Finite Group Databasebeta

← #25981530

Subgroups — #25981530

Order 11008.

2178 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148436C211yesmaximal, characteristic, complemented
2C2×#14583568C211yesmaximal, characteristic, complemented
3#19146714C214yesmaximal, complemented
4#19146602C214yesmaximal, complemented
5#19146174C214yesmaximal, complemented
6#19146138C214yesmaximal, complemented
7#19145616C212yesmaximal, complemented
8#19145397C211yesmaximal, characteristic, complemented
9#19145395C211yesmaximal, characteristic, complemented
10#19145363C212yesmaximal, complemented
11#19144767C212yesmaximal, complemented
12#19143847C211yesmaximal, characteristic, complemented
13#19143818C212yesmaximal, complemented
14#19143622C211yesmaximal, characteristic, complemented
15C43×#3007C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic, complemented
17C2×#13063350C2212yescomplemented
18C2×#13063348C2214yescomplemented
19#14583597—22no—
20#14583597C2212yescomplemented
21#14583591C2212yescomplemented
22#14583576—22no—
23#14583568—22no—
24#14583568—22no—
25#14583568C2214yes—
26#14583568C2214yescomplemented
27#14583560C2212yescomplemented
28#14583540C2212yescomplemented
29#14583498—21no—
30#14583489—21no—
31#14583461—21no—
32C2×#13063321—21no—
33C2×#13063321C2211yescharacteristic, complemented
34#14583435C2212yes—
35#14583412C2212yes—
36C2×#13063299—21no—
37C2×#13063299C2211yescharacteristic
38C2×#13063299C2211yescharacteristic
39C2×#13063296—21no—
40C2×#13063296C2211yescharacteristic, complemented
41#14583372—21no—
42C2×Q8×Dic43C2211yescharacteristic, complemented
43C2×C4×C22⋊D43—21no—
44C2×C4×C22⋊D43C2211yescharacteristic
45#14583285C2214yescomplemented
46#14583262C2214yescomplemented
47#14583232C2212yescomplemented
48#14583222C2214yescomplemented
49#14583218C2212yes—
50#14583218C2212yescomplemented
51#14583212C2212yescomplemented
52#14583204C2214yescomplemented
53#14583152C2214yescomplemented
54#14583147C2214yescomplemented
55#14583134C2214yescomplemented
56#14583125C2214yescomplemented
57#14583123C2214yescomplemented
58#14583097C2214yescomplemented
59#14583093C2214yescomplemented
60#14583060C2214yescomplemented
61#14583049C2212yescomplemented
62#14583047C2214yescomplemented
63#14583044C2214yescomplemented
64#14583043C2214yescomplemented
65#14583038C2212yes—
66#14583038C2212yescomplemented
67#14583035C2212yes—
68#14583035C2212yescomplemented
69#14583033C2212yes—
70#14583006C2214yescomplemented
71#14583002C2214yescomplemented
72#14582973C2214yescomplemented
73#14582968C2214yescomplemented
74#14582953C2212yescomplemented
75#14582900C2212yescomplemented
76#14582894C2214yescomplemented
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×#10621902—22no—
88C2×#10621902—44no—
89C2×#10621902C2314yes—
90C2×#10621902C2312yes—
91C22×D172—21no—
92C22×D172C2311yescharacteristic
93C22×D172C2311yescharacteristic
94C22×C22⋊D43—21no—
95C22×C22⋊D43—21no—
96C22×C22⋊D43—21no—
97C22×C22⋊D43—21no—
98C22×C22⋊D43—21no—
99C22×C22⋊D43D411yescharacteristic
100C22×C4×D43—21no—
101C22×C4×D43C2311yescharacteristic
102#13063350—44no—
103#13063348—48no—
104C2×#10621884C2314yes—
105C2×#10621884C2314yes—
106C2×D344C2314yes—
107C2×#10621882C2314yes—
108C2×#10621877C2312yes—
109C2×C8×D43C2314yes—
110#13063321—24no—
111#13063321—24no—
112#13063321—22no—
113#13063321C2314yes—
114#13063320—22no—
115#13063320—22no—
116#13063320—22no—
117#13063316—22no—
118#13063316C2312yes—
119#13063314—22no—
120#13063314C2312yes—
121#13063310—22no—
122#13063310—22no—
123#13063310—22no—
124#13063309—22no—
125#13063309—22no—
126#13063301—22no—
127#13063301C2312yes—
128#13063300—22no—
129#13063300C2312yes—
130#13063299—21no—
131#13063299—21no—
132#13063299—21no—
133#13063299—21no—
134#13063299—22no—
135#13063299—22no—
136#13063299—24no—
137#13063299—24no—
138#13063299C2312yes—
139#13063299C2312yes—
140#13063299C2312yes—
141#13063299C2312yes—
142#13063296—22no—
143#13063296—24no—
144#13063296—24no—
145#13063296C2314yes—
146#13063295—22no—
147#13063295—22no—
148Q8×Dic43—22no—
149Q8×Dic43C2312yes—
150Q8×Dic43C2314yes—
151#13063287—22no—
152#13063287C2312yes—
153C4×C22⋊D43—22no—
154C4×C22⋊D43—22no—
155C4×C22⋊D43—24no—
156C4×C22⋊D43—24no—
157C4×C22⋊D43D412yes—
158C4×C22⋊D43D412yes—
159C4×C22⋊D43C2312yes—
160C4×C22⋊D43C2312yes—
161(C22⋊D43)⋊C4—22no—
162(C22⋊D43)⋊C4—22no—
163#13063283—22no—
164#13063283C2312yes—
165#13063281—22no—
166C2×C4⋊Dic43—21no—
167C2×C4⋊Dic43C2311yescharacteristic
168C2×C4⋊Dic43C2311yescharacteristic
169C2×Dic43⋊C4D411yescharacteristic
170C2×C22⋊Dic43—21no—
171C2×C22⋊Dic43D411yescharacteristic
172C2×(C2×D43)⋊C4—21no—
173C2×(C2×D43)⋊C4—21no—
174C2×(C2×D43)⋊C4D411yescharacteristic
175C22⋊C4×D43—22no—
176C2×C4×Dic43—21no—
177C2×C4×Dic43C2311yescharacteristic
178#13063258C2314yes—
179#13063257C2314yes—
180Dic43⋊C8C2314yes—
181#13063249C2314yes—
182#13063249C2314yes—
183#13063247C2314yes—
184#13063247C2314yes—
185#13063246C2314yes—
186#13063245C2314yes—
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×D43—21no—
221C23×D43C2×D411yescharacteristic
222#41×C43—24no—
223#41×C43—24no—
224#41×C43—42no—
225#41×C43—42no—
226#41×C43—44no—
227#41×C43—44no—
228C2×Q8×C43—24no—
229C2×Q8×C43—21no—
230C2×Q8×C43—21no—
231C2×Q8×C43—42no—
232C2×Q8×C43C2412yes—
233C2×Q8×C43C2412yes—
234C2×D4×C43—21no—
235C2×D4×C43—22no—
236C2×D4×C43—22no—
237C2×D4×C43—42no—
238C2×D4×C43—44no—
239C2×D4×C43C2412yes—
240C22×C4×C43—22no—
241C22×C4×C43—22no—
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43—21no—
245C22×C4×C43—42no—
246C22×C4×C43—44no—
247C22×C4×C43C2×D411yescharacteristic
248C22×C4×C43C2×D411yescharacteristic
249C22×C4×C43C2×D411yescharacteristic
250C22×C4×C43C2411yescharacteristic
251C22×C4×C43C2411yescharacteristic
252C22×C4×C43C2411yescharacteristic
253C2×C22⋊D43—24no—
254C2×C22⋊D43—24no—
255C2×C22⋊D43—22no—
256C2×C22⋊D43—22no—
257C2×C22⋊D43—22no—
258C2×C22⋊D43—22no—
259C2×C22⋊D43—24no—
260C2×C22⋊D43—42no—
261C2×C22⋊D43—44no—
262C2×C22⋊D43—44no—
263C2×C22⋊D43—82no—
264C2×C22⋊D43—82no—
265C2×C22⋊D43—82no—
266C2×C22⋊D43C2×D412yes—
267C2×C22⋊D43C2×D412yes—
268C22×Dic43—21no—
269C22×Dic43—21no—
270C22×Dic43C2×D411yescharacteristic
271C22×Dic43C2×D411yescharacteristic
272C22×Dic43C2×D411yescharacteristic
273#10621902—28no—
274#10621902—44no—
275#10621902—44no—
276#10621902—48no—
277C2×D172—21no—
278C2×D172—21no—
279C2×D172—24no—
280C2×D172—22no—
281C2×D172—22no—
282C2×D172—42no—
283C2×D172—44no—
284C2×D172—42no—
285C2×D172C2412yes—
286C2×D172C2412yes—
287C2×C4×D43—24no—
288C2×C4×D43—22no—
289C2×C4×D43—22no—
290C2×C4×D43—42no—
291C2×C4×D43—44no—
292C2×C4×D43C2×D412yes—
293C2×C4×D43C2412yes—
294Q16×C43—28no—
295SD16×C43—44no—
296M16×C43—42no—
297C2×C8×C43C2414yes—
298C4⋊C4×C43—22no—
299C4⋊C4×C43—22no—
300C4⋊C4×C43—21no—
301C4⋊C4×C43C2412yes—
302C22⋊C4×C43—22no—
303C22⋊C4×C43—22no—
304C22⋊Dic43—24no—
305C22⋊Dic43C2×D412yes—
306C22⋊Dic43C2×D412yes—
307#10621884—28no—
308#10621884—44no—
309#10621882—44no—
310(C2×D43)⋊C4—22no—
311(C2×D43)⋊C4—22no—
312(C2×D43)⋊C4—22no—
313(C2×D43)⋊C4—22no—
314(C2×D43)⋊C4—22no—
315(C2×D43)⋊C4—22no—
316(C2×D43)⋊C4—22no—
317(C2×D43)⋊C4—22no—
318(C2×D43)⋊C4—22no—
319(C2×D43)⋊C4—22no—
320(C2×D43)⋊C4C2×D412yes—
321(C2×D43)⋊C4C2×D412yes—
322C4⋊Dic43—21no—
323C4⋊Dic43—21no—
324C4⋊Dic43—24no—
325C4⋊Dic43—22no—
326C4⋊Dic43—22no—
327C4⋊Dic43C2412yes—
328C4⋊Dic43C2412yes—
329Dic43⋊C4—22no—
330Dic43⋊C4—22no—
331Dic43⋊C4C2×D412yes—
332Dic43⋊C4C2×D412yes—
333C4×Dic43—24no—
334C4×Dic43—22no—
335C4×Dic43—22no—
336C4×Dic43C2×D412yes—
337C4×Dic43C2412yes—
338#10621877—42no—
339C2×C43⋊C8C2414yes—
340D344—44no—
341C8×D43—44no—
342C23×C43—22no—
343C23×C43—22no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—42no—
347C23×C43—42no—
348C23×C43—42no—
349C23×C43C22×D411yescharacteristic
350C23×C43C22×D411yescharacteristic
351C23×C43C22×D411yescharacteristic
352C22×D43—22no—
353C22×D43—22no—
354C22×D43—22no—
355C22×D43—41no—
356C22×D43—41no—
357C22×D43—42no—
358C22×D43—42no—
359C22×D43—42no—
360C22×D43—42no—
361C22×D43—81no—
362C22×D43—81no—
363C22×D43C22×D412yes—
364Q8×C43—24no—
365Q8×C43—22no—
366Q8×C43—24no—
367Q8×C43—81no—
368Q8×C43H(5,𝔽2)14yes—
369D4×C43—22no—
370D4×C43—22no—
371D4×C43—44no—
372D4×C43—44no—
373D4×C43—42no—
374C2×C4×C43—24no—
375C2×C4×C43—22no—
376C2×C4×C43—22no—
377C2×C4×C43—22no—
378C2×C4×C43—22no—
379C2×C4×C43—22no—
380C2×C4×C43—22no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—44no—
385C2×C4×C43—44no—
386C2×C4×C43—81no—
387C2×C4×C43—81no—
388C2×C4×C43C22×D411yescharacteristic
389C2×C4×C43C22×D411yescharacteristic
390C2×C4×C43C22×D411yescharacteristic
391C2×C4×C43C2511yescharacteristic
392C22⋊D43—42no—
393C22⋊D43—42no—
394C22⋊D43—48no—
395C22⋊D43—44no—
396C22⋊D43—44no—
397C22⋊D43—84no—
398C22⋊D43—84no—
399C22⋊D43—82no—
400C22⋊D43—82no—
401C2×Dic43—22no—
402C2×Dic43—22no—
403C2×Dic43—22no—
404C2×Dic43—41no—
405C2×Dic43—41no—
406C2×Dic43—42no—
407C2×Dic43—42no—
408C2×Dic43C22×D412yes—
409C2×Dic43C22×D412yes—
410C2×Dic43C22×D412yes—
411D172—24no—
412D172—24no—
413D172—48no—
414D172—42no—
415D172—81no—
416D172—82no—
417D172—82no—
418C4×D43—24no—
419C4×D43—42no—
420C4×D43—48no—
421C4×D43—82no—
422C4×D43—82no—
423C8×C43—24no—
424C43⋊C8—24no—
425#61577—431nomaximal, Sylow
426C22×C43—21no—
427C22×C43—21no—
428C22×C43—21no—
429C22×C43—21no—
430C22×C43—21no—
431C22×C43—21no—
432C22×C43—21no—
433C22×C43—21no—
434C22×C43—42no—
435C22×C43—42no—
436C22×C43—42no—
437C22×C43—82no—
438C22×C43—84no—
439C22×C43#57512yes—
440C22×C43C23×D411yescharacteristic
441C2×D43—22no—
442C2×D43—22no—
443C2×D43—22no—
444C2×D43—42no—
445C2×D43—42no—
446C2×D43—42no—
447C2×D43—42no—
448C2×D43—42no—
449C2×D43—42no—
450C2×D43—82no—
451C2×D43—84no—
452C2×D43—162no—
453C4×C43—24no—
454C4×C43—21no—
455C4×C43—21no—
456C4×C43—21no—
457C4×C43—42no—
458C4×C43—42no—
459C4×C43C2×H(5,𝔽2)12yes—
460Dic43—22no—
461Dic43—22no—
462Dic43—22no—
463Dic43—42no—
464Dic43—42no—
465#3505—431no—
466C2×#550—431no—
467#3317—434no—
468#3309—434no—
469#3271—434no—
470#3268—434no—
471#3217—432no—
472#3193—431no—
473#3192—431no—
474#3188—432no—
475#3117—432no—
476#3007D4311yescharacteristic, complemented
477#3006—431no—
478#3002—432no—
479#2973—431no—
480C2×C43—22no—
481C2×C43—41no—
482C2×C43—41no—
483C2×C43—82no—
484C2×C43#348411yescharacteristic
485C2×C43C2×#57511yescharacteristic
486C2×C43#358511yescharacteristic
487D43—42no—
488D43—82no—
489D43—82no—
490C22×#41—431no—
491C22×#41C2×D4311yescharacteristic
492C2×#137C2×D4312yescomplemented
493C2×AGL(1,ℤ/8)—432no—
494C2×#135—434no—
495#553—432no—
496#553—862no—
497#552—432no—
498#551—862no—
499#550—434no—
500#550—434no—
501#550—862no—
502#550—862no—
503#548—432no—
504#546—432no—
505#539—861no—
506#538—861no—
507#534—861no—
508C2×#127—431no—
509C2×#127—861no—
510#529—432no—
511#525—432no—
512C2×C22⋊Q8C2×D4311yescharacteristic
513C2×#121—431no—
514C2×#121—431no—
515C2×#121—431no—
516C2×#121—861no—
517C2×#121—861no—
518#518—861no—
519C2×C4×Q8—431no—
520C2×C4×D4—431no—
521C2×C4×D4—861no—
522#496—434no—
523#490—434no—
524#484—432no—
525#482—434no—
526#481—432no—
527#481—432no—
528#480—432no—
529#479—434no—
530#469—434no—
531#468—434no—
532#466—434no—
533#465—434no—
534#464—434no—
535#460—434no—
536#459—434no—
537#452—434no—
538#452C2×D4314yescomplemented
539#451C2×D4312yescomplemented
540#450—432no—
541#450C2×D4312yescomplemented
542#449—434no—
543#449—434no—
544#449—434no—
545#448—432no—
546#448—432no—
547#447—432no—
548#447—432no—
549#447—432no—
550#441—434no—
551#440—434no—
552#435—434no—
553#435—434no—
554#432—432no—
555#417—432no—
556#417C2×D4312yescomplemented
557#416—434no—
558#407—431no—
559#407C2×D4311yescharacteristic
560C2×C22⋊C8—432no—
561C43#6157711yescharacteristic, complemented, Sylow
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—44no—
565C2×#41—434no—
566C2×#41—432no—
567C2×#41—862no—
568C2×#41—1724no—
569C2×#41C22×D4312yes—
570C2×#41C22×D4312yes—
571C22×Q8C22×D4311yescharacteristic
572C22×Q8C22×D4311yescharacteristic
573C22×D4—21no—
574C22×D4—431no—
575C22×D4—431no—
576C22×D4—431no—
577C22×D4—861no—
578C22×D4—861no—
579C22×D4—861no—
580C22×D4—861no—
581C22×D4—861no—
582C22×D4—861no—
583C22×D4C22×D4311yescharacteristic
584C23×C4—21no—
585C23×C4—431no—
586C23×C4—861no—
587C23×C4C22×D4311yescharacteristic
588#137—44no—
589AGL(1,ℤ/8)—1724no—
590#135—1728no—
591C2×Q16C22×D4314yes—
592C2×SD16—434no—
593C2×SD16—434no—
594C2×SD16C22×D4314yes—
595C2×D8—434no—
596C2×D8—434no—
597C2×M16—432no—
598C2×M16C22×D4312yes—
599C22×C8—434no—
600#127—434no—
601#127—862no—
602#127—864no—
603#127—864no—
604#126—862no—
605#126—862no—
606#126—862no—
607#125—432no—
608#125—862no—
609#124—432no—
610#124—862no—
611#123—862no—
612#123—862no—
613#123—862no—
614#123—862no—
615#123—862no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618C22⋊Q8—432no—
619C22⋊Q8—862no—
620C22⋊Q8C22×D4312yes—
621C22⋊Q8C22×D4312yes—
622#121—434no—
623#121—432no—
624#121—432no—
625#121—432no—
626#121—432no—
627#121—432no—
628#121—862no—
629#121—864no—
630#121—864no—
631#121—864no—
632#121—864no—
633#121—862no—
634#121—862no—
635#121—862no—
636#121—861no—
637#121—861no—
638#121—861no—
639#121—861no—
640#120—862no—
641#120—862no—
642C4×Q8—434no—
643C4×Q8—432no—
644C4×Q8—862no—
645C4×D4—432no—
646C4×D4—432no—
647C4×D4—432no—
648C4×D4—432no—
649C4×D4—432no—
650C4×D4—862no—
651C4×D4—862no—
652C4×D4—862no—
653C4×D4—862no—
654C4×D4—862no—
655C4×D4—864no—
656C4×D4—864no—
657#117—432no—
658#117—862no—
659#117—862no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—431no—
662C2×C4⋊C4—431no—
663C2×C4⋊C4—431no—
664C2×C4⋊C4—861no—
665C2×C4⋊C4C22×D4311yescharacteristic
666C2×C22⋊C4—21no—
667C2×C22⋊C4—431no—
668C2×C22⋊C4—431no—
669C2×C22⋊C4—862no—
670C2×C22⋊C4—861no—
671C2×C22⋊C4—861no—
672C2×C22⋊C4—861no—
673C2×C42—431no—
674C2×C42—861no—
675#107—434no—
676#106—434no—
677C4⋊C8—434no—
678#103—434no—
679#103—434no—
680#103C22×D4314yes—
681#102—434no—
682#102—434no—
683#102—434no—
684#102—434no—
685#102C22×D4314yes—
686C22⋊C8—432no—
687C22⋊C8—432no—
688C22⋊C8—434no—
689C22⋊C8C22×D4312yes—
690C22⋊C8C22×D4312yes—
691#97—434no—
692C24—21no—
693C24—431no—
694C24—861no—
695C24—861no—
696C24D4×D4311yescharacteristic
697#41—24no—
698#41—24no—
699#41—42no—
700#41—42no—
701#41—44no—
702#41—44no—
703#41—868no—
704#41—1724no—
705#41—1724no—
706#41—1728no—
707C2×Q8—24no—
708C2×Q8—21no—
709C2×Q8—21no—
710C2×Q8—42no—
711C2×Q8C23×D4312yes—
712C2×Q8C23×D4312yes—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—21no—
716C2×D4—42no—
717C2×D4—44no—
718C2×D4—432no—
719C2×D4—432no—
720C2×D4—432no—
721C2×D4—432no—
722C2×D4—862no—
723C2×D4—862no—
724C2×D4—864no—
725C2×D4—864no—
726C2×D4—864no—
727C2×D4—864no—
728C2×D4—862no—
729C2×D4—862no—
730C2×D4—862no—
731C2×D4—862no—
732C2×D4—861no—
733C2×D4—861no—
734C2×D4—3442no—
735C2×D4—3442no—
736C2×D4—3442no—
737C2×D4—1722no—
738C2×D4—1722no—
739C2×D4—1724no—
740C2×D4—1722no—
741C2×D4—1724no—
742C2×D4—1724no—
743C2×D4C23×D4312yes—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—42no—
750C22×C4—44no—
751C22×C4—431no—
752C22×C4—431no—
753C22×C4—431no—
754C22×C4—432no—
755C22×C4—432no—
756C22×C4—862no—
757C22×C4—862no—
758C22×C4—864no—
759C22×C4—861no—
760C22×C4—861no—
761C22×C4—1722no—
762C22×C4—1724no—
763C22×C4D4×D4311yescharacteristic
764C22×C4D4×D4311yescharacteristic
765C22×C4D4×D4311yescharacteristic
766C22×C4C23×D4311yescharacteristic
767C22×C4C23×D4311yescharacteristic
768C22×C4C23×D4311yescharacteristic
769Q16—28no—
770SD16—44no—
771SD16—868no—
772SD16—1724no—
773D8—1724no—
774D8—1724no—
775M16—42no—
776M16—1722no—
777C2×C8—434no—
778C2×C8—1724no—
779C2×C8C23×D4314yes—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—21no—
783C4⋊C4—432no—
784C4⋊C4—432no—
785C4⋊C4—432no—
786C4⋊C4—432no—
787C4⋊C4—864no—
788C4⋊C4—862no—
789C4⋊C4—862no—
790C4⋊C4—862no—
791C4⋊C4—862no—
792C4⋊C4—861no—
793C4⋊C4—861no—
794C4⋊C4C23×D4312yes—
795C22⋊C4—22no—
796C22⋊C4—22no—
797C22⋊C4—432no—
798C22⋊C4—432no—
799C22⋊C4—432no—
800C22⋊C4—432no—
801C22⋊C4—862no—
802C22⋊C4—862no—
803C22⋊C4—862no—
804C22⋊C4—862no—
805C22⋊C4—862no—
806C22⋊C4—862no—
807C22⋊C4—864no—
808C22⋊C4—862no—
809C22⋊C4—862no—
810C22⋊C4—862no—
811C22⋊C4—862no—
812C42—432no—
813C42—432no—
814C42—864no—
815C42—862no—
816C42—862no—
817C23—22no—
818C23—22no—
819C23—41no—
820C23—41no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—432no—
825C23—862no—
826C23—862no—
827C23—862no—
828C23—3441no—
829C23—3441no—
830C23—1721no—
831C23—1721no—
832C23—1722no—
833C23—1722no—
834C23—1722no—
835C23—1722no—
836C23C2×D4×D4311yescharacteristic
837C23C2×D4×D4311yescharacteristic
838C23C2×D4×D4311yescharacteristic
839Q8—24no—
840Q8—22no—
841Q8—24no—
842Q8—81no—
843Q8#1306337014yes—
844D4—22no—
845D4—22no—
846D4—44no—
847D4—44no—
848D4—42no—
849D4—864no—
850D4—864no—
851D4—3441no—
852D4—3442no—
853D4—3442no—
854D4—3444no—
855D4—3442no—
856D4—3442no—
857D4—3444no—
858D4—1728no—
859D4—1722no—
860D4—1722no—
861D4—1722no—
862D4—1728no—
863D4—1724no—
864D4—1724no—
865C2×C4—24no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—44no—
876C2×C4—44no—
877C2×C4—81no—
878C2×C4—81no—
879C2×C4—432no—
880C2×C4—432no—
881C2×C4—432no—
882C2×C4—862no—
883C2×C4—864no—
884C2×C4—862no—
885C2×C4—862no—
886C2×C4—3442no—
887C2×C4—3442no—
888C2×C4—1722no—
889C2×C4—1728no—
890C2×C4—1721no—
891C2×C4—1721no—
892C2×C4—1722no—
893C2×C4—1722no—
894C2×C4C2×D4×D4311yescharacteristic
895C2×C4C2×D4×D4311yescharacteristic
896C2×C4C2×D4×D4311yescharacteristic
897C2×C4C24×D4311yescharacteristic
898C8—24no—
899C8—864no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—82no—
912C22—84no—
913C22—862no—
914C22—862no—
915C22—862no—
916C22—3444no—
917C22—3442no—
918C22—1722no—
919C22—1722no—
920C22—1722no—
921C22—1722no—
922C22—1722no—
923C22—1722no—
924C22—6882no—
925C22#1458369812yes—
926C22C22×D4×D4311yescharacteristic
927C4—24no—
928C4—21no—
929C4—21no—
930C4—21no—
931C4—42no—
932C4—42no—
933C4—862no—
934C4—862no—
935C4—862no—
936C4—1722no—
937C4—1722no—
938C4C2×#1306337012yes—
939C2—22no—
940C2—41no—
941C2—41no—
942C2—82no—
943C2—3442no—
944C2—3442no—
945C2—1722no—
946C2#1914822411yescharacteristic
947C2C2×#1458369811yescharacteristic
948C2#1914937211yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3007C2
socleC22×C43C23×D4
hypercenter#3007D43
hypocenterC43#61577
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×#14583568C2semidirect
3. #19146714C2semidirect
4. #19146602C2semidirect
5. #19146174C2semidirect
6. #19146138C2semidirect
7. #19145616C2semidirect
8. #19145397C2semidirect
9. #19145395C2semidirect
10. #19145363C2semidirect
11. #19144767C2semidirect
12. #19143847C2semidirect
13. #19143818C2semidirect
14. #19143622C2semidirect
15. C43×#3007C2semidirect
16. C22×#10621902C22semidirect
17. C2×#13063350C22semidirect
18. C2×#13063348C22semidirect
20. #14583597C22semidirect
21. #14583591C22semidirect
26. #14583568C22semidirect
27. #14583560C22semidirect
28. #14583540C22semidirect
33. C2×#13063321C22semidirect
40. C2×#13063296C22semidirect
42. C2×Q8×Dic43C22semidirect
45. #14583285C22semidirect
46. #14583262C22semidirect
47. #14583232C22semidirect
48. #14583222C22semidirect
50. #14583218C22semidirect
51. #14583212C22semidirect
52. #14583204C22semidirect
53. #14583152C22semidirect
54. #14583147C22semidirect
55. #14583134C22semidirect
56. #14583125C22semidirect
57. #14583123C22semidirect
58. #14583097C22semidirect
59. #14583093C22semidirect
60. #14583060C22semidirect
61. #14583049C22semidirect
62. #14583047C22semidirect
63. #14583044C22semidirect
64. #14583043C22semidirect
66. #14583038C22semidirect
68. #14583035C22semidirect
70. #14583006C22semidirect
71. #14583002C22semidirect
72. #14582973C22semidirect
73. #14582968C22semidirect
74. #14582953C22semidirect
75. #14582900C22semidirect
76. #14582894C22semidirect
78. C22⋊C8×D43C22semidirect
80. C2×#137×C43C22semidirect
82. C43×#452C22semidirect
83. C43×#451C22semidirect
84. C43×#450C22semidirect
85. C43×#417C22semidirect
476. #3007D43semidirect
492. C2×#137C2×D43semidirect
538. #452C2×D43semidirect
539. #451C2×D43semidirect
541. #450C2×D43semidirect
556. #417C2×D43semidirect
561. C43#61577semidirect

Maximal subgroups

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

subgroupindex
#191484362
C2×#145835682
#191467142
#191466022
#191461742
#191461382
#191456162
#191453972
#191453952
#191453632
#191447672
#191438472
#191438182
#191436222
C43×#30072
#6157743