Finite Group Databasebeta

← #25981500

Subgroups — #25981500

Order 11008.

2126 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148436C211yesmaximal, characteristic, complemented
2C2×#14583548C211yesmaximal, characteristic, complemented
3#19146684C214yesmaximal, complemented
4#19146572C214yesmaximal, complemented
5#19146144C214yesmaximal, complemented
6#19146123C214yesmaximal, complemented
7#19145625C212yesmaximal, complemented
8#19145416C211yesmaximal, characteristic, complemented
9#19145402C211yesmaximal, characteristic, complemented
10#19145379C212yesmaximal, complemented
11#19144734C212yesmaximal, complemented
12#19143847C211yesmaximal, characteristic, complemented
13#19143814C212yesmaximal, complemented
14#19143622C211yesmaximal, characteristic, complemented
15C43×#3007C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic, complemented
17C2×#13063350C2212yescomplemented
18C2×#13063346C2214yescomplemented
19#14583597—22no—
20#14583597C2212yescomplemented
21#14583591C2212yescomplemented
22#14583576—22no—
23#14583560C2212yescomplemented
24#14583548—22no—
25#14583548—22no—
26#14583548C2214yes—
27#14583548C2214yescomplemented
28#14583540C2212yescomplemented
29#14583498—21no—
30#14583489—21no—
31#14583461—21no—
32C2×#13063323C2211yescharacteristic, complemented
33#14583435C2212yes—
34#14583412C2212yes—
35C2×#13063308—21no—
36C2×#13063306—21no—
37C2×#13063304C2211yescharacteristic
38C2×#13063301C2211yescharacteristic, complemented
39C2×#13063299C2211yescharacteristic
40C2×#13063297—21no—
41#14583372—21no—
42C2×D4×Dic43C2211yescharacteristic, complemented
43C2×C4×C22⋊D43C2211yescharacteristic
44C22×Dic43⋊C4—21no—
45#14583292C2214yescomplemented
46#14583266C2214yescomplemented
47#14583239C2214yescomplemented
48#14583235C2212yescomplemented
49#14583229C2212yescomplemented
50#14583227C2212yescomplemented
51#14583213C2212yes—
52#14583197C2214yescomplemented
53#14583155C2214yescomplemented
54#14583145C2214yescomplemented
55#14583137C2214yescomplemented
56#14583131C2214yescomplemented
57#14583116C2214yescomplemented
58#14583107C2214yescomplemented
59#14583103C2214yescomplemented
60#14583060C2214yescomplemented
61#14583058C2214yescomplemented
62#14583055C2212yescomplemented
63#14583054C2212yescomplemented
64#14583052C2212yescomplemented
65#14583045C2214yescomplemented
66#14583044C2214yescomplemented
67#14583040C2212yes—
68#14583038C2212yes—
69#14583033C2212yes—
70#14583008C2214yescomplemented
71#14583000C2214yescomplemented
72#14582973C2214yescomplemented
73#14582968C2214yescomplemented
74#14582953C2212yescomplemented
75#14582900C2212yescomplemented
76#14582892C2214yescomplemented
77#14582863C2211yescharacteristic
78C22⋊C8×D43C2212yescomplemented
79C22×#41×C43C2211yescharacteristic
80C2×#137×C43C2212yescomplemented
81C2×C22⋊Q8×C43C2211yescharacteristic
82C43×#452C2214yescomplemented
83C43×#451C2212yescomplemented
84C43×#450C2212yescomplemented
85C43×#417C2212yescomplemented
86C43×#407C2211yescharacteristic
87C2×#10621902C2312yes—
88C2×#10621900—22no—
89C2×#10621900—44no—
90C2×#10621900C2314yes—
91C22×Dic86C2311yescharacteristic
92C22×D172C2311yescharacteristic
93C22×C22⋊D43—21no—
94C22×C22⋊D43—21no—
95C22×C22⋊D43D411yescharacteristic
96C23×Dic43—21no—
97C23×Dic43—21no—
98C22×C4×D43C2311yescharacteristic
99#13063350—44no—
100#13063346—48no—
101C2×#10621885C2314yes—
102C2×#10621873C2314yes—
103C2×#10621884C2314yes—
104C2×#10621882C2314yes—
105C2×#10621877C2312yes—
106C2×C8×D43C2314yes—
107#13063323—22no—
108#13063323C2314yes—
109#13063320—22no—
110#13063320—22no—
111#13063320—22no—
112#13063316—22no—
113#13063316C2312yes—
114#13063314—22no—
115#13063314C2312yes—
116#13063310—22no—
117#13063310—22no—
118#13063310—22no—
119#13063309—22no—
120#13063309—22no—
121#13063308—24no—
122#13063308—24no—
123#13063306—24no—
124#13063306—24no—
125#13063304—21no—
126#13063304—21no—
127#13063304C2312yes—
128#13063304C2312yes—
129#13063301—22no—
130#13063301—22no—
131#13063301C2312yes—
132#13063301C2314yes—
133#13063300—22no—
134#13063300C2312yes—
135#13063299—21no—
136#13063299—21no—
137#13063299—22no—
138#13063299—22no—
139#13063299C2312yes—
140#13063299C2312yes—
141#13063297—24no—
142#13063297—24no—
143#13063295—22no—
144#13063295—22no—
145Q8×Dic43C2312yes—
146D4×Dic43—22no—
147D4×Dic43C2314yes—
148#13063287—22no—
149#13063287C2312yes—
150C4×C22⋊D43—22no—
151C4×C22⋊D43—22no—
152C4×C22⋊D43D412yes—
153C4×C22⋊D43D412yes—
154C4×C22⋊D43C2312yes—
155C4×C22⋊D43C2312yes—
156(C22⋊D43)⋊C4—22no—
157(C22⋊D43)⋊C4—22no—
158#13063283—22no—
159#13063283C2312yes—
160#13063281—22no—
161C2×C4⋊Dic43C2311yescharacteristic
162C2×C4⋊Dic43C2311yescharacteristic
163C2×Dic43⋊C4—21no—
164C2×Dic43⋊C4—21no—
165C2×Dic43⋊C4—21no—
166C2×Dic43⋊C4—21no—
167C2×Dic43⋊C4—24no—
168C2×Dic43⋊C4—24no—
169C2×Dic43⋊C4D411yescharacteristic
170C2×C22⋊Dic43—21no—
171C2×C22⋊Dic43—21no—
172C2×C22⋊Dic43D411yescharacteristic
173C2×(C2×D43)⋊C4—21no—
174C2×(C2×D43)⋊C4—21no—
175C2×(C2×D43)⋊C4D411yescharacteristic
176C22⋊C4×D43—22no—
177C2×C4×Dic43C2311yescharacteristic
178#13063259C2314yes—
179#13063256C2314yes—
180Dic43⋊C8C2314yes—
181#13063250C2314yes—
182#13063249C2314yes—
183#13063249C2314yes—
184#13063248C2314yes—
185#13063247C2314yes—
186#13063246C2314yes—
187C22⋊(C43⋊C8)C2312yes—
188C22⋊(C43⋊C8)C2312yes—
189(C2×D43)⋊C8C2314yes—
190#13063235C2314yes—
191C2×#41×C43—21no—
192C2×#41×C43—21no—
193C2×#41×C43—44no—
194C2×#41×C43C2312yes—
195C2×#41×C43C2312yes—
196C22×Q8×C43C2311yescharacteristic
197C22×Q8×C43C2311yescharacteristic
198C22×D4×C43—21no—
199C22×D4×C43C2311yescharacteristic
200C23×C4×C43—21no—
201C23×C4×C43C2311yescharacteristic
202#137×C43—44no—
203C2×Q16×C43C2314yes—
204C2×SD16×C43C2314yes—
205C2×M16×C43C2312yes—
206C22⋊Q8×C43—21no—
207C22⋊Q8×C43—21no—
208C22⋊Q8×C43C2312yes—
209C22⋊Q8×C43C2312yes—
210C2×C4⋊C4×C43—21no—
211C2×C4⋊C4×C43C2311yescharacteristic
212C2×C22⋊C4×C43—21no—
213#103×C43C2314yes—
214#102×C43C2314yes—
215C22⋊C8×C43C2312yes—
216C22⋊C8×C43C2312yes—
217C24×C43—21no—
218C24×C43C2×D411yescharacteristic
219C23×D43—21no—
220C23×D43C2×D411yescharacteristic
221#41×C43—24no—
222#41×C43—24no—
223#41×C43—42no—
224#41×C43—42no—
225#41×C43—44no—
226#41×C43—44no—
227C2×Q8×C43—21no—
228C2×Q8×C43—21no—
229C2×Q8×C43—42no—
230C2×Q8×C43—42no—
231C2×Q8×C43C2412yes—
232C2×Q8×C43C2412yes—
233C2×D4×C43—24no—
234C2×D4×C43—21no—
235C2×D4×C43—22no—
236C2×D4×C43—22no—
237C2×D4×C43—44no—
238C2×D4×C43C2412yes—
239C22×C4×C43—22no—
240C22×C4×C43—22no—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43—44no—
245C22×C4×C43—42no—
246C22×C4×C43C2×D411yescharacteristic
247C22×C4×C43C2×D411yescharacteristic
248C22×C4×C43C2×D411yescharacteristic
249C22×C4×C43C2411yescharacteristic
250C22×C4×C43C2411yescharacteristic
251C22×C4×C43C2411yescharacteristic
252C2×C22⋊D43—22no—
253C2×C22⋊D43—22no—
254C2×C22⋊D43—24no—
255C2×C22⋊D43—42no—
256C2×C22⋊D43—44no—
257C2×C22⋊D43—44no—
258C2×C22⋊D43C2×D412yes—
259C2×C22⋊D43C2×D412yes—
260C22×Dic43—24no—
261C22×Dic43—24no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—44no—
266C22×Dic43—44no—
267C22×Dic43C2×D411yescharacteristic
268C22×Dic43C2×D411yescharacteristic
269C22×Dic43C2×D411yescharacteristic
270#10621902—44no—
271#10621900—28no—
272#10621900—44no—
273#10621900—48no—
274C2×D172—21no—
275C2×D172—22no—
276C2×D172—22no—
277C2×D172—42no—
278C2×D172C2412yes—
279C2×C4×D43—22no—
280C2×C4×D43—22no—
281C2×C4×D43—42no—
282C2×C4×D43C2×D412yes—
283C2×C4×D43C2412yes—
284C2×Dic86—21no—
285C2×Dic86—42no—
286C2×Dic86C2412yes—
287Q16×C43—44no—
288SD16×C43—28no—
289M16×C43—42no—
290C2×C8×C43C2414yes—
291C4⋊C4×C43—22no—
292C4⋊C4×C43—22no—
293C4⋊C4×C43—21no—
294C4⋊C4×C43C2412yes—
295C22⋊C4×C43—22no—
296C22⋊C4×C43—22no—
297C22⋊Dic43—24no—
298C22⋊Dic43—22no—
299C22⋊Dic43—22no—
300C22⋊Dic43C2×D412yes—
301C22⋊Dic43C2×D412yes—
302#10621885—44no—
303#10621884—44no—
304#10621882—28no—
305(C2×D43)⋊C4—22no—
306(C2×D43)⋊C4—22no—
307(C2×D43)⋊C4—22no—
308(C2×D43)⋊C4—22no—
309(C2×D43)⋊C4—22no—
310(C2×D43)⋊C4—22no—
311(C2×D43)⋊C4—24no—
312(C2×D43)⋊C4—22no—
313(C2×D43)⋊C4—22no—
314(C2×D43)⋊C4C2×D412yes—
315(C2×D43)⋊C4C2×D412yes—
316C4⋊Dic43—21no—
317C4⋊Dic43—21no—
318C4⋊Dic43—22no—
319C4⋊Dic43—22no—
320C4⋊Dic43C2412yes—
321C4⋊Dic43C2412yes—
322Dic43⋊C4—22no—
323Dic43⋊C4—22no—
324Dic43⋊C4—24no—
325Dic43⋊C4—24no—
326Dic43⋊C4—24no—
327Dic43⋊C4—22no—
328Dic43⋊C4—22no—
329Dic43⋊C4C2×D412yes—
330Dic43⋊C4C2×D412yes—
331C4×Dic43—22no—
332C4×Dic43—22no—
333C4×Dic43C2×D412yes—
334C4×Dic43C2412yes—
335#10621877—42no—
336C2×C43⋊C8C2414yes—
337#10621873—44no—
338C8×D43—44no—
339C23×C43—24no—
340C23×C43—22no—
341C23×C43—22no—
342C23×C43—41no—
343C23×C43—41no—
344C23×C43—42no—
345C23×C43—42no—
346C23×C43C22×D411yescharacteristic
347C23×C43C22×D411yescharacteristic
348C23×C43C22×D411yescharacteristic
349C22×D43—22no—
350C22×D43—22no—
351C22×D43—41no—
352C22×D43—41no—
353C22×D43—42no—
354C22×D43—81no—
355C22×D43—81no—
356C22×D43C22×D412yes—
357Q8×C43—22no—
358Q8×C43—24no—
359Q8×C43—22no—
360Q8×C43—42no—
361Q8×C43—81no—
362D4×C43—24no—
363D4×C43—22no—
364D4×C43—44no—
365D4×C43—44no—
366D4×C43H(5,𝔽2)14yes—
367C2×C4×C43—22no—
368C2×C4×C43—22no—
369C2×C4×C43—22no—
370C2×C4×C43—22no—
371C2×C4×C43—22no—
372C2×C4×C43—22no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—44no—
377C2×C4×C43—44no—
378C2×C4×C43—42no—
379C2×C4×C43—81no—
380C2×C4×C43—81no—
381C2×C4×C43C22×D411yescharacteristic
382C2×C4×C43C22×D411yescharacteristic
383C2×C4×C43C22×D411yescharacteristic
384C2×C4×C43C2511yescharacteristic
385C22⋊D43—42no—
386C22⋊D43—42no—
387C22⋊D43—48no—
388C22⋊D43—44no—
389C22⋊D43—44no—
390C2×Dic43—22no—
391C2×Dic43—22no—
392C2×Dic43—22no—
393C2×Dic43—22no—
394C2×Dic43—41no—
395C2×Dic43—41no—
396C2×Dic43—48no—
397C2×Dic43—48no—
398C2×Dic43—42no—
399C2×Dic43—42no—
400C2×Dic43—42no—
401C2×Dic43C22×D412yes—
402C2×Dic43C22×D412yes—
403C2×Dic43C22×D412yes—
404D172—24no—
405D172—81no—
406D172—82no—
407D172—82no—
408C4×D43—24no—
409C4×D43—42no—
410C4×D43—82no—
411C4×D43—82no—
412Dic86—24no—
413Dic86—42no—
414C8×C43—24no—
415C43⋊C8—24no—
416#61575—431nomaximal, Sylow
417C22×C43—21no—
418C22×C43—21no—
419C22×C43—21no—
420C22×C43—21no—
421C22×C43—21no—
422C22×C43—24no—
423C22×C43—21no—
424C22×C43—21no—
425C22×C43—21no—
426C22×C43—48no—
427C22×C43—42no—
428C22×C43—42no—
429C22×C43—82no—
430C22×C43#57512yes—
431C22×C43C23×D411yescharacteristic
432C2×D43—22no—
433C2×D43—22no—
434C2×D43—22no—
435C2×D43—42no—
436C2×D43—42no—
437C2×D43—42no—
438C2×D43—82no—
439C2×D43—162no—
440C4×C43—21no—
441C4×C43—21no—
442C4×C43—21no—
443C4×C43—42no—
444C4×C43—42no—
445C4×C43—42no—
446C4×C43C2×H(5,𝔽2)12yes—
447Dic43—22no—
448Dic43—22no—
449Dic43—22no—
450Dic43—42no—
451Dic43—42no—
452Dic43—42no—
453#3505—431no—
454C2×#547—431no—
455#3315—434no—
456#3307—434no—
457#3269—434no—
458#3267—434no—
459#3218—432no—
460#3195—431no—
461#3193—431no—
462#3190—432no—
463#3114—432no—
464#3007D4311yescharacteristic, complemented
465#3006—431no—
466#3002—432no—
467#2973—431no—
468C2×C43—22no—
469C2×C43—41no—
470C2×C43—41no—
471C2×C43—44no—
472C2×C43#348411yescharacteristic
473C2×C43C2×#57511yescharacteristic
474C2×C43#358611yescharacteristic
475D43—42no—
476D43—82no—
477C22×#41—431no—
478C22×#41C2×D4311yescharacteristic
479C2×#137C2×D4312yescomplemented
480C2×AGL(1,ℤ/8)—432no—
481C2×#135—434no—
482#553—432no—
483#553—862no—
484#552—432no—
485#551—862no—
486#548—432no—
487#547—434no—
488#547—434no—
489#547—862no—
490#547—862no—
491#546—432no—
492#539—861no—
493#538—861no—
494#534—861no—
495C2×C4⋊Q8—431no—
496#529—432no—
497#525—432no—
498C2×#123—861no—
499C2×#123—861no—
500C2×C22⋊Q8—431no—
501C2×C22⋊Q8—431no—
502C2×C22⋊Q8C2×D4311yescharacteristic
503C2×#121—431no—
504C2×#121—861no—
505#518—861no—
506C2×C4×D4—431no—
507C2×C4×D4—431no—
508C22×C4⋊C4—861no—
509#497—434no—
510#491—434no—
511#485—434no—
512#484—432no—
513#483—432no—
514#483—432no—
515#480—432no—
516#478—434no—
517#470—434no—
518#468—434no—
519#467—434no—
520#465—434no—
521#463—434no—
522#462—434no—
523#461—434no—
524#452—434no—
525#452—434no—
526#452C2×D4314yescomplemented
527#451—432no—
528#451—432no—
529#451C2×D4312yescomplemented
530#450—432no—
531#450C2×D4312yescomplemented
532#449—434no—
533#449—434no—
534#448—432no—
535#448—432no—
536#447—432no—
537#442—434no—
538#440—434no—
539#435—434no—
540#435—434no—
541#432—432no—
542#417—432no—
543#417C2×D4312yescomplemented
544#416—434no—
545#407—431no—
546#407C2×D4311yescharacteristic
547C2×C22⋊C8—432no—
548C43#6157511yescharacteristic, complemented, Sylow
549C2×#41—21no—
550C2×#41—21no—
551C2×#41—44no—
552C2×#41—432no—
553C2×#41—434no—
554C2×#41—862no—
555C2×#41—1724no—
556C2×#41C22×D4312yes—
557C2×#41C22×D4312yes—
558C22×Q8—431no—
559C22×Q8C22×D4311yescharacteristic
560C22×Q8C22×D4311yescharacteristic
561C22×D4—21no—
562C22×D4—431no—
563C22×D4—431no—
564C22×D4—861no—
565C22×D4—861no—
566C22×D4C22×D4311yescharacteristic
567C23×C4—21no—
568C23×C4—431no—
569C23×C4—861no—
570C23×C4—861no—
571C23×C4C22×D4311yescharacteristic
572#137—44no—
573AGL(1,ℤ/8)—1724no—
574#135—1728no—
575C2×Q16—434no—
576C2×Q16C22×D4314yes—
577C2×SD16—434no—
578C2×SD16—434no—
579C2×SD16C22×D4314yes—
580C2×D8—434no—
581C2×M16—432no—
582C2×M16C22×D4312yes—
583C22×C8—434no—
584C4⋊Q8—434no—
585C4⋊Q8—862no—
586#126—862no—
587#126—862no—
588#126—862no—
589#125—432no—
590#125—862no—
591#124—432no—
592#124—862no—
593#123—862no—
594#123—862no—
595#123—862no—
596#123—864no—
597#123—864no—
598#123—864no—
599#123—864no—
600#123—862no—
601#123—862no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—434no—
605C22⋊Q8—432no—
606C22⋊Q8—432no—
607C22⋊Q8—432no—
608C22⋊Q8—862no—
609C22⋊Q8—862no—
610C22⋊Q8—861no—
611C22⋊Q8—861no—
612C22⋊Q8C22×D4312yes—
613C22⋊Q8C22×D4312yes—
614#121—432no—
615#121—432no—
616#121—432no—
617#121—862no—
618#121—862no—
619#121—862no—
620#121—864no—
621#121—864no—
622#121—861no—
623#121—861no—
624#120—862no—
625#120—862no—
626C4×Q8—432no—
627C4×D4—432no—
628C4×D4—432no—
629C4×D4—432no—
630C4×D4—432no—
631C4×D4—434no—
632C4×D4—432no—
633C4×D4—862no—
634C4×D4—862no—
635C4×D4—862no—
636C4×D4—862no—
637C4×D4—862no—
638C4×D4—862no—
639#117—432no—
640#117—862no—
641#117—862no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—431no—
644C2×C4⋊C4—431no—
645C2×C4⋊C4—431no—
646C2×C4⋊C4—864no—
647C2×C4⋊C4—864no—
648C2×C4⋊C4—861no—
649C2×C4⋊C4—861no—
650C2×C4⋊C4—861no—
651C2×C4⋊C4—861no—
652C2×C4⋊C4C22×D4311yescharacteristic
653C2×C22⋊C4—21no—
654C2×C22⋊C4—431no—
655C2×C22⋊C4—431no—
656C2×C22⋊C4—862no—
657C2×C22⋊C4—861no—
658C2×C22⋊C4—861no—
659C2×C22⋊C4—861no—
660C2×C22⋊C4—861no—
661C2×C42—431no—
662#107—434no—
663#106—434no—
664C4⋊C8—434no—
665#103—434no—
666#103—434no—
667#103—434no—
668#103—434no—
669#103C22×D4314yes—
670#102—434no—
671#102—434no—
672#102C22×D4314yes—
673C22⋊C8—432no—
674C22⋊C8—432no—
675C22⋊C8—434no—
676C22⋊C8C22×D4312yes—
677C22⋊C8C22×D4312yes—
678#97—434no—
679C24—21no—
680C24—431no—
681C24—861no—
682C24D4×D4311yescharacteristic
683#41—24no—
684#41—24no—
685#41—42no—
686#41—42no—
687#41—44no—
688#41—44no—
689#41—868no—
690#41—1724no—
691#41—1724no—
692#41—1728no—
693C2×Q8—21no—
694C2×Q8—21no—
695C2×Q8—42no—
696C2×Q8—42no—
697C2×Q8—432no—
698C2×Q8—861no—
699C2×Q8—1722no—
700C2×Q8C23×D4312yes—
701C2×Q8C23×D4312yes—
702C2×D4—24no—
703C2×D4—22no—
704C2×D4—22no—
705C2×D4—21no—
706C2×D4—44no—
707C2×D4—432no—
708C2×D4—432no—
709C2×D4—432no—
710C2×D4—862no—
711C2×D4—862no—
712C2×D4—864no—
713C2×D4—862no—
714C2×D4—862no—
715C2×D4—861no—
716C2×D4—1722no—
717C2×D4—1722no—
718C2×D4—1724no—
719C2×D4—1724no—
720C2×D4C23×D4312yes—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—42no—
727C22×C4—44no—
728C22×C4—431no—
729C22×C4—431no—
730C22×C4—431no—
731C22×C4—432no—
732C22×C4—432no—
733C22×C4—862no—
734C22×C4—862no—
735C22×C4—864no—
736C22×C4—864no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—861no—
740C22×C4—1722no—
741C22×C4—1724no—
742C22×C4—1724no—
743C22×C4D4×D4311yescharacteristic
744C22×C4D4×D4311yescharacteristic
745C22×C4D4×D4311yescharacteristic
746C22×C4C23×D4311yescharacteristic
747C22×C4C23×D4311yescharacteristic
748C22×C4C23×D4311yescharacteristic
749Q16—44no—
750Q16—1724no—
751SD16—28no—
752SD16—1724no—
753SD16—1724no—
754D8—868no—
755M16—42no—
756M16—1722no—
757C2×C8—434no—
758C2×C8—1724no—
759C2×C8C23×D4314yes—
760C4⋊C4—22no—
761C4⋊C4—22no—
762C4⋊C4—21no—
763C4⋊C4—432no—
764C4⋊C4—432no—
765C4⋊C4—432no—
766C4⋊C4—432no—
767C4⋊C4—864no—
768C4⋊C4—864no—
769C4⋊C4—864no—
770C4⋊C4—862no—
771C4⋊C4—862no—
772C4⋊C4—862no—
773C4⋊C4—862no—
774C4⋊C4—861no—
775C4⋊C4—861no—
776C4⋊C4—862no—
777C4⋊C4—862no—
778C4⋊C4C23×D4312yes—
779C22⋊C4—22no—
780C22⋊C4—22no—
781C22⋊C4—432no—
782C22⋊C4—432no—
783C22⋊C4—432no—
784C22⋊C4—432no—
785C22⋊C4—862no—
786C22⋊C4—862no—
787C22⋊C4—862no—
788C22⋊C4—862no—
789C22⋊C4—864no—
790C22⋊C4—862no—
791C22⋊C4—862no—
792C22⋊C4—864no—
793C22⋊C4—862no—
794C22⋊C4—862no—
795C22⋊C4—862no—
796C22⋊C4—862no—
797C42—432no—
798C42—432no—
799C42—862no—
800C42—862no—
801C23—24no—
802C23—22no—
803C23—22no—
804C23—41no—
805C23—41no—
806C23—42no—
807C23—42no—
808C23—432no—
809C23—862no—
810C23—862no—
811C23—3441no—
812C23—3441no—
813C23—1721no—
814C23—1721no—
815C23—1722no—
816C23C2×D4×D4311yescharacteristic
817C23C2×D4×D4311yescharacteristic
818C23C2×D4×D4311yescharacteristic
819Q8—24no—
820Q8—22no—
821Q8—22no—
822Q8—42no—
823Q8—81no—
824Q8—864no—
825Q8—1722no—
826D4—24no—
827D4—22no—
828D4—44no—
829D4—44no—
830D4—864no—
831D4—3441no—
832D4—3442no—
833D4—3442no—
834D4—1722no—
835D4—1722no—
836D4—1728no—
837D4—1724no—
838D4—1724no—
839D4#1306337014yes—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—42no—
852C2×C4—81no—
853C2×C4—81no—
854C2×C4—432no—
855C2×C4—432no—
856C2×C4—432no—
857C2×C4—862no—
858C2×C4—864no—
859C2×C4—862no—
860C2×C4—862no—
861C2×C4—862no—
862C2×C4—3442no—
863C2×C4—3442no—
864C2×C4—1722no—
865C2×C4—1721no—
866C2×C4—1721no—
867C2×C4—1728no—
868C2×C4—1728no—
869C2×C4—1722no—
870C2×C4—1722no—
871C2×C4—1722no—
872C2×C4C2×D4×D4311yescharacteristic
873C2×C4C2×D4×D4311yescharacteristic
874C2×C4C2×D4×D4311yescharacteristic
875C2×C4C24×D4311yescharacteristic
876C8—24no—
877C8—864no—
878C22—21no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—24no—
887C22—48no—
888C22—42no—
889C22—42no—
890C22—82no—
891C22—862no—
892C22—862no—
893C22—862no—
894C22—3442no—
895C22—1722no—
896C22—1722no—
897C22—1722no—
898C22—6882no—
899C22#1458369812yes—
900C22C22×D4×D4311yescharacteristic
901C4—21no—
902C4—21no—
903C4—21no—
904C4—42no—
905C4—42no—
906C4—42no—
907C4—862no—
908C4—862no—
909C4—862no—
910C4—1722no—
911C4—1722no—
912C4—1722no—
913C4C2×#1306337012yes—
914C2—22no—
915C2—41no—
916C2—41no—
917C2—44no—
918C2—3442no—
919C2—1722no—
920C2#1914822411yescharacteristic
921C2C2×#1458369811yescharacteristic
922C2#1914937911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3007C2
socleC22×C43C23×D4
hypercenter#3007D43
hypocenterC43#61575
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
1. #19148436C2semidirect
2. C2×#14583548C2semidirect
3. #19146684C2semidirect
4. #19146572C2semidirect
5. #19146144C2semidirect
6. #19146123C2semidirect
7. #19145625C2semidirect
8. #19145416C2semidirect
9. #19145402C2semidirect
10. #19145379C2semidirect
11. #19144734C2semidirect
12. #19143847C2semidirect
13. #19143814C2semidirect
14. #19143622C2semidirect
15. C43×#3007C2semidirect
16. C22×#10621900C22semidirect
17. C2×#13063350C22semidirect
18. C2×#13063346C22semidirect
20. #14583597C22semidirect
21. #14583591C22semidirect
23. #14583560C22semidirect
27. #14583548C22semidirect
28. #14583540C22semidirect
32. C2×#13063323C22semidirect
38. C2×#13063301C22semidirect
42. C2×D4×Dic43C22semidirect
45. #14583292C22semidirect
46. #14583266C22semidirect
47. #14583239C22semidirect
48. #14583235C22semidirect
49. #14583229C22semidirect
50. #14583227C22semidirect
52. #14583197C22semidirect
53. #14583155C22semidirect
54. #14583145C22semidirect
55. #14583137C22semidirect
56. #14583131C22semidirect
57. #14583116C22semidirect
58. #14583107C22semidirect
59. #14583103C22semidirect
60. #14583060C22semidirect
61. #14583058C22semidirect
62. #14583055C22semidirect
63. #14583054C22semidirect
64. #14583052C22semidirect
65. #14583045C22semidirect
66. #14583044C22semidirect
70. #14583008C22semidirect
71. #14583000C22semidirect
72. #14582973C22semidirect
73. #14582968C22semidirect
74. #14582953C22semidirect
75. #14582900C22semidirect
76. #14582892C22semidirect
78. C22⋊C8×D43C22semidirect
80. C2×#137×C43C22semidirect
82. C43×#452C22semidirect
83. C43×#451C22semidirect
84. C43×#450C22semidirect
85. C43×#417C22semidirect
464. #3007D43semidirect
479. C2×#137C2×D43semidirect
526. #452C2×D43semidirect
529. #451C2×D43semidirect
531. #450C2×D43semidirect
543. #417C2×D43semidirect
548. C43#61575semidirect

Maximal subgroups

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

subgroupindex
#191484362
C2×#145835482
#191466842
#191465722
#191461442
#191461232
#191456252
#191454162
#191454022
#191453792
#191447342
#191438472
#191438142
#191436222
C43×#30072
#6157543