Finite Group Databasebeta

← #25147366

Subgroups — #25147366

Order 11008.

1116 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583133C211yesmaximal, characteristic, complemented
2C2×#14583126C211yesmaximal, characteristic, complemented
3C2×#14583114C211yesmaximal, characteristic, complemented
4C2×D4×C43⋊C8C211yesmaximal, characteristic, complemented
5#19139534C211yesmaximal, characteristic, complemented
6#19135798C211yesmaximal, characteristic, complemented
7#19135784C211yesmaximal, characteristic, complemented
8#19135598C211yesmaximal, characteristic, complemented
9#19135591C211yesmaximal, characteristic, complemented
10#19135404C211yesmaximal, characteristic, complemented
11#19135361C211yesmaximal, characteristic, complemented
12#19135021C211yesmaximal, characteristic, complemented
13#19135016C211yesmaximal, characteristic, complemented
14C4×#13063246C211yesmaximal, characteristic, complemented
15C43×#2535C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C23×C43⋊C8C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×#13063313C2211yescharacteristic
21C2×#13063304C2211yescharacteristic
22C2×#13063304C2211yescharacteristic
23C2×#13063299C2211yescharacteristic
24C2×#13063299C2211yescharacteristic
25#14583133—24no—
26#14583126—24no—
27#14583114—24no—
28D4×C43⋊C8—24no—
29C2×#13063258C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×C4×C43⋊C8C2211yescharacteristic
43#14582834—21no—
44#14582807—21no—
45#14582799—21no—
46#14582799—21no—
47C4×C4⋊Dic43C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52C2×#121×C43C2211yescharacteristic
53C2×#121×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C43×#397—21no—
57C43×#392—21no—
58C43×#386—21no—
59C43×#386—21no—
60C43×#382C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C43×#380C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C22×C22⋊D43—21no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883—41no—
70C2×#10621882—22no—
71C2×#10621882—22no—
72C2×#10621882—41no—
73C22×C43⋊C8—22no—
74C22×C43⋊C8—22no—
75C22×C43⋊C8—22no—
76C22×C43⋊C8—22no—
77C22×C43⋊C8—41no—
78C22×C43⋊C8—41no—
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063313—22no—
84#13063313—22no—
85#13063304—22no—
86#13063304—22no—
87#13063304—41no—
88#13063304—41no—
89#13063299—22no—
90#13063299—22no—
91#13063299—41no—
92#13063299—41no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×C4×Dic43—21no—
104#13063258—22no—
105#13063256—22no—
106C4⋊(C43⋊C8)D414yescomplemented
107#13063248—22no—
108#13063248—22no—
109#13063248—41no—
110#13063246—22no—
111#13063246D414yescomplemented
112#13063245—22no—
113#13063245—22no—
114#13063245—41no—
115C22⋊(C43⋊C8)—22no—
116C22⋊(C43⋊C8)—22no—
117C4×C43⋊C8—22no—
118C43⋊#95—21no—
119C22×D4×C43—21no—
120C22×D4×C43—21no—
121C22×D4×C43D411yescharacteristic
122C22×D4×C43C2311yescharacteristic
123C23×C4×C43—21no—
124C23×C4×C43C2311yescharacteristic
125C23×C4×C43C2311yescharacteristic
126#121×C43—22no—
127#121×C43—22no—
128#121×C43—41no—
129#121×C43—41no—
130C4×D4×C43—22no—
131C4×D4×C43—22no—
132C4×D4×C43—22no—
133C4×D4×C43—22no—
134C2×C4⋊C4×C43D411yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43D411yescharacteristic
144C2×C22⋊C4×C43D411yescharacteristic
145C2×C42×C43C2311yescharacteristic
146#95×C43—21no—
147#95×C43—21no—
148#95×C43—21no—
149#95×C43—21no—
150C24×C43—21no—
151C24×C43C2×D411yescharacteristic
152C24×C43C2×D411yescharacteristic
153C23×D43—21no—
154C2×D4×C43—22no—
155C2×D4×C43—21no—
156C2×D4×C43—22no—
157C2×D4×C43—22no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—81no—
167C2×D4×C43—81no—
168C2×D4×C43C2×D412yes—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—42no—
185C22×C4×C43—81no—
186C22×C4×C43—81no—
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2411yescharacteristic
192C2×C22⋊D43—42no—
193C2×C22⋊D43—42no—
194C2×C22⋊D43—42no—
195C2×C22⋊D43—42no—
196C2×C22⋊D43—81no—
197C2×C22⋊D43—81no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C2×D172—21no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—21no—
207C2×Dic86—21no—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86—21no—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C4⋊C4×C43—22no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—21no—
220C22⋊C4×C43—22no—
221C22⋊C4×C43—22no—
222C22⋊C4×C43—42no—
223C22⋊C4×C43—42no—
224C22⋊C4×C43—42no—
225C22⋊C4×C43—81no—
226C22⋊C4×C43—81no—
227C42×C43C2×D412yes—
228C42×C43#4112yes—
229C22⋊Dic43—42no—
230C22⋊Dic43—42no—
231#10621883—44no—
232#10621882—44no—
233(C2×D43)⋊C4—42no—
234(C2×D43)⋊C4—42no—
235(C2×D43)⋊C4—42no—
236(C2×D43)⋊C4—42no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43C2×D412yes—
240C4⋊Dic43#4112yes—
241Dic43⋊C4—42no—
242Dic43⋊C4—42no—
243C4×Dic43—81no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—44no—
254C2×C43⋊C8—44no—
255C2×C43⋊C8C2×D412yes—
256C2×C43⋊C8C2×D412yes—
257C2×C43⋊C8C2×D412yes—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—22no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43#13512yes—
278C23×C43#13512yes—
279C23×C43C22×D411yescharacteristic
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—41no—
286C22×D43—41no—
287D4×C43—28no—
288D4×C43—22no—
289D4×C43—22no—
290D4×C43—41no—
291D4×C43—41no—
292D4×C43—84no—
293D4×C43—84no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—84no—
322C2×C4×C43#12112yes—
323C2×C4×C43#12112yes—
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C2×#4111yescharacteristic
327C2×C4×C43C2×#4111yescharacteristic
328C2×C4×C43H(5,𝔽2)11yescharacteristic
329C2×C4×C43H(5,𝔽2)11yescharacteristic
330C22⋊D43—84no—
331C22⋊D43—84no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341D172—41no—
342D172—41no—
343D172—41no—
344D172—41no—
345Dic86—41no—
346Dic86—41no—
347Dic86—41no—
348Dic86—41no—
349C43⋊C8—22no—
350C43⋊C8—22no—
351C43⋊C8—22no—
352C43⋊C8—41no—
353#25388—431nomaximal, Sylow
354C22×C43—22no—
355C22×C43—22no—
356C22×C43—22no—
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—22no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—41no—
367C22×C43—41no—
368C22×C43—42no—
369C22×C43—42no—
370C22×C43—42no—
371C22×C43—81no—
372C22×C43—81no—
373C22×C43—81no—
374C22×C43—81no—
375C22×C43C2×#12111yescharacteristic
376C22×C43D4211yescharacteristic
377C22×C43#54611yescharacteristic
378C22×C43C2×#13511yescharacteristic
379C22×C43C2×#13511yescharacteristic
380C22×C43#57611yescharacteristic
381C22×C43#57711yescharacteristic
382C2×D43—81no—
383C2×D43—81no—
384C2×D43—81no—
385C2×D43—81no—
386C2×D43—81no—
387C2×D43—81no—
388C2×D43—81no—
389C4×C43—22no—
390C4×C43—22no—
391C4×C43—41no—
392C4×C43—41no—
393C4×C43—81no—
394C4×C43—81no—
395C4×C43—81no—
396C4×C43#53211yescharacteristic
397C4×C43#54011yescharacteristic
398C4×C43D4211yescharacteristic
399C4×C43#55011yescharacteristic
400Dic43—42no—
401Dic43—42no—
402Dic43—81no—
403C2×#466—431no—
404C2×#465—431no—
405C2×#463—431no—
406C2×C8×D4—431no—
407#2540—431no—
408#2535D4311yescharacteristic, complemented
409#2036—431no—
410#2034—431no—
411#2000—431no—
412#1999—431no—
413#1958—431no—
414#1949—431no—
415#1893—431no—
416#1892—431no—
417C4×#102—431no—
418C2×C43—42no—
419C2×C43—42no—
420C2×C43—82no—
421C2×C43#242811yescharacteristic
422C2×C43#305011yescharacteristic
423C2×C43#306211yescharacteristic
424C2×C43#328011yescharacteristic
425C2×C43#328211yescharacteristic
426C2×C43#329711yescharacteristic
427C2×C43#330111yescharacteristic
428D43—161no—
429C22×SD16—431no—
430C22×D8—431no—
431C23×C8—431no—
432C23×C8—431no—
433C2×#124—431no—
434C2×C22⋊Q8—431no—
435C2×C22⋊Q8—431no—
436C2×#121—431no—
437C2×#121—431no—
438C2×#121C2×D4311yescharacteristic
439C2×#121C2×D4311yescharacteristic
440C2×C4×D4C2×D4311yescharacteristic
441C2×C4×D4C2×D4311yescharacteristic
442#466—864no—
443#465—864no—
444#463—864no—
445C8×D4—864no—
446C2×#107—431no—
447C2×#106—431no—
448C2×C4⋊C8—431no—
449C2×#103—431no—
450C2×#103—431no—
451C2×#103—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102—431no—
455C2×#102—431no—
456C2×#102—431no—
457C2×C22⋊C8—431no—
458C2×C22⋊C8—431no—
459C2×C4×C8—431no—
460#399—861no—
461#397—21no—
462#392—21no—
463#392—861no—
464#390—861no—
465#390—861no—
466#386—21no—
467#386—21no—
468#382C2×D4311yescharacteristic
469#380C2×D4311yescharacteristic
470#380C2×D4311yescharacteristic
471C4×C4⋊C4—431no—
472#340—431no—
473#340—431no—
474#340—431no—
475#340—431no—
476C43#2538811yescharacteristic, complemented, Sylow
477C22×Q8—431no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—431no—
481C22×D4—861no—
482C22×D4—861no—
483C22×D4C22⋊D4311yescharacteristic
484C22×D4C22×D4311yescharacteristic
485C23×C4—21no—
486C23×C4C22×D4311yescharacteristic
487C23×C4C22×D4311yescharacteristic
488C2×SD16—862no—
489C2×SD16—862no—
490C2×SD16—1721no—
491C2×D8—862no—
492C2×D8—862no—
493C2×D8—1721no—
494C22×C8—431no—
495C22×C8—431no—
496C22×C8—431no—
497C22×C8—431no—
498C22×C8—862no—
499C22×C8—862no—
500C22×C8—862no—
501C22×C8—862no—
502C22×C8—1721no—
503C22×C8—1721no—
504#124—862no—
505#124—862no—
506C22⋊Q8—862no—
507C22⋊Q8—862no—
508C22⋊Q8—1721no—
509C22⋊Q8—1721no—
510#121—22no—
511#121—22no—
512#121—41no—
513#121—41no—
514#121—862no—
515#121—862no—
516#121—1721no—
517#121—1721no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—22no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4—431no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4C22⋊D4311yescharacteristic
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C4⋊C4C22×D4311yescharacteristic
529C2×C4⋊C4C22×D4311yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4C22⋊D4311yescharacteristic
542C2×C22⋊C4C22⋊D4311yescharacteristic
543C2×C42—861no—
544C2×C42C22×D4311yescharacteristic
545#107—862no—
546#106—862no—
547C4⋊C8—434no—
548#103—862no—
549#103—862no—
550#103—1721no—
551#102—434no—
552#102—862no—
553#102—862no—
554#102—862no—
555#102—1721no—
556C22⋊C8—862no—
557C22⋊C8—862no—
558C4×C8—862no—
559#95—21no—
560#95—21no—
561#95—21no—
562#95—21no—
563#95—861no—
564C24—21no—
565C24—861no—
566C24C2×C22⋊D4311yescharacteristic
567C24C2×C22⋊D4311yescharacteristic
568C2×Q8—861no—
569C2×Q8—861no—
570C2×Q8—861no—
571C2×Q8—861no—
572C2×Q8—861no—
573C2×Q8—861no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—861no—
589C2×D4—861no—
590C2×D4—861no—
591C2×D4—861no—
592C2×D4—861no—
593C2×D4—861no—
594C2×D4—3441no—
595C2×D4—3441no—
596C2×D4—1722no—
597C2×D4—1722no—
598C2×D4—1722no—
599C2×D4—1722no—
600C2×D4D4×D4312yes—
601C22×C4—21no—
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—21no—
615C22×C4—21no—
616C22×C4—42no—
617C22×C4—81no—
618C22×C4—81no—
619C22×C4—861no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4C2×C22⋊D4311yescharacteristic
623C22×C4C2×C22⋊D4311yescharacteristic
624C22×C4C2×C22⋊D4311yescharacteristic
625C22×C4C2×C22⋊D4311yescharacteristic
626C22×C4C23×D4311yescharacteristic
627SD16—1724no—
628D8—1724no—
629C2×C8—432no—
630C2×C8—432no—
631C2×C8—432no—
632C2×C8—861no—
633C2×C8—861no—
634C2×C8—861no—
635C2×C8—861no—
636C2×C8—861no—
637C2×C8—861no—
638C2×C8—861no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8—1724no—
642C2×C8—1724no—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—432no—
651C4⋊C4—432no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—1722no—
655C4⋊C4—1722no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—81no—
662C22⋊C4—81no—
663C22⋊C4—1722no—
664C22⋊C4—1722no—
665C22⋊C4—1722no—
666C22⋊C4—1722no—
667C22⋊C4—1722no—
668C22⋊C4—1722no—
669C42—3441no—
670C42D4×D4312yes—
671C42#1062190012yes—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—22no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—1721no—
692C23—1721no—
693C23—1721no—
694C23—1721no—
695C23—1721no—
696C23—1721no—
697C23—1721no—
698C23#1306334512yes—
699C23#1306334512yes—
700C23C22×C22⋊D4311yescharacteristic
701Q8—1721no—
702Q8—1721no—
703Q8—1721no—
704Q8—1721no—
705D4—28no—
706D4—22no—
707D4—22no—
708D4—41no—
709D4—41no—
710D4—84no—
711D4—84no—
712D4—3444no—
713D4—3444no—
714D4—1721no—
715D4—1721no—
716D4—1721no—
717D4—1721no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
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—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—84no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4#1306329712yes—
756C2×C4#1306329712yes—
757C2×C4C2×D4×D4311yescharacteristic
758C2×C4C2×D4×D4311yescharacteristic
759C2×C4#41×D4311yescharacteristic
760C2×C4C2×#1062190011yescharacteristic
761C2×C4#1306337011yescharacteristic
762C2×C4#1306337111yescharacteristic
763C8—862no—
764C8—862no—
765C8—862no—
766C8—1721no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—3441no—
789C22—3441no—
790C22—3441no—
791C22—3441no—
792C22—3441no—
793C22—3441no—
794C22—3441no—
795C22C2×#1306329711yescharacteristic
796C22D4×C22⋊D4311yescharacteristic
797C22#1458353711yescharacteristic
798C22C2×#1306334511yescharacteristic
799C22C2×#1306334511yescharacteristic
800C22#1458370211yescharacteristic
801C22#1458371011yescharacteristic
802C4—22no—
803C4—22no—
804C4—41no—
805C4—41no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4—3441no—
810C4—1722no—
811C4—1722no—
812C4#1458344411yescharacteristic
813C4#1458350211yescharacteristic
814C4#1458353311yescharacteristic
815C4#1458356711yescharacteristic
816C2—42no—
817C2—42no—
818C2—82no—
819C2—6881no—
820C2#1913818511yescharacteristic
821C2#1914417311yescharacteristic
822C2#1914427111yescharacteristic
823C2#1914627611yescharacteristic
824C2#1914629811yescharacteristic
825C2#1914643911yescharacteristic
826C2#1914649111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2535C2
socleC23×C43C22×D4
hypercenter#2535D43
hypocenterC43#25388
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. C2×#14583133C2semidirect
2. C2×#14583126C2semidirect
3. C2×#14583114C2semidirect
4. C2×D4×C43⋊C8C2semidirect
5. #19139534C2semidirect
6. #19135798C2semidirect
7. #19135784C2semidirect
8. #19135598C2semidirect
9. #19135591C2semidirect
10. #19135404C2semidirect
11. #19135361C2semidirect
12. #19135021C2semidirect
13. #19135016C2semidirect
14. C4×#13063246C2semidirect
15. C43×#2535C2semidirect
106. C4⋊(C43⋊C8)D4semidirect
111. #13063246D4semidirect
408. #2535D43semidirect
476. C43#25388semidirect

Maximal subgroups

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

subgroupindex
C2×#145831332
C2×#145831262
C2×#145831142
C2×D4×C43⋊C82
#191395342
#191357982
#191357842
#191355982
#191355912
#191354042
#191353612
#191350212
#191350162
C4×#130632462
C43×#25352
#2538843