Finite Group Databasebeta

← #25968018

Subgroups — #25968018

Order 11008.

2822 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147887C211yesmaximal, characteristic, complemented
2C22×#13063321C211yesmaximal, characteristic, complemented
3#19145616C214yesmaximal, complemented
4#19145611C214yesmaximal, complemented
5#19145534C214yesmaximal, complemented
6#19145511C214yesmaximal, complemented
7#19145043C212yesmaximal, complemented
8#19144967C212yesmaximal, complemented
9#19144074C212yesmaximal, complemented
10#19144073C212yesmaximal, complemented
11#19143825C211yesmaximal, characteristic, complemented
12#19143822C211yesmaximal, characteristic, complemented
13#19143821C211yesmaximal, characteristic, complemented
14#19143224C211yesmaximal, characteristic, complemented
15C43×#3003C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C22⋊D43—22no—
18C2×#13063353C2212yescomplemented
19C2×#13063351C2212yescomplemented
20C2×#13063350C2212yescomplemented
21#14583452C2211yescharacteristic, complemented
22#14583451C2212yescomplemented
23#14583445C2211yescharacteristic, complemented
24#14583444C2212yescomplemented
25C2×#13063321—22no—
26C2×#13063321—22no—
27C2×#13063321—22no—
28C2×#13063321C2212yes—
29C2×#13063321C2214yes—
30C2×#13063321C2212yes—
31C2×#13063321C2214yes—
32#14583435C2212yescomplemented
33#14583430C2212yescomplemented
34#14583429—22no—
35#14583426—22no—
36#14583410C2211yescharacteristic
37#14583405—22no—
38#41×Dic43C2211yescharacteristic, complemented
39#14583367C2211yescharacteristic, complemented
40C4×#10621900—22no—
41C22×C4×Dic43C2211yescharacteristic
42#14583287C2214yescomplemented
43#14583285C2214yescomplemented
44#14583274C2214yescomplemented
45#14583270C2214yescomplemented
46#14583262C2218yescomplemented
47#14583244C2218yescomplemented
48#14583098C2218yescomplemented
49#14583097C2218yescomplemented
50#14583093C2218yescomplemented
51#14583092C2218yescomplemented
52#14583052C2214yescomplemented
53#14583050C2214yescomplemented
54#14583049C2214yescomplemented
55#14583035C2214yescomplemented
56#14583033C2214yescomplemented
57#14583032C2214yescomplemented
58#14582953C2214yescomplemented
59#14582949C2214yescomplemented
60#14582922C2212yescomplemented
61#14582905C2212yescomplemented
62#14582904C2212yescomplemented
63#14582903C2212yescomplemented
64#14582863C2211yescharacteristic
65M16×Dic43C2212yescomplemented
66C23×D4×C43C2211yescharacteristic
67C2×AGL(1,ℤ/8)×C43C2212yescomplemented
68C43×#525C2211yescharacteristic
69C43×#450C2214yescomplemented
70C43×#447C2214yescomplemented
71C43×#418C2212yescomplemented
72C43×#407C2211yescharacteristic
73C24×D43—21no—
74C2×#10621898C2311yescharacteristic
75C2×#10621900—22no—
76C22×D172—22no—
77C22×D172—21no—
78C22×D172—44no—
79C22×D172C2312yes—
80C22×D172C2314yes—
81C22×C22⋊D43—24no—
82C22×C22⋊D43—24no—
83C22×C22⋊D43—24no—
84C22×C22⋊D43—24no—
85C22×C22⋊D43—24no—
86C22×C22⋊D43—24no—
87C22×C22⋊D43—416no—
88C23×Dic43D412yes—
89#13063353—44no—
90#13063351—44no—
91#13063350—44no—
92C2×#10621873C2314yescomplemented
93C2×#10621883C2314yescomplemented
94C2×#10621884C2314yescomplemented
95C2×D344C2314yescomplemented
96C2×#10621882C2314yescomplemented
97C2×#10621882C2314yescomplemented
98C2×#10621877C2312yes—
99#13063324C2312yescomplemented
100#13063323C2311yescharacteristic, complemented
101#13063321—22no—
102#13063321—24no—
103#13063321—22no—
104#13063321—24no—
105#13063321—24no—
106#13063321—24no—
107#13063321—24no—
108#13063321C2318yes—
109#13063321C2314yes—
110#13063321C2314yes—
111#13063321C2311yescharacteristic, complemented
112#13063320—22no—
113#13063318—22no—
114#13063316C2312yescomplemented
115#13063315—22no—
116#13063314C2311yescharacteristic, complemented
117#13063312C2311yescharacteristic, complemented
118#13063311—22no—
119#13063309—22no—
120#13063308—21no—
121#13063306—22no—
122#13063304C2312yes—
123#13063302—22no—
124#13063302—22no—
125#13063299C2312yes—
126#13063297—22no—
127#13063297—22no—
128#13063294—21no—
129Q8×Dic43C2312yescomplemented
130C4×Dic86—22no—
131#13063290—22no—
132#13063290C2312yescomplemented
133D4×Dic43—22no—
134D4×Dic43—22no—
135D4×Dic43C2312yescomplemented
136#13063287C2312yescomplemented
137C4×C22⋊D43—22no—
138C4×C22⋊D43—22no—
139(C22⋊D43)⋊C4—22no—
140(C22⋊D43)⋊C4—22no—
141(C22⋊D43)⋊C4—22no—
142#13063284—21no—
143#13063284C2311yescharacteristic
144#13063283—22no—
145#13063282—21no—
146#13063281—22no—
147#13063281—22no—
148C2×C4×Dic43—21no—
149C2×C4×Dic43D412yes—
150C2×C4×Dic43D412yes—
151C2×C4×Dic43D412yes—
152C2×C4×Dic43C2311yescharacteristic
153C2×C4×Dic43C2311yescharacteristic
154C2×C4×Dic43C2312yes—
155C2×C4×Dic43C2312yes—
156C42×D43—21no—
157Dic43⋊C8C2318yescomplemented
158#13063247C2318yescomplemented
159#13063246C2318yescomplemented
160#13063245C2318yescomplemented
161C22⋊(C43⋊C8)C2314yes—
162#13063235C2314yescomplemented
163C8×Dic43C2314yescomplemented
164C25×C43—21no—
165C2×#41×C43C2311yescharacteristic
166C22×D4×C43—22no—
167C22×D4×C43—21no—
168C22×D4×C43—44no—
169C22×D4×C43C2312yes—
170C22×D4×C43C2314yes—
171C23×C4×C43C2311yescharacteristic
172AGL(1,ℤ/8)×C43—44no—
173C2×SD16×C43C2314yescomplemented
174C2×D8×C43C2314yescomplemented
175C2×M16×C43C2312yes—
176#123×C43—21no—
177C22⋊Q8×C43C2312yes—
178#121×C43C2312yes—
179#120×C43—21no—
180C4×D4×C43—22no—
181#117×C43C2311yescharacteristic
182#102×C43C2318yescomplemented
183C22⋊C8×C43C2314yes—
184C24×C43—22no—
185C24×C43—24no—
186C24×C43—44no—
187C24×C43—48no—
188C24×C43C2×D411yescharacteristic
189C23×D43—24no—
190C23×D43—22no—
191C23×D43—48no—
192C23×D43—44no—
193#41×C43—24no—
194C2×Q8×C43C2411yescharacteristic
195C2×D4×C43—24no—
196C2×D4×C43—22no—
197C2×D4×C43—22no—
198C2×D4×C43—21no—
199C2×D4×C43—24no—
200C2×D4×C43—24no—
201C2×D4×C43—48no—
202C2×D4×C43—48no—
203C2×D4×C43—44no—
204C2×D4×C43C2414yes—
205C2×D4×C43C2411yescharacteristic
206C22×C4×C43—24no—
207C22×C4×C43—21no—
208C22×C4×C43C2×D412yes—
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2412yes—
211C22×C4×C43C2411yescharacteristic
212C2×C22⋊D43—22no—
213C2×C22⋊D43—28no—
214C2×C22⋊D43—28no—
215C2×C22⋊D43—28no—
216C2×C22⋊D43—28no—
217C2×C22⋊D43—21no—
218C2×C22⋊D43—22no—
219C2×C22⋊D43—416no—
220C2×C22⋊D43—416no—
221C2×C22⋊D43—416no—
222C2×C22⋊D43—416no—
223C2×C22⋊D43—416no—
224C2×C22⋊D43—416no—
225C22×Dic43—28no—
226C22×Dic43—22no—
227C22×Dic43C2×D412yes—
228C22×Dic43C2×D412yes—
229C22×Dic43C2×D412yes—
230C22×Dic43C2×D412yes—
231C22×Dic43C2×D412yes—
232C22×Dic43C2×D412yes—
233#10621900—48no—
234#10621898—24no—
235C2×D172—24no—
236C2×D172—22no—
237C2×D172—24no—
238C2×D172—24no—
239C2×D172—48no—
240C2×D172—48no—
241C2×D172—44no—
242C2×D172C2414yes—
243C2×D172C2411yescharacteristic
244C2×C4×D43—21no—
245C2×C4×D43—22no—
246C2×Dic86—22no—
247C2×Dic86C2411yescharacteristic
248SD16×C43—44no—
249D8×C43—44no—
250M16×C43—24no—
251C2×C8×C43C2414yes—
252C4⋊C4×C43—22no—
253C4⋊C4×C43C2412yes—
254C22⋊C4×C43—22no—
255C22⋊C4×C43—21no—
256C22⋊C4×C43—22no—
257C42×C43—21no—
258C22⋊Dic43—22no—
259C22⋊Dic43—22no—
260C22⋊Dic43—22no—
261C22⋊Dic43—21no—
262#10621884—44no—
263#10621883—44no—
264#10621882—44no—
265#10621882—44no—
266(C2×D43)⋊C4—22no—
267(C2×D43)⋊C4—22no—
268(C2×D43)⋊C4—22no—
269C4⋊Dic43—22no—
270C4⋊Dic43—22no—
271C4⋊Dic43C2412yes—
272Dic43⋊C4—22no—
273Dic43⋊C4—22no—
274Dic43⋊C4—22no—
275Dic43⋊C4—22no—
276Dic43⋊C4—22no—
277C4×Dic43—21no—
278C4×Dic43—22no—
279C4×Dic43—22no—
280C4×Dic43C2×D411yescharacteristic
281C4×Dic43C2×D412yes—
282C4×Dic43C2×D411yescharacteristic
283C4×Dic43C2×D412yes—
284C4×Dic43C2×D412yes—
285C4×Dic43C2×D412yes—
286C4×Dic43C2×D412yes—
287C4×Dic43C2411yescharacteristic
288C4×Dic43C2411yescharacteristic
289C4×Dic43C2412yes—
290#10621877—24no—
291C2×C43⋊C8C2414yes—
292D344—44no—
293#10621873—44no—
294C23×C43—22no—
295C23×C43—24no—
296C23×C43—21no—
297C23×C43—24no—
298C23×C43—48no—
299C23×C43—48no—
300C23×C43—48no—
301C23×C43—44no—
302C23×C43—48no—
303C23×C43—816no—
304C23×C43C22×D411yescharacteristic
305C23×C43C22×D412yes—
306C22×D43—21no—
307C22×D43—24no—
308C22×D43—48no—
309C22×D43—48no—
310C22×D43—48no—
311C22×D43—44no—
312C22×D43—48no—
313C22×D43—816no—
314Q8×C43—22no—
315D4×C43—22no—
316D4×C43—24no—
317D4×C43—24no—
318D4×C43—48no—
319D4×C43—42no—
320D4×C43—44no—
321D4×C43—44no—
322C2×C4×C43—22no—
323C2×C4×C43—24no—
324C2×C4×C43—24no—
325C2×C4×C43—21no—
326C2×C4×C43—22no—
327C2×C4×C43—42no—
328C2×C4×C43C22×D412yes—
329C2×C4×C43C22×D411yescharacteristic
330C2×C4×C43H(5,𝔽2)14yes—
331C2×C4×C43C2511yescharacteristic
332C22⋊D43—416no—
333C22⋊D43—416no—
334C22⋊D43—42no—
335C22⋊D43—44no—
336C22⋊D43—44no—
337C22⋊D43—416no—
338C22⋊D43—416no—
339C2×Dic43—24no—
340C2×Dic43—24no—
341C2×Dic43—24no—
342C2×Dic43—24no—
343C2×Dic43—24no—
344C2×Dic43—21no—
345C2×Dic43—22no—
346C2×Dic43—44no—
347C2×Dic43AGL(1,ℤ/8)18yescomplemented
348C2×Dic43C22×D412yes—
349C2×Dic43C22×D412yes—
350C2×Dic43C22×D412yes—
351C2×Dic43C22×D412yes—
352D172—24no—
353D172—22no—
354D172—24no—
355D172—48no—
356D172—44no—
357C4×D43—42no—
358C4×D43—44no—
359Dic86—22no—
360Dic86—44no—
361C8×C43—24no—
362C43⋊C8—24no—
363#60798—431nomaximal, Sylow
364C22×C43—28no—
365C22×C43—22no—
366C22×C43—22no—
367C22×C43—22no—
368C22×C43—44no—
369C22×C43—41no—
370C22×C43—48no—
371C22×C43—42no—
372C22×C43—88no—
373C22×C43—816no—
374C22×C43#53512yes—
375C22×C43C2×AGL(1,ℤ/8)14yes—
376C22×C43C23×D411yescharacteristic
377C2×D43—44no—
378C2×D43—41no—
379C2×D43—48no—
380C2×D43—42no—
381C2×D43—88no—
382C2×D43—816no—
383C4×C43—22no—
384C4×C43—41no—
385C4×C43—42no—
386C4×C43#53512yes—
387C4×C43C2×H(5,𝔽2)12yes—
388Dic43—22no—
389Dic43—22no—
390Dic43—41no—
391Dic43—42no—
392Dic43C2×AGL(1,ℤ/8)14yes—
393Dic43C2×AGL(1,ℤ/8)14yes—
394#3444—431no—
395C22×#127—431no—
396#3217—434no—
397#3217—434no—
398#3208—434no—
399#3205—434no—
400#3151—432no—
401#3138—432no—
402#3038—432no—
403#3038—432no—
404#3003—431no—
405#3003—431no—
406#3003—431no—
407#3003D4311yescharacteristic, complemented
408#2920—431no—
409C2×C43—22no—
410C2×C43—24no—
411C2×C43—81no—
412C2×C43—84no—
413C2×C43C2×#53511yescharacteristic
414C2×C43C22×AGL(1,ℤ/8)12yes—
415D43—81no—
416D43—84no—
417C23×D4—431no—
418C23×D4—862no—
419C23×D4C2×D4311yescharacteristic
420C2×AGL(1,ℤ/8)—432no—
421C2×AGL(1,ℤ/8)—432no—
422C2×AGL(1,ℤ/8)—432no—
423C2×AGL(1,ℤ/8)C2×D4312yescomplemented
424#533—431no—
425#533—432no—
426#532—432no—
427#532—431no—
428C2×#127—432no—
429C2×#127—434no—
430C2×#127—434no—
431C2×#127—432no—
432C2×#127—862no—
433C2×#127—862no—
434C2×#127—862no—
435#529—432no—
436#529—432no—
437#529—862no—
438#529—862no—
439#525—431no—
440#525—862no—
441#525C2×D4311yescharacteristic
442C4×#41—431no—
443C4×#41—431no—
444C4×#41—862no—
445C22×C42—431no—
446#496—434no—
447#496—434no—
448#493—434no—
449#492—434no—
450#490—438no—
451#486—438no—
452#460—438no—
453#460—438no—
454#459—438no—
455#459—438no—
456#450—434no—
457#450—434no—
458#450—434no—
459#450C2×D4314yescomplemented
460#447—434no—
461#447—434no—
462#447—434no—
463#447C2×D4314yescomplemented
464#432—434no—
465#431—434no—
466#423—432no—
467#418—432no—
468#418—432no—
469#418—432no—
470#418C2×D4312yescomplemented
471#407—431no—
472#407C2×D4311yescharacteristic
473C4×M16—432no—
474C43#6079811yescharacteristic, complemented, Sylow
475C25—21no—
476C25—861no—
477C2×#41—431no—
478C2×#41—862no—
479C2×#41C22×D4311yescharacteristic
480C22×D4—22no—
481C22×D4—21no—
482C22×D4—44no—
483C22×D4—432no—
484C22×D4—434no—
485C22×D4—864no—
486C22×D4—864no—
487C22×D4—864no—
488C22×D4—864no—
489C22×D4—864no—
490C22×D4—864no—
491C22×D4—862no—
492C22×D4—861no—
493C22×D4—1724no—
494C22×D4—17216no—
495C22×D4C22×D4312yes—
496C22×D4C22×D4314yes—
497C23×C4—432no—
498C23×C4C22×D4311yescharacteristic
499AGL(1,ℤ/8)—44no—
500AGL(1,ℤ/8)—1724no—
501AGL(1,ℤ/8)—1724no—
502AGL(1,ℤ/8)—1724no—
503C2×SD16—434no—
504C2×SD16—434no—
505C2×SD16—434no—
506C2×SD16C22×D4314yescomplemented
507C2×D8—434no—
508C2×D8—434no—
509C2×D8—434no—
510C2×D8C22×D4314yescomplemented
511C2×M16—432no—
512C2×M16C22×D4312yes—
513C4⋊Q8—432no—
514C4⋊Q8—431no—
515#127—438no—
516#127—434no—
517#127—434no—
518#127—431no—
519#127—862no—
520#127—864no—
521#127—862no—
522#127—864no—
523#127—864no—
524#127—864no—
525#127—864no—
526#126—862no—
527#126—862no—
528#125—432no—
529#125—862no—
530#124—431no—
531#124—431no—
532#124—862no—
533#123—21no—
534#123—862no—
535#123—862no—
536#123—861no—
537C22⋊Q8—432no—
538C22⋊Q8—862no—
539C22⋊Q8—862no—
540C22⋊Q8C22×D4312yes—
541#121—432no—
542#121—862no—
543#121—862no—
544#121C22×D4312yes—
545#120—21no—
546#120—861no—
547C4×Q8—432no—
548C4×Q8—432no—
549C4×Q8—862no—
550C4×Q8—862no—
551C4×D4—22no—
552C4×D4—432no—
553C4×D4—432no—
554C4×D4—862no—
555C4×D4—862no—
556C4×D4—862no—
557C4×D4—862no—
558C4×D4—862no—
559C4×D4—862no—
560C4×D4—862no—
561#117—431no—
562#117—861no—
563#117—862no—
564#117—862no—
565#117—861no—
566#117—862no—
567#117C22×D4311yescharacteristic
568C2×C42—432no—
569C2×C42—432no—
570C2×C42—432no—
571C2×C42—431no—
572C2×C42—432no—
573C2×C42—431no—
574C2×C42—432no—
575C2×C42—861no—
576C2×C42—861no—
577C4⋊C8—438no—
578#102—438no—
579#102—438no—
580#102—438no—
581#102C22×D4318yescomplemented
582C22⋊C8—434no—
583C22⋊C8C22×D4314yes—
584#97—434no—
585C4×C8—434no—
586C24—24no—
587C24—22no—
588C24—44no—
589C24—48no—
590C24—864no—
591C24—862no—
592C24—1728no—
593C24—1724no—
594C24D4×D4311yescharacteristic
595#41—24no—
596#41—864no—
597#41—1728no—
598C2×Q8—431no—
599C2×Q8—862no—
600C2×Q8C23×D4311yescharacteristic
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—24no—
604C2×D4—22no—
605C2×D4—24no—
606C2×D4—24no—
607C2×D4—48no—
608C2×D4—44no—
609C2×D4—48no—
610C2×D4—434no—
611C2×D4—431no—
612C2×D4—862no—
613C2×D4—868no—
614C2×D4—868no—
615C2×D4—868no—
616C2×D4—868no—
617C2×D4—862no—
618C2×D4—861no—
619C2×D4—864no—
620C2×D4—862no—
621C2×D4—864no—
622C2×D4—864no—
623C2×D4—1728no—
624C2×D4—1724no—
625C2×D4—1728no—
626C2×D4—17216no—
627C2×D4—17216no—
628C2×D4—17216no—
629C2×D4—17216no—
630C2×D4—17216no—
631C2×D4—17216no—
632C2×D4C23×D4314yes—
633C2×D4C23×D4311yescharacteristic
634C22×C4—24no—
635C22×C4—21no—
636C22×C4—432no—
637C22×C4—432no—
638C22×C4—432no—
639C22×C4—432no—
640C22×C4—432no—
641C22×C4—432no—
642C22×C4—862no—
643C22×C4—868no—
644C22×C4—862no—
645C22×C4—861no—
646C22×C4D4×D4312yes—
647C22×C4D4×D4311yescharacteristic
648C22×C4C23×D4312yes—
649C22×C4C23×D4311yescharacteristic
650SD16—44no—
651SD16—1724no—
652SD16—1724no—
653SD16—1724no—
654D8—44no—
655D8—1724no—
656D8—1724no—
657D8—1724no—
658M16—24no—
659M16—864no—
660C2×C8—434no—
661C2×C8C23×D4314yes—
662C4⋊C4—22no—
663C4⋊C4—432no—
664C4⋊C4—862no—
665C4⋊C4—862no—
666C4⋊C4—862no—
667C4⋊C4—862no—
668C4⋊C4—862no—
669C4⋊C4—862no—
670C4⋊C4—862no—
671C4⋊C4C23×D4312yes—
672C22⋊C4—22no—
673C22⋊C4—21no—
674C22⋊C4—22no—
675C22⋊C4—862no—
676C22⋊C4—862no—
677C22⋊C4—862no—
678C22⋊C4—862no—
679C22⋊C4—861no—
680C22⋊C4—862no—
681C22⋊C4—862no—
682C42—21no—
683C42—431no—
684C42—432no—
685C42—431no—
686C42—432no—
687C42—432no—
688C42—432no—
689C42—432no—
690C42—431no—
691C42—431no—
692C42—432no—
693C42—862no—
694C42—862no—
695C42—861no—
696C23—24no—
697C23—22no—
698C23—21no—
699C23—24no—
700C23—48no—
701C23—48no—
702C23—48no—
703C23—48no—
704C23—44no—
705C23—816no—
706C23—861no—
707C23—864no—
708C23—34416no—
709C23—1728no—
710C23—1728no—
711C23—1728no—
712C23—1728no—
713C23—1724no—
714C23C2×D4×D4312yes—
715C23C2×D4×D4311yescharacteristic
716Q8—22no—
717Q8—862no—
718Q8—1724no—
719D4—22no—
720D4—24no—
721D4—24no—
722D4—48no—
723D4—44no—
724D4—42no—
725D4—44no—
726D4—862no—
727D4—864no—
728D4—864no—
729D4—1728no—
730D4—17216no—
731D4—17216no—
732D4—1724no—
733D4—17216no—
734D4—17216no—
735D4—1724no—
736D4—1722no—
737D4—1724no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—42no—
744C2×C4—438no—
745C2×C4—432no—
746C2×C4—432no—
747C2×C4—432no—
748C2×C4—432no—
749C2×C4—864no—
750C2×C4—864no—
751C2×C4—864no—
752C2×C4—864no—
753C2×C4—864no—
754C2×C4—862no—
755C2×C4—861no—
756C2×C4—1724no—
757C2×C4—1724no—
758C2×C4—1722no—
759C2×C4C2×D4×D4312yes—
760C2×C4C2×D4×D4311yescharacteristic
761C2×C4#1306337014yes—
762C2×C4C24×D4311yescharacteristic
763C8—24no—
764C8—864no—
765C22—28no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—42no—
770C22—48no—
771C22—41no—
772C22—44no—
773C22—816no—
774C22—88no—
775C22—34416no—
776C22—3448no—
777C22—1722no—
778C22—1728no—
779C22—1721no—
780C22—1724no—
781C22#1458346412yes—
782C22AGL(1,ℤ/8)×D4314yes—
783C22C22×D4×D4311yescharacteristic
784C4—22no—
785C4—42no—
786C4—41no—
787C4—434no—
788C4—434no—
789C4—862no—
790C4—862no—
791C4—1722no—
792C4—1721no—
793C4#1458346412yes—
794C4C2×#1306337012yes—
795C2—24no—
796C2—22no—
797C2—84no—
798C2—81no—
799C2—3444no—
800C2—3441no—
801C2C2×#1458346411yescharacteristic
802C2C2×AGL(1,ℤ/8)×D4312yes—
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3003C2
socleC22×C43C23×D4
hypercenter#3003D43
hypocenterC43#60798
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3003

Complements

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

NH ≅ G/Ntype
1. #19147887C2semidirect
2. C22×#13063321C2semidirect
3. #19145616C2semidirect
4. #19145611C2semidirect
5. #19145534C2semidirect
6. #19145511C2semidirect
7. #19145043C2semidirect
8. #19144967C2semidirect
9. #19144074C2semidirect
10. #19144073C2semidirect
11. #19143825C2semidirect
12. #19143822C2semidirect
13. #19143821C2semidirect
14. #19143224C2semidirect
15. C43×#3003C2semidirect
18. C2×#13063353C22semidirect
19. C2×#13063351C22semidirect
20. C2×#13063350C22semidirect
21. #14583452C22semidirect
22. #14583451C22semidirect
23. #14583445C22semidirect
24. #14583444C22semidirect
32. #14583435C22semidirect
33. #14583430C22semidirect
38. #41×Dic43C22semidirect
39. #14583367C22semidirect
42. #14583287C22semidirect
43. #14583285C22semidirect
44. #14583274C22semidirect
45. #14583270C22semidirect
46. #14583262C22semidirect
47. #14583244C22semidirect
48. #14583098C22semidirect
49. #14583097C22semidirect
50. #14583093C22semidirect
51. #14583092C22semidirect
52. #14583052C22semidirect
53. #14583050C22semidirect
54. #14583049C22semidirect
55. #14583035C22semidirect
56. #14583033C22semidirect
57. #14583032C22semidirect
58. #14582953C22semidirect
59. #14582949C22semidirect
60. #14582922C22semidirect
61. #14582905C22semidirect
62. #14582904C22semidirect
63. #14582903C22semidirect
65. M16×Dic43C22semidirect
67. C2×AGL(1,ℤ/8)×C43C22semidirect
69. C43×#450C22semidirect
70. C43×#447C22semidirect
71. C43×#418C22semidirect
92. C2×#10621873C23semidirect
93. C2×#10621883C23semidirect
94. C2×#10621884C23semidirect
95. C2×D344C23semidirect
96. C2×#10621882C23semidirect
97. C2×#10621882C23semidirect
99. #13063324C23semidirect
100. #13063323C23semidirect
111. #13063321C23semidirect
114. #13063316C23semidirect
116. #13063314C23semidirect
117. #13063312C23semidirect
129. Q8×Dic43C23semidirect
132. #13063290C23semidirect
135. D4×Dic43C23semidirect
136. #13063287C23semidirect
157. Dic43⋊C8C23semidirect
158. #13063247C23semidirect
159. #13063246C23semidirect
160. #13063245C23semidirect
162. #13063235C23semidirect
163. C8×Dic43C23semidirect
173. C2×SD16×C43C23semidirect
174. C2×D8×C43C23semidirect
182. #102×C43C23semidirect
347. C2×Dic43AGL(1,ℤ/8)semidirect
407. #3003D43semidirect
423. C2×AGL(1,ℤ/8)C2×D43semidirect
459. #450C2×D43semidirect
463. #447C2×D43semidirect
470. #418C2×D43semidirect
474. C43#60798semidirect
506. C2×SD16C22×D43semidirect
510. C2×D8C22×D43semidirect
581. #102C22×D43semidirect

Maximal subgroups

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

subgroupindex
#191478872
C22×#130633212
#191456162
#191456112
#191455342
#191455112
#191450432
#191449672
#191440742
#191440732
#191438252
#191438222
#191438212
#191432242
C43×#30032
#6079843