C8—111no—
410C2×C22⋊C8—111no—
411C2×#97—111no—
412#388—21no—
413#387—21no—
414#386—21no—
415#382C2×D1111yescharacteristic
416#380C2×D1111yescharacteristic
417#380C2×D1111yescharacteristic
418C4×C4⋊C4C2×D1111yescharacteristic
419C4×C22⋊C4—21no—
420#340—111no—
421#340—111no—
422#340—111no—
423#340—111no—
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—22no—
428C22×C11—22no—
429C22×C11—22no—
430C22×C11—22no—
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—41no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11#41914yescomplemented
438C22×C11C22×C22⋊C411yescharacteristic
439C22×C11D4211yescharacteristic
440C22×C11#54611yescharacteristic
441C22×C11C2×#13711yescharacteristic
442C22×C11C2×#13711yescharacteristic
443C22×C11#57711yescharacteristic
444C22×C11#57811yescharacteristic
445C4×C11—22no—
446C4×C11—22no—
447C4×C11—22no—
448C4×C11—22no—
449C4×C11—42no—
450C4×C11—81no—
451C4×C11—81no—
452C4×C11—81no—
453C4×C11C2×C4×D411yescharacteristic
454C4×C11#51811yescharacteristic
455C4×C11D4211yescharacteristic
456C4×C11#54611yescharacteristic
457Dic11—24no—
458Dic11—42no—
459Dic11—42no—
460Dic11—42no—
461C22×Q8—114no—
462C22×Q8—114no—
463C22×Q8—111no—
464C22×Q8—111no—
465C22×Q8—111no—
466C22×Q8—222no—
467C22×Q8—222no—
468C22×Q8—222no—
469C22×Q8—222no—
470C22×Q8—222no—
471C22×Q8—222no—
472C22×Q8—221no—
473C22×Q8—221no—
474C22×Q8—441no—
475C22×Q8—441no—
476C22×Q8—441no—
477C22×Q8—441no—
478C22×D4C22⋊D1111yescharacteristic
479C23×C4—21no—
480C23×C4—221no—
481C23×C4—221no—
482C23×C4C22×D1111yescharacteristic
483C23×C4C22×D1111yescharacteristic
484C2×M16—222no—
485C2×M16—222no—
486C2×M16—441no—
487C22×C8—111no—
488C22×C8—111no—
489C22×C8—111no—
490C22×C8—111no—
491C22×C8—222no—
492C22×C8—222no—
493C22×C8—441no—
494C4⋊Q8—114no—
495C4⋊Q8—228no—
496C4⋊Q8—222no—
497C22⋊Q8—114no—
498C22⋊Q8—114no—
499C22⋊Q8—222no—
500C22⋊Q8—222no—
501C22⋊Q8—228no—
502C22⋊Q8—228no—
503C4×Q8—114no—
504C4×Q8—222no—
505C4×D4—228no—
506C4×D4C4×D1114yes—
507C4×D4D4414yes—
508#117—22no—
509#117—41no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—41no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—221no—
515C2×C4⋊C4—221no—
516C2×C4⋊C4—221no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4C22⋊D1111yescharacteristic
520C2×C4⋊C4C22×D1111yescharacteristic
521C2×C4⋊C4C22×D1111yescharacteristic
522C2×C4⋊C4C22×D1111yescharacteristic
523C2×C4⋊C4C22×D1111yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C22⋊C4C22⋊D1111yescharacteristic
530C2×C22⋊C4C22⋊D1111yescharacteristic
531C2×C42—21no—
532C2×C42—21no—
533C2×C42—221no—
534C2×C42C22×D1111yescharacteristic
535C4⋊C8—222no—
536#103—114no—
537#103—222no—
538#103—222no—
539#103—222no—
540#103—222no—
541#103—222no—
542#103—222no—
543#103—222no—
544#103—441no—
545#103—441no—
546#103—441no—
547#103—441no—
548C22⋊C8—222no—
549C22⋊C8—222no—
550#97—222no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556C2×C11—24no—
557C2×C11—42no—
558C2×C11D4×C22⋊C411yescharacteristic
559C2×C11C2×#41911yescharacteristic
560C2×C11#289811yescharacteristic
561C2×C11#326611yescharacteristic
562C2×C11#327011yescharacteristic
563C2×C11#331211yescharacteristic
564C2×C11#332011yescharacteristic
565C24C2×C22⋊D1111yescharacteristic
566C24C2×C22⋊D1111yescharacteristic
567C2×Q8—112no—
568C2×Q8—112no—
569C2×Q8—112no—
570C2×Q8—112no—
571C2×Q8—112no—
572C2×Q8—228no—
573C2×Q8—228no—
574C2×Q8—224no—
575C2×Q8—224no—
576C2×Q8—221no—
577C2×Q8—221no—
578C2×Q8—221no—
579C2×Q8—221no—
580C2×Q8—221no—
581C2×Q8—221no—
582C2×Q8—221no—
583C2×Q8—221no—
584C2×Q8—221no—
585C2×Q8—221no—
586C2×Q8—221no—
587C2×Q8—221no—
588C2×Q8—221no—
589C2×Q8—442no—
590C2×Q8—442no—
591C2×Q8—442no—
592C2×Q8—442no—
593C2×Q8—444no—
594C2×Q8—444no—
595C2×Q8—444no—
596C2×Q8—444no—
597C2×Q8—444no—
598C2×Q8—444no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4(C2×D11)⋊C414yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—81no—
617C22×C4—221no—
618C22×C4—224no—
619C22×C4—224no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4—442no—
624C22×C4—442no—
625C22×C4—442no—
626C22×C4—442no—
627C22×C4C2×C4×D1112yes—
628C22×C4C2×C4×D1112yes—
629C22×C4C2×D4412yes—
630C22×C4C2×D4412yes—
631C22×C4C2×C22⋊D1111yescharacteristic
632C22×C4C2×C22⋊D1111yescharacteristic
633C22×C4C2×C22⋊D1111yescharacteristic
634C22×C4C2×C22⋊D1111yescharacteristic
635C22×C4C23×D1111yescharacteristic
636M16—444no—
637C2×C8—112no—
638C2×C8—221no—
639C2×C8—221no—
640C2×C8—221no—
641C2×C8—221no—
642C2×C8—221no—
643C2×C8—221no—
644C2×C8—221no—
645C2×C8—221no—
646C2×C8—221no—
647C2×C8—221no—
648C2×C8—221no—
649C2×C8—444no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—42no—
658C4⋊C4—112no—
659C4⋊C4—224no—
660C4⋊C4—224no—
661C4⋊C4—224no—
662C4⋊C4—224no—
663C4⋊C4—224no—
664C4⋊C4—221no—
665C4⋊C4(C2×D11)⋊C414yes—
666C4⋊C4D4×D1112yes—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—81no—
670C22⋊C4—224no—
671C22⋊C4—224no—
672C22⋊C4(C2×D11)⋊C414yes—
673C22⋊C4(C2×D11)⋊C414yes—
674C42—42no—
675C42—81no—
676C42—224no—
677C42C2×C4×D1112yes—
678C42C2×D4412yes—
679C11#2242511yescharacteristic, complemented, Sylow
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23C2×(C2×D11)⋊C412yes—
691C23C2×(C2×D11)⋊C412yes—
692C23#6700412yes—
693C23#6700412yes—
694C23C22×C22⋊D1111yescharacteristic
695Q8—114no—
696Q8—222no—
697Q8—222no—
698Q8—222no—
699Q8—222no—
700Q8—222no—
701Q8—222no—
702Q8—222no—
703Q8—448no—
704Q8—448no—
705Q8—441no—
706Q8—441no—
707Q8—441no—
708Q8—441no—
709D4—28no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—448no—
746C2×C4—448no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4—441no—
750C2×C4—441no—
751C2×C4—441no—
752C2×C4—441no—
753C2×C4C2×(C2×D11)⋊C412yes—
754C2×C4C2×(C2×D11)⋊C412yes—
755C2×C4C2×(C2×D11)⋊C412yes—
756C2×C4C2×(C2×D11)⋊C412yes—
757C2×C4C22×C4×D1111yescharacteristic
758C2×C4C22×D4411yescharacteristic
759C2×C4C2×D4×D1111yescharacteristic
760C2×C4#6703711yescharacteristic
761C2×C4#41×D1111yescharacteristic
762C2×C4#6704211yescharacteristic
763C8—222no—
764C8—441no—
765C8—441no—
766C8—441no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22#1062261714yescomplemented
781C22C22×(C2×D11)⋊C411yescharacteristic
782C22D4×C22⋊D1111yescharacteristic
783C22C2×#6700411yescharacteristic
784C22C2×#6700411yescharacteristic
785C22#1062336011yescharacteristic
786C22#1062336711yescharacteristic
787C22#1062336911yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—42no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4—224no—
797C4—442no—
798C4—442no—
799C4—442no—
800C4C4×D4×D1111yescharacteristic
801C4#1062307611yescharacteristic
802C4D4×D4411yescharacteristic
803C4#1062308511yescharacteristic
804C2—24no—
805C2—42no—
806C2D4×(C2×D11)⋊C411yescharacteristic
807C2C2×#1062261711yescharacteristic
808C2#1307714611yescharacteristic
809C2#1308012211yescharacteristic
810C2#1308018211yescharacteristic
811C2#1308066111yescharacteristic
812C2#1308078111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2352C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
cosocleC22×C4×C11C24
hypercenter#2352D11
hypocenterC11#22425
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
3. C2×#10622617C2semidirect
4. C22×#66874C2semidirect
5. #13069539C2semidirect
6. #13069435C2semidirect
7. #13069047C2semidirect
8. #13069037C2semidirect
9. #13068928C2semidirect
10. #13068923C2semidirect
11. #13068628C2semidirect
12. #13068550C2semidirect
13. #13068550C2semidirect
14. #13068449C2semidirect
27. D4×Dic22C4semidirect
83. C22×Dic22C2×C4semidirect
116. #66977C2×C4semidirect
135. #66922C2×C4semidirect
137. C4×Dic22C2×C4semidirect
156. #66874D4semidirect
437. C22×C11#419semidirect
679. C11#22425semidirect
780. C22#10622617semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic222
C2×#106226242
C2×#106226172
C22×#668742
#130695392
#130694352
#130690472
#130690372
#130689282
#130689232
#130686282
#130685502
#130684492
C11×#23522
#2242511