Finite Group Databasebeta

← #25968399

Subgroups — #25968399

Order 11008.

2146 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148470C211yesmaximal, characteristic, complemented
2#19148389C211yesmaximal, characteristic, complemented
3#19145652C214yesmaximal, complemented
4#19145643C214yesmaximal, complemented
5#19145587C214yesmaximal, complemented
6#19145581C214yesmaximal, complemented
7#19145043C211yesmaximal, characteristic, complemented
8C2×#14583285C211yesmaximal, characteristic, complemented
9#19144983C211yesmaximal, characteristic, complemented
10#19144938C211yesmaximal, characteristic, complemented
11#19144106C211yesmaximal, characteristic, complemented
12#19144104C211yesmaximal, characteristic, complemented
13#19144101C211yesmaximal, characteristic, complemented
14#19144100C211yesmaximal, characteristic, complemented
15#19143881C211yesmaximal, characteristic, complemented
16#19143865C211yesmaximal, characteristic, complemented
17#19143861C211yesmaximal, characteristic, complemented
18#19143242C211yesmaximal, characteristic, complemented
19C43×#3010C211yesmaximal, characteristic, complemented
20C2×#13063371C2211yescharacteristic
21C2×#13063353C2211yescharacteristic
22C2×#13063351C2211yescharacteristic
23C2×#13063350C2211yescharacteristic, complemented
24C22×#10621884C2211yescharacteristic, complemented
25C22×D344C2211yescharacteristic
26C22×#10621882C2211yescharacteristic
27#14583631—22no—
28#14583569—22no—
29#14583560—22no—
30#14583537—24no—
31#14583537—22no—
32#14583536—24no—
33#14583502C2214yescomplemented
34#14583473C2211yescharacteristic
35#14583473C2212yescomplemented
36#14583463C2211yescharacteristic
37#14583463C2211yescharacteristic
38#14583463C2212yescomplemented
39#14583452C2211yescharacteristic, complemented
40#14583445C2211yescharacteristic
41#14583445C2212yescomplemented
42#14583444C2214yescomplemented
43C2×#13063321C2211yescharacteristic, complemented
44C2×#13063314C2211yescharacteristic
45C2×#13063314C2212yescomplemented
46#14583374C2211yescharacteristic, complemented
47#14583373C2211yescharacteristic, complemented
48#41×Dic43C2211yescharacteristic
49#14583287C2212yescomplemented
50#14583285C2214yescomplemented
51#14583285C2214yescomplemented
52#14583285C2212yescomplemented
53#14583274C2212yescomplemented
54#14583270C2212yescomplemented
55#14583266C2212yescomplemented
56#14583262C2212yescomplemented
57#14583260C2214yescomplemented
58#14583260C2212yescomplemented
59#14583257C2212yescomplemented
60#14583255C2214yescomplemented
61#14583117C2214yescomplemented
62#14583117C2214yescomplemented
63#14583116C2214yescomplemented
64#14583116C2214yescomplemented
65#14583103C2214yescomplemented
66#14583102C2214yescomplemented
67#14583093C2214yescomplemented
68#14583092C2214yescomplemented
69#14583046C2214yescomplemented
70#14583044C2214yescomplemented
71#14583042C2214yescomplemented
72#14583038C2214yescomplemented
73#14583035C2214yescomplemented
74#14583032C2214yescomplemented
75#14582957C2214yescomplemented
76#14582953C2214yescomplemented
77#14582927C2211yescharacteristic, complemented
78#14582925C2211yescharacteristic, complemented
79#14582908C2211yescharacteristic, complemented
80#14582905C2211yescharacteristic
81#14582903C2211yescharacteristic
82#14582896C2211yescharacteristic
83#14582895C2211yescharacteristic, complemented
84#14582893C2211yescharacteristic
85#14582866C2211yescharacteristic
86M16×Dic43C2211yescharacteristic, complemented
87C2×#13063235C2211yescharacteristic, complemented
88C2×2−1+4×C43C2211yescharacteristic
89C2×AGL(1,ℤ/8)×C43C2211yescharacteristic, complemented
90C22×SD16×C43C2211yescharacteristic, complemented
91C43×#535C2211yescharacteristic
92C43×#449C2214yescomplemented
93C43×#448C2214yescomplemented
94C43×#419C2211yescharacteristic, complemented
95C43×#416C2211yescharacteristic, complemented
96C43×#408C2211yescharacteristic
97#13063371—42no—
98#13063371—42no—
99C2×#10621902—21no—
100C2×#10621898C2311yescharacteristic
101C2×#10621898C2312yes—
102C2×#10621900—24no—
103C22×D172C2311yescharacteristic
104C22×D172C2311yescharacteristic
105C22×D172C2312yes—
106C22×C22⋊D43—22no—
107C2×D4×D43—22no—
108C2×D4×D43—21no—
109#13063353—42no—
110#13063351—42no—
111#13063350—42no—
112C2×#10621873C2312yes—
113C2×#10621883C2312yes—
114C2×#10621884—42no—
115C2×#10621884C2314yes—
116C2×#10621884C2312yes—
117C2×D344—42no—
118C2×D344C2314yes—
119C2×D344C2312yes—
120C2×#10621882—42no—
121C2×#10621882C2314yes—
122C2×#10621882C2312yes—
123C2×#10621882C2312yes—
124C2×#10621877C2311yescharacteristic
125C22×C43⋊C8C2311yescharacteristic
126#13063324C2312yes—
127#13063323C2312yes—
128#13063323C2311yescharacteristic
129#13063321—21no—
130#13063321—22no—
131#13063321C2312yes—
132#13063321C2312yes—
133#13063321C2312yes—
134#13063321C2311yescharacteristic
135#13063316C2312yes—
136#13063314—21no—
137#13063314—22no—
138#13063314—24no—
139#13063314C2312yes—
140#13063314C2312yes—
141#13063314C2312yes—
142#13063314C2312yes—
143#13063314C2311yescharacteristic
144#13063312C2311yescharacteristic
145#13063311—24no—
146#13063309—24no—
147#13063308—22no—
148#13063308—24no—
149#13063307—24no—
150#13063302—22no—
151#13063301—22no—
152#13063301—24no—
153#13063299—22no—
154#13063299—24no—
155#13063299C2314yes—
156#13063297—24no—
157#13063297—22no—
158#13063297—24no—
159#13063297—24no—
160#13063296—24no—
161#13063293—22no—
162#13063293—22no—
163#13063293—24no—
164Q8×Dic43D412yes—
165C4×Dic86—22no—
166C4×D172—22no—
167D4×Dic43—22no—
168D4×Dic43D412yes—
169D4×Dic43D414yes—
170D4×Dic43C2314yes—
171#13063287C2314yes—
172C4×C22⋊D43—22no—
173C4×C22⋊D43—24no—
174(C22⋊D43)⋊C4—24no—
175#13063284C2311yescharacteristic
176#13063284C2311yescharacteristic
177#13063284C2312yes—
178C2×C22⋊Dic43—22no—
179C2×(C2×D43)⋊C4—22no—
180C2×(C2×D43)⋊C4—24no—
181C22⋊C4×D43—22no—
182C2×C4×Dic43C2311yescharacteristic
183C2×C4×Dic43C2312yes—
184Dic43⋊C8C2314yes—
185Dic43⋊C8C2314yes—
186#13063250C2312yes—
187#13063249C2314yes—
188#13063249C2312yes—
189#13063248C2312yes—
190#13063247C2314yes—
191#13063247C2312yes—
192#13063246C2312yes—
193#13063245C2314yes—
194#13063245C2312yes—
195C22⋊(C43⋊C8)C2314yes—
196#13063235C2312yes—
197#13063235C2312yes—
198#13063235C2312yes—
199C8×Dic43C2312yes—
2002−1+4×C43—42no—
2012−1+4×C43—42no—
202C2×#41×C43—22no—
203C2×#41×C43—21no—
204C2×#41×C43C2311yescharacteristic
205C2×#41×C43C2312yes—
206C2×#41×C43C2311yescharacteristic
207C22×Q8×C43—21no—
208C22×Q8×C43C2311yescharacteristic
209C22×Q8×C43C2312yes—
210C22×D4×C43C2311yescharacteristic
211AGL(1,ℤ/8)×C43—42no—
212C2×SD16×C43—42no—
213C2×SD16×C43C2314yes—
214C2×SD16×C43C2312yes—
215C2×D8×C43C2312yes—
216C2×M16×C43C2311yescharacteristic
217C22×C8×C43C2311yescharacteristic
218#127×C43—21no—
219#124×C43—21no—
220#121×C43C2314yes—
221#120×C43—22no—
222#117×C43C2311yescharacteristic
223#103×C43C2314yes—
224#103×C43C2312yes—
225#102×C43C2312yes—
226C22⋊C8×C43C2314yes—
227C24×C43—21no—
228C23×D43—21no—
229C23×D43—22no—
230C23×D43—21no—
231#41×C43—22no—
232#41×C43—22no—
233#41×C43—22no—
234#41×C43—22no—
235#41×C43—42no—
236#41×C43—42no—
237#41×C43—48no—
238#41×C43—44no—
239C2×Q8×C43—22no—
240C2×Q8×C43—21no—
241C2×Q8×C43—22no—
242C2×Q8×C43—22no—
243C2×Q8×C43—42no—
244C2×Q8×C43—42no—
245C2×Q8×C43—44no—
246C2×Q8×C43C2×D411yescharacteristic
247C2×Q8×C43C2412yes—
248C2×Q8×C43C2411yescharacteristic
249C2×D4×C43—21no—
250C2×D4×C43—22no—
251C2×D4×C43—21no—
252C2×D4×C43—24no—
253C2×D4×C43—22no—
254C2×D4×C43—22no—
255C2×D4×C43C2×D412yes—
256C2×D4×C43C2×D411yescharacteristic
257C2×D4×C43C2411yescharacteristic
258C2×D4×C43C2412yes—
259C22×C4×C43—22no—
260C22×C4×C43—21no—
261C22×C4×C43—22no—
262C22×C4×C43—21no—
263C22×C4×C43C2412yes—
264C22×C4×C43C2411yescharacteristic
265C2×C22⋊D43—24no—
266C2×C22⋊D43—22no—
267C2×C22⋊D43—24no—
268C2×C22⋊D43—24no—
269C2×C22⋊D43—22no—
270C2×C22⋊D43—21no—
271C2×C22⋊D43—24no—
272C2×C22⋊D43—84no—
273C22×Dic43—24no—
274C22×Dic43C2×D414yes—
275C22×Dic43C2×D412yes—
276#10621902—44no—
277#10621900—88no—
278D4×D43—44no—
279D4×D43—48no—
280#10621898—22no—
281#10621898—22no—
282#10621898—42no—
283#10621898—42no—
284C2×D172—21no—
285C2×D172—22no—
286C2×D172—21no—
287C2×D172—22no—
288C2×D172—22no—
289C2×D172—22no—
290C2×D172—22no—
291C2×D172—42no—
292C2×D172—42no—
293C2×D172C2412yes—
294C2×D172C2411yescharacteristic
295C2×D172C2412yes—
296C2×C4×D43—22no—
297C2×C4×D43—21no—
298C2×C4×D43—24no—
299C2×Dic86—22no—
300C2×Dic86C2411yescharacteristic
301SD16×C43—44no—
302SD16×C43—42no—
303D8×C43—42no—
304M16×C43—22no—
305C2×C8×C43—22no—
306C2×C8×C43C2412yes—
307C2×C8×C43C2412yes—
308C4⋊C4×C43C2412yes—
309C22⋊C4×C43—24no—
310C22⋊C4×C43—21no—
311C42×C43—21no—
312C22⋊Dic43—24no—
313C22⋊Dic43—22no—
314C22⋊Dic43—21no—
315C22⋊Dic43C2×D412yes—
316C22⋊Dic43C2×D414yes—
317#10621884—44no—
318#10621884—42no—
319#10621883—42no—
320#10621882—44no—
321#10621882—42no—
322#10621882—42no—
323(C2×D43)⋊C4—24no—
324(C2×D43)⋊C4—24no—
325(C2×D43)⋊C4—24no—
326(C2×D43)⋊C4—22no—
327(C2×D43)⋊C4—24no—
328(C2×D43)⋊C4—24no—
329(C2×D43)⋊C4—24no—
330C4⋊Dic43—22no—
331C4⋊Dic43C2×D412yes—
332C4⋊Dic43C2×D414yes—
333C4⋊Dic43C2412yes—
334Dic43⋊C4—22no—
335Dic43⋊C4—22no—
336Dic43⋊C4—24no—
337Dic43⋊C4—22no—
338C4×Dic43—21no—
339C4×Dic43C2×D414yes—
340C4×Dic43C2×D412yes—
341C4×Dic43C2411yescharacteristic
342C4×Dic43C2411yescharacteristic
343C4×Dic43C2412yes—
344#10621877—22no—
345C2×C43⋊C8—22no—
346C2×C43⋊C8C2412yes—
347C2×C43⋊C8C2412yes—
348D344—44no—
349D344—42no—
350#10621873—42no—
351C23×C43—22no—
352C23×C43—21no—
353C23×C43—42no—
354C23×C43—82no—
355C23×C43C22×D412yes—
356C23×C43C22×D411yescharacteristic
357C22×D43—21no—
358C22×D43—22no—
359C22×D43—22no—
360C22×D43—44no—
361C22×D43—42no—
362C22×D43—42no—
363C22×D43—82no—
364C22×D43—82no—
365C22×D43—84no—
366Q8×C43—22no—
367Q8×C43—22no—
368Q8×C43—21no—
369Q8×C43—22no—
370Q8×C43—21no—
371Q8×C43—44no—
372Q8×C43—42no—
373D4×C43—24no—
374D4×C43—22no—
375D4×C43—22no—
376D4×C43—21no—
377D4×C43—22no—
378D4×C43—21no—
379D4×C43—44no—
380D4×C43—42no—
381D4×C43—42no—
382D4×C43—84no—
383C2×C4×C43—22no—
384C2×C4×C43—22no—
385C2×C4×C43—22no—
386C2×C4×C43—22no—
387C2×C4×C43—21no—
388C2×C4×C43—44no—
389C2×C4×C43—44no—
390C2×C4×C43—42no—
391C2×C4×C43—42no—
392C2×C4×C43C22×D412yes—
393C2×C4×C43C22×D411yescharacteristic
394C2×C4×C43H(5,𝔽2)12yes—
395C2×C4×C43H(5,𝔽2)12yes—
396C2×C4×C43C2511yescharacteristic
397C22⋊D43—48no—
398C22⋊D43—44no—
399C22⋊D43—42no—
400C22⋊D43—84no—
401C22⋊D43—82no—
402C22⋊D43—84no—
403C22⋊D43—84no—
404C2×Dic43—22no—
405C2×Dic43—21no—
406C2×Dic43—44no—
407C2×Dic43—42no—
408C2×Dic43—84no—
409C2×Dic43C22×D412yes—
410C2×Dic43C22×D412yes—
411C2×Dic43C22×D414yes—
412D172—22no—
413D172—22no—
414D172—22no—
415D172—21no—
416D172—22no—
417D172—21no—
418D172—44no—
419D172—42no—
420D172—42no—
421C4×D43—44no—
422C4×D43—42no—
423C4×D43—84no—
424Dic86—21no—
425Dic86—21no—
426Dic86—44no—
427C8×C43—22no—
428C8×C43—22no—
429C43⋊C8—22no—
430C43⋊C8—22no—
431#60825—431nomaximal, Sylow
432C22×C43—22no—
433C22×C43—24no—
434C22×C43—22no—
435C22×C43—44no—
436C22×C43—42no—
437C22×C43—42no—
438C22×C43—41no—
439C22×C43—162no—
440C22×C43#53512yes—
441C22×C43C23×D411yescharacteristic
442C2×D43—44no—
443C2×D43—42no—
444C2×D43—44no—
445C2×D43—41no—
446C2×D43—42no—
447C2×D43—42no—
448C2×D43—162no—
449C2×D43—162no—
450C2×D43—164no—
451C4×C43—22no—
452C4×C43—42no—
453C4×C43—42no—
454C4×C43—41no—
455C4×C43#53512yes—
456C4×C43C2×H(5,𝔽2)11yescharacteristic
457C4×C43C2×H(5,𝔽2)11yescharacteristic
458Dic43—22no—
459Dic43—24no—
460Dic43—22no—
461Dic43—42no—
462Dic43—41no—
463#3508—431no—
464#3500—431no—
465#3221—434no—
466#3220—434no—
467#3214—434no—
468#3213—434no—
469#3151—431no—
470C2×#496—431no—
471#3140—431no—
472#3135—431no—
473#3042—431no—
474#3042—431no—
475#3041—431no—
476#3041—431no—
477#3010—431no—
478#3010D4311yescharacteristic, complemented
479#3008—431no—
480#3008—431no—
481#2923—431no—
482C2×C43—22no—
483C2×C43—42no—
484C2×C43—81no—
485C2×C43—82no—
486C2×C43C2×#53511yescharacteristic
487C2×C43#358512yes—
488D43—82no—
489D43—82no—
490D43—81no—
491C2×2−1+4C2×D4311yescharacteristic
492C2×H(5,𝔽2)—431no—
493C2×AGL(1,ℤ/8)—431no—
494C2×AGL(1,ℤ/8)—431no—
495C2×AGL(1,ℤ/8)—431no—
496C2×AGL(1,ℤ/8)C2×D4311yescharacteristic, complemented
497C22×SD16—431no—
498C22×SD16C2×D4311yescharacteristic, complemented
499C22×D8—431no—
500C22×D8—431no—
501#559—862no—
502#550—862no—
503#548—862no—
504#546—864no—
505#546—864no—
506#546—862no—
507#540—434no—
508#536—432no—
509#536—431no—
510#535—431no—
511#535—432no—
512#535—431no—
513#535C2×D4311yescharacteristic
514#533—431no—
515#532—434no—
516#532—431no—
517#532—432no—
518C2×#127—431no—
519C2×#124—431no—
520C2×#124—432no—
521#518—431no—
522#518—431no—
523C4×#41—431no—
524#496—434no—
525#496—434no—
526#496—432no—
527#496—432no—
528#493—432no—
529#492—432no—
530#491—432no—
531#490—432no—
532#489—432no—
533#489—434no—
534#489—432no—
535#488—434no—
536#463—434no—
537#463—434no—
538#463—434no—
539#463—434no—
540#461—434no—
541#461—434no—
542#459—434no—
543#459—434no—
544#449—434no—
545#449—434no—
546#449—434no—
547#449C2×D4314yescomplemented
548#448—434no—
549#448C2×D4314yescomplemented
550#447—434no—
551#447—434no—
552#433—434no—
553#432—434no—
554#424—431no—
555#424—431no—
556#419—431no—
557#419C2×D4311yescharacteristic, complemented
558#418—431no—
559#418—431no—
560#416—431no—
561#416—431no—
562#416—431no—
563#416C2×D4311yescharacteristic, complemented
564#408—431no—
565#408C2×D4311yescharacteristic
566C4×M16—431no—
567C2×#97—431no—
568C43#6082511yescharacteristic, complemented, Sylow
5692−1+4—42no—
5702−1+4—42no—
571H(5,𝔽2)—1722no—
572H(5,𝔽2)—1722no—
573C2×#41—22no—
574C2×#41—21no—
575C2×#41—431no—
576C2×#41—432no—
577C2×#41—864no—
578C2×#41—861no—
579C2×#41C22×D4311yescharacteristic
580C2×#41C22×D4312yes—
581C2×#41C22×D4311yescharacteristic
582C22×Q8—21no—
583C22×Q8C22×D4311yescharacteristic
584C22×Q8C22×D4312yes—
585C22×D4—431no—
586C22×D4—431no—
587C22×D4—432no—
588C22×D4—862no—
589C22×D4—862no—
590C22×D4—861no—
591C22×D4C22×D4311yescharacteristic
592AGL(1,ℤ/8)—42no—
593AGL(1,ℤ/8)—1722no—
594AGL(1,ℤ/8)—1722no—
595AGL(1,ℤ/8)—1722no—
596C2×SD16—42no—
597C2×SD16—434no—
598C2×SD16—432no—
599C2×SD16—432no—
600C2×SD16—432no—
601C2×SD16—1722no—
602C2×SD16C22×D4314yes—
603C2×SD16C22×D4312yes—
604C2×D8—434no—
605C2×D8—432no—
606C2×D8—432no—
607C2×D8—434no—
608C2×D8—432no—
609C2×D8—1722no—
610C2×D8—1722no—
611C2×D8C22×D4312yes—
612C2×M16—431no—
613C2×M16C22×D4311yescharacteristic
614C22×C8—431no—
615C22×C8C22×D4311yescharacteristic
616C4⋊Q8—432no—
617C4⋊Q8—432no—
618C4⋊Q8—431no—
619#127—21no—
620#127—432no—
621#127—432no—
622#127—432no—
623#127—431no—
624#127—862no—
625#127—861no—
626#125—432no—
627#124—21no—
628#124—432no—
629#124—431no—
630#124—432no—
631#124—432no—
632#124—432no—
633#124—431no—
634#124—864no—
635#124—864no—
636#124—862no—
637#124—861no—
638#123—864no—
639#123—864no—
640#123—862no—
641#123—864no—
642C22⋊Q8—862no—
643C22⋊Q8—862no—
644C22⋊Q8—864no—
645#121—434no—
646#121—864no—
647#121—864no—
648#121—862no—
649#121—864no—
650#121—864no—
651#121—862no—
652#121—864no—
653#121C22×D4314yes—
654#120—22no—
655#120—862no—
656#120—864no—
657#120—862no—
658C4×Q8—432no—
659C4×Q8—862no—
660C4×D4—434no—
661C4×D4—432no—
662C4×D4—434no—
663C4×D4—434no—
664C4×D4—862no—
665C4×D4—864no—
666C4×D4—864no—
667C4×D4—862no—
668C4×D4—862no—
669#117—431no—
670#117—432no—
671#117—431no—
672#117C22×D4311yescharacteristic
673C2×C22⋊C4—862no—
674C2×C22⋊C4—862no—
675C2×C22⋊C4—864no—
676C2×C22⋊C4—862no—
677C2×C42—431no—
678C2×C42—432no—
679C4⋊C8—434no—
680C4⋊C8—434no—
681#103—432no—
682#103—434no—
683#103—432no—
684#103—432no—
685#103C22×D4312yes—
686#103C22×D4314yes—
687#102—432no—
688#102—432no—
689#102—434no—
690#102—432no—
691#102—434no—
692#102C22×D4312yes—
693C22⋊C8—434no—
694C22⋊C8C22×D4314yes—
695#97—432no—
696#97—432no—
697#97—432no—
698C4×C8—432no—
699C24—21no—
700C24—862no—
701C24—861no—
702C24—861no—
703#41—22no—
704#41—22no—
705#41—22no—
706#41—22no—
707#41—42no—
708#41—42no—
709#41—48no—
710#41—44no—
711#41—862no—
712#41—862no—
713#41—3448no—
714#41—1722no—
715#41—1722no—
716#41—1724no—
717C2×Q8—22no—
718C2×Q8—21no—
719C2×Q8—22no—
720C2×Q8—22no—
721C2×Q8—42no—
722C2×Q8—42no—
723C2×Q8—44no—
724C2×Q8—431no—
725C2×Q8—862no—
726C2×Q8D4×D4311yescharacteristic
727C2×Q8C23×D4312yes—
728C2×Q8C23×D4311yescharacteristic
729C2×D4—22no—
730C2×D4—21no—
731C2×D4—24no—
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—432no—
736C2×D4—431no—
737C2×D4—432no—
738C2×D4—864no—
739C2×D4—862no—
740C2×D4—864no—
741C2×D4—864no—
742C2×D4—864no—
743C2×D4—862no—
744C2×D4—861no—
745C2×D4—861no—
746C2×D4—862no—
747C2×D4—861no—
748C2×D4—862no—
749C2×D4—862no—
750C2×D4—862no—
751C2×D4—862no—
752C2×D4—3444no—
753C2×D4—1722no—
754C2×D4—1722no—
755C2×D4—1728no—
756C2×D4—1724no—
757C2×D4D4×D4312yes—
758C2×D4D4×D4311yescharacteristic
759C2×D4C23×D4311yescharacteristic
760C2×D4C23×D4312yes—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—434no—
766C22×C4—432no—
767C22×C4—864no—
768C22×C4—864no—
769C22×C4—862no—
770C22×C4—861no—
771C22×C4C23×D4312yes—
772C22×C4C23×D4311yescharacteristic
773SD16—44no—
774SD16—42no—
775SD16—1722no—
776SD16—1722no—
777SD16—1724no—
778SD16—1722no—
779D8—42no—
780D8—1724no—
781D8—1722no—
782D8—1724no—
783D8—1722no—
784D8—1722no—
785M16—22no—
786M16—862no—
787C2×C8—22no—
788C2×C8—432no—
789C2×C8—432no—
790C2×C8—862no—
791C2×C8C23×D4312yes—
792C2×C8C23×D4312yes—
793C4⋊C4—432no—
794C4⋊C4—434no—
795C4⋊C4—432no—
796C4⋊C4—862no—
797C4⋊C4—864no—
798C4⋊C4—862no—
799C4⋊C4—862no—
800C4⋊C4—862no—
801C4⋊C4C23×D4312yes—
802C22⋊C4—21no—
803C22⋊C4—24no—
804C22⋊C4—432no—
805C22⋊C4—434no—
806C22⋊C4—862no—
807C22⋊C4—864no—
808C22⋊C4—864no—
809C22⋊C4—864no—
810C22⋊C4—864no—
811C22⋊C4—864no—
812C22⋊C4—864no—
813C22⋊C4—862no—
814C22⋊C4—861no—
815C22⋊C4—864no—
816C42—21no—
817C42—434no—
818C42—432no—
819C42—431no—
820C42—431no—
821C42—432no—
822C42—861no—
823C23—22no—
824C23—21no—
825C23—42no—
826C23—82no—
827C23—862no—
828C23—861no—
829C23—862no—
830C23—3442no—
831C23—3442no—
832C23—3444no—
833C23—1724no—
834C23—1722no—
835C23—1722no—
836C23C2×D4×D4312yes—
837C23C2×D4×D4311yescharacteristic
838Q8—22no—
839Q8—22no—
840Q8—21no—
841Q8—22no—
842Q8—21no—
843Q8—44no—
844Q8—42no—
845Q8—861no—
846Q8—861no—
847Q8—1724no—
848D4—24no—
849D4—22no—
850D4—21no—
851D4—22no—
852D4—21no—
853D4—22no—
854D4—44no—
855D4—42no—
856D4—42no—
857D4—84no—
858D4—862no—
859D4—862no—
860D4—862no—
861D4—861no—
862D4—861no—
863D4—862no—
864D4—3444no—
865D4—3444no—
866D4—3442no—
867D4—3444no—
868D4—1724no—
869D4—1728no—
870D4—1724no—
871D4—1722no—
872D4—1722no—
873D4—1722no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—21no—
879C2×C4—44no—
880C2×C4—44no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—432no—
884C2×C4—434no—
885C2×C4—432no—
886C2×C4—862no—
887C2×C4—861no—
888C2×C4—3444no—
889C2×C4—3444no—
890C2×C4—1724no—
891C2×C4—1722no—
892C2×C4—1724no—
893C2×C4—1722no—
894C2×C4C2×D4×D4312yes—
895C2×C4C2×D4×D4311yescharacteristic
896C2×C4#1306337012yes—
897C2×C4#1306337012yes—
898C2×C4C24×D4311yescharacteristic
899C8—22no—
900C8—22no—
901C8—862no—
902C8—862no—
903C22—22no—
904C22—24no—
905C22—22no—
906C22—44no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—162no—
911C22—1724no—
912C22—1724no—
913C22—1722no—
914C22—1722no—
915C22—1721no—
916C22—1722no—
917C22—6882no—
918C22—6882no—
919C22—6884no—
920C22#1458346412yes—
921C22C22×D4×D4311yescharacteristic
922C4—22no—
923C4—42no—
924C4—42no—
925C4—41no—
926C4—864no—
927C4—862no—
928C4—862no—
929C4—1722no—
930C4—1721no—
931C4#1458346412yes—
932C4C2×#1306337011yescharacteristic
933C4C2×#1306337011yescharacteristic
934C2—22no—
935C2—42no—
936C2—82no—
937C2—81no—
938C2—3442no—
939C2—3441no—
940C2—3442no—
941C2C2×#1458346411yescharacteristic
942C2#1914937312yes—
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3010C2
socleC22×C43C23×D4
hypercenter#3010D43
hypocenterC43#60825
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3010

Complements

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

NH ≅ G/Ntype
1. #19148470C2semidirect
2. #19148389C2semidirect
3. #19145652C2semidirect
4. #19145643C2semidirect
5. #19145587C2semidirect
6. #19145581C2semidirect
7. #19145043C2semidirect
8. C2×#14583285C2semidirect
9. #19144983C2semidirect
10. #19144938C2semidirect
11. #19144106C2semidirect
12. #19144104C2semidirect
13. #19144101C2semidirect
14. #19144100C2semidirect
15. #19143881C2semidirect
16. #19143865C2semidirect
17. #19143861C2semidirect
18. #19143242C2semidirect
19. C43×#3010C2semidirect
23. C2×#13063350C22semidirect
24. C22×#10621884C22semidirect
33. #14583502C22semidirect
35. #14583473C22semidirect
38. #14583463C22semidirect
39. #14583452C22semidirect
41. #14583445C22semidirect
42. #14583444C22semidirect
43. C2×#13063321C22semidirect
45. C2×#13063314C22semidirect
46. #14583374C22semidirect
47. #14583373C22semidirect
49. #14583287C22semidirect
50. #14583285C22semidirect
51. #14583285C22semidirect
52. #14583285C22semidirect
53. #14583274C22semidirect
54. #14583270C22semidirect
55. #14583266C22semidirect
56. #14583262C22semidirect
57. #14583260C22semidirect
58. #14583260C22semidirect
59. #14583257C22semidirect
60. #14583255C22semidirect
61. #14583117C22semidirect
62. #14583117C22semidirect
63. #14583116C22semidirect
64. #14583116C22semidirect
65. #14583103C22semidirect
66. #14583102C22semidirect
67. #14583093C22semidirect
68. #14583092C22semidirect
69. #14583046C22semidirect
70. #14583044C22semidirect
71. #14583042C22semidirect
72. #14583038C22semidirect
73. #14583035C22semidirect
74. #14583032C22semidirect
75. #14582957C22semidirect
76. #14582953C22semidirect
77. #14582927C22semidirect
78. #14582925C22semidirect
79. #14582908C22semidirect
83. #14582895C22semidirect
86. M16×Dic43C22semidirect
87. C2×#13063235C22semidirect
89. C2×AGL(1,ℤ/8)×C43C22semidirect
90. C22×SD16×C43C22semidirect
92. C43×#449C22semidirect
93. C43×#448C22semidirect
94. C43×#419C22semidirect
95. C43×#416C22semidirect
478. #3010D43semidirect
496. C2×AGL(1,ℤ/8)C2×D43semidirect
498. C22×SD16C2×D43semidirect
547. #449C2×D43semidirect
549. #448C2×D43semidirect
557. #419C2×D43semidirect
563. #416C2×D43semidirect
568. C43#60825semidirect

Maximal subgroups

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

subgroupindex
#191484702
#191483892
#191456522
#191456432
#191455872
#191455812
#191450432
C2×#145832852
#191449832
#191449382
#191441062
#191441042
#191441012
#191441002
#191438812
#191438652
#191438612
#191432422
C43×#30102
#6082543